TSTP Solution File: SWW394+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW394+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:26:06 EDT 2023

% Result   : Theorem 47.22s 46.13s
% Output   : Proof 47.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWW394+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.14  % Command  : nanocop.sh %s %d
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May 18 22:07:32 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 47.22/46.13  
% 47.22/46.13  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 47.22/46.13  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.22/46.13  %-----------------------------------------------------
% 47.22/46.13  ncf(matrix, plain, [(52751 ^ _2084997) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))], !, (30419 ^ _778495) ^ [_1333111, _1333113, _1333115, _1333117, _1333119, _1333121] : [-(hBOOL(hAPP(hAPP(c_member(_1333111), _1333113), c_SetInterval_Oord_OgreaterThanAtMost(_1333111, _1333115, _1333117, _1333119, _1333121)))), hBOOL(hAPP(hAPP(_1333117, _1333119), _1333113)), hBOOL(hAPP(hAPP(_1333115, _1333113), _1333121))], (38917 ^ _778495) ^ [_1532318, _1532320] : [-(c_FunDef_Oreduction__pair(_1532318, _1532320)), c_Wellfounded_Owf(_1532318, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool), tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool)), _1532320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1532318, _1532318, _1532318), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool), tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool)), _1532320)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool), tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool)), _1532320))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool), tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool)), _1532320)))], (18930 ^ _778495) ^ [_1118802, _1118804, _1118806, _1118808, _1118810, _1118812] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1118802, _1118804, _1118806, _1118808, c_Nitpick_Opair__box_OPairBox(_1118802, _1118804, _1118810, _1118812)) = hAPP(hAPP(_1118808, _1118810), _1118812))], (29184 ^ _778495) ^ [_1309185, _1309187, _1309189, _1309191] : [-(hAPP(c_Nat_Onat_Onat__rec(_1309185, _1309187, _1309189), hAPP(c_Nat_OSuc, _1309191)) = hAPP(hAPP(_1309189, _1309191), hAPP(c_Nat_Onat_Onat__rec(_1309185, _1309187, _1309189), _1309191)))], (42828 ^ _778495) ^ [_1631833, _1631835, _1631837] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631833), tc_List_Olist(_1631833))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631833), tc_List_Olist(_1631833)), _1631835), c_List_Olist_ONil(_1631833))), c_List_Olistrel1(_1631833, _1631837)))], (26566 ^ _778495) ^ [_1253768, _1253770, _1253772, _1253774] : [class_Rings_Olinordered__semidom(_1253768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253768), c_Groups_Oone__class_Oone(_1253768)), _1253770)), 26573 ^ _778495 : [(26580 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253772), _1253774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253768), hAPP(hAPP(c_Power_Opower__class_Opower(_1253768), _1253770), _1253772)), hAPP(hAPP(c_Power_Opower__class_Opower(_1253768), _1253770), _1253774))))], (26574 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253768), hAPP(hAPP(c_Power_Opower__class_Opower(_1253768), _1253770), _1253772)), hAPP(hAPP(c_Power_Opower__class_Opower(_1253768), _1253770), _1253774))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253772), _1253774)))]]], (32550 ^ _778495) ^ [_1378210] : [-(_1378210 = 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)), _1378210), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (11284 ^ _778495) ^ [_973244, _973246, _973248] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973246), _973248)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973244), _973248)))], (3472 ^ _778495) ^ [_830418, _830420, _830422, _830424, _830426, _830428] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_830428, _830424, _830420) = c_SetInterval_Oord__class_OgreaterThanAtMost(_830426, _830422, _830418)), _830428 = _830426, _830424 = _830422, _830420 = _830418], (19640 ^ _778495) ^ [_1131273, _1131275, _1131277] : [class_Orderings_Olinorder(_1131273), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131273), _1131275)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131273), _1131277)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1131273, tc_HOL_Obool)), _1131275), _1131277) = c_Orderings_Obot__class_Obot(tc_fun(_1131273, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1131273), c_Big__Operators_Olinorder__class_OMin(_1131273, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1131273, tc_HOL_Obool)), _1131275), _1131277))), c_Big__Operators_Olinorder__class_OMin(_1131273, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1131273, tc_HOL_Obool)), _1131275), _1131277))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1131273), c_Big__Operators_Olinorder__class_OMin(_1131273, _1131275)), c_Big__Operators_Olinorder__class_OMin(_1131273, _1131277)))], (9238 ^ _778495) ^ [_934648, _934650, _934652, _934654] : [class_Lattices_Odistrib__lattice(_934648), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934648), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934648), _934650), _934652)), _934654) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934648), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934648), _934650), _934654)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934648), _934652), _934654)))], (21156 ^ _778495) ^ [_1157550, _1157552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1157550)), c_Int_OBit1(_1157552))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157550), _1157552)))], (22866 ^ _778495) ^ [_1187217, _1187219, _1187221, _1187223] : [class_Int_Onumber__ring(_1187217), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187217), hAPP(c_Int_Onumber__class_Onumber__of(_1187217), _1187219)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1187217), _1187221), hAPP(c_Int_Onumber__class_Onumber__of(_1187217), _1187223))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187217), hAPP(c_Int_Onumber__class_Onumber__of(_1187217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1187219), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187223)))), _1187221))], (29498 ^ _778495) ^ [_1315123, _1315125, _1315127, _1315129, _1315131, _1315133] : [-(hAPP(hAPP(c_Product__Type_OPair(_1315123, _1315125), _1315127), _1315129) = hAPP(hAPP(c_Product__Type_OPair(_1315123, _1315125), _1315131), _1315133)), _1315127 = _1315131, _1315129 = _1315133], (6088 ^ _778495) ^ [_876048, _876050, _876052, _876054] : [6089 ^ _778495 : [(6092 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_876048), _876050), _876054))], (6090 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_876048), _876050), _876052))]], -(hBOOL(hAPP(hAPP(c_member(_876048), _876050), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876048, tc_HOL_Obool)), _876052), _876054))))], (33044 ^ _778495) ^ [_1388112, _1388114, _1388116, _1388118] : [class_Orderings_Olinorder(_1388112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388112), _1388114), _1388116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388112), _1388116), _1388118)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1388112, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1388112, _1388114, _1388116)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1388112, _1388116, _1388118)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1388112, _1388114, _1388118))], (22886 ^ _778495) ^ [_1187669] : [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, _1187669)))))], (48298 ^ _778495) ^ [_1752335, _1752337, _1752339, _1752341] : [-(hAPP(hAPP(c_List_Oappend(_1752335), c_List_Oreplicate(_1752335, _1752337, _1752339)), c_List_Oreplicate(_1752335, _1752341, _1752339)) = hAPP(hAPP(c_List_Oappend(_1752335), c_List_Oreplicate(_1752335, _1752341, _1752339)), c_List_Oreplicate(_1752335, _1752337, _1752339)))], (39096 ^ _778495) ^ [_1536616, _1536618] : [c_Wellfounded_OwfP(_1536616, hAPP(hAPP(c_COMBC(_1536616, tc_fun(tc_prod(_1536616, _1536616), tc_HOL_Obool), tc_fun(_1536616, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536616, tc_fun(tc_fun(tc_prod(_1536616, _1536616), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1536616, _1536616), tc_HOL_Obool), tc_fun(_1536616, tc_HOL_Obool)), _1536616), c_COMBC(_1536616, tc_fun(tc_prod(_1536616, _1536616), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536616, tc_prod(_1536616, _1536616)), tc_fun(_1536616, tc_fun(tc_fun(tc_prod(_1536616, _1536616), tc_HOL_Obool), tc_HOL_Obool)), _1536616), hAPP(c_COMBB(tc_prod(_1536616, _1536616), tc_fun(tc_fun(tc_prod(_1536616, _1536616), tc_HOL_Obool), tc_HOL_Obool), _1536616), c_member(tc_prod(_1536616, _1536616)))), c_Product__Type_OPair(_1536616, _1536616)))), _1536618)), -(c_Wellfounded_Owf(_1536616, _1536618))], (33407 ^ _778495) ^ [_1398303, _1398305, _1398307, _1398309, _1398311] : [_1398303 = c_Orderings_Obot__class_Obot(tc_fun(_1398305, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398305, tc_fun(_1398307, tc_HOL_Obool)), _1398303), hAPP(hAPP(c_COMBB(tc_fun(_1398307, tc_HOL_Obool), tc_fun(_1398307, tc_HOL_Obool), _1398305), hAPP(c_Set_Oinsert(_1398307), _1398309)), _1398311)) = c_Orderings_Obot__class_Obot(tc_fun(_1398307, tc_HOL_Obool)))], (40752 ^ _778495) ^ [_1577095, _1577097, _1577099, _1577101, _1577103] : [-(hAPP(c_Relation_Oconverse(_1577095, _1577097), hAPP(hAPP(c_Relation_Orel__comp(_1577095, _1577099, _1577097), _1577101), _1577103)) = hAPP(hAPP(c_Relation_Orel__comp(_1577097, _1577099, _1577095), hAPP(c_Relation_Oconverse(_1577099, _1577097), _1577103)), hAPP(c_Relation_Oconverse(_1577095, _1577099), _1577101)))], (51775 ^ _778495) ^ [_1823695, _1823697, _1823699, _1823701] : [class_Rings_Ocomm__ring(_1823695), class_Rings_Odvd(_1823695), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823695), _1823697), _1823699)), 51786 ^ _778495 : [(51793 ^ _778495) ^ [_1824121, _1824123] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823695), _1823697), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1823695), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1823695), _1824123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1823695), _1824121), _1823699))), _1823701))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823695), _1823697), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1823695), _1824123), _1823701))))], (51787 ^ _778495) ^ [_1823948, _1823950] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823695), _1823697), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1823695), _1823950), _1823701))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823695), _1823697), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1823695), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1823695), _1823950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1823695), _1823948), _1823699))), _1823701))))]]], (37765 ^ _778495) ^ [_1496989, _1496991] : [-(hAPP(c_Set_OCollect(_1496989), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1496989), c_fNot), _1496991)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1496989, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1496989), _1496991)))], (21262 ^ _778495) ^ [_1159438, _1159440, _1159442] : [class_Groups_Oordered__ab__group__add__abs(_1159438), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159438), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1159438), hAPP(c_Groups_Oabs__class_Oabs(_1159438), _1159440)), hAPP(c_Groups_Oabs__class_Oabs(_1159438), _1159442))), hAPP(c_Groups_Oabs__class_Oabs(_1159438), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1159438), _1159440), _1159442)))))], (40461 ^ _778495) ^ [_1570468, _1570470] : [-(hAPP(c_Relation_OImage(_1570468, _1570468, c_Relation_OId(_1570468)), _1570470) = _1570470)], (11264 ^ _778495) ^ [_972866, _972868, _972870] : [_972866 = _972870, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972866), _972868) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972870), _972868))], (32964 ^ _778495) ^ [_1386610, _1386612, _1386614] : [class_Orderings_Oorder(_1386610), 32967 ^ _778495 : [(32974 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386610), _1386612), _1386614))), -(c_Orderings_Obot__class_Obot(tc_fun(_1386610, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1386610, _1386612, _1386614))], (32968 ^ _778495) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1386610, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1386610, _1386612, _1386614), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386610), _1386612), _1386614))]]], (31839 ^ _778495) ^ [_1361871, _1361873, _1361875, _1361877] : [-(hAPP(c_Set_OPow(_1361871), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361873, tc_fun(_1361871, tc_HOL_Obool)), _1361875), _1361877)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361873, tc_fun(tc_fun(_1361871, tc_HOL_Obool), tc_HOL_Obool)), _1361875), hAPP(hAPP(c_COMBB(tc_fun(_1361871, tc_HOL_Obool), tc_fun(tc_fun(_1361871, tc_HOL_Obool), tc_HOL_Obool), _1361873), c_Set_OPow(_1361871)), _1361877)))], (49449 ^ _778495) ^ [_1777997, _1777999] : [c_Relation_Osym(_1777997, _1777999), -(c_Relation_Osym(_1777997, hAPP(c_Relation_Oconverse(_1777997, _1777997), _1777999)))], (19912 ^ _778495) ^ [_1136262, _1136264, _1136266] : [class_Nat_Osemiring__char__0(_1136262), 19915 ^ _778495 : [(19922 ^ _778495) ^ [] : [_1136264 = _1136266, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1136262), _1136264) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1136262), _1136266))], (19916 ^ _778495) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1136262), _1136264) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1136262), _1136266), -(_1136264 = _1136266)]]], (33395 ^ _778495) ^ [_1397887, _1397889, _1397891, _1397893] : [hBOOL(hAPP(hAPP(c_member(_1397889), _1397893), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397887, tc_fun(_1397889, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397887, tc_HOL_Obool))), _1397891))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397887, tc_fun(_1397889, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397887, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1397889, tc_HOL_Obool), tc_fun(_1397889, tc_HOL_Obool), _1397887), hAPP(c_COMBC(_1397889, tc_fun(_1397889, tc_HOL_Obool), tc_HOL_Obool), c_member(_1397889))), _1397891)), _1397893)))], (7880 ^ _778495) ^ [_908465, _908467, _908469] : [class_Orderings_Olinorder(_908465), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908465), _908467), _908469))), 7887 ^ _778495 : [(7894 ^ _778495) ^ [] : [_908467 = _908469, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908465), _908467), _908469)))], (7888 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908465), _908467), _908469)), -(_908467 = _908469)]]], (13316 ^ _778495) ^ [_1015438] : [hAPP(c_Nat_OSuc, _1015438) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (52695 ^ _778495) ^ [_1836141, _1836143] : [hBOOL(hAPP(hAPP(c_fconj, _1836141), _1836143)), -(hBOOL(_1836141))], (15107 ^ _778495) ^ [_1046650, _1046652, _1046654, _1046656, _1046658] : [class_Rings_Olinordered__semiring__strict(_1046650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046650), _1046652), _1046654)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046650), _1046656), _1046658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1046650), c_Groups_Ozero__class_Ozero(_1046650)), _1046652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1046650), c_Groups_Ozero__class_Ozero(_1046650)), _1046656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046650), _1046652), _1046656)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046650), _1046654), _1046658))))], (40399 ^ _778495) ^ [_1568950, _1568952] : [-(c_Transitive__Closure_Ortrancl(_1568950, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568950, _1568950), tc_HOL_Obool)), _1568952), c_Relation_OId(_1568950))) = c_Transitive__Closure_Ortrancl(_1568950, _1568952))], (9701 ^ _778495) ^ [_944719, _944721, _944723] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_944719), _944721)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_944719, tc_HOL_Obool)), _944721), _944723) = hAPP(hAPP(c_Finite__Set_Ofold(_944719, tc_fun(_944719, tc_HOL_Obool), c_Set_Oinsert(_944719)), _944723), _944721))], (18814 ^ _778495) ^ [_1116527, _1116529, _1116531, _1116533] : [class_Fields_Olinordered__field__inverse__zero(_1116527), class_Int_Onumber(_1116527), 18821 ^ _778495 : [(18822 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116527), hAPP(c_Int_Onumber__class_Onumber__of(_1116527), _1116529)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116527), _1116531), _1116533))), 18825 ^ _778495 : [(18832 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116527), c_Groups_Ozero__class_Ozero(_1116527)), _1116533))), 18835 ^ _778495 : [(18842 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116527), _1116533), c_Groups_Ozero__class_Ozero(_1116527)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116527), hAPP(c_Int_Onumber__class_Onumber__of(_1116527), _1116529)), c_Groups_Ozero__class_Ozero(_1116527))))], (18836 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116527), _1116533), c_Groups_Ozero__class_Ozero(_1116527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116527), _1116531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116527), hAPP(c_Int_Onumber__class_Onumber__of(_1116527), _1116529)), _1116533))))]]], (18826 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116527), c_Groups_Ozero__class_Ozero(_1116527)), _1116533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116527), hAPP(c_Int_Onumber__class_Onumber__of(_1116527), _1116529)), _1116533)), _1116531)))]]], (18848 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116527), hAPP(c_Int_Onumber__class_Onumber__of(_1116527), _1116529)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116527), _1116531), _1116533)))), 18851 ^ _778495 : [(18854 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116527), hAPP(c_Int_Onumber__class_Onumber__of(_1116527), _1116529)), _1116533)), _1116531))], (18852 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116527), c_Groups_Ozero__class_Ozero(_1116527)), _1116533)))]], 18855 ^ _778495 : [(18858 ^ _778495) ^ [] : [18859 ^ _778495 : [(18862 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116527), _1116531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116527), hAPP(c_Int_Onumber__class_Onumber__of(_1116527), _1116529)), _1116533)))], (18860 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116527), _1116533), c_Groups_Ozero__class_Ozero(_1116527))))]], 18863 ^ _778495 : [(18866 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116527), hAPP(c_Int_Onumber__class_Onumber__of(_1116527), _1116529)), c_Groups_Ozero__class_Ozero(_1116527)))], (18864 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116527), _1116533), c_Groups_Ozero__class_Ozero(_1116527)))]]], (18856 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116527), c_Groups_Ozero__class_Ozero(_1116527)), _1116533))]]]]], (9785 ^ _778495) ^ [_946217, _946219, _946221, _946223, _946225, _946227] : [c_Finite__Set_Ofun__left__comm__idem(_946217, _946219, _946221), hBOOL(hAPP(c_Finite__Set_Ofinite(_946217), _946223)), -(hAPP(hAPP(c_Finite__Set_Ofold(_946217, _946219, _946221), _946225), hAPP(hAPP(c_Set_Oinsert(_946217), _946227), _946223)) = hAPP(hAPP(c_Finite__Set_Ofold(_946217, _946219, _946221), hAPP(hAPP(_946221, _946227), _946225)), _946223))], (24848 ^ _778495) ^ [_1223119] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1223119)), -(hAPP(c_Int_Onat, _1223119) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45213 ^ _778495) ^ [_1685344, _1685346, _1685348, _1685350, _1685352, _1685354] : [c_List_Olist__all2(_1685344, _1685346, _1685348, _1685350, _1685352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685354), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685344)), _1685350))), -(hBOOL(hAPP(hAPP(_1685348, hAPP(hAPP(c_List_Onth(_1685344), _1685350), _1685354)), hAPP(hAPP(c_List_Onth(_1685346), _1685352), _1685354))))], (3800 ^ _778495) ^ [_835598, _835600, _835602, _835604, _835606, _835608] : [-(c_List_Olinorder__class_Oinsort__key(_835608, _835604, _835600) = c_List_Olinorder__class_Oinsort__key(_835606, _835602, _835598)), _835608 = _835606, _835604 = _835602, _835600 = _835598], (33272 ^ _778495) ^ [_1393863, _1393865, _1393867, _1393869, _1393871] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393863, tc_fun(_1393865, tc_HOL_Obool)), _1393867), hAPP(hAPP(c_COMBB(tc_fun(_1393865, tc_HOL_Obool), tc_fun(_1393865, tc_HOL_Obool), _1393863), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1393865, tc_HOL_Obool)), _1393869)), _1393871)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1393865, tc_HOL_Obool)), _1393869), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393863, tc_fun(_1393865, tc_HOL_Obool)), _1393867), _1393871)))], (3008 ^ _778495) ^ [_823248, _823250, _823252, _823254] : [-(c_Wellfounded_Oacc(_823254, _823250) = c_Wellfounded_Oacc(_823252, _823248)), _823254 = _823252, _823250 = _823248], (27687 ^ _778495) ^ [_1272619, _1272621] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272619, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272619, tc_HOL_Obool)), _1272621)), _1272621) = c_Orderings_Otop__class_Otop(tc_fun(_1272619, tc_HOL_Obool)))], (40199 ^ _778495) ^ [_1563413, _1563415] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563413, _1563413)), hAPP(hAPP(c_Product__Type_OPair(_1563413, _1563413), 40200 ^ [_1563413, _1563415]), 40200 ^ [_1563413, _1563415])), c_Transitive__Closure_Otrancl(_1563413, _1563415)))), -(c_Wellfounded_Oacyclic(_1563413, _1563415))], (34377 ^ _778495) ^ [_1420436, _1420438, _1420440, _1420442, _1420444, _1420446] : [hBOOL(hAPP(hAPP(c_member(_1420436), _1420438), _1420440)), _1420442 = hAPP(_1420444, _1420438), -(hBOOL(hAPP(hAPP(c_member(_1420446), _1420442), hAPP(c_Set_Oimage(_1420436, _1420446, _1420444), _1420440))))], (49198 ^ _778495) ^ [_1773614, _1773616] : [c_Relation_Oantisym(_1773614, _1773616), -(c_Relation_Oantisym(_1773614, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1773614, _1773614), tc_HOL_Obool)), _1773616), c_Relation_OId(_1773614))))], (19080 ^ _778495) ^ [_1121517, _1121519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121517), _1121519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1121517), _1121519)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (2430 ^ _778495) ^ [_814277, _814279, _814281, _814283] : [-(c_Orderings_Oord_Omin(_814283, _814279) = c_Orderings_Oord_Omin(_814281, _814277)), _814283 = _814281, _814279 = _814277], (15709 ^ _778495) ^ [_1058067, _1058069] : [_1058067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058067), _1058069) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35579 ^ _778495) ^ [] : [-(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))))))], (27011 ^ _778495) ^ [] : [-(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))], (51311 ^ _778495) ^ [_1815664, _1815666, _1815668, _1815670] : [class_Rings_Ocomm__semiring__1(_1815664), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815664), _1815666), _1815668)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815664), _1815668), _1815670)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815664), _1815666), _1815670)))], (902 ^ _778495) ^ [_792020, _792022, _792024, _792026, _792028, _792030, _792032, _792034] : [-(c_Fun_Oinj__on(_792032, _792028, _792024, _792020)), c_Fun_Oinj__on(_792034, _792030, _792026, _792022), _792034 = _792032, _792030 = _792028, _792026 = _792024, _792022 = _792020], (26588 ^ _778495) ^ [] : [-(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))))], (44205 ^ _778495) ^ [_1662863, _1662865, _1662867] : [-(_1662863 = c_List_Olist_ONil(_1662865)), -(c_List_Olast(_1662865, hAPP(hAPP(c_List_Olist_OCons(_1662865), _1662867), _1662863)) = c_List_Olast(_1662865, _1662863))], (22958 ^ _778495) ^ [_1188823, _1188825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1188823), 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)))), _1188825)), 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)))), _1188823)) = 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), _1188825), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1188823))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (16214 ^ _778495) ^ [_1068193, _1068195, _1068197] : [class_Rings_Odivision__ring(_1068193), -(_1068195 = c_Groups_Ozero__class_Ozero(_1068193)), 16221 ^ _778495 : [(16228 ^ _778495) ^ [] : [_1068197 = _1068195, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1068193), _1068197), _1068195) = c_Groups_Oone__class_Oone(_1068193))], (16222 ^ _778495) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1068193), _1068197), _1068195) = c_Groups_Oone__class_Oone(_1068193), -(_1068197 = _1068195)]]], (23827 ^ _778495) ^ [_1205127, _1205129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205127)), 23830 ^ _778495 : [(23837 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205129)), -(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), _1205129), _1205127))))], (23831 ^ _778495) ^ [] : [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), _1205129), _1205127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205129)))]]], (21434 ^ _778495) ^ [_1162759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1162759))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1162759)))], (49576 ^ _778495) ^ [_1779939, _1779941] : [c_Equiv__Relations_Opart__equivp(_1779939, _1779941), 49580 ^ _778495 : [(49585 ^ _778495) ^ [] : [-(c_Predicate_Otransp(_1779939, _1779941))], (49583 ^ _778495) ^ [] : [-(c_Predicate_Osymp(_1779939, _1779941))], (49581 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1779941, 49579 ^ [_1779939, _1779941]), 49579 ^ [_1779939, _1779941])))]]], (11270 ^ _778495) ^ [_972989, _972991, _972993] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972989), _972991) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972989), _972993), -(_972991 = _972993)], (41332 ^ _778495) ^ [_1592488] : [-(c_Nitpick_Odenom(_1592488) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1592488, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1592488)))], (48710 ^ _778495) ^ [_1761226, _1761228, _1761230] : [c_List_Oall__interval__int(_1761226, _1761228, _1761230), 48713 ^ _778495 : [(48714 ^ _778495) ^ [_1761304] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1761304), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1761228, _1761230))), -(hBOOL(hAPP(_1761226, _1761304)))]]], (14715 ^ _778495) ^ [_1039472, _1039474, _1039476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1039472)), 14718 ^ _778495 : [(14725 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039474), _1039476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039472), _1039474)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039472), _1039476))))], (14719 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039472), _1039474)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039472), _1039476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039474), _1039476)))]]], (2340 ^ _778495) ^ [_812818, _812820, _812822, _812824] : [-(c_Divides_Odivmod__int(_812824, _812820) = c_Divides_Odivmod__int(_812822, _812818)), _812824 = _812822, _812820 = _812818], (37045 ^ _778495) ^ [_1477191, _1477193, _1477195, _1477197, _1477199] : [c_Finite__Set_Ofolding__one__idem(_1477191, _1477193, _1477195), hAPP(_1477197, hAPP(hAPP(_1477193, 37050 ^ [_1477191, _1477193, _1477195, _1477197, _1477199]), 37051 ^ [_1477191, _1477193, _1477195, _1477197, _1477199])) = hAPP(hAPP(_1477193, hAPP(_1477197, 37050 ^ [_1477191, _1477193, _1477195, _1477197, _1477199])), hAPP(_1477197, 37051 ^ [_1477191, _1477193, _1477195, _1477197, _1477199])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477191), _1477199)), -(_1477199 = c_Orderings_Obot__class_Obot(tc_fun(_1477191, tc_HOL_Obool))), -(hAPP(_1477197, hAPP(_1477195, _1477199)) = hAPP(_1477195, hAPP(c_Set_Oimage(_1477191, _1477191, _1477197), _1477199)))], (48566 ^ _778495) ^ [_1757948, _1757950, _1757952] : [-(c_List_Olist__ex1(_1757948, _1757950, _1757952)), 48567 ^ _778495 : [(48568 ^ _778495) ^ [_1758042] : [hBOOL(hAPP(hAPP(c_member(_1757948), _1758042), hAPP(c_List_Oset(_1757948), _1757952))), hBOOL(hAPP(_1757950, _1758042)), 48576 ^ _778495 : [(48581 ^ _778495) ^ [] : [48575 ^ [_1757948, _1757950, _1757952, _1758042] = _1758042], (48579 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1757950, 48575 ^ [_1757948, _1757950, _1757952, _1758042])))], (48577 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757948), 48575 ^ [_1757948, _1757950, _1757952, _1758042]), hAPP(c_List_Oset(_1757948), _1757952))))]]]]], (15737 ^ _778495) ^ [_1058495, _1058497, _1058499, _1058501, _1058503] : [class_Groups_Oordered__comm__monoid__add(_1058495), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058497), _1058499)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1058497, tc_HOL_Obool)), _1058501), _1058499)), 15751 ^ _778495 : [(15754 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058495), c_Groups_Ozero__class_Ozero(_1058495)), hAPP(_1058503, 15750 ^ [_1058495, _1058497, _1058499, _1058501, _1058503])))], (15752 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1058497), 15750 ^ [_1058495, _1058497, _1058499, _1058501, _1058503]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058497, tc_HOL_Obool)), _1058499), _1058501))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058495), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058497, _1058495), _1058503), _1058501)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058497, _1058495), _1058503), _1058499))))], (21342 ^ _778495) ^ [_1160863, _1160865, _1160867] : [class_Rings_Olinordered__idom(_1160863), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160863), c_Groups_Ozero__class_Ozero(_1160863)), _1160865)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160863), hAPP(c_Groups_Oabs__class_Oabs(_1160863), _1160867)), _1160865) = hAPP(c_Groups_Oabs__class_Oabs(_1160863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160863), _1160867), _1160865)))], (50387 ^ _778495) ^ [_1797213, _1797215, _1797217] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1797213, _1797213)), hAPP(hAPP(c_Product__Type_OPair(_1797213, _1797213), hAPP(_1797215, hAPP(c_Nat_OSuc, 50388 ^ [_1797213, _1797215, _1797217]))), hAPP(_1797215, 50388 ^ [_1797213, _1797215, _1797217]))), c_Transitive__Closure_Ortrancl(_1797213, _1797217))), c_Wellfounded_Owf(_1797213, c_Transitive__Closure_Otrancl(_1797213, _1797217)), 50396 ^ _778495 : [(50397 ^ _778495) ^ [_1797479] : [-(hAPP(_1797215, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50395 ^ [_1797213, _1797215, _1797217]), _1797479)) = hAPP(_1797215, 50395 ^ [_1797213, _1797215, _1797217]))]]], (46915 ^ _778495) ^ [_1721935, _1721937, _1721939, _1721941, _1721943] : [hBOOL(hAPP(hAPP(c_member(_1721935), _1721937), hAPP(c_List_Oset(_1721935), _1721939))), -(hBOOL(hAPP(_1721941, _1721937))), -(c_List_OtakeWhile(_1721935, _1721941, hAPP(hAPP(c_List_Oappend(_1721935), _1721939), _1721943)) = c_List_OtakeWhile(_1721935, _1721941, _1721939))], (6106 ^ _778495) ^ [_876535, _876537, _876539, _876541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876535, tc_HOL_Obool)), _876537), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876535, tc_HOL_Obool)), _876539), _876541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876535, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_876535, tc_HOL_Obool)), _876537), _876539)), _876541)))], (41133 ^ _778495) ^ [_1586999, _1587001, _1587003, _1587005, _1587007] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586999, _1586999)), hAPP(hAPP(c_Product__Type_OPair(_1586999, _1586999), _1587001), _1587003)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586999, _1586999), tc_HOL_Obool), _1587005), _1587007))), 41138 ^ _778495 : [(41141 ^ _778495) ^ [] : [-(_1587001 = _1587003)], (41139 ^ _778495) ^ [] : [-(_1587005 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41144 ^ _778495 : [(41149 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586999, _1586999)), hAPP(hAPP(c_Product__Type_OPair(_1586999, _1586999), 41142 ^ [_1586999, _1587001, _1587003, _1587005, _1587007]), _1587003)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586999, _1586999), tc_HOL_Obool), 41143 ^ [_1586999, _1587001, _1587003, _1587005, _1587007]), _1587007))))], (41147 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586999, _1586999)), hAPP(hAPP(c_Product__Type_OPair(_1586999, _1586999), _1587001), 41142 ^ [_1586999, _1587001, _1587003, _1587005, _1587007])), _1587007)))], (41145 ^ _778495) ^ [] : [-(_1587005 = hAPP(c_Nat_OSuc, 41143 ^ [_1586999, _1587001, _1587003, _1587005, _1587007]))]]], (45320 ^ _778495) ^ [_1687979, _1687981] : [-(_1687979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1687981, _1687979, c_List_Olist_ONil(_1687981)) = c_List_Olist_ONil(tc_List_Olist(_1687981)))], (27293 ^ _778495) ^ [_1265782, _1265784] : [class_Rings_Olinordered__idom(_1265782), 27296 ^ _778495 : [(27303 ^ _778495) ^ [] : [_1265784 = c_Groups_Ozero__class_Ozero(_1265782), -(c_Groups_Osgn__class_Osgn(_1265782, _1265784) = c_Groups_Ozero__class_Ozero(_1265782))], (27297 ^ _778495) ^ [] : [c_Groups_Osgn__class_Osgn(_1265782, _1265784) = c_Groups_Ozero__class_Ozero(_1265782), -(_1265784 = c_Groups_Ozero__class_Ozero(_1265782))]]], (51471 ^ _778495) ^ [_1818418] : [_1818418 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818418), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (10983 ^ _778495) ^ [_967441, _967443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967441), _967443)), 10986 ^ _778495 : [(10989 ^ _778495) ^ [] : [_967441 = _967443], (10987 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967441), _967443)))]]], (29894 ^ _778495) ^ [_1322300, _1322302, _1322304, _1322306, _1322308] : [hAPP(c_Product__Type_Osnd(_1322300, _1322302), hAPP(hAPP(c_Product__Type_OPair(_1322300, _1322302), _1322304), _1322306)) = _1322308, -(_1322306 = _1322308)], (46120 ^ _778495) ^ [_1706378, _1706380, _1706382] : [class_Orderings_Olinorder(_1706378), c_List_Olinorder__class_Osorted(_1706378, _1706380), -(c_List_Olinorder__class_Osorted(_1706378, hAPP(hAPP(c_List_Odrop(_1706378), _1706382), _1706380)))], (46987 ^ _778495) ^ [_1723597, _1723599, _1723601] : [-(hAPP(hAPP(c_List_Oappend(_1723597), c_List_OtakeWhile(_1723597, _1723599, _1723601)), c_List_OdropWhile(_1723597, _1723599, _1723601)) = _1723601)], (28685 ^ _778495) ^ [_1298491, _1298493] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1298491) = hAPP(c_Nat_OSuc, _1298493), -(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(_1298491))), 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)), _1298493))))))], (34701 ^ _778495) ^ [_1427438, _1427440, _1427442, _1427444] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1427438, tc_fun(_1427440, tc_HOL_Obool)), _1427442), _1427444) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1427440, tc_HOL_Obool), hAPP(c_Set_Oimage(_1427438, tc_fun(_1427440, tc_HOL_Obool), _1427444), _1427442)))], (47217 ^ _778495) ^ [_1728309, _1728311, _1728313] : [hBOOL(hAPP(c_List_Odistinct(_1728309), _1728311)), -(hBOOL(hAPP(c_List_Odistinct(_1728309), c_List_Oinsert(_1728309, _1728313, _1728311))))], (48362 ^ _778495) ^ [_1753483, _1753485, _1753487] : [-(hAPP(hAPP(c_List_Oappend(_1753483), c_List_Oreplicate(_1753483, _1753485, _1753487)), hAPP(hAPP(c_List_Olist_OCons(_1753483), _1753487), c_List_Olist_ONil(_1753483))) = hAPP(hAPP(c_List_Olist_OCons(_1753483), _1753487), c_List_Oreplicate(_1753483, _1753485, _1753487)))], (23006 ^ _778495) ^ [_1189729, _1189731, _1189733] : [class_Divides_Osemiring__div(_1189729), -(c_Divides_Odiv__class_Omod(_1189729, c_Divides_Odiv__class_Omod(_1189729, _1189731, _1189733), _1189733) = c_Divides_Odiv__class_Omod(_1189729, _1189731, _1189733))], (41831 ^ _778495) ^ [_1608084, _1608086, _1608088] : [_1608084 = _1608086, 41834 ^ _778495 : [(41837 ^ _778495) ^ [_1608232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1608232), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608088)), _1608084))), -(hAPP(hAPP(c_List_Onth(_1608088), _1608084), _1608232) = hAPP(hAPP(c_List_Onth(_1608088), _1608086), _1608232))], (41835 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608088)), _1608084) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608088)), _1608086))]]], (27583 ^ _778495) ^ [_1270807, _1270809] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1270807, _1270809)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1270807, _1270809), tc_HOL_Obool)))), 27586 ^ _778495 : [(27589 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1270809), c_Orderings_Otop__class_Otop(tc_fun(_1270809, tc_HOL_Obool)))))], (27587 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1270807), c_Orderings_Otop__class_Otop(tc_fun(_1270807, tc_HOL_Obool)))))]]], (5775 ^ _778495) ^ [_870037, _870039, _870041, _870043] : [c_Finite__Set_Ofolding__one(_870037, _870039, _870041), -(hAPP(_870041, hAPP(hAPP(c_Set_Oinsert(_870037), _870043), c_Orderings_Obot__class_Obot(tc_fun(_870037, tc_HOL_Obool)))) = _870043)], (46104 ^ _778495) ^ [_1706142, _1706144] : [class_Orderings_Olinorder(_1706142), -(c_List_Olinorder__class_Osorted(_1706142, c_List_Olinorder__class_Osort__key(_1706142, _1706142, c_COMBI(_1706142), _1706144)))], (47705 ^ _778495) ^ [_1739792, _1739794] : [c_List_Olist__ex(_1739792, _1739794, c_List_Olist_ONil(_1739792))], (20202 ^ _778495) ^ [_1141391, _1141393] : [class_Rings_Osemiring__1(_1141391), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1141391), hAPP(c_Nat_OSuc, _1141393)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141391), c_Groups_Oone__class_Oone(_1141391)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1141391), _1141393)))], (52347 ^ _778495) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (3160 ^ _778495) ^ [_825566, _825568, _825570, _825572, _825574, _825576] : [-(c_Big__Operators_Olattice_OSup__fin(_825576, _825572, _825568) = c_Big__Operators_Olattice_OSup__fin(_825574, _825570, _825566)), _825576 = _825574, _825572 = _825570, _825568 = _825566], (13482 ^ _778495) ^ [_1017793] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1017793) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40804 ^ _778495) ^ [_1578483, _1578485, _1578487, _1578489] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578483, _1578483)), hAPP(hAPP(c_Product__Type_OPair(_1578483, _1578483), _1578485), _1578487)), c_Transitive__Closure_Ortrancl(_1578483, _1578489))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578483, _1578483)), hAPP(hAPP(c_Product__Type_OPair(_1578483, _1578483), _1578487), _1578485)), c_Transitive__Closure_Ortrancl(_1578483, hAPP(c_Relation_Oconverse(_1578483, _1578483), _1578489)))))], (13231 ^ _778495) ^ [_1014068, _1014070, _1014072] : [class_Groups_Ogroup__add(_1014068), 13234 ^ _778495 : [(13241 ^ _778495) ^ [] : [_1014070 = _1014072, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014068), _1014070), _1014072) = c_Groups_Ozero__class_Ozero(_1014068))], (13235 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014068), _1014070), _1014072) = c_Groups_Ozero__class_Ozero(_1014068), -(_1014070 = _1014072)]]], (22784 ^ _778495) ^ [_1185764, _1185766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185764), _1185766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1185764)), c_Int_OBit1(_1185766))))], (40621 ^ _778495) ^ [_1574163, _1574165, _1574167, _1574169] : [-(c_Wellfounded_Oacyclic(_1574163, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1574163, _1574163)), hAPP(hAPP(c_Product__Type_OPair(_1574163, _1574163), _1574165), _1574167)), _1574169))), c_Wellfounded_Oacyclic(_1574163, _1574169), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574163, _1574163)), hAPP(hAPP(c_Product__Type_OPair(_1574163, _1574163), _1574167), _1574165)), c_Transitive__Closure_Ortrancl(_1574163, _1574169))))], (11466 ^ _778495) ^ [_977023, _977025, _977027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977023), _977025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977023), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977025), _977027))))], (38312 ^ _778495) ^ [_1515110, _1515112] : [c_Predicate_Oreflp(_1515110, _1515112), -(c_Relation_Orefl__on(_1515110, c_Orderings_Otop__class_Otop(tc_fun(_1515110, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1515110, _1515110)), hAPP(c_Product__Type_Oprod_Oprod__case(_1515110, _1515110, tc_HOL_Obool), _1515112))))], (48078 ^ _778495) ^ [_1747313, _1747315, _1747317, _1747319, _1747321, _1747323, _1747325] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1747313, _1747315, _1747317, _1747319), _1747321), _1747323), _1747325) = c_New__DSequence_Opos__bind(_1747313, _1747315, hAPP(hAPP(hAPP(_1747317, _1747321), _1747323), _1747325), hAPP(hAPP(c_COMBC(_1747313, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1747315))), hAPP(hAPP(c_COMBC(_1747313, 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(_1747315)))), hAPP(hAPP(c_COMBC(_1747313, 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(_1747315))))), _1747319), _1747321)), _1747323)), _1747325)))], (34955 ^ _778495) ^ [_1432369, _1432371, _1432373, _1432375, _1432377, _1432379] : [_1432369 = _1432371, -(hAPP(c_Fun_Ofun__upd(_1432373, _1432375, _1432377, _1432371, _1432379), _1432369) = _1432379)], (30843 ^ _778495) ^ [_1341570, _1341572, _1341574] : [class_Orderings_Olinorder(_1341570), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341570), _1341572), _1341574) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341570), _1341574), _1341572))], (43253 ^ _778495) ^ [_1641428, _1641430, _1641432] : [_1641432 = c_List_Olist_ONil(_1641430), -(_1641428 = hAPP(hAPP(c_List_Oappend(_1641430), _1641428), _1641432))], (26722 ^ _778495) ^ [_1256301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1256301), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1256301)), c_Int_OMin)))], (41087 ^ _778495) ^ [_1585885, _1585887] : [-(c_Transitive__Closure_Ortrancl(_1585885, _1585887) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1585885, _1585885), 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(_1585885, _1585885), tc_HOL_Obool), tc_fun(tc_prod(_1585885, _1585885), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1585885, _1585885), tc_HOL_Obool)), _1585887)))], (48547 ^ _778495) ^ [_1757515, _1757517, _1757519] : [c_List_Olist__ex1(_1757515, _1757517, _1757519), 48551 ^ _778495 : [(48556 ^ _778495) ^ [_1757761] : [-(_1757761 = 48550 ^ [_1757515, _1757517, _1757519]), hBOOL(hAPP(hAPP(c_member(_1757515), _1757761), hAPP(c_List_Oset(_1757515), _1757519))), hBOOL(hAPP(_1757517, _1757761))], (48554 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1757517, 48550 ^ [_1757515, _1757517, _1757519])))], (48552 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757515), 48550 ^ [_1757515, _1757517, _1757519]), hAPP(c_List_Oset(_1757515), _1757519))))]]], (22080 ^ _778495) ^ [_1173531, _1173533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1173531)), c_Int_OBit0(_1173533))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1173531), _1173533)))], (46925 ^ _778495) ^ [_1722093, _1722095, _1722097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722093)), c_List_OtakeWhile(_1722093, _1722095, _1722097))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722093)), _1722097))), hBOOL(hAPP(_1722095, hAPP(hAPP(c_List_Onth(_1722093), _1722097), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722093)), c_List_OtakeWhile(_1722093, _1722095, _1722097)))))], (31642 ^ _778495) ^ [_1356880, _1356882, _1356884, _1356886, _1356888] : [-(hAPP(c_Product__Type_Ofst(_1356880, _1356882), hAPP(c_Product__Type_Oapfst(_1356884, _1356880, _1356882, _1356886), _1356888)) = hAPP(_1356886, hAPP(c_Product__Type_Ofst(_1356884, _1356882), _1356888)))], (41115 ^ _778495) ^ [_1586557, _1586559, _1586561, _1586563, _1586565] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586557, _1586557)), hAPP(hAPP(c_Product__Type_OPair(_1586557, _1586557), _1586559), _1586561)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586557, _1586557), tc_HOL_Obool), _1586563), _1586565))), 41120 ^ _778495 : [(41123 ^ _778495) ^ [] : [-(_1586559 = _1586561)], (41121 ^ _778495) ^ [] : [-(_1586563 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41126 ^ _778495 : [(41131 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586557, _1586557)), hAPP(hAPP(c_Product__Type_OPair(_1586557, _1586557), 41124 ^ [_1586557, _1586559, _1586561, _1586563, _1586565]), _1586561)), _1586565)))], (41129 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586557, _1586557)), hAPP(hAPP(c_Product__Type_OPair(_1586557, _1586557), _1586559), 41124 ^ [_1586557, _1586559, _1586561, _1586563, _1586565])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586557, _1586557), tc_HOL_Obool), 41125 ^ [_1586557, _1586559, _1586561, _1586563, _1586565]), _1586565))))], (41127 ^ _778495) ^ [] : [-(_1586563 = hAPP(c_Nat_OSuc, 41125 ^ [_1586557, _1586559, _1586561, _1586563, _1586565]))]]], (50575 ^ _778495) ^ [_1803102, _1803104, _1803106] : [-(c_Lazy__Sequence_Omap(_1803102, _1803104, _1803106, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1803102)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1803104))], (11923 ^ _778495) ^ [_986154, _986156, _986158, _986160, _986162, _986164] : [class_Rings_Oordered__ring(_986154), 11926 ^ _778495 : [(11933 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986154), _986160), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986154), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_986154), _986162), _986156)), _986158)), _986164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986154), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986154), _986156), _986158)), _986160)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986154), _986162), _986158)), _986164))))], (11927 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986154), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986154), _986156), _986158)), _986160)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986154), _986162), _986158)), _986164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986154), _986160), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986154), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_986154), _986162), _986156)), _986158)), _986164))))]]], (22366 ^ _778495) ^ [_1178466, _1178468] : [class_Rings_Ocomm__ring__1(_1178466), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1178466), _1178468) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178466), hAPP(c_Groups_Ouminus__class_Ouminus(_1178466), c_Groups_Oone__class_Oone(_1178466))), _1178468))], (39836 ^ _778495) ^ [_1554918, _1554920, _1554922, _1554924, _1554926] : [c_Finite__Set_Ofolding__idem(_1554918, _1554920, _1554922, _1554924), -(hAPP(c_Fun_Ocomp(_1554920, _1554920, _1554920, hAPP(_1554922, _1554926)), hAPP(_1554922, _1554926)) = hAPP(_1554922, _1554926))], (5020 ^ _778495) ^ [_855134, _855136, _855138, _855140, _855142, _855144] : [-(c_Set_Oimage(_855144, _855140, _855136) = c_Set_Oimage(_855142, _855138, _855134)), _855144 = _855142, _855140 = _855138, _855136 = _855134], (30049 ^ _778495) ^ [_1325601, _1325603, _1325605] : [-(hAPP(c_Product__Type_Ofst(_1325601, _1325603), _1325605) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1325601, _1325603, _1325601), c_COMBK(_1325601, _1325603)), _1325605))], (6866 ^ _778495) ^ [_891178, _891180] : [class_Lattices_Obounded__lattice__bot(_891178), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891178), c_Orderings_Obot__class_Obot(_891178)), _891180) = _891180)], (46658 ^ _778495) ^ [_1716635, _1716637, _1716639, _1716641, _1716643] : [c_List_Olist__all2(_1716635, _1716637, _1716639, hAPP(c_List_Orev(_1716635), _1716641), _1716643), -(c_List_Olist__all2(_1716635, _1716637, _1716639, _1716641, hAPP(c_List_Orev(_1716637), _1716643)))], (32994 ^ _778495) ^ [_1387094, _1387096, _1387098, _1387100] : [class_Orderings_Oorder(_1387094), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1387094, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1387094, _1387096, _1387098)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1387094, _1387098, _1387100)) = c_Orderings_Obot__class_Obot(tc_fun(_1387094, tc_HOL_Obool)))], (15355 ^ _778495) ^ [_1051185, _1051187, _1051189] : [hBOOL(hAPP(_1051185, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051187), _1051189))), 15358 ^ _778495 : [(15365 ^ _778495) ^ [_1051376] : [_1051187 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051189), _1051376), -(hBOOL(hAPP(_1051185, _1051376)))], (15359 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051187), _1051189)), -(hBOOL(hAPP(_1051185, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (12452 ^ _778495) ^ [_998160, _998162, _998164] : [12454 ^ _778495 : [(12457 ^ _778495) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998160, tc_HOL_Obool)), 12453 ^ [_998160, _998162, _998164]), _998164) = c_Orderings_Obot__class_Obot(tc_fun(_998160, tc_HOL_Obool))], (12455 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_998160, tc_HOL_Obool)), 12453 ^ [_998160, _998162, _998164]), _998162)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998160, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_998160, tc_HOL_Obool), _998162)), _998164) = c_Orderings_Obot__class_Obot(tc_fun(_998160, tc_HOL_Obool)))], (42209 ^ _778495) ^ [_1619059, _1619061] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1619059, _1619061) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1619059), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1619061), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (33509 ^ _778495) ^ [_1401414, _1401416, _1401418, _1401420, _1401422] : [_1401414 = c_Orderings_Obot__class_Obot(tc_fun(_1401416, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401418, tc_HOL_Obool)), _1401420), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401416, tc_fun(_1401418, tc_HOL_Obool)), _1401414), _1401422)) = _1401420)], (41228 ^ _778495) ^ [_1590011, _1590013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590011, _1590011)), _1590013), c_Relation_OId(_1590011))), -(_1590013 = hAPP(hAPP(c_Product__Type_OPair(_1590011, _1590011), 41231 ^ [_1590011, _1590013]), 41231 ^ [_1590011, _1590013]))], (12693 ^ _778495) ^ [_1003296, _1003298, _1003300, _1003302, _1003304] : [class_Groups_Ocomm__monoid__add(_1003296), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003298), _1003300)), -(hBOOL(hAPP(hAPP(c_member(_1003298), _1003302), _1003300))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003298, _1003296), _1003304), hAPP(hAPP(c_Set_Oinsert(_1003298), _1003302), _1003300)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003296), hAPP(_1003304, _1003302)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003298, _1003296), _1003304), _1003300)))], (49634 ^ _778495) ^ [_1781356, _1781358, _1781360, _1781362] : [c_Fun_Oinj__on(_1781356, _1781358, _1781360, c_Orderings_Otop__class_Otop(tc_fun(_1781356, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781358, _1781356, c_Hilbert__Choice_Oinv__into(_1781356, _1781358, c_Orderings_Otop__class_Otop(tc_fun(_1781356, tc_HOL_Obool)), _1781360)), hAPP(c_Set_Oimage(_1781356, _1781358, _1781360), _1781362)) = _1781362)], (20972 ^ _778495) ^ [_1154147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154147)), 20976 ^ _778495 : [(20979 ^ _778495) ^ [] : [-(_1154147 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20975 ^ [_1154147]))], (20977 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20975 ^ [_1154147])))]]], (5877 ^ _778495) ^ [_872091, _872093] : [hBOOL(hAPP(hAPP(c_member(_872091), _872093), c_Orderings_Obot__class_Obot(tc_fun(_872091, tc_HOL_Obool))))], (9937 ^ _778495) ^ [_949236, _949238, _949240, _949242, _949244] : [c_Finite__Set_Ofolding__one(_949236, _949238, _949240), hBOOL(hAPP(c_Finite__Set_Ofinite(_949236), _949242)), hBOOL(hAPP(c_Finite__Set_Ofinite(_949236), _949244)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949236, tc_HOL_Obool)), _949242), _949244) = c_Orderings_Obot__class_Obot(tc_fun(_949236, tc_HOL_Obool))), -(hAPP(hAPP(_949238, hAPP(_949240, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_949236, tc_HOL_Obool)), _949242), _949244))), hAPP(_949240, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949236, tc_HOL_Obool)), _949242), _949244))) = hAPP(hAPP(_949238, hAPP(_949240, _949242)), hAPP(_949240, _949244)))], (36228 ^ _778495) ^ [_1460400, _1460402, _1460404, _1460406, _1460408] : [c_Fun_Oinj__on(_1460400, _1460402, _1460404, _1460406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1460400, tc_HOL_Obool)), _1460408), _1460406)), -(c_Fun_Oinj__on(_1460400, _1460402, _1460404, _1460408))], (34907 ^ _778495) ^ [_1431600, _1431602, _1431604, _1431606] : [-(c_Fun_Ofun__upd(_1431600, _1431602, _1431604, _1431606, hAPP(_1431604, _1431606)) = _1431604)], (48870 ^ _778495) ^ [_1766152, _1766154, _1766156, _1766158] : [class_Complete__Lattice_Ocomplete__lattice(_1766152), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1766154, _1766152), _1766156), _1766158) = c_Complete__Lattice_OInf__class_OInf(_1766152, hAPP(c_Set_OCollect(_1766152), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1766154, _1766152), tc_HOL_Obool), tc_HOL_Obool, _1766152), c_HOL_OEx(tc_fun(_1766154, _1766152))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1766154, _1766152), tc_HOL_Obool), tc_fun(tc_fun(_1766154, _1766152), tc_HOL_Obool), _1766152), hAPP(c_COMBS(tc_fun(_1766154, _1766152), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1766154, _1766152)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1766154, _1766152), tc_fun(tc_fun(_1766154, _1766152), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1766154, _1766152))), _1766156)))), hAPP(hAPP(c_COMBC(_1766152, tc_fun(tc_fun(_1766154, _1766152), _1766152), tc_fun(tc_fun(_1766154, _1766152), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1766152, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1766154, _1766152), _1766152), tc_fun(tc_fun(_1766154, _1766152), tc_HOL_Obool)), _1766152), c_COMBB(_1766152, tc_HOL_Obool, tc_fun(_1766154, _1766152))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1766154, _1766152), _1766154, _1766152), c_COMBI(tc_fun(_1766154, _1766152))), _1766158)))))))], (52113 ^ _778495) ^ [_1830001, _1830003] : [class_Lattices_Odistrib__lattice(_1830001), -(class_Lattices_Odistrib__lattice(tc_fun(_1830003, _1830001)))], (36606 ^ _778495) ^ [_1467717, _1467719, _1467721, _1467723, _1467725, _1467727] : [c_Fun_Oinj__on(_1467717, _1467719, _1467721, _1467723), -(hBOOL(hAPP(hAPP(c_member(_1467719), _1467725), hAPP(c_Set_Oimage(_1467717, _1467719, _1467721), _1467723)))), -(c_Fun_Oinj__on(_1467717, _1467719, c_Fun_Ofun__upd(_1467717, _1467719, _1467721, _1467727, _1467725), _1467723))], (28333 ^ _778495) ^ [_1286732, _1286734, _1286736, _1286738, _1286740, _1286742] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1286732, _1286734)), hAPP(hAPP(c_Product__Type_OPair(_1286732, _1286734), _1286740), _1286742)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool)), _1286736), _1286738))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286732, tc_fun(_1286734, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1286732, tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_fun(_1286734, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1286734, tc_fun(tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_fun(_1286734, tc_HOL_Obool)), _1286732), c_COMBC(_1286734, tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1286734, tc_prod(_1286732, _1286734)), tc_fun(_1286734, tc_fun(tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_HOL_Obool)), _1286732), hAPP(c_COMBB(tc_prod(_1286732, _1286734), tc_fun(tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_HOL_Obool), _1286734), c_member(tc_prod(_1286732, _1286734)))), c_Product__Type_OPair(_1286732, _1286734)))), _1286736)), hAPP(hAPP(c_COMBC(_1286732, tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_fun(_1286734, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1286734, tc_fun(tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_fun(_1286734, tc_HOL_Obool)), _1286732), c_COMBC(_1286734, tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1286734, tc_prod(_1286732, _1286734)), tc_fun(_1286734, tc_fun(tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_HOL_Obool)), _1286732), hAPP(c_COMBB(tc_prod(_1286732, _1286734), tc_fun(tc_fun(tc_prod(_1286732, _1286734), tc_HOL_Obool), tc_HOL_Obool), _1286734), c_member(tc_prod(_1286732, _1286734)))), c_Product__Type_OPair(_1286732, _1286734)))), _1286738)), _1286740), _1286742)))], (49606 ^ _778495) ^ [_1780740, _1780742, _1780744] : [hAPP(c_Fun_Ocomp(_1780742, _1780740, _1780740, c_Hilbert__Choice_Oinv__into(_1780740, _1780742, c_Orderings_Otop__class_Otop(tc_fun(_1780740, tc_HOL_Obool)), _1780744)), _1780744) = c_Fun_Oid(_1780740), -(c_Fun_Oinj__on(_1780740, _1780742, _1780744, c_Orderings_Otop__class_Otop(tc_fun(_1780740, tc_HOL_Obool))))], (37773 ^ _778495) ^ [_1497210, _1497212, _1497214] : [-(hAPP(c_Set_OCollect(_1497210), hAPP(hAPP(c_COMBS(_1497210, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497210), c_fconj), _1497212)), _1497214)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1497210, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1497210), _1497212)), hAPP(c_Set_OCollect(_1497210), _1497214)))], (11895 ^ _778495) ^ [_985612, _985614, _985616, _985618, _985620] : [class_Groups_Oordered__cancel__ab__semigroup__add(_985612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985612), _985614), _985616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985612), _985618), _985620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985612), _985614), _985618)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985612), _985616), _985620))))], (42433 ^ _778495) ^ [_1624100, _1624102, _1624104, _1624106] : [hBOOL(hAPP(c_List_Odistinct(_1624100), _1624102)), -(hBOOL(hAPP(hAPP(c_member(_1624100), _1624104), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1624100, tc_HOL_Obool)), hAPP(c_List_Oset(_1624100), _1624102)), hAPP(hAPP(c_Set_Oinsert(_1624100), hAPP(hAPP(c_List_Onth(_1624100), _1624102), _1624106)), c_Orderings_Obot__class_Obot(tc_fun(_1624100, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1624100), hAPP(hAPP(c_List_Olist__update(_1624100, _1624102), _1624106), _1624104))))], (35985 ^ _778495) ^ [_1454036, _1454038] : [c_Equiv__Relations_Oequivp(_1454036, _1454038), 35988 ^ _778495 : [(35995 ^ _778495) ^ [_1454229, _1454231] : [hAPP(_1454038, _1454231) = hAPP(_1454038, _1454229), -(hBOOL(hAPP(hAPP(_1454038, _1454231), _1454229)))], (35989 ^ _778495) ^ [_1454130, _1454132] : [hBOOL(hAPP(hAPP(_1454038, _1454132), _1454130)), -(hAPP(_1454038, _1454132) = hAPP(_1454038, _1454130))]]], (30249 ^ _778495) ^ [_1329649] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1329649)) = _1329649)], (10767 ^ _778495) ^ [_963941, _963943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963941), _963943)), -(hAPP(c_Nat_OSuc, _963941) = _963943), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963941)), _963943)))], (33938 ^ _778495) ^ [_1410438, _1410440] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1410438)), _1410440) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1410438, _1410440))], (31011 ^ _778495) ^ [_1345007, _1345009, _1345011] : [class_Groups_Olinordered__ab__group__add(_1345007), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1345007), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345007), _1345009), _1345011)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345007), hAPP(c_Groups_Ouminus__class_Ouminus(_1345007), _1345009)), hAPP(c_Groups_Ouminus__class_Ouminus(_1345007), _1345011)))], (43880 ^ _778495) ^ [_1656222, _1656224, _1656226, _1656228] : [-(hAPP(c_List_Ofoldl(_1656222, _1656224, _1656226, _1656228), c_List_Olist_ONil(_1656224)) = _1656228)], (20442 ^ _778495) ^ [] : [-(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))))], (52293 ^ _778495) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (34402 ^ _778495) ^ [_1420968, _1420970, _1420972, _1420974, _1420976] : [-(hBOOL(hAPP(hAPP(c_member(_1420968), _1420970), hAPP(c_Set_Oimage(_1420972, _1420968, _1420974), _1420976)))), 34403 ^ _778495 : [(34404 ^ _778495) ^ [_1421038] : [hBOOL(hAPP(hAPP(c_member(_1420972), _1421038), _1420976)), _1420970 = hAPP(_1420974, _1421038)]]], (42571 ^ _778495) ^ [_1627186, _1627188] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1627186), _1627188))), -(c_Nitpick_Ocard_H(_1627186, _1627188) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37682 ^ _778495) ^ [_1494513, _1494515, _1494517, _1494519, _1494521, _1494523, _1494525] : [-(hAPP(c_Product__Type_Osnd(_1494513, _1494515), hAPP(c_Product__Type_Omap__pair(_1494517, _1494513, _1494519, _1494515, _1494521, _1494523), _1494525)) = hAPP(_1494523, hAPP(c_Product__Type_Osnd(_1494517, _1494519), _1494525)))], (27557 ^ _778495) ^ [_1270276] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1270276)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1270276), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1270276), c_Orderings_Otop__class_Otop(tc_fun(_1270276, tc_HOL_Obool)))))], (33814 ^ _778495) ^ [_1408001, _1408003, _1408005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1408001), _1408003)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408001), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408003), _1408005)) = 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, _1408001), _1408003)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408003), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408003), _1408005))))], (12749 ^ _778495) ^ [_1004474, _1004476, _1004478, _1004480] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1004474), _1004476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1004474, tc_HOL_Obool)), _1004476), _1004478)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004474, tc_Nat_Onat), _1004480), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1004474, tc_HOL_Obool)), _1004478), _1004476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004474, tc_Nat_Onat), _1004480), _1004478)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004474, tc_Nat_Onat), _1004480), _1004476)))], (33002 ^ _778495) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (30187 ^ _778495) ^ [_1328402, _1328404, _1328406] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1328402, _1328404), _1328406))), _1328402 = 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), _1328406)), _1328404)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1328406)), 30194 ^ _778495 : [(30197 ^ _778495) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1328406) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30195 ^ _778495) ^ [] : [-(_1328404 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 30198 ^ _778495 : [(30201 ^ _778495) ^ [] : [30202 ^ _778495 : [(30205 ^ _778495) ^ [] : [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), _1328406))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1328406)), _1328404))], (30203 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1328404)))]], 30210 ^ _778495 : [(30213 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1328404), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1328406))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1328406)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (30211 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1328404))]]], (30199 ^ _778495) ^ [] : [_1328404 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (7350 ^ _778495) ^ [_900623, _900625, _900627, _900629, _900631] : [c_Finite__Set_Ofolding__one(_900623, _900625, _900627), hBOOL(hAPP(c_Finite__Set_Ofinite(_900623), _900629)), -(hBOOL(hAPP(hAPP(c_member(_900623), _900631), _900629))), -(_900629 = c_Orderings_Obot__class_Obot(tc_fun(_900623, tc_HOL_Obool))), -(hAPP(_900627, hAPP(hAPP(c_Set_Oinsert(_900623), _900631), _900629)) = hAPP(hAPP(_900625, _900631), hAPP(_900627, _900629)))], (50399 ^ _778495) ^ [_1797538, _1797540, _1797542, _1797544, _1797546] : [50401 ^ _778495 : [(50404 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797542, tc_HOL_Obool)), _1797544), hAPP(_1797546, 50400 ^ [_1797538, _1797540, _1797542, _1797544, _1797546])))], (50402 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797538), 50400 ^ [_1797538, _1797540, _1797542, _1797544, _1797546]), _1797540)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797542, tc_HOL_Obool)), _1797544), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797538, tc_fun(_1797542, tc_HOL_Obool)), _1797540), _1797546))))], (22942 ^ _778495) ^ [_1188564, _1188566] : [class_Int_Onumber__ring(_1188564), 22945 ^ _778495 : [(22952 ^ _778495) ^ [] : [c_Int_Oiszero(_1188564, hAPP(c_Int_Onumber__class_Onumber__of(_1188564), 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), _1188566)))), -(c_Groups_Oone__class_Oone(_1188564) = hAPP(c_Int_Onumber__class_Onumber__of(_1188564), _1188566))], (22946 ^ _778495) ^ [] : [c_Groups_Oone__class_Oone(_1188564) = hAPP(c_Int_Onumber__class_Onumber__of(_1188564), _1188566), -(c_Int_Oiszero(_1188564, hAPP(c_Int_Onumber__class_Onumber__of(_1188564), 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), _1188566)))))]]], (4612 ^ _778495) ^ [_848682, _848684] : [_848684 = _848682, -(c_DSequence_Oempty(_848684) = c_DSequence_Oempty(_848682))], (27723 ^ _778495) ^ [_1273244, _1273246, _1273248] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1273244, _1273246, _1273248, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1273246)], (50542 ^ _778495) ^ [_1802461, _1802463, _1802465] : [c_List_Olist__ex(tc_Nat_Onat, _1802461, c_List_Oupt(_1802463, _1802465)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1802461), _1802463, _1802465)], (34623 ^ _778495) ^ [_1425940, _1425942] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1425940), _1425942) = 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)), _1425940)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1425942))))], (41151 ^ _778495) ^ [_1587441, _1587443, _1587445, _1587447, _1587449] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587441, _1587441)), hAPP(hAPP(c_Product__Type_OPair(_1587441, _1587441), _1587443), _1587445)), c_Transitive__Closure_Ortrancl(_1587441, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587441, _1587441), tc_HOL_Obool)), _1587447), _1587449)))), 41157 ^ _778495 : [(41163 ^ _778495) ^ [] : [41156 ^ [_1587441, _1587443, _1587445, _1587447, _1587449] = 41159 ^ [_1587441, _1587443, _1587445, _1587447, _1587449]], (41161 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587441, _1587441)), hAPP(hAPP(c_Product__Type_OPair(_1587441, _1587441), 41156 ^ [_1587441, _1587443, _1587445, _1587447, _1587449]), 41159 ^ [_1587441, _1587443, _1587445, _1587447, _1587449])), _1587449)))], (41158 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587441, _1587441)), hAPP(hAPP(c_Product__Type_OPair(_1587441, _1587441), _1587443), 41156 ^ [_1587441, _1587443, _1587445, _1587447, _1587449])), c_Transitive__Closure_Ortrancl(_1587441, _1587447))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587441, _1587441)), hAPP(hAPP(c_Product__Type_OPair(_1587441, _1587441), _1587443), _1587445)), c_Transitive__Closure_Ortrancl(_1587441, _1587447))))], (40682 ^ _778495) ^ [_1575719, _1575721, _1575723] : [c_Relation_Ototal__on(_1575719, _1575721, _1575723), -(c_Relation_Ototal__on(_1575719, _1575721, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1575719, _1575719), tc_HOL_Obool)), _1575723), c_Relation_OId(_1575719))))], (40904 ^ _778495) ^ [_1581205, _1581207, _1581209] : [-(hAPP(c_Relation_Oconverse(_1581205, _1581207), _1581209) = hAPP(c_Set_OCollect(tc_prod(_1581207, _1581205)), hAPP(c_Product__Type_Oprod_Oprod__case(_1581207, _1581205, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1581207, tc_fun(tc_prod(_1581205, _1581207), tc_HOL_Obool), tc_fun(_1581205, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581205, tc_fun(tc_fun(tc_prod(_1581205, _1581207), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1581205, _1581207), tc_HOL_Obool), tc_fun(_1581205, tc_HOL_Obool)), _1581207), c_COMBC(_1581205, tc_fun(tc_prod(_1581205, _1581207), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581205, tc_prod(_1581205, _1581207)), tc_fun(_1581205, tc_fun(tc_fun(tc_prod(_1581205, _1581207), tc_HOL_Obool), tc_HOL_Obool)), _1581207), hAPP(c_COMBB(tc_prod(_1581205, _1581207), tc_fun(tc_fun(tc_prod(_1581205, _1581207), tc_HOL_Obool), tc_HOL_Obool), _1581205), c_member(tc_prod(_1581205, _1581207)))), hAPP(c_COMBC(_1581205, _1581207, tc_prod(_1581205, _1581207)), c_Product__Type_OPair(_1581205, _1581207))))), _1581209))))], (30639 ^ _778495) ^ [_1337879, _1337881, _1337883, _1337885] : [class_Orderings_Olinorder(_1337879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337879), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1337879), _1337881), _1337883)), _1337885)), 30646 ^ _778495 : [(30649 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337879), _1337883), _1337885)))], (30647 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337879), _1337881), _1337885)))]]], (4554 ^ _778495) ^ [_847777, _847779, _847781, _847783, _847785, _847787, _847789, _847791] : [-(c_Random__Sequence_ORandom(_847791, _847787, _847783, _847779) = c_Random__Sequence_ORandom(_847789, _847785, _847781, _847777)), _847791 = _847789, _847787 = _847785, _847783 = _847781, _847779 = _847777], (26628 ^ _778495) ^ [_1254847] : [_1254847 = c_Int_OMin, -(c_Int_OBit1(_1254847) = c_Int_OMin)], (28825 ^ _778495) ^ [_1301690, _1301692] : [-(c_Divides_OnegDivAlg(_1301690, _1301692) = hAPP(c_Divides_Oadjust(_1301692), c_Divides_OnegDivAlg(_1301690, 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)))), _1301692)))), -(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), _1301690), _1301692)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1301692), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (5831 ^ _778495) ^ [_871130, _871132, _871134] : [-(hAPP(hAPP(c_Set_Oinsert(_871130), _871132), _871134) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_871130, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_871130), _871132), c_Orderings_Obot__class_Obot(tc_fun(_871130, tc_HOL_Obool)))), _871134))], (38769 ^ _778495) ^ [_1528910, _1528912, _1528914] : [c_Wellfounded_Owf(_1528910, _1528912), c_Wellfounded_Owf(_1528910, _1528914), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1528910, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1528910, _1528910), _1528912)), hAPP(c_Relation_ORange(_1528910, _1528910), _1528914)) = c_Orderings_Obot__class_Obot(tc_fun(_1528910, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1528910, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528910, _1528910), tc_HOL_Obool)), _1528912), _1528914)))], (2890 ^ _778495) ^ [_821385, _821387, _821389, _821391] : [-(c_Nitpick_OAbs__Frac(_821391, _821387) = c_Nitpick_OAbs__Frac(_821389, _821385)), _821391 = _821389, _821387 = _821385], (44502 ^ _778495) ^ [_1669688, _1669690, _1669692, _1669694, _1669696] : [-(c_List_Olist_Olist__size(_1669688, _1669690, hAPP(hAPP(c_List_Omap(_1669692, _1669688), _1669694), _1669696)) = c_List_Olist_Olist__size(_1669692, hAPP(c_Fun_Ocomp(_1669688, tc_Nat_Onat, _1669692, _1669690), _1669694), _1669696))], (45034 ^ _778495) ^ [_1681294, _1681296, _1681298] : [hBOOL(hAPP(c_List_Olistsp(_1681294, hAPP(hAPP(c_COMBC(_1681294, tc_fun(_1681294, tc_HOL_Obool), tc_HOL_Obool), c_member(_1681294)), _1681296)), _1681298)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1681294)), _1681298), c_List_Olists(_1681294, _1681296))))], (44161 ^ _778495) ^ [_1662091, _1662093, _1662095] : [class_Orderings_Olinorder(_1662091), -(hAPP(c_List_Oset(_1662091), c_List_Olinorder__class_Oinsort__insert__key(_1662091, _1662091, c_COMBI(_1662091), _1662093, _1662095)) = hAPP(hAPP(c_Set_Oinsert(_1662091), _1662093), hAPP(c_List_Oset(_1662091), _1662095)))], (17467 ^ _778495) ^ [_1091290, _1091292, _1091294] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1091290), _1091292)), 17473 ^ _778495 : [(17476 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1091294, 17472 ^ [_1091290, _1091292, _1091294])))], (17474 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1091290), 17472 ^ [_1091290, _1091292, _1091294]), _1091292)))]], -(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(_1091290, tc_Nat_Onat), _1091294), _1091292))))], (40637 ^ _778495) ^ [_1574621, _1574623] : [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), _1574621), _1574623)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1574621), _1574623)))], (46618 ^ _778495) ^ [_1715638, _1715640, _1715642] : [hAPP(c_List_Orev(_1715638), _1715640) = hAPP(hAPP(c_List_Olist_OCons(_1715638), _1715642), c_List_Olist_ONil(_1715638)), -(_1715640 = hAPP(hAPP(c_List_Olist_OCons(_1715638), _1715642), c_List_Olist_ONil(_1715638)))], (23755 ^ _778495) ^ [_1203990, _1203992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203990), _1203992)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203990), _1203992) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (12707 ^ _778495) ^ [_1003546, _1003548, _1003550, _1003552, _1003554] : [class_Groups_Ocomm__monoid__add(_1003546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003548), _1003550)), -(hBOOL(hAPP(hAPP(c_member(_1003548), _1003552), _1003550))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003548, _1003546), _1003554), hAPP(hAPP(c_Set_Oinsert(_1003548), _1003552), _1003550)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003546), hAPP(_1003554, _1003552)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003548, _1003546), _1003554), _1003550)))], (14993 ^ _778495) ^ [_1044459, _1044461, _1044463, _1044465] : [class_Rings_Olinordered__semiring__strict(_1044459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044459), _1044461), _1044463)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044459), _1044465), _1044463))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044459), c_Groups_Ozero__class_Ozero(_1044459)), _1044463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044459), _1044461), _1044465)))], (16476 ^ _778495) ^ [_1072884, _1072886, _1072888, _1072890] : [class_Fields_Olinordered__field(_1072884), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072884), c_Groups_Ozero__class_Ozero(_1072884)), _1072886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072884), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072884), _1072888), _1072886)), _1072890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072884), _1072888), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1072884), _1072890), _1072886))))], (32548 ^ _778495) ^ [_1378180] : [-(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)), _1378180), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (25383 ^ _778495) ^ [_1232059, _1232061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232061)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1232059), _1232061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1232059)), hAPP(c_Int_Onat, _1232061)))], (47231 ^ _778495) ^ [_1728572, _1728574] : [-(c_List_Oinsert(_1728572, _1728574, c_List_Olist_ONil(_1728572)) = hAPP(hAPP(c_List_Olist_OCons(_1728572), _1728574), c_List_Olist_ONil(_1728572)))], (44720 ^ _778495) ^ [_1674305, _1674307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1674305), _1674307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1674305)), hAPP(c_Code__Numeral_Oof__nat, _1674307))))], (14073 ^ _778495) ^ [_1028407, _1028409, _1028411, _1028413] : [class_Rings_Olinordered__semidom(_1028407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028407), c_Groups_Ozero__class_Ozero(_1028407)), _1028409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028407), _1028411), _1028413)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028407), _1028411), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028407), _1028409), _1028413))))], (43133 ^ _778495) ^ [_1639015, _1639017, _1639019, _1639021] : [hAPP(hAPP(c_List_Oappend(_1639015), _1639017), _1639019) = hAPP(hAPP(c_List_Oappend(_1639015), _1639017), _1639021), -(_1639019 = _1639021)], (30455 ^ _778495) ^ [_1333850, _1333852, _1333854, _1333856, _1333858] : [-(hBOOL(hAPP(hAPP(c_member(_1333850), _1333852), c_SetInterval_Oord_OgreaterThanLessThan(_1333850, _1333854, _1333856, _1333858)))), hBOOL(hAPP(hAPP(_1333854, _1333856), _1333852)), hBOOL(hAPP(hAPP(_1333854, _1333852), _1333858))], (28303 ^ _778495) ^ [_1284647, _1284649, _1284651] : [hAPP(hAPP(c_COMBC(_1284647, tc_fun(_1284647, tc_HOL_Obool), tc_HOL_Obool), c_member(_1284647)), _1284649) = hAPP(hAPP(c_COMBC(_1284647, tc_fun(_1284647, tc_HOL_Obool), tc_HOL_Obool), c_member(_1284647)), _1284651), -(_1284649 = _1284651)], (40349 ^ _778495) ^ [_1567721, _1567723] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567721, _1567721), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1567721, _1567723)), c_Relation_OId(_1567721)) = c_Transitive__Closure_Ortrancl(_1567721, _1567723))], (48068 ^ _778495) ^ [_1746980, _1746982, _1746984, _1746986] : [-(c_New__Random__Sequence_Opos__empty(_1746980, _1746982, _1746984, _1746986) = c_New__DSequence_Opos__empty(_1746980))], (45590 ^ _778495) ^ [_1693325, _1693327] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693325)), c_List_Oconcat(_1693325, _1693327)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1693325), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1693325))), _1693327)))], (6058 ^ _778495) ^ [_875398, _875400, _875402, _875404] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875398, tc_HOL_Obool)), _875400), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875398, tc_HOL_Obool)), _875402), _875404)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875398, tc_HOL_Obool)), _875402), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875398, tc_HOL_Obool)), _875400), _875404)))], (3018 ^ _778495) ^ [_823397, _823399, _823401, _823403] : [-(c_Nitpick_Ocard_H(_823403, _823399) = c_Nitpick_Ocard_H(_823401, _823397)), _823403 = _823401, _823399 = _823397], (6568 ^ _778495) ^ [_885358, _885360, _885362, _885364] : [-(hBOOL(hAPP(hAPP(c_member(_885358), _885360), _885362))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_885358, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_885358), _885360), _885364)), _885362) = hAPP(hAPP(c_Set_Oinsert(_885358), _885360), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_885358, tc_HOL_Obool)), _885364), _885362)))], (24842 ^ _778495) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37073 ^ _778495) ^ [_1477960, _1477962] : [-(c_Divides_Odivmod__nat(_1477960, _1477962) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1477960, _1477962)))], (11119 ^ _778495) ^ [_969837, _969839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969837), _969839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969837), hAPP(c_Nat_OSuc, _969839))))], (36817 ^ _778495) ^ [_1472730] : [class_Nat_Osemiring__char__0(_1472730), -(c_Fun_Oinj__on(tc_Nat_Onat, _1472730, c_Nat_Osemiring__1__class_Oof__nat(_1472730), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (22360 ^ _778495) ^ [_1178347, _1178349, _1178351] : [class_Groups_Ogroup__add(_1178347), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1178347), _1178349), _1178351) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178347), _1178349), hAPP(c_Groups_Ouminus__class_Ouminus(_1178347), _1178351)))], (44335 ^ _778495) ^ [_1665016, _1665018, _1665020, _1665022] : [-(_1665016 = c_List_Olist_ONil(_1665018)), -(c_List_Olast(_1665020, hAPP(hAPP(c_List_Omap(_1665018, _1665020), _1665022), _1665016)) = hAPP(_1665022, c_List_Olast(_1665018, _1665016)))], (22970 ^ _778495) ^ [_1189130, _1189132] : [-(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), _1189130)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1189132)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1189130))) = 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), _1189132)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1189130)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (48876 ^ _778495) ^ [_1766595, _1766597, _1766599, _1766601] : [class_Complete__Lattice_Ocomplete__lattice(_1766595), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1766597, _1766595), _1766599), _1766601) = c_Complete__Lattice_OInf__class_OInf(_1766595, hAPP(c_Set_OCollect(_1766595), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1766597, _1766595), tc_HOL_Obool), tc_HOL_Obool, _1766595), c_HOL_OEx(tc_fun(_1766597, _1766595))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1766597, _1766595), tc_HOL_Obool), tc_fun(tc_fun(_1766597, _1766595), tc_HOL_Obool), _1766595), hAPP(c_COMBS(tc_fun(_1766597, _1766595), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1766597, _1766595)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1766597, _1766595), tc_fun(tc_fun(_1766597, _1766595), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1766597, _1766595))), _1766599)))), hAPP(hAPP(c_COMBC(_1766595, tc_fun(tc_fun(_1766597, _1766595), _1766595), tc_fun(tc_fun(_1766597, _1766595), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1766595, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1766597, _1766595), _1766595), tc_fun(tc_fun(_1766597, _1766595), tc_HOL_Obool)), _1766595), c_COMBB(_1766595, tc_HOL_Obool, tc_fun(_1766597, _1766595))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1766597, _1766595), _1766597, _1766595), c_COMBI(tc_fun(_1766597, _1766595))), _1766601)))))))], (32890 ^ _778495) ^ [_1385317, _1385319, _1385321, _1385323] : [class_Orderings_Oorder(_1385317), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385317, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1385317, _1385319, _1385321)), c_SetInterval_Oord__class_OatLeastAtMost(_1385317, _1385321, _1385323)) = c_Orderings_Obot__class_Obot(tc_fun(_1385317, tc_HOL_Obool)))], (50711 ^ _778495) ^ [_1805482, _1805484, _1805486] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1805482), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1805484), _1805486))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1805482), _1805486)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1805486), _1805484)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1805482), _1805484)))], (7730 ^ _778495) ^ [_906306, _906308, _906310, _906312] : [class_Orderings_Oord(_906306), 7733 ^ _778495 : [(7742 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_906308, _906306)), _906310), _906312))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906308, _906306)), _906310), _906312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906308, _906306)), _906312), _906310)))], (7734 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_906308, _906306)), _906310), _906312)), 7737 ^ _778495 : [(7740 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906308, _906306)), _906312), _906310))], (7738 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906308, _906306)), _906310), _906312)))]]]]], (47636 ^ _778495) ^ [_1738214, _1738216, _1738218, _1738220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738214), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738216)), _1738218))), 47642 ^ _778495 : [(47645 ^ _778495) ^ [] : [hBOOL(hAPP(_1738220, 47641 ^ [_1738214, _1738216, _1738218, _1738220]))], (47643 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738216), 47641 ^ [_1738214, _1738216, _1738218, _1738220]), hAPP(c_List_Oset(_1738216), _1738218))))]], -(hBOOL(hAPP(_1738220, hAPP(hAPP(c_List_Onth(_1738216), _1738218), _1738214))))], (39143 ^ _778495) ^ [_1538448, _1538450, _1538452] : [-(c_Relation_Orefl__on(_1538448, _1538450, _1538452)), 39147 ^ _778495 : [(39150 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1538448, _1538448, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1538448, tc_fun(_1538448, tc_HOL_Obool), tc_fun(_1538448, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1538448, tc_HOL_Obool), tc_fun(_1538448, tc_HOL_Obool)), _1538448), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1538448)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538448), c_fconj), hAPP(hAPP(c_COMBC(_1538448, tc_fun(_1538448, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538448)), _1538450)))), hAPP(hAPP(c_COMBC(_1538448, tc_fun(_1538448, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538448)), _1538450))), 39146 ^ [_1538448, _1538450, _1538452]))], (39148 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1538448, _1538448)), 39146 ^ [_1538448, _1538450, _1538452]), _1538452)))]], 39152 ^ _778495 : [(39155 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1538448, _1538448)), hAPP(hAPP(c_Product__Type_OPair(_1538448, _1538448), 39151 ^ [_1538448, _1538450, _1538452]), 39151 ^ [_1538448, _1538450, _1538452])), _1538452))], (39153 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538448), 39151 ^ [_1538448, _1538450, _1538452]), _1538450)))]]], (43804 ^ _778495) ^ [_1654644, _1654646, _1654648] : [-(hAPP(c_List_Oset(_1654644), hAPP(c_List_Orotate(_1654644, _1654646), _1654648)) = hAPP(c_List_Oset(_1654644), _1654648))], (42327 ^ _778495) ^ [_1621475, _1621477, _1621479, _1621481, _1621483] : [-(hAPP(hAPP(c_List_Olist__update(_1621475, hAPP(hAPP(c_List_Olist__update(_1621475, _1621477), _1621479), _1621481)), _1621479), _1621483) = hAPP(hAPP(c_List_Olist__update(_1621475, _1621477), _1621479), _1621483))], (44446 ^ _778495) ^ [_1668415, _1668417, _1668419, _1668421, _1668423] : [c_Fun_Oinj__on(_1668415, _1668417, _1668419, c_Orderings_Otop__class_Otop(tc_fun(_1668415, tc_HOL_Obool))), 44449 ^ _778495 : [(44456 ^ _778495) ^ [] : [_1668421 = _1668423, -(hAPP(hAPP(c_List_Omap(_1668415, _1668417), _1668419), _1668421) = hAPP(hAPP(c_List_Omap(_1668415, _1668417), _1668419), _1668423))], (44450 ^ _778495) ^ [] : [hAPP(hAPP(c_List_Omap(_1668415, _1668417), _1668419), _1668421) = hAPP(hAPP(c_List_Omap(_1668415, _1668417), _1668419), _1668423), -(_1668421 = _1668423)]]], (9911 ^ _778495) ^ [_948735, _948737, _948739, _948741, _948743] : [c_Finite__Set_Ofolding__one(_948735, _948737, _948739), hBOOL(hAPP(c_Finite__Set_Ofinite(_948735), _948741)), -(_948741 = c_Orderings_Obot__class_Obot(tc_fun(_948735, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_948735), _948743)), -(_948743 = c_Orderings_Obot__class_Obot(tc_fun(_948735, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_948735, tc_HOL_Obool)), _948741), _948743) = c_Orderings_Obot__class_Obot(tc_fun(_948735, tc_HOL_Obool)), -(hAPP(_948739, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948735, tc_HOL_Obool)), _948741), _948743)) = hAPP(hAPP(_948737, hAPP(_948739, _948741)), hAPP(_948739, _948743)))], (23512 ^ _778495) ^ [_1199625, _1199627] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199625, _1199627) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1199625 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1199627), 23515 ^ [_1199625, _1199627]))], (43796 ^ _778495) ^ [_1654458, _1654460, _1654462, _1654464] : [-(hAPP(c_List_Orotate(_1654458, _1654460), hAPP(c_List_Orotate(_1654458, _1654462), _1654464)) = hAPP(c_List_Orotate(_1654458, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1654460), _1654462)), _1654464))], (29362 ^ _778495) ^ [_1312431, _1312433] : [-(_1312431 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29365 ^ _778495 : [(29372 ^ _778495) ^ [] : [-(_1312433 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1312431, _1312433) = 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, _1312433))), 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, _1312431)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1312433))), c_Divides_Opdivmod(_1312431, _1312433)), 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), _1312433))))), c_Divides_Opdivmod(_1312431, _1312433)))))], (29366 ^ _778495) ^ [] : [_1312433 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1312431, _1312433) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1312431))]]], (13123 ^ _778495) ^ [_1012456, _1012458] : [class_Groups_Ocomm__monoid__add(_1012456), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012456), c_Groups_Ozero__class_Ozero(_1012456)), _1012458) = _1012458)], (13418 ^ _778495) ^ [_1016833, _1016835, _1016837] : [13419 ^ _778495 : [(13422 ^ _778495) ^ [] : [_1016835 = _1016837], (13420 ^ _778495) ^ [] : [_1016833 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016833), _1016835) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016833), _1016837))], (37947 ^ _778495) ^ [_1501081, _1501083, _1501085, _1501087, _1501089] : [c_Relation_Orefl__on(_1501081, _1501083, _1501085), c_Relation_Orefl__on(_1501081, _1501087, _1501089), -(c_Relation_Orefl__on(_1501081, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501081, tc_HOL_Obool)), _1501083), _1501087), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1501081, _1501081), tc_HOL_Obool)), _1501085), _1501089)))], (21936 ^ _778495) ^ [_1170811, _1170813, _1170815] : [class_Groups_Oordered__ab__group__add(_1170811), 21939 ^ _778495 : [(21946 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170811), hAPP(c_Groups_Ouminus__class_Ouminus(_1170811), _1170815)), _1170813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170811), hAPP(c_Groups_Ouminus__class_Ouminus(_1170811), _1170813)), _1170815)))], (21940 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170811), hAPP(c_Groups_Ouminus__class_Ouminus(_1170811), _1170813)), _1170815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170811), hAPP(c_Groups_Ouminus__class_Ouminus(_1170811), _1170815)), _1170813)))]]], (43279 ^ _778495) ^ [_1641874, _1641876] : [-(hAPP(hAPP(c_List_Oappend(_1641874), c_List_Olist_ONil(_1641874)), _1641876) = _1641876)], (39287 ^ _778495) ^ [_1542056, _1542058] : [39289 ^ _778495 : [(39292 ^ _778495) ^ [] : [hBOOL(hAPP(_1542056, hAPP(c_Int_OAbs__Integ, 39288 ^ [_1542056, _1542058])))], (39290 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39288 ^ [_1542056, _1542058]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1542056, _1542058)))], (28697 ^ _778495) ^ [_1298758, _1298760] : [hAPP(c_Nat_OSuc, _1298758) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1298760), -(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(_1298760))), 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)), _1298758))))))], (32448 ^ _778495) ^ [_1376348] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1376348)), -(_1376348 = 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))), _1376348)), c_FunDef_Omax__strict)))], (36534 ^ _778495) ^ [_1466084, _1466086, _1466088, _1466090, _1466092, _1466094] : [c_Fun_Oinj__on(_1466084, _1466086, _1466088, _1466090), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466084, tc_HOL_Obool)), _1466092), _1466090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466084, tc_HOL_Obool)), _1466094), _1466090)), -(hAPP(c_Set_Oimage(_1466084, _1466086, _1466088), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466084, tc_HOL_Obool)), _1466092), _1466094)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466086, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466084, _1466086, _1466088), _1466092)), hAPP(c_Set_Oimage(_1466084, _1466086, _1466088), _1466094)))], (7914 ^ _778495) ^ [_908984, _908986, _908988] : [class_Orderings_Oorder(_908984), -(_908986 = _908988), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908984), _908988), _908986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908984), _908988), _908986)))], (27829 ^ _778495) ^ [_1275096, _1275098] : [c_Nat__Transfer_Ois__nat(_1275096), c_Nat__Transfer_Ois__nat(_1275098), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1275096), _1275098)))], (33608 ^ _778495) ^ [_1403735, _1403737, _1403739, _1403741, _1403743] : [33610 ^ _778495 : [(33616 ^ _778495) ^ [] : [hBOOL(hAPP(_1403743, 33612 ^ [_1403735, _1403737, _1403739, _1403741, _1403743]))], (33614 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403735), 33612 ^ [_1403735, _1403737, _1403739, _1403741, _1403743]), hAPP(_1403741, 33609 ^ [_1403735, _1403737, _1403739, _1403741, _1403743]))))], (33611 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403737), 33609 ^ [_1403735, _1403737, _1403739, _1403741, _1403743]), _1403739)))]], 33617 ^ _778495 : [(33618 ^ _778495) ^ [_1404045] : [hBOOL(hAPP(hAPP(c_member(_1403735), _1404045), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403737, tc_fun(_1403735, tc_HOL_Obool)), _1403739), _1403741))), -(hBOOL(hAPP(_1403743, _1404045)))]]], (52417 ^ _778495) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (43678 ^ _778495) ^ [_1652129, _1652131, _1652133, _1652135] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652129) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1652131), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652129)), hAPP(hAPP(c_List_Olist_OCons(_1652131), _1652133), _1652135)) = hAPP(hAPP(c_List_Olist_OCons(_1652131), _1652133), _1652135))], (24832 ^ _778495) ^ [_1222804, _1222806] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1222804), _1222806)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222804)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222806)))], (29751 ^ _778495) ^ [_1319493, _1319495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1319493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1319495)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1319493, _1319495), c_Divides_OposDivAlg(_1319493, _1319495))))], (27133 ^ _778495) ^ [_1263109, _1263111, _1263113] : [class_Rings_Oring__1(_1263109), -(hAPP(c_Int_Oring__1__class_Oof__int(_1263109), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1263111), _1263113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1263109), hAPP(c_Int_Oring__1__class_Oof__int(_1263109), _1263111)), hAPP(c_Int_Oring__1__class_Oof__int(_1263109), _1263113)))], (22020 ^ _778495) ^ [_1172341, _1172343, _1172345] : [class_Rings_Oring(_1172341), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172341), hAPP(c_Groups_Ouminus__class_Ouminus(_1172341), _1172343)), _1172345) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172341), _1172343), hAPP(c_Groups_Ouminus__class_Ouminus(_1172341), _1172345)))], (27139 ^ _778495) ^ [_1263244, _1263246] : [class_Rings_Oring__1(_1263244), -(hAPP(c_Int_Oring__1__class_Oof__int(_1263244), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1263246)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1263244), _1263246))], (48268 ^ _778495) ^ [_1751885, _1751887, _1751889, _1751891, _1751893] : [c_List_Oreplicate(_1751885, _1751887, _1751889) = c_List_Oreplicate(_1751885, _1751891, _1751893), 48271 ^ _778495 : [(48274 ^ _778495) ^ [] : [-(_1751887 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1751889 = _1751893)], (48272 ^ _778495) ^ [] : [-(_1751887 = _1751891)]]], (35581 ^ _778495) ^ [_1444159, _1444161, _1444163, _1444165] : [-(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), _1444159), _1444161)), 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), _1444163), _1444165)), 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), _1444159), _1444163)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1444161), _1444165))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1444159), _1444165)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1444161), _1444163)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (34915 ^ _778495) ^ [_1431735, _1431737, _1431739, _1431741, _1431743, _1431745] : [-(_1431735 = _1431737), -(hAPP(c_Fun_Ofun__upd(_1431739, _1431741, _1431743, _1431737, _1431745), _1431735) = hAPP(_1431743, _1431735))], (9010 ^ _778495) ^ [_930506, _930508, _930510] : [class_Lattices_Olattice(_930506), hBOOL(hAPP(c_Finite__Set_Ofinite(_930506), _930508)), hBOOL(hAPP(hAPP(c_member(_930506), _930510), _930508)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930506), _930510), c_Big__Operators_Olattice__class_OSup__fin(_930506, _930508)) = _930510)], (43596 ^ _778495) ^ [_1650043, _1650045, _1650047, _1650049] : [-(hAPP(hAPP(c_List_Oappend(_1650043), _1650045), _1650047) = _1650049), _1650045 = hAPP(hAPP(c_List_Otake(_1650043), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650043)), _1650045)), _1650049), _1650047 = hAPP(hAPP(c_List_Odrop(_1650043), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650043)), _1650045)), _1650049)], (35340 ^ _778495) ^ [_1438684, _1438686] : [class_Groups_Oordered__ab__group__add(_1438684), -(hAPP(c_Set_Oimage(_1438684, _1438684, c_Groups_Ouminus__class_Ouminus(_1438684)), hAPP(c_SetInterval_Oord__class_OatMost(_1438684), _1438686)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1438684), hAPP(c_Groups_Ouminus__class_Ouminus(_1438684), _1438686)))], (20196 ^ _778495) ^ [_1141262, _1141264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1141262), _1141264)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1141264)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1141262)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1141264), _1141262)))], (49136 ^ _778495) ^ [_1772329, _1772331] : [c_Relation_Oantisym(_1772329, hAPP(c_Relation_Oconverse(_1772329, _1772329), _1772331)), -(c_Relation_Oantisym(_1772329, _1772331))], (41334 ^ _778495) ^ [_1592523] : [-(c_Nitpick_Onum(_1592523) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1592523, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1592523)))], (29136 ^ _778495) ^ [_1307687] : [-(c_Divides_Oadjust(_1307687) = 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)), _1307687))))), 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)), _1307687))))), 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))))))))], (1458 ^ _778495) ^ [_799748, _799750] : [-(class_Lattices_Oboolean__algebra(_799748)), _799750 = _799748, class_Lattices_Oboolean__algebra(_799750)], (41320 ^ _778495) ^ [_1592260, _1592262, _1592264] : [c_Nitpick_Oless__eq__frac(_1592260, _1592262, _1592264), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592260), c_Nitpick_Oplus__frac(_1592260, _1592262, c_Nitpick_Ouminus__frac(_1592260, _1592264)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52499 ^ _778495) ^ [_1833908, _1833910] : [-(class_Nat_Osize(tc_sum(_1833908, _1833910)))], (20349 ^ _778495) ^ [_1144034, _1144036] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1144034), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144034)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144036)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1144034), _1144036)))], (42037 ^ _778495) ^ [_1613178, _1613180, _1613182] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1613178)), _1613180), c_List_Olists(_1613178, _1613182))), 42040 ^ _778495 : [(42041 ^ _778495) ^ [_1613286] : [hBOOL(hAPP(hAPP(c_member(_1613178), _1613286), hAPP(c_List_Oset(_1613178), _1613180))), -(hBOOL(hAPP(hAPP(c_member(_1613178), _1613286), _1613182)))]]], (42077 ^ _778495) ^ [_1614095, _1614097, _1614099] : [-(hBOOL(hAPP(hAPP(c_member(_1614095), _1614097), hAPP(c_List_Oset(_1614095), _1614099)))), 42078 ^ _778495 : [(42079 ^ _778495) ^ [_1614169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1614169), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614095)), _1614099))), hAPP(hAPP(c_List_Onth(_1614095), _1614099), _1614169) = _1614097]]], (44359 ^ _778495) ^ [_1666072, _1666074] : [-(hAPP(hAPP(c_List_Ozip(_1666072, _1666072), _1666074), _1666074) = hAPP(hAPP(c_List_Omap(_1666072, tc_prod(_1666072, _1666072)), hAPP(hAPP(c_COMBS(_1666072, _1666072, tc_prod(_1666072, _1666072)), c_Product__Type_OPair(_1666072, _1666072)), c_COMBI(_1666072))), _1666074))], (25319 ^ _778495) ^ [_1230833, _1230835, _1230837] : [hBOOL(hAPP(_1230833, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1230835, _1230837))), 25322 ^ _778495 : [(25329 ^ _778495) ^ [] : [-(_1230837 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25332 ^ _778495 : [(25333 ^ _778495) ^ [_1231081, _1231083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1231081), _1230837)), _1230835 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1230837), _1231083)), _1231081), -(hBOOL(hAPP(_1230833, _1231081)))]]], (25323 ^ _778495) ^ [] : [_1230837 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1230833, _1230835)))]]], (50887 ^ _778495) ^ [_1808697, _1808699, _1808701, _1808703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808697, _1808699)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808701, _1808703))), 50890 ^ _778495 : [(50891 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808697), _1808699)), 50894 ^ _778495 : [(50899 ^ _778495) ^ [] : [50900 ^ _778495 : [(50903 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808697), _1808701))], (50901 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808701), _1808697)))]], 50904 ^ _778495 : [(50907 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808703), _1808699))], (50905 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808699), _1808703)))]]], (50897 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808699), _1808703)))], (50895 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808701), _1808697)))]]], (50909 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808701), _1808703)))]]], (9530 ^ _778495) ^ [_941182, _941184, _941186, _941188] : [hBOOL(hAPP(hAPP(c_member(_941182), _941184), _941186)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941182, tc_HOL_Obool)), _941186), hAPP(hAPP(c_Set_Oinsert(_941182), _941184), _941188)) = hAPP(hAPP(c_Set_Oinsert(_941182), _941184), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941182, tc_HOL_Obool)), _941186), _941188)))], (1288 ^ _778495) ^ [_797623, _797625] : [-(class_Divides_Oring__div(_797623)), _797625 = _797623, class_Divides_Oring__div(_797625)], (38949 ^ _778495) ^ [_1533204, _1533206] : [-(hAPP(c_Relation_OField(_1533204), _1533206) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1533204, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533204, _1533204), _1533206)), hAPP(c_Relation_ORange(_1533204, _1533204), _1533206)))], (43054 ^ _778495) ^ [_1637134, _1637136, _1637138, _1637140, _1637142] : [-(hAPP(hAPP(c_List_Oappend(_1637134), _1637136), _1637138) = hAPP(hAPP(c_List_Olist_OCons(_1637134), _1637140), _1637142)), 43055 ^ _778495 : [(43062 ^ _778495) ^ [_1637317] : [_1637136 = hAPP(hAPP(c_List_Olist_OCons(_1637134), _1637140), _1637317), hAPP(hAPP(c_List_Oappend(_1637134), _1637317), _1637138) = _1637142], (43056 ^ _778495) ^ [] : [_1637136 = c_List_Olist_ONil(_1637134), _1637138 = hAPP(hAPP(c_List_Olist_OCons(_1637134), _1637140), _1637142)]]], (44484 ^ _778495) ^ [_1669246, _1669248, _1669250, _1669252] : [-(_1669246 = c_List_Olist_ONil(_1669248)), -(hAPP(c_List_Ohd(_1669250), hAPP(hAPP(c_List_Omap(_1669248, _1669250), _1669252), _1669246)) = hAPP(_1669252, hAPP(c_List_Ohd(_1669248), _1669246)))], (22896 ^ _778495) ^ [_1187857, _1187859] : [class_Int_Onumber__ring(_1187857), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187857), _1187859), hAPP(c_Int_Onumber__class_Onumber__of(_1187857), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187857), _1187859), _1187859))], (48198 ^ _778495) ^ [_1750585, _1750587, _1750589] : [-(hAPP(c_List_Orev(_1750585), c_List_Oreplicate(_1750585, _1750587, _1750589)) = c_List_Oreplicate(_1750585, _1750587, _1750589))], (7596 ^ _778495) ^ [_904151, _904153, _904155, _904157] : [class_Orderings_Oorder(_904151), _904153 = _904155, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904151), _904157), _904155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904151), _904157), _904153)))], (36272 ^ _778495) ^ [_1461166, _1461168, _1461170, _1461172, _1461174, _1461176] : [c_Fun_Oinj__on(_1461166, _1461168, _1461170, _1461172), hBOOL(hAPP(hAPP(c_member(_1461166), _1461174), _1461172)), hBOOL(hAPP(hAPP(c_member(_1461166), _1461176), _1461172)), 36283 ^ _778495 : [(36290 ^ _778495) ^ [] : [_1461174 = _1461176, -(hAPP(_1461170, _1461174) = hAPP(_1461170, _1461176))], (36284 ^ _778495) ^ [] : [hAPP(_1461170, _1461174) = hAPP(_1461170, _1461176), -(_1461174 = _1461176)]]], (37597 ^ _778495) ^ [_1492189, _1492191, _1492193, _1492195, _1492197, _1492199] : [class_Groups_Ocomm__monoid__mult(_1492189), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492191), _1492193)), 37607 ^ _778495 : [(37610 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492195), hAPP(_1492197, 37606 ^ [_1492189, _1492191, _1492193, _1492195, _1492197, _1492199])))], (37608 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492191), 37606 ^ [_1492189, _1492191, _1492193, _1492195, _1492197, _1492199]), _1492193)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1492191, _1492189), hAPP(hAPP(c_COMBS(_1492191, tc_fun(_1492195, tc_HOL_Obool), _1492189), hAPP(hAPP(c_COMBB(tc_fun(_1492195, _1492189), tc_fun(tc_fun(_1492195, tc_HOL_Obool), _1492189), _1492191), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1492195, _1492189)), _1492199)), _1492197)), _1492193) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1492191, _1492195), _1492189), hAPP(c_Product__Type_Oprod_Oprod__case(_1492191, _1492195, _1492189), _1492199)), hAPP(hAPP(c_Product__Type_OSigma(_1492191, _1492195), _1492193), _1492197)))], (23460 ^ _778495) ^ [_1198708] : [-(_1198708 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1198708), _1198708) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (33674 ^ _778495) ^ [_1405574, _1405576] : [_1405574 = _1405576, -(hAPP(c_Int_ORep__Integ, _1405574) = hAPP(c_Int_ORep__Integ, _1405576))], (35332 ^ _778495) ^ [] : [-(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)))], (13348 ^ _778495) ^ [_1015820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015820), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31821 ^ _778495) ^ [_1361210, _1361212, _1361214, _1361216, _1361218] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361210, tc_fun(_1361212, tc_HOL_Obool)), _1361214), hAPP(hAPP(c_COMBS(_1361210, tc_fun(_1361212, tc_HOL_Obool), tc_fun(_1361212, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361212, tc_HOL_Obool), tc_fun(tc_fun(_1361212, tc_HOL_Obool), tc_fun(_1361212, tc_HOL_Obool)), _1361210), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361212, tc_HOL_Obool))), _1361216)), _1361218)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361212, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361210, tc_fun(_1361212, tc_HOL_Obool)), _1361214), _1361216)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361210, tc_fun(_1361212, tc_HOL_Obool)), _1361214), _1361218)))], (34927 ^ _778495) ^ [_1431878, _1431880, _1431882, _1431884, _1431886, _1431888] : [_1431878 = _1431880, -(hAPP(c_Fun_Ofun__upd(_1431882, _1431884, _1431886, _1431880, _1431888), _1431878) = _1431888)], (25946 ^ _778495) ^ [_1242307, _1242309, _1242311] : [class_Int_Onumber__ring(_1242307), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1242307), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1242307), _1242309), _1242311)), 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(_1242307), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1242307), hAPP(hAPP(c_Power_Opower__class_Opower(_1242307), _1242309), 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(_1242307), _1242311), 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(_1242307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242307), hAPP(c_Int_Onumber__class_Onumber__of(_1242307), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1242309)), _1242311)))], (5360 ^ _778495) ^ [_860436, _860438, _860440, _860442, _860444, _860446, _860448, _860450] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_860450, _860446, _860442, _860438) = c_SetInterval_Oord_OgreaterThanLessThan(_860448, _860444, _860440, _860436)), _860450 = _860448, _860446 = _860444, _860442 = _860440, _860438 = _860436], (16370 ^ _778495) ^ [_1070900, _1070902, _1070904, _1070906] : [class_Fields_Olinordered__field__inverse__zero(_1070900), 16373 ^ _778495 : [(16374 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070900), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1070900), _1070902), _1070904)), _1070906)), 16377 ^ _778495 : [(16384 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070900), c_Groups_Ozero__class_Ozero(_1070900)), _1070904))), 16387 ^ _778495 : [(16394 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070900), _1070904), c_Groups_Ozero__class_Ozero(_1070900)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070900), c_Groups_Ozero__class_Ozero(_1070900)), _1070906)))], (16388 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070900), _1070904), c_Groups_Ozero__class_Ozero(_1070900))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070900), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070900), _1070906), _1070904)), _1070902)))]]], (16378 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070900), c_Groups_Ozero__class_Ozero(_1070900)), _1070904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070900), _1070902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070900), _1070906), _1070904))))]]], (16400 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070900), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1070900), _1070902), _1070904)), _1070906))), 16403 ^ _778495 : [(16406 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070900), _1070902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070900), _1070906), _1070904)))], (16404 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070900), c_Groups_Ozero__class_Ozero(_1070900)), _1070904)))]], 16407 ^ _778495 : [(16410 ^ _778495) ^ [] : [16411 ^ _778495 : [(16414 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070900), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070900), _1070906), _1070904)), _1070902))], (16412 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070900), _1070904), c_Groups_Ozero__class_Ozero(_1070900))))]], 16415 ^ _778495 : [(16418 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070900), c_Groups_Ozero__class_Ozero(_1070900)), _1070906))], (16416 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070900), _1070904), c_Groups_Ozero__class_Ozero(_1070900)))]]], (16408 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070900), c_Groups_Ozero__class_Ozero(_1070900)), _1070904))]]]]], (52267 ^ _778495) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (23649 ^ _778495) ^ [_1202080, _1202082, _1202084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202080)), 23652 ^ _778495 : [(23653 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1202082, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202084), _1202080)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202084, _1202080))), 23656 ^ _778495 : [(23657 ^ _778495) ^ [_1202281, _1202283] : [-(hBOOL(hAPP(hAPP(_1202082, _1202283), _1202281))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202281), _1202080)), _1202084 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202080), _1202283)), _1202281)]]], (23671 ^ _778495) ^ [] : [23674 ^ _778495 : [(23677 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23673 ^ [_1202080, _1202082, _1202084]), _1202080)))], (23679 ^ _778495) ^ [] : [-(_1202084 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202080), 23672 ^ [_1202080, _1202082, _1202084])), 23673 ^ [_1202080, _1202082, _1202084]))], (23681 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1202082, 23672 ^ [_1202080, _1202082, _1202084]), 23673 ^ [_1202080, _1202082, _1202084]))], (23675 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23673 ^ [_1202080, _1202082, _1202084])))]], -(hBOOL(hAPP(hAPP(_1202082, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202084), _1202080)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202084, _1202080))))]]], (45201 ^ _778495) ^ [_1685088, _1685090, _1685092] : [-(c_Enum_Oproduct(_1685088, _1685090, c_List_Olist_ONil(_1685088), _1685092) = c_List_Olist_ONil(tc_prod(_1685088, _1685090)))], (7080 ^ _778495) ^ [_895134, _895136, _895138, _895140] : [hBOOL(hAPP(_895134, _895136)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895138, tc_HOL_Obool)), _895134), _895140), _895136)))], (35456 ^ _778495) ^ [_1441118, _1441120, _1441122, _1441124, _1441126] : [class_Groups_Ocomm__monoid__add(_1441118), class_Groups_Ocomm__monoid__mult(_1441118), _1441120 = _1441122, c_Nat__Transfer_Onat__set(_1441122), 35474 ^ _778495 : [(35477 ^ _778495) ^ [] : [hAPP(_1441124, 35473 ^ [_1441118, _1441120, _1441122, _1441124, _1441126]) = hAPP(_1441126, 35473 ^ [_1441118, _1441120, _1441122, _1441124, _1441126])], (35475 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35473 ^ [_1441118, _1441120, _1441122, _1441124, _1441126])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1441118), _1441124), _1441120) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1441118), _1441126), _1441122))], (19474 ^ _778495) ^ [_1128208, _1128210, _1128212] : [class_Orderings_Olinorder(_1128208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128208), _1128210)), -(_1128210 = c_Orderings_Obot__class_Obot(tc_fun(_1128208, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128208), _1128212)), -(_1128212 = c_Orderings_Obot__class_Obot(tc_fun(_1128208, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1128208, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1128208, tc_HOL_Obool)), _1128210), _1128212)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1128208), c_Big__Operators_Olinorder__class_OMin(_1128208, _1128210)), c_Big__Operators_Olinorder__class_OMin(_1128208, _1128212)))], (13281 ^ _778495) ^ [_1014822] : [class_Rings_Ozero__neq__one(_1014822), c_Groups_Oone__class_Oone(_1014822) = c_Groups_Ozero__class_Ozero(_1014822)], (20372 ^ _778495) ^ [_1144477, _1144479] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144477) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144479), -(_1144477 = _1144479)], (280 ^ _778495) ^ [_782905, _782907, _782909, _782911] : [-(c_Nitpick_Orefl_H(_782909, _782905)), c_Nitpick_Orefl_H(_782911, _782907), _782911 = _782909, _782907 = _782905], (24347 ^ _778495) ^ [_1214325] : [class_Int_Onumber__ring(_1214325), c_Int_Oiszero(_1214325, hAPP(c_Int_Onumber__class_Onumber__of(_1214325), c_Int_OBit1(c_Int_OPls)))], (31866 ^ _778495) ^ [_1362726, _1362728, _1362730, _1362732, _1362734] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362726, tc_fun(_1362728, tc_HOL_Obool)), _1362730), hAPP(hAPP(c_COMBC(_1362726, tc_fun(_1362728, tc_HOL_Obool), tc_fun(_1362728, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1362728, tc_HOL_Obool), tc_fun(tc_fun(_1362728, tc_HOL_Obool), tc_fun(_1362728, tc_HOL_Obool)), _1362726), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362728, tc_HOL_Obool))), _1362732)), _1362734)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362728, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362726, tc_fun(_1362728, tc_HOL_Obool)), _1362730), _1362732)), _1362734))], (11752 ^ _778495) ^ [_982569, _982571] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _982569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982569), _982571))))], (48814 ^ _778495) ^ [_1763791, _1763793] : [48815 ^ _778495 : [(48816 ^ _778495) ^ [_1763857] : [hBOOL(hAPP(_1763793, _1763857))]], 48818 ^ _778495 : [(48821 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1763793, 48817 ^ [_1763791, _1763793])))], (48819 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763791), 48817 ^ [_1763791, _1763793]), c_Orderings_Otop__class_Otop(tc_fun(_1763791, tc_HOL_Obool)))))]]], (9586 ^ _778495) ^ [_942410, _942412, _942414, _942416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942410, tc_HOL_Obool)), _942416), _942412)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942410, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942410, tc_HOL_Obool)), _942412), _942414)), _942416) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942410, tc_HOL_Obool)), _942412), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942410, tc_HOL_Obool)), _942414), _942416)))], (37384 ^ _778495) ^ [_1485954, _1485956, _1485958] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1485954, _1485956), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1485954, _1485956), _1485958), hAPP(c_COMBK(tc_fun(_1485956, tc_HOL_Obool), _1485954), c_Orderings_Otop__class_Otop(tc_fun(_1485956, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1485954, _1485956), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1485954, tc_HOL_Obool)), _1485958)), hAPP(c_COMBK(tc_fun(_1485956, tc_HOL_Obool), _1485954), c_Orderings_Otop__class_Otop(tc_fun(_1485956, tc_HOL_Obool)))))], (8930 ^ _778495) ^ [_928720, _928722, _928724, _928726] : [class_Lattices_Olattice(_928720), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928720), _928722), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928720), _928724), _928726)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928720), _928724), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928720), _928722), _928726)))], (50655 ^ _778495) ^ [_1804491, _1804493, _1804495, _1804497] : [class_Divides_Osemiring__div(_1804491), -(_1804493 = c_Groups_Ozero__class_Ozero(_1804491)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804491), _1804493), _1804495)), 50666 ^ _778495 : [(50673 ^ _778495) ^ [] : [_1804495 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804491), _1804497), _1804493), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1804491), _1804495), _1804493) = _1804497)], (50667 ^ _778495) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1804491), _1804495), _1804493) = _1804497, -(_1804495 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804491), _1804497), _1804493))]]], (24846 ^ _778495) ^ [_1223077, _1223079] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223077), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223079)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223077, _1223079)))], (51959 ^ _778495) ^ [_1827487, _1827489, _1827491] : [class_Rings_Ocomm__semiring__1(_1827487), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827487), _1827489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827487), _1827491), _1827489))))], (30495 ^ _778495) ^ [_1334663, _1334665, _1334667, _1334669] : [hBOOL(hAPP(hAPP(c_member(_1334663), _1334665), c_SetInterval_Oord_OgreaterThan(_1334663, _1334667, _1334669))), -(hBOOL(hAPP(hAPP(_1334667, _1334669), _1334665)))], (10467 ^ _778495) ^ [_959095] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _959095)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _959095)], (6804 ^ _778495) ^ [_890031, _890033, _890035, _890037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890031, tc_HOL_Obool)), _890033), _890035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890031, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_890031), _890037), _890033)), hAPP(hAPP(c_Set_Oinsert(_890031), _890037), _890035))))], (6342 ^ _778495) ^ [_881155, _881157, _881159, _881161] : [class_Orderings_Oorder(_881155), _881157 = _881159, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881155), _881161), _881159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881155), _881161), _881157)))], (50833 ^ _778495) ^ [_1807765, _1807767] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807765), 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, 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_839830)), _839836 = _839834, _839832 = _839830], (23593 ^ _778495) ^ [_1201071, _1201073, _1201075, _1201077] : [class_Divides_Osemiring__div(_1201071), -(_1201073 = c_Groups_Ozero__class_Ozero(_1201071)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1201071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201071), _1201073), _1201075)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201071), _1201073), _1201077)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1201071), _1201075), _1201077))], (19984 ^ _778495) ^ [_1137486, _1137488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137486)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1137486), _1137488)))], (33878 ^ _778495) ^ [_1409080, _1409082, _1409084, _1409086, _1409088] : [class_Orderings_Olinorder(_1409080), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1409080, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409080, _1409082), _1409084)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409080, _1409086), _1409088))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409080), _1409084), _1409082))), 33889 ^ _778495 : [(33892 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409080), _1409084), _1409088)))], (33890 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409080), _1409086), _1409082)))]]], (37172 ^ _778495) ^ [_1480362, _1480364, _1480366] : [-(hAPP(c_Set_Ovimage(_1480362, _1480364, _1480366), c_Orderings_Otop__class_Otop(tc_fun(_1480364, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1480362, tc_HOL_Obool)))], (21690 ^ _778495) ^ [_1166827, _1166829, _1166831] : [class_Lattices_Oboolean__algebra(_1166827), 21693 ^ _778495 : [(21700 ^ _778495) ^ [] : [_1166829 = _1166831, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1166827), _1166829) = hAPP(c_Groups_Ouminus__class_Ouminus(_1166827), _1166831))], (21694 ^ _778495) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1166827), _1166829) = hAPP(c_Groups_Ouminus__class_Ouminus(_1166827), _1166831), -(_1166829 = _1166831)]]], (39642 ^ _778495) ^ [_1550371, _1550373, _1550375, _1550377, _1550379, _1550381, _1550383, _1550385, _1550387, _1550389, _1550391] : [c_Finite__Set_Ofolding(_1550371, _1550373, _1550375, _1550377), -(hAPP(c_Fun_Ocomp(_1550379, _1550381, _1550383, _1550385), hAPP(c_Fun_Ocomp(_1550387, _1550379, _1550383, _1550389), _1550391)) = hAPP(c_Fun_Ocomp(_1550387, _1550381, _1550383, hAPP(c_Fun_Ocomp(_1550379, _1550381, _1550387, _1550385), _1550389)), _1550391))], (22126 ^ _778495) ^ [_1174224, _1174226] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1174224)), c_Int_OBit0(_1174226)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1174224), _1174226)))], (28127 ^ _778495) ^ [_1280287] : [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), _1280287))), 28130 ^ _778495 : [(28137 ^ _778495) ^ [] : [-(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), _1280287))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1280287)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1280287)), 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), _1280287)))))], (28131 ^ _778495) ^ [] : [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), _1280287)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1280287)) = 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), _1280287))))]]], (32904 ^ _778495) ^ [] : [-(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)))], (39159 ^ _778495) ^ [_1539089, _1539091, _1539093] : [hBOOL(hAPP(hAPP(c_member(_1539091), _1539089), c_Orderings_Obot__class_Obot(tc_fun(_1539091, tc_HOL_Obool)))), -(hBOOL(hAPP(_1539093, _1539089)))], (35595 ^ _778495) ^ [_1444592] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1444592) = 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, _1444592)), 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))))))))], (24665 ^ _778495) ^ [_1220130, _1220132, _1220134] : [class_Rings_Ocomm__semiring__1(_1220130), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220130), hAPP(hAPP(c_Power_Opower__class_Opower(_1220130), _1220132), _1220134)), _1220132) = hAPP(hAPP(c_Power_Opower__class_Opower(_1220130), _1220132), hAPP(c_Nat_OSuc, _1220134)))], (28627 ^ _778495) ^ [_1297135, _1297137, _1297139] : [class_Int_Onumber__ring(_1297135), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1297135), hAPP(c_Int_Onumber__class_Onumber__of(_1297135), _1297137)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1297139))) = hAPP(hAPP(c_HOL_OLet(_1297135, _1297135), hAPP(hAPP(c_Power_Opower__class_Opower(_1297135), hAPP(c_Int_Onumber__class_Onumber__of(_1297135), _1297137)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1297139))), hAPP(hAPP(c_COMBS(_1297135, _1297135, _1297135), c_Groups_Otimes__class_Otimes(_1297135)), c_COMBI(_1297135))))], (38363 ^ _778495) ^ [_1517511, _1517513] : [-(c_Product__Type_Oapsnd(_1517511, _1517511, _1517513, c_Fun_Oid(_1517511)) = c_Fun_Oid(tc_prod(_1517513, _1517511)))], (17848 ^ _778495) ^ [_1098476, _1098478, _1098480, _1098482] : [class_Orderings_Olinorder(_1098476), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098476), _1098478), _1098480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098476), _1098478), _1098482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098476), _1098478), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1098476), _1098480), _1098482))))], (51695 ^ _778495) ^ [_1822307, _1822309] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822307, _1822309) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822307), _1822309)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822309), _1822307)))], (47001 ^ _778495) ^ [_1723847, _1723849, _1723851] : [c_List_OdropWhile(_1723847, _1723849, _1723851) = c_List_Olist_ONil(_1723847), 47004 ^ _778495 : [(47005 ^ _778495) ^ [_1723938] : [hBOOL(hAPP(hAPP(c_member(_1723847), _1723938), hAPP(c_List_Oset(_1723847), _1723851))), -(hBOOL(hAPP(_1723849, _1723938)))]]], (19028 ^ _778495) ^ [_1120709, _1120711] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120709)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120711)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120709), _1120711)))], (34316 ^ _778495) ^ [_1418687, _1418689, _1418691, _1418693] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1418687), _1418689)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1418691), hAPP(c_Set_Oimage(_1418687, _1418691, _1418693), _1418689))))], (37656 ^ _778495) ^ [_1493782, _1493784, _1493786, _1493788, _1493790, _1493792] : [hAPP(c_Set_Oimage(_1493782, _1493784, _1493786), c_Orderings_Otop__class_Otop(tc_fun(_1493782, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1493784, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493788, _1493790, _1493792), c_Orderings_Otop__class_Otop(tc_fun(_1493788, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1493790, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1493782, _1493788), tc_prod(_1493784, _1493790), c_Product__Type_Omap__pair(_1493782, _1493784, _1493788, _1493790, _1493786, _1493792)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1493782, _1493788), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1493784, _1493790), tc_HOL_Obool)))], (37801 ^ _778495) ^ [_1497887, _1497889] : [-(hBOOL(hAPP(_1497889, 37802 ^ [_1497887, _1497889]))), -(hAPP(c_Set_OCollect(_1497887), _1497889) = c_Orderings_Obot__class_Obot(tc_fun(_1497887, tc_HOL_Obool)))], (19194 ^ _778495) ^ [_1123413, _1123415, _1123417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123413), _1123415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123415), _1123417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123413), _1123417)))], (29212 ^ _778495) ^ [] : [-(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)))))], (19140 ^ _778495) ^ [_1122576, _1122578, _1122580] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122576), _1122578)), _1122580) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122576), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122578), _1122580)))], (32458 ^ _778495) ^ [_1376467, _1376469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376467), _1376469)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1376469, _1376467) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (48112 ^ _778495) ^ [_1748227, _1748229, _1748231, _1748233] : [-(c_Predicate_Oconversep(_1748227, _1748229, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1748227, tc_fun(_1748229, tc_HOL_Obool))), _1748231), _1748233)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1748229, tc_fun(_1748227, tc_HOL_Obool))), c_Predicate_Oconversep(_1748227, _1748229, _1748231)), c_Predicate_Oconversep(_1748227, _1748229, _1748233)))], (23789 ^ _778495) ^ [_1204549, _1204551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204549)), 23792 ^ _778495 : [(23801 ^ _778495) ^ [] : [-(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), _1204549), _1204551)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204551), _1204549)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204551))], (23793 ^ _778495) ^ [] : [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), _1204549), _1204551))), 23796 ^ _778495 : [(23799 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204551)))], (23797 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204551), _1204549)))]]]]], (2620 ^ _778495) ^ [_817196, _817198, _817200, _817202, _817204, _817206] : [-(c_Wellfounded_Omlex__prod(_817206, _817202, _817198) = c_Wellfounded_Omlex__prod(_817204, _817200, _817196)), _817206 = _817204, _817202 = _817200, _817198 = _817196], (52407 ^ _778495) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (30609 ^ _778495) ^ [_1337385, _1337387] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1337385)), hAPP(c_Nat_OSuc, _1337387)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1337385))), 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, _1337387))), 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)), _1337387)))))], (5925 ^ _778495) ^ [_872963, _872965] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872963, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_872963, tc_HOL_Obool))), _872965)))], (43852 ^ _778495) ^ [_1655605, _1655607] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655605)), hAPP(c_List_Otl(_1655605), _1655607)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655605)), _1655607)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12525 ^ _778495) ^ [_999633] : [class_Complete__Lattice_Ocomplete__lattice(_999633), -(c_Complete__Lattice_OSup__class_OSup(_999633, c_Orderings_Obot__class_Obot(tc_fun(_999633, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_999633))], (41860 ^ _778495) ^ [_1608785, _1608787, _1608789, _1608791] : [-(hAPP(hAPP(c_List_Onth(_1608785), hAPP(hAPP(c_List_Olist_OCons(_1608785), _1608787), _1608789)), _1608791) = c_Nat_Onat_Onat__case(_1608785, _1608787, hAPP(c_List_Onth(_1608785), _1608789), _1608791))], (27315 ^ _778495) ^ [_1266095, _1266097, _1266099] : [class_Rings_Olinordered__idom(_1266095), -(c_Groups_Osgn__class_Osgn(_1266095, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266095), _1266097), _1266099)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266095), c_Groups_Osgn__class_Osgn(_1266095, _1266097)), c_Groups_Osgn__class_Osgn(_1266095, _1266099)))], (52449 ^ _778495) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (20488 ^ _778495) ^ [_1146119] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146119) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146119), c_Int_OPls)))], (7024 ^ _778495) ^ [_893946, _893948, _893950, _893952] : [class_Lattices_Osemilattice__sup(_893946), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893946), _893948), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893946), _893950), _893952)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893946), _893950), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893946), _893948), _893952)))], (41340 ^ _778495) ^ [_1592611, _1592613, _1592615, _1592617, _1592619, _1592621] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1592611, _1592613, _1592615), _1592617), hAPP(hAPP(c_Product__Type_OPair(_1592611, _1592613), _1592619), _1592621)) = hAPP(hAPP(_1592617, _1592619), _1592621))], (52405 ^ _778495) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (43818 ^ _778495) ^ [_1654901] : [-(hAPP(c_List_Otl(_1654901), c_List_Olist_ONil(_1654901)) = c_List_Olist_ONil(_1654901))], (37702 ^ _778495) ^ [_1495169, _1495171, _1495173, _1495175, _1495177, _1495179, _1495181, _1495183] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1495169, _1495171)), _1495173), hAPP(c_Set_Oimage(tc_prod(_1495175, _1495177), tc_prod(_1495169, _1495171), c_Product__Type_Omap__pair(_1495175, _1495169, _1495177, _1495171, _1495179, _1495181)), _1495183))), 37707 ^ _778495 : [(37710 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1495175, _1495177)), hAPP(hAPP(c_Product__Type_OPair(_1495175, _1495177), 37705 ^ [_1495169, _1495171, _1495173, _1495175, _1495177, _1495179, _1495181, _1495183]), 37706 ^ [_1495169, _1495171, _1495173, _1495175, _1495177, _1495179, _1495181, _1495183])), _1495183)))], (37708 ^ _778495) ^ [] : [-(_1495173 = hAPP(hAPP(c_Product__Type_OPair(_1495169, _1495171), hAPP(_1495179, 37705 ^ [_1495169, _1495171, _1495173, _1495175, _1495177, _1495179, _1495181, _1495183])), hAPP(_1495181, 37706 ^ [_1495169, _1495171, _1495173, _1495175, _1495177, _1495179, _1495181, _1495183])))]]], (3638 ^ _778495) ^ [_833075, _833077] : [_833077 = _833075, -(c_List_Oreturn__list(_833077) = c_List_Oreturn__list(_833075))], (31178 ^ _778495) ^ [_1348312, _1348314] : [class_Orderings_Olinorder(_1348312), -(c_Big__Operators_Olattice_OSup__fin(_1348312, c_Orderings_Oord__class_Omax(_1348312), hAPP(hAPP(c_Set_Oinsert(_1348312), _1348314), c_Orderings_Obot__class_Obot(tc_fun(_1348312, tc_HOL_Obool)))) = _1348314)], (44877 ^ _778495) ^ [_1677498] : [-(c_Code__Numeral_OSuc__code__numeral(_1677498) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1677498))))], (3136 ^ _778495) ^ [_825196, _825198, _825200, _825202] : [-(c_Big__Operators_Olinorder__class_OMax(_825202, _825198) = c_Big__Operators_Olinorder__class_OMax(_825200, _825196)), _825202 = _825200, _825198 = _825196], (49985 ^ _778495) ^ [_1789537] : [-(c_Fun_Obij__betw(_1789537, _1789537, c_Fun_Oid(_1789537), c_Orderings_Otop__class_Otop(tc_fun(_1789537, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1789537, tc_HOL_Obool))))], (9176 ^ _778495) ^ [_933505, _933507, _933509] : [class_Lattices_Osemilattice__inf(_933505), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933505), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933505), _933507), _933509)), _933509)))], (28369 ^ _778495) ^ [_1289427, _1289429, _1289431] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289427, tc_Nat_Onat), _1289429), _1289431)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289427, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1289427), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1289429)), _1289431))], (41981 ^ _778495) ^ [_1611858, _1611860, _1611862] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611858)), hAPP(hAPP(c_List_Otake(_1611858), _1611860), _1611862)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611858)), _1611862)), _1611860))], (46286 ^ _778495) ^ [_1708941, _1708943, _1708945, _1708947, _1708949] : [class_Orderings_Olinorder(_1708941), c_List_Olinorder__class_Osorted(_1708941, hAPP(hAPP(c_List_Omap(_1708943, _1708941), _1708945), _1708947)), -(c_List_Olinorder__class_Osorted(_1708941, hAPP(hAPP(c_List_Omap(_1708943, _1708941), _1708945), c_List_Oremove1(_1708943, _1708949, _1708947))))], (25002 ^ _778495) ^ [_1225670, _1225672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225672)), 25009 ^ _778495 : [(25016 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225670), _1225672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1225670)), hAPP(c_Int_Onat, _1225672))))], (25010 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1225670)), hAPP(c_Int_Onat, _1225672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225670), _1225672)))]]], (7184 ^ _778495) ^ [_896939, _896941, _896943, _896945, _896947] : [class_Groups_Oordered__ab__group__add(_896939), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_896939), _896941), _896943) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_896939), _896945), _896947), 7191 ^ _778495 : [(7198 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896939), _896945), _896947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896939), _896941), _896943)))], (7192 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896939), _896941), _896943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896939), _896945), _896947)))]]], (7498 ^ _778495) ^ [_902719, _902721, _902723] : [class_Orderings_Olinorder(_902719), -(_902721 = _902723), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902719), _902721), _902723))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902719), _902723), _902721)))], (30831 ^ _778495) ^ [_1341336, _1341338, _1341340] : [class_Orderings_Olinorder(_1341336), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341336), _1341338), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341336), _1341338), _1341340)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341336), _1341338), _1341340))], (43524 ^ _778495) ^ [_1648332, _1648334, _1648336, _1648338] : [-(hAPP(hAPP(c_List_Odrop(_1648332), _1648334), hAPP(hAPP(c_List_Otake(_1648332), _1648336), _1648338)) = hAPP(hAPP(c_List_Otake(_1648332), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1648336), _1648334)), hAPP(hAPP(c_List_Odrop(_1648332), _1648334), _1648338)))], (21118 ^ _778495) ^ [_1156834] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1156834)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1156834))], (33270 ^ _778495) ^ [_1393773, _1393775, _1393777, _1393779] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1393773, tc_HOL_Obool), tc_fun(_1393775, tc_HOL_Obool)), _1393777), hAPP(hAPP(c_COMBC(tc_fun(_1393773, tc_HOL_Obool), tc_fun(_1393773, tc_fun(_1393775, tc_HOL_Obool)), tc_fun(_1393775, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393773, tc_fun(_1393775, tc_HOL_Obool))), _1393779)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393773, tc_fun(_1393775, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1393773, tc_HOL_Obool), _1393777)), _1393779))], (28157 ^ _778495) ^ [_1280806, _1280808, _1280810, _1280812] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1280806, _1280808, _1280810, c_Code__Numeral_OSuc__code__numeral(_1280812)) = hAPP(hAPP(_1280810, _1280812), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1280806, _1280808, _1280810, _1280812)))], (49833 ^ _778495) ^ [_1786316] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786316), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1786316 = hAPP(c_Code__Numeral_Onat__of, 49836 ^ [_1786316]))], (23434 ^ _778495) ^ [_1198291, _1198293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198291), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23437 ^ _778495 : [(23444 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1198293), _1198291)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23438 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1198293), _1198291)), 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)), _1198293)))]]], (33445 ^ _778495) ^ [_1399214, _1399216, _1399218, _1399220, _1399222] : [_1399214 = c_Orderings_Obot__class_Obot(tc_fun(_1399216, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399216, tc_fun(_1399218, tc_HOL_Obool)), _1399214), hAPP(hAPP(c_COMBC(_1399216, tc_fun(_1399218, tc_HOL_Obool), tc_fun(_1399218, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1399218, tc_HOL_Obool), tc_fun(tc_fun(_1399218, tc_HOL_Obool), tc_fun(_1399218, tc_HOL_Obool)), _1399216), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399218, tc_HOL_Obool))), _1399220)), _1399222)) = c_Orderings_Obot__class_Obot(tc_fun(_1399218, tc_HOL_Obool)))], (26774 ^ _778495) ^ [_1257091, _1257093, _1257095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257091, tc_HOL_Obool)), _1257093), _1257095)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1257091, tc_HOL_Obool)), _1257093), hAPP(c_Set_OPow(_1257091), _1257095))))], (13384 ^ _778495) ^ [_1016354] : [_1016354 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016354), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38971 ^ _778495) ^ [_1533921, _1533923, _1533925, _1533927] : [hBOOL(hAPP(hAPP(c_member(_1533921), _1533927), hAPP(c_Relation_ODomain(_1533921, _1533923), _1533925))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1533921, _1533923, hAPP(hAPP(c_COMBC(_1533921, tc_fun(tc_prod(_1533921, _1533923), tc_HOL_Obool), tc_fun(_1533923, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533923, tc_fun(tc_fun(tc_prod(_1533921, _1533923), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1533921, _1533923), tc_HOL_Obool), tc_fun(_1533923, tc_HOL_Obool)), _1533921), c_COMBC(_1533923, tc_fun(tc_prod(_1533921, _1533923), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533923, tc_prod(_1533921, _1533923)), tc_fun(_1533923, tc_fun(tc_fun(tc_prod(_1533921, _1533923), tc_HOL_Obool), tc_HOL_Obool)), _1533921), hAPP(c_COMBB(tc_prod(_1533921, _1533923), tc_fun(tc_fun(tc_prod(_1533921, _1533923), tc_HOL_Obool), tc_HOL_Obool), _1533923), c_member(tc_prod(_1533921, _1533923)))), c_Product__Type_OPair(_1533921, _1533923)))), _1533925)), _1533927)))], (7542 ^ _778495) ^ [_903320, _903322, _903324] : [class_Orderings_Oorder(_903320), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903320), _903322), _903324)), _903322 = _903324], (12461 ^ _778495) ^ [_998423, _998425, _998427] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998423, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_998423, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_998423, tc_HOL_Obool), tc_HOL_Obool)), _998425), _998427))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998423, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_998423, tc_HOL_Obool), _998425)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_998423, tc_HOL_Obool), _998427)))))], (12882 ^ _778495) ^ [_1007731, _1007733, _1007735, _1007737, _1007739] : [class_Groups_Ocomm__monoid__mult(_1007731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007733), _1007735)), hBOOL(hAPP(hAPP(c_member(_1007733), _1007737), _1007735)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1007733, _1007731), _1007739), _1007735) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007731), hAPP(_1007739, _1007737)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1007733, _1007731), _1007739), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007733, tc_HOL_Obool)), _1007735), hAPP(hAPP(c_Set_Oinsert(_1007733), _1007737), c_Orderings_Obot__class_Obot(tc_fun(_1007733, tc_HOL_Obool)))))))], (9128 ^ _778495) ^ [_932690, _932692, _932694, _932696] : [class_Lattices_Osemilattice__inf(_932690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932690), _932692), _932694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932690), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932690), _932692), _932696)), _932694)))], (46870 ^ _778495) ^ [_1721056, _1721058, _1721060] : [46872 ^ _778495 : [(46875 ^ _778495) ^ [] : [hBOOL(hAPP(_1721058, 46871 ^ [_1721056, _1721058, _1721060]))], (46873 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1721056), 46871 ^ [_1721056, _1721058, _1721060]), hAPP(c_List_Oset(_1721056), _1721060))))]], -(c_List_OtakeWhile(_1721056, _1721058, _1721060) = _1721060)], (19144 ^ _778495) ^ [_1122684, _1122686, _1122688] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122684), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122686), _1122688)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122684), _1122686)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122684), _1122688)))], (32230 ^ _778495) ^ [_1371734, _1371736, _1371738, _1371740, _1371742] : [class_Orderings_Oorder(_1371734), 32233 ^ _778495 : [(32254 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1371734, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1371734, _1371736, _1371738)), c_SetInterval_Oord__class_OatLeastAtMost(_1371734, _1371740, _1371742)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371734), _1371740), _1371742)), 32257 ^ _778495 : [(32260 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371734), _1371740), _1371736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371734), _1371738), _1371742)), 32267 ^ _778495 : [(32270 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371734), _1371738), _1371742))], (32268 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371734), _1371740), _1371736))]]], (32258 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371734), _1371736), _1371738)))]]], (32234 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1371734, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1371734, _1371736, _1371738)), c_SetInterval_Oord__class_OatLeastAtMost(_1371734, _1371740, _1371742))), 32237 ^ _778495 : [(32238 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371734), _1371736), _1371738)), 32241 ^ _778495 : [(32246 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371734), _1371740), _1371736))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371734), _1371738), _1371742)))], (32244 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371734), _1371738), _1371742)))], (32242 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371734), _1371740), _1371736)))]]], (32252 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371734), _1371740), _1371742)))]]]]], (7104 ^ _778495) ^ [_895570, _895572, _895574] : [class_Lattices_Olattice(_895570), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895570), _895572), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895570), _895574), _895572))))], (13207 ^ _778495) ^ [_1013672, _1013674] : [class_Rings_Ocomm__semiring__1(_1013672), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013672), _1013674), c_Groups_Ozero__class_Ozero(_1013672)) = c_Groups_Ozero__class_Ozero(_1013672))], (33262 ^ _778495) ^ [_1393532, _1393534, _1393536, _1393538, _1393540, _1393542] : [class_Complete__Lattice_Ocomplete__lattice(_1393532), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393534, tc_fun(_1393536, _1393532)), _1393538), _1393540), _1393542) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393534, _1393532), _1393538), hAPP(hAPP(c_COMBC(_1393534, _1393536, _1393532), _1393540), _1393542)))], (21044 ^ _778495) ^ [_1155453, _1155455, _1155457] : [class_Groups_Oordered__ab__group__add__abs(_1155453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155453), hAPP(c_Groups_Oabs__class_Oabs(_1155453), _1155455)), _1155457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155453), _1155455), _1155457)))], (46072 ^ _778495) ^ [_1705563, _1705565, _1705567, _1705569, _1705571] : [class_Orderings_Olinorder(_1705563), hBOOL(hAPP(hAPP(c_member(_1705565), _1705567), hAPP(c_List_Oset(_1705565), _1705569))), c_List_Olinorder__class_Osorted(_1705563, hAPP(hAPP(c_List_Omap(_1705565, _1705563), _1705571), _1705569)), hAPP(c_List_Ohd(_1705565), hAPP(c_List_Ofilter(_1705565, hAPP(hAPP(c_COMBB(_1705563, tc_HOL_Obool, _1705565), hAPP(c_fequal, hAPP(_1705571, _1705567))), _1705571)), _1705569)) = _1705567, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705565, _1705563, _1705571), _1705567), c_List_Oremove1(_1705565, _1705567, _1705569)) = _1705569)], (26114 ^ _778495) ^ [_1245344, _1245346] : [class_Groups_Omonoid__mult(_1245344), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1245344), c_Groups_Oone__class_Oone(_1245344)), _1245346) = c_Groups_Oone__class_Oone(_1245344))], (31448 ^ _778495) ^ [_1352976, _1352978, _1352980] : [class_Orderings_Olinorder(_1352976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352976), _1352978)), -(_1352978 = c_Orderings_Obot__class_Obot(tc_fun(_1352976, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352976), _1352980)), -(_1352980 = c_Orderings_Obot__class_Obot(tc_fun(_1352976, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1352976, tc_HOL_Obool)), _1352978), _1352980) = c_Orderings_Obot__class_Obot(tc_fun(_1352976, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1352976, c_Orderings_Oord__class_Omax(_1352976), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352976, tc_HOL_Obool)), _1352978), _1352980)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352976), c_Big__Operators_Olattice_OSup__fin(_1352976, c_Orderings_Oord__class_Omax(_1352976), _1352978)), c_Big__Operators_Olattice_OSup__fin(_1352976, c_Orderings_Oord__class_Omax(_1352976), _1352980)))], (17658 ^ _778495) ^ [_1095210, _1095212, _1095214] : [class_Orderings_Olinorder(_1095210), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095210), _1095212), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095210), _1095212), _1095214)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095210), _1095212), _1095214))], (28715 ^ _778495) ^ [_1299105] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1299105)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1299105)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1299105)), 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)))))], (22560 ^ _778495) ^ [_1181798, _1181800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181798), _1181800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1181798)), c_Int_OBit1(_1181800))))], (49336 ^ _778495) ^ [_1775950, _1775952] : [-(c_Relation_Osym(_1775950, c_Relation_OId__on(_1775950, _1775952)))], (42231 ^ _778495) ^ [_1619489] : [42233 ^ _778495 : [(42236 ^ _778495) ^ [] : [42232 ^ [_1619489] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42234 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42232 ^ [_1619489]), hAPP(c_List_Oset(tc_Nat_Onat), _1619489))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619489) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43812 ^ _778495) ^ [_1654800, _1654802, _1654804] : [_1654804 = c_List_Olist_ONil(_1654800), -(hAPP(c_List_Orotate(_1654800, _1654802), _1654804) = c_List_Olist_ONil(_1654800))], (21856 ^ _778495) ^ [_1169612, _1169614] : [class_Groups_Ogroup__add(_1169612), 21859 ^ _778495 : [(21866 ^ _778495) ^ [] : [c_Groups_Ozero__class_Ozero(_1169612) = _1169614, -(c_Groups_Ozero__class_Ozero(_1169612) = hAPP(c_Groups_Ouminus__class_Ouminus(_1169612), _1169614))], (21860 ^ _778495) ^ [] : [c_Groups_Ozero__class_Ozero(_1169612) = hAPP(c_Groups_Ouminus__class_Ouminus(_1169612), _1169614), -(c_Groups_Ozero__class_Ozero(_1169612) = _1169614)]]], (14793 ^ _778495) ^ [_1040887, _1040889, _1040891] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040887), _1040889)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040887), _1040891)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040889), _1040891))], (13117 ^ _778495) ^ [_1012361, _1012363] : [class_Groups_Omonoid__add(_1012361), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012361), c_Groups_Ozero__class_Ozero(_1012361)), _1012363) = _1012363)], (11837 ^ _778495) ^ [_984239, _984241, _984243, _984245, _984247] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_984239, _984241, _984243), _984245), _984247), c_Orderings_Obot__class_Obot(tc_fun(_984241, tc_HOL_Obool))) = _984247)], (24471 ^ _778495) ^ [_1216332, _1216334, _1216336] : [class_Rings_Olinordered__idom(_1216332), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216332), _1216334), c_Groups_Ozero__class_Ozero(_1216332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216332), hAPP(hAPP(c_Power_Opower__class_Opower(_1216332), _1216334), 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)))), _1216336)))), c_Groups_Ozero__class_Ozero(_1216332))))], (40972 ^ _778495) ^ [_1582849, _1582851, _1582853] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582849, _1582849)), _1582851), c_Transitive__Closure_Ortrancl(_1582849, _1582853))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582849, _1582849)), _1582851), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582849, _1582849), tc_HOL_Obool), 40975 ^ [_1582849, _1582851, _1582853]), _1582853))))], (35302 ^ _778495) ^ [_1437891] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1437891)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1437891))], (42487 ^ _778495) ^ [_1625183, _1625185] : [hAPP(c_Finite__Set_Ocard(_1625183), hAPP(c_List_Oset(_1625183), _1625185)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625183)), _1625185), -(hBOOL(hAPP(c_List_Odistinct(_1625183), _1625185)))], (52255 ^ _778495) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (23162 ^ _778495) ^ [_1193135, _1193137, _1193139, _1193141] : [class_Divides_Osemiring__div(_1193135), -(c_Divides_Odiv__class_Omod(_1193135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193135), _1193137), _1193139), _1193141) = c_Divides_Odiv__class_Omod(_1193135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193135), c_Divides_Odiv__class_Omod(_1193135, _1193137, _1193141)), c_Divides_Odiv__class_Omod(_1193135, _1193139, _1193141)), _1193141))], (9390 ^ _778495) ^ [_938246, _938248, _938250, _938252] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938246, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938246, tc_HOL_Obool)), _938248), _938250)), _938252) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938246, tc_HOL_Obool)), _938248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938246, tc_HOL_Obool)), _938250), _938252)))], (10633 ^ _778495) ^ [_961778, _961780, _961782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961778), _961780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961778), _961782)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961780), _961782))))], (44131 ^ _778495) ^ [_1661597, _1661599, _1661601] : [class_Orderings_Olinorder(_1661597), -(hBOOL(hAPP(hAPP(c_member(_1661597), _1661599), hAPP(c_List_Oset(_1661597), _1661601)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661597, _1661597, c_COMBI(_1661597), _1661599, _1661601) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661597, _1661597, c_COMBI(_1661597)), _1661599), _1661601))], (27247 ^ _778495) ^ [_1265044] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1265044)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1265044)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38540 ^ _778495) ^ [_1522519, _1522521, _1522523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522519, _1522519), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1522519, _1522519, _1522519), _1522521), _1522523)), _1522521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1522519, tc_HOL_Obool), tc_fun(_1522519, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1522519, tc_HOL_Obool), tc_fun(_1522519, tc_HOL_Obool), tc_fun(_1522519, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1522519, _1522521)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1522519, tc_HOL_Obool), tc_fun(_1522519, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1522519, _1522523)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1522519, tc_HOL_Obool), tc_fun(_1522519, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1522519, tc_HOL_Obool), tc_fun(_1522519, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1522519, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1522519, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1522519, tc_HOL_Obool), tc_fun(_1522519, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1522519, _1522521))))], (37676 ^ _778495) ^ [_1494294, _1494296, _1494298, _1494300, _1494302, _1494304, _1494306, _1494308, _1494310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494294, _1494296)), hAPP(hAPP(c_Product__Type_OPair(_1494294, _1494296), _1494298), _1494300)), _1494302)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494304, _1494306)), hAPP(hAPP(c_Product__Type_OPair(_1494304, _1494306), hAPP(_1494308, _1494298)), hAPP(_1494310, _1494300))), hAPP(c_Set_Oimage(tc_prod(_1494294, _1494296), tc_prod(_1494304, _1494306), c_Product__Type_Omap__pair(_1494294, _1494304, _1494296, _1494306, _1494308, _1494310)), _1494302))))], (40371 ^ _778495) ^ [_1568221, _1568223, _1568225, _1568227, _1568229] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568221, _1568221)), hAPP(hAPP(c_Product__Type_OPair(_1568221, _1568221), _1568223), _1568225)), c_Transitive__Closure_Ortrancl(_1568221, _1568227))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568221, _1568221)), hAPP(hAPP(c_Product__Type_OPair(_1568221, _1568221), _1568225), _1568229)), _1568227)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568221, _1568221)), hAPP(hAPP(c_Product__Type_OPair(_1568221, _1568221), _1568223), _1568229)), c_Transitive__Closure_Ortrancl(_1568221, _1568227))))], (31342 ^ _778495) ^ [_1351019, _1351021, _1351023] : [class_Orderings_Olinorder(_1351019), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351019), _1351021)), -(_1351023 = c_Orderings_Obot__class_Obot(tc_fun(_1351019, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1351019, tc_HOL_Obool)), _1351023), _1351021)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351019), c_Big__Operators_Olinorder__class_OMax(_1351019, _1351023)), c_Big__Operators_Olinorder__class_OMax(_1351019, _1351021)) = c_Big__Operators_Olinorder__class_OMax(_1351019, _1351021))], (45292 ^ _778495) ^ [_1687212] : [-(c_Enum_Osublists(_1687212, c_List_Olist_ONil(_1687212)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687212)), c_List_Olist_ONil(_1687212)), c_List_Olist_ONil(tc_List_Olist(_1687212))))], (42565 ^ _778495) ^ [_1626949, _1626951] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1626949), _1626951)), -(c_Nitpick_Ocard_H(_1626949, _1626951) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626949)), c_Hilbert__Choice_OEps(tc_List_Olist(_1626949), hAPP(hAPP(c_COMBS(tc_List_Olist(_1626949), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1626949)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1626949), tc_fun(_1626949, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1626949, tc_HOL_Obool), tc_fun(tc_fun(_1626949, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1626949)), c_fequal), c_List_Oset(_1626949))), _1626951))), c_List_Odistinct(_1626949)))))], (44670 ^ _778495) ^ [_1673333, _1673335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673333), _1673335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673333)), hAPP(c_Code__Numeral_Oof__nat, _1673335))))], (31870 ^ _778495) ^ [_1362925, _1362927, _1362929, _1362931, _1362933] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362925, tc_HOL_Obool)), _1362927), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362929, tc_fun(_1362925, tc_HOL_Obool)), _1362931), _1362933)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362929, tc_fun(_1362925, tc_HOL_Obool)), _1362931), hAPP(hAPP(c_COMBB(tc_fun(_1362925, tc_HOL_Obool), tc_fun(_1362925, tc_HOL_Obool), _1362929), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362925, tc_HOL_Obool)), _1362927)), _1362933)))], (45851 ^ _778495) ^ [_1700745, _1700747, _1700749, _1700751] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700745)), _1700747))), c_List_Ofoldr(tc_List_Olist(_1700749), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700749)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700749))), _1700751, 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(_1700745)), _1700747)), c_List_Ofoldr(tc_List_Olist(_1700749), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700749)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700749), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700749)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700749)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1700749), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700749)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700749), tc_List_Olist(_1700749), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700749)))), _1700751), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (14731 ^ _778495) ^ [_1039755, _1039757, _1039759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1039755)), 14734 ^ _778495 : [(14741 ^ _778495) ^ [] : [_1039757 = _1039759, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039755), _1039757) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039755), _1039759))], (14735 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039755), _1039757) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039755), _1039759), -(_1039757 = _1039759)]]], (20208 ^ _778495) ^ [_1141512, _1141514, _1141516] : [class_Rings_Oring__1(_1141512), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1141514), _1141516)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1141512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1141516), _1141514)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1141512), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1141512), _1141516)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1141512), _1141514)))], (32748 ^ _778495) ^ [_1382559, _1382561, _1382563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1382559)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1382561), _1382563)), 32755 ^ _778495 : [(32756 ^ _778495) ^ [_1382755] : [32758 ^ _778495 : [(32764 ^ _778495) ^ [] : [-(_1382755 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32760 ^ [_1382559, _1382561, _1382563, _1382755]), 32757 ^ [_1382559, _1382561, _1382563, _1382755]))], (32762 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32760 ^ [_1382559, _1382561, _1382563, _1382755]), _1382563)))], (32759 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32757 ^ [_1382559, _1382561, _1382563, _1382755]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1382559))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1382755), _1382561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382755), _1382559)), _1382561)))]]], (6238 ^ _778495) ^ [_879379, _879381, _879383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879379, tc_HOL_Obool)), _879381), _879383)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879379, tc_HOL_Obool)), _879381), _879383) = _879383)], (34769 ^ _778495) ^ [_1428914] : [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)), _1428914))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1428914)))], (42335 ^ _778495) ^ [_1621752, _1621754, _1621756] : [hBOOL(hAPP(hAPP(c_member(_1621752), _1621754), hAPP(c_List_Oset(_1621752), c_List_Obutlast(_1621752, _1621756)))), -(hBOOL(hAPP(hAPP(c_member(_1621752), _1621754), hAPP(c_List_Oset(_1621752), _1621756))))], (41473 ^ _778495) ^ [_1597252, _1597254, _1597256, _1597258] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597252), tc_List_Olist(_1597252))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597252), tc_List_Olist(_1597252)), _1597254), _1597256)), c_List_Olex(_1597252, _1597258))), 41476 ^ _778495 : [(41479 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597252)), _1597254) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597252)), _1597256))], (41477 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597252), tc_List_Olist(_1597252))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597252), tc_List_Olist(_1597252)), _1597254), _1597256)), c_List_Olexord(_1597252, _1597258))))]]], (9160 ^ _778495) ^ [_933249, _933251, _933253] : [class_Lattices_Osemilattice__inf(_933249), 9163 ^ _778495 : [(9170 ^ _778495) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933249), _933251), _933253) = _933251, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933249), _933251), _933253)))], (9164 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933249), _933251), _933253)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933249), _933251), _933253) = _933251)]]], (5813 ^ _778495) ^ [_870785, _870787, _870789] : [hBOOL(hAPP(hAPP(c_member(_870785), _870787), hAPP(hAPP(c_Set_Oinsert(_870785), _870789), c_Orderings_Obot__class_Obot(tc_fun(_870785, tc_HOL_Obool))))), -(_870787 = _870789)], (7634 ^ _778495) ^ [_904786, _904788, _904790, _904792] : [class_Orderings_Oorder(_904786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904786), _904788), _904790)), _904788 = _904792, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904786), _904792), _904790)))], (7340 ^ _778495) ^ [_900360, _900362, _900364, _900366, _900368, _900370, _900372, _900374] : [c_Finite__Set_Ofolding__image__simple(_900360, _900362, _900364, _900366, _900368, _900370), hBOOL(hAPP(c_Finite__Set_Ofinite(_900362), _900372)), -(hAPP(_900370, hAPP(hAPP(c_Set_Oinsert(_900362), _900374), _900372)) = hAPP(hAPP(_900364, hAPP(_900368, _900374)), hAPP(_900370, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900362, tc_HOL_Obool)), _900372), hAPP(hAPP(c_Set_Oinsert(_900362), _900374), c_Orderings_Obot__class_Obot(tc_fun(_900362, tc_HOL_Obool)))))))], (43904 ^ _778495) ^ [_1656792] : [class_Groups_Omonoid__add(_1656792), -(c_List_Omonoid__add__class_Olistsum(_1656792) = c_List_Ofoldl(_1656792, _1656792, c_Groups_Oplus__class_Oplus(_1656792), c_Groups_Ozero__class_Ozero(_1656792)))], (38848 ^ _778495) ^ [_1530695, _1530697, _1530699] : [-(hAPP(c_Set_Oimage(tc_prod(_1530695, _1530697), _1530695, c_Product__Type_Ofst(_1530695, _1530697)), _1530699) = hAPP(c_Relation_ODomain(_1530695, _1530697), _1530699))], (15299 ^ _778495) ^ [_1050247, _1050249] : [15300 ^ _778495 : [(15303 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050247), _1050249)))], (15301 ^ _778495) ^ [] : [_1050249 = c_Orderings_Obot__class_Obot(tc_fun(_1050247, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1050247), _1050249) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38721 ^ _778495) ^ [_1528037, _1528039] : [-(hAPP(c_Relation_ODomain(_1528037, _1528037), c_Relation_OId__on(_1528037, _1528039)) = _1528039)], (2808 ^ _778495) ^ [_820156, _820158, _820160, _820162] : [-(c_Relation_ODomain(_820162, _820158) = c_Relation_ODomain(_820160, _820156)), _820162 = _820160, _820158 = _820156], (30247 ^ _778495) ^ [] : [-(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)))], (7242 ^ _778495) ^ [_898141, _898143, _898145, _898147, _898149] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_898141, _898141, _898143, _898145, _898147), _898149)), -(hBOOL(hAPP(hAPP(c_member(_898141), _898145), _898147))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_898141, _898143, hAPP(hAPP(c_Set_Oinsert(_898141), _898145), _898147)), _898149)))], (31045 ^ _778495) ^ [_1345696, _1345698, _1345700, _1345702] : [class_Orderings_Olinorder(_1345696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345696), _1345698)), hBOOL(hAPP(hAPP(c_member(_1345696), _1345700), _1345698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345696), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345696), _1345700), _1345702)), hAPP(hAPP(c_Finite__Set_Ofold(_1345696, _1345696, c_Orderings_Oord__class_Omax(_1345696)), _1345702), _1345698))))], (6836 ^ _778495) ^ [_890619, _890621, _890623, _890625] : [6837 ^ _778495 : [(6840 ^ _778495) ^ [] : [hBOOL(hAPP(_890623, _890621))], (6838 ^ _778495) ^ [] : [hBOOL(hAPP(_890619, _890621))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890625, tc_HOL_Obool)), _890623), _890619), _890621)))], (40669 ^ _778495) ^ [_1575297, _1575299, _1575301, _1575303, _1575305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575297, _1575297)), hAPP(hAPP(c_Product__Type_OPair(_1575297, _1575297), hAPP(_1575299, hAPP(c_Nat_OSuc, 40670 ^ [_1575297, _1575299, _1575301, _1575303, _1575305]))), hAPP(_1575299, 40670 ^ [_1575297, _1575299, _1575301, _1575303, _1575305]))), c_Transitive__Closure_Ortrancl(_1575297, _1575301))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575297, _1575297)), hAPP(hAPP(c_Product__Type_OPair(_1575297, _1575297), hAPP(_1575299, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1575303), _1575305))), hAPP(_1575299, _1575303))), c_Transitive__Closure_Ortrancl(_1575297, _1575301))))], (3556 ^ _778495) ^ [_831784, _831786, _831788, _831790, _831792, _831794] : [-(c_List_Oremove1(_831794, _831790, _831786) = c_List_Oremove1(_831792, _831788, _831784)), _831794 = _831792, _831790 = _831788, _831786 = _831784], (9536 ^ _778495) ^ [_941349, _941351, _941353, _941355] : [-(hBOOL(hAPP(hAPP(c_member(_941349), _941351), _941353))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941349, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_941349), _941351), _941355)), _941353) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941349, tc_HOL_Obool)), _941355), _941353))], (23843 ^ _778495) ^ [_1205383, _1205385] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205383), _1205385) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1205385 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23852 ^ _778495 : [(23855 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205383), _1205385)))], (23853 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205383)))]], 23856 ^ _778495 : [(23859 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205385), _1205383)))], (23857 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205383), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (49791 ^ _778495) ^ [_1785030, _1785032, _1785034, _1785036, _1785038] : [c_Fun_Oinj__on(_1785030, _1785032, _1785034, c_Orderings_Otop__class_Otop(tc_fun(_1785030, tc_HOL_Obool))), 49797 ^ _778495 : [(49800 ^ _778495) ^ [] : [hBOOL(hAPP(_1785036, hAPP(c_Hilbert__Choice_Oinv__into(_1785030, _1785032, c_Orderings_Otop__class_Otop(tc_fun(_1785030, tc_HOL_Obool)), _1785034), 49796 ^ [_1785030, _1785032, _1785034, _1785036, _1785038])))], (49798 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785032), 49796 ^ [_1785030, _1785032, _1785034, _1785036, _1785038]), hAPP(c_Set_Oimage(_1785030, _1785032, _1785034), c_Orderings_Otop__class_Otop(tc_fun(_1785030, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1785036, _1785038)))], (44223 ^ _778495) ^ [_1663084, _1663086, _1663088] : [_1663084 = c_List_Olist_ONil(_1663086), -(c_List_Olast(_1663086, hAPP(hAPP(c_List_Oappend(_1663086), _1663088), _1663084)) = c_List_Olast(_1663086, _1663088))], (30029 ^ _778495) ^ [_1325208, _1325210, _1325212, _1325214] : [hAPP(c_Product__Type_Ofst(_1325208, _1325210), _1325212) = hAPP(c_Product__Type_Ofst(_1325208, _1325210), _1325214), hAPP(c_Product__Type_Osnd(_1325208, _1325210), _1325212) = hAPP(c_Product__Type_Osnd(_1325208, _1325210), _1325214), -(_1325212 = _1325214)], (31232 ^ _778495) ^ [_1349160, _1349162, _1349164] : [class_Orderings_Olinorder(_1349160), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349160), _1349162)), -(_1349162 = c_Orderings_Obot__class_Obot(tc_fun(_1349160, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1349160, c_Orderings_Oord__class_Omax(_1349160), hAPP(hAPP(c_Set_Oinsert(_1349160), _1349164), _1349162)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349160), _1349164), c_Big__Operators_Olattice_OSup__fin(_1349160, c_Orderings_Oord__class_Omax(_1349160), _1349162)))], (41235 ^ _778495) ^ [_1590153, _1590155] : [-(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)))), _1590153)) = 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)))), _1590155))), 41237 ^ _778495 : [(41240 ^ _778495) ^ [] : [41241 ^ _778495 : [(41244 ^ _778495) ^ [] : [hBOOL(hAPP(_1590155, 41236 ^ [_1590153, _1590155]))], (41242 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1590153, 41236 ^ [_1590153, _1590155])))]], 41245 ^ _778495 : [(41248 ^ _778495) ^ [] : [hBOOL(hAPP(_1590153, 41236 ^ [_1590153, _1590155]))], (41246 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1590155, 41236 ^ [_1590153, _1590155])))]]], (41238 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41236 ^ [_1590153, _1590155])))]]], (33820 ^ _778495) ^ [] : [-(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)))], (22276 ^ _778495) ^ [_1176885, _1176887] : [class_Groups_Olinordered__ab__group__add(_1176885), 22279 ^ _778495 : [(22286 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176885), c_Groups_Ozero__class_Ozero(_1176885)), _1176887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176885), hAPP(c_Groups_Ouminus__class_Ouminus(_1176885), _1176887)), _1176887)))], (22280 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176885), hAPP(c_Groups_Ouminus__class_Ouminus(_1176885), _1176887)), _1176887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176885), c_Groups_Ozero__class_Ozero(_1176885)), _1176887)))]]], (34218 ^ _778495) ^ [_1416237, _1416239] : [c_Relation_Oirrefl(_1416237, _1416239), 34221 ^ _778495 : [(34222 ^ _778495) ^ [_1416319] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1416237, _1416237)), hAPP(hAPP(c_Product__Type_OPair(_1416237, _1416237), _1416319), _1416319)), _1416239))]]], (48663 ^ _778495) ^ [_1760389, _1760391] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1760389)), _1760391)), 48667 ^ _778495 : [(48668 ^ _778495) ^ [_1760490] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1760389)), _1760490), _1760391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760389)), _1760490)), 48666 ^ [_1760389, _1760391])))]]], (38538 ^ _778495) ^ [_1522437, _1522439, _1522441, _1522443] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522437, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1522437, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1522439, _1522437), _1522441)), hAPP(c_Relation_ORange(_1522439, _1522437), _1522443))), hAPP(c_Relation_ORange(_1522439, _1522437), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1522439, _1522437), tc_HOL_Obool)), _1522441), _1522443)))))], (42329 ^ _778495) ^ [_1621533, _1621535, _1621537, _1621539, _1621541] : [-(hAPP(hAPP(c_List_Olist__update(_1621533, hAPP(hAPP(c_List_Olist_OCons(_1621533), _1621535), _1621537)), _1621539), _1621541) = c_Nat_Onat_Onat__case(tc_List_Olist(_1621533), hAPP(hAPP(c_List_Olist_OCons(_1621533), _1621541), _1621537), hAPP(hAPP(c_COMBB(tc_List_Olist(_1621533), tc_List_Olist(_1621533), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1621533), _1621535)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1621533, tc_List_Olist(_1621533)), c_List_Olist__update(_1621533, _1621537)), _1621541)), _1621539))], (15697 ^ _778495) ^ [_1057916, _1057918] : [_1057916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1057916), _1057918) = _1057918)], (24449 ^ _778495) ^ [_1215950, _1215952] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215950))), -(c_SMT_Oz3mod(_1215952, _1215950) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215952, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1215950)))], (30963 ^ _778495) ^ [_1343951, _1343953, _1343955, _1343957] : [class_Orderings_Olinorder(_1343951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343951), _1343953), _1343955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343951), _1343953), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343951), _1343955), _1343957))))], (48674 ^ _778495) ^ [_1760629] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1760629)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760629)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29482 ^ _778495) ^ [_1314802, _1314804, _1314806, _1314808, _1314810, _1314812] : [hAPP(hAPP(c_Product__Type_OPair(_1314802, _1314804), _1314806), _1314808) = hAPP(hAPP(c_Product__Type_OPair(_1314802, _1314804), _1314810), _1314812), 29485 ^ _778495 : [(29488 ^ _778495) ^ [] : [-(_1314808 = _1314812)], (29486 ^ _778495) ^ [] : [-(_1314806 = _1314810)]]], (26704 ^ _778495) ^ [_1255998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1255998)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255998), c_Int_OMin)))], (52229 ^ _778495) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (52707 ^ _778495) ^ [_1836315, _1836317] : [hBOOL(_1836315), -(hBOOL(hAPP(hAPP(c_fdisj, _1836315), _1836317)))], (34799 ^ _778495) ^ [_1429405, _1429407] : [-(hAPP(c_Set_Oimage(_1429405, _1429405, c_COMBI(_1429405)), _1429407) = _1429407)], (48404 ^ _778495) ^ [_1754437, _1754439, _1754441, _1754443] : [-(hAPP(c_New__DSequence_Opos__union(_1754437, _1754439, _1754441), _1754443) = c_Lazy__Sequence_Oappend(_1754437, hAPP(_1754439, _1754443), hAPP(_1754441, _1754443)))], (45794 ^ _778495) ^ [_1698666, _1698668, _1698670] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1698666, tc_HOL_Obool)), hAPP(c_List_Oset(_1698666), _1698668)), hAPP(hAPP(c_Set_Oinsert(_1698666), _1698670), c_Orderings_Obot__class_Obot(tc_fun(_1698666, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1698666), hAPP(c_List_Ofilter(_1698666, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698666), c_fNot), hAPP(hAPP(c_COMBC(_1698666, _1698666, tc_HOL_Obool), c_fequal), _1698670))), _1698668)))], (7012 ^ _778495) ^ [_893696, _893698, _893700] : [class_Lattices_Olattice(_893696), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893696), _893698), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893696), _893698), _893700)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893696), _893698), _893700))], (23510 ^ _778495) ^ [_1199557, _1199559] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1199557))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1199559))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1199557)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1199559)))], (41967 ^ _778495) ^ [_1611526, _1611528, _1611530, _1611532] : [hBOOL(hAPP(hAPP(c_member(_1611526), _1611528), hAPP(c_List_Oset(_1611526), hAPP(hAPP(c_List_Otake(_1611526), _1611530), _1611532)))), -(hBOOL(hAPP(hAPP(c_member(_1611526), _1611528), hAPP(c_List_Oset(_1611526), _1611532))))], (52443 ^ _778495) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (48126 ^ _778495) ^ [_1748544, _1748546, _1748548, _1748550, _1748552] : [hBOOL(hAPP(hAPP(_1748548, _1748552), _1748550)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748544, _1748546, _1748548), _1748550), _1748552)))], (45524 ^ _778495) ^ [_1691990, _1691992, _1691994, _1691996] : [class_Orderings_Olinorder(_1691990), -(hAPP(c_List_Oset(_1691992), c_List_Olinorder__class_Osort__key(_1691992, _1691990, _1691994, _1691996)) = hAPP(c_List_Oset(_1691992), _1691996))], (44416 ^ _778495) ^ [_1667442, _1667444, _1667446, _1667448, _1667450] : [class_Groups_Ocomm__monoid__add(_1667442), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667442), hAPP(hAPP(c_List_Omap(_1667444, _1667442), hAPP(hAPP(c_COMBS(_1667444, _1667442, _1667442), hAPP(hAPP(c_COMBB(_1667442, tc_fun(_1667442, _1667442), _1667444), c_Groups_Oplus__class_Oplus(_1667442)), _1667446)), _1667448)), _1667450)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1667442), hAPP(c_List_Omonoid__add__class_Olistsum(_1667442), hAPP(hAPP(c_List_Omap(_1667444, _1667442), _1667446), _1667450))), hAPP(c_List_Omonoid__add__class_Olistsum(_1667442), hAPP(hAPP(c_List_Omap(_1667444, _1667442), _1667448), _1667450))))], (42824 ^ _778495) ^ [_1631691, _1631693, _1631695] : [-(hAPP(hAPP(c_List_Otake(_1631691), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1631691), _1631693), _1631695)) = hAPP(hAPP(c_List_Olist_OCons(_1631691), _1631693), c_List_Olist_ONil(_1631691)))], (20079 ^ _778495) ^ [_1139196, _1139198] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1139196)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1139198)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1139196), _1139198)))], (22162 ^ _778495) ^ [_1174942, _1174944] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1174942)), _1174944) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1174942), _1174944)))], (1818 ^ _778495) ^ [_804248, _804250] : [-(class_Groups_Omonoid__add(_804248)), _804250 = _804248, class_Groups_Omonoid__add(_804250)], (814 ^ _778495) ^ [_790786, _790788, _790790, _790792, _790794, _790796] : [-(c_Equiv__Relations_Oequiv(_790794, _790790, _790786)), c_Equiv__Relations_Oequiv(_790796, _790792, _790788), _790796 = _790794, _790792 = _790790, _790788 = _790786], (34823 ^ _778495) ^ [_1429884, _1429886] : [class_Groups_Oordered__ab__group__add(_1429884), -(hAPP(c_Set_Oimage(_1429884, _1429884, c_Groups_Ouminus__class_Ouminus(_1429884)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1429884), _1429886)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1429884), hAPP(c_Groups_Ouminus__class_Ouminus(_1429884), _1429886)))], (48098 ^ _778495) ^ [_1747870, _1747872] : [c_Wellfounded_Oacyclic(_1747870, hAPP(c_Set_OCollect(tc_prod(_1747870, _1747870)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747870, _1747870, tc_HOL_Obool), c_Predicate_Oconversep(_1747870, _1747870, _1747872)))), -(c_Wellfounded_Oacyclic(_1747870, hAPP(c_Set_OCollect(tc_prod(_1747870, _1747870)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747870, _1747870, tc_HOL_Obool), _1747872))))], (35334 ^ _778495) ^ [_1438557, _1438559, _1438561] : [class_Orderings_Oorder(_1438557), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438557, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1438557, _1438559, _1438561)), hAPP(c_SetInterval_Oord__class_OatLeast(_1438557), _1438561)) = c_Orderings_Obot__class_Obot(tc_fun(_1438557, tc_HOL_Obool)))], (20476 ^ _778495) ^ [_1145909, _1145911] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1145909), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1145911)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1145909), _1145911)))], (41338 ^ _778495) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33028 ^ _778495) ^ [_1387744, _1387746, _1387748, _1387750, _1387752] : [class_Orderings_Olinorder(_1387744), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1387744, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1387744, _1387746, _1387748)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1387744, _1387750, _1387752)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1387744, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1387744), _1387746), _1387750), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1387744), _1387748), _1387752)))], (45510 ^ _778495) ^ [_1691726, _1691728, _1691730] : [class_Orderings_Olinorder(_1691726), -(c_List_Olinorder__class_Osort__key(_1691728, _1691726, _1691730, c_List_Olist_ONil(_1691728)) = c_List_Olist_ONil(_1691728))], (7042 ^ _778495) ^ [_894375, _894377, _894379, _894381] : [class_Lattices_Osemilattice__sup(_894375), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894375), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894375), _894377), _894379)), _894381) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894375), _894377), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894375), _894379), _894381)))], (16282 ^ _778495) ^ [_1069355] : [class_Rings_Oring__1(_1069355), -(hBOOL(hAPP(hAPP(c_member(_1069355), c_Groups_Oone__class_Oone(_1069355)), c_Int_Oring__1__class_OInts(_1069355))))], (12436 ^ _778495) ^ [_997669, _997671, _997673] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_997669, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_997669, tc_HOL_Obool)), _997671), _997673)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_997669, tc_HOL_Obool)), _997671), c_Complete__Lattice_OSup__class_OSup(tc_fun(_997669, tc_HOL_Obool), _997673)))], (35593 ^ _778495) ^ [_1444540, _1444542] : [-(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), _1444540), _1444542)), 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), _1444540), _1444542))], (26768 ^ _778495) ^ [_1256966, _1256968, _1256970] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1256966, tc_HOL_Obool)), _1256968), hAPP(c_Set_OPow(_1256966), _1256970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256966, tc_HOL_Obool)), _1256968), _1256970)))], (22996 ^ _778495) ^ [_1189571, _1189573, _1189575] : [class_Divides_Osemiring__div(_1189571), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1189571), c_Divides_Odiv__class_Omod(_1189571, _1189573, _1189575)), _1189575) = c_Groups_Ozero__class_Ozero(_1189571))], (40780 ^ _778495) ^ [_1577962, _1577964, _1577966, _1577968, _1577970] : [-(hAPP(c_Relation_Oconverse(_1577962, _1577964), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1577966, tc_fun(tc_prod(_1577962, _1577964), tc_HOL_Obool)), _1577968), _1577970)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1577966, tc_fun(tc_prod(_1577964, _1577962), tc_HOL_Obool)), _1577968), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1577962, _1577964), tc_HOL_Obool), tc_fun(tc_prod(_1577964, _1577962), tc_HOL_Obool), _1577966), c_Relation_Oconverse(_1577962, _1577964)), _1577970)))], (47409 ^ _778495) ^ [_1733012, _1733014, _1733016, _1733018] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1733012, _1733014, _1733016, _1733018) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1733012, _1733014), _1733016), _1733018)))], (29210 ^ _778495) ^ [_1309651, _1309653, _1309655, _1309657] : [-(hAPP(c_Nat_Onat_Onat__rec(_1309651, _1309653, _1309655), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1309657)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1309651), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1309657))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1309651, _1309651), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1309651, tc_fun(_1309651, _1309651)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1309651, tc_fun(_1309651, _1309651)), tc_Int_Oint), c_If(_1309651)), c_Nat__Numeral_Oneg)), _1309653)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1309651, _1309651), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1309651, _1309651), tc_Int_Oint), _1309655), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1309651, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1309651, _1309653, _1309655)), c_Int_Onat)))))], (15035 ^ _778495) ^ [_1045266, _1045268, _1045270, _1045272] : [class_Rings_Olinordered__semiring__strict(_1045266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045266), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045266), _1045268), _1045270)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045266), _1045272), _1045270))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045266), c_Groups_Ozero__class_Ozero(_1045266)), _1045270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045266), _1045268), _1045272)))], (40419 ^ _778495) ^ [_1569420, _1569422, _1569424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569420, _1569420), tc_HOL_Obool)), _1569422), c_Transitive__Closure_Ortrancl(_1569420, _1569424))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569420, _1569420), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1569420, _1569422)), c_Transitive__Closure_Ortrancl(_1569420, _1569424))))], (7676 ^ _778495) ^ [_905471, _905473, _905475] : [class_Orderings_Opreorder(_905471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905471), _905473), _905475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905471), _905475), _905473))], (32492 ^ _778495) ^ [_1377084, _1377086, _1377088, _1377090] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1377084), _1377086)), 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)), _1377088), _1377084)), 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)), _1377090), _1377086)), 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)), _1377088), _1377090)), _1377086)), c_FunDef_Omax__weak)))], (41001 ^ _778495) ^ [_1583586, _1583588, _1583590, _1583592, _1583594, _1583596] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583586, _1583586)), hAPP(hAPP(c_Product__Type_OPair(_1583586, _1583586), _1583588), _1583590)), _1583592)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583586, _1583586)), hAPP(hAPP(c_Product__Type_OPair(_1583586, _1583586), _1583590), _1583594)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583586, _1583586), tc_HOL_Obool), _1583596), _1583592))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583586, _1583586)), hAPP(hAPP(c_Product__Type_OPair(_1583586, _1583586), _1583588), _1583594)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583586, _1583586), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1583596)), _1583592))))], (39428 ^ _778495) ^ [_1545751, _1545753, _1545755, _1545757, _1545759, _1545761, _1545763, _1545765, _1545767, _1545769, _1545771] : [-(hAPP(c_Product__Type_Omap__pair(_1545751, _1545753, _1545755, _1545757, _1545759, _1545761), hAPP(c_Product__Type_Omap__pair(_1545763, _1545751, _1545765, _1545755, _1545767, _1545769), _1545771)) = hAPP(c_Product__Type_Omap__pair(_1545763, _1545753, _1545765, _1545757, hAPP(c_Fun_Ocomp(_1545751, _1545753, _1545763, _1545759), _1545767), hAPP(c_Fun_Ocomp(_1545755, _1545757, _1545765, _1545761), _1545769)), _1545771))], (45432 ^ _778495) ^ [_1690246, _1690248] : [c_List_Oremdups(_1690246, _1690248) = c_List_Olist_ONil(_1690246), -(_1690248 = c_List_Olist_ONil(_1690246))], (24019 ^ _778495) ^ [_1208307] : [class_Int_Onumber__ring(_1208307), -(c_Int_Oiszero(_1208307, hAPP(c_Int_Onumber__class_Onumber__of(_1208307), c_Int_OPls)))], (31876 ^ _778495) ^ [_1363354, _1363356, _1363358, _1363360, _1363362, _1363364] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363354, tc_fun(_1363356, tc_fun(_1363358, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1363354, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1363356, _1363358), tc_HOL_Obool), tc_fun(_1363356, tc_fun(_1363358, tc_HOL_Obool)), _1363354), hAPP(c_COMBC(_1363356, tc_fun(tc_prod(_1363356, _1363358), tc_HOL_Obool), tc_fun(_1363358, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363358, tc_fun(tc_fun(tc_prod(_1363356, _1363358), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1363356, _1363358), tc_HOL_Obool), tc_fun(_1363358, tc_HOL_Obool)), _1363356), c_COMBC(_1363358, tc_fun(tc_prod(_1363356, _1363358), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363358, tc_prod(_1363356, _1363358)), tc_fun(_1363358, tc_fun(tc_fun(tc_prod(_1363356, _1363358), tc_HOL_Obool), tc_HOL_Obool)), _1363356), hAPP(c_COMBB(tc_prod(_1363356, _1363358), tc_fun(tc_fun(tc_prod(_1363356, _1363358), tc_HOL_Obool), tc_HOL_Obool), _1363358), c_member(tc_prod(_1363356, _1363358)))), c_Product__Type_OPair(_1363356, _1363358))))), _1363360)), _1363362), _1363364)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1363356, _1363358)), hAPP(hAPP(c_Product__Type_OPair(_1363356, _1363358), _1363362), _1363364)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363354, tc_fun(tc_prod(_1363356, _1363358), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1363354, tc_HOL_Obool))), _1363360))))], (45312 ^ _778495) ^ [_1687810, _1687812] : [-(c_Enum_On__lists(_1687810, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1687812) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687810)), c_List_Olist_ONil(_1687810)), c_List_Olist_ONil(tc_List_Olist(_1687810))))], (46907 ^ _778495) ^ [_1721804, _1721806, _1721808] : [hBOOL(hAPP(c_List_Odistinct(_1721804), _1721806)), -(hBOOL(hAPP(c_List_Odistinct(_1721804), c_List_OtakeWhile(_1721804, _1721808, _1721806))))], (31360 ^ _778495) ^ [_1351333, _1351335, _1351337] : [class_Orderings_Olinorder(_1351333), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351333), _1351335)), -(_1351335 = c_Orderings_Obot__class_Obot(tc_fun(_1351333, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351333), _1351337)), -(_1351337 = c_Orderings_Obot__class_Obot(tc_fun(_1351333, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1351333, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351333, tc_HOL_Obool)), _1351335), _1351337)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351333), c_Big__Operators_Olinorder__class_OMax(_1351333, _1351335)), c_Big__Operators_Olinorder__class_OMax(_1351333, _1351337)))], (34026 ^ _778495) ^ [_1412206, _1412208, _1412210, _1412212] : [class_Orderings_Oorder(_1412206), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412206, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1412206, _1412208), _1412210)), c_SetInterval_Oord__class_OatLeastAtMost(_1412206, _1412210, _1412212)) = c_Orderings_Obot__class_Obot(tc_fun(_1412206, tc_HOL_Obool)))], (4068 ^ _778495) ^ [_840128, _840130, _840132, _840134, _840136, _840138, _840140, _840142] : [-(c_New__Random__Sequence_Opos__map(_840142, _840138, _840134, _840130) = c_New__Random__Sequence_Opos__map(_840140, _840136, _840132, _840128)), _840142 = _840140, _840138 = _840136, _840134 = _840132, _840130 = _840128], (18609 ^ _778495) ^ [_1112638, _1112640, _1112642] : [class_Orderings_Olinorder(_1112638), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112638), _1112640)), -(_1112640 = c_Orderings_Obot__class_Obot(tc_fun(_1112638, tc_HOL_Obool))), 18620 ^ _778495 : [(18621 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112638), _1112642), hAPP(c_Finite__Set_Ofold1(_1112638, c_Orderings_Oord__class_Omin(_1112638)), _1112640))), 18624 ^ _778495 : [(18625 ^ _778495) ^ [_1112931] : [hBOOL(hAPP(hAPP(c_member(_1112638), _1112931), _1112640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112638), _1112642), _1112931)))]]], (18631 ^ _778495) ^ [] : [18633 ^ _778495 : [(18636 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112638), _1112642), 18632 ^ [_1112638, _1112640, _1112642]))], (18634 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112638), 18632 ^ [_1112638, _1112640, _1112642]), _1112640)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112638), _1112642), hAPP(c_Finite__Set_Ofold1(_1112638, c_Orderings_Oord__class_Omin(_1112638)), _1112640))))]]], (30795 ^ _778495) ^ [_1340548, _1340550] : [class_Orderings_Olinorder(_1340548), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340548), _1340550), _1340550) = _1340550)], (11298 ^ _778495) ^ [_973499, _973501, _973503, _973505] : [class_Groups_Ocancel__ab__semigroup__add(_973499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973499), _973501), _973503) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973499), _973501), _973505), -(_973503 = _973505)], (22658 ^ _778495) ^ [_1183535, _1183537] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1183535), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183537)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1183535), _1183537))], (8738 ^ _778495) ^ [_924765, _924767, _924769, _924771, _924773, _924775, _924777, _924779] : [c_Finite__Set_Ofolding__image__simple__idem(_924765, _924767, _924769, _924771, _924773, _924775), hBOOL(hAPP(c_Finite__Set_Ofinite(_924767), _924777)), -(hAPP(_924775, hAPP(hAPP(c_Set_Oinsert(_924767), _924779), _924777)) = hAPP(hAPP(_924769, hAPP(_924773, _924779)), hAPP(_924775, _924777)))], (10163 ^ _778495) ^ [_953695, _953697] : [class_Lattices_Olattice(_953695), -(c_Big__Operators_Olattice__class_OInf__fin(_953695, hAPP(hAPP(c_Set_Oinsert(_953695), _953697), c_Orderings_Obot__class_Obot(tc_fun(_953695, tc_HOL_Obool)))) = _953697)], (51137 ^ _778495) ^ [_1812908, _1812910, _1812912] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812908), _1812910)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812910), _1812912)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812908), _1812912)))], (20125 ^ _778495) ^ [] : [-(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))], (52363 ^ _778495) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (52469 ^ _778495) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (46688 ^ _778495) ^ [_1717228, _1717230, _1717232] : [_1717230 = _1717232, -(hAPP(c_List_Orev(_1717228), _1717230) = hAPP(c_List_Orev(_1717228), _1717232))], (37394 ^ _778495) ^ [_1486374, _1486376, _1486378, _1486380, _1486382] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1486374, _1486376), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1486374, tc_HOL_Obool)), _1486378), _1486380)), hAPP(c_COMBK(tc_fun(_1486376, tc_HOL_Obool), _1486374), _1486382)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1486374, _1486376), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486374, _1486376), _1486378), hAPP(c_COMBK(tc_fun(_1486376, tc_HOL_Obool), _1486374), _1486382))), hAPP(hAPP(c_Product__Type_OSigma(_1486374, _1486376), _1486380), hAPP(c_COMBK(tc_fun(_1486376, tc_HOL_Obool), _1486374), _1486382))))], (23889 ^ _778495) ^ [_1206068, _1206070, _1206072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206068)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1206072), _1206068)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206070), _1206072)), _1206068))], (34070 ^ _778495) ^ [_1413158, _1413160, _1413162, _1413164] : [class_Groups_Ocomm__monoid__add(_1413158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1413160), _1413162)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1413158), _1413164), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1413160), _1413162)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1413158), hAPP(_1413164, _1413160)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1413158), _1413164), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1413160)), _1413162))))], (21968 ^ _778495) ^ [_1171377, _1171379, _1171381] : [class_Groups_Oab__group__add(_1171377), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1171377), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171377), _1171379), _1171381)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171377), hAPP(c_Groups_Ouminus__class_Ouminus(_1171377), _1171379)), hAPP(c_Groups_Ouminus__class_Ouminus(_1171377), _1171381)))], (15605 ^ _778495) ^ [_1056134, _1056136, _1056138, _1056140, _1056142] : [class_Groups_Ocomm__monoid__mult(_1056134), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056136), _1056138)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056136), _1056140)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056136, tc_HOL_Obool)), _1056138), _1056140) = c_Orderings_Obot__class_Obot(tc_fun(_1056136, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056136, _1056134), _1056142), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1056136, tc_HOL_Obool)), _1056138), _1056140)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056134), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056136, _1056134), _1056142), _1056138)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056136, _1056134), _1056142), _1056140)))], (20384 ^ _778495) ^ [_1144668, _1144670] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144668) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144670), -(_1144668 = _1144670)], (8868 ^ _778495) ^ [_927530, _927532, _927534] : [8869 ^ _778495 : [(8872 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_927530), _927534))], (8870 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_927530), _927532))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_927530), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927530, tc_HOL_Obool)), _927532), _927534))))], (27703 ^ _778495) ^ [_1272899, _1272901] : [class_Lattices_Oboolean__algebra(_1272899), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272899), hAPP(c_Groups_Ouminus__class_Ouminus(_1272899), _1272901)), _1272901) = c_Orderings_Otop__class_Otop(_1272899))], (51147 ^ _778495) ^ [_1813071, _1813073] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813071), _1813073)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813073), _1813071)), -(_1813071 = _1813073)], (34715 ^ _778495) ^ [_1427726, _1427728, _1427730] : [class_Orderings_Oord(_1427726), 34718 ^ _778495 : [(34725 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427726), _1427730), _1427728)), -(hBOOL(hAPP(hAPP(c_member(_1427726), _1427728), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1427726), _1427730))))], (34719 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1427726), _1427728), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1427726), _1427730))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427726), _1427730), _1427728)))]]], (26688 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (10217 ^ _778495) ^ [_954668, _954670] : [class_Lattices_Olattice(_954668), hBOOL(hAPP(c_Finite__Set_Ofinite(_954668), _954670)), -(c_Big__Operators_Olattice__class_OInf__fin(_954668, _954670) = hAPP(c_Finite__Set_Ofold1(_954668, c_Lattices_Osemilattice__inf__class_Oinf(_954668)), _954670))], (52213 ^ _778495) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (43947 ^ _778495) ^ [_1657599, _1657601] : [class_Complete__Lattice_Ocomplete__lattice(_1657599), -(c_Complete__Lattice_OInf__class_OInf(_1657599, hAPP(c_List_Oset(_1657599), _1657601)) = hAPP(c_List_Ofoldl(_1657599, _1657599, c_Lattices_Osemilattice__inf__class_Oinf(_1657599), c_Orderings_Otop__class_Otop(_1657599)), _1657601))], (3506 ^ _778495) ^ [_830945, _830947, _830949, _830951, _830953, _830955, _830957, _830959] : [-(c_List_Olinorder__class_Osort__key(_830959, _830955, _830951, _830947) = c_List_Olinorder__class_Osort__key(_830957, _830953, _830949, _830945)), _830959 = _830957, _830955 = _830953, _830951 = _830949, _830947 = _830945], (8822 ^ _778495) ^ [_926605, _926607, _926609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_926605), _926607)), hBOOL(hAPP(hAPP(c_member(_926605), _926609), _926607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_926605), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926605, tc_HOL_Obool)), _926607), hAPP(hAPP(c_Set_Oinsert(_926605), _926609), c_Orderings_Obot__class_Obot(tc_fun(_926605, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_926605), _926607))))], (6155 ^ _778495) ^ [_877703, _877705, _877707, _877709] : [6157 ^ _778495 : [(6160 ^ _778495) ^ [] : [hBOOL(hAPP(_877709, 6156 ^ [_877703, _877705, _877707, _877709]))], (6158 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877703), 6156 ^ [_877703, _877705, _877707, _877709]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_877703, tc_HOL_Obool)), _877705), _877707))))]], 6161 ^ _778495 : [(6168 ^ _778495) ^ [_878020] : [hBOOL(hAPP(hAPP(c_member(_877703), _878020), _877707)), -(hBOOL(hAPP(_877709, _878020)))], (6162 ^ _778495) ^ [_877923] : [hBOOL(hAPP(hAPP(c_member(_877703), _877923), _877705)), -(hBOOL(hAPP(_877709, _877923)))]]], (45304 ^ _778495) ^ [_1687672, _1687674] : [-(c_Enum_Oenum__the(_1687672, _1687674) = c_HOL_OThe(_1687672, _1687674))], (27325 ^ _778495) ^ [_1266290, _1266292] : [class_Rings_Olinordered__idom(_1266290), 27328 ^ _778495 : [(27335 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266290), _1266292), c_Groups_Ozero__class_Ozero(_1266290))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266290), c_Groups_Osgn__class_Osgn(_1266290, _1266292)), c_Groups_Ozero__class_Ozero(_1266290))))], (27329 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266290), c_Groups_Osgn__class_Osgn(_1266290, _1266292)), c_Groups_Ozero__class_Ozero(_1266290))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266290), _1266292), c_Groups_Ozero__class_Ozero(_1266290))))]]], (9548 ^ _778495) ^ [_941514, _941516, _941518, _941520] : [hBOOL(hAPP(hAPP(c_member(_941514), _941516), _941518)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941514, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_941514), _941516), _941520)), _941518) = hAPP(hAPP(c_Set_Oinsert(_941514), _941516), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941514, tc_HOL_Obool)), _941520), _941518)))], (23765 ^ _778495) ^ [_1204145, _1204147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204147), 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), _1204145), _1204147)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34783 ^ _778495) ^ [_1429148, _1429150] : [class_Orderings_Olinorder(_1429148), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1429148, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1429148), _1429150)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1429148), _1429150))], (51021 ^ _778495) ^ [_1811023, _1811025, _1811027] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811023), _1811025)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811025), _1811023))), _1811025 = _1811027, 51032 ^ _778495 : [(51035 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811027), _1811023))], (51033 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811023), _1811027)))]]], (46642 ^ _778495) ^ [_1716168, _1716170, _1716172] : [-(hAPP(c_List_Orev(_1716168), hAPP(hAPP(c_List_Oappend(_1716168), _1716170), _1716172)) = hAPP(hAPP(c_List_Oappend(_1716168), hAPP(c_List_Orev(_1716168), _1716172)), hAPP(c_List_Orev(_1716168), _1716170)))], (45550 ^ _778495) ^ [_1692453, _1692455] : [c_List_Olist_ONil(_1692453) = c_List_Oconcat(_1692453, _1692455), 45553 ^ _778495 : [(45554 ^ _778495) ^ [_1692544] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692453)), _1692544), hAPP(c_List_Oset(tc_List_Olist(_1692453)), _1692455))), -(_1692544 = c_List_Olist_ONil(_1692453))]]], (42283 ^ _778495) ^ [_1620554, _1620556, _1620558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1620554), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620556)), _1620558))), -(c_List_Obutlast(_1620556, hAPP(hAPP(c_List_Otake(_1620556), _1620554), _1620558)) = hAPP(hAPP(c_List_Otake(_1620556), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1620554), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1620558))], (28061 ^ _778495) ^ [_1279236, _1279238] : [-(c_Random_Olog(_1279236, _1279238) = 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(_1279236, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1279238), _1279236)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1279236), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1279238), _1279236)))], (43560 ^ _778495) ^ [_1649176, _1649178] : [-(hAPP(hAPP(c_List_Odrop(_1649176), _1649178), c_List_Olist_ONil(_1649176)) = c_List_Olist_ONil(_1649176))], (7522 ^ _778495) ^ [_903000, _903002, _903004] : [class_Orderings_Opreorder(_903000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903000), _903002), _903004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903000), _903004), _903002))], (48120 ^ _778495) ^ [_1748437, _1748439, _1748441, _1748443, _1748445] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748437, _1748439, _1748441), _1748443), _1748445)), -(hBOOL(hAPP(hAPP(_1748441, _1748445), _1748443)))], (20167 ^ _778495) ^ [_1140769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1140769)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1140769 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6318 ^ _778495) ^ [_880771, _880773, _880775, _880777] : [_880771 = _880773, hBOOL(hAPP(hAPP(c_member(_880775), _880773), _880777)), -(hBOOL(hAPP(hAPP(c_member(_880775), _880771), _880777)))], (47020 ^ _778495) ^ [_1724254, _1724256, _1724258, _1724260] : [hBOOL(hAPP(_1724254, _1724256)), -(c_List_OdropWhile(_1724258, _1724254, hAPP(hAPP(c_List_Olist_OCons(_1724258), _1724256), _1724260)) = c_List_OdropWhile(_1724258, _1724254, _1724260))], (46822 ^ _778495) ^ [_1719966, _1719968, _1719970] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719966), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719966))), _1719968))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719970), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719966))), _1719968))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719966))), hAPP(c_List_Ofilter(tc_List_Olist(_1719966), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1719966)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719970)), c_Nat_Osize__class_Osize(tc_List_Olist(_1719966)))), c_List_Otranspose(_1719966, _1719968))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719966)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719966)), _1719968), _1719970)))], (52231 ^ _778495) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (25610 ^ _778495) ^ [_1236125, _1236127] : [class_Rings_Oring__1__no__zero__divisors(_1236125), 25613 ^ _778495 : [(25620 ^ _778495) ^ [] : [_1236127 = c_Groups_Ozero__class_Ozero(_1236125), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1236125), _1236127), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1236125))], (25614 ^ _778495) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1236125), _1236127), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1236125), -(_1236127 = c_Groups_Ozero__class_Ozero(_1236125))]]], (28971 ^ _778495) ^ [_1304275, _1304277, _1304279, _1304281, _1304283, _1304285] : [hBOOL(hAPP(hAPP(_1304275, _1304277), _1304279)), hBOOL(hAPP(hAPP(_1304281, _1304277), _1304279)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304283, tc_fun(_1304285, tc_HOL_Obool))), _1304275), _1304281), _1304277), _1304279)))], (14237 ^ _778495) ^ [_1031383, _1031385, _1031387] : [class_Rings_Olinordered__semiring__strict(_1031383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031383), c_Groups_Ozero__class_Ozero(_1031383)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031383), _1031385), _1031387))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031383), c_Groups_Ozero__class_Ozero(_1031383)), _1031387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031383), c_Groups_Ozero__class_Ozero(_1031383)), _1031385)))], (3524 ^ _778495) ^ [_831246, _831248, _831250, _831252, _831254, _831256, _831258, _831260, _831262, _831264] : [-(c_List_Olinorder__class_Oinsort__insert__key(_831264, _831260, _831256, _831252, _831248) = c_List_Olinorder__class_Oinsort__insert__key(_831262, _831258, _831254, _831250, _831246)), _831264 = _831262, _831260 = _831258, _831256 = _831254, _831252 = _831250, _831248 = _831246], (51081 ^ _778495) ^ [_1811987, _1811989] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811987), _1811989)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811989), _1811987))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811989), _1811987)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811987), _1811989)))], (36879 ^ _778495) ^ [_1473871, _1473873, _1473875, _1473877, _1473879] : [c_Typedef_Otype__definition(_1473871, _1473873, _1473875, _1473877, _1473879), -(hAPP(c_Set_Oimage(_1473873, _1473871, _1473877), _1473879) = c_Orderings_Otop__class_Otop(tc_fun(_1473871, tc_HOL_Obool)))], (260 ^ _778495) ^ [_782655, _782657] : [-(class_Fields_Olinordered__field(_782655)), _782657 = _782655, class_Fields_Olinordered__field(_782657)], (34669 ^ _778495) ^ [_1426736, _1426738] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1426736), _1426738) = 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)), _1426736)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1426738))))], (584 ^ _778495) ^ [_787293, _787295, _787297, _787299, _787301, _787303, _787305, _787307, _787309, _787311] : [-(c_Typedef_Otype__definition(_787309, _787305, _787301, _787297, _787293)), c_Typedef_Otype__definition(_787311, _787307, _787303, _787299, _787295), _787311 = _787309, _787307 = _787305, _787303 = _787301, _787299 = _787297, _787295 = _787293], (44001 ^ _778495) ^ [_1658842, _1658844] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1658842), hAPP(c_List_Oset(tc_Nat_Onat), _1658844))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1658842), 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)), _1658844))))], (17634 ^ _778495) ^ [_1094638, _1094640, _1094642, _1094644] : [class_Orderings_Olinorder(_1094638), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094638), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094638), _1094640), _1094642)), _1094644) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094638), _1094640), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094638), _1094642), _1094644)))], (39171 ^ _778495) ^ [_1539291, _1539293, _1539295] : [hBOOL(hAPP(c_Predicate_OPowp(_1539291, _1539293), _1539295)), 39174 ^ _778495 : [(39175 ^ _778495) ^ [_1539375] : [hBOOL(hAPP(hAPP(c_member(_1539291), _1539375), _1539295)), -(hBOOL(hAPP(_1539293, _1539375)))]]], (1268 ^ _778495) ^ [_797373, _797375] : [-(class_Rings_Ocomm__ring__1(_797373)), _797375 = _797373, class_Rings_Ocomm__ring__1(_797375)], (33834 ^ _778495) ^ [_1408423, _1408425] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408423), _1408425)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1408425), _1408423))], (19360 ^ _778495) ^ [_1126270, _1126272, _1126274] : [class_Orderings_Olinorder(_1126270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126270), _1126272)), -(_1126272 = c_Orderings_Obot__class_Obot(tc_fun(_1126270, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1126270, c_Orderings_Oord__class_Omin(_1126270), hAPP(hAPP(c_Set_Oinsert(_1126270), _1126274), _1126272)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1126270), _1126274), c_Big__Operators_Olattice_OInf__fin(_1126270, c_Orderings_Oord__class_Omin(_1126270), _1126272)))], (19562 ^ _778495) ^ [_1129851, _1129853, _1129855] : [class_Orderings_Olinorder(_1129851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1129851), _1129853)), -(_1129853 = c_Orderings_Obot__class_Obot(tc_fun(_1129851, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1129851), _1129855)), -(_1129855 = c_Orderings_Obot__class_Obot(tc_fun(_1129851, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129851, tc_HOL_Obool)), _1129853), _1129855) = c_Orderings_Obot__class_Obot(tc_fun(_1129851, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1129851, c_Orderings_Oord__class_Omin(_1129851), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1129851, tc_HOL_Obool)), _1129853), _1129855)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1129851), c_Big__Operators_Olattice_OInf__fin(_1129851, c_Orderings_Oord__class_Omin(_1129851), _1129853)), c_Big__Operators_Olattice_OInf__fin(_1129851, c_Orderings_Oord__class_Omin(_1129851), _1129855)))], (52671 ^ _778495) ^ [] : [-(hBOOL(c_fTrue))], (37825 ^ _778495) ^ [_1498239, _1498241] : [-(c_Relation_Orefl__on(_1498239, _1498241, c_Relation_OId__on(_1498239, _1498241)))], (37071 ^ _778495) ^ [_1477910, _1477912, _1477914, _1477916, _1477918] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1477910, _1477912, _1477914), _1477916), _1477918) = c_HOL_OThe(_1477912, c_Finite__Set_Ofold__graph(_1477910, _1477912, _1477914, _1477916, _1477918)))], (15835 ^ _778495) ^ [_1060670, _1060672, _1060674, _1060676, _1060678] : [class_Groups_Ocomm__monoid__add(_1060670), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060672), _1060674)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060672), _1060676)), 15849 ^ _778495 : [(15852 ^ _778495) ^ [] : [hAPP(_1060678, 15848 ^ [_1060670, _1060672, _1060674, _1060676, _1060678]) = c_Groups_Ozero__class_Ozero(_1060670)], (15850 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1060672), 15848 ^ [_1060670, _1060672, _1060674, _1060676, _1060678]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1060672, tc_HOL_Obool)), _1060674), _1060676))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1060672, _1060670), _1060678), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1060672, tc_HOL_Obool)), _1060674), _1060676)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060670), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1060672, _1060670), _1060678), _1060674)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1060672, _1060670), _1060678), _1060676)))], (30267 ^ _778495) ^ [_1329919] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1329919)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1329919), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1329919)))], (5620 ^ _778495) ^ [_864478, _864480] : [_864480 = _864478, -(c_Set_Oinsert(_864480) = c_Set_Oinsert(_864478))], (39251 ^ _778495) ^ [_1541276, _1541278] : [class_Complete__Lattice_Ocomplete__lattice(_1541276), -(c_Complete__Lattice_OSup__class_OSup(_1541276, _1541278) = c_Complete__Lattice_OInf__class_OInf(_1541276, hAPP(c_Set_OCollect(_1541276), hAPP(hAPP(c_COMBB(tc_fun(_1541276, tc_HOL_Obool), tc_HOL_Obool, _1541276), c_HOL_OAll(_1541276)), hAPP(hAPP(c_COMBB(tc_fun(_1541276, tc_HOL_Obool), tc_fun(_1541276, tc_HOL_Obool), _1541276), hAPP(c_COMBS(_1541276, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541276), c_fimplies), hAPP(hAPP(c_COMBC(_1541276, tc_fun(_1541276, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541276)), _1541278)))), hAPP(c_COMBC(_1541276, _1541276, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1541276)))))))], (21660 ^ _778495) ^ [] : [-(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))], (2204 ^ _778495) ^ [_810710, _810712, _810714, _810716, _810718, _810720] : [-(c_Random_Ominus__shift(_810720, _810716, _810712) = c_Random_Ominus__shift(_810718, _810714, _810710)), _810720 = _810718, _810716 = _810714, _810712 = _810710], (44770 ^ _778495) ^ [_1675277, _1675279, _1675281, _1675283] : [class_Groups_Ocomm__monoid__add(_1675277), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1675277), _1675279), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1675281, _1675283))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1675277), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1675277), _1675279), c_List_Oupto(_1675281, _1675283))))], (30051 ^ _778495) ^ [_1325647, _1325649, _1325651] : [-(hAPP(hAPP(c_Product__Type_OPair(_1325647, _1325649), hAPP(c_Product__Type_Ofst(_1325647, _1325649), _1325651)), hAPP(c_Product__Type_Osnd(_1325647, _1325649), _1325651)) = _1325651)], (15814 ^ _778495) ^ [_1060175, _1060177, _1060179, _1060181, _1060183] : [class_Groups_Ocomm__monoid__mult(_1060175), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060177), _1060179)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060177), _1060181)), 15828 ^ _778495 : [(15831 ^ _778495) ^ [] : [hAPP(_1060183, 15827 ^ [_1060175, _1060177, _1060179, _1060181, _1060183]) = c_Groups_Oone__class_Oone(_1060175)], (15829 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1060177), 15827 ^ [_1060175, _1060177, _1060179, _1060181, _1060183]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1060177, tc_HOL_Obool)), _1060179), _1060181))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1060177, _1060175), _1060183), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1060177, tc_HOL_Obool)), _1060179), _1060181)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060175), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1060177, _1060175), _1060183), _1060179)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1060177, _1060175), _1060183), _1060181)))], (1618 ^ _778495) ^ [_801748, _801750] : [-(class_Rings_Oordered__cancel__semiring(_801748)), _801750 = _801748, class_Rings_Oordered__cancel__semiring(_801750)], (40357 ^ _778495) ^ [_1567875, _1567877] : [-(hAPP(c_Relation_ORange(_1567875, _1567875), c_Transitive__Closure_Ortrancl(_1567875, _1567877)) = c_Orderings_Otop__class_Otop(tc_fun(_1567875, tc_HOL_Obool)))], (32164 ^ _778495) ^ [_1370148, _1370150, _1370152, _1370154, _1370156] : [_1370148 = c_Orderings_Obot__class_Obot(tc_fun(_1370150, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370150, tc_fun(_1370152, tc_HOL_Obool)), _1370148), hAPP(hAPP(c_COMBB(tc_fun(_1370152, tc_HOL_Obool), tc_fun(_1370152, tc_HOL_Obool), _1370150), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370152, tc_HOL_Obool)), _1370154)), _1370156)) = c_Orderings_Otop__class_Otop(tc_fun(_1370152, tc_HOL_Obool)))], (21992 ^ _778495) ^ [_1171893, _1171895, _1171897] : [class_Rings_Oidom(_1171893), 21995 ^ _778495 : [(21996 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171893), _1171895), _1171895) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171893), _1171897), _1171897), -(_1171895 = _1171897), -(_1171895 = hAPP(c_Groups_Ouminus__class_Ouminus(_1171893), _1171897))], (22006 ^ _778495) ^ [] : [22007 ^ _778495 : [(22010 ^ _778495) ^ [] : [_1171895 = hAPP(c_Groups_Ouminus__class_Ouminus(_1171893), _1171897)], (22008 ^ _778495) ^ [] : [_1171895 = _1171897]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171893), _1171895), _1171895) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171893), _1171897), _1171897))]]], (20194 ^ _778495) ^ [_1141227] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1141227)) = 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), _1141227)))], (35352 ^ _778495) ^ [_1438930, _1438932] : [class_Orderings_Oorder(_1438930), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438930, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1438930), _1438932)), hAPP(c_SetInterval_Oord__class_OatLeast(_1438930), _1438932)) = hAPP(hAPP(c_Set_Oinsert(_1438930), _1438932), c_Orderings_Obot__class_Obot(tc_fun(_1438930, tc_HOL_Obool))))], (20272 ^ _778495) ^ [_1142652, _1142654, _1142656] : [-(hBOOL(hAPP(_1142652, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1142654), _1142656))))), 20275 ^ _778495 : [(20278 ^ _778495) ^ [] : [hBOOL(hAPP(_1142652, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142654)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142656))))], (20276 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1142656), _1142654)))]], 20279 ^ _778495 : [(20282 ^ _778495) ^ [] : [hBOOL(hAPP(_1142652, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20280 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1142654), _1142656)))]]], (20832 ^ _778495) ^ [_1151611, _1151613] : [class_Int_Onumber__ring(_1151611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1151613)), -(hBOOL(hAPP(hAPP(c_member(_1151611), hAPP(c_Int_Onumber__class_Onumber__of(_1151611), _1151613)), c_Nat_Osemiring__1__class_ONats(_1151611))))], (34536 ^ _778495) ^ [_1424092, _1424094, _1424096, _1424098] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1424092), _1424094)), -(hAPP(c_Set_Oimage(_1424092, _1424096, _1424098), _1424094) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1424096, tc_HOL_Obool), _1424092, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424096, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1424092, tc_fun(_1424096, tc_HOL_Obool), tc_fun(_1424096, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1424096, tc_fun(tc_fun(_1424096, tc_HOL_Obool), tc_fun(_1424096, tc_HOL_Obool)), _1424092), c_Set_Oinsert(_1424096)), _1424098)), c_Orderings_Obot__class_Obot(tc_fun(_1424096, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1424096, tc_HOL_Obool))), _1424094))], (34259 ^ _778495) ^ [_1417378, _1417380, _1417382] : [-(hAPP(c_Relation_OField(_1417378), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1417378, _1417378), tc_HOL_Obool)), _1417380), _1417382)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417378, tc_HOL_Obool)), hAPP(c_Relation_OField(_1417378), _1417380)), hAPP(c_Relation_OField(_1417378), _1417382)))], (24065 ^ _778495) ^ [_1208998, _1209000, _1209002, _1209004] : [_1208998 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1209000), _1209002)), _1209004), -(_1209000 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1208998), _1209000) = _1209002), 24072 ^ _778495 : [(24075 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209004), _1209000))], (24073 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209000)))]], 24080 ^ _778495 : [(24083 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209000), _1209004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1209004), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24081 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209000))]]], (42702 ^ _778495) ^ [_1629584, _1629586] : [-(c_List_Osublist(_1629584, c_List_Olist_ONil(_1629584), _1629586) = c_List_Olist_ONil(_1629584))], (27577 ^ _778495) ^ [_1270688, _1270690] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270688, tc_HOL_Obool)), _1270690), c_Orderings_Otop__class_Otop(tc_fun(_1270688, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1270688, tc_HOL_Obool)))], (27569 ^ _778495) ^ [_1270512, _1270514] : [-(c_Sum__Type_OPlus(_1270512, _1270514, c_Orderings_Otop__class_Otop(tc_fun(_1270512, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1270514, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1270512, _1270514), tc_HOL_Obool)))], (7860 ^ _778495) ^ [_908225, _908227, _908229] : [class_Orderings_Olinorder(_908225), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908225), _908227), _908229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908225), _908229), _908227)))], (20464 ^ _778495) ^ [_1145733] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1145733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145733), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13225 ^ _778495) ^ [_1013969, _1013971] : [class_Rings_Omult__zero(_1013969), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013969), c_Groups_Ozero__class_Ozero(_1013969)), _1013971) = c_Groups_Ozero__class_Ozero(_1013969))], (8556 ^ _778495) ^ [_921387, _921389, _921391] : [class_Lattices_Oab__semigroup__idem__mult(_921387), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921387), _921389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921387), _921389), _921391)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921387), _921389), _921391))], (52171 ^ _778495) ^ [_1830762, _1830764] : [class_Groups_Ouminus(_1830762), -(class_Groups_Ouminus(tc_fun(_1830764, _1830762)))], (15856 ^ _778495) ^ [_1061165, _1061167, _1061169, _1061171, _1061173] : [class_Groups_Ocomm__monoid__add(_1061165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061167), _1061169)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061167), _1061171)), 15870 ^ _778495 : [(15873 ^ _778495) ^ [] : [hAPP(_1061173, 15869 ^ [_1061165, _1061167, _1061169, _1061171, _1061173]) = c_Groups_Ozero__class_Ozero(_1061165)], (15871 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1061167), 15869 ^ [_1061165, _1061167, _1061169, _1061171, _1061173]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1061167, tc_HOL_Obool)), _1061169), _1061171))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1061167, _1061165), _1061173), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061167, tc_HOL_Obool)), _1061169), _1061171)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061165), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1061167, _1061165), _1061173), _1061169)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1061167, _1061165), _1061173), _1061171)))], (37775 ^ _778495) ^ [_1497283] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1497283, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1497283), hAPP(c_COMBK(tc_HOL_Obool, _1497283), c_fFalse)))], (4572 ^ _778495) ^ [_848078, _848080] : [_848080 = _848078, -(c_DSequence_Ounion(_848080) = c_DSequence_Ounion(_848078))], (3814 ^ _778495) ^ [_835819, _835821] : [_835821 = _835819, -(c_Enum_Oenum__class_Oenum__all(_835821) = c_Enum_Oenum__class_Oenum__all(_835819))], (47562 ^ _778495) ^ [_1736879, _1736881, _1736883, _1736885] : [class_Orderings_Oorder(_1736879), class_Enum_Oenum(_1736881), 47569 ^ _778495 : [(47576 ^ _778495) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736881), hAPP(hAPP(c_COMBS(_1736881, _1736879, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736879, tc_fun(_1736879, tc_HOL_Obool), _1736881), c_Orderings_Oord__class_Oless__eq(_1736879)), _1736883)), _1736885))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736881, _1736879)), _1736883), _1736885)))], (47570 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736881, _1736879)), _1736883), _1736885)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736881), hAPP(hAPP(c_COMBS(_1736881, _1736879, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736879, tc_fun(_1736879, tc_HOL_Obool), _1736881), c_Orderings_Oord__class_Oless__eq(_1736879)), _1736883)), _1736885))))]]], (23563 ^ _778495) ^ [_1200653, _1200655, _1200657] : [class_Divides_Osemiring__div(_1200653), -(_1200655 = c_Groups_Ozero__class_Ozero(_1200653)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200653), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200653), _1200657), _1200655)), _1200655) = _1200657)], (52297 ^ _778495) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (28213 ^ _778495) ^ [_1282100, _1282102, _1282104, _1282106, _1282108] : [class_Groups_Ocomm__monoid__mult(_1282100), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1282102, _1282100), hAPP(hAPP(c_COMBS(_1282102, _1282100, _1282100), hAPP(hAPP(c_COMBB(_1282100, tc_fun(_1282100, _1282100), _1282102), c_Groups_Otimes__class_Otimes(_1282100)), _1282104)), _1282106)), _1282108) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282100), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1282102, _1282100), _1282104), _1282108)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1282102, _1282100), _1282106), _1282108)))], (20000 ^ _778495) ^ [] : [-(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)))], (38961 ^ _778495) ^ [_1533448, _1533450, _1533452] : [-(hAPP(c_Relation_ODomain(_1533448, _1533450), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1533448, _1533450), tc_HOL_Obool), _1533452)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1533448, _1533450), tc_HOL_Obool), tc_fun(_1533448, tc_HOL_Obool)), _1533452), c_Relation_ODomain(_1533448, _1533450)))], (27281 ^ _778495) ^ [_1265614, _1265616] : [c_Code__Numeral_OSuc__code__numeral(_1265614) = c_Code__Numeral_OSuc__code__numeral(_1265616), -(_1265614 = _1265616)], (10469 ^ _778495) ^ [_959127, _959129, _959131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _959127), _959129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959131), _959127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959127), _959131)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959129), _959131))))], (46220 ^ _778495) ^ [_1707878, _1707880, _1707882, _1707884] : [class_Orderings_Olinorder(_1707878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707878), _1707880), _1707882)), c_List_Olinorder__class_Osorted(_1707878, hAPP(hAPP(c_List_Olist_OCons(_1707878), _1707882), _1707884)), -(c_List_Olinorder__class_Osorted(_1707878, hAPP(hAPP(c_List_Olist_OCons(_1707878), _1707880), hAPP(hAPP(c_List_Olist_OCons(_1707878), _1707882), _1707884))))], (39740 ^ _778495) ^ [_1552656, _1552658, _1552660, _1552662, _1552664, _1552666] : [c_Finite__Set_Ofolding(_1552656, _1552658, _1552660, _1552662), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552656), _1552664)), -(hBOOL(hAPP(hAPP(c_member(_1552656), _1552666), _1552664))), -(hAPP(_1552662, hAPP(hAPP(c_Set_Oinsert(_1552656), _1552666), _1552664)) = hAPP(c_Fun_Ocomp(_1552658, _1552658, _1552658, hAPP(_1552662, _1552664)), hAPP(_1552660, _1552666)))], (33491 ^ _778495) ^ [_1400492, _1400494, _1400496, _1400498] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1400492, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1400494, tc_fun(_1400492, tc_HOL_Obool)), _1400496), _1400498)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400494, tc_fun(_1400492, tc_HOL_Obool)), _1400496), hAPP(hAPP(c_COMBB(tc_fun(_1400492, tc_HOL_Obool), tc_fun(_1400492, tc_HOL_Obool), _1400494), c_Groups_Ouminus__class_Ouminus(tc_fun(_1400492, tc_HOL_Obool))), _1400498)))], (20912 ^ _778495) ^ [_1153004, _1153006] : [class_Int_Onumber__ring(_1153004), -(hAPP(c_Int_Onumber__class_Onumber__of(_1153004), c_Int_Osucc(_1153006)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153004), c_Groups_Oone__class_Oone(_1153004)), hAPP(c_Int_Onumber__class_Onumber__of(_1153004), _1153006)))], (43241 ^ _778495) ^ [_1641214, _1641216, _1641218] : [_1641218 = c_List_Olist_ONil(_1641216), -(_1641214 = hAPP(hAPP(c_List_Oappend(_1641216), _1641218), _1641214))], (49689 ^ _778495) ^ [_1782752, _1782754, _1782756, _1782758, _1782760, _1782762] : [hAPP(c_Hilbert__Choice_Oinv__into(_1782752, _1782754, _1782756, _1782758), _1782760) = hAPP(c_Hilbert__Choice_Oinv__into(_1782752, _1782754, _1782756, _1782758), _1782762), hBOOL(hAPP(hAPP(c_member(_1782754), _1782760), hAPP(c_Set_Oimage(_1782752, _1782754, _1782758), _1782756))), hBOOL(hAPP(hAPP(c_member(_1782754), _1782762), hAPP(c_Set_Oimage(_1782752, _1782754, _1782758), _1782756))), -(_1782760 = _1782762)], (45664 ^ _778495) ^ [_1695896, _1695898, _1695900] : [hBOOL(hAPP(c_List_Odistinct(_1695896), _1695898)), -(hBOOL(hAPP(c_List_Odistinct(_1695896), hAPP(c_List_Ofilter(_1695896, _1695900), _1695898))))], (29077 ^ _778495) ^ [_1306483, _1306485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1306483)), 29080 ^ _778495 : [(29087 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306485), _1306483))), -(c_Divides_OposDivAlg(_1306485, _1306483) = hAPP(c_Divides_Oadjust(_1306483), c_Divides_OposDivAlg(_1306485, 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)))), _1306483))))], (29081 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306485), _1306483)), -(c_Divides_OposDivAlg(_1306485, _1306483) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1306485))]]], (46832 ^ _778495) ^ [_1720275, _1720277] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1720275), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1720275))), _1720277))), -(c_List_Otranspose(_1720275, c_List_Otranspose(_1720275, _1720277)) = c_List_OtakeWhile(tc_List_Olist(_1720275), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1720275)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1720275), tc_List_Olist(_1720275), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1720275))), _1720277))], (35358 ^ _778495) ^ [_1439073, _1439075] : [class_Orderings_Olinorder(_1439073), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439073, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1439073), _1439075), c_Orderings_Obot__class_Obot(tc_fun(_1439073, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439073), _1439075)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1439073), _1439075))], (6032 ^ _778495) ^ [_874951, _874953, _874955] : [class_Orderings_Oorder(_874951), 6035 ^ _778495 : [(6044 ^ _778495) ^ [] : [-(_874953 = _874955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874951), _874953), _874955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874951), _874955), _874953))], (6036 ^ _778495) ^ [] : [_874953 = _874955, 6039 ^ _778495 : [(6042 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874951), _874955), _874953)))], (6040 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874951), _874953), _874955)))]]]]], (52043 ^ _778495) ^ [_1828919, _1828921, _1828923, _1828925, _1828927] : [class_Rings_Ocomm__semiring__1(_1828919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1828921), _1828923)), hBOOL(hAPP(hAPP(c_member(_1828921), _1828925), _1828923)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828919), hAPP(_1828927, _1828925)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1828921, _1828919), _1828927), _1828923))))], (46881 ^ _778495) ^ [_1721318, _1721320, _1721322, _1721324, _1721326] : [-(hAPP(hAPP(c_List_Ozip(_1721318, _1721320), c_List_OtakeWhile(_1721318, _1721322, _1721324)), _1721326) = c_List_OtakeWhile(tc_prod(_1721318, _1721320), hAPP(c_Fun_Ocomp(_1721318, tc_HOL_Obool, tc_prod(_1721318, _1721320), _1721322), c_Product__Type_Ofst(_1721318, _1721320)), hAPP(hAPP(c_List_Ozip(_1721318, _1721320), _1721324), _1721326)))], (25678 ^ _778495) ^ [_1237335, _1237337] : [class_Rings_Olinordered__idom(_1237335), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1237335), hAPP(c_Groups_Oabs__class_Oabs(_1237335), _1237337)), 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(_1237335), _1237337), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19456 ^ _778495) ^ [_1127894, _1127896, _1127898] : [class_Orderings_Olinorder(_1127894), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127894), _1127896)), -(_1127898 = c_Orderings_Obot__class_Obot(tc_fun(_1127894, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1127894, tc_HOL_Obool)), _1127898), _1127896)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1127894), c_Big__Operators_Olinorder__class_OMin(_1127894, _1127898)), c_Big__Operators_Olinorder__class_OMin(_1127894, _1127896)) = c_Big__Operators_Olinorder__class_OMin(_1127894, _1127896))], (45977 ^ _778495) ^ [_1703443, _1703445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703443)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703445))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703443), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703445)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703443)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703443)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703445))))], (38840 ^ _778495) ^ [_1530510, _1530512, _1530514, _1530516] : [-(hAPP(c_Relation_ODomain(_1530510, _1530512), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530510, _1530512), tc_HOL_Obool)), _1530514), _1530516)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530510, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1530510, _1530512), _1530514)), hAPP(c_Relation_ODomain(_1530510, _1530512), _1530516)))], (38820 ^ _778495) ^ [_1530083, _1530085, _1530087] : [hAPP(c_Relation_ODomain(_1530083, _1530085), _1530087) = c_Orderings_Obot__class_Obot(tc_fun(_1530083, tc_HOL_Obool)), -(_1530087 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530083, _1530085), tc_HOL_Obool)))], (51613 ^ _778495) ^ [_1821033] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821033), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1821033 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (39898 ^ _778495) ^ [_1556297, _1556299] : [39899 ^ _778495 : [(39900 ^ _778495) ^ [_1556343] : [hBOOL(hAPP(_1556297, _1556343))]], -(hBOOL(hAPP(_1556297, c_Hilbert__Choice_OEps(_1556299, _1556297))))], (22212 ^ _778495) ^ [_1175801, _1175803] : [class_Groups_Olinordered__ab__group__add(_1175801), 22215 ^ _778495 : [(22222 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175801), c_Groups_Ozero__class_Ozero(_1175801)), _1175803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175801), hAPP(c_Groups_Ouminus__class_Ouminus(_1175801), _1175803)), _1175803)))], (22216 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175801), hAPP(c_Groups_Ouminus__class_Ouminus(_1175801), _1175803)), _1175803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175801), c_Groups_Ozero__class_Ozero(_1175801)), _1175803)))]]], (23613 ^ _778495) ^ [_1201347, _1201349, _1201351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201347), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23616 ^ _778495 : [(23617 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1201349, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1201351), _1201347)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1201351, _1201347))), 23620 ^ _778495 : [(23621 ^ _778495) ^ [_1201557, _1201559] : [-(hBOOL(hAPP(hAPP(_1201349, _1201559), _1201557))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201347), _1201557)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1201557), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1201351 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201347), _1201559)), _1201557)]]], (23635 ^ _778495) ^ [] : [23638 ^ _778495 : [(23641 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23637 ^ [_1201347, _1201349, _1201351]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23643 ^ _778495) ^ [] : [-(_1201351 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201347), 23636 ^ [_1201347, _1201349, _1201351])), 23637 ^ [_1201347, _1201349, _1201351]))], (23645 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1201349, 23636 ^ [_1201347, _1201349, _1201351]), 23637 ^ [_1201347, _1201349, _1201351]))], (23639 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201347), 23637 ^ [_1201347, _1201349, _1201351])))]], -(hBOOL(hAPP(hAPP(_1201349, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1201351), _1201347)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1201351, _1201347))))]]], (30053 ^ _778495) ^ [_1325695, _1325697, _1325699] : [-(_1325695 = hAPP(hAPP(c_Product__Type_OPair(_1325697, _1325699), hAPP(c_Product__Type_Ofst(_1325697, _1325699), _1325695)), hAPP(c_Product__Type_Osnd(_1325697, _1325699), _1325695)))], (19070 ^ _778495) ^ [_1121321, _1121323, _1121325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121321), _1121323)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121325)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121325), _1121321)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121325), _1121323))))], (10949 ^ _778495) ^ [_966959, _966961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966959), _966961)), -(_966959 = _966961), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _966959), _966961)))], (17750 ^ _778495) ^ [_1096804, _1096806, _1096808] : [class_Orderings_Olinorder(_1096804), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096804), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096804), _1096806), _1096808)), _1096808)))], (27667 ^ _778495) ^ [_1272251] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272251, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1272251, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1272251, tc_HOL_Obool)))], (3964 ^ _778495) ^ [_838456, _838458] : [_838458 = _838456, -(c_New__DSequence_Opos__empty(_838458) = c_New__DSequence_Opos__empty(_838456))], (40039 ^ _778495) ^ [_1559610, _1559612, _1559614] : [class_Orderings_Olinorder(_1559610), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559610), _1559612)), 40049 ^ _778495 : [(40052 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1559610), 40048 ^ [_1559610, _1559612, _1559614]), _1559614))], (40050 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559610), 40048 ^ [_1559610, _1559612, _1559614]), _1559612)))]], hBOOL(hAPP(hAPP(c_member(_1559610), _1559614), _1559612)), -(c_Big__Operators_Olinorder__class_OMax(_1559610, _1559612) = _1559614)], (332 ^ _778495) ^ [_783617, _783619, _783621, _783623] : [-(c_FunDef_Oreduction__pair(_783621, _783617)), c_FunDef_Oreduction__pair(_783623, _783619), _783623 = _783621, _783619 = _783617], (48823 ^ _778495) ^ [_1763960, _1763962, _1763964, _1763966] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1763960), _1763962)), 48826 ^ _778495 : [(48827 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1763964), hAPP(c_Set_OCollect(_1763964), hAPP(hAPP(c_COMBB(tc_fun(_1763960, tc_HOL_Obool), tc_HOL_Obool, _1763964), c_HOL_OEx(_1763960)), hAPP(hAPP(c_COMBB(tc_fun(_1763960, tc_HOL_Obool), tc_fun(_1763960, tc_HOL_Obool), _1763964), hAPP(c_COMBS(_1763960, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1763960), c_fconj), hAPP(hAPP(c_COMBC(_1763960, tc_fun(_1763960, tc_HOL_Obool), tc_HOL_Obool), c_member(_1763960)), _1763962)))), _1763966))))), 48830 ^ _778495 : [(48831 ^ _778495) ^ [_1764268] : [hBOOL(hAPP(hAPP(c_member(_1763960), _1764268), _1763962)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1763964), hAPP(c_Set_OCollect(_1763964), hAPP(hAPP(c_COMBC(_1763964, _1763960, tc_HOL_Obool), _1763966), _1764268)))))]]], (48837 ^ _778495) ^ [] : [48839 ^ _778495 : [(48842 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1763964), hAPP(c_Set_OCollect(_1763964), hAPP(hAPP(c_COMBC(_1763964, _1763960, tc_HOL_Obool), _1763966), 48838 ^ [_1763960, _1763962, _1763964, _1763966]))))], (48840 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763960), 48838 ^ [_1763960, _1763962, _1763964, _1763966]), _1763962)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1763964), hAPP(c_Set_OCollect(_1763964), hAPP(hAPP(c_COMBB(tc_fun(_1763960, tc_HOL_Obool), tc_HOL_Obool, _1763964), c_HOL_OEx(_1763960)), hAPP(hAPP(c_COMBB(tc_fun(_1763960, tc_HOL_Obool), tc_fun(_1763960, tc_HOL_Obool), _1763964), hAPP(c_COMBS(_1763960, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1763960), c_fconj), hAPP(hAPP(c_COMBC(_1763960, tc_fun(_1763960, tc_HOL_Obool), tc_HOL_Obool), c_member(_1763960)), _1763962)))), _1763966))))))]]], (42359 ^ _778495) ^ [_1622323, _1622325, _1622327, _1622329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622323), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622325)), _1622327))), 42362 ^ _778495 : [(42369 ^ _778495) ^ [] : [hAPP(hAPP(c_List_Onth(_1622325), _1622327), _1622323) = _1622329, -(hAPP(hAPP(c_List_Olist__update(_1622325, _1622327), _1622323), _1622329) = _1622327)], (42363 ^ _778495) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1622325, _1622327), _1622323), _1622329) = _1622327, -(hAPP(hAPP(c_List_Onth(_1622325), _1622327), _1622323) = _1622329)]]], (50258 ^ _778495) ^ [_1794785, _1794787] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1794785), _1794787)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1794785, 50261 ^ [_1794785, _1794787], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1794785), _1794787)), _1794787))], (44792 ^ _778495) ^ [_1675932, _1675934, _1675936, _1675938, _1675940] : [class_Groups_Omonoid__add(_1675932), class_Groups_Oordered__ab__semigroup__add(_1675932), 44802 ^ _778495 : [(44805 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675932), hAPP(_1675938, 44801 ^ [_1675932, _1675934, _1675936, _1675938, _1675940])), hAPP(_1675940, 44801 ^ [_1675932, _1675934, _1675936, _1675938, _1675940])))], (44803 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1675934), 44801 ^ [_1675932, _1675934, _1675936, _1675938, _1675940]), hAPP(c_List_Oset(_1675934), _1675936))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675932), hAPP(c_List_Omonoid__add__class_Olistsum(_1675932), hAPP(hAPP(c_List_Omap(_1675934, _1675932), _1675938), _1675936))), hAPP(c_List_Omonoid__add__class_Olistsum(_1675932), hAPP(hAPP(c_List_Omap(_1675934, _1675932), _1675940), _1675936)))))], (26652 ^ _778495) ^ [_1255182, _1255184] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1255182, tc_HOL_Obool)), _1255184), hAPP(c_Set_OPow(_1255182), _1255184))))], (34008 ^ _778495) ^ [_1411817, _1411819, _1411821, _1411823] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1411817, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1411819)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1411817, tc_HOL_Obool), tc_Nat_Onat), _1411821), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1411823))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1411817, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1411823, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1411819), _1411823))), _1411821))], (15553 ^ _778495) ^ [_1055064, _1055066, _1055068, _1055070] : [class_Groups_Ocomm__monoid__mult(_1055064), 15556 ^ _778495 : [(15563 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1055066), _1055068))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1055066, _1055064), _1055070), _1055068) = c_Groups_Oone__class_Oone(_1055064))], (15557 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055066), _1055068)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1055066, _1055064), _1055070), _1055068) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1055064, _1055066, c_Groups_Otimes__class_Otimes(_1055064)), _1055070), c_Groups_Oone__class_Oone(_1055064)), _1055068))]]], (52271 ^ _778495) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (51477 ^ _778495) ^ [_1818520, _1818522] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818520), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1818522), _1818520))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818520), _1818522)))], (47124 ^ _778495) ^ [_1726448, _1726450, _1726452, _1726454] : [47126 ^ _778495 : [(47131 ^ _778495) ^ [] : [hBOOL(hAPP(_1726454, hAPP(hAPP(c_List_Onth(_1726450), _1726452), 47125 ^ [_1726448, _1726450, _1726452, _1726454])))], (47129 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47125 ^ [_1726448, _1726450, _1726452, _1726454]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726450)), _1726452))))], (47127 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47125 ^ [_1726448, _1726450, _1726452, _1726454]), _1726448)))]], 47134 ^ _778495 : [(47137 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1726454, hAPP(hAPP(c_List_Onth(_1726450), _1726452), _1726448))))], (47135 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726448), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726450)), _1726452))))]], -(c_List_OtakeWhile(_1726450, _1726454, _1726452) = hAPP(hAPP(c_List_Otake(_1726450), _1726448), _1726452))], (28279 ^ _778495) ^ [_1283967, _1283969, _1283971, _1283973] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1283967, _1283969)), hAPP(hAPP(c_Product__Type_OPair(_1283967, _1283969), _1283971), _1283973)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1283967, _1283969), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1283967, tc_fun(_1283969, tc_HOL_Obool))), _1283971), _1283973)))], (49927 ^ _778495) ^ [_1788282, _1788284, _1788286, _1788288, _1788290, _1788292] : [c_Fun_Obij__betw(_1788282, _1788284, _1788286, _1788288, _1788290), hBOOL(hAPP(hAPP(c_member(_1788282), _1788292), _1788288)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1788284, _1788282, _1788290, c_Hilbert__Choice_Oinv__into(_1788282, _1788284, _1788288, _1788286)), _1788292) = hAPP(_1788286, _1788292))], (33006 ^ _778495) ^ [_1387313, _1387315, _1387317, _1387319] : [class_Orderings_Olinorder(_1387313), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387313), _1387315), _1387317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387313), _1387317), _1387319)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387313, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1387313, _1387315, _1387317)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1387313, _1387317, _1387319)) = c_SetInterval_Oord__class_OatLeastAtMost(_1387313, _1387315, _1387319))], (47766 ^ _778495) ^ [_1740801, _1740803, _1740805, _1740807] : [47767 ^ _778495 : [(47770 ^ _778495) ^ [] : [c_List_Olist__ex(_1740801, _1740803, _1740807)], (47768 ^ _778495) ^ [] : [hBOOL(hAPP(_1740803, _1740805))]], -(c_List_Olist__ex(_1740801, _1740803, hAPP(hAPP(c_List_Olist_OCons(_1740801), _1740805), _1740807)))], (35424 ^ _778495) ^ [_1440412, _1440414, _1440416] : [class_Lattices_Oab__semigroup__idem__mult(_1440412), hAPP(_1440414, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1440412), 35429 ^ [_1440412, _1440414, _1440416]), 35430 ^ [_1440412, _1440414, _1440416])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1440412), hAPP(_1440414, 35429 ^ [_1440412, _1440414, _1440416])), hAPP(_1440414, 35430 ^ [_1440412, _1440414, _1440416])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440412), _1440416)), -(_1440416 = c_Orderings_Obot__class_Obot(tc_fun(_1440412, tc_HOL_Obool))), -(hAPP(_1440414, hAPP(c_Finite__Set_Ofold1(_1440412, c_Groups_Otimes__class_Otimes(_1440412)), _1440416)) = hAPP(c_Finite__Set_Ofold1(_1440412, c_Groups_Otimes__class_Otimes(_1440412)), hAPP(c_Set_Oimage(_1440412, _1440412, _1440414), _1440416)))], (22320 ^ _778495) ^ [_1177619, _1177621] : [class_Groups_Oab__group__add(_1177619), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177619), hAPP(c_Groups_Ouminus__class_Ouminus(_1177619), _1177621)), _1177621) = c_Groups_Ozero__class_Ozero(_1177619))], (10655 ^ _778495) ^ [_962215, _962217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962215), _962217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962217), _962215)), -(_962215 = _962217)], (37885 ^ _778495) ^ [_1499689, _1499691, _1499693] : [-(hBOOL(hAPP(_1499689, _1499691))), -(hAPP(c_Set_OCollect(_1499693), hAPP(hAPP(c_COMBS(_1499693, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499693), c_fconj), hAPP(hAPP(c_COMBC(_1499693, _1499693, tc_HOL_Obool), c_fequal), _1499691))), _1499689)) = c_Orderings_Obot__class_Obot(tc_fun(_1499693, tc_HOL_Obool)))], (8894 ^ _778495) ^ [_927984, _927986, _927988] : [class_Lattices_Olattice(_927984), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927984), _927986), _927988) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927984), _927988), _927986))], (9608 ^ _778495) ^ [_943020, _943022, _943024] : [class_Lattices_Olattice(_943020), hBOOL(hAPP(c_Finite__Set_Ofinite(_943020), _943022)), hBOOL(hAPP(hAPP(c_member(_943020), _943024), _943022)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_943020), _943024), c_Big__Operators_Olattice__class_OSup__fin(_943020, _943022)) = c_Big__Operators_Olattice__class_OSup__fin(_943020, _943022))], (36057 ^ _778495) ^ [_1455473, _1455475, _1455477, _1455479, _1455481, _1455483, _1455485, _1455487, _1455489] : [c_Equiv__Relations_Oequiv(_1455473, _1455475, _1455477), c_Equiv__Relations_Oequiv(_1455479, _1455481, _1455483), c_Equiv__Relations_Ocongruent2(_1455473, _1455479, tc_fun(_1455485, tc_HOL_Obool), _1455477, _1455483, _1455487), hBOOL(hAPP(hAPP(c_member(_1455479), _1455489), _1455481)), -(c_Equiv__Relations_Ocongruent(_1455473, tc_fun(_1455485, tc_HOL_Obool), _1455477, hAPP(hAPP(c_COMBB(tc_fun(_1455479, tc_fun(_1455485, tc_HOL_Obool)), tc_fun(_1455485, tc_HOL_Obool), _1455473), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1455479, tc_fun(_1455485, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1455479, _1455479, _1455483), hAPP(hAPP(c_Set_Oinsert(_1455479), _1455489), c_Orderings_Obot__class_Obot(tc_fun(_1455479, tc_HOL_Obool)))))), _1455487)))], (22372 ^ _778495) ^ [_1178581, _1178583] : [class_Rings_Oring__1__no__zero__divisors(_1178581), 22375 ^ _778495 : [(22376 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178581), _1178583), _1178583) = c_Groups_Oone__class_Oone(_1178581), -(_1178583 = c_Groups_Oone__class_Oone(_1178581)), -(_1178583 = hAPP(c_Groups_Ouminus__class_Ouminus(_1178581), c_Groups_Oone__class_Oone(_1178581)))], (22386 ^ _778495) ^ [] : [22387 ^ _778495 : [(22390 ^ _778495) ^ [] : [_1178583 = hAPP(c_Groups_Ouminus__class_Ouminus(_1178581), c_Groups_Oone__class_Oone(_1178581))], (22388 ^ _778495) ^ [] : [_1178583 = c_Groups_Oone__class_Oone(_1178581)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178581), _1178583), _1178583) = c_Groups_Oone__class_Oone(_1178581))]]], (45973 ^ _778495) ^ [_1703367, _1703369] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1703367, _1703369))))], (6054 ^ _778495) ^ [_875278, _875280, _875282] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875278, tc_HOL_Obool)), _875280), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_875278, tc_HOL_Obool)), _875282), _875280)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875278, tc_HOL_Obool)), _875280), _875282))], (37508 ^ _778495) ^ [_1489475, _1489477, _1489479, _1489481] : [_1489475 = c_Orderings_Obot__class_Obot(tc_fun(_1489477, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1489479, _1489477), _1489479, c_Product__Type_Ofst(_1489479, _1489477)), hAPP(hAPP(c_Product__Type_OSigma(_1489479, _1489477), _1489481), hAPP(c_COMBK(tc_fun(_1489477, tc_HOL_Obool), _1489479), _1489475))) = c_Orderings_Obot__class_Obot(tc_fun(_1489479, tc_HOL_Obool)))], (51665 ^ _778495) ^ [_1821772, _1821774] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821772), _1821774)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821774, _1821772) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (44285 ^ _778495) ^ [_1664102, _1664104] : [-(_1664102 = c_List_Olist_ONil(_1664104)), -(hAPP(hAPP(c_List_Oappend(_1664104), c_List_Obutlast(_1664104, _1664102)), hAPP(hAPP(c_List_Olist_OCons(_1664104), c_List_Olast(_1664104, _1664102)), c_List_Olist_ONil(_1664104))) = _1664102)], (28511 ^ _778495) ^ [_1294033, _1294035, _1294037, _1294039, _1294041] : [class_Groups_Ocomm__monoid__add(_1294033), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294035), _1294037)), 28518 ^ _778495 : [(28525 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1294035), _1294039), _1294037))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1294035, _1294033), hAPP(hAPP(c_COMBC(_1294035, _1294033, _1294033), hAPP(hAPP(c_COMBS(_1294035, _1294033, tc_fun(_1294033, _1294033)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1294033, tc_fun(_1294033, _1294033)), _1294035), c_If(_1294033)), hAPP(hAPP(c_COMBC(_1294035, _1294035, tc_HOL_Obool), c_fequal), _1294039))), _1294041)), c_Groups_Ozero__class_Ozero(_1294033))), _1294037) = c_Groups_Ozero__class_Ozero(_1294033))], (28519 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1294035), _1294039), _1294037)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1294035, _1294033), hAPP(hAPP(c_COMBC(_1294035, _1294033, _1294033), hAPP(hAPP(c_COMBS(_1294035, _1294033, tc_fun(_1294033, _1294033)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1294033, tc_fun(_1294033, _1294033)), _1294035), c_If(_1294033)), hAPP(hAPP(c_COMBC(_1294035, _1294035, tc_HOL_Obool), c_fequal), _1294039))), _1294041)), c_Groups_Ozero__class_Ozero(_1294033))), _1294037) = hAPP(_1294041, _1294039))]]], (36770 ^ _778495) ^ [_1471414, _1471416, _1471418, _1471420] : [c_Fun_Oinj__on(_1471414, tc_fun(tc_fun(_1471414, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1471414, tc_fun(tc_prod(_1471414, _1471414), tc_HOL_Obool), tc_fun(tc_fun(_1471414, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471414, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1471414, _1471414), tc_HOL_Obool), tc_fun(tc_fun(_1471414, tc_HOL_Obool), tc_HOL_Obool)), _1471414), c_Equiv__Relations_Oquotient(_1471414)), hAPP(hAPP(c_COMBC(_1471414, tc_fun(_1471414, tc_HOL_Obool), tc_fun(_1471414, tc_HOL_Obool)), c_Set_Oinsert(_1471414)), c_Orderings_Obot__class_Obot(tc_fun(_1471414, tc_HOL_Obool))))), _1471416), _1471418), hBOOL(hAPP(hAPP(c_member(_1471414), _1471420), _1471418)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1471414, tc_HOL_Obool)), _1471418), hAPP(hAPP(c_Set_Oinsert(_1471414), _1471420), c_Orderings_Obot__class_Obot(tc_fun(_1471414, tc_HOL_Obool))))), _1471416) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1471414, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471414), _1471418), _1471416)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471414), hAPP(hAPP(c_Set_Oinsert(_1471414), _1471420), c_Orderings_Obot__class_Obot(tc_fun(_1471414, tc_HOL_Obool)))), _1471416)))], (42321 ^ _778495) ^ [_1621395, _1621397, _1621399, _1621401, _1621403, _1621405] : [-(_1621395 = _1621397), -(hAPP(hAPP(c_List_Olist__update(_1621399, hAPP(hAPP(c_List_Olist__update(_1621399, _1621401), _1621395), _1621403)), _1621397), _1621405) = hAPP(hAPP(c_List_Olist__update(_1621399, hAPP(hAPP(c_List_Olist__update(_1621399, _1621401), _1621397), _1621405)), _1621395), _1621403))], (52307 ^ _778495) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (50066 ^ _778495) ^ [_1790925, _1790927, _1790929, _1790931, _1790933] : [c_Fun_Obij__betw(_1790925, _1790927, _1790929, _1790931, _1790933), -(c_Fun_Oinj__on(_1790925, _1790927, _1790929, _1790931))], (20566 ^ _778495) ^ [_1147413] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147413)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147413)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147413))], (21296 ^ _778495) ^ [_1160110, _1160112] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1160110), _1160112)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1160110) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (26710 ^ _778495) ^ [_1256093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1256093), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1256093)), c_Int_OMin)))], (25564 ^ _778495) ^ [_1235300, _1235302] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1235300)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1235302)) = 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)))), _1235300)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1235302)))], (38874 ^ _778495) ^ [_1531237, _1531239, _1531241] : [c_Wellfounded_Owf(_1531237, _1531239), c_Wellfounded_Owf(_1531237, _1531241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531237, _1531237), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531237, _1531237, _1531237), _1531239), _1531241)), _1531239)), -(c_Wellfounded_Owf(_1531237, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531237, _1531237), tc_HOL_Obool)), _1531239), _1531241)))], (46682 ^ _778495) ^ [_1717133, _1717135, _1717137] : [hAPP(c_List_Orev(_1717133), _1717135) = hAPP(c_List_Orev(_1717133), _1717137), -(_1717135 = _1717137)], (40866 ^ _778495) ^ [_1580134, _1580136, _1580138] : [c_Relation_Ototal__on(_1580134, _1580136, _1580138), 40869 ^ _778495 : [(40870 ^ _778495) ^ [_1580278] : [hBOOL(hAPP(hAPP(c_member(_1580134), _1580278), _1580136)), 40873 ^ _778495 : [(40874 ^ _778495) ^ [_1580418] : [hBOOL(hAPP(hAPP(c_member(_1580134), _1580418), _1580136)), -(_1580278 = _1580418), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580134, _1580134)), hAPP(hAPP(c_Product__Type_OPair(_1580134, _1580134), _1580278), _1580418)), _1580138))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580134, _1580134)), hAPP(hAPP(c_Product__Type_OPair(_1580134, _1580134), _1580418), _1580278)), _1580138)))]]]]], (42818 ^ _778495) ^ [_1631642, _1631644] : [-(_1631644 = c_List_Olist_ONil(_1631642)), -(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(_1631642)), _1631644))))], (7726 ^ _778495) ^ [_906230, _906232, _906234, _906236] : [-(c_Nitpick_Ofold__graph_H(_906230, _906232, _906234, _906236, c_Orderings_Obot__class_Obot(tc_fun(_906230, tc_HOL_Obool)), _906236))], (32018 ^ _778495) ^ [_1367345, _1367347, _1367349, _1367351, _1367353] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367345, tc_fun(_1367347, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1367345, tc_HOL_Obool)), _1367349), _1367351)), _1367353) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367347, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367345, tc_fun(_1367347, tc_HOL_Obool)), _1367349), _1367353)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367345, tc_fun(_1367347, tc_HOL_Obool)), _1367351), _1367353)))], (45672 ^ _778495) ^ [_1696079, _1696081, _1696083] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1696079, tc_HOL_Obool)), hAPP(c_List_Oset(_1696079), hAPP(c_List_Ofilter(_1696079, _1696081), _1696083))), hAPP(c_List_Oset(_1696079), _1696083))))], (24539 ^ _778495) ^ [_1217847, _1217849] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1217847), _1217849) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1217847, _1217849)), _1217849))], (10179 ^ _778495) ^ [_954021, _954023, _954025] : [class_Lattices_Olattice(_954021), hBOOL(hAPP(c_Finite__Set_Ofinite(_954021), _954023)), hBOOL(hAPP(hAPP(c_member(_954021), _954025), _954023)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_954021), _954025), c_Big__Operators_Olattice__class_OInf__fin(_954021, _954023)) = _954025)], (1968 ^ _778495) ^ [_806119, _806121, _806123, _806125, _806127, _806129] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_806127, _806123, _806119)), c_Hoare__Mirabelle_Ohoare__derivs(_806129, _806125, _806121), _806129 = _806127, _806125 = _806123, _806121 = _806119], (17932 ^ _778495) ^ [_1099917, _1099919, _1099921, _1099923] : [class_Orderings_Olinorder(_1099917), 17935 ^ _778495 : [(17944 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099917), _1099919), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099917), _1099921), _1099923)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099917), _1099919), _1099921)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099917), _1099919), _1099923))], (17936 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099917), _1099919), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099917), _1099921), _1099923))), 17939 ^ _778495 : [(17942 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099917), _1099919), _1099923)))], (17940 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099917), _1099919), _1099921)))]]]]], (52627 ^ _778495) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (38808 ^ _778495) ^ [_1529661, _1529663, _1529665] : [c_Wellfounded_Owf(_1529661, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529661, _1529661), tc_HOL_Obool)), _1529663), _1529665)), -(c_Wellfounded_Owf(_1529661, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529661, _1529661), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529661, _1529661), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1529661, _1529661, _1529661), _1529663), _1529663)), hAPP(hAPP(c_Relation_Orel__comp(_1529661, _1529661, _1529661), _1529665), _1529663))), _1529665)))], (32624 ^ _778495) ^ [_1379733, _1379735, _1379737, _1379739] : [c_Wellfounded_Omax__extp(_1379733, hAPP(hAPP(c_COMBC(_1379733, tc_fun(tc_prod(_1379733, _1379733), tc_HOL_Obool), tc_fun(_1379733, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1379733, tc_fun(tc_fun(tc_prod(_1379733, _1379733), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1379733, _1379733), tc_HOL_Obool), tc_fun(_1379733, tc_HOL_Obool)), _1379733), c_COMBC(_1379733, tc_fun(tc_prod(_1379733, _1379733), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1379733, tc_prod(_1379733, _1379733)), tc_fun(_1379733, tc_fun(tc_fun(tc_prod(_1379733, _1379733), tc_HOL_Obool), tc_HOL_Obool)), _1379733), hAPP(c_COMBB(tc_prod(_1379733, _1379733), tc_fun(tc_fun(tc_prod(_1379733, _1379733), tc_HOL_Obool), tc_HOL_Obool), _1379733), c_member(tc_prod(_1379733, _1379733)))), c_Product__Type_OPair(_1379733, _1379733)))), _1379735), _1379737, _1379739), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1379733, tc_HOL_Obool), tc_fun(_1379733, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1379733, tc_HOL_Obool), tc_fun(_1379733, tc_HOL_Obool)), _1379737), _1379739)), c_Wellfounded_Omax__ext(_1379733, _1379735))))], (34253 ^ _778495) ^ [_1417233, _1417235, _1417237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1417233, _1417233), tc_HOL_Obool)), _1417235), _1417237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1417233, tc_HOL_Obool)), hAPP(c_Relation_OField(_1417233), _1417235)), hAPP(c_Relation_OField(_1417233), _1417237))))], (11506 ^ _778495) ^ [_977774, _977776, _977778, _977780] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_977774), 11509 ^ _778495 : [(11516 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977774), _977778), _977780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977774), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977774), _977776), _977778)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977774), _977776), _977780))))], (11510 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977774), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977774), _977776), _977778)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977774), _977776), _977780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977774), _977778), _977780)))]]], (22146 ^ _778495) ^ [_1174654, _1174656] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1174654)), _1174656) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1174654), _1174656)))], (46600 ^ _778495) ^ [_1715320, _1715322] : [_1715322 = c_List_Olist_ONil(_1715320), -(c_List_Olist_ONil(_1715320) = hAPP(c_List_Orev(_1715320), _1715322))], (160 ^ _778495) ^ [_781097, _781099, _781101, _781103, _781105, _781107, _781109, _781111, _781113, _781115, _781117, _781119] : [-(c_Finite__Set_Ofolding__image__simple(_781117, _781113, _781109, _781105, _781101, _781097)), c_Finite__Set_Ofolding__image__simple(_781119, _781115, _781111, _781107, _781103, _781099), _781119 = _781117, _781115 = _781113, _781111 = _781109, _781107 = _781105, _781103 = _781101, _781099 = _781097], (43766 ^ _778495) ^ [_1653909, _1653911, _1653913] : [-(_1653909 = c_List_Olist_ONil(_1653911)), -(hAPP(c_List_Ohd(_1653911), hAPP(c_List_Orotate(_1653911, _1653913), _1653909)) = hAPP(hAPP(c_List_Onth(_1653911), _1653909), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1653913, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653911)), _1653909))))], (1198 ^ _778495) ^ [_796498, _796500] : [-(class_Rings_Olinordered__semiring__1(_796498)), _796500 = _796498, class_Rings_Olinordered__semiring__1(_796500)], (52225 ^ _778495) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (49362 ^ _778495) ^ [_1776379, _1776381] : [c_Equiv__Relations_Opart__equivp(_1776379, _1776381), 49366 ^ _778495 : [(49379 ^ _778495) ^ [_1776721, _1776723] : [-(hBOOL(hAPP(hAPP(_1776381, _1776723), _1776721))), hBOOL(hAPP(hAPP(_1776381, _1776723), _1776723)), hBOOL(hAPP(hAPP(_1776381, _1776721), _1776721)), hAPP(_1776381, _1776723) = hAPP(_1776381, _1776721)], (49369 ^ _778495) ^ [_1776552, _1776554] : [hBOOL(hAPP(hAPP(_1776381, _1776554), _1776552)), 49372 ^ _778495 : [(49377 ^ _778495) ^ [] : [-(hAPP(_1776381, _1776554) = hAPP(_1776381, _1776552))], (49375 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1776381, _1776552), _1776552)))], (49373 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1776381, _1776554), _1776554)))]]], (49367 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1776381, 49365 ^ [_1776379, _1776381]), 49365 ^ [_1776379, _1776381])))]]], (42730 ^ _778495) ^ [_1630072, _1630074] : [_1630074 = c_List_Olist_ONil(_1630072), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630072)), _1630074) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23212 ^ _778495) ^ [_1194244, _1194246, _1194248, _1194250] : [class_Divides_Oring__div(_1194244), c_Divides_Odiv__class_Omod(_1194244, _1194246, _1194248) = c_Divides_Odiv__class_Omod(_1194244, _1194250, _1194248), -(c_Divides_Odiv__class_Omod(_1194244, hAPP(c_Groups_Ouminus__class_Ouminus(_1194244), _1194246), _1194248) = c_Divides_Odiv__class_Omod(_1194244, hAPP(c_Groups_Ouminus__class_Ouminus(_1194244), _1194250), _1194248))], (46722 ^ _778495) ^ [_1717925, _1717927, _1717929, _1717931] : [hAPP(c_List_Orev(_1717925), _1717927) = hAPP(hAPP(c_List_Olist_OCons(_1717925), _1717929), _1717931), -(_1717927 = hAPP(hAPP(c_List_Oappend(_1717925), hAPP(c_List_Orev(_1717925), _1717931)), hAPP(hAPP(c_List_Olist_OCons(_1717925), _1717929), c_List_Olist_ONil(_1717925))))], (29115 ^ _778495) ^ [_1307200, _1307202, _1307204, _1307206, _1307208] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1307200, _1307202)), hAPP(hAPP(c_Product__Type_OPair(_1307200, _1307202), _1307206), _1307208)), _1307204)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1307200, _1307202, _1307204), _1307206), _1307208)))], (46586 ^ _778495) ^ [_1715077, _1715079] : [hBOOL(hAPP(c_List_Odistinct(_1715077), _1715079)), -(hBOOL(hAPP(c_List_Odistinct(_1715077), hAPP(c_List_Orev(_1715077), _1715079))))], (43874 ^ _778495) ^ [_1656026, _1656028, _1656030, _1656032] : [43875 ^ _778495 : [(43876 ^ _778495) ^ [_1656123, _1656125] : [_1656026 = hAPP(hAPP(c_List_Olist_OCons(_1656028), _1656125), _1656123)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656028), tc_List_Olist(_1656028))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656028), tc_List_Olist(_1656028)), _1656030), hAPP(hAPP(c_List_Oappend(_1656028), _1656030), _1656026))), c_List_Olexord(_1656028, _1656032))))], (37420 ^ _778495) ^ [_1487271, _1487273, _1487275, _1487277, _1487279] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1487271, _1487273), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487271, tc_HOL_Obool)), _1487275), _1487277)), _1487279) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1487271, _1487273), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1487271, _1487273), _1487275), _1487279)), hAPP(hAPP(c_Product__Type_OSigma(_1487271, _1487273), _1487277), _1487279)))], (44550 ^ _778495) ^ [_1670703, _1670705, _1670707, _1670709] : [-(hBOOL(hAPP(c_List_Odistinct(_1670703), hAPP(hAPP(c_List_Omap(_1670705, _1670703), _1670707), _1670709)))), hBOOL(hAPP(c_List_Odistinct(_1670705), _1670709)), c_Fun_Oinj__on(_1670705, _1670703, _1670707, hAPP(c_List_Oset(_1670705), _1670709))], (43953 ^ _778495) ^ [_1657714, _1657716, _1657718] : [class_Lattices_Olattice(_1657714), -(c_Big__Operators_Olattice__class_OSup__fin(_1657714, hAPP(c_List_Oset(_1657714), hAPP(hAPP(c_List_Olist_OCons(_1657714), _1657716), _1657718))) = hAPP(c_List_Ofoldl(_1657714, _1657714, c_Lattices_Osemilattice__sup__class_Osup(_1657714), _1657716), _1657718))], (52625 ^ _778495) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (45592 ^ _778495) ^ [_1693378, _1693380] : [-(hAPP(c_List_Oset(_1693378), c_List_Oconcat(_1693378, _1693380)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1693378), tc_fun(_1693378, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1693378)), _1693380)), c_List_Oset(_1693378)))], (44361 ^ _778495) ^ [_1666157, _1666159, _1666161, _1666163] : [c_List_Olist_ONil(_1666157) = hAPP(hAPP(c_List_Omap(_1666159, _1666157), _1666161), _1666163), -(_1666163 = c_List_Olist_ONil(_1666159))], (49094 ^ _778495) ^ [_1771631, _1771633] : [c_Relation_Otrans(_1771631, hAPP(c_Set_OCollect(tc_prod(_1771631, _1771631)), hAPP(c_Product__Type_Oprod_Oprod__case(_1771631, _1771631, tc_HOL_Obool), _1771633))), -(c_Predicate_Otransp(_1771631, _1771633))], (38375 ^ _778495) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (19928 ^ _778495) ^ [] : [-(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)))], (11276 ^ _778495) ^ [_973088, _973090, _973092] : [_973090 = _973092, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973088), _973090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973088), _973092))], (2446 ^ _778495) ^ [_814511, _814513, _814515, _814517] : [-(c_FunDef_Orp__inv__image(_814517, _814513) = c_FunDef_Orp__inv__image(_814515, _814511)), _814517 = _814515, _814513 = _814511], (44638 ^ _778495) ^ [_1672749, _1672751, _1672753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672749), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672751)), _1672753))), -(hAPP(c_Random_Opick(_1672751, hAPP(hAPP(c_List_Omap(_1672751, tc_prod(tc_Code__Numeral_Ocode__numeral, _1672751)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1672751), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1672753)), hAPP(c_Code__Numeral_Oof__nat, _1672749)) = hAPP(hAPP(c_List_Onth(_1672751), _1672753), _1672749))], (8986 ^ _778495) ^ [_930012, _930014, _930016, _930018] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930012, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930012, tc_HOL_Obool)), _930014), _930016)), _930018) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930012, tc_HOL_Obool)), _930014), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930012, tc_HOL_Obool)), _930016), _930018)))], (8832 ^ _778495) ^ [_926838, _926840, _926842, _926844] : [hBOOL(hAPP(_926838, _926840)), hBOOL(hAPP(_926842, _926840)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926844, tc_HOL_Obool)), _926838), _926842), _926840)))], (44536 ^ _778495) ^ [_1670451, _1670453, _1670455, _1670457, _1670459, _1670461] : [-(hBOOL(hAPP(hAPP(c_member(_1670451), _1670453), hAPP(c_List_Oset(_1670451), _1670455)))), -(hAPP(hAPP(c_List_Omap(_1670451, _1670457), c_Fun_Ofun__upd(_1670451, _1670457, _1670459, _1670453, _1670461)), _1670455) = hAPP(hAPP(c_List_Omap(_1670451, _1670457), _1670459), _1670455))], (40359 ^ _778495) ^ [_1567914, _1567916] : [-(c_Relation_Orefl__on(_1567914, c_Orderings_Otop__class_Otop(tc_fun(_1567914, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1567914, _1567916)))], (39392 ^ _778495) ^ [_1544757, _1544759, _1544761, _1544763] : [c_Finite__Set_Ofun__left__comm__idem(_1544757, _1544759, _1544761), -(hAPP(c_Fun_Ocomp(_1544759, _1544759, _1544759, hAPP(_1544761, _1544763)), hAPP(_1544761, _1544763)) = hAPP(_1544761, _1544763))], (32386 ^ _778495) ^ [_1374862, _1374864, _1374866, _1374868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1374862), _1374864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1374866), _1374868)), -(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), _1374862), _1374866)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1374864), _1374868))), c_FunDef_Opair__leq)))], (8586 ^ _778495) ^ [_921868, _921870, _921872, _921874, _921876] : [class_Groups_Oab__semigroup__mult(_921868), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_921868, _921868, c_Groups_Otimes__class_Otimes(_921868), _921870, _921872), _921874)), -(hBOOL(hAPP(hAPP(c_member(_921868), _921870), _921872))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_921868, _921868, c_Groups_Otimes__class_Otimes(_921868), _921876, hAPP(hAPP(c_Set_Oinsert(_921868), _921870), _921872)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921868), _921876), _921874))))], (46650 ^ _778495) ^ [_1716390, _1716392, _1716394, _1716396] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716390)), _1716392) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716394)), _1716396), -(hAPP(hAPP(c_List_Ozip(_1716390, _1716394), hAPP(c_List_Orev(_1716390), _1716392)), hAPP(c_List_Orev(_1716394), _1716396)) = hAPP(c_List_Orev(tc_prod(_1716390, _1716394)), hAPP(hAPP(c_List_Ozip(_1716390, _1716394), _1716392), _1716396)))], (12284 ^ _778495) ^ [_993896, _993898, _993900, _993902, _993904] : [class_Groups_Ocomm__monoid__mult(_993896), hBOOL(hAPP(c_Finite__Set_Ofinite(_993898), _993900)), hBOOL(hAPP(c_Finite__Set_Ofinite(_993898), _993902)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993896), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_993896, _993898, c_Groups_Otimes__class_Otimes(_993896)), _993904), c_Groups_Oone__class_Oone(_993896)), _993900)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_993896, _993898, c_Groups_Otimes__class_Otimes(_993896)), _993904), c_Groups_Oone__class_Oone(_993896)), _993902)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993896), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_993896, _993898, c_Groups_Otimes__class_Otimes(_993896)), _993904), c_Groups_Oone__class_Oone(_993896)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993898, tc_HOL_Obool)), _993900), _993902))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_993896, _993898, c_Groups_Otimes__class_Otimes(_993896)), _993904), c_Groups_Oone__class_Oone(_993896)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_993898, tc_HOL_Obool)), _993900), _993902))))], (1298 ^ _778495) ^ [_797748, _797750] : [-(class_Rings_Ocomm__ring(_797748)), _797750 = _797748, class_Rings_Ocomm__ring(_797750)], (41308 ^ _778495) ^ [_1592014, _1592016, _1592018] : [c_Nitpick_Oless__frac(_1592014, _1592016, _1592018), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592014), c_Nitpick_Oplus__frac(_1592014, _1592016, c_Nitpick_Ouminus__frac(_1592014, _1592018)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (2694 ^ _778495) ^ [_818343, _818345] : [_818345 = _818343, -(c_HOL_OAll(_818345) = c_HOL_OAll(_818343))], (45719 ^ _778495) ^ [_1697012, _1697014, _1697016] : [-(c_List_Opartition(_1697012, _1697014, _1697016) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1697012), tc_List_Olist(_1697012)), hAPP(c_List_Ofilter(_1697012, _1697014), _1697016)), hAPP(c_List_Ofilter(_1697012, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1697012, c_fNot), _1697014)), _1697016)))], (35481 ^ _778495) ^ [_1441581, _1441583, _1441585, _1441587, _1441589] : [class_Groups_Ocomm__monoid__add(_1441581), class_Groups_Ocomm__monoid__mult(_1441581), _1441583 = _1441585, c_Nat__Transfer_Onat__set(_1441585), 35499 ^ _778495 : [(35502 ^ _778495) ^ [] : [hAPP(_1441587, 35498 ^ [_1441581, _1441583, _1441585, _1441587, _1441589]) = hAPP(_1441589, 35498 ^ [_1441581, _1441583, _1441585, _1441587, _1441589])], (35500 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35498 ^ [_1441581, _1441583, _1441585, _1441587, _1441589])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1441581), _1441587), _1441583) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1441581), _1441589), _1441585))], (26816 ^ _778495) ^ [_1257949, _1257951] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1257949, tc_HOL_Obool), tc_HOL_Obool)), _1257951), hAPP(c_Set_OPow(_1257949), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1257949, tc_HOL_Obool), _1257951)))))], (5853 ^ _778495) ^ [_871643, _871645, _871647, _871649] : [_871643 = _871645, 5858 ^ _778495 : [(5861 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_871647), _871649), _871645)))], (5859 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_871647), _871649), _871643)))]], 5862 ^ _778495 : [(5865 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_871647), _871649), _871645))], (5863 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_871647), _871649), _871643))]]], (48210 ^ _778495) ^ [_1750766, _1750768, _1750770] : [-(_1750766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1750768, c_List_Oreplicate(_1750768, _1750766, _1750770)) = _1750770)], (32938 ^ _778495) ^ [_1386228, _1386230, _1386232] : [class_Orderings_Oorder(_1386228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386228), _1386230), _1386232)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1386228, _1386232, _1386230) = c_Orderings_Obot__class_Obot(tc_fun(_1386228, tc_HOL_Obool)))], (29304 ^ _778495) ^ [_1311336, _1311338, _1311340] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1311336, _1311338), _1311340)), -(c_Divides_Odivmod__nat(_1311336, _1311338) = _1311340)], (27951 ^ _778495) ^ [_1277124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277124)), -(c_Nat__Transfer_Ois__nat(_1277124))], (6250 ^ _778495) ^ [_879621, _879623, _879625, _879627] : [_879621 = _879623, 6253 ^ _778495 : [(6260 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_879625), _879627), _879623)), -(hBOOL(hAPP(hAPP(c_member(_879625), _879627), _879621)))], (6254 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_879625), _879627), _879621)), -(hBOOL(hAPP(hAPP(c_member(_879625), _879627), _879623)))]]], (22102 ^ _778495) ^ [_1173862] : [c_Int_OPls = _1173862, -(c_Int_OPls = c_Int_OBit0(_1173862))], (49739 ^ _778495) ^ [_1783745, _1783747, _1783749, _1783751] : [c_Fun_Oinj__on(_1783745, _1783747, _1783749, c_Orderings_Otop__class_Otop(tc_fun(_1783745, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1783745, _1783747, c_Orderings_Otop__class_Otop(tc_fun(_1783745, tc_HOL_Obool)), _1783749), hAPP(_1783749, _1783751)) = _1783751)], (44584 ^ _778495) ^ [_1671494, _1671496, _1671498] : [c_Fun_Oinj__on(tc_List_Olist(_1671494), tc_List_Olist(_1671496), hAPP(c_List_Omap(_1671494, _1671496), _1671498), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671494), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1671494, _1671496, _1671498, c_Orderings_Otop__class_Otop(tc_fun(_1671494, tc_HOL_Obool))))], (6724 ^ _778495) ^ [_888521, _888523] : [hBOOL(hAPP(hAPP(c_member(_888521), _888523), c_Orderings_Obot__class_Obot(tc_fun(_888521, tc_HOL_Obool))))], (40690 ^ _778495) ^ [_1575879] : [-(hAPP(c_Relation_Oconverse(_1575879, _1575879), c_Relation_OId(_1575879)) = c_Relation_OId(_1575879))], (10869 ^ _778495) ^ [_965644, _965646, _965648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965646), _965648)), -(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, _965644)), _965646)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965644)), _965648))))], (732 ^ _778495) ^ [_789585, _789587, _789589, _789591, _789593, _789595] : [-(c_List_Oall__interval__int(_789593, _789589, _789585)), c_List_Oall__interval__int(_789595, _789591, _789587), _789595 = _789593, _789591 = _789589, _789587 = _789585], (22228 ^ _778495) ^ [_1176069, _1176071] : [class_Rings_Olinordered__idom(_1176069), 22231 ^ _778495 : [(22238 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176069), _1176071), c_Groups_Ozero__class_Ozero(_1176069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176069), _1176071), hAPP(c_Groups_Ouminus__class_Ouminus(_1176069), _1176071))))], (22232 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176069), _1176071), hAPP(c_Groups_Ouminus__class_Ouminus(_1176069), _1176071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176069), _1176071), c_Groups_Ozero__class_Ozero(_1176069))))]]], (2764 ^ _778495) ^ [_819472, _819474, _819476, _819478] : [-(c_Wellfounded_Omax__ext(_819478, _819474) = c_Wellfounded_Omax__ext(_819476, _819472)), _819478 = _819476, _819474 = _819472], (29944 ^ _778495) ^ [_1323324, _1323326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1323324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1323326), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323324, _1323326) = 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), _1323324), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1323326)))))], (34048 ^ _778495) ^ [_1412707, _1412709, _1412711] : [class_Orderings_Oorder(_1412707), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412707, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1412707), _1412709)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1412707, _1412709), _1412711)) = c_Orderings_Obot__class_Obot(tc_fun(_1412707, tc_HOL_Obool)))], (34178 ^ _778495) ^ [_1415402, _1415404] : [class_Orderings_Olinorder(_1415402), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415402, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1415402), _1415404)), hAPP(hAPP(c_Set_Oinsert(_1415402), _1415404), c_Orderings_Obot__class_Obot(tc_fun(_1415402, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1415402), _1415404))], (45901 ^ _778495) ^ [_1702205, _1702207] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702205), _1702207))), -(c_List_Oupt(_1702205, hAPP(c_Nat_OSuc, _1702207)) = c_List_Olist_ONil(tc_Nat_Onat))], (47675 ^ _778495) ^ [_1739004, _1739006, _1739008] : [-(c_List_Olist__ex(_1739004, _1739006, _1739008)), 47676 ^ _778495 : [(47677 ^ _778495) ^ [_1739069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1739069), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739004)), _1739008))), hBOOL(hAPP(_1739006, hAPP(hAPP(c_List_Onth(_1739004), _1739008), _1739069)))]]], (9394 ^ _778495) ^ [_938403, _938405, _938407, _938409] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938403, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938403, tc_HOL_Obool)), _938405), _938407)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938403, tc_HOL_Obool)), _938409), _938407)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938403, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938403, tc_HOL_Obool)), _938405), _938407)), _938409))], (47998 ^ _778495) ^ [_1745407, _1745409, _1745411] : [c_List_Olist__ex1(_1745407, _1745409, _1745411), 48002 ^ _778495 : [(48007 ^ _778495) ^ [_1745653] : [-(_1745653 = 48001 ^ [_1745407, _1745409, _1745411]), hBOOL(hAPP(hAPP(c_member(_1745407), _1745653), hAPP(c_List_Oset(_1745407), _1745411))), hBOOL(hAPP(_1745409, _1745653))], (48005 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1745409, 48001 ^ [_1745407, _1745409, _1745411])))], (48003 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745407), 48001 ^ [_1745407, _1745409, _1745411]), hAPP(c_List_Oset(_1745407), _1745411))))]]], (21440 ^ _778495) ^ [_1162842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1162842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1162842))))], (2252 ^ _778495) ^ [_811466, _811468, _811470, _811472] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_811472, _811468) = c_Code__Numeral_Odiv__mod__code__numeral(_811470, _811466)), _811472 = _811470, _811468 = _811466], (25626 ^ _778495) ^ [_1236366] : [class_Rings_Osemiring__1(_1236366), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1236366), c_Groups_Ozero__class_Ozero(_1236366)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1236366))], (29278 ^ _778495) ^ [_1310854, _1310856, _1310858, _1310860, _1310862] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1310854, _1310856), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1310858), _1310860))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1310856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1310862)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1310854, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1310856), _1310862)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1310858), _1310862)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1310856), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1310858, _1310862))), _1310860)))))], (34909 ^ _778495) ^ [_1431638, _1431640, _1431642, _1431644, _1431646] : [hAPP(_1431638, _1431640) = _1431642, -(c_Fun_Ofun__upd(_1431644, _1431646, _1431638, _1431640, _1431642) = _1431638)], (52713 ^ _778495) ^ [_1836402, _1836404] : [hBOOL(_1836402), -(hBOOL(hAPP(hAPP(c_fdisj, _1836404), _1836402)))], (40635 ^ _778495) ^ [_1574565, _1574567] : [-(c_Relation_Oirrefl(_1574565, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1574565, _1574565), tc_HOL_Obool)), _1574567), c_Relation_OId(_1574565))))], (25598 ^ _778495) ^ [_1235881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235881)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1235881)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1235881)))], (37450 ^ _778495) ^ [_1488090, _1488092, _1488094, _1488096, _1488098, _1488100] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1488090, _1488092)), hAPP(hAPP(c_Product__Type_OPair(_1488090, _1488092), _1488094), _1488096)), hAPP(hAPP(c_Product__Type_OSigma(_1488090, _1488092), _1488098), _1488100))), -(hBOOL(hAPP(hAPP(c_member(_1488092), _1488096), hAPP(_1488100, _1488094))))], (26876 ^ _778495) ^ [_1258917] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1258917)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1258917)))], (48967 ^ _778495) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (52617 ^ _778495) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (22908 ^ _778495) ^ [] : [-(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))))], (29328 ^ _778495) ^ [_1311779, _1311781, _1311783, _1311785, _1311787, _1311789, _1311791] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1311779, _1311781), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1311783), _1311785))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1311787, _1311781), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1311789), _1311791))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1311781)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1311779), _1311787), _1311781), 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), _1311783), _1311789)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1311785), _1311791)), _1311781))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1311785), _1311791), _1311781)))))], (52107 ^ _778495) ^ [_1829922, _1829924] : [class_Lattices_Olattice(_1829922), -(class_Lattices_Osemilattice__inf(tc_fun(_1829924, _1829922)))], (11374 ^ _778495) ^ [_974901, _974903, _974905, _974907] : [class_Rings_Ocomm__semiring__1(_974901), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974901), _974903), _974905)), _974907) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974901), _974903), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974901), _974905), _974907)))], (12537 ^ _778495) ^ [_999833, _999835, _999837] : [class_Complete__Lattice_Ocomplete__lattice(_999833), -(c_Complete__Lattice_OSup__class_OSup(_999833, hAPP(hAPP(c_Set_Oinsert(_999833), _999835), _999837)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_999833), _999835), c_Complete__Lattice_OSup__class_OSup(_999833, _999837)))], (45103 ^ _778495) ^ [_1683219, _1683221, _1683223, _1683225, _1683227, _1683229, _1683231] : [c_List_Olist__all2(_1683219, _1683221, _1683223, _1683225, _1683227), c_List_Olist__all2(_1683219, _1683221, _1683223, _1683229, _1683231), -(c_List_Olist__all2(_1683219, _1683221, _1683223, hAPP(hAPP(c_List_Oappend(_1683219), _1683225), _1683229), hAPP(hAPP(c_List_Oappend(_1683221), _1683227), _1683231)))], (52325 ^ _778495) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (7900 ^ _778495) ^ [_908768, _908770, _908772] : [class_Orderings_Oorder(_908768), -(_908770 = _908772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908768), _908770), _908772)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908768), _908770), _908772)))], (31760 ^ _778495) ^ [_1359623, _1359625] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1359623, _1359625))))], (19414 ^ _778495) ^ [_1127189, _1127191, _1127193] : [class_Orderings_Olinorder(_1127189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1127189, tc_HOL_Obool)), _1127191), _1127193)), -(_1127191 = c_Orderings_Obot__class_Obot(tc_fun(_1127189, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127189), _1127193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127189), c_Big__Operators_Olinorder__class_OMin(_1127189, _1127193)), c_Big__Operators_Olinorder__class_OMin(_1127189, _1127191))))], (28491 ^ _778495) ^ [_1293523, _1293525, _1293527, _1293529, _1293531] : [class_Groups_Ocomm__monoid__add(_1293523), hBOOL(hAPP(c_Finite__Set_Ofinite(_1293525), _1293527)), 28498 ^ _778495 : [(28505 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1293525), _1293529), _1293527))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293525, _1293523), hAPP(hAPP(c_COMBC(_1293525, _1293523, _1293523), hAPP(hAPP(c_COMBS(_1293525, _1293523, tc_fun(_1293523, _1293523)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1293523, tc_fun(_1293523, _1293523)), _1293525), c_If(_1293523)), hAPP(c_fequal, _1293529))), _1293531)), c_Groups_Ozero__class_Ozero(_1293523))), _1293527) = c_Groups_Ozero__class_Ozero(_1293523))], (28499 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1293525), _1293529), _1293527)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293525, _1293523), hAPP(hAPP(c_COMBC(_1293525, _1293523, _1293523), hAPP(hAPP(c_COMBS(_1293525, _1293523, tc_fun(_1293523, _1293523)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1293523, tc_fun(_1293523, _1293523)), _1293525), c_If(_1293523)), hAPP(c_fequal, _1293529))), _1293531)), c_Groups_Ozero__class_Ozero(_1293523))), _1293527) = hAPP(_1293531, _1293529))]]], (34671 ^ _778495) ^ [_1426797, _1426799] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1426797), _1426799)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1426797)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1426799))))], (21422 ^ _778495) ^ [_1162573] : [class_Int_Onumber__ring(_1162573), -(c_Groups_Oone__class_Oone(_1162573) = hAPP(c_Int_Onumber__class_Onumber__of(_1162573), c_Int_OBit1(c_Int_OPls)))], (28989 ^ _778495) ^ [_1304669, _1304671, _1304673, _1304675] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1304669, tc_fun(_1304671, tc_HOL_Obool))), _1304673), _1304675))], (30437 ^ _778495) ^ [_1333484, _1333486, _1333488, _1333490, _1333492, _1333494] : [-(hBOOL(hAPP(hAPP(c_member(_1333484), _1333486), c_SetInterval_Oord_OatLeastLessThan(_1333484, _1333488, _1333490, _1333492, _1333494)))), hBOOL(hAPP(hAPP(_1333488, _1333492), _1333486)), hBOOL(hAPP(hAPP(_1333490, _1333486), _1333494))], (32622 ^ _778495) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (5691 ^ _778495) ^ [_868458, _868460, _868462, _868464, _868466] : [hAPP(hAPP(c_Set_Oinsert(_868458), _868460), hAPP(hAPP(c_Set_Oinsert(_868458), _868462), c_Orderings_Obot__class_Obot(tc_fun(_868458, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_868458), _868464), hAPP(hAPP(c_Set_Oinsert(_868458), _868466), c_Orderings_Obot__class_Obot(tc_fun(_868458, tc_HOL_Obool)))), 5696 ^ _778495 : [(5699 ^ _778495) ^ [] : [-(_868462 = _868466)], (5697 ^ _778495) ^ [] : [-(_868460 = _868464)]], 5700 ^ _778495 : [(5703 ^ _778495) ^ [] : [-(_868462 = _868464)], (5701 ^ _778495) ^ [] : [-(_868460 = _868466)]]], (28855 ^ _778495) ^ [_1302280, _1302282, _1302284] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1302280, _1302282, _1302284, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1302282)], (20 ^ _778495) ^ [_778755, _778757, _778759, _778761, _778763, _778765] : [-(c_Hoare__Mirabelle_Ohoare__valids(_778763, _778759, _778755)), c_Hoare__Mirabelle_Ohoare__valids(_778765, _778761, _778757), _778765 = _778763, _778761 = _778759, _778757 = _778755], (44907 ^ _778495) ^ [_1678063, _1678065, _1678067, _1678069, _1678071] : [c_List_Opartition(_1678063, _1678065, _1678067) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678063), tc_List_Olist(_1678063)), _1678069), _1678071), 44910 ^ _778495 : [(44917 ^ _778495) ^ [_1678325] : [hBOOL(hAPP(hAPP(c_member(_1678063), _1678325), hAPP(c_List_Oset(_1678063), _1678071))), hBOOL(hAPP(_1678065, _1678325))], (44911 ^ _778495) ^ [_1678216] : [hBOOL(hAPP(hAPP(c_member(_1678063), _1678216), hAPP(c_List_Oset(_1678063), _1678069))), -(hBOOL(hAPP(_1678065, _1678216)))]]], (39933 ^ _778495) ^ [_1556887, _1556889, _1556891] : [39934 ^ _778495 : [(39935 ^ _778495) ^ [_1556941] : [hBOOL(hAPP(_1556887, _1556941))]], _1556889 = c_Hilbert__Choice_OEps(_1556891, _1556887), -(hBOOL(hAPP(_1556887, _1556889)))], (52331 ^ _778495) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (46806 ^ _778495) ^ [_1719656, _1719658] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719656), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719656))), _1719658))), 46809 ^ _778495 : [(46816 ^ _778495) ^ [] : [-(_1719658 = c_List_Olist_ONil(tc_List_Olist(_1719656))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719656))), c_List_Otranspose(_1719656, _1719658)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719656)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719656)), _1719658), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46810 ^ _778495) ^ [] : [_1719658 = c_List_Olist_ONil(tc_List_Olist(_1719656)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719656))), c_List_Otranspose(_1719656, _1719658)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7278 ^ _778495) ^ [_898845, _898847, _898849, _898851] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898845, tc_HOL_Obool)), _898847), hAPP(hAPP(c_Set_Oinsert(_898845), _898849), _898851)))), 7281 ^ _778495 : [(7284 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898845, tc_HOL_Obool)), _898847), _898851))], (7282 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898845), _898849), _898851)))]], 7285 ^ _778495 : [(7288 ^ _778495) ^ [] : [7289 ^ _778495 : [(7292 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898845, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898845, tc_HOL_Obool)), _898847), hAPP(hAPP(c_Set_Oinsert(_898845), _898849), c_Orderings_Obot__class_Obot(tc_fun(_898845, tc_HOL_Obool))))), _898851))], (7290 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898845), _898849), _898847)))]], 7293 ^ _778495 : [(7296 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898845, tc_HOL_Obool)), _898847), _898851))], (7294 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898845), _898849), _898847))]]], (7286 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898845), _898849), _898851))]]], (3408 ^ _778495) ^ [_829428, _829430, _829432, _829434, _829436, _829438, _829440, _829442] : [-(c_List_Olist_Olist__case(_829442, _829438, _829434, _829430) = c_List_Olist_Olist__case(_829440, _829436, _829432, _829428)), _829442 = _829440, _829438 = _829436, _829434 = _829432, _829430 = _829428], (44077 ^ _778495) ^ [_1660618, _1660620, _1660622, _1660624, _1660626, _1660628] : [class_Orderings_Olinorder(_1660618), -(hAPP(_1660620, _1660622) = hAPP(_1660620, _1660624)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660626, _1660618, _1660620), _1660624), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660626, _1660618, _1660620), _1660622), _1660628)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660626, _1660618, _1660620), _1660622), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660626, _1660618, _1660620), _1660624), _1660628)))], (11398 ^ _778495) ^ [_975523, _975525, _975527, _975529, _975531] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_975523), 11401 ^ _778495 : [(11402 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975523), _975525), _975529)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975523), _975527), _975531)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975523), _975525), _975531)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975523), _975527), _975529)), -(_975525 = _975527), -(_975529 = _975531)], (11412 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975523), _975525), _975529)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975523), _975527), _975531)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975523), _975525), _975531)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975523), _975527), _975529))), 11415 ^ _778495 : [(11418 ^ _778495) ^ [] : [_975529 = _975531], (11416 ^ _778495) ^ [] : [_975525 = _975527]]]]], (25560 ^ _778495) ^ [_1235202, _1235204] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235202), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1235204)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235202), 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)))), _1235204)))], (24876 ^ _778495) ^ [_1223539, _1223541] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223539)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223539)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223541)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223539)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223541))))], (22994 ^ _778495) ^ [_1189536, _1189538] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189536, _1189538)), _1189538) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8966 ^ _778495) ^ [_929572, _929574, _929576, _929578] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929572, tc_HOL_Obool)), _929574), _929576), _929578)), -(hBOOL(hAPP(_929574, _929578)))], (44373 ^ _778495) ^ [_1666369, _1666371, _1666373] : [-(hAPP(hAPP(c_List_Omap(_1666369, _1666371), _1666373), c_List_Olist_ONil(_1666369)) = c_List_Olist_ONil(_1666371))], (28953 ^ _778495) ^ [_1303934, _1303936, _1303938, _1303940, _1303942, _1303944] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1303934, tc_fun(_1303936, tc_HOL_Obool))), _1303938), _1303940), _1303942), _1303944)), -(hBOOL(hAPP(hAPP(_1303938, _1303942), _1303944))), -(hBOOL(hAPP(hAPP(_1303940, _1303942), _1303944)))], (36851 ^ _778495) ^ [_1473313, _1473315, _1473317, _1473319] : [c_Fun_Oinj__on(_1473313, _1473315, _1473317, _1473319), -(c_Fun_Oinj__on(_1473315, _1473313, c_Fun_Othe__inv__into(_1473313, _1473315, _1473319, _1473317), hAPP(c_Set_Oimage(_1473313, _1473315, _1473317), _1473319)))], (49322 ^ _778495) ^ [_1775745, _1775747] : [-(c_Relation_Osym(_1775745, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1775745, _1775745), tc_HOL_Obool)), _1775747), hAPP(c_Relation_Oconverse(_1775745, _1775745), _1775747))))], (42087 ^ _778495) ^ [_1614331, _1614333] : [-(c_List_Olists(_1614331, _1614333) = hAPP(c_Set_OCollect(tc_List_Olist(_1614331)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614331), tc_fun(_1614331, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614331, tc_HOL_Obool), tc_fun(tc_fun(_1614331, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614331)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614331, tc_HOL_Obool))), c_List_Oset(_1614331))), _1614333)))], (31644 ^ _778495) ^ [_1356934, _1356936, _1356938, _1356940, _1356942] : [-(hAPP(c_Product__Type_Osnd(_1356934, _1356936), hAPP(c_Product__Type_Oapfst(_1356938, _1356934, _1356936, _1356940), _1356942)) = hAPP(c_Product__Type_Osnd(_1356938, _1356936), _1356942))], (42004 ^ _778495) ^ [_1612443, _1612445, _1612447] : [42006 ^ _778495 : [(42009 ^ _778495) ^ [] : [hBOOL(hAPP(_1612447, hAPP(hAPP(c_List_Onth(_1612443), _1612445), 42005 ^ [_1612443, _1612445, _1612447])))], (42007 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42005 ^ [_1612443, _1612445, _1612447]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612443)), _1612445))))]], 42010 ^ _778495 : [(42011 ^ _778495) ^ [_1612645] : [hBOOL(hAPP(hAPP(c_member(_1612443), _1612645), hAPP(c_List_Oset(_1612443), _1612445))), -(hBOOL(hAPP(_1612447, _1612645)))]]], (51177 ^ _778495) ^ [_1813522, _1813524, _1813526] : [_1813522 = _1813524, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813524), _1813526)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813522), _1813526)))], (46720 ^ _778495) ^ [_1717841, _1717843, _1717845] : [-(hAPP(c_List_Orev(_1717841), hAPP(hAPP(c_List_Olist_OCons(_1717841), _1717843), _1717845)) = hAPP(hAPP(c_List_Oappend(_1717841), hAPP(c_List_Orev(_1717841), _1717845)), hAPP(hAPP(c_List_Olist_OCons(_1717841), _1717843), c_List_Olist_ONil(_1717841))))], (24607 ^ _778495) ^ [_1219090, _1219092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219090)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1219090), _1219092)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1219090)), hAPP(c_Int_Onat, _1219092)))], (38029 ^ _778495) ^ [_1503635, _1503637, _1503639, _1503641] : [-(hAPP(c_Relation_OImage(_1503635, _1503637, _1503639), hAPP(hAPP(c_Set_Oinsert(_1503635), _1503641), c_Orderings_Obot__class_Obot(tc_fun(_1503635, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1503637), hAPP(hAPP(c_COMBC(_1503637, tc_fun(tc_prod(_1503635, _1503637), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1503635, _1503637), tc_fun(tc_fun(tc_prod(_1503635, _1503637), tc_HOL_Obool), tc_HOL_Obool), _1503637), c_member(tc_prod(_1503635, _1503637))), hAPP(c_Product__Type_OPair(_1503635, _1503637), _1503641))), _1503639)))], (28321 ^ _778495) ^ [_1285493, _1285495, _1285497, _1285499] : [_1285497 = _1285499, -(hAPP(hAPP(c_COMBC(_1285493, tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_fun(_1285495, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285495, tc_fun(tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_fun(_1285495, tc_HOL_Obool)), _1285493), c_COMBC(_1285495, tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285495, tc_prod(_1285493, _1285495)), tc_fun(_1285495, tc_fun(tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_HOL_Obool)), _1285493), hAPP(c_COMBB(tc_prod(_1285493, _1285495), tc_fun(tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_HOL_Obool), _1285495), c_member(tc_prod(_1285493, _1285495)))), c_Product__Type_OPair(_1285493, _1285495)))), _1285497) = hAPP(hAPP(c_COMBC(_1285493, tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_fun(_1285495, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285495, tc_fun(tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_fun(_1285495, tc_HOL_Obool)), _1285493), c_COMBC(_1285495, tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285495, tc_prod(_1285493, _1285495)), tc_fun(_1285495, tc_fun(tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_HOL_Obool)), _1285493), hAPP(c_COMBB(tc_prod(_1285493, _1285495), tc_fun(tc_fun(tc_prod(_1285493, _1285495), tc_HOL_Obool), tc_HOL_Obool), _1285495), c_member(tc_prod(_1285493, _1285495)))), c_Product__Type_OPair(_1285493, _1285495)))), _1285499))], (40924 ^ _778495) ^ [_1581844, _1581846] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581844, _1581844), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1581846) = _1581846)], (42890 ^ _778495) ^ [_1633111, _1633113] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1633111), tc_List_Olist(_1633111), c_List_Olistrel(_1633111, _1633113)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633111)), c_List_Olist_ONil(_1633111)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633111), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633111)), c_List_Olist_ONil(_1633111)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633111), tc_HOL_Obool))))], (1328 ^ _778495) ^ [_798123, _798125] : [-(class_Groups_Osgn__if(_798123)), _798125 = _798123, class_Groups_Osgn__if(_798125)], (33567 ^ _778495) ^ [_1402817, _1402819, _1402821] : [class_Orderings_Olinorder(_1402817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402817), _1402819), _1402821)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402817, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1402817), _1402819)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1402817, _1402819, _1402821)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1402817), _1402821))], (19186 ^ _778495) ^ [_1123343] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123343), _1123343)))], (43536 ^ _778495) ^ [_1648678, _1648680, _1648682] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648678)), hAPP(hAPP(c_List_Odrop(_1648678), _1648680), _1648682)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648678)), _1648682)), _1648680))], (38278 ^ _778495) ^ [_1513879, _1513881, _1513883] : [class_Orderings_Olinorder(_1513879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513879), _1513881)), -(_1513881 = c_Orderings_Obot__class_Obot(tc_fun(_1513879, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1513879), _1513883), c_Big__Operators_Olattice_OInf__fin(_1513879, c_Orderings_Oord__class_Omin(_1513879), _1513881)) = c_Big__Operators_Olattice_OInf__fin(_1513879, c_Orderings_Oord__class_Omin(_1513879), hAPP(c_Set_OCollect(_1513879), hAPP(hAPP(c_COMBB(tc_fun(_1513879, tc_HOL_Obool), tc_HOL_Obool, _1513879), c_HOL_OEx(_1513879)), hAPP(hAPP(c_COMBC(_1513879, tc_fun(_1513879, tc_HOL_Obool), tc_fun(_1513879, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513879, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1513879, tc_HOL_Obool), tc_fun(_1513879, tc_HOL_Obool)), _1513879), c_COMBS(_1513879, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513879, tc_HOL_Obool), tc_fun(_1513879, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1513879), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513879), c_fconj)), hAPP(hAPP(c_COMBC(_1513879, tc_fun(_1513879, _1513879), tc_fun(_1513879, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513879, tc_HOL_Obool), tc_fun(tc_fun(_1513879, _1513879), tc_fun(_1513879, tc_HOL_Obool)), _1513879), c_COMBB(_1513879, tc_HOL_Obool, _1513879)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1513879), _1513883))))), hAPP(hAPP(c_COMBC(_1513879, tc_fun(_1513879, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513879)), _1513881))))))], (51363 ^ _778495) ^ [_1816522, _1816524, _1816526] : [class_Rings_Olinordered__idom(_1816522), hAPP(c_Groups_Oabs__class_Oabs(_1816522), _1816524) = hAPP(c_Groups_Oabs__class_Oabs(_1816522), _1816526), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816522), _1816524), _1816526)))], (37352 ^ _778495) ^ [_1485063, _1485065, _1485067] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1485063, _1485065), c_Orderings_Obot__class_Obot(tc_fun(_1485063, tc_HOL_Obool))), _1485067) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool)))], (22716 ^ _778495) ^ [_1184574, _1184576] : [class_Groups_Oordered__ab__group__add__abs(_1184574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184574), _1184576), c_Groups_Ozero__class_Ozero(_1184574))), -(hAPP(c_Groups_Oabs__class_Oabs(_1184574), _1184576) = hAPP(c_Groups_Ouminus__class_Ouminus(_1184574), _1184576))], (4968 ^ _778495) ^ [_854306, _854308, _854310, _854312, _854314, _854316] : [-(c_Set_Ovimage(_854316, _854312, _854308) = c_Set_Ovimage(_854314, _854310, _854306)), _854316 = _854314, _854312 = _854310, _854308 = _854306], (37835 ^ _778495) ^ [_1498434, _1498436, _1498438] : [hBOOL(hAPP(_1498438, _1498436)), -(hBOOL(hAPP(hAPP(c_member(_1498434), _1498436), hAPP(c_Set_OCollect(_1498434), _1498438))))], (3680 ^ _778495) ^ [_833700, _833702, _833704, _833706, _833708, _833710, _833712, _833714] : [-(c_List_Omaps(_833714, _833710, _833706, _833702) = c_List_Omaps(_833712, _833708, _833704, _833700)), _833714 = _833712, _833710 = _833708, _833706 = _833704, _833702 = _833700], (51687 ^ _778495) ^ [_1822144, _1822146] : [51688 ^ _778495 : [(51691 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822146), _1822144))], (51689 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822144), _1822146)))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822144, _1822146) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (48017 ^ _778495) ^ [_1745840, _1745842, _1745844] : [-(c_List_Olist__ex1(_1745840, _1745842, _1745844)), 48018 ^ _778495 : [(48019 ^ _778495) ^ [_1745934] : [hBOOL(hAPP(hAPP(c_member(_1745840), _1745934), hAPP(c_List_Oset(_1745840), _1745844))), hBOOL(hAPP(_1745842, _1745934)), 48027 ^ _778495 : [(48032 ^ _778495) ^ [] : [48026 ^ [_1745840, _1745842, _1745844, _1745934] = _1745934], (48030 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1745842, 48026 ^ [_1745840, _1745842, _1745844, _1745934])))], (48028 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745840), 48026 ^ [_1745840, _1745842, _1745844, _1745934]), hAPP(c_List_Oset(_1745840), _1745844))))]]]]], (34438 ^ _778495) ^ [_1421728, _1421730, _1421732, _1421734, _1421736] : [hBOOL(hAPP(hAPP(c_member(_1421728), _1421730), _1421732)), -(hAPP(hAPP(c_Set_Oinsert(_1421734), hAPP(_1421736, _1421730)), hAPP(c_Set_Oimage(_1421728, _1421734, _1421736), _1421732)) = hAPP(c_Set_Oimage(_1421728, _1421734, _1421736), _1421732))], (6356 ^ _778495) ^ [_881374, _881376, _881378, _881380] : [hBOOL(hAPP(hAPP(c_member(_881374), _881376), _881378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881374, tc_HOL_Obool)), _881378), _881380)), -(hBOOL(hAPP(hAPP(c_member(_881374), _881376), _881380)))], (37330 ^ _778495) ^ [_1484402, _1484404, _1484406, _1484408, _1484410, _1484412] : [hBOOL(hAPP(hAPP(c_member(_1484402), _1484404), _1484406)), 37333 ^ _778495 : [(37340 ^ _778495) ^ [] : [_1484410 = _1484412, -(hAPP(hAPP(c_Product__Type_OSigma(_1484408, _1484402), _1484410), hAPP(c_COMBK(tc_fun(_1484402, tc_HOL_Obool), _1484408), _1484406)) = hAPP(hAPP(c_Product__Type_OSigma(_1484408, _1484402), _1484412), hAPP(c_COMBK(tc_fun(_1484402, tc_HOL_Obool), _1484408), _1484406)))], (37334 ^ _778495) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1484408, _1484402), _1484410), hAPP(c_COMBK(tc_fun(_1484402, tc_HOL_Obool), _1484408), _1484406)) = hAPP(hAPP(c_Product__Type_OSigma(_1484408, _1484402), _1484412), hAPP(c_COMBK(tc_fun(_1484402, tc_HOL_Obool), _1484408), _1484406)), -(_1484410 = _1484412)]]], (42768 ^ _778495) ^ [_1630758, _1630760, _1630762, _1630764] : [_1630760 = c_List_Olist_ONil(_1630758), -(hAPP(hAPP(c_List_Olist__update(_1630758, _1630760), _1630762), _1630764) = c_List_Olist_ONil(_1630758))], (10857 ^ _778495) ^ [_965389, _965391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965391), hAPP(c_Nat_OSuc, _965389))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965389), _965391))], (17794 ^ _778495) ^ [_1097547, _1097549, _1097551, _1097553] : [class_Orderings_Olinorder(_1097547), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097547), _1097549), _1097551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097547), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1097547), _1097549), _1097553)), _1097551)))], (19272 ^ _778495) ^ [_1124841, _1124843] : [class_Orderings_Olinorder(_1124841), -(c_Big__Operators_Olinorder__class_OMin(_1124841, hAPP(hAPP(c_Set_Oinsert(_1124841), _1124843), c_Orderings_Obot__class_Obot(tc_fun(_1124841, tc_HOL_Obool)))) = _1124843)], (46905 ^ _778495) ^ [_1721754, _1721756, _1721758] : [-(c_List_OtakeWhile(_1721754, _1721756, _1721758) = hAPP(hAPP(c_List_Otake(_1721754), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721754)), c_List_OtakeWhile(_1721754, _1721756, _1721758))), _1721758))], (29705 ^ _778495) ^ [_1318909, _1318911, _1318913] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1318909, _1318909), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1318911), _1318913))), -(_1318909 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1318911 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (40964 ^ _778495) ^ [_1582618, _1582620, _1582622, _1582624] : [-(hAPP(hAPP(c_Nat_Ocompow(_1582618, _1582618), _1582620), hAPP(hAPP(c_Nat_Ocompow(_1582618, _1582618), _1582622), _1582624)) = hAPP(hAPP(c_Nat_Ocompow(_1582618, _1582618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1582622), _1582620)), _1582624))], (13352 ^ _778495) ^ [_1015874] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015874), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1015874)], (41201 ^ _778495) ^ [_1589179, _1589181, _1589183, _1589185, _1589187] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589179, _1589179)), hAPP(hAPP(c_Product__Type_OPair(_1589179, _1589179), _1589181), _1589183)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589179, _1589179), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1589185)), _1589187))), 41205 ^ _778495 : [(41208 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589179, _1589179)), hAPP(hAPP(c_Product__Type_OPair(_1589179, _1589179), 41204 ^ [_1589179, _1589181, _1589183, _1589185, _1589187]), _1589183)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589179, _1589179), tc_HOL_Obool), _1589185), _1589187))))], (41206 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589179, _1589179)), hAPP(hAPP(c_Product__Type_OPair(_1589179, _1589179), _1589181), 41204 ^ [_1589179, _1589181, _1589183, _1589185, _1589187])), _1589187)))]]], (15371 ^ _778495) ^ [_1051477, _1051479, _1051481] : [-(hBOOL(hAPP(_1051477, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051479), _1051481)))), 15374 ^ _778495 : [(15377 ^ _778495) ^ [] : [hBOOL(hAPP(_1051477, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15375 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051479), _1051481)))]], 15379 ^ _778495 : [(15382 ^ _778495) ^ [] : [hBOOL(hAPP(_1051477, 15378 ^ [_1051477, _1051479, _1051481]))], (15380 ^ _778495) ^ [] : [-(_1051479 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051481), 15378 ^ [_1051477, _1051479, _1051481]))]]], (8900 ^ _778495) ^ [_928093, _928095, _928097] : [class_Lattices_Osemilattice__inf(_928093), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928093), _928095), _928097) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928093), _928097), _928095))], (31740 ^ _778495) ^ [_1359168, _1359170, _1359172, _1359174, _1359176, _1359178, _1359180, _1359182] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1359168, tc_fun(_1359170, tc_fun(_1359172, tc_HOL_Obool))), _1359174), _1359176), _1359178), _1359180)), -(hBOOL(hAPP(hAPP(hAPP(_1359176, _1359182), _1359178), _1359180))), hBOOL(hAPP(hAPP(c_member(_1359168), _1359182), _1359174))], (40337 ^ _778495) ^ [_1567423, _1567425, _1567427, _1567429] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567423, _1567423)), hAPP(hAPP(c_Product__Type_OPair(_1567423, _1567423), _1567425), _1567427)), c_Transitive__Closure_Otrancl(_1567423, _1567429))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567423, _1567423)), hAPP(hAPP(c_Product__Type_OPair(_1567423, _1567423), _1567425), _1567427)), c_Transitive__Closure_Ortrancl(_1567423, _1567429))))], (27981 ^ _778495) ^ [_1277638, _1277640, _1277642] : [class_Complete__Lattice_Ocomplete__lattice(_1277638), -(c_Complete__Lattice_OInf__class_OInf(_1277638, hAPP(hAPP(c_Set_Oinsert(_1277638), _1277640), _1277642)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1277638), _1277640), c_Complete__Lattice_OInf__class_OInf(_1277638, _1277642)))], (36174 ^ _778495) ^ [_1458768, _1458770, _1458772] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1458768, hAPP(hAPP(c_COMBC(_1458768, tc_fun(tc_prod(_1458768, _1458768), tc_HOL_Obool), tc_fun(_1458768, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458768, tc_fun(tc_fun(tc_prod(_1458768, _1458768), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1458768, _1458768), tc_HOL_Obool), tc_fun(_1458768, tc_HOL_Obool)), _1458768), c_COMBC(_1458768, tc_fun(tc_prod(_1458768, _1458768), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458768, tc_prod(_1458768, _1458768)), tc_fun(_1458768, tc_fun(tc_fun(tc_prod(_1458768, _1458768), tc_HOL_Obool), tc_HOL_Obool)), _1458768), hAPP(c_COMBB(tc_prod(_1458768, _1458768), tc_fun(tc_fun(tc_prod(_1458768, _1458768), tc_HOL_Obool), tc_HOL_Obool), _1458768), c_member(tc_prod(_1458768, _1458768)))), c_Product__Type_OPair(_1458768, _1458768)))), _1458770)), _1458772)), -(hBOOL(hAPP(hAPP(c_member(_1458768), _1458772), c_Wellfounded_Oacc(_1458768, _1458770))))], (31968 ^ _778495) ^ [_1366328, _1366330, _1366332, _1366334] : [class_Complete__Lattice_Ocomplete__lattice(_1366328), -(_1366330 = c_Orderings_Obot__class_Obot(tc_fun(_1366332, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1366332, _1366328), _1366330), hAPP(c_COMBK(_1366328, _1366332), _1366334)) = _1366334)], (50591 ^ _778495) ^ [_1803392, _1803394] : [class_Rings_Ocomm__semiring__1(_1803392), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1803392), _1803394), c_Groups_Ozero__class_Ozero(_1803392))))], (40802 ^ _778495) ^ [_1578452, _1578454] : [-(c_Relation_Ototal__on(_1578452, c_Orderings_Obot__class_Obot(tc_fun(_1578452, tc_HOL_Obool)), _1578454))], (20864 ^ _778495) ^ [_1152170] : [-(c_Int_Osucc(_1152170) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1152170), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (26160 ^ _778495) ^ [_1246269, _1246271, _1246273, _1246275] : [class_Rings_Olinordered__semidom(_1246269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246269), _1246271), _1246273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246269), c_Groups_Ozero__class_Ozero(_1246269)), _1246271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246269), hAPP(hAPP(c_Power_Opower__class_Opower(_1246269), _1246271), _1246275)), hAPP(hAPP(c_Power_Opower__class_Opower(_1246269), _1246273), _1246275))))], (8808 ^ _778495) ^ [_926250, _926252, _926254, _926256] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_926250), _926252)), hBOOL(hAPP(hAPP(c_member(_926250), _926254), _926252)), hBOOL(hAPP(hAPP(c_member(_926250), _926256), _926252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_926250), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926250, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926250, tc_HOL_Obool)), _926252), hAPP(hAPP(c_Set_Oinsert(_926250), _926254), c_Orderings_Obot__class_Obot(tc_fun(_926250, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_926250), _926256), c_Orderings_Obot__class_Obot(tc_fun(_926250, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_926250), _926252))))], (31864 ^ _778495) ^ [_1362636, _1362638, _1362640, _1362642, _1362644] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362636, tc_fun(_1362638, tc_HOL_Obool)), _1362640), hAPP(hAPP(c_COMBB(tc_fun(_1362638, tc_HOL_Obool), tc_fun(_1362638, tc_HOL_Obool), _1362636), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362638, tc_HOL_Obool)), _1362642)), _1362644)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362638, tc_HOL_Obool)), _1362642), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362636, tc_fun(_1362638, tc_HOL_Obool)), _1362640), _1362644)))], (10307 ^ _778495) ^ [_956148, _956150] : [class_Lattices_Olattice(_956148), hBOOL(hAPP(c_Finite__Set_Ofinite(_956148), _956150)), -(_956150 = c_Orderings_Obot__class_Obot(tc_fun(_956148, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956148), c_Big__Operators_Olattice__class_OInf__fin(_956148, _956150)), c_Big__Operators_Olattice__class_OSup__fin(_956148, _956150))))], (21458 ^ _778495) ^ [_1163139, _1163141] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163139), _1163141), hAPP(c_Int_Onumber__class_Onumber__of(_1163139), c_Int_OBit1(c_Int_OPls))) = _1163141), class_Fields_Ofield(_1163139), class_Int_Onumber__ring(_1163139)], (628 ^ _778495) ^ [_788007, _788009] : [-(c_List_Onat__list(_788007)), _788009 = _788007, c_List_Onat__list(_788009)], (49455 ^ _778495) ^ [_1778103, _1778105] : [c_Relation_Osym(_1778103, _1778105), -(hAPP(c_Relation_Oconverse(_1778103, _1778103), _1778105) = _1778105)], (23466 ^ _778495) ^ [_1198763, _1198765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198763, tc_HOL_Obool)), _1198765), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1198763, tc_HOL_Obool)), _1198765))), -(_1198765 = c_Orderings_Obot__class_Obot(tc_fun(_1198763, tc_HOL_Obool)))], (1248 ^ _778495) ^ [_797123, _797125] : [-(class_Groups_Oab__group__add(_797123)), _797125 = _797123, class_Groups_Oab__group__add(_797125)], (39802 ^ _778495) ^ [_1554209, _1554211, _1554213, _1554215, _1554217, _1554219] : [c_Finite__Set_Ofolding__idem(_1554209, _1554211, _1554213, _1554215), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554209), _1554217)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554209), _1554219)), -(hAPP(_1554215, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1554209, tc_HOL_Obool)), _1554217), _1554219)) = hAPP(c_Fun_Ocomp(_1554211, _1554211, _1554211, hAPP(_1554215, _1554217)), hAPP(_1554215, _1554219)))], (45859 ^ _778495) ^ [_1701069, _1701071, _1701073] : [class_Groups_Oab__semigroup__add(_1701069), -(c_List_Ofoldr(_1701069, _1701069, c_Groups_Oplus__class_Oplus(_1701069), _1701071, _1701073) = hAPP(c_List_Ofoldl(_1701069, _1701069, c_Groups_Oplus__class_Oplus(_1701069), _1701073), _1701071))], (48729 ^ _778495) ^ [_1761598, _1761600, _1761602, _1761604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761598), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1761600, _1761602, _1761598, _1761604) = 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(_1761600)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1761600)))], (21020 ^ _778495) ^ [_1155066, _1155068] : [class_Groups_Oordered__ab__group__add__abs(_1155066), -(hAPP(c_Groups_Oabs__class_Oabs(_1155066), hAPP(c_Groups_Oabs__class_Oabs(_1155066), _1155068)) = hAPP(c_Groups_Oabs__class_Oabs(_1155066), _1155068))], (20089 ^ _778495) ^ [_1139375, _1139377, _1139379] : [class_Rings_Olinordered__semidom(_1139375), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139375), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1139375), _1139377)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1139375), _1139379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1139377), _1139379)))], (42185 ^ _778495) ^ [_1618364, _1618366, _1618368, _1618370, _1618372, _1618374] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618364, _1618366)), hAPP(hAPP(c_Product__Type_OPair(_1618364, _1618366), _1618368), _1618370)), hAPP(c_List_Oset(tc_prod(_1618364, _1618366)), hAPP(hAPP(c_List_Ozip(_1618364, _1618366), _1618372), _1618374)))), -(hBOOL(hAPP(hAPP(c_member(_1618366), _1618370), hAPP(c_List_Oset(_1618366), _1618374))))], (43471 ^ _778495) ^ [_1647017, _1647019, _1647021, _1647023, _1647025] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647017), tc_List_Olist(_1647017))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647017), tc_List_Olist(_1647017)), hAPP(hAPP(c_List_Oappend(_1647017), _1647019), _1647021)), hAPP(hAPP(c_List_Oappend(_1647017), _1647019), _1647023))), c_List_Olexord(_1647017, _1647025))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1647017, _1647017)), hAPP(hAPP(c_Product__Type_OPair(_1647017, _1647017), 43476 ^ [_1647017, _1647019, _1647021, _1647023, _1647025]), 43476 ^ [_1647017, _1647019, _1647021, _1647023, _1647025])), _1647025))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647017), tc_List_Olist(_1647017))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647017), tc_List_Olist(_1647017)), _1647021), _1647023)), c_List_Olexord(_1647017, _1647025))))], (44211 ^ _778495) ^ [_1662929, _1662931, _1662933] : [_1662929 = c_List_Olist_ONil(_1662931), -(c_List_Olast(_1662931, hAPP(hAPP(c_List_Olist_OCons(_1662931), _1662933), _1662929)) = _1662933)], (49785 ^ _778495) ^ [_1784875, _1784877, _1784879] : [hAPP(c_Fun_Ocomp(_1784875, _1784877, _1784877, _1784879), c_Hilbert__Choice_Oinv__into(_1784875, _1784877, c_Orderings_Otop__class_Otop(tc_fun(_1784875, tc_HOL_Obool)), _1784879)) = c_Fun_Oid(_1784877), -(hAPP(c_Set_Oimage(_1784875, _1784877, _1784879), c_Orderings_Otop__class_Otop(tc_fun(_1784875, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784877, tc_HOL_Obool)))], (21416 ^ _778495) ^ [_1162472, _1162474] : [class_Int_Onumber__ring(_1162472), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162472), _1162474), hAPP(c_Int_Onumber__class_Onumber__of(_1162472), c_Int_OBit1(c_Int_OPls))) = _1162474)], (45079 ^ _778495) ^ [_1682515, _1682517, _1682519, _1682521, _1682523, _1682525, _1682527] : [c_List_Olist__all2(_1682521, _1682517, hAPP(hAPP(c_COMBB(_1682515, tc_fun(_1682517, tc_HOL_Obool), _1682521), _1682519), _1682523), _1682525, _1682527), -(c_List_Olist__all2(_1682515, _1682517, _1682519, hAPP(hAPP(c_List_Omap(_1682521, _1682515), _1682523), _1682525), _1682527))], (26616 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (35739 ^ _778495) ^ [_1448241, _1448243, _1448245, _1448247, _1448249] : [c_Equiv__Relations_Oequiv(_1448241, _1448243, _1448245), hBOOL(hAPP(hAPP(c_member(tc_prod(_1448241, _1448241)), hAPP(hAPP(c_Product__Type_OPair(_1448241, _1448241), _1448247), _1448249)), _1448245)), -(hAPP(c_Relation_OImage(_1448241, _1448241, _1448245), hAPP(hAPP(c_Set_Oinsert(_1448241), _1448247), c_Orderings_Obot__class_Obot(tc_fun(_1448241, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1448241, _1448241, _1448245), hAPP(hAPP(c_Set_Oinsert(_1448241), _1448249), c_Orderings_Obot__class_Obot(tc_fun(_1448241, tc_HOL_Obool)))))], (20802 ^ _778495) ^ [_1151243] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1151243), 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), _1151243)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1151243)))], (29799 ^ _778495) ^ [_1320388, _1320390, _1320392, _1320394] : [_1320388 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1320390), _1320392)), _1320394), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1320388, _1320390), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1320392), _1320394)))), 29806 ^ _778495 : [(29809 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1320394)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1320394), _1320390))], (29807 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1320390)))]], 29814 ^ _778495 : [(29817 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1320390), _1320394)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1320394), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29815 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1320390))]]], (44839 ^ _778495) ^ [_1676825, _1676827] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1676825), _1676827) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676825)), hAPP(c_Code__Numeral_Onat__of, _1676827))))], (44389 ^ _778495) ^ [_1666738, _1666740, _1666742, _1666744, _1666746] : [hAPP(hAPP(c_List_Omap(_1666738, _1666740), _1666742), _1666744) = hAPP(hAPP(c_List_Omap(_1666738, _1666740), _1666746), _1666744), 44392 ^ _778495 : [(44393 ^ _778495) ^ [_1666861] : [hBOOL(hAPP(hAPP(c_member(_1666738), _1666861), hAPP(c_List_Oset(_1666738), _1666744))), -(hAPP(_1666742, _1666861) = hAPP(_1666746, _1666861))]]], (13579 ^ _778495) ^ [_1019466, _1019468, _1019470, _1019472] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1019466, _1019470)), c_Sum__Type_OPlus(_1019466, _1019470, _1019468, _1019472)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1019466), _1019468)), hAPP(c_Finite__Set_Ocard(_1019470), _1019472))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019466), _1019468)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019470), _1019472))], (30861 ^ _778495) ^ [_1341879, _1341881, _1341883] : [class_Orderings_Olinorder(_1341879), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1341879), _1341881), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341879), _1341881), _1341883)) = _1341881)], (30873 ^ _778495) ^ [_1342147, _1342149, _1342151, _1342153] : [class_Orderings_Olinorder(_1342147), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342147), _1342149), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342147), _1342151), _1342153)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342147), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342147), _1342149), _1342151)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342147), _1342149), _1342153)))], (25210 ^ _778495) ^ [_1229126, _1229128] : [hAPP(c_Int_Onat, _1229126) = _1229128, 25213 ^ _778495 : [(25220 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229126))), -(_1229128 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25214 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229126)), -(_1229126 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229128))]]], (14895 ^ _778495) ^ [_1042664, _1042666, _1042668] : [class_Groups_Oordered__comm__monoid__add(_1042664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042664), _1042666), c_Groups_Ozero__class_Ozero(_1042664))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042664), _1042668), c_Groups_Ozero__class_Ozero(_1042664))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042664), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042664), _1042666), _1042668)), c_Groups_Ozero__class_Ozero(_1042664))))], (5108 ^ _778495) ^ [_856486, _856488, _856490, _856492] : [-(c_Product__Type_OPair(_856492, _856488) = c_Product__Type_OPair(_856490, _856486)), _856492 = _856490, _856488 = _856486], (10097 ^ _778495) ^ [_952639, _952641] : [class_Groups_Oone(_952639), 10100 ^ _778495 : [(10107 ^ _778495) ^ [] : [_952641 = c_Groups_Oone__class_Oone(_952639), -(c_Groups_Oone__class_Oone(_952639) = _952641)], (10101 ^ _778495) ^ [] : [c_Groups_Oone__class_Oone(_952639) = _952641, -(_952641 = c_Groups_Oone__class_Oone(_952639))]]], (41292 ^ _778495) ^ [_1591636, _1591638, _1591640] : [-(c_Nitpick_Otimes__frac(_1591636, _1591638, _1591640) = hAPP(hAPP(c_Nitpick_Ofrac(_1591636), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591636), _1591638)), hAPP(c_Nitpick_Onum(_1591636), _1591640))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1591636), _1591638)), hAPP(c_Nitpick_Odenom(_1591636), _1591640))))], (19156 ^ _778495) ^ [_1122790, _1122792, _1122794] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1122790), _1122792)), _1122794) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122790), _1122794)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122792), _1122794)))], (23124 ^ _778495) ^ [_1192322, _1192324, _1192326] : [class_Divides_Osemiring__div(_1192322), -(c_Divides_Odiv__class_Omod(_1192322, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192322), _1192324), _1192326), _1192326) = c_Divides_Odiv__class_Omod(_1192322, _1192324, _1192326))], (46754 ^ _778495) ^ [_1718556, _1718558, _1718560] : [-(hAPP(c_List_Orotate(_1718556, _1718558), hAPP(c_List_Orev(_1718556), _1718560)) = hAPP(c_List_Orev(_1718556), hAPP(c_List_Orotate(_1718556, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718556)), _1718560)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1718558, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718556)), _1718560)))), _1718560)))], (47384 ^ _778495) ^ [_1732357, _1732359] : [class_Enum_Oenum(_1732357), 47387 ^ _778495 : [(47395 ^ _778495) ^ [] : [47396 ^ _778495 : [(47397 ^ _778495) ^ [_1732537] : [hBOOL(hAPP(_1732359, _1732537))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732357), _1732359)))], (47388 ^ _778495) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732357), _1732359)), -(hBOOL(hAPP(_1732359, 47391 ^ [_1732357, _1732359])))]]], (43175 ^ _778495) ^ [_1639894, _1639896, _1639898, _1639900, _1639902, _1639904] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639894)), _1639896) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639898)), _1639900), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639894)), _1639902) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639898)), _1639904), -(hAPP(hAPP(c_List_Ozip(_1639894, _1639898), hAPP(hAPP(c_List_Oappend(_1639894), _1639896), _1639902)), hAPP(hAPP(c_List_Oappend(_1639898), _1639900), _1639904)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1639894, _1639898)), hAPP(hAPP(c_List_Ozip(_1639894, _1639898), _1639896), _1639900)), hAPP(hAPP(c_List_Ozip(_1639894, _1639898), _1639902), _1639904)))], (5705 ^ _778495) ^ [_868720, _868722, _868724, _868726, _868728] : [-(hAPP(hAPP(c_Set_Oinsert(_868720), _868722), hAPP(hAPP(c_Set_Oinsert(_868720), _868724), c_Orderings_Obot__class_Obot(tc_fun(_868720, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_868720), _868726), hAPP(hAPP(c_Set_Oinsert(_868720), _868728), c_Orderings_Obot__class_Obot(tc_fun(_868720, tc_HOL_Obool))))), 5706 ^ _778495 : [(5713 ^ _778495) ^ [] : [_868722 = _868728, _868724 = _868726], (5707 ^ _778495) ^ [] : [_868722 = _868726, _868724 = _868728]]], (52451 ^ _778495) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (30381 ^ _778495) ^ [_1332394, _1332396, _1332398, _1332400] : [hBOOL(hAPP(hAPP(c_member(_1332394), _1332396), c_SetInterval_Oord_OatMost(_1332394, _1332398, _1332400))), -(hBOOL(hAPP(hAPP(_1332398, _1332396), _1332400)))], (44065 ^ _778495) ^ [_1660352, _1660354, _1660356, _1660358] : [class_Orderings_Olinorder(_1660352), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660352, _1660352, c_COMBI(_1660352)), _1660354), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660352, _1660352, c_COMBI(_1660352)), _1660356), _1660358)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660352, _1660352, c_COMBI(_1660352)), _1660356), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660352, _1660352, c_COMBI(_1660352)), _1660354), _1660358)))], (44962 ^ _778495) ^ [_1679812, _1679814, _1679816, _1679818] : [hBOOL(hAPP(c_List_Olistsp(_1679812, hAPP(hAPP(c_COMBS(_1679812, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1679812), c_fconj), _1679814)), _1679816)), _1679818)), 44965 ^ _778495 : [(44968 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1679812, _1679816), _1679818)))], (44966 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1679812, _1679814), _1679818)))]]], (27993 ^ _778495) ^ [_1277931, _1277933, _1277935] : [class_Complete__Lattice_Ocomplete__lattice(_1277931), -(c_Complete__Lattice_OInf__class_OInf(_1277931, hAPP(hAPP(c_Set_Oinsert(_1277931), _1277933), hAPP(hAPP(c_Set_Oinsert(_1277931), _1277935), c_Orderings_Obot__class_Obot(tc_fun(_1277931, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1277931), _1277933), _1277935))], (24838 ^ _778495) ^ [_1222928] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1222928) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222928)))], (5184 ^ _778495) ^ [_857676, _857678, _857680, _857682] : [-(c_Lazy__Sequence_Oflat(_857682, _857678) = c_Lazy__Sequence_Oflat(_857680, _857676)), _857682 = _857680, _857678 = _857676], (3126 ^ _778495) ^ [_825047, _825049, _825051, _825053] : [-(c_Big__Operators_Olinorder__class_OMin(_825053, _825049) = c_Big__Operators_Olinorder__class_OMin(_825051, _825047)), _825053 = _825051, _825049 = _825047], (3326 ^ _778495) ^ [_828169, _828171, _828173, _828175] : [-(c_HOL_OLet(_828175, _828171) = c_HOL_OLet(_828173, _828169)), _828175 = _828173, _828171 = _828169], (42303 ^ _778495) ^ [_1620952, _1620954, _1620956, _1620958] : [_1620952 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620954)), _1620956)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1620954, hAPP(hAPP(c_List_Olist__update(_1620954, _1620956), _1620952), _1620958)) = c_List_Obutlast(_1620954, _1620956))], (52441 ^ _778495) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (25086 ^ _778495) ^ [_1227012] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1227012)))), -(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), _1227012)) = 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), _1227012))))], (51257 ^ _778495) ^ [_1814781, _1814783] : [51264 ^ _778495 : [(51267 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814783), _1814781))], (51265 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814781), _1814783)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814781), _1814783)), -(_1814781 = _1814783)], (44291 ^ _778495) ^ [_1664182, _1664184, _1664186] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664182)), _1664184), c_List_Olists(_1664182, _1664186))), -(_1664184 = c_List_Olist_ONil(_1664182)), 44300 ^ _778495 : [(44305 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664182)), 44299 ^ [_1664182, _1664184, _1664186]), c_List_Olists(_1664182, _1664186))))], (44303 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664182), 44298 ^ [_1664182, _1664184, _1664186]), _1664186)))], (44301 ^ _778495) ^ [] : [-(_1664184 = hAPP(hAPP(c_List_Olist_OCons(_1664182), 44298 ^ [_1664182, _1664184, _1664186]), 44299 ^ [_1664182, _1664184, _1664186]))]]], (2456 ^ _778495) ^ [_814660, _814662] : [_814662 = _814660, -(c_SetInterval_Oord__class_OatLeast(_814662) = c_SetInterval_Oord__class_OatLeast(_814660))], (29699 ^ _778495) ^ [_1318865, _1318867] : [-(_1318865 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1318867, _1318865), c_Divides_Odivmod__int(_1318867, _1318865))))], (50445 ^ _778495) ^ [_1799326, _1799328, _1799330, _1799332, _1799334, _1799336, _1799338] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799326, _1799328), tc_prod(_1799326, _1799328))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799326, _1799328), tc_prod(_1799326, _1799328)), hAPP(hAPP(c_Product__Type_OPair(_1799326, _1799328), _1799330), _1799332)), hAPP(hAPP(c_Product__Type_OPair(_1799326, _1799328), _1799334), _1799336))), c_Transitive__Closure_Ortrancl(tc_prod(_1799326, _1799328), _1799338))), -(hAPP(hAPP(c_Product__Type_OPair(_1799326, _1799328), _1799330), _1799332) = hAPP(hAPP(c_Product__Type_OPair(_1799326, _1799328), _1799334), _1799336)), 50454 ^ _778495 : [(50457 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799326, _1799328), tc_prod(_1799326, _1799328))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799326, _1799328), tc_prod(_1799326, _1799328)), hAPP(hAPP(c_Product__Type_OPair(_1799326, _1799328), 50452 ^ [_1799326, _1799328, _1799330, _1799332, _1799334, _1799336, _1799338]), 50453 ^ [_1799326, _1799328, _1799330, _1799332, _1799334, _1799336, _1799338])), hAPP(hAPP(c_Product__Type_OPair(_1799326, _1799328), _1799334), _1799336))), c_Transitive__Closure_Ortrancl(tc_prod(_1799326, _1799328), _1799338))))], (50455 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799326, _1799328), tc_prod(_1799326, _1799328))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799326, _1799328), tc_prod(_1799326, _1799328)), hAPP(hAPP(c_Product__Type_OPair(_1799326, _1799328), _1799330), _1799332)), hAPP(hAPP(c_Product__Type_OPair(_1799326, _1799328), 50452 ^ [_1799326, _1799328, _1799330, _1799332, _1799334, _1799336, _1799338]), 50453 ^ [_1799326, _1799328, _1799330, _1799332, _1799334, _1799336, _1799338]))), _1799338)))]]], (41535 ^ _778495) ^ [_1599196, _1599198, _1599200, _1599202] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599196), tc_List_Olist(_1599196))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599196), tc_List_Olist(_1599196)), _1599198), _1599200)), c_List_Olistrel1(_1599196, _1599202))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599196)), _1599198) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599196)), _1599200))], (50060 ^ _778495) ^ [_1790806, _1790808, _1790810] : [c_Fun_Obij__betw(_1790806, _1790808, _1790810, c_Orderings_Otop__class_Otop(tc_fun(_1790806, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790808, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1790806, _1790808, _1790810, c_Orderings_Otop__class_Otop(tc_fun(_1790806, tc_HOL_Obool))))], (37426 ^ _778495) ^ [_1487501, _1487503, _1487505, _1487507, _1487509, _1487511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1487501, _1487503)), hAPP(hAPP(c_Product__Type_OPair(_1487501, _1487503), _1487505), _1487507)), hAPP(hAPP(c_Product__Type_OSigma(_1487501, _1487503), _1487509), _1487511))), 37429 ^ _778495 : [(37432 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487503), _1487507), hAPP(_1487511, _1487505))))], (37430 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487501), _1487505), _1487509)))]]], (41559 ^ _778495) ^ [_1600029, _1600031, _1600033, _1600035, _1600037] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600029, _1600029)), hAPP(hAPP(c_Product__Type_OPair(_1600029, _1600029), _1600031), _1600033)), _1600035)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600029), tc_List_Olist(_1600029))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600029), tc_List_Olist(_1600029)), hAPP(hAPP(c_List_Olist_OCons(_1600029), _1600031), _1600037)), hAPP(hAPP(c_List_Olist_OCons(_1600029), _1600033), _1600037))), c_List_Olistrel1(_1600029, _1600035))))], (49873 ^ _778495) ^ [_1786966, _1786968] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1786966), _1786968))), -(c_Quickcheck_Obeyond(_1786966, _1786968) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (38963 ^ _778495) ^ [_1533511, _1533513] : [-(c_HOL_OThe(_1533511, hAPP(hAPP(c_COMBC(_1533511, _1533511, tc_HOL_Obool), c_fequal), _1533513)) = _1533513)], (42976 ^ _778495) ^ [_1635233, _1635235, _1635237, _1635239, _1635241] : [_1635233 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1635235, _1635237, _1635239), _1635233), _1635241) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635237), _1635235), c_List_Olist_ONil(_1635237)), _1635241))], (42089 ^ _778495) ^ [_1614409, _1614411] : [-(hAPP(c_List_Oset(_1614409), _1614411) = hAPP(c_Set_OCollect(_1614409), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1614409), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1614409, 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)), _1614409), 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)), _1614409), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1614409, tc_fun(tc_Nat_Onat, _1614409), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614409, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1614409), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1614409), c_COMBB(_1614409, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1614409), _1614411))))), 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(_1614409)), _1614411))))))], (45306 ^ _778495) ^ [_1687703, _1687705, _1687707] : [hBOOL(hAPP(c_List_Odistinct(_1687703), _1687705)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1687703)), c_Enum_On__lists(_1687703, _1687707, _1687705))))], (43185 ^ _778495) ^ [_1640203, _1640205, _1640207] : [-(hAPP(c_List_Oset(_1640203), hAPP(hAPP(c_List_Oappend(_1640203), _1640205), _1640207)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640203, tc_HOL_Obool)), hAPP(c_List_Oset(_1640203), _1640205)), hAPP(c_List_Oset(_1640203), _1640207)))], (43297 ^ _778495) ^ [_1642216, _1642218, _1642220, _1642222] : [-(hAPP(hAPP(c_List_Otake(_1642216), _1642218), hAPP(hAPP(c_List_Oappend(_1642216), _1642220), _1642222)) = hAPP(hAPP(c_List_Oappend(_1642216), hAPP(hAPP(c_List_Otake(_1642216), _1642218), _1642220)), hAPP(hAPP(c_List_Otake(_1642216), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1642218), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642216)), _1642220))), _1642222)))], (52239 ^ _778495) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (40720 ^ _778495) ^ [_1576427, _1576429, _1576431] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576427, _1576429)), hAPP(c_Relation_Oconverse(_1576429, _1576427), _1576431))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576429, _1576427)), _1576431)))], (42199 ^ _778495) ^ [_1618780, _1618782, _1618784, _1618786, _1618788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618780), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618782)), _1618784))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618780), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618786)), _1618788))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1618782, _1618786)), hAPP(hAPP(c_List_Ozip(_1618782, _1618786), _1618784), _1618788)), _1618780) = hAPP(hAPP(c_Product__Type_OPair(_1618782, _1618786), hAPP(hAPP(c_List_Onth(_1618782), _1618784), _1618780)), hAPP(hAPP(c_List_Onth(_1618786), _1618788), _1618780)))], (40345 ^ _778495) ^ [_1567633, _1567635] : [-(c_Transitive__Closure_Otrancl(_1567633, _1567635) = hAPP(hAPP(c_Relation_Orel__comp(_1567633, _1567633, _1567633), _1567635), c_Transitive__Closure_Ortrancl(_1567633, _1567635)))], (18032 ^ _778495) ^ [_1101770, _1101772, _1101774] : [class_Int_Onumber__ring(_1101770), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101770), hAPP(c_Int_Onumber__class_Onumber__of(_1101770), _1101772)), hAPP(c_Int_Onumber__class_Onumber__of(_1101770), _1101774)) = hAPP(c_Int_Onumber__class_Onumber__of(_1101770), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1101772), _1101774)))], (40343 ^ _778495) ^ [_1567592, _1567594] : [-(c_Transitive__Closure_Otrancl(_1567592, _1567594) = hAPP(hAPP(c_Relation_Orel__comp(_1567592, _1567592, _1567592), c_Transitive__Closure_Ortrancl(_1567592, _1567594)), _1567594))], (31488 ^ _778495) ^ [_1353691, _1353693, _1353695] : [class_Orderings_Olinorder(_1353691), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353691), _1353693)), -(hBOOL(hAPP(hAPP(c_member(_1353691), _1353695), _1353693))), -(_1353693 = c_Orderings_Obot__class_Obot(tc_fun(_1353691, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1353691, hAPP(hAPP(c_Set_Oinsert(_1353691), _1353695), _1353693)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353691), _1353695), c_Big__Operators_Olinorder__class_OMax(_1353691, _1353693)))], (42748 ^ _778495) ^ [_1630399, _1630401] : [c_Orderings_Obot__class_Obot(tc_fun(_1630399, tc_HOL_Obool)) = hAPP(c_List_Oset(_1630399), _1630401), -(_1630401 = c_List_Olist_ONil(_1630399))], (44217 ^ _778495) ^ [_1663028, _1663030, _1663032] : [-(_1663028 = c_List_Olist_ONil(_1663030)), -(c_List_Olast(_1663030, hAPP(hAPP(c_List_Olist_OCons(_1663030), _1663032), _1663028)) = c_List_Olast(_1663030, _1663028))], (5582 ^ _778495) ^ [_863887, _863889, _863891, _863893, _863895, _863897] : [-(c_COMBC(_863897, _863893, _863889) = c_COMBC(_863895, _863891, _863887)), _863897 = _863895, _863893 = _863891, _863889 = _863887], (50589 ^ _778495) ^ [_1803364] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803364), _1803364)))], (38564 ^ _778495) ^ [_1523990, _1523992, _1523994, _1523996] : [hBOOL(hAPP(hAPP(c_member(_1523990), _1523992), hAPP(c_Relation_ORange(_1523994, _1523990), _1523996))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523994, _1523990)), hAPP(hAPP(c_Product__Type_OPair(_1523994, _1523990), 38567 ^ [_1523990, _1523992, _1523994, _1523996]), _1523992)), _1523996)))], (15669 ^ _778495) ^ [_1057441, _1057443, _1057445, _1057447] : [class_Groups_Ocomm__monoid__add(_1057441), 15672 ^ _778495 : [(15679 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1057443), _1057445))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057443, _1057441), _1057447), _1057445) = c_Groups_Ozero__class_Ozero(_1057441))], (15673 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1057443), _1057445)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057443, _1057441), _1057447), _1057445) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057441, _1057443, c_Groups_Oplus__class_Oplus(_1057441)), _1057447), c_Groups_Ozero__class_Ozero(_1057441)), _1057445))]]], (3580 ^ _778495) ^ [_832154, _832156, _832158, _832160] : [-(c_List_Olist__update(_832160, _832156) = c_List_Olist__update(_832158, _832154)), _832160 = _832158, _832156 = _832154], (45823 ^ _778495) ^ [_1699408, _1699410] : [-(c_List_Oconcat(tc_List_Olist(_1699408), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699408), tc_List_Olist(tc_List_Olist(_1699408))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1699408)), _1699408, c_List_Olist_ONil(tc_List_Olist(_1699408)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1699408), tc_List_Olist(tc_List_Olist(_1699408))), _1699408), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699408), tc_List_Olist(tc_List_Olist(_1699408)), tc_List_Olist(tc_List_Olist(_1699408))), c_List_Olist_OCons(tc_List_Olist(_1699408))), c_List_Olist_ONil(tc_List_Olist(_1699408)))))), _1699410)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699408), tc_List_Olist(_1699408)), c_List_Otl(_1699408)), hAPP(c_List_Ofilter(tc_List_Olist(_1699408), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1699408)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699408), tc_List_Olist(_1699408), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1699408)))), _1699410)))], (49150 ^ _778495) ^ [_1772536, _1772538] : [-(c_Relation_Oantisym(_1772536, c_Relation_OId__on(_1772536, _1772538)))], (15766 ^ _778495) ^ [_1059151, _1059153, _1059155, _1059157] : [-(c_Sum__Type_OPlus(_1059151, _1059153, _1059155, _1059157) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1059151, _1059153), tc_HOL_Obool))), _1059155 = c_Orderings_Obot__class_Obot(tc_fun(_1059151, tc_HOL_Obool)), _1059157 = c_Orderings_Obot__class_Obot(tc_fun(_1059153, tc_HOL_Obool))], (19930 ^ _778495) ^ [_1136521] : [-(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), _1136521))))], (11478 ^ _778495) ^ [_977245, _977247, _977249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977245), _977247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977245), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977247), _977249))))], (26978 ^ _778495) ^ [_1260593, _1260595] : [class_Int_Onumber__ring(_1260593), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1260593), hAPP(c_Int_Onumber__class_Onumber__of(_1260593), 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)))), _1260595)) = c_Groups_Oone__class_Oone(_1260593))], (52551 ^ _778495) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (8724 ^ _778495) ^ [_924541, _924543, _924545] : [class_Groups_Oab__semigroup__mult(_924541), hBOOL(hAPP(c_Finite__Set_Ofinite(_924541), _924543)), -(hBOOL(hAPP(hAPP(c_member(_924541), _924545), _924543))), -(hAPP(c_Finite__Set_Ofold1(_924541, c_Groups_Otimes__class_Otimes(_924541)), hAPP(hAPP(c_Set_Oinsert(_924541), _924545), _924543)) = hAPP(hAPP(c_Finite__Set_Ofold(_924541, _924541, c_Groups_Otimes__class_Otimes(_924541)), _924545), _924543))], (26002 ^ _778495) ^ [_1243388, _1243390, _1243392, _1243394] : [class_Fields_Ofield(_1243388), -(_1243390 = c_Groups_Ozero__class_Ozero(_1243388)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243392), _1243394)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1243388), _1243390), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243394), _1243392)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243388), hAPP(hAPP(c_Power_Opower__class_Opower(_1243388), _1243390), _1243394)), hAPP(hAPP(c_Power_Opower__class_Opower(_1243388), _1243390), _1243392)))], (41435 ^ _778495) ^ [_1596220, _1596222, _1596224, _1596226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1596220), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1596222), _1596224))), -(hAPP(c_Random_Opick(_1596222, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1596222)), _1596224), _1596226)), _1596220) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1596222), _1596224))], (18020 ^ _778495) ^ [_1101476, _1101478, _1101480, _1101482] : [class_Groups_Oordered__ab__group__add(_1101476), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101476), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1101476), _1101478), _1101480)), _1101482) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1101476), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101476), _1101478), _1101482)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101476), _1101480), _1101482)))], (50556 ^ _778495) ^ [_1802645, _1802647, _1802649, _1802651, _1802653, _1802655, _1802657, _1802659] : [c_Finite__Set_Ofolding__image(_1802645, _1802647, _1802649, _1802651, _1802653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1802647), _1802655)), 50566 ^ _778495 : [(50569 ^ _778495) ^ [] : [hAPP(_1802657, 50565 ^ [_1802645, _1802647, _1802649, _1802651, _1802653, _1802655, _1802657, _1802659]) = hAPP(_1802659, 50565 ^ [_1802645, _1802647, _1802649, _1802651, _1802653, _1802655, _1802657, _1802659])], (50567 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802647), 50565 ^ [_1802645, _1802647, _1802649, _1802651, _1802653, _1802655, _1802657, _1802659]), _1802655)))]], -(hAPP(hAPP(_1802653, _1802657), _1802655) = hAPP(hAPP(_1802653, _1802659), _1802655))], (41688 ^ _778495) ^ [_1604342, _1604344, _1604346, _1604348, _1604350, _1604352] : [c_List_Olistrelp(_1604342, _1604344, hAPP(hAPP(c_List_Olist_OCons(_1604342), _1604346), _1604348), hAPP(hAPP(c_List_Olist_OCons(_1604342), _1604350), _1604352)), 41691 ^ _778495 : [(41694 ^ _778495) ^ [] : [-(c_List_Olistrelp(_1604342, _1604344, _1604348, _1604352))], (41692 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1604344, _1604346), _1604350)))]]], (48418 ^ _778495) ^ [_1754724, _1754726, _1754728, _1754730, _1754732] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1754724, _1754726, _1754728) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754724, _1754730, _1754732)), _1754726 = _1754730, _1754728 = _1754732], (13827 ^ _778495) ^ [_1023960, _1023962, _1023964, _1023966] : [class_Rings_Oordered__comm__semiring(_1023960), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023960), _1023962), _1023964)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023960), c_Groups_Ozero__class_Ozero(_1023960)), _1023966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023960), _1023966), _1023962)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023960), _1023966), _1023964))))], (30819 ^ _778495) ^ [_1341068, _1341070, _1341072, _1341074] : [class_Orderings_Olinorder(_1341068), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341068), _1341070), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341068), _1341072), _1341074)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341068), _1341072), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341068), _1341070), _1341074)))], (35512 ^ _778495) ^ [_1442246, _1442248, _1442250, _1442252, _1442254] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1442246, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442248, _1442246, _1442250), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442248, tc_HOL_Obool)), _1442252), _1442254))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442246, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442248, _1442246, _1442250), _1442252)), hAPP(c_Relation_OImage(_1442248, _1442246, _1442250), _1442254)))))], (17410 ^ _778495) ^ [_1089994, _1089996, _1089998, _1090000, _1090002] : [class_Fields_Ofield(_1089994), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089996), _1089998)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089996), _1090000)), 17424 ^ _778495 : [(17427 ^ _778495) ^ [] : [-(hAPP(_1090002, 17423 ^ [_1089994, _1089996, _1089998, _1090000, _1090002]) = c_Groups_Ozero__class_Ozero(_1089994))], (17425 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1089996), 17423 ^ [_1089994, _1089996, _1089998, _1090000, _1090002]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1089996, tc_HOL_Obool)), _1089998), _1090000))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089996, _1089994), _1090002), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1089996, tc_HOL_Obool)), _1089998), _1090000)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1089994), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089994), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089996, _1089994), _1090002), _1089998)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089996, _1089994), _1090002), _1090000))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089996, _1089994), _1090002), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1089996, tc_HOL_Obool)), _1089998), _1090000))))], (26298 ^ _778495) ^ [_1248677, _1248679, _1248681] : [class_Fields_Ofield__inverse__zero(_1248677), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248677), c_Groups_Oone__class_Oone(_1248677)), hAPP(hAPP(c_Power_Opower__class_Opower(_1248677), _1248679), _1248681)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1248677), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248677), c_Groups_Oone__class_Oone(_1248677)), _1248679)), _1248681))], (9396 ^ _778495) ^ [_938487] : [class_Lattices_Osemilattice__inf(_938487), -(c_Finite__Set_Ofun__left__comm__idem(_938487, _938487, c_Lattices_Osemilattice__inf__class_Oinf(_938487)))], (44408 ^ _778495) ^ [_1667239, _1667241, _1667243, _1667245, _1667247, _1667249, _1667251] : [hAPP(hAPP(c_List_Omap(_1667239, _1667241), _1667243), _1667245) = hAPP(hAPP(c_List_Omap(_1667247, _1667241), _1667249), _1667251), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667239)), _1667245) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667247)), _1667251))], (29545 ^ _778495) ^ [_1316255, _1316257] : [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), _1316255), _1316257))), 29548 ^ _778495 : [(29557 ^ _778495) ^ [] : [-(c_Divides_OposDivAlg(_1316255, _1316257) = hAPP(c_Divides_Oadjust(_1316257), c_Divides_OposDivAlg(_1316255, 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)))), _1316257)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1316255), _1316257))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1316257), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29549 ^ _778495) ^ [] : [29550 ^ _778495 : [(29553 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1316257), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29551 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1316255), _1316257))]], -(c_Divides_OposDivAlg(_1316255, _1316257) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1316255))]]], (15529 ^ _778495) ^ [_1054508, _1054510, _1054512, _1054514, _1054516] : [class_Groups_Ocomm__monoid__mult(_1054508), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054510), _1054512)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054510), _1054514)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054508), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054510, _1054508), _1054516), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1054510, tc_HOL_Obool)), _1054512), _1054514))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054510, _1054508), _1054516), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1054510, tc_HOL_Obool)), _1054512), _1054514))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054508), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054510, _1054508), _1054516), _1054512)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054510, _1054508), _1054516), _1054514)))], (21446 ^ _778495) ^ [_1162943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1162943)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162943), c_Int_OPls)))], (19854 ^ _778495) ^ [_1135110, _1135112] : [class_Orderings_Olinorder(_1135110), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135110), _1135112)), -(_1135112 = c_Orderings_Obot__class_Obot(tc_fun(_1135110, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1135110), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1135110), 19867 ^ [_1135110, _1135112]), 19868 ^ [_1135110, _1135112])), hAPP(hAPP(c_Set_Oinsert(_1135110), 19867 ^ [_1135110, _1135112]), hAPP(hAPP(c_Set_Oinsert(_1135110), 19868 ^ [_1135110, _1135112]), c_Orderings_Obot__class_Obot(tc_fun(_1135110, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1135110), c_Big__Operators_Olattice_OInf__fin(_1135110, c_Orderings_Oord__class_Omin(_1135110), _1135112)), _1135112)))], (4578 ^ _778495) ^ [_848163, _848165, _848167, _848169] : [-(c_Product__Type_Osnd(_848169, _848165) = c_Product__Type_Osnd(_848167, _848163)), _848169 = _848167, _848165 = _848163], (48482 ^ _778495) ^ [_1755903, _1755905] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1755903)), _1755905) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1755903, tc_Lazy__Sequence_Olazy__sequence(_1755903)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1755903, tc_Lazy__Sequence_Olazy__sequence(_1755903), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755903), tc_Nat_Onat), _1755903), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1755903), 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(_1755903)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1755903)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1755903), _1755905)))], (44855 ^ _778495) ^ [_1677120] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677120)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (45203 ^ _778495) ^ [_1685127, _1685129, _1685131, _1685133, _1685135, _1685137] : [c_List_Olist__all2(_1685127, _1685129, _1685131, _1685133, _1685135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685137), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685129)), _1685135))), -(hBOOL(hAPP(hAPP(_1685131, hAPP(hAPP(c_List_Onth(_1685127), _1685133), _1685137)), hAPP(hAPP(c_List_Onth(_1685129), _1685135), _1685137))))], (48162 ^ _778495) ^ [_1749279, _1749281, _1749283] : [-(_1749281 = _1749283), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749279, _1749279, hAPP(hAPP(c_COMBB(tc_fun(_1749279, tc_HOL_Obool), tc_fun(_1749279, tc_HOL_Obool), _1749279), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1749279), c_fNot)), c_fequal)), _1749281), _1749283)))], (16702 ^ _778495) ^ [_1077113, _1077115, _1077117] : [class_Fields_Olinordered__field(_1077113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077113), c_Groups_Ozero__class_Ozero(_1077113)), _1077115)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077113), c_Groups_Ozero__class_Ozero(_1077113)), _1077117)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077113), c_Groups_Ozero__class_Ozero(_1077113)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1077113), _1077115), _1077117))))], (20446 ^ _778495) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32004 ^ _778495) ^ [_1367027, _1367029, _1367031, _1367033, _1367035] : [_1367027 = c_Orderings_Obot__class_Obot(tc_fun(_1367029, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367031, tc_HOL_Obool)), _1367033), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367029, tc_fun(_1367031, tc_HOL_Obool)), _1367027), _1367035)) = _1367033)], (27691 ^ _778495) ^ [_1272717] : [class_Lattices_Oboolean__algebra(_1272717), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1272717), c_Orderings_Otop__class_Otop(_1272717)) = c_Orderings_Obot__class_Obot(_1272717))], (39654 ^ _778495) ^ [_1550751, _1550753, _1550755, _1550757, _1550759, _1550761, _1550763, _1550765] : [c_Finite__Set_Ofolding__image(_1550751, _1550753, _1550755, _1550757, _1550759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550753), _1550761)), -(hAPP(hAPP(_1550759, hAPP(hAPP(c_COMBS(_1550753, _1550751, _1550751), hAPP(hAPP(c_COMBB(_1550751, tc_fun(_1550751, _1550751), _1550753), _1550755), _1550763)), _1550765)), _1550761) = hAPP(hAPP(_1550755, hAPP(hAPP(_1550759, _1550763), _1550761)), hAPP(hAPP(_1550759, _1550765), _1550761)))], (45326 ^ _778495) ^ [_1688027, _1688029, _1688031] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1688027))), c_Enum_On__lists(_1688027, _1688029, _1688031)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688027)), _1688031)), _1688029))], (19684 ^ _778495) ^ [_1132098, _1132100, _1132102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132098)), _1132098 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1132100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132098), _1132102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132100), _1132098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1132102)))], (2874 ^ _778495) ^ [_821151, _821153, _821155, _821157] : [-(c_Nitpick_Oinverse__frac(_821157, _821153) = c_Nitpick_Oinverse__frac(_821155, _821151)), _821157 = _821155, _821153 = _821151], (41371 ^ _778495) ^ [_1593871, _1593873, _1593875] : [-(hAPP(c_List_Olexn(_1593871, _1593873), hAPP(c_Nat_OSuc, _1593875)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1593871), tc_List_Olist(_1593871)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1593871, tc_List_Olist(_1593871)), tc_prod(_1593871, tc_List_Olist(_1593871))), tc_prod(tc_List_Olist(_1593871), tc_List_Olist(_1593871)), c_Product__Type_Omap__pair(tc_prod(_1593871, tc_List_Olist(_1593871)), tc_List_Olist(_1593871), tc_prod(_1593871, tc_List_Olist(_1593871)), tc_List_Olist(_1593871), hAPP(c_Product__Type_Oprod_Oprod__case(_1593871, tc_List_Olist(_1593871), tc_List_Olist(_1593871)), c_List_Olist_OCons(_1593871)), hAPP(c_Product__Type_Oprod_Oprod__case(_1593871, tc_List_Olist(_1593871), tc_List_Olist(_1593871)), c_List_Olist_OCons(_1593871)))), c_Wellfounded_Olex__prod(_1593871, tc_List_Olist(_1593871), _1593873, hAPP(c_List_Olexn(_1593871, _1593873), _1593875)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1593871), tc_List_Olist(_1593871))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1593871), tc_List_Olist(_1593871), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593871), tc_fun(tc_List_Olist(_1593871), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593871), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593871), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593871), tc_HOL_Obool)), tc_List_Olist(_1593871)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1593871))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593871)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593871), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593871)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593871)))), hAPP(c_Nat_OSuc, _1593875))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593871), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593871)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593871)))), hAPP(c_Nat_OSuc, _1593875)))))))], (13247 ^ _778495) ^ [_1014309, _1014311, _1014313] : [class_Groups_Oab__group__add(_1014309), 13250 ^ _778495 : [(13257 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014309), _1014311), _1014313) = c_Groups_Ozero__class_Ozero(_1014309), -(_1014311 = _1014313)], (13251 ^ _778495) ^ [] : [_1014311 = _1014313, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014309), _1014311), _1014313) = c_Groups_Ozero__class_Ozero(_1014309))]]], (22630 ^ _778495) ^ [_1183052] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183052)), _1183052) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47734 ^ _778495) ^ [_1740268, _1740270, _1740272] : [-(c_List_Olist__ex(_1740268, _1740270, _1740272)), 47735 ^ _778495 : [(47736 ^ _778495) ^ [_1740325] : [hBOOL(hAPP(hAPP(c_member(_1740268), _1740325), hAPP(c_List_Oset(_1740268), _1740272))), hBOOL(hAPP(_1740270, _1740325))]]], (35549 ^ _778495) ^ [_1443294, _1443296, _1443298, _1443300, _1443302, _1443304] : [hBOOL(hAPP(hAPP(c_member(_1443294), _1443296), _1443298)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1443294, _1443300)), hAPP(hAPP(c_Product__Type_OPair(_1443294, _1443300), _1443296), _1443302)), _1443304)), -(hBOOL(hAPP(hAPP(c_member(_1443300), _1443302), hAPP(c_Relation_OImage(_1443294, _1443300, _1443304), _1443298))))], (27813 ^ _778495) ^ [_1274876] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1274876, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1274876, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1274876, tc_HOL_Obool)))], (29466 ^ _778495) ^ [_1314498, _1314500, _1314502, _1314504] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1314498, _1314500), _1314502)), hBOOL(hAPP(hAPP(_1314500, _1314504), _1314502)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1314498, _1314500), _1314504)))], (28751 ^ _778495) ^ [_1299906, _1299908] : [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(_1299908))), 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), _1299906)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1299906)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1299908))))], (34112 ^ _778495) ^ [_1414038, _1414040, _1414042] : [class_Orderings_Olinorder(_1414038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414038), _1414040), _1414042)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414038, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1414038), _1414040)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1414038, _1414040, _1414042)) = hAPP(c_SetInterval_Oord__class_OatMost(_1414038), _1414042))], (7086 ^ _778495) ^ [_895245, _895247, _895249, _895251] : [hBOOL(hAPP(_895245, _895247)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895249, tc_HOL_Obool)), _895251), _895245), _895247)))], (44053 ^ _778495) ^ [_1660080, _1660082, _1660084, _1660086, _1660088] : [class_Orderings_Olinorder(_1660080), -(hAPP(c_List_Oset(_1660082), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660082, _1660080, _1660084), _1660086), _1660088)) = hAPP(hAPP(c_Set_Oinsert(_1660082), _1660086), hAPP(c_List_Oset(_1660082), _1660088)))], (43748 ^ _778495) ^ [_1653744, _1653746] : [-(_1653744 = c_List_Olist_ONil(_1653746)), -(hBOOL(hAPP(hAPP(c_member(_1653746), hAPP(c_List_Ohd(_1653746), _1653744)), hAPP(c_List_Oset(_1653746), _1653744))))], (25491 ^ _778495) ^ [_1233913, _1233915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1233913)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1233913), _1233915)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1233915), _1233913) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1233915), _1233913)), _1233913)))], (37767 ^ _778495) ^ [_1497042, _1497044, _1497046, _1497048] : [-(hAPP(c_Set_Ovimage(_1497042, _1497044, _1497046), hAPP(c_Set_OCollect(_1497044), _1497048)) = hAPP(c_Set_OCollect(_1497042), hAPP(hAPP(c_COMBB(_1497044, tc_HOL_Obool, _1497042), _1497048), _1497046)))], (33040 ^ _778495) ^ [_1388030, _1388032] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1388030, _1388032)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1388032), hAPP(c_Nat_OSuc, _1388030)))], (29312 ^ _778495) ^ [_1311464, _1311466, _1311468, _1311470] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1311464, _1311466), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1311468), _1311470))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1311464, _1311466) = _1311470)], (52437 ^ _778495) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (43008 ^ _778495) ^ [_1636177, _1636179, _1636181, _1636183, _1636185] : [hAPP(hAPP(c_List_Olist_OCons(_1636177), _1636179), _1636181) = hAPP(hAPP(c_List_Oappend(_1636177), _1636183), _1636185), 43013 ^ _778495 : [(43016 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636177), _1636179), _1636181) = _1636185)], (43014 ^ _778495) ^ [] : [-(_1636183 = c_List_Olist_ONil(_1636177))]], 43018 ^ _778495 : [(43021 ^ _778495) ^ [] : [-(_1636181 = hAPP(hAPP(c_List_Oappend(_1636177), 43017 ^ [_1636177, _1636179, _1636181, _1636183, _1636185]), _1636185))], (43019 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636177), _1636179), 43017 ^ [_1636177, _1636179, _1636181, _1636183, _1636185]) = _1636183)]]], (48110 ^ _778495) ^ [_1748158, _1748160, _1748162, _1748164] : [-(c_Predicate_Oconversep(_1748158, _1748160, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1748158, tc_fun(_1748160, tc_HOL_Obool))), _1748162), _1748164)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1748160, tc_fun(_1748158, tc_HOL_Obool))), c_Predicate_Oconversep(_1748158, _1748160, _1748162)), c_Predicate_Oconversep(_1748158, _1748160, _1748164)))], (11833 ^ _778495) ^ [_984137, _984139, _984141] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _984137), _984139)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _984137), _984141)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984139), _984141))], (24641 ^ _778495) ^ [_1219695, _1219697, _1219699] : [_1219695 = 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), _1219695), _1219697)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1219695), _1219699)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28087 ^ _778495) ^ [_1279621, _1279623, _1279625] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1279621), _1279623))), -(c_Random_Ominus__shift(_1279625, _1279621, _1279623) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1279621), _1279623))], (28415 ^ _778495) ^ [_1291141, _1291143, _1291145, _1291147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool)), _1291145), _1291147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291141, tc_fun(_1291143, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1291141, tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_fun(_1291143, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1291143, tc_fun(tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_fun(_1291143, tc_HOL_Obool)), _1291141), c_COMBC(_1291143, tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1291143, tc_prod(_1291141, _1291143)), tc_fun(_1291143, tc_fun(tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_HOL_Obool)), _1291141), hAPP(c_COMBB(tc_prod(_1291141, _1291143), tc_fun(tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_HOL_Obool), _1291143), c_member(tc_prod(_1291141, _1291143)))), c_Product__Type_OPair(_1291141, _1291143)))), _1291145)), hAPP(hAPP(c_COMBC(_1291141, tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_fun(_1291143, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1291143, tc_fun(tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_fun(_1291143, tc_HOL_Obool)), _1291141), c_COMBC(_1291143, tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1291143, tc_prod(_1291141, _1291143)), tc_fun(_1291143, tc_fun(tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_HOL_Obool)), _1291141), hAPP(c_COMBB(tc_prod(_1291141, _1291143), tc_fun(tc_fun(tc_prod(_1291141, _1291143), tc_HOL_Obool), tc_HOL_Obool), _1291143), c_member(tc_prod(_1291141, _1291143)))), c_Product__Type_OPair(_1291141, _1291143)))), _1291147))))], (40732 ^ _778495) ^ [_1576681, _1576683, _1576685] : [c_Relation_Ototal__on(_1576681, _1576683, hAPP(c_Relation_Oconverse(_1576681, _1576681), _1576685)), -(c_Relation_Ototal__on(_1576681, _1576683, _1576685))], (25882 ^ _778495) ^ [_1240902, _1240904, _1240906] : [class_Rings_Olinordered__idom(_1240902), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240902), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1240902), hAPP(hAPP(c_Power_Opower__class_Opower(_1240902), _1240904), 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(_1240902), _1240906), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1240902)))], (45085 ^ _778495) ^ [_1682690, _1682692, _1682694, _1682696, _1682698, _1682700, _1682702] : [c_List_Olist__all2(_1682690, _1682692, _1682694, _1682696, hAPP(hAPP(c_List_Omap(_1682698, _1682692), _1682700), _1682702)), -(c_List_Olist__all2(_1682690, _1682698, hAPP(hAPP(c_COMBC(_1682690, tc_fun(_1682698, _1682692), tc_fun(_1682698, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682692, tc_HOL_Obool), tc_fun(tc_fun(_1682698, _1682692), tc_fun(_1682698, tc_HOL_Obool)), _1682690), c_COMBB(_1682692, tc_HOL_Obool, _1682698)), _1682694)), _1682700), _1682696, _1682702))], (2490 ^ _778495) ^ [_815149, _815151, _815153, _815155] : [-(c_Nitpick_Onorm__frac(_815155, _815151) = c_Nitpick_Onorm__frac(_815153, _815149)), _815155 = _815153, _815151 = _815149], (41886 ^ _778495) ^ [_1609270, _1609272, _1609274, _1609276] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609270), tc_List_Olist(_1609270))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609270), tc_List_Olist(_1609270)), _1609272), _1609274)), c_List_Olexord(_1609270, _1609276))), 41891 ^ _778495 : [(41894 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1609270), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609270)), _1609272)), _1609274) = _1609272)], (41892 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609270)), _1609272)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609270)), _1609274))))]], 41896 ^ _778495 : [(41901 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609270, _1609270)), hAPP(hAPP(c_Product__Type_OPair(_1609270, _1609270), hAPP(hAPP(c_List_Onth(_1609270), _1609272), 41895 ^ [_1609270, _1609272, _1609274, _1609276])), hAPP(hAPP(c_List_Onth(_1609270), _1609274), 41895 ^ [_1609270, _1609272, _1609274, _1609276]))), _1609276)))], (41899 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1609270), 41895 ^ [_1609270, _1609272, _1609274, _1609276]), _1609272) = hAPP(hAPP(c_List_Otake(_1609270), 41895 ^ [_1609270, _1609272, _1609274, _1609276]), _1609274))], (41897 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41895 ^ [_1609270, _1609272, _1609274, _1609276]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609270)), _1609272)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609270)), _1609274)))))]]], (14161 ^ _778495) ^ [_1029982, _1029984, _1029986, _1029988] : [class_Rings_Olinordered__ring__strict(_1029982), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029982), c_Groups_Ozero__class_Ozero(_1029982)), _1029984)), 14168 ^ _778495 : [(14175 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029982), _1029986), _1029988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029982), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029982), _1029984), _1029986)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029982), _1029984), _1029988))))], (14169 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029982), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029982), _1029984), _1029986)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029982), _1029984), _1029988))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029982), _1029986), _1029988)))]]], (37737 ^ _778495) ^ [_1496186, _1496188] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1496186)), -(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)), _1496186))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1496188))))) = 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)), _1496186))), 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, _1496188))))))], (44827 ^ _778495) ^ [_1676649, _1676651] : [hAPP(c_Code__Numeral_Onat__of, _1676649) = hAPP(c_Code__Numeral_Onat__of, _1676651), -(_1676649 = _1676651)], (42936 ^ _778495) ^ [_1634149, _1634151, _1634153] : [-(c_List_Olistset(_1634149, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1634149, tc_HOL_Obool)), _1634151), _1634153)) = c_List_Oset__Cons(_1634149, _1634151, c_List_Olistset(_1634149, _1634153)))], (43834 ^ _778495) ^ [_1655193, _1655195, _1655197] : [-(hAPP(hAPP(c_List_Odrop(_1655193), hAPP(c_Nat_OSuc, _1655195)), _1655197) = hAPP(hAPP(c_List_Odrop(_1655193), _1655195), hAPP(c_List_Otl(_1655193), _1655197)))], (39636 ^ _778495) ^ [_1550226, _1550228, _1550230, _1550232, _1550234, _1550236] : [c_Finite__Set_Ofolding(_1550226, _1550228, _1550230, _1550232), -(hAPP(c_Fun_Ocomp(_1550228, _1550228, _1550228, hAPP(_1550230, _1550234)), hAPP(_1550230, _1550236)) = hAPP(c_Fun_Ocomp(_1550228, _1550228, _1550228, hAPP(_1550230, _1550236)), hAPP(_1550230, _1550234)))], (46090 ^ _778495) ^ [_1705942] : [class_Orderings_Olinorder(_1705942), -(c_List_Olinorder__class_Osorted(_1705942, c_List_Olist_ONil(_1705942)))], (42836 ^ _778495) ^ [_1632114, _1632116, _1632118] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632114), tc_List_Olist(_1632114))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632114), tc_List_Olist(_1632114)), _1632116), c_List_Olist_ONil(_1632114))), c_List_Olex(_1632114, _1632118)))], (11686 ^ _778495) ^ [_981255, _981257] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _981255)), _981257) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _981255), _981257)))], (45235 ^ _778495) ^ [_1685901, _1685903, _1685905, _1685907, _1685909] : [-(c_List_Olist__all2(_1685901, _1685903, _1685905, _1685907, _1685909)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685901)), _1685907) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685903)), _1685909), 45241 ^ _778495 : [(45244 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1685905, hAPP(hAPP(c_List_Onth(_1685901), _1685907), 45240 ^ [_1685901, _1685903, _1685905, _1685907, _1685909])), hAPP(hAPP(c_List_Onth(_1685903), _1685909), 45240 ^ [_1685901, _1685903, _1685905, _1685907, _1685909])))], (45242 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45240 ^ [_1685901, _1685903, _1685905, _1685907, _1685909]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685901)), _1685907))))]]], (41541 ^ _778495) ^ [_1599365, _1599367, _1599369, _1599371] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599365), tc_List_Olist(_1599365))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599365), tc_List_Olist(_1599365)), _1599367), _1599369)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1599365), c_List_Olistrel1(_1599365, _1599371)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599365)), _1599367) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599365)), _1599369))], (38453 ^ _778495) ^ [_1520052, _1520054, _1520056, _1520058, _1520060, _1520062] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1520052, _1520054, _1520056), _1520058), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520054, _1520056), tc_HOL_Obool)), _1520060), _1520062)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520052, _1520056), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1520052, _1520054, _1520056), _1520058), _1520060)), hAPP(hAPP(c_Relation_Orel__comp(_1520052, _1520054, _1520056), _1520058), _1520062)))], (34247 ^ _778495) ^ [_1417131, _1417133] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1417131), _1417133))))], (45925 ^ _778495) ^ [_1702563, _1702565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702563), _1702565)), -(c_List_Oupt(_1702563, _1702565) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702563), c_List_Oupt(hAPP(c_Nat_OSuc, _1702563), _1702565)))], (35080 ^ _778495) ^ [_1434222, _1434224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1434222)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1434222, _1434224)))], (40439 ^ _778495) ^ [_1569927, _1569929] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1569927, _1569927, _1569927), _1569929), c_Transitive__Closure_Ortrancl(_1569927, _1569929)) = hAPP(hAPP(c_Relation_Orel__comp(_1569927, _1569927, _1569927), c_Transitive__Closure_Ortrancl(_1569927, _1569929)), _1569929))], (36394 ^ _778495) ^ [_1463315, _1463317, _1463319, _1463321, _1463323] : [c_Fun_Oinj__on(_1463315, _1463317, _1463319, _1463321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1463315, tc_HOL_Obool)), _1463323), _1463321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1463317, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1463315, _1463317, _1463319), _1463323)), hAPP(c_Set_Oimage(_1463315, _1463317, _1463319), _1463321))))], (12368 ^ _778495) ^ [_996056, _996058, _996060, _996062, _996064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996056), _996058)), 12371 ^ _778495 : [(12378 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996062), 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), _996058), _996056)), _996060)), _996064))), -(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), _996056), _996060)), _996062)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996058), _996060)), _996064))))], (12372 ^ _778495) ^ [] : [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), _996056), _996060)), _996062)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996058), _996060)), _996064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996062), 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), _996058), _996056)), _996060)), _996064))))]]], (22614 ^ _778495) ^ [_1182758, _1182760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1182758)), c_Int_OBit0(_1182760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182758), _1182760)))], (30825 ^ _778495) ^ [_1341211, _1341213, _1341215] : [class_Orderings_Olinorder(_1341211), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341211), _1341213), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341211), _1341213), _1341215)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341211), _1341213), _1341215))], (4488 ^ _778495) ^ [_846704, _846706] : [_846706 = _846704, -(c_Nat_Osize__class_Osize(_846706) = c_Nat_Osize__class_Osize(_846704))], (9358 ^ _778495) ^ [_937223, _937225, _937227, _937229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937223, tc_HOL_Obool)), _937225), _937227)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937223, tc_HOL_Obool)), _937225), _937229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937223, tc_HOL_Obool)), _937225), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937223, tc_HOL_Obool)), _937227), _937229))))], (38351 ^ _778495) ^ [_1517333, _1517335] : [-(c_Fun_Oinj__on(_1517333, _1517333, c_Fun_Oid(_1517333), _1517335))], (49545 ^ _778495) ^ [_1779457, _1779459] : [c_Relation_Osym(_1779457, hAPP(c_Set_OCollect(tc_prod(_1779457, _1779457)), hAPP(c_Product__Type_Oprod_Oprod__case(_1779457, _1779457, tc_HOL_Obool), _1779459))), -(c_Predicate_Osymp(_1779457, _1779459))], (24141 ^ _778495) ^ [_1210445, _1210447, _1210449] : [-(hBOOL(hAPP(_1210445, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1210447), _1210449)))), 24144 ^ _778495 : [(24147 ^ _778495) ^ [] : [hBOOL(hAPP(_1210445, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24145 ^ _778495) ^ [] : [-(_1210449 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 24150 ^ _778495 : [(24151 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210449)))], (24157 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24153 ^ [_1210445, _1210447, _1210449]), _1210449)))], (24161 ^ _778495) ^ [] : [hBOOL(hAPP(_1210445, 24152 ^ [_1210445, _1210447, _1210449]))], (24159 ^ _778495) ^ [] : [-(_1210447 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1210449), 24152 ^ [_1210445, _1210447, _1210449])), 24153 ^ [_1210445, _1210447, _1210449]))], (24155 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24153 ^ [_1210445, _1210447, _1210449])))]], 24162 ^ _778495 : [(24163 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210449), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24169 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24165 ^ [_1210445, _1210447, _1210449]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24173 ^ _778495) ^ [] : [hBOOL(hAPP(_1210445, 24164 ^ [_1210445, _1210447, _1210449]))], (24171 ^ _778495) ^ [] : [-(_1210447 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1210449), 24164 ^ [_1210445, _1210447, _1210449])), 24165 ^ [_1210445, _1210447, _1210449]))], (24167 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210449), 24165 ^ [_1210445, _1210447, _1210449])))]]], (28351 ^ _778495) ^ [_1288742, _1288744, _1288746, _1288748, _1288750] : [class_Rings_Osemiring__0(_1288742), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288742), _1288744), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1288746, _1288742), _1288748), _1288750)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1288746, _1288742), hAPP(hAPP(c_COMBB(_1288742, _1288742, _1288746), hAPP(c_Groups_Otimes__class_Otimes(_1288742), _1288744)), _1288748)), _1288750))], (47048 ^ _778495) ^ [_1724735, _1724737, _1724739, _1724741, _1724743] : [hBOOL(hAPP(hAPP(c_member(_1724735), _1724737), hAPP(c_List_Oset(_1724735), _1724739))), -(hBOOL(hAPP(_1724741, _1724737))), -(c_List_OdropWhile(_1724735, _1724741, hAPP(hAPP(c_List_Oappend(_1724735), _1724739), _1724743)) = hAPP(hAPP(c_List_Oappend(_1724735), c_List_OdropWhile(_1724735, _1724741, _1724739)), _1724743))], (4894 ^ _778495) ^ [_853143, _853145] : [_853145 = _853143, -(c_Set_OCollect(_853145) = c_Set_OCollect(_853143))], (29342 ^ _778495) ^ [_1312140, _1312142] : [-(c_Divides_Opdivmod(_1312140, _1312142) = 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), _1312140)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1312142))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1312140), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1312142))))], (35326 ^ _778495) ^ [_1438396, _1438398, _1438400, _1438402] : [class_Orderings_Olinorder(_1438396), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438396, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1438396, _1438398, _1438400)), hAPP(c_SetInterval_Oord__class_OatLeast(_1438396), _1438402)) = c_SetInterval_Oord__class_OatLeastAtMost(_1438396, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1438396), _1438398), _1438402), _1438400))], (36033 ^ _778495) ^ [_1454937, _1454939, _1454941, _1454943, _1454945, _1454947, _1454949, _1454951, _1454953, _1454955] : [c_Equiv__Relations_Ocongruent2(_1454937, _1454939, _1454941, _1454943, _1454945, _1454947), hBOOL(hAPP(hAPP(c_member(tc_prod(_1454937, _1454937)), hAPP(hAPP(c_Product__Type_OPair(_1454937, _1454937), _1454949), _1454951)), _1454943)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1454939, _1454939)), hAPP(hAPP(c_Product__Type_OPair(_1454939, _1454939), _1454953), _1454955)), _1454945)), -(hAPP(hAPP(_1454947, _1454949), _1454953) = hAPP(hAPP(_1454947, _1454951), _1454955))], (12052 ^ _778495) ^ [_989180, _989182, _989184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989180), _989182)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989184), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989182), _989180)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989184), _989182)), _989180))], (5757 ^ _778495) ^ [_869697, _869699, _869701] : [c_Hoare__Mirabelle_Ohoare__derivs(_869697, _869699, _869701), -(c_Hoare__Mirabelle_Ohoare__valids(_869697, _869699, _869701))], (27931 ^ _778495) ^ [_1276698, _1276700, _1276702] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1276698, tc_HOL_Obool)), _1276700), _1276702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276698, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1276698, tc_HOL_Obool), _1276702)), _1276700)))], (19802 ^ _778495) ^ [_1134231] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134231) = _1134231)], (35648 ^ _778495) ^ [_1446163, _1446165, _1446167] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446163, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446163), _1446165), _1446167), -(_1446165 = c_Orderings_Obot__class_Obot(tc_fun(_1446163, tc_HOL_Obool)))], (14883 ^ _778495) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5626 ^ _778495) ^ [_864563, _864565] : [_864565 = _864563, -(c_Orderings_Obot__class_Obot(_864565) = c_Orderings_Obot__class_Obot(_864563))], (52397 ^ _778495) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (28895 ^ _778495) ^ [_1303039, _1303041] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303039), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 28898 ^ _778495 : [(28907 ^ _778495) ^ [] : [-(c_Nitpick_Onorm__frac(_1303041, _1303039) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1303041), _1303039)), 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), _1303041))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1303039)))), -(_1303041 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1303039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28899 ^ _778495) ^ [] : [28900 ^ _778495 : [(28903 ^ _778495) ^ [] : [_1303039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (28901 ^ _778495) ^ [] : [_1303041 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1303041, _1303039) = 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)))]]], (42872 ^ _778495) ^ [_1632805, _1632807, _1632809, _1632811] : [-(_1632805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1632807), _1632805), hAPP(hAPP(c_List_Olist_OCons(_1632807), _1632809), _1632811)) = hAPP(hAPP(c_List_Olist_OCons(_1632807), _1632809), hAPP(hAPP(c_List_Otake(_1632807), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1632805), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1632811)))], (33181 ^ _778495) ^ [_1391147, _1391149, _1391151, _1391153] : [c_Orderings_Obot__class_Obot(tc_fun(_1391147, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391149, tc_fun(_1391147, tc_HOL_Obool)), _1391151), _1391153), 33184 ^ _778495 : [(33185 ^ _778495) ^ [_1391263] : [hBOOL(hAPP(hAPP(c_member(_1391149), _1391263), _1391151)), -(hAPP(_1391153, _1391263) = c_Orderings_Obot__class_Obot(tc_fun(_1391147, tc_HOL_Obool)))]]], (39059 ^ _778495) ^ [_1536005] : [-(c_Wellfounded_OwfP(_1536005, hAPP(c_COMBK(tc_fun(_1536005, tc_HOL_Obool), _1536005), hAPP(c_COMBK(tc_HOL_Obool, _1536005), c_fFalse))))], (1888 ^ _778495) ^ [_805123, _805125] : [-(class_Groups_Ominus(_805123)), _805125 = _805123, class_Groups_Ominus(_805125)], (19162 ^ _778495) ^ [_1122941, _1122943, _1122945] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122941), _1122943)), _1122945) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122943), _1122945)))], (49461 ^ _778495) ^ [_1778188, _1778190] : [hAPP(c_Relation_Oconverse(_1778188, _1778188), _1778190) = _1778190, -(c_Relation_Osym(_1778188, _1778190))], (25800 ^ _778495) ^ [_1239352, _1239354, _1239356] : [class_Rings_Ocomm__semiring__1(_1239352), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1239352), _1239354), 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)))), _1239356)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239352), hAPP(hAPP(c_Power_Opower__class_Opower(_1239352), _1239354), _1239356)), hAPP(hAPP(c_Power_Opower__class_Opower(_1239352), _1239354), _1239356)))], (8168 ^ _778495) ^ [_913142, _913144, _913146] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913142), _913146)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_913142), hAPP(hAPP(c_Set_Oinsert(_913142), _913144), _913146))))], (20436 ^ _778495) ^ [_1145398, _1145400] : [class_Int_Onumber__ring(_1145398), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1145398), _1145400), hAPP(c_Int_Onumber__class_Onumber__of(_1145398), c_Int_OPls)) = _1145400)], (27601 ^ _778495) ^ [_1271169, _1271171] : [class_Orderings_Otop(_1271169), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271169), _1271171), c_Orderings_Otop__class_Otop(_1271169))))], (20424 ^ _778495) ^ [_1145210] : [class_Int_Onumber__ring(_1145210), -(hAPP(c_Int_Onumber__class_Onumber__of(_1145210), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1145210))], (48322 ^ _778495) ^ [_1752772, _1752774, _1752776] : [_1752774 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1752772, _1752774, _1752776) = c_List_Olist_ONil(_1752772))], (40397 ^ _778495) ^ [_1568883, _1568885, _1568887] : [-(c_Transitive__Closure_Ortrancl(_1568883, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568883, _1568883), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568883, _1568885)), c_Transitive__Closure_Ortrancl(_1568883, _1568887))) = c_Transitive__Closure_Ortrancl(_1568883, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568883, _1568883), tc_HOL_Obool)), _1568885), _1568887)))], (38749 ^ _778495) ^ [_1528528, _1528530, _1528532, _1528534] : [c_Wellfounded_Owf(_1528528, _1528530), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528528, _1528528)), hAPP(hAPP(c_Product__Type_OPair(_1528528, _1528528), _1528532), _1528534)), _1528530)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528528, _1528528)), hAPP(hAPP(c_Product__Type_OPair(_1528528, _1528528), _1528534), _1528532)), _1528530))], (800 ^ _778495) ^ [_790593, _790595, _790597, _790599] : [-(c_Predicate_Oreflp(_790597, _790593)), c_Predicate_Oreflp(_790599, _790595), _790599 = _790597, _790595 = _790593], (33311 ^ _778495) ^ [_1395660, _1395662, _1395664, _1395666, _1395668, _1395670] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1395662, _1395664)), hAPP(hAPP(c_Product__Type_OPair(_1395662, _1395664), _1395668), _1395670)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395660, tc_fun(tc_prod(_1395662, _1395664), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1395660, tc_HOL_Obool))), _1395666))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395660, tc_fun(_1395662, tc_fun(_1395664, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1395660, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1395662, _1395664), tc_HOL_Obool), tc_fun(_1395662, tc_fun(_1395664, tc_HOL_Obool)), _1395660), hAPP(c_COMBC(_1395662, tc_fun(tc_prod(_1395662, _1395664), tc_HOL_Obool), tc_fun(_1395664, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395664, tc_fun(tc_fun(tc_prod(_1395662, _1395664), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1395662, _1395664), tc_HOL_Obool), tc_fun(_1395664, tc_HOL_Obool)), _1395662), c_COMBC(_1395664, tc_fun(tc_prod(_1395662, _1395664), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395664, tc_prod(_1395662, _1395664)), tc_fun(_1395664, tc_fun(tc_fun(tc_prod(_1395662, _1395664), tc_HOL_Obool), tc_HOL_Obool)), _1395662), hAPP(c_COMBB(tc_prod(_1395662, _1395664), tc_fun(tc_fun(tc_prod(_1395662, _1395664), tc_HOL_Obool), tc_HOL_Obool), _1395664), c_member(tc_prod(_1395662, _1395664)))), c_Product__Type_OPair(_1395662, _1395664))))), _1395666)), _1395668), _1395670)))], (6670 ^ _778495) ^ [_887585, _887587, _887589] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887585, tc_HOL_Obool)), _887587), _887589) = c_Orderings_Obot__class_Obot(tc_fun(_887585, tc_HOL_Obool)), 6673 ^ _778495 : [(6676 ^ _778495) ^ [] : [-(_887589 = c_Orderings_Obot__class_Obot(tc_fun(_887585, tc_HOL_Obool)))], (6674 ^ _778495) ^ [] : [-(_887587 = c_Orderings_Obot__class_Obot(tc_fun(_887585, tc_HOL_Obool)))]]], (48076 ^ _778495) ^ [_1747265, _1747267, _1747269, _1747271, _1747273] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1747265), _1747267), _1747269), _1747271), _1747273) = c_New__DSequence_Oneg__single(_1747265, _1747267))], (14603 ^ _778495) ^ [_1037834, _1037836] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037834), _1037836) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 14604 ^ _778495 : [(14611 ^ _778495) ^ [] : [_1037834 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1037836 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14605 ^ _778495) ^ [] : [_1037834 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1037836 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (51993 ^ _778495) ^ [_1828059, _1828061, _1828063, _1828065] : [class_Rings_Oidom(_1828059), 51996 ^ _778495 : [(51997 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828059), _1828061), _1828063)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828059), _1828061), _1828065))), -(_1828061 = c_Groups_Ozero__class_Ozero(_1828059)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828059), _1828063), _1828065)))], (52007 ^ _778495) ^ [] : [52008 ^ _778495 : [(52011 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828059), _1828063), _1828065))], (52009 ^ _778495) ^ [] : [_1828061 = c_Groups_Ozero__class_Ozero(_1828059)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828059), _1828061), _1828063)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828059), _1828061), _1828065))))]]], (52199 ^ _778495) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (44440 ^ _778495) ^ [_1668184, _1668186, _1668188, _1668190, _1668192] : [class_Groups_Oab__group__add(_1668184), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1668184), hAPP(hAPP(c_List_Omap(_1668186, _1668184), hAPP(hAPP(c_COMBS(_1668186, _1668184, _1668184), hAPP(hAPP(c_COMBB(_1668184, tc_fun(_1668184, _1668184), _1668186), c_Groups_Ominus__class_Ominus(_1668184)), _1668188)), _1668190)), _1668192)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1668184), hAPP(c_List_Omonoid__add__class_Olistsum(_1668184), hAPP(hAPP(c_List_Omap(_1668186, _1668184), _1668188), _1668192))), hAPP(c_List_Omonoid__add__class_Olistsum(_1668184), hAPP(hAPP(c_List_Omap(_1668186, _1668184), _1668190), _1668192))))], (12074 ^ _778495) ^ [_989606, _989608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989606), _989608)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989608), _989606)), _989606) = _989608)], (29017 ^ _778495) ^ [_1305214, _1305216, _1305218, _1305220, _1305222, _1305224] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305214, tc_fun(_1305216, tc_HOL_Obool))), _1305218), _1305220), _1305222), _1305224)), -(hBOOL(hAPP(hAPP(_1305218, _1305222), _1305224)))], (28053 ^ _778495) ^ [_1279101, _1279103] : [28054 ^ _778495 : [(28057 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1279103), _1279101))], (28055 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1279101), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1279101, _1279103) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (34204 ^ _778495) ^ [_1415953, _1415955, _1415957, _1415959] : [class_Orderings_Olinorder(_1415953), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1415953), _1415955), _1415957)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415953), _1415957), _1415959)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415953, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1415953, _1415955, _1415957)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1415953, _1415957, _1415959)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1415953, _1415955), _1415959))], (8194 ^ _778495) ^ [_913611, _913613, _913615] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913611), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913611, tc_HOL_Obool)), _913613), _913615))), 8197 ^ _778495 : [(8200 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_913611), _913615)))], (8198 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_913611), _913613)))]]], (6798 ^ _778495) ^ [_889894, _889896, _889898, _889900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889894, tc_HOL_Obool)), _889896), _889898)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889894, tc_HOL_Obool)), _889896), hAPP(hAPP(c_Set_Oinsert(_889894), _889900), _889898))))], (46746 ^ _778495) ^ [_1718323, _1718325] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1718323), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1718323))), c_List_Otranspose(_1718323, _1718325)))))], (20230 ^ _778495) ^ [_1141899, _1141901, _1141903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141899), _1141901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1141903)), -(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), _1141903)), _1141899)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1141903)), _1141901))))], (48682 ^ _778495) ^ [_1760788, _1760790, _1760792] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760788) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1760788, _1760790, _1760792)], (42710 ^ _778495) ^ [_1629726, _1629728] : [-(c_List_Olistrelp(_1629726, _1629728, c_List_Olist_ONil(_1629726), c_List_Olist_ONil(_1629726)))], (6116 ^ _778495) ^ [_876880, _876882, _876884, _876886] : [6117 ^ _778495 : [(6118 ^ _778495) ^ [_876990] : [hBOOL(hAPP(hAPP(c_member(_876880), _876990), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876880, tc_HOL_Obool)), _876882), _876884))), hBOOL(hAPP(_876886, _876990))]], 6126 ^ _778495 : [(6129 ^ _778495) ^ [] : [-(hBOOL(hAPP(_876886, 6125 ^ [_876880, _876882, _876884, _876886])))], (6127 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_876880), 6125 ^ [_876880, _876882, _876884, _876886]), _876882)))]], 6131 ^ _778495 : [(6134 ^ _778495) ^ [] : [-(hBOOL(hAPP(_876886, 6130 ^ [_876880, _876882, _876884, _876886])))], (6132 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_876880), 6130 ^ [_876880, _876882, _876884, _876886]), _876884)))]]], (33824 ^ _778495) ^ [_1408218] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408218), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (50801 ^ _778495) ^ [_1807174, _1807176] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807174), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807176))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807176), _1807174)))], (21662 ^ _778495) ^ [_1166370] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1166370)) = _1166370)], (22772 ^ _778495) ^ [_1185541, _1185543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185541), _1185543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1185541)), c_Int_OBit1(_1185543))))], (27969 ^ _778495) ^ [_1277438, _1277440] : [class_Complete__Lattice_Ocomplete__lattice(_1277438), -(c_Complete__Lattice_OInf__class_OInf(_1277438, hAPP(hAPP(c_Set_Oinsert(_1277438), _1277440), c_Orderings_Obot__class_Obot(tc_fun(_1277438, tc_HOL_Obool)))) = _1277440)], (46110 ^ _778495) ^ [_1706231, _1706233, _1706235] : [class_Orderings_Olinorder(_1706231), c_List_Olinorder__class_Osorted(_1706231, _1706233), -(c_List_Olinorder__class_Osorted(_1706231, c_List_Olinorder__class_Oinsort__insert__key(_1706231, _1706231, c_COMBI(_1706231), _1706235, _1706233)))], (11286 ^ _778495) ^ [_973295, _973297] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973295), _973297) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973297), _973295))], (28733 ^ _778495) ^ [_1299486, _1299488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1299486)), hAPP(c_Nat_OSuc, _1299488))), -(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(_1299486))), 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)), _1299488)))))], (24531 ^ _778495) ^ [_1217688, _1217690] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217688), _1217690)), _1217688)))], (31005 ^ _778495) ^ [_1344868, _1344870, _1344872] : [class_Groups_Olinordered__ab__group__add(_1344868), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1344868), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1344868), _1344870), _1344872)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344868), hAPP(c_Groups_Ouminus__class_Ouminus(_1344868), _1344870)), hAPP(c_Groups_Ouminus__class_Ouminus(_1344868), _1344872)))], (52419 ^ _778495) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (13883 ^ _778495) ^ [_1025022, _1025024, _1025026] : [class_Rings_Oordered__cancel__semiring(_1025022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025022), _1025024), c_Groups_Ozero__class_Ozero(_1025022))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025022), c_Groups_Ozero__class_Ozero(_1025022)), _1025026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025022), _1025024), _1025026)), c_Groups_Ozero__class_Ozero(_1025022))))], (46025 ^ _778495) ^ [_1704310, _1704312, _1704314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704310), _1704312)), _1704314)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1704310, _1704314)), _1704312) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704310), _1704312))], (26890 ^ _778495) ^ [_1259085, _1259087] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1259085), _1259087) = c_Groups_Oone__class_Oone(tc_Int_Oint), 26895 ^ _778495 : [(26898 ^ _778495) ^ [] : [-(_1259087 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (26896 ^ _778495) ^ [] : [-(_1259085 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 26899 ^ _778495 : [(26902 ^ _778495) ^ [] : [-(_1259087 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (26900 ^ _778495) ^ [] : [-(_1259085 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (44323 ^ _778495) ^ [_1664827, _1664829] : [-(_1664827 = c_List_Olist_ONil(_1664829)), -(c_Random_Oselect__weight(_1664829, hAPP(hAPP(c_List_Omap(_1664829, tc_prod(tc_Code__Numeral_Ocode__numeral, _1664829)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1664829), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1664827)) = c_Random_Oselect(_1664829, _1664827))], (38649 ^ _778495) ^ [_1526824, _1526826, _1526828, _1526830] : [c_Wellfounded_Owf(_1526824, _1526826), -(c_Wellfounded_Owf(_1526828, hAPP(hAPP(c_Relation_Oinv__image(_1526824, _1526828), _1526826), _1526830)))], (30447 ^ _778495) ^ [_1333701, _1333703, _1333705, _1333707, _1333709] : [hBOOL(hAPP(hAPP(c_member(_1333701), _1333703), c_SetInterval_Oord_OgreaterThanLessThan(_1333701, _1333705, _1333707, _1333709))), 30450 ^ _778495 : [(30453 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1333705, _1333703), _1333709)))], (30451 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1333705, _1333707), _1333703)))]]], (29422 ^ _778495) ^ [_1313617] : [class_Orderings_Olinorder(_1313617), -(c_Orderings_Oord_Omax(_1313617, hAPP(c_COMBC(_1313617, _1313617, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1313617))) = c_Orderings_Oord__class_Omin(_1313617))], (37382 ^ _778495) ^ [_1485862, _1485864, _1485866] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1485862, _1485864), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1485862, _1485864), c_Orderings_Otop__class_Otop(tc_fun(_1485862, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1485864, tc_HOL_Obool), _1485862), _1485866))) = hAPP(hAPP(c_Product__Type_OSigma(_1485862, _1485864), c_Orderings_Otop__class_Otop(tc_fun(_1485862, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1485864, tc_HOL_Obool), _1485862), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1485864, tc_HOL_Obool)), _1485866))))], (3080 ^ _778495) ^ [_824366, _824368, _824370, _824372] : [-(c_Nat_Ocompow(_824372, _824368) = c_Nat_Ocompow(_824370, _824366)), _824372 = _824370, _824368 = _824366], (41403 ^ _778495) ^ [_1594816, _1594818, _1594820, _1594822, _1594824, _1594826] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594816), tc_List_Olist(_1594816))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594816), tc_List_Olist(_1594816)), hAPP(hAPP(c_List_Olist_OCons(_1594816), _1594818), _1594820)), hAPP(hAPP(c_List_Olist_OCons(_1594816), _1594822), _1594824))), c_List_Olex(_1594816, _1594826))), 41408 ^ _778495 : [(41411 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594816)), _1594820) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594816)), _1594824))], (41409 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594816, _1594816)), hAPP(hAPP(c_Product__Type_OPair(_1594816, _1594816), _1594818), _1594822)), _1594826)))]], 41412 ^ _778495 : [(41415 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594816), tc_List_Olist(_1594816))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594816), tc_List_Olist(_1594816)), _1594820), _1594824)), c_List_Olex(_1594816, _1594826))))], (41413 ^ _778495) ^ [] : [-(_1594818 = _1594822)]]], (46786 ^ _778495) ^ [_1719342, _1719344, _1719346] : [class_Orderings_Olinorder(_1719342), c_List_Olinorder__class_Osorted(_1719342, hAPP(c_List_Orev(_1719342), _1719344)), 46793 ^ _778495 : [(46800 ^ _778495) ^ [] : [-(_1719344 = c_List_Olist_ONil(_1719342)), -(c_List_Ofoldr(_1719342, _1719342, c_Orderings_Oord__class_Omax(_1719342), _1719344, _1719346) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1719342), hAPP(hAPP(c_List_Onth(_1719342), _1719344), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1719346))], (46794 ^ _778495) ^ [] : [_1719344 = c_List_Olist_ONil(_1719342), -(c_List_Ofoldr(_1719342, _1719342, c_Orderings_Oord__class_Omax(_1719342), _1719344, _1719346) = _1719346)]]], (37552 ^ _778495) ^ [_1490974, _1490976, _1490978] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490974), _1490976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1490974, _1490974), tc_HOL_Obool)), _1490978), hAPP(hAPP(c_Product__Type_OSigma(_1490974, _1490974), _1490976), hAPP(c_COMBK(tc_fun(_1490974, tc_HOL_Obool), _1490974), _1490976)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1490974, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490974), _1490976), _1490978))))], (48527 ^ _778495) ^ [_1757082, _1757084, _1757086, _1757088] : [48528 ^ _778495 : [(48531 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757082), _1757086), _1757088))], (48529 ^ _778495) ^ [] : [_1757084 = _1757088]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1757082), hAPP(hAPP(c_List_Olist_OCons(_1757082), _1757084), _1757086)), _1757088)))], (5476 ^ _778495) ^ [_862326, _862328] : [_862328 = _862326, -(c_Finite__Set_Ofinite(_862328) = c_Finite__Set_Ofinite(_862326))], (21766 ^ _778495) ^ [_1168031, _1168033, _1168035] : [class_Groups_Oordered__ab__group__add(_1168031), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168031), _1168033), _1168035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168031), hAPP(c_Groups_Ouminus__class_Ouminus(_1168031), _1168035)), hAPP(c_Groups_Ouminus__class_Ouminus(_1168031), _1168033))))], (27341 ^ _778495) ^ [_1266558, _1266560] : [class_Rings_Olinordered__idom(_1266558), 27344 ^ _778495 : [(27351 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266558), c_Groups_Ozero__class_Ozero(_1266558)), _1266560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266558), c_Groups_Ozero__class_Ozero(_1266558)), c_Groups_Osgn__class_Osgn(_1266558, _1266560))))], (27345 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266558), c_Groups_Ozero__class_Ozero(_1266558)), c_Groups_Osgn__class_Osgn(_1266558, _1266560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266558), c_Groups_Ozero__class_Ozero(_1266558)), _1266560)))]]], (29916 ^ _778495) ^ [_1322852, _1322854] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1322852, _1322854) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1322852, _1322854)))], (12046 ^ _778495) ^ [_989069, _989071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989069), _989071)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989069), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989071), _989069)) = _989071)], (48366 ^ _778495) ^ [_1753589, _1753591, _1753593] : [-(_1753589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753591), c_List_Oreplicate(_1753591, _1753589, _1753593)) = hAPP(hAPP(c_Set_Oinsert(_1753591), _1753593), c_Orderings_Obot__class_Obot(tc_fun(_1753591, tc_HOL_Obool))))], (37814 ^ _778495) ^ [_1498067, _1498069] : [-(hBOOL(hAPP(_1498069, 37815 ^ [_1498067, _1498069]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1498067, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1498067), _1498069))], (19292 ^ _778495) ^ [_1125195, _1125197] : [class_Orderings_Olinorder(_1125195), -(c_Big__Operators_Olattice_OInf__fin(_1125195, c_Orderings_Oord__class_Omin(_1125195), hAPP(hAPP(c_Set_Oinsert(_1125195), _1125197), c_Orderings_Obot__class_Obot(tc_fun(_1125195, tc_HOL_Obool)))) = _1125197)], (29655 ^ _778495) ^ [_1318228, _1318230, _1318232] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1318228, _1318228), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1318230), _1318232))), -(_1318228 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1318232 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47582 ^ _778495) ^ [_1737269, _1737271] : [class_Enum_Oenum(_1737269), 47585 ^ _778495 : [(47592 ^ _778495) ^ [] : [hBOOL(hAPP(_1737271, 47593 ^ [_1737269, _1737271])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737269), _1737271)))], (47586 ^ _778495) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737269), _1737271)), 47589 ^ _778495 : [(47590 ^ _778495) ^ [_1737395] : [-(hBOOL(hAPP(_1737271, _1737395)))]]]]], (3628 ^ _778495) ^ [_832926, _832928, _832930, _832932] : [-(c_List_Obutlast(_832932, _832928) = c_List_Obutlast(_832930, _832926)), _832932 = _832930, _832928 = _832926], (30059 ^ _778495) ^ [_1325839, _1325841] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1325839, _1325841) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1325839, _1325841)))], (44887 ^ _778495) ^ [_1677675, _1677677] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1677675), _1677677) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677675)), hAPP(c_Code__Numeral_Onat__of, _1677677))))], (21792 ^ _778495) ^ [_1168493, _1168495, _1168497] : [class_Groups_Oordered__ab__group__add(_1168493), 21795 ^ _778495 : [(21802 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168493), hAPP(c_Groups_Ouminus__class_Ouminus(_1168493), _1168497)), _1168495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168493), hAPP(c_Groups_Ouminus__class_Ouminus(_1168493), _1168495)), _1168497)))], (21796 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168493), hAPP(c_Groups_Ouminus__class_Ouminus(_1168493), _1168495)), _1168497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168493), hAPP(c_Groups_Ouminus__class_Ouminus(_1168493), _1168497)), _1168495)))]]], (49587 ^ _778495) ^ [_1780099, _1780101] : [c_Equiv__Relations_Opart__equivp(_1780099, _1780101), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1780099, tc_HOL_Obool)), 49590 ^ [_1780099, _1780101]), hAPP(hAPP(c_COMBB(tc_fun(_1780099, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1780099, tc_HOL_Obool)), c_HOL_OEx(_1780099)), hAPP(hAPP(c_COMBB(tc_fun(_1780099, tc_HOL_Obool), tc_fun(_1780099, tc_HOL_Obool), tc_fun(_1780099, tc_HOL_Obool)), hAPP(c_COMBS(_1780099, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1780099), c_fconj), hAPP(hAPP(c_COMBS(_1780099, _1780099, tc_HOL_Obool), _1780101), c_COMBI(_1780099))))), hAPP(hAPP(c_COMBC(tc_fun(_1780099, tc_HOL_Obool), tc_fun(_1780099, tc_fun(_1780099, tc_HOL_Obool)), tc_fun(_1780099, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1780099, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1780099, tc_fun(_1780099, tc_HOL_Obool)), tc_fun(_1780099, tc_HOL_Obool)), tc_fun(_1780099, tc_HOL_Obool)), c_COMBB(tc_fun(_1780099, tc_HOL_Obool), tc_HOL_Obool, _1780099)), c_fequal)), _1780101))))))], (10565 ^ _778495) ^ [_960863, _960865, _960867] : [10566 ^ _778495 : [(10569 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_960867, _960865), _960863))], (10567 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960863), _960865)))]], 10572 ^ _778495 : [(10575 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_960867, _960865), _960863))], (10573 ^ _778495) ^ [] : [-(_960863 = _960865)]], 10578 ^ _778495 : [(10581 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_960867, _960865), _960863))], (10579 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960865), _960863)))]], -(hBOOL(hAPP(hAPP(_960867, _960865), _960863)))], (27457 ^ _778495) ^ [_1268278, _1268280] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1268278), _1268280) = 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), _1268278)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1268280)))))], (34353 ^ _778495) ^ [_1419750, _1419752, _1419754, _1419756, _1419758] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1419750, tc_HOL_Obool)), _1419752), hAPP(c_Set_Oimage(_1419754, _1419750, _1419756), _1419758)))), 34354 ^ _778495 : [(34355 ^ _778495) ^ [_1419830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1419754, tc_HOL_Obool)), _1419830), _1419758)), _1419752 = hAPP(c_Set_Oimage(_1419754, _1419750, _1419756), _1419830)]]], (8238 ^ _778495) ^ [_914396, _914398, _914400, _914402] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_914396, _914398, _914400, _914402, c_Orderings_Obot__class_Obot(tc_fun(_914396, tc_HOL_Obool))), _914402)))], (9893 ^ _778495) ^ [_948346, _948348, _948350, _948352, _948354, _948356, _948358, _948360] : [c_Finite__Set_Ofolding__image__simple(_948346, _948348, _948350, _948352, _948354, _948356), hBOOL(hAPP(c_Finite__Set_Ofinite(_948348), _948358)), hBOOL(hAPP(c_Finite__Set_Ofinite(_948348), _948360)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_948348, tc_HOL_Obool)), _948358), _948360) = c_Orderings_Obot__class_Obot(tc_fun(_948348, tc_HOL_Obool)), -(hAPP(_948356, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948348, tc_HOL_Obool)), _948358), _948360)) = hAPP(hAPP(_948350, hAPP(_948356, _948358)), hAPP(_948356, _948360)))], (30801 ^ _778495) ^ [_1340639, _1340641, _1340643, _1340645] : [class_Orderings_Olinorder(_1340639), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340639), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340639), _1340641), _1340643)), _1340645) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340639), _1340641), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340639), _1340643), _1340645)))], (28805 ^ _778495) ^ [_1301311, _1301313] : [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), _1301311))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1301313), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1301311))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1301313), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1301311))), 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), _1301313))), c_COMBI(tc_Int_Oint))))], (44889 ^ _778495) ^ [_1677721, _1677723] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1677721), _1677723) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677721)), hAPP(c_Code__Numeral_Onat__of, _1677723))))], (42219 ^ _778495) ^ [_1619274, _1619276] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619274, _1619276)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1619274, _1619276))], (35943 ^ _778495) ^ [_1452898, _1452900] : [c_Equiv__Relations_Oequiv(_1452898, c_Orderings_Otop__class_Otop(tc_fun(_1452898, tc_HOL_Obool)), _1452900), -(c_Equiv__Relations_Oequivp(_1452898, hAPP(hAPP(c_COMBC(_1452898, tc_fun(tc_prod(_1452898, _1452898), tc_HOL_Obool), tc_fun(_1452898, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452898, tc_fun(tc_fun(tc_prod(_1452898, _1452898), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452898, _1452898), tc_HOL_Obool), tc_fun(_1452898, tc_HOL_Obool)), _1452898), c_COMBC(_1452898, tc_fun(tc_prod(_1452898, _1452898), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452898, tc_prod(_1452898, _1452898)), tc_fun(_1452898, tc_fun(tc_fun(tc_prod(_1452898, _1452898), tc_HOL_Obool), tc_HOL_Obool)), _1452898), hAPP(c_COMBB(tc_prod(_1452898, _1452898), tc_fun(tc_fun(tc_prod(_1452898, _1452898), tc_HOL_Obool), tc_HOL_Obool), _1452898), c_member(tc_prod(_1452898, _1452898)))), c_Product__Type_OPair(_1452898, _1452898)))), _1452900)))], (13426 ^ _778495) ^ [_1016994, _1016996, _1016998] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016994), _1016996) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016998), _1016996), -(_1016994 = _1016998), -(_1016996 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35290 ^ _778495) ^ [_1437669, _1437671] : [class_Orderings_Olinorder(_1437669), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1437669, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1437669), _1437671)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1437669), _1437671))], (51245 ^ _778495) ^ [_1814589, _1814591] : [51252 ^ _778495 : [(51255 ^ _778495) ^ [] : [_1814589 = _1814591], (51253 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814589), _1814591)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814589), _1814591)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814591), _1814589)))], (51677 ^ _778495) ^ [_1821983, _1821985] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821983, _1821985) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821983), _1821985)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821985), _1821983)))], (22834 ^ _778495) ^ [_1186618, _1186620] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1186618)), c_Int_OBit1(_1186620)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1186618)), _1186620)))], (44843 ^ _778495) ^ [_1676904, _1676906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1676904), _1676906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676904)), hAPP(c_Code__Numeral_Onat__of, _1676906))))], (38220 ^ _778495) ^ [_1511177, _1511179, _1511181] : [class_Lattices_Odistrib__lattice(_1511177), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511177), _1511179)), -(_1511179 = c_Orderings_Obot__class_Obot(tc_fun(_1511177, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511177), _1511181)), -(_1511181 = c_Orderings_Obot__class_Obot(tc_fun(_1511177, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1511177), c_Big__Operators_Olattice__class_OSup__fin(_1511177, _1511179)), c_Big__Operators_Olattice__class_OSup__fin(_1511177, _1511181)) = c_Big__Operators_Olattice__class_OSup__fin(_1511177, hAPP(c_Set_OCollect(_1511177), hAPP(hAPP(c_COMBB(tc_fun(_1511177, tc_HOL_Obool), tc_HOL_Obool, _1511177), c_HOL_OEx(_1511177)), hAPP(hAPP(c_COMBB(tc_fun(_1511177, tc_fun(_1511177, tc_HOL_Obool)), tc_fun(_1511177, tc_HOL_Obool), _1511177), hAPP(c_COMBB(tc_fun(_1511177, tc_HOL_Obool), tc_HOL_Obool, _1511177), c_HOL_OEx(_1511177))), hAPP(hAPP(c_COMBC(_1511177, tc_fun(_1511177, tc_fun(_1511177, tc_HOL_Obool)), tc_fun(_1511177, tc_fun(_1511177, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511177, tc_fun(tc_fun(_1511177, tc_HOL_Obool), tc_fun(_1511177, tc_HOL_Obool))), tc_fun(tc_fun(_1511177, tc_fun(_1511177, tc_HOL_Obool)), tc_fun(_1511177, tc_fun(_1511177, tc_HOL_Obool))), _1511177), c_COMBS(_1511177, tc_fun(_1511177, tc_HOL_Obool), tc_fun(_1511177, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511177, tc_fun(_1511177, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1511177, tc_fun(tc_fun(_1511177, tc_HOL_Obool), tc_fun(_1511177, tc_HOL_Obool))), _1511177), hAPP(c_COMBB(tc_fun(_1511177, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1511177, tc_HOL_Obool), tc_fun(_1511177, tc_HOL_Obool)), _1511177), c_COMBS(_1511177, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511177, tc_fun(_1511177, tc_HOL_Obool)), tc_fun(_1511177, tc_fun(_1511177, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1511177), hAPP(c_COMBB(tc_fun(_1511177, tc_HOL_Obool), tc_fun(_1511177, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1511177), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511177), c_fconj))), hAPP(hAPP(c_COMBC(_1511177, tc_fun(_1511177, tc_fun(_1511177, _1511177)), tc_fun(_1511177, tc_fun(_1511177, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1511177, _1511177), tc_fun(_1511177, tc_HOL_Obool)), tc_fun(tc_fun(_1511177, tc_fun(_1511177, _1511177)), tc_fun(_1511177, tc_fun(_1511177, tc_HOL_Obool))), _1511177), c_COMBB(tc_fun(_1511177, _1511177), tc_fun(_1511177, tc_HOL_Obool), _1511177)), hAPP(hAPP(c_COMBB(tc_fun(_1511177, tc_HOL_Obool), tc_fun(tc_fun(_1511177, _1511177), tc_fun(_1511177, tc_HOL_Obool)), _1511177), c_COMBB(_1511177, tc_HOL_Obool, _1511177)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1511177)))))), hAPP(hAPP(c_COMBC(_1511177, tc_fun(_1511177, tc_HOL_Obool), tc_fun(_1511177, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1511177, tc_HOL_Obool), tc_fun(_1511177, tc_HOL_Obool)), _1511177), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1511177)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511177), c_fconj), hAPP(hAPP(c_COMBC(_1511177, tc_fun(_1511177, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511177)), _1511179)))), hAPP(hAPP(c_COMBC(_1511177, tc_fun(_1511177, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511177)), _1511181))))))))], (25270 ^ _778495) ^ [_1229973, _1229975] : [25271 ^ _778495 : [(25274 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229975))], (25272 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229973))]], 25275 ^ _778495 : [(25282 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1229973), _1229975)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1229973)), hAPP(c_Int_Onat, _1229975))))], (25276 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1229973)), hAPP(c_Int_Onat, _1229975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1229973), _1229975)))]]], (52357 ^ _778495) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (37144 ^ _778495) ^ [_1479631, _1479633, _1479635, _1479637, _1479639] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1479631, _1479633, _1479635), _1479637), _1479639)), -(hBOOL(hAPP(_1479637, hAPP(_1479635, _1479639))))], (5322 ^ _778495) ^ [_859875, _859877, _859879, _859881, _859883, _859885] : [-(c_Divides_Odiv__class_Omod(_859885, _859881, _859877) = c_Divides_Odiv__class_Omod(_859883, _859879, _859875)), _859885 = _859883, _859881 = _859879, _859877 = _859875], (52259 ^ _778495) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (50957 ^ _778495) ^ [_1809944, _1809946] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809944), _1809946)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809946), _1809944))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809946), _1809944)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809944), _1809946)))], (9232 ^ _778495) ^ [_934489, _934491, _934493, _934495] : [class_Lattices_Odistrib__lattice(_934489), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934489), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934489), _934491), _934493)), _934495) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934489), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934489), _934491), _934495)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934489), _934493), _934495)))], (42706 ^ _778495) ^ [_1629650, _1629652, _1629654, _1629656] : [-(c_List_Oremove1(_1629650, _1629652, c_List_Oremove1(_1629650, _1629654, _1629656)) = c_List_Oremove1(_1629650, _1629654, c_List_Oremove1(_1629650, _1629652, _1629656)))], (5733 ^ _778495) ^ [_869264, _869266] : [-(c_Set_Othe__elem(_869264, hAPP(hAPP(c_Set_Oinsert(_869264), _869266), c_Orderings_Obot__class_Obot(tc_fun(_869264, tc_HOL_Obool)))) = _869266)], (40527 ^ _778495) ^ [_1572123, _1572125, _1572127, _1572129] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572123, _1572123)), hAPP(hAPP(c_Product__Type_OPair(_1572123, _1572123), _1572125), _1572127)), c_Transitive__Closure_Ortrancl(_1572123, _1572129))), -(_1572125 = _1572127), 40534 ^ _778495 : [(40537 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572123, _1572123)), hAPP(hAPP(c_Product__Type_OPair(_1572123, _1572123), _1572125), _1572127)), c_Transitive__Closure_Otrancl(_1572123, _1572129))))], (40535 ^ _778495) ^ [] : [_1572125 = _1572127]]], (28477 ^ _778495) ^ [_1293217, _1293219] : [-(hAPP(c_Finite__Set_Ocard(_1293217), _1293219) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293217, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1293217), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1293219))], (10399 ^ _778495) ^ [_957870, _957872, _957874] : [class_Lattices_Olattice(_957870), hBOOL(hAPP(c_Finite__Set_Ofinite(_957870), _957872)), -(_957872 = c_Orderings_Obot__class_Obot(tc_fun(_957870, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_957870), _957874)), -(_957874 = c_Orderings_Obot__class_Obot(tc_fun(_957870, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957870, tc_HOL_Obool)), _957872), _957874) = c_Orderings_Obot__class_Obot(tc_fun(_957870, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_957870, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_957870, tc_HOL_Obool)), _957872), _957874)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_957870), c_Big__Operators_Olattice__class_OInf__fin(_957870, _957872)), c_Big__Operators_Olattice__class_OInf__fin(_957870, _957874)))], (28943 ^ _778495) ^ [_1303865, _1303867] : [-(c_Divides_OposDivAlg(_1303865, _1303867) = hAPP(c_Divides_Oadjust(_1303867), c_Divides_OposDivAlg(_1303865, 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)))), _1303867)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303865), _1303867))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1303867), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22094 ^ _778495) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (9622 ^ _778495) ^ [_943255, _943257] : [class_Lattices_Olattice(_943255), hBOOL(hAPP(c_Finite__Set_Ofinite(_943255), _943257)), -(c_Big__Operators_Olattice__class_OSup__fin(_943255, _943257) = hAPP(c_Finite__Set_Ofold1(_943255, c_Lattices_Osemilattice__sup__class_Osup(_943255)), _943257))], (39584 ^ _778495) ^ [_1549070, _1549072, _1549074, _1549076, _1549078, _1549080] : [c_Finite__Set_Ofolding(_1549070, _1549072, _1549074, _1549076), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549070), _1549078)), hBOOL(hAPP(hAPP(c_member(_1549070), _1549080), _1549078)), -(hAPP(_1549076, _1549078) = hAPP(c_Fun_Ocomp(_1549072, _1549072, _1549072, hAPP(_1549076, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1549070, tc_HOL_Obool)), _1549078), hAPP(hAPP(c_Set_Oinsert(_1549070), _1549080), c_Orderings_Obot__class_Obot(tc_fun(_1549070, tc_HOL_Obool)))))), hAPP(_1549074, _1549080)))], (4738 ^ _778495) ^ [_850713, _850715, _850717, _850719, _850721, _850723, _850725, _850727] : [-(c_Wellfounded_Olex__prod(_850727, _850723, _850719, _850715) = c_Wellfounded_Olex__prod(_850725, _850721, _850717, _850713)), _850727 = _850725, _850723 = _850721, _850719 = _850717, _850715 = _850713], (38113 ^ _778495) ^ [_1506921, _1506923] : [-(hAPP(c_Set_OPow(_1506921), _1506923) = hAPP(c_Set_OCollect(tc_fun(_1506921, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1506921, tc_HOL_Obool), tc_fun(_1506921, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1506921, tc_HOL_Obool))), _1506923)))], (40692 ^ _778495) ^ [_1575927, _1575929] : [c_Wellfounded_Oacyclic(_1575927, hAPP(c_Relation_Oconverse(_1575927, _1575927), _1575929)), -(c_Wellfounded_Oacyclic(_1575927, _1575929))], (22710 ^ _778495) ^ [_1184461, _1184463] : [class_Groups_Oordered__ab__group__add__abs(_1184461), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184461), hAPP(c_Groups_Ouminus__class_Ouminus(_1184461), hAPP(c_Groups_Oabs__class_Oabs(_1184461), _1184463))), c_Groups_Ozero__class_Ozero(_1184461))))], (23342 ^ _778495) ^ [_1196876, _1196878] : [class_Divides_Osemiring__div(_1196876), -(c_Divides_Odiv__class_Omod(_1196876, _1196878, c_Groups_Oone__class_Oone(_1196876)) = c_Groups_Ozero__class_Ozero(_1196876))], (34168 ^ _778495) ^ [_1415189, _1415191, _1415193] : [class_Orderings_Olinorder(_1415189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1415189), _1415191), _1415193)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415189, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1415189, _1415191), _1415193)), hAPP(hAPP(c_Set_Oinsert(_1415189), _1415193), c_Orderings_Obot__class_Obot(tc_fun(_1415189, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1415189, _1415191, _1415193))], (40698 ^ _778495) ^ [_1576012, _1576014] : [c_Wellfounded_Oacyclic(_1576012, _1576014), -(c_Wellfounded_Oacyclic(_1576012, hAPP(c_Relation_Oconverse(_1576012, _1576012), _1576014)))], (51397 ^ _778495) ^ [_1817134, _1817136, _1817138, _1817140] : [class_Divides_Osemiring__div(_1817134), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817134), _1817136), _1817138)), 51404 ^ _778495 : [(51411 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817134), _1817136), _1817140)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817134), _1817136), c_Divides_Odiv__class_Omod(_1817134, _1817140, _1817138))))], (51405 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817134), _1817136), c_Divides_Odiv__class_Omod(_1817134, _1817140, _1817138))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817134), _1817136), _1817140)))]]], (10033 ^ _778495) ^ [_951307, _951309, _951311, _951313, _951315, _951317] : [c_Finite__Set_Ofun__left__comm(_951307, _951309, _951311), hBOOL(hAPP(c_Finite__Set_Ofinite(_951307), _951313)), -(hBOOL(hAPP(hAPP(c_member(_951307), _951315), _951313))), -(hAPP(hAPP(c_Finite__Set_Ofold(_951307, _951309, _951311), _951317), hAPP(hAPP(c_Set_Oinsert(_951307), _951315), _951313)) = hAPP(hAPP(_951311, _951315), hAPP(hAPP(c_Finite__Set_Ofold(_951307, _951309, _951311), _951317), _951313)))], (24221 ^ _778495) ^ [_1211883, _1211885, _1211887, _1211889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211883)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211885), _1211887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211887), 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), _1211885), _1211883)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1211885), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1211889, _1211883))), _1211887))))], (39350 ^ _778495) ^ [_1543585, _1543587, _1543589, _1543591, _1543593, _1543595] : [39353 ^ _778495 : [(39356 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1543591), _1543593), hAPP(hAPP(_1543595, 39351 ^ [_1543585, _1543587, _1543589, _1543591, _1543593, _1543595]), 39352 ^ [_1543585, _1543587, _1543589, _1543591, _1543593, _1543595])))], (39354 ^ _778495) ^ [] : [-(_1543585 = hAPP(hAPP(c_Product__Type_OPair(_1543587, _1543589), 39351 ^ [_1543585, _1543587, _1543589, _1543591, _1543593, _1543595]), 39352 ^ [_1543585, _1543587, _1543589, _1543591, _1543593, _1543595]))]], -(hBOOL(hAPP(hAPP(c_member(_1543591), _1543593), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1543587, _1543589, tc_fun(_1543591, tc_HOL_Obool)), _1543595), _1543585))))], (44434 ^ _778495) ^ [_1667981, _1667983, _1667985, _1667987, _1667989] : [class_Rings_Osemiring__0(_1667981), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667981), hAPP(hAPP(c_List_Omap(_1667983, _1667981), hAPP(hAPP(c_COMBC(_1667983, _1667981, _1667981), hAPP(hAPP(c_COMBB(_1667981, tc_fun(_1667981, _1667981), _1667983), c_Groups_Otimes__class_Otimes(_1667981)), _1667985)), _1667987)), _1667989)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1667981), hAPP(c_List_Omonoid__add__class_Olistsum(_1667981), hAPP(hAPP(c_List_Omap(_1667983, _1667981), _1667985), _1667989))), _1667987))], (38242 ^ _778495) ^ [_1512276, _1512278, _1512280] : [class_Lattices_Odistrib__lattice(_1512276), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512276), _1512278)), -(_1512278 = c_Orderings_Obot__class_Obot(tc_fun(_1512276, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1512276), _1512280), c_Big__Operators_Olattice__class_OSup__fin(_1512276, _1512278)) = c_Big__Operators_Olattice__class_OSup__fin(_1512276, hAPP(c_Set_OCollect(_1512276), hAPP(hAPP(c_COMBB(tc_fun(_1512276, tc_HOL_Obool), tc_HOL_Obool, _1512276), c_HOL_OEx(_1512276)), hAPP(hAPP(c_COMBC(_1512276, tc_fun(_1512276, tc_HOL_Obool), tc_fun(_1512276, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512276, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1512276, tc_HOL_Obool), tc_fun(_1512276, tc_HOL_Obool)), _1512276), c_COMBS(_1512276, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512276, tc_HOL_Obool), tc_fun(_1512276, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1512276), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512276), c_fconj)), hAPP(hAPP(c_COMBC(_1512276, tc_fun(_1512276, _1512276), tc_fun(_1512276, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512276, tc_HOL_Obool), tc_fun(tc_fun(_1512276, _1512276), tc_fun(_1512276, tc_HOL_Obool)), _1512276), c_COMBB(_1512276, tc_HOL_Obool, _1512276)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1512276), _1512280))))), hAPP(hAPP(c_COMBC(_1512276, tc_fun(_1512276, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512276)), _1512278))))))], (52263 ^ _778495) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (23478 ^ _778495) ^ [_1199007, _1199009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199009)), -(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, _1199007, _1199009))))], (38405 ^ _778495) ^ [_1518325, _1518327] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518325), _1518327)), -(_1518327 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1518325, 38409 ^ [_1518325, _1518327]), 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)), 38408 ^ [_1518325, _1518327]))))], (40224 ^ _778495) ^ [_1563990, _1563992, _1563994] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563990, _1563990)), _1563992), _1563994)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563990, _1563990)), _1563992), c_Transitive__Closure_Otrancl(_1563990, _1563994))))], (21274 ^ _778495) ^ [_1159744, _1159746, _1159748] : [class_Fields_Olinordered__field(_1159744), -(_1159746 = c_Groups_Ozero__class_Ozero(_1159744)), -(hAPP(c_Groups_Oabs__class_Oabs(_1159744), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159744), _1159748), _1159746)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159744), hAPP(c_Groups_Oabs__class_Oabs(_1159744), _1159748)), hAPP(c_Groups_Oabs__class_Oabs(_1159744), _1159746)))], (1908 ^ _778495) ^ [_805373, _805375] : [-(class_Groups_Ozero(_805373)), _805375 = _805373, class_Groups_Ozero(_805375)], (52387 ^ _778495) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (45360 ^ _778495) ^ [_1688850, _1688852, _1688854, _1688856, _1688858] : [c_Finite__Set_Ofun__left__comm(_1688850, _1688852, _1688854), -(hAPP(hAPP(c_Finite__Set_Ofold(_1688850, _1688852, _1688854), _1688856), hAPP(c_List_Oset(_1688850), _1688858)) = hAPP(c_List_Ofoldl(_1688852, _1688850, hAPP(c_COMBC(_1688850, _1688852, _1688852), _1688854), _1688856), c_List_Oremdups(_1688850, _1688858)))], (23240 ^ _778495) ^ [_1194818, _1194820, _1194822] : [hBOOL(hAPP(hAPP(c_member(_1194818), _1194820), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1194818, tc_HOL_Obool)), _1194822))), hBOOL(hAPP(hAPP(c_member(_1194818), _1194820), _1194822))], (41734 ^ _778495) ^ [_1605525] : [-(c_List_Olists(_1605525, c_Orderings_Otop__class_Otop(tc_fun(_1605525, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1605525), tc_HOL_Obool)))], (46957 ^ _778495) ^ [_1722857] : [c_List_Onat__list(_1722857), -(c_List_Oembed__list(c_List_Oreturn__list(_1722857)) = _1722857)], (42832 ^ _778495) ^ [_1631966, _1631968, _1631970] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631966), tc_List_Olist(_1631966))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631966), tc_List_Olist(_1631966)), _1631968), c_List_Olist_ONil(_1631966))), c_List_Olexord(_1631966, _1631970)))], (25860 ^ _778495) ^ [_1240527, _1240529, _1240531] : [class_Rings_Olinordered__idom(_1240527), 25863 ^ _778495 : [(25864 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240527), c_Groups_Ozero__class_Ozero(_1240527)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1240527), hAPP(hAPP(c_Power_Opower__class_Opower(_1240527), _1240529), 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(_1240527), _1240531), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1240529 = c_Groups_Ozero__class_Ozero(_1240527), _1240531 = c_Groups_Ozero__class_Ozero(_1240527)], (25874 ^ _778495) ^ [] : [25875 ^ _778495 : [(25878 ^ _778495) ^ [] : [-(_1240531 = c_Groups_Ozero__class_Ozero(_1240527))], (25876 ^ _778495) ^ [] : [-(_1240529 = c_Groups_Ozero__class_Ozero(_1240527))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240527), c_Groups_Ozero__class_Ozero(_1240527)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1240527), hAPP(hAPP(c_Power_Opower__class_Opower(_1240527), _1240529), 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(_1240527), _1240531), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (46838 ^ _778495) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (42894 ^ _778495) ^ [_1633275, _1633277, _1633279] : [hBOOL(hAPP(hAPP(c_member(_1633275), _1633277), hAPP(c_List_Oset(_1633275), _1633279))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633275)), c_List_Oremove1(_1633275, _1633277, _1633279)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633275)), _1633279)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (39420 ^ _778495) ^ [_1545433, _1545435, _1545437, _1545439, _1545441, _1545443, _1545445] : [-(hAPP(c_Fun_Ocomp(_1545433, _1545435, _1545437, _1545439), c_Fun_Ofun__upd(_1545437, _1545433, _1545441, _1545443, _1545445)) = c_Fun_Ofun__upd(_1545437, _1545435, hAPP(c_Fun_Ocomp(_1545433, _1545435, _1545437, _1545439), _1545441), _1545443, hAPP(_1545439, _1545445)))], (37097 ^ _778495) ^ [_1478596] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1478596), c_Int_OInteg)), -(_1478596 = hAPP(c_Int_ORep__Integ, 37100 ^ [_1478596]))], (36296 ^ _778495) ^ [_1461567, _1461569, _1461571, _1461573, _1461575, _1461577] : [c_Fun_Oinj__on(_1461567, _1461569, _1461571, _1461573), -(_1461575 = _1461577), hBOOL(hAPP(hAPP(c_member(_1461567), _1461575), _1461573)), hBOOL(hAPP(hAPP(c_member(_1461567), _1461577), _1461573)), hAPP(_1461571, _1461575) = hAPP(_1461571, _1461577)], (47401 ^ _778495) ^ [_1732600, _1732602, _1732604, _1732606, _1732608] : [47402 ^ _778495 : [(47405 ^ _778495) ^ [] : [hBOOL(hAPP(_1732608, hAPP(hAPP(c_List_Ozip(_1732600, _1732604), hAPP(hAPP(c_List_Otake(_1732600), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732600)), _1732602)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732604)), _1732606))), _1732602)), hAPP(hAPP(c_List_Otake(_1732604), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732600)), _1732602)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732604)), _1732606))), _1732606))))], (47403 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732600)), hAPP(hAPP(c_List_Otake(_1732600), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732600)), _1732602)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732604)), _1732606))), _1732602)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732604)), hAPP(hAPP(c_List_Otake(_1732604), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732600)), _1732602)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732604)), _1732606))), _1732606)))]], -(hBOOL(hAPP(_1732608, hAPP(hAPP(c_List_Ozip(_1732600, _1732604), _1732602), _1732606))))], (11005 ^ _778495) ^ [_967822, _967824, _967826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967822), _967824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967822), _967826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967826), _967824)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967826), _967822))))], (45372 ^ _778495) ^ [_1689180, _1689182] : [-(hBOOL(hAPP(c_List_Odistinct(_1689180), c_List_Oremdups(_1689180, _1689182))))], (36320 ^ _778495) ^ [_1462027, _1462029, _1462031, _1462033, _1462035] : [c_Fun_Oinj__on(_1462027, _1462029, _1462031, c_Orderings_Otop__class_Otop(tc_fun(_1462027, tc_HOL_Obool))), 36323 ^ _778495 : [(36330 ^ _778495) ^ [] : [_1462033 = _1462035, -(hAPP(_1462031, _1462033) = hAPP(_1462031, _1462035))], (36324 ^ _778495) ^ [] : [hAPP(_1462031, _1462033) = hAPP(_1462031, _1462035), -(_1462033 = _1462035)]]], (34987 ^ _778495) ^ [_1432858, _1432860, _1432862] : [class_Groups_Ocomm__monoid__add(_1432858), class_Groups_Ocomm__monoid__mult(_1432858), c_Nat__Transfer_Onat__set(_1432860), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1432858), _1432862), _1432860) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1432858), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1432858, tc_Nat_Onat), _1432862), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1432860)))], (41304 ^ _778495) ^ [_1591900, _1591902] : [-(c_Nitpick_Oinverse__frac(_1591900, _1591902) = hAPP(hAPP(c_Nitpick_Ofrac(_1591900), hAPP(c_Nitpick_Odenom(_1591900), _1591902)), hAPP(c_Nitpick_Onum(_1591900), _1591902)))], (52435 ^ _778495) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (50252 ^ _778495) ^ [_1794630, _1794632, _1794634, _1794636] : [c_Fun_Obij__betw(_1794630, _1794632, _1794634, c_Orderings_Otop__class_Otop(tc_fun(_1794630, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794632, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1794630, _1794632, _1794634), _1794636) = hAPP(c_Set_Oimage(_1794632, _1794630, c_Hilbert__Choice_Oinv__into(_1794630, _1794632, c_Orderings_Otop__class_Otop(tc_fun(_1794630, tc_HOL_Obool)), _1794634)), _1794636))], (40232 ^ _778495) ^ [_1564157, _1564159] : [-(hAPP(c_Relation_ODomain(_1564157, _1564157), c_Transitive__Closure_Otrancl(_1564157, _1564159)) = hAPP(c_Relation_ODomain(_1564157, _1564157), _1564159))], (20862 ^ _778495) ^ [_1152139] : [-(c_Int_Opred(_1152139) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1152139), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20412 ^ _778495) ^ [_1145046] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1145046), c_Int_OPls) = _1145046)], (43167 ^ _778495) ^ [_1639693, _1639695, _1639697] : [class_Groups_Omonoid__add(_1639693), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1639693), hAPP(hAPP(c_List_Oappend(_1639693), _1639695), _1639697)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1639693), hAPP(c_List_Omonoid__add__class_Olistsum(_1639693), _1639695)), hAPP(c_List_Omonoid__add__class_Olistsum(_1639693), _1639697)))], (42017 ^ _778495) ^ [_1612762, _1612764, _1612766, _1612768, _1612770] : [hBOOL(hAPP(hAPP(c_member(_1612762), _1612764), hAPP(c_List_Oset(_1612762), _1612766))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612768), hAPP(_1612770, _1612764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612768), c_List_Olist_Olist__size(_1612762, _1612770, _1612766))))], (44899 ^ _778495) ^ [_1677856, _1677858] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1677856), _1677858) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1677856, 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)))), _1677858))))], (8416 ^ _778495) ^ [_918221, _918223, _918225, _918227, _918229] : [c_Finite__Set_Ofolding__one__idem(_918221, _918223, _918225), hBOOL(hAPP(c_Finite__Set_Ofinite(_918221), _918227)), -(_918229 = c_Orderings_Obot__class_Obot(tc_fun(_918221, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918221, tc_HOL_Obool)), _918229), _918227)), -(hAPP(hAPP(_918223, hAPP(_918225, _918229)), hAPP(_918225, _918227)) = hAPP(_918225, _918227))], (2700 ^ _778495) ^ [_818428, _818430, _818432, _818434, _818436, _818438] : [-(c_Predicate_ODomainP(_818438, _818434, _818430) = c_Predicate_ODomainP(_818436, _818432, _818428)), _818438 = _818436, _818434 = _818432, _818430 = _818428], (45376 ^ _778495) ^ [_1689274, _1689276] : [c_List_Oremdups(_1689274, _1689276) = _1689276, -(hBOOL(hAPP(c_List_Odistinct(_1689274), _1689276)))], (8980 ^ _778495) ^ [_929830, _929832, _929834] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929830, tc_HOL_Obool)), _929832), _929834) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929830, tc_HOL_Obool)), _929834), _929832))], (39887 ^ _778495) ^ [_1556019, _1556021, _1556023] : [-(c_Hilbert__Choice_OEps(tc_prod(_1556019, _1556021), hAPP(c_Product__Type_Oprod_Oprod__case(_1556019, _1556021, tc_HOL_Obool), _1556023)) = c_Hilbert__Choice_OEps(tc_prod(_1556019, _1556021), hAPP(hAPP(c_COMBS(tc_prod(_1556019, _1556021), _1556021, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1556019, tc_fun(_1556021, tc_HOL_Obool), tc_prod(_1556019, _1556021)), _1556023), c_Product__Type_Ofst(_1556019, _1556021))), c_Product__Type_Osnd(_1556019, _1556021))))], (27259 ^ _778495) ^ [_1265244, _1265246] : [class_Rings_Olinordered__idom(_1265244), 27262 ^ _778495 : [(27269 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265244), _1265246), c_Groups_Ozero__class_Ozero(_1265244))), -(c_Groups_Osgn__class_Osgn(_1265244, _1265246) = hAPP(c_Groups_Ouminus__class_Ouminus(_1265244), c_Groups_Oone__class_Oone(_1265244)))], (27263 ^ _778495) ^ [] : [c_Groups_Osgn__class_Osgn(_1265244, _1265246) = hAPP(c_Groups_Ouminus__class_Ouminus(_1265244), c_Groups_Oone__class_Oone(_1265244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265244), _1265246), c_Groups_Ozero__class_Ozero(_1265244))))]]], (21986 ^ _778495) ^ [_1171774, _1171776, _1171778] : [class_Groups_Ogroup__add(_1171774), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171774), hAPP(c_Groups_Ouminus__class_Ouminus(_1171774), _1171776)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171774), _1171776), _1171778)) = _1171778)], (6940 ^ _778495) ^ [_892438, _892440, _892442, _892444] : [class_Lattices_Osemilattice__sup(_892438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892438), _892440), _892442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892438), _892444), _892442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892438), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892438), _892440), _892444)), _892442)))], (34887 ^ _778495) ^ [_1431185, _1431187, _1431189] : [class_Orderings_Olinorder(_1431185), hAPP(_1431187, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1431185), 34892 ^ [_1431185, _1431187, _1431189]), 34893 ^ [_1431185, _1431187, _1431189])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1431185), hAPP(_1431187, 34892 ^ [_1431185, _1431187, _1431189])), hAPP(_1431187, 34893 ^ [_1431185, _1431187, _1431189])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431185), _1431189)), -(_1431189 = c_Orderings_Obot__class_Obot(tc_fun(_1431185, tc_HOL_Obool))), -(hAPP(_1431187, c_Big__Operators_Olattice_OInf__fin(_1431185, c_Orderings_Oord__class_Omin(_1431185), _1431189)) = c_Big__Operators_Olattice_OInf__fin(_1431185, c_Orderings_Oord__class_Omin(_1431185), hAPP(c_Set_Oimage(_1431185, _1431185, _1431187), _1431189)))], (47960 ^ _778495) ^ [_1744711, _1744713, _1744715, _1744717] : [c_List_Olist__ex1(_1744711, _1744713, hAPP(hAPP(c_List_Olist_OCons(_1744711), _1744715), _1744717)), 47963 ^ _778495 : [(47970 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1744713, _1744715))), -(c_List_Olist__ex1(_1744711, _1744713, _1744717))], (47964 ^ _778495) ^ [] : [hBOOL(hAPP(_1744713, _1744715)), -(c_List_Olist__all(_1744711, hAPP(hAPP(c_COMBS(_1744711, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1744711), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1744711), c_fNot), _1744713))), hAPP(c_fequal, _1744715)), _1744717))]]], (1128 ^ _778495) ^ [_795623, _795625] : [-(class_Lattices_Obounded__lattice(_795623)), _795625 = _795623, class_Lattices_Obounded__lattice(_795625)], (19961 ^ _778495) ^ [_1137049] : [hBOOL(hAPP(_1137049, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 19962 ^ [_1137049]))), 19965 ^ _778495 : [(19966 ^ _778495) ^ [_1137149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137149)), -(hBOOL(hAPP(_1137049, _1137149)))]]], (46192 ^ _778495) ^ [_1707415] : [class_Orderings_Olinorder(_1707415), -(c_List_Olinorder__class_Osorted(_1707415, c_List_Olist_ONil(_1707415)))], (23074 ^ _778495) ^ [_1191247, _1191249, _1191251, _1191253, _1191255, _1191257] : [class_Divides_Osemiring__div(_1191247), c_Divides_Odiv__class_Omod(_1191247, _1191249, _1191251) = c_Divides_Odiv__class_Omod(_1191247, _1191253, _1191251), c_Divides_Odiv__class_Omod(_1191247, _1191255, _1191251) = c_Divides_Odiv__class_Omod(_1191247, _1191257, _1191251), -(c_Divides_Odiv__class_Omod(_1191247, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191247), _1191249), _1191255), _1191251) = c_Divides_Odiv__class_Omod(_1191247, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191247), _1191253), _1191257), _1191251))], (29123 ^ _778495) ^ [_1307400, _1307402] : [c_Nitpick_Orefl_H(_1307400, _1307402), 29126 ^ _778495 : [(29127 ^ _778495) ^ [_1307478] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1307400, _1307400)), hAPP(hAPP(c_Product__Type_OPair(_1307400, _1307400), _1307478), _1307478)), _1307402)))]]], (52673 ^ _778495) ^ [_1835891] : [hBOOL(hAPP(c_fNot, _1835891)), hBOOL(_1835891)], (28225 ^ _778495) ^ [_1282416, _1282418, _1282420, _1282422, _1282424] : [class_Fields_Ofield(_1282416), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1282416), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1282418, _1282416), _1282420), _1282422)), _1282424) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1282418, _1282416), hAPP(hAPP(c_COMBC(_1282418, _1282416, _1282416), hAPP(hAPP(c_COMBB(_1282416, tc_fun(_1282416, _1282416), _1282418), c_Rings_Oinverse__class_Odivide(_1282416)), _1282420)), _1282424)), _1282422))], (37128 ^ _778495) ^ [_1479254, _1479256, _1479258, _1479260, _1479262] : [hBOOL(hAPP(hAPP(c_member(_1479254), _1479256), hAPP(c_Set_Ovimage(_1479254, _1479258, _1479260), _1479262))), -(hBOOL(hAPP(hAPP(c_member(_1479258), hAPP(_1479260, _1479256)), _1479262)))], (21644 ^ _778495) ^ [_1166049, _1166051] : [-(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), _1166049))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1166051))))], (52333 ^ _778495) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (27369 ^ _778495) ^ [_1267040] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1267040)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1267040)], (33340 ^ _778495) ^ [_1396643, _1396645, _1396647, _1396649, _1396651] : [class_Complete__Lattice_Ocomplete__lattice(_1396643), class_Orderings_Olinorder(_1396643), 33347 ^ _778495 : [(33357 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396643), _1396645), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396647, _1396643), _1396649), _1396651)))), 33358 ^ _778495 : [(33359 ^ _778495) ^ [_1396991] : [hBOOL(hAPP(hAPP(c_member(_1396647), _1396991), _1396649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396643), _1396645), hAPP(_1396651, _1396991)))]]], (33348 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396643), _1396645), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396647, _1396643), _1396649), _1396651))), 33352 ^ _778495 : [(33355 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396643), _1396645), hAPP(_1396651, 33351 ^ [_1396643, _1396645, _1396647, _1396649, _1396651]))))], (33353 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1396647), 33351 ^ [_1396643, _1396645, _1396647, _1396649, _1396651]), _1396649)))]]]]], (32906 ^ _778495) ^ [_1385639, _1385641, _1385643, _1385645] : [class_Orderings_Olinorder(_1385639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385639), _1385641), _1385643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385639), _1385643), _1385645)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385639, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1385639, _1385641, _1385643)), c_SetInterval_Oord__class_OatLeastAtMost(_1385639, _1385643, _1385645)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1385639, _1385641, _1385645))], (6668 ^ _778495) ^ [_887526, _887528] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887526, tc_HOL_Obool)), _887528), c_Orderings_Obot__class_Obot(tc_fun(_887526, tc_HOL_Obool))) = _887528)], (44596 ^ _778495) ^ [_1671754, _1671756, _1671758, _1671760] : [class_Groups_Ocomm__monoid__add(_1671754), hBOOL(hAPP(c_List_Odistinct(_1671756), _1671758)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671754), hAPP(hAPP(c_List_Omap(_1671756, _1671754), _1671760), _1671758)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1671756, _1671754), _1671760), hAPP(c_List_Oset(_1671756), _1671758)))], (38665 ^ _778495) ^ [_1527076, _1527078] : [-(c_Wellfounded_Owf(_1527076, hAPP(c_Wellfounded_Omeasure(_1527076), _1527078)))], (20149 ^ _778495) ^ [_1140432, _1140434, _1140436] : [class_Rings_Osemiring__1(_1140432), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140432), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1140434), _1140436)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140432), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140432), _1140434)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140432), _1140436)))], (44980 ^ _778495) ^ [_1680194, _1680196, _1680198] : [-(c_List_Olistsp(_1680194, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680194, tc_HOL_Obool)), _1680196), _1680198)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1680194), tc_HOL_Obool)), c_List_Olistsp(_1680194, _1680196)), c_List_Olistsp(_1680194, _1680198)))], (48864 ^ _778495) ^ [_1765709, _1765711, _1765713, _1765715] : [class_Complete__Lattice_Ocomplete__lattice(_1765709), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1765711, _1765709), _1765713), _1765715) = c_Complete__Lattice_OSup__class_OSup(_1765709, hAPP(c_Set_OCollect(_1765709), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1765711, _1765709), tc_HOL_Obool), tc_HOL_Obool, _1765709), c_HOL_OEx(tc_fun(_1765711, _1765709))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1765711, _1765709), tc_HOL_Obool), tc_fun(tc_fun(_1765711, _1765709), tc_HOL_Obool), _1765709), hAPP(c_COMBS(tc_fun(_1765711, _1765709), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1765711, _1765709)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1765711, _1765709), tc_fun(tc_fun(_1765711, _1765709), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1765711, _1765709))), _1765713)))), hAPP(hAPP(c_COMBC(_1765709, tc_fun(tc_fun(_1765711, _1765709), _1765709), tc_fun(tc_fun(_1765711, _1765709), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1765709, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1765711, _1765709), _1765709), tc_fun(tc_fun(_1765711, _1765709), tc_HOL_Obool)), _1765709), c_COMBB(_1765709, tc_HOL_Obool, tc_fun(_1765711, _1765709))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1765711, _1765709), _1765711, _1765709), c_COMBI(tc_fun(_1765711, _1765709))), _1765715)))))))], (41989 ^ _778495) ^ [_1612067, _1612069] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1612067), hAPP(c_List_Oset(_1612067), _1612069))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612067)), _1612069))))], (28193 ^ _778495) ^ [_1281624, _1281626, _1281628, _1281630] : [class_Groups_Oab__group__add(_1281624), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1281626, _1281624), hAPP(hAPP(c_COMBB(_1281624, _1281624, _1281626), c_Groups_Ouminus__class_Ouminus(_1281624)), _1281628)), _1281630) = hAPP(c_Groups_Ouminus__class_Ouminus(_1281624), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1281626, _1281624), _1281628), _1281630)))], (43608 ^ _778495) ^ [_1650349, _1650351, _1650353, _1650355] : [_1650349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1650351), _1650349), hAPP(hAPP(c_List_Olist_OCons(_1650351), _1650353), _1650355)) = hAPP(hAPP(c_List_Olist_OCons(_1650351), _1650353), _1650355))], (46648 ^ _778495) ^ [_1716341, _1716343, _1716345] : [-(hAPP(c_List_Orev(_1716341), hAPP(c_List_Ofilter(_1716341, _1716343), _1716345)) = hAPP(c_List_Ofilter(_1716341, _1716343), hAPP(c_List_Orev(_1716341), _1716345)))], (50941 ^ _778495) ^ [_1809702, _1809704] : [class_Rings_Ocomm__semiring__1(_1809702), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809702), c_Groups_Ozero__class_Ozero(_1809702)), _1809704)), -(_1809704 = c_Groups_Ozero__class_Ozero(_1809702))], (17708 ^ _778495) ^ [_1096161, _1096163, _1096165] : [class_Int_Onumber__ring(_1096161), class_Int_Oring__char__0(_1096161), 17715 ^ _778495 : [(17722 ^ _778495) ^ [] : [_1096163 = _1096165, -(hAPP(c_Int_Onumber__class_Onumber__of(_1096161), _1096163) = hAPP(c_Int_Onumber__class_Onumber__of(_1096161), _1096165))], (17716 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1096161), _1096163) = hAPP(c_Int_Onumber__class_Onumber__of(_1096161), _1096165), -(_1096163 = _1096165)]]], (10793 ^ _778495) ^ [_964314, _964316] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964314), _964316))), 10796 ^ _778495 : [(10803 ^ _778495) ^ [] : [_964314 = _964316, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964314), hAPP(c_Nat_OSuc, _964316))))], (10797 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964314), hAPP(c_Nat_OSuc, _964316))), -(_964314 = _964316)]]], (43514 ^ _778495) ^ [_1648123, _1648125, _1648127] : [hBOOL(hAPP(c_List_Odistinct(_1648123), _1648125)), -(hBOOL(hAPP(c_List_Odistinct(_1648123), hAPP(hAPP(c_List_Odrop(_1648123), _1648127), _1648125))))], (50554 ^ _778495) ^ [_1802599, _1802601, _1802603, _1802605] : [-(hAPP(c_Lazy__Sequence_Obind(_1802599, _1802601, _1802603), _1802605) = c_Lazy__Sequence_Oflat(_1802601, c_Lazy__Sequence_Omap(_1802599, tc_Lazy__Sequence_Olazy__sequence(_1802601), _1802605, _1802603)))], (16240 ^ _778495) ^ [_1068590, _1068592, _1068594] : [class_Rings_Oring__1(_1068590), hBOOL(hAPP(hAPP(c_member(_1068590), _1068592), c_Int_Oring__1__class_OInts(_1068590))), hBOOL(hAPP(hAPP(c_member(_1068590), _1068594), c_Int_Oring__1__class_OInts(_1068590))), -(hBOOL(hAPP(hAPP(c_member(_1068590), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068590), _1068592), _1068594)), c_Int_Oring__1__class_OInts(_1068590))))], (41728 ^ _778495) ^ [_1605280, _1605282, _1605284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1605280, _1605280), tc_HOL_Obool)), _1605282), hAPP(hAPP(c_Product__Type_OSigma(_1605280, _1605280), _1605284), hAPP(c_COMBK(tc_fun(_1605280, tc_HOL_Obool), _1605280), _1605284)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1605280), tc_List_Olist(_1605280)), tc_HOL_Obool)), c_List_Olistrel(_1605280, _1605282)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1605280), tc_List_Olist(_1605280)), c_List_Olists(_1605280, _1605284)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1605280), tc_HOL_Obool), tc_List_Olist(_1605280)), c_List_Olists(_1605280, _1605284))))))], (34514 ^ _778495) ^ [_1423544, _1423546, _1423548] : [class_Groups_Oordered__ab__group__add(_1423544), -(hAPP(c_Set_Oimage(_1423544, _1423544, c_Groups_Ouminus__class_Ouminus(_1423544)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1423544, _1423546), _1423548)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1423544, hAPP(c_Groups_Ouminus__class_Ouminus(_1423544), _1423548), hAPP(c_Groups_Ouminus__class_Ouminus(_1423544), _1423546)))], (33096 ^ _778495) ^ [_1389264, _1389266, _1389268, _1389270] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1389264), _1389270) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1389268), _1389266), -(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), _1389264), _1389266)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1389268), _1389270))), c_Int_Ointrel)))], (25672 ^ _778495) ^ [_1237218, _1237220] : [class_Rings_Olinordered__idom(_1237218), -(hAPP(c_Groups_Oabs__class_Oabs(_1237218), hAPP(hAPP(c_Power_Opower__class_Opower(_1237218), _1237220), 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(_1237218), _1237220), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (27409 ^ _778495) ^ [_1267613] : [_1267613 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1267613) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6266 ^ _778495) ^ [_879882, _879884, _879886, _879888] : [_879882 = _879884, 6269 ^ _778495 : [(6276 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_879886), _879884), _879888)), -(hBOOL(hAPP(hAPP(c_member(_879886), _879882), _879888)))], (6270 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_879886), _879882), _879888)), -(hBOOL(hAPP(hAPP(c_member(_879886), _879884), _879888)))]]], (6711 ^ _778495) ^ [_888343, _888345] : [6712 ^ _778495 : [(6713 ^ _778495) ^ [_888396] : [hBOOL(hAPP(hAPP(c_member(_888343), _888396), _888345))]], _888345 = c_Orderings_Obot__class_Obot(tc_fun(_888343, tc_HOL_Obool))], (22916 ^ _778495) ^ [_1188167] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1188167), 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, _1188167)))], (9542 ^ _778495) ^ [_941422, _941424, _941426, _941428] : [-(hBOOL(hAPP(hAPP(c_member(_941422), _941424), _941426))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941422, tc_HOL_Obool)), _941426), hAPP(hAPP(c_Set_Oinsert(_941422), _941424), _941428)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941422, tc_HOL_Obool)), _941426), _941428))], (24397 ^ _778495) ^ [_1215174, _1215176] : [class_Int_Onumber__ring(_1215174), 24400 ^ _778495 : [(24407 ^ _778495) ^ [] : [c_Int_Oiszero(_1215174, hAPP(c_Int_Onumber__class_Onumber__of(_1215174), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1215176)))), -(c_Groups_Ozero__class_Ozero(_1215174) = hAPP(c_Int_Onumber__class_Onumber__of(_1215174), _1215176))], (24401 ^ _778495) ^ [] : [c_Groups_Ozero__class_Ozero(_1215174) = hAPP(c_Int_Onumber__class_Onumber__of(_1215174), _1215176), -(c_Int_Oiszero(_1215174, hAPP(c_Int_Onumber__class_Onumber__of(_1215174), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1215176)))))]]], (33652 ^ _778495) ^ [_1404864, _1404866, _1404868, _1404870, _1404872, _1404874, _1404876] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404864, tc_fun(_1404866, tc_fun(_1404868, tc_HOL_Obool))), _1404870), _1404872), _1404874), _1404876))), 33653 ^ _778495 : [(33654 ^ _778495) ^ [_1404949] : [hBOOL(hAPP(hAPP(c_member(_1404864), _1404949), _1404870)), hBOOL(hAPP(hAPP(hAPP(_1404872, _1404949), _1404874), _1404876))]]], (34763 ^ _778495) ^ [_1428829] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1428829)), -(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)), _1428829))))], (43520 ^ _778495) ^ [_1648234, _1648236, _1648238] : [-(hAPP(hAPP(c_List_Odrop(_1648234), _1648236), c_List_Obutlast(_1648234, _1648238)) = c_List_Obutlast(_1648234, hAPP(hAPP(c_List_Odrop(_1648234), _1648236), _1648238)))], (37196 ^ _778495) ^ [_1480971, _1480973, _1480975, _1480977, _1480979] : [-(hAPP(c_Set_Ovimage(_1480971, _1480973, _1480975), hAPP(hAPP(c_Set_Oinsert(_1480973), _1480977), _1480979)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480971, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1480971, _1480973, _1480975), hAPP(hAPP(c_Set_Oinsert(_1480973), _1480977), c_Orderings_Obot__class_Obot(tc_fun(_1480973, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1480971, _1480973, _1480975), _1480979)))], (24888 ^ _778495) ^ [_1223720, _1223722] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223720)))), 24891 ^ _778495 : [(24898 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223722)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223720), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223722)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223720), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223722))))], (24892 ^ _778495) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223722))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223720), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223722)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223720))]]], (2500 ^ _778495) ^ [_815298, _815300, _815302, _815304] : [-(c_Set_Othe__elem(_815304, _815300) = c_Set_Othe__elem(_815302, _815298)), _815304 = _815302, _815300 = _815298], (22032 ^ _778495) ^ [_1172599, _1172601, _1172603] : [class_Rings_Oring(_1172599), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1172599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172599), _1172601), _1172603)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172599), _1172601), hAPP(c_Groups_Ouminus__class_Ouminus(_1172599), _1172603)))], (12346 ^ _778495) ^ [_995494, _995496, _995498, _995500, _995502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995494), _995496)), -(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), _995496), _995498)), _995500)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995494), _995498)), _995502)) = 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), _995496), _995494)), _995498)), _995500)), _995502))], (40288 ^ _778495) ^ [_1565540, _1565542, _1565544, _1565546] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565540, _1565540)), _1565542), c_Transitive__Closure_Otrancl(_1565540, _1565544))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565540, _1565540), tc_HOL_Obool)), _1565544), _1565546)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565540, _1565540)), _1565542), c_Transitive__Closure_Otrancl(_1565540, _1565546))))], (3266 ^ _778495) ^ [_827251, _827253] : [_827253 = _827251, -(c_Int_OBit1(_827253) = c_Int_OBit1(_827251))], (25940 ^ _778495) ^ [_1242200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242200)), -(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), _1242200), 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)))))))], (26766 ^ _778495) ^ [_1256903, _1256905] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1256903, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1256903, tc_HOL_Obool))), hAPP(c_Set_OPow(_1256903), _1256905))))], (21226 ^ _778495) ^ [_1158656, _1158658] : [class_Groups_Oordered__ab__group__add__abs(_1158656), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158656), c_Groups_Ozero__class_Ozero(_1158656)), _1158658)), -(hAPP(c_Groups_Oabs__class_Oabs(_1158656), _1158658) = _1158658)], (35603 ^ _778495) ^ [_1444844, _1444846, _1444848, _1444850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444844), _1444850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444848), _1444846))), -(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), _1444844), _1444846)), 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), _1444848), _1444850)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (21070 ^ _778495) ^ [_1155854] : [class_Groups_Oordered__ab__group__add__abs(_1155854), -(hAPP(c_Groups_Oabs__class_Oabs(_1155854), c_Groups_Ozero__class_Ozero(_1155854)) = c_Groups_Ozero__class_Ozero(_1155854))], (36194 ^ _778495) ^ [_1459594, _1459596, _1459598, _1459600] : [c_Fun_Oinj__on(_1459594, _1459596, _1459598, _1459600), 36197 ^ _778495 : [(36198 ^ _778495) ^ [_1459702] : [hBOOL(hAPP(hAPP(c_member(_1459594), _1459702), _1459600)), 36201 ^ _778495 : [(36202 ^ _778495) ^ [_1459804] : [hBOOL(hAPP(hAPP(c_member(_1459594), _1459804), _1459600)), hAPP(_1459598, _1459702) = hAPP(_1459598, _1459804), -(_1459702 = _1459804)]]]]], (10991 ^ _778495) ^ [_967568, _967570] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967568), _967570))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967568), _967570)), -(_967568 = _967570)], (29164 ^ _778495) ^ [_1308661, _1308663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1308661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1308661), _1308663)), -(c_Divides_Odivmod__nat(_1308663, _1308661) = 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), _1308663), _1308661)), _1308661))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1308663), _1308661), _1308661)))], (15049 ^ _778495) ^ [_1045535, _1045537, _1045539, _1045541] : [class_Rings_Olinordered__semiring(_1045535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045535), _1045537), _1045539)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045535), _1045541), _1045539))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045535), c_Groups_Ozero__class_Ozero(_1045535)), _1045539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045535), _1045537), _1045541)))], (47154 ^ _778495) ^ [_1727160, _1727162] : [class_Orderings_Olinorder(_1727160), 47157 ^ _778495 : [(47178 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727160, _1727162)), 47179 ^ _778495 : [(47182 ^ _778495) ^ [_1727720, _1727722] : [_1727162 = hAPP(hAPP(c_List_Olist_OCons(_1727160), _1727720), _1727722), 47188 ^ _778495 : [(47191 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727160), _1727720), 47187 ^ [_1727160, _1727162, _1727720, _1727722]))], (47189 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1727160), 47187 ^ [_1727160, _1727162, _1727720, _1727722]), hAPP(c_List_Oset(_1727160), _1727722))))]], c_List_Olinorder__class_Osorted(_1727160, _1727722)], (47180 ^ _778495) ^ [] : [_1727162 = c_List_Olist_ONil(_1727160)]]], (47158 ^ _778495) ^ [] : [c_List_Olinorder__class_Osorted(_1727160, _1727162), -(_1727162 = c_List_Olist_ONil(_1727160)), 47167 ^ _778495 : [(47170 ^ _778495) ^ [_1727494] : [hBOOL(hAPP(hAPP(c_member(_1727160), _1727494), hAPP(c_List_Oset(_1727160), 47165 ^ [_1727160, _1727162]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727160), 47166 ^ [_1727160, _1727162]), _1727494)))], (47176 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727160, 47165 ^ [_1727160, _1727162]))], (47168 ^ _778495) ^ [] : [-(_1727162 = hAPP(hAPP(c_List_Olist_OCons(_1727160), 47166 ^ [_1727160, _1727162]), 47165 ^ [_1727160, _1727162]))]]]]], (25568 ^ _778495) ^ [_1235399] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1235399), _1235399)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1235399)], (45762 ^ _778495) ^ [_1697901, _1697903, _1697905, _1697907] : [-(hBOOL(hAPP(_1697901, _1697903))), -(hAPP(c_List_OremoveAll(_1697905, _1697903), hAPP(c_List_Ofilter(_1697905, _1697901), _1697907)) = hAPP(c_List_Ofilter(_1697905, _1697901), _1697907))], (12000 ^ _778495) ^ [_988158, _988160] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988158), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988160), _988158)))))], (28691 ^ _778495) ^ [_1298614, _1298616] : [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(_1298614))), 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)), _1298616))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1298614) = hAPP(c_Nat_OSuc, _1298616))], (52571 ^ _778495) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (27889 ^ _778495) ^ [_1276125, _1276127] : [c_Nat__Transfer_Ois__nat(_1276125), c_Nat__Transfer_Ois__nat(_1276127), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1276125, _1276127)))], (6078 ^ _778495) ^ [_875894, _875896, _875898, _875900] : [hBOOL(hAPP(hAPP(c_member(_875894), _875896), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875894, tc_HOL_Obool)), _875898), _875900))), -(hBOOL(hAPP(hAPP(c_member(_875894), _875896), _875898))), -(hBOOL(hAPP(hAPP(c_member(_875894), _875896), _875900)))], (37999 ^ _778495) ^ [_1502620, _1502622, _1502624, _1502626, _1502628] : [c_Relation_Orefl__on(_1502620, _1502622, _1502624), hBOOL(hAPP(hAPP(c_member(tc_prod(_1502620, _1502620)), hAPP(hAPP(c_Product__Type_OPair(_1502620, _1502620), _1502626), _1502628)), _1502624)), -(hBOOL(hAPP(hAPP(c_member(_1502620), _1502626), _1502622)))], (20004 ^ _778495) ^ [_1137842] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137842) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1137842 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28467 ^ _778495) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28873 ^ _778495) ^ [_1302576, _1302578] : [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), _1302576))), 28876 ^ _778495 : [(28883 ^ _778495) ^ [] : [-(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), _1302578)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302576))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302578), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302576)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302576)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302578), 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), _1302576)))))], (28877 ^ _778495) ^ [] : [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), _1302578)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302576)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302578), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302576)) = 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), _1302578)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302576))))]]], (24551 ^ _778495) ^ [_1218070, _1218072, _1218074] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218070), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1218072, _1218074)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218070), _1218072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218070), _1218074)))], (34795 ^ _778495) ^ [_1429313, _1429315] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1429313, _1429315) = 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), _1429313), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1429315))))], (23278 ^ _778495) ^ [_1195590, _1195592] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195590), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195592)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195590)), _1195592))], (45703 ^ _778495) ^ [_1696715, _1696717, _1696719, _1696721] : [-(hAPP(c_List_Ofilter(_1696715, _1696717), c_List_Oremove1(_1696715, _1696719, _1696721)) = c_List_Oremove1(_1696715, _1696719, hAPP(c_List_Ofilter(_1696715, _1696717), _1696721)))], (52657 ^ _778495) ^ [_1835671, _1835673] : [hBOOL(hAPP(hAPP(c_fequal, _1835671), _1835673)), -(_1835671 = _1835673)], (44925 ^ _778495) ^ [_1678493, _1678495, _1678497, _1678499] : [-(c_List_Opartition(_1678493, _1678495, hAPP(hAPP(c_List_Olist_OCons(_1678493), _1678497), _1678499)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1678493), tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1678493), tc_fun(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493))), tc_fun(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1678493), tc_fun(tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)))), tc_fun(tc_fun(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493))), tc_fun(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)))), tc_List_Olist(_1678493)), c_COMBS(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493))), tc_fun(tc_List_Olist(_1678493), tc_fun(tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)))), tc_List_Olist(_1678493)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)), tc_fun(tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493))), tc_List_Olist(_1678493)), hAPP(c_If(tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493))), hAPP(_1678495, _1678497)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1678493), tc_fun(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493))), tc_List_Olist(_1678493)), c_Product__Type_OPair(tc_List_Olist(_1678493), tc_List_Olist(_1678493))), hAPP(c_List_Olist_OCons(_1678493), _1678497))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1678493), tc_fun(tc_List_Olist(_1678493), tc_List_Olist(_1678493)), tc_fun(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493))), tc_fun(tc_fun(tc_List_Olist(_1678493), tc_List_Olist(_1678493)), tc_fun(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)))), tc_List_Olist(_1678493)), c_COMBB(tc_List_Olist(_1678493), tc_prod(tc_List_Olist(_1678493), tc_List_Olist(_1678493)), tc_List_Olist(_1678493))), c_Product__Type_OPair(tc_List_Olist(_1678493), tc_List_Olist(_1678493)))), hAPP(c_List_Olist_OCons(_1678493), _1678497)))), c_List_Opartition(_1678493, _1678495, _1678499)))], (14885 ^ _778495) ^ [_1042562, _1042564] : [_1042562 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042562), _1042564), -(_1042564 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1042562 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41066 ^ _778495) ^ [_1585383, _1585385] : [-(hAPP(hAPP(c_Nat_Ocompow(_1585383, _1585383), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1585385) = c_Fun_Oid(_1585383))], (48042 ^ _778495) ^ [_1746384, _1746386, _1746388, _1746390, _1746392] : [-(_1746384 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1746386, _1746388, _1746390, _1746392), _1746384) = c_Lazy__Sequence_Ohb__bind(_1746386, _1746388, hAPP(_1746390, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1746384), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1746386, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746388))), _1746392), _1746384)))], (36109 ^ _778495) ^ [_1456870, _1456872, _1456874, _1456876, _1456878, _1456880, _1456882, _1456884, _1456886, _1456888, _1456890] : [c_Equiv__Relations_Oequiv(_1456870, _1456872, _1456874), c_Equiv__Relations_Oequiv(_1456876, _1456878, _1456880), c_Equiv__Relations_Ocongruent2(_1456870, _1456876, tc_fun(_1456882, tc_HOL_Obool), _1456874, _1456880, _1456884), hBOOL(hAPP(hAPP(c_member(tc_fun(_1456870, tc_HOL_Obool)), _1456886), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1456870), _1456872), _1456874))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1456876, tc_HOL_Obool)), _1456888), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1456876), _1456878), _1456880))), 36131 ^ _778495 : [(36137 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1456882, tc_HOL_Obool)), hAPP(hAPP(_1456884, 36130 ^ [_1456870, _1456872, _1456874, _1456876, _1456878, _1456880, _1456882, _1456884, _1456886, _1456888, _1456890]), 36133 ^ [_1456870, _1456872, _1456874, _1456876, _1456878, _1456880, _1456882, _1456884, _1456886, _1456888, _1456890])), _1456890))], (36135 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456876), 36133 ^ [_1456870, _1456872, _1456874, _1456876, _1456878, _1456880, _1456882, _1456884, _1456886, _1456888, _1456890]), _1456878)))], (36132 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456870), 36130 ^ [_1456870, _1456872, _1456874, _1456876, _1456878, _1456880, _1456882, _1456884, _1456886, _1456888, _1456890]), _1456872)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1456882, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1456870, tc_fun(_1456882, tc_HOL_Obool)), _1456886), hAPP(hAPP(c_COMBB(tc_fun(_1456876, tc_fun(_1456882, tc_HOL_Obool)), tc_fun(_1456882, tc_HOL_Obool), _1456870), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1456876, tc_fun(_1456882, tc_HOL_Obool)), _1456888)), _1456884))), _1456890)))], (30713 ^ _778495) ^ [_1339193, _1339195, _1339197, _1339199] : [class_Orderings_Olinorder(_1339193), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339193), _1339195), _1339197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339193), _1339195), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339193), _1339199), _1339197))))], (49921 ^ _778495) ^ [_1788131, _1788133, _1788135] : [c_Fun_Obij__betw(_1788131, _1788133, _1788135, c_Orderings_Otop__class_Otop(tc_fun(_1788131, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788133, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1788133, _1788131, c_Hilbert__Choice_Oinv__into(_1788131, _1788133, c_Orderings_Otop__class_Otop(tc_fun(_1788131, tc_HOL_Obool)), _1788135), c_Orderings_Otop__class_Otop(tc_fun(_1788133, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788131, tc_HOL_Obool))))], (42252 ^ _778495) ^ [_1619895, _1619897] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1619895), _1619897) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619895, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1619897), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (35384 ^ _778495) ^ [_1439606, _1439608, _1439610] : [class_Lattices_Olattice(_1439606), hAPP(_1439608, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1439606), 35389 ^ [_1439606, _1439608, _1439610]), 35390 ^ [_1439606, _1439608, _1439610])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1439606), hAPP(_1439608, 35389 ^ [_1439606, _1439608, _1439610])), hAPP(_1439608, 35390 ^ [_1439606, _1439608, _1439610])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1439606), _1439610)), -(_1439610 = c_Orderings_Obot__class_Obot(tc_fun(_1439606, tc_HOL_Obool))), -(hAPP(_1439608, c_Big__Operators_Olattice__class_OInf__fin(_1439606, _1439610)) = c_Big__Operators_Olattice__class_OInf__fin(_1439606, hAPP(c_Set_Oimage(_1439606, _1439606, _1439608), _1439610)))], (37077 ^ _778495) ^ [_1478034, _1478036, _1478038] : [-(c_HOL_OThe(tc_prod(_1478034, _1478036), hAPP(c_Product__Type_Oprod_Oprod__case(_1478034, _1478036, tc_HOL_Obool), _1478038)) = c_HOL_OThe(tc_prod(_1478034, _1478036), hAPP(hAPP(c_COMBS(tc_prod(_1478034, _1478036), _1478036, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1478034, tc_fun(_1478036, tc_HOL_Obool), tc_prod(_1478034, _1478036)), _1478038), c_Product__Type_Ofst(_1478034, _1478036))), c_Product__Type_Osnd(_1478034, _1478036))))], (15758 ^ _778495) ^ [_1059002, _1059004, _1059006, _1059008] : [c_Sum__Type_OPlus(_1059002, _1059004, _1059006, _1059008) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1059002, _1059004), tc_HOL_Obool)), 15761 ^ _778495 : [(15764 ^ _778495) ^ [] : [-(_1059008 = c_Orderings_Obot__class_Obot(tc_fun(_1059004, tc_HOL_Obool)))], (15762 ^ _778495) ^ [] : [-(_1059006 = c_Orderings_Obot__class_Obot(tc_fun(_1059002, tc_HOL_Obool)))]]], (12010 ^ _778495) ^ [_988373, _988375, _988377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988373), _988377)), _988375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988373), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988375), _988377))))], (51465 ^ _778495) ^ [_1818337] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818337), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1818337 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (37925 ^ _778495) ^ [_1500528, _1500530, _1500532] : [-(hAPP(hAPP(c_Set_Oinsert(_1500528), _1500530), _1500532) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1500528, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1500528), hAPP(hAPP(c_COMBC(_1500528, _1500528, tc_HOL_Obool), c_fequal), _1500530))), _1500532))], (52279 ^ _778495) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (45177 ^ _778495) ^ [_1684691, _1684693, _1684695, _1684697] : [c_List_Olist__all2(_1684691, _1684693, _1684695, _1684697, c_List_Olist_ONil(_1684693)), -(_1684697 = c_List_Olist_ONil(_1684691))], (16204 ^ _778495) ^ [_1068079, _1068081] : [class_Rings_Odivision__ring(_1068079), -(_1068081 = c_Groups_Ozero__class_Ozero(_1068079)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1068079), _1068081), _1068081) = c_Groups_Oone__class_Oone(_1068079))], (45248 ^ _778495) ^ [_1686261, _1686263, _1686265, _1686267, _1686269, _1686271, _1686273, _1686275] : [c_List_Olist__all2(_1686261, _1686263, _1686265, _1686267, _1686269), hBOOL(hAPP(hAPP(_1686265, _1686271), _1686273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686275), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686263)), _1686269))), -(c_List_Olist__all2(_1686261, _1686263, _1686265, hAPP(hAPP(c_List_Olist__update(_1686261, _1686267), _1686275), _1686271), hAPP(hAPP(c_List_Olist__update(_1686263, _1686269), _1686275), _1686273)))], (39490 ^ _778495) ^ [_1547071, _1547073, _1547075, _1547077, _1547079, _1547081] : [class_Groups_Ocomm__monoid__add(_1547071), c_Fun_Oinj__on(_1547073, _1547075, _1547077, _1547079), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1547075, _1547071), _1547081), hAPP(c_Set_Oimage(_1547073, _1547075, _1547077), _1547079)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1547073, _1547071), hAPP(c_Fun_Ocomp(_1547075, _1547071, _1547073, _1547081), _1547077)), _1547079))], (44572 ^ _778495) ^ [_1671196, _1671198, _1671200, _1671202] : [c_Fun_Oinj__on(_1671196, _1671198, _1671200, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671196, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1671196), tc_fun(_1671196, tc_HOL_Obool), c_List_Oset(_1671196)), _1671202))), -(c_Fun_Oinj__on(tc_List_Olist(_1671196), tc_List_Olist(_1671198), hAPP(c_List_Omap(_1671196, _1671198), _1671200), _1671202))], (52309 ^ _778495) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (52477 ^ _778495) ^ [_1833626] : [-(class_Nat_Osize(tc_List_Olist(_1833626)))], (11188 ^ _778495) ^ [_971242, _971244, _971246] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_971242), _971244)), hBOOL(hAPP(hAPP(c_member(_971242), _971246), _971244)), -(hAPP(c_Finite__Set_Ocard(_971242), _971244) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_971242), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971242, tc_HOL_Obool)), _971244), hAPP(hAPP(c_Set_Oinsert(_971242), _971246), c_Orderings_Obot__class_Obot(tc_fun(_971242, tc_HOL_Obool)))))))], (45721 ^ _778495) ^ [_1697076, _1697078, _1697080, _1697082, _1697084] : [-(hAPP(c_List_Ofilter(_1697076, _1697078), hAPP(hAPP(c_List_Omap(_1697080, _1697076), _1697082), _1697084)) = hAPP(hAPP(c_List_Omap(_1697080, _1697076), _1697082), hAPP(c_List_Ofilter(_1697080, hAPP(c_Fun_Ocomp(_1697076, tc_HOL_Obool, _1697080, _1697078), _1697082)), _1697084)))], (49804 ^ _778495) ^ [_1785356, _1785358, _1785360, _1785362, _1785364, _1785366] : [class_Groups_Ocomm__monoid__mult(_1785356), hBOOL(hAPP(c_Finite__Set_Ofinite(_1785358), _1785360)), 49814 ^ _778495 : [(49817 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785362), hAPP(_1785364, 49813 ^ [_1785356, _1785358, _1785360, _1785362, _1785364, _1785366])))], (49815 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785358), 49813 ^ [_1785356, _1785358, _1785360, _1785362, _1785364, _1785366]), _1785360)))]], 49821 ^ _778495 : [(49825 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785358), 49823 ^ [_1785356, _1785358, _1785360, _1785362, _1785364, _1785366]), _1785360)))], (49827 ^ _778495) ^ [] : [49820 ^ [_1785356, _1785358, _1785360, _1785362, _1785364, _1785366] = 49823 ^ [_1785356, _1785358, _1785360, _1785362, _1785364, _1785366]], (49829 ^ _778495) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785362, tc_HOL_Obool)), hAPP(_1785364, 49820 ^ [_1785356, _1785358, _1785360, _1785362, _1785364, _1785366])), hAPP(_1785364, 49823 ^ [_1785356, _1785358, _1785360, _1785362, _1785364, _1785366])) = c_Orderings_Obot__class_Obot(tc_fun(_1785362, tc_HOL_Obool))], (49822 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785358), 49820 ^ [_1785356, _1785358, _1785360, _1785362, _1785364, _1785366]), _1785360)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785356, _1785362, c_Groups_Otimes__class_Otimes(_1785356)), _1785366), c_Groups_Oone__class_Oone(_1785356)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1785358, tc_fun(_1785362, tc_HOL_Obool)), _1785360), _1785364)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785356, _1785358, c_Groups_Otimes__class_Otimes(_1785356)), hAPP(hAPP(c_COMBB(tc_fun(_1785362, tc_HOL_Obool), _1785356, _1785358), hAPP(hAPP(c_Finite__Set_Ofold__image(_1785356, _1785362, c_Groups_Otimes__class_Otimes(_1785356)), _1785366), c_Groups_Oone__class_Oone(_1785356))), _1785364)), c_Groups_Oone__class_Oone(_1785356)), _1785360))], (35654 ^ _778495) ^ [_1446280, _1446282, _1446284] : [_1446282 = c_Orderings_Obot__class_Obot(tc_fun(_1446280, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446280, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446280), _1446282), _1446284))], (37808 ^ _778495) ^ [_1497959, _1497961] : [c_Orderings_Obot__class_Obot(tc_fun(_1497959, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1497959), _1497961), 37811 ^ _778495 : [(37812 ^ _778495) ^ [_1498044] : [hBOOL(hAPP(_1497961, _1498044))]]], (9707 ^ _778495) ^ [_944858, _944860, _944862] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_944858), _944860)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944858, tc_HOL_Obool)), _944862), _944860)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_944858), _944862)), hAPP(c_Finite__Set_Ocard(_944858), _944860))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944858, tc_HOL_Obool)), _944862), _944860)))], (39947 ^ _778495) ^ [_1557231, _1557233, _1557235, _1557237, _1557239, _1557241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1557231, tc_HOL_Obool)), _1557233), _1557235)), 39953 ^ _778495 : [(39956 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1557237, tc_HOL_Obool)), hAPP(_1557239, 39952 ^ [_1557231, _1557233, _1557235, _1557237, _1557239, _1557241])), hAPP(_1557241, 39952 ^ [_1557231, _1557233, _1557235, _1557237, _1557239, _1557241])))], (39954 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1557231), 39952 ^ [_1557231, _1557233, _1557235, _1557237, _1557239, _1557241]), _1557233)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557231, _1557237), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1557231, _1557237), _1557233), _1557239)), hAPP(hAPP(c_Product__Type_OSigma(_1557231, _1557237), _1557235), _1557241))))], (11971 ^ _778495) ^ [_987471, _987473, _987475, _987477, _987479, _987481] : [class_Rings_Oordered__ring(_987471), 11974 ^ _778495 : [(11981 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987471), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_987471), _987473), _987479)), _987475)), _987477)), _987481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987471), _987473), _987475)), _987477)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987471), _987479), _987475)), _987481))))], (11975 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987471), _987473), _987475)), _987477)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987471), _987479), _987475)), _987481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987471), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_987471), _987473), _987479)), _987475)), _987477)), _987481)))]]], (25702 ^ _778495) ^ [_1237759, _1237761, _1237763] : [class_Rings_Olinordered__semidom(_1237759), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237759), hAPP(hAPP(c_Power_Opower__class_Opower(_1237759), _1237761), 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(_1237759), _1237763), 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(_1237759), c_Groups_Ozero__class_Ozero(_1237759)), _1237763)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237759), _1237761), _1237763)))], (26516 ^ _778495) ^ [_1252829, _1252831, _1252833] : [class_Rings_Olinordered__semidom(_1252829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252829), c_Groups_Ozero__class_Ozero(_1252829)), _1252831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252829), _1252831), c_Groups_Oone__class_Oone(_1252829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252829), hAPP(hAPP(c_Power_Opower__class_Opower(_1252829), _1252831), hAPP(c_Nat_OSuc, _1252833))), c_Groups_Oone__class_Oone(_1252829))))], (37158 ^ _778495) ^ [_1479895, _1479897, _1479899, _1479901, _1479903, _1479905] : [-(hAPP(c_Set_Ovimage(_1479895, _1479897, _1479899), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479901, tc_fun(_1479897, tc_HOL_Obool)), _1479903), _1479905)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479901, tc_fun(_1479895, tc_HOL_Obool)), _1479903), hAPP(hAPP(c_COMBB(tc_fun(_1479897, tc_HOL_Obool), tc_fun(_1479895, tc_HOL_Obool), _1479901), c_Set_Ovimage(_1479895, _1479897, _1479899)), _1479905)))], (2972 ^ _778495) ^ [_822614, _822616, _822618, _822620, _822622, _822624, _822626, _822628, _822630, _822632, _822634, _822636] : [-(c_Product__Type_Omap__pair(_822636, _822632, _822628, _822624, _822620, _822616) = c_Product__Type_Omap__pair(_822634, _822630, _822626, _822622, _822618, _822614)), _822636 = _822634, _822632 = _822630, _822628 = _822626, _822624 = _822622, _822620 = _822618, _822616 = _822614], (4900 ^ _778495) ^ [_853228, _853230, _853232, _853234, _853236, _853238] : [-(c_Product__Type_Oprod_Oprod__case(_853238, _853234, _853230) = c_Product__Type_Oprod_Oprod__case(_853236, _853232, _853228)), _853238 = _853236, _853234 = _853232, _853230 = _853228], (20500 ^ _778495) ^ [_1146311] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146311), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146311), c_Int_OPls)))], (11350 ^ _778495) ^ [_974363, _974365, _974367, _974369] : [class_Groups_Oab__semigroup__add(_974363), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974363), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974363), _974365), _974367)), _974369) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974363), _974365), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974363), _974367), _974369)))], (38459 ^ _778495) ^ [_1520309, _1520311, _1520313, _1520315] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1520309, _1520311, _1520313), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520309, _1520311), tc_HOL_Obool))), _1520315) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520309, _1520313), tc_HOL_Obool)))], (50072 ^ _778495) ^ [_1791042, _1791044, _1791046, _1791048, _1791050] : [c_Fun_Obij__betw(_1791042, _1791044, _1791046, _1791048, _1791050), 50075 ^ _778495 : [(50078 ^ _778495) ^ [] : [-(hAPP(c_Set_Oimage(_1791042, _1791044, _1791046), _1791048) = _1791050)], (50076 ^ _778495) ^ [] : [-(c_Fun_Oinj__on(_1791042, _1791044, _1791046, _1791048))]]], (19496 ^ _778495) ^ [_1128557, _1128559, _1128561] : [class_Orderings_Olinorder(_1128557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128557), _1128559)), -(c_Big__Operators_Olinorder__class_OMin(_1128557, hAPP(hAPP(c_Set_Oinsert(_1128557), _1128561), _1128559)) = hAPP(hAPP(c_Finite__Set_Ofold(_1128557, _1128557, c_Orderings_Oord__class_Omin(_1128557)), _1128561), _1128559))], (8332 ^ _778495) ^ [_916324, _916326, _916328, _916330, _916332, _916334, _916336] : [-(c_Nitpick_Ofold__graph_H(_916324, _916326, _916328, _916330, _916332, hAPP(hAPP(_916328, _916334), _916336))), 8333 ^ _778495 : [(8340 ^ _778495) ^ [_916553, _916555] : [hAPP(hAPP(_916328, _916334), _916336) = hAPP(hAPP(_916328, _916555), _916553), hBOOL(hAPP(hAPP(c_member(_916324), _916555), _916332)), c_Nitpick_Ofold__graph_H(_916324, _916326, _916328, _916330, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916324, tc_HOL_Obool)), _916332), hAPP(hAPP(c_Set_Oinsert(_916324), _916555), c_Orderings_Obot__class_Obot(tc_fun(_916324, tc_HOL_Obool)))), _916553)], (8334 ^ _778495) ^ [] : [_916332 = c_Orderings_Obot__class_Obot(tc_fun(_916324, tc_HOL_Obool)), hAPP(hAPP(_916328, _916334), _916336) = _916330]]], (30531 ^ _778495) ^ [_1335638, _1335640, _1335642] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1335638, tc_HOL_Obool), tc_fun(_1335638, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1335638, tc_HOL_Obool), tc_fun(_1335638, tc_HOL_Obool)), _1335640), _1335642)), c_Wellfounded_Ofinite__psubset(_1335638))), 30534 ^ _778495 : [(30537 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1335638), _1335642)))], (30535 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1335638, tc_HOL_Obool)), _1335640), _1335642)))]]], (41369 ^ _778495) ^ [_1593805, _1593807, _1593809] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593805)), c_List_Osublist(_1593805, _1593807, _1593809)) = 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(_1593805)), _1593807)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1593809)))))], (42626 ^ _778495) ^ [_1628370, _1628372] : [-(_1628370 = c_List_Olist_ONil(_1628372)), hBOOL(hAPP(c_List_Odistinct(_1628372), _1628370)), -(hBOOL(hAPP(c_List_Odistinct(_1628372), c_List_Obutlast(_1628372, _1628370))))], (40663 ^ _778495) ^ [_1575111, _1575113, _1575115] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1575111, _1575111), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1575111, _1575111), _1575113)), c_Transitive__Closure_Ortrancl(_1575111, _1575113)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575111, _1575111), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575111, _1575111)), hAPP(hAPP(c_Product__Type_OPair(_1575111, _1575111), _1575115), _1575115)), c_Transitive__Closure_Otrancl(_1575111, _1575113)))], (19176 ^ _778495) ^ [_1123189, _1123191] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123189), _1123191))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123189), _1123191)), -(_1123189 = _1123191)], (52501 ^ _778495) ^ [_1833935] : [class_Finite__Set_Ofinite(_1833935), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1833935)))], (37168 ^ _778495) ^ [_1480204, _1480206, _1480208, _1480210, _1480212] : [-(hAPP(c_Set_Ovimage(_1480204, _1480206, _1480208), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480206, tc_HOL_Obool)), _1480210), _1480212)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480204, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1480204, _1480206, _1480208), _1480210)), hAPP(c_Set_Ovimage(_1480204, _1480206, _1480208), _1480212)))], (12118 ^ _778495) ^ [_990448, _990450, _990452, _990454, _990456, _990458, _990460] : [c_Finite__Set_Ofolding__image__simple(_990448, _990450, _990452, _990454, _990456, _990458), hBOOL(hAPP(c_Finite__Set_Ofinite(_990450), _990460)), -(hAPP(_990458, _990460) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_990448, _990450, _990452), _990456), _990454), _990460))], (40193 ^ _778495) ^ [_1563285, _1563287] : [c_Wellfounded_Oacyclic(_1563285, _1563287), 40196 ^ _778495 : [(40197 ^ _778495) ^ [_1563370] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563285, _1563285)), hAPP(hAPP(c_Product__Type_OPair(_1563285, _1563285), _1563370), _1563370)), c_Transitive__Closure_Otrancl(_1563285, _1563287)))]]], (6994 ^ _778495) ^ [_893353, _893355, _893357] : [class_Lattices_Olattice(_893353), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893353), _893355), _893357) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893353), _893357), _893355))], (48364 ^ _778495) ^ [_1753544, _1753546, _1753548] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1753544), hAPP(c_COMBK(_1753544, tc_Nat_Onat), _1753546)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1753548)) = c_List_Oreplicate(_1753544, _1753548, _1753546))], (30077 ^ _778495) ^ [_1326260, _1326262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1326260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1326262)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1326260), _1326262) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1326260, _1326262)))], (42846 ^ _778495) ^ [_1632388, _1632390] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1632388), _1632390))), -(c_List_Oupto(_1632388, _1632390) = c_List_Olist_ONil(tc_Int_Oint))], (15425 ^ _778495) ^ [_1052495, _1052497] : [-(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), _1052495), _1052497)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1052495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1052497))], (12543 ^ _778495) ^ [_999954, _999956, _999958, _999960, _999962, _999964, _999966] : [c_Big__Operators_Ocomm__monoid__big(_999954, _999956, _999958, _999960, _999962), 12546 ^ _778495 : [(12553 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_999956), _999964))), -(hAPP(hAPP(_999962, _999966), _999964) = _999960)], (12547 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_999956), _999964)), -(hAPP(hAPP(_999962, _999966), _999964) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_999954, _999956, _999958), _999966), _999960), _999964))]]], (12531 ^ _778495) ^ [_999726, _999728] : [class_Complete__Lattice_Ocomplete__lattice(_999726), -(c_Complete__Lattice_OSup__class_OSup(_999726, hAPP(hAPP(c_Set_Oinsert(_999726), _999728), c_Orderings_Obot__class_Obot(tc_fun(_999726, tc_HOL_Obool)))) = _999728)], (52427 ^ _778495) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (27827 ^ _778495) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23088 ^ _778495) ^ [_1191530, _1191532, _1191534, _1191536] : [class_Divides_Osemiring__div(_1191530), -(c_Divides_Odiv__class_Omod(_1191530, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191530), c_Divides_Odiv__class_Omod(_1191530, _1191532, _1191534)), _1191536), _1191534) = c_Divides_Odiv__class_Omod(_1191530, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191530), _1191532), _1191536), _1191534))], (1418 ^ _778495) ^ [_799248, _799250] : [-(class_Lattices_Obounded__lattice__bot(_799248)), _799250 = _799248, class_Lattices_Obounded__lattice__bot(_799250)], (40888 ^ _778495) ^ [_1580623, _1580625, _1580627] : [40890 ^ _778495 : [(40891 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1580623), 40889 ^ [_1580623, _1580625, _1580627]), _1580625)))], (40896 ^ _778495) ^ [] : [40889 ^ [_1580623, _1580625, _1580627] = 40892 ^ [_1580623, _1580625, _1580627]], (40900 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580623, _1580623)), hAPP(hAPP(c_Product__Type_OPair(_1580623, _1580623), 40892 ^ [_1580623, _1580625, _1580627]), 40889 ^ [_1580623, _1580625, _1580627])), _1580627))], (40898 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580623, _1580623)), hAPP(hAPP(c_Product__Type_OPair(_1580623, _1580623), 40889 ^ [_1580623, _1580625, _1580627]), 40892 ^ [_1580623, _1580625, _1580627])), _1580627))], (40894 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1580623), 40892 ^ [_1580623, _1580625, _1580627]), _1580625)))]], -(c_Relation_Ototal__on(_1580623, _1580625, _1580627))], (36488 ^ _778495) ^ [_1465174, _1465176, _1465178] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465174), _1465176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465174, tc_HOL_Obool)), _1465176), hAPP(c_Set_Oimage(_1465174, _1465174, _1465178), _1465176))), -(c_Fun_Oinj__on(_1465174, _1465174, _1465178, _1465176))], (370 ^ _778495) ^ [_784128, _784130, _784132, _784134] : [-(c_Wellfounded_OwfP(_784132, _784128)), c_Wellfounded_OwfP(_784134, _784130), _784134 = _784132, _784130 = _784128], (2106 ^ _778495) ^ [_809185, _809187] : [_809187 = _809185, -(c_Int_Osucc(_809187) = c_Int_Osucc(_809185))], (16442 ^ _778495) ^ [_1072234, _1072236, _1072238, _1072240] : [class_Fields_Olinordered__field(_1072234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072234), c_Groups_Ozero__class_Ozero(_1072234)), _1072236)), 16449 ^ _778495 : [(16456 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072234), _1072238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072234), _1072240), _1072236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072234), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1072234), _1072238), _1072236)), _1072240)))], (16450 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072234), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1072234), _1072238), _1072236)), _1072240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072234), _1072238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072234), _1072240), _1072236))))]]], (40840 ^ _778495) ^ [_1579643, _1579645, _1579647] : [c_Relation_Orefl__on(_1579643, _1579645, _1579647), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1579643, _1579643), tc_HOL_Obool)), _1579647), hAPP(hAPP(c_Relation_Orel__comp(_1579643, _1579643, _1579643), hAPP(c_Relation_Oconverse(_1579643, _1579643), _1579647)), _1579647))))], (41314 ^ _778495) ^ [_1592125, _1592127, _1592129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592125), c_Nitpick_Oplus__frac(_1592125, _1592127, c_Nitpick_Ouminus__frac(_1592125, _1592129)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1592125, _1592127, _1592129))], (48492 ^ _778495) ^ [_1756336, _1756338, _1756340, _1756342, _1756344] : [48494 ^ _778495 : [(48497 ^ _778495) ^ [] : [c_Relation_Orefl__on(_1756340, hAPP(_1756342, 48493 ^ [_1756336, _1756338, _1756340, _1756342, _1756344]), hAPP(_1756344, 48493 ^ [_1756336, _1756338, _1756340, _1756342, _1756344]))], (48495 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756336), 48493 ^ [_1756336, _1756338, _1756340, _1756342, _1756344]), _1756338)))]], -(c_Relation_Orefl__on(_1756340, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756336, tc_fun(_1756340, tc_HOL_Obool)), _1756338), _1756342), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756336, tc_fun(tc_prod(_1756340, _1756340), tc_HOL_Obool)), _1756338), _1756344)))], (23330 ^ _778495) ^ [_1196622, _1196624, _1196626, _1196628] : [class_Divides_Osemiring__div(_1196622), -(c_Divides_Odiv__class_Omod(_1196622, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1196622), _1196624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196622), _1196626), _1196628)), _1196628) = c_Divides_Odiv__class_Omod(_1196622, _1196624, _1196628))], (22806 ^ _778495) ^ [_1186201, _1186203] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186201)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186203))))), _1186201 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1186203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48062 ^ _778495) ^ [_1746776, _1746778, _1746780, _1746782, _1746784, _1746786, _1746788] : [-(c_New__Random__Sequence_Opos__decr__bind(_1746776, _1746778, _1746780, _1746782, _1746784, _1746786, _1746788) = c_New__DSequence_Opos__decr__bind(_1746776, _1746778, hAPP(hAPP(hAPP(_1746780, _1746784), _1746786), _1746788), hAPP(hAPP(c_COMBC(_1746776, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746778))), hAPP(hAPP(c_COMBC(_1746776, 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(_1746778)))), hAPP(hAPP(c_COMBC(_1746776, 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(_1746778))))), _1746782), _1746784)), _1746786)), _1746788)))], (20143 ^ _778495) ^ [_1140297, _1140299, _1140301] : [class_Rings_Osemiring__1(_1140297), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140297), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1140299), _1140301)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140297), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140297), _1140299)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140297), _1140301)))], (11490 ^ _778495) ^ [_977467, _977469, _977471, _977473] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_977467), 11493 ^ _778495 : [(11500 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977467), _977469), _977473)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977467), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977467), _977469), _977471)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977467), _977473), _977471))))], (11494 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977467), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977467), _977469), _977471)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977467), _977473), _977471))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977467), _977469), _977473)))]]], (48144 ^ _778495) ^ [_1748901, _1748903, _1748905, _1748907, _1748909] : [hBOOL(hAPP(hAPP(_1748901, _1748903), _1748905)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748907, _1748909, _1748901), _1748905), _1748903)))], (42644 ^ _778495) ^ [_1628653] : [-(c_List_Obutlast(_1628653, c_List_Olist_ONil(_1628653)) = c_List_Olist_ONil(_1628653))], (26602 ^ _778495) ^ [_1254418, _1254420] : [class_Int_Onumber__ring(_1254418), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1254418), hAPP(c_Int_Onumber__class_Onumber__of(_1254418), 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)))), _1254420))) = hAPP(c_Int_Onumber__class_Onumber__of(_1254418), c_Int_OMin))], (46852 ^ _778495) ^ [_1720675, _1720677, _1720679, _1720681] : [hBOOL(hAPP(hAPP(c_member(_1720675), _1720677), hAPP(c_List_Oset(_1720675), c_List_OtakeWhile(_1720675, _1720679, _1720681)))), 46855 ^ _778495 : [(46858 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1720679, _1720677)))], (46856 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720675), _1720677), hAPP(c_List_Oset(_1720675), _1720681))))]]], (44271 ^ _778495) ^ [_1663856, _1663858, _1663860, _1663862] : [-(hAPP(hAPP(c_List_Oappend(_1663856), _1663858), hAPP(hAPP(c_List_Olist_OCons(_1663856), _1663860), c_List_Olist_ONil(_1663856))) = _1663862), -(_1663862 = c_List_Olist_ONil(_1663856)), c_List_Obutlast(_1663856, _1663862) = _1663858, c_List_Olast(_1663856, _1663862) = _1663860], (6470 ^ _778495) ^ [_883271, _883273, _883275, _883277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883271, tc_HOL_Obool)), _883273), _883275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883271, tc_HOL_Obool)), _883277), _883275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883271, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_883271, tc_HOL_Obool)), _883273), _883277)), _883275)))], (44375 ^ _778495) ^ [_1666430, _1666432, _1666434, _1666436] : [hAPP(hAPP(c_List_Omap(_1666430, _1666432), _1666434), _1666436) = c_List_Olist_ONil(_1666432), -(_1666436 = c_List_Olist_ONil(_1666430))], (28181 ^ _778495) ^ [_1281358, _1281360, _1281362, _1281364] : [class_Rings_Oring__1(_1281358), -(hAPP(c_Int_Oring__1__class_Oof__int(_1281358), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1281360, tc_Int_Oint), _1281362), _1281364)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1281360, _1281358), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1281358, _1281360), c_Int_Oring__1__class_Oof__int(_1281358)), _1281362)), _1281364))], (45697 ^ _778495) ^ [_1696657, _1696659, _1696661, _1696663] : [-(hBOOL(hAPP(_1696657, _1696659))), -(c_List_Oremove1(_1696661, _1696659, hAPP(c_List_Ofilter(_1696661, _1696657), _1696663)) = hAPP(c_List_Ofilter(_1696661, _1696657), _1696663))], (27758 ^ _778495) ^ [_1273820, _1273822, _1273824] : [27760 ^ _778495 : [(27765 ^ _778495) ^ [] : [hBOOL(hAPP(_1273822, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 27759 ^ [_1273820, _1273822, _1273824]), _1273820)))], (27763 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1273822, 27759 ^ [_1273820, _1273822, _1273824])))], (27761 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27759 ^ [_1273820, _1273822, _1273824]), _1273820)))]], hBOOL(hAPP(_1273822, _1273824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1273824), _1273820)), -(hBOOL(hAPP(_1273822, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21588 ^ _778495) ^ [_1165106, _1165108] : [class_Int_Onumber__ring(_1165106), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1165106), hAPP(c_Int_Onumber__class_Onumber__of(_1165106), _1165108)), c_Groups_Oone__class_Oone(_1165106)) = hAPP(c_Int_Onumber__class_Onumber__of(_1165106), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1165108), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (5208 ^ _778495) ^ [_858046, _858048] : [_858048 = _858046, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_858048) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_858046))], (40934 ^ _778495) ^ [_1582059, _1582061, _1582063, _1582065] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1582059, _1582061), tc_fun(_1582059, _1582061)), _1582063), c_Fun_Ocomp(_1582061, _1582061, _1582059, _1582065)) = c_Fun_Ocomp(_1582061, _1582061, _1582059, hAPP(hAPP(c_Nat_Ocompow(_1582061, _1582061), _1582063), _1582065)))], (45402 ^ _778495) ^ [_1689705, _1689707] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689705)), c_List_Oremdups(_1689705, _1689707)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689705)), _1689707), -(c_List_Oremdups(_1689705, _1689707) = _1689707)], (36047 ^ _778495) ^ [_1455274, _1455276, _1455278, _1455280, _1455282, _1455284] : [c_Equiv__Relations_Ocongruent(_1455274, _1455276, _1455278, _1455280), hBOOL(hAPP(hAPP(c_member(tc_prod(_1455274, _1455274)), hAPP(hAPP(c_Product__Type_OPair(_1455274, _1455274), _1455282), _1455284)), _1455278)), -(hAPP(_1455280, _1455282) = hAPP(_1455280, _1455284))], (2914 ^ _778495) ^ [_821755, _821757, _821759, _821761] : [-(c_Nitpick_Ouminus__frac(_821761, _821757) = c_Nitpick_Ouminus__frac(_821759, _821755)), _821761 = _821759, _821757 = _821755], (1718 ^ _778495) ^ [_802998, _803000] : [-(class_Groups_Ocomm__monoid__add(_802998)), _803000 = _802998, class_Groups_Ocomm__monoid__add(_803000)], (41515 ^ _778495) ^ [_1598508, _1598510] : [-(c_List_Olistrel1(_1598508, hAPP(c_Relation_Oconverse(_1598508, _1598508), _1598510)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1598508), tc_List_Olist(_1598508)), c_List_Olistrel1(_1598508, _1598510)))], (46405 ^ _778495) ^ [_1711269, _1711271, _1711273, _1711275, _1711277, _1711279] : [class_Orderings_Olinorder(_1711269), c_List_Olinorder__class_Osorted(_1711269, hAPP(hAPP(c_List_Omap(_1711271, _1711269), _1711273), _1711275)), hBOOL(hAPP(_1711277, _1711279)), -(hAPP(c_List_Ofilter(_1711271, _1711277), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1711271, _1711269, _1711273), _1711279), _1711275)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1711271, _1711269, _1711273), _1711279), hAPP(c_List_Ofilter(_1711271, _1711277), _1711275)))], (4166 ^ _778495) ^ [_841661, _841663] : [_841663 = _841661, -(c_List_Odrop(_841663) = c_List_Odrop(_841661))], (5879 ^ _778495) ^ [_872128, _872130, _872132, _872134] : [hBOOL(hAPP(hAPP(c_member(_872128), _872130), hAPP(hAPP(c_Set_Oinsert(_872128), _872132), _872134))), -(_872130 = _872132), -(hBOOL(hAPP(hAPP(c_member(_872128), _872130), _872134)))], (6060 ^ _778495) ^ [_875492, _875494, _875496, _875498] : [hBOOL(hAPP(hAPP(c_member(_875492), _875494), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_875492, tc_HOL_Obool)), _875496), _875498))), 6063 ^ _778495 : [(6066 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_875492), _875494), _875498))], (6064 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_875492), _875494), _875496)))]]], (52431 ^ _778495) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (6664 ^ _778495) ^ [_887444, _887446] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887444, tc_HOL_Obool)), _887446), _887446) = c_Orderings_Obot__class_Obot(tc_fun(_887444, tc_HOL_Obool)))], (14979 ^ _778495) ^ [_1044190, _1044192, _1044194, _1044196] : [class_Rings_Olinordered__semiring__strict(_1044190), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044190), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044190), _1044192), _1044194)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044190), _1044192), _1044196))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044190), c_Groups_Ozero__class_Ozero(_1044190)), _1044192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044190), _1044194), _1044196)))], (16646 ^ _778495) ^ [_1076079, _1076081, _1076083, _1076085] : [class_Fields_Olinordered__field(_1076079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076079), _1076081), _1076083)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076079), c_Groups_Ozero__class_Ozero(_1076079)), _1076085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076079), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1076079), _1076081), _1076085)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1076079), _1076083), _1076085))))], (32020 ^ _778495) ^ [_1367434, _1367436, _1367438] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1367434, tc_HOL_Obool)), _1367436), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1367434, tc_HOL_Obool), _1367438)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1367434, tc_HOL_Obool), tc_fun(_1367434, tc_HOL_Obool)), _1367438), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1367434, tc_HOL_Obool)), _1367436)))], (19146 ^ _778495) ^ [_1122737, _1122739] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122737), _1122739))), -(_1122737 = _1122739), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122739), _1122737)))], (6366 ^ _778495) ^ [_881559, _881561, _881563, _881565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881559, tc_HOL_Obool)), _881561), _881563)), hBOOL(hAPP(hAPP(c_member(_881559), _881565), _881561)), -(hBOOL(hAPP(hAPP(c_member(_881559), _881565), _881563)))], (17652 ^ _778495) ^ [_1095067, _1095069, _1095071, _1095073] : [class_Orderings_Olinorder(_1095067), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095067), _1095069), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095067), _1095071), _1095073)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095067), _1095071), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095067), _1095069), _1095073)))], (28675 ^ _778495) ^ [_1298094] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1298094) = 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), _1298094), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (45889 ^ _778495) ^ [_1701944, _1701946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701944), _1701946)), -(c_List_Oupt(_1701944, hAPP(c_Nat_OSuc, _1701946)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701944, _1701946)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1701946), c_List_Olist_ONil(tc_Nat_Onat))))], (23729 ^ _778495) ^ [_1203569, _1203571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203569), 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)), _1203571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203569), _1203571)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39676 ^ _778495) ^ [_1551302, _1551304, _1551306, _1551308, _1551310, _1551312, _1551314, _1551316] : [c_Finite__Set_Ofolding(_1551302, _1551304, _1551306, _1551308), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551302), _1551310)), -(hAPP(c_Fun_Ocomp(_1551304, _1551304, _1551312, hAPP(_1551306, _1551314)), hAPP(c_Fun_Ocomp(_1551304, _1551304, _1551312, hAPP(_1551308, _1551310)), _1551316)) = hAPP(c_Fun_Ocomp(_1551304, _1551304, _1551312, hAPP(_1551308, _1551310)), hAPP(c_Fun_Ocomp(_1551304, _1551304, _1551312, hAPP(_1551306, _1551314)), _1551316)))], (34273 ^ _778495) ^ [_1417670, _1417672] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1417670), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1417672) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1417670, _1417672))], (51765 ^ _778495) ^ [_1823538, _1823540, _1823542] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823538, _1823540) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1823542), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1823538 = _1823540, _1823540 = _1823542], (50493 ^ _778495) ^ [_1801225, _1801227, _1801229, _1801231, _1801233, _1801235] : [50496 ^ _778495 : [(50503 ^ _778495) ^ [] : [hAPP(hAPP(_1801233, 50494 ^ [_1801225, _1801227, _1801229, _1801231, _1801233, _1801235]), 50498 ^ [_1801225, _1801227, _1801229, _1801231, _1801233, _1801235]) = hAPP(hAPP(_1801233, 50495 ^ [_1801225, _1801227, _1801229, _1801231, _1801233, _1801235]), 50499 ^ [_1801225, _1801227, _1801229, _1801231, _1801233, _1801235])], (50501 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801229, _1801229)), hAPP(hAPP(c_Product__Type_OPair(_1801229, _1801229), 50498 ^ [_1801225, _1801227, _1801229, _1801231, _1801233, _1801235]), 50499 ^ [_1801225, _1801227, _1801229, _1801231, _1801233, _1801235])), _1801231)))], (50497 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801225, _1801225)), hAPP(hAPP(c_Product__Type_OPair(_1801225, _1801225), 50494 ^ [_1801225, _1801227, _1801229, _1801231, _1801233, _1801235]), 50495 ^ [_1801225, _1801227, _1801229, _1801231, _1801233, _1801235])), _1801227)))]], -(c_Equiv__Relations_Ocongruent2(_1801225, _1801229, _1801235, _1801227, _1801231, _1801233))], (22062 ^ _778495) ^ [_1173186, _1173188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1173186), _1173188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1173186)), c_Int_OBit0(_1173188))))], (20993 ^ _778495) ^ [_1154571, _1154573, _1154575] : [class_Orderings_Olinorder(_1154571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1154571), _1154573)), 21003 ^ _778495 : [(21006 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154571), _1154575), 21002 ^ [_1154571, _1154573, _1154575]))], (21004 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1154571), 21002 ^ [_1154571, _1154573, _1154575]), _1154573)))]], hBOOL(hAPP(hAPP(c_member(_1154571), _1154575), _1154573)), -(c_Big__Operators_Olinorder__class_OMin(_1154571, _1154573) = _1154575)], (27363 ^ _778495) ^ [_1266933, _1266935] : [class_Rings_Olinordered__idom(_1266933), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266933), c_Groups_Osgn__class_Osgn(_1266933, _1266935)), hAPP(c_Groups_Oabs__class_Oabs(_1266933), _1266935)) = _1266935)], (41772 ^ _778495) ^ [_1606315, _1606317, _1606319] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606315)), _1606317), c_List_Olists(_1606315, c_Wellfounded_Oacc(_1606315, _1606319)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606315)), _1606317), c_Wellfounded_Oacc(tc_List_Olist(_1606315), c_List_Olistrel1(_1606315, _1606319)))))], (12058 ^ _778495) ^ [_989317, _989319, _989321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989317), _989319)), 12061 ^ _778495 : [(12068 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989321), _989317)), _989319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989321), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989319), _989317))))], (12062 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989321), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989319), _989317))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989321), _989317)), _989319)))]]], (24701 ^ _778495) ^ [_1220685, _1220687, _1220689, _1220691] : [class_Rings_Ocomm__semiring__1(_1220685), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220685), hAPP(hAPP(c_Power_Opower__class_Opower(_1220685), _1220687), _1220689)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220685), _1220687), _1220691)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1220685), _1220687), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220689), _1220691)))], (45895 ^ _778495) ^ [_1702082, _1702084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702082), _1702084)), -(c_List_Oupt(_1702082, hAPP(c_Nat_OSuc, _1702084)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1702082, _1702084)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702084), c_List_Olist_ONil(tc_Nat_Onat))))], (36314 ^ _778495) ^ [_1461880, _1461882, _1461884, _1461886] : [c_Fun_Oinj__on(_1461880, _1461882, _1461884, c_Orderings_Otop__class_Otop(tc_fun(_1461880, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1461880, tc_fun(_1461886, _1461882), hAPP(hAPP(c_COMBB(_1461882, tc_fun(_1461886, _1461882), _1461880), c_COMBK(_1461882, _1461886)), _1461884), c_Orderings_Otop__class_Otop(tc_fun(_1461880, tc_HOL_Obool))))], (42211 ^ _778495) ^ [_1619106, _1619108] : [class_Groups_Ocomm__monoid__add(_1619106), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1619106), _1619108) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1619106), hAPP(c_List_Onth(_1619106), _1619108)), 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(_1619106)), _1619108))))], (42254 ^ _778495) ^ [_1619938, _1619940] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1619938, _1619940) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1619938), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1619940)))], (43562 ^ _778495) ^ [_1649213, _1649215, _1649217, _1649219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1649213), _1649215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1649217, tc_HOL_Obool)), hAPP(c_List_Oset(_1649217), hAPP(hAPP(c_List_Odrop(_1649217), _1649215), _1649219))), hAPP(c_List_Oset(_1649217), hAPP(hAPP(c_List_Odrop(_1649217), _1649213), _1649219)))))], (43281 ^ _778495) ^ [_1641921, _1641923, _1641925] : [_1641921 = c_List_Olist_ONil(_1641923), -(c_List_Obutlast(_1641923, hAPP(hAPP(c_List_Oappend(_1641923), _1641925), _1641921)) = c_List_Obutlast(_1641923, _1641925))], (46312 ^ _778495) ^ [_1709431, _1709433, _1709435, _1709437, _1709439] : [class_Orderings_Olinorder(_1709431), c_List_Olinorder__class_Osorted(_1709431, hAPP(hAPP(c_List_Omap(_1709433, _1709431), _1709435), _1709437)), -(c_List_Olinorder__class_Osorted(_1709431, hAPP(hAPP(c_List_Omap(_1709433, _1709431), _1709435), hAPP(c_List_Ofilter(_1709433, _1709439), _1709437))))], (32022 ^ _778495) ^ [_1367501, _1367503, _1367505] : [class_Orderings_Oorder(_1367501), 32025 ^ _778495 : [(32032 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367501), _1367503), _1367505))), -(c_Orderings_Obot__class_Obot(tc_fun(_1367501, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1367501, _1367503, _1367505))], (32026 ^ _778495) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1367501, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1367501, _1367503, _1367505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367501), _1367503), _1367505))]]], (48168 ^ _778495) ^ [_1749375, _1749377, _1749379, _1749381, _1749383] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749375, _1749377, hAPP(hAPP(c_COMBC(_1749375, tc_fun(tc_prod(_1749375, _1749377), tc_HOL_Obool), tc_fun(_1749377, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749377, tc_fun(tc_fun(tc_prod(_1749375, _1749377), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1749375, _1749377), tc_HOL_Obool), tc_fun(_1749377, tc_HOL_Obool)), _1749375), c_COMBC(_1749377, tc_fun(tc_prod(_1749375, _1749377), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749377, tc_prod(_1749375, _1749377)), tc_fun(_1749377, tc_fun(tc_fun(tc_prod(_1749375, _1749377), tc_HOL_Obool), tc_HOL_Obool)), _1749375), hAPP(c_COMBB(tc_prod(_1749375, _1749377), tc_fun(tc_fun(tc_prod(_1749375, _1749377), tc_HOL_Obool), tc_HOL_Obool), _1749377), c_member(tc_prod(_1749375, _1749377)))), c_Product__Type_OPair(_1749375, _1749377)))), _1749379)), _1749381), _1749383)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1749377, _1749375)), hAPP(hAPP(c_Product__Type_OPair(_1749377, _1749375), _1749381), _1749383)), hAPP(c_Relation_Oconverse(_1749375, _1749377), _1749379))))], (28917 ^ _778495) ^ [_1303337, _1303339, _1303341, _1303343, _1303345] : [-(c_Nat_Onat_Onat__case(_1303337, _1303339, _1303341, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1303343)), _1303345)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1303337), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1303343))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1303337, _1303337), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1303337, tc_fun(_1303337, _1303337)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1303337, tc_fun(_1303337, _1303337)), tc_Int_Oint), c_If(_1303337)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1303337, _1303339, _1303341, _1303345))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1303337, tc_Int_Oint), _1303341), 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)), _1303345)))))], (20494 ^ _778495) ^ [_1146206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146206), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146206) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31868 ^ _778495) ^ [_1362835, _1362837, _1362839, _1362841, _1362843] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362835, tc_HOL_Obool)), _1362837), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362839, tc_fun(_1362835, tc_HOL_Obool)), _1362841), _1362843)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362839, tc_fun(_1362835, tc_HOL_Obool)), _1362841), hAPP(hAPP(c_COMBB(tc_fun(_1362835, tc_HOL_Obool), tc_fun(_1362835, tc_HOL_Obool), _1362839), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362835, tc_HOL_Obool)), _1362837)), _1362843)))], (46700 ^ _778495) ^ [_1717442, _1717444, _1717446] : [_1717444 = hAPP(c_List_Orev(_1717442), _1717446), -(hAPP(c_List_Orev(_1717442), _1717444) = _1717446)], (51755 ^ _778495) ^ [_1823363] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823363, _1823363) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1823363), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (27527 ^ _778495) ^ [_1269746] : [class_Finite__Set_Ofinite(_1269746), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1269746), c_Orderings_Otop__class_Otop(tc_fun(_1269746, tc_HOL_Obool)))))], (20458 ^ _778495) ^ [_1145635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145635)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1145635))], (52605 ^ _778495) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (5659 ^ _778495) ^ [_867817, _867819, _867821, _867823] : [c_Hoare__Mirabelle_Ohoare__derivs(_867817, _867819, _867821), c_Hoare__Mirabelle_Ohoare__derivs(_867817, _867823, _867819), -(c_Hoare__Mirabelle_Ohoare__derivs(_867817, _867823, _867821))], (9298 ^ _778495) ^ [_935996, _935998, _936000, _936002] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_935996, _935998, _936000), _936002), c_Orderings_Obot__class_Obot(tc_fun(_935996, tc_HOL_Obool))) = _936002)], (31584 ^ _778495) ^ [_1355437, _1355439] : [class_Orderings_Olinorder(_1355437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355437), _1355439)), -(_1355439 = c_Orderings_Obot__class_Obot(tc_fun(_1355437, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1355437), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355437), 31597 ^ [_1355437, _1355439]), 31598 ^ [_1355437, _1355439])), hAPP(hAPP(c_Set_Oinsert(_1355437), 31597 ^ [_1355437, _1355439]), hAPP(hAPP(c_Set_Oinsert(_1355437), 31598 ^ [_1355437, _1355439]), c_Orderings_Obot__class_Obot(tc_fun(_1355437, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1355437), c_Big__Operators_Olattice_OSup__fin(_1355437, c_Orderings_Oord__class_Omax(_1355437), _1355439)), _1355439)))], (48803 ^ _778495) ^ [_1763591, _1763593] : [-(hBOOL(hAPP(_1763593, 48810 ^ [_1763591, _1763593]))), 48804 ^ _778495 : [(48805 ^ _778495) ^ [_1763652] : [hBOOL(hAPP(hAPP(c_member(_1763591), _1763652), c_Orderings_Otop__class_Otop(tc_fun(_1763591, tc_HOL_Obool)))), hBOOL(hAPP(_1763593, _1763652))]]], (43157 ^ _778495) ^ [_1639484, _1639486, _1639488, _1639490, _1639492, _1639494] : [hAPP(hAPP(c_List_Oappend(_1639484), _1639486), _1639488) = _1639490, _1639492 = hAPP(hAPP(c_List_Oappend(_1639484), _1639488), _1639494), -(hAPP(hAPP(c_List_Oappend(_1639484), _1639486), _1639492) = hAPP(hAPP(c_List_Oappend(_1639484), _1639490), _1639494))], (29735 ^ _778495) ^ [_1319281, _1319283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1319281), 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)), _1319283)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1319281, _1319283), c_Divides_OnegDivAlg(_1319281, _1319283))))], (42191 ^ _778495) ^ [_1618545, _1618547, _1618549, _1618551, _1618553, _1618555] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618545, _1618547)), hAPP(hAPP(c_Product__Type_OPair(_1618545, _1618547), _1618549), _1618551)), hAPP(c_List_Oset(tc_prod(_1618545, _1618547)), hAPP(hAPP(c_List_Ozip(_1618545, _1618547), _1618553), _1618555)))), 42194 ^ _778495 : [(42197 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618547), _1618551), hAPP(c_List_Oset(_1618547), _1618555))))], (42195 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618545), _1618549), hAPP(c_List_Oset(_1618545), _1618553))))]]], (17542 ^ _778495) ^ [_1092776, _1092778, _1092780] : [hBOOL(hAPP(hAPP(c_member(_1092776), _1092778), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1092776, tc_HOL_Obool), _1092780))), 17546 ^ _778495 : [(17549 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1092776, tc_HOL_Obool)), 17545 ^ [_1092776, _1092778, _1092780]), _1092780)))], (17547 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1092776), _1092778), 17545 ^ [_1092776, _1092778, _1092780])))]]], (11308 ^ _778495) ^ [_973666, _973668, _973670, _973672] : [class_Groups_Ocancel__semigroup__add(_973666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973666), _973668), _973670) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973666), _973668), _973672), -(_973670 = _973672)], (7928 ^ _778495) ^ [_909200, _909202, _909204] : [class_Orderings_Olinorder(_909200), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909200), _909202), _909204)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909200), _909204), _909202))], (42405 ^ _778495) ^ [_1623249, _1623251] : [-(c_List_Obutlast(_1623249, _1623251) = hAPP(hAPP(c_List_Otake(_1623249), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623249)), _1623251)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1623251))], (39360 ^ _778495) ^ [_1543910, _1543912, _1543914, _1543916, _1543918, _1543920] : [-(hAPP(c_Set_Ovimage(_1543910, tc_prod(_1543912, _1543914), _1543916), hAPP(hAPP(c_Product__Type_OSigma(_1543912, _1543914), _1543918), hAPP(c_COMBK(tc_fun(_1543914, tc_HOL_Obool), _1543912), _1543920))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543910, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1543910, _1543912, hAPP(c_Fun_Ocomp(tc_prod(_1543912, _1543914), _1543912, _1543910, c_Product__Type_Ofst(_1543912, _1543914)), _1543916)), _1543918)), hAPP(c_Set_Ovimage(_1543910, _1543914, hAPP(c_Fun_Ocomp(tc_prod(_1543912, _1543914), _1543914, _1543910, c_Product__Type_Osnd(_1543912, _1543914)), _1543916)), _1543920)))], (50036 ^ _778495) ^ [_1790378, _1790380, _1790382, _1790384] : [c_Fun_Obij__betw(_1790378, _1790380, _1790382, c_Orderings_Obot__class_Obot(tc_fun(_1790378, tc_HOL_Obool)), _1790384), -(_1790384 = c_Orderings_Obot__class_Obot(tc_fun(_1790380, tc_HOL_Obool)))], (52095 ^ _778495) ^ [_1829764, _1829766] : [class_Lattices_Obounded__lattice(_1829764), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1829766, _1829764)))], (7036 ^ _778495) ^ [_894232, _894234, _894236, _894238] : [class_Lattices_Osemilattice__sup(_894232), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894232), _894234), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894232), _894236), _894238)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894232), _894236), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894232), _894234), _894238)))], (44151 ^ _778495) ^ [_1661920, _1661922, _1661924] : [class_Orderings_Olinorder(_1661920), hBOOL(hAPP(hAPP(c_member(_1661920), _1661922), hAPP(c_List_Oset(_1661920), _1661924))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661920, _1661920, c_COMBI(_1661920), _1661922, _1661924) = _1661924)], (5348 ^ _778495) ^ [_860266, _860268] : [_860268 = _860266, -(c_Groups_Ouminus__class_Ouminus(_860268) = c_Groups_Ouminus__class_Ouminus(_860266))], (51533 ^ _778495) ^ [_1819552, _1819554, _1819556] : [class_Rings_Ocomm__ring__1(_1819552), 51536 ^ _778495 : [(51543 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819552), _1819554), _1819556)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819552), _1819554), hAPP(c_Groups_Ouminus__class_Ouminus(_1819552), _1819556))))], (51537 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819552), _1819554), hAPP(c_Groups_Ouminus__class_Ouminus(_1819552), _1819556))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819552), _1819554), _1819556)))]]], (9220 ^ _778495) ^ [_934291, _934293] : [class_Lattices_Obounded__lattice__bot(_934291), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934291), c_Orderings_Obot__class_Obot(_934291)), _934293) = c_Orderings_Obot__class_Obot(_934291))], (37220 ^ _778495) ^ [_1481565, _1481567, _1481569, _1481571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1481565), _1481567)), c_Fun_Oinj__on(_1481569, _1481565, _1481571, c_Orderings_Otop__class_Otop(tc_fun(_1481569, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1481569), hAPP(c_Set_Ovimage(_1481569, _1481565, _1481571), _1481567))))], (30411 ^ _778495) ^ [_1332958, _1332960, _1332962, _1332964, _1332966, _1332968] : [hBOOL(hAPP(hAPP(c_member(_1332958), _1332960), c_SetInterval_Oord_OgreaterThanAtMost(_1332958, _1332962, _1332964, _1332966, _1332968))), 30414 ^ _778495 : [(30417 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1332962, _1332960), _1332968)))], (30415 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1332964, _1332966), _1332960)))]]], (24517 ^ _778495) ^ [_1217353, _1217355] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217353), _1217355)), _1217355) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1217353), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1217353, _1217355)))], (47992 ^ _778495) ^ [_1745325, _1745327] : [c_List_Olist__ex1(_1745325, _1745327, c_List_Olist_ONil(_1745325))], (25518 ^ _778495) ^ [_1234420, _1234422, _1234424] : [-(hBOOL(hAPP(_1234420, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1234422), _1234424)))), 25519 ^ _778495 : [(25526 ^ _778495) ^ [_1234588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1234424), _1234588)), _1234422)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1234422), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1234424), hAPP(c_Nat_OSuc, _1234588)))), hBOOL(hAPP(_1234420, _1234588))], (25520 ^ _778495) ^ [] : [_1234424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1234420, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10537 ^ _778495) ^ [_960396, _960398, _960400] : [_960398 = _960400, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _960396)), _960398) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _960396)), _960400))], (32932 ^ _778495) ^ [_1386135, _1386137] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1386135, _1386137))))], (18084 ^ _778495) ^ [_1102878, _1102880, _1102882] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102878), _1102880)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102882), _1102880)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1102878), _1102882)), _1102880))], (22662 ^ _778495) ^ [_1183615, _1183617] : [class_Rings_Oring__1(_1183615), hBOOL(hAPP(hAPP(c_member(_1183615), _1183617), c_Int_Oring__1__class_OInts(_1183615))), -(hBOOL(hAPP(hAPP(c_member(_1183615), hAPP(c_Groups_Ouminus__class_Ouminus(_1183615), _1183617)), c_Int_Oring__1__class_OInts(_1183615))))], (10735 ^ _778495) ^ [_963442, _963444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963442)), hAPP(c_Nat_OSuc, _963444))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963442), _963444)))], (14841 ^ _778495) ^ [_1041710, _1041712, _1041714] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041710), _1041712)), 14844 ^ _778495 : [(14864 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1041710, tc_Nat_Onat), _1041714), _1041712) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 14865 ^ _778495 : [(14866 ^ _778495) ^ [_1042191] : [hBOOL(hAPP(hAPP(c_member(_1041710), _1042191), _1041712)), hAPP(_1041714, _1042191) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 14874 ^ _778495 : [(14879 ^ _778495) ^ [] : [hAPP(_1041714, 14873 ^ [_1041710, _1041712, _1041714, _1042191]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14877 ^ _778495) ^ [] : [_1042191 = 14873 ^ [_1041710, _1041712, _1041714, _1042191]], (14875 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1041710), 14873 ^ [_1041710, _1041712, _1041714, _1042191]), _1041712)))]]]]], (14845 ^ _778495) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1041710, tc_Nat_Onat), _1041714), _1041712) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 14849 ^ _778495 : [(14854 ^ _778495) ^ [_1042030] : [hBOOL(hAPP(hAPP(c_member(_1041710), _1042030), _1041712)), -(14848 ^ [_1041710, _1041712, _1041714] = _1042030), -(hAPP(_1041714, _1042030) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14852 ^ _778495) ^ [] : [-(hAPP(_1041714, 14848 ^ [_1041710, _1041712, _1041714]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (14850 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1041710), 14848 ^ [_1041710, _1041712, _1041714]), _1041712)))]]]]], (22014 ^ _778495) ^ [_1172212, _1172214, _1172216] : [class_Rings_Oring(_1172212), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172212), hAPP(c_Groups_Ouminus__class_Ouminus(_1172212), _1172214)), hAPP(c_Groups_Ouminus__class_Ouminus(_1172212), _1172216)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172212), _1172214), _1172216))], (24443 ^ _778495) ^ [_1215861, _1215863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215861)), -(c_SMT_Oz3mod(_1215863, _1215861) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215863, _1215861))], (35955 ^ _778495) ^ [_1453546, _1453548, _1453550, _1453552, _1453554] : [c_Equiv__Relations_Oequivp(_1453546, _1453548), hBOOL(hAPP(hAPP(_1453548, _1453550), _1453552)), hBOOL(hAPP(hAPP(_1453548, _1453552), _1453554)), -(hBOOL(hAPP(hAPP(_1453548, _1453550), _1453554)))], (43319 ^ _778495) ^ [_1642792, _1642794, _1642796, _1642798] : [43320 ^ _778495 : [(43323 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642792), _1642794), hAPP(c_List_Oset(_1642792), c_List_Obutlast(_1642792, _1642798))))], (43321 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642792), _1642794), hAPP(c_List_Oset(_1642792), c_List_Obutlast(_1642792, _1642796))))]], -(hBOOL(hAPP(hAPP(c_member(_1642792), _1642794), hAPP(c_List_Oset(_1642792), c_List_Obutlast(_1642792, hAPP(hAPP(c_List_Oappend(_1642792), _1642796), _1642798))))))], (15515 ^ _778495) ^ [_1054147, _1054149, _1054151, _1054153, _1054155] : [class_Groups_Ocomm__monoid__mult(_1054147), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054149), _1054151)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054149), _1054153)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054147), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054149, _1054147), _1054155), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1054149, tc_HOL_Obool)), _1054151), _1054153))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054149, _1054147), _1054155), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1054149, tc_HOL_Obool)), _1054151), _1054153))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054147), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054149, _1054147), _1054155), _1054151)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054149, _1054147), _1054155), _1054153)))], (21256 ^ _778495) ^ [_1159275, _1159277, _1159279] : [class_Groups_Oordered__ab__group__add__abs(_1159275), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159275), hAPP(c_Groups_Oabs__class_Oabs(_1159275), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1159275), hAPP(c_Groups_Oabs__class_Oabs(_1159275), _1159277)), hAPP(c_Groups_Oabs__class_Oabs(_1159275), _1159279)))), hAPP(c_Groups_Oabs__class_Oabs(_1159275), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1159275), _1159277), _1159279)))))], (49765 ^ _778495) ^ [_1784345, _1784347, _1784349, _1784351, _1784353, _1784355, _1784357] : [c_Fun_Oinj__on(_1784345, _1784347, _1784349, hAPP(c_Set_Oimage(_1784351, _1784345, _1784353), _1784355)), c_Fun_Oinj__on(_1784351, _1784345, _1784353, _1784355), hBOOL(hAPP(hAPP(c_member(_1784347), _1784357), hAPP(c_Set_Oimage(_1784345, _1784347, _1784349), hAPP(c_Set_Oimage(_1784351, _1784345, _1784353), _1784355)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1784351, _1784347, _1784355, hAPP(c_Fun_Ocomp(_1784345, _1784347, _1784351, _1784349), _1784353)), _1784357) = hAPP(hAPP(c_Fun_Ocomp(_1784345, _1784351, _1784347, c_Hilbert__Choice_Oinv__into(_1784351, _1784345, _1784355, _1784353)), c_Hilbert__Choice_Oinv__into(_1784345, _1784347, hAPP(c_Set_Oimage(_1784351, _1784345, _1784353), _1784355), _1784349)), _1784357))], (39181 ^ _778495) ^ [_1539474, _1539476, _1539478] : [39183 ^ _778495 : [(39186 ^ _778495) ^ [] : [hBOOL(hAPP(_1539476, 39182 ^ [_1539474, _1539476, _1539478]))], (39184 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539474), 39182 ^ [_1539474, _1539476, _1539478]), _1539478)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1539474, _1539476), _1539478)))], (10909 ^ _778495) ^ [_966357, _966359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966357), hAPP(c_Nat_OSuc, _966359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966357), _966359))), -(_966357 = hAPP(c_Nat_OSuc, _966359))], (2688 ^ _778495) ^ [_818258, _818260] : [_818260 = _818258, -(c_Set_OBall(_818260) = c_Set_OBall(_818258))], (17640 ^ _778495) ^ [_1094781, _1094783, _1094785, _1094787] : [class_Orderings_Olinorder(_1094781), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094781), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094781), _1094783), _1094785)), _1094787) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094781), _1094783), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094781), _1094785), _1094787)))], (45602 ^ _778495) ^ [_1693625, _1693627] : [class_Orderings_Olinorder(_1693625), -(c_List_Olinorder__class_Osort__key(_1693625, _1693625, c_COMBI(_1693625), _1693627) = hAPP(c_List_Ofoldl(tc_List_Olist(_1693625), _1693625, hAPP(c_COMBC(_1693625, tc_List_Olist(_1693625), tc_List_Olist(_1693625)), c_List_Olinorder__class_Oinsort__key(_1693625, _1693625, c_COMBI(_1693625))), c_List_Olist_ONil(_1693625)), _1693627))], (33284 ^ _778495) ^ [_1394578, _1394580, _1394582, _1394584, _1394586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1394578, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394580, tc_fun(_1394578, tc_HOL_Obool)), _1394582), _1394584)), _1394586)), 33287 ^ _778495 : [(33288 ^ _778495) ^ [_1394711] : [hBOOL(hAPP(hAPP(c_member(_1394580), _1394711), _1394582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1394578, tc_HOL_Obool)), hAPP(_1394584, _1394711)), _1394586)))]]], (37346 ^ _778495) ^ [_1484755, _1484757, _1484759, _1484761, _1484763] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1484755, _1484757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1484755, tc_HOL_Obool)), _1484759), _1484761)), _1484763) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1484755, _1484757), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1484755, _1484757), _1484759), _1484763)), hAPP(hAPP(c_Product__Type_OSigma(_1484755, _1484757), _1484761), _1484763)))], (41417 ^ _778495) ^ [_1595214, _1595216, _1595218, _1595220, _1595222, _1595224] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595214), tc_List_Olist(_1595214))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595214), tc_List_Olist(_1595214)), hAPP(hAPP(c_List_Olist_OCons(_1595214), _1595216), _1595218)), hAPP(hAPP(c_List_Olist_OCons(_1595214), _1595220), _1595222))), c_List_Olex(_1595214, _1595224)))), 41418 ^ _778495 : [(41425 ^ _778495) ^ [] : [_1595216 = _1595220, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595214), tc_List_Olist(_1595214))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595214), tc_List_Olist(_1595214)), _1595218), _1595222)), c_List_Olex(_1595214, _1595224)))], (41419 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595214, _1595214)), hAPP(hAPP(c_Product__Type_OPair(_1595214, _1595214), _1595216), _1595220)), _1595224)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595214)), _1595218) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595214)), _1595222)]]], (38292 ^ _778495) ^ [_1514377, _1514379, _1514381] : [class_Orderings_Olinorder(_1514377), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514377), _1514379)), -(_1514379 = c_Orderings_Obot__class_Obot(tc_fun(_1514377, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1514377), _1514381), c_Big__Operators_Olattice_OSup__fin(_1514377, c_Orderings_Oord__class_Omax(_1514377), _1514379)) = c_Big__Operators_Olattice_OSup__fin(_1514377, c_Orderings_Oord__class_Omax(_1514377), hAPP(c_Set_OCollect(_1514377), hAPP(hAPP(c_COMBB(tc_fun(_1514377, tc_HOL_Obool), tc_HOL_Obool, _1514377), c_HOL_OEx(_1514377)), hAPP(hAPP(c_COMBC(_1514377, tc_fun(_1514377, tc_HOL_Obool), tc_fun(_1514377, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514377, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1514377, tc_HOL_Obool), tc_fun(_1514377, tc_HOL_Obool)), _1514377), c_COMBS(_1514377, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514377, tc_HOL_Obool), tc_fun(_1514377, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1514377), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1514377), c_fconj)), hAPP(hAPP(c_COMBC(_1514377, tc_fun(_1514377, _1514377), tc_fun(_1514377, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514377, tc_HOL_Obool), tc_fun(tc_fun(_1514377, _1514377), tc_fun(_1514377, tc_HOL_Obool)), _1514377), c_COMBB(_1514377, tc_HOL_Obool, _1514377)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1514377), _1514381))))), hAPP(hAPP(c_COMBC(_1514377, tc_fun(_1514377, tc_HOL_Obool), tc_HOL_Obool), c_member(_1514377)), _1514379))))))], (27515 ^ _778495) ^ [_1269501, _1269503] : [-(hBOOL(hAPP(hAPP(c_member(_1269501), _1269503), c_Orderings_Otop__class_Otop(tc_fun(_1269501, tc_HOL_Obool)))))], (49088 ^ _778495) ^ [_1771528, _1771530] : [c_Predicate_Otransp(_1771528, _1771530), -(c_Relation_Otrans(_1771528, hAPP(c_Set_OCollect(tc_prod(_1771528, _1771528)), hAPP(c_Product__Type_Oprod_Oprod__case(_1771528, _1771528, tc_HOL_Obool), _1771530))))], (11845 ^ _778495) ^ [_984397, _984399, _984401, _984403, _984405, _984407] : [class_Rings_Oring(_984397), 11848 ^ _778495 : [(11855 ^ _778495) ^ [] : [_984403 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_984397), _984405), _984399)), _984401)), _984407), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984397), _984399), _984401)), _984403) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984397), _984405), _984401)), _984407))], (11849 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984397), _984399), _984401)), _984403) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984397), _984405), _984401)), _984407), -(_984403 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_984397), _984405), _984399)), _984401)), _984407))]]], (51331 ^ _778495) ^ [_1815986, _1815988, _1815990] : [class_Rings_Olinordered__idom(_1815986), 51334 ^ _778495 : [(51341 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815986), _1815988), _1815990)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815986), _1815988), hAPP(c_Groups_Oabs__class_Oabs(_1815986), _1815990))))], (51335 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815986), _1815988), hAPP(c_Groups_Oabs__class_Oabs(_1815986), _1815990))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815986), _1815988), _1815990)))]]], (6056 ^ _778495) ^ [_875338, _875340, _875342] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875338, tc_HOL_Obool)), _875340), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875338, tc_HOL_Obool)), _875340), _875342)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875338, tc_HOL_Obool)), _875340), _875342))], (2008 ^ _778495) ^ [_807574, _807576, _807578, _807580, _807582, _807584, _807586, _807588, _807590, _807592] : [-(c_Nitpick_Opair__box_Opair__box__case(_807592, _807588, _807584, _807580, _807576) = c_Nitpick_Opair__box_Opair__box__case(_807590, _807586, _807582, _807578, _807574)), _807592 = _807590, _807588 = _807586, _807584 = _807582, _807580 = _807578, _807576 = _807574], (46752 ^ _778495) ^ [_1718490, _1718492, _1718494] : [-(hAPP(c_List_Orev(_1718490), hAPP(hAPP(c_List_Odrop(_1718490), _1718492), _1718494)) = hAPP(hAPP(c_List_Otake(_1718490), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718490)), _1718494)), _1718492)), hAPP(c_List_Orev(_1718490), _1718494)))], (45825 ^ _778495) ^ [_1699560, _1699562, _1699564, _1699566] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1699560)), c_List_Otranspose__rel(_1699560)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699560)), hAPP(hAPP(c_List_Olist_OCons(_1699560), _1699562), _1699564)), _1699566))), -(c_List_Otranspose(_1699560, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699560)), hAPP(hAPP(c_List_Olist_OCons(_1699560), _1699562), _1699564)), _1699566)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699560)), hAPP(hAPP(c_List_Olist_OCons(_1699560), _1699562), c_List_Oconcat(_1699560, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699560), tc_List_Olist(_1699560)), c_List_Olist_Olist__case(tc_List_Olist(_1699560), _1699560, c_List_Olist_ONil(_1699560), hAPP(hAPP(c_COMBB(tc_List_Olist(_1699560), tc_fun(tc_List_Olist(_1699560), tc_List_Olist(_1699560)), _1699560), c_COMBK(tc_List_Olist(_1699560), tc_List_Olist(_1699560))), hAPP(hAPP(c_COMBC(_1699560, tc_List_Olist(_1699560), tc_List_Olist(_1699560)), c_List_Olist_OCons(_1699560)), c_List_Olist_ONil(_1699560))))), _1699566)))), c_List_Otranspose(_1699560, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699560)), _1699564), c_List_Oconcat(tc_List_Olist(_1699560), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699560), tc_List_Olist(tc_List_Olist(_1699560))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1699560)), _1699560, c_List_Olist_ONil(tc_List_Olist(_1699560)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1699560), tc_List_Olist(tc_List_Olist(_1699560))), _1699560), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699560), tc_List_Olist(tc_List_Olist(_1699560)), tc_List_Olist(tc_List_Olist(_1699560))), c_List_Olist_OCons(tc_List_Olist(_1699560))), c_List_Olist_ONil(tc_List_Olist(_1699560)))))), _1699566))))))], (45414 ^ _778495) ^ [_1689937, _1689939] : [-(c_List_Oremdups(_1689937, c_List_Oremdups(_1689937, _1689939)) = c_List_Oremdups(_1689937, _1689939))], (33822 ^ _778495) ^ [_1408180, _1408182] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408180), hAPP(c_Nat_OSuc, _1408182)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1408180, _1408182))], (34012 ^ _778495) ^ [_1411937, _1411939, _1411941, _1411943] : [class_Orderings_Olinorder(_1411937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411937), _1411939), _1411941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411937), _1411941), _1411943)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411937, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1411937, _1411939), _1411941)), c_SetInterval_Oord__class_OatLeastAtMost(_1411937, _1411941, _1411943)) = c_SetInterval_Oord__class_OatLeastAtMost(_1411937, _1411939, _1411943))], (44341 ^ _778495) ^ [_1665076] : [-(hAPP(c_List_Omap(_1665076, _1665076), c_Fun_Oid(_1665076)) = c_Fun_Oid(tc_List_Olist(_1665076)))], (19036 ^ _778495) ^ [_1120856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1120856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120856)))], (5040 ^ _778495) ^ [_855440, _855442, _855444, _855446] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855446, _855442) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855444, _855440)), _855446 = _855444, _855442 = _855440], (10009 ^ _778495) ^ [_950801, _950803, _950805] : [class_Lattices_Olattice(_950801), hBOOL(hAPP(c_Finite__Set_Ofinite(_950801), _950803)), hBOOL(hAPP(hAPP(c_member(_950801), _950805), _950803)), 10020 ^ _778495 : [(10027 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950801, tc_HOL_Obool)), _950803), hAPP(hAPP(c_Set_Oinsert(_950801), _950805), c_Orderings_Obot__class_Obot(tc_fun(_950801, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_950801, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_950801, _950803) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950801), _950805), c_Big__Operators_Olattice__class_OInf__fin(_950801, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950801, tc_HOL_Obool)), _950803), hAPP(hAPP(c_Set_Oinsert(_950801), _950805), c_Orderings_Obot__class_Obot(tc_fun(_950801, tc_HOL_Obool)))))))], (10021 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950801, tc_HOL_Obool)), _950803), hAPP(hAPP(c_Set_Oinsert(_950801), _950805), c_Orderings_Obot__class_Obot(tc_fun(_950801, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_950801, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_950801, _950803) = _950805)]]], (43299 ^ _778495) ^ [_1642298, _1642300, _1642302, _1642304, _1642306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642298), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642300)), _1642302))), -(hAPP(hAPP(c_List_Olist__update(_1642300, hAPP(hAPP(c_List_Oappend(_1642300), _1642302), _1642304)), _1642298), _1642306) = hAPP(hAPP(c_List_Oappend(_1642300), hAPP(hAPP(c_List_Olist__update(_1642300, _1642302), _1642298), _1642306)), _1642304))], (33439 ^ _778495) ^ [_1399088, _1399090, _1399092, _1399094, _1399096] : [-(_1399088 = c_Orderings_Obot__class_Obot(tc_fun(_1399090, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399090, tc_fun(_1399092, tc_HOL_Obool)), _1399088), hAPP(hAPP(c_COMBB(tc_fun(_1399092, tc_HOL_Obool), tc_fun(_1399092, tc_HOL_Obool), _1399090), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399092, tc_HOL_Obool)), _1399094)), _1399096)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399092, tc_HOL_Obool)), _1399094), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399090, tc_fun(_1399092, tc_HOL_Obool)), _1399088), _1399096)))], (10965 ^ _778495) ^ [_967183, _967185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967183), _967185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967183), _967185))), -(_967183 = _967185)], (22650 ^ _778495) ^ [_1183365] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1183365)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1183365)))], (34106 ^ _778495) ^ [_1413895, _1413897, _1413899, _1413901] : [class_Orderings_Olinorder(_1413895), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413895, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1413895, _1413897, _1413899)), hAPP(c_SetInterval_Oord__class_OatMost(_1413895), _1413901)) = c_SetInterval_Oord__class_OatLeastAtMost(_1413895, _1413897, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1413895), _1413899), _1413901)))], (32098 ^ _778495) ^ [_1368714, _1368716, _1368718, _1368720] : [class_Orderings_Oorder(_1368714), 32101 ^ _778495 : [(32110 ^ _778495) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1368714, _1368716, _1368718) = hAPP(hAPP(c_Set_Oinsert(_1368714), _1368720), c_Orderings_Obot__class_Obot(tc_fun(_1368714, tc_HOL_Obool)))), _1368716 = _1368718, _1368718 = _1368720], (32102 ^ _778495) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1368714, _1368716, _1368718) = hAPP(hAPP(c_Set_Oinsert(_1368714), _1368720), c_Orderings_Obot__class_Obot(tc_fun(_1368714, tc_HOL_Obool))), 32105 ^ _778495 : [(32108 ^ _778495) ^ [] : [-(_1368718 = _1368720)], (32106 ^ _778495) ^ [] : [-(_1368716 = _1368718)]]]]], (37989 ^ _778495) ^ [_1502425, _1502427, _1502429, _1502431, _1502433] : [c_Relation_Orefl__on(_1502425, _1502427, _1502429), hBOOL(hAPP(hAPP(c_member(tc_prod(_1502425, _1502425)), hAPP(hAPP(c_Product__Type_OPair(_1502425, _1502425), _1502431), _1502433)), _1502429)), -(hBOOL(hAPP(hAPP(c_member(_1502425), _1502433), _1502427)))], (26108 ^ _778495) ^ [_1245185, _1245187, _1245189, _1245191] : [class_Groups_Ocomm__monoid__mult(_1245185), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1245185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245185), _1245187), _1245189)), _1245191) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245185), hAPP(hAPP(c_Power_Opower__class_Opower(_1245185), _1245187), _1245191)), hAPP(hAPP(c_Power_Opower__class_Opower(_1245185), _1245189), _1245191)))], (52165 ^ _778495) ^ [_1830683, _1830685] : [class_Orderings_Obot(_1830683), -(class_Orderings_Obot(tc_fun(_1830685, _1830683)))], (5927 ^ _778495) ^ [_873003, _873005, _873007, _873009] : [hBOOL(hAPP(hAPP(c_member(_873003), _873005), _873007)), -(hBOOL(hAPP(hAPP(c_member(_873003), _873005), _873009))), -(hBOOL(hAPP(hAPP(c_member(_873003), _873005), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_873003, tc_HOL_Obool)), _873007), _873009))))], (43546 ^ _778495) ^ [_1648918, _1648920, _1648922] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648918, tc_HOL_Obool)), hAPP(c_List_Oset(_1648918), hAPP(hAPP(c_List_Odrop(_1648918), _1648920), _1648922))), hAPP(c_List_Oset(_1648918), _1648922))))], (20918 ^ _778495) ^ [_1153135] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1153135)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1153135) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14465 ^ _778495) ^ [_1035535, _1035537, _1035539] : [class_Groups_Ocomm__monoid__add(_1035535), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1035537, _1035535), _1035539), c_Orderings_Obot__class_Obot(tc_fun(_1035537, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1035535))], (28267 ^ _778495) ^ [_1283584, _1283586, _1283588, _1283590] : [hBOOL(hAPP(hAPP(c_member(_1283584), _1283590), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1283584, tc_HOL_Obool)), _1283586), _1283588))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1283584, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1283584, tc_fun(_1283584, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283584)), _1283586)), hAPP(hAPP(c_COMBC(_1283584, tc_fun(_1283584, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283584)), _1283588)), _1283590)))], (9775 ^ _778495) ^ [_945994, _945996, _945998, _946000, _946002, _946004] : [c_Finite__Set_Ofun__left__comm__idem(_945994, _945996, _945998), hBOOL(hAPP(c_Finite__Set_Ofinite(_945994), _946000)), -(hAPP(hAPP(c_Finite__Set_Ofold(_945994, _945996, _945998), _946002), hAPP(hAPP(c_Set_Oinsert(_945994), _946004), _946000)) = hAPP(hAPP(_945998, _946004), hAPP(hAPP(c_Finite__Set_Ofold(_945994, _945996, _945998), _946002), _946000)))], (22578 ^ _778495) ^ [_1182140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1182140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1182140)))], (21172 ^ _778495) ^ [_1157826, _1157828] : [class_Groups_Oordered__ab__group__add__abs(_1157826), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157826), c_Groups_Ozero__class_Ozero(_1157826)), _1157828)), -(hAPP(c_Groups_Oabs__class_Oabs(_1157826), _1157828) = _1157828)], (41929 ^ _778495) ^ [_1610704, _1610706, _1610708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610704)), _1610706)), _1610708)), -(hAPP(hAPP(c_List_Otake(_1610704), _1610708), _1610706) = _1610706)], (48645 ^ _778495) ^ [_1759905, _1759907, _1759909, _1759911, _1759913, _1759915, _1759917] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1759905, tc_fun(_1759907, tc_fun(_1759909, tc_HOL_Obool))), _1759911), _1759913), _1759915), _1759917)), 48649 ^ _778495 : [(48652 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1759913, 48648 ^ [_1759905, _1759907, _1759909, _1759911, _1759913, _1759915, _1759917]), _1759915), _1759917)))], (48650 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759905), 48648 ^ [_1759905, _1759907, _1759909, _1759911, _1759913, _1759915, _1759917]), _1759911)))]]], (11680 ^ _778495) ^ [_981126, _981128] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981126), hAPP(c_Nat_OSuc, _981128)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981126), _981128)))], (23062 ^ _778495) ^ [_1191073, _1191075] : [class_Divides_Osemiring__div(_1191073), -(c_Divides_Odiv__class_Omod(_1191073, _1191075, c_Groups_Ozero__class_Ozero(_1191073)) = _1191075)], (26682 ^ _778495) ^ [_1255671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1255671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1255671))))], (23222 ^ _778495) ^ [_1194431, _1194433, _1194435] : [class_Divides_Oring__div(_1194431), -(c_Divides_Odiv__class_Omod(_1194431, hAPP(c_Groups_Ouminus__class_Ouminus(_1194431), _1194433), _1194435) = c_Divides_Odiv__class_Omod(_1194431, hAPP(c_Groups_Ouminus__class_Ouminus(_1194431), c_Divides_Odiv__class_Omod(_1194431, _1194433, _1194435)), _1194435))], (49192 ^ _778495) ^ [_1773509, _1773511] : [c_Relation_Oantisym(_1773509, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1773509, _1773509), tc_HOL_Obool)), _1773511), c_Relation_OId(_1773509))), -(c_Relation_Oantisym(_1773509, _1773511))], (52323 ^ _778495) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (31474 ^ _778495) ^ [_1353471, _1353473, _1353475] : [class_Orderings_Olinorder(_1353471), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353471), _1353473)), -(hBOOL(hAPP(hAPP(c_member(_1353471), _1353475), _1353473))), -(c_Big__Operators_Olattice_OSup__fin(_1353471, c_Orderings_Oord__class_Omax(_1353471), hAPP(hAPP(c_Set_Oinsert(_1353471), _1353475), _1353473)) = hAPP(hAPP(c_Finite__Set_Ofold(_1353471, _1353471, c_Orderings_Oord__class_Omax(_1353471)), _1353475), _1353473))], (52429 ^ _778495) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (32410 ^ _778495) ^ [_1375370, _1375372, _1375374, _1375376, _1375378] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1375370, tc_fun(_1375372, tc_HOL_Obool)), _1375374), _1375376), _1375378)), 32413 ^ _778495 : [(32414 ^ _778495) ^ [_1375479] : [hBOOL(hAPP(hAPP(c_member(_1375370), _1375479), _1375374)), -(hBOOL(hAPP(hAPP(_1375376, _1375479), _1375378)))]]], (34641 ^ _778495) ^ [_1426279, _1426281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1426279), _1426281)), -(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)), _1426279)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1426281))))], (52729 ^ _778495) ^ [_1836583, _1836585] : [-(hBOOL(_1836583)), -(hBOOL(hAPP(hAPP(c_fimplies, _1836583), _1836585)))], (33836 ^ _778495) ^ [_1408463, _1408465, _1408467] : [class_Orderings_Oorder(_1408463), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408463), _1408465), _1408467)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408463, _1408467), _1408465) = c_Orderings_Obot__class_Obot(tc_fun(_1408463, tc_HOL_Obool)))], (40922 ^ _778495) ^ [_1581818] : [-(c_Relation_Osingle__valued(_1581818, _1581818, c_Relation_OId(_1581818)))], (15417 ^ _778495) ^ [_1052372, _1052374] : [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), _1052372), _1052374))), 15420 ^ _778495 : [(15423 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1052374)))], (15421 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1052372)))]]], (24489 ^ _778495) ^ [_1216693, _1216695, _1216697] : [_1216695 = _1216697, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1216693, tc_HOL_Obool)), _1216695) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1216693, tc_HOL_Obool)), _1216697))], (14835 ^ _778495) ^ [_1041609, _1041611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041609), _1041611)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041609), _1041611) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43508 ^ _778495) ^ [_1648018, _1648020] : [hBOOL(hAPP(c_List_Odistinct(_1648018), _1648020)), -(hBOOL(hAPP(c_List_Odistinct(_1648018), hAPP(c_List_Orotate1(_1648018), _1648020))))], (39464 ^ _778495) ^ [_1546592, _1546594, _1546596, _1546598, _1546600, _1546602] : [c_Fun_Oinj__on(_1546592, _1546594, _1546596, _1546598), c_Fun_Oinj__on(_1546594, _1546600, _1546602, hAPP(c_Set_Oimage(_1546592, _1546594, _1546596), _1546598)), -(c_Fun_Oinj__on(_1546592, _1546600, hAPP(c_Fun_Ocomp(_1546594, _1546600, _1546592, _1546602), _1546596), _1546598))], (23418 ^ _778495) ^ [_1198032, _1198034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198032)), 23421 ^ _778495 : [(23428 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198034), 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), _1198034), _1198032)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23422 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1198034), _1198032)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198034), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (27665 ^ _778495) ^ [_1272210] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272210, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1272210, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1272210, tc_HOL_Obool)))], (46850 ^ _778495) ^ [_1720625, _1720627, _1720629] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720625)), c_List_OtakeWhile(_1720625, _1720627, _1720629))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720625)), _1720629))))], (23288 ^ _778495) ^ [_1195837, _1195839] : [-(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, _1195837, _1195839)), _1195839) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195837), _1195839))], (51105 ^ _778495) ^ [_1812370, _1812372, _1812374] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812370), _1812372)), 51116 ^ _778495 : [(51119 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812374), _1812370))], (51117 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812370), _1812374)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812372), _1812374)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812374), _1812372)))], (23252 ^ _778495) ^ [_1194998] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194998) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17320 ^ _778495) ^ [_1088243, _1088245, _1088247, _1088249] : [class_Fields_Ofield(_1088243), -(_1088245 = c_Groups_Ozero__class_Ozero(_1088243)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088243), _1088247), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1088243), _1088249), _1088245)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1088243), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088243), _1088245), _1088247)), _1088249)), _1088245))], (15487 ^ _778495) ^ [_1053647, _1053649, _1053651, _1053653, _1053655] : [class_Groups_Ocomm__monoid__mult(_1053647), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053649), _1053651)), -(hBOOL(hAPP(hAPP(c_member(_1053649), _1053653), _1053651))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1053649, _1053647), _1053655), hAPP(hAPP(c_Set_Oinsert(_1053649), _1053653), _1053651)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053647), hAPP(_1053655, _1053653)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1053649, _1053647), _1053655), _1053651)))], (44037 ^ _778495) ^ [_1659698, _1659700, _1659702, _1659704, _1659706, _1659708] : [class_Orderings_Olinorder(_1659698), 44040 ^ _778495 : [(44047 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659698), hAPP(_1659700, _1659702)), hAPP(_1659700, _1659704)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659706, _1659698, _1659700), _1659702), hAPP(hAPP(c_List_Olist_OCons(_1659706), _1659704), _1659708)) = hAPP(hAPP(c_List_Olist_OCons(_1659706), _1659704), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659706, _1659698, _1659700), _1659702), _1659708)))], (44041 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659698), hAPP(_1659700, _1659702)), hAPP(_1659700, _1659704))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659706, _1659698, _1659700), _1659702), hAPP(hAPP(c_List_Olist_OCons(_1659706), _1659704), _1659708)) = hAPP(hAPP(c_List_Olist_OCons(_1659706), _1659702), hAPP(hAPP(c_List_Olist_OCons(_1659706), _1659704), _1659708)))]]], (39452 ^ _778495) ^ [_1546360, _1546362, _1546364, _1546366, _1546368, _1546370] : [c_Fun_Oinj__on(_1546360, _1546362, hAPP(c_Fun_Ocomp(_1546364, _1546362, _1546360, _1546366), _1546368), _1546370), -(c_Fun_Oinj__on(_1546360, _1546364, _1546368, _1546370))], (27653 ^ _778495) ^ [_1271977, _1271979] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1271977, tc_HOL_Obool)), _1271979), c_Orderings_Otop__class_Otop(tc_fun(_1271977, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1271977, tc_HOL_Obool)))], (22742 ^ _778495) ^ [_1184994, _1184996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1184994)), c_Int_OBit0(_1184996))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184994), _1184996)))], (28433 ^ _778495) ^ [_1292122, _1292124, _1292126, _1292128, _1292130] : [class_Groups_Ocomm__monoid__add(_1292122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292124), _1292126)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1292124, _1292122), hAPP(hAPP(c_COMBS(_1292124, _1292122, _1292122), hAPP(hAPP(c_COMBB(_1292122, tc_fun(_1292122, _1292122), _1292124), c_Groups_Oplus__class_Oplus(_1292122)), _1292128)), _1292130)), _1292126) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1292122), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1292124, _1292122), _1292128), _1292126)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1292124, _1292122), _1292130), _1292126)))], (42027 ^ _778495) ^ [_1612961, _1612963, _1612965, _1612967, _1612969] : [hBOOL(hAPP(hAPP(c_member(_1612961), _1612963), hAPP(c_List_Oset(_1612961), _1612965))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1612967), hAPP(_1612969, _1612963))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1612967), c_List_Olist_Olist__size(_1612961, _1612969, _1612965))))], (46903 ^ _778495) ^ [_1721721, _1721723] : [-(c_List_OtakeWhile(_1721721, _1721723, c_List_Olist_ONil(_1721721)) = c_List_Olist_ONil(_1721721))], (20343 ^ _778495) ^ [_1143929, _1143931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1143929), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143929)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143931)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11071 ^ _778495) ^ [_968997, _968999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968997), _968999)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968999), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968999), _968997)) = _968997)], (9070 ^ _778495) ^ [_931691, _931693, _931695, _931697] : [class_Lattices_Osemilattice__inf(_931691), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931691), _931693), _931695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931691), _931693), _931697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931691), _931693), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931691), _931695), _931697))))], (46860 ^ _778495) ^ [_1720860, _1720862, _1720864] : [c_List_OtakeWhile(_1720860, _1720862, _1720864) = _1720864, 46863 ^ _778495 : [(46864 ^ _778495) ^ [_1720947] : [hBOOL(hAPP(hAPP(c_member(_1720860), _1720947), hAPP(c_List_Oset(_1720860), _1720864))), -(hBOOL(hAPP(_1720862, _1720947)))]]], (47026 ^ _778495) ^ [_1724365, _1724367, _1724369, _1724371] : [-(hBOOL(hAPP(_1724365, _1724367))), -(c_List_OdropWhile(_1724369, _1724365, hAPP(hAPP(c_List_Olist_OCons(_1724369), _1724367), _1724371)) = hAPP(hAPP(c_List_Olist_OCons(_1724369), _1724367), _1724371))], (22418 ^ _778495) ^ [_1179356, _1179358, _1179360] : [class_Lattices_Oboolean__algebra(_1179356), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1179356), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1179356), _1179358), _1179360)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1179356), hAPP(c_Groups_Ouminus__class_Ouminus(_1179356), _1179358)), hAPP(c_Groups_Ouminus__class_Ouminus(_1179356), _1179360)))], (1788 ^ _778495) ^ [_803873, _803875] : [-(class_Orderings_Opreorder(_803873)), _803875 = _803873, class_Orderings_Opreorder(_803875)], (33589 ^ _778495) ^ [_1403242, _1403244] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1403242), _1403244))))], (566 ^ _778495) ^ [_787024, _787026, _787028, _787030, _787032, _787034] : [-(c_Finite__Set_Ofun__left__comm__idem(_787032, _787028, _787024)), c_Finite__Set_Ofun__left__comm__idem(_787034, _787030, _787026), _787034 = _787032, _787030 = _787028, _787026 = _787024], (52101 ^ _778495) ^ [_1829843, _1829845] : [class_Lattices_Olattice(_1829843), -(class_Lattices_Osemilattice__sup(tc_fun(_1829845, _1829843)))], (442 ^ _778495) ^ [_785220, _785222, _785224, _785226, _785228, _785230] : [-(c_Relation_Ototal__on(_785228, _785224, _785220)), c_Relation_Ototal__on(_785230, _785226, _785222), _785230 = _785228, _785226 = _785224, _785222 = _785220], (21974 ^ _778495) ^ [_1171516, _1171518, _1171520] : [class_Groups_Ogroup__add(_1171516), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1171516), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171516), _1171518), _1171520)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171516), hAPP(c_Groups_Ouminus__class_Ouminus(_1171516), _1171520)), hAPP(c_Groups_Ouminus__class_Ouminus(_1171516), _1171518)))], (17431 ^ _778495) ^ [_1090490, _1090492, _1090494, _1090496, _1090498] : [class_Groups_Ocomm__monoid__add(_1090490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090492), _1090494)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1090492, tc_HOL_Obool)), _1090496), _1090494)), 17445 ^ _778495 : [(17448 ^ _778495) ^ [] : [hAPP(_1090498, 17444 ^ [_1090490, _1090492, _1090494, _1090496, _1090498]) = c_Groups_Ozero__class_Ozero(_1090490)], (17446 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1090492), 17444 ^ [_1090490, _1090492, _1090494, _1090496, _1090498]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090492, tc_HOL_Obool)), _1090494), _1090496))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1090492, _1090490), _1090498), _1090494) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1090492, _1090490), _1090498), _1090496))], (22836 ^ _778495) ^ [_1186663, _1186665] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1186663)), c_Int_OBit1(_1186665)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186663), c_Int_Osucc(_1186665))))], (39053 ^ _778495) ^ [_1535896, _1535898] : [c_Wellfounded_Owf(_1535896, hAPP(c_Set_OCollect(tc_prod(_1535896, _1535896)), hAPP(c_Product__Type_Oprod_Oprod__case(_1535896, _1535896, tc_HOL_Obool), _1535898))), -(c_Wellfounded_OwfP(_1535896, _1535898))], (21514 ^ _778495) ^ [_1163907, _1163909] : [class_Int_Onumber__ring(_1163907), class_Rings_Olinordered__idom(_1163907), 21521 ^ _778495 : [(21528 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1163909), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163907), hAPP(c_Int_Onumber__class_Onumber__of(_1163907), _1163909)), c_Groups_Oone__class_Oone(_1163907))))], (21522 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163907), hAPP(c_Int_Onumber__class_Onumber__of(_1163907), _1163909)), c_Groups_Oone__class_Oone(_1163907))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1163909), c_Int_OBit1(c_Int_OPls))))]]], (11472 ^ _778495) ^ [_977134, _977136, _977138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977134), _977136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977134), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977138), _977136))))], (5302 ^ _778495) ^ [_859569, _859571, _859573, _859575, _859577, _859579] : [-(c_SetInterval_Oord_OgreaterThan(_859579, _859575, _859571) = c_SetInterval_Oord_OgreaterThan(_859577, _859573, _859569)), _859579 = _859577, _859575 = _859573, _859571 = _859569], (24613 ^ _778495) ^ [_1219213, _1219215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219215)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1219213), hAPP(c_Int_Onat, _1219215)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1219213, _1219215)))], (43580 ^ _778495) ^ [_1649636, _1649638, _1649640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649636)), _1649640)), _1649638)), -(hAPP(hAPP(c_List_Odrop(_1649636), _1649638), _1649640) = c_List_Olist_ONil(_1649636))], (35597 ^ _778495) ^ [_1444651, _1444653, _1444655, _1444657] : [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), _1444651), _1444653)), 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), _1444655), _1444657)), 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), _1444651), _1444657)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444655), _1444653))))], (26356 ^ _778495) ^ [_1249842, _1249844, _1249846] : [class_Rings_Olinordered__semidom(_1249842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249842), c_Groups_Oone__class_Oone(_1249842)), _1249844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249842), hAPP(hAPP(c_Power_Opower__class_Opower(_1249842), _1249844), _1249846)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249842), _1249844), hAPP(hAPP(c_Power_Opower__class_Opower(_1249842), _1249844), _1249846)))))], (48216 ^ _778495) ^ [_1750811, _1750813, _1750815, _1750817, _1750819, _1750821] : [-(hAPP(hAPP(c_List_Ozip(_1750811, _1750813), c_List_Oreplicate(_1750811, _1750815, _1750817)), c_List_Oreplicate(_1750813, _1750819, _1750821)) = c_List_Oreplicate(tc_prod(_1750811, _1750813), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750815), _1750819), hAPP(hAPP(c_Product__Type_OPair(_1750811, _1750813), _1750817), _1750821)))], (2714 ^ _778495) ^ [_818649, _818651, _818653, _818655, _818657, _818659] : [-(c_Predicate_ORangeP(_818659, _818655, _818651) = c_Predicate_ORangeP(_818657, _818653, _818649)), _818659 = _818657, _818655 = _818653, _818651 = _818649], (3384 ^ _778495) ^ [_829058, _829060, _829062, _829064, _829066, _829068] : [-(c_List_Opartition(_829068, _829064, _829060) = c_List_Opartition(_829066, _829062, _829058)), _829068 = _829066, _829064 = _829062, _829060 = _829058], (6744 ^ _778495) ^ [_888909, _888911, _888913] : [-(hBOOL(hAPP(hAPP(c_member(_888909), _888911), hAPP(hAPP(c_Set_Oinsert(_888909), _888911), _888913))))], (5907 ^ _778495) ^ [_872618, _872620, _872622, _872624] : [hBOOL(hAPP(hAPP(c_member(_872618), _872620), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_872618, tc_HOL_Obool)), _872622), _872624))), -(hBOOL(hAPP(hAPP(c_member(_872618), _872620), _872622))), -(hBOOL(hAPP(hAPP(c_member(_872618), _872620), _872624)))], (24555 ^ _778495) ^ [_1218176] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218176)) = _1218176)], (29129 ^ _778495) ^ [_1307520, _1307522] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1307520, _1307520)), hAPP(hAPP(c_Product__Type_OPair(_1307520, _1307520), 29130 ^ [_1307520, _1307522]), 29130 ^ [_1307520, _1307522])), _1307522)), -(c_Nitpick_Orefl_H(_1307520, _1307522))], (17994 ^ _778495) ^ [_1100986, _1100988, _1100990] : [class_Int_Onumber__ring(_1100986), class_Rings_Olinordered__idom(_1100986), 18001 ^ _778495 : [(18008 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100988), _1100990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100986), hAPP(c_Int_Onumber__class_Onumber__of(_1100986), _1100988)), hAPP(c_Int_Onumber__class_Onumber__of(_1100986), _1100990))))], (18002 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100986), hAPP(c_Int_Onumber__class_Onumber__of(_1100986), _1100988)), hAPP(c_Int_Onumber__class_Onumber__of(_1100986), _1100990))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100988), _1100990)))]]], (21328 ^ _778495) ^ [_1160649] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1160649)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160649))))], (37444 ^ _778495) ^ [_1487935, _1487937, _1487939, _1487941, _1487943, _1487945] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1487935, _1487937)), hAPP(hAPP(c_Product__Type_OPair(_1487935, _1487937), _1487939), _1487941)), hAPP(hAPP(c_Product__Type_OSigma(_1487935, _1487937), _1487943), _1487945))), -(hBOOL(hAPP(hAPP(c_member(_1487935), _1487939), _1487943)))], (21094 ^ _778495) ^ [_1156370, _1156372, _1156374] : [class_Groups_Oordered__ab__group__add__abs(_1156370), -(hAPP(c_Groups_Oabs__class_Oabs(_1156370), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1156370), _1156372), _1156374)) = hAPP(c_Groups_Oabs__class_Oabs(_1156370), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1156370), _1156374), _1156372)))], (37354 ^ _778495) ^ [_1485112, _1485114, _1485116, _1485118] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1485112, _1485114)), hAPP(hAPP(c_Product__Type_OSigma(_1485112, _1485114), _1485116), hAPP(c_COMBK(tc_fun(_1485114, tc_HOL_Obool), _1485112), _1485118))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1485112), _1485116)), hAPP(c_Finite__Set_Ocard(_1485114), _1485118)))], (15085 ^ _778495) ^ [_1046227, _1046229, _1046231, _1046233, _1046235] : [class_Rings_Olinordered__semiring__strict(_1046227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046227), _1046229), _1046231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1046227), _1046233), _1046235)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1046227), c_Groups_Ozero__class_Ozero(_1046227)), _1046229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046227), c_Groups_Ozero__class_Ozero(_1046227)), _1046233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046227), _1046229), _1046233)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046227), _1046231), _1046235))))], (25038 ^ _778495) ^ [_1226206, _1226208] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1226206) = _1226208, 25041 ^ _778495 : [(25044 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226208)))], (25042 ^ _778495) ^ [] : [-(_1226206 = hAPP(c_Int_Onat, _1226208))]]], (41336 ^ _778495) ^ [_1592558, _1592560, _1592562] : [-(c_Product__Type_Ointernal__split(_1592558, _1592560, _1592562) = c_Product__Type_Oprod_Oprod__case(_1592558, _1592560, _1592562))], (14385 ^ _778495) ^ [_1034157, _1034159, _1034161] : [class_Groups_Oordered__ab__group__add(_1034157), 14388 ^ _778495 : [(14395 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1034157), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034157), _1034159), _1034161)), c_Groups_Ozero__class_Ozero(_1034157))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1034157), _1034159), _1034161)))], (14389 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1034157), _1034159), _1034161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1034157), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034157), _1034159), _1034161)), c_Groups_Ozero__class_Ozero(_1034157))))]]], (33662 ^ _778495) ^ [_1405117, _1405119, _1405121, _1405123, _1405125, _1405127] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405117, tc_fun(_1405119, tc_HOL_Obool)), _1405121), hAPP(hAPP(c_COMBC(_1405117, tc_fun(_1405123, tc_fun(_1405119, tc_HOL_Obool)), tc_fun(_1405119, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405123, tc_HOL_Obool), tc_fun(tc_fun(_1405123, tc_fun(_1405119, tc_HOL_Obool)), tc_fun(_1405119, tc_HOL_Obool)), _1405117), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405123, tc_fun(_1405119, tc_HOL_Obool))), _1405125)), _1405127)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405123, tc_fun(_1405119, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405117, tc_fun(_1405123, tc_HOL_Obool)), _1405121), _1405125)), _1405127))], (48392 ^ _778495) ^ [_1754237, _1754239] : [-(c_Predicate_Opred__comp(_1754237, _1754237, _1754237, c_fequal, c_Predicate_Opred__comp(_1754237, _1754237, _1754237, _1754239, c_fequal)) = _1754239)], (22120 ^ _778495) ^ [_1174123, _1174125] : [c_Int_OBit0(_1174123) = c_Int_OBit1(_1174125)], (27035 ^ _778495) ^ [_1261497] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261497) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1261497))], (23525 ^ _778495) ^ [_1199842, _1199844, _1199846] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199842, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1199842, tc_HOL_Obool)), _1199844), _1199846)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1199842, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199842, tc_HOL_Obool)), _1199844)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199842, tc_HOL_Obool)), _1199846)))], (34122 ^ _778495) ^ [_1414233, _1414235, _1414237] : [class_Orderings_Oorder(_1414233), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414233, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1414233), _1414235)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1414233, _1414235, _1414237)) = c_Orderings_Obot__class_Obot(tc_fun(_1414233, tc_HOL_Obool)))], (45821 ^ _778495) ^ [_1699328, _1699330, _1699332] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699328)), hAPP(c_List_Ofilter(_1699328, _1699330), _1699332)) = 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(_1699328)), _1699332)))), hAPP(hAPP(c_COMBB(_1699328, tc_HOL_Obool, tc_Nat_Onat), _1699330), hAPP(c_List_Onth(_1699328), _1699332))))))], (30793 ^ _778495) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (32194 ^ _778495) ^ [_1370960, _1370962, _1370964, _1370966, _1370968] : [-(_1370960 = c_Orderings_Obot__class_Obot(tc_fun(_1370962, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370962, tc_fun(_1370964, tc_HOL_Obool)), _1370960), hAPP(hAPP(c_COMBC(_1370962, tc_fun(_1370964, tc_HOL_Obool), tc_fun(_1370964, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370964, tc_HOL_Obool), tc_fun(tc_fun(_1370964, tc_HOL_Obool), tc_fun(_1370964, tc_HOL_Obool)), _1370962), c_Groups_Ominus__class_Ominus(tc_fun(_1370964, tc_HOL_Obool))), _1370966)), _1370968)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370964, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370962, tc_fun(_1370964, tc_HOL_Obool)), _1370960), _1370966)), _1370968))], (11256 ^ _778495) ^ [_972692, _972694, _972696] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972692), _972694)), _972696) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972692), _972696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972694), _972696)))], (43293 ^ _778495) ^ [_1642090, _1642092, _1642094, _1642096] : [-(hAPP(hAPP(c_List_Onth(_1642090), hAPP(hAPP(c_List_Oappend(_1642090), _1642092), hAPP(hAPP(c_List_Olist_OCons(_1642090), _1642094), _1642096))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642090)), _1642092)) = _1642094)], (20778 ^ _778495) ^ [_1150931, _1150933] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150931)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150931)), _1150933)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1150931))), _1150933))], (28757 ^ _778495) ^ [_1300072, _1300074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1300072)), hAPP(c_Nat_OSuc, _1300074))), -(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(_1300072))), 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)), _1300074)))))], (48334 ^ _778495) ^ [_1752970, _1752972, _1752974] : [_1752972 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1752970) = c_List_Oreplicate(_1752970, _1752972, _1752974))], (45516 ^ _778495) ^ [_1691821, _1691823, _1691825] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1691821), tc_List_Olist(_1691821), c_List_Oappend(_1691821), _1691823), _1691825) = hAPP(hAPP(c_List_Oappend(_1691821), _1691823), c_List_Oconcat(_1691821, _1691825)))], (38857 ^ _778495) ^ [_1530959, _1530961] : [38859 ^ _778495 : [(38860 ^ _778495) ^ [_1530984] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530959, _1530959)), hAPP(hAPP(c_Product__Type_OPair(_1530959, _1530959), hAPP(38858 ^ [_1530959, _1530961], hAPP(c_Nat_OSuc, _1530984))), hAPP(38858 ^ [_1530959, _1530961], _1530984))), _1530961)))]], -(c_Wellfounded_Owf(_1530959, _1530961))], (47300 ^ _778495) ^ [_1730463, _1730465, _1730467, _1730469, _1730471] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730463, _1730463)), hAPP(hAPP(c_Product__Type_OPair(_1730463, _1730463), _1730465), _1730467)), c_List_Omeasures(_1730463, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1730463, tc_Nat_Onat)), _1730469), _1730471))))), 47301 ^ _778495 : [(47304 ^ _778495) ^ [] : [hAPP(_1730469, _1730465) = hAPP(_1730469, _1730467), hBOOL(hAPP(hAPP(c_member(tc_prod(_1730463, _1730463)), hAPP(hAPP(c_Product__Type_OPair(_1730463, _1730463), _1730465), _1730467)), c_List_Omeasures(_1730463, _1730471)))], (47302 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1730469, _1730465)), hAPP(_1730469, _1730467)))]]], (10645 ^ _778495) ^ [_962024, _962026, _962028, _962030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962024), _962026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962028), _962030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962024), _962028)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962026), _962030))))], (37069 ^ _778495) ^ [_1477810, _1477812, _1477814, _1477816, _1477818] : [-(hAPP(c_Fun_Othe__inv__into(_1477810, _1477812, _1477814, _1477816), _1477818) = c_HOL_OThe(_1477810, hAPP(hAPP(c_COMBS(_1477810, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1477810), c_fconj), hAPP(hAPP(c_COMBC(_1477810, tc_fun(_1477810, tc_HOL_Obool), tc_HOL_Obool), c_member(_1477810)), _1477814))), hAPP(hAPP(c_COMBC(_1477810, _1477812, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1477812, tc_fun(_1477812, tc_HOL_Obool), _1477810), c_fequal), _1477816)), _1477818))))], (7154 ^ _778495) ^ [_896420, _896422, _896424, _896426] : [class_Lattices_Osemilattice__sup(_896420), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896420), _896422), _896424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896420), _896422), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896420), _896424), _896426))))], (44367 ^ _778495) ^ [_1666260, _1666262, _1666264, _1666266] : [_1666266 = c_List_Olist_ONil(_1666262), -(c_List_Olist_ONil(_1666260) = hAPP(hAPP(c_List_Omap(_1666262, _1666260), _1666264), _1666266))], (26258 ^ _778495) ^ [_1247890, _1247892, _1247894] : [class_Groups_Omonoid__mult(_1247890), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1247890), _1247892), hAPP(c_Nat_OSuc, _1247894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247890), hAPP(hAPP(c_Power_Opower__class_Opower(_1247890), _1247892), _1247894)), _1247892))], (50337 ^ _778495) ^ [_1796290, _1796292, _1796294] : [hBOOL(hAPP(hAPP(_1796292, _1796294), _1796294)), -(hBOOL(hAPP(c_Quotient_ORespects(_1796290, _1796292), _1796294)))], (22134 ^ _778495) ^ [_1174396, _1174398, _1174400] : [class_Fields_Ofield__inverse__zero(_1174396), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1174396), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174396), _1174398), _1174400)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174396), _1174398), hAPP(c_Groups_Ouminus__class_Ouminus(_1174396), _1174400)))], (48372 ^ _778495) ^ [_1753661, _1753663, _1753665] : [_1753661 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1753663), c_List_Oreplicate(_1753663, _1753661, _1753665)) = c_Orderings_Obot__class_Obot(tc_fun(_1753663, tc_HOL_Obool)))], (31793 ^ _778495) ^ [_1360435, _1360437, _1360439, _1360441] : [31795 ^ _778495 : [(31798 ^ _778495) ^ [] : [hAPP(_1360441, 31794 ^ [_1360435, _1360437, _1360439, _1360441]) = c_Orderings_Otop__class_Otop(tc_fun(_1360435, tc_HOL_Obool))], (31796 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1360437), 31794 ^ [_1360435, _1360437, _1360439, _1360441]), _1360439)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1360435, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1360437, tc_fun(_1360435, tc_HOL_Obool)), _1360439), _1360441))], (14775 ^ _778495) ^ [_1040537, _1040539, _1040541] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040537), _1040539)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040541), _1040539)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040537), _1040541))], (44662 ^ _778495) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (40278 ^ _778495) ^ [_1565279, _1565281, _1565283, _1565285, _1565287] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565279, _1565279)), hAPP(hAPP(c_Product__Type_OPair(_1565279, _1565279), _1565281), _1565283)), _1565285)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565279, _1565279)), hAPP(hAPP(c_Product__Type_OPair(_1565279, _1565279), _1565283), _1565287)), _1565285)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565279, _1565279)), hAPP(hAPP(c_Product__Type_OPair(_1565279, _1565279), _1565281), _1565287)), c_Transitive__Closure_Otrancl(_1565279, _1565285))))], (34444 ^ _778495) ^ [_1421875, _1421877, _1421879, _1421881] : [-(hBOOL(hAPP(hAPP(c_member(_1421875), hAPP(_1421877, _1421879)), hAPP(c_Set_Oimage(_1421881, _1421875, _1421877), c_Orderings_Otop__class_Otop(tc_fun(_1421881, tc_HOL_Obool))))))], (34269 ^ _778495) ^ [_1417595] : [-(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)), _1417595)) = hAPP(c_Int_Onat, _1417595))], (52237 ^ _778495) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (12384 ^ _778495) ^ [_996447, _996449, _996451, _996453, _996455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996447), _996449)), -(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), _996447), _996451)), _996453)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996449), _996451)), _996455)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996453), 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), _996449), _996447)), _996451)), _996455)))], (29693 ^ _778495) ^ [_1318752, _1318754, _1318756] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1318752), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1318754)), _1318756)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1318752, _1318754), hAPP(c_Divides_OnegateSnd, _1318756))))], (10597 ^ _778495) ^ [_961394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961394), _961394))], (42375 ^ _778495) ^ [_1622617, _1622619, _1622621, _1622623, _1622625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622617), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622619)), _1622621))), 42378 ^ _778495 : [(42385 ^ _778495) ^ [] : [-(_1622617 = _1622623), -(hAPP(hAPP(c_List_Onth(_1622619), hAPP(hAPP(c_List_Olist__update(_1622619, _1622621), _1622617), _1622625)), _1622623) = hAPP(hAPP(c_List_Onth(_1622619), _1622621), _1622623))], (42379 ^ _778495) ^ [] : [_1622617 = _1622623, -(hAPP(hAPP(c_List_Onth(_1622619), hAPP(hAPP(c_List_Olist__update(_1622619, _1622621), _1622617), _1622625)), _1622623) = _1622625)]]], (1648 ^ _778495) ^ [_802123, _802125] : [-(class_Rings_Olinordered__semiring(_802123)), _802125 = _802123, class_Rings_Olinordered__semiring(_802125)], (48882 ^ _778495) ^ [_1767038, _1767040, _1767042, _1767044] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1767038), _1767040)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1767038), _1767042)), -(_1767042 = c_Orderings_Obot__class_Obot(tc_fun(_1767038, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1767038, _1767044, _1767040, _1767042)), 48896 ^ _778495 : [(48899 ^ _778495) ^ [_1767383] : [hBOOL(hAPP(hAPP(c_member(_1767038), _1767383), _1767042)), hBOOL(hAPP(hAPP(_1767044, 48895 ^ [_1767038, _1767040, _1767042, _1767044]), _1767383))], (48897 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767038), 48895 ^ [_1767038, _1767040, _1767042, _1767044]), _1767040)))]]], (22348 ^ _778495) ^ [_1178109, _1178111, _1178113] : [class_Groups_Ogroup__add(_1178109), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1178109), _1178111), hAPP(c_Groups_Ouminus__class_Ouminus(_1178109), _1178113)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178109), _1178111), _1178113))], (18050 ^ _778495) ^ [_1102243, _1102245, _1102247] : [class_Int_Onumber__ring(_1102243), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102243), hAPP(c_Int_Onumber__class_Onumber__of(_1102243), _1102245)), hAPP(c_Int_Onumber__class_Onumber__of(_1102243), _1102247)) = hAPP(c_Int_Onumber__class_Onumber__of(_1102243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1102245), _1102247)))], (20355 ^ _778495) ^ [_1144098, _1144100, _1144102, _1144104] : [class_Orderings_Olinorder(_1144098), hBOOL(hAPP(c_Finite__Set_Ofinite(_1144098), _1144100)), 20365 ^ _778495 : [(20368 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144098), _1144102), 20364 ^ [_1144098, _1144100, _1144102, _1144104]))], (20366 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1144098), 20364 ^ [_1144098, _1144100, _1144102, _1144104]), _1144100)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144098), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144098), _1144102), _1144104)), hAPP(hAPP(c_Finite__Set_Ofold(_1144098, _1144098, c_Orderings_Oord__class_Omin(_1144098)), _1144104), _1144100))))], (37182 ^ _778495) ^ [_1480602, _1480604, _1480606, _1480608] : [-(hAPP(c_Set_Ovimage(_1480602, _1480604, _1480606), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1480604, tc_HOL_Obool), _1480608)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1480604, tc_HOL_Obool), tc_fun(_1480602, tc_HOL_Obool)), _1480608), c_Set_Ovimage(_1480602, _1480604, _1480606)))], (23386 ^ _778495) ^ [_1197590, _1197592] : [class_Rings_Osemiring__1(_1197590), 23389 ^ _778495 : [(23396 ^ _778495) ^ [] : [_1197592 = c_Groups_Ozero__class_Ozero(_1197590), -(c_Int_Oiszero(_1197590, _1197592))], (23390 ^ _778495) ^ [] : [c_Int_Oiszero(_1197590, _1197592), -(_1197592 = c_Groups_Ozero__class_Ozero(_1197590))]]], (40393 ^ _778495) ^ [_1568789, _1568791] : [-(c_Transitive__Closure_Ortrancl(_1568789, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1568789, _1568789), tc_HOL_Obool)), _1568791), c_Relation_OId(_1568789))) = c_Transitive__Closure_Ortrancl(_1568789, _1568791))], (47078 ^ _778495) ^ [_1725378, _1725380, _1725382, _1725384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725378), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725380)), c_List_OdropWhile(_1725380, _1725382, _1725384)))), -(hAPP(hAPP(c_List_Onth(_1725380), c_List_OdropWhile(_1725380, _1725382, _1725384)), _1725378) = hAPP(hAPP(c_List_Onth(_1725380), _1725384), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1725378), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725380)), c_List_OtakeWhile(_1725380, _1725382, _1725384)))))], (8270 ^ _778495) ^ [_915135, _915137, _915139, _915141] : [c_Finite__Set_Ofolding__one(_915135, _915137, _915139), hBOOL(hAPP(c_Finite__Set_Ofinite(_915135), _915141)), -(hAPP(_915139, _915141) = hAPP(c_Finite__Set_Ofold1(_915135, _915137), _915141))], (39257 ^ _778495) ^ [_1541517, _1541519] : [class_Complete__Lattice_Ocomplete__lattice(_1541517), -(c_Complete__Lattice_OInf__class_OInf(_1541517, _1541519) = c_Complete__Lattice_OSup__class_OSup(_1541517, hAPP(c_Set_OCollect(_1541517), hAPP(hAPP(c_COMBB(tc_fun(_1541517, tc_HOL_Obool), tc_HOL_Obool, _1541517), c_HOL_OAll(_1541517)), hAPP(hAPP(c_COMBB(tc_fun(_1541517, tc_HOL_Obool), tc_fun(_1541517, tc_HOL_Obool), _1541517), hAPP(c_COMBS(_1541517, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541517), c_fimplies), hAPP(hAPP(c_COMBC(_1541517, tc_fun(_1541517, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541517)), _1541519)))), c_Orderings_Oord__class_Oless__eq(_1541517))))))], (35364 ^ _778495) ^ [_1439216, _1439218, _1439220] : [class_Orderings_Olinorder(_1439216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439216), _1439218), _1439220)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439216, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1439216, _1439218, _1439220)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439216), _1439220)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1439216), _1439218))], (48378 ^ _778495) ^ [_1753762, _1753764, _1753766] : [-(_1753762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753764), c_List_Oreplicate(_1753764, _1753762, _1753766)) = hAPP(hAPP(c_Set_Oinsert(_1753764), _1753766), c_Orderings_Obot__class_Obot(tc_fun(_1753764, tc_HOL_Obool))))], (28633 ^ _778495) ^ [_1297326, _1297328] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1297326), _1297328)), -(hAPP(c_Finite__Set_Ocard(_1297326), _1297328) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1297326, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1297326), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1297328))], (36162 ^ _778495) ^ [] : [-(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))], (30909 ^ _778495) ^ [_1343043, _1343045, _1343047, _1343049] : [class_Orderings_Olinorder(_1343043), 30912 ^ _778495 : [(30921 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343043), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343043), _1343045), _1343047)), _1343049))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343043), _1343045), _1343049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343043), _1343047), _1343049))], (30913 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343043), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343043), _1343045), _1343047)), _1343049)), 30916 ^ _778495 : [(30919 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343043), _1343047), _1343049)))], (30917 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343043), _1343045), _1343049)))]]]]], (40926 ^ _778495) ^ [_1581881, _1581883, _1581885] : [c_Relation_Osingle__valued(_1581881, _1581881, _1581883), -(c_Relation_Osingle__valued(_1581881, _1581881, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581881, _1581881), tc_HOL_Obool), _1581885), _1581883)))], (28273 ^ _778495) ^ [_1283810, _1283812, _1283814, _1283816] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1283810, tc_fun(_1283812, tc_HOL_Obool))), _1283814), _1283816)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1283810, _1283812)), hAPP(hAPP(c_Product__Type_OPair(_1283810, _1283812), _1283814), _1283816)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1283810, _1283812), tc_HOL_Obool)))))], (24515 ^ _778495) ^ [_1217306, _1217308] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1217306), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217308), _1217306)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1217308), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1217308, _1217306)))], (24844 ^ _778495) ^ [_1223035, _1223037] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223035, _1223037)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223035), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223037)))], (40962 ^ _778495) ^ [_1582559, _1582561, _1582563, _1582565] : [-(hAPP(_1582559, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1582561, _1582561), _1582563), _1582559), _1582565)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1582561, _1582561), _1582563), _1582559), hAPP(_1582559, _1582565)))], (15685 ^ _778495) ^ [_1057713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1057713)), -(_1057713 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057713), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (24513 ^ _778495) ^ [_1217259, _1217261] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1217259, _1217261) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1217259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217259), _1217261)), _1217261)))], (20018 ^ _778495) ^ [_1138039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138039)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8924 ^ _778495) ^ [_928577, _928579, _928581, _928583] : [class_Lattices_Osemilattice__inf(_928577), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928577), _928579), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928577), _928581), _928583)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928577), _928581), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928577), _928579), _928583)))], (20784 ^ _778495) ^ [_1151003] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1151003))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151003)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17618 ^ _778495) ^ [_1094380, _1094382, _1094384, _1094386, _1094388, _1094390] : [-(c_Nitpick_Opair__box_OPairBox(_1094380, _1094382, _1094384, _1094386) = c_Nitpick_Opair__box_OPairBox(_1094380, _1094382, _1094388, _1094390)), _1094384 = _1094388, _1094386 = _1094390], (26880 ^ _778495) ^ [_1258968, _1258970] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1258968), _1258970) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1258968 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1258968 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (23112 ^ _778495) ^ [_1192078, _1192080, _1192082, _1192084] : [class_Divides_Osemiring__div(_1192078), -(c_Divides_Odiv__class_Omod(_1192078, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192078), _1192080), _1192082), _1192084) = c_Divides_Odiv__class_Omod(_1192078, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192078), _1192080), c_Divides_Odiv__class_Omod(_1192078, _1192082, _1192084)), _1192084))], (25022 ^ _778495) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (38324 ^ _778495) ^ [_1515346, _1515348, _1515350, _1515352, _1515354, _1515356, _1515358] : [class_Rings_Osemiring__0(_1515346), c_Fun_Oinj__on(tc_prod(_1515348, _1515350), _1515346, hAPP(c_Product__Type_Oprod_Oprod__case(_1515348, _1515350, _1515346), hAPP(hAPP(c_COMBC(_1515348, tc_fun(_1515350, _1515346), tc_fun(_1515350, _1515346)), hAPP(hAPP(c_COMBB(tc_fun(_1515346, _1515346), tc_fun(tc_fun(_1515350, _1515346), tc_fun(_1515350, _1515346)), _1515348), c_COMBB(_1515346, _1515346, _1515350)), hAPP(hAPP(c_COMBB(_1515346, tc_fun(_1515346, _1515346), _1515348), c_Groups_Otimes__class_Otimes(_1515346)), _1515352))), _1515354)), hAPP(hAPP(c_Product__Type_OSigma(_1515348, _1515350), _1515356), hAPP(c_COMBK(tc_fun(_1515350, tc_HOL_Obool), _1515348), _1515358))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1515346), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1515348, _1515346), _1515352), _1515356)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1515350, _1515346), _1515354), _1515358)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1515346, _1515346), c_Fun_Oid(_1515346)), hAPP(c_Set_OCollect(_1515346), hAPP(hAPP(c_COMBB(tc_fun(_1515348, tc_HOL_Obool), tc_HOL_Obool, _1515346), c_HOL_OEx(_1515348)), hAPP(hAPP(c_COMBB(tc_fun(_1515348, tc_fun(_1515350, tc_HOL_Obool)), tc_fun(_1515348, tc_HOL_Obool), _1515346), hAPP(c_COMBB(tc_fun(_1515350, tc_HOL_Obool), tc_HOL_Obool, _1515348), c_HOL_OEx(_1515350))), hAPP(hAPP(c_COMBC(_1515346, tc_fun(_1515348, tc_fun(_1515350, tc_HOL_Obool)), tc_fun(_1515348, tc_fun(_1515350, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1515348, tc_fun(tc_fun(_1515350, tc_HOL_Obool), tc_fun(_1515350, tc_HOL_Obool))), tc_fun(tc_fun(_1515348, tc_fun(_1515350, tc_HOL_Obool)), tc_fun(_1515348, tc_fun(_1515350, tc_HOL_Obool))), _1515346), c_COMBS(_1515348, tc_fun(_1515350, tc_HOL_Obool), tc_fun(_1515350, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1515348, tc_fun(_1515350, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1515348, tc_fun(tc_fun(_1515350, tc_HOL_Obool), tc_fun(_1515350, tc_HOL_Obool))), _1515346), hAPP(c_COMBB(tc_fun(_1515350, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1515350, tc_HOL_Obool), tc_fun(_1515350, tc_HOL_Obool)), _1515348), c_COMBS(_1515350, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1515348, tc_fun(_1515350, tc_HOL_Obool)), tc_fun(_1515348, tc_fun(_1515350, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1515346), hAPP(c_COMBB(tc_fun(_1515350, tc_HOL_Obool), tc_fun(_1515350, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1515348), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515350), c_fconj))), hAPP(hAPP(c_COMBC(_1515346, tc_fun(_1515348, tc_fun(_1515350, _1515346)), tc_fun(_1515348, tc_fun(_1515350, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1515350, _1515346), tc_fun(_1515350, tc_HOL_Obool)), tc_fun(tc_fun(_1515348, tc_fun(_1515350, _1515346)), tc_fun(_1515348, tc_fun(_1515350, tc_HOL_Obool))), _1515346), c_COMBB(tc_fun(_1515350, _1515346), tc_fun(_1515350, tc_HOL_Obool), _1515348)), hAPP(hAPP(c_COMBB(tc_fun(_1515346, tc_HOL_Obool), tc_fun(tc_fun(_1515350, _1515346), tc_fun(_1515350, tc_HOL_Obool)), _1515346), c_COMBB(_1515346, tc_HOL_Obool, _1515350)), c_fequal))), hAPP(hAPP(c_COMBC(_1515348, tc_fun(_1515350, _1515346), tc_fun(_1515350, _1515346)), hAPP(hAPP(c_COMBB(tc_fun(_1515346, _1515346), tc_fun(tc_fun(_1515350, _1515346), tc_fun(_1515350, _1515346)), _1515348), c_COMBB(_1515346, _1515346, _1515350)), hAPP(hAPP(c_COMBB(_1515346, tc_fun(_1515346, _1515346), _1515348), c_Groups_Otimes__class_Otimes(_1515346)), _1515352))), _1515354)))))), hAPP(hAPP(c_COMBC(_1515348, tc_fun(_1515350, tc_HOL_Obool), tc_fun(_1515350, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1515350, tc_HOL_Obool), tc_fun(_1515350, tc_HOL_Obool)), _1515348), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1515350)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515348), c_fconj), hAPP(hAPP(c_COMBC(_1515348, tc_fun(_1515348, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515348)), _1515356)))), hAPP(hAPP(c_COMBC(_1515350, tc_fun(_1515350, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515350)), _1515358))))))))], (41547 ^ _778495) ^ [_1599565, _1599567, _1599569, _1599571] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599565), tc_List_Olist(_1599565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599565), tc_List_Olist(_1599565)), _1599567), _1599569)), c_List_Olistrel1(_1599565, hAPP(c_Relation_Oconverse(_1599565, _1599565), _1599571)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599565), tc_List_Olist(_1599565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599565), tc_List_Olist(_1599565)), _1599567), _1599569)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1599565), tc_List_Olist(_1599565)), c_List_Olistrel1(_1599565, _1599571)))))], (43421 ^ _778495) ^ [_1645514, _1645516, _1645518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645514), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645516)), _1645518))), -(hAPP(hAPP(c_List_Otake(_1645516), hAPP(c_Nat_OSuc, _1645514)), _1645518) = hAPP(hAPP(c_List_Oappend(_1645516), hAPP(hAPP(c_List_Otake(_1645516), _1645514), _1645518)), hAPP(hAPP(c_List_Olist_OCons(_1645516), hAPP(hAPP(c_List_Onth(_1645516), _1645518), _1645514)), c_List_Olist_ONil(_1645516))))], (35609 ^ _778495) ^ [_1445064, _1445066, _1445068, _1445070] : [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), _1445064), _1445066)), 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), _1445068), _1445070)), 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), _1445064), _1445070)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1445068), _1445066))))], (21452 ^ _778495) ^ [_1163038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163038), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1163038)), c_Int_OPls)))], (26958 ^ _778495) ^ [_1260190] : [-(hAPP(c_Set_OPow(_1260190), c_Orderings_Obot__class_Obot(tc_fun(_1260190, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1260190, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1260190, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1260190, tc_HOL_Obool), tc_HOL_Obool))))], (6008 ^ _778495) ^ [_874494, _874496, _874498] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_874494, tc_HOL_Obool)), _874496), _874498) = _874498, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874494, tc_HOL_Obool)), _874496), _874498)))], (4802 ^ _778495) ^ [_851703, _851705, _851707, _851709] : [-(c_List_Olistrel(_851709, _851705) = c_List_Olistrel(_851707, _851703)), _851709 = _851707, _851705 = _851703], (42760 ^ _778495) ^ [_1630599] : [-(hAPP(c_List_Oset(_1630599), c_List_Olist_ONil(_1630599)) = c_Orderings_Obot__class_Obot(tc_fun(_1630599, tc_HOL_Obool)))], (50911 ^ _778495) ^ [_1809159, _1809161, _1809163, _1809165] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809159, _1809161)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809163, _1809165)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809163), _1809165)), 50914 ^ _778495 : [(50917 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809163), _1809159)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809161), _1809165)), 50924 ^ _778495 : [(50931 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809161), _1809165)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809165), _1809161)))], (50925 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809163), _1809159)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809159), _1809163)))]]], (50915 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809159), _1809161)))]]], (924 ^ _778495) ^ [_792373, _792375, _792377, _792379, _792381, _792383, _792385, _792387, _792389, _792391] : [-(c_Fun_Obij__betw(_792389, _792385, _792381, _792377, _792373)), c_Fun_Obij__betw(_792391, _792387, _792383, _792379, _792375), _792391 = _792389, _792387 = _792385, _792383 = _792381, _792379 = _792377, _792375 = _792373], (33515 ^ _778495) ^ [_1401547, _1401549, _1401551, _1401553, _1401555] : [-(_1401547 = c_Orderings_Obot__class_Obot(tc_fun(_1401549, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401551, tc_HOL_Obool)), _1401553), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401549, tc_fun(_1401551, tc_HOL_Obool)), _1401547), _1401555)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401549, tc_fun(_1401551, tc_HOL_Obool)), _1401547), hAPP(hAPP(c_COMBB(tc_fun(_1401551, tc_HOL_Obool), tc_fun(_1401551, tc_HOL_Obool), _1401549), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401551, tc_HOL_Obool)), _1401553)), _1401555)))], (52633 ^ _778495) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (47288 ^ _778495) ^ [_1730184, _1730186, _1730188, _1730190, _1730192] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1730184, _1730184)), hAPP(hAPP(c_Product__Type_OPair(_1730184, _1730184), _1730186), _1730188)), c_List_Omeasures(_1730184, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1730184, tc_Nat_Onat)), _1730190), _1730192)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1730190, _1730186)), hAPP(_1730190, _1730188)))), 47295 ^ _778495 : [(47298 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730184, _1730184)), hAPP(hAPP(c_Product__Type_OPair(_1730184, _1730184), _1730186), _1730188)), c_List_Omeasures(_1730184, _1730192))))], (47296 ^ _778495) ^ [] : [-(hAPP(_1730190, _1730186) = hAPP(_1730190, _1730188))]]], (4352 ^ _778495) ^ [_844618, _844620] : [_844620 = _844618, -(c_Lazy__Sequence_Osingle(_844620) = c_Lazy__Sequence_Osingle(_844618))], (26960 ^ _778495) ^ [_1260247, _1260249, _1260251] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1260247, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1260247, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1260247), _1260249)), hAPP(c_Set_OPow(_1260247), _1260251))), hAPP(c_Set_OPow(_1260247), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260247, tc_HOL_Obool)), _1260249), _1260251)))))], (39904 ^ _778495) ^ [_1556401, _1556403, _1556405] : [hBOOL(hAPP(_1556401, _1556403)), -(hBOOL(hAPP(_1556401, c_Hilbert__Choice_OEps(_1556405, _1556401))))], (45975 ^ _778495) ^ [_1703397, _1703399] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1703397, _1703399)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1703399), _1703397))], (47849 ^ _778495) ^ [_1742621] : [class_Nat_Osize(_1742621), -(c_FunDef_Ois__measure(_1742621, c_Nat_Osize__class_Osize(_1742621)))], (23412 ^ _778495) ^ [_1197954] : [class_Rings_Osemiring__1(_1197954), c_Int_Oiszero(_1197954, c_Groups_Oone__class_Oone(_1197954))], (7464 ^ _778495) ^ [_902329, _902331, _902333] : [class_Orderings_Olinorder(_902329), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902329), _902331), _902333))), -(_902331 = _902333), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902329), _902333), _902331)))], (35845 ^ _778495) ^ [_1450564, _1450566, _1450568, _1450570, _1450572] : [c_Equiv__Relations_Oequiv(_1450564, _1450566, _1450568), 35848 ^ _778495 : [(35859 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1450564, _1450564)), hAPP(hAPP(c_Product__Type_OPair(_1450564, _1450564), _1450570), _1450572)), _1450568))), hAPP(c_Relation_OImage(_1450564, _1450564, _1450568), hAPP(hAPP(c_Set_Oinsert(_1450564), _1450570), c_Orderings_Obot__class_Obot(tc_fun(_1450564, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1450564, _1450564, _1450568), hAPP(hAPP(c_Set_Oinsert(_1450564), _1450572), c_Orderings_Obot__class_Obot(tc_fun(_1450564, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1450564), _1450570), _1450566)), hBOOL(hAPP(hAPP(c_member(_1450564), _1450572), _1450566))], (35849 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1450564, _1450564)), hAPP(hAPP(c_Product__Type_OPair(_1450564, _1450564), _1450570), _1450572)), _1450568)), 35852 ^ _778495 : [(35857 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450564), _1450572), _1450566)))], (35855 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450564), _1450570), _1450566)))], (35853 ^ _778495) ^ [] : [-(hAPP(c_Relation_OImage(_1450564, _1450564, _1450568), hAPP(hAPP(c_Set_Oinsert(_1450564), _1450570), c_Orderings_Obot__class_Obot(tc_fun(_1450564, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1450564, _1450564, _1450568), hAPP(hAPP(c_Set_Oinsert(_1450564), _1450572), c_Orderings_Obot__class_Obot(tc_fun(_1450564, tc_HOL_Obool)))))]]]]], (14341 ^ _778495) ^ [_1033336, _1033338, _1033340, _1033342] : [class_Rings_Olinordered__ring__strict(_1033336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033336), _1033338), _1033340)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033336), _1033342), c_Groups_Ozero__class_Ozero(_1033336))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033336), _1033340), _1033342)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033336), _1033338), _1033342))))], (49043 ^ _778495) ^ [_1770267] : [-(c_Relation_Otrans(tc_fun(_1770267, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1770267)))], (49883 ^ _778495) ^ [_1787096, _1787098, _1787100, _1787102] : [c_Fun_Obij__betw(_1787096, _1787098, _1787100, c_Orderings_Otop__class_Otop(tc_fun(_1787096, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787098, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1787096, _1787098, _1787100), hAPP(c_Set_OCollect(_1787096), _1787102)) = hAPP(c_Set_OCollect(_1787098), hAPP(hAPP(c_COMBB(_1787096, tc_HOL_Obool, _1787098), _1787102), c_Hilbert__Choice_Oinv__into(_1787096, _1787098, c_Orderings_Otop__class_Otop(tc_fun(_1787096, tc_HOL_Obool)), _1787100))))], (19002 ^ _778495) ^ [_1120216, _1120218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120216)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120218))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120216), _1120218)))], (4006 ^ _778495) ^ [_839143, _839145, _839147, _839149, _839151, _839153, _839155, _839157] : [-(c_New__Random__Sequence_Oneg__bind(_839157, _839153, _839149, _839145) = c_New__Random__Sequence_Oneg__bind(_839155, _839151, _839147, _839143)), _839157 = _839155, _839153 = _839151, _839149 = _839147, _839145 = _839143], (42445 ^ _778495) ^ [_1624348, _1624350, _1624352] : [hBOOL(hAPP(c_List_Odistinct(_1624348), _1624350)), -(hBOOL(hAPP(c_List_Odistinct(_1624348), hAPP(hAPP(c_List_Otake(_1624348), _1624352), _1624350))))], (8300 ^ _778495) ^ [_915613, _915615, _915617, _915619, _915621, _915623, _915625, _915627] : [c_Finite__Set_Ofolding__image__simple(_915613, _915615, _915617, _915619, _915621, _915623), hBOOL(hAPP(c_Finite__Set_Ofinite(_915615), _915625)), -(hBOOL(hAPP(hAPP(c_member(_915615), _915627), _915625))), -(hAPP(_915623, hAPP(hAPP(c_Set_Oinsert(_915615), _915627), _915625)) = hAPP(hAPP(_915617, hAPP(_915621, _915627)), hAPP(_915623, _915625)))], (42928 ^ _778495) ^ [_1633804] : [-(c_List_Olistset(_1633804, c_List_Olist_ONil(tc_fun(_1633804, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633804)), c_List_Olist_ONil(_1633804)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633804), tc_HOL_Obool))))], (32478 ^ _778495) ^ [_1376803, _1376805, _1376807, _1376809] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1376803), _1376805)), 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)), _1376803), _1376807)), 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)), _1376805), _1376809)), 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)), _1376805), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1376807), _1376809))), c_FunDef_Omin__weak)))], (52635 ^ _778495) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (17954 ^ _778495) ^ [_1100297, _1100299, _1100301, _1100303] : [class_Orderings_Olinorder(_1100297), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100297), _1100299), _1100301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100297), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100297), _1100303), _1100299)), _1100301)))], (34010 ^ _778495) ^ [_1411899] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411899), hAPP(c_Nat_OSuc, _1411899)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1411899), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (52439 ^ _778495) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (44017 ^ _778495) ^ [_1659208, _1659210, _1659212] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659208), tc_List_Olist(_1659208))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659208), tc_List_Olist(_1659208)), c_List_Olist_ONil(_1659208)), _1659210)), c_List_Olexord(_1659208, _1659212))), -(_1659210 = hAPP(hAPP(c_List_Olist_OCons(_1659208), 44020 ^ [_1659208, _1659210, _1659212]), 44021 ^ [_1659208, _1659210, _1659212]))], (39430 ^ _778495) ^ [_1545840, _1545842, _1545844, _1545846, _1545848, _1545850] : [-(hAPP(c_Set_Oimage(_1545840, _1545842, hAPP(c_Fun_Ocomp(_1545844, _1545842, _1545840, _1545846), _1545848)), _1545850) = hAPP(c_Set_Oimage(_1545844, _1545842, _1545846), hAPP(c_Set_Oimage(_1545840, _1545844, _1545848), _1545850)))], (20900 ^ _778495) ^ [_1152806] : [class_Rings_Osemiring__1(_1152806), -(hBOOL(hAPP(hAPP(c_member(_1152806), c_Groups_Oone__class_Oone(_1152806)), c_Nat_Osemiring__1__class_ONats(_1152806))))], (46965 ^ _778495) ^ [_1722981] : [-(c_List_Oembed__list(_1722981) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1722981))], (16002 ^ _778495) ^ [_1064244, _1064246] : [-(hBOOL(hAPP(_1064244, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1064244, _1064246)), 16010 ^ _778495 : [(16013 ^ _778495) ^ [_1064482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1064482), 16009 ^ [_1064244, _1064246])), hBOOL(hAPP(_1064244, _1064482))], (16019 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1064244, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 16009 ^ [_1064244, _1064246]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (16011 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16009 ^ [_1064244, _1064246]), _1064246)))]]], (38475 ^ _778495) ^ [_1520726, _1520728, _1520730, _1520732] : [hAPP(hAPP(c_Relation_Orel__comp(_1520726, _1520726, _1520726), _1520728), _1520730) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520726, _1520726), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1520726, _1520726, _1520726), _1520732), _1520730) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520726, _1520726), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1520726, _1520726, _1520726), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520726, _1520726), tc_HOL_Obool)), _1520728), _1520732)), _1520730) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520726, _1520726), tc_HOL_Obool)))], (9578 ^ _778495) ^ [_942150, _942152, _942154] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942150, tc_HOL_Obool)), _942152), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942150, tc_HOL_Obool)), _942154), _942152)) = c_Orderings_Obot__class_Obot(tc_fun(_942150, tc_HOL_Obool)))], (17480 ^ _778495) ^ [_1091551, _1091553, _1091555, _1091557] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1091551, tc_Nat_Onat), _1091553), _1091555) = hAPP(c_Nat_OSuc, _1091557), 17484 ^ _778495 : [(17487 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1091553, 17483 ^ [_1091551, _1091553, _1091555, _1091557]))))], (17485 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1091551), 17483 ^ [_1091551, _1091553, _1091555, _1091557]), _1091555)))]]], (49033 ^ _778495) ^ [_1770128, _1770130] : [c_Relation_Otrans(_1770128, _1770130), -(c_Transitive__Closure_Otrancl(_1770128, _1770130) = _1770130)], (5132 ^ _778495) ^ [_856856, _856858, _856860, _856862] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_856862, _856858) = c_SetInterval_Oord__class_OatLeastLessThan(_856860, _856856)), _856862 = _856860, _856858 = _856856], (48654 ^ _778495) ^ [_1760131, _1760133, _1760135, _1760137, _1760139, _1760141, _1760143] : [48656 ^ _778495 : [(48659 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1760135, 48655 ^ [_1760131, _1760133, _1760135, _1760137, _1760139, _1760141, _1760143]), _1760137), _1760139))], (48657 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760131), 48655 ^ [_1760131, _1760133, _1760135, _1760137, _1760139, _1760141, _1760143]), _1760133)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1760131, tc_fun(_1760141, tc_fun(_1760143, tc_HOL_Obool))), _1760133), _1760135), _1760137), _1760139)))], (478 ^ _778495) ^ [_785758, _785760] : [-(class_Rings_Oinverse(_785758)), _785760 = _785758, class_Rings_Oinverse(_785760)], (29902 ^ _778495) ^ [_1322494, _1322496, _1322498, _1322500, _1322502, _1322504] : [hAPP(c_Product__Type_Oapsnd(_1322494, _1322496, _1322498, _1322500), _1322502) = hAPP(c_Product__Type_Oapsnd(_1322494, _1322496, _1322498, _1322504), _1322502), -(hAPP(_1322500, hAPP(c_Product__Type_Osnd(_1322498, _1322494), _1322502)) = hAPP(_1322504, hAPP(c_Product__Type_Osnd(_1322498, _1322494), _1322502)))], (26102 ^ _778495) ^ [_1245044, _1245046, _1245048] : [class_Groups_Omonoid__mult(_1245044), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245044), hAPP(hAPP(c_Power_Opower__class_Opower(_1245044), _1245046), _1245048)), _1245046) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245044), _1245046), hAPP(hAPP(c_Power_Opower__class_Opower(_1245044), _1245046), _1245048)))], (21654 ^ _778495) ^ [_1166241, _1166243] : [class_Int_Onumber__ring(_1166241), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1166241), hAPP(c_Int_Onumber__class_Onumber__of(_1166241), _1166243)) = hAPP(c_Int_Onumber__class_Onumber__of(_1166241), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1166243)))], (21952 ^ _778495) ^ [_1171094, _1171096, _1171098] : [class_Groups_Oordered__ab__group__add(_1171094), 21955 ^ _778495 : [(21962 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171094), _1171098), hAPP(c_Groups_Ouminus__class_Ouminus(_1171094), _1171096))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171094), _1171096), hAPP(c_Groups_Ouminus__class_Ouminus(_1171094), _1171098))))], (21956 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171094), _1171096), hAPP(c_Groups_Ouminus__class_Ouminus(_1171094), _1171098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171094), _1171098), hAPP(c_Groups_Ouminus__class_Ouminus(_1171094), _1171096))))]]], (48118 ^ _778495) ^ [_1748378, _1748380, _1748382] : [-(c_Predicate_Oconversep(_1748378, _1748380, c_Predicate_Oconversep(_1748380, _1748378, _1748382)) = _1748382)], (37879 ^ _778495) ^ [_1499516, _1499518, _1499520] : [hBOOL(hAPP(_1499516, _1499518)), -(hAPP(c_Set_OCollect(_1499520), hAPP(hAPP(c_COMBS(_1499520, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499520), c_fconj), hAPP(hAPP(c_COMBC(_1499520, _1499520, tc_HOL_Obool), c_fequal), _1499518))), _1499516)) = hAPP(hAPP(c_Set_Oinsert(_1499520), _1499518), c_Orderings_Obot__class_Obot(tc_fun(_1499520, tc_HOL_Obool))))], (25722 ^ _778495) ^ [_1238131, _1238133] : [class_Rings_Olinordered__idom(_1238131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238131), hAPP(hAPP(c_Power_Opower__class_Opower(_1238131), _1238133), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1238131)))], (6244 ^ _778495) ^ [_879500, _879502, _879504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879500, tc_HOL_Obool)), _879502), _879504)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879500, tc_HOL_Obool)), _879504), _879502) = _879504)], (45018 ^ _778495) ^ [_1680956, _1680958, _1680960, _1680962] : [-(hBOOL(hAPP(c_List_Olistsp(_1680956, _1680958), hAPP(hAPP(c_List_Oappend(_1680956), _1680960), _1680962)))), hBOOL(hAPP(c_List_Olistsp(_1680956, _1680958), _1680960)), hBOOL(hAPP(c_List_Olistsp(_1680956, _1680958), _1680962))], (28023 ^ _778495) ^ [_1278429, _1278431] : [-(hBOOL(hAPP(hAPP(c_member(_1278429), _1278431), c_Orderings_Otop__class_Otop(tc_fun(_1278429, tc_HOL_Obool)))))], (38184 ^ _778495) ^ [_1509592, _1509594, _1509596] : [class_Lattices_Odistrib__lattice(_1509592), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509592), _1509594)), -(_1509594 = c_Orderings_Obot__class_Obot(tc_fun(_1509592, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509592), _1509596)), -(_1509596 = c_Orderings_Obot__class_Obot(tc_fun(_1509592, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1509592), c_Big__Operators_Olattice__class_OInf__fin(_1509592, _1509594)), c_Big__Operators_Olattice__class_OInf__fin(_1509592, _1509596)) = c_Big__Operators_Olattice__class_OInf__fin(_1509592, hAPP(c_Set_OCollect(_1509592), hAPP(hAPP(c_COMBB(tc_fun(_1509592, tc_HOL_Obool), tc_HOL_Obool, _1509592), c_HOL_OEx(_1509592)), hAPP(hAPP(c_COMBB(tc_fun(_1509592, tc_fun(_1509592, tc_HOL_Obool)), tc_fun(_1509592, tc_HOL_Obool), _1509592), hAPP(c_COMBB(tc_fun(_1509592, tc_HOL_Obool), tc_HOL_Obool, _1509592), c_HOL_OEx(_1509592))), hAPP(hAPP(c_COMBC(_1509592, tc_fun(_1509592, tc_fun(_1509592, tc_HOL_Obool)), tc_fun(_1509592, tc_fun(_1509592, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1509592, tc_fun(tc_fun(_1509592, tc_HOL_Obool), tc_fun(_1509592, tc_HOL_Obool))), tc_fun(tc_fun(_1509592, tc_fun(_1509592, tc_HOL_Obool)), tc_fun(_1509592, tc_fun(_1509592, tc_HOL_Obool))), _1509592), c_COMBS(_1509592, tc_fun(_1509592, tc_HOL_Obool), tc_fun(_1509592, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1509592, tc_fun(_1509592, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1509592, tc_fun(tc_fun(_1509592, tc_HOL_Obool), tc_fun(_1509592, tc_HOL_Obool))), _1509592), hAPP(c_COMBB(tc_fun(_1509592, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1509592, tc_HOL_Obool), tc_fun(_1509592, tc_HOL_Obool)), _1509592), c_COMBS(_1509592, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1509592, tc_fun(_1509592, tc_HOL_Obool)), tc_fun(_1509592, tc_fun(_1509592, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1509592), hAPP(c_COMBB(tc_fun(_1509592, tc_HOL_Obool), tc_fun(_1509592, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1509592), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509592), c_fconj))), hAPP(hAPP(c_COMBC(_1509592, tc_fun(_1509592, tc_fun(_1509592, _1509592)), tc_fun(_1509592, tc_fun(_1509592, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1509592, _1509592), tc_fun(_1509592, tc_HOL_Obool)), tc_fun(tc_fun(_1509592, tc_fun(_1509592, _1509592)), tc_fun(_1509592, tc_fun(_1509592, tc_HOL_Obool))), _1509592), c_COMBB(tc_fun(_1509592, _1509592), tc_fun(_1509592, tc_HOL_Obool), _1509592)), hAPP(hAPP(c_COMBB(tc_fun(_1509592, tc_HOL_Obool), tc_fun(tc_fun(_1509592, _1509592), tc_fun(_1509592, tc_HOL_Obool)), _1509592), c_COMBB(_1509592, tc_HOL_Obool, _1509592)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1509592)))))), hAPP(hAPP(c_COMBC(_1509592, tc_fun(_1509592, tc_HOL_Obool), tc_fun(_1509592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1509592, tc_HOL_Obool), tc_fun(_1509592, tc_HOL_Obool)), _1509592), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1509592)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509592), c_fconj), hAPP(hAPP(c_COMBC(_1509592, tc_fun(_1509592, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509592)), _1509594)))), hAPP(hAPP(c_COMBC(_1509592, tc_fun(_1509592, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509592)), _1509596))))))))], (21170 ^ _778495) ^ [_1157801] : [c_Int_OPls = c_Int_OBit1(_1157801)], (12679 ^ _778495) ^ [_1002971, _1002973, _1002975, _1002977, _1002979] : [class_Groups_Ocomm__monoid__add(_1002971), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002973), _1002975)), hBOOL(hAPP(hAPP(c_member(_1002973), _1002977), _1002975)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1002973, _1002971), _1002979), _1002975) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002971), hAPP(_1002979, _1002977)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1002973, _1002971), _1002979), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002973, tc_HOL_Obool)), _1002975), hAPP(hAPP(c_Set_Oinsert(_1002973), _1002977), c_Orderings_Obot__class_Obot(tc_fun(_1002973, tc_HOL_Obool)))))))], (46033 ^ _778495) ^ [_1704482, _1704484] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1704482, _1704484) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1704482), _1704484)))], (23861 ^ _778495) ^ [_1205614, _1205616] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205614), _1205616) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23862 ^ _778495 : [(23871 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205614), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205616), _1205614))], (23865 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205614), _1205616))], (23863 ^ _778495) ^ [] : [_1205616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (52221 ^ _778495) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (46019 ^ _778495) ^ [_1704200, _1704202] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1704200, _1704202)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1704200), hAPP(c_Nat_OSuc, _1704202)))], (47209 ^ _778495) ^ [_1728204, _1728206, _1728208] : [-(hBOOL(hAPP(hAPP(c_member(_1728204), _1728206), hAPP(c_List_Oset(_1728204), _1728208)))), -(c_List_Oinsert(_1728204, _1728206, _1728208) = hAPP(hAPP(c_List_Olist_OCons(_1728204), _1728206), _1728208))], (12246 ^ _778495) ^ [_993267, _993269] : [class_Complete__Lattice_Ocomplete__lattice(_993267), hBOOL(hAPP(c_Finite__Set_Ofinite(_993267), _993269)), -(_993269 = c_Orderings_Obot__class_Obot(tc_fun(_993267, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_993267, _993269) = c_Complete__Lattice_OSup__class_OSup(_993267, _993269))], (20808 ^ _778495) ^ [_1151301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1151301), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151301)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (22124 ^ _778495) ^ [_1174193] : [-(c_Int_OBit0(_1174193) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1174193), _1174193))], (12430 ^ _778495) ^ [_997538, _997540, _997542] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_997538, tc_HOL_Obool)), _997540), _997542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997538, tc_HOL_Obool)), _997540), c_Complete__Lattice_OSup__class_OSup(tc_fun(_997538, tc_HOL_Obool), _997542))))], (28919 ^ _778495) ^ [_1303455] : [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), _1303455))), 28922 ^ _778495 : [(28929 ^ _778495) ^ [] : [-(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), _1303455)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1303455)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1303455)), 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), _1303455)))))], (28923 ^ _778495) ^ [] : [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), _1303455))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1303455)) = 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)))]]], (17577 ^ _778495) ^ [_1093560, _1093562, _1093564] : [class_Orderings_Olinorder(_1093560), -(_1093562 = c_Orderings_Obot__class_Obot(tc_fun(_1093560, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1093560, tc_HOL_Obool)), _1093562), _1093564)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093560), _1093564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093560), hAPP(c_Finite__Set_Ofold1(_1093560, c_Orderings_Oord__class_Omin(_1093560)), _1093564)), hAPP(c_Finite__Set_Ofold1(_1093560, c_Orderings_Oord__class_Omin(_1093560)), _1093562))))], (4822 ^ _778495) ^ [_852001, _852003, _852005, _852007] : [-(c_Relation_Oconverse(_852007, _852003) = c_Relation_Oconverse(_852005, _852001)), _852007 = _852005, _852003 = _852001], (44648 ^ _778495) ^ [_1673001, _1673003] : [hAPP(c_Code__Numeral_Oof__nat, _1673001) = hAPP(c_Code__Numeral_Oof__nat, _1673003), -(_1673001 = _1673003)], (34494 ^ _778495) ^ [_1422971, _1422973, _1422975, _1422977, _1422979] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1422971), hAPP(c_Set_Oimage(_1422973, _1422971, _1422975), c_Orderings_Otop__class_Otop(tc_fun(_1422973, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1422977), hAPP(c_Set_Oimage(_1422973, _1422977, hAPP(hAPP(c_COMBB(_1422971, _1422977, _1422973), _1422979), _1422975)), c_Orderings_Otop__class_Otop(tc_fun(_1422973, tc_HOL_Obool))))))], (24671 ^ _778495) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10629 ^ _778495) ^ [_961704] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961704), _961704))))], (48801 ^ _778495) ^ [_1763548] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1763548, tc_HOL_Obool) = c_Set_OBex(_1763548))], (29388 ^ _778495) ^ [_1313012, _1313014, _1313016, _1313018, _1313020] : [hBOOL(hAPP(hAPP(_1313012, _1313014), _1313016)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1313018, _1313020, tc_HOL_Obool), _1313012), hAPP(hAPP(c_Product__Type_OPair(_1313018, _1313020), _1313014), _1313016))))], (45135 ^ _778495) ^ [_1683870, _1683872, _1683874, _1683876, _1683878, _1683880, _1683882] : [c_List_Olist__all2(_1683870, _1683872, _1683874, hAPP(hAPP(c_List_Olist_OCons(_1683870), _1683876), _1683878), hAPP(hAPP(c_List_Olist_OCons(_1683872), _1683880), _1683882)), 45138 ^ _778495 : [(45141 ^ _778495) ^ [] : [-(c_List_Olist__all2(_1683870, _1683872, _1683874, _1683878, _1683882))], (45139 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1683874, _1683876), _1683880)))]]], (45768 ^ _778495) ^ [_1697961, _1697963, _1697965] : [-(c_List_Oremdups(_1697961, hAPP(c_List_Ofilter(_1697961, _1697963), _1697965)) = hAPP(c_List_Ofilter(_1697961, _1697963), c_List_Oremdups(_1697961, _1697965)))], (13151 ^ _778495) ^ [_1012887, _1012889] : [class_Groups_Ocomm__monoid__add(_1012887), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012887), _1012889), c_Groups_Ozero__class_Ozero(_1012887)) = _1012889)], (34941 ^ _778495) ^ [_1432073, _1432075, _1432077, _1432079, _1432081, _1432083] : [-(c_Fun_Ofun__upd(_1432073, _1432075, c_Fun_Ofun__upd(_1432073, _1432075, _1432077, _1432079, _1432081), _1432079, _1432083) = c_Fun_Ofun__upd(_1432073, _1432075, _1432077, _1432079, _1432083))], (38144 ^ _778495) ^ [_1507989, _1507991] : [-(c_Fun_Oinj__on(tc_fun(_1507989, _1507991), tc_fun(tc_prod(_1507989, _1507991), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1507989, _1507991), tc_HOL_Obool), tc_fun(tc_prod(_1507989, _1507991), tc_HOL_Obool), tc_fun(_1507989, _1507991)), c_Set_OCollect(tc_prod(_1507989, _1507991))), hAPP(hAPP(c_COMBB(tc_fun(_1507989, tc_fun(_1507991, tc_HOL_Obool)), tc_fun(tc_prod(_1507989, _1507991), tc_HOL_Obool), tc_fun(_1507989, _1507991)), c_Product__Type_Oprod_Oprod__case(_1507989, _1507991, tc_HOL_Obool)), hAPP(c_COMBB(_1507991, tc_fun(_1507991, tc_HOL_Obool), _1507989), hAPP(c_COMBC(_1507991, _1507991, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1507989, _1507991), tc_HOL_Obool))))], (7562 ^ _778495) ^ [_903612, _903614, _903616] : [class_Orderings_Opreorder(_903612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903612), _903614), _903616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903612), _903616), _903614))], (23450 ^ _778495) ^ [_1198547, _1198549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198547), 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)), _1198549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1198547), _1198549)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (48704 ^ _778495) ^ [_1761160, _1761162, _1761164] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1761160), _1761162, _1761164)), -(c_List_Olist__ex(tc_Int_Oint, _1761160, c_List_Oupto(_1761162, _1761164)))], (21600 ^ _778495) ^ [_1165360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1165360), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1165360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1165360 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4838 ^ _778495) ^ [_852235, _852237, _852239, _852241] : [-(c_Hilbert__Choice_OEps(_852241, _852237) = c_Hilbert__Choice_OEps(_852239, _852235)), _852241 = _852239, _852237 = _852235], (22672 ^ _778495) ^ [_1183800] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1183800)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1183800))))], (31019 ^ _778495) ^ [_1345189, _1345191] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1345189)), _1345191) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1345189), 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), _1345189)), _1345191))], (38789 ^ _778495) ^ [_1529298, _1529300] : [hBOOL(hAPP(hAPP(c_member(_1529298), 38790 ^ [_1529298, _1529300]), c_Wellfounded_Oacc(_1529298, _1529300))), -(c_Wellfounded_Owf(_1529298, _1529300))], (13735 ^ _778495) ^ [_1022200, _1022202, _1022204] : [class_Rings_Oordered__ring(_1022200), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022200), c_Groups_Ozero__class_Ozero(_1022200)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022200), _1022202), _1022204)))), 13740 ^ _778495 : [(13747 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022200), _1022202), c_Groups_Ozero__class_Ozero(_1022200))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022200), _1022204), c_Groups_Ozero__class_Ozero(_1022200)))], (13741 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022200), c_Groups_Ozero__class_Ozero(_1022200)), _1022202)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022200), c_Groups_Ozero__class_Ozero(_1022200)), _1022204))]]], (35781 ^ _778495) ^ [_1449146, _1449148, _1449150, _1449152, _1449154, _1449156, _1449158] : [c_Equiv__Relations_Oequiv(_1449146, _1449148, _1449150), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449146, tc_HOL_Obool)), _1449152), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449146), _1449148), _1449150))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449146, tc_HOL_Obool)), _1449154), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449146), _1449148), _1449150))), hBOOL(hAPP(hAPP(c_member(_1449146), _1449156), _1449152)), hBOOL(hAPP(hAPP(c_member(_1449146), _1449158), _1449154)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1449146, _1449146)), hAPP(hAPP(c_Product__Type_OPair(_1449146, _1449146), _1449156), _1449158)), _1449150)), -(_1449152 = _1449154)], (6860 ^ _778495) ^ [_891041, _891043, _891045, _891047, _891049] : [class_Lattices_Olattice(_891041), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891043, _891041)), _891045), _891047), _891049) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891041), hAPP(_891045, _891049)), hAPP(_891047, _891049)))], (20560 ^ _778495) ^ [_1147322] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147322))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147322)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27243 ^ _778495) ^ [_1264964, _1264966] : [-(c_Nitpick_Onat__lcm(_1264964, _1264966) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1264964), _1264966)), c_Nitpick_Onat__gcd(_1264964, _1264966)))], (4526 ^ _778495) ^ [_847327, _847329, _847331, _847333] : [-(c_List_Oupto(_847333, _847329) = c_List_Oupto(_847331, _847327)), _847333 = _847331, _847329 = _847327], (1528 ^ _778495) ^ [_800623, _800625] : [-(class_Enum_Oenum(_800623)), _800625 = _800623, class_Enum_Oenum(_800625)], (236 ^ _778495) ^ [_782337, _782339] : [-(class_Rings_Odivision__ring(_782337)), _782339 = _782337, class_Rings_Odivision__ring(_782339)], (40206 ^ _778495) ^ [_1563487, _1563489, _1563491, _1563493] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563487, _1563487)), hAPP(hAPP(c_Product__Type_OPair(_1563487, _1563487), _1563489), _1563491)), _1563493)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563487, _1563487)), hAPP(hAPP(c_Product__Type_OPair(_1563487, _1563487), _1563489), _1563491)), c_Transitive__Closure_Otrancl(_1563487, _1563493))))], (14558 ^ _778495) ^ [_1037131] : [_1037131 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037131), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (6014 ^ _778495) ^ [_874635, _874637, _874639] : [_874635 = _874637, 6017 ^ _778495 : [(6020 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874639, tc_HOL_Obool)), _874637), _874635)))], (6018 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874639, tc_HOL_Obool)), _874635), _874637)))]]], (33138 ^ _778495) ^ [_1390145, _1390147, _1390149, _1390151, _1390153, _1390155, _1390157, _1390159] : [hBOOL(hAPP(hAPP(c_member(_1390145), _1390147), _1390149)), hBOOL(hAPP(hAPP(hAPP(_1390151, _1390147), _1390153), _1390155)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390145, tc_fun(_1390157, tc_fun(_1390159, tc_HOL_Obool))), _1390149), _1390151), _1390153), _1390155)))], (8078 ^ _778495) ^ [_911464, _911466, _911468, _911470] : [class_Lattices_Osemilattice__sup(_911464), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911464), _911466), _911468)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911464), _911466), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911464), _911470), _911468))))], (24431 ^ _778495) ^ [_1215704, _1215706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215704)), -(c_SMT_Oz3div(_1215706, _1215704) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215706), _1215704))], (6624 ^ _778495) ^ [_886508, _886510, _886512, _886514] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886508, tc_HOL_Obool)), _886510), hAPP(hAPP(c_Set_Oinsert(_886508), _886512), _886514)))), 6627 ^ _778495 : [(6630 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886508, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886508, tc_HOL_Obool)), _886510), hAPP(hAPP(c_Set_Oinsert(_886508), _886512), c_Orderings_Obot__class_Obot(tc_fun(_886508, tc_HOL_Obool))))), _886514))], (6628 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886508), _886512), _886510)))]], 6631 ^ _778495 : [(6634 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886508, tc_HOL_Obool)), _886510), _886514))], (6632 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886508), _886512), _886510))]]], (41991 ^ _778495) ^ [_1612132, _1612134, _1612136] : [41993 ^ _778495 : [(41996 ^ _778495) ^ [] : [hBOOL(hAPP(_1612136, 41992 ^ [_1612132, _1612134, _1612136]))], (41994 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612132), 41992 ^ [_1612132, _1612134, _1612136]), hAPP(c_List_Oset(_1612132), _1612134))))]], 41997 ^ _778495 : [(41998 ^ _778495) ^ [_1612316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612316), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612132)), _1612134))), -(hBOOL(hAPP(_1612136, hAPP(hAPP(c_List_Onth(_1612132), _1612134), _1612316))))]]], (47831 ^ _778495) ^ [_1742335, _1742337, _1742339, _1742341] : [c_List_Olist__all(_1742335, _1742337, hAPP(hAPP(c_List_Oappend(_1742335), _1742339), _1742341)), 47834 ^ _778495 : [(47837 ^ _778495) ^ [] : [-(c_List_Olist__all(_1742335, _1742337, _1742341))], (47835 ^ _778495) ^ [] : [-(c_List_Olist__all(_1742335, _1742337, _1742339))]]], (36797 ^ _778495) ^ [] : [-(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))], (12422 ^ _778495) ^ [_997347] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_997347, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_997347, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_997347, tc_HOL_Obool)))], (10457 ^ _778495) ^ [_958909] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958909), hAPP(c_Nat_OSuc, _958909))))], (48231 ^ _778495) ^ [_1751111, _1751113, _1751115, _1751117] : [48232 ^ _778495 : [(48235 ^ _778495) ^ [] : [_1751113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48233 ^ _778495) ^ [] : [hBOOL(hAPP(_1751117, _1751115))]], 48236 ^ _778495 : [(48237 ^ _778495) ^ [_1751236] : [hBOOL(hAPP(hAPP(c_member(_1751111), _1751236), hAPP(c_List_Oset(_1751111), c_List_Oreplicate(_1751111, _1751113, _1751115)))), -(hBOOL(hAPP(_1751117, _1751236)))]]], (34482 ^ _778495) ^ [_1422777, _1422779, _1422781, _1422783] : [_1422777 = c_Orderings_Obot__class_Obot(tc_fun(_1422779, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1422779, _1422781, hAPP(c_COMBK(_1422781, _1422779), _1422783)), _1422777) = c_Orderings_Obot__class_Obot(tc_fun(_1422781, tc_HOL_Obool)))], (52611 ^ _778495) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (26460 ^ _778495) ^ [_1251741, _1251743, _1251745, _1251747] : [class_Rings_Olinordered__semidom(_1251741), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1251743), _1251745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251741), c_Groups_Oone__class_Oone(_1251741)), _1251747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251741), hAPP(hAPP(c_Power_Opower__class_Opower(_1251741), _1251747), _1251743)), hAPP(hAPP(c_Power_Opower__class_Opower(_1251741), _1251747), _1251745))))], (36837 ^ _778495) ^ [_1473068, _1473070, _1473072, _1473074, _1473076, _1473078] : [c_Fun_Oinj__on(_1473068, _1473070, _1473072, _1473074), hAPP(_1473072, _1473076) = _1473078, hBOOL(hAPP(hAPP(c_member(_1473068), _1473076), _1473074)), -(hAPP(c_Fun_Othe__inv__into(_1473068, _1473070, _1473074, _1473072), _1473078) = _1473076)], (8162 ^ _778495) ^ [_913035, _913037, _913039] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913035), hAPP(hAPP(c_Set_Oinsert(_913035), _913037), _913039))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_913035), _913039)))], (12114 ^ _778495) ^ [_990387] : [-(hAPP(c_Nat_OSuc, _990387) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _990387))], (16946 ^ _778495) ^ [_1081242, _1081244, _1081246, _1081248, _1081250] : [class_Fields_Olinordered__field(_1081242), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081242), c_Groups_Ozero__class_Ozero(_1081242)), _1081244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081242), _1081244), _1081246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081242), c_Groups_Ozero__class_Ozero(_1081242)), _1081248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081242), _1081248), _1081250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081242), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1081242), _1081244), _1081250)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1081242), _1081246), _1081248))))], (41501 ^ _778495) ^ [_1598151, _1598153, _1598155, _1598157] : [-(c_List_Olist_Olist__size(_1598151, _1598153, hAPP(hAPP(c_List_Olist_OCons(_1598151), _1598155), _1598157)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1598153, _1598155)), c_List_Olist_Olist__size(_1598151, _1598153, _1598157))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43696 ^ _778495) ^ [_1652554, _1652556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652554)), _1652556)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1652554), _1652556) = _1652556)], (33475 ^ _778495) ^ [_1399958, _1399960, _1399962, _1399964, _1399966] : [-(_1399958 = c_Orderings_Obot__class_Obot(tc_fun(_1399960, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399962, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399960, tc_fun(_1399962, tc_HOL_Obool)), _1399958), _1399964)), _1399966) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399960, tc_fun(_1399962, tc_HOL_Obool)), _1399958), hAPP(hAPP(c_COMBC(_1399960, tc_fun(_1399962, tc_HOL_Obool), tc_fun(_1399962, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1399962, tc_HOL_Obool), tc_fun(tc_fun(_1399962, tc_HOL_Obool), tc_fun(_1399962, tc_HOL_Obool)), _1399960), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399962, tc_HOL_Obool))), _1399964)), _1399966)))], (38558 ^ _778495) ^ [_1523633, _1523635, _1523637, _1523639] : [hBOOL(hAPP(hAPP(c_member(_1523635), _1523639), hAPP(c_Relation_ORange(_1523633, _1523635), _1523637))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1523633, _1523635, hAPP(hAPP(c_COMBC(_1523633, tc_fun(tc_prod(_1523633, _1523635), tc_HOL_Obool), tc_fun(_1523635, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523635, tc_fun(tc_fun(tc_prod(_1523633, _1523635), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1523633, _1523635), tc_HOL_Obool), tc_fun(_1523635, tc_HOL_Obool)), _1523633), c_COMBC(_1523635, tc_fun(tc_prod(_1523633, _1523635), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523635, tc_prod(_1523633, _1523635)), tc_fun(_1523635, tc_fun(tc_fun(tc_prod(_1523633, _1523635), tc_HOL_Obool), tc_HOL_Obool)), _1523633), hAPP(c_COMBB(tc_prod(_1523633, _1523635), tc_fun(tc_fun(tc_prod(_1523633, _1523635), tc_HOL_Obool), tc_HOL_Obool), _1523635), c_member(tc_prod(_1523633, _1523635)))), c_Product__Type_OPair(_1523633, _1523635)))), _1523637)), _1523639)))], (52555 ^ _778495) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (32902 ^ _778495) ^ [] : [-(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)))], (39384 ^ _778495) ^ [_1544540, _1544542, _1544544, _1544546, _1544548, _1544550] : [-(hAPP(hAPP(c_Fun_Ocomp(_1544540, _1544542, _1544544, _1544546), _1544548), _1544550) = hAPP(_1544546, hAPP(_1544548, _1544550)))], (29825 ^ _778495) ^ [_1320850, _1320852, _1320854, _1320856, _1320858] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1320850, _1320852), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1320854), _1320856))), -(_1320852 = 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), _1320858), _1320850), _1320852), 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), _1320858), _1320854)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1320858), _1320856)), _1320852))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1320858), _1320856), _1320852)))))], (48515 ^ _778495) ^ [_1756900] : [-(c_List_Omember(_1756900) = c_List_Oset(_1756900))], (32218 ^ _778495) ^ [_1371452, _1371454] : [hAPP(_1371452, 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), _1371452), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1371454)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1371452), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1371454)))], (41829 ^ _778495) ^ [_1608030] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1608030)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1608030), tc_HOL_Obool))))], (20658 ^ _778495) ^ [_1148798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1148798)), -(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), _1148798))))], (45784 ^ _778495) ^ [_1698492, _1698494, _1698496, _1698498] : [hBOOL(hAPP(hAPP(c_member(_1698492), _1698494), hAPP(c_List_Oset(_1698492), _1698496))), -(hBOOL(hAPP(_1698498, _1698494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698492)), hAPP(c_List_Ofilter(_1698492, _1698498), _1698496))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698492)), _1698496))))], (31039 ^ _778495) ^ [_1345595] : [class_Orderings_Olinorder(_1345595), -(c_Orderings_Oord_Omin(_1345595, hAPP(c_COMBC(_1345595, _1345595, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1345595))) = c_Orderings_Oord__class_Omax(_1345595))], (29837 ^ _778495) ^ [_1321187, _1321189, _1321191] : [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), _1321187), _1321189))), -(hBOOL(hAPP(hAPP(_1321191, _1321187), _1321189))), 29844 ^ _778495 : [(29847 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1321191, 29842 ^ [_1321187, _1321189, _1321191]), 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)))), 29843 ^ [_1321187, _1321189, _1321191])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 29842 ^ [_1321187, _1321189, _1321191]), 29843 ^ [_1321187, _1321189, _1321191]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 29843 ^ [_1321187, _1321189, _1321191]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29857 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1321191, 29842 ^ [_1321187, _1321189, _1321191]), 29843 ^ [_1321187, _1321189, _1321191]))], (29845 ^ _778495) ^ [] : [-(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), 29842 ^ [_1321187, _1321189, _1321191]), 29843 ^ [_1321187, _1321189, _1321191]))))]]], (32292 ^ _778495) ^ [_1372857, _1372859, _1372861, _1372863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1372857), _1372859)), -(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), _1372857), _1372861)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1372859), _1372863))), c_FunDef_Opair__less)))], (8066 ^ _778495) ^ [_911227, _911229, _911231, _911233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_911227, tc_HOL_Obool)), _911229), _911231)), hBOOL(hAPP(hAPP(c_member(_911227), _911233), _911229)), -(hBOOL(hAPP(hAPP(c_member(_911227), _911233), _911231)))], (4230 ^ _778495) ^ [_842597, _842599] : [_842599 = _842597, -(c_List_Oappend(_842599) = c_List_Oappend(_842597))], (33158 ^ _778495) ^ [_1390618, _1390620, _1390622, _1390624] : [33160 ^ _778495 : [(33163 ^ _778495) ^ [] : [hAPP(_1390624, 33159 ^ [_1390618, _1390620, _1390622, _1390624]) = c_Orderings_Obot__class_Obot(tc_fun(_1390620, tc_HOL_Obool))], (33161 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1390618), 33159 ^ [_1390618, _1390620, _1390622, _1390624]), _1390622)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390618, tc_fun(_1390620, tc_HOL_Obool)), _1390622), _1390624) = c_Orderings_Obot__class_Obot(tc_fun(_1390620, tc_HOL_Obool)))], (33128 ^ _778495) ^ [_1389948, _1389950, _1389952, _1389954, _1389956, _1389958] : [hBOOL(hAPP(hAPP(c_member(_1389948), _1389950), _1389952)), hBOOL(hAPP(hAPP(_1389954, _1389950), _1389956)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389948, tc_fun(_1389958, tc_HOL_Obool)), _1389952), _1389954), _1389956)))], (40409 ^ _778495) ^ [_1569217, _1569219, _1569221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569217, _1569217), tc_HOL_Obool)), _1569219), _1569221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569217, _1569217), tc_HOL_Obool)), _1569221), c_Transitive__Closure_Ortrancl(_1569217, _1569219))), -(c_Transitive__Closure_Ortrancl(_1569217, _1569221) = c_Transitive__Closure_Ortrancl(_1569217, _1569219))], (39927 ^ _778495) ^ [_1556783, _1556785] : [39928 ^ _778495 : [(39929 ^ _778495) ^ [_1556829] : [hBOOL(hAPP(_1556783, _1556829))]], -(hBOOL(hAPP(_1556783, c_Hilbert__Choice_OEps(_1556785, _1556783))))], (8010 ^ _778495) ^ [_910295, _910297, _910299, _910301] : [class_Orderings_Opreorder(_910295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910295), _910297), _910299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910295), _910299), _910301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910295), _910297), _910301)))], (44809 ^ 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034778), _1034782), _1034782)) = c_Groups_Ozero__class_Ozero(_1034778)), _1034780 = c_Groups_Ozero__class_Ozero(_1034778), _1034782 = c_Groups_Ozero__class_Ozero(_1034778)], (14423 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034778), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034778), _1034780), _1034780)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034778), _1034782), _1034782)) = c_Groups_Ozero__class_Ozero(_1034778), 14426 ^ _778495 : [(14429 ^ _778495) ^ [] : [-(_1034782 = c_Groups_Ozero__class_Ozero(_1034778))], (14427 ^ _778495) ^ [] : [-(_1034780 = c_Groups_Ozero__class_Ozero(_1034778))]]]]], (37242 ^ _778495) ^ [_1482009, _1482011, _1482013, _1482015] : [-(hBOOL(hAPP(hAPP(c_member(_1482009), _1482011), _1482013))), -(hAPP(c_Set_Ovimage(_1482015, _1482009, hAPP(c_COMBK(_1482009, _1482015), _1482011)), _1482013) = c_Orderings_Obot__class_Obot(tc_fun(_1482015, tc_HOL_Obool)))], (29075 ^ _778495) ^ [_1306381, _1306383, _1306385, _1306387] : [-(c_Nat_Onat_Onat__case(_1306381, _1306383, _1306385, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1306387)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1306381), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1306387))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1306381, _1306381), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1306381, tc_fun(_1306381, _1306381)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1306381, tc_fun(_1306381, _1306381)), tc_Int_Oint), c_If(_1306381)), c_Nat__Numeral_Oneg)), _1306383)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1306381, tc_Int_Oint), _1306385), c_Int_Onat))))], (43965 ^ _778495) ^ [_1657972, _1657974, _1657976] : [class_Orderings_Olinorder(_1657972), -(c_Big__Operators_Olinorder__class_OMin(_1657972, hAPP(c_List_Oset(_1657972), hAPP(hAPP(c_List_Olist_OCons(_1657972), _1657974), _1657976))) = hAPP(c_List_Ofoldl(_1657972, _1657972, c_Orderings_Oord__class_Omin(_1657972), _1657974), _1657976))], (30340 ^ _778495) ^ [_1331320] : [30342 ^ _778495 : [(30345 ^ _778495) ^ [_1331430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30341 ^ [_1331320, _1331430]), _1331430))], (30343 ^ _778495) ^ [_1331396] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30341 ^ [_1331320, _1331396]), _1331320)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1331320)))], (24623 ^ _778495) ^ [_1219384, _1219386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219386)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1219384, _1219386)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1219384), hAPP(c_Int_Onat, _1219386)))], (40846 ^ _778495) ^ [_1579782, _1579784, _1579786] : [hAPP(hAPP(c_Relation_Orel__comp(_1579782, _1579782, _1579782), hAPP(c_Relation_Oconverse(_1579782, _1579782), _1579784)), _1579784) = _1579784, hAPP(c_Relation_ODomain(_1579782, _1579782), _1579784) = _1579786, -(c_Equiv__Relations_Oequiv(_1579782, _1579786, _1579784))], (11690 ^ _778495) ^ [_981359, _981361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981359), _981361)), _981359))], (30067 ^ _778495) ^ [_1326093, _1326095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1326093), 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)), _1326095)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1326093), _1326095) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1326093, _1326095)))], (41945 ^ _778495) ^ [_1611092, _1611094, _1611096, _1611098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1611092), _1611094)), -(hAPP(hAPP(c_List_Onth(_1611096), hAPP(hAPP(c_List_Otake(_1611096), _1611094), _1611098)), _1611092) = hAPP(hAPP(c_List_Onth(_1611096), _1611098), _1611092))], (20930 ^ _778495) ^ [_1153323, _1153325, _1153327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153323)), 20936 ^ _778495 : [(20939 ^ _778495) ^ [] : [hBOOL(hAPP(_1153325, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 20935 ^ [_1153323, _1153325, _1153327]), _1153323)))], (20937 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1153325, 20935 ^ [_1153323, _1153325, _1153327])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153327)), 20944 ^ _778495 : [(20945 ^ _778495) ^ [_1153612] : [hBOOL(hAPP(_1153325, _1153612)), -(hBOOL(hAPP(_1153325, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1153612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1153327), _1153323)))))]]], (27999 ^ _778495) ^ [_1278072, _1278074, _1278076] : [class_Complete__Lattice_Ocomplete__lattice(_1278072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278072), _1278074)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1278072), _1278076), c_Complete__Lattice_OInf__class_OInf(_1278072, _1278074)) = hAPP(hAPP(c_Finite__Set_Ofold(_1278072, _1278072, c_Lattices_Osemilattice__inf__class_Oinf(_1278072)), _1278076), _1278074))], (19784 ^ _778495) ^ [_1133876, _1133878, _1133880, _1133882, _1133884] : [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), _1133876), _1133878)), _1133880)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133876), _1133882)), _1133884))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1133884), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133876), _1133884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133876), _1133880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1133882), _1133878)))], (41858 ^ _778495) ^ [_1608742, _1608744, _1608746] : [-(hAPP(hAPP(c_List_Onth(_1608742), hAPP(hAPP(c_List_Olist_OCons(_1608742), _1608744), _1608746)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1608744)], (24978 ^ _778495) ^ [_1225269, _1225271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1225269)), hAPP(c_Int_Onat, _1225271))), 24981 ^ _778495 : [(24984 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225269), _1225271)))], (24982 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225271)))]]], (5955 ^ _778495) ^ [_873504, _873506, _873508] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873504, tc_HOL_Obool)), _873506), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873504, tc_HOL_Obool)), _873508), _873506))))], (29533 ^ _778495) ^ [_1315890, _1315892, _1315894, _1315896, _1315898] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1315890, _1315892, tc_HOL_Obool), _1315894), hAPP(hAPP(c_Product__Type_OPair(_1315890, _1315892), _1315896), _1315898))), -(hBOOL(hAPP(hAPP(_1315894, _1315896), _1315898)))], (43676 ^ _778495) ^ [_1652052, _1652054, _1652056, _1652058] : [-(hAPP(c_List_Orotate1(_1652054), hAPP(hAPP(c_List_Olist_OCons(_1652054), _1652056), _1652058)) = hAPP(hAPP(c_List_Oappend(_1652054), _1652058), hAPP(hAPP(c_List_Olist_OCons(_1652054), _1652056), c_List_Olist_ONil(_1652054))))], (27613 ^ _778495) ^ [_1271361, _1271363] : [class_Lattices_Obounded__lattice__top(_1271361), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271361), _1271363), c_Orderings_Otop__class_Otop(_1271361)) = c_Orderings_Otop__class_Otop(_1271361))], (17004 ^ _778495) ^ [_1082343, _1082345, _1082347] : [class_Fields_Olinordered__field(_1082343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082343), _1082345), c_Groups_Ozero__class_Ozero(_1082343))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082343), _1082347), c_Groups_Ozero__class_Ozero(_1082343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082343), c_Groups_Ozero__class_Ozero(_1082343)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1082343), _1082345), _1082347))))], (8254 ^ _778495) ^ [_914763, _914765, _914767, _914769] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_914763), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914763, tc_HOL_Obool)), _914765), _914769))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_914763), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914763, tc_HOL_Obool)), _914765), hAPP(hAPP(c_Set_Oinsert(_914763), _914767), _914769)))))], (24035 ^ _778495) ^ [_1208530, _1208532] : [class_Int_Onumber__ring(_1208530), class_Int_Oring__char__0(_1208530), 24042 ^ _778495 : [(24049 ^ _778495) ^ [] : [c_Int_Oiszero(_1208530, hAPP(c_Int_Onumber__class_Onumber__of(_1208530), _1208532)), -(c_Int_Oiszero(_1208530, hAPP(c_Int_Onumber__class_Onumber__of(_1208530), c_Int_OBit0(_1208532))))], (24043 ^ _778495) ^ [] : [c_Int_Oiszero(_1208530, hAPP(c_Int_Onumber__class_Onumber__of(_1208530), c_Int_OBit0(_1208532))), -(c_Int_Oiszero(_1208530, hAPP(c_Int_Onumber__class_Onumber__of(_1208530), _1208532)))]]], (19096 ^ _778495) ^ [_1121780] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121780) = _1121780)], (52311 ^ _778495) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (2824 ^ _778495) ^ [_820390, _820392, _820394, _820396] : [-(c_Nitpick_Oint__lcm(_820396, _820392) = c_Nitpick_Oint__lcm(_820394, _820390)), _820396 = _820394, _820392 = _820390], (34338 ^ _778495) ^ [_1419371, _1419373, _1419375, _1419377, _1419379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1419371, tc_HOL_Obool)), _1419373), _1419375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1419377, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1419371, _1419377, _1419379), _1419373)), hAPP(c_Set_Oimage(_1419371, _1419377, _1419379), _1419375))))], (12002 ^ _778495) ^ [_988197, _988199] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988197), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988197), _988199)))))], (11939 ^ _778495) ^ [_986593, _986595, _986597, _986599, _986601, _986603] : [class_Rings_Oordered__ring(_986593), 11942 ^ _778495 : [(11949 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986593), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986593), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_986593), _986595), _986601)), _986597)), _986599)), _986603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986593), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986593), _986595), _986597)), _986599)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986593), _986601), _986597)), _986603))))], (11943 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986593), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986593), _986595), _986597)), _986599)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986593), _986601), _986597)), _986603))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986593), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986593), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_986593), _986595), _986601)), _986597)), _986599)), _986603)))]]], (17670 ^ _778495) ^ [_1095460, _1095462, _1095464] : [class_Orderings_Olinorder(_1095460), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095460), _1095462), _1095464) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095460), _1095464), _1095462))], (38433 ^ _778495) ^ [_1519402, _1519404, _1519406, _1519408, _1519410] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1519402, _1519404)), hAPP(hAPP(c_Product__Type_OPair(_1519402, _1519404), _1519406), _1519408)), _1519410)), -(hBOOL(hAPP(hAPP(c_member(_1519404), _1519408), hAPP(c_Relation_ORange(_1519402, _1519404), _1519410))))], (25576 ^ _778495) ^ [_1235531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1235531)), -(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, _1235531))))], (47859 ^ _778495) ^ [_1742748, _1742750] : [-(c_FunDef_Ois__measure(_1742748, _1742750))], (7000 ^ _778495) ^ [_893462, _893464, _893466] : [class_Lattices_Osemilattice__sup(_893462), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893462), _893464), _893466) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893462), _893466), _893464))], (8126 ^ _778495) ^ [_912313, _912315, _912317] : [8127 ^ _778495 : [(8130 ^ _778495) ^ [] : [_912315 = _912317], (8128 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_912313, tc_HOL_Obool)), _912315), _912317))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912313, tc_HOL_Obool)), _912315), _912317)))], (34534 ^ _778495) ^ [_1424053] : [-(c_Relation_OId__on(_1424053, c_Orderings_Obot__class_Obot(tc_fun(_1424053, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1424053, _1424053), tc_HOL_Obool)))], (10143 ^ _778495) ^ [_953371] : [class_Groups_Oab__semigroup__mult(_953371), -(c_Finite__Set_Ofun__left__comm(_953371, _953371, c_Groups_Otimes__class_Otimes(_953371)))], (42638 ^ _778495) ^ [_1628550, _1628552, _1628554] : [hBOOL(hAPP(c_List_Odistinct(_1628550), _1628552)), -(hBOOL(hAPP(c_List_Odistinct(_1628550), c_List_Oremove1(_1628550, _1628554, _1628552))))], (31113 ^ _778495) ^ [_1346974, _1346976, _1346978] : [class_Orderings_Olinorder(_1346974), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346974), _1346976)), hBOOL(hAPP(hAPP(c_member(_1346974), _1346978), _1346976)), 31124 ^ _778495 : [(31131 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346974, tc_HOL_Obool)), _1346976), hAPP(hAPP(c_Set_Oinsert(_1346974), _1346978), c_Orderings_Obot__class_Obot(tc_fun(_1346974, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1346974, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1346974, c_Orderings_Oord__class_Omax(_1346974), _1346976) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346974), _1346978), c_Big__Operators_Olattice_OSup__fin(_1346974, c_Orderings_Oord__class_Omax(_1346974), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346974, tc_HOL_Obool)), _1346976), hAPP(hAPP(c_Set_Oinsert(_1346974), _1346978), c_Orderings_Obot__class_Obot(tc_fun(_1346974, tc_HOL_Obool)))))))], (31125 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346974, tc_HOL_Obool)), _1346976), hAPP(hAPP(c_Set_Oinsert(_1346974), _1346978), c_Orderings_Obot__class_Obot(tc_fun(_1346974, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1346974, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1346974, c_Orderings_Oord__class_Omax(_1346974), _1346976) = _1346978)]]], (42940 ^ _778495) ^ [_1634424, _1634426, _1634428] : [class_Orderings_Olinorder(_1634424), hBOOL(hAPP(c_Finite__Set_Ofinite(_1634424), _1634426)), -(c_List_Olinorder__class_Osorted__list__of__set(_1634424, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1634424, tc_HOL_Obool)), _1634426), hAPP(hAPP(c_Set_Oinsert(_1634424), _1634428), c_Orderings_Obot__class_Obot(tc_fun(_1634424, tc_HOL_Obool))))) = c_List_Oremove1(_1634424, _1634428, c_List_Olinorder__class_Osorted__list__of__set(_1634424, _1634426)))], (31328 ^ _778495) ^ [_1350811, _1350813, _1350815] : [class_Orderings_Olinorder(_1350811), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350811), _1350813)), -(_1350813 = c_Orderings_Obot__class_Obot(tc_fun(_1350811, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1350811, hAPP(hAPP(c_Set_Oinsert(_1350811), _1350815), _1350813)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350811), _1350815), c_Big__Operators_Olinorder__class_OMax(_1350811, _1350813)))], (5354 ^ _778495) ^ [_860351, _860353] : [_860353 = _860351, -(c_Orderings_Oord__class_Oless(_860353) = c_Orderings_Oord__class_Oless(_860351))], (2112 ^ _778495) ^ [_809270, _809272, _809274, _809276, _809278, _809280] : [-(c_Power_Opower_Opower(_809280, _809276, _809272) = c_Power_Opower_Opower(_809278, _809274, _809270)), _809280 = _809278, _809276 = _809274, _809272 = _809270], (11668 ^ _778495) ^ [_980908, _980910, _980912] : [class_Groups_Ogroup__add(_980908), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980908), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_980908), _980910), _980912)), _980912) = _980910)], (14369 ^ _778495) ^ [_1033874, _1033876, _1033878] : [class_Groups_Oordered__ab__group__add(_1033874), 14372 ^ _778495 : [(14379 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033874), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033874), _1033876), _1033878)), c_Groups_Ozero__class_Ozero(_1033874))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033874), _1033876), _1033878)))], (14373 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033874), _1033876), _1033878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033874), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033874), _1033876), _1033878)), c_Groups_Ozero__class_Ozero(_1033874))))]]], (22608 ^ _778495) ^ [_1182636, _1182638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182636), _1182638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1182636)), c_Int_OBit0(_1182638))))], (26756 ^ _778495) ^ [_1256770] : [class_Int_Onumber__ring(_1256770), c_Int_Oiszero(_1256770, hAPP(c_Int_Onumber__class_Onumber__of(_1256770), c_Int_OMin))], (26238 ^ _778495) ^ [_1247551, _1247553, _1247555, _1247557] : [class_Rings_Olinordered__semidom(_1247551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247551), c_Groups_Oone__class_Oone(_1247551)), _1247553)), 26245 ^ _778495 : [(26252 ^ _778495) ^ [] : [_1247555 = _1247557, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1247551), _1247553), _1247555) = hAPP(hAPP(c_Power_Opower__class_Opower(_1247551), _1247553), _1247557))], (26246 ^ _778495) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1247551), _1247553), _1247555) = hAPP(hAPP(c_Power_Opower__class_Opower(_1247551), _1247553), _1247557), -(_1247555 = _1247557)]]], (9044 ^ _778495) ^ [_931197, _931199, _931201, _931203] : [class_Lattices_Osemilattice__inf(_931197), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931197), _931199), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931197), _931201), _931203))), 9051 ^ _778495 : [(9054 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931197), _931199), _931203)))], (9052 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931197), _931199), _931201)))]]], (4666 ^ _778495) ^ [_849539, _849541, _849543, _849545, _849547, _849549] : [-(c_Relation_OImage(_849549, _849545, _849541) = c_Relation_OImage(_849547, _849543, _849539)), _849549 = _849547, _849545 = _849543, _849541 = _849539], (29623 ^ _778495) ^ [_1317565, _1317567, _1317569, _1317571, _1317573] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1317565, _1317567), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1317569), _1317571))), -(_1317567 = 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)), _1317573)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1317565, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1317567), _1317573)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1317569), _1317573)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1317567), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1317569, _1317573))), _1317571)))))], (52455 ^ _778495) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (48761 ^ _778495) ^ [_1762686, _1762688, _1762690, _1762692] : [-(hAPP(c_Relation_OImage(_1762686, _1762688, hAPP(c_Set_OCollect(tc_prod(_1762686, _1762688)), hAPP(c_Product__Type_Oprod_Oprod__case(_1762686, _1762688, tc_HOL_Obool), _1762690))), _1762692) = hAPP(c_Set_OCollect(_1762688), hAPP(hAPP(c_COMBB(tc_fun(_1762686, tc_HOL_Obool), tc_HOL_Obool, _1762688), c_HOL_OEx(_1762686)), hAPP(hAPP(c_COMBB(tc_fun(_1762686, tc_HOL_Obool), tc_fun(_1762686, tc_HOL_Obool), _1762688), hAPP(c_COMBS(_1762686, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1762686), c_fconj), hAPP(hAPP(c_COMBC(_1762686, tc_fun(_1762686, tc_HOL_Obool), tc_HOL_Obool), c_member(_1762686)), _1762692)))), hAPP(c_COMBC(_1762686, _1762688, tc_HOL_Obool), _1762690)))))], (36248 ^ _778495) ^ [_1460744, _1460746, _1460748, _1460750, _1460752] : [c_Fun_Oinj__on(_1460744, _1460746, _1460748, _1460750), -(c_Fun_Oinj__on(_1460744, _1460746, _1460748, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1460744, tc_HOL_Obool)), _1460750), _1460752)))], (44970 ^ _778495) ^ [_1679985, _1679987, _1679989, _1679991] : [-(hBOOL(hAPP(c_List_Olistsp(_1679985, hAPP(hAPP(c_COMBS(_1679985, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1679985), c_fconj), _1679987)), _1679989)), _1679991))), hBOOL(hAPP(c_List_Olistsp(_1679985, _1679987), _1679991)), hBOOL(hAPP(c_List_Olistsp(_1679985, _1679989), _1679991))], (7204 ^ _778495) ^ [_897294, _897296, _897298, _897300, _897302] : [c_Finite__Set_Ofolding__one(_897294, _897296, _897298), hBOOL(hAPP(c_Finite__Set_Ofinite(_897294), _897300)), hBOOL(hAPP(hAPP(c_member(_897294), _897302), _897300)), 7215 ^ _778495 : [(7222 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897294, tc_HOL_Obool)), _897300), hAPP(hAPP(c_Set_Oinsert(_897294), _897302), c_Orderings_Obot__class_Obot(tc_fun(_897294, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_897294, tc_HOL_Obool))), -(hAPP(_897298, _897300) = hAPP(hAPP(_897296, _897302), hAPP(_897298, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897294, tc_HOL_Obool)), _897300), hAPP(hAPP(c_Set_Oinsert(_897294), _897302), c_Orderings_Obot__class_Obot(tc_fun(_897294, tc_HOL_Obool)))))))], (7216 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897294, tc_HOL_Obool)), _897300), hAPP(hAPP(c_Set_Oinsert(_897294), _897302), c_Orderings_Obot__class_Obot(tc_fun(_897294, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_897294, tc_HOL_Obool)), -(hAPP(_897298, _897300) = _897302)]]], (41068 ^ _778495) ^ [_1585437, _1585439, _1585441] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585437, _1585437)), _1585439), c_Transitive__Closure_Otrancl(_1585437, _1585441))), 41072 ^ _778495 : [(41075 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585437, _1585437)), _1585439), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585437, _1585437), tc_HOL_Obool), 41071 ^ [_1585437, _1585439, _1585441]), _1585441))))], (41073 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41071 ^ [_1585437, _1585439, _1585441])))]]], (34939 ^ _778495) ^ [_1432033, _1432035, _1432037, _1432039, _1432041] : [-(hAPP(c_Fun_Ofun__upd(_1432033, _1432035, _1432037, _1432039, _1432041), _1432039) = _1432041)], (26986 ^ _778495) ^ [_1260722, _1260724] : [class_Rings_Oring__1(_1260722), 26989 ^ _778495 : [(26996 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1260724), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1260722), _1260724) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1260722), hAPP(c_Int_Onat, _1260724)))], (26990 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1260724), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1260722), _1260724) = hAPP(c_Groups_Ouminus__class_Ouminus(_1260722), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1260722), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1260724)))))]]], (9795 ^ _778495) ^ [_946440, _946442] : [class_Lattices_Olattice(_946440), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_946440), _946442), _946442) = _946442)], (48406 ^ _778495) ^ [_1754483, _1754485, _1754487] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754483)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1754483, _1754485, _1754487)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754483)), _1754487)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29985 ^ _778495) ^ [_1324243, _1324245, _1324247] : [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), _1324243), _1324245))), -(hBOOL(hAPP(hAPP(_1324247, _1324243), _1324245))), 29992 ^ _778495 : [(29995 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 29991 ^ [_1324243, _1324245, _1324247]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1324247, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 29990 ^ [_1324243, _1324245, _1324247])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 29991 ^ [_1324243, _1324245, _1324247]))))], (30001 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1324247, 29990 ^ [_1324243, _1324245, _1324247]), 29991 ^ [_1324243, _1324245, _1324247]))], (29993 ^ _778495) ^ [] : [-(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), 29990 ^ [_1324243, _1324245, _1324247]), 29991 ^ [_1324243, _1324245, _1324247]))))]]], (46897 ^ _778495) ^ [_1721663, _1721665, _1721667, _1721669] : [-(hBOOL(hAPP(_1721663, _1721665))), -(c_List_OtakeWhile(_1721667, _1721663, hAPP(hAPP(c_List_Olist_OCons(_1721667), _1721665), _1721669)) = c_List_Olist_ONil(_1721667))], (31843 ^ _778495) ^ [_1362037, _1362039, _1362041, _1362043, _1362045] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362037, tc_fun(_1362039, tc_HOL_Obool)), _1362041), hAPP(hAPP(c_COMBB(tc_fun(_1362039, tc_HOL_Obool), tc_fun(_1362039, tc_HOL_Obool), _1362037), hAPP(c_Set_Oinsert(_1362039), _1362043)), _1362045)) = hAPP(hAPP(c_Set_Oinsert(_1362039), _1362043), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362037, tc_fun(_1362039, tc_HOL_Obool)), _1362041), _1362045)))], (64 ^ _778495) ^ [_779469, _779471, _779473, _779475, _779477, _779479, _779481, _779483, _779485, _779487, _779489, _779491] : [-(c_Nitpick_Ofold__graph_H(_779489, _779485, _779481, _779477, _779473, _779469)), c_Nitpick_Ofold__graph_H(_779491, _779487, _779483, _779479, _779475, _779471), _779491 = _779489, _779487 = _779485, _779483 = _779481, _779479 = _779477, _779475 = _779473, _779471 = _779469], (45028 ^ _778495) ^ [_1681141, _1681143, _1681145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1681141, tc_HOL_Obool)), _1681143), _1681145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1681141), tc_HOL_Obool)), c_List_Olistsp(_1681141, _1681143)), c_List_Olistsp(_1681141, _1681145))))], (30379 ^ _778495) ^ [_1332319, _1332321, _1332323, _1332325, _1332327, _1332329] : [-(c_Product__Type_Oprod_Oprod__rec(_1332319, _1332321, _1332323, _1332325, hAPP(hAPP(c_Product__Type_OPair(_1332319, _1332321), _1332327), _1332329)) = hAPP(hAPP(_1332325, _1332327), _1332329))], (47886 ^ _778495) ^ [_1743280, _1743282, _1743284] : [c_FunDef_Ois__measure(_1743280, _1743282), -(c_FunDef_Ois__measure(tc_prod(_1743284, _1743280), hAPP(hAPP(c_COMBB(_1743280, tc_Nat_Onat, tc_prod(_1743284, _1743280)), _1743282), c_Product__Type_Osnd(_1743284, _1743280))))], (5735 ^ _778495) ^ [_869305, _869307, _869309] : [-(hAPP(hAPP(c_Set_Oinsert(_869305), _869307), hAPP(hAPP(c_Set_Oinsert(_869305), _869307), _869309)) = hAPP(hAPP(c_Set_Oinsert(_869305), _869307), _869309))], (47707 ^ _778495) ^ [_1739841, _1739843, _1739845, _1739847] : [c_List_Olist__ex(_1739841, _1739843, hAPP(hAPP(c_List_Oappend(_1739841), _1739845), _1739847)), -(c_List_Olist__ex(_1739841, _1739843, _1739845)), -(c_List_Olist__ex(_1739841, _1739843, _1739847))], (2480 ^ _778495) ^ [_815000, _815002, _815004, _815006] : [-(c_Nitpick_Onumber__of__frac(_815006, _815002) = c_Nitpick_Onumber__of__frac(_815004, _815000)), _815006 = _815004, _815002 = _815000], (14327 ^ _778495) ^ [_1033067, _1033069, _1033071, _1033073] : [class_Rings_Olinordered__comm__semiring__strict(_1033067), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033067), _1033069), _1033071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033067), c_Groups_Ozero__class_Ozero(_1033067)), _1033073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033067), _1033073), _1033069)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033067), _1033073), _1033071))))], (13318 ^ _778495) ^ [_1015473] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1015473)], (48300 ^ _778495) ^ [_1752396, _1752398, _1752400, _1752402] : [-(c_List_Oreplicate(_1752396, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1752398), _1752400), _1752402) = hAPP(hAPP(c_List_Oappend(_1752396), c_List_Oreplicate(_1752396, _1752398, _1752402)), c_List_Oreplicate(_1752396, _1752400, _1752402)))], (40557 ^ _778495) ^ [] : [-(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))))], (40633 ^ _778495) ^ [_1574436] : [-(c_Relation_OId(_1574436) = hAPP(c_Set_OCollect(tc_prod(_1574436, _1574436)), hAPP(hAPP(c_COMBB(tc_fun(_1574436, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1574436, _1574436)), c_HOL_OEx(_1574436)), hAPP(hAPP(c_COMBC(tc_prod(_1574436, _1574436), tc_fun(_1574436, tc_prod(_1574436, _1574436)), tc_fun(_1574436, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1574436, _1574436), tc_HOL_Obool), tc_fun(tc_fun(_1574436, tc_prod(_1574436, _1574436)), tc_fun(_1574436, tc_HOL_Obool)), tc_prod(_1574436, _1574436)), c_COMBB(tc_prod(_1574436, _1574436), tc_HOL_Obool, _1574436)), c_fequal)), hAPP(hAPP(c_COMBS(_1574436, _1574436, tc_prod(_1574436, _1574436)), c_Product__Type_OPair(_1574436, _1574436)), c_COMBI(_1574436))))))], (43790 ^ _778495) ^ [_1654355, _1654357] : [hBOOL(hAPP(c_List_Odistinct(_1654355), _1654357)), -(hBOOL(hAPP(c_List_Odistinct(_1654355), hAPP(c_List_Otl(_1654355), _1654357))))], (52623 ^ _778495) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (28401 ^ _778495) ^ [_1290260, _1290262, _1290264] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1290260, tc_Nat_Onat), _1290262), _1290264)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1290260, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1290260), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1290262)), _1290264))], (20396 ^ _778495) ^ [_1144853] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144853)))], (40327 ^ _778495) ^ [_1567203, _1567205, _1567207] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567203, _1567203)), _1567205), _1567207)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567203, _1567203)), _1567205), c_Transitive__Closure_Ortrancl(_1567203, _1567207))))], (32926 ^ _778495) ^ [_1386024, _1386026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1386024), _1386026)), -(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), _1386024), _1386026)), c_Wellfounded_Oless__than)))], (34502 ^ _778495) ^ [_1423199, _1423201, _1423203] : [-(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)), _1423199)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1423201, _1423203)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423201), _1423199), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423203), _1423199)))], (19844 ^ _778495) ^ [_1134957, _1134959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134957)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134959)), -(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), _1134957), _1134959))))], (23573 ^ _778495) ^ [_1200781, _1200783, _1200785] : [class_Divides_Osemiring__div(_1200781), -(_1200783 = c_Groups_Ozero__class_Ozero(_1200781)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200781), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200781), _1200783), _1200785)), _1200783) = _1200785)], (25194 ^ _778495) ^ [_1228852, _1228854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228852)), 25197 ^ _778495 : [(25204 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228852), _1228854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1228852)), hAPP(c_Int_Onat, _1228854))))], (25198 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1228852)), hAPP(c_Int_Onat, _1228854))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228852), _1228854)))]]], (48757 ^ _778495) ^ [_1762554, _1762556, _1762558, _1762560] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1762554), _1762556), _1762558), _1762560) = 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(_1762554)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1762554), _1762556)))], (23494 ^ _778495) ^ [_1199255, _1199257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199257, _1199255)), _1199255)))], (40782 ^ _778495) ^ [_1578054, _1578056] : [-(c_Transitive__Closure_Otrancl(_1578054, hAPP(c_Relation_Oconverse(_1578054, _1578054), _1578056)) = hAPP(c_Relation_Oconverse(_1578054, _1578054), c_Transitive__Closure_Otrancl(_1578054, _1578056)))], (52423 ^ _778495) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (37208 ^ _778495) ^ [_1481256, _1481258, _1481260, _1481262, _1481264] : [hAPP(c_Set_Oimage(_1481256, _1481258, _1481260), c_Orderings_Otop__class_Otop(tc_fun(_1481256, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1481258, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481256, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1481256, _1481258, _1481260), _1481262)), _1481264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481258, tc_HOL_Obool)), _1481262), hAPP(c_Set_Oimage(_1481256, _1481258, _1481260), _1481264))))], (14471 ^ _778495) ^ [_1035644, _1035646, _1035648] : [class_Groups_Ocomm__monoid__add(_1035644), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1035646, _1035644), _1035648), c_Orderings_Obot__class_Obot(tc_fun(_1035646, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1035644))], (33246 ^ _778495) ^ [_1392772, _1392774, _1392776, _1392778, _1392780, _1392782] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392772, tc_fun(_1392774, tc_HOL_Obool)), _1392776), hAPP(hAPP(c_COMBC(_1392772, tc_fun(_1392778, tc_fun(_1392774, tc_HOL_Obool)), tc_fun(_1392774, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392778, tc_HOL_Obool), tc_fun(tc_fun(_1392778, tc_fun(_1392774, tc_HOL_Obool)), tc_fun(_1392774, tc_HOL_Obool)), _1392772), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392778, tc_fun(_1392774, tc_HOL_Obool))), _1392780)), _1392782)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392778, tc_fun(_1392774, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392772, tc_fun(_1392778, tc_HOL_Obool)), _1392776), _1392780)), _1392782))], (23228 ^ _778495) ^ [_1194552, _1194554, _1194556] : [hBOOL(hAPP(hAPP(c_member(_1194552), _1194554), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1194552, tc_HOL_Obool)), _1194556))), hBOOL(hAPP(hAPP(c_member(_1194552), _1194554), _1194556))], (24263 ^ _778495) ^ [_1212684, _1212686, _1212688] : [hBOOL(hAPP(_1212684, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212686, _1212688))), 24266 ^ _778495 : [(24291 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212688), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24294 ^ _778495 : [(24295 ^ _778495) ^ [_1213306, _1213308] : [-(hBOOL(hAPP(_1212684, _1213306))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212688), _1213306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213306), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1212686 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1212688), _1213308)), _1213306)]]], (24273 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212688)), 24276 ^ _778495 : [(24277 ^ _778495) ^ [_1213014, _1213016] : [-(hBOOL(hAPP(_1212684, _1213014))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213014), _1212688)), _1212686 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1212688), _1213016)), _1213014)]]], (24267 ^ _778495) ^ [] : [_1212688 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1212684, _1212686)))]]], (40353 ^ _778495) ^ [_1567802, _1567804] : [-(c_Transitive__Closure_Otrancl(_1567802, c_Transitive__Closure_Ortrancl(_1567802, _1567804)) = c_Transitive__Closure_Ortrancl(_1567802, _1567804))], (27004 ^ _778495) ^ [_1261030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261030), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1261030 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 27007 ^ [_1261030]))))], (40300 ^ _778495) ^ [_1565810, _1565812, _1565814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565810, _1565810), tc_HOL_Obool)), _1565812), hAPP(hAPP(c_Product__Type_OSigma(_1565810, _1565810), _1565814), hAPP(c_COMBK(tc_fun(_1565810, tc_HOL_Obool), _1565810), _1565814)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565810, _1565810), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1565810, _1565812)), hAPP(hAPP(c_Product__Type_OSigma(_1565810, _1565810), _1565814), hAPP(c_COMBK(tc_fun(_1565810, tc_HOL_Obool), _1565810), _1565814)))))], (37979 ^ _778495) ^ [_1502234, _1502236, _1502238, _1502240] : [c_Relation_Orefl__on(_1502234, _1502236, _1502238), hBOOL(hAPP(hAPP(c_member(_1502234), _1502240), _1502236)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1502234, _1502234)), hAPP(hAPP(c_Product__Type_OPair(_1502234, _1502234), _1502240), _1502240)), _1502238)))], (28327 ^ _778495) ^ [_1286075, _1286077, _1286079, _1286081, _1286083, _1286085] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286075, tc_fun(_1286077, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1286075, tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_fun(_1286077, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1286077, tc_fun(tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_fun(_1286077, tc_HOL_Obool)), _1286075), c_COMBC(_1286077, tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1286077, tc_prod(_1286075, _1286077)), tc_fun(_1286077, tc_fun(tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_HOL_Obool)), _1286075), hAPP(c_COMBB(tc_prod(_1286075, _1286077), tc_fun(tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_HOL_Obool), _1286077), c_member(tc_prod(_1286075, _1286077)))), c_Product__Type_OPair(_1286075, _1286077)))), _1286079)), hAPP(hAPP(c_COMBC(_1286075, tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_fun(_1286077, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1286077, tc_fun(tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_fun(_1286077, tc_HOL_Obool)), _1286075), c_COMBC(_1286077, tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1286077, tc_prod(_1286075, _1286077)), tc_fun(_1286077, tc_fun(tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_HOL_Obool)), _1286075), hAPP(c_COMBB(tc_prod(_1286075, _1286077), tc_fun(tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool), tc_HOL_Obool), _1286077), c_member(tc_prod(_1286075, _1286077)))), c_Product__Type_OPair(_1286075, _1286077)))), _1286081)), _1286083), _1286085)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1286075, _1286077)), hAPP(hAPP(c_Product__Type_OPair(_1286075, _1286077), _1286083), _1286085)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1286075, _1286077), tc_HOL_Obool)), _1286079), _1286081))))], (37749 ^ _778495) ^ [_1496470, _1496472, _1496474] : [37750 ^ _778495 : [(37753 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496470), hAPP(c_Set_OCollect(_1496470), _1496474)))], (37751 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496470), hAPP(c_Set_OCollect(_1496470), _1496472)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1496470), hAPP(c_Set_OCollect(_1496470), hAPP(hAPP(c_COMBS(_1496470, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1496470), c_fconj), _1496472)), _1496474)))))], (40553 ^ _778495) ^ [_1572683] : [-(hAPP(c_Relation_ORange(_1572683, _1572683), c_Relation_OId(_1572683)) = c_Orderings_Otop__class_Otop(tc_fun(_1572683, tc_HOL_Obool)))], (35703 ^ _778495) ^ [] : [-(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))], (45159 ^ _778495) ^ [_1684385, _1684387, _1684389] : [_1684385 = _1684387, -(c_List_Olist__all2(_1684389, _1684389, c_fequal, _1684385, _1684387))], (21712 ^ _778495) ^ [_1167163, _1167165, _1167167] : [class_Groups_Ogroup__add(_1167163), 21715 ^ _778495 : [(21722 ^ _778495) ^ [] : [_1167167 = hAPP(c_Groups_Ouminus__class_Ouminus(_1167163), _1167165), -(_1167165 = hAPP(c_Groups_Ouminus__class_Ouminus(_1167163), _1167167))], (21716 ^ _778495) ^ [] : [_1167165 = hAPP(c_Groups_Ouminus__class_Ouminus(_1167163), _1167167), -(_1167167 = hAPP(c_Groups_Ouminus__class_Ouminus(_1167163), _1167165))]]], (27151 ^ _778495) ^ [_1263456, _1263458] : [class_Rings_Oring__1(_1263456), -(hBOOL(hAPP(hAPP(c_member(_1263456), hAPP(c_Int_Oring__1__class_Oof__int(_1263456), _1263458)), c_Int_Oring__1__class_OInts(_1263456))))], (49031 ^ _778495) ^ [_1770103] : [-(c_Relation_Otrans(_1770103, c_Relation_OId(_1770103)))], (45171 ^ _778495) ^ [_1684553, _1684555, _1684557, _1684559, _1684561] : [c_List_Olist__all2(_1684553, _1684555, _1684557, _1684559, _1684561), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684553)), _1684559) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684555)), _1684561))], (28617 ^ _778495) ^ [_1296814, _1296816, _1296818, _1296820, _1296822] : [class_Groups_Ocomm__monoid__add(_1296814), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296816), _1296818)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1296816, _1296814), _1296820), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296816, tc_HOL_Obool)), _1296818), _1296822)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1296816, _1296814), hAPP(hAPP(c_COMBC(_1296816, _1296814, _1296814), hAPP(hAPP(c_COMBS(_1296816, _1296814, tc_fun(_1296814, _1296814)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1296814, tc_fun(_1296814, _1296814)), _1296816), c_If(_1296814)), hAPP(hAPP(c_COMBC(_1296816, tc_fun(_1296816, tc_HOL_Obool), tc_HOL_Obool), c_member(_1296816)), _1296822))), _1296820)), c_Groups_Ozero__class_Ozero(_1296814))), _1296818))], (2360 ^ _778495) ^ [_813116, _813118, _813120, _813122] : [-(c_Divides_OposDivAlg(_813122, _813118) = c_Divides_OposDivAlg(_813120, _813116)), _813122 = _813120, _813118 = _813116], (23895 ^ _778495) ^ [_1206199, _1206201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1206199), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206201), _1206199)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206199, _1206201) = _1206199)], (33481 ^ _778495) ^ [_1400085, _1400087, _1400089, _1400091, _1400093] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400085, tc_fun(_1400087, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1400085), _1400089), _1400091)), _1400093) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400087, tc_HOL_Obool)), hAPP(_1400093, _1400089)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400085, tc_fun(_1400087, tc_HOL_Obool)), _1400091), _1400093)))], (39700 ^ _778495) ^ [_1551836, _1551838, _1551840, _1551842, _1551844, _1551846, _1551848, _1551850] : [c_Finite__Set_Ofolding(_1551836, _1551838, _1551840, _1551842), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551836), _1551844)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551836), _1551846)), -(hAPP(c_Fun_Ocomp(_1551838, _1551838, _1551848, hAPP(_1551842, _1551846)), hAPP(c_Fun_Ocomp(_1551838, _1551838, _1551848, hAPP(_1551842, _1551844)), _1551850)) = hAPP(c_Fun_Ocomp(_1551838, _1551838, _1551848, hAPP(_1551842, _1551844)), hAPP(c_Fun_Ocomp(_1551838, _1551838, _1551848, hAPP(_1551842, _1551846)), _1551850)))], (44815 ^ _778495) ^ [_1676458, _1676460] : [hAPP(c_Code__Numeral_Onat__of, _1676458) = hAPP(c_Code__Numeral_Onat__of, _1676460), -(_1676458 = _1676460)], (42443 ^ _778495) ^ [_1624318, _1624320] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1624318, _1624320))))], (8954 ^ _778495) ^ [_929292, _929294, _929296, _929298] : [class_Lattices_Osemilattice__inf(_929292), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929292), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929292), _929294), _929296)), _929298) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929292), _929294), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929292), _929296), _929298)))], (25046 ^ _778495) ^ [_1226321, _1226323] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1226321) = _1226323), _1226321 = hAPP(c_Int_Onat, _1226323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226323))], (32472 ^ _778495) ^ [_1376666, _1376668, _1376670, _1376672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1376666), _1376668)), -(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), _1376666), _1376670)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1376668), _1376672))), c_FunDef_Opair__leq)))], (52251 ^ _778495) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (26376 ^ _778495) ^ [_1250252, _1250254] : [class_Power_Opower(_1250252), class_Rings_Osemiring__0(_1250252), 26383 ^ _778495 : [(26390 ^ _778495) ^ [] : [-(_1250254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1250252), c_Groups_Ozero__class_Ozero(_1250252)), _1250254) = c_Groups_Ozero__class_Ozero(_1250252))], (26384 ^ _778495) ^ [] : [_1250254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1250252), c_Groups_Ozero__class_Ozero(_1250252)), _1250254) = c_Groups_Oone__class_Oone(_1250252))]]], (52507 ^ _778495) ^ [_1834010] : [class_Enum_Oenum(_1834010), -(class_Enum_Oenum(tc_Option_Ooption(_1834010)))], (19214 ^ _778495) ^ [_1123740, _1123742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123740), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1123742), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123740), _1123742)))], (10465 ^ _778495) ^ [_959049, _959051] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959049), hAPP(c_Nat_OSuc, _959051)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959049), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _959051))], (42694 ^ _778495) ^ [_1629441, _1629443, _1629445] : [42695 ^ _778495 : [(42698 ^ _778495) ^ [] : [_1629445 = c_List_Olist_ONil(_1629441)], (42696 ^ _778495) ^ [] : [_1629443 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1629441), _1629443), _1629445) = c_List_Olist_ONil(_1629441))], (25433 ^ _778495) ^ [_1232976, _1232978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232976), _1232978)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1232978), _1232976)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1232978)), hAPP(c_Int_Onat, _1232976)))], (6328 ^ _778495) ^ [_880936, _880938, _880940, _880942] : [class_Orderings_Oord(_880936), _880938 = _880940, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880936), _880940), _880942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880936), _880938), _880942)))], (11706 ^ _778495) ^ [_981705, _981707, _981709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981705), _981707)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981705), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981707), _981709))))], (20016 ^ _778495) ^ [_1138002] : [-(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), _1138002))))], (1938 ^ _778495) ^ [_805748, _805750] : [-(class_Rings_Odvd(_805748)), _805750 = _805748, class_Rings_Odvd(_805750)], (29061 ^ _778495) ^ [_1306116, _1306118] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1306116)), _1306118) = 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), _1306116)), _1306118))], (21320 ^ _778495) ^ [_1160502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160502), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1160502)), c_Int_OPls)))], (3666 ^ _778495) ^ [_833479, _833481, _833483, _833485, _833487, _833489] : [-(c_List_Oinsert(_833489, _833485, _833481) = c_List_Oinsert(_833487, _833483, _833479)), _833489 = _833487, _833485 = _833483, _833481 = _833479], (32630 ^ _778495) ^ [_1380118, _1380120, _1380122, _1380124] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1380118, tc_HOL_Obool), tc_fun(_1380118, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1380118, tc_HOL_Obool), tc_fun(_1380118, tc_HOL_Obool)), _1380122), _1380124)), c_Wellfounded_Omax__ext(_1380118, _1380120))), -(c_Wellfounded_Omax__extp(_1380118, hAPP(hAPP(c_COMBC(_1380118, tc_fun(tc_prod(_1380118, _1380118), tc_HOL_Obool), tc_fun(_1380118, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1380118, tc_fun(tc_fun(tc_prod(_1380118, _1380118), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1380118, _1380118), tc_HOL_Obool), tc_fun(_1380118, tc_HOL_Obool)), _1380118), c_COMBC(_1380118, tc_fun(tc_prod(_1380118, _1380118), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1380118, tc_prod(_1380118, _1380118)), tc_fun(_1380118, tc_fun(tc_fun(tc_prod(_1380118, _1380118), tc_HOL_Obool), tc_HOL_Obool)), _1380118), hAPP(c_COMBB(tc_prod(_1380118, _1380118), tc_fun(tc_fun(tc_prod(_1380118, _1380118), tc_HOL_Obool), tc_HOL_Obool), _1380118), c_member(tc_prod(_1380118, _1380118)))), c_Product__Type_OPair(_1380118, _1380118)))), _1380120), _1380122, _1380124))], (52621 ^ _778495) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (41606 ^ _778495) ^ [_1601424, _1601426, _1601428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601424, _1601424), tc_HOL_Obool)), _1601426), _1601428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1601424), tc_List_Olist(_1601424)), tc_HOL_Obool)), c_List_Olistrel(_1601424, _1601426)), c_List_Olistrel(_1601424, _1601428))))], (35304 ^ _778495) ^ [_1437923, _1437925, _1437927] : [class_Orderings_Olinorder(_1437923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437923), _1437925), _1437927)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437923, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1437923, _1437925), _1437927)), hAPP(c_SetInterval_Oord__class_OatLeast(_1437923), _1437927)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1437923), _1437925))], (40704 ^ _778495) ^ [_1576121, _1576123, _1576125] : [c_Relation_Orefl__on(_1576121, _1576123, hAPP(c_Relation_Oconverse(_1576121, _1576121), _1576125)), -(c_Relation_Orefl__on(_1576121, _1576123, _1576125))], (38577 ^ _778495) ^ [_1524820, _1524822, _1524824, _1524826, _1524828, _1524830, _1524832] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524820, _1524824)), hAPP(hAPP(c_Product__Type_OPair(_1524820, _1524824), _1524830), _1524832)), hAPP(hAPP(c_Relation_Orel__comp(_1524820, _1524822, _1524824), _1524826), _1524828))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1524820, _1524822, _1524824, hAPP(hAPP(c_COMBC(_1524820, tc_fun(tc_prod(_1524820, _1524822), tc_HOL_Obool), tc_fun(_1524822, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524822, tc_fun(tc_fun(tc_prod(_1524820, _1524822), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1524820, _1524822), tc_HOL_Obool), tc_fun(_1524822, tc_HOL_Obool)), _1524820), c_COMBC(_1524822, tc_fun(tc_prod(_1524820, _1524822), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524822, tc_prod(_1524820, _1524822)), tc_fun(_1524822, tc_fun(tc_fun(tc_prod(_1524820, _1524822), tc_HOL_Obool), tc_HOL_Obool)), _1524820), hAPP(c_COMBB(tc_prod(_1524820, _1524822), tc_fun(tc_fun(tc_prod(_1524820, _1524822), tc_HOL_Obool), tc_HOL_Obool), _1524822), c_member(tc_prod(_1524820, _1524822)))), c_Product__Type_OPair(_1524820, _1524822)))), _1524826), hAPP(hAPP(c_COMBC(_1524822, tc_fun(tc_prod(_1524822, _1524824), tc_HOL_Obool), tc_fun(_1524824, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524824, tc_fun(tc_fun(tc_prod(_1524822, _1524824), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1524822, _1524824), tc_HOL_Obool), tc_fun(_1524824, tc_HOL_Obool)), _1524822), c_COMBC(_1524824, tc_fun(tc_prod(_1524822, _1524824), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524824, tc_prod(_1524822, _1524824)), tc_fun(_1524824, tc_fun(tc_fun(tc_prod(_1524822, _1524824), tc_HOL_Obool), tc_HOL_Obool)), _1524822), hAPP(c_COMBB(tc_prod(_1524822, _1524824), tc_fun(tc_fun(tc_prod(_1524822, _1524824), tc_HOL_Obool), tc_HOL_Obool), _1524824), c_member(tc_prod(_1524822, _1524824)))), c_Product__Type_OPair(_1524822, _1524824)))), _1524828)), _1524830), _1524832)))], (37392 ^ _778495) ^ [_1486291, _1486293, _1486295, _1486297, _1486299] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1486291, _1486293), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1486291, tc_HOL_Obool)), _1486295), _1486297)), _1486299) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1486291, _1486293), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486291, _1486293), _1486295), _1486299)), hAPP(hAPP(c_Product__Type_OSigma(_1486291, _1486293), _1486297), _1486299)))], (1468 ^ _778495) ^ [_799873, _799875] : [-(class_Lattices_Olattice(_799873)), _799875 = _799873, class_Lattices_Olattice(_799875)], (13287 ^ _778495) ^ [_1014904, _1014906, _1014908] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1014904), _1014906)), 13290 ^ _778495 : [(13291 ^ _778495) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1014904, tc_Nat_Onat), _1014908), _1014906) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 13294 ^ _778495 : [(13295 ^ _778495) ^ [_1015066] : [hBOOL(hAPP(hAPP(c_member(_1014904), _1015066), _1014906)), -(hAPP(_1014908, _1015066) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (13301 ^ _778495) ^ [] : [13303 ^ _778495 : [(13306 ^ _778495) ^ [] : [hAPP(_1014908, 13302 ^ [_1014904, _1014906, _1014908]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13304 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014904), 13302 ^ [_1014904, _1014906, _1014908]), _1014906)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1014904, tc_Nat_Onat), _1014908), _1014906) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (17876 ^ _778495) ^ [_1098996, _1098998, _1099000, _1099002] : [class_Orderings_Olinorder(_1098996), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098996), _1098998), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1098996), _1099000), _1099002))), 17883 ^ _778495 : [(17886 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098996), _1098998), _1099002)))], (17884 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098996), _1098998), _1099000)))]]], (3042 ^ _778495) ^ [_823767, _823769, _823771, _823773] : [-(c_List_Olistset(_823773, _823769) = c_List_Olistset(_823771, _823767)), _823773 = _823771, _823769 = _823767], (40946 ^ _778495) ^ [_1582289, _1582291, _1582293] : [c_Wellfounded_Owf(_1582289, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582289, _1582289), tc_HOL_Obool), _1582291), _1582293)), -(c_Wellfounded_Owf(_1582289, _1582293))], (10639 ^ _778495) ^ [_961901, _961903, _961905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961901), _961903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961905), _961901)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961905), _961903))))], (25393 ^ _778495) ^ [_1232238, _1232240] : [class_Groups_Omonoid__mult(_1232238), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1232238), _1232240), 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(_1232238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232238), _1232240), _1232240)), _1232240))], (29715 ^ _778495) ^ [_1319025, _1319027, _1319029, _1319031] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1319025, _1319027), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1319029), _1319031))), -(_1319027 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1319025, _1319027) = _1319031)], (36695 ^ _778495) ^ [_1469730, _1469732, _1469734, _1469736, _1469738] : [-(c_Fun_Oinj__on(_1469730, _1469732, _1469734, hAPP(hAPP(c_Set_Oinsert(_1469730), _1469736), _1469738))), c_Fun_Oinj__on(_1469730, _1469732, _1469734, _1469738), -(hBOOL(hAPP(hAPP(c_member(_1469732), hAPP(_1469734, _1469736)), hAPP(c_Set_Oimage(_1469730, _1469732, _1469734), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469730, tc_HOL_Obool)), _1469738), hAPP(hAPP(c_Set_Oinsert(_1469730), _1469736), c_Orderings_Obot__class_Obot(tc_fun(_1469730, tc_HOL_Obool))))))))], (41210 ^ _778495) ^ [_1589491, _1589493, _1589495, _1589497] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589491, _1589491)), hAPP(hAPP(c_Product__Type_OPair(_1589491, _1589491), _1589493), _1589495)), c_Transitive__Closure_Otrancl(_1589491, _1589497))), 41214 ^ _778495 : [(41217 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589491, _1589491)), hAPP(hAPP(c_Product__Type_OPair(_1589491, _1589491), 41213 ^ [_1589491, _1589493, _1589495, _1589497]), _1589495)), c_Transitive__Closure_Ortrancl(_1589491, _1589497))))], (41215 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589491, _1589491)), hAPP(hAPP(c_Product__Type_OPair(_1589491, _1589491), _1589493), 41213 ^ [_1589491, _1589493, _1589495, _1589497])), _1589497)))]]], (30783 ^ _778495) ^ [_1340401] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1340401) = c_Orderings_Oord__class_Omax(_1340401)), class_Lattices_Osemilattice__sup(_1340401), class_Orderings_Olinorder(_1340401)], (21326 ^ _778495) ^ [_1160603] : [-(c_Int_OBit1(_1160603) = 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)), _1160603)), _1160603))], (4772 ^ _778495) ^ [_851248, _851250, _851252, _851254, _851256, _851258] : [-(c_Relation_Orel__comp(_851258, _851254, _851250) = c_Relation_Orel__comp(_851256, _851252, _851248)), _851258 = _851256, _851254 = _851252, _851250 = _851248], (17862 ^ _778495) ^ [_1098725, _1098727, _1098729, _1098731, _1098733] : [class_Orderings_Olinorder(_1098725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098725), _1098727), _1098729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098725), _1098731), _1098733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098725), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1098725), _1098727), _1098731)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1098725), _1098729), _1098733))))], (49292 ^ _778495) ^ [_1775004, _1775006] : [c_Relation_Osym(_1775004, _1775006), 49295 ^ _778495 : [(49296 ^ _778495) ^ [_1775110, _1775112] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775004, _1775004)), hAPP(hAPP(c_Product__Type_OPair(_1775004, _1775004), _1775112), _1775110)), _1775006)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775004, _1775004)), hAPP(hAPP(c_Product__Type_OPair(_1775004, _1775004), _1775110), _1775112)), _1775006)))]]], (37690 ^ _778495) ^ [_1494745, _1494747, _1494749, _1494751, _1494753, _1494755] : [-(c_Product__Type_Omap__pair(_1494745, _1494747, _1494749, _1494751, _1494753, _1494755) = hAPP(c_Product__Type_Oprod_Oprod__case(_1494745, _1494749, tc_prod(_1494747, _1494751)), hAPP(hAPP(c_COMBC(_1494745, tc_fun(_1494749, _1494751), tc_fun(_1494749, tc_prod(_1494747, _1494751))), hAPP(hAPP(c_COMBB(tc_fun(_1494751, tc_prod(_1494747, _1494751)), tc_fun(tc_fun(_1494749, _1494751), tc_fun(_1494749, tc_prod(_1494747, _1494751))), _1494745), c_COMBB(_1494751, tc_prod(_1494747, _1494751), _1494749)), hAPP(hAPP(c_COMBB(_1494747, tc_fun(_1494751, tc_prod(_1494747, _1494751)), _1494745), c_Product__Type_OPair(_1494747, _1494751)), _1494753))), _1494755)))], (32092 ^ _778495) ^ [_1368605, _1368607] : [class_Orderings_Oorder(_1368605), -(c_SetInterval_Oord__class_OatLeastAtMost(_1368605, _1368607, _1368607) = hAPP(hAPP(c_Set_Oinsert(_1368605), _1368607), c_Orderings_Obot__class_Obot(tc_fun(_1368605, tc_HOL_Obool))))], (38383 ^ _778495) ^ [_1517881, _1517883] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1517881, _1517883, tc_prod(_1517881, _1517883)), c_Product__Type_OPair(_1517881, _1517883)) = c_Fun_Oid(tc_prod(_1517881, _1517883)))], (35625 ^ _778495) ^ [_1445507, _1445509, _1445511] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1445507), _1445509), _1445511) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1445507, tc_fun(tc_fun(_1445507, tc_HOL_Obool), tc_HOL_Obool)), _1445509), hAPP(hAPP(c_COMBC(_1445507, tc_fun(tc_fun(_1445507, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1445507, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445507, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1445507, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1445507, tc_HOL_Obool), tc_HOL_Obool)), _1445507), c_Set_Oinsert(tc_fun(_1445507, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1445507, tc_HOL_Obool), tc_fun(_1445507, tc_HOL_Obool), _1445507), c_Relation_OImage(_1445507, _1445507, _1445511)), hAPP(hAPP(c_COMBC(_1445507, tc_fun(_1445507, tc_HOL_Obool), tc_fun(_1445507, tc_HOL_Obool)), c_Set_Oinsert(_1445507)), c_Orderings_Obot__class_Obot(tc_fun(_1445507, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1445507, tc_HOL_Obool), tc_HOL_Obool)))))], (38947 ^ _778495) ^ [_1533122, _1533124, _1533126, _1533128] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533122, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1533122, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533122, _1533124), _1533126)), hAPP(c_Relation_ODomain(_1533122, _1533124), _1533128))), hAPP(c_Relation_ODomain(_1533122, _1533124), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1533122, _1533124), tc_HOL_Obool)), _1533126), _1533128)))))], (14251 ^ _778495) ^ [_1031638, _1031640, _1031642, _1031644] : [class_Rings_Olinordered__ring__strict(_1031638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031638), _1031640), c_Groups_Ozero__class_Ozero(_1031638))), 14258 ^ _778495 : [(14265 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031638), _1031644), _1031642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031638), _1031640), _1031642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031638), _1031640), _1031644))))], (14259 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031638), _1031640), _1031642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031638), _1031640), _1031644))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031638), _1031644), _1031642)))]]], (32314 ^ _778495) ^ [_1373330, _1373332, _1373334, _1373336, _1373338] : [class_Complete__Lattice_Ocomplete__lattice(_1373330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373332), _1373334)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1373330), _1373336), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1373332, _1373330), _1373334), _1373338)) = hAPP(hAPP(c_Finite__Set_Ofold(_1373332, _1373330, hAPP(hAPP(c_COMBB(_1373330, tc_fun(_1373330, _1373330), _1373332), c_Lattices_Osemilattice__inf__class_Oinf(_1373330)), _1373338)), _1373336), _1373334))], (39432 ^ _778495) ^ [_1545902, _1545904, _1545906, _1545908, _1545910] : [hAPP(c_Set_Oimage(_1545902, _1545904, _1545906), c_Orderings_Otop__class_Otop(tc_fun(_1545902, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1545904, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1545904, _1545908, _1545910), c_Orderings_Otop__class_Otop(tc_fun(_1545904, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1545908, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1545902, _1545908, hAPP(c_Fun_Ocomp(_1545904, _1545908, _1545902, _1545910), _1545906)), c_Orderings_Otop__class_Otop(tc_fun(_1545902, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1545908, tc_HOL_Obool)))], (5689 ^ _778495) ^ [_868394, _868396, _868398] : [hAPP(hAPP(c_Set_Oinsert(_868394), _868396), _868398) = c_Orderings_Obot__class_Obot(tc_fun(_868394, tc_HOL_Obool))], (34306 ^ _778495) ^ [_1418494, _1418496, _1418498, _1418500, _1418502, _1418504] : [_1418494 = hAPP(_1418496, _1418498), hBOOL(hAPP(hAPP(c_member(_1418500), _1418498), _1418502)), -(hBOOL(hAPP(hAPP(c_member(_1418504), _1418494), hAPP(c_Set_Oimage(_1418500, _1418504, _1418496), _1418502))))], (46037 ^ _778495) ^ [_1704555, _1704557] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704555), hAPP(c_List_Onth(_1704555), _1704557)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704555)), _1704557))) = _1704557)], (5568 ^ _778495) ^ [_863666, _863668, _863670, _863672, _863674, _863676] : [-(c_COMBB(_863676, _863672, _863668) = c_COMBB(_863674, _863670, _863666)), _863676 = _863674, _863672 = _863670, _863668 = _863666], (14299 ^ _778495) ^ [_1032529, _1032531, _1032533, _1032535] : [class_Rings_Olinordered__semiring__strict(_1032529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032529), _1032531), _1032533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032529), c_Groups_Ozero__class_Ozero(_1032529)), _1032535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032529), _1032531), _1032535)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032529), _1032533), _1032535))))], (10843 ^ _778495) ^ [_965192, _965194] : [10844 ^ _778495 : [(10847 ^ _778495) ^ [] : [_965192 = _965194], (10845 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965192), _965194))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965192), hAPP(c_Nat_OSuc, _965194))))], (17054 ^ _778495) ^ [_1083316, _1083318, _1083320, _1083322] : [class_Fields_Olinordered__field(_1083316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083316), _1083318), c_Groups_Ozero__class_Ozero(_1083316))), 17061 ^ _778495 : [(17068 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083316), _1083322), _1083318)), _1083320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083316), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1083316), _1083320), _1083318)), _1083322)))], (17062 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083316), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1083316), _1083320), _1083318)), _1083322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083316), _1083322), _1083318)), _1083320)))]]], (37859 ^ _778495) ^ [_1499020, _1499022, _1499024] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499020, tc_HOL_Obool)), _1499022), _1499024) = hAPP(c_Set_OCollect(_1499020), hAPP(hAPP(c_COMBS(_1499020, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499020), c_fconj), hAPP(hAPP(c_COMBC(_1499020, tc_fun(_1499020, tc_HOL_Obool), tc_HOL_Obool), c_member(_1499020)), _1499022))), hAPP(hAPP(c_COMBC(_1499020, tc_fun(_1499020, tc_HOL_Obool), tc_HOL_Obool), c_member(_1499020)), _1499024))))], (39652 ^ _778495) ^ [_1550680, _1550682, _1550684, _1550686, _1550688, _1550690] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1550680, _1550682), _1550682, tc_prod(_1550684, _1550686), c_Product__Type_Osnd(_1550680, _1550682)), c_Product__Type_Omap__pair(_1550684, _1550680, _1550686, _1550682, _1550688, _1550690)) = hAPP(c_Fun_Ocomp(_1550686, _1550682, tc_prod(_1550684, _1550686), _1550690), c_Product__Type_Osnd(_1550684, _1550686)))], (34949 ^ _778495) ^ [_1432245, _1432247, _1432249, _1432251, _1432253] : [hAPP(_1432249, _1432251) = _1432253, -(c_Fun_Ofun__upd(_1432245, _1432247, _1432249, _1432251, _1432253) = _1432249)], (41481 ^ _778495) ^ [_1597503, _1597505, _1597507, _1597509] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597503), tc_List_Olist(_1597503))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597503), tc_List_Olist(_1597503)), _1597505), _1597507)), c_List_Olex(_1597503, _1597509)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597503), tc_List_Olist(_1597503))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597503), tc_List_Olist(_1597503)), _1597505), _1597507)), c_List_Olexord(_1597503, _1597509))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597503)), _1597505) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597503)), _1597507)], (42674 ^ _778495) ^ [_1629146, _1629148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1629146), _1629148)), -(c_List_Oupto(_1629148, _1629146) = c_List_Olist_ONil(tc_Int_Oint))], (35680 ^ _778495) ^ [_1447008, _1447010, _1447012, _1447014, _1447016] : [c_Equiv__Relations_Oequiv(_1447008, _1447010, _1447012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447008, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1447008, _1447008, _1447012), hAPP(hAPP(c_Set_Oinsert(_1447008), _1447014), c_Orderings_Obot__class_Obot(tc_fun(_1447008, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1447008, _1447008, _1447012), hAPP(hAPP(c_Set_Oinsert(_1447008), _1447016), c_Orderings_Obot__class_Obot(tc_fun(_1447008, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1447008), _1447014), _1447010)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447008, _1447008)), hAPP(hAPP(c_Product__Type_OPair(_1447008, _1447008), _1447016), _1447014)), _1447012)))], (14453 ^ _778495) ^ [_1035344] : [class_Rings_Olinordered__semidom(_1035344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1035344), c_Groups_Oone__class_Oone(_1035344)), c_Groups_Ozero__class_Ozero(_1035344)))], (25256 ^ _778495) ^ [_1229749, _1229751] : [-(_1229749 = hAPP(c_Int_Onat, _1229751)), 25259 ^ _778495 : [(25262 ^ _778495) ^ [] : [_1229751 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229749)], (25260 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229751)))]], 25263 ^ _778495 : [(25266 ^ _778495) ^ [] : [_1229749 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25264 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229751))]]], (38154 ^ _778495) ^ [_1508579] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1508579) = 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), _1508579), c_Int_Onat)))))], (35124 ^ _778495) ^ [_1434846, _1434848] : [c_Nat__Transfer_Ois__nat(_1434846), c_Nat__Transfer_Onat__set(_1434848), 35131 ^ _778495 : [(35138 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1434846)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1434848))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1434846), _1434848)))], (35132 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1434846), _1434848)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1434846)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1434848))))]]], (15461 ^ _778495) ^ [_1053128, _1053130, _1053132] : [15462 ^ _778495 : [(15465 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053128), _1053132))], (15463 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1053130)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053128), _1053130)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053132), _1053130))))], (22982 ^ _778495) ^ [_1189339, _1189341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1189339), 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)))), _1189341))), 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)))), _1189339)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1189341), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1189339))], (2398 ^ _778495) ^ [_813739, _813741, _813743, _813745, _813747, _813749, _813751, _813753, _813755, _813757] : [-(c_Product__Type_Oprod_Oprod__rec(_813757, _813753, _813749, _813745, _813741) = c_Product__Type_Oprod_Oprod__rec(_813755, _813751, _813747, _813743, _813739)), _813757 = _813755, _813753 = _813751, _813749 = _813747, _813745 = _813743, _813741 = _813739], (45456 ^ _778495) ^ [_1690626, _1690628, _1690630, _1690632] : [-(hAPP(c_List_OremoveAll(_1690626, _1690628), hAPP(hAPP(c_List_Oappend(_1690626), _1690630), _1690632)) = hAPP(hAPP(c_List_Oappend(_1690626), hAPP(c_List_OremoveAll(_1690626, _1690628), _1690630)), hAPP(c_List_OremoveAll(_1690626, _1690628), _1690632)))], (7816 ^ _778495) ^ [_907570, _907572, _907574] : [class_Orderings_Opreorder(_907570), 7819 ^ _778495 : [(7828 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907570), _907572), _907574))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907570), _907572), _907574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907570), _907574), _907572)))], (7820 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907570), _907572), _907574)), 7823 ^ _778495 : [(7826 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907570), _907574), _907572))], (7824 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907570), _907572), _907574)))]]]]], (9811 ^ _778495) ^ [_946724, _946726, _946728, _946730, _946732, _946734, _946736, _946738] : [c_Finite__Set_Ofolding__image__simple(_946724, _946726, _946728, _946730, _946732, _946734), hBOOL(hAPP(c_Finite__Set_Ofinite(_946726), _946736)), hBOOL(hAPP(c_Finite__Set_Ofinite(_946726), _946738)), -(hAPP(hAPP(_946728, hAPP(_946734, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946726, tc_HOL_Obool)), _946736), _946738))), hAPP(_946734, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946726, tc_HOL_Obool)), _946736), _946738))) = hAPP(hAPP(_946728, hAPP(_946734, _946736)), hAPP(_946734, _946738)))], (37065 ^ _778495) ^ [_1477626, _1477628, _1477630, _1477632] : [-(c_HOL_OThe(tc_prod(_1477626, _1477628), hAPP(c_Product__Type_Oprod_Oprod__case(_1477626, _1477628, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1477626, tc_fun(_1477628, tc_HOL_Obool), tc_fun(_1477628, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1477628, tc_HOL_Obool), tc_fun(_1477628, tc_HOL_Obool)), _1477626), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1477628)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1477626), c_fconj), hAPP(c_fequal, _1477630)))), hAPP(c_fequal, _1477632)))) = hAPP(hAPP(c_Product__Type_OPair(_1477626, _1477628), _1477630), _1477632))], (38455 ^ _778495) ^ [_1520143, _1520145, _1520147, _1520149, _1520151, _1520153] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1520143, _1520145, _1520147), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520143, _1520145), tc_HOL_Obool)), _1520149), _1520151)), _1520153) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520143, _1520147), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1520143, _1520145, _1520147), _1520149), _1520153)), hAPP(hAPP(c_Relation_Orel__comp(_1520143, _1520145, _1520147), _1520151), _1520153)))], (50819 ^ _778495) ^ [_1807498, _1807500] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807498), _1807500)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807498), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807500))))], (16852 ^ _778495) ^ [_1079536, _1079538, _1079540, _1079542] : [class_Fields_Ofield__inverse__zero(_1079536), -(_1079538 = c_Groups_Ozero__class_Ozero(_1079536)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1079536), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079536), _1079540), _1079538)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079536), _1079542), _1079538)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1079536), _1079540), _1079542))], (34387 ^ _778495) ^ [_1420629, _1420631, _1420633, _1420635, _1420637] : [hBOOL(hAPP(hAPP(c_member(_1420629), _1420631), _1420633)), -(hBOOL(hAPP(hAPP(c_member(_1420635), hAPP(_1420637, _1420631)), hAPP(c_Set_Oimage(_1420629, _1420635, _1420637), _1420633))))], (44193 ^ _778495) ^ [_1662700, _1662702] : [-(_1662700 = c_List_Olist_ONil(_1662702)), -(c_List_Olast(_1662702, _1662700) = hAPP(hAPP(c_List_Onth(_1662702), _1662700), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662702)), _1662700)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (33942 ^ _778495) ^ [_1410506] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410506)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1410506))], (23044 ^ _778495) ^ [_1190646, _1190648] : [-(_1190646 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1190648), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1190646), _1190648))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190646, _1190648)))], (15225 ^ _778495) ^ [_1048941, _1048943, _1048945] : [class_Rings_Olinordered__ring__strict(_1048941), 15228 ^ _778495 : [(15229 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048941), c_Groups_Ozero__class_Ozero(_1048941)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048941), _1048943), _1048943)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048941), _1048945), _1048945)))), _1048943 = c_Groups_Ozero__class_Ozero(_1048941), _1048945 = c_Groups_Ozero__class_Ozero(_1048941)], (15239 ^ _778495) ^ [] : [15240 ^ _778495 : [(15243 ^ _778495) ^ [] : [-(_1048945 = c_Groups_Ozero__class_Ozero(_1048941))], (15241 ^ _778495) ^ [] : [-(_1048943 = c_Groups_Ozero__class_Ozero(_1048941))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048941), c_Groups_Ozero__class_Ozero(_1048941)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048941), _1048943), _1048943)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048941), _1048945), _1048945)))))]]], (29892 ^ _778495) ^ [_1322256, _1322258, _1322260, _1322262] : [-(hAPP(c_Product__Type_Osnd(_1322256, _1322258), hAPP(hAPP(c_Product__Type_OPair(_1322256, _1322258), _1322260), _1322262)) = _1322262)], (17330 ^ _778495) ^ [_1088421, _1088423, _1088425, _1088427] : [class_Fields_Ofield(_1088421), -(_1088423 = c_Groups_Ozero__class_Ozero(_1088421)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088421), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1088421), _1088425), _1088423)), _1088427) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1088421), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088421), _1088425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088421), _1088423), _1088427))), _1088423))], (9472 ^ _778495) ^ [_939885, _939887, _939889, _939891] : [class_Lattices_Olattice(_939885), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939885), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939885), _939887), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939885), _939889), _939891))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939885), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939885), _939887), _939889)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939885), _939887), _939891)))))], (1518 ^ _778495) ^ [_800498, _800500] : [-(class_Finite__Set_Ofinite(_800498)), _800500 = _800498, class_Finite__Set_Ofinite(_800500)], (45727 ^ _778495) ^ [_1697229, _1697231, _1697233, _1697235] : [hBOOL(hAPP(_1697229, _1697231)), -(hAPP(c_List_Ofilter(_1697233, _1697229), hAPP(hAPP(c_List_Olist_OCons(_1697233), _1697231), _1697235)) = hAPP(hAPP(c_List_Olist_OCons(_1697233), _1697231), hAPP(c_List_Ofilter(_1697233, _1697229), _1697235)))], (39025 ^ _778495) ^ [_1535139, _1535141] : [-(hAPP(c_List_Olexn(_1535139, _1535141), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1535139), tc_List_Olist(_1535139)), tc_HOL_Obool)))], (34677 ^ _778495) ^ [_1426902, _1426904] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1426902)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1426904))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1426902), _1426904)))], (48517 ^ _778495) ^ [_1756948, _1756950, _1756952, _1756954] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756948), hAPP(hAPP(c_List_Olist_OCons(_1756948), _1756950), _1756952)), _1756954)), -(_1756950 = _1756954), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756948), _1756952), _1756954)))], (23506 ^ _778495) ^ [_1199459, _1199461] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1199459, tc_HOL_Obool)), _1199461), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199459, tc_HOL_Obool)), _1199461)) = c_Orderings_Obot__class_Obot(tc_fun(_1199459, tc_HOL_Obool)))], (20416 ^ _778495) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (24523 ^ _778495) ^ [_1217486, _1217488] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217486)), _1217488) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1217486), _1217488)))], (36164 ^ _778495) ^ [_1458401, _1458403, _1458405] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1458401), _1458403)), c_Fun_Oinj__on(_1458401, tc_fun(tc_fun(_1458401, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1458401, tc_fun(tc_prod(_1458401, _1458401), tc_HOL_Obool), tc_fun(tc_fun(_1458401, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458401, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1458401, _1458401), tc_HOL_Obool), tc_fun(tc_fun(_1458401, tc_HOL_Obool), tc_HOL_Obool)), _1458401), c_Equiv__Relations_Oquotient(_1458401)), hAPP(hAPP(c_COMBC(_1458401, tc_fun(_1458401, tc_HOL_Obool), tc_fun(_1458401, tc_HOL_Obool)), c_Set_Oinsert(_1458401)), c_Orderings_Obot__class_Obot(tc_fun(_1458401, tc_HOL_Obool))))), _1458405), _1458403), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1458401, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1458401), _1458403), _1458405)) = hAPP(c_Finite__Set_Ocard(_1458401), _1458403))], (42934 ^ _778495) ^ [_1634110, _1634112, _1634114, _1634116] : [-(hAPP(c_List_Olist_Olist__case(_1634110, _1634112, _1634114, _1634116), c_List_Olist_ONil(_1634112)) = _1634114)], (34363 ^ _778495) ^ [_1419995, _1419997, _1419999, _1420001, _1420003] : [-(hAPP(c_Set_Oimage(_1419995, _1419997, hAPP(hAPP(c_COMBB(_1419999, _1419997, _1419995), _1420001), _1420003)), c_Orderings_Otop__class_Otop(tc_fun(_1419995, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1419999, _1419997, _1420001), hAPP(c_Set_Oimage(_1419995, _1419999, _1420003), c_Orderings_Otop__class_Otop(tc_fun(_1419995, tc_HOL_Obool)))))], (13897 ^ _778495) ^ [_1025277, _1025279, _1025281] : [class_Rings_Oordered__cancel__semiring(_1025277), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025277), c_Groups_Ozero__class_Ozero(_1025277)), _1025279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025277), _1025281), c_Groups_Ozero__class_Ozero(_1025277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025277), _1025281), _1025279)), c_Groups_Ozero__class_Ozero(_1025277))))], (21334 ^ _778495) ^ [_1160744] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160744))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1160744)))))], (5845 ^ _778495) ^ [_871525] : [-(c_Finite__Set_Ofun__left__comm__idem(_871525, tc_fun(_871525, tc_HOL_Obool), c_Set_Oinsert(_871525)))], (31841 ^ _778495) ^ [_1361953, _1361955, _1361957, _1361959, _1361961] : [-(hAPP(hAPP(c_Set_Oinsert(_1361953), _1361955), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361957, tc_fun(_1361953, tc_HOL_Obool)), _1361959), _1361961)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361957, tc_fun(_1361953, tc_HOL_Obool)), _1361959), hAPP(hAPP(c_COMBB(tc_fun(_1361953, tc_HOL_Obool), tc_fun(_1361953, tc_HOL_Obool), _1361957), hAPP(c_Set_Oinsert(_1361953), _1361955)), _1361961)))], (4346 ^ _778495) ^ [_844533, _844535] : [_844535 = _844533, -(c_Lazy__Sequence_Oempty(_844535) = c_Lazy__Sequence_Oempty(_844533))], (17824 ^ _778495) ^ [_1098066, _1098068, _1098070] : [class_Orderings_Olinorder(_1098066), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098066), _1098068), _1098070)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1098066), _1098070), _1098068) = _1098068)], (26426 ^ _778495) ^ [_1251090, _1251092, _1251094, _1251096] : [class_Rings_Olinordered__semidom(_1251090), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251090), c_Groups_Oone__class_Oone(_1251090)), _1251092)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251090), hAPP(hAPP(c_Power_Opower__class_Opower(_1251090), _1251092), _1251094)), hAPP(hAPP(c_Power_Opower__class_Opower(_1251090), _1251092), _1251096))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1251094), _1251096)))], (23050 ^ _778495) ^ [_1190827, _1190829, _1190831] : [-(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), _1190827), _1190829)), _1190829)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190827, _1190829))), _1190831) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190827), _1190831))], (45113 ^ _778495) ^ [_1683418, _1683420, _1683422, _1683424, _1683426, _1683428, _1683430] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683418)), _1683420) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683422)), _1683424), 45116 ^ _778495 : [(45125 ^ _778495) ^ [] : [-(c_List_Olist__all2(_1683418, _1683422, _1683426, hAPP(hAPP(c_List_Oappend(_1683418), _1683420), _1683428), hAPP(hAPP(c_List_Oappend(_1683422), _1683424), _1683430))), c_List_Olist__all2(_1683418, _1683422, _1683426, _1683420, _1683424), c_List_Olist__all2(_1683418, _1683422, _1683426, _1683428, _1683430)], (45117 ^ _778495) ^ [] : [c_List_Olist__all2(_1683418, _1683422, _1683426, hAPP(hAPP(c_List_Oappend(_1683418), _1683420), _1683428), hAPP(hAPP(c_List_Oappend(_1683422), _1683424), _1683430)), 45120 ^ _778495 : [(45123 ^ _778495) ^ [] : [-(c_List_Olist__all2(_1683418, _1683422, _1683426, _1683428, _1683430))], (45121 ^ _778495) ^ [] : [-(c_List_Olist__all2(_1683418, _1683422, _1683426, _1683420, _1683424))]]]]], (30063 ^ _778495) ^ [_1325975, _1325977, _1325979, _1325981, _1325983] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1325975, _1325977, _1325979), _1325981), _1325983) = hAPP(hAPP(_1325981, hAPP(c_Product__Type_Ofst(_1325975, _1325977), _1325983)), hAPP(c_Product__Type_Osnd(_1325975, _1325977), _1325983)))], (46879 ^ _778495) ^ [_1721244, _1721246, _1721248, _1721250, _1721252] : [-(hAPP(hAPP(c_List_Ozip(_1721244, _1721246), _1721248), c_List_OtakeWhile(_1721246, _1721250, _1721252)) = c_List_OtakeWhile(tc_prod(_1721244, _1721246), hAPP(c_Fun_Ocomp(_1721246, tc_HOL_Obool, tc_prod(_1721244, _1721246), _1721250), c_Product__Type_Osnd(_1721244, _1721246)), hAPP(hAPP(c_List_Ozip(_1721244, _1721246), _1721248), _1721252)))], (2552 ^ _778495) ^ [_816134, _816136, _816138, _816140, _816142, _816144] : [-(c_Finite__Set_Ofold1Set(_816144, _816140, _816136) = c_Finite__Set_Ofold1Set(_816142, _816138, _816134)), _816144 = _816142, _816140 = _816138, _816136 = _816134], (33946 ^ _778495) ^ [_1410570] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410570)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410570)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1410570)))], (12488 ^ _778495) ^ [_999008, _999010, _999012] : [class_Complete__Lattice_Ocomplete__lattice(_999008), class_Orderings_Olinorder(_999008), 12495 ^ _778495 : [(12505 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999008), _999010), c_Complete__Lattice_OSup__class_OSup(_999008, _999012)))), 12506 ^ _778495 : [(12507 ^ _778495) ^ [_999314] : [hBOOL(hAPP(hAPP(c_member(_999008), _999314), _999012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999008), _999010), _999314))]]], (12496 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999008), _999010), c_Complete__Lattice_OSup__class_OSup(_999008, _999012))), 12500 ^ _778495 : [(12503 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999008), _999010), 12499 ^ [_999008, _999010, _999012])))], (12501 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_999008), 12499 ^ [_999008, _999010, _999012]), _999012)))]]]]], (40347 ^ _778495) ^ [_1567674, _1567676] : [-(c_Transitive__Closure_Otrancl(_1567674, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567674, _1567674), tc_HOL_Obool)), _1567676), c_Relation_OId(_1567674))) = c_Transitive__Closure_Ortrancl(_1567674, _1567676))], (29745 ^ _778495) ^ [_1319436, _1319438] : [-(_1319436 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1319438, _1319436), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1319438), _1319436)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1319438, _1319436)))))], (16536 ^ _778495) ^ [_1074092, _1074094, _1074096] : [class_Fields_Olinordered__field__inverse__zero(_1074092), 16539 ^ _778495 : [(16554 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074092), c_Groups_Ozero__class_Ozero(_1074092)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1074092), _1074094), _1074096)))), 16555 ^ _778495 : [(16562 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074092), _1074094), c_Groups_Ozero__class_Ozero(_1074092))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074092), _1074096), c_Groups_Ozero__class_Ozero(_1074092)))], (16556 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074092), c_Groups_Ozero__class_Ozero(_1074092)), _1074094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074092), c_Groups_Ozero__class_Ozero(_1074092)), _1074096))]]], (16540 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074092), c_Groups_Ozero__class_Ozero(_1074092)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1074092), _1074094), _1074096))), 16545 ^ _778495 : [(16548 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074092), c_Groups_Ozero__class_Ozero(_1074092)), _1074096)))], (16546 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074092), c_Groups_Ozero__class_Ozero(_1074092)), _1074094)))]], 16549 ^ _778495 : [(16552 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074092), _1074096), c_Groups_Ozero__class_Ozero(_1074092))))], (16550 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074092), _1074094), c_Groups_Ozero__class_Ozero(_1074092))))]]]]], (24962 ^ _778495) ^ [_1224995, _1224997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224995)), 24965 ^ _778495 : [(24972 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224997), _1224995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1224997)), hAPP(c_Int_Onat, _1224995))))], (24966 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1224997)), hAPP(c_Int_Onat, _1224995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224997), _1224995)))]]], (4236 ^ _778495) ^ [_842682, _842684, _842686, _842688] : [-(c_List_Omap(_842688, _842684) = c_List_Omap(_842686, _842682)), _842688 = _842686, _842684 = _842682], (2 ^ _778495) ^ [_778522] : [-(_778522 = _778522)], (35013 ^ _778495) ^ [_1433256, _1433258] : [c_Nat__Transfer_Onat__set(_1433256), c_Nat__Transfer_Onat__set(_1433258), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1433256), _1433258)))], (6666 ^ _778495) ^ [_887485, _887487] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887485, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_887485, tc_HOL_Obool))), _887487) = _887487)], (33004 ^ _778495) ^ [_1387275, _1387277] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1387275, _1387277)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1387277), _1387275))], (46244 ^ _778495) ^ [_1708264, _1708266, _1708268] : [class_Orderings_Olinorder(_1708264), c_List_Olinorder__class_Osorted(_1708264, _1708266), hBOOL(hAPP(c_List_Odistinct(_1708264), _1708266)), c_List_Olinorder__class_Osorted(_1708264, _1708268), hBOOL(hAPP(c_List_Odistinct(_1708264), _1708268)), hAPP(c_List_Oset(_1708264), _1708266) = hAPP(c_List_Oset(_1708264), _1708268), -(_1708266 = _1708268)], (42864 ^ _778495) ^ [_1632629] : [-(c_List_Olists(_1632629, c_Orderings_Obot__class_Obot(tc_fun(_1632629, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632629)), c_List_Olist_ONil(_1632629)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632629), tc_HOL_Obool))))], (26618 ^ _778495) ^ [] : [c_Int_OPls = c_Int_OMin], (2868 ^ _778495) ^ [_821066, _821068] : [_821068 = _821066, -(c_Int_Oring__1__class_Oof__int(_821068) = c_Int_Oring__1__class_Oof__int(_821066))], (40234 ^ _778495) ^ [_1564197, _1564199] : [-(hAPP(c_Relation_ORange(_1564197, _1564197), c_Transitive__Closure_Otrancl(_1564197, _1564199)) = hAPP(c_Relation_ORange(_1564197, _1564197), _1564199))], (32660 ^ _778495) ^ [_1380959, _1380961, _1380963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380959)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1380961), _1380963)), 32667 ^ _778495 : [(32668 ^ _778495) ^ [_1381149] : [32670 ^ _778495 : [(32676 ^ _778495) ^ [] : [-(_1381149 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32672 ^ [_1380959, _1380961, _1380963, _1381149]), 32669 ^ [_1380959, _1380961, _1380963, _1381149]))], (32674 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32672 ^ [_1380959, _1380961, _1380963, _1381149]), _1380963)))], (32671 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32669 ^ [_1380959, _1380961, _1380963, _1381149]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1380959))))]], -(_1381149 = _1380961), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1381149), _1380959) = _1380961]]], (43620 ^ _778495) ^ [_1650544, _1650546, _1650548, _1650550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650544), _1650546)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650548)), _1650550))), -(hAPP(hAPP(c_List_Onth(_1650548), hAPP(hAPP(c_List_Odrop(_1650548), _1650544), _1650550)), _1650546) = hAPP(hAPP(c_List_Onth(_1650548), _1650550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650544), _1650546)))], (142 ^ _778495) ^ [_780828, _780830, _780832, _780834, _780836, _780838] : [-(c_Big__Operators_Osemilattice__big(_780836, _780832, _780828)), c_Big__Operators_Osemilattice__big(_780838, _780834, _780830), _780838 = _780836, _780834 = _780832, _780830 = _780828], (7396 ^ _778495) ^ [_901448, _901450, _901452] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_901448), _901450)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_901448), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901448, tc_HOL_Obool)), _901450), _901452))))], (52289 ^ _778495) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (34921 ^ _778495) ^ [_1431787, _1431789, _1431791, _1431793, _1431795, _1431797, _1431799] : [-(_1431787 = _1431789), -(c_Fun_Ofun__upd(_1431791, _1431793, c_Fun_Ofun__upd(_1431791, _1431793, _1431795, _1431787, _1431797), _1431789, _1431799) = c_Fun_Ofun__upd(_1431791, _1431793, c_Fun_Ofun__upd(_1431791, _1431793, _1431795, _1431789, _1431799), _1431787, _1431797))], (26646 ^ _778495) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (34251 ^ _778495) ^ [_1417192] : [-(hAPP(c_Relation_OField(_1417192), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1417192, _1417192), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1417192, tc_HOL_Obool)))], (3254 ^ _778495) ^ [_827081, _827083] : [_827083 = _827081, -(c_Code__Numeral_OSuc__code__numeral(_827083) = c_Code__Numeral_OSuc__code__numeral(_827081))], (28371 ^ _778495) ^ [_1289485, _1289487, _1289489, _1289491] : [class_Fields_Olinordered__field(_1289485), -(hAPP(c_Groups_Oabs__class_Oabs(_1289485), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1289487, _1289485), _1289489), _1289491)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1289487, _1289485), hAPP(hAPP(c_COMBB(_1289485, _1289485, _1289487), c_Groups_Oabs__class_Oabs(_1289485)), _1289489)), _1289491))], (43261 ^ _778495) ^ [_1641582, _1641584, _1641586] : [c_List_Olist_ONil(_1641582) = hAPP(hAPP(c_List_Oappend(_1641582), _1641584), _1641586), 43264 ^ _778495 : [(43267 ^ _778495) ^ [] : [-(_1641586 = c_List_Olist_ONil(_1641582))], (43265 ^ _778495) ^ [] : [-(_1641584 = c_List_Olist_ONil(_1641582))]]], (9989 ^ _778495) ^ [_950357, _950359] : [class_Lattices_Olattice(_950357), hBOOL(hAPP(c_Finite__Set_Ofinite(_950357), _950359)), -(_950359 = c_Orderings_Obot__class_Obot(tc_fun(_950357, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_950357), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_950357), 10002 ^ [_950357, _950359]), 10003 ^ [_950357, _950359])), hAPP(hAPP(c_Set_Oinsert(_950357), 10002 ^ [_950357, _950359]), hAPP(hAPP(c_Set_Oinsert(_950357), 10003 ^ [_950357, _950359]), c_Orderings_Obot__class_Obot(tc_fun(_950357, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_950357), c_Big__Operators_Olattice__class_OSup__fin(_950357, _950359)), _950359)))], (13911 ^ _778495) ^ [_1025532, _1025534, _1025536] : [class_Rings_Oordered__cancel__semiring(_1025532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025532), c_Groups_Ozero__class_Ozero(_1025532)), _1025534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025532), _1025536), c_Groups_Ozero__class_Ozero(_1025532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025532), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025532), _1025534), _1025536)), c_Groups_Ozero__class_Ozero(_1025532))))], (39038 ^ _778495) ^ [_1535385, _1535387, _1535389, _1535391] : [39040 ^ _778495 : [(39043 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1535387, hAPP(_1535389, 39039 ^ [_1535385, _1535387, _1535389, _1535391]))), hAPP(_1535387, 39039 ^ [_1535385, _1535387, _1535389, _1535391])))], (39041 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1535385, 39039 ^ [_1535385, _1535387, _1535389, _1535391])))]], -(c_Wellfounded_Owf(_1535391, hAPP(c_Set_OCollect(tc_prod(_1535391, _1535391)), hAPP(c_Product__Type_Oprod_Oprod__case(_1535391, _1535391, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1535391, tc_HOL_Obool), tc_fun(_1535391, tc_HOL_Obool), _1535391), hAPP(c_COMBS(_1535391, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535391), c_fconj), _1535385))), hAPP(hAPP(c_COMBC(_1535391, tc_fun(_1535391, _1535391), tc_fun(_1535391, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535391, tc_HOL_Obool), tc_fun(tc_fun(_1535391, _1535391), tc_fun(_1535391, tc_HOL_Obool)), _1535391), c_COMBB(_1535391, tc_HOL_Obool, _1535391)), c_fequal)), _1535389))))))], (27619 ^ _778495) ^ [_1271460, _1271462, _1271464] : [class_Lattices_Obounded__lattice__top(_1271460), 27622 ^ _778495 : [(27631 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1271460), _1271462), _1271464) = c_Orderings_Otop__class_Otop(_1271460)), _1271462 = c_Orderings_Otop__class_Otop(_1271460), _1271464 = c_Orderings_Otop__class_Otop(_1271460)], (27623 ^ _778495) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1271460), _1271462), _1271464) = c_Orderings_Otop__class_Otop(_1271460), 27626 ^ _778495 : [(27629 ^ _778495) ^ [] : [-(_1271464 = c_Orderings_Otop__class_Otop(_1271460))], (27627 ^ _778495) ^ [] : [-(_1271462 = c_Orderings_Otop__class_Otop(_1271460))]]]]], (31882 ^ _778495) ^ [_1363837, _1363839, _1363841, _1363843, _1363845, _1363847] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1363839, _1363841)), hAPP(hAPP(c_Product__Type_OPair(_1363839, _1363841), _1363845), _1363847)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363837, tc_fun(tc_prod(_1363839, _1363841), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1363837, tc_HOL_Obool))), _1363843))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363837, tc_fun(_1363839, tc_fun(_1363841, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1363837, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1363839, _1363841), tc_HOL_Obool), tc_fun(_1363839, tc_fun(_1363841, tc_HOL_Obool)), _1363837), hAPP(c_COMBC(_1363839, tc_fun(tc_prod(_1363839, _1363841), tc_HOL_Obool), tc_fun(_1363841, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363841, tc_fun(tc_fun(tc_prod(_1363839, _1363841), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1363839, _1363841), tc_HOL_Obool), tc_fun(_1363841, tc_HOL_Obool)), _1363839), c_COMBC(_1363841, tc_fun(tc_prod(_1363839, _1363841), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363841, tc_prod(_1363839, _1363841)), tc_fun(_1363841, tc_fun(tc_fun(tc_prod(_1363839, _1363841), tc_HOL_Obool), tc_HOL_Obool)), _1363839), hAPP(c_COMBB(tc_prod(_1363839, _1363841), tc_fun(tc_fun(tc_prod(_1363839, _1363841), tc_HOL_Obool), tc_HOL_Obool), _1363841), c_member(tc_prod(_1363839, _1363841)))), c_Product__Type_OPair(_1363839, _1363841))))), _1363843)), _1363845), _1363847)))], (22496 ^ _778495) ^ [_1180704, _1180706, _1180708] : [class_Rings_Olinordered__idom(_1180704), 22499 ^ _778495 : [(22508 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180704), hAPP(c_Groups_Oabs__class_Oabs(_1180704), _1180706)), _1180708))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180704), _1180706), _1180708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180704), hAPP(c_Groups_Ouminus__class_Ouminus(_1180704), _1180706)), _1180708))], (22500 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180704), hAPP(c_Groups_Oabs__class_Oabs(_1180704), _1180706)), _1180708)), 22503 ^ _778495 : [(22506 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180704), hAPP(c_Groups_Ouminus__class_Ouminus(_1180704), _1180706)), _1180708)))], (22504 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180704), _1180706), _1180708)))]]]]], (43941 ^ _778495) ^ [_1657484, _1657486] : [class_Complete__Lattice_Ocomplete__lattice(_1657484), -(c_Complete__Lattice_OSup__class_OSup(_1657484, hAPP(c_List_Oset(_1657484), _1657486)) = hAPP(c_List_Ofoldl(_1657484, _1657484, c_Lattices_Osemilattice__sup__class_Osup(_1657484), c_Orderings_Obot__class_Obot(_1657484)), _1657486))], (35539 ^ _778495) ^ [_1443028, _1443030, _1443032, _1443034, _1443036] : [-(hBOOL(hAPP(hAPP(c_member(_1443028), _1443030), hAPP(c_Relation_OImage(_1443032, _1443028, _1443034), _1443036)))), 35540 ^ _778495 : [(35541 ^ _778495) ^ [_1443114] : [hBOOL(hAPP(hAPP(c_member(_1443032), _1443114), _1443036)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1443032, _1443028)), hAPP(hAPP(c_Product__Type_OPair(_1443032, _1443028), _1443114), _1443030)), _1443034))]]], (5050 ^ _778495) ^ [_855589, _855591, _855593, _855595] : [-(c_Quotient_ORespects(_855595, _855591) = c_Quotient_ORespects(_855593, _855589)), _855595 = _855593, _855591 = _855589], (30239 ^ _778495) ^ [_1329452, _1329454, _1329456, _1329458, _1329460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1329452, _1329454)), hAPP(_1329452, _1329456))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1329458, _1329458)), hAPP(hAPP(c_Product__Type_OPair(_1329458, _1329458), _1329454), _1329456)), c_Wellfounded_Omlex__prod(_1329458, _1329452, _1329460))))], (17108 ^ _778495) ^ [_1084347, _1084349, _1084351, _1084353] : [class_Fields_Olinordered__field(_1084347), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084347), c_Groups_Ozero__class_Ozero(_1084347)), _1084349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084347), _1084351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084347), _1084353), _1084349))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084347), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1084347), _1084351), _1084349)), _1084353)))], (38647 ^ _778495) ^ [_1526793] : [-(c_Wellfounded_Owf(_1526793, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1526793, _1526793), tc_HOL_Obool))))], (40112 ^ _778495) ^ [_1561299, _1561301, _1561303, _1561305, _1561307, _1561309, _1561311, _1561313] : [class_Groups_Ocomm__monoid__add(_1561299), class_Orderings_Oord(_1561301), _1561303 = _1561305, _1561307 = _1561309, 40130 ^ _778495 : [(40135 ^ _778495) ^ [] : [hAPP(_1561311, 40129 ^ [_1561299, _1561301, _1561303, _1561305, _1561307, _1561309, _1561311, _1561313]) = hAPP(_1561313, 40129 ^ [_1561299, _1561301, _1561303, _1561305, _1561307, _1561309, _1561311, _1561313])], (40133 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1561301), 40129 ^ [_1561299, _1561301, _1561303, _1561305, _1561307, _1561309, _1561311, _1561313]), _1561309)))], (40131 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1561301), _1561305), 40129 ^ [_1561299, _1561301, _1561303, _1561305, _1561307, _1561309, _1561311, _1561313])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561301, _1561299), _1561311), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1561301, _1561303), _1561307)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561301, _1561299), _1561313), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1561301, _1561305), _1561309)))], (44734 ^ _778495) ^ [_1674653, _1674655, _1674657, _1674659, _1674661] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674653)), _1674655) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674657)), _1674659), 44737 ^ _778495 : [(44746 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1674653, _1674657), _1674655), _1674659) = _1674661), hAPP(hAPP(c_List_Omap(tc_prod(_1674653, _1674657), _1674653), c_Product__Type_Ofst(_1674653, _1674657)), _1674661) = _1674655, hAPP(hAPP(c_List_Omap(tc_prod(_1674653, _1674657), _1674657), c_Product__Type_Osnd(_1674653, _1674657)), _1674661) = _1674659], (44738 ^ _778495) ^ [] : [hAPP(hAPP(c_List_Ozip(_1674653, _1674657), _1674655), _1674659) = _1674661, 44741 ^ _778495 : [(44744 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674653, _1674657), _1674657), c_Product__Type_Osnd(_1674653, _1674657)), _1674661) = _1674659)], (44742 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674653, _1674657), _1674653), c_Product__Type_Ofst(_1674653, _1674657)), _1674661) = _1674655)]]]]], (44349 ^ _778495) ^ [_1665331, _1665333, _1665335, _1665337, _1665339, _1665341] : [-(hAPP(hAPP(c_List_Ozip(_1665331, _1665333), _1665335), hAPP(hAPP(c_List_Omap(_1665337, _1665333), _1665339), _1665341)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665331, _1665337), tc_prod(_1665331, _1665333)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665331, _1665337, tc_prod(_1665331, _1665333)), hAPP(hAPP(c_COMBC(_1665331, tc_fun(_1665337, _1665333), tc_fun(_1665337, tc_prod(_1665331, _1665333))), hAPP(hAPP(c_COMBB(tc_fun(_1665333, tc_prod(_1665331, _1665333)), tc_fun(tc_fun(_1665337, _1665333), tc_fun(_1665337, tc_prod(_1665331, _1665333))), _1665331), c_COMBB(_1665333, tc_prod(_1665331, _1665333), _1665337)), c_Product__Type_OPair(_1665331, _1665333))), _1665339))), hAPP(hAPP(c_List_Ozip(_1665331, _1665337), _1665335), _1665341)))], (48218 ^ _778495) ^ [_1750904, _1750906, _1750908, _1750910] : [48220 ^ _778495 : [(48223 ^ _778495) ^ [] : [hBOOL(hAPP(_1750910, 48219 ^ [_1750904, _1750906, _1750908, _1750910]))], (48221 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750904), 48219 ^ [_1750904, _1750906, _1750908, _1750910]), hAPP(c_List_Oset(_1750904), c_List_Oreplicate(_1750904, _1750906, _1750908)))))]], -(hBOOL(hAPP(_1750910, _1750908))), -(_1750906 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22164 ^ _778495) ^ [_1174985, _1174987] : [class_Groups_Oordered__ab__group__add(_1174985), 22167 ^ _778495 : [(22174 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174985), _1174987), c_Groups_Ozero__class_Ozero(_1174985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174985), c_Groups_Ozero__class_Ozero(_1174985)), hAPP(c_Groups_Ouminus__class_Ouminus(_1174985), _1174987))))], (22168 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174985), c_Groups_Ozero__class_Ozero(_1174985)), hAPP(c_Groups_Ouminus__class_Ouminus(_1174985), _1174987))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174985), _1174987), c_Groups_Ozero__class_Ozero(_1174985))))]]], (23879 ^ _778495) ^ [_1205909, _1205911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1205911)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205909), _1205911)), _1205909)))], (33022 ^ _778495) ^ [_1387617, _1387619, _1387621, _1387623] : [class_Orderings_Oorder(_1387617), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1387617, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1387617, _1387619, _1387621)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1387617, _1387621, _1387623)) = c_Orderings_Obot__class_Obot(tc_fun(_1387617, tc_HOL_Obool)))], (34032 ^ _778495) ^ [_1412337, _1412339, _1412341, _1412343, _1412345] : [class_Orderings_Olinorder(_1412337), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412337, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1412337, _1412339), _1412341)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1412337, _1412343), _1412345)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1412337, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1412337), _1412339), _1412343)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1412337), _1412341), _1412345)))], (39542 ^ _778495) ^ [_1548121, _1548123, _1548125, _1548127, _1548129] : [class_Groups_Ocomm__monoid__mult(_1548121), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548123), _1548125)), c_Fun_Oinj__on(_1548123, _1548123, _1548127, _1548125), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1548123, _1548121), _1548129), hAPP(c_Set_Oimage(_1548123, _1548123, _1548127), _1548125)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1548123, _1548121), hAPP(c_Fun_Ocomp(_1548123, _1548121, _1548123, _1548129), _1548127)), _1548125))], (5679 ^ _778495) ^ [_868157, _868159, _868161, _868163] : [c_Hoare__Mirabelle_Ohoare__derivs(_868157, _868159, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_868157)), _868161), _868163)), 5682 ^ _778495 : [(5685 ^ _778495) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_868157, _868159, _868163))], (5683 ^ _778495) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_868157, _868159, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_868157)), _868161), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_868157), tc_HOL_Obool)))))]]], (40106 ^ _778495) ^ [_1561102, _1561104, _1561106, _1561108, _1561110, _1561112, _1561114] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1561102, _1561104, _1561106, _1561108), _1561110), _1561112), _1561114) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1561104, _1561106, _1561108), _1561112), hAPP(_1561110, _1561114)))], (49670 ^ _778495) ^ [_1782237, _1782239, _1782241, _1782243] : [hAPP(c_Set_Oimage(_1782237, _1782239, _1782241), c_Orderings_Otop__class_Otop(tc_fun(_1782237, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782239, tc_HOL_Obool)), -(hAPP(_1782241, hAPP(c_Hilbert__Choice_Oinv__into(_1782237, _1782239, c_Orderings_Otop__class_Otop(tc_fun(_1782237, tc_HOL_Obool)), _1782241), _1782243)) = _1782243)], (43836 ^ _778495) ^ [_1655244, _1655246, _1655248] : [-(hAPP(c_List_Orotate(_1655244, hAPP(c_Nat_OSuc, _1655246)), _1655248) = hAPP(c_List_Orotate1(_1655244), hAPP(c_List_Orotate(_1655244, _1655246), _1655248)))], (46636 ^ _778495) ^ [_1716037, _1716039, _1716041] : [_1716041 = hAPP(hAPP(c_List_Olist_OCons(_1716037), _1716039), c_List_Olist_ONil(_1716037)), -(hAPP(hAPP(c_List_Olist_OCons(_1716037), _1716039), c_List_Olist_ONil(_1716037)) = hAPP(c_List_Orev(_1716037), _1716041))], (49729 ^ _778495) ^ [_1783564, _1783566, _1783568, _1783570, _1783572] : [c_Fun_Oinj__on(_1783564, _1783566, _1783568, _1783570), hBOOL(hAPP(hAPP(c_member(_1783564), _1783572), _1783570)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1783564, _1783566, _1783570, _1783568), hAPP(_1783568, _1783572)) = _1783572)], (28171 ^ _778495) ^ [_1281155, _1281157, _1281159, _1281161] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1281155), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1281157, tc_Int_Oint), _1281159), _1281161)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1281157, _1281155), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1281155, _1281157), c_Int_Oring__1__class_Oof__int(_1281155)), _1281159)), _1281161)), class_Groups_Ocomm__monoid__mult(_1281155), class_Rings_Oring__1(_1281155)], (48188 ^ _778495) ^ [_1750321, _1750323, _1750325] : [-(c_List_Oreplicate(_1750321, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750321)), hAPP(c_List_Ofilter(_1750321, hAPP(c_fequal, _1750323)), _1750325)), _1750323) = hAPP(c_List_Ofilter(_1750321, hAPP(c_fequal, _1750323)), _1750325))], (6705 ^ _778495) ^ [_888212, _888214] : [_888214 = c_Orderings_Obot__class_Obot(tc_fun(_888212, tc_HOL_Obool)), 6708 ^ _778495 : [(6709 ^ _778495) ^ [_888292] : [hBOOL(hAPP(hAPP(c_member(_888212), _888292), _888214))]]], (21904 ^ _778495) ^ [_1170302, _1170304] : [class_Groups_Olinordered__ab__group__add(_1170302), 21907 ^ _778495 : [(21914 ^ _778495) ^ [] : [_1170304 = c_Groups_Ozero__class_Ozero(_1170302), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1170302), _1170304) = _1170304)], (21908 ^ _778495) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1170302), _1170304) = _1170304, -(_1170304 = c_Groups_Ozero__class_Ozero(_1170302))]]], (9402 ^ _778495) ^ [_938566, _938568] : [class_Lattices_Olattice(_938566), -(c_Big__Operators_Olattice__class_OSup__fin(_938566, hAPP(hAPP(c_Set_Oinsert(_938566), _938568), c_Orderings_Obot__class_Obot(tc_fun(_938566, tc_HOL_Obool)))) = _938568)], (27275 ^ _778495) ^ [_1265506, _1265508] : [class_Rings_Olinordered__idom(_1265506), -(c_Groups_Osgn__class_Osgn(_1265506, c_Groups_Osgn__class_Osgn(_1265506, _1265508)) = c_Groups_Osgn__class_Osgn(_1265506, _1265508))], (9646 ^ _778495) ^ [_943679, _943681, _943683] : [class_Lattices_Osemilattice__inf(_943679), hBOOL(hAPP(c_Finite__Set_Ofinite(_943679), _943681)), hBOOL(hAPP(hAPP(c_member(_943679), _943683), _943681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943679), hAPP(c_Finite__Set_Ofold1(_943679, c_Lattices_Osemilattice__inf__class_Oinf(_943679)), _943681)), _943683)))], (26174 ^ _778495) ^ [_1246538, _1246540, _1246542] : [class_Rings_Olinordered__semidom(_1246538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246538), c_Groups_Ozero__class_Ozero(_1246538)), _1246540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246538), c_Groups_Ozero__class_Ozero(_1246538)), hAPP(hAPP(c_Power_Opower__class_Opower(_1246538), _1246540), _1246542))))], (17036 ^ _778495) ^ [_1082957, _1082959, _1082961, _1082963] : [class_Fields_Olinordered__field(_1082957), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082957), _1082959), _1082961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082957), c_Groups_Ozero__class_Ozero(_1082957)), _1082963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082957), c_Groups_Ozero__class_Ozero(_1082957)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082957), _1082961), _1082959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082957), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1082957), _1082963), _1082961)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1082957), _1082963), _1082959))))], (13392 ^ _778495) ^ [_1016466, _1016468] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016466), _1016468) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016468), _1016466) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1016466 = _1016468)], (14552 ^ _778495) ^ [_1037050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037050), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1037050 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17682 ^ _778495) ^ [_1095678, _1095680] : [class_Orderings_Olinorder(_1095678), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095678), _1095680), _1095680) = _1095680)], (7006 ^ _778495) ^ [_893571, _893573, _893575] : [class_Lattices_Osemilattice__sup(_893571), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893571), _893573), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893571), _893573), _893575)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893571), _893573), _893575))], (23519 ^ _778495) ^ [_1199730, _1199732] : [23520 ^ _778495 : [(23521 ^ _778495) ^ [_1199779] : [_1199730 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1199732), _1199779)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199730, _1199732) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10125 ^ _778495) ^ [_953086, _953088] : [class_Groups_Omonoid__mult(_953086), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953086), _953088), c_Groups_Oone__class_Oone(_953086)) = _953088)], (51925 ^ _778495) ^ [_1826858, _1826860, _1826862, _1826864, _1826866] : [class_Rings_Ocomm__semiring__1(_1826858), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826858), _1826860), _1826862)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826858), _1826864), _1826866)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826858), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826858), _1826860), _1826864)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826858), _1826862), _1826866))))], (428 ^ _778495) ^ [_785027, _785029, _785031, _785033] : [-(c_Relation_Oirrefl(_785031, _785027)), c_Relation_Oirrefl(_785033, _785029), _785033 = _785031, _785029 = _785027], (33401 ^ _778495) ^ [_1398112, _1398114, _1398116, _1398118, _1398120] : [hBOOL(hAPP(hAPP(c_member(_1398112), _1398114), _1398116)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398118, tc_HOL_Obool)), hAPP(_1398120, _1398114)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398112, tc_fun(_1398118, tc_HOL_Obool)), _1398116), _1398120)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398112, tc_fun(_1398118, tc_HOL_Obool)), _1398116), _1398120))], (23254 ^ _778495) ^ [_1195024] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1195024) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6574 ^ _778495) ^ [_885444, _885446, _885448, _885450] : [-(hBOOL(hAPP(hAPP(c_member(_885444), _885446), _885448))), 6577 ^ _778495 : [(6584 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885444, tc_HOL_Obool)), _885448), _885450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885444, tc_HOL_Obool)), _885448), hAPP(hAPP(c_Set_Oinsert(_885444), _885446), _885450))))], (6578 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885444, tc_HOL_Obool)), _885448), hAPP(hAPP(c_Set_Oinsert(_885444), _885446), _885450))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885444, tc_HOL_Obool)), _885448), _885450)))]]], (41359 ^ _778495) ^ [_1593046, _1593048, _1593050, _1593052, _1593054] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593046), tc_List_Olist(_1593046))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593046), tc_List_Olist(_1593046)), _1593048), _1593050)), hAPP(c_List_Olexn(_1593046, _1593052), _1593054))), 41362 ^ _778495 : [(41365 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593046)), _1593050) = _1593054)], (41363 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593046)), _1593048) = _1593054)]]], (1178 ^ _778495) ^ [_796248, _796250] : [-(class_Rings_Olinordered__ring__strict(_796248)), _796250 = _796248, class_Rings_Olinordered__ring__strict(_796250)], (43117 ^ _778495) ^ [_1638606, _1638608, _1638610, _1638612, _1638614] : [-(hAPP(hAPP(c_List_Oappend(_1638606), _1638608), _1638610) = hAPP(hAPP(c_List_Oappend(_1638606), _1638612), _1638614)), 43118 ^ _778495 : [(43125 ^ _778495) ^ [_1638830] : [hAPP(hAPP(c_List_Oappend(_1638606), _1638608), _1638830) = _1638612, _1638610 = hAPP(hAPP(c_List_Oappend(_1638606), _1638830), _1638614)], (43119 ^ _778495) ^ [_1638718] : [_1638608 = hAPP(hAPP(c_List_Oappend(_1638606), _1638612), _1638718), hAPP(hAPP(c_List_Oappend(_1638606), _1638718), _1638610) = _1638614]]], (41433 ^ _778495) ^ [_1595670, _1595672, _1595674] : [-(c_List_Oset__Cons(_1595670, _1595672, _1595674) = hAPP(c_Set_OCollect(tc_List_Olist(_1595670)), hAPP(hAPP(c_COMBB(tc_fun(_1595670, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1595670)), c_HOL_OEx(_1595670)), hAPP(hAPP(c_COMBB(tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool)), tc_fun(_1595670, tc_HOL_Obool), tc_List_Olist(_1595670)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), tc_HOL_Obool, _1595670), c_HOL_OEx(tc_List_Olist(_1595670)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595670), tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool)), tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595670, tc_fun(tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool))), tc_fun(tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool)), tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool))), tc_List_Olist(_1595670)), c_COMBS(_1595670, tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1595670, tc_fun(tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool))), tc_List_Olist(_1595670)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595670), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool)), _1595670), c_COMBS(tc_List_Olist(_1595670), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool)), tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1595670)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595670), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1595670), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1595670)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595670), tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_List_Olist(_1595670))), tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1595670), tc_List_Olist(_1595670)), tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool)), tc_fun(tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_List_Olist(_1595670))), tc_fun(_1595670, tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool))), tc_List_Olist(_1595670)), c_COMBB(tc_fun(tc_List_Olist(_1595670), tc_List_Olist(_1595670)), tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), _1595670)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1595670), tc_List_Olist(_1595670)), tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool)), tc_List_Olist(_1595670)), c_COMBB(tc_List_Olist(_1595670), tc_HOL_Obool, tc_List_Olist(_1595670))), c_fequal))), c_List_Olist_OCons(_1595670)))))), hAPP(hAPP(c_COMBC(_1595670, tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool)), _1595670), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1595670))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1595670), c_fconj), hAPP(hAPP(c_COMBC(_1595670, tc_fun(_1595670, tc_HOL_Obool), tc_HOL_Obool), c_member(_1595670)), _1595672)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595670), tc_fun(tc_List_Olist(_1595670), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1595670))), _1595674)))))))], (45492 ^ _778495) ^ [_1691275, _1691277, _1691279, _1691281, _1691283] : [c_Fun_Oinj__on(_1691275, _1691277, _1691279, c_Orderings_Otop__class_Otop(tc_fun(_1691275, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1691275, _1691277), _1691279), hAPP(c_List_OremoveAll(_1691275, _1691281), _1691283)) = hAPP(c_List_OremoveAll(_1691277, hAPP(_1691279, _1691281)), hAPP(hAPP(c_List_Omap(_1691275, _1691277), _1691279), _1691283)))], (51647 ^ _778495) ^ [_1821533, _1821535] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821533, _1821535), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821533), _1821535))], (19242 ^ _778495) ^ [_1124285, _1124287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124285), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124287), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124285), _1124287)))], (47040 ^ _778495) ^ [_1724564, _1724566, _1724568] : [-(c_List_OdropWhile(_1724564, _1724566, _1724568) = c_List_Olist_ONil(_1724564)), hBOOL(hAPP(_1724566, hAPP(c_List_Ohd(_1724564), c_List_OdropWhile(_1724564, _1724566, _1724568))))], (1428 ^ _778495) ^ [_799373, _799375] : [-(class_Lattices_Osemilattice__sup(_799373)), _799375 = _799373, class_Lattices_Osemilattice__sup(_799375)], (51121 ^ _778495) ^ [_1812644, _1812646, _1812648] : [_1812644 = _1812646, 51132 ^ _778495 : [(51135 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812648), _1812644))], (51133 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812644), _1812648)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812646), _1812648)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812648), _1812646)))], (47420 ^ _778495) ^ [_1733275, _1733277, _1733279, _1733281, _1733283] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733275)), _1733277) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733279)), _1733281), 47426 ^ _778495 : [(47429 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1733283, hAPP(hAPP(c_List_Onth(_1733275), _1733277), 47425 ^ [_1733275, _1733277, _1733279, _1733281, _1733283])), hAPP(hAPP(c_List_Onth(_1733279), _1733281), 47425 ^ [_1733275, _1733277, _1733279, _1733281, _1733283])))], (47427 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47425 ^ [_1733275, _1733277, _1733279, _1733281, _1733283]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733275)), _1733277))))]], -(c_List_Olist__all2(_1733275, _1733279, _1733283, _1733277, _1733281))], (29400 ^ _778495) ^ [_1313270, _1313272] : [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), _1313270), _1313272))), 29403 ^ _778495 : [(29412 ^ _778495) ^ [] : [-(c_Divides_OnegDivAlg(_1313270, _1313272) = hAPP(c_Divides_Oadjust(_1313272), c_Divides_OnegDivAlg(_1313270, 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)))), _1313272)))), -(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), _1313270), _1313272)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1313272), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29404 ^ _778495) ^ [] : [29405 ^ _778495 : [(29408 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1313272), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29406 ^ _778495) ^ [] : [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), _1313270), _1313272)))]], -(c_Divides_OnegDivAlg(_1313270, _1313272) = 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), _1313270), _1313272)))]]], (42493 ^ _778495) ^ [_1625302, _1625304] : [hBOOL(hAPP(c_List_Odistinct(_1625302), _1625304)), -(hAPP(c_Finite__Set_Ocard(_1625302), hAPP(c_List_Oset(_1625302), _1625304)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625302)), _1625304))], (34807 ^ _778495) ^ [_1429566, _1429568, _1429570] : [class_Orderings_Olinorder(_1429566), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1429566), _1429568), _1429570)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1429566, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1429566, _1429568, _1429570)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1429566), _1429570)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1429566), _1429568))], (29928 ^ _778495) ^ [_1323050, _1323052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1323050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1323052)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323050, _1323052) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1323050, _1323052)))], (4358 ^ _778495) ^ [_844703, _844705, _844707, _844709] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_844709, _844705) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_844707, _844703)), _844709 = _844707, _844705 = _844703], (28383 ^ _778495) ^ [_1289807, _1289809, _1289811] : [class_Groups_Ocomm__monoid__add(_1289807), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289809, _1289807), hAPP(c_COMBK(_1289807, _1289809), c_Groups_Ozero__class_Ozero(_1289807))), _1289811) = c_Groups_Ozero__class_Ozero(_1289807))], (38318 ^ _778495) ^ [_1515225, _1515227] : [c_Relation_Orefl__on(_1515225, c_Orderings_Otop__class_Otop(tc_fun(_1515225, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1515225, _1515225)), hAPP(c_Product__Type_Oprod_Oprod__case(_1515225, _1515225, tc_HOL_Obool), _1515227))), -(c_Predicate_Oreflp(_1515225, _1515227))], (12851 ^ _778495) ^ [_1007063, _1007065, _1007067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1007063, tc_HOL_Obool)), _1007065), _1007067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1007063, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1007063, _1007065)), c_Predicate_OPowp(_1007063, _1007067))))], (19524 ^ _778495) ^ [_1128991, _1128993, _1128995] : [class_Orderings_Olinorder(_1128991), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128991), _1128993)), 19531 ^ _778495 : [(19538 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1128991, tc_HOL_Obool)), _1128993), hAPP(hAPP(c_Set_Oinsert(_1128991), _1128995), c_Orderings_Obot__class_Obot(tc_fun(_1128991, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1128991, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1128991, c_Orderings_Oord__class_Omin(_1128991), hAPP(hAPP(c_Set_Oinsert(_1128991), _1128995), _1128993)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1128991), _1128995), c_Big__Operators_Olattice_OInf__fin(_1128991, c_Orderings_Oord__class_Omin(_1128991), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1128991, tc_HOL_Obool)), _1128993), hAPP(hAPP(c_Set_Oinsert(_1128991), _1128995), c_Orderings_Obot__class_Obot(tc_fun(_1128991, tc_HOL_Obool)))))))], (19532 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1128991, tc_HOL_Obool)), _1128993), hAPP(hAPP(c_Set_Oinsert(_1128991), _1128995), c_Orderings_Obot__class_Obot(tc_fun(_1128991, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1128991, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1128991, c_Orderings_Oord__class_Omin(_1128991), hAPP(hAPP(c_Set_Oinsert(_1128991), _1128995), _1128993)) = _1128995)]]], (43588 ^ _778495) ^ [_1649864, _1649866, _1649868, _1649870] : [hAPP(hAPP(c_List_Oappend(_1649864), _1649866), _1649868) = _1649870, 43591 ^ _778495 : [(43594 ^ _778495) ^ [] : [-(_1649868 = hAPP(hAPP(c_List_Odrop(_1649864), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649864)), _1649866)), _1649870))], (43592 ^ _778495) ^ [] : [-(_1649866 = hAPP(hAPP(c_List_Otake(_1649864), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649864)), _1649866)), _1649870))]]], (21198 ^ _778495) ^ [_1158234, _1158236] : [class_Groups_Oordered__ab__group__add__abs(_1158234), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158234), c_Groups_Ozero__class_Ozero(_1158234)), hAPP(c_Groups_Oabs__class_Oabs(_1158234), _1158236))))], (5536 ^ _778495) ^ [_863198, _863200, _863202, _863204] : [-(tc_prod(_863204, _863200) = tc_prod(_863202, _863198)), _863204 = _863202, _863200 = _863198], (20512 ^ _778495) ^ [_1146506, _1146508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146506)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146508))), 20515 ^ _778495 : [(20516 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1146506), _1146508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1146508)))], (20522 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1146506), _1146508)))]]], (25962 ^ _778495) ^ [_1242723] : [_1242723 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1242723) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4134 ^ _778495) ^ [_841185, _841187, _841189, _841191, _841193, _841195] : [-(c_Predicate_Oconversep(_841195, _841191, _841187) = c_Predicate_Oconversep(_841193, _841189, _841185)), _841195 = _841193, _841191 = _841189, _841187 = _841185], (40746 ^ _778495) ^ [_1576908, _1576910] : [-(hAPP(c_Relation_Oconverse(_1576908, _1576908), c_Relation_OId__on(_1576908, _1576910)) = c_Relation_OId__on(_1576908, _1576910))], (10941 ^ _778495) ^ [_966824, _966826] : [10942 ^ _778495 : [(10945 ^ _778495) ^ [] : [_966824 = _966826], (10943 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _966824), _966826))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966824), _966826)))], (25240 ^ _778495) ^ [_1229557, _1229559] : [_1229557 = hAPP(c_Int_Onat, _1229559), 25243 ^ _778495 : [(25250 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229559))), -(_1229557 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25244 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229559)), -(_1229559 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229557))]]], (44141 ^ _778495) ^ [_1661753, _1661755, _1661757, _1661759, _1661761] : [class_Orderings_Olinorder(_1661753), hBOOL(hAPP(c_List_Odistinct(_1661755), _1661757)), -(hBOOL(hAPP(c_List_Odistinct(_1661755), c_List_Olinorder__class_Oinsort__insert__key(_1661755, _1661753, _1661759, _1661761, _1661757))))], (45919 ^ _778495) ^ [_1702517, _1702519] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702517), _1702519))), -(c_List_Oupt(_1702517, _1702519) = c_List_Olist_ONil(tc_Nat_Onat))], (45812 ^ _778495) ^ [_1699133, _1699135] : [45814 ^ _778495 : [(45817 ^ _778495) ^ [] : [45813 ^ [_1699133, _1699135] = c_List_Olist_ONil(_1699133)], (45815 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699133)), 45813 ^ [_1699133, _1699135]), hAPP(c_List_Oset(tc_List_Olist(_1699133)), _1699135))))]], -(c_List_Otranspose(_1699133, _1699135) = c_List_Olist_ONil(tc_List_Olist(_1699133)))], (37644 ^ _778495) ^ [_1493480, _1493482, _1493484, _1493486, _1493488] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1493480, _1493482)), _1493484), hAPP(hAPP(c_Product__Type_OSigma(_1493480, _1493482), _1493486), _1493488))), 37648 ^ _778495 : [(37654 ^ _778495) ^ [] : [-(_1493484 = hAPP(hAPP(c_Product__Type_OPair(_1493480, _1493482), 37647 ^ [_1493480, _1493482, _1493484, _1493486, _1493488]), 37650 ^ [_1493480, _1493482, _1493484, _1493486, _1493488]))], (37652 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493482), 37650 ^ [_1493480, _1493482, _1493484, _1493486, _1493488]), hAPP(_1493488, 37647 ^ [_1493480, _1493482, _1493484, _1493486, _1493488]))))], (37649 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493480), 37647 ^ [_1493480, _1493482, _1493484, _1493486, _1493488]), _1493486)))]]], (46476 ^ _778495) ^ [_1712546, _1712548] : [class_Orderings_Olinorder(_1712546), 46479 ^ _778495 : [(46480 ^ _778495) ^ [] : [c_List_Olinorder__class_Osorted(_1712546, _1712548), 46483 ^ _778495 : [(46484 ^ _778495) ^ [_1712717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712717), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712546)), _1712548))), 46487 ^ _778495 : [(46488 ^ _778495) ^ [_1712834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712834), _1712717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712546), hAPP(hAPP(c_List_Onth(_1712546), _1712548), _1712834)), hAPP(hAPP(c_List_Onth(_1712546), _1712548), _1712717))))]]]]], (46494 ^ _778495) ^ [] : [46496 ^ _778495 : [(46502 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712546), hAPP(hAPP(c_List_Onth(_1712546), _1712548), 46498 ^ [_1712546, _1712548])), hAPP(hAPP(c_List_Onth(_1712546), _1712548), 46495 ^ [_1712546, _1712548])))], (46500 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46498 ^ [_1712546, _1712548]), 46495 ^ [_1712546, _1712548])))], (46497 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46495 ^ [_1712546, _1712548]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712546)), _1712548))))]], -(c_List_Olinorder__class_Osorted(_1712546, _1712548))]]], (45855 ^ _778495) ^ [_1700951, _1700953, _1700955, _1700957, _1700959, _1700961] : [-(c_List_Ofoldr(_1700951, _1700953, _1700955, hAPP(hAPP(c_List_Olist_OCons(_1700951), _1700957), _1700959), _1700961) = hAPP(hAPP(_1700955, _1700957), c_List_Ofoldr(_1700951, _1700953, _1700955, _1700959, _1700961)))], (27799 ^ _778495) ^ [_1274619, _1274621, _1274623, _1274625] : [hBOOL(hAPP(hAPP(c_member(_1274619), _1274621), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1274619, tc_HOL_Obool), _1274623))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1274619, tc_HOL_Obool)), _1274625), _1274623)), -(hBOOL(hAPP(hAPP(c_member(_1274619), _1274621), _1274625)))], (35374 ^ _778495) ^ [_1439411, _1439413, _1439415] : [class_Orderings_Olinorder(_1439411), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439411), _1439413), _1439415)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439411, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1439411, _1439413, _1439415)), hAPP(c_SetInterval_Oord__class_OatLeast(_1439411), _1439415)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439411), _1439413))], (45183 ^ _778495) ^ [_1684782, _1684784, _1684786, _1684788] : [_1684788 = c_List_Olist_ONil(_1684782), -(c_List_Olist__all2(_1684782, _1684784, _1684786, _1684788, c_List_Olist_ONil(_1684784)))], (678 ^ _778495) ^ [_788770, _788772, _788774, _788776] : [-(c_FunDef_Ois__measure(_788774, _788770)), c_FunDef_Ois__measure(_788776, _788772), _788776 = _788774, _788772 = _788770], (37328 ^ _778495) ^ [_1484312, _1484314, _1484316, _1484318] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1484312, _1484314), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484312, tc_HOL_Obool), _1484316)), _1484318) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1484312, tc_HOL_Obool), tc_fun(tc_prod(_1484312, _1484314), tc_HOL_Obool)), _1484316), hAPP(hAPP(c_COMBC(tc_fun(_1484312, tc_HOL_Obool), tc_fun(_1484312, tc_fun(_1484314, tc_HOL_Obool)), tc_fun(tc_prod(_1484312, _1484314), tc_HOL_Obool)), c_Product__Type_OSigma(_1484312, _1484314)), _1484318)))], (38907 ^ _778495) ^ [_1531943, _1531945, _1531947, _1531949, _1531951] : [-(hAPP(c_Relation_ODomain(_1531943, _1531945), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1531943, _1531945)), hAPP(hAPP(c_Product__Type_OPair(_1531943, _1531945), _1531947), _1531949)), _1531951)) = hAPP(hAPP(c_Set_Oinsert(_1531943), _1531947), hAPP(c_Relation_ODomain(_1531943, _1531945), _1531951)))], (3272 ^ _778495) ^ [_827336, _827338, _827340, _827342] : [-(c_List_Olistsp(_827342, _827338) = c_List_Olistsp(_827340, _827336)), _827342 = _827340, _827338 = _827336], (10897 ^ _778495) ^ [_966126, _966128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966126)), hAPP(c_Nat_OSuc, _966128))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966126), _966128)))], (384 ^ _778495) ^ [_784321, _784323, _784325, _784327, _784329, _784331, _784333, _784335] : [-(c_Finite__Set_Ofolding(_784333, _784329, _784325, _784321)), c_Finite__Set_Ofolding(_784335, _784331, _784327, _784323), _784335 = _784333, _784331 = _784329, _784327 = _784325, _784323 = _784321], (27459 ^ _778495) ^ [_1268327, _1268329, _1268331, _1268333] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1268327, _1268329, _1268331, c_Code__Numeral_OSuc__code__numeral(_1268333)) = hAPP(_1268331, _1268333))], (2218 ^ _778495) ^ [_810931, _810933, _810935, _810937] : [-(c_Random_Oinc__shift(_810937, _810933) = c_Random_Oinc__shift(_810935, _810931)), _810937 = _810935, _810933 = _810931], (8134 ^ _778495) ^ [_912472, _912474, _912476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_912472, tc_HOL_Obool)), _912474), _912476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912472, tc_HOL_Obool)), _912474), _912476)))], (49045 ^ _778495) ^ [_1770295, _1770297] : [-(c_Relation_Otrans(_1770295, c_Transitive__Closure_Ortrancl(_1770295, _1770297)))], (50122 ^ _778495) ^ [_1791988, _1791990, _1791992] : [c_Fun_Obij__betw(_1791988, _1791990, _1791992, c_Orderings_Otop__class_Otop(tc_fun(_1791988, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1791990, tc_HOL_Obool))), 50125 ^ _778495 : [(50128 ^ _778495) ^ [] : [-(hAPP(c_Set_Oimage(_1791988, _1791990, _1791992), c_Orderings_Otop__class_Otop(tc_fun(_1791988, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1791990, tc_HOL_Obool)))], (50126 ^ _778495) ^ [] : [-(c_Fun_Oinj__on(_1791988, _1791990, _1791992, c_Orderings_Otop__class_Otop(tc_fun(_1791988, tc_HOL_Obool))))]]], (37769 ^ _778495) ^ [_1497098] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1497098, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1497098), hAPP(c_COMBK(tc_HOL_Obool, _1497098), c_fTrue)))], (43102 ^ _778495) ^ [_1638275, _1638277, _1638279, _1638281, _1638283] : [hAPP(hAPP(c_List_Oappend(_1638275), _1638277), _1638279) = hAPP(hAPP(c_List_Oappend(_1638275), _1638281), _1638283), 43108 ^ _778495 : [(43111 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1638275), 43105 ^ [_1638275, _1638277, _1638279, _1638281, _1638283]), _1638279) = _1638283)], (43109 ^ _778495) ^ [] : [-(_1638277 = hAPP(hAPP(c_List_Oappend(_1638275), _1638281), 43105 ^ [_1638275, _1638277, _1638279, _1638281, _1638283]))]], 43112 ^ _778495 : [(43115 ^ _778495) ^ [] : [-(_1638279 = hAPP(hAPP(c_List_Oappend(_1638275), 43105 ^ [_1638275, _1638277, _1638279, _1638281, _1638283]), _1638283))], (43113 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1638275), _1638277), 43105 ^ [_1638275, _1638277, _1638279, _1638281, _1638283]) = _1638281)]]], (24934 ^ _778495) ^ [_1224553, _1224555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1224553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1224555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1224555), _1224553)), _1224555)))], (45153 ^ _778495) ^ [_1684238, _1684240, _1684242, _1684244, _1684246, _1684248] : [c_List_Olist__all2(_1684238, _1684240, _1684242, _1684244, _1684246), -(c_List_Olist__all2(_1684238, _1684240, _1684242, hAPP(hAPP(c_List_Otake(_1684238), _1684248), _1684244), hAPP(hAPP(c_List_Otake(_1684240), _1684248), _1684246)))], (36548 ^ _778495) ^ [_1466419, _1466421, _1466423, _1466425, _1466427] : [c_Fun_Oinj__on(_1466419, _1466421, _1466423, c_Orderings_Otop__class_Otop(tc_fun(_1466419, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1466419, _1466421, _1466423), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466419, tc_HOL_Obool)), _1466425), _1466427)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466421, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466419, _1466421, _1466423), _1466425)), hAPP(c_Set_Oimage(_1466419, _1466421, _1466423), _1466427)))], (30393 ^ _778495) ^ [_1332639, _1332641, _1332643, _1332645] : [hBOOL(hAPP(hAPP(c_member(_1332639), _1332641), c_SetInterval_Oord_OatLeast(_1332639, _1332643, _1332645))), -(hBOOL(hAPP(hAPP(_1332643, _1332645), _1332641)))], (38083 ^ _778495) ^ [_1505367, _1505369, _1505371] : [class_Orderings_Olinorder(_1505367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505367), _1505369)), -(_1505369 = c_Orderings_Obot__class_Obot(tc_fun(_1505367, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505367), _1505371)), -(_1505371 = c_Orderings_Obot__class_Obot(tc_fun(_1505367, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1505367), c_Big__Operators_Olattice_OSup__fin(_1505367, c_Orderings_Oord__class_Omax(_1505367), _1505369)), c_Big__Operators_Olattice_OSup__fin(_1505367, c_Orderings_Oord__class_Omax(_1505367), _1505371)) = c_Big__Operators_Olattice_OSup__fin(_1505367, c_Orderings_Oord__class_Omax(_1505367), hAPP(c_Set_OCollect(_1505367), hAPP(hAPP(c_COMBB(tc_fun(_1505367, tc_HOL_Obool), tc_HOL_Obool, _1505367), c_HOL_OEx(_1505367)), hAPP(hAPP(c_COMBB(tc_fun(_1505367, tc_fun(_1505367, tc_HOL_Obool)), tc_fun(_1505367, tc_HOL_Obool), _1505367), hAPP(c_COMBB(tc_fun(_1505367, tc_HOL_Obool), tc_HOL_Obool, _1505367), c_HOL_OEx(_1505367))), hAPP(hAPP(c_COMBC(_1505367, tc_fun(_1505367, tc_fun(_1505367, tc_HOL_Obool)), tc_fun(_1505367, tc_fun(_1505367, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1505367, tc_fun(tc_fun(_1505367, tc_HOL_Obool), tc_fun(_1505367, tc_HOL_Obool))), tc_fun(tc_fun(_1505367, tc_fun(_1505367, tc_HOL_Obool)), tc_fun(_1505367, tc_fun(_1505367, tc_HOL_Obool))), _1505367), c_COMBS(_1505367, tc_fun(_1505367, tc_HOL_Obool), tc_fun(_1505367, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1505367, tc_fun(_1505367, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1505367, tc_fun(tc_fun(_1505367, tc_HOL_Obool), tc_fun(_1505367, tc_HOL_Obool))), _1505367), hAPP(c_COMBB(tc_fun(_1505367, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1505367, tc_HOL_Obool), tc_fun(_1505367, tc_HOL_Obool)), _1505367), c_COMBS(_1505367, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1505367, tc_fun(_1505367, tc_HOL_Obool)), tc_fun(_1505367, tc_fun(_1505367, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1505367), hAPP(c_COMBB(tc_fun(_1505367, tc_HOL_Obool), tc_fun(_1505367, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1505367), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1505367), c_fconj))), hAPP(hAPP(c_COMBC(_1505367, tc_fun(_1505367, tc_fun(_1505367, _1505367)), tc_fun(_1505367, tc_fun(_1505367, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1505367, _1505367), tc_fun(_1505367, tc_HOL_Obool)), tc_fun(tc_fun(_1505367, tc_fun(_1505367, _1505367)), tc_fun(_1505367, tc_fun(_1505367, tc_HOL_Obool))), _1505367), c_COMBB(tc_fun(_1505367, _1505367), tc_fun(_1505367, tc_HOL_Obool), _1505367)), hAPP(hAPP(c_COMBB(tc_fun(_1505367, tc_HOL_Obool), tc_fun(tc_fun(_1505367, _1505367), tc_fun(_1505367, tc_HOL_Obool)), _1505367), c_COMBB(_1505367, tc_HOL_Obool, _1505367)), c_fequal))), c_Orderings_Oord__class_Omin(_1505367)))))), hAPP(hAPP(c_COMBC(_1505367, tc_fun(_1505367, tc_HOL_Obool), tc_fun(_1505367, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1505367, tc_HOL_Obool), tc_fun(_1505367, tc_HOL_Obool)), _1505367), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1505367)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1505367), c_fconj), hAPP(hAPP(c_COMBC(_1505367, tc_fun(_1505367, tc_HOL_Obool), tc_HOL_Obool), c_member(_1505367)), _1505369)))), hAPP(hAPP(c_COMBC(_1505367, tc_fun(_1505367, tc_HOL_Obool), tc_HOL_Obool), c_member(_1505367)), _1505371))))))))], (27013 ^ _778495) ^ [_1261161, _1261163, _1261165] : [class_Int_Oring__char__0(_1261161), 27016 ^ _778495 : [(27023 ^ _778495) ^ [] : [_1261163 = _1261165, -(hAPP(c_Int_Oring__1__class_Oof__int(_1261161), _1261163) = hAPP(c_Int_Oring__1__class_Oof__int(_1261161), _1261165))], (27017 ^ _778495) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1261161), _1261163) = hAPP(c_Int_Oring__1__class_Oof__int(_1261161), _1261165), -(_1261163 = _1261165)]]], (1738 ^ _778495) ^ [_803248, _803250] : [-(class_Groups_Osemigroup__add(_803248)), _803250 = _803248, class_Groups_Osemigroup__add(_803250)], (48080 ^ _778495) ^ [_1747430, _1747432, _1747434] : [-(hAPP(c_New__DSequence_Oneg__single(_1747430, _1747432), _1747434) = c_Lazy__Sequence_Ohb__single(_1747430, _1747432))], (37743 ^ _778495) ^ [_1496363, _1496365, _1496367] : [hBOOL(hAPP(_1496363, _1496365)), -(hBOOL(hAPP(hAPP(c_member(_1496367), _1496365), hAPP(c_Set_OCollect(_1496367), _1496363))))], (21144 ^ _778495) ^ [_1157327, _1157329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1157327)), c_Int_OBit1(_1157329))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157327), _1157329)))], (52433 ^ _778495) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (20224 ^ _778495) ^ [_1141808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1141808)), -(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), _1141808))))], (43269 ^ _778495) ^ [_1641711, _1641713, _1641715] : [-(c_List_Olist_ONil(_1641711) = hAPP(hAPP(c_List_Oappend(_1641711), _1641713), _1641715)), _1641713 = c_List_Olist_ONil(_1641711), _1641715 = c_List_Olist_ONil(_1641711)], (18382 ^ _778495) ^ [_1108332, _1108334, _1108336, _1108338] : [class_Fields_Olinordered__field__inverse__zero(_1108332), class_Int_Onumber(_1108332), 18389 ^ _778495 : [(18390 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), hAPP(c_Int_Onumber__class_Onumber__of(_1108332), _1108334)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108332), _1108336), _1108338))), 18393 ^ _778495 : [(18400 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), c_Groups_Ozero__class_Ozero(_1108332)), _1108338))), 18403 ^ _778495 : [(18410 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), _1108338), c_Groups_Ozero__class_Ozero(_1108332)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), hAPP(c_Int_Onumber__class_Onumber__of(_1108332), _1108334)), c_Groups_Ozero__class_Ozero(_1108332))))], (18404 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), _1108338), c_Groups_Ozero__class_Ozero(_1108332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), _1108336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108332), hAPP(c_Int_Onumber__class_Onumber__of(_1108332), _1108334)), _1108338))))]]], (18394 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), c_Groups_Ozero__class_Ozero(_1108332)), _1108338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108332), hAPP(c_Int_Onumber__class_Onumber__of(_1108332), _1108334)), _1108338)), _1108336)))]]], (18416 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), hAPP(c_Int_Onumber__class_Onumber__of(_1108332), _1108334)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108332), _1108336), _1108338)))), 18419 ^ _778495 : [(18422 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108332), hAPP(c_Int_Onumber__class_Onumber__of(_1108332), _1108334)), _1108338)), _1108336))], (18420 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), c_Groups_Ozero__class_Ozero(_1108332)), _1108338)))]], 18423 ^ _778495 : [(18426 ^ _778495) ^ [] : [18427 ^ _778495 : [(18430 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), _1108336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108332), hAPP(c_Int_Onumber__class_Onumber__of(_1108332), _1108334)), _1108338)))], (18428 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), _1108338), c_Groups_Ozero__class_Ozero(_1108332))))]], 18431 ^ _778495 : [(18434 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), hAPP(c_Int_Onumber__class_Onumber__of(_1108332), _1108334)), c_Groups_Ozero__class_Ozero(_1108332)))], (18432 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), _1108338), c_Groups_Ozero__class_Ozero(_1108332)))]]], (18424 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108332), c_Groups_Ozero__class_Ozero(_1108332)), _1108338))]]]]], (19048 ^ _778495) ^ [_1121020, _1121022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121020)), 19051 ^ _778495 : [(19060 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121020), _1121022) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1121020 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1121022 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (19052 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121020), _1121022) = c_Groups_Oone__class_Oone(tc_Int_Oint), 19055 ^ _778495 : [(19058 ^ _778495) ^ [] : [-(_1121022 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (19056 ^ _778495) ^ [] : [-(_1121020 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (52597 ^ _778495) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (40816 ^ _778495) ^ [_1578845, _1578847, _1578849, _1578851] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578845, _1578845)), hAPP(hAPP(c_Product__Type_OPair(_1578845, _1578845), _1578847), _1578849)), hAPP(c_Relation_Oconverse(_1578845, _1578845), c_Transitive__Closure_Otrancl(_1578845, _1578851)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578845, _1578845)), hAPP(hAPP(c_Product__Type_OPair(_1578845, _1578845), _1578847), _1578849)), c_Transitive__Closure_Otrancl(_1578845, hAPP(c_Relation_Oconverse(_1578845, _1578845), _1578851)))))], (23264 ^ _778495) ^ [_1195247, _1195249, _1195251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195247, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1195247, tc_HOL_Obool)), _1195249)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1195247, tc_HOL_Obool)), _1195251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195247, tc_HOL_Obool)), _1195251), _1195249)))], (23961 ^ _778495) ^ [_1207403, _1207405] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207403, _1207405) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207403, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1207405)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207403, _1207405)), _1207405))], (11216 ^ _778495) ^ [_971758, _971760, _971762, _971764, _971766] : [class_Groups_Ocomm__monoid__mult(_971758), hBOOL(hAPP(c_Finite__Set_Ofinite(_971760), _971762)), hBOOL(hAPP(c_Finite__Set_Ofinite(_971760), _971764)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971760, tc_HOL_Obool)), _971762), _971764) = c_Orderings_Obot__class_Obot(tc_fun(_971760, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_971758, _971760, c_Groups_Otimes__class_Otimes(_971758)), _971766), c_Groups_Oone__class_Oone(_971758)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971760, tc_HOL_Obool)), _971762), _971764)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971758), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_971758, _971760, c_Groups_Otimes__class_Otimes(_971758)), _971766), c_Groups_Oone__class_Oone(_971758)), _971762)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_971758, _971760, c_Groups_Otimes__class_Otimes(_971758)), _971766), c_Groups_Oone__class_Oone(_971758)), _971764)))], (47996 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17074 ^ _778495) ^ [_1083697, _1083699, _1083701, _1083703] : [class_Fields_Olinordered__field(_1083697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083697), _1083699), c_Groups_Ozero__class_Ozero(_1083697))), 17081 ^ _778495 : [(17088 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083697), _1083703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083697), _1083701), _1083699))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083697), _1083701), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1083697), _1083703), _1083699))))], (17082 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083697), _1083701), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1083697), _1083703), _1083699))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083697), _1083703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083697), _1083701), _1083699))))]]], (28443 ^ _778495) ^ [_1292389, _1292391, _1292393, _1292395, _1292397] : [class_Groups_Ocomm__monoid__mult(_1292389), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292391), _1292393)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292391, _1292389), hAPP(hAPP(c_COMBS(_1292391, _1292389, _1292389), hAPP(hAPP(c_COMBB(_1292389, tc_fun(_1292389, _1292389), _1292391), c_Groups_Otimes__class_Otimes(_1292389)), _1292395)), _1292397)), _1292393) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292389), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292391, _1292389), _1292395), _1292393)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292391, _1292389), _1292397), _1292393)))], (6456 ^ _778495) ^ [_883038, _883040, _883042, _883044] : [class_Orderings_Oorder(_883038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883038), _883040), _883042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883038), _883044), _883040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883038), _883044), _883042)))], (12997 ^ _778495) ^ [_1010361] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1010361)))], (3062 ^ _778495) ^ [_824065, _824067, _824069, _824071, _824073, _824075, _824077, _824079] : [-(c_Nat_Onat_Onat__case(_824079, _824075, _824071, _824067) = c_Nat_Onat_Onat__case(_824077, _824073, _824069, _824065)), _824079 = _824077, _824075 = _824073, _824071 = _824069, _824067 = _824065], (22692 ^ _778495) ^ [_1184122] : [-(c_Int_Osucc(c_Int_OBit0(_1184122)) = c_Int_OBit1(_1184122))], (48755 ^ _778495) ^ [_1762505, _1762507, _1762509] : [-(c_Random__Sequence_Oempty(_1762505, _1762507, _1762509) = 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(_1762505)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1762505)))], (18926 ^ _778495) ^ [_1118710, _1118712, _1118714, _1118716] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1118710, _1118712)), c_Nitpick_Opair__box_OPairBox(_1118710, _1118712, _1118714, _1118716)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7070 ^ _778495) ^ [_894969, _894971, _894973, _894975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894969, tc_HOL_Obool)), _894971), _894973)), hBOOL(hAPP(_894971, _894975)), -(hBOOL(hAPP(_894973, _894975)))], (20179 ^ _778495) ^ [] : [-(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))], (35198 ^ _778495) ^ [_1436000] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1436000)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1436000)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1436000), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (41716 ^ _778495) ^ [_1604891, _1604893, _1604895, _1604897, _1604899] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604891), tc_List_Olist(_1604891))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604891), tc_List_Olist(_1604891)), hAPP(hAPP(c_List_Olist_OCons(_1604891), _1604893), _1604895)), _1604897)), c_List_Olistrel(_1604891, _1604899))), 41721 ^ _778495 : [(41726 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604891), tc_List_Olist(_1604891))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604891), tc_List_Olist(_1604891)), _1604895), 41720 ^ [_1604891, _1604893, _1604895, _1604897, _1604899])), c_List_Olistrel(_1604891, _1604899))))], (41724 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604891, _1604891)), hAPP(hAPP(c_Product__Type_OPair(_1604891, _1604891), _1604893), 41719 ^ [_1604891, _1604893, _1604895, _1604897, _1604899])), _1604899)))], (41722 ^ _778495) ^ [] : [-(_1604897 = hAPP(hAPP(c_List_Olist_OCons(_1604891), 41719 ^ [_1604891, _1604893, _1604895, _1604897, _1604899]), 41720 ^ [_1604891, _1604893, _1604895, _1604897, _1604899]))]]], (36729 ^ _778495) ^ [_1470612, _1470614, _1470616, _1470618] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1470612), _1470614)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470616), _1470618)), 36736 ^ _778495 : [(36737 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470612), _1470614)), hAPP(c_Finite__Set_Ocard(_1470616), _1470618)))), 36738 ^ _778495 : [(36739 ^ _778495) ^ [_1470823] : [c_Fun_Oinj__on(_1470612, _1470616, _1470823, _1470614), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470616, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470612, _1470616, _1470823), _1470614)), _1470618))]]], (36747 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470612), _1470614)), hAPP(c_Finite__Set_Ocard(_1470616), _1470618))), 36751 ^ _778495 : [(36754 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470616, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470612, _1470616, 36750 ^ [_1470612, _1470614, _1470616, _1470618]), _1470614)), _1470618)))], (36752 ^ _778495) ^ [] : [-(c_Fun_Oinj__on(_1470612, _1470616, 36750 ^ [_1470612, _1470614, _1470616, _1470618], _1470614))]]]]], (14659 ^ _778495) ^ [_1038610, _1038612] : [14660 ^ _778495 : [(14663 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1038612))], (14661 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1038610))]], -(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), _1038610), _1038612))))], (10881 ^ _778495) ^ [_965884, _965886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965884), hAPP(c_Nat_OSuc, _965886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965884), _965886))), -(_965884 = hAPP(c_Nat_OSuc, _965886))], (43864 ^ _778495) ^ [_1655866, _1655868] : [class_Lattices_Oab__semigroup__idem__mult(_1655866), -(_1655868 = c_List_Olist_ONil(_1655866)), -(hAPP(c_Finite__Set_Ofold1(_1655866, c_Groups_Otimes__class_Otimes(_1655866)), hAPP(c_List_Oset(_1655866), _1655868)) = hAPP(c_List_Ofoldl(_1655866, _1655866, c_Groups_Otimes__class_Otimes(_1655866), hAPP(c_List_Ohd(_1655866), _1655868)), hAPP(c_List_Otl(_1655866), _1655868)))], (9318 ^ _778495) ^ [_936464, _936466, _936468] : [9320 ^ _778495 : [(9326 ^ _778495) ^ [] : [-(9319 ^ [_936464, _936466, _936468] = 9322 ^ [_936464, _936466, _936468])], (9324 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_936464), 9322 ^ [_936464, _936466, _936468]), _936468)))], (9321 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_936464), 9319 ^ [_936464, _936466, _936468]), _936466)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936464, tc_HOL_Obool)), _936466), _936468) = c_Orderings_Obot__class_Obot(tc_fun(_936464, tc_HOL_Obool)))], (4504 ^ _778495) ^ [_846938, _846940, _846942, _846944, _846946, _846948, _846950, _846952, _846954, _846956] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_846956, _846952, _846948, _846944, _846940) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_846954, _846950, _846946, _846942, _846938)), _846956 = _846954, _846952 = _846950, _846948 = _846946, _846944 = _846942, _846940 = _846938], (48342 ^ _778495) ^ [_1753094, _1753096, _1753098, _1753100, _1753102] : [-(hAPP(hAPP(c_List_Omap(_1753094, _1753096), _1753098), c_List_Oreplicate(_1753094, _1753100, _1753102)) = c_List_Oreplicate(_1753096, _1753100, hAPP(_1753098, _1753102)))], (29970 ^ _778495) ^ [_1323860, _1323862, _1323864, _1323866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1323866, _1323862)), hAPP(_1323866, _1323864))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1323860, _1323860)), hAPP(hAPP(c_Product__Type_OPair(_1323860, _1323860), _1323862), _1323864)), hAPP(c_Wellfounded_Omeasure(_1323860), _1323866))))], (30837 ^ _778495) ^ [_1341461, _1341463, _1341465] : [class_Orderings_Olinorder(_1341461), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341461), _1341463), _1341465) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341461), _1341465), _1341463))], (42810 ^ _778495) ^ [_1631482, _1631484, _1631486] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1631482, tc_HOL_Obool)), hAPP(c_List_Oset(_1631482), c_List_Oremove1(_1631482, _1631484, _1631486))), hAPP(c_List_Oset(_1631482), _1631486))))], (40308 ^ _778495) ^ [_1566287, _1566289, _1566291, _1566293] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1566287, tc_fun(_1566287, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1566287, tc_fun(tc_prod(_1566287, _1566287), tc_HOL_Obool), tc_fun(_1566287, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566287, tc_fun(tc_fun(tc_prod(_1566287, _1566287), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1566287, _1566287), tc_HOL_Obool), tc_fun(_1566287, tc_HOL_Obool)), _1566287), c_COMBC(_1566287, tc_fun(tc_prod(_1566287, _1566287), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566287, tc_prod(_1566287, _1566287)), tc_fun(_1566287, tc_fun(tc_fun(tc_prod(_1566287, _1566287), tc_HOL_Obool), tc_HOL_Obool)), _1566287), hAPP(c_COMBB(tc_prod(_1566287, _1566287), tc_fun(tc_fun(tc_prod(_1566287, _1566287), tc_HOL_Obool), tc_HOL_Obool), _1566287), c_member(tc_prod(_1566287, _1566287)))), c_Product__Type_OPair(_1566287, _1566287)))), _1566289)), c_fequal), _1566291), _1566293)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566287, _1566287)), hAPP(hAPP(c_Product__Type_OPair(_1566287, _1566287), _1566291), _1566293)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566287, _1566287), tc_HOL_Obool)), _1566289), c_Relation_OId(_1566287)))))], (50825 ^ _778495) ^ [_1807620, _1807622] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807620), 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)))), _1807622))), 50828 ^ _778495 : [(50831 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807622), _1807620))], (50829 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807620), _1807622)))]]], (2294 ^ _778495) ^ [_812137, _812139, _812141, _812143] : [-(c_Groups_Osgn__class_Osgn(_812143, _812139) = c_Groups_Osgn__class_Osgn(_812141, _812137)), _812143 = _812141, _812139 = _812137], (52193 ^ _778495) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (43329 ^ _778495) ^ [_1643065, _1643067, _1643069, _1643071, _1643073, _1643075] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643065), tc_List_Olist(_1643065))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643065), tc_List_Olist(_1643065)), hAPP(hAPP(c_List_Oappend(_1643065), _1643067), _1643073)), hAPP(hAPP(c_List_Oappend(_1643065), _1643069), _1643075))), c_List_Olistrel1(_1643065, _1643071)))), 43330 ^ _778495 : [(43337 ^ _778495) ^ [] : [_1643067 = _1643069, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643065), tc_List_Olist(_1643065))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643065), tc_List_Olist(_1643065)), _1643073), _1643075)), c_List_Olistrel1(_1643065, _1643071)))], (43331 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643065), tc_List_Olist(_1643065))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643065), tc_List_Olist(_1643065)), _1643067), _1643069)), c_List_Olistrel1(_1643065, _1643071))), _1643073 = _1643075]]], (45347 ^ _778495) ^ [_1688554, _1688556, _1688558, _1688560] : [45349 ^ _778495 : [(45352 ^ _778495) ^ [] : [hBOOL(hAPP(_1688558, hAPP(hAPP(c_List_Onth(_1688554), _1688556), 45348 ^ [_1688554, _1688556, _1688558, _1688560])))], (45350 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45348 ^ [_1688554, _1688556, _1688558, _1688560]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688554)), _1688556))))]], hBOOL(hAPP(hAPP(c_member(_1688554), _1688560), hAPP(c_List_Oset(_1688554), _1688556))), -(hBOOL(hAPP(_1688558, _1688560)))], (51635 ^ _778495) ^ [_1821378, _1821380] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821378, _1821380) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821378), _1821380))], (15691 ^ _778495) ^ [_1057810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1057810)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057810), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1057810)], (44414 ^ _778495) ^ [_1667390, _1667392, _1667394, _1667396] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667390)), hAPP(hAPP(c_List_Omap(_1667392, _1667390), _1667394), _1667396)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667392)), _1667396))], (51671 ^ _778495) ^ [_1821871, _1821873] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821871), _1821873)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821873, _1821871) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (15978 ^ _778495) ^ [_1063704, _1063706, _1063708, _1063710, _1063712] : [class_Fields_Ofield(_1063704), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063706), _1063708)), -(hAPP(_1063710, _1063712) = c_Groups_Ozero__class_Ozero(_1063704)), 15989 ^ _778495 : [(15996 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1063706), _1063712), _1063708))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1063706, _1063704), _1063710), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1063706, tc_HOL_Obool)), _1063708), hAPP(hAPP(c_Set_Oinsert(_1063706), _1063712), c_Orderings_Obot__class_Obot(tc_fun(_1063706, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1063706, _1063704), _1063710), _1063708))], (15990 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1063706), _1063712), _1063708)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1063706, _1063704), _1063710), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1063706, tc_HOL_Obool)), _1063708), hAPP(hAPP(c_Set_Oinsert(_1063706), _1063712), c_Orderings_Obot__class_Obot(tc_fun(_1063706, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1063704), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1063706, _1063704), _1063710), _1063708)), hAPP(_1063710, _1063712)))]]], (52119 ^ _778495) ^ [_1830080, _1830082] : [class_Lattices_Oboolean__algebra(_1830080), -(class_Lattices_Oboolean__algebra(tc_fun(_1830082, _1830080)))], (3988 ^ _778495) ^ [_838842, _838844, _838846, _838848, _838850, _838852, _838854, _838856] : [-(c_New__Random__Sequence_Oneg__map(_838856, _838852, _838848, _838844) = c_New__Random__Sequence_Oneg__map(_838854, _838850, _838846, _838842)), _838856 = _838854, _838852 = _838850, _838848 = _838846, _838844 = _838842], (44859 ^ _778495) ^ [] : [-(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))], (50483 ^ _778495) ^ [_1800967, _1800969, _1800971, _1800973] : [50486 ^ _778495 : [(50489 ^ _778495) ^ [] : [hAPP(_1800971, 50484 ^ [_1800967, _1800969, _1800971, _1800973]) = hAPP(_1800971, 50485 ^ [_1800967, _1800969, _1800971, _1800973])], (50487 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1800967, _1800967)), hAPP(hAPP(c_Product__Type_OPair(_1800967, _1800967), 50484 ^ [_1800967, _1800969, _1800971, _1800973]), 50485 ^ [_1800967, _1800969, _1800971, _1800973])), _1800969)))]], -(c_Equiv__Relations_Ocongruent(_1800967, _1800973, _1800969, _1800971))], (43090 ^ _778495) ^ [_1637963, _1637965, _1637967, _1637969] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637963)), hAPP(hAPP(c_List_Oappend(_1637963), _1637965), _1637967)), c_List_Olists(_1637963, _1637969)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637963)), _1637965), c_List_Olists(_1637963, _1637969))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637963)), _1637967), c_List_Olists(_1637963, _1637969)))], (2314 ^ _778495) ^ [_812435, _812437] : [_812437 = _812435, -(c_Divides_Oadjust(_812437) = c_Divides_Oadjust(_812435))], (34128 ^ _778495) ^ [_1414360, _1414362, _1414364] : [class_Orderings_Oorder(_1414360), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414360, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1414360), _1414362)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1414360, _1414362, _1414364)) = c_Orderings_Obot__class_Obot(tc_fun(_1414360, tc_HOL_Obool)))], (29240 ^ _778495) ^ [_1310179, _1310181] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310179))), 29243 ^ _778495 : [(29250 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310181))), -(c_Divides_Odivmod__int(_1310179, _1310181) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1310179), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1310181))))], (29244 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310181)), -(c_Divides_Odivmod__int(_1310179, _1310181) = c_Divides_OnegDivAlg(_1310179, _1310181))]]], (20886 ^ _778495) ^ [_1152551, _1152553, _1152555] : [class_Rings_Osemiring__1(_1152551), hBOOL(hAPP(hAPP(c_member(_1152551), _1152553), c_Nat_Osemiring__1__class_ONats(_1152551))), hBOOL(hAPP(hAPP(c_member(_1152551), _1152555), c_Nat_Osemiring__1__class_ONats(_1152551))), -(hBOOL(hAPP(hAPP(c_member(_1152551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152551), _1152553), _1152555)), c_Nat_Osemiring__1__class_ONats(_1152551))))], (20536 ^ _778495) ^ [_1146934, _1146936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146934)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146936))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146934), _1146936))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146934), c_Int_OPls)))], (52607 ^ _778495) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (19016 ^ _778495) ^ [_1120493, _1120495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120493)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120495))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120493), _1120495)))], (45294 ^ _778495) ^ [_1687256, _1687258, _1687260] : [-(c_Enum_Osublists(_1687256, hAPP(hAPP(c_List_Olist_OCons(_1687256), _1687258), _1687260)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1687256)), tc_List_Olist(tc_List_Olist(_1687256))), c_Enum_Osublists(_1687256, _1687260)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1687256)), tc_List_Olist(tc_List_Olist(_1687256)), tc_List_Olist(tc_List_Olist(_1687256))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1687256)), tc_fun(tc_List_Olist(tc_List_Olist(_1687256)), tc_List_Olist(tc_List_Olist(_1687256))), tc_List_Olist(tc_List_Olist(_1687256))), c_List_Oappend(tc_List_Olist(_1687256))), hAPP(c_List_Omap(tc_List_Olist(_1687256), tc_List_Olist(_1687256)), hAPP(c_List_Olist_OCons(_1687256), _1687258)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1687256))))))], (52559 ^ _778495) ^ [_1834640] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1834640)))], (38796 ^ _778495) ^ [_1529431, _1529433, _1529435] : [c_Wellfounded_Owf(_1529431, _1529433), -(hBOOL(hAPP(hAPP(c_member(_1529431), _1529435), c_Wellfounded_Oacc(_1529431, _1529433))))], (48180 ^ _778495) ^ [_1750147, _1750149, _1750151, _1750153] : [-(c_Lazy__Sequence_Oproduct(_1750147, _1750149, _1750151, _1750153) = hAPP(c_Lazy__Sequence_Obind(_1750147, tc_prod(_1750147, _1750149), _1750151), hAPP(hAPP(c_COMBB(tc_fun(_1750149, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750147, _1750149))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750147, _1750149)), _1750147), c_Lazy__Sequence_Obind(_1750149, tc_prod(_1750147, _1750149), _1750153)), hAPP(hAPP(c_COMBB(tc_fun(_1750149, tc_prod(_1750147, _1750149)), tc_fun(_1750149, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750147, _1750149))), _1750147), hAPP(c_COMBB(tc_prod(_1750147, _1750149), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750147, _1750149)), _1750149), c_Lazy__Sequence_Osingle(tc_prod(_1750147, _1750149)))), c_Product__Type_OPair(_1750147, _1750149)))))], (5642 ^ _778495) ^ [_864793, _864795] : [_864795 = _864793, -(tc_Hoare__Mirabelle_Otriple(_864795) = tc_Hoare__Mirabelle_Otriple(_864793))], (49180 ^ _778495) ^ [_1773173, _1773175] : [49183 ^ _778495 : [(49188 ^ _778495) ^ [] : [49181 ^ [_1773173, _1773175] = 49182 ^ [_1773173, _1773175]], (49186 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773173, _1773173)), hAPP(hAPP(c_Product__Type_OPair(_1773173, _1773173), 49182 ^ [_1773173, _1773175]), 49181 ^ [_1773173, _1773175])), _1773175)))], (49184 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773173, _1773173)), hAPP(hAPP(c_Product__Type_OPair(_1773173, _1773173), 49181 ^ [_1773173, _1773175]), 49182 ^ [_1773173, _1773175])), _1773175)))]], -(c_Relation_Oantisym(_1773173, _1773175))], (43457 ^ _778495) ^ [_1646612, _1646614, _1646616, _1646618] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646612), tc_List_Olist(_1646612))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646612), tc_List_Olist(_1646612)), _1646614), _1646616)), c_List_Olistrel1(_1646612, _1646618))), 43462 ^ _778495 : [(43469 ^ _778495) ^ [] : [-(_1646616 = hAPP(hAPP(c_List_Oappend(_1646612), 43464 ^ [_1646612, _1646614, _1646616, _1646618]), hAPP(hAPP(c_List_Olist_OCons(_1646612), 43461 ^ [_1646612, _1646614, _1646616, _1646618]), 43465 ^ [_1646612, _1646614, _1646616, _1646618])))], (43467 ^ _778495) ^ [] : [-(_1646614 = hAPP(hAPP(c_List_Oappend(_1646612), 43464 ^ [_1646612, _1646614, _1646616, _1646618]), hAPP(hAPP(c_List_Olist_OCons(_1646612), 43460 ^ [_1646612, _1646614, _1646616, _1646618]), 43465 ^ [_1646612, _1646614, _1646616, _1646618])))], (43463 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646612, _1646612)), hAPP(hAPP(c_Product__Type_OPair(_1646612, _1646612), 43460 ^ [_1646612, _1646614, _1646616, _1646618]), 43461 ^ [_1646612, _1646614, _1646616, _1646618])), _1646618)))]]], (43415 ^ _778495) ^ [_1645265, _1645267, _1645269, _1645271, _1645273, _1645275, _1645277] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1645265, _1645265)), hAPP(hAPP(c_Product__Type_OPair(_1645265, _1645265), _1645267), _1645269)), _1645271)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645265), tc_List_Olist(_1645265))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645265), tc_List_Olist(_1645265)), hAPP(hAPP(c_List_Oappend(_1645265), _1645273), hAPP(hAPP(c_List_Olist_OCons(_1645265), _1645267), _1645275))), hAPP(hAPP(c_List_Oappend(_1645265), _1645273), hAPP(hAPP(c_List_Olist_OCons(_1645265), _1645269), _1645277)))), c_List_Olexord(_1645265, _1645271))))], (11987 ^ _778495) ^ [_987925, _987927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987925), _987927)), -(_987927 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987925), 11990 ^ [_987925, _987927])))], (52609 ^ _778495) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (38645 ^ _778495) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (40441 ^ _778495) ^ [_1569978, _1569980] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1569978, _1569978, _1569978), c_Transitive__Closure_Ortrancl(_1569978, _1569980)), c_Transitive__Closure_Ortrancl(_1569978, _1569980)) = c_Transitive__Closure_Ortrancl(_1569978, _1569980))], (40756 ^ _778495) ^ [_1577256, _1577258, _1577260, _1577262, _1577264] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577256, _1577258)), hAPP(hAPP(c_Product__Type_OPair(_1577256, _1577258), _1577260), _1577262)), hAPP(c_Relation_Oconverse(_1577258, _1577256), _1577264))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577258, _1577256)), hAPP(hAPP(c_Product__Type_OPair(_1577258, _1577256), _1577262), _1577260)), _1577264)))], (15265 ^ _778495) ^ [_1049639, _1049641, _1049643] : [class_Rings_Olinordered__idom(_1049639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049639), c_Groups_Ozero__class_Ozero(_1049639)), _1049641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049639), c_Groups_Ozero__class_Ozero(_1049639)), _1049643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049639), _1049643), c_Groups_Oone__class_Oone(_1049639))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049639), _1049641), _1049643)), _1049641)))], (38895 ^ _778495) ^ [_1531676, _1531678, _1531680, _1531682] : [38896 ^ _778495 : [(38897 ^ _778495) ^ [_1531751] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531676, _1531680)), hAPP(hAPP(c_Product__Type_OPair(_1531676, _1531680), _1531678), _1531751)), _1531682))]], -(hBOOL(hAPP(hAPP(c_member(_1531676), _1531678), hAPP(c_Relation_ODomain(_1531676, _1531680), _1531682))))], (10499 ^ _778495) ^ [_959667, _959669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959667), _959669)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _959669)), _959667) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959669), _959667)))], (15289 ^ _778495) ^ [_1050092, _1050094] : [hAPP(c_Finite__Set_Ocard(_1050092), _1050094) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1050094 = c_Orderings_Obot__class_Obot(tc_fun(_1050092, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050092), _1050094))], (20020 ^ _778495) ^ [_1138085, _1138087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138085)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138087))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1138085), _1138087)))], (41373 ^ _778495) ^ [_1594162, _1594164, _1594166, _1594168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594162)), _1594164)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594162)), _1594166))), _1594164 = hAPP(hAPP(c_List_Olist_OCons(_1594162), _1594168), _1594166)], (41923 ^ _778495) ^ [_1610471, _1610473, _1610475] : [-(hAPP(c_List_Oset(_1610471), c_List_Osublist(_1610471, _1610473, _1610475)) = hAPP(c_Set_OCollect(_1610471), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1610471), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1610471, 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)), _1610471), 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)), _1610471), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1610471, tc_fun(tc_Nat_Onat, _1610471), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1610471, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1610471), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1610471), c_COMBB(_1610471, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1610471), _1610473))))), 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(_1610471)), _1610473)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1610475))))))], (45654 ^ _778495) ^ [_1695573, _1695575] : [-(c_List_Oconcat(_1695573, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695573), tc_List_Olist(_1695573)), c_List_Olist_Olist__case(tc_List_Olist(_1695573), _1695573, c_List_Olist_ONil(_1695573), hAPP(hAPP(c_COMBB(tc_List_Olist(_1695573), tc_fun(tc_List_Olist(_1695573), tc_List_Olist(_1695573)), _1695573), c_COMBK(tc_List_Olist(_1695573), tc_List_Olist(_1695573))), hAPP(hAPP(c_COMBC(_1695573, tc_List_Olist(_1695573), tc_List_Olist(_1695573)), c_List_Olist_OCons(_1695573)), c_List_Olist_ONil(_1695573))))), _1695575)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695573), _1695573), c_List_Ohd(_1695573)), hAPP(c_List_Ofilter(tc_List_Olist(_1695573), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1695573)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695573), tc_List_Olist(_1695573), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1695573)))), _1695575)))], (18278 ^ _778495) ^ [_1106385, _1106387, _1106389, _1106391] : [class_Fields_Ofield__inverse__zero(_1106385), class_Int_Onumber(_1106385), 18285 ^ _778495 : [(18286 ^ _778495) ^ [] : [_1106387 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106385), _1106389), hAPP(c_Int_Onumber__class_Onumber__of(_1106385), _1106391)), 18289 ^ _778495 : [(18296 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1106385), _1106391) = c_Groups_Ozero__class_Ozero(_1106385), -(_1106387 = c_Groups_Ozero__class_Ozero(_1106385))], (18290 ^ _778495) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1106385), _1106391) = c_Groups_Ozero__class_Ozero(_1106385)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106385), _1106387), hAPP(c_Int_Onumber__class_Onumber__of(_1106385), _1106391)) = _1106389)]]], (18302 ^ _778495) ^ [] : [-(_1106387 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106385), _1106389), hAPP(c_Int_Onumber__class_Onumber__of(_1106385), _1106391))), 18305 ^ _778495 : [(18308 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106385), _1106387), hAPP(c_Int_Onumber__class_Onumber__of(_1106385), _1106391)) = _1106389], (18306 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1106385), _1106391) = c_Groups_Ozero__class_Ozero(_1106385)]], 18309 ^ _778495 : [(18312 ^ _778495) ^ [] : [_1106387 = c_Groups_Ozero__class_Ozero(_1106385)], (18310 ^ _778495) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1106385), _1106391) = c_Groups_Ozero__class_Ozero(_1106385))]]]]], (29789 ^ _778495) ^ [_1320323, _1320325] : [-(c_Divides_Odivmod__nat(_1320325, _1320323) = 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), _1320325), _1320323), _1320323))), -(_1320323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1320325), _1320323)))], (44702 ^ _778495) ^ [_1673898, _1673900, _1673902, _1673904] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673898)), _1673900) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673902)), _1673904), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673898, _1673902), _1673902), c_Product__Type_Osnd(_1673898, _1673902)), hAPP(hAPP(c_List_Ozip(_1673898, _1673902), _1673900), _1673904)) = _1673904)], (17608 ^ _778495) ^ [_1094164, _1094166, _1094168, _1094170, _1094172, _1094174] : [-(c_Nitpick_Opair__box_Opair__box__size(_1094164, _1094166, _1094168, _1094170, c_Nitpick_Opair__box_OPairBox(_1094164, _1094166, _1094172, _1094174)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1094168, _1094172)), hAPP(_1094170, _1094174))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20450 ^ _778495) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (36827 ^ _778495) ^ [_1472887, _1472889, _1472891, _1472893, _1472895] : [c_Fun_Oinj__on(_1472887, _1472889, _1472891, _1472893), hBOOL(hAPP(hAPP(c_member(_1472887), _1472895), _1472893)), -(hAPP(c_Fun_Othe__inv__into(_1472887, _1472889, _1472893, _1472891), hAPP(_1472891, _1472895)) = _1472895)], (45418 ^ _778495) ^ [_1690016, _1690018] : [c_List_Olist_ONil(_1690016) = c_List_Oremdups(_1690016, _1690018), -(_1690018 = c_List_Olist_ONil(_1690016))], (49473 ^ _778495) ^ [_1778366, _1778368, _1778370] : [c_Relation_Osym(_1778366, _1778368), c_Relation_Osym(_1778366, _1778370), -(c_Relation_Osym(_1778366, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1778366, _1778366), tc_HOL_Obool)), _1778368), _1778370)))], (32152 ^ _778495) ^ [_1369796, _1369798, _1369800, _1369802, _1369804] : [_1369796 = c_Orderings_Obot__class_Obot(tc_fun(_1369798, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1369798, tc_fun(_1369800, tc_HOL_Obool)), _1369796), hAPP(hAPP(c_COMBC(_1369798, tc_fun(_1369800, tc_HOL_Obool), tc_fun(_1369800, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1369800, tc_HOL_Obool), tc_fun(tc_fun(_1369800, tc_HOL_Obool), tc_fun(_1369800, tc_HOL_Obool)), _1369798), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369800, tc_HOL_Obool))), _1369802)), _1369804)) = c_Orderings_Otop__class_Otop(tc_fun(_1369800, tc_HOL_Obool)))], (43399 ^ _778495) ^ [_1644807, _1644809, _1644811, _1644813] : [-(c_List_Osublist(_1644807, hAPP(hAPP(c_List_Oappend(_1644807), _1644809), _1644811), _1644813) = hAPP(hAPP(c_List_Oappend(_1644807), c_List_Osublist(_1644807, _1644809, _1644813)), c_List_Osublist(_1644807, _1644811, 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(_1644807)), _1644809)))), _1644813)))))], (506 ^ _778495) ^ [_786152, _786154, _786156, _786158, _786160, _786162] : [-(c_Nitpick_Oless__eq__frac(_786160, _786156, _786152)), c_Nitpick_Oless__eq__frac(_786162, _786158, _786154), _786162 = _786160, _786158 = _786156, _786154 = _786152], (27415 ^ _778495) ^ [_1267689] : [-(_1267689 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27418 ^ _778495 : [(27425 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1267689))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1267689) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (27419 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1267689)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1267689) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (10543 ^ _778495) ^ [_960513, _960515] : [hAPP(c_Nat_OSuc, _960513) = hAPP(c_Nat_OSuc, _960515), -(_960513 = _960515)], (11750 ^ _778495) ^ [_982533, _982535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _982533), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982535), _982533))))], (34424 ^ _778495) ^ [_1421435, _1421437, _1421439] : [-(hAPP(c_Set_Oimage(_1421435, _1421437, _1421439), c_Orderings_Obot__class_Obot(tc_fun(_1421435, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1421437, tc_HOL_Obool)))], (25118 ^ _778495) ^ [_1227490, _1227492, _1227494] : [hBOOL(hAPP(_1227490, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227492), _1227494))), 25121 ^ _778495 : [(25128 ^ _778495) ^ [] : [-(_1227494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25131 ^ _778495 : [(25132 ^ _778495) ^ [_1227742, _1227744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227742), _1227494)), _1227492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227494), _1227744)), _1227742), -(hBOOL(hAPP(_1227490, _1227744)))]]], (25122 ^ _778495) ^ [] : [_1227494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1227490, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (48088 ^ _778495) ^ [_1747635, _1747637, _1747639, _1747641, _1747643] : [-(c_List_Osplice(_1747635, hAPP(hAPP(c_List_Olist_OCons(_1747635), _1747637), _1747639), hAPP(hAPP(c_List_Olist_OCons(_1747635), _1747641), _1747643)) = hAPP(hAPP(c_List_Olist_OCons(_1747635), _1747637), hAPP(hAPP(c_List_Olist_OCons(_1747635), _1747641), c_List_Osplice(_1747635, _1747639, _1747643))))], (19392 ^ _778495) ^ [_1126822, _1126824, _1126826] : [class_Orderings_Olinorder(_1126822), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126822), _1126824)), -(_1126824 = c_Orderings_Obot__class_Obot(tc_fun(_1126822, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126822), _1126826)), -(_1126826 = c_Orderings_Obot__class_Obot(tc_fun(_1126822, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1126822, c_Orderings_Oord__class_Omin(_1126822), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1126822, tc_HOL_Obool)), _1126824), _1126826)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1126822), c_Big__Operators_Olattice_OInf__fin(_1126822, c_Orderings_Oord__class_Omin(_1126822), _1126824)), c_Big__Operators_Olattice_OInf__fin(_1126822, c_Orderings_Oord__class_Omin(_1126822), _1126826)))], (52409 ^ _778495) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (32936 ^ _778495) ^ [_1386197, _1386199] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1386197, _1386199))))], (8202 ^ _778495) ^ [_913758, _913760, _913762] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_913758), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913758, tc_HOL_Obool)), _913760), _913762)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_913758), _913760)), hBOOL(hAPP(c_Finite__Set_Ofinite(_913758), _913762))], (35615 ^ _778495) ^ [_1445257, _1445259, _1445261, _1445263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1445257), _1445263)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1445261), _1445259))), -(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), _1445257), _1445259)), 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), _1445261), _1445263)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (21744 ^ _778495) ^ [_1167645, _1167647, _1167649] : [class_Groups_Ogroup__add(_1167645), 21747 ^ _778495 : [(21754 ^ _778495) ^ [] : [_1167647 = _1167649, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1167645), _1167647) = hAPP(c_Groups_Ouminus__class_Ouminus(_1167645), _1167649))], (21748 ^ _778495) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1167645), _1167647) = hAPP(c_Groups_Ouminus__class_Ouminus(_1167645), _1167649), -(_1167647 = _1167649)]]], (26366 ^ _778495) ^ [_1250053, _1250055, _1250057] : [class_Rings_Olinordered__semidom(_1250053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250053), c_Groups_Oone__class_Oone(_1250053)), _1250055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250053), c_Groups_Oone__class_Oone(_1250053)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250053), _1250055), hAPP(hAPP(c_Power_Opower__class_Opower(_1250053), _1250055), _1250057)))))], (49352 ^ _778495) ^ [_1776207, _1776209, _1776211, _1776213] : [c_Equiv__Relations_Opart__equivp(_1776207, _1776209), hBOOL(hAPP(hAPP(_1776209, _1776211), _1776213)), -(hBOOL(hAPP(hAPP(_1776209, _1776213), _1776211)))], (34699 ^ _778495) ^ [_1427381, _1427383, _1427385, _1427387] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1427381, tc_HOL_Obool), hAPP(c_Set_Oimage(_1427383, tc_fun(_1427381, tc_HOL_Obool), _1427385), _1427387)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1427383, tc_fun(_1427381, tc_HOL_Obool)), _1427387), _1427385))], (52389 ^ _778495) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (45733 ^ _778495) ^ [_1697364, _1697366, _1697368, _1697370] : [-(hBOOL(hAPP(_1697364, _1697366))), -(hAPP(c_List_Ofilter(_1697368, _1697364), hAPP(hAPP(c_List_Olist_OCons(_1697368), _1697366), _1697370)) = hAPP(c_List_Ofilter(_1697368, _1697364), _1697370))], (44696 ^ _778495) ^ [_1673741, _1673743, _1673745, _1673747] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673741)), _1673743) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673745)), _1673747), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673741, _1673745), _1673741), c_Product__Type_Ofst(_1673741, _1673745)), hAPP(hAPP(c_List_Ozip(_1673741, _1673745), _1673743), _1673747)) = _1673743)], (44764 ^ _778495) ^ [_1675195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1675195)), _1675195 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40822 ^ _778495) ^ [_1579038, _1579040, _1579042, _1579044] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579038, _1579038)), hAPP(hAPP(c_Product__Type_OPair(_1579038, _1579038), _1579040), _1579042)), c_Transitive__Closure_Otrancl(_1579038, hAPP(c_Relation_Oconverse(_1579038, _1579038), _1579044)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579038, _1579038)), hAPP(hAPP(c_Product__Type_OPair(_1579038, _1579038), _1579040), _1579042)), hAPP(c_Relation_Oconverse(_1579038, _1579038), c_Transitive__Closure_Otrancl(_1579038, _1579044)))))], (39378 ^ _778495) ^ [_1544393, _1544395, _1544397, _1544399, _1544401, _1544403, _1544405, _1544407, _1544409] : [hAPP(c_Fun_Ocomp(_1544393, _1544395, _1544397, _1544399), _1544401) = hAPP(c_Fun_Ocomp(_1544403, _1544395, _1544397, _1544405), _1544407), -(hAPP(_1544399, hAPP(_1544401, _1544409)) = hAPP(_1544405, hAPP(_1544407, _1544409)))], (10555 ^ _778495) ^ [_960702, _960704] : [_960702 = _960704, -(hAPP(c_Nat_OSuc, _960702) = hAPP(c_Nat_OSuc, _960704))], (50807 ^ _778495) ^ [_1807275, _1807277] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807277), _1807275)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807275), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807277))))], (34080 ^ _778495) ^ [_1413400, _1413402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1413400), _1413402)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1413400), hAPP(c_Nat_OSuc, _1413402)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1413402), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1413400), _1413402)))], (13269 ^ _778495) ^ [_1014645, _1014647] : [class_Groups_Ogroup__add(_1014645), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014645), _1014647), c_Groups_Ozero__class_Ozero(_1014645)) = _1014647)], (33020 ^ _778495) ^ [_1387578, _1387580] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1387578), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1387580) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1387578, _1387580))], (13263 ^ _778495) ^ [_1014550, _1014552] : [class_Groups_Ogroup__add(_1014550), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014550), _1014552), _1014552) = c_Groups_Ozero__class_Ozero(_1014550))], (29964 ^ _778495) ^ [_1323713, _1323715, _1323717, _1323719] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1323713, _1323713)), hAPP(hAPP(c_Product__Type_OPair(_1323713, _1323713), _1323715), _1323717)), hAPP(c_Wellfounded_Omeasure(_1323713), _1323719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1323719, _1323715)), hAPP(_1323719, _1323717))))], (39364 ^ _778495) ^ [_1544061, _1544063, _1544065] : [-(hAPP(c_Fun_Ocomp(_1544061, _1544061, _1544063, c_Fun_Oid(_1544061)), _1544065) = _1544065)], (52447 ^ _778495) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (12184 ^ _778495) ^ [_991759, _991761, _991763, _991765, _991767] : [class_Rings_Ocomm__semiring__1(_991759), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991759), _991761), _991763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991759), _991765), _991767)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991759), _991761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991759), _991763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991759), _991765), _991767))))], (11003 ^ _778495) ^ [_967779, _967781] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967779)), hAPP(c_Nat_OSuc, _967781)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967779), _967781))], (38593 ^ _778495) ^ [_1525656, _1525658, _1525660, _1525662, _1525664] : [hBOOL(hAPP(hAPP(_1525656, _1525658), _1525660)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1525662, _1525664, _1525656), _1525660)))], (29047 ^ _778495) ^ [_1305859, _1305861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1305859)), _1305861)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1305859), _1305861)))], (39225 ^ _778495) ^ [_1540912, _1540914] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1540912, _1540912)), _1540914)), c_Wellfounded_Oacyclic(_1540912, _1540914), -(c_Wellfounded_Owf(_1540912, _1540914))], (29725 ^ _778495) ^ [_1319151, _1319153, _1319155, _1319157] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1319151, _1319153), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1319155), _1319157))), -(_1319153 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1319151), _1319153) = _1319155)], (30229 ^ _778495) ^ [_1329205, _1329207, _1329209, _1329211, _1329213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1329205, _1329207)), hAPP(_1329205, _1329209))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1329211, _1329211)), hAPP(hAPP(c_Product__Type_OPair(_1329211, _1329211), _1329207), _1329209)), _1329213)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1329211, _1329211)), hAPP(hAPP(c_Product__Type_OPair(_1329211, _1329211), _1329207), _1329209)), c_Wellfounded_Omlex__prod(_1329211, _1329205, _1329213))))], (32158 ^ _778495) ^ [_1370003, _1370005, _1370007, _1370009, _1370011] : [-(_1370003 = c_Orderings_Obot__class_Obot(tc_fun(_1370005, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370005, tc_fun(_1370007, tc_HOL_Obool)), _1370003), hAPP(hAPP(c_COMBC(_1370005, tc_fun(_1370007, tc_HOL_Obool), tc_fun(_1370007, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370007, tc_HOL_Obool), tc_fun(tc_fun(_1370007, tc_HOL_Obool), tc_fun(_1370007, tc_HOL_Obool)), _1370005), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370007, tc_HOL_Obool))), _1370009)), _1370011)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370007, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370005, tc_fun(_1370007, tc_HOL_Obool)), _1370003), _1370009)), _1370011))], (8240 ^ _778495) ^ [_914438, _914440, _914442, _914444] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_914438, _914440, _914442, _914444, c_Orderings_Obot__class_Obot(tc_fun(_914438, tc_HOL_Obool))), _914444)))], (6654 ^ _778495) ^ [_887200, _887202, _887204] : [hBOOL(hAPP(hAPP(c_member(_887200), _887202), _887204)), -(hAPP(hAPP(c_Set_Oinsert(_887200), _887202), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887200, tc_HOL_Obool)), _887204), hAPP(hAPP(c_Set_Oinsert(_887200), _887202), c_Orderings_Obot__class_Obot(tc_fun(_887200, tc_HOL_Obool))))) = _887204)], (13462 ^ _778495) ^ [_1017537, _1017539] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017537), _1017539) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1017537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1017539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51895 ^ _778495) ^ [_1826335, _1826337, _1826339, _1826341] : [class_Rings_Ocomm__semiring__1(_1826335), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826335), _1826337), _1826339)), _1826341)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826335), _1826339), _1826341)))], (47321 ^ _778495) ^ [_1731155, _1731157, _1731159, _1731161] : [class_Orderings_Oorder(_1731155), class_Enum_Oenum(_1731157), 47328 ^ _778495 : [(47337 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1731157, _1731155)), _1731159), _1731161))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731157, _1731155)), _1731159), _1731161)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731157), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1731157), c_fNot), hAPP(hAPP(c_COMBS(_1731157, _1731155, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1731155, tc_fun(_1731155, tc_HOL_Obool), _1731157), c_fequal), _1731159)), _1731161))))], (47329 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1731157, _1731155)), _1731159), _1731161)), 47332 ^ _778495 : [(47335 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731157), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1731157), c_fNot), hAPP(hAPP(c_COMBS(_1731157, _1731155, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1731155, tc_fun(_1731155, tc_HOL_Obool), _1731157), c_fequal), _1731159)), _1731161)))))], (47333 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731157, _1731155)), _1731159), _1731161)))]]]]], (49338 ^ _778495) ^ [_1775978, _1775980, _1775982, _1775984, _1775986] : [c_Equiv__Relations_Opart__equivp(_1775978, _1775980), hBOOL(hAPP(hAPP(_1775980, _1775982), _1775984)), hBOOL(hAPP(hAPP(_1775980, _1775984), _1775986)), -(hBOOL(hAPP(hAPP(_1775980, _1775982), _1775986)))], (43151 ^ _778495) ^ [_1639369, _1639371, _1639373, _1639375] : [_1639371 = _1639375, -(hAPP(hAPP(c_List_Oappend(_1639369), _1639371), _1639373) = hAPP(hAPP(c_List_Oappend(_1639369), _1639375), _1639373))], (5739 ^ _778495) ^ [_869438, _869440, _869442, _869444] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_869438), _869440), _869442), _869444)), -(_869440 = _869444), -(hBOOL(hAPP(_869442, _869444)))], (38534 ^ _778495) ^ [_1522284, _1522286, _1522288, _1522290, _1522292] : [-(hAPP(c_Relation_ORange(_1522284, _1522286), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1522284, _1522286)), hAPP(hAPP(c_Product__Type_OPair(_1522284, _1522286), _1522288), _1522290)), _1522292)) = hAPP(hAPP(c_Set_Oinsert(_1522286), _1522290), hAPP(c_Relation_ORange(_1522284, _1522286), _1522292)))], (47462 ^ _778495) ^ [_1734190, _1734192, _1734194, _1734196] : [47464 ^ _778495 : [(47467 ^ _778495) ^ [] : [hBOOL(hAPP(_1734194, 47463 ^ [_1734190, _1734192, _1734194, _1734196]))], (47465 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734190), 47463 ^ [_1734190, _1734192, _1734194, _1734196]), hAPP(c_List_Oset(_1734190), _1734192))))]], -(c_List_OtakeWhile(_1734190, _1734194, hAPP(hAPP(c_List_Oappend(_1734190), _1734192), _1734196)) = hAPP(hAPP(c_List_Oappend(_1734190), _1734192), c_List_OtakeWhile(_1734190, _1734194, _1734196)))], (11835 ^ _778495) ^ [_984188, _984190, _984192] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _984188), _984190)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _984192), _984190)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984188), _984192))], (33920 ^ _778495) ^ [_1410000, _1410002, _1410004, _1410006] : [class_Orderings_Olinorder(_1410000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410000), _1410002), _1410004)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410000, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1410000, _1410002), _1410006)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1410000, _1410002), _1410004)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1410000, _1410004), _1410006))], (28081 ^ _778495) ^ [_1279506, _1279508, _1279510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1279506), _1279508)), -(c_Random_Ominus__shift(_1279510, _1279506, _1279508) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1279510), _1279506)), _1279508))], (45760 ^ _778495) ^ [_1697831, _1697833, _1697835, _1697837, _1697839] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697831)), hAPP(c_List_Ofilter(_1697831, _1697833), hAPP(hAPP(c_List_Omap(_1697835, _1697831), _1697837), _1697839))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697835)), hAPP(c_List_Ofilter(_1697835, hAPP(c_Fun_Ocomp(_1697831, tc_HOL_Obool, _1697835, _1697833), _1697837)), _1697839)))], (3146 ^ _778495) ^ [_825345, _825347, _825349, _825351, _825353, _825355] : [-(c_Big__Operators_Olattice_OInf__fin(_825355, _825351, _825347) = c_Big__Operators_Olattice_OInf__fin(_825353, _825349, _825345)), _825355 = _825353, _825351 = _825349, _825347 = _825345], (14829 ^ _778495) ^ [_1041514, _1041516] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041514), _1041516) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041514), _1041516)))], (19106 ^ _778495) ^ [_1121968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121968), 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)), _1121968)), _1121968)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29029 ^ _778495) ^ [_1305480, _1305482, _1305484, _1305486, _1305488, _1305490] : [hBOOL(hAPP(hAPP(_1305480, _1305482), _1305484)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305486, tc_fun(_1305488, tc_HOL_Obool))), _1305480), _1305490), _1305482), _1305484)))], (37022 ^ _778495) ^ [_1476727] : [-(c_Nitpick_Ozero__frac(_1476727) = c_Nitpick_OAbs__Frac(_1476727, 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))))], (49441 ^ _778495) ^ [_1777872] : [-(c_Relation_Osym(_1777872, c_Relation_OId(_1777872)))], (1858 ^ _778495) ^ [_804748, _804750] : [-(class_Orderings_Oorder(_804748)), _804750 = _804748, class_Orderings_Oorder(_804750)], (46051 ^ _778495) ^ [_1704890, _1704892, _1704894, _1704896, _1704898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704890), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1704892), _1704894))), -(hAPP(hAPP(c_List_Onth(_1704896), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704896), _1704898), c_List_Oupt(_1704894, _1704892))), _1704890) = hAPP(_1704898, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704894), _1704890)))], (17300 ^ _778495) ^ [_1087887, _1087889, _1087891, _1087893] : [class_Fields_Ofield(_1087887), -(_1087889 = c_Groups_Ozero__class_Ozero(_1087887)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087887), _1087891), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1087887), _1087893), _1087889)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1087887), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087887), _1087889), _1087891)), _1087893)), _1087889))], (47994 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9262 ^ _778495) ^ [_935234, _935236, _935238] : [class_Lattices_Olattice(_935234), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935234), _935236), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935234), _935236), _935238)) = _935236)], (47941 ^ _778495) ^ [_1744318, _1744320, _1744322] : [c_List_Olist__all(_1744318, _1744320, _1744322), 47944 ^ _778495 : [(47945 ^ _778495) ^ [_1744399] : [hBOOL(hAPP(hAPP(c_member(_1744318), _1744399), hAPP(c_List_Oset(_1744318), _1744322))), -(hBOOL(hAPP(_1744320, _1744399)))]]], (25632 ^ _778495) ^ [_1236463, _1236465] : [class_Rings_Ocomm__semiring__1(_1236463), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236463), _1236465), _1236465) = hAPP(hAPP(c_Power_Opower__class_Opower(_1236463), _1236465), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (30407 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (46768 ^ _778495) ^ [_1719005, _1719007, _1719009, _1719011] : [class_Orderings_Olinorder(_1719005), c_List_Olinorder__class_Osorted(_1719005, hAPP(c_List_Orev(_1719005), _1719007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1719009), _1719011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719011), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719005)), _1719007))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719005), hAPP(hAPP(c_List_Onth(_1719005), _1719007), _1719011)), hAPP(hAPP(c_List_Onth(_1719005), _1719007), _1719009))))], (28237 ^ _778495) ^ [_1282725, _1282727] : [hBOOL(hAPP(hAPP(c_member(_1282725), _1282727), c_Orderings_Obot__class_Obot(tc_fun(_1282725, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1282725, tc_HOL_Obool)), _1282727)))], (7378 ^ _778495) ^ [_901089, _901091] : [_901089 = c_Orderings_Obot__class_Obot(tc_fun(_901091, tc_HOL_Obool)), 7379 ^ _778495 : [(7380 ^ _778495) ^ [_901158, _901160] : [_901089 = hAPP(hAPP(c_Set_Oinsert(_901091), _901160), _901158), -(hBOOL(hAPP(hAPP(c_member(_901091), _901160), _901158)))]]], (43305 ^ _778495) ^ [_1642473, _1642475, _1642477, _1642479, _1642481] : [-(hAPP(hAPP(c_List_Olist__update(_1642473, hAPP(hAPP(c_List_Oappend(_1642473), _1642475), hAPP(hAPP(c_List_Olist_OCons(_1642473), _1642477), _1642479))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642473)), _1642475)), _1642481) = hAPP(hAPP(c_List_Oappend(_1642473), _1642475), hAPP(hAPP(c_List_Olist_OCons(_1642473), _1642481), _1642479)))], (26548 ^ _778495) ^ [_1253429, _1253431, _1253433, _1253435] : [class_Rings_Olinordered__semidom(_1253429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253431), _1253433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253429), c_Groups_Ozero__class_Ozero(_1253429)), _1253435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253429), _1253435), c_Groups_Oone__class_Oone(_1253429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253429), hAPP(hAPP(c_Power_Opower__class_Opower(_1253429), _1253435), _1253433)), hAPP(hAPP(c_Power_Opower__class_Opower(_1253429), _1253435), _1253431))))], (18240 ^ _778495) ^ [_1105790, _1105792, _1105794, _1105796] : [class_Fields_Ofield__inverse__zero(_1105790), class_Int_Onumber(_1105790), 18247 ^ _778495 : [(18248 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1105790), _1105792) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105790), _1105794), _1105796), 18251 ^ _778495 : [(18258 ^ _778495) ^ [] : [_1105796 = c_Groups_Ozero__class_Ozero(_1105790), -(hAPP(c_Int_Onumber__class_Onumber__of(_1105790), _1105792) = c_Groups_Ozero__class_Ozero(_1105790))], (18252 ^ _778495) ^ [] : [-(_1105796 = c_Groups_Ozero__class_Ozero(_1105790)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105790), hAPP(c_Int_Onumber__class_Onumber__of(_1105790), _1105792)), _1105796) = _1105794)]]], (18264 ^ _778495) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1105790), _1105792) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105790), _1105794), _1105796)), 18267 ^ _778495 : [(18270 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105790), hAPP(c_Int_Onumber__class_Onumber__of(_1105790), _1105792)), _1105796) = _1105794], (18268 ^ _778495) ^ [] : [_1105796 = c_Groups_Ozero__class_Ozero(_1105790)]], 18271 ^ _778495 : [(18274 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1105790), _1105792) = c_Groups_Ozero__class_Ozero(_1105790)], (18272 ^ _778495) ^ [] : [-(_1105796 = c_Groups_Ozero__class_Ozero(_1105790))]]]]], (35524 ^ _778495) ^ [_1442569, _1442571, _1442573, _1442575, _1442577] : [-(hAPP(c_Relation_OImage(_1442569, _1442571, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1442569, _1442571), tc_HOL_Obool)), _1442573), _1442575)), _1442577) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442571, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442569, _1442571, _1442573), _1442577)), hAPP(c_Relation_OImage(_1442569, _1442571, _1442575), _1442577)))], (52269 ^ _778495) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (27789 ^ _778495) ^ [_1274422, _1274424, _1274426, _1274428] : [hBOOL(hAPP(hAPP(c_member(_1274422), _1274424), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1274422, tc_HOL_Obool), _1274426))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1274422, tc_HOL_Obool)), _1274428), _1274426)), -(hBOOL(hAPP(hAPP(c_member(_1274422), _1274424), _1274428)))], (52515 ^ _778495) ^ [_1834109, _1834111] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1834109, _1834111)))], (45548 ^ _778495) ^ [_1692387, _1692389, _1692391] : [-(c_List_Oconcat(_1692387, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1692387)), _1692389), _1692391)) = hAPP(hAPP(c_List_Oappend(_1692387), _1692389), c_List_Oconcat(_1692387, _1692391)))], (15623 ^ _778495) ^ [_1056529, _1056531, _1056533, _1056535, _1056537] : [class_Groups_Ocomm__monoid__mult(_1056529), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056531), _1056533)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056531), _1056535)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056531, tc_HOL_Obool)), _1056533), _1056535) = c_Orderings_Obot__class_Obot(tc_fun(_1056531, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056531, _1056529), _1056537), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1056531, tc_HOL_Obool)), _1056533), _1056535)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056529), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056531, _1056529), _1056537), _1056533)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056531, _1056529), _1056537), _1056535)))], (19602 ^ _778495) ^ [_1130566, _1130568, _1130570] : [class_Orderings_Olinorder(_1130566), hBOOL(hAPP(c_Finite__Set_Ofinite(_1130566), _1130568)), -(hBOOL(hAPP(hAPP(c_member(_1130566), _1130570), _1130568))), -(_1130568 = c_Orderings_Obot__class_Obot(tc_fun(_1130566, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1130566, hAPP(hAPP(c_Set_Oinsert(_1130566), _1130570), _1130568)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1130566), _1130570), c_Big__Operators_Olinorder__class_OMin(_1130566, _1130568)))], (34328 ^ _778495) ^ [_1419036, _1419038, _1419040, _1419042, _1419044] : [-(hAPP(c_Set_Oimage(_1419036, _1419038, _1419040), hAPP(hAPP(c_Set_Oinsert(_1419036), _1419042), _1419044)) = hAPP(hAPP(c_Set_Oinsert(_1419038), hAPP(_1419040, _1419042)), hAPP(c_Set_Oimage(_1419036, _1419038, _1419040), _1419044)))], (29001 ^ _778495) ^ [_1304902, _1304904, _1304906, _1304908, _1304910, _1304912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304902, tc_fun(_1304904, tc_HOL_Obool))), _1304906), _1304908)), hBOOL(hAPP(hAPP(_1304906, _1304910), _1304912)), -(hBOOL(hAPP(hAPP(_1304908, _1304910), _1304912)))], (15913 ^ _778495) ^ [_1062355, _1062357, _1062359] : [-(hAPP(c_Finite__Set_Ocard(_1062355), _1062357) = hAPP(c_Nat_OSuc, _1062359)), 15914 ^ _778495 : [(15915 ^ _778495) ^ [_1062455, _1062457] : [_1062357 = hAPP(hAPP(c_Set_Oinsert(_1062355), _1062457), _1062455), -(hBOOL(hAPP(hAPP(c_member(_1062355), _1062457), _1062455))), hAPP(c_Finite__Set_Ocard(_1062355), _1062455) = _1062359, 15926 ^ _778495 : [(15929 ^ _778495) ^ [] : [_1062455 = c_Orderings_Obot__class_Obot(tc_fun(_1062355, tc_HOL_Obool))], (15927 ^ _778495) ^ [] : [-(_1062359 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (4454 ^ _778495) ^ [_846185, _846187, _846189, _846191] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846191, _846187) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846189, _846185)), _846191 = _846189, _846187 = _846185], (33633 ^ _778495) ^ [_1404392, _1404394, _1404396, _1404398, _1404400] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404392, tc_fun(_1404394, tc_HOL_Obool)), _1404396), _1404398), _1404400))), 33634 ^ _778495 : [(33635 ^ _778495) ^ [_1404464] : [hBOOL(hAPP(hAPP(c_member(_1404392), _1404464), _1404396)), hBOOL(hAPP(hAPP(_1404398, _1404464), _1404400))]]], (24834 ^ _778495) ^ [_1222850, _1222852] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222850)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222852)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1222850), _1222852)))], (23943 ^ _778495) ^ [_1207009, _1207011, _1207013] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1207009, tc_HOL_Obool)), _1207011), _1207013) = c_Orderings_Obot__class_Obot(tc_fun(_1207009, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1207009, tc_HOL_Obool)), _1207011), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1207009, tc_HOL_Obool)), _1207013))))], (39650 ^ _778495) ^ [_1550609, _1550611, _1550613, _1550615, _1550617, _1550619] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1550609, _1550611), _1550609, tc_prod(_1550613, _1550615), c_Product__Type_Ofst(_1550609, _1550611)), c_Product__Type_Omap__pair(_1550613, _1550609, _1550615, _1550611, _1550617, _1550619)) = hAPP(c_Fun_Ocomp(_1550613, _1550609, tc_prod(_1550613, _1550615), _1550617), c_Product__Type_Ofst(_1550613, _1550615)))], (20010 ^ _778495) ^ [_1137919] : [_1137919 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137919) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6222 ^ _778495) ^ [_879063, _879065, _879067, _879069] : [hBOOL(hAPP(hAPP(c_member(_879063), _879065), _879067)), -(hBOOL(hAPP(hAPP(c_member(_879063), _879065), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879063, tc_HOL_Obool)), _879069), _879067))))], (7098 ^ _778495) ^ [_895463, _895465, _895467] : [class_Lattices_Osemilattice__sup(_895463), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895463), _895465), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895463), _895465), _895467))))], (29093 ^ _778495) ^ [_1306723, _1306725] : [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), _1306723))), 29096 ^ _778495 : [(29103 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306725)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306723)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306725), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306723)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306723)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306725), 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), _1306723)))))], (29097 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306725)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306723))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306725), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306723)) = 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), _1306725)))]]], (5867 ^ _778495) ^ [_871906, _871908, _871910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871906, tc_HOL_Obool)), _871908), _871910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871906, tc_HOL_Obool)), _871910), _871908)), -(_871908 = _871910)], (41441 ^ _778495) ^ [_1596363, _1596365, _1596367, _1596369] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1596363), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1596365), _1596367)))), -(hAPP(c_Random_Opick(_1596365, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1596365)), _1596367), _1596369)), _1596363) = hAPP(c_Random_Opick(_1596365, _1596369), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1596363), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1596365), _1596367))))], (22068 ^ _778495) ^ [_1173308, _1173310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1173308)), c_Int_OBit0(_1173310))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1173308), _1173310)))], (38521 ^ _778495) ^ [_1521967, _1521969, _1521971, _1521973] : [hBOOL(hAPP(hAPP(c_member(_1521967), _1521969), hAPP(c_Relation_ORange(_1521971, _1521967), _1521973))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1521971, _1521967)), hAPP(hAPP(c_Product__Type_OPair(_1521971, _1521967), 38524 ^ [_1521967, _1521969, _1521971, _1521973]), _1521969)), _1521973)))], (4598 ^ _778495) ^ [_848461, _848463, _848465, _848467, _848469, _848471] : [-(c_Random__Sequence_Oempty(_848471, _848467, _848463) = c_Random__Sequence_Oempty(_848469, _848465, _848461)), _848471 = _848469, _848467 = _848465, _848463 = _848461], (40335 ^ _778495) ^ [_1567377, _1567379] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567377, _1567377)), hAPP(hAPP(c_Product__Type_OPair(_1567377, _1567377), _1567379), _1567379)), c_Relation_OId(_1567377))))], (39325 ^ _778495) ^ [_1542876, _1542878, _1542880] : [c_Wellfounded_OwfP(_1542876, hAPP(_1542878, 39326 ^ [_1542876, _1542878, _1542880])), 39333 ^ _778495 : [(39336 ^ _778495) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1542876, tc_HOL_Obool)), c_Predicate_ODomainP(_1542876, _1542876, hAPP(_1542878, 39331 ^ [_1542876, _1542878, _1542880]))), c_Predicate_ORangeP(_1542876, _1542876, hAPP(_1542878, 39332 ^ [_1542876, _1542878, _1542880]))) = c_Orderings_Obot__class_Obot(tc_fun(_1542876, tc_HOL_Obool))], (39334 ^ _778495) ^ [] : [hAPP(_1542878, 39331 ^ [_1542876, _1542878, _1542880]) = hAPP(_1542878, 39332 ^ [_1542876, _1542878, _1542880])]], -(c_Wellfounded_OwfP(_1542876, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542880, tc_fun(_1542876, tc_fun(_1542876, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1542880, tc_HOL_Obool))), _1542878)))], (24425 ^ _778495) ^ [_1215642, _1215644] : [-(_1215642 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1215642, _1215644) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1215642), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1215644)))], (11015 ^ _778495) ^ [_968009, _968011, _968013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968009), _968011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968009), _968013)), _968011)))], (45841 ^ _778495) ^ [_1700458, _1700460] : [-(c_Random_Opick(_1700458, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1700458), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1700458, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1700458, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1700458)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1700460)) = c_Random_Opick(_1700458, _1700460))], (20820 ^ _778495) ^ [_1151459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1151459), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151459)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14441 ^ _778495) ^ [_1035153] : [class_Rings_Olinordered__semidom(_1035153), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035153), c_Groups_Ozero__class_Ozero(_1035153)), c_Groups_Oone__class_Oone(_1035153))))], (21302 ^ _778495) ^ [_1160223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1160223))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1160223)))], (47282 ^ _778495) ^ [_1729989, _1729991, _1729993, _1729995, _1729997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1729989, _1729991)), hAPP(_1729989, _1729993))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729995, _1729995)), hAPP(hAPP(c_Product__Type_OPair(_1729995, _1729995), _1729991), _1729993)), c_List_Omeasures(_1729995, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729995, tc_Nat_Onat)), _1729989), _1729997)))))], (5400 ^ _778495) ^ [_861126, _861128, _861130, _861132, _861134, _861136, _861138, _861140, _861142, _861144] : [-(c_SetInterval_Oord_OatLeastLessThan(_861144, _861140, _861136, _861132, _861128) = c_SetInterval_Oord_OatLeastLessThan(_861142, _861138, _861134, _861130, _861126)), _861144 = _861142, _861140 = _861138, _861136 = _861134, _861132 = _861130, _861128 = _861126], (12028 ^ _778495) ^ [_988702, _988704, _988706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988702), _988704)), _988706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988702), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988706), _988704))))], (49254 ^ _778495) ^ [_1774415, _1774417] : [-(c_Equiv__Relations_Oequivp(_1774415, _1774417)), c_Predicate_Oreflp(_1774415, _1774417), c_Predicate_Osymp(_1774415, _1774417), c_Predicate_Otransp(_1774415, _1774417)], (26406 ^ _778495) ^ [_1250715, _1250717, _1250719, _1250721] : [class_Rings_Olinordered__semidom(_1250715), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250715), c_Groups_Oone__class_Oone(_1250715)), _1250717)), 26413 ^ _778495 : [(26420 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1250719), _1250721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250715), hAPP(hAPP(c_Power_Opower__class_Opower(_1250715), _1250717), _1250719)), hAPP(hAPP(c_Power_Opower__class_Opower(_1250715), _1250717), _1250721))))], (26414 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250715), hAPP(hAPP(c_Power_Opower__class_Opower(_1250715), _1250717), _1250719)), hAPP(hAPP(c_Power_Opower__class_Opower(_1250715), _1250717), _1250721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1250719), _1250721)))]]], (46554 ^ _778495) ^ [_1714180, _1714182, _1714184] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714180), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1714180))), _1714182))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714184), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714180))), _1714182))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714180), _1714180), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714180), tc_Nat_Onat, _1714180), c_List_Onth(_1714180)), _1714184)), hAPP(c_List_Ofilter(tc_List_Olist(_1714180), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714180)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714184)), c_Nat_Osize__class_Osize(tc_List_Olist(_1714180)))), c_List_Otranspose(_1714180, _1714182))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714180)), _1714182), _1714184))], (30483 ^ _778495) ^ [_1334418, _1334420, _1334422, _1334424] : [hBOOL(hAPP(hAPP(c_member(_1334418), _1334420), c_SetInterval_Oord_OlessThan(_1334418, _1334422, _1334424))), -(hBOOL(hAPP(hAPP(_1334422, _1334420), _1334424)))], (48194 ^ _778495) ^ [_1750470, _1750472, _1750474, _1750476] : [-(hAPP(hAPP(c_List_Oappend(_1750470), c_List_Oreplicate(_1750470, _1750472, _1750474)), hAPP(hAPP(c_List_Olist_OCons(_1750470), _1750474), _1750476)) = hAPP(hAPP(c_List_Olist_OCons(_1750470), _1750474), hAPP(hAPP(c_List_Oappend(_1750470), c_List_Oreplicate(_1750470, _1750472, _1750474)), _1750476)))], (21106 ^ _778495) ^ [_1156590, _1156592] : [class_Rings_Olinordered__idom(_1156590), -(hAPP(c_Groups_Oabs__class_Oabs(_1156590), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1156590), _1156592)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1156590), _1156592))], (270 ^ _778495) ^ [_782780, _782782] : [-(class_Fields_Ofield__inverse__zero(_782780)), _782782 = _782780, class_Fields_Ofield__inverse__zero(_782782)], (44841 ^ _778495) ^ [] : [-(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))))], (13701 ^ _778495) ^ [_1021569, _1021571, _1021573] : [class_Groups_Oordered__comm__monoid__add(_1021569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021569), _1021571), c_Groups_Ozero__class_Ozero(_1021569))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021569), _1021573), c_Groups_Ozero__class_Ozero(_1021569))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021569), _1021571), _1021573)), c_Groups_Ozero__class_Ozero(_1021569))))], (37190 ^ _778495) ^ [_1480826, _1480828, _1480830, _1480832, _1480834] : [hAPP(_1480832, _1480828) = _1480834, -(hBOOL(hAPP(hAPP(c_member(_1480826), _1480828), hAPP(c_Set_Ovimage(_1480826, _1480830, _1480832), hAPP(hAPP(c_Set_Oinsert(_1480830), _1480834), c_Orderings_Obot__class_Obot(tc_fun(_1480830, tc_HOL_Obool)))))))], (11785 ^ _778495) ^ [_983214, _983216, _983218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983214), _983216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983214), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983218), _983216))))], (49967 ^ _778495) ^ [_1789138, _1789140, _1789142, _1789144, _1789146, _1789148, _1789150] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1789138, tc_HOL_Obool)), _1789140), _1789142) = c_Orderings_Obot__class_Obot(tc_fun(_1789138, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1789144, tc_HOL_Obool)), _1789146), _1789148) = c_Orderings_Obot__class_Obot(tc_fun(_1789144, tc_HOL_Obool)), c_Fun_Obij__betw(_1789138, _1789144, _1789150, _1789140, _1789146), c_Fun_Obij__betw(_1789138, _1789144, _1789150, _1789142, _1789148), -(c_Fun_Obij__betw(_1789138, _1789144, _1789150, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1789138, tc_HOL_Obool)), _1789140), _1789142), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1789144, tc_HOL_Obool)), _1789146), _1789148)))], (27145 ^ _778495) ^ [_1263345, _1263347] : [class_Rings_Oring__1(_1263345), -(hAPP(c_Int_Oring__1__class_Oof__int(_1263345), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1263347)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1263345), hAPP(c_Int_Oring__1__class_Oof__int(_1263345), _1263347)))], (51861 ^ _778495) ^ [_1825624, _1825626, _1825628] : [class_Divides_Osemiring__div(_1825624), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825624), _1825626), _1825628)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825624), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825624), _1825628), _1825626)), _1825626) = _1825628)], (23364 ^ _778495) ^ [_1197239, _1197241] : [-(_1197239 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23367 ^ _778495 : [(23374 ^ _778495) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1197241, _1197239) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1197241), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197239)) = 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), _1197241), _1197239))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23368 ^ _778495) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1197241, _1197239) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1197241), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197239)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1197241), _1197239)))]]], (29914 ^ _778495) ^ [_1322798, _1322800, _1322802] : [-(hAPP(c_Product__Type_Osnd(_1322798, _1322800), _1322802) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1322798, _1322800, _1322800), hAPP(c_COMBK(tc_fun(_1322800, _1322800), _1322798), c_COMBI(_1322800))), _1322802))], (41706 ^ _778495) ^ [_1604696, _1604698, _1604700, _1604702, _1604704, _1604706] : [hBOOL(hAPP(hAPP(_1604696, _1604698), _1604700)), c_List_Olistrelp(_1604702, _1604696, _1604704, _1604706), -(c_List_Olistrelp(_1604702, _1604696, hAPP(hAPP(c_List_Olist_OCons(_1604702), _1604698), _1604704), hAPP(hAPP(c_List_Olist_OCons(_1604702), _1604700), _1604706)))], (49110 ^ _778495) ^ [_1771901, _1771903, _1771905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1771901, _1771901), tc_HOL_Obool)), _1771903), _1771905)), c_Relation_Oantisym(_1771901, _1771905), -(c_Relation_Oantisym(_1771901, _1771903))], (26586 ^ _778495) ^ [_1254143, _1254145] : [-(c_Int_Onat__aux(_1254143, _1254145) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1254143)), _1254145))], (52227 ^ _778495) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (4204 ^ _778495) ^ [_842214, _842216] : [_842216 = _842214, -(c_List_Onth(_842216) = c_List_Onth(_842214))], (16750 ^ _778495) ^ [_1077958, _1077960, _1077962] : [class_Fields_Olinordered__field__inverse__zero(_1077958), 16753 ^ _778495 : [(16768 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077958), c_Groups_Ozero__class_Ozero(_1077958)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1077958), _1077960), _1077962)))), 16769 ^ _778495 : [(16776 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077958), _1077960), c_Groups_Ozero__class_Ozero(_1077958))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077958), _1077962), c_Groups_Ozero__class_Ozero(_1077958)))], (16770 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077958), c_Groups_Ozero__class_Ozero(_1077958)), _1077960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077958), c_Groups_Ozero__class_Ozero(_1077958)), _1077962))]]], (16754 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077958), c_Groups_Ozero__class_Ozero(_1077958)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1077958), _1077960), _1077962))), 16759 ^ _778495 : [(16762 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077958), c_Groups_Ozero__class_Ozero(_1077958)), _1077962)))], (16760 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077958), c_Groups_Ozero__class_Ozero(_1077958)), _1077960)))]], 16763 ^ _778495 : [(16766 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077958), _1077962), c_Groups_Ozero__class_Ozero(_1077958))))], (16764 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077958), _1077960), c_Groups_Ozero__class_Ozero(_1077958))))]]]]], (45588 ^ _778495) ^ [_1693262, _1693264, _1693266, _1693268] : [-(hAPP(hAPP(c_List_Omap(_1693262, _1693264), _1693266), c_List_Oconcat(_1693262, _1693268)) = c_List_Oconcat(_1693264, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1693262), tc_List_Olist(_1693264)), hAPP(c_List_Omap(_1693262, _1693264), _1693266)), _1693268)))], (6784 ^ _778495) ^ [_889615, _889617, _889619, _889621] : [hBOOL(hAPP(hAPP(c_member(_889615), _889617), _889619)), -(hBOOL(hAPP(hAPP(c_member(_889615), _889617), hAPP(hAPP(c_Set_Oinsert(_889615), _889621), _889619))))], (26650 ^ _778495) ^ [_1255157] : [c_Int_OBit0(_1255157) = c_Int_OMin], (20470 ^ _778495) ^ [_1145818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145818), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1145818)))], (10959 ^ _778495) ^ [_967071, _967073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967071), _967073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967071), _967073)))], (1158 ^ _778495) ^ [_795998, _796000] : [-(class_Groups_Olinordered__ab__group__add(_795998)), _796000 = _795998, class_Groups_Olinordered__ab__group__add(_796000)], (1084 ^ _778495) ^ [_794909, _794911, _794913, _794915, _794917, _794919] : [-(c_List_Oall__interval__nat(_794917, _794913, _794909)), c_List_Oall__interval__nat(_794919, _794915, _794911), _794919 = _794917, _794915 = _794913, _794911 = _794909], (43684 ^ _778495) ^ [_1652264, _1652266, _1652268, _1652270] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652264) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1652266), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652264)), hAPP(hAPP(c_List_Olist_OCons(_1652266), _1652268), _1652270)) = hAPP(hAPP(c_List_Odrop(_1652266), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652264)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1652270))], (9056 ^ _778495) ^ [_931420, _931422, _931424, _931426, _931428] : [class_Lattices_Osemilattice__inf(_931420), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931420), _931422), _931424)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931420), _931426), _931428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931420), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931420), _931422), _931426)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931420), _931424), _931428))))], (5458 ^ _778495) ^ [_862071, _862073] : [_862073 = _862071, -(c_Groups_Oplus__class_Oplus(_862073) = c_Groups_Oplus__class_Oplus(_862071))], (47032 ^ _778495) ^ [_1724429, _1724431] : [-(c_List_OdropWhile(_1724429, _1724431, c_List_Olist_ONil(_1724429)) = c_List_Olist_ONil(_1724429))], (5917 ^ _778495) ^ [_872778, _872780, _872782, _872784] : [5918 ^ _778495 : [(5921 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_872778), _872780), _872784))], (5919 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_872778), _872780), _872782))]], -(hBOOL(hAPP(hAPP(c_member(_872778), _872780), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_872778, tc_HOL_Obool)), _872784), _872782))))], (21026 ^ _778495) ^ [_1155186, _1155188] : [c_Int_OBit1(_1155186) = c_Int_OBit1(_1155188), -(_1155186 = _1155188)], (1808 ^ _778495) ^ [_804123, _804125] : [-(class_Groups_Omonoid__mult(_804123)), _804125 = _804123, class_Groups_Omonoid__mult(_804125)], (48490 ^ _778495) ^ [_1756287, _1756289, _1756291, _1756293, _1756295, _1756297] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1756287, _1756289, _1756291, _1756293, c_Lazy__Sequence_Olazy__sequence_OInsert(_1756289, _1756295, _1756297)) = hAPP(hAPP(_1756293, _1756295), _1756297))], (23685 ^ _778495) ^ [_1202795, _1202797, _1202799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202795), _1202797)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202799), 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), _1202797), _1202799)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202795), _1202799))))], (43854 ^ _778495) ^ [_1655655, _1655657, _1655659] : [-(hAPP(c_List_Otl(_1655655), hAPP(hAPP(c_List_Otake(_1655655), _1655657), _1655659)) = hAPP(hAPP(c_List_Otake(_1655655), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655657), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1655655), _1655659)))], (11041 ^ _778495) ^ [_968473, _968475, _968477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968473), _968475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968473), _968477)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968475), _968473)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968477), _968473)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968475), _968477))], (14181 ^ _778495) ^ [_1030363, _1030365, _1030367] : [class_Rings_Olinordered__semiring__strict(_1030363), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030363), c_Groups_Ozero__class_Ozero(_1030363)), _1030365)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030363), c_Groups_Ozero__class_Ozero(_1030363)), _1030367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030363), c_Groups_Ozero__class_Ozero(_1030363)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030363), _1030365), _1030367))))], (38759 ^ _778495) ^ [_1528742, _1528744, _1528746] : [c_Wellfounded_Owf(_1528742, _1528744), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528742, _1528742)), hAPP(hAPP(c_Product__Type_OPair(_1528742, _1528742), _1528746), _1528746)), _1528744))], (17804 ^ _778495) ^ [_1097726, _1097728, _1097730, _1097732] : [class_Orderings_Olinorder(_1097726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097726), _1097728), _1097730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097726), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1097726), _1097732), _1097728)), _1097730)))], (42594 ^ _778495) ^ [_1627648, _1627650, _1627652] : [hBOOL(hAPP(c_List_Odistinct(_1627648), _1627650)), -(hAPP(c_List_Oset(_1627648), c_List_Oremove1(_1627648, _1627652, _1627650)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627648, tc_HOL_Obool)), hAPP(c_List_Oset(_1627648), _1627650)), hAPP(hAPP(c_Set_Oinsert(_1627648), _1627652), c_Orderings_Obot__class_Obot(tc_fun(_1627648, tc_HOL_Obool)))))], (37931 ^ _778495) ^ [_1500724, _1500726, _1500728] : [-(hAPP(c_Set_OCollect(_1500724), hAPP(hAPP(c_COMBS(_1500724, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1500724), c_fimplies), _1500726)), _1500728)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1500724, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1500724, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1500724), _1500726))), hAPP(c_Set_OCollect(_1500724), _1500728)))], (5422 ^ _778495) ^ [_861515, _861517, _861519, _861521, _861523, _861525, _861527, _861529] : [-(c_SetInterval_Oord_OatLeastAtMost(_861529, _861525, _861521, _861517) = c_SetInterval_Oord_OatLeastAtMost(_861527, _861523, _861519, _861515)), _861529 = _861527, _861525 = _861523, _861521 = _861519, _861517 = _861515], (26932 ^ _778495) ^ [_1259759, _1259761] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1259759), hAPP(c_Int_Onumber__class_Onumber__of(_1259759), c_Int_OMin)), _1259761) = hAPP(c_Groups_Ouminus__class_Ouminus(_1259759), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1259759), c_Groups_Oone__class_Oone(_1259759)), _1259761))), class_Fields_Ofield__inverse__zero(_1259759), class_Int_Onumber__ring(_1259759)], (40595 ^ _778495) ^ [_1573526, _1573528, _1573530, _1573532] : [c_Wellfounded_Owf(_1573526, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1573526, _1573526)), hAPP(hAPP(c_Product__Type_OPair(_1573526, _1573526), _1573528), _1573530)), _1573532)), 40598 ^ _778495 : [(40601 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573526, _1573526)), hAPP(hAPP(c_Product__Type_OPair(_1573526, _1573526), _1573530), _1573528)), c_Transitive__Closure_Ortrancl(_1573526, _1573532)))], (40599 ^ _778495) ^ [] : [-(c_Wellfounded_Owf(_1573526, _1573532))]]], (38256 ^ _778495) ^ [_1512762, _1512764, _1512766] : [class_Orderings_Olinorder(_1512762), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512762), _1512764)), -(_1512764 = c_Orderings_Obot__class_Obot(tc_fun(_1512762, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512762), _1512766)), -(_1512766 = c_Orderings_Obot__class_Obot(tc_fun(_1512762, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1512762), c_Big__Operators_Olattice_OInf__fin(_1512762, c_Orderings_Oord__class_Omin(_1512762), _1512764)), c_Big__Operators_Olattice_OInf__fin(_1512762, c_Orderings_Oord__class_Omin(_1512762), _1512766)) = c_Big__Operators_Olattice_OInf__fin(_1512762, c_Orderings_Oord__class_Omin(_1512762), hAPP(c_Set_OCollect(_1512762), hAPP(hAPP(c_COMBB(tc_fun(_1512762, tc_HOL_Obool), tc_HOL_Obool, _1512762), c_HOL_OEx(_1512762)), hAPP(hAPP(c_COMBB(tc_fun(_1512762, tc_fun(_1512762, tc_HOL_Obool)), tc_fun(_1512762, tc_HOL_Obool), _1512762), hAPP(c_COMBB(tc_fun(_1512762, tc_HOL_Obool), tc_HOL_Obool, _1512762), c_HOL_OEx(_1512762))), hAPP(hAPP(c_COMBC(_1512762, tc_fun(_1512762, tc_fun(_1512762, tc_HOL_Obool)), tc_fun(_1512762, tc_fun(_1512762, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512762, tc_fun(tc_fun(_1512762, tc_HOL_Obool), tc_fun(_1512762, tc_HOL_Obool))), tc_fun(tc_fun(_1512762, tc_fun(_1512762, tc_HOL_Obool)), tc_fun(_1512762, tc_fun(_1512762, tc_HOL_Obool))), _1512762), c_COMBS(_1512762, tc_fun(_1512762, tc_HOL_Obool), tc_fun(_1512762, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512762, tc_fun(_1512762, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1512762, tc_fun(tc_fun(_1512762, tc_HOL_Obool), tc_fun(_1512762, tc_HOL_Obool))), _1512762), hAPP(c_COMBB(tc_fun(_1512762, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1512762, tc_HOL_Obool), tc_fun(_1512762, tc_HOL_Obool)), _1512762), c_COMBS(_1512762, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512762, tc_fun(_1512762, tc_HOL_Obool)), tc_fun(_1512762, tc_fun(_1512762, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1512762), hAPP(c_COMBB(tc_fun(_1512762, tc_HOL_Obool), tc_fun(_1512762, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1512762), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512762), c_fconj))), hAPP(hAPP(c_COMBC(_1512762, tc_fun(_1512762, tc_fun(_1512762, _1512762)), tc_fun(_1512762, tc_fun(_1512762, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1512762, _1512762), tc_fun(_1512762, tc_HOL_Obool)), tc_fun(tc_fun(_1512762, tc_fun(_1512762, _1512762)), tc_fun(_1512762, tc_fun(_1512762, tc_HOL_Obool))), _1512762), c_COMBB(tc_fun(_1512762, _1512762), tc_fun(_1512762, tc_HOL_Obool), _1512762)), hAPP(hAPP(c_COMBB(tc_fun(_1512762, tc_HOL_Obool), tc_fun(tc_fun(_1512762, _1512762), tc_fun(_1512762, tc_HOL_Obool)), _1512762), c_COMBB(_1512762, tc_HOL_Obool, _1512762)), c_fequal))), c_Orderings_Oord__class_Omax(_1512762)))))), hAPP(hAPP(c_COMBC(_1512762, tc_fun(_1512762, tc_HOL_Obool), tc_fun(_1512762, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1512762, tc_HOL_Obool), tc_fun(_1512762, tc_HOL_Obool)), _1512762), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1512762)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512762), c_fconj), hAPP(hAPP(c_COMBC(_1512762, tc_fun(_1512762, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512762)), _1512764)))), hAPP(hAPP(c_COMBC(_1512762, tc_fun(_1512762, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512762)), _1512766))))))))], (51071 ^ _778495) ^ [_1811825, _1811827] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811825), _1811827))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811825), _1811827)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811827), _1811825)))], (30771 ^ _778495) ^ [_1340187, _1340189, _1340191] : [class_Orderings_Olinorder(_1340187), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340187), _1340189), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340187), _1340191), _1340189))))], (35506 ^ _778495) ^ [_1442044, _1442046, _1442048, _1442050, _1442052, _1442054] : [-(hAPP(c_Relation_OImage(_1442044, _1442046, _1442048), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1442050, tc_fun(_1442044, tc_HOL_Obool)), _1442052), _1442054)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1442050, tc_fun(_1442046, tc_HOL_Obool)), _1442052), hAPP(hAPP(c_COMBB(tc_fun(_1442044, tc_HOL_Obool), tc_fun(_1442046, tc_HOL_Obool), _1442050), c_Relation_OImage(_1442044, _1442046, _1442048)), _1442054)))], (33664 ^ _778495) ^ [_1405236, _1405238, _1405240, _1405242, _1405244, _1405246] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405236, tc_fun(_1405238, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405240, tc_fun(_1405236, tc_HOL_Obool)), _1405242), _1405244)), _1405246) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405240, tc_fun(_1405238, tc_HOL_Obool)), _1405242), hAPP(hAPP(c_COMBC(_1405240, tc_fun(_1405236, tc_fun(_1405238, tc_HOL_Obool)), tc_fun(_1405238, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405236, tc_HOL_Obool), tc_fun(tc_fun(_1405236, tc_fun(_1405238, tc_HOL_Obool)), tc_fun(_1405238, tc_HOL_Obool)), _1405240), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405236, tc_fun(_1405238, tc_HOL_Obool))), _1405244)), _1405246)))], (37043 ^ _778495) ^ [_1477121, _1477123] : [-(c_Set_Othe__elem(_1477121, _1477123) = c_HOL_OThe(_1477121, hAPP(hAPP(c_COMBB(tc_fun(_1477121, tc_HOL_Obool), tc_HOL_Obool, _1477121), hAPP(c_fequal, _1477123)), hAPP(hAPP(c_COMBC(_1477121, tc_fun(_1477121, tc_HOL_Obool), tc_fun(_1477121, tc_HOL_Obool)), c_Set_Oinsert(_1477121)), c_Orderings_Obot__class_Obot(tc_fun(_1477121, tc_HOL_Obool))))))], (14675 ^ _778495) ^ [_1038840, _1038842] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1038840), _1038842) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14678 ^ _778495 : [(14681 ^ _778495) ^ [] : [-(_1038842 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14679 ^ _778495) ^ [] : [-(_1038840 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (42852 ^ _778495) ^ [_1632446, _1632448, _1632450] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1632446)), -(c_List_Osublist(_1632448, hAPP(hAPP(c_List_Olist_OCons(_1632448), _1632450), c_List_Olist_ONil(_1632448)), _1632446) = hAPP(hAPP(c_List_Olist_OCons(_1632448), _1632450), c_List_Olist_ONil(_1632448)))], (6872 ^ _778495) ^ [_891273, _891275] : [class_Lattices_Obounded__lattice__bot(_891273), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891273), _891275), c_Orderings_Obot__class_Obot(_891273)) = _891275)], (22778 ^ _778495) ^ [_1185663, _1185665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1185663)), c_Int_OBit1(_1185665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185663), _1185665)))], (22154 ^ _778495) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (8650 ^ _778495) ^ [_923004, _923006] : [class_Groups_Oab__semigroup__mult(_923004), hBOOL(hAPP(c_Finite__Set_Ofinite(_923004), _923006)), -(_923006 = c_Orderings_Obot__class_Obot(tc_fun(_923004, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_923004), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923004), 8663 ^ [_923004, _923006]), 8664 ^ [_923004, _923006])), hAPP(hAPP(c_Set_Oinsert(_923004), 8663 ^ [_923004, _923006]), hAPP(hAPP(c_Set_Oinsert(_923004), 8664 ^ [_923004, _923006]), c_Orderings_Obot__class_Obot(tc_fun(_923004, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_923004), hAPP(c_Finite__Set_Ofold1(_923004, c_Groups_Otimes__class_Otimes(_923004)), _923006)), _923006)))], (41342 ^ _778495) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25604 ^ _778495) ^ [_1235984, _1235986] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1235984, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1235986)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1235984, 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)))), _1235986)))], (5937 ^ _778495) ^ [_873163, _873165, _873167, _873169] : [hBOOL(hAPP(hAPP(c_member(_873163), _873165), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_873163, tc_HOL_Obool)), _873167), _873169))), 5940 ^ _778495 : [(5943 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873163), _873165), _873169))], (5941 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_873163), _873165), _873167)))]]], (22336 ^ _778495) ^ [_1177885, _1177887] : [class_Groups_Ogroup__add(_1177885), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1177885), c_Groups_Ozero__class_Ozero(_1177885)), _1177887) = hAPP(c_Groups_Ouminus__class_Ouminus(_1177885), _1177887))], (42134 ^ _778495) ^ [_1616998, _1617000, _1617002, _1617004, _1617006, _1617008] : [-(hAPP(hAPP(c_List_Ozip(_1616998, _1617000), hAPP(hAPP(c_List_Olist_OCons(_1616998), _1617002), _1617004)), hAPP(hAPP(c_List_Olist_OCons(_1617000), _1617006), _1617008)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1616998, _1617000)), hAPP(hAPP(c_Product__Type_OPair(_1616998, _1617000), _1617002), _1617006)), hAPP(hAPP(c_List_Ozip(_1616998, _1617000), _1617004), _1617008)))], (52565 ^ _778495) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (6228 ^ _778495) ^ [_879194, _879196, _879198, _879200, _879202] : [class_Orderings_Oord(_879194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879196, _879194)), _879198), _879200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879194), hAPP(_879198, _879202)), hAPP(_879200, _879202))))], (42407 ^ _778495) ^ [_1623319, _1623321, _1623323, _1623325] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623319), tc_List_Olist(_1623319))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623319), tc_List_Olist(_1623319)), _1623321), _1623323)), c_List_Olistrel1(_1623319, _1623325))), 42412 ^ _778495 : [(42417 ^ _778495) ^ [] : [-(_1623323 = hAPP(hAPP(c_List_Olist__update(_1623319, _1623321), 42411 ^ [_1623319, _1623321, _1623323, _1623325]), 42410 ^ [_1623319, _1623321, _1623323, _1623325]))], (42415 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42411 ^ [_1623319, _1623321, _1623323, _1623325]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623319)), _1623321))))], (42413 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623319, _1623319)), hAPP(hAPP(c_Product__Type_OPair(_1623319, _1623319), hAPP(hAPP(c_List_Onth(_1623319), _1623321), 42411 ^ [_1623319, _1623321, _1623323, _1623325])), 42410 ^ [_1623319, _1623321, _1623323, _1623325])), _1623325)))]]], (34275 ^ _778495) ^ [_1417711, _1417713, _1417715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1417711, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1417711, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34276 ^ [_1417711, _1417713, _1417715])), _1417713)), _1417715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1417711, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1417711, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1417713)), _1417715)))], (51037 ^ _778495) ^ [_1811289, _1811291] : [_1811291 = _1811289, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811289), _1811291)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811291), _1811289)))], (28427 ^ _778495) ^ [_1291941, _1291943, _1291945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291941, tc_HOL_Obool)), _1291943), _1291945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291941, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1291941, tc_fun(_1291941, tc_HOL_Obool), tc_HOL_Obool), c_member(_1291941)), _1291943)), hAPP(hAPP(c_COMBC(_1291941, tc_fun(_1291941, tc_HOL_Obool), tc_HOL_Obool), c_member(_1291941)), _1291945))))], (42950 ^ _778495) ^ [_1634631, _1634633, _1634635] : [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), _1634631), _1634633))), -(hBOOL(hAPP(hAPP(_1634635, _1634631), _1634633))), 42957 ^ _778495 : [(42960 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 42955 ^ [_1634631, _1634633, _1634635]), 42956 ^ [_1634631, _1634633, _1634635])), -(hBOOL(hAPP(hAPP(_1634635, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 42955 ^ [_1634631, _1634633, _1634635]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 42956 ^ [_1634631, _1634633, _1634635])))], (42966 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1634635, 42955 ^ [_1634631, _1634633, _1634635]), 42956 ^ [_1634631, _1634633, _1634635]))], (42958 ^ _778495) ^ [] : [-(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), 42955 ^ [_1634631, _1634633, _1634635]), 42956 ^ [_1634631, _1634633, _1634635]))))]]], (48204 ^ _778495) ^ [_1750723, _1750725, _1750727] : [-(_1750723 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1750725), c_List_Oreplicate(_1750725, _1750723, _1750727)) = _1750727)], (31829 ^ _778495) ^ [_1361540, _1361542, _1361544, _1361546, _1361548, _1361550] : [class_Complete__Lattice_Ocomplete__lattice(_1361540), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361542, tc_fun(_1361544, _1361540)), _1361546), _1361548), _1361550) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361542, _1361540), _1361546), hAPP(hAPP(c_COMBC(_1361542, _1361544, _1361540), _1361548), _1361550)))], (22596 ^ _778495) ^ [_1182419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182419), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1182419)), c_Int_OPls)))], (3612 ^ _778495) ^ [_832692, _832694] : [_832694 = _832692, -(c_Orderings_Oord__class_Omax(_832694) = c_Orderings_Oord__class_Omax(_832692))], (20109 ^ _778495) ^ [_1139725, _1139727, _1139729] : [class_Rings_Olinordered__semidom(_1139725), 20112 ^ _778495 : [(20119 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1139727), _1139729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139725), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1139725), _1139727)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1139725), _1139729))))], (20113 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139725), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1139725), _1139727)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1139725), _1139729))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1139727), _1139729)))]]], (1448 ^ _778495) ^ [_799623, _799625] : [-(class_Lattices_Odistrib__lattice(_799623)), _799625 = _799623, class_Lattices_Odistrib__lattice(_799625)], (12440 ^ _778495) ^ [_997804, _997806, _997808] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_997804, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_997804, tc_HOL_Obool), tc_HOL_Obool)), _997806), _997808)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_997804, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_997804, tc_HOL_Obool), _997806)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_997804, tc_HOL_Obool), _997808)))], (14497 ^ _778495) ^ [_1036001, _1036003, _1036005] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1036001), _1036003)), 14500 ^ _778495 : [(14520 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1036001, tc_Nat_Onat), _1036005), _1036003) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 14521 ^ _778495 : [(14522 ^ _778495) ^ [_1036482] : [hBOOL(hAPP(hAPP(c_member(_1036001), _1036482), _1036003)), hAPP(_1036005, _1036482) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14530 ^ _778495 : [(14535 ^ _778495) ^ [] : [hAPP(_1036005, 14529 ^ [_1036001, _1036003, _1036005, _1036482]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14533 ^ _778495) ^ [] : [_1036482 = 14529 ^ [_1036001, _1036003, _1036005, _1036482]], (14531 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1036001), 14529 ^ [_1036001, _1036003, _1036005, _1036482]), _1036003)))]]]]], (14501 ^ _778495) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1036001, tc_Nat_Onat), _1036005), _1036003) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14505 ^ _778495 : [(14510 ^ _778495) ^ [_1036321] : [hBOOL(hAPP(hAPP(c_member(_1036001), _1036321), _1036003)), -(14504 ^ [_1036001, _1036003, _1036005] = _1036321), -(hAPP(_1036005, _1036321) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14508 ^ _778495) ^ [] : [-(hAPP(_1036005, 14504 ^ [_1036001, _1036003, _1036005]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14506 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1036001), 14504 ^ [_1036001, _1036003, _1036005]), _1036003)))]]]]], (13342 ^ _778495) ^ [_1015729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1015729)), _1015729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26614 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (2566 ^ _778495) ^ [_816355, _816357, _816359, _816361, _816363, _816365] : [-(c_Partial__Function_Oflat__lub(_816365, _816361, _816357) = c_Partial__Function_Oflat__lub(_816363, _816359, _816355)), _816365 = _816363, _816361 = _816359, _816357 = _816355], (36624 ^ _778495) ^ [_1468058] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1468058)), c_Int_OInteg)))], (33624 ^ _778495) ^ [_1404204, _1404206, _1404208, _1404210, _1404212] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404204, tc_fun(_1404206, tc_HOL_Obool)), _1404208), _1404210), _1404212)), 33628 ^ _778495 : [(33631 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1404210, 33627 ^ [_1404204, _1404206, _1404208, _1404210, _1404212]), _1404212)))], (33629 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404204), 33627 ^ [_1404204, _1404206, _1404208, _1404210, _1404212]), _1404208)))]]], (49278 ^ _778495) ^ [_1774785, _1774787] : [49279 ^ _778495 : [(49280 ^ _778495) ^ [_1774841] : [hBOOL(hAPP(hAPP(_1774785, _1774841), _1774841))]], c_Predicate_Osymp(_1774787, _1774785), c_Predicate_Otransp(_1774787, _1774785), -(c_Equiv__Relations_Opart__equivp(_1774787, _1774785))], (21088 ^ _778495) ^ [_1156231, _1156233, _1156235] : [class_Rings_Olinordered__idom(_1156231), -(hAPP(c_Groups_Oabs__class_Oabs(_1156231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156231), _1156233), _1156235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156231), hAPP(c_Groups_Oabs__class_Oabs(_1156231), _1156233)), hAPP(c_Groups_Oabs__class_Oabs(_1156231), _1156235)))], (39200 ^ _778495) ^ [_1539813] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1539813, tc_HOL_Obool) = c_Set_OBall(_1539813))], (45937 ^ _778495) ^ [_1702788, _1702790] : [c_List_Oupt(_1702788, _1702790) = c_List_Olist_ONil(tc_Nat_Onat), -(_1702790 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702790), _1702788)))], (46644 ^ _778495) ^ [_1716226, _1716228] : [-(hAPP(c_List_Orev(_1716226), c_List_Oconcat(_1716226, _1716228)) = c_List_Oconcat(_1716226, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1716226), tc_List_Olist(_1716226)), c_List_Orev(_1716226)), hAPP(c_List_Orev(tc_List_Olist(_1716226)), _1716228))))], (24055 ^ _778495) ^ [_1208823, _1208825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1208823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1208823), _1208825)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208823, _1208825) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1208823), _1208825))], (45394 ^ _778495) ^ [_1689561, _1689563] : [hBOOL(hAPP(c_List_Odistinct(_1689561), _1689563)), -(c_List_Oremdups(_1689561, _1689563) = _1689563)], (33828 ^ _778495) ^ [_1408276, _1408278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1408276), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408278), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1408276))))), -(_1408276 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408278), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1408276))))], (37085 ^ _778495) ^ [_1478254, _1478256, _1478258] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478254, tc_HOL_Obool)), _1478256), hAPP(hAPP(c_Set_Oinsert(_1478254), _1478258), c_Orderings_Obot__class_Obot(tc_fun(_1478254, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1478254, _1478258, _1478256) = c_HOL_OThe(_1478254, hAPP(hAPP(c_COMBC(_1478254, tc_fun(_1478254, tc_HOL_Obool), tc_HOL_Obool), c_member(_1478254)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1478254, tc_HOL_Obool)), _1478256), hAPP(hAPP(c_Set_Oinsert(_1478254), _1478258), c_Orderings_Obot__class_Obot(tc_fun(_1478254, tc_HOL_Obool)))))))], (32010 ^ _778495) ^ [_1367160, _1367162, _1367164, _1367166, _1367168] : [-(_1367160 = c_Orderings_Obot__class_Obot(tc_fun(_1367162, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367164, tc_HOL_Obool)), _1367166), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367162, tc_fun(_1367164, tc_HOL_Obool)), _1367160), _1367168)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367162, tc_fun(_1367164, tc_HOL_Obool)), _1367160), hAPP(hAPP(c_COMBB(tc_fun(_1367164, tc_HOL_Obool), tc_fun(_1367164, tc_HOL_Obool), _1367162), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367164, tc_HOL_Obool)), _1367166)), _1367168)))], (37122 ^ _778495) ^ [_1479099, _1479101, _1479103, _1479105, _1479107] : [hBOOL(hAPP(hAPP(c_member(_1479099), _1479101), hAPP(c_Set_Ovimage(_1479099, _1479103, _1479105), _1479107))), -(hBOOL(hAPP(hAPP(c_member(_1479103), hAPP(_1479105, _1479101)), _1479107)))], (16924 ^ _778495) ^ [_1080819, _1080821, _1080823, _1080825, _1080827] : [class_Fields_Olinordered__field(_1080819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080819), c_Groups_Ozero__class_Ozero(_1080819)), _1080821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080819), _1080821), _1080823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080819), c_Groups_Ozero__class_Ozero(_1080819)), _1080825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080819), _1080825), _1080827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080819), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1080819), _1080821), _1080827)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1080819), _1080823), _1080825))))], (49489 ^ _778495) ^ [_1778626, _1778628] : [-(c_Relation_Osym(_1778626, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1778626, _1778626), tc_HOL_Obool)), _1778628), hAPP(c_Relation_Oconverse(_1778626, _1778626), _1778628))))], (45843 ^ _778495) ^ [_1700521] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1700521)), c_List_Otranspose__rel(_1700521)), c_List_Olist_ONil(tc_List_Olist(_1700521)))), -(c_List_Otranspose(_1700521, c_List_Olist_ONil(tc_List_Olist(_1700521))) = c_List_Olist_ONil(tc_List_Olist(_1700521)))], (29877 ^ _778495) ^ [_1321891, _1321893, _1321895] : [29879 ^ _778495 : [(29882 ^ _778495) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1321895, 29878 ^ [_1321891, _1321893, _1321895]))], (29880 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1321891), 29878 ^ [_1321891, _1321893, _1321895]), _1321893)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1321891, tc_Int_Oint), _1321895), _1321893) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1321891, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1321891), c_Int_Onat), _1321895)), _1321893)))], (44992 ^ _778495) ^ [_1680464, _1680466, _1680468, _1680470] : [hBOOL(hAPP(c_List_Olistsp(_1680464, _1680466), hAPP(hAPP(c_List_Olist_OCons(_1680464), _1680468), _1680470))), 44995 ^ _778495 : [(44998 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1680464, _1680466), _1680470)))], (44996 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1680466, _1680468)))]]], (50096 ^ _778495) ^ [_1791443, _1791445, _1791447, _1791449] : [c_Fun_Obij__betw(_1791443, _1791445, _1791447, _1791449, c_Orderings_Otop__class_Otop(tc_fun(_1791445, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1791443, _1791445, _1791447), c_Orderings_Otop__class_Otop(tc_fun(_1791443, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1791445, tc_HOL_Obool)))], (23052 ^ _778495) ^ [_1190888, _1190890] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190888, _1190890) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1190888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1190888), _1190890)), _1190890)))], (15151 ^ _778495) ^ [_1047496, _1047498, _1047500, _1047502] : [class_Rings_Olinordered__ring__strict(_1047496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047496), _1047498), c_Groups_Ozero__class_Ozero(_1047496))), 15158 ^ _778495 : [(15165 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047496), _1047502), _1047500)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047496), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047496), _1047498), _1047500)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047496), _1047498), _1047502))))], (15159 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047496), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047496), _1047498), _1047500)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047496), _1047498), _1047502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047496), _1047502), _1047500)))]]], (47855 ^ _778495) ^ [_1742698, _1742700] : [-(c_FunDef_Ois__measure(_1742698, _1742700))], (26030 ^ _778495) ^ [_1243913, _1243915, _1243917, _1243919] : [class_Rings_Olinordered__semidom(_1243913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243913), c_Groups_Oone__class_Oone(_1243913)), _1243915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243913), hAPP(hAPP(c_Power_Opower__class_Opower(_1243913), _1243915), _1243917)), hAPP(hAPP(c_Power_Opower__class_Opower(_1243913), _1243915), _1243919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243917), _1243919)))], (17364 ^ _778495) ^ [_1089061, _1089063, _1089065] : [class_Fields_Olinordered__field(_1089061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089061), _1089063), _1089065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089061), _1089063), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1089061), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089061), _1089063), _1089065)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089061), c_Groups_Oone__class_Oone(_1089061)), c_Groups_Oone__class_Oone(_1089061))))))], (27815 ^ _778495) ^ [_1274918, _1274920] : [c_Nat__Transfer_Ois__nat(_1274918), c_Nat__Transfer_Ois__nat(_1274920), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1274918), _1274920)))], (1218 ^ _778495) ^ [_796748, _796750] : [-(class_Rings_Oordered__ring__abs(_796748)), _796750 = _796748, class_Rings_Oordered__ring__abs(_796750)], (2420 ^ _778495) ^ [_814128, _814130, _814132, _814134] : [-(c_Orderings_Oord_Omax(_814134, _814130) = c_Orderings_Oord_Omax(_814132, _814128)), _814134 = _814132, _814130 = _814128], (34685 ^ _778495) ^ [_1427076, _1427078, _1427080] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1427076), _1427078), _1427080) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1427076), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1427076, tc_Int_Oint), _1427078), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1427080))), class_Groups_Ocomm__monoid__add(_1427076), class_Groups_Ocomm__monoid__mult(_1427076)], (12515 ^ _778495) ^ [_999468, _999470, _999472] : [class_Complete__Lattice_Ocomplete__lattice(_999468), hBOOL(hAPP(hAPP(c_member(_999468), _999470), _999472)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999468), _999470), c_Complete__Lattice_OSup__class_OSup(_999468, _999472))))], (24455 ^ _778495) ^ [_1216000, _1216002] : [class_Rings_Osemiring__1(_1216000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216002)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216000), 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)))), _1216002))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216000), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216000), hAPP(c_Int_Onat, _1216002))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216000), hAPP(c_Int_Onat, _1216002))))], (25646 ^ _778495) ^ [_1236714] : [class_Rings_Osemiring__1(_1236714), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1236714), c_Groups_Oone__class_Oone(_1236714)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1236714))], (33276 ^ _778495) ^ [_1394062, _1394064, _1394066, _1394068, _1394070] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394062, tc_HOL_Obool)), _1394064), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394066, tc_fun(_1394062, tc_HOL_Obool)), _1394068), _1394070)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394066, tc_fun(_1394062, tc_HOL_Obool)), _1394068), hAPP(hAPP(c_COMBB(tc_fun(_1394062, tc_HOL_Obool), tc_fun(_1394062, tc_HOL_Obool), _1394066), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394062, tc_HOL_Obool)), _1394064)), _1394070)))], (52287 ^ _778495) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (42724 ^ _778495) ^ [_1629981, _1629983] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629981)), _1629983) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1629983 = c_List_Olist_ONil(_1629981))], (36017 ^ _778495) ^ [_1454663] : [-(c_Equiv__Relations_Oequivp(_1454663, c_fequal))], (51625 ^ _778495) ^ [_1821201, _1821203] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821203, _1821201) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821201), _1821203)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821203), _1821201)))], (38019 ^ _778495) ^ [_1503224, _1503226, _1503228, _1503230, _1503232, _1503234] : [class_Groups_Ocomm__monoid__add(_1503224), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503226), _1503228)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503226, _1503224), _1503230), _1503228) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503232, _1503224), hAPP(hAPP(c_COMBB(tc_fun(_1503226, tc_HOL_Obool), _1503224, _1503232), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503226, _1503224), _1503230)), hAPP(hAPP(c_COMBB(tc_fun(_1503226, tc_HOL_Obool), tc_fun(_1503226, tc_HOL_Obool), _1503232), c_Set_OCollect(_1503226)), hAPP(hAPP(c_COMBB(tc_fun(_1503226, tc_HOL_Obool), tc_fun(_1503226, tc_HOL_Obool), _1503232), hAPP(c_COMBS(_1503226, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1503226), c_fconj), hAPP(hAPP(c_COMBC(_1503226, tc_fun(_1503226, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503226)), _1503228)))), hAPP(c_COMBC(_1503226, _1503232, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1503232, tc_fun(_1503232, tc_HOL_Obool), _1503226), c_fequal), _1503234)))))), hAPP(c_Set_Oimage(_1503226, _1503232, _1503234), _1503228)))], (37079 ^ _778495) ^ [_1478127, _1478129, _1478131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478127, tc_HOL_Obool)), _1478129), hAPP(hAPP(c_Set_Oinsert(_1478127), _1478131), c_Orderings_Obot__class_Obot(tc_fun(_1478127, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1478127, _1478131, _1478129) = _1478131)], (40796 ^ _778495) ^ [_1578317, _1578319, _1578321] : [-(hAPP(c_Relation_ORange(_1578317, _1578319), hAPP(c_Relation_Oconverse(_1578319, _1578317), _1578321)) = hAPP(c_Relation_ODomain(_1578319, _1578317), _1578321))], (28709 ^ _778495) ^ [_1299016] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1299016))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1299016)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10585 ^ _778495) ^ [_961209, _961211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961209), _961211)), _961209 = _961211], (47695 ^ _778495) ^ [_1739497, _1739499, _1739501] : [-(hBOOL(hAPP(hAPP(c_member(_1739497), _1739499), hAPP(c_List_Oset(_1739497), _1739501)))), 47696 ^ _778495 : [(47697 ^ _778495) ^ [_1739586] : [47698 ^ _778495 : [(47699 ^ _778495) ^ [_1739659] : [_1739501 = hAPP(hAPP(c_List_Oappend(_1739497), _1739586), hAPP(hAPP(c_List_Olist_OCons(_1739497), _1739499), _1739659))]], -(hBOOL(hAPP(hAPP(c_member(_1739497), _1739499), hAPP(c_List_Oset(_1739497), _1739586))))]]], (52147 ^ _778495) ^ [_1830446, _1830448] : [class_Orderings_Oorder(_1830446), -(class_Orderings_Oorder(tc_fun(_1830448, _1830446)))], (26126 ^ _778495) ^ [_1245568, _1245570, _1245572, _1245574] : [class_Groups_Omonoid__mult(_1245568), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1245568), _1245570), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1245572), _1245574)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1245568), hAPP(hAPP(c_Power_Opower__class_Opower(_1245568), _1245570), _1245572)), _1245574))], (26748 ^ _778495) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (26750 ^ _778495) ^ [_1256693] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1256693), c_Int_OMin) = c_Int_Opred(_1256693))], (23280 ^ _778495) ^ [_1195633, _1195635, _1195637] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195633), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195635, _1195637)), _1195637) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195633), _1195635), _1195637))], (786 ^ _778495) ^ [_790400, _790402, _790404, _790406] : [-(c_Relation_Oantisym(_790404, _790400)), c_Relation_Oantisym(_790406, _790402), _790406 = _790404, _790402 = _790400], (13687 ^ _778495) ^ [_1021316, _1021318, _1021320, _1021322] : [class_Groups_Oordered__comm__monoid__add(_1021316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021316), c_Groups_Ozero__class_Ozero(_1021316)), _1021318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021316), _1021320), _1021322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021316), _1021320), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021316), _1021322), _1021318))))], (25343 ^ _778495) ^ [_1231266, _1231268, _1231270] : [-(hBOOL(hAPP(_1231266, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1231268, _1231270)))), 25346 ^ _778495 : [(25349 ^ _778495) ^ [] : [hBOOL(hAPP(_1231266, _1231268))], (25347 ^ _778495) ^ [] : [-(_1231270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25350 ^ _778495 : [(25355 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25353 ^ [_1231266, _1231268, _1231270]), _1231270)))], (25357 ^ _778495) ^ [] : [-(_1231268 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1231270), 25352 ^ [_1231266, _1231268, _1231270])), 25353 ^ [_1231266, _1231268, _1231270]))], (25359 ^ _778495) ^ [] : [hBOOL(hAPP(_1231266, 25353 ^ [_1231266, _1231268, _1231270]))], (25351 ^ _778495) ^ [] : [_1231270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (50048 ^ _778495) ^ [_1790592, _1790594, _1790596, _1790598, _1790600] : [c_Fun_Obij__betw(_1790592, _1790594, _1790596, _1790598, _1790600), -(hAPP(c_Finite__Set_Ocard(_1790592), _1790598) = hAPP(c_Finite__Set_Ocard(_1790594), _1790600))], (52233 ^ _778495) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (35023 ^ _778495) ^ [_1433403] : [c_Nat__Transfer_Onat__set(_1433403), 35026 ^ _778495 : [(35027 ^ _778495) ^ [_1433469] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1433469), _1433403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1433469)))]]], (3780 ^ _778495) ^ [_835292, _835294] : [_835294 = _835292, -(c_List_Odistinct(_835294) = c_List_Odistinct(_835292))], (39442 ^ _778495) ^ [_1546161, _1546163, _1546165, _1546167, _1546169] : [c_Fun_Oinj__on(_1546161, _1546163, _1546165, c_Orderings_Otop__class_Otop(tc_fun(_1546161, tc_HOL_Obool))), c_Fun_Oinj__on(_1546167, _1546161, _1546169, c_Orderings_Otop__class_Otop(tc_fun(_1546167, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1546167, _1546163, hAPP(c_Fun_Ocomp(_1546161, _1546163, _1546167, _1546165), _1546169), c_Orderings_Otop__class_Otop(tc_fun(_1546167, tc_HOL_Obool))))], (43490 ^ _778495) ^ [_1647623, _1647625, _1647627] : [-(hAPP(hAPP(c_List_Oappend(_1647623), hAPP(hAPP(c_List_Otake(_1647623), _1647625), _1647627)), hAPP(hAPP(c_List_Odrop(_1647623), _1647625), _1647627)) = _1647627)], (44480 ^ _778495) ^ [_1669108, _1669110, _1669112, _1669114, _1669116] : [-(hAPP(hAPP(c_List_Omap(_1669108, _1669110), _1669112), hAPP(hAPP(c_List_Olist_OCons(_1669108), _1669114), _1669116)) = hAPP(hAPP(c_List_Olist_OCons(_1669110), hAPP(_1669112, _1669114)), hAPP(hAPP(c_List_Omap(_1669108, _1669110), _1669112), _1669116)))], (23100 ^ _778495) ^ [_1191800, _1191802, _1191804, _1191806] : [class_Divides_Osemiring__div(_1191800), -(c_Divides_Odiv__class_Omod(_1191800, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191800), _1191802), _1191804), _1191806) = c_Divides_Odiv__class_Omod(_1191800, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191800), c_Divides_Odiv__class_Omod(_1191800, _1191802, _1191806)), c_Divides_Odiv__class_Omod(_1191800, _1191804, _1191806)), _1191806))], (13496 ^ _778495) ^ [_1018037, _1018039, _1018041, _1018043] : [class_Groups_Ocomm__monoid__mult(_1018037), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1018039), _1018041))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1018039, _1018037), _1018043), _1018041) = c_Groups_Oone__class_Oone(_1018037))], (18870 ^ _778495) ^ [_1117596, _1117598, _1117600, _1117602] : [class_Fields_Olinordered__field__inverse__zero(_1117596), class_Int_Onumber(_1117596), 18877 ^ _778495 : [(18878 ^ _778495) ^ [] : 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117596), _1117598), hAPP(c_Int_Onumber__class_Onumber__of(_1117596), _1117602)))))]]], (18882 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117596), c_Groups_Ozero__class_Ozero(_1117596)), hAPP(c_Int_Onumber__class_Onumber__of(_1117596), _1117602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117596), _1117598), hAPP(c_Int_Onumber__class_Onumber__of(_1117596), _1117602))), _1117600)))]]], (18904 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117596), _1117598), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117596), _1117600), hAPP(c_Int_Onumber__class_Onumber__of(_1117596), _1117602))))), 18907 ^ _778495 : [(18910 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117596), _1117598), hAPP(c_Int_Onumber__class_Onumber__of(_1117596), _1117602))), _1117600))], (18908 ^ 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c_Groups_Ozero__class_Ozero(_1117596)))]]], (18912 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117596), c_Groups_Ozero__class_Ozero(_1117596)), hAPP(c_Int_Onumber__class_Onumber__of(_1117596), _1117602)))]]]]], (20448 ^ _778495) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (16134 ^ _778495) ^ [_1066971, _1066973, _1066975, _1066977] : [class_Rings_Odivision__ring(_1066971), -(_1066973 = c_Groups_Ozero__class_Ozero(_1066971)), _1066975 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066971), _1066977), _1066973), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066971), _1066975), _1066973) = _1066977)], (47717 ^ _778495) ^ [_1739953, _1739955, _1739957, _1739959] : [47718 ^ _778495 : [(47721 ^ _778495) ^ [] : [c_List_Olist__ex(_1739953, _1739955, _1739959)], (47719 ^ _778495) ^ [] : [c_List_Olist__ex(_1739953, _1739955, _1739957)]], -(c_List_Olist__ex(_1739953, _1739955, hAPP(hAPP(c_List_Oappend(_1739953), _1739957), _1739959)))], (37757 ^ _778495) ^ [_1496681] : [-(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)), _1496681)))))], (28651 ^ _778495) ^ [_1297642] : [-(c_Finite__Set_Ofun__left__comm__idem(_1297642, tc_fun(_1297642, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1297642, tc_HOL_Obool), tc_fun(tc_fun(_1297642, tc_HOL_Obool), tc_fun(_1297642, tc_HOL_Obool)), _1297642), hAPP(c_COMBC(tc_fun(_1297642, tc_HOL_Obool), tc_fun(_1297642, tc_HOL_Obool), tc_fun(_1297642, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1297642, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1297642, tc_fun(_1297642, tc_HOL_Obool), tc_fun(_1297642, tc_HOL_Obool)), c_Set_Oinsert(_1297642)), c_Orderings_Obot__class_Obot(tc_fun(_1297642, tc_HOL_Obool))))))], (9660 ^ _778495) ^ [_943916, _943918, _943920] : [class_Lattices_Osemilattice__inf(_943916), hBOOL(hAPP(c_Finite__Set_Ofinite(_943916), _943918)), -(_943918 = c_Orderings_Obot__class_Obot(tc_fun(_943916, tc_HOL_Obool))), 9671 ^ _778495 : [(9672 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943916), _943920), hAPP(c_Finite__Set_Ofold1(_943916, c_Lattices_Osemilattice__inf__class_Oinf(_943916)), _943918))), 9675 ^ _778495 : [(9676 ^ _778495) ^ [_944209] : [hBOOL(hAPP(hAPP(c_member(_943916), _944209), _943918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943916), _943920), _944209)))]]], (9682 ^ _778495) ^ [] : [9684 ^ _778495 : [(9687 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943916), _943920), 9683 ^ [_943916, _943918, _943920]))], (9685 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_943916), 9683 ^ [_943916, _943918, _943920]), _943918)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943916), _943920), hAPP(c_Finite__Set_Ofold1(_943916, c_Lattices_Osemilattice__inf__class_Oinf(_943916)), _943918))))]]], (26092 ^ _778495) ^ [_1244863, _1244865, _1244867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1244863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1244863), _1244865)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1244863), _1244867))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1244865), _1244867)))], (46734 ^ _778495) ^ [_1718225, _1718227] : [-(_1718225 = c_List_Olist_ONil(_1718227)), -(c_List_Olast(_1718227, hAPP(c_List_Orev(_1718227), _1718225)) = hAPP(c_List_Ohd(_1718227), _1718225))], (44428 ^ _778495) ^ [_1667798, _1667800, _1667802, _1667804, _1667806] : [class_Rings_Osemiring__0(_1667798), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667798), hAPP(hAPP(c_List_Omap(_1667800, _1667798), hAPP(hAPP(c_COMBB(_1667798, _1667798, _1667800), hAPP(c_Groups_Otimes__class_Otimes(_1667798), _1667802)), _1667804)), _1667806)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1667798), _1667802), hAPP(c_List_Omonoid__add__class_Olistsum(_1667798), hAPP(hAPP(c_List_Omap(_1667800, _1667798), _1667804), _1667806))))], (8500 ^ _778495) ^ [_920240, _920242, _920244, _920246, _920248] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_920240, _920242, hAPP(hAPP(c_Set_Oinsert(_920240), _920244), _920246)), _920248))), 8501 ^ _778495 : [(8502 ^ _778495) ^ [_920344, _920346] : [hAPP(hAPP(c_Set_Oinsert(_920240), _920244), _920246) = hAPP(hAPP(c_Set_Oinsert(_920240), _920346), _920344), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_920240, _920240, _920242, _920346, _920344), _920248)), -(hBOOL(hAPP(hAPP(c_member(_920240), _920346), _920344)))]]], (9386 ^ _778495) ^ [_938023, _938025, _938027, _938029] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938023, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938023, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938023, tc_HOL_Obool)), _938025), _938027)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938023, tc_HOL_Obool)), _938027), _938029))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938023, tc_HOL_Obool)), _938029), _938025)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938023, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938023, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938023, tc_HOL_Obool)), _938025), _938027)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938023, tc_HOL_Obool)), _938027), _938029))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938023, tc_HOL_Obool)), _938029), _938025)))], (25744 ^ _778495) ^ [_1238465, _1238467, _1238469] : [class_Rings_Olinordered__idom(_1238465), 25747 ^ _778495 : [(25756 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1238465), hAPP(hAPP(c_Power_Opower__class_Opower(_1238465), _1238467), 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(_1238465), _1238469), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1238465)), _1238467 = c_Groups_Ozero__class_Ozero(_1238465), _1238469 = c_Groups_Ozero__class_Ozero(_1238465)], (25748 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1238465), hAPP(hAPP(c_Power_Opower__class_Opower(_1238465), _1238467), 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(_1238465), _1238469), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1238465), 25751 ^ _778495 : [(25754 ^ _778495) ^ [] : [-(_1238469 = c_Groups_Ozero__class_Ozero(_1238465))], (25752 ^ _778495) ^ [] : [-(_1238467 = c_Groups_Ozero__class_Ozero(_1238465))]]]]], (42938 ^ _778495) ^ [_1634197, _1634199, _1634201, _1634203, _1634205] : [-(hAPP(hAPP(c_List_Ozip(_1634197, _1634199), _1634201), hAPP(hAPP(c_List_Olist_OCons(_1634199), _1634203), _1634205)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1634197, _1634199)), _1634197, c_List_Olist_ONil(tc_prod(_1634197, _1634199)), hAPP(hAPP(c_COMBC(_1634197, tc_fun(tc_List_Olist(_1634197), tc_List_Olist(tc_prod(_1634197, _1634199))), tc_fun(tc_List_Olist(_1634197), tc_List_Olist(tc_prod(_1634197, _1634199)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1634197, _1634199)), tc_List_Olist(tc_prod(_1634197, _1634199))), tc_fun(tc_fun(tc_List_Olist(_1634197), tc_List_Olist(tc_prod(_1634197, _1634199))), tc_fun(tc_List_Olist(_1634197), tc_List_Olist(tc_prod(_1634197, _1634199)))), _1634197), c_COMBB(tc_List_Olist(tc_prod(_1634197, _1634199)), tc_List_Olist(tc_prod(_1634197, _1634199)), tc_List_Olist(_1634197))), hAPP(hAPP(c_COMBB(tc_prod(_1634197, _1634199), tc_fun(tc_List_Olist(tc_prod(_1634197, _1634199)), tc_List_Olist(tc_prod(_1634197, _1634199))), _1634197), c_List_Olist_OCons(tc_prod(_1634197, _1634199))), hAPP(hAPP(c_COMBC(_1634197, _1634199, tc_prod(_1634197, _1634199)), c_Product__Type_OPair(_1634197, _1634199)), _1634203)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1634197), tc_List_Olist(_1634199), tc_List_Olist(tc_prod(_1634197, _1634199))), c_List_Ozip(_1634197, _1634199)), _1634205))), _1634201))], (20073 ^ _778495) ^ [_1139092, _1139094] : [class_Rings_Olinordered__semidom(_1139092), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139092), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1139092), _1139094)), c_Groups_Ozero__class_Ozero(_1139092)))], (9030 ^ _778495) ^ [_930930, _930932, _930934, _930936] : [class_Lattices_Osemilattice__inf(_930930), hBOOL(hAPP(c_Finite__Set_Ofinite(_930930), _930932)), hBOOL(hAPP(hAPP(c_member(_930930), _930934), _930932)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930930), hAPP(hAPP(c_Finite__Set_Ofold(_930930, _930930, c_Lattices_Osemilattice__inf__class_Oinf(_930930)), _930936), _930932)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930930), _930934), _930936))))], (34224 ^ _778495) ^ [_1416359, _1416361] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1416359, _1416359)), hAPP(hAPP(c_Product__Type_OPair(_1416359, _1416359), 34225 ^ [_1416359, _1416361]), 34225 ^ [_1416359, _1416361])), _1416361))), -(c_Relation_Oirrefl(_1416359, _1416361))], (14127 ^ _778495) ^ [_1029376, _1029378, _1029380, _1029382] : [class_Rings_Olinordered__ring__strict(_1029376), 14130 ^ _778495 : [(14145 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029376), _1029378), _1029380)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029376), _1029378), _1029382)))), 14146 ^ _778495 : [(14153 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029376), _1029378), c_Groups_Ozero__class_Ozero(_1029376))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029376), _1029382), _1029380))], (14147 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029376), c_Groups_Ozero__class_Ozero(_1029376)), _1029378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029376), _1029380), _1029382))]]], (14131 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029376), _1029378), _1029380)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029376), _1029378), _1029382))), 14136 ^ _778495 : [(14139 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029376), _1029380), _1029382)))], (14137 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029376), c_Groups_Ozero__class_Ozero(_1029376)), _1029378)))]], 14140 ^ _778495 : [(14143 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029376), _1029382), _1029380)))], (14141 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029376), _1029378), c_Groups_Ozero__class_Ozero(_1029376))))]]]]], (45674 ^ _778495) ^ [_1696150, _1696152, _1696154] : [hAPP(c_List_Ofilter(_1696150, _1696152), _1696154) = _1696154, 45677 ^ _778495 : [(45678 ^ _778495) ^ [_1696241] : [hBOOL(hAPP(hAPP(c_member(_1696150), _1696241), hAPP(c_List_Oset(_1696150), _1696154))), -(hBOOL(hAPP(_1696152, _1696241)))]]], (34324 ^ _778495) ^ [_1418875, _1418877, _1418879, _1418881, _1418883, _1418885] : [-(hAPP(c_Set_Oimage(_1418875, _1418877, _1418879), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418881, tc_fun(_1418875, tc_HOL_Obool)), _1418883), _1418885)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418881, tc_fun(_1418877, tc_HOL_Obool)), _1418883), hAPP(hAPP(c_COMBB(tc_fun(_1418875, tc_HOL_Obool), tc_fun(_1418877, tc_HOL_Obool), _1418881), c_Set_Oimage(_1418875, _1418877, _1418879)), _1418885)))], (22602 ^ _778495) ^ [_1182535, _1182537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1182535)), c_Int_OBit0(_1182537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182535), _1182537)))], (38977 ^ _778495) ^ [_1534278, _1534280] : [c_Wellfounded_Owf(_1534278, _1534280), -(c_Wellfounded_Owf(tc_List_Olist(_1534278), c_List_Olenlex(_1534278, _1534280)))], (33383 ^ _778495) ^ [_1397500, _1397502, _1397504, _1397506, _1397508] : [hBOOL(hAPP(hAPP(c_member(_1397500), _1397502), _1397504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1397506, tc_HOL_Obool)), hAPP(_1397508, _1397502)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397500, tc_fun(_1397506, tc_HOL_Obool)), _1397504), _1397508))))], (4332 ^ _778495) ^ [_844312, _844314, _844316, _844318, _844320, _844322] : [-(c_New__DSequence_Opos__union(_844322, _844318, _844314) = c_New__DSequence_Opos__union(_844320, _844316, _844312)), _844322 = _844320, _844318 = _844316, _844314 = _844312], (43668 ^ _778495) ^ [_1651846, _1651848, _1651850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651846), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651848)), _1651850))), -(hAPP(hAPP(c_List_Olist_OCons(_1651848), hAPP(hAPP(c_List_Onth(_1651848), _1651850), _1651846)), hAPP(hAPP(c_List_Odrop(_1651848), hAPP(c_Nat_OSuc, _1651846)), _1651850)) = hAPP(hAPP(c_List_Odrop(_1651848), _1651846), _1651850))], (1102 ^ _778495) ^ [_795178, _795180, _795182, _795184, _795186, _795188, _795190, _795192, _795194, _795196] : [-(c_Finite__Set_Ofolding__image(_795194, _795190, _795186, _795182, _795178)), c_Finite__Set_Ofolding__image(_795196, _795192, _795188, _795184, _795180), _795196 = _795194, _795192 = _795190, _795188 = _795186, _795184 = _795182, _795180 = _795178], (3446 ^ _778495) ^ [_830027, _830029] : [_830029 = _830027, -(c_List_Otranspose__rel(_830029) = c_List_Otranspose__rel(_830027))], (37935 ^ _778495) ^ [_1500847] : [-(c_Relation_Orefl__on(_1500847, c_Orderings_Obot__class_Obot(tc_fun(_1500847, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500847, _1500847), tc_HOL_Obool))))], (34817 ^ _778495) ^ [_1429761, _1429763] : [class_Groups_Oordered__ab__group__add(_1429761), -(hAPP(c_Set_Oimage(_1429761, _1429761, c_Groups_Ouminus__class_Ouminus(_1429761)), hAPP(c_SetInterval_Oord__class_OlessThan(_1429761), _1429763)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1429761), hAPP(c_Groups_Ouminus__class_Ouminus(_1429761), _1429763)))], (30897 ^ _778495) ^ [_1342725, _1342727, _1342729, _1342731] : [class_Groups_Oordered__ab__group__add(_1342725), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1342725), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342725), _1342727), _1342729)), _1342731) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342725), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1342725), _1342727), _1342731)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1342725), _1342729), _1342731)))], (22924 ^ _778495) ^ [] : [-(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))))], (26648 ^ _778495) ^ [_1255123] : [c_Int_OMin = c_Int_OBit0(_1255123)], (45796 ^ _778495) ^ [_1698753, _1698755, _1698757] : [hBOOL(hAPP(c_List_Odistinct(_1698753), _1698755)), -(hAPP(c_List_Ofilter(_1698753, hAPP(hAPP(c_COMBC(_1698753, tc_fun(_1698753, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698753)), hAPP(c_List_Oset(_1698753), c_List_Osublist(_1698753, _1698755, _1698757)))), _1698755) = c_List_Osublist(_1698753, _1698755, _1698757))], (47827 ^ _778495) ^ [] : [-(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))))], (19544 ^ _778495) ^ [_1129479, _1129481, _1129483] : [class_Orderings_Olinorder(_1129479), hBOOL(hAPP(c_Finite__Set_Ofinite(_1129479), _1129481)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1129479), _1129483)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129479, tc_HOL_Obool)), _1129481), _1129483) = c_Orderings_Obot__class_Obot(tc_fun(_1129479, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1129479), c_Big__Operators_Olattice_OInf__fin(_1129479, c_Orderings_Oord__class_Omin(_1129479), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1129479, tc_HOL_Obool)), _1129481), _1129483))), c_Big__Operators_Olattice_OInf__fin(_1129479, c_Orderings_Oord__class_Omin(_1129479), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129479, tc_HOL_Obool)), _1129481), _1129483))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1129479), c_Big__Operators_Olattice_OInf__fin(_1129479, c_Orderings_Oord__class_Omin(_1129479), _1129481)), c_Big__Operators_Olattice_OInf__fin(_1129479, c_Orderings_Oord__class_Omin(_1129479), _1129483)))], (12978 ^ _778495) ^ [_1009919, _1009921, _1009923, _1009925, _1009927, _1009929] : [class_Groups_Oab__semigroup__mult(_1009919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009921), _1009923)), 12988 ^ _778495 : [(12991 ^ _778495) ^ [] : [hAPP(_1009925, 12987 ^ [_1009919, _1009921, _1009923, _1009925, _1009927, _1009929]) = hAPP(_1009927, 12987 ^ [_1009919, _1009921, _1009923, _1009925, _1009927, _1009929])], (12989 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1009921), 12987 ^ [_1009919, _1009921, _1009923, _1009925, _1009927, _1009929]), _1009923)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1009919, _1009921, c_Groups_Otimes__class_Otimes(_1009919)), _1009925), _1009929), _1009923) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1009919, _1009921, c_Groups_Otimes__class_Otimes(_1009919)), _1009927), _1009929), _1009923))], (37024 ^ _778495) ^ [_1476755] : [-(c_Nitpick_Oone__frac(_1476755) = c_Nitpick_OAbs__Frac(_1476755, 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))))], (40688 ^ _778495) ^ [_1575836, _1575838] : [-(c_Transitive__Closure_Ortrancl(_1575836, hAPP(c_Relation_Oconverse(_1575836, _1575836), _1575838)) = hAPP(c_Relation_Oconverse(_1575836, _1575836), c_Transitive__Closure_Ortrancl(_1575836, _1575838)))], (20686 ^ _778495) ^ [_1149298, _1149300] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149298) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149300), 20689 ^ _778495 : [(20696 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149298)))), 20699 ^ _778495 : [(20706 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149300)))), -(_1149298 = _1149300)], (20700 ^ _778495) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149300))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149298) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (20690 ^ _778495) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149298))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149300)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (50861 ^ _778495) ^ [_1808269, _1808271, _1808273] : [class_Divides_Osemiring__div(_1808269), 50864 ^ _778495 : [(50871 ^ _778495) ^ [] : [c_Divides_Odiv__class_Omod(_1808269, _1808273, _1808271) = c_Groups_Ozero__class_Ozero(_1808269), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808269), _1808271), _1808273)))], (50865 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808269), _1808271), _1808273)), -(c_Divides_Odiv__class_Omod(_1808269, _1808273, _1808271) = c_Groups_Ozero__class_Ozero(_1808269))]]], (40073 ^ _778495) ^ [_1560306, _1560308, _1560310, _1560312, _1560314] : [-(_1560306 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1560308, _1560310, _1560306, _1560312), _1560314) = hAPP(hAPP(c_Product__Type_Oscomp(_1560310, _1560308, _1560310, tc_prod(_1560308, _1560310)), hAPP(_1560312, _1560314)), c_Random_Oiterate(_1560308, _1560310, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1560306), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1560312)))], (52141 ^ _778495) ^ [_1830367, _1830369] : [class_Lattices_Olattice(_1830367), -(class_Lattices_Olattice(tc_fun(_1830369, _1830367)))], (42778 ^ _778495) ^ [_1630947, _1630949] : [-(c_List_Olist_Olist__size(_1630947, _1630949, c_List_Olist_ONil(_1630947)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31980 ^ _778495) ^ [_1366526, _1366528, _1366530, _1366532] : [_1366526 = c_Orderings_Obot__class_Obot(tc_fun(_1366528, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1366528, tc_fun(_1366530, tc_HOL_Obool)), _1366526), hAPP(c_COMBK(tc_fun(_1366530, tc_HOL_Obool), _1366528), _1366532)) = c_Orderings_Otop__class_Otop(tc_fun(_1366530, tc_HOL_Obool)))], (5727 ^ _778495) ^ [_869167, _869169, _869171] : [class_Orderings_Obot(_869167), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_869169, _869167)), _869171) = c_Orderings_Obot__class_Obot(_869167))], (37821 ^ _778495) ^ [_1498124, _1498126] : [-(hAPP(c_Set_OCollect(_1498124), _1498126) = _1498126)], (4494 ^ _778495) ^ [_846789, _846791, _846793, _846795] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_846795, _846791) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_846793, _846789)), _846795 = _846793, _846791 = _846789], (28199 ^ _778495) ^ [_1281773, _1281775, _1281777, _1281779] : [-(hAPP(c_Finite__Set_Ofold__image(_1281773, _1281775, _1281777), _1281779) = c_Finite__Set_Ofold(_1281775, _1281773, hAPP(hAPP(c_COMBB(_1281773, tc_fun(_1281773, _1281773), _1281775), _1281777), _1281779)))], (30777 ^ _778495) ^ [_1340294, _1340296, _1340298] : [class_Orderings_Olinorder(_1340294), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340294), _1340296), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340294), _1340296), _1340298))))], (44756 ^ _778495) ^ [_1675101, _1675103, _1675105] : [-(c_List_Olist_Olist__size(_1675101, _1675103, _1675105) = 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(_1675101, tc_Nat_Onat), _1675103), _1675105))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675101)), _1675105)))], (23286 ^ _778495) ^ [_1195786, _1195788, _1195790] : [-(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, _1195786, _1195788)), _1195790), _1195788) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1195786), _1195790), _1195788))], (19298 ^ _778495) ^ [_1125308, _1125310, _1125312] : [class_Orderings_Olinorder(_1125308), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125308), _1125310)), hBOOL(hAPP(hAPP(c_member(_1125308), _1125312), _1125310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125308), c_Big__Operators_Olinorder__class_OMin(_1125308, _1125310)), _1125312)))], (32542 ^ _778495) ^ [_1378085] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1378085)), -(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))), _1378085)), c_FunDef_Omax__weak)))], (41461 ^ _778495) ^ [_1596858, _1596860, _1596862, _1596864, _1596866, _1596868] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596858), tc_List_Olist(_1596858))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596858), tc_List_Olist(_1596858)), hAPP(hAPP(c_List_Olist_OCons(_1596858), _1596860), _1596862)), hAPP(hAPP(c_List_Olist_OCons(_1596858), _1596864), _1596866))), c_List_Olexord(_1596858, _1596868)))), 41462 ^ _778495 : [(41465 ^ _778495) ^ [] : [_1596860 = _1596864, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596858), tc_List_Olist(_1596858))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596858), tc_List_Olist(_1596858)), _1596862), _1596866)), c_List_Olexord(_1596858, _1596868)))], (41463 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596858, _1596858)), hAPP(hAPP(c_Product__Type_OPair(_1596858, _1596858), _1596860), _1596864)), _1596868))]]], (35721 ^ _778495) ^ [_1447923, _1447925, _1447927, _1447929, _1447931] : [c_Equiv__Relations_Oequiv(_1447923, _1447925, _1447927), hBOOL(hAPP(hAPP(c_member(tc_fun(_1447923, tc_HOL_Obool)), _1447929), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447923), _1447925), _1447927))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1447923, tc_HOL_Obool)), _1447931), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447923), _1447925), _1447927))), -(_1447929 = _1447931), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447923, tc_HOL_Obool)), _1447929), _1447931) = c_Orderings_Obot__class_Obot(tc_fun(_1447923, tc_HOL_Obool)))], (43100 ^ _778495) ^ [_1638190, _1638192, _1638194, _1638196] : [-(hAPP(hAPP(c_List_Oappend(_1638190), hAPP(hAPP(c_List_Oappend(_1638190), _1638192), _1638194)), _1638196) = hAPP(hAPP(c_List_Oappend(_1638190), _1638192), hAPP(hAPP(c_List_Oappend(_1638190), _1638194), _1638196)))], (28219 ^ _778495) ^ [_1282301, _1282303, _1282305] : [class_Groups_Ocomm__monoid__mult(_1282301), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1282303, _1282301), hAPP(c_COMBK(_1282301, _1282303), c_Groups_Oone__class_Oone(_1282301))), _1282305) = c_Groups_Oone__class_Oone(_1282301))], (22890 ^ _778495) ^ [_1187740, _1187742] : [class_Int_Onumber__ring(_1187740), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187740), hAPP(c_Int_Onumber__class_Onumber__of(_1187740), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1187742) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187740), _1187742), _1187742))], (4660 ^ _778495) ^ [_849454, _849456] : [_849456 = _849454, -(c_Random__Sequence_Osingle(_849456) = c_Random__Sequence_Osingle(_849454))], (13406 ^ _778495) ^ [_1016677] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1016677) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2728 ^ _778495) ^ [_818870, _818872, _818874, _818876, _818878, _818880, _818882, _818884] : [-(c_Product__Type_Oapsnd(_818884, _818880, _818876, _818872) = c_Product__Type_Oapsnd(_818882, _818878, _818874, _818870)), _818884 = _818882, _818880 = _818878, _818876 = _818874, _818872 = _818870], (48676 ^ _778495) ^ [_1760661, _1760663] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1760661, _1760663), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760661)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49443 ^ _778495) ^ [_1777912, _1777914] : [c_Relation_Osym(_1777912, hAPP(c_Relation_Oconverse(_1777912, _1777912), _1777914)), -(c_Relation_Osym(_1777912, _1777914))], (21370 ^ _778495) ^ [_1161459, _1161461, _1161463] : [class_Groups_Oordered__ab__group__add__abs(_1161459), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161459), hAPP(c_Groups_Oabs__class_Oabs(_1161459), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161459), _1161461), _1161463))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161459), hAPP(c_Groups_Oabs__class_Oabs(_1161459), _1161461)), hAPP(c_Groups_Oabs__class_Oabs(_1161459), _1161463)))))], (46748 ^ _778495) ^ [_1718369, _1718371] : [-(hAPP(c_List_Orev(_1718369), _1718371) = hAPP(c_List_Ofoldl(tc_List_Olist(_1718369), _1718369, hAPP(c_COMBC(_1718369, tc_List_Olist(_1718369), tc_List_Olist(_1718369)), c_List_Olist_OCons(_1718369)), c_List_Olist_ONil(_1718369)), _1718371))], (2792 ^ _778495) ^ [_819922, _819924] : [_819924 = _819922, -(c_Relation_OField(_819924) = c_Relation_OField(_819922))], (19204 ^ _778495) ^ [_1123576, _1123578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123576), _1123578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123578), _1123576)), -(_1123576 = _1123578)], (27747 ^ _778495) ^ [_1273623, _1273625, _1273627] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1273623, _1273625) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1273627, _1273625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1273627), _1273623)), -(_1273623 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1273625), 27754 ^ [_1273623, _1273625, _1273627])))], (19896 ^ _778495) ^ [_1136022, _1136024] : [class_Int_Onumber__ring(_1136022), 19899 ^ _778495 : [(19906 ^ _778495) ^ [] : [-(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), _1136024)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1136022), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1136024)) = c_Groups_Ozero__class_Ozero(_1136022))], (19900 ^ _778495) ^ [] : [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), _1136024))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1136022), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1136024)) = hAPP(c_Int_Onumber__class_Onumber__of(_1136022), _1136024))]]], (23715 ^ _778495) ^ [_1203324, _1203326, _1203328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203324), 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)), _1203326)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203326), _1203328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203324), _1203326)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203324), _1203328))))], (20155 ^ _778495) ^ [_1140567] : [class_Rings_Osemiring__1(_1140567), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140567), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1140567))], (36815 ^ _778495) ^ [_1472705] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1472705))], (45416 ^ _778495) ^ [_1689971] : [-(c_List_Oremdups(_1689971, c_List_Olist_ONil(_1689971)) = c_List_Olist_ONil(_1689971))], (25952 ^ _778495) ^ [_1242522, _1242524, _1242526] : [class_Rings_Olinordered__idom(_1242522), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242522), c_Groups_Ozero__class_Ozero(_1242522)), hAPP(hAPP(c_Power_Opower__class_Opower(_1242522), _1242524), 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)))), _1242526))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242522), c_Groups_Ozero__class_Ozero(_1242522)), _1242524)))], (9332 ^ _778495) ^ [_936700, _936702, _936704] : [class_Lattices_Olattice(_936700), hBOOL(hAPP(c_Finite__Set_Ofinite(_936700), _936702)), -(c_Big__Operators_Olattice__class_OSup__fin(_936700, hAPP(hAPP(c_Set_Oinsert(_936700), _936704), _936702)) = hAPP(hAPP(c_Finite__Set_Ofold(_936700, _936700, c_Lattices_Osemilattice__sup__class_Osup(_936700)), _936704), _936702))], (6688 ^ _778495) ^ [_887925, _887927, _887929, _887931] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887925, tc_HOL_Obool)), _887927), hAPP(hAPP(c_Set_Oinsert(_887925), _887929), _887931)) = hAPP(hAPP(c_Set_Oinsert(_887925), _887929), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887925, tc_HOL_Obool)), _887927), _887931)))], (48969 ^ _778495) ^ [_1769093, _1769095, _1769097, _1769099] : [c_Relation_Otrans(_1769093, _1769095), c_Relation_Otrans(_1769097, _1769099), -(c_Relation_Otrans(tc_prod(_1769093, _1769097), c_Wellfounded_Olex__prod(_1769093, _1769097, _1769095, _1769099)))], (5546 ^ _778495) ^ [_863347, _863349] : [_863349 = _863347, -(tc_Lazy__Sequence_Olazy__sequence(_863349) = tc_Lazy__Sequence_Olazy__sequence(_863347))], (38379 ^ _778495) ^ [_1517795, _1517797, _1517799, _1517801] : [-(c_Product__Type_Oapsnd(_1517795, _1517797, _1517799, _1517801) = c_Product__Type_Omap__pair(_1517799, _1517799, _1517795, _1517797, c_Fun_Oid(_1517799), _1517801))], (7662 ^ _778495) ^ [_905238, _905240, _905242, _905244] : [class_Orderings_Oorder(_905238), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905238), _905240), _905242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905238), _905244), _905240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905238), _905244), _905242)))], (21646 ^ _778495) ^ [_1166088, _1166090] : [-(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, _1166088)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1166090))))], (46646 ^ _778495) ^ [_1716284, _1716286, _1716288, _1716290] : [-(hAPP(c_List_Orev(_1716284), hAPP(hAPP(c_List_Omap(_1716286, _1716284), _1716288), _1716290)) = hAPP(hAPP(c_List_Omap(_1716286, _1716284), _1716288), hAPP(c_List_Orev(_1716286), _1716290)))], (30501 ^ _778495) ^ [_1334772, _1334774, _1334776, _1334778] : [hBOOL(hAPP(hAPP(_1334776, _1334778), _1334774)), -(hBOOL(hAPP(hAPP(c_member(_1334772), _1334774), c_SetInterval_Oord_OgreaterThan(_1334772, _1334776, _1334778))))], (2194 ^ _778495) ^ [_810561, _810563, _810565, _810567] : [-(c_Random_Olog(_810567, _810563) = c_Random_Olog(_810565, _810561)), _810567 = _810565, _810563 = _810561], (42477 ^ _778495) ^ [_1624989, _1624991, _1624993] : [-(hBOOL(hAPP(c_List_Odistinct(_1624989), hAPP(hAPP(c_List_Olist_OCons(_1624989), _1624991), _1624993)))), -(hBOOL(hAPP(hAPP(c_member(_1624989), _1624991), hAPP(c_List_Oset(_1624989), _1624993)))), hBOOL(hAPP(c_List_Odistinct(_1624989), _1624993))], (45458 ^ _778495) ^ [_1690689, _1690691, _1690693, _1690695] : [-(c_List_Oremdups(_1690689, hAPP(hAPP(c_List_Omap(_1690691, _1690689), _1690693), c_List_Oremdups(_1690691, _1690695))) = c_List_Oremdups(_1690689, hAPP(hAPP(c_List_Omap(_1690691, _1690689), _1690693), _1690695)))], (45913 ^ _778495) ^ [_1702406, _1702408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702406), _1702408)), -(c_List_Oupt(_1702406, _1702408) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702406), c_List_Oupt(hAPP(c_Nat_OSuc, _1702406), _1702408)))], (38631 ^ _778495) ^ [_1526455, _1526457, _1526459] : [c_Wellfounded_Owf(_1526455, _1526457), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526455, _1526455), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1526455, _1526455, _1526455), _1526457), _1526459)), _1526457)), -(c_FunDef_Oreduction__pair(_1526455, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1526455, _1526455), tc_HOL_Obool), tc_fun(tc_prod(_1526455, _1526455), tc_HOL_Obool)), _1526457), _1526459)))], (13145 ^ _778495) ^ [_1012792, _1012794] : [class_Groups_Omonoid__add(_1012792), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012792), _1012794), c_Groups_Ozero__class_Ozero(_1012792)) = _1012794)], (45466 ^ _778495) ^ [_1690856, _1690858, _1690860] : [-(hBOOL(hAPP(hAPP(c_member(_1690856), _1690858), hAPP(c_List_Oset(_1690856), _1690860)))), -(hAPP(c_List_OremoveAll(_1690856, _1690858), _1690860) = _1690860)], (46716 ^ _778495) ^ [_1717727, _1717729, _1717731, _1717733, _1717735] : [-(c_List_Ofoldr(_1717727, _1717729, _1717731, _1717733, _1717735) = hAPP(c_List_Ofoldl(_1717729, _1717727, hAPP(c_COMBC(_1717727, _1717729, _1717729), _1717731), _1717735), hAPP(c_List_Orev(_1717727), _1717733)))], (49745 ^ _778495) ^ [_1783872, _1783874, _1783876, _1783878, _1783880] : [c_Fun_Oinj__on(_1783872, _1783874, _1783876, c_Orderings_Otop__class_Otop(tc_fun(_1783872, tc_HOL_Obool))), hAPP(_1783876, _1783878) = _1783880, -(hAPP(c_Hilbert__Choice_Oinv__into(_1783872, _1783874, c_Orderings_Otop__class_Otop(tc_fun(_1783872, tc_HOL_Obool)), _1783876), _1783880) = _1783878)], (25092 ^ _778495) ^ [_1227070, _1227072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227070)), 25095 ^ _778495 : [(25102 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227072), _1227070))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227072), _1227070) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1227072), _1227070)), _1227070)))], (25096 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227072), _1227070)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227072), _1227070) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11652 ^ _778495) ^ [_980602, _980604, _980606, _980608] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_980602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980602), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980602), _980604), _980606)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980602), _980604), _980608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980602), _980606), _980608)))], (44644 ^ _778495) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11258 ^ _778495) ^ [_972767, _972769, _972771] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972767), _972769) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972771), _972769), -(_972767 = _972771)], (24738 ^ _778495) ^ [_1221371] : [24740 ^ _778495 : [(24743 ^ _778495) ^ [] : [hBOOL(hAPP(_1221371, hAPP(c_Int_Onat, 24739 ^ [_1221371])))], (24741 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24739 ^ [_1221371])))]], 24744 ^ _778495 : [(24745 ^ _778495) ^ [_1221504] : [-(hBOOL(hAPP(_1221371, _1221504)))]]], (31646 ^ _778495) ^ [_1356985, _1356987, _1356989, _1356991, _1356993, _1356995, _1356997] : [-(hAPP(c_Product__Type_Oapsnd(_1356985, _1356987, _1356989, _1356991), hAPP(c_Product__Type_Oapfst(_1356993, _1356989, _1356985, _1356995), _1356997)) = hAPP(c_Product__Type_Oapfst(_1356993, _1356989, _1356987, _1356995), hAPP(c_Product__Type_Oapsnd(_1356985, _1356987, _1356993, _1356991), _1356997)))], (30045 ^ _778495) ^ [_1325506, _1325508, _1325510, _1325512] : [-(hAPP(c_Product__Type_Ofst(_1325506, _1325508), hAPP(hAPP(c_Product__Type_OPair(_1325506, _1325508), _1325510), _1325512)) = _1325510)], (34238 ^ _778495) ^ [_1416760, _1416762, _1416764, _1416766] : [-(hAPP(c_Relation_OField(_1416760), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1416760, _1416760)), hAPP(hAPP(c_Product__Type_OPair(_1416760, _1416760), _1416762), _1416764)), _1416766)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1416760, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1416760), _1416762), hAPP(hAPP(c_Set_Oinsert(_1416760), _1416764), c_Orderings_Obot__class_Obot(tc_fun(_1416760, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1416760), _1416766)))], (43995 ^ _778495) ^ [_1658671, _1658673, _1658675, _1658677] : [class_Complete__Lattice_Ocomplete__lattice(_1658671), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658673, _1658671), hAPP(c_List_Oset(_1658673), _1658675)), _1658677) = hAPP(c_List_Ofoldl(_1658671, _1658673, hAPP(c_COMBC(_1658673, _1658671, _1658671), hAPP(hAPP(c_COMBB(_1658671, tc_fun(_1658671, _1658671), _1658673), c_Lattices_Osemilattice__inf__class_Oinf(_1658671)), _1658677)), c_Orderings_Otop__class_Otop(_1658671)), _1658675))], (16660 ^ _778495) ^ [_1076348, _1076350, _1076352] : [class_Fields_Olinordered__field(_1076348), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076348), _1076350), c_Groups_Ozero__class_Ozero(_1076348))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076348), _1076352), c_Groups_Ozero__class_Ozero(_1076348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076348), c_Groups_Ozero__class_Ozero(_1076348)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1076348), _1076350), _1076352))))], (12769 ^ _778495) ^ [_1004996, _1004998, _1005000, _1005002, _1005004] : [class_Groups_Ocomm__monoid__add(_1004996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004998), _1005000)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004998), _1005002)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1004998, tc_HOL_Obool)), _1005000), _1005002) = c_Orderings_Obot__class_Obot(tc_fun(_1004998, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004998, _1004996), _1005004), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004998, tc_HOL_Obool)), _1005000), _1005002)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004996), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004998, _1004996), _1005004), _1005000)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004998, _1004996), _1005004), _1005002)))], (2900 ^ _778495) ^ [_821534, _821536, _821538, _821540, _821542, _821544] : [-(c_Nitpick_Oplus__frac(_821544, _821540, _821536) = c_Nitpick_Oplus__frac(_821542, _821538, _821534)), _821544 = _821542, _821540 = _821538, _821536 = _821534], (11684 ^ _778495) ^ [_981212, _981214] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _981212)), _981214) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981212), hAPP(c_Nat_OSuc, _981214)))], (26074 ^ _778495) ^ [_1244620, _1244622] : [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), _1244620), _1244622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1244620))), -(_1244622 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35144 ^ _778495) ^ [_1435149, _1435151] : [c_Nat__Transfer_Onat__set(_1435149), c_Nat__Transfer_Onat__set(_1435151), 35151 ^ _778495 : [(35158 ^ _778495) ^ [] : [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), _1435149)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1435151))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1435149), _1435151)))], (35152 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1435149), _1435151)), -(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), _1435149)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1435151))))]]], (14487 ^ _778495) ^ [_1035877, _1035879, _1035881, _1035883] : [class_Groups_Ocomm__monoid__add(_1035877), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035879), _1035881))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1035879, _1035877), _1035883), _1035881) = c_Groups_Ozero__class_Ozero(_1035877))], (22434 ^ _778495) ^ [_1179643, _1179645, _1179647] : [class_Rings_Odivision__ring(_1179643), -(_1179645 = c_Groups_Ozero__class_Ozero(_1179643)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179643), hAPP(c_Groups_Ouminus__class_Ouminus(_1179643), _1179647)), hAPP(c_Groups_Ouminus__class_Ouminus(_1179643), _1179645)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179643), _1179647), _1179645))], (26924 ^ _778495) ^ [_1259561, _1259563, _1259565, _1259567] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1259561, _1259563, _1259565), _1259567), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1259563)], (8918 ^ _778495) ^ [_928452, _928454, _928456] : [class_Lattices_Osemilattice__inf(_928452), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928452), _928454), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928452), _928454), _928456)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928452), _928454), _928456))], (38457 ^ _778495) ^ [_1520234, _1520236, _1520238, _1520240, _1520242, _1520244, _1520246] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1520234, _1520236, _1520238), hAPP(hAPP(c_Relation_Orel__comp(_1520234, _1520240, _1520236), _1520242), _1520244)), _1520246) = hAPP(hAPP(c_Relation_Orel__comp(_1520234, _1520240, _1520238), _1520242), hAPP(hAPP(c_Relation_Orel__comp(_1520240, _1520236, _1520238), _1520244), _1520246)))], (48951 ^ _778495) ^ [_1768483, _1768485, _1768487, _1768489, _1768491, _1768493] : [-(c_Partial__Function_Ofun__lub(_1768483, _1768485, _1768487, _1768489, _1768491, _1768493) = hAPP(_1768489, hAPP(c_Set_OCollect(_1768483), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768487, _1768483), tc_HOL_Obool), tc_HOL_Obool, _1768483), c_HOL_OEx(tc_fun(_1768487, _1768483))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768487, _1768483), tc_HOL_Obool), tc_fun(tc_fun(_1768487, _1768483), tc_HOL_Obool), _1768483), hAPP(c_COMBS(tc_fun(_1768487, _1768483), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768487, _1768483)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768487, _1768483), tc_fun(tc_fun(_1768487, _1768483), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768487, _1768483))), _1768491)))), hAPP(hAPP(c_COMBC(_1768483, tc_fun(tc_fun(_1768487, _1768483), _1768483), tc_fun(tc_fun(_1768487, _1768483), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768483, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768487, _1768483), _1768483), tc_fun(tc_fun(_1768487, _1768483), tc_HOL_Obool)), _1768483), c_COMBB(_1768483, tc_HOL_Obool, tc_fun(_1768487, _1768483))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768487, _1768483), _1768487, _1768483), c_COMBI(tc_fun(_1768487, _1768483))), _1768493)))))))], (41903 ^ _778495) ^ [_1609810, _1609812, _1609814, _1609816] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609810), tc_List_Olist(_1609810))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609810), tc_List_Olist(_1609810)), _1609812), _1609814)), c_List_Olexord(_1609810, _1609816)))), 41904 ^ _778495 : [(41911 ^ _778495) ^ [_1610117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610117), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609810)), _1609812)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609810)), _1609814)))), hAPP(hAPP(c_List_Otake(_1609810), _1610117), _1609812) = hAPP(hAPP(c_List_Otake(_1609810), _1610117), _1609814), hBOOL(hAPP(hAPP(c_member(tc_prod(_1609810, _1609810)), hAPP(hAPP(c_Product__Type_OPair(_1609810, _1609810), hAPP(hAPP(c_List_Onth(_1609810), _1609812), _1610117)), hAPP(hAPP(c_List_Onth(_1609810), _1609814), _1610117))), _1609816))], (41905 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609810)), _1609812)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609810)), _1609814))), hAPP(hAPP(c_List_Otake(_1609810), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609810)), _1609812)), _1609814) = _1609812]]], (47788 ^ _778495) ^ [_1741301, _1741303, _1741305] : [hBOOL(hAPP(hAPP(c_member(_1741301), _1741303), hAPP(c_List_Oset(_1741301), _1741305))), 47793 ^ _778495 : [(47796 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1741301), _1741303), hAPP(c_List_Oset(_1741301), 47792 ^ [_1741301, _1741303, _1741305])))], (47794 ^ _778495) ^ [] : [-(_1741305 = hAPP(hAPP(c_List_Oappend(_1741301), 47791 ^ [_1741301, _1741303, _1741305]), hAPP(hAPP(c_List_Olist_OCons(_1741301), _1741303), 47792 ^ [_1741301, _1741303, _1741305])))]]], (34562 ^ _778495) ^ [_1424748, _1424750, _1424752, _1424754] : [_1424748 = _1424750, hBOOL(hAPP(hAPP(c_member(_1424752), _1424748), _1424754)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1424752, _1424752)), hAPP(hAPP(c_Product__Type_OPair(_1424752, _1424752), _1424748), _1424750)), c_Relation_OId__on(_1424752, _1424754))))], (39816 ^ _778495) ^ [_1554490, _1554492, _1554494, _1554496, _1554498, _1554500] : [c_Finite__Set_Ofolding__idem(_1554490, _1554492, _1554494, _1554496), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554490), _1554498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1554490, tc_HOL_Obool)), _1554500), _1554498)), -(hAPP(c_Fun_Ocomp(_1554492, _1554492, _1554492, hAPP(_1554496, _1554498)), hAPP(_1554496, _1554500)) = hAPP(_1554496, _1554498))], (49268 ^ _778495) ^ [_1774598, _1774600] : [c_Relation_Osym(_1774598, _1774600), c_Relation_Otrans(_1774598, _1774600), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1774598, _1774598), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1774598, _1774598, _1774598), hAPP(c_Relation_Oconverse(_1774598, _1774598), _1774600)), _1774600)), _1774600)))], (51641 ^ _778495) ^ [_1821470, _1821472] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821470), _1821472))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821470, _1821472) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (16108 ^ _778495) ^ [_1066487, _1066489, _1066491, _1066493] : [class_Rings_Odivision__ring(_1066487), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066487), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1066487), _1066489), _1066491)), _1066493) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1066487), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066487), _1066489), _1066493)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066487), _1066491), _1066493)))], (32560 ^ _778495) ^ [_1378291, _1378293, _1378295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1378291)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1378293), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1378295)), 32567 ^ _778495 : [(32568 ^ _778495) ^ [_1378499] : [32570 ^ _778495 : [(32576 ^ _778495) ^ [] : [-(_1378499 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32572 ^ [_1378291, _1378293, _1378295, _1378499]), 32569 ^ [_1378291, _1378293, _1378295, _1378499]))], (32574 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32572 ^ [_1378291, _1378293, _1378295, _1378499]), _1378295)))], (32571 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32569 ^ [_1378291, _1378293, _1378295, _1378499]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1378291))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1378499), _1378293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1378499), _1378291)), _1378293)))]]], (39866 ^ _778495) ^ [_1555511, _1555513, _1555515, _1555517, _1555519, _1555521, _1555523, _1555525] : [class_Groups_Ocomm__monoid__mult(_1555511), c_Fun_Oinj__on(_1555513, _1555515, _1555517, _1555519), _1555521 = hAPP(c_Set_Oimage(_1555513, _1555515, _1555517), _1555519), 39880 ^ _778495 : [(39883 ^ _778495) ^ [] : [hAPP(_1555523, 39879 ^ [_1555511, _1555513, _1555515, _1555517, _1555519, _1555521, _1555523, _1555525]) = hAPP(hAPP(c_Fun_Ocomp(_1555515, _1555511, _1555513, _1555525), _1555517), 39879 ^ [_1555511, _1555513, _1555515, _1555517, _1555519, _1555521, _1555523, _1555525])], (39881 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555513), 39879 ^ [_1555511, _1555513, _1555515, _1555517, _1555519, _1555521, _1555523, _1555525]), _1555519)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555515, _1555511), _1555525), _1555521) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555513, _1555511), _1555523), _1555519))], (29490 ^ _778495) ^ [_1314980, _1314982, _1314984, _1314986, _1314988, _1314990] : [hAPP(hAPP(c_Product__Type_OPair(_1314980, _1314982), _1314984), _1314986) = hAPP(hAPP(c_Product__Type_OPair(_1314980, _1314982), _1314988), _1314990), 29493 ^ _778495 : [(29496 ^ _778495) ^ [] : [-(_1314986 = _1314990)], (29494 ^ _778495) ^ [] : [-(_1314984 = _1314988)]]], (45444 ^ _778495) ^ [_1690441, _1690443, _1690445, _1690447] : [_1690441 = _1690443, -(hAPP(c_List_OremoveAll(_1690445, _1690441), hAPP(hAPP(c_List_Olist_OCons(_1690445), _1690443), _1690447)) = hAPP(c_List_OremoveAll(_1690445, _1690441), _1690447))], (11674 ^ _778495) ^ [_981017, _981019, _981021] : [class_Groups_Ogroup__add(_981017), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_981017), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981017), _981019), _981021)), _981021) = _981019)], (15543 ^ _778495) ^ [_1054869, _1054871, _1054873, _1054875] : [class_Groups_Ocomm__monoid__mult(_1054869), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054871), _1054873)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054871, _1054869), _1054875), _1054873) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1054869, _1054871, c_Groups_Otimes__class_Otimes(_1054869)), _1054875), c_Groups_Oone__class_Oone(_1054869)), _1054873))], (38571 ^ _778495) ^ [_1524185, _1524187, _1524189, _1524191, _1524193, _1524195, _1524197] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1524185, _1524187, _1524189, hAPP(hAPP(c_COMBC(_1524185, tc_fun(tc_prod(_1524185, _1524187), tc_HOL_Obool), tc_fun(_1524187, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524187, tc_fun(tc_fun(tc_prod(_1524185, _1524187), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1524185, _1524187), tc_HOL_Obool), tc_fun(_1524187, tc_HOL_Obool)), _1524185), c_COMBC(_1524187, tc_fun(tc_prod(_1524185, _1524187), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524187, tc_prod(_1524185, _1524187)), tc_fun(_1524187, tc_fun(tc_fun(tc_prod(_1524185, _1524187), tc_HOL_Obool), tc_HOL_Obool)), _1524185), hAPP(c_COMBB(tc_prod(_1524185, _1524187), tc_fun(tc_fun(tc_prod(_1524185, _1524187), tc_HOL_Obool), tc_HOL_Obool), _1524187), c_member(tc_prod(_1524185, _1524187)))), c_Product__Type_OPair(_1524185, _1524187)))), _1524191), hAPP(hAPP(c_COMBC(_1524187, tc_fun(tc_prod(_1524187, _1524189), tc_HOL_Obool), tc_fun(_1524189, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524189, tc_fun(tc_fun(tc_prod(_1524187, _1524189), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1524187, _1524189), tc_HOL_Obool), tc_fun(_1524189, tc_HOL_Obool)), _1524187), c_COMBC(_1524189, tc_fun(tc_prod(_1524187, _1524189), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524189, tc_prod(_1524187, _1524189)), tc_fun(_1524189, tc_fun(tc_fun(tc_prod(_1524187, _1524189), tc_HOL_Obool), tc_HOL_Obool)), _1524187), hAPP(c_COMBB(tc_prod(_1524187, _1524189), tc_fun(tc_fun(tc_prod(_1524187, _1524189), tc_HOL_Obool), tc_HOL_Obool), _1524189), c_member(tc_prod(_1524187, _1524189)))), c_Product__Type_OPair(_1524187, _1524189)))), _1524193)), _1524195), _1524197)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524185, _1524189)), hAPP(hAPP(c_Product__Type_OPair(_1524185, _1524189), _1524195), _1524197)), hAPP(hAPP(c_Relation_Orel__comp(_1524185, _1524187, _1524189), _1524191), _1524193))))], (2086 ^ _778495) ^ [_808887, _808889, _808891, _808893] : [-(c_SMT_Oz3mod(_808893, _808889) = c_SMT_Oz3mod(_808891, _808887)), _808893 = _808891, _808889 = _808887], (22654 ^ _778495) ^ [_1183441, _1183443] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1183441)), c_Int_OBit1(_1183443)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1183441), _1183443)))], (41676 ^ _778495) ^ [_1603926, _1603928, _1603930, _1603932, _1603934] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603926), tc_List_Olist(_1603926))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603926), tc_List_Olist(_1603926)), _1603928), hAPP(hAPP(c_List_Olist_OCons(_1603926), _1603930), _1603932))), c_List_Olistrel(_1603926, _1603934))), 41681 ^ _778495 : [(41686 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603926), tc_List_Olist(_1603926))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603926), tc_List_Olist(_1603926)), 41680 ^ [_1603926, _1603928, _1603930, _1603932, _1603934]), _1603932)), c_List_Olistrel(_1603926, _1603934))))], (41684 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603926, _1603926)), hAPP(hAPP(c_Product__Type_OPair(_1603926, _1603926), 41679 ^ [_1603926, _1603928, _1603930, _1603932, _1603934]), _1603930)), _1603934)))], (41682 ^ _778495) ^ [] : [-(_1603928 = hAPP(hAPP(c_List_Olist_OCons(_1603926), 41679 ^ [_1603926, _1603928, _1603930, _1603932, _1603934]), 41680 ^ [_1603926, _1603928, _1603930, _1603932, _1603934]))]]], (44708 ^ _778495) ^ [] : [-(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))], (39570 ^ _778495) ^ [_1548759, _1548761, _1548763, _1548765, _1548767, _1548769, _1548771] : [class_Groups_Oab__semigroup__mult(_1548759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548761), _1548763)), c_Fun_Oinj__on(_1548761, _1548765, _1548767, _1548763), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1548759, _1548765, c_Groups_Otimes__class_Otimes(_1548759)), _1548769), _1548771), hAPP(c_Set_Oimage(_1548761, _1548765, _1548767), _1548763)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1548759, _1548761, c_Groups_Otimes__class_Otimes(_1548759)), hAPP(c_Fun_Ocomp(_1548765, _1548759, _1548761, _1548769), _1548767)), _1548771), _1548763))], (20478 ^ _778495) ^ [_1145952, _1145954] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145952), _1145954), hAPP(c_Int_Onumber__class_Onumber__of(_1145952), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1145952)), class_Fields_Ofield__inverse__zero(_1145952), class_Int_Onumber__ring(_1145952)], (24571 ^ _778495) ^ [_1218486, _1218488, _1218490] : [-(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, _1218486, _1218488)), _1218490), _1218488) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1218486), _1218490), _1218488))], (52561 ^ _778495) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (17551 ^ _778495) ^ [_1092968, _1092970, _1092972, _1092974] : [class_Rings_Olinordered__semidom(_1092968), 17557 ^ _778495 : [(17560 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092968), c_Groups_Ozero__class_Ozero(_1092968)), hAPP(_1092974, 17556 ^ [_1092968, _1092970, _1092972, _1092974])))], (17558 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1092970), 17556 ^ [_1092968, _1092970, _1092972, _1092974]), _1092972)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092968), c_Groups_Ozero__class_Ozero(_1092968)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1092970, _1092968), _1092974), _1092972))))], (45040 ^ _778495) ^ [_1681433, _1681435, _1681437] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1681433)), _1681437), c_List_Olists(_1681433, _1681435))), -(hBOOL(hAPP(c_List_Olistsp(_1681433, hAPP(hAPP(c_COMBC(_1681433, tc_fun(_1681433, tc_HOL_Obool), tc_HOL_Obool), c_member(_1681433)), _1681435)), _1681437)))], (2228 ^ _778495) ^ [_811080, _811082] : [_811082 = _811080, -(c_Nat_Onat_Onat__size(_811082) = c_Nat_Onat_Onat__size(_811080))], (28739 ^ _778495) ^ [_1299613, _1299615] : [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(_1299613))), 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)), _1299615)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1299613)), hAPP(c_Nat_OSuc, _1299615))))], (21808 ^ _778495) ^ [_1168776, _1168778, _1168780] : [class_Groups_Oordered__ab__group__add(_1168776), 21811 ^ _778495 : [(21818 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168776), _1168780), hAPP(c_Groups_Ouminus__class_Ouminus(_1168776), _1168778))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168776), _1168778), hAPP(c_Groups_Ouminus__class_Ouminus(_1168776), _1168780))))], (21812 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168776), _1168778), hAPP(c_Groups_Ouminus__class_Ouminus(_1168776), _1168780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168776), _1168780), hAPP(c_Groups_Ouminus__class_Ouminus(_1168776), _1168778))))]]], (50843 ^ _778495) ^ [_1807952, _1807954] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807952), 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)))), _1807954))), 50846 ^ _778495 : [(50849 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807952), _1807954))], (50847 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807954), _1807952)))]]], (50108 ^ _778495) ^ [_1791713, _1791715, _1791717, _1791719, _1791721, _1791723, _1791725] : [c_Fun_Obij__betw(_1791713, _1791715, _1791717, _1791719, _1791721), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1791713, tc_HOL_Obool)), _1791723), _1791719)), hAPP(c_Set_Oimage(_1791713, _1791715, _1791717), _1791723) = _1791725, -(c_Fun_Obij__betw(_1791713, _1791715, _1791717, _1791723, _1791725))], (4086 ^ _778495) ^ [_840429, _840431, _840433, _840435, _840437, _840439, _840441, _840443] : [-(c_New__Random__Sequence_Opos__bind(_840443, _840439, _840435, _840431) = c_New__Random__Sequence_Opos__bind(_840441, _840437, _840433, _840429)), _840443 = _840441, _840439 = _840437, _840435 = _840433, _840431 = _840429], (10725 ^ _778495) ^ [_963299, _963301] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _963299), _963301) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _963299 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _963301 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (10347 ^ _778495) ^ [_956883, _956885, _956887, _956889] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_956883), _956885)), hBOOL(hAPP(hAPP(c_member(_956883), _956887), _956885)), -(hBOOL(hAPP(hAPP(c_member(_956883), _956887), _956889))), -(hAPP(c_Finite__Set_Ocard(_956883), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_956883, tc_HOL_Obool)), _956885), hAPP(hAPP(c_Set_Oinsert(_956883), _956887), _956889))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_956883), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_956883, tc_HOL_Obool)), _956885), _956889))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (28165 ^ _778495) ^ [_1281016, _1281018, _1281020, _1281022] : [class_Groups_Oordered__ab__group__add__abs(_1281016), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281016), c_Groups_Ozero__class_Ozero(_1281016)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1281018, _1281016), hAPP(hAPP(c_COMBB(_1281016, _1281016, _1281018), c_Groups_Oabs__class_Oabs(_1281016)), _1281020)), _1281022))))], (24591 ^ _778495) ^ [_1218847, _1218849] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1218847)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1218847)), _1218849) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1218847)), _1218849)))], (3832 ^ _778495) ^ [_836074, _836076, _836078, _836080, _836082, _836084, _836086, _836088, _836090, _836092, _836094, _836096, _836098, _836100] : [-(c_New__Random__Sequence_Oneg__decr__bind(_836100, _836096, _836092, _836088, _836084, _836080, _836076) = c_New__Random__Sequence_Oneg__decr__bind(_836098, _836094, _836090, _836086, _836082, _836078, _836074)), _836100 = _836098, _836096 = _836094, _836092 = _836090, _836088 = _836086, _836084 = _836082, _836080 = _836078, _836076 = _836074], (33746 ^ _778495) ^ [_1406760, _1406762, _1406764] : [class_Orderings_Olinorder(_1406760), 33749 ^ _778495 : [(33756 ^ _778495) ^ [] : [_1406762 = _1406764, -(hAPP(c_SetInterval_Oord__class_OatMost(_1406760), _1406762) = hAPP(c_SetInterval_Oord__class_OatMost(_1406760), _1406764))], (33750 ^ _778495) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1406760), _1406762) = hAPP(c_SetInterval_Oord__class_OatMost(_1406760), _1406764), -(_1406762 = _1406764)]]], (45296 ^ _778495) ^ [_1687390, _1687392] : [hBOOL(hAPP(c_List_Odistinct(_1687390), _1687392)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1687390, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1687390), tc_fun(_1687390, tc_HOL_Obool)), c_List_Oset(_1687390)), c_Enum_Osublists(_1687390, _1687392)))))], (52329 ^ _778495) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (20430 ^ _778495) ^ [_1145297, _1145299] : [class_Int_Onumber__ring(_1145297), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1145297), hAPP(c_Int_Onumber__class_Onumber__of(_1145297), c_Int_OPls)), _1145299) = _1145299)], (32298 ^ _778495) ^ [_1372994, _1372996, _1372998, _1373000] : [class_Groups_Ocomm__monoid__add(_1372994), 32301 ^ _778495 : [(32308 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1372996)), _1372998))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1372994), _1373000), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1372998, hAPP(c_Nat_OSuc, _1372996))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1372994), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1372994), _1373000), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1372998, _1372996))), hAPP(_1373000, hAPP(c_Nat_OSuc, _1372996))))], (32302 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1372996)), _1372998)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1372994), _1373000), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1372998, hAPP(c_Nat_OSuc, _1372996))) = c_Groups_Ozero__class_Ozero(_1372994))]]], (2030 ^ _778495) ^ [_807963, _807965, _807967, _807969, _807971, _807973, _807975, _807977, _807979, _807981] : [-(c_Nitpick_Opair__box_Opair__box__rec(_807981, _807977, _807973, _807969, _807965) = c_Nitpick_Opair__box_Opair__box__rec(_807979, _807975, _807971, _807967, _807963)), _807981 = _807979, _807977 = _807975, _807973 = _807971, _807969 = _807967, _807965 = _807963], (27093 ^ _778495) ^ [_1262374, _1262376, _1262378] : [class_Rings_Olinordered__idom(_1262374), 27096 ^ _778495 : [(27103 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1262376), _1262378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262374), hAPP(c_Int_Oring__1__class_Oof__int(_1262374), _1262376)), hAPP(c_Int_Oring__1__class_Oof__int(_1262374), _1262378))))], (27097 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262374), hAPP(c_Int_Oring__1__class_Oof__int(_1262374), _1262376)), hAPP(c_Int_Oring__1__class_Oof__int(_1262374), _1262378))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1262376), _1262378)))]]], (22180 ^ _778495) ^ [_1175259, _1175261] : [class_Groups_Olinordered__ab__group__add(_1175259), 22183 ^ _778495 : [(22190 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175259), _1175261), c_Groups_Ozero__class_Ozero(_1175259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175259), _1175261), hAPP(c_Groups_Ouminus__class_Ouminus(_1175259), _1175261))))], (22184 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175259), _1175261), hAPP(c_Groups_Ouminus__class_Ouminus(_1175259), _1175261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175259), _1175261), c_Groups_Ozero__class_Ozero(_1175259))))]]], (45837 ^ _778495) ^ [_1700252, _1700254, _1700256, _1700258] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1700252, tc_Nat_Onat), _1700252), c_Product__Type_Ofst(_1700252, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1700252, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1700252, tc_Nat_Onat)), _1700254), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1700252, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1700252, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1700252, tc_Nat_Onat), _1700256), _1700258))) = hAPP(hAPP(c_List_Omap(tc_prod(_1700252, tc_Nat_Onat), _1700252), c_Product__Type_Ofst(_1700252, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1700252, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1700252, tc_Nat_Onat)), _1700254), c_Product__Type_Osnd(_1700252, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1700252, tc_Nat_Onat), _1700256), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1700258)))))], (29679 ^ _778495) ^ [_1318548, _1318550, _1318552, _1318554, _1318556, _1318558] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1318548, _1318550), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1318552), _1318554))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1318548, _1318550), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1318556), _1318558))), -(_1318550 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1318554 = _1318558)], (52089 ^ _778495) ^ [_1829685, _1829687] : [class_Lattices_Obounded__lattice(_1829685), -(class_Lattices_Obounded__lattice__top(tc_fun(_1829687, _1829685)))], (39598 ^ _778495) ^ [_1549383, _1549385, _1549387, _1549389, _1549391, _1549393, _1549395, _1549397] : [c_Finite__Set_Ofolding__image(_1549383, _1549385, _1549387, _1549389, _1549391), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549385), _1549393)), c_Fun_Oinj__on(_1549385, _1549385, _1549395, _1549393), -(hAPP(hAPP(_1549391, _1549397), hAPP(c_Set_Oimage(_1549385, _1549385, _1549395), _1549393)) = hAPP(hAPP(_1549391, hAPP(c_Fun_Ocomp(_1549385, _1549383, _1549385, _1549397), _1549395)), _1549393))], (28099 ^ _778495) ^ [_1279762, _1279764] : [-(_1279762 = _1279764), -(c_Random_Oinc__shift(_1279762, _1279764) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1279764), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (28469 ^ _778495) ^ [_1293010, _1293012, _1293014, _1293016] : [class_Rings_Osemiring__1(_1293010), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1293010), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293012, tc_Nat_Onat), _1293014), _1293016)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293012, _1293010), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1293010, _1293012), c_Nat_Osemiring__1__class_Oof__nat(_1293010)), _1293014)), _1293016))], (24996 ^ _778495) ^ [_1225571, _1225573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1225573, _1225571)), _1225571)))], (45302 ^ _778495) ^ [_1687527, _1687529, _1687531] : [-(hAPP(c_List_Oset(tc_List_Olist(_1687527)), c_Enum_On__lists(_1687527, _1687529, _1687531)) = hAPP(c_Set_OCollect(tc_List_Olist(_1687527)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1687527), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1687527)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687527), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1687527)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1687527)))), _1687529))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687527), tc_fun(_1687527, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1687527, tc_HOL_Obool), tc_fun(tc_fun(_1687527, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1687527)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1687527, tc_HOL_Obool))), c_List_Oset(_1687527))), hAPP(c_List_Oset(_1687527), _1687531)))))], (16254 ^ _778495) ^ [_1068845, _1068847, _1068849] : [class_Rings_Oring__1(_1068845), hBOOL(hAPP(hAPP(c_member(_1068845), _1068847), c_Int_Oring__1__class_OInts(_1068845))), hBOOL(hAPP(hAPP(c_member(_1068845), _1068849), c_Int_Oring__1__class_OInts(_1068845))), -(hBOOL(hAPP(hAPP(c_member(_1068845), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068845), _1068847), _1068849)), c_Int_Oring__1__class_OInts(_1068845))))], (24922 ^ _778495) ^ [_1224343, _1224345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1224343)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1224345), _1224343)), _1224343) = _1224345)], (42148 ^ _778495) ^ [_1617414, _1617416, _1617418] : [-(_1617414 = _1617416), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617418)), _1617414) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617418)), _1617416), 42154 ^ _778495 : [(42157 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1617418, _1617418, tc_HOL_Obool), c_fequal), 42153 ^ [_1617414, _1617416, _1617418]))], (42155 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617418, _1617418)), 42153 ^ [_1617414, _1617416, _1617418]), hAPP(c_List_Oset(tc_prod(_1617418, _1617418)), hAPP(hAPP(c_List_Ozip(_1617418, _1617418), _1617414), _1617416)))))]]], (4536 ^ _778495) ^ [_847476, _847478, _847480, _847482, _847484, _847486, _847488, _847490] : [-(c_Product__Type_Oscomp(_847490, _847486, _847482, _847478) = c_Product__Type_Oscomp(_847488, _847484, _847480, _847476)), _847490 = _847488, _847486 = _847484, _847482 = _847480, _847478 = _847476], (27689 ^ _778495) ^ [_1272668, _1272670] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272668, tc_HOL_Obool)), _1272670) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272668, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1272668, tc_HOL_Obool))), _1272670))], (38765 ^ _778495) ^ [_1528860] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1528860)))], (19266 ^ _778495) ^ [_1124732, _1124734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124732), _1124734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124732), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1124734)))], (15469 ^ _778495) ^ [_1053308, _1053310, _1053312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053308), _1053310)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053308), _1053312))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1053308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053310), _1053312)))], (6648 ^ _778495) ^ [_887123, _887125, _887127] : [-(hBOOL(hAPP(hAPP(c_member(_887123), _887125), _887127))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887123, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_887123), _887125), _887127)), hAPP(hAPP(c_Set_Oinsert(_887123), _887125), c_Orderings_Obot__class_Obot(tc_fun(_887123, tc_HOL_Obool)))) = _887127)], (33940 ^ _778495) ^ [_1410476] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1410476) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1410476))], (38733 ^ _778495) ^ [_1528196, _1528198, _1528200] : [c_Wellfounded_Owf(_1528196, _1528198), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528196, _1528196)), hAPP(hAPP(c_Product__Type_OPair(_1528196, _1528196), _1528200), _1528200)), _1528198))], (16084 ^ _778495) ^ [_1065987, _1065989] : [class_Rings_Odivision__ring(_1065987), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1065987), c_Groups_Ozero__class_Ozero(_1065987)), _1065989) = c_Groups_Ozero__class_Ozero(_1065987))], (30867 ^ _778495) ^ [_1341988, _1341990, _1341992, _1341994] : [class_Orderings_Olinorder(_1341988), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341988), _1341990), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1341988), _1341992), _1341994)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1341988), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341988), _1341990), _1341992)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341988), _1341990), _1341994)))], (5951 ^ _778495) ^ [_873421, _873423] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873421, tc_HOL_Obool)), _873423), _873423)))], (3736 ^ _778495) ^ [_834600, _834602] : [_834602 = _834600, -(c_Enum_Oenum__class_Oenum__ex(_834602) = c_Enum_Oenum__class_Oenum__ex(_834600))], (20256 ^ _778495) ^ [_1142363, _1142365, _1142367] : [hBOOL(hAPP(_1142363, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1142365), _1142367)))), 20259 ^ _778495 : [(20266 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1142365), _1142367)), -(hBOOL(hAPP(_1142363, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20260 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1142367), _1142365)), -(hBOOL(hAPP(_1142363, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142365)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142367)))))]]], (3766 ^ _778495) ^ [_835071, _835073, _835075, _835077, _835079, _835081] : [-(c_List_OdropWhile(_835081, _835077, _835073) = c_List_OdropWhile(_835079, _835075, _835071)), _835081 = _835079, _835077 = _835075, _835073 = _835071], (8988 ^ _778495) ^ [_930085, _930087] : [class_Lattices_Olattice(_930085), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930085), _930087), _930087) = _930087)], (49204 ^ _778495) ^ [_1773725, _1773727] : [c_Wellfounded_Oacyclic(_1773725, _1773727), -(c_Relation_Oantisym(_1773725, c_Transitive__Closure_Ortrancl(_1773725, _1773727)))], (21706 ^ _778495) ^ [_1167068, _1167070] : [class_Groups_Ogroup__add(_1167068), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1167068), hAPP(c_Groups_Ouminus__class_Ouminus(_1167068), _1167070)) = _1167070)], (30055 ^ _778495) ^ [_1325743, _1325745, _1325747, _1325749, _1325751] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1325743, _1325745, _1325747), _1325749), _1325751) = hAPP(hAPP(_1325749, hAPP(c_Product__Type_Ofst(_1325743, _1325745), _1325751)), hAPP(c_Product__Type_Osnd(_1325743, _1325745), _1325751)))], (52587 ^ _778495) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (30301 ^ _778495) ^ [_1330517, _1330519, _1330521] : [class_Groups_Ocomm__monoid__add(_1330517), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1330517), _1330519), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1330521))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1330517), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1330517), _1330519), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1330521))), hAPP(_1330519, _1330521)))], (52401 ^ _778495) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (37466 ^ _778495) ^ [_1488529, _1488531, _1488533, _1488535, _1488537, _1488539] : [hBOOL(hAPP(hAPP(c_member(_1488529), _1488531), _1488533)), 37469 ^ _778495 : [(37476 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488535, tc_HOL_Obool)), _1488537), _1488539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1488535, _1488529), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1488535, _1488529), _1488537), hAPP(c_COMBK(tc_fun(_1488529, tc_HOL_Obool), _1488535), _1488533))), hAPP(hAPP(c_Product__Type_OSigma(_1488535, _1488529), _1488539), hAPP(c_COMBK(tc_fun(_1488529, tc_HOL_Obool), _1488535), _1488533)))))], (37470 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1488535, _1488529), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1488535, _1488529), _1488537), hAPP(c_COMBK(tc_fun(_1488529, tc_HOL_Obool), _1488535), _1488533))), hAPP(hAPP(c_Product__Type_OSigma(_1488535, _1488529), _1488539), hAPP(c_COMBK(tc_fun(_1488529, tc_HOL_Obool), _1488535), _1488533)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488535, tc_HOL_Obool)), _1488537), _1488539)))]]], (46670 ^ _778495) ^ [_1716887, _1716889, _1716891, _1716893, _1716895] : [c_List_Olist__all2(_1716887, _1716889, _1716891, hAPP(c_List_Orev(_1716887), _1716893), hAPP(c_List_Orev(_1716889), _1716895)), -(c_List_Olist__all2(_1716887, _1716889, _1716891, _1716893, _1716895))], (24579 ^ _778495) ^ [_1218663, _1218665] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1218663)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1218663)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1218665)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1218663)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1218665))))], (27607 ^ _778495) ^ [_1271262, _1271264] : [class_Lattices_Obounded__lattice__top(_1271262), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271262), c_Orderings_Otop__class_Otop(_1271262)), _1271264) = c_Orderings_Otop__class_Otop(_1271262))], (40079 ^ _778495) ^ [_1560386, _1560388, _1560390, _1560392, _1560394, _1560396, _1560398, _1560400] : [class_Groups_Ocomm__monoid__add(_1560386), c_Fun_Oinj__on(_1560388, _1560390, _1560392, _1560394), _1560396 = hAPP(c_Set_Oimage(_1560388, _1560390, _1560392), _1560394), 40093 ^ _778495 : [(40096 ^ _778495) ^ [] : [hAPP(_1560398, 40092 ^ [_1560386, _1560388, _1560390, _1560392, _1560394, _1560396, _1560398, _1560400]) = hAPP(_1560400, hAPP(_1560392, 40092 ^ [_1560386, _1560388, _1560390, _1560392, _1560394, _1560396, _1560398, _1560400]))], (40094 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560388), 40092 ^ [_1560386, _1560388, _1560390, _1560392, _1560394, _1560396, _1560398, _1560400]), _1560394)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560390, _1560386), _1560400), _1560396) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560388, _1560386), _1560398), _1560394))], (37422 ^ _778495) ^ [_1487354, _1487356] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1487354, _1487354), tc_HOL_Obool)), c_Relation_OId__on(_1487354, _1487356)), hAPP(hAPP(c_Product__Type_OSigma(_1487354, _1487354), _1487356), hAPP(c_COMBK(tc_fun(_1487354, tc_HOL_Obool), _1487354), _1487356)))))], (45831 ^ _778495) ^ [_1700093, _1700095] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1700093)), c_List_Otranspose__rel(_1700093)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700093)), c_List_Olist_ONil(_1700093)), _1700095))), -(c_List_Otranspose(_1700093, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700093)), c_List_Olist_ONil(_1700093)), _1700095)) = c_List_Otranspose(_1700093, _1700095))], (5807 ^ _778495) ^ [_870648, _870650, _870652] : [hBOOL(hAPP(hAPP(c_member(_870648), _870650), hAPP(hAPP(c_Set_Oinsert(_870648), _870652), c_Orderings_Obot__class_Obot(tc_fun(_870648, tc_HOL_Obool))))), -(_870650 = _870652)], (52343 ^ _778495) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (26056 ^ _778495) ^ [_1244378, _1244380] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1244378), _1244380) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1244380 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1244378 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50609 ^ _778495) ^ [_1803663, _1803665, _1803667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1803663)), 50612 ^ _778495 : [(50619 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803665), _1803667)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803663), _1803665)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803663), _1803667))))], (50613 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803663), _1803665)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803663), _1803667))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803665), _1803667)))]]], (24543 ^ _778495) ^ [_1217941, _1217943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1217941), _1217943)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1217941, _1217943) = _1217941)], (23130 ^ _778495) ^ [_1192431, _1192433, _1192435, _1192437, _1192439, _1192441] : [class_Divides_Osemiring__div(_1192431), c_Divides_Odiv__class_Omod(_1192431, _1192433, _1192435) = c_Divides_Odiv__class_Omod(_1192431, _1192437, _1192435), c_Divides_Odiv__class_Omod(_1192431, _1192439, _1192435) = c_Divides_Odiv__class_Omod(_1192431, _1192441, _1192435), -(c_Divides_Odiv__class_Omod(_1192431, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192431), _1192433), _1192439), _1192435) = c_Divides_Odiv__class_Omod(_1192431, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192431), _1192437), _1192441), _1192435))], (51373 ^ _778495) ^ [_1816687, _1816689, _1816691, _1816693] : [class_Divides_Osemiring__div(_1816687), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816687), _1816689), _1816691)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816687), _1816689), _1816693)), 51384 ^ _778495 : [(51391 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816687), _1816691), _1816693)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816687), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1816687), _1816691), _1816689)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1816687), _1816693), _1816689))))], (51385 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816687), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1816687), _1816691), _1816689)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1816687), _1816693), _1816689))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816687), _1816691), _1816693)))]]], (27185 ^ _778495) ^ [_1264030, _1264032] : [class_Rings_Olinordered__idom(_1264030), 27188 ^ _778495 : [(27195 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1264032), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264030), hAPP(c_Int_Oring__1__class_Oof__int(_1264030), _1264032)), c_Groups_Ozero__class_Ozero(_1264030))))], (27189 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264030), hAPP(c_Int_Oring__1__class_Oof__int(_1264030), _1264032)), c_Groups_Ozero__class_Ozero(_1264030))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1264032), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (10563 ^ _778495) ^ [_960837] : [_960837 = hAPP(c_Nat_OSuc, _960837)], (15595 ^ _778495) ^ [_1055865, _1055867, _1055869, _1055871, _1055873] : [class_Groups_Ocomm__monoid__mult(_1055865), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055867), _1055869)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1055867, _1055865), _1055871), hAPP(hAPP(c_Set_Oinsert(_1055867), _1055873), _1055869)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055865), hAPP(_1055871, _1055873)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1055867, _1055865), _1055871), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055867, tc_HOL_Obool)), _1055869), hAPP(hAPP(c_Set_Oinsert(_1055867), _1055873), c_Orderings_Obot__class_Obot(tc_fun(_1055867, tc_HOL_Obool)))))))], (29011 ^ _778495) ^ [_1305093, _1305095, _1305097] : [_1305093 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1305095, _1305095), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1305095, _1305095), tc_HOL_Obool)), _1305093), _1305097)))], (29194 ^ _778495) ^ [_1309353, _1309355, _1309357, _1309359] : [class_Rings_Osemiring__1(_1309353), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1309353, _1309355, hAPP(c_Nat_OSuc, _1309357), _1309359) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1309353, _1309355, _1309357, hAPP(_1309355, _1309359)))], (19260 ^ _778495) ^ [_1124621, _1124623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124621), _1124623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124621), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1124623)))], (13372 ^ _778495) ^ [_1016172, _1016174] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016172), _1016174) = _1016172, -(_1016174 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25288 ^ _778495) ^ [_1230289, _1230291] : [hBOOL(hAPP(_1230289, hAPP(c_Int_Onat, _1230291))), 25291 ^ _778495 : [(25298 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230291), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1230289, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25292 ^ _778495) ^ [_1230389] : [_1230291 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230389), -(hBOOL(hAPP(_1230289, _1230389)))]]], (39340 ^ _778495) ^ [_1543316, _1543318, _1543320, _1543322, _1543324, _1543326] : [hBOOL(hAPP(hAPP(c_member(_1543316), _1543318), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1543320, _1543322, tc_fun(_1543316, tc_HOL_Obool)), _1543324), _1543326))), 39345 ^ _778495 : [(39348 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543316), _1543318), hAPP(hAPP(_1543324, 39343 ^ [_1543316, _1543318, _1543320, _1543322, _1543324, _1543326]), 39344 ^ [_1543316, _1543318, _1543320, _1543322, _1543324, _1543326]))))], (39346 ^ _778495) ^ [] : [-(_1543326 = hAPP(hAPP(c_Product__Type_OPair(_1543320, _1543322), 39343 ^ [_1543316, _1543318, _1543320, _1543322, _1543324, _1543326]), 39344 ^ [_1543316, _1543318, _1543320, _1543322, _1543324, _1543326]))]]], (9188 ^ _778495) ^ [_933719, _933721, _933723] : [class_Lattices_Osemilattice__inf(_933719), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933719), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933719), _933721), _933723)), _933721)))], (20444 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (42331 ^ _778495) ^ [_1621630, _1621632, _1621634, _1621636, _1621638] : [-(hAPP(hAPP(c_List_Olist__update(_1621630, hAPP(hAPP(c_List_Olist_OCons(_1621630), _1621632), _1621634)), hAPP(c_Nat_OSuc, _1621636)), _1621638) = hAPP(hAPP(c_List_Olist_OCons(_1621630), _1621632), hAPP(hAPP(c_List_Olist__update(_1621630, _1621634), _1621636), _1621638)))], (26840 ^ _778495) ^ [_1258337, _1258339] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1258337), _1258339), hAPP(c_Int_Onumber__class_Onumber__of(_1258337), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1258337), _1258339)), class_Fields_Ofield__inverse__zero(_1258337), class_Int_Onumber__ring(_1258337)], (12580 ^ _778495) ^ [_1000765, _1000767] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1000765, tc_HOL_Obool)), _1000767)), 12586 ^ _778495 : [(12589 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1000765), 12585 ^ [_1000765, _1000767]))], (12587 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1000765, tc_HOL_Obool)), 12585 ^ [_1000765, _1000767]), _1000767)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1000765), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1000765, tc_HOL_Obool), _1000767))))], (2280 ^ _778495) ^ [_811916, _811918, _811920, _811922, _811924, _811926] : [-(c_Nat_Onat_Onat__rec(_811926, _811922, _811918) = c_Nat_Onat_Onat__rec(_811924, _811920, _811916)), _811926 = _811924, _811922 = _811920, _811918 = _811916], (1778 ^ _778495) ^ [_803748, _803750] : [-(class_Rings_Ozero__neq__one(_803748)), _803750 = _803748, class_Rings_Ozero__neq__one(_803750)], (24659 ^ _778495) ^ [_1219999, _1220001, _1220003] : [class_Rings_Ocomm__semiring__1(_1219999), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219999), _1220001), hAPP(hAPP(c_Power_Opower__class_Opower(_1219999), _1220001), _1220003)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1219999), _1220001), hAPP(c_Nat_OSuc, _1220003)))], (37250 ^ _778495) ^ [_1482167, _1482169, _1482171, _1482173, _1482175] : [c_Fun_Oinj__on(_1482167, _1482169, _1482171, c_Orderings_Otop__class_Otop(tc_fun(_1482167, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1482169, tc_HOL_Obool)), _1482173), hAPP(c_Set_Oimage(_1482167, _1482169, _1482171), _1482175))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1482167, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1482167, _1482169, _1482171), _1482173)), _1482175)))], (25457 ^ _778495) ^ [_1233378, _1233380] : [-(_1233378 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1233380), _1233378) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233380), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1233380), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1233378), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (47197 ^ _778495) ^ [_1728025, _1728027, _1728029] : [-(hBOOL(hAPP(hAPP(c_member(_1728025), _1728027), hAPP(c_List_Oset(_1728025), _1728029)))), -(c_List_Oinsert(_1728025, _1728027, _1728029) = hAPP(hAPP(c_List_Olist_OCons(_1728025), _1728027), _1728029))], (9478 ^ _778495) ^ [_940058, _940060, _940062] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_940058), _940060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_940058), _940060)), hAPP(c_Finite__Set_Ocard(_940058), hAPP(hAPP(c_Set_Oinsert(_940058), _940062), _940060)))))], (41951 ^ _778495) ^ [_1611231, _1611233, _1611235, _1611237] : [hBOOL(hAPP(hAPP(c_member(_1611231), _1611233), hAPP(c_List_Oset(_1611231), hAPP(hAPP(c_List_Olist_OCons(_1611231), _1611235), _1611237)))), -(_1611233 = _1611235), -(hBOOL(hAPP(hAPP(c_member(_1611231), _1611233), hAPP(c_List_Oset(_1611231), _1611237))))], (32464 ^ _778495) ^ [_1376556, _1376558] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376556), _1376558))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1376558, _1376556) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1376558), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1376558), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1376556)))], (39362 ^ _778495) ^ [_1544024, _1544026, _1544028] : [-(hAPP(c_Fun_Ocomp(_1544024, _1544026, _1544024, _1544028), c_Fun_Oid(_1544024)) = _1544028)], (33980 ^ _778495) ^ [_1411171, _1411173, _1411175, _1411177, _1411179] : [class_Groups_Ocomm__monoid__add(_1411171), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1411173), _1411175)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1411175), _1411177)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411171), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411171), _1411179), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411173), _1411175))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411171), _1411179), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411175), _1411177))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411171), _1411179), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411173), _1411177)))], (6790 ^ _778495) ^ [_889740, _889742, _889744] : [hBOOL(hAPP(hAPP(c_member(_889740), _889742), _889744)), -(hAPP(hAPP(c_Set_Oinsert(_889740), _889742), _889744) = _889744)], (44849 ^ _778495) ^ [_1677009, _1677011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677009)), hAPP(c_Code__Numeral_Onat__of, _1677011))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1677009), _1677011)))], (26754 ^ _778495) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (2330 ^ _778495) ^ [_812669, _812671, _812673, _812675] : [-(c_Nitpick_Onat__gcd(_812675, _812671) = c_Nitpick_Onat__gcd(_812673, _812669)), _812675 = _812673, _812671 = _812669], (50579 ^ _778495) ^ [_1803183, _1803185, _1803187] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1803183), _1803185)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1803183), _1803187))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1803183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1803185), _1803187)))], (52679 ^ _778495) ^ [_1835967] : [-(hBOOL(_1835967)), -(hBOOL(hAPP(c_fNot, _1835967)))], (27715 ^ _778495) ^ [_1273109] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1273109), c_Orderings_Otop__class_Otop(tc_fun(_1273109, 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(_1273109), c_Orderings_Otop__class_Otop(tc_fun(_1273109, tc_HOL_Obool))))))], (21138 ^ _778495) ^ [_1157205, _1157207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1157205), _1157207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1157205)), c_Int_OBit1(_1157207))))], (4618 ^ _778495) ^ [_848767, _848769] : [_848769 = _848767, -(c_DSequence_Osingle(_848769) = c_DSequence_Osingle(_848767))], (21580 ^ _778495) ^ [_1164967, _1164969] : [class_Int_Onumber__ring(_1164967), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164967), c_Groups_Oone__class_Oone(_1164967)), hAPP(c_Int_Onumber__class_Onumber__of(_1164967), _1164969)) = hAPP(c_Int_Onumber__class_Onumber__of(_1164967), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1164969)))], (8948 ^ _778495) ^ [_929149, _929151, _929153, _929155] : [class_Lattices_Olattice(_929149), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929149), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929149), _929151), _929153)), _929155) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929149), _929151), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929149), _929153), _929155)))], (21480 ^ _778495) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (38723 ^ _778495) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (17280 ^ _778495) ^ [_1087531, _1087533, _1087535, _1087537] : [class_Fields_Ofield(_1087531), -(_1087533 = c_Groups_Ozero__class_Ozero(_1087531)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087531), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1087531), _1087535), _1087533)), _1087537) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1087531), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087531), _1087535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087531), _1087533), _1087537))), _1087533))], (33042 ^ _778495) ^ [_1388071, _1388073] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1388071, _1388073)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1388073), _1388071)))], (35508 ^ _778495) ^ [_1442128, _1442130, _1442132] : [-(hAPP(c_Relation_OImage(_1442128, _1442130, _1442132), c_Orderings_Obot__class_Obot(tc_fun(_1442128, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1442130, tc_HOL_Obool)))], (34520 ^ _778495) ^ [_1423679, _1423681, _1423683] : [class_Groups_Oordered__ab__group__add(_1423679), -(hAPP(c_Set_Oimage(_1423679, _1423679, c_Groups_Ouminus__class_Ouminus(_1423679)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1423679, _1423681, _1423683)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1423679, hAPP(c_Groups_Ouminus__class_Ouminus(_1423679), _1423683)), hAPP(c_Groups_Ouminus__class_Ouminus(_1423679), _1423681)))], (22620 ^ _778495) ^ [_1182859, _1182861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182859), _1182861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1182859)), c_Int_OBit0(_1182861))))], (24381 ^ _778495) ^ [_1214915, _1214917] : [class_Int_Onumber__ring(_1214915), 24384 ^ _778495 : [(24391 ^ _778495) ^ [] : [c_Int_Oiszero(_1214915, hAPP(c_Int_Onumber__class_Onumber__of(_1214915), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214917), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1214915), _1214917) = c_Groups_Ozero__class_Ozero(_1214915))], (24385 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1214915), _1214917) = c_Groups_Ozero__class_Ozero(_1214915), -(c_Int_Oiszero(_1214915, hAPP(c_Int_Onumber__class_Onumber__of(_1214915), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214917), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (15219 ^ _778495) ^ [_1048797, _1048799, _1048801] : [class_Rings_Olinordered__ring(_1048797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048797), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048797), _1048799), _1048799)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048797), _1048801), _1048801))), c_Groups_Ozero__class_Ozero(_1048797)))], (20081 ^ _778495) ^ [_1139242, _1139244] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1139242), _1139244)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1139242)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1139244)))], (52197 ^ _778495) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (1758 ^ _778495) ^ [_803498, _803500] : [-(class_Rings_Ocomm__semiring(_803498)), _803500 = _803498, class_Rings_Ocomm__semiring(_803500)], (27157 ^ _778495) ^ [_1263559, _1263561, _1263563] : [class_Rings_Oring__1(_1263559), -(hAPP(c_Int_Oring__1__class_Oof__int(_1263559), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1263561), _1263563)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1263559), hAPP(c_Int_Oring__1__class_Oof__int(_1263559), _1263561)), _1263563))], (38783 ^ _778495) ^ [_1529196, _1529198] : [c_Wellfounded_Owf(_1529196, _1529198), 38786 ^ _778495 : [(38787 ^ _778495) ^ [_1529265] : [-(hBOOL(hAPP(hAPP(c_member(_1529196), _1529265), c_Wellfounded_Oacc(_1529196, _1529198))))]]], (3644 ^ _778495) ^ [_833160, _833162] : [_833162 = _833160, -(c_List_Oembed__list(_833162) = c_List_Oembed__list(_833160))], (34326 ^ _778495) ^ [_1418959, _1418961, _1418963, _1418965, _1418967, _1418969] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418959, tc_fun(_1418961, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1418963, _1418959, _1418965), _1418967)), _1418969) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418963, tc_fun(_1418961, tc_HOL_Obool)), _1418967), hAPP(hAPP(c_COMBB(_1418959, tc_fun(_1418961, tc_HOL_Obool), _1418963), _1418969), _1418965)))], (48507 ^ _778495) ^ [_1756735, _1756737, _1756739] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756735), _1756739), _1756737)), -(hBOOL(hAPP(hAPP(c_member(_1756735), _1756737), hAPP(c_List_Oset(_1756735), _1756739))))], (26740 ^ _778495) ^ [] : [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)], (40748 ^ _778495) ^ [_1576945, _1576947, _1576949, _1576951] : [-(hAPP(c_Relation_Oconverse(_1576945, _1576947), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1576945, _1576947), tc_HOL_Obool)), _1576949), _1576951)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1576947, _1576945), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1576945, _1576947), _1576949)), hAPP(c_Relation_Oconverse(_1576945, _1576947), _1576951)))], (31802 ^ _778495) ^ [_1360689, _1360691, _1360693, _1360695, _1360697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360689, tc_HOL_Obool)), _1360691), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1360693, tc_fun(_1360689, tc_HOL_Obool)), _1360695), _1360697))), 31805 ^ _778495 : [(31806 ^ _778495) ^ [_1360822] : [hBOOL(hAPP(hAPP(c_member(_1360693), _1360822), _1360695)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360689, tc_HOL_Obool)), _1360691), hAPP(_1360697, _1360822))))]]], (35567 ^ _778495) ^ [_1443805, _1443807, _1443809, _1443811, _1443813] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1443809, _1443805)), hAPP(hAPP(c_Product__Type_OPair(_1443809, _1443805), _1443813), _1443807)), _1443811)), -(hBOOL(hAPP(hAPP(c_member(_1443805), _1443807), hAPP(c_Relation_OImage(_1443809, _1443805, _1443811), hAPP(hAPP(c_Set_Oinsert(_1443809), _1443813), c_Orderings_Obot__class_Obot(tc_fun(_1443809, tc_HOL_Obool)))))))], (3282 ^ _778495) ^ [_827485, _827487, _827489, _827491] : [-(c_List_Olists(_827491, _827487) = c_List_Olists(_827489, _827485)), _827491 = _827489, _827487 = _827485], (13275 ^ _778495) ^ [_1014740] : [class_Rings_Ozero__neq__one(_1014740), c_Groups_Ozero__class_Ozero(_1014740) = c_Groups_Oone__class_Oone(_1014740)], (7752 ^ _778495) ^ [_906698, _906700, _906702] : [class_Orderings_Olinorder(_906698), 7755 ^ _778495 : [(7762 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906698), _906702), _906700)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906698), _906700), _906702))], (7756 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906698), _906700), _906702))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906698), _906702), _906700)))]]], (44121 ^ _778495) ^ [_1661425, _1661427, _1661429, _1661431, _1661433] : [class_Orderings_Olinorder(_1661425), -(hBOOL(hAPP(hAPP(c_member(_1661425), hAPP(_1661427, _1661429)), hAPP(c_Set_Oimage(_1661431, _1661425, _1661427), hAPP(c_List_Oset(_1661431), _1661433))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661431, _1661425, _1661427, _1661429, _1661433) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661431, _1661425, _1661427), _1661429), _1661433))], (43307 ^ _778495) ^ [_1642567, _1642569, _1642571, _1642573] : [hBOOL(hAPP(hAPP(c_member(_1642567), _1642569), hAPP(c_List_Oset(_1642567), _1642571))), -(c_List_Oremove1(_1642567, _1642569, hAPP(hAPP(c_List_Oappend(_1642567), _1642571), _1642573)) = hAPP(hAPP(c_List_Oappend(_1642567), c_List_Oremove1(_1642567, _1642569, _1642571)), _1642573))], (26590 ^ _778495) ^ [_1254198, _1254200] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1254198), _1254200)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1254198, tc_HOL_Obool)), hAPP(c_Set_OPow(_1254198), _1254200)) = 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(_1254198), _1254200)))], (10513 ^ _778495) ^ [_959943, _959945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _959943)), _959945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _959943), _959945)))], (42722 ^ _778495) ^ [_1629934] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629934)), c_List_Olist_ONil(_1629934)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7648 ^ _778495) ^ [_905005, _905007, _905009, _905011] : [class_Orderings_Opreorder(_905005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905005), _905007), _905009)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905005), _905009), _905011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905005), _905007), _905011)))], (5721 ^ _778495) ^ [_869036, _869038, _869040] : [hAPP(hAPP(c_Set_Oinsert(_869036), _869038), c_Orderings_Obot__class_Obot(tc_fun(_869036, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_869036), _869040), c_Orderings_Obot__class_Obot(tc_fun(_869036, tc_HOL_Obool))), -(_869038 = _869040)], (12202 ^ _778495) ^ [_992290, _992292, _992294] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_992290), _992292)), hBOOL(hAPP(c_Finite__Set_Ofinite(_992290), _992294)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_992290), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_992290, tc_HOL_Obool)), _992292), _992294))), hAPP(c_Finite__Set_Ocard(_992290), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_992290, tc_HOL_Obool)), _992292), _992294))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_992290), _992292)), hAPP(c_Finite__Set_Ocard(_992290), _992294)))], (42256 ^ _778495) ^ [_1619991] : [c_List_Onat__list(_1619991), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1619991)))], (51549 ^ _778495) ^ [_1819820, _1819822, _1819824, _1819826] : [class_Rings_Ocomm__ring__1(_1819820), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819820), _1819822), _1819824)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819820), _1819822), _1819826)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819820), _1819822), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1819820), _1819824), _1819826))))], (51293 ^ _778495) ^ [_1815394, _1815396] : [_1815394 = _1815396, 51296 ^ _778495 : [(51299 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815396), _1815394)))], (51297 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815394), _1815396)))]]], (12390 ^ _778495) ^ [_996648, _996650, _996652, _996654, _996656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996648), _996650)), 12393 ^ _778495 : [(12400 ^ _778495) ^ [] : [_996654 = 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), _996650), _996648)), _996652)), _996656), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996648), _996652)), _996654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996650), _996652)), _996656))], (12394 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996648), _996652)), _996654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996650), _996652)), _996656), -(_996654 = 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), _996650), _996648)), _996652)), _996656))]]], (51583 ^ _778495) ^ [_1820473, _1820475, _1820477] : [class_Divides_Oring__div(_1820473), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820473), _1820475), _1820477)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820473), hAPP(c_Groups_Ouminus__class_Ouminus(_1820473), _1820477)), _1820475) = hAPP(c_Groups_Ouminus__class_Ouminus(_1820473), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820473), _1820477), _1820475)))], (22922 ^ _778495) ^ [] : [-(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)))))], (38105 ^ _778495) ^ [_1506484, _1506486] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506484), _1506486)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1506484, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1506484, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1506484, tc_HOL_Obool), tc_fun(_1506484, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1506484, tc_HOL_Obool))), _1506486)))))], (30103 ^ _778495) ^ [_1326721, _1326723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1326721), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1326723), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1326721), _1326723) = 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), _1326721), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1326723)))))], (52375 ^ _778495) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (30703 ^ _778495) ^ [_1339032, _1339034, _1339036] : [class_Orderings_Olinorder(_1339032), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339032), _1339034), _1339036)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339032), _1339034), _1339036) = _1339036)], (52177 ^ _778495) ^ [_1830841, _1830843] : [class_Groups_Ominus(_1830841), -(class_Groups_Ominus(tc_fun(_1830843, _1830841)))], (1318 ^ _778495) ^ [_797998, _798000] : [-(class_Int_Onumber__ring(_797998)), _798000 = _797998, class_Int_Onumber__ring(_798000)], (27579 ^ _778495) ^ [_1270734, _1270736] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270734, tc_HOL_Obool)), _1270736), c_Orderings_Otop__class_Otop(tc_fun(_1270734, tc_HOL_Obool)))))], (11807 ^ _778495) ^ [_983639, _983641, _983643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983639), _983641)), _983643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983641), _983643)))], (41252 ^ _778495) ^ [_1590474, _1590476, _1590478, _1590480, _1590482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590474, tc_HOL_Obool)), _1590476), _1590478)), 41258 ^ _778495 : [(41263 ^ _778495) ^ [] : [hBOOL(hAPP(_1590482, 41257 ^ [_1590474, _1590476, _1590478, _1590480, _1590482]))], (41261 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1590480, 41257 ^ [_1590474, _1590476, _1590478, _1590480, _1590482])))], (41259 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590474), 41257 ^ [_1590474, _1590476, _1590478, _1590480, _1590482]), _1590476)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590474, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1590474, tc_HOL_Obool)), _1590476), hAPP(c_Set_OCollect(_1590474), _1590480))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1590474, tc_HOL_Obool)), _1590478), hAPP(c_Set_OCollect(_1590474), _1590482)))))], (16308 ^ _778495) ^ [_1069761, _1069763] : [class_Int_Oring__char__0(_1069761), hBOOL(hAPP(hAPP(c_member(_1069761), _1069763), c_Int_Oring__1__class_OInts(_1069761))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069761), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069761), c_Groups_Oone__class_Oone(_1069761)), _1069763)), _1069763) = c_Groups_Ozero__class_Ozero(_1069761)], (43540 ^ _778495) ^ [_1648773, _1648775, _1648777, _1648779] : [hBOOL(hAPP(hAPP(c_member(_1648773), _1648775), hAPP(c_List_Oset(_1648773), hAPP(hAPP(c_List_Odrop(_1648773), _1648777), _1648779)))), -(hBOOL(hAPP(hAPP(c_member(_1648773), _1648775), hAPP(c_List_Oset(_1648773), _1648779))))], (27899 ^ _778495) ^ [_1276256, _1276258] : [c_Nat__Transfer_Ois__nat(_1276256), c_Nat__Transfer_Ois__nat(_1276258), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1276256), _1276258)))], (52205 ^ _778495) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (42808 ^ _778495) ^ [_1631451, _1631453] : [-(c_List_Osublist(_1631451, _1631453, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1631451))], (30903 ^ _778495) ^ [_1342884, _1342886, _1342888, _1342890] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1342884), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1342884), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342884), _1342886), _1342888)), _1342890) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342884), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1342884), _1342886), _1342890)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1342884), _1342888), _1342890)))], (46419 ^ _778495) ^ [_1711558, _1711560, _1711562] : [class_Orderings_Olinorder(_1711558), 46422 ^ _778495 : [(46435 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711558, hAPP(hAPP(c_List_Olist_OCons(_1711558), _1711560), _1711562))), 46439 ^ _778495 : [(46442 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711558), _1711560), 46438 ^ [_1711558, _1711560, _1711562]))], (46440 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1711558), 46438 ^ [_1711558, _1711560, _1711562]), hAPP(c_List_Oset(_1711558), _1711562))))]], c_List_Olinorder__class_Osorted(_1711558, _1711562)], (46423 ^ _778495) ^ [] : [c_List_Olinorder__class_Osorted(_1711558, hAPP(hAPP(c_List_Olist_OCons(_1711558), _1711560), _1711562)), 46426 ^ _778495 : [(46427 ^ _778495) ^ [_1711726] : [hBOOL(hAPP(hAPP(c_member(_1711558), _1711726), hAPP(c_List_Oset(_1711558), _1711562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711558), _1711560), _1711726)))], (46433 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711558, _1711562))]]]]], (46756 ^ _778495) ^ [_1718629, _1718631, _1718633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718629), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718631)), _1718633))), -(hAPP(hAPP(c_List_Onth(_1718631), hAPP(c_List_Orev(_1718631), _1718633)), _1718629) = hAPP(hAPP(c_List_Onth(_1718631), _1718633), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718631)), _1718633)), hAPP(c_Nat_OSuc, _1718629))))], (22326 ^ _778495) ^ [_1177724, _1177726, _1177728] : [class_Groups_Ogroup__add(_1177724), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177724), _1177726), _1177728) = c_Groups_Ozero__class_Ozero(_1177724), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1177724), _1177726) = _1177728)], (8314 ^ _778495) ^ [_915887, _915889, _915891, _915893, _915895, _915897, _915899] : [c_Nitpick_Ofold__graph_H(_915887, _915889, _915891, _915893, _915895, hAPP(hAPP(_915891, _915897), _915899)), 8319 ^ _778495 : [(8322 ^ _778495) ^ [] : [-(hAPP(hAPP(_915891, _915897), _915899) = _915893)], (8320 ^ _778495) ^ [] : [-(_915895 = c_Orderings_Obot__class_Obot(tc_fun(_915887, tc_HOL_Obool)))]], 8325 ^ _778495 : [(8330 ^ _778495) ^ [] : [-(c_Nitpick_Ofold__graph_H(_915887, _915889, _915891, _915893, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915887, tc_HOL_Obool)), _915895), hAPP(hAPP(c_Set_Oinsert(_915887), 8323 ^ [_915887, _915889, _915891, _915893, _915895, _915897, _915899]), c_Orderings_Obot__class_Obot(tc_fun(_915887, tc_HOL_Obool)))), 8324 ^ [_915887, _915889, _915891, _915893, _915895, _915897, _915899]))], (8328 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_915887), 8323 ^ [_915887, _915889, _915891, _915893, _915895, _915897, _915899]), _915895)))], (8326 ^ _778495) ^ [] : [-(hAPP(hAPP(_915891, _915897), _915899) = hAPP(hAPP(_915891, 8323 ^ [_915887, _915889, _915891, _915893, _915895, _915897, _915899]), 8324 ^ [_915887, _915889, _915891, _915893, _915895, _915897, _915899]))]]], (44758 ^ _778495) ^ [_1675163] : [-(_1675163 = 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)), _1675163)))], (34446 ^ _778495) ^ [_1421926, _1421928, _1421930, _1421932, _1421934] : [_1421926 = hAPP(_1421928, _1421930), -(hBOOL(hAPP(hAPP(c_member(_1421932), _1421926), hAPP(c_Set_Oimage(_1421934, _1421932, _1421928), c_Orderings_Otop__class_Otop(tc_fun(_1421934, tc_HOL_Obool))))))], (39214 ^ _778495) ^ [_1540372, _1540374, _1540376, _1540378] : [39216 ^ _778495 : [(39219 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1540372, _1540372, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1540372, tc_fun(_1540372, _1540374), tc_fun(_1540372, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540374, tc_HOL_Obool), tc_fun(tc_fun(_1540372, _1540374), tc_fun(_1540372, tc_HOL_Obool)), _1540372), c_COMBB(_1540374, tc_HOL_Obool, _1540372)), hAPP(hAPP(c_COMBB(_1540374, tc_fun(_1540374, tc_HOL_Obool), _1540372), c_fequal), _1540378))), _1540378)), 39215 ^ [_1540372, _1540374, _1540376, _1540378]))], (39217 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540372, _1540372)), 39215 ^ [_1540372, _1540374, _1540376, _1540378]), _1540376)))]], -(c_Equiv__Relations_Ocongruent(_1540372, _1540374, _1540376, _1540378))], (47347 ^ _778495) ^ [_1731675, _1731677, _1731679] : [class_Enum_Oenum(_1731675), class_Enum_Oenum(_1731677), 47354 ^ _778495 : [(47361 ^ _778495) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731677), hAPP(hAPP(c_COMBB(tc_fun(_1731675, tc_HOL_Obool), tc_HOL_Obool, _1731677), c_Enum_Oenum__class_Oenum__ex(_1731675)), hAPP(hAPP(c_COMBB(tc_fun(_1731675, tc_prod(_1731677, _1731675)), tc_fun(_1731675, tc_HOL_Obool), _1731677), hAPP(c_COMBB(tc_prod(_1731677, _1731675), tc_HOL_Obool, _1731675), _1731679)), c_Product__Type_OPair(_1731677, _1731675))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731677, _1731675)), _1731679)))], (47355 ^ _778495) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731677, _1731675)), _1731679)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731677), hAPP(hAPP(c_COMBB(tc_fun(_1731675, tc_HOL_Obool), tc_HOL_Obool, _1731677), c_Enum_Oenum__class_Oenum__ex(_1731675)), hAPP(hAPP(c_COMBB(tc_fun(_1731675, tc_prod(_1731677, _1731675)), tc_fun(_1731675, tc_HOL_Obool), _1731677), hAPP(c_COMBB(tc_prod(_1731677, _1731675), tc_HOL_Obool, _1731675), _1731679)), c_Product__Type_OPair(_1731677, _1731675))))))]]], (33191 ^ _778495) ^ [_1391376, _1391378, _1391380, _1391382] : [33193 ^ _778495 : [(33196 ^ _778495) ^ [] : [hAPP(_1391382, 33192 ^ [_1391376, _1391378, _1391380, _1391382]) = c_Orderings_Obot__class_Obot(tc_fun(_1391376, tc_HOL_Obool))], (33194 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391378), 33192 ^ [_1391376, _1391378, _1391380, _1391382]), _1391380)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1391376, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391378, tc_fun(_1391376, tc_HOL_Obool)), _1391380), _1391382))], (32170 ^ _778495) ^ [_1370317, _1370319, _1370321, _1370323, _1370325] : [-(_1370317 = c_Orderings_Obot__class_Obot(tc_fun(_1370319, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370319, tc_fun(_1370321, tc_HOL_Obool)), _1370317), hAPP(hAPP(c_COMBB(tc_fun(_1370321, tc_HOL_Obool), tc_fun(_1370321, tc_HOL_Obool), _1370319), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370321, tc_HOL_Obool)), _1370323)), _1370325)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370321, tc_HOL_Obool)), _1370323), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370319, tc_fun(_1370321, tc_HOL_Obool)), _1370317), _1370325)))], (5034 ^ _778495) ^ [_855355, _855357] : [_855357 = _855355, -(c_Finite__Set_Ocard(_855357) = c_Finite__Set_Ocard(_855355))], (47235 ^ _778495) ^ [_1728661, _1728663, _1728665, _1728667] : [-(c_List_Omaps(_1728661, _1728663, _1728665, _1728667) = c_List_Oconcat(_1728663, hAPP(hAPP(c_List_Omap(_1728661, tc_List_Olist(_1728663)), _1728665), _1728667)))], (35807 ^ _778495) ^ [_1449683, _1449685, _1449687, _1449689, _1449691] : [hAPP(c_Relation_OImage(_1449683, _1449683, _1449685), hAPP(hAPP(c_Set_Oinsert(_1449683), _1449687), c_Orderings_Obot__class_Obot(tc_fun(_1449683, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1449683, _1449683, _1449685), hAPP(hAPP(c_Set_Oinsert(_1449683), _1449689), c_Orderings_Obot__class_Obot(tc_fun(_1449683, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1449683, _1449691, _1449685), hBOOL(hAPP(hAPP(c_member(_1449683), _1449689), _1449691)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1449683, _1449683)), hAPP(hAPP(c_Product__Type_OPair(_1449683, _1449683), _1449687), _1449689)), _1449685)))], (47523 ^ _778495) ^ [_1735835, _1735837, _1735839, _1735841, _1735843] : [hAPP(hAPP(c_List_Olist_OCons(_1735835), _1735837), _1735839) = hAPP(c_List_Ofilter(_1735835, _1735841), _1735843), 47528 ^ _778495 : [(47537 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1735841, _1735837)))], (47539 ^ _778495) ^ [] : [-(_1735839 = hAPP(c_List_Ofilter(_1735835, _1735841), 47527 ^ [_1735835, _1735837, _1735839, _1735841, _1735843]))], (47531 ^ _778495) ^ [_1736149] : [hBOOL(hAPP(hAPP(c_member(_1735835), _1736149), hAPP(c_List_Oset(_1735835), 47526 ^ [_1735835, _1735837, _1735839, _1735841, _1735843]))), hBOOL(hAPP(_1735841, _1736149))], (47529 ^ _778495) ^ [] : [-(_1735843 = hAPP(hAPP(c_List_Oappend(_1735835), 47526 ^ [_1735835, _1735837, _1735839, _1735841, _1735843]), hAPP(hAPP(c_List_Olist_OCons(_1735835), _1735837), 47527 ^ [_1735835, _1735837, _1735839, _1735841, _1735843])))]]], (28309 ^ _778495) ^ [_1284782, _1284784, _1284786] : [_1284784 = _1284786, -(hAPP(hAPP(c_COMBC(_1284782, tc_fun(_1284782, tc_HOL_Obool), tc_HOL_Obool), c_member(_1284782)), _1284784) = hAPP(hAPP(c_COMBC(_1284782, tc_fun(_1284782, tc_HOL_Obool), tc_HOL_Obool), c_member(_1284782)), _1284786))], (1538 ^ _778495) ^ [_800748, _800750] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_800748)), _800750 = _800748, class_Groups_Oordered__cancel__ab__semigroup__add(_800750)], (47034 ^ _778495) ^ [_1724462, _1724464, _1724466] : [hBOOL(hAPP(c_List_Odistinct(_1724462), _1724464)), -(hBOOL(hAPP(c_List_Odistinct(_1724462), c_List_OdropWhile(_1724462, _1724466, _1724464))))], (1918 ^ _778495) ^ [_805498, _805500] : [-(class_Int_Onumber(_805498)), _805500 = _805498, class_Int_Onumber(_805500)], (42179 ^ _778495) ^ [_1618183, _1618185, _1618187, _1618189, _1618191, _1618193] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618183, _1618185)), hAPP(hAPP(c_Product__Type_OPair(_1618183, _1618185), _1618187), _1618189)), hAPP(c_List_Oset(tc_prod(_1618183, _1618185)), hAPP(hAPP(c_List_Ozip(_1618183, _1618185), _1618191), _1618193)))), -(hBOOL(hAPP(hAPP(c_member(_1618183), _1618187), hAPP(c_List_Oset(_1618183), _1618191))))], (46270 ^ _778495) ^ [_1708647, _1708649, _1708651, _1708653] : [class_Orderings_Olinorder(_1708647), -(c_List_Olinorder__class_Osorted(_1708647, hAPP(hAPP(c_List_Omap(_1708649, _1708647), _1708651), c_List_Olinorder__class_Osort__key(_1708649, _1708647, _1708651, _1708653))))], (39921 ^ _778495) ^ [_1556677, _1556679] : [39922 ^ _778495 : [(39923 ^ _778495) ^ [_1556723] : [hBOOL(hAPP(_1556677, _1556723))]], -(hBOOL(hAPP(_1556677, c_Hilbert__Choice_OEps(_1556679, _1556677))))], (48460 ^ _778495) ^ [_1755419] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1755419) = c_Lazy__Sequence_Osmall__lazy_H(_1755419, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1755419)))], (22156 ^ _778495) ^ [_1174818, _1174820] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1174818), _1174820)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1174818)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1174820)))], (23056 ^ _778495) ^ [_1190982, _1190984] : [class_Divides_Osemiring__div(_1190982), -(c_Divides_Odiv__class_Omod(_1190982, c_Groups_Ozero__class_Ozero(_1190982), _1190984) = c_Groups_Ozero__class_Ozero(_1190982))], (39372 ^ _778495) ^ [_1544239, _1544241, _1544243, _1544245, _1544247, _1544249, _1544251, _1544253] : [hAPP(c_Fun_Ocomp(_1544239, _1544241, _1544243, _1544245), _1544247) = hAPP(c_Fun_Ocomp(_1544249, _1544241, _1544243, _1544251), _1544253), 39375 ^ _778495 : [(39376 ^ _778495) ^ [_1544354] : [-(hAPP(_1544245, hAPP(_1544247, _1544354)) = hAPP(_1544251, hAPP(_1544253, _1544354)))]]], (36903 ^ _778495) ^ [_1474311, _1474313, _1474315, _1474317, _1474319, _1474321, _1474323] : [c_Typedef_Otype__definition(_1474311, _1474313, _1474315, _1474317, _1474319), 36906 ^ _778495 : [(36913 ^ _778495) ^ [] : [_1474321 = _1474323, -(hAPP(_1474315, _1474321) = hAPP(_1474315, _1474323))], (36907 ^ _778495) ^ [] : [hAPP(_1474315, _1474321) = hAPP(_1474315, _1474323), -(_1474321 = _1474323)]]], (25638 ^ _778495) ^ [_1236570, _1236572] : [class_Groups_Omonoid__mult(_1236570), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1236570), _1236572), 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(_1236570), _1236572), _1236572))], (27987 ^ _778495) ^ [_1277759, _1277761, _1277763] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1277759, tc_HOL_Obool)), _1277761), _1277763) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1277759, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1277759, tc_HOL_Obool)), _1277761), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1277759, tc_HOL_Obool)), _1277763), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1277759, tc_HOL_Obool), tc_HOL_Obool))))))], (9440 ^ _778495) ^ [_939235, _939237, _939239] : [class_Lattices_Olattice(_939235), hBOOL(hAPP(c_Finite__Set_Ofinite(_939235), _939237)), -(_939237 = c_Orderings_Obot__class_Obot(tc_fun(_939235, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_939235), _939239)), -(_939239 = c_Orderings_Obot__class_Obot(tc_fun(_939235, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939235, tc_HOL_Obool)), _939237), _939239) = c_Orderings_Obot__class_Obot(tc_fun(_939235, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_939235, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_939235, tc_HOL_Obool)), _939237), _939239)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939235), c_Big__Operators_Olattice__class_OSup__fin(_939235, _939237)), c_Big__Operators_Olattice__class_OSup__fin(_939235, _939239)))], (52273 ^ _778495) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (21554 ^ _778495) ^ [_1164526, _1164528] : [class_Int_Onumber__ring(_1164526), class_Rings_Olinordered__idom(_1164526), 21561 ^ _778495 : [(21568 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1164528), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164526), hAPP(c_Int_Onumber__class_Onumber__of(_1164526), _1164528)), c_Groups_Oone__class_Oone(_1164526))))], (21562 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164526), hAPP(c_Int_Onumber__class_Onumber__of(_1164526), _1164528)), c_Groups_Oone__class_Oone(_1164526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1164528), c_Int_OBit1(c_Int_OPls))))]]], (20315 ^ _778495) ^ [_1143471, _1143473] : [class_Int_Onumber__ring(_1143471), 20318 ^ _778495 : [(20325 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143473)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1143471), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143473)) = hAPP(c_Int_Onumber__class_Onumber__of(_1143471), _1143473))], (20319 ^ _778495) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143473))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1143471), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143473)) = c_Groups_Ozero__class_Ozero(_1143471))]]], (29447 ^ _778495) ^ [_1314126, _1314128, _1314130] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1314126, _1314128), _1314130)), 29450 ^ _778495 : [(29451 ^ _778495) ^ [_1314211] : [hBOOL(hAPP(hAPP(_1314128, _1314211), _1314130)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1314126, _1314128), _1314211)))]]], (25080 ^ _778495) ^ [_1226919] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1226919))), -(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), _1226919)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14013 ^ _778495) ^ [_1027331, _1027333] : [class_Groups_Olinordered__ab__group__add(_1027331), 14016 ^ _778495 : [(14023 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027331), c_Groups_Ozero__class_Ozero(_1027331)), _1027333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027331), c_Groups_Ozero__class_Ozero(_1027331)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027331), _1027333), _1027333))))], (14017 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027331), c_Groups_Ozero__class_Ozero(_1027331)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027331), _1027333), _1027333))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027331), c_Groups_Ozero__class_Ozero(_1027331)), _1027333)))]]], (7478 ^ _778495) ^ [_902460, _902462, _902464] : [class_Orderings_Olinorder(_902460), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902460), _902462), _902464))), 7485 ^ _778495 : [(7492 ^ _778495) ^ [] : [_902464 = _902462, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902460), _902464), _902462))], (7486 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902460), _902464), _902462))), -(_902464 = _902462)]]], (38842 ^ _778495) ^ [_1530582, _1530584, _1530586] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1530582, _1530584)), _1530586)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1530582), hAPP(c_Relation_ODomain(_1530582, _1530584), _1530586))))], (24653 ^ _778495) ^ [_1219868, _1219870, _1219872] : [class_Rings_Ocomm__semiring__1(_1219868), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1219868), _1219870), hAPP(c_Nat_OSuc, _1219872)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219868), _1219870), hAPP(hAPP(c_Power_Opower__class_Opower(_1219868), _1219870), _1219872)))], (6534 ^ _778495) ^ [_884666, _884668, _884670, _884672] : [hBOOL(hAPP(hAPP(c_member(_884666), _884668), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_884666, tc_HOL_Obool)), _884670), _884672))), hBOOL(hAPP(hAPP(c_member(_884666), _884668), _884672))], (36508 ^ _778495) ^ [_1465548, _1465550] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465548), c_Orderings_Otop__class_Otop(tc_fun(_1465548, tc_HOL_Obool)))), c_Fun_Oinj__on(_1465548, _1465548, _1465550, c_Orderings_Otop__class_Otop(tc_fun(_1465548, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1465548, _1465548, _1465550), c_Orderings_Otop__class_Otop(tc_fun(_1465548, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1465548, tc_HOL_Obool)))], (27735 ^ _778495) ^ [_1273436, _1273438] : [class_Complete__Lattice_Ocomplete__lattice(_1273436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273436), _1273438)), -(c_Complete__Lattice_OInf__class_OInf(_1273436, _1273438) = hAPP(hAPP(c_Finite__Set_Ofold(_1273436, _1273436, c_Lattices_Osemilattice__inf__class_Oinf(_1273436)), c_Orderings_Otop__class_Otop(_1273436)), _1273438))], (24695 ^ _778495) ^ [_1220590, _1220592] : [class_Rings_Ocomm__semiring__1(_1220590), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1220590), _1220592), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1220590))], (43614 ^ _778495) ^ [_1650472, _1650474, _1650476, _1650478] : [-(_1650472 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1650474), _1650472), hAPP(hAPP(c_List_Olist_OCons(_1650474), _1650476), _1650478)) = hAPP(hAPP(c_List_Odrop(_1650474), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1650472), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1650478))], (19098 ^ _778495) ^ [_1121815] : [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)), _1121815)), _1121815) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (27591 ^ _778495) ^ [_1270972, _1270974] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1270972, _1270974)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1270972, _1270974), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270972), c_Orderings_Otop__class_Otop(tc_fun(_1270972, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270974), c_Orderings_Otop__class_Otop(tc_fun(_1270974, tc_HOL_Obool))))], (31658 ^ _778495) ^ [_1357255, _1357257, _1357259, _1357261] : [class_Groups_Oab__group__add(_1357255), 31661 ^ _778495 : [(31668 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1357257), _1357259))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1357255), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1357255, _1357255), hAPP(hAPP(c_COMBB(_1357255, tc_fun(_1357255, _1357255), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1357255)), _1357261)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1357255, tc_Nat_Onat), _1357261), 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, _1357257, _1357259)) = c_Groups_Ozero__class_Ozero(_1357255))], (31662 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1357257), _1357259)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1357255), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1357255, _1357255), hAPP(hAPP(c_COMBB(_1357255, tc_fun(_1357255, _1357255), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1357255)), _1357261)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1357255, tc_Nat_Onat), _1357261), 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, _1357257, _1357259)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357255), hAPP(_1357261, _1357257)), hAPP(_1357261, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1357259), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (2774 ^ _778495) ^ [_819621, _819623, _819625, _819627, _819629, _819631, _819633, _819635] : [-(c_Random_Oiterate(_819635, _819631, _819627, _819623) = c_Random_Oiterate(_819633, _819629, _819625, _819621)), _819635 = _819633, _819631 = _819629, _819627 = _819625, _819623 = _819621], (14703 ^ _778495) ^ [_1039268, _1039270] : [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), _1039268), _1039270))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039270), _1039268)))], (48979 ^ _778495) ^ [_1769246, _1769248] : [c_Relation_Otrans(_1769246, _1769248), -(c_Relation_Otrans(_1769246, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1769246, _1769246), tc_HOL_Obool)), _1769248), c_Relation_OId(_1769246))))], (24689 ^ _778495) ^ [_1220491, _1220493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1220491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1220493, _1220491)), _1220491)))], (35969 ^ _778495) ^ [_1453775, _1453777, _1453779, _1453781] : [c_Equiv__Relations_Oequivp(_1453775, _1453777), hBOOL(hAPP(hAPP(_1453777, _1453779), _1453781)), -(hBOOL(hAPP(hAPP(_1453777, _1453781), _1453779)))], (7784 ^ _778495) ^ [_907116, _907118, _907120] : [class_Orderings_Olinorder(_907116), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907116), _907118), _907120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907116), _907120), _907118)))], (42391 ^ _778495) ^ [_1622913, _1622915, _1622917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622913), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622915)), _1622917))), -(hAPP(hAPP(c_List_Otake(_1622915), _1622913), c_List_Obutlast(_1622915, _1622917)) = hAPP(hAPP(c_List_Otake(_1622915), _1622913), _1622917))], (20856 ^ _778495) ^ [_1152036, _1152038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1152036)), _1152038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1152036), _1152038)))], (29954 ^ _778495) ^ [_1323505, _1323507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1323505), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1323507), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323505, _1323507) = 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), _1323505), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1323507)))))], (39518 ^ _778495) ^ [_1547633, _1547635, _1547637, _1547639, _1547641, _1547643] : [class_Groups_Ocomm__monoid__mult(_1547633), c_Fun_Oinj__on(_1547635, _1547637, _1547639, _1547641), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1547637, _1547633), _1547643), hAPP(c_Set_Oimage(_1547635, _1547637, _1547639), _1547641)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1547635, _1547633), hAPP(c_Fun_Ocomp(_1547637, _1547633, _1547635, _1547643), _1547639)), _1547641))], (1828 ^ _778495) ^ [_804373, _804375] : [-(class_Rings_Osemiring__1(_804373)), _804375 = _804373, class_Rings_Osemiring__1(_804375)], (41654 ^ _778495) ^ [_1602810, _1602812, _1602814, _1602816, _1602818, _1602820] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602810, _1602810)), hAPP(hAPP(c_Product__Type_OPair(_1602810, _1602810), _1602812), _1602814)), _1602816)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602810), tc_List_Olist(_1602810))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602810), tc_List_Olist(_1602810)), _1602818), _1602820)), c_List_Olistrel(_1602810, _1602816))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602810), tc_List_Olist(_1602810))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602810), tc_List_Olist(_1602810)), hAPP(hAPP(c_List_Olist_OCons(_1602810), _1602812), _1602818)), hAPP(hAPP(c_List_Olist_OCons(_1602810), _1602814), _1602820))), c_List_Olistrel(_1602810, _1602816))))], (33225 ^ _778495) ^ [_1392170, _1392172, _1392174, _1392176, _1392178] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392170, tc_fun(_1392172, tc_HOL_Obool)), _1392174), hAPP(hAPP(c_COMBS(_1392170, tc_fun(_1392172, tc_HOL_Obool), tc_fun(_1392172, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392172, tc_HOL_Obool), tc_fun(tc_fun(_1392172, tc_HOL_Obool), tc_fun(_1392172, tc_HOL_Obool)), _1392170), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392172, tc_HOL_Obool))), _1392176)), _1392178)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392172, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392170, tc_fun(_1392172, tc_HOL_Obool)), _1392174), _1392176)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392170, tc_fun(_1392172, tc_HOL_Obool)), _1392174), _1392178)))], (45000 ^ _778495) ^ [_1680607, _1680609, _1680611, _1680613] : [-(hBOOL(hAPP(c_List_Olistsp(_1680607, _1680609), hAPP(hAPP(c_List_Olist_OCons(_1680607), _1680611), _1680613)))), hBOOL(hAPP(_1680609, _1680611)), hBOOL(hAPP(c_List_Olistsp(_1680607, _1680609), _1680613))], (52583 ^ _778495) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (34504 ^ _778495) ^ [_1423256, _1423258] : [-(c_Relation_OId__on(_1423256, _1423258) = hAPP(c_Product__Type_Oprod_Oprod__case(_1423256, _1423256, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1423256, tc_HOL_Obool, tc_fun(_1423256, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1423256, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1423256, tc_HOL_Obool)), _1423256), c_COMBC(_1423256, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1423256, tc_HOL_Obool), tc_fun(_1423256, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1423256), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1423256), c_fconj)), c_fequal))), _1423258)))], (19588 ^ _778495) ^ [_1130346, _1130348, _1130350] : [class_Orderings_Olinorder(_1130346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1130346), _1130348)), -(hBOOL(hAPP(hAPP(c_member(_1130346), _1130350), _1130348))), -(c_Big__Operators_Olattice_OInf__fin(_1130346, c_Orderings_Oord__class_Omin(_1130346), hAPP(hAPP(c_Set_Oinsert(_1130346), _1130350), _1130348)) = hAPP(hAPP(c_Finite__Set_Ofold(_1130346, _1130346, c_Orderings_Oord__class_Omin(_1130346)), _1130350), _1130348))], (51489 ^ _778495) ^ [_1818736, _1818738, _1818740, _1818742] : [class_Rings_Ocomm__semiring__1(_1818736), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818736), _1818738), _1818740)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818736), _1818738), _1818742)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818736), _1818738), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1818736), _1818740), _1818742))))], (24413 ^ _778495) ^ [_1215433, _1215435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215433)), -(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)))), _1215435))), 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)))), _1215433)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215435), _1215433))], (5274 ^ _778495) ^ [_859127, _859129, _859131, _859133, _859135, _859137] : [-(c_SetInterval_Oord_OatMost(_859137, _859133, _859129) = c_SetInterval_Oord_OatMost(_859135, _859131, _859127)), _859137 = _859135, _859133 = _859131, _859129 = _859127], (36677 ^ _778495) ^ [_1469272, _1469274, _1469276, _1469278] : [hBOOL(hAPP(hAPP(c_member(_1469272), _1469274), c_Wellfounded_Oacc(_1469272, _1469276))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1469272, _1469272)), hAPP(hAPP(c_Product__Type_OPair(_1469272, _1469272), _1469278), _1469274)), _1469276)), -(hBOOL(hAPP(hAPP(c_member(_1469272), _1469278), c_Wellfounded_Oacc(_1469272, _1469276))))], (25888 ^ _778495) ^ [_1241046, _1241048, _1241050] : [class_Int_Onumber__ring(_1241046), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1241046), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1241046), _1241048), _1241050)), 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(_1241046), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1241046), hAPP(hAPP(c_Power_Opower__class_Opower(_1241046), _1241048), 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(_1241046), _1241050), 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(_1241046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241046), hAPP(c_Int_Onumber__class_Onumber__of(_1241046), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1241048)), _1241050)))], (20772 ^ _778495) ^ [_1150820, _1150822] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150820))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150820)), _1150822)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1150822))], (8150 ^ _778495) ^ [_912788, _912790, _912792, _912794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912788, tc_HOL_Obool)), _912790), _912792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_912788, tc_HOL_Obool)), _912792), _912794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_912788, tc_HOL_Obool)), _912790), _912794)))], (48686 ^ _778495) ^ [_1760876, _1760878, _1760880] : [c_List_Olist__all(tc_Int_Oint, _1760876, c_List_Oupto(_1760878, _1760880)), -(c_List_Oall__interval__int(_1760876, _1760878, _1760880))], (20790 ^ _778495) ^ [_1151094] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1151094)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151094)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1151094)))], (17214 ^ _778495) ^ [_1086331, _1086333, _1086335, _1086337] : [class_Fields_Olinordered__field__inverse__zero(_1086331), 17217 ^ _778495 : [(17218 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), _1086333), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1086331), _1086335), _1086337))), 17221 ^ _778495 : [(17228 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), c_Groups_Ozero__class_Ozero(_1086331)), _1086337))), 17231 ^ _778495 : [(17238 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), _1086337), c_Groups_Ozero__class_Ozero(_1086331)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), _1086333), c_Groups_Ozero__class_Ozero(_1086331))))], (17232 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), _1086337), c_Groups_Ozero__class_Ozero(_1086331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), _1086335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086331), _1086333), _1086337))))]]], (17222 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), c_Groups_Ozero__class_Ozero(_1086331)), _1086337)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086331), _1086333), _1086337)), _1086335)))]]], (17244 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), _1086333), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1086331), _1086335), _1086337)))), 17247 ^ _778495 : [(17250 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086331), _1086333), _1086337)), _1086335))], (17248 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), c_Groups_Ozero__class_Ozero(_1086331)), _1086337)))]], 17251 ^ _778495 : [(17254 ^ _778495) ^ [] : [17255 ^ _778495 : [(17258 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), _1086335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086331), _1086333), _1086337)))], (17256 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), _1086337), c_Groups_Ozero__class_Ozero(_1086331))))]], 17259 ^ _778495 : [(17262 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), _1086333), c_Groups_Ozero__class_Ozero(_1086331)))], (17260 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), _1086337), c_Groups_Ozero__class_Ozero(_1086331)))]]], (17252 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086331), c_Groups_Ozero__class_Ozero(_1086331)), _1086337))]]]]], (5170 ^ _778495) ^ [_857455, _857457, _857459, _857461, _857463, _857465] : [-(c_Lazy__Sequence_Obind(_857465, _857461, _857457) = c_Lazy__Sequence_Obind(_857463, _857459, _857455)), _857465 = _857463, _857461 = _857459, _857457 = _857455], (28721 ^ _778495) ^ [_1299175, _1299177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1299175)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1299177))), -(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(_1299177))), 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), _1299175)), c_Int_Onat))))))], (32188 ^ _778495) ^ [_1370753, _1370755, _1370757, _1370759, _1370761] : [_1370753 = c_Orderings_Obot__class_Obot(tc_fun(_1370755, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370755, tc_fun(_1370757, tc_HOL_Obool)), _1370753), hAPP(hAPP(c_COMBC(_1370755, tc_fun(_1370757, tc_HOL_Obool), tc_fun(_1370757, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370757, tc_HOL_Obool), tc_fun(tc_fun(_1370757, tc_HOL_Obool), tc_fun(_1370757, tc_HOL_Obool)), _1370755), c_Groups_Ominus__class_Ominus(tc_fun(_1370757, tc_HOL_Obool))), _1370759)), _1370761)) = c_Orderings_Otop__class_Otop(tc_fun(_1370757, tc_HOL_Obool)))], (36705 ^ _778495) ^ [_1470006, _1470008, _1470010, _1470012, _1470014] : [c_Fun_Oinj__on(_1470006, _1470008, _1470010, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470006, tc_HOL_Obool)), _1470012), _1470014)), 36708 ^ _778495 : [(36713 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470008, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470006, _1470008, _1470010), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470006, tc_HOL_Obool)), _1470012), _1470014))), hAPP(c_Set_Oimage(_1470006, _1470008, _1470010), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470006, tc_HOL_Obool)), _1470014), _1470012))) = c_Orderings_Obot__class_Obot(tc_fun(_1470008, tc_HOL_Obool)))], (36711 ^ _778495) ^ [] : [-(c_Fun_Oinj__on(_1470006, _1470008, _1470010, _1470014))], (36709 ^ _778495) ^ [] : [-(c_Fun_Oinj__on(_1470006, _1470008, _1470010, _1470012))]]], (33930 ^ _778495) ^ [_1410207, _1410209] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1410207, 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(_1410207, tc_HOL_Obool)), tc_fun(_1410207, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1410207, tc_HOL_Obool)), tc_fun(_1410207, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1410207, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1410209)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1410207, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1410209))], (5482 ^ _778495) ^ [_862411, _862413] : [_862413 = _862411, -(c_Orderings_Oord__class_Oless__eq(_862413) = c_Orderings_Oord__class_Oless__eq(_862411))], (31099 ^ _778495) ^ [_1346776, _1346778] : [class_Orderings_Olinorder(_1346776), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346776), _1346778)), -(_1346778 = c_Orderings_Obot__class_Obot(tc_fun(_1346776, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346776), c_Big__Operators_Olattice_OInf__fin(_1346776, c_Orderings_Oord__class_Omin(_1346776), _1346778)), c_Big__Operators_Olattice_OSup__fin(_1346776, c_Orderings_Oord__class_Omax(_1346776), _1346778))))], (21728 ^ _778495) ^ [_1167404, _1167406, _1167408] : [class_Groups_Ogroup__add(_1167404), 21731 ^ _778495 : [(21738 ^ _778495) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1167404), _1167408) = _1167406, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1167404), _1167406) = _1167408)], (21732 ^ _778495) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1167404), _1167406) = _1167408, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1167404), _1167408) = _1167406)]]], (29438 ^ _778495) ^ [_1313922, _1313924, _1313926] : [29440 ^ _778495 : [(29443 ^ _778495) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1313922, _1313924), 29439 ^ [_1313922, _1313924, _1313926]))], (29441 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1313924, 29439 ^ [_1313922, _1313924, _1313926]), _1313926)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1313922, _1313924), _1313926)))], (24727 ^ _778495) ^ [_1221186] : [hBOOL(hAPP(_1221186, 24728 ^ [_1221186])), 24731 ^ _778495 : [(24732 ^ _778495) ^ [_1221280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221280)), -(hBOOL(hAPP(_1221186, hAPP(c_Int_Onat, _1221280))))]]], (29665 ^ _778495) ^ [_1318344, _1318346, _1318348, _1318350, _1318352, _1318354] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1318344, _1318346), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1318348), _1318350))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1318344, _1318346), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1318352), _1318354))), -(_1318346 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1318348 = _1318352)], (37028 ^ _778495) ^ [_1476820, _1476822, _1476824] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1476820), _1476822), _1476824) = c_Nitpick_OAbs__Frac(_1476820, c_Nitpick_Onorm__frac(_1476822, _1476824)))], (13408 ^ _778495) ^ [_1016721, _1016723, _1016725] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016721), _1016723) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016721), _1016725), -(_1016721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1016723 = _1016725)], (52615 ^ _778495) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (9825 ^ _778495) ^ [_947057, _947059, _947061] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_947057), _947059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_947057), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947057, tc_HOL_Obool)), _947059), hAPP(hAPP(c_Set_Oinsert(_947057), _947061), c_Orderings_Obot__class_Obot(tc_fun(_947057, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_947057), _947059))))], (41523 ^ _778495) ^ [_1598706, _1598708, _1598710, _1598712, _1598714] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598706), tc_List_Olist(_1598706))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598706), tc_List_Olist(_1598706)), _1598708), _1598710)), c_List_Olistrel1(_1598706, _1598712))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598706), tc_List_Olist(_1598706))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598706), tc_List_Olist(_1598706)), hAPP(hAPP(c_List_Olist_OCons(_1598706), _1598714), _1598708)), hAPP(hAPP(c_List_Olist_OCons(_1598706), _1598714), _1598710))), c_List_Olistrel1(_1598706, _1598712))))], (19374 ^ _778495) ^ [_1126490, _1126492, _1126494] : [class_Orderings_Olinorder(_1126490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126490), _1126492)), -(_1126494 = c_Orderings_Obot__class_Obot(tc_fun(_1126490, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1126490, tc_HOL_Obool)), _1126494), _1126492)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1126490), c_Big__Operators_Olattice_OInf__fin(_1126490, c_Orderings_Oord__class_Omin(_1126490), _1126494)), c_Big__Operators_Olattice_OInf__fin(_1126490, c_Orderings_Oord__class_Omin(_1126490), _1126492)) = c_Big__Operators_Olattice_OInf__fin(_1126490, c_Orderings_Oord__class_Omin(_1126490), _1126492))], (30011 ^ _778495) ^ [_1324870, _1324872, _1324874, _1324876] : [_1324870 = _1324872, 30014 ^ _778495 : [(30017 ^ _778495) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1324874, _1324876), _1324870) = hAPP(c_Product__Type_Osnd(_1324874, _1324876), _1324872))], (30015 ^ _778495) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1324874, _1324876), _1324870) = hAPP(c_Product__Type_Ofst(_1324874, _1324876), _1324872))]]], (39404 ^ _778495) ^ [_1545037, _1545039, _1545041, _1545043, _1545045] : [c_Finite__Set_Ofun__left__comm(_1545037, _1545039, _1545041), -(hAPP(c_Fun_Ocomp(_1545039, _1545039, _1545039, hAPP(_1545041, _1545043)), hAPP(_1545041, _1545045)) = hAPP(c_Fun_Ocomp(_1545039, _1545039, _1545039, hAPP(_1545041, _1545045)), hAPP(_1545041, _1545043)))], (30893 ^ _778495) ^ [_1342670] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1342670), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1342670)], (33303 ^ _778495) ^ [_1395099, _1395101] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1395099, tc_HOL_Obool), _1395101) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1395099, tc_HOL_Obool), tc_fun(_1395099, tc_HOL_Obool)), _1395101), c_COMBI(tc_fun(_1395099, tc_HOL_Obool))))], (52463 ^ _778495) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (23156 ^ _778495) ^ [_1192992, _1192994, _1192996, _1192998] : [class_Divides_Osemiring__div(_1192992), -(c_Divides_Odiv__class_Omod(_1192992, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192992), _1192994), _1192996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192992), _1192994), _1192998)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192992), _1192994), c_Divides_Odiv__class_Omod(_1192992, _1192996, _1192998)))], (52549 ^ _778495) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (46592 ^ _778495) ^ [_1715182] : [-(hAPP(c_List_Orev(_1715182), c_List_Olist_ONil(_1715182)) = c_List_Olist_ONil(_1715182))], (33668 ^ _778495) ^ [_1405489, _1405491] : [hAPP(c_Int_ORep__Integ, _1405489) = hAPP(c_Int_ORep__Integ, _1405491), -(_1405489 = _1405491)], (26218 ^ _778495) ^ [_1247213, _1247215, _1247217] : [class_Rings_Olinordered__semidom(_1247213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247213), c_Groups_Oone__class_Oone(_1247213)), _1247215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247213), c_Groups_Oone__class_Oone(_1247213)), hAPP(hAPP(c_Power_Opower__class_Opower(_1247213), _1247215), _1247217))))], (12406 ^ _778495) ^ [_997009, _997011, _997013] : [class_Complete__Lattice_Ocomplete__lattice(_997009), -(c_Complete__Lattice_OSup__class_OSup(_997009, hAPP(hAPP(c_Set_Oinsert(_997009), _997011), hAPP(hAPP(c_Set_Oinsert(_997009), _997013), c_Orderings_Obot__class_Obot(tc_fun(_997009, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_997009), _997011), _997013))], (23705 ^ _778495) ^ [_1203163, _1203165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203163), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203165), _1203163)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203163), _1203165) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11556 ^ _778495) ^ [_978742, _978744, _978746, _978748] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_978742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978742), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978742), _978744), _978746)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978742), _978748), _978746))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978742), _978744), _978748)))], (52351 ^ _778495) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (5657 ^ _778495) ^ [_867784, _867786] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_867784, _867786, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867784), tc_HOL_Obool))))], (13629 ^ _778495) ^ [_1020337, _1020339, _1020341] : [class_Groups_Oordered__comm__monoid__add(_1020337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020337), c_Groups_Ozero__class_Ozero(_1020337)), _1020339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020337), c_Groups_Ozero__class_Ozero(_1020337)), _1020341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020337), c_Groups_Ozero__class_Ozero(_1020337)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020337), _1020339), _1020341))))], (39666 ^ _778495) ^ [_1551089, _1551091, _1551093, _1551095, _1551097, _1551099] : [c_Finite__Set_Ofolding(_1551089, _1551091, _1551093, _1551095), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551089), _1551097)), -(hAPP(c_Fun_Ocomp(_1551091, _1551091, _1551091, hAPP(_1551093, _1551099)), hAPP(_1551095, _1551097)) = hAPP(c_Fun_Ocomp(_1551091, _1551091, _1551091, hAPP(_1551095, _1551097)), hAPP(_1551093, _1551099)))], (44712 ^ _778495) ^ [_1674139, _1674141] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1674139)), hAPP(c_Code__Numeral_Oof__nat, _1674141)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1674139), _1674141)))], (41367 ^ _778495) ^ [_1593249, _1593251] : [-(c_List_Olenlex(_1593249, _1593251) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1593249), tc_List_Olist(_1593249))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1593249), tc_List_Olist(_1593249), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1593249), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593249), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool)), tc_List_Olist(_1593249)), c_COMBS(tc_List_Olist(_1593249), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593249), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1593249)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593249)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593249), tc_fun(tc_List_Olist(_1593249), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593249), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool)), tc_List_Olist(_1593249)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1593249))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593249)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1593249))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1593249)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1593249), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593249), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool)), tc_List_Olist(_1593249)), c_COMBS(tc_List_Olist(_1593249), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593249), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1593249)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593249)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593249), tc_fun(tc_List_Olist(_1593249), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593249), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool)), tc_List_Olist(_1593249)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1593249))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593249)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593249))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1593249)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593249), tc_fun(tc_prod(tc_List_Olist(_1593249), tc_List_Olist(_1593249)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593249), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593249), tc_List_Olist(_1593249)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593249), tc_List_Olist(_1593249)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593249), tc_HOL_Obool)), tc_List_Olist(_1593249)), c_COMBC(tc_List_Olist(_1593249), tc_fun(tc_prod(tc_List_Olist(_1593249), tc_List_Olist(_1593249)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593249), tc_prod(tc_List_Olist(_1593249), tc_List_Olist(_1593249))), tc_fun(tc_List_Olist(_1593249), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593249), tc_List_Olist(_1593249)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1593249)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1593249), tc_List_Olist(_1593249)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593249), tc_List_Olist(_1593249)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1593249)), c_member(tc_prod(tc_List_Olist(_1593249), tc_List_Olist(_1593249))))), c_Product__Type_OPair(tc_List_Olist(_1593249), tc_List_Olist(_1593249))))), c_List_Olex(_1593249, _1593251)))))))], (40676 ^ _778495) ^ [_1575608, _1575610, _1575612] : [c_Relation_Ototal__on(_1575608, _1575610, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1575608, _1575608), tc_HOL_Obool)), _1575612), c_Relation_OId(_1575608))), -(c_Relation_Ototal__on(_1575608, _1575610, _1575612))], (24511 ^ _778495) ^ [_1217196, _1217198, _1217200] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1217196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1217198), _1217200)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1217198), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217196), _1217198), _1217200))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1217196, _1217198)))], (42297 ^ _778495) ^ [_1620870, _1620872, _1620874, _1620876, _1620878] : [-(_1620870 = _1620872), -(hAPP(hAPP(c_List_Onth(_1620874), hAPP(hAPP(c_List_Olist__update(_1620874, _1620876), _1620870), _1620878)), _1620872) = hAPP(hAPP(c_List_Onth(_1620874), _1620876), _1620872))], (28291 ^ _778495) ^ [_1284403, _1284405, _1284407, _1284409, _1284411] : [c_Finite__Set_Ofun__left__comm__idem(_1284403, _1284405, _1284407), -(c_Finite__Set_Ofun__left__comm__idem(_1284409, _1284405, hAPP(hAPP(c_COMBB(_1284403, tc_fun(_1284405, _1284405), _1284409), _1284407), _1284411)))], (29310 ^ _778495) ^ [_1311431, _1311433] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1311431, _1311433), c_Divides_Odivmod__nat(_1311431, _1311433))))], (11210 ^ _778495) ^ [_971663, _971665] : [class_Rings_Ocomm__semiring__1(_971663), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971663), c_Groups_Oone__class_Oone(_971663)), _971665) = _971665)], (21404 ^ _778495) ^ [_1162278] : [_1162278 = 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), _1162278)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (40320 ^ _778495) ^ [_1567131, _1567133] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567131, _1567131)), hAPP(hAPP(c_Product__Type_OPair(_1567131, _1567131), 40321 ^ [_1567131, _1567133]), 40321 ^ [_1567131, _1567133])), c_Transitive__Closure_Otrancl(_1567131, _1567133)))), -(c_Wellfounded_Oacyclic(_1567131, _1567133))], (11542 ^ _778495) ^ [_978471, _978473, _978475, _978477, _978479] : [class_Groups_Oordered__ab__semigroup__add(_978471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978471), _978473), _978475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978471), _978477), _978479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978471), _978473), _978477)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978471), _978475), _978479))))], (38385 ^ _778495) ^ [_1517924, _1517926, _1517928, _1517930] : [class_Groups_Ocomm__monoid__add(_1517924), c_Fun_Oinj__on(_1517926, _1517924, _1517928, _1517930), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1517926, _1517924), _1517928), _1517930) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1517924, _1517924), c_Fun_Oid(_1517924)), hAPP(c_Set_Oimage(_1517926, _1517924, _1517928), _1517930)))], (33108 ^ _778495) ^ [_1389516, _1389518, _1389520, _1389522] : [class_Complete__Lattice_Ocomplete__lattice(_1389516), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389518), _1389520)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389518, _1389516), _1389520), _1389522) = hAPP(hAPP(c_Finite__Set_Ofold(_1389518, _1389516, hAPP(hAPP(c_COMBB(_1389516, tc_fun(_1389516, _1389516), _1389518), c_Lattices_Osemilattice__sup__class_Osup(_1389516)), _1389522)), c_Orderings_Obot__class_Obot(_1389516)), _1389520))], (21574 ^ _778495) ^ [_1164840, _1164842] : [class_Int_Onumber__ring(_1164840), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164840), hAPP(c_Int_Onumber__class_Onumber__of(_1164840), _1164842)), c_Groups_Oone__class_Oone(_1164840)) = hAPP(c_Int_Onumber__class_Onumber__of(_1164840), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1164842), c_Int_OBit1(c_Int_OPls))))], (24707 ^ _778495) ^ [_1220852] : [24708 ^ _778495 : [(24709 ^ _778495) ^ [_1220909] : [hBOOL(hAPP(_1220852, _1220909))]], 24711 ^ _778495 : [(24714 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1220852, hAPP(c_Int_Onat, 24710 ^ [_1220852]))))], (24712 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24710 ^ [_1220852])))]]], (44982 ^ _778495) ^ [_1680254, _1680256, _1680258, _1680260] : [hBOOL(hAPP(c_List_Olistsp(_1680254, _1680256), _1680258)), hBOOL(hAPP(c_List_Olistsp(_1680254, _1680260), _1680258)), -(hBOOL(hAPP(c_List_Olistsp(_1680254, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680254, tc_HOL_Obool)), _1680256), _1680260)), _1680258)))], (2818 ^ _778495) ^ [_820305, _820307] : [_820307 = _820305, -(c_Nat_Ofunpow(_820307) = c_Nat_Ofunpow(_820305))], (43894 ^ _778495) ^ [_1656513, _1656515, _1656517, _1656519] : [class_Groups_Osemigroup__add(_1656513), -(hAPP(c_List_Ofoldl(_1656513, _1656513, c_Groups_Oplus__class_Oplus(_1656513), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656513), _1656515), _1656517)), _1656519) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656513), _1656515), hAPP(c_List_Ofoldl(_1656513, _1656513, c_Groups_Oplus__class_Oplus(_1656513), _1656517), _1656519)))], (27825 ^ _778495) ^ [_1275053] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1275053)))], (9382 ^ _778495) ^ [_937855, _937857, _937859, _937861] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937855, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937855, tc_HOL_Obool)), _937857), _937859)), _937861) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937855, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937855, tc_HOL_Obool)), _937857), _937861)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937855, tc_HOL_Obool)), _937859), _937861)))], (10851 ^ _778495) ^ [_965344, _965346] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965344), _965346))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965346), hAPP(c_Nat_OSuc, _965344))))], (51915 ^ _778495) ^ [_1826693, _1826695, _1826697, _1826699] : [class_Rings_Odvd(_1826693), _1826695 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826693), _1826697), _1826699), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826693), _1826697), _1826695)))], (41089 ^ _778495) ^ [_1585956, _1585958, _1585960, _1585962, _1585964] : [c_Relation_Osingle__valued(_1585956, _1585956, _1585958), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585956, _1585956)), hAPP(hAPP(c_Product__Type_OPair(_1585956, _1585956), _1585960), _1585962)), c_Transitive__Closure_Ortrancl(_1585956, _1585958))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585956, _1585956)), hAPP(hAPP(c_Product__Type_OPair(_1585956, _1585956), _1585960), _1585964)), c_Transitive__Closure_Ortrancl(_1585956, _1585958))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585956, _1585956)), hAPP(hAPP(c_Product__Type_OPair(_1585956, _1585956), _1585962), _1585964)), c_Transitive__Closure_Ortrancl(_1585956, _1585958)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585956, _1585956)), hAPP(hAPP(c_Product__Type_OPair(_1585956, _1585956), _1585964), _1585962)), c_Transitive__Closure_Ortrancl(_1585956, _1585958))))], (25766 ^ _778495) ^ [] : [-(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))))], (11877 ^ _778495) ^ [_985191, _985193, _985195] : [class_Rings_Ocomm__semiring__1(_985191), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985191), _985193), _985195)), _985195) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985191), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985191), _985193), c_Groups_Oone__class_Oone(_985191))), _985195))], (21168 ^ _778495) ^ [_1157767] : [c_Int_OBit1(_1157767) = c_Int_OPls], (36756 ^ _778495) ^ [_1471139, _1471141, _1471143, _1471145, _1471147] : [c_Fun_Oinj__on(_1471139, _1471141, _1471143, _1471145), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471141, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471139, _1471141, _1471143), _1471145)), _1471147)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471141), _1471147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1471139), _1471145)), hAPP(c_Finite__Set_Ocard(_1471141), _1471147))))], (30251 ^ _778495) ^ [_1329678, _1329680, _1329682] : [class_Orderings_Olinorder(_1329678), 30254 ^ _778495 : [(30261 ^ _778495) ^ [] : [_1329680 = _1329682, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1329678), _1329680) = hAPP(c_SetInterval_Oord__class_OlessThan(_1329678), _1329682))], (30255 ^ _778495) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1329678), _1329680) = hAPP(c_SetInterval_Oord__class_OlessThan(_1329678), _1329682), -(_1329680 = _1329682)]]], (26920 ^ _778495) ^ [_1259495] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1259495)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1259495)))], (34184 ^ _778495) ^ [_1415545, _1415547, _1415549] : [class_Orderings_Olinorder(_1415545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415545), _1415547), _1415549)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415545, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1415545), _1415547), c_Orderings_Obot__class_Obot(tc_fun(_1415545, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1415545, _1415547, _1415549)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1415545, _1415547), _1415549))], (18758 ^ _778495) ^ [_1115458, _1115460, _1115462, _1115464] : [class_Fields_Olinordered__field__inverse__zero(_1115458), class_Int_Onumber(_1115458), 18765 ^ _778495 : [(18766 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115458), _1115460), _1115462)), hAPP(c_Int_Onumber__class_Onumber__of(_1115458), _1115464))), 18769 ^ _778495 : [(18776 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115458), c_Groups_Ozero__class_Ozero(_1115458)), _1115462))), 18779 ^ _778495 : [(18786 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115458), _1115462), c_Groups_Ozero__class_Ozero(_1115458)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115458), c_Groups_Ozero__class_Ozero(_1115458)), hAPP(c_Int_Onumber__class_Onumber__of(_1115458), _1115464))))], (18780 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115458), _1115462), c_Groups_Ozero__class_Ozero(_1115458))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115458), hAPP(c_Int_Onumber__class_Onumber__of(_1115458), _1115464)), _1115462)), _1115460)))]]], (18770 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115458), c_Groups_Ozero__class_Ozero(_1115458)), _1115462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115458), _1115460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115458), hAPP(c_Int_Onumber__class_Onumber__of(_1115458), _1115464)), _1115462))))]]], (18792 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115458), _1115460), _1115462)), hAPP(c_Int_Onumber__class_Onumber__of(_1115458), _1115464)))), 18795 ^ _778495 : [(18798 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115458), _1115460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115458), hAPP(c_Int_Onumber__class_Onumber__of(_1115458), _1115464)), _1115462)))], (18796 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115458), c_Groups_Ozero__class_Ozero(_1115458)), _1115462)))]], 18799 ^ _778495 : [(18802 ^ _778495) ^ [] : [18803 ^ _778495 : [(18806 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115458), hAPP(c_Int_Onumber__class_Onumber__of(_1115458), _1115464)), _1115462)), _1115460))], (18804 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115458), _1115462), c_Groups_Ozero__class_Ozero(_1115458))))]], 18807 ^ _778495 : [(18810 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115458), c_Groups_Ozero__class_Ozero(_1115458)), hAPP(c_Int_Onumber__class_Onumber__of(_1115458), _1115464)))], (18808 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115458), _1115462), c_Groups_Ozero__class_Ozero(_1115458)))]]], (18800 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115458), c_Groups_Ozero__class_Ozero(_1115458)), _1115462))]]]]], (4410 ^ _778495) ^ [_845539, _845541] : [_845541 = _845539, -(c_Lazy__Sequence_Oyieldn(_845541) = c_Lazy__Sequence_Oyieldn(_845539))], (48678 ^ _778495) ^ [_1760694, _1760696] : [-(c_Lazy__Sequence_Oappend(_1760694, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760694), _1760696) = _1760696)], (41983 ^ _778495) ^ [_1611913, _1611915, _1611917, _1611919] : [-(hAPP(hAPP(c_List_Otake(_1611913), _1611915), hAPP(hAPP(c_List_Otake(_1611913), _1611917), _1611919)) = hAPP(hAPP(c_List_Otake(_1611913), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1611915), _1611917)), _1611919))], (40100 ^ _778495) ^ [_1560878, _1560880, _1560882, _1560884, _1560886, _1560888, _1560890, _1560892, _1560894] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1560878, _1560880, _1560882, _1560884), hAPP(hAPP(c_Product__Type_Oscomp(_1560878, _1560886, _1560888, tc_prod(_1560880, _1560882)), _1560890), _1560892)), _1560894) = hAPP(hAPP(c_Product__Type_Oscomp(_1560878, _1560886, _1560888, _1560884), _1560890), hAPP(hAPP(c_COMBC(_1560886, tc_fun(_1560880, tc_fun(_1560882, _1560884)), tc_fun(_1560888, _1560884)), hAPP(hAPP(c_COMBB(tc_fun(_1560888, tc_prod(_1560880, _1560882)), tc_fun(tc_fun(_1560880, tc_fun(_1560882, _1560884)), tc_fun(_1560888, _1560884)), _1560886), c_Product__Type_Oscomp(_1560888, _1560880, _1560882, _1560884)), _1560892)), _1560894)))], (38047 ^ _778495) ^ [_1504200, _1504202] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1504200)), 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)), _1504200))), 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, _1504202))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (52321 ^ _778495) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (24904 ^ _778495) ^ [_1223993] : [-(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), _1223993)) = 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), _1223993))))], (48132 ^ _778495) ^ [_1748681, _1748683, _1748685, _1748687, _1748689] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748681, _1748683, _1748685), _1748687), _1748689)), -(hBOOL(hAPP(hAPP(_1748685, _1748689), _1748687)))], (48444 ^ _778495) ^ [_1755163, _1755165] : [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), _1755163), _1755165))), 48447 ^ _778495 : [(48454 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755163), _1755165))), -(c_Lazy__Sequence_Osmall__lazy_H(_1755163, _1755165) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1755165), c_Lazy__Sequence_Osmall__lazy_H(_1755163, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1755165), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48448 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755163), _1755165)), -(c_Lazy__Sequence_Osmall__lazy_H(_1755163, _1755165) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (7310 ^ _778495) ^ [_899623, _899625, _899627, _899629, _899631, _899633, _899635] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_899623, _899625, _899627, _899629, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899623, tc_HOL_Obool)), _899631), hAPP(hAPP(c_Set_Oinsert(_899623), _899633), c_Orderings_Obot__class_Obot(tc_fun(_899623, tc_HOL_Obool))))), _899635)), hBOOL(hAPP(hAPP(c_member(_899623), _899633), _899631)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_899623, _899625, _899627, _899629, _899631), hAPP(hAPP(_899627, _899633), _899635))))], (27787 ^ _778495) ^ [_1274390, _1274392] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1274390, tc_HOL_Obool)), _1274392)))], (17340 ^ _778495) ^ [_1088599, _1088601, _1088603, _1088605, _1088607] : [class_Fields_Ofield(_1088599), -(_1088601 = c_Groups_Ozero__class_Ozero(_1088599)), -(_1088603 = c_Groups_Ozero__class_Ozero(_1088599)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088599), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1088599), _1088605), _1088601)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1088599), _1088607), _1088603)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1088599), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088599), _1088605), _1088603)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088599), _1088607), _1088601))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088599), _1088601), _1088603)))], (8876 ^ _778495) ^ [_927693, _927695] : [class_Lattices_Osemilattice__inf(_927693), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927693), _927695), _927695) = _927695)], (26952 ^ _778495) ^ [_1260105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260105)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1260105) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (40104 ^ _778495) ^ [_1561051, _1561053, _1561055, _1561057, _1561059] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1561051, _1561053, _1561051, _1561055), hAPP(c_Product__Type_OPair(_1561053, _1561051), _1561057)), _1561059) = hAPP(_1561059, _1561057))], (48066 ^ _778495) ^ [_1746948, _1746950] : [-(hAPP(c_New__DSequence_Opos__empty(_1746948), _1746950) = c_Lazy__Sequence_Oempty(_1746948))], (37584 ^ _778495) ^ [_1491902, _1491904, _1491906, _1491908] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491902), _1491904)), 37590 ^ _778495 : [(37593 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491906), hAPP(_1491908, 37589 ^ [_1491902, _1491904, _1491906, _1491908])))], (37591 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491902), 37589 ^ [_1491902, _1491904, _1491906, _1491908]), _1491904)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1491902, _1491906)), hAPP(hAPP(c_Product__Type_OSigma(_1491902, _1491906), _1491904), _1491908))))], (48926 ^ _778495) ^ [_1767970, _1767972, _1767974, _1767976] : [-(c_Wellfounded_Omax__extp(_1767970, _1767972, _1767974, _1767976)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1767970), _1767974)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1767970), _1767976)), -(_1767976 = c_Orderings_Obot__class_Obot(tc_fun(_1767970, tc_HOL_Obool))), 48940 ^ _778495 : [(48943 ^ _778495) ^ [_1768315] : [hBOOL(hAPP(hAPP(c_member(_1767970), _1768315), _1767976)), hBOOL(hAPP(hAPP(_1767972, 48939 ^ [_1767970, _1767972, _1767974, _1767976]), _1768315))], (48941 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767970), 48939 ^ [_1767970, _1767972, _1767974, _1767976]), _1767974)))]]], (46977 ^ _778495) ^ [_1723300, _1723302, _1723304] : [hBOOL(hAPP(c_List_Odistinct(_1723300), _1723302)), hBOOL(hAPP(hAPP(c_member(_1723300), _1723304), hAPP(c_List_Oset(_1723300), _1723302))), -(c_List_OdropWhile(_1723300, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723300), c_fNot), hAPP(hAPP(c_COMBC(_1723300, _1723300, tc_HOL_Obool), c_fequal), _1723304)), hAPP(c_List_Orev(_1723300), _1723302)) = hAPP(hAPP(c_List_Olist_OCons(_1723300), _1723304), hAPP(c_List_Orev(_1723300), c_List_OtakeWhile(_1723300, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723300), c_fNot), hAPP(hAPP(c_COMBC(_1723300, _1723300, tc_HOL_Obool), c_fequal), _1723304)), _1723302))))], (17519 ^ _778495) ^ [_1092297, _1092299, _1092301, _1092303] : [class_Lattices_Osemilattice__sup(_1092297), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092297), _1092299)), 17529 ^ _778495 : [(17532 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092297), 17528 ^ [_1092297, _1092299, _1092301, _1092303]), _1092301))], (17530 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1092297), 17528 ^ [_1092297, _1092299, _1092301, _1092303]), _1092299)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092297), hAPP(hAPP(c_Finite__Set_Ofold(_1092297, _1092297, c_Lattices_Osemilattice__sup__class_Osup(_1092297)), _1092303), _1092299)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1092297), _1092301), _1092303))))], (15659 ^ _778495) ^ [_1057246, _1057248, _1057250, _1057252] : [class_Groups_Ocomm__monoid__add(_1057246), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057248), _1057250)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057248, _1057246), _1057252), _1057250) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057246, _1057248, c_Groups_Oplus__class_Oplus(_1057246)), _1057252), c_Groups_Ozero__class_Ozero(_1057246)), _1057250))], (11692 ^ _778495) ^ [_981407, _981409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981407), _981409)), _981409))], (12236 ^ _778495) ^ [_993082, _993084, _993086] : [class_Complete__Lattice_Ocomplete__lattice(_993082), hBOOL(hAPP(c_Finite__Set_Ofinite(_993082), _993084)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_993082), _993086), c_Complete__Lattice_OSup__class_OSup(_993082, _993084)) = hAPP(hAPP(c_Finite__Set_Ofold(_993082, _993082, c_Lattices_Osemilattice__sup__class_Osup(_993082)), _993086), _993084))], (26640 ^ _778495) ^ [_1255015] : [c_Int_OMin = _1255015, -(c_Int_OMin = c_Int_OBit1(_1255015))], (47976 ^ _778495) ^ [_1744987, _1744989, _1744991, _1744993] : [-(c_List_Olist__ex1(_1744987, _1744989, hAPP(hAPP(c_List_Olist_OCons(_1744987), _1744991), _1744993))), 47979 ^ _778495 : [(47982 ^ _778495) ^ [] : [c_List_Olist__all(_1744987, hAPP(hAPP(c_COMBS(_1744987, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1744987), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1744987), c_fNot), _1744989))), hAPP(c_fequal, _1744991)), _1744993)], (47980 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1744989, _1744991)))]], 47983 ^ _778495 : [(47986 ^ _778495) ^ [] : [c_List_Olist__ex1(_1744987, _1744989, _1744993)], (47984 ^ _778495) ^ [] : [hBOOL(hAPP(_1744989, _1744991))]]], (39102 ^ _778495) ^ [_1536925, _1536927] : [c_Wellfounded_Owf(_1536925, _1536927), -(c_Wellfounded_OwfP(_1536925, hAPP(hAPP(c_COMBC(_1536925, tc_fun(tc_prod(_1536925, _1536925), tc_HOL_Obool), tc_fun(_1536925, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536925, tc_fun(tc_fun(tc_prod(_1536925, _1536925), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1536925, _1536925), tc_HOL_Obool), tc_fun(_1536925, tc_HOL_Obool)), _1536925), c_COMBC(_1536925, tc_fun(tc_prod(_1536925, _1536925), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536925, tc_prod(_1536925, _1536925)), tc_fun(_1536925, tc_fun(tc_fun(tc_prod(_1536925, _1536925), tc_HOL_Obool), tc_HOL_Obool)), _1536925), hAPP(c_COMBB(tc_prod(_1536925, _1536925), tc_fun(tc_fun(tc_prod(_1536925, _1536925), tc_HOL_Obool), tc_HOL_Obool), _1536925), c_member(tc_prod(_1536925, _1536925)))), c_Product__Type_OPair(_1536925, _1536925)))), _1536927)))], (46162 ^ _778495) ^ [_1706976, _1706978, _1706980] : [class_Orderings_Olinorder(_1706976), 46165 ^ _778495 : [(46172 ^ _778495) ^ [] : [c_List_Olinorder__class_Osorted(_1706976, _1706980), -(c_List_Olinorder__class_Osorted(_1706976, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706976, _1706976, c_COMBI(_1706976)), _1706978), _1706980)))], (46166 ^ _778495) ^ [] : [c_List_Olinorder__class_Osorted(_1706976, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706976, _1706976, c_COMBI(_1706976)), _1706978), _1706980)), -(c_List_Olinorder__class_Osorted(_1706976, _1706980))]]], (18158 ^ _778495) ^ [_1104482, _1104484] : [class_Int_Onumber__ring(_1104482), -(hBOOL(hAPP(hAPP(c_member(_1104482), hAPP(c_Int_Onumber__class_Onumber__of(_1104482), _1104484)), c_Int_Oring__1__class_OInts(_1104482))))], (34038 ^ _778495) ^ [_1412508, _1412510, _1412512] : [class_Orderings_Olinorder(_1412508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412508), _1412510), _1412512)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412508, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1412508), _1412510)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1412508, _1412510), _1412512)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1412508), _1412512))], (15402 ^ _778495) ^ [_1052072, _1052074, _1052076] : [-(hBOOL(hAPP(_1052072, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052074), _1052076)))), 15405 ^ _778495 : [(15408 ^ _778495) ^ [] : [hBOOL(hAPP(_1052072, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15406 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052074), _1052076)))]], 15410 ^ _778495 : [(15413 ^ _778495) ^ [] : [hBOOL(hAPP(_1052072, 15409 ^ [_1052072, _1052074, _1052076]))], (15411 ^ _778495) ^ [] : [-(_1052074 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052076), 15409 ^ [_1052072, _1052074, _1052076]))]]], (38357 ^ _778495) ^ [_1517422, _1517424, _1517426] : [c_Predicate_Oreflp(_1517422, _1517424), -(hBOOL(hAPP(hAPP(_1517424, _1517426), _1517426)))], (30539 ^ _778495) ^ [_1335833, _1335835, _1335837] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1335833, tc_HOL_Obool), tc_fun(_1335833, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1335833, tc_HOL_Obool), tc_fun(_1335833, tc_HOL_Obool)), _1335835), _1335837)), c_Wellfounded_Ofinite__psubset(_1335833)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1335833, tc_HOL_Obool)), _1335835), _1335837)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335833), _1335837))], (31944 ^ _778495) ^ [_1365543, _1365545, _1365547, _1365549, _1365551] : [hBOOL(hAPP(hAPP(c_member(_1365543), _1365545), _1365547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1365549, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365543, tc_fun(_1365549, tc_HOL_Obool)), _1365547), _1365551)), hAPP(_1365551, _1365545))))], (24928 ^ _778495) ^ [_1224448, _1224450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1224448)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1224448), _1224450)), _1224448) = _1224450)], (31938 ^ _778495) ^ [_1365338, _1365340, _1365342, _1365344, _1365346, _1365348] : [hBOOL(hAPP(hAPP(c_member(_1365338), _1365340), _1365342)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365338, tc_fun(_1365344, tc_HOL_Obool)), _1365342), hAPP(hAPP(c_COMBB(tc_fun(_1365344, tc_HOL_Obool), tc_fun(_1365344, tc_HOL_Obool), _1365338), hAPP(c_Set_Oinsert(_1365344), _1365346)), _1365348)) = hAPP(hAPP(c_Set_Oinsert(_1365344), _1365346), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365338, tc_fun(_1365344, tc_HOL_Obool)), _1365342), _1365348)))], (6796 ^ _778495) ^ [_889849, _889851, _889853] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889849, tc_HOL_Obool)), _889851), hAPP(hAPP(c_Set_Oinsert(_889849), _889853), _889851))))], (24747 ^ _778495) ^ [_1221537, _1221539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221539)), 24754 ^ _778495 : [(24761 ^ _778495) ^ [] : [_1221537 = _1221539, -(hAPP(c_Int_Onat, _1221537) = hAPP(c_Int_Onat, _1221539))], (24755 ^ _778495) ^ [] : [hAPP(c_Int_Onat, _1221537) = hAPP(c_Int_Onat, _1221539), -(_1221537 = _1221539)]]], (45579 ^ _778495) ^ [_1693071, _1693073] : [45581 ^ _778495 : [(45584 ^ _778495) ^ [] : [45580 ^ [_1693071, _1693073] = c_List_Olist_ONil(_1693071)], (45582 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1693071)), 45580 ^ [_1693071, _1693073]), hAPP(c_List_Oset(tc_List_Olist(_1693071)), _1693073))))]], -(c_List_Oconcat(_1693071, _1693073) = c_List_Olist_ONil(_1693071))], (52277 ^ _778495) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (20099 ^ _778495) ^ [_1139550, _1139552, _1139554] : [class_Rings_Olinordered__semidom(_1139550), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1139552), _1139554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139550), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1139550), _1139552)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1139550), _1139554))))], (45751 ^ _778495) ^ [_1697714, _1697716, _1697718] : [45753 ^ _778495 : [(45756 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1697716, 45752 ^ [_1697714, _1697716, _1697718])))], (45754 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1697714), 45752 ^ [_1697714, _1697716, _1697718]), hAPP(c_List_Oset(_1697714), _1697718))))]], -(hAPP(c_List_Ofilter(_1697714, _1697716), _1697718) = c_List_Olist_ONil(_1697714))], (20712 ^ _778495) ^ [_1149683, _1149685] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149683) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149685)), 20715 ^ _778495 : [(20718 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149685)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20716 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149683))))]], 20719 ^ _778495 : [(20722 ^ _778495) ^ [] : [20723 ^ _778495 : [(20726 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149683) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (20724 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149685))))]], 20727 ^ _778495 : [(20730 ^ _778495) ^ [] : [_1149683 = _1149685], (20728 ^ _778495) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149685)))]]], (20720 ^ _778495) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149683)))]]], (46328 ^ _778495) ^ [_1709781, _1709783, _1709785] : [class_Orderings_Olinorder(_1709781), -(c_List_Olinorder__class_Osorted(_1709781, hAPP(c_List_Ofilter(_1709781, hAPP(hAPP(c_COMBC(_1709781, _1709781, tc_HOL_Obool), c_fequal), hAPP(_1709783, _1709785))), _1709785)))], (51653 ^ _778495) ^ [_1821625, _1821627] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821625), _1821627))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821625, _1821627))], (49025 ^ _778495) ^ [_1770016, _1770018] : [c_Relation_Otrans(_1770016, _1770018), -(c_Relation_Otrans(tc_List_Olist(_1770016), c_List_Olexord(_1770016, _1770018)))], (30999 ^ _778495) ^ [_1344695, _1344697, _1344699, _1344701] : [class_Orderings_Olinorder(_1344695), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344695), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344695), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1344695), _1344697), _1344699)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1344695), _1344697), _1344701))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1344695), _1344697), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344695), _1344699), _1344701)))))], (5610 ^ _778495) ^ [_864329, _864331, _864333, _864335] : [-(hAPP(_864335, _864331) = hAPP(_864333, _864329)), _864335 = _864333, _864331 = _864329], (26454 ^ _778495) ^ [_1251620, _1251622, _1251624] : [class_Rings_Olinordered__idom(_1251620), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251620), c_Groups_Ozero__class_Ozero(_1251620)), hAPP(hAPP(c_Power_Opower__class_Opower(_1251620), hAPP(c_Groups_Oabs__class_Oabs(_1251620), _1251622)), _1251624))))], (42309 ^ _778495) ^ [_1621083, _1621085, _1621087, _1621089] : [-(_1621083 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621085)), _1621087)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1621085, hAPP(hAPP(c_List_Olist__update(_1621085, _1621087), _1621083), _1621089)) = hAPP(hAPP(c_List_Olist__update(_1621085, c_List_Obutlast(_1621085, _1621087)), _1621083), _1621089))], (37823 ^ _778495) ^ [_1498154, _1498156, _1498158] : [-(hAPP(hAPP(c_Set_Oinsert(_1498154), _1498156), hAPP(c_Set_OCollect(_1498154), _1498158)) = hAPP(c_Set_OCollect(_1498154), hAPP(hAPP(c_COMBS(_1498154, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498154), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1498154), c_fNot), hAPP(hAPP(c_COMBC(_1498154, _1498154, tc_HOL_Obool), c_fequal), _1498156)))), _1498158)))], (7164 ^ _778495) ^ [_896599, _896601, _896603, _896605] : [class_Lattices_Osemilattice__sup(_896599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896599), _896601), _896603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896599), _896601), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896599), _896605), _896603))))], (31630 ^ _778495) ^ [_1356576, _1356578, _1356580, _1356582, _1356584, _1356586] : [hAPP(c_Product__Type_Oapfst(_1356576, _1356578, _1356580, _1356582), _1356584) = hAPP(c_Product__Type_Oapfst(_1356576, _1356578, _1356580, _1356586), _1356584), -(hAPP(_1356582, hAPP(c_Product__Type_Ofst(_1356576, _1356580), _1356584)) = hAPP(_1356586, hAPP(c_Product__Type_Ofst(_1356576, _1356580), _1356584)))], (4796 ^ _778495) ^ [_851618, _851620] : [_851620 = _851618, -(c_Relation_OId(_851620) = c_Relation_OId(_851618))], (50090 ^ _778495) ^ [_1791338, _1791340, _1791342, _1791344] : [c_Fun_Oinj__on(_1791338, _1791340, _1791342, _1791344), -(c_Fun_Obij__betw(_1791338, _1791340, _1791342, _1791344, hAPP(c_Set_Oimage(_1791338, _1791340, _1791342), _1791344)))], (2462 ^ _778495) ^ [_814745, _814747] : [_814747 = _814745, -(c_SetInterval_Oord__class_OgreaterThan(_814747) = c_SetInterval_Oord__class_OgreaterThan(_814745))], (23695 ^ _778495) ^ [_1202982, _1202984, _1202986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202982), _1202984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202982), _1202986)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202984), _1202986))))], (23937 ^ _778495) ^ [_1206898, _1206900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206898)), -(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, _1206900, _1206898))))], (12833 ^ _778495) ^ [_1006469, _1006471, _1006473] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1006469, tc_HOL_Obool)), _1006471), _1006473))), 12839 ^ _778495 : [(12843 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1006469, tc_HOL_Obool)), 12841 ^ [_1006469, _1006471, _1006473]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1006469, tc_HOL_Obool)), _1006471), _1006473))))], (12845 ^ _778495) ^ [] : [12838 ^ [_1006469, _1006471, _1006473] = 12841 ^ [_1006469, _1006471, _1006473]], (12847 ^ _778495) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006469, tc_HOL_Obool)), 12838 ^ [_1006469, _1006471, _1006473]), 12841 ^ [_1006469, _1006471, _1006473]) = c_Orderings_Obot__class_Obot(tc_fun(_1006469, tc_HOL_Obool))], (12840 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1006469, tc_HOL_Obool)), 12838 ^ [_1006469, _1006471, _1006473]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1006469, tc_HOL_Obool)), _1006471), _1006473))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006469, tc_HOL_Obool)), _1006471), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1006469, tc_HOL_Obool), _1006473)) = c_Orderings_Obot__class_Obot(tc_fun(_1006469, tc_HOL_Obool)))], (47951 ^ _778495) ^ [_1744508, _1744510, _1744512] : [47953 ^ _778495 : [(47956 ^ _778495) ^ [] : [hBOOL(hAPP(_1744510, 47952 ^ [_1744508, _1744510, _1744512]))], (47954 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744508), 47952 ^ [_1744508, _1744510, _1744512]), hAPP(c_List_Oset(_1744508), _1744512))))]], -(c_List_Olist__all(_1744508, _1744510, _1744512))], (21162 ^ _778495) ^ [_1157651, _1157653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157651), _1157653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1157651)), c_Int_OBit1(_1157653))))], (45500 ^ _778495) ^ [_1691505, _1691507] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691505)), c_List_Oremdups(_1691505, c_List_Oconcat(_1691505, _1691507))) = hAPP(c_Finite__Set_Ocard(_1691505), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1691505), tc_fun(_1691505, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1691505)), _1691507)), c_List_Oset(_1691505))))], (23472 ^ _778495) ^ [_1198882, _1198884] : [_1198884 = c_Orderings_Obot__class_Obot(tc_fun(_1198882, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198882, tc_HOL_Obool)), _1198884), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1198882, tc_HOL_Obool)), _1198884))))], (36869 ^ _778495) ^ [_1473676, _1473678, _1473680, _1473682, _1473684] : [c_Fun_Oinj__on(_1473676, _1473678, _1473680, _1473682), hBOOL(hAPP(hAPP(c_member(_1473678), _1473684), hAPP(c_Set_Oimage(_1473676, _1473678, _1473680), _1473682))), -(hAPP(_1473680, hAPP(c_Fun_Othe__inv__into(_1473676, _1473678, _1473682, _1473680), _1473684)) = _1473684)], (6292 ^ _778495) ^ [_880328, _880330, _880332] : [class_Orderings_Oorder(_880328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880328), _880330), _880332)), 6299 ^ _778495 : [(6306 ^ _778495) ^ [] : [_880332 = _880330, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880328), _880332), _880330)))], (6300 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880328), _880332), _880330)), -(_880332 = _880330)]]], (1658 ^ _778495) ^ [_802248, _802250] : [-(class_Rings_Olinordered__semidom(_802248)), _802250 = _802248, class_Rings_Olinordered__semidom(_802250)], (52159 ^ _778495) ^ [_1830604, _1830606] : [class_Orderings_Oord(_1830604), -(class_Orderings_Oord(tc_fun(_1830606, _1830604)))], (23256 ^ _778495) ^ [_1195051] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195051, _1195051) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (2350 ^ _778495) ^ [_812967, _812969, _812971, _812973] : [-(c_Divides_OnegDivAlg(_812973, _812969) = c_Divides_OnegDivAlg(_812971, _812967)), _812973 = _812971, _812969 = _812967], (37927 ^ _778495) ^ [_1500589, _1500591] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1500589, tc_HOL_Obool)), _1500591) = hAPP(c_Set_OCollect(_1500589), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1500589), c_fNot), hAPP(hAPP(c_COMBC(_1500589, tc_fun(_1500589, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500589)), _1500591))))], (31222 ^ _778495) ^ [_1349003, _1349005] : [class_Orderings_Olinorder(_1349003), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349003), _1349005)), -(c_Big__Operators_Olinorder__class_OMax(_1349003, _1349005) = hAPP(c_Finite__Set_Ofold1(_1349003, c_Orderings_Oord__class_Omax(_1349003)), _1349005))], (46363 ^ _778495) ^ [_1710421, _1710423, _1710425] : [class_Orderings_Olinorder(_1710421), 46366 ^ _778495 : [(46385 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710421, hAPP(hAPP(c_List_Oappend(_1710421), _1710423), _1710425))), c_List_Olinorder__class_Osorted(_1710421, _1710423), c_List_Olinorder__class_Osorted(_1710421, _1710425), 46395 ^ _778495 : [(46401 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710421), 46394 ^ [_1710421, _1710423, _1710425]), 46397 ^ [_1710421, _1710423, _1710425]))], (46399 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710421), 46397 ^ [_1710421, _1710423, _1710425]), hAPP(c_List_Oset(_1710421), _1710425))))], (46396 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710421), 46394 ^ [_1710421, _1710423, _1710425]), hAPP(c_List_Oset(_1710421), _1710423))))]]], (46367 ^ _778495) ^ [] : [c_List_Olinorder__class_Osorted(_1710421, hAPP(hAPP(c_List_Oappend(_1710421), _1710423), _1710425)), 46370 ^ _778495 : [(46375 ^ _778495) ^ [_1710657] : [hBOOL(hAPP(hAPP(c_member(_1710421), _1710657), hAPP(c_List_Oset(_1710421), _1710423))), 46378 ^ _778495 : [(46379 ^ _778495) ^ [_1710767] : [hBOOL(hAPP(hAPP(c_member(_1710421), _1710767), hAPP(c_List_Oset(_1710421), _1710425))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710421), _1710657), _1710767)))]]], (46373 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710421, _1710425))], (46371 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710421, _1710423))]]]]], (43039 ^ _778495) ^ [_1636841, _1636843, _1636845, _1636847, _1636849] : [hAPP(hAPP(c_List_Oappend(_1636841), _1636843), _1636845) = hAPP(hAPP(c_List_Olist_OCons(_1636841), _1636847), _1636849), 43044 ^ _778495 : [(43047 ^ _778495) ^ [] : [-(_1636845 = hAPP(hAPP(c_List_Olist_OCons(_1636841), _1636847), _1636849))], (43045 ^ _778495) ^ [] : [-(_1636843 = c_List_Olist_ONil(_1636841))]], 43049 ^ _778495 : [(43052 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1636841), 43048 ^ [_1636841, _1636843, _1636845, _1636847, _1636849]), _1636845) = _1636849)], (43050 ^ _778495) ^ [] : [-(_1636843 = hAPP(hAPP(c_List_Olist_OCons(_1636841), _1636847), 43048 ^ [_1636841, _1636843, _1636845, _1636847, _1636849]))]]], (7132 ^ _778495) ^ [_896040, _896042, _896044, _896046] : [class_Lattices_Osemilattice__sup(_896040), 7135 ^ _778495 : [(7144 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896040), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896040), _896042), _896044)), _896046))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896040), _896042), _896046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896040), _896044), _896046))], (7136 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896040), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896040), _896042), _896044)), _896046)), 7139 ^ _778495 : [(7142 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896040), _896044), _896046)))], (7140 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896040), _896042), _896046)))]]]]], (35821 ^ _778495) ^ [_1450016, _1450018, _1450020, _1450022, _1450024] : [c_Equiv__Relations_Oequiv(_1450016, _1450018, _1450020), hBOOL(hAPP(hAPP(c_member(_1450016), _1450022), _1450018)), hBOOL(hAPP(hAPP(c_member(_1450016), _1450024), _1450018)), 35832 ^ _778495 : [(35839 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1450016, _1450016)), hAPP(hAPP(c_Product__Type_OPair(_1450016, _1450016), _1450022), _1450024)), _1450020)), -(hAPP(c_Relation_OImage(_1450016, _1450016, _1450020), hAPP(hAPP(c_Set_Oinsert(_1450016), _1450022), c_Orderings_Obot__class_Obot(tc_fun(_1450016, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1450016, _1450016, _1450020), hAPP(hAPP(c_Set_Oinsert(_1450016), _1450024), c_Orderings_Obot__class_Obot(tc_fun(_1450016, tc_HOL_Obool)))))], (35833 ^ _778495) ^ [] : [hAPP(c_Relation_OImage(_1450016, _1450016, _1450020), hAPP(hAPP(c_Set_Oinsert(_1450016), _1450022), c_Orderings_Obot__class_Obot(tc_fun(_1450016, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1450016, _1450016, _1450020), hAPP(hAPP(c_Set_Oinsert(_1450016), _1450024), c_Orderings_Obot__class_Obot(tc_fun(_1450016, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1450016, _1450016)), hAPP(hAPP(c_Product__Type_OPair(_1450016, _1450016), _1450022), _1450024)), _1450020)))]]], (9801 ^ _778495) ^ [_946531, _946533, _946535, _946537, _946539] : [c_Finite__Set_Ofolding__one__idem(_946531, _946533, _946535), hBOOL(hAPP(c_Finite__Set_Ofinite(_946531), _946537)), -(hAPP(_946535, hAPP(hAPP(c_Set_Oinsert(_946531), _946539), _946537)) = hAPP(hAPP(c_Finite__Set_Ofold(_946531, _946531, _946533), _946539), _946537))], (35670 ^ _778495) ^ [_1446707, _1446709, _1446711, _1446713, _1446715, _1446717] : [c_Equiv__Relations_Oequiv(_1446707, _1446709, _1446711), hBOOL(hAPP(hAPP(c_member(_1446707), _1446713), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446707, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446707, _1446707, _1446711), hAPP(hAPP(c_Set_Oinsert(_1446707), _1446715), c_Orderings_Obot__class_Obot(tc_fun(_1446707, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1446707, _1446707, _1446711), hAPP(hAPP(c_Set_Oinsert(_1446707), _1446717), c_Orderings_Obot__class_Obot(tc_fun(_1446707, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446707, _1446707)), hAPP(hAPP(c_Product__Type_OPair(_1446707, _1446707), _1446715), _1446717)), _1446711)))], (34709 ^ _778495) ^ [_1427615, _1427617] : [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)), _1427615)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1427617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1427615), _1427617)))], (50265 ^ _778495) ^ [_1794906, _1794908, _1794910, _1794912, _1794914, _1794916] : [c_Fun_Oinj__on(_1794906, _1794908, _1794910, _1794912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794908, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1794906, _1794908, _1794910), _1794912)), _1794914)), c_Fun_Oinj__on(_1794908, _1794906, _1794916, _1794914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794906, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1794908, _1794906, _1794916), _1794914)), _1794912)), -(c_Fun_Obij__betw(_1794906, _1794908, 50280 ^ [_1794906, _1794908, _1794910, _1794912, _1794914, _1794916], _1794912, _1794914))], (45957 ^ _778495) ^ [_1703049, _1703051, _1703053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703049), _1703051)), _1703053)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1703051), c_List_Oupt(_1703049, _1703053)) = c_List_Oupt(_1703049, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703049), _1703051)))], (29200 ^ _778495) ^ [_1309464, _1309466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1309464), _1309466)), -(c_Divides_Odivmod__nat(_1309464, _1309466) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1309464))], (18086 ^ _778495) ^ [_1102935] : [class_Orderings_Olinorder(_1102935), -(c_Finite__Set_Ofun__left__comm__idem(_1102935, _1102935, c_Orderings_Oord__class_Omin(_1102935)))], (43351 ^ _778495) ^ [_1643766, _1643768, _1643770] : [hBOOL(hAPP(c_List_Odistinct(_1643766), hAPP(hAPP(c_List_Oappend(_1643766), _1643768), _1643770))), 43354 ^ _778495 : [(43359 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643766, tc_HOL_Obool)), hAPP(c_List_Oset(_1643766), _1643768)), hAPP(c_List_Oset(_1643766), _1643770)) = c_Orderings_Obot__class_Obot(tc_fun(_1643766, tc_HOL_Obool)))], (43357 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643766), _1643770)))], (43355 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643766), _1643768)))]]], (26184 ^ _778495) ^ [_1246721, _1246723, 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c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1384541))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384545), _1384675)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384545), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1384675), _1384541))))]]], (534 ^ _778495) ^ [_786546, _786548, _786550, _786552, _786554, _786556, _786558, _786560] : [-(c_List_Olistrelp(_786558, _786554, _786550, _786546)), c_List_Olistrelp(_786560, _786556, _786552, _786548), _786560 = _786558, _786556 = _786554, _786552 = _786550, _786548 = _786546], (2542 ^ _778495) ^ [_815985, _815987, _815989, _815991] : [-(c_Divides_Odivmod__nat__rel(_815991, _815987) = c_Divides_Odivmod__nat__rel(_815989, _815985)), _815991 = _815989, _815987 = _815985], (5787 ^ _778495) ^ [_870271, _870273, _870275] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_870271, _870273, c_Orderings_Obot__class_Obot(tc_fun(_870271, tc_HOL_Obool))), _870275))], (5510 ^ _778495) ^ [_862815, _862817, _862819, _862821] : [-(tc_sum(_862821, _862817) = tc_sum(_862819, _862815)), _862821 = _862819, _862817 = _862815], (17910 ^ _778495) ^ [_1099568, _1099570, _1099572, _1099574] : [class_Orderings_Olinorder(_1099568), 17913 ^ _778495 : [(17914 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099568), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099568), _1099570), _1099572)), _1099574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099568), _1099570), _1099574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099568), _1099572), _1099574)))], (17924 ^ _778495) ^ [] : [17925 ^ _778495 : [(17928 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099568), _1099572), _1099574))], (17926 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099568), _1099570), _1099574))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099568), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099568), _1099570), _1099572)), _1099574)))]]], (34500 ^ _778495) ^ [_1423138, _1423140, _1423142] : [-(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)), _1423138)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1423140), _1423142)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423140), _1423138)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423142), _1423138)))], (17974 ^ _778495) ^ [_1100655, _1100657, _1100659] : [class_Int_Onumber__ring(_1100655), class_Rings_Olinordered__idom(_1100655), 17981 ^ _778495 : [(17988 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100657), _1100659)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100655), hAPP(c_Int_Onumber__class_Onumber__of(_1100655), _1100657)), hAPP(c_Int_Onumber__class_Onumber__of(_1100655), _1100659))))], (17982 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100655), hAPP(c_Int_Onumber__class_Onumber__of(_1100655), _1100657)), hAPP(c_Int_Onumber__class_Onumber__of(_1100655), _1100659))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100657), _1100659)))]]], (20181 ^ _778495) ^ [_1140982, _1140984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140982), _1140984)), -(_1140984 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140982), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 20184 ^ [_1140982, _1140984]))))], (36626 ^ _778495) ^ [_1468089, _1468091, _1468093, _1468095, _1468097, _1468099] : [c_Fun_Oinj__on(_1468089, _1468091, _1468093, _1468095), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468091, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468089, _1468091, _1468093), _1468095)), _1468097)), c_Fun_Oinj__on(_1468091, _1468089, _1468099, _1468097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468089, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468091, _1468089, _1468099), _1468097)), _1468095)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468089), _1468095)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468091), _1468097)), -(hAPP(c_Finite__Set_Ocard(_1468089), _1468095) = hAPP(c_Finite__Set_Ocard(_1468091), _1468097))], (27431 ^ _778495) ^ [_1267881, _1267883] : [class_Groups_Osgn__if(_1267881), 27434 ^ _778495 : [(27441 ^ _778495) ^ [] : [-(_1267883 = c_Groups_Ozero__class_Ozero(_1267881)), 27444 ^ _778495 : [(27451 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267881), c_Groups_Ozero__class_Ozero(_1267881)), _1267883))), -(c_Groups_Osgn__class_Osgn(_1267881, _1267883) = hAPP(c_Groups_Ouminus__class_Ouminus(_1267881), c_Groups_Oone__class_Oone(_1267881)))], (27445 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267881), c_Groups_Ozero__class_Ozero(_1267881)), _1267883)), -(c_Groups_Osgn__class_Osgn(_1267881, _1267883) = c_Groups_Oone__class_Oone(_1267881))]]], (27435 ^ _778495) ^ [] : [_1267883 = c_Groups_Ozero__class_Ozero(_1267881), -(c_Groups_Osgn__class_Osgn(_1267881, _1267883) = c_Groups_Ozero__class_Ozero(_1267881))]]], (29918 ^ _778495) ^ [_1322887, _1322889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1322887), 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)), _1322889)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1322887, _1322889) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1322887, _1322889)))], (12134 ^ _778495) ^ [_990794, _990796, _990798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990794), _990796)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990796), _990794))), _990798) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _990796)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990794), _990798)))], (25451 ^ _778495) ^ [_1233295, _1233297] : [_1233295 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1233297), _1233295) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (24095 ^ _778495) ^ [_1209485, _1209487, _1209489] : [hBOOL(hAPP(_1209485, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1209487), _1209489))), 24098 ^ _778495 : [(24123 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209489), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24126 ^ _778495 : [(24127 ^ _778495) ^ [_1210149] : [-(hBOOL(hAPP(_1209485, _1210149))), 24128 ^ _778495 : [(24129 ^ _778495) ^ [_1210223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209489), _1210223)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210223), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1209487 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1209489), _1210149)), _1210223)]]]]], (24105 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209489)), 24108 ^ _778495 : [(24109 ^ _778495) ^ [_1209819] : [-(hBOOL(hAPP(_1209485, _1209819))), 24110 ^ _778495 : [(24111 ^ _778495) ^ [_1209890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209890), _1209489)), _1209487 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1209489), _1209819)), _1209890)]]]]], (24099 ^ _778495) ^ [] : [_1209489 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1209485, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (6480 ^ _778495) ^ [_883490, _883492, _883494, _883496, _883498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883490, tc_HOL_Obool)), _883492), _883494)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883490, tc_HOL_Obool)), _883496), _883498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883490, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_883490, tc_HOL_Obool)), _883492), _883496)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_883490, tc_HOL_Obool)), _883494), _883498))))], (46152 ^ _778495) ^ [_1706839, _1706841] : [class_Orderings_Olinorder(_1706839), c_List_Olinorder__class_Osorted(_1706839, _1706841), -(c_List_Olinorder__class_Osorted(_1706839, hAPP(c_List_Otl(_1706839), _1706841)))], (21410 ^ _778495) ^ [_1162371, _1162373] : [class_Int_Onumber__ring(_1162371), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162371), hAPP(c_Int_Onumber__class_Onumber__of(_1162371), c_Int_OBit1(c_Int_OPls))), _1162373) = _1162373)], (37855 ^ _778495) ^ [_1498842, _1498844, _1498846] : [-(hAPP(hAPP(c_Set_Oinsert(_1498842), _1498844), _1498846) = hAPP(c_Set_OCollect(_1498842), hAPP(hAPP(c_COMBS(_1498842, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498842), c_fdisj), hAPP(hAPP(c_COMBC(_1498842, _1498842, tc_HOL_Obool), c_fequal), _1498844))), hAPP(hAPP(c_COMBC(_1498842, tc_fun(_1498842, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498842)), _1498846))))], (26660 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (47484 ^ _778495) ^ [_1734767, _1734769, _1734771, _1734773, _1734775] : [hAPP(c_List_Ofilter(_1734767, _1734769), _1734771) = hAPP(hAPP(c_List_Olist_OCons(_1734767), _1734773), _1734775), 47489 ^ _778495 : [(47498 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1734769, _1734773)))], (47500 ^ _778495) ^ [] : [-(_1734775 = hAPP(c_List_Ofilter(_1734767, _1734769), 47488 ^ [_1734767, _1734769, _1734771, _1734773, _1734775]))], (47492 ^ _778495) ^ [_1735081] : [hBOOL(hAPP(hAPP(c_member(_1734767), _1735081), hAPP(c_List_Oset(_1734767), 47487 ^ [_1734767, _1734769, _1734771, _1734773, _1734775]))), hBOOL(hAPP(_1734769, _1735081))], (47490 ^ _778495) ^ [] : [-(_1734771 = hAPP(hAPP(c_List_Oappend(_1734767), 47487 ^ [_1734767, _1734769, _1734771, _1734773, _1734775]), hAPP(hAPP(c_List_Olist_OCons(_1734767), _1734773), 47488 ^ [_1734767, _1734769, _1734771, _1734773, _1734775])))]]], (30679 ^ _778495) ^ [_1338622, _1338624, _1338626, _1338628] : [class_Orderings_Olinorder(_1338622), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338622), _1338624), _1338626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338622), _1338628), _1338626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338622), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338622), _1338624), _1338628)), _1338626)))], (52209 ^ _778495) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (15776 ^ _778495) ^ [_1059336, _1059338, _1059340] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1059336), _1059338)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059336), _1059340)), 15786 ^ _778495 : [(15789 ^ _778495) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15787 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1059336), 15785 ^ [_1059336, _1059338, _1059340]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1059336, tc_HOL_Obool)), _1059338), _1059340))))]], -(hAPP(c_Finite__Set_Ocard(_1059336), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1059336, tc_HOL_Obool)), _1059338), _1059340)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1059336), _1059338)), hAPP(c_Finite__Set_Ocard(_1059336), _1059340)))], (21242 ^ _778495) ^ [_1158964, _1158966, _1158968, _1158970, _1158972] : [class_Rings_Olinordered__idom(_1158964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158964), hAPP(c_Groups_Oabs__class_Oabs(_1158964), _1158966)), _1158968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158964), hAPP(c_Groups_Oabs__class_Oabs(_1158964), _1158970)), _1158972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158964), hAPP(c_Groups_Oabs__class_Oabs(_1158964), _1158966)), hAPP(c_Groups_Oabs__class_Oabs(_1158964), _1158970))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158964), _1158968), _1158972))))], (45328 ^ _778495) ^ [_1688080, _1688082, _1688084, _1688086] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688080)), _1688082), hAPP(c_List_Oset(tc_List_Olist(_1688080)), c_Enum_On__lists(_1688080, _1688084, _1688086)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688080)), _1688082) = _1688084)], (10933 ^ _778495) ^ [_966678, _966680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966680)), _966678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966678), _966680))], (37276 ^ _778495) ^ [_1482902, _1482904, _1482906, _1482908, _1482910, _1482912] : [-(hBOOL(hAPP(hAPP(c_member(_1482902), _1482904), _1482906))), 37279 ^ _778495 : [(37286 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482902), _1482908), _1482906))), -(hAPP(c_Set_Ovimage(_1482910, _1482902, hAPP(hAPP(c_COMBC(_1482910, _1482902, _1482902), hAPP(hAPP(c_COMBC(_1482910, _1482902, tc_fun(_1482902, _1482902)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1482902, tc_fun(_1482902, _1482902)), _1482910), c_If(_1482902)), hAPP(hAPP(c_COMBC(_1482910, tc_fun(_1482910, tc_HOL_Obool), tc_HOL_Obool), c_member(_1482910)), _1482912))), _1482904)), _1482908)), _1482906) = c_Orderings_Obot__class_Obot(tc_fun(_1482910, tc_HOL_Obool)))], (37280 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1482902), _1482908), _1482906)), -(hAPP(c_Set_Ovimage(_1482910, _1482902, hAPP(hAPP(c_COMBC(_1482910, _1482902, _1482902), hAPP(hAPP(c_COMBC(_1482910, _1482902, tc_fun(_1482902, _1482902)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1482902, tc_fun(_1482902, _1482902)), _1482910), c_If(_1482902)), hAPP(hAPP(c_COMBC(_1482910, tc_fun(_1482910, tc_HOL_Obool), tc_HOL_Obool), c_member(_1482910)), _1482912))), _1482904)), _1482908)), _1482906) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1482910, tc_HOL_Obool)), _1482912))]]], (49937 ^ _778495) ^ [_1788479, _1788481, _1788483, _1788485, _1788487] : [c_Fun_Obij__betw(_1788479, _1788481, _1788483, _1788485, _1788487), -(c_Fun_Obij__betw(_1788481, _1788479, c_Hilbert__Choice_Oinv__into(_1788479, _1788481, _1788485, _1788483), _1788487, _1788485))], (27535 ^ _778495) ^ [_1269879, _1269881, _1269883] : [class_Orderings_Otop(_1269879), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1269881, _1269879)), _1269883) = c_Orderings_Otop__class_Otop(_1269879))], (20240 ^ _778495) ^ [_1142092, _1142094] : [class_Rings_Olinordered__semidom(_1142092), 20243 ^ _778495 : [(20250 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1142094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142092), c_Groups_Ozero__class_Ozero(_1142092)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1142092), _1142094))))], (20244 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142092), c_Groups_Ozero__class_Ozero(_1142092)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1142092), _1142094))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1142094)))]]], (37933 ^ _778495) ^ [_1500805, _1500807] : [-(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), _1500805)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1500807))))))], (8670 ^ _778495) ^ [_923458, _923460, _923462] : [class_Groups_Oab__semigroup__mult(_923458), hBOOL(hAPP(c_Finite__Set_Ofinite(_923458), _923460)), -(_923460 = c_Orderings_Obot__class_Obot(tc_fun(_923458, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_923458), _923462)), -(_923462 = c_Orderings_Obot__class_Obot(tc_fun(_923458, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923458, tc_HOL_Obool)), _923460), _923462) = c_Orderings_Obot__class_Obot(tc_fun(_923458, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_923458, c_Groups_Otimes__class_Otimes(_923458)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923458, tc_HOL_Obool)), _923460), _923462)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923458), hAPP(c_Finite__Set_Ofold1(_923458, c_Groups_Otimes__class_Otimes(_923458)), _923460)), hAPP(c_Finite__Set_Ofold1(_923458, c_Groups_Otimes__class_Otimes(_923458)), _923462)))], (22902 ^ _778495) ^ [_1187974] : [class_Int_Onumber__ring(_1187974), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187974), c_Groups_Oone__class_Oone(_1187974)), c_Groups_Oone__class_Oone(_1187974)) = hAPP(c_Int_Onumber__class_Onumber__of(_1187974), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (35711 ^ _778495) ^ [_1447716, _1447718, _1447720, _1447722] : [c_Equiv__Relations_Oequiv(_1447716, _1447718, _1447720), hBOOL(hAPP(hAPP(c_member(_1447716), _1447722), _1447718)), -(hBOOL(hAPP(hAPP(c_member(_1447716), _1447722), hAPP(c_Relation_OImage(_1447716, _1447716, _1447720), hAPP(hAPP(c_Set_Oinsert(_1447716), _1447722), c_Orderings_Obot__class_Obot(tc_fun(_1447716, tc_HOL_Obool)))))))], (25608 ^ _778495) ^ [_1236074, _1236076] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1236074))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1236076)) = 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)))), _1236074), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1236076)))], (39047 ^ _778495) ^ [_1535793, _1535795] : [c_Wellfounded_OwfP(_1535793, _1535795), -(c_Wellfounded_Owf(_1535793, hAPP(c_Set_OCollect(tc_prod(_1535793, _1535793)), hAPP(c_Product__Type_Oprod_Oprod__case(_1535793, _1535793, tc_HOL_Obool), _1535795))))], (6114 ^ _778495) ^ [_876775, _876777, _876779, _876781] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_876775, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876775, tc_HOL_Obool)), _876777), _876779)), _876781) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876775, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_876775, tc_HOL_Obool)), _876777), _876781)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_876775, tc_HOL_Obool)), _876779), _876781)))], (14937 ^ _778495) ^ [_1043427, _1043429, _1043431, _1043433] : [class_Groups_Oordered__comm__monoid__add(_1043427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043427), c_Groups_Ozero__class_Ozero(_1043427)), _1043429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043427), _1043431), _1043433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043427), _1043431), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043427), _1043429), _1043433))))], (44229 ^ _778495) ^ [_1663191, _1663193, _1663195] : [-(_1663191 = c_List_Olist_ONil(_1663193)), -(c_List_Olast(_1663193, hAPP(hAPP(c_List_Oappend(_1663193), _1663195), _1663191)) = c_List_Olast(_1663193, _1663191))], (52453 ^ _778495) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (22122 ^ _778495) ^ [_1174164, _1174166] : [c_Int_OBit1(_1174164) = c_Int_OBit0(_1174166)], (37160 ^ _778495) ^ [_1479979, _1479981, _1479983, _1479985, _1479987] : [-(hAPP(c_Set_Ovimage(_1479979, _1479981, _1479983), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479981, tc_HOL_Obool)), _1479985), _1479987)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479979, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1479979, _1479981, _1479983), _1479985)), hAPP(c_Set_Ovimage(_1479979, _1479981, _1479983), _1479987)))], (41796 ^ _778495) ^ [_1607030, _1607032, _1607034, _1607036] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607030), tc_List_Olist(_1607030))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607030), tc_List_Olist(_1607030)), _1607032), _1607034)), c_List_Olistrel(_1607030, _1607036)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607030)), _1607032) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607030)), _1607034), 41802 ^ _778495 : [(41805 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607030, _1607030)), hAPP(hAPP(c_Product__Type_OPair(_1607030, _1607030), hAPP(hAPP(c_List_Onth(_1607030), _1607032), 41801 ^ [_1607030, _1607032, _1607034, _1607036])), hAPP(hAPP(c_List_Onth(_1607030), _1607034), 41801 ^ [_1607030, _1607032, _1607034, _1607036]))), _1607036))], (41803 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41801 ^ [_1607030, _1607032, _1607034, _1607036]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607030)), _1607032))))]]], (23258 ^ _778495) ^ [_1195078, _1195080, _1195082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195078, tc_HOL_Obool)), _1195080), _1195082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195078, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1195078, tc_HOL_Obool)), _1195082)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1195078, tc_HOL_Obool)), _1195080))))], (44307 ^ _778495) ^ [_1664465, _1664467, _1664469] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664465)), _1664467), c_List_Olists(_1664465, _1664469)))), 44308 ^ _778495 : [(44311 ^ _778495) ^ [_1664593, _1664595] : [_1664467 = hAPP(hAPP(c_List_Olist_OCons(_1664465), _1664595), _1664593), hBOOL(hAPP(hAPP(c_member(_1664465), _1664595), _1664469)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664465)), _1664593), c_List_Olists(_1664465, _1664469)))], (44309 ^ _778495) ^ [] : [_1664467 = c_List_Olist_ONil(_1664465)]]], (35907 ^ _778495) ^ [_1451999, _1452001, _1452003, _1452005, _1452007, _1452009, _1452011, _1452013, _1452015, _1452017] : [c_Equiv__Relations_Oequiv(_1451999, _1452001, _1452003), c_Equiv__Relations_Oequiv(_1452005, _1452007, _1452009), c_Equiv__Relations_Ocongruent2(_1451999, _1452005, tc_fun(_1452011, tc_HOL_Obool), _1452003, _1452009, _1452013), hBOOL(hAPP(hAPP(c_member(_1451999), _1452015), _1452001)), hBOOL(hAPP(hAPP(c_member(_1452005), _1452017), _1452007)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451999, tc_fun(_1452011, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1451999, _1451999, _1452003), hAPP(hAPP(c_Set_Oinsert(_1451999), _1452015), c_Orderings_Obot__class_Obot(tc_fun(_1451999, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1452005, tc_fun(_1452011, tc_HOL_Obool)), tc_fun(_1452011, tc_HOL_Obool), _1451999), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1452005, tc_fun(_1452011, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1452005, _1452005, _1452009), hAPP(hAPP(c_Set_Oinsert(_1452005), _1452017), c_Orderings_Obot__class_Obot(tc_fun(_1452005, tc_HOL_Obool)))))), _1452013)) = hAPP(hAPP(_1452013, _1452015), _1452017))], (25894 ^ _778495) ^ [_1241261, _1241263, _1241265] : [class_Rings_Olinordered__idom(_1241261), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241261), c_Groups_Ozero__class_Ozero(_1241261)), hAPP(hAPP(c_Power_Opower__class_Opower(_1241261), _1241263), 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)))), _1241265)))))], (33058 ^ _778495) ^ [_1388377, _1388379, _1388381, _1388383] : [class_Groups_Ocomm__monoid__add(_1388377), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1388379), _1388381)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1388377), _1388383), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1388379, _1388381)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1388377), hAPP(_1388383, _1388379)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1388377), _1388383), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1388379, _1388381))))], (24519 ^ _778495) ^ [_1217400, _1217402] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1217400), _1217402)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217400)), _1217402))], (35064 ^ _778495) ^ [_1434006, _1434008] : [c_Nat__Transfer_Ois__nat(_1434006), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1434006, _1434008)))], (10119 ^ _778495) ^ [_952991, _952993] : [class_Groups_Ocomm__monoid__mult(_952991), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952991), _952993), c_Groups_Oone__class_Oone(_952991)) = _952993)], (49100 ^ _778495) ^ [_1771740, _1771742] : [c_Relation_Otrans(_1771740, _1771742), c_Relation_Oantisym(_1771740, _1771742), -(c_Relation_Otrans(_1771740, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1771740, _1771740), tc_HOL_Obool)), _1771742), c_Relation_OId(_1771740))))], (24419 ^ _778495) ^ [_1215565, _1215567] : [_1215565 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1215565, _1215567) = _1215567)], (32396 ^ _778495) ^ [_1375065, _1375067, _1375069, _1375071] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1375065), _1375067)), 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)), _1375069), _1375065)), 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)), _1375071), _1375067)), 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)), _1375069), _1375071)), _1375067)), c_FunDef_Omax__strict)))], (38519 ^ _778495) ^ [_1521900, _1521902, _1521904] : [-(hAPP(c_Set_Oimage(tc_prod(_1521900, _1521902), _1521902, c_Product__Type_Osnd(_1521900, _1521902)), _1521904) = hAPP(c_Relation_ORange(_1521900, _1521902), _1521904))], (10821 ^ _778495) ^ [_964849, _964851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _964849)), hAPP(c_Nat_OSuc, _964851))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964849), _964851)))], (11282 ^ _778495) ^ [_973193, _973195, _973197] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973193), _973195)), _973197) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973193), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973195), _973197)))], (12260 ^ _778495) ^ [_993439, _993441, _993443] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_993439), _993441)), hBOOL(hAPP(c_Finite__Set_Ofinite(_993439), _993443)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_993439, tc_HOL_Obool)), _993441), _993443) = c_Orderings_Obot__class_Obot(tc_fun(_993439, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_993439), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993439, tc_HOL_Obool)), _993441), _993443)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_993439), _993441)), hAPP(c_Finite__Set_Ocard(_993439), _993443)))], (6400 ^ _778495) ^ [_882160, _882162, _882164, _882166] : [class_Orderings_Oorder(_882160), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882160), _882162), _882164)), _882162 = _882166, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882160), _882166), _882164)))], (19340 ^ _778495) ^ [_1125950, _1125952] : [class_Orderings_Olinorder(_1125950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125950), _1125952)), -(c_Big__Operators_Olattice_OInf__fin(_1125950, c_Orderings_Oord__class_Omin(_1125950), _1125952) = hAPP(c_Finite__Set_Ofold1(_1125950, c_Orderings_Oord__class_Omin(_1125950)), _1125952))], (17502 ^ _778495) ^ [_1091933, _1091935, _1091937, _1091939] : [class_Lattices_Osemilattice__inf(_1091933), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091933), _1091935)), 17512 ^ _778495 : [(17515 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091933), _1091937), 17511 ^ [_1091933, _1091935, _1091937, _1091939]))], (17513 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1091933), 17511 ^ [_1091933, _1091935, _1091937, _1091939]), _1091935)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091933), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091933), _1091937), _1091939)), hAPP(hAPP(c_Finite__Set_Ofold(_1091933, _1091933, c_Lattices_Osemilattice__inf__class_Oinf(_1091933)), _1091939), _1091935))))], (43345 ^ _778495) ^ [_1643513, _1643515, _1643517, _1643519, _1643521] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643513), tc_List_Olist(_1643513))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643513), tc_List_Olist(_1643513)), _1643515), _1643517)), c_List_Olexord(_1643513, _1643519))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643513), tc_List_Olist(_1643513))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643513), tc_List_Olist(_1643513)), hAPP(hAPP(c_List_Oappend(_1643513), _1643521), _1643515)), hAPP(hAPP(c_List_Oappend(_1643513), _1643521), _1643517))), c_List_Olexord(_1643513, _1643519))))], (19164 ^ _778495) ^ [_1122992] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1122992) = _1122992)], (45472 ^ _778495) ^ [_1690912, _1690914, _1690916] : [hBOOL(hAPP(c_List_Odistinct(_1690912), _1690914)), -(c_List_Oremove1(_1690912, _1690916, _1690914) = hAPP(c_List_OremoveAll(_1690912, _1690916), _1690914))], (32202 ^ _778495) ^ [_1371128, _1371130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1371128), hAPP(c_Nat_OSuc, _1371130))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1371128, hAPP(c_Nat_OSuc, _1371130)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1371130)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1371128, _1371130)))], (34092 ^ _778495) ^ [_1413575, _1413577, _1413579] : [class_Groups_Ocomm__monoid__add(_1413575), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1413575), _1413577), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1413579))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1413575), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1413575), _1413577), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1413579))), hAPP(_1413577, hAPP(c_Nat_OSuc, _1413579))))], (23535 ^ _778495) ^ [_1200077, _1200079] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1200077, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1200079)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1200077, _1200079) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (6844 ^ _778495) ^ [_890774, _890776, _890778, _890780] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890774, tc_HOL_Obool)), _890776), _890778), _890780)), -(hBOOL(hAPP(_890776, _890780))), -(hBOOL(hAPP(_890778, _890780)))], (39027 ^ _778495) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (41742 ^ _778495) ^ [_1605698, _1605700, _1605702] : [c_Equiv__Relations_Oequiv(_1605698, _1605700, _1605702), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1605698), c_List_Olists(_1605698, _1605700), c_List_Olistrel(_1605698, _1605702)))], (28187 ^ _778495) ^ [_1281507, _1281509, _1281511, _1281513] : [class_Groups_Ouminus(_1281507), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1281509, _1281507)), _1281511), _1281513) = hAPP(c_Groups_Ouminus__class_Ouminus(_1281507), hAPP(_1281511, _1281513)))], (51157 ^ _778495) ^ [_1813220, _1813222] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813220), _1813222)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813222), _1813220)), -(_1813220 = _1813222)], (52275 ^ _778495) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (16716 ^ _778495) ^ [_1077368, _1077370, _1077372] : [class_Fields_Olinordered__field__inverse__zero(_1077368), 16719 ^ _778495 : [(16734 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077368), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1077368), _1077370), _1077372)), c_Groups_Ozero__class_Ozero(_1077368)))), 16735 ^ _778495 : [(16742 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077368), _1077370), c_Groups_Ozero__class_Ozero(_1077368))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077368), c_Groups_Ozero__class_Ozero(_1077368)), _1077372))], (16736 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077368), c_Groups_Ozero__class_Ozero(_1077368)), _1077370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077368), _1077372), c_Groups_Ozero__class_Ozero(_1077368)))]]], (16720 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077368), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1077368), _1077370), _1077372)), c_Groups_Ozero__class_Ozero(_1077368))), 16725 ^ _778495 : [(16728 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077368), _1077372), c_Groups_Ozero__class_Ozero(_1077368))))], (16726 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077368), c_Groups_Ozero__class_Ozero(_1077368)), _1077370)))]], 16729 ^ _778495 : [(16732 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077368), c_Groups_Ozero__class_Ozero(_1077368)), _1077372)))], (16730 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077368), _1077370), c_Groups_Ozero__class_Ozero(_1077368))))]]]]], (52461 ^ _778495) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (28009 ^ _778495) ^ [_1278257, _1278259] : [class_Complete__Lattice_Ocomplete__lattice(_1278257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278257), _1278259)), -(_1278259 = c_Orderings_Obot__class_Obot(tc_fun(_1278257, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1278257, _1278259) = c_Complete__Lattice_OInf__class_OInf(_1278257, _1278259))], (50421 ^ _778495) ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798196, _1798198), tc_prod(_1798196, _1798198))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798196, _1798198), tc_prod(_1798196, _1798198)), hAPP(hAPP(c_Product__Type_OPair(_1798196, _1798198), _1798200), _1798202)), hAPP(hAPP(c_Product__Type_OPair(_1798196, _1798198), _1798204), _1798206))), c_Transitive__Closure_Ortrancl(tc_prod(_1798196, _1798198), _1798208))), hBOOL(hAPP(hAPP(_1798210, _1798200), _1798202)), 50432 ^ _778495 : [(50437 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798196, _1798198), tc_prod(_1798196, _1798198))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798196, _1798198), tc_prod(_1798196, _1798198)), hAPP(hAPP(c_Product__Type_OPair(_1798196, _1798198), 50430 ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210]), 50431 ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210])), hAPP(hAPP(c_Product__Type_OPair(_1798196, _1798198), 50434 ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210]), 50435 ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210]))), _1798208)))], (50439 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1798210, 50430 ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210]), 50431 ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210])))], (50441 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1798210, 50434 ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210]), 50435 ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210]))], (50433 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798196, _1798198), tc_prod(_1798196, _1798198))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798196, _1798198), tc_prod(_1798196, _1798198)), hAPP(hAPP(c_Product__Type_OPair(_1798196, _1798198), _1798200), _1798202)), hAPP(hAPP(c_Product__Type_OPair(_1798196, _1798198), 50430 ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210]), 50431 ^ [_1798196, _1798198, _1798200, _1798202, _1798204, _1798206, _1798208, _1798210]))), c_Transitive__Closure_Ortrancl(tc_prod(_1798196, _1798198), _1798208))))]], -(hBOOL(hAPP(hAPP(_1798210, _1798204), _1798206)))], (16990 ^ _778495) ^ [_1082088, _1082090, _1082092] : [class_Fields_Olinordered__field(_1082088), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082088), _1082090), c_Groups_Ozero__class_Ozero(_1082088))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082088), c_Groups_Ozero__class_Ozero(_1082088)), _1082092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082088), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1082088), _1082090), _1082092)), c_Groups_Ozero__class_Ozero(_1082088))))], (39067 ^ _778495) ^ [_1536150, _1536152] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1536150, _1536152), 39068 ^ [_1536150, _1536152])), -(c_Wellfounded_OwfP(_1536150, _1536152))], (33587 ^ _778495) ^ [_1403214] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1403214))))], (12486 ^ _778495) ^ [_998937, _998939, _998941, _998943] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _998937), _998939)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _998941), _998939)), _998943)) = 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), _998937), _998941)), _998939)), _998943))], (21486 ^ _778495) ^ [] : [-(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)))))], (26288 ^ _778495) ^ [_1248499, _1248501, _1248503, _1248505] : [class_Fields_Ofield(_1248499), -(_1248501 = c_Groups_Ozero__class_Ozero(_1248499)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1248499), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248499), _1248503), _1248501)), _1248505) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248499), hAPP(hAPP(c_Power_Opower__class_Opower(_1248499), _1248503), _1248505)), hAPP(hAPP(c_Power_Opower__class_Opower(_1248499), _1248501), _1248505)))], (39424 ^ _778495) ^ [_1545561, _1545563, _1545565, _1545567, _1545569, _1545571, _1545573, _1545575, _1545577, _1545579] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1545561, _1545563), tc_prod(_1545565, _1545567), tc_prod(_1545569, _1545571), c_Product__Type_Omap__pair(_1545561, _1545565, _1545563, _1545567, _1545573, _1545575)), c_Product__Type_Omap__pair(_1545569, _1545561, _1545571, _1545563, _1545577, _1545579)) = c_Product__Type_Omap__pair(_1545569, _1545565, _1545571, _1545567, hAPP(c_Fun_Ocomp(_1545561, _1545565, _1545569, _1545573), _1545577), hAPP(c_Fun_Ocomp(_1545563, _1545567, _1545571, _1545575), _1545579)))], (17392 ^ _778495) ^ [_1089635, _1089637, _1089639, _1089641] : [class_Fields_Olinordered__field(_1089635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089635), _1089637), _1089639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089635), c_Groups_Ozero__class_Ozero(_1089635)), _1089641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089635), c_Groups_Ozero__class_Ozero(_1089635)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089635), _1089639), _1089637))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089635), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1089635), _1089641), _1089639)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1089635), _1089641), _1089637))))], (33485 ^ _778495) ^ [_1400252, _1400254, _1400256, _1400258, _1400260] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400252, tc_HOL_Obool)), _1400254), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1400256, tc_fun(_1400252, tc_HOL_Obool)), _1400258), _1400260)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400256, tc_fun(_1400252, tc_HOL_Obool)), _1400258), hAPP(hAPP(c_COMBB(tc_fun(_1400252, tc_HOL_Obool), tc_fun(_1400252, tc_HOL_Obool), _1400256), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400252, tc_HOL_Obool)), _1400254)), _1400260)))], (31029 ^ _778495) ^ [_1345372, _1345374, _1345376, _1345378] : [class_Orderings_Olinorder(_1345372), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345372), _1345374)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1345372, _1345372, c_Orderings_Oord__class_Omax(_1345372)), _1345376), hAPP(hAPP(c_Set_Oinsert(_1345372), _1345378), _1345374)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345372), _1345378), hAPP(hAPP(c_Finite__Set_Ofold(_1345372, _1345372, c_Orderings_Oord__class_Omax(_1345372)), _1345376), _1345374)))], (15479 ^ _778495) ^ [_1053485, _1053487, _1053489] : [15480 ^ _778495 : [(15483 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053487), _1053489))], (15481 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1053485)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053485), _1053487)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053485), _1053489))))], (18578 ^ _778495) ^ [_1112088, _1112090, _1112092] : [class_Orderings_Olinorder(_1112088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112088), _1112090)), -(_1112090 = c_Orderings_Obot__class_Obot(tc_fun(_1112088, tc_HOL_Obool))), 18589 ^ _778495 : [(18599 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112088), hAPP(c_Finite__Set_Ofold1(_1112088, c_Orderings_Oord__class_Omin(_1112088)), _1112090)), _1112092))), 18600 ^ _778495 : [(18601 ^ _778495) ^ [_1112477] : [hBOOL(hAPP(hAPP(c_member(_1112088), _1112477), _1112090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112088), _1112477), _1112092))]]], (18590 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112088), hAPP(c_Finite__Set_Ofold1(_1112088, c_Orderings_Oord__class_Omin(_1112088)), _1112090)), _1112092)), 18594 ^ _778495 : [(18597 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112088), 18593 ^ [_1112088, _1112090, _1112092]), _1112092)))], (18595 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112088), 18593 ^ [_1112088, _1112090, _1112092]), _1112090)))]]]]], (26928 ^ _778495) ^ [_1259660] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1259660), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1259660))], (21376 ^ _778495) ^ [_1161612, _1161614, _1161616, _1161618, _1161620] : [class_Groups_Oordered__ab__group__add__abs(_1161612), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161612), hAPP(c_Groups_Oabs__class_Oabs(_1161612), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161612), _1161614), _1161616)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161612), _1161618), _1161620)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161612), hAPP(c_Groups_Oabs__class_Oabs(_1161612), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161612), _1161614), _1161618))), hAPP(c_Groups_Oabs__class_Oabs(_1161612), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161612), _1161616), _1161620))))))], (18550 ^ _778495) ^ [_1111584, _1111586, _1111588, _1111590] : [class_Orderings_Olinorder(_1111584), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111584), _1111586)), hBOOL(hAPP(hAPP(c_member(_1111584), _1111588), _1111586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111584), hAPP(hAPP(c_Finite__Set_Ofold(_1111584, _1111584, c_Orderings_Oord__class_Omin(_1111584)), _1111590), _1111586)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1111584), _1111588), _1111590))))], (45780 ^ _778495) ^ [_1698336, _1698338, _1698340, _1698342] : [-(c_List_Otranspose(_1698336, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698338), tc_List_Olist(_1698336)), hAPP(c_List_Omap(_1698338, _1698336), _1698340)), _1698342)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698338), tc_List_Olist(_1698336)), hAPP(c_List_Omap(_1698338, _1698336), _1698340)), c_List_Otranspose(_1698338, _1698342)))], (40230 ^ _778495) ^ [_1564115] : [-(c_Transitive__Closure_Otrancl(_1564115, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564115, _1564115), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564115, _1564115), tc_HOL_Obool)))], (28025 ^ _778495) ^ [_1278466, _1278468, _1278470, _1278472] : [28027 ^ _778495 : [(28032 ^ _778495) ^ [] : [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(_1278470, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 28026 ^ [_1278466, _1278468, _1278470, _1278472]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1278470, 28026 ^ [_1278466, _1278468, _1278470, _1278472])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28030 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 28026 ^ [_1278466, _1278468, _1278470, _1278472]), _1278468)))], (28028 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1278466), 28026 ^ [_1278466, _1278468, _1278470, _1278472])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1278466), _1278468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1278470, _1278466)), _1278472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1278472), hAPP(_1278470, _1278468))), 28046 ^ _778495 : [(28051 ^ _778495) ^ [] : [-(hAPP(_1278470, 28045 ^ [_1278466, _1278468, _1278470, _1278472]) = _1278472)], (28049 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 28045 ^ [_1278466, _1278468, _1278470, _1278472]), _1278468)))], (28047 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1278466), 28045 ^ [_1278466, _1278468, _1278470, _1278472])))]]], (9979 ^ _778495) ^ [_950086, _950088, _950090, _950092, _950094, _950096] : [c_Finite__Set_Ofun__left__comm(_950086, _950088, _950090), hBOOL(hAPP(c_Finite__Set_Ofinite(_950086), _950092)), -(hAPP(hAPP(c_Finite__Set_Ofold(_950086, _950088, _950090), _950094), hAPP(hAPP(c_Set_Oinsert(_950086), _950096), _950092)) = hAPP(hAPP(_950090, _950096), hAPP(hAPP(c_Finite__Set_Ofold(_950086, _950088, _950090), _950094), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950086, tc_HOL_Obool)), _950092), hAPP(hAPP(c_Set_Oinsert(_950086), _950096), c_Orderings_Obot__class_Obot(tc_fun(_950086, tc_HOL_Obool)))))))], (22354 ^ _778495) ^ [_1178228, _1178230, _1178232] : [class_Groups_Oab__group__add(_1178228), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1178228), _1178230), _1178232) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178228), _1178230), hAPP(c_Groups_Ouminus__class_Ouminus(_1178228), _1178232)))], (51047 ^ _778495) ^ [_1811442, _1811444] : [_1811442 = _1811444, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811442), _1811444)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811444), _1811442)))], (46524 ^ _778495) ^ [_1713597, _1713599, _1713601, _1713603, _1713605] : [class_Orderings_Olinorder(_1713597), c_Fun_Oinj__on(_1713599, _1713597, _1713601, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1713599, tc_HOL_Obool)), hAPP(c_List_Oset(_1713599), _1713603)), hAPP(c_List_Oset(_1713599), _1713605))), c_List_Olinorder__class_Osorted(_1713597, hAPP(hAPP(c_List_Omap(_1713599, _1713597), _1713601), _1713603)), hBOOL(hAPP(c_List_Odistinct(_1713597), hAPP(hAPP(c_List_Omap(_1713599, _1713597), _1713601), _1713603))), c_List_Olinorder__class_Osorted(_1713597, hAPP(hAPP(c_List_Omap(_1713599, _1713597), _1713601), _1713605)), hBOOL(hAPP(c_List_Odistinct(_1713597), hAPP(hAPP(c_List_Omap(_1713599, _1713597), _1713601), _1713605))), hAPP(c_List_Oset(_1713599), _1713603) = hAPP(c_List_Oset(_1713599), _1713605), -(_1713603 = _1713605)], (19142 ^ _778495) ^ [_1122627, _1122629, _1122631] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122627), _1122629)), _1122631) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122627), _1122631)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122629), _1122631)))], (41351 ^ _778495) ^ [_1592847, _1592849] : [-(c_List_Olenlex(_1592847, _1592849) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1592847)), tc_List_Olist(_1592847)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1592847), c_Wellfounded_Oless__than, c_List_Olex(_1592847, _1592849))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592847), tc_List_Olist(_1592847), tc_prod(tc_Nat_Onat, tc_List_Olist(_1592847))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1592847), tc_prod(tc_Nat_Onat, tc_List_Olist(_1592847))), tc_List_Olist(_1592847)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1592847))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592847)))), c_COMBI(tc_List_Olist(_1592847)))))], (10321 ^ _778495) ^ [_956334, _956336, _956338] : [class_Lattices_Olattice(_956334), hBOOL(hAPP(c_Finite__Set_Ofinite(_956334), _956336)), -(c_Big__Operators_Olattice__class_OInf__fin(_956334, hAPP(hAPP(c_Set_Oinsert(_956334), _956338), _956336)) = hAPP(hAPP(c_Finite__Set_Ofold(_956334, _956334, c_Lattices_Osemilattice__inf__class_Oinf(_956334)), _956338), _956336))], (13089 ^ _778495) ^ [_1011930, _1011932, _1011934] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1011930), 13092 ^ _778495 : [(13099 ^ _778495) ^ [] : [_1011934 = c_Groups_Ozero__class_Ozero(_1011930), -(_1011932 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011930), _1011932), _1011934))], (13093 ^ _778495) ^ [] : [_1011932 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011930), _1011932), _1011934), -(_1011934 = c_Groups_Ozero__class_Ozero(_1011930))]]], (31774 ^ _778495) ^ [_1359955, _1359957, _1359959, _1359961] : [31776 ^ _778495 : [(31779 ^ _778495) ^ [] : [hAPP(_1359961, 31775 ^ [_1359955, _1359957, _1359959, _1359961]) = c_Orderings_Otop__class_Otop(tc_fun(_1359957, tc_HOL_Obool))], (31777 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359955), 31775 ^ [_1359955, _1359957, _1359959, _1359961]), _1359959)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1359955, tc_fun(_1359957, tc_HOL_Obool)), _1359959), _1359961) = c_Orderings_Otop__class_Otop(tc_fun(_1359957, tc_HOL_Obool)))], (25660 ^ _778495) ^ [_1236946, _1236948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236946), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236946), _1236948)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1236946))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1236948))))], (1728 ^ _778495) ^ [_803123, _803125] : [-(class_Rings_Ocomm__semiring__1(_803123)), _803125 = _803123, class_Rings_Ocomm__semiring__1(_803125)], (37248 ^ _778495) ^ [_1482076, _1482078, _1482080, _1482082] : [-(hAPP(c_Set_Ovimage(_1482076, _1482078, _1482080), _1482082) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482078, tc_fun(_1482076, tc_HOL_Obool)), _1482082), hAPP(hAPP(c_COMBB(tc_fun(_1482078, tc_HOL_Obool), tc_fun(_1482076, tc_HOL_Obool), _1482078), c_Set_Ovimage(_1482076, _1482078, _1482080)), hAPP(hAPP(c_COMBC(_1482078, tc_fun(_1482078, tc_HOL_Obool), tc_fun(_1482078, tc_HOL_Obool)), c_Set_Oinsert(_1482078)), c_Orderings_Obot__class_Obot(tc_fun(_1482078, tc_HOL_Obool))))))], (8098 ^ _778495) ^ [_911840, _911842, _911844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_911840, tc_HOL_Obool)), _911842), _911844)), 8101 ^ _778495 : [(8104 ^ _778495) ^ [] : [_911842 = _911844], (8102 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911840, tc_HOL_Obool)), _911842), _911844)))]]], (34526 ^ _778495) ^ [_1423814, _1423816, _1423818, _1423820, _1423822] : [hBOOL(hAPP(hAPP(c_member(_1423814), _1423816), _1423818)), -(hAPP(c_Set_Oimage(_1423814, _1423820, hAPP(c_COMBK(_1423820, _1423814), _1423822)), _1423818) = hAPP(hAPP(c_Set_Oinsert(_1423820), _1423822), c_Orderings_Obot__class_Obot(tc_fun(_1423820, tc_HOL_Obool))))], (2510 ^ _778495) ^ [_815447, _815449, _815451, _815453, _815455, _815457, _815459, _815461, _815463, _815465] : [-(c_Finite__Set_Ofold__graph(_815465, _815461, _815457, _815453, _815449) = c_Finite__Set_Ofold__graph(_815463, _815459, _815455, _815451, _815447)), _815465 = _815463, _815461 = _815459, _815457 = _815455, _815453 = _815451, _815449 = _815447], (45772 ^ _778495) ^ [_1698050, _1698052] : [-(c_List_Otranspose(_1698050, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698050)), c_List_Olist_ONil(_1698050)), _1698052)) = c_List_Otranspose(_1698050, _1698052))], (20414 ^ _778495) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (48302 ^ _778495) ^ [_1752466, _1752468, _1752470, _1752472] : [hBOOL(hAPP(_1752466, _1752468)), -(hAPP(c_List_Ofilter(_1752470, _1752466), c_List_Oreplicate(_1752470, _1752472, _1752468)) = c_List_Oreplicate(_1752470, _1752472, _1752468))], (40314 ^ _778495) ^ [_1566708, _1566710, _1566712, _1566714] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566708, _1566708)), hAPP(hAPP(c_Product__Type_OPair(_1566708, _1566708), _1566712), _1566714)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566708, _1566708), tc_HOL_Obool)), _1566710), c_Relation_OId(_1566708)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1566708, tc_fun(_1566708, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1566708, tc_fun(tc_prod(_1566708, _1566708), tc_HOL_Obool), tc_fun(_1566708, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566708, tc_fun(tc_fun(tc_prod(_1566708, _1566708), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1566708, _1566708), tc_HOL_Obool), tc_fun(_1566708, tc_HOL_Obool)), _1566708), c_COMBC(_1566708, tc_fun(tc_prod(_1566708, _1566708), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566708, tc_prod(_1566708, _1566708)), tc_fun(_1566708, tc_fun(tc_fun(tc_prod(_1566708, _1566708), tc_HOL_Obool), tc_HOL_Obool)), _1566708), hAPP(c_COMBB(tc_prod(_1566708, _1566708), tc_fun(tc_fun(tc_prod(_1566708, _1566708), tc_HOL_Obool), tc_HOL_Obool), _1566708), c_member(tc_prod(_1566708, _1566708)))), c_Product__Type_OPair(_1566708, _1566708)))), _1566710)), c_fequal), _1566712), _1566714)))], (40236 ^ _778495) ^ [_1564252, _1564254] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564252, _1564252)), c_Transitive__Closure_Otrancl(_1564252, _1564254))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564252, _1564252)), _1564254)))], (40649 ^ _778495) ^ [_1574837, _1574839, _1574841, _1574843, _1574845] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574837, _1574837)), hAPP(hAPP(c_Product__Type_OPair(_1574837, _1574837), _1574839), _1574841)), c_Transitive__Closure_Ortrancl(_1574837, _1574843))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574837, _1574837), tc_HOL_Obool)), _1574843), hAPP(hAPP(c_Product__Type_OSigma(_1574837, _1574837), _1574845), hAPP(c_COMBK(tc_fun(_1574837, tc_HOL_Obool), _1574837), _1574845)))), -(_1574839 = _1574841), -(hBOOL(hAPP(hAPP(c_member(_1574837), _1574839), _1574845)))], (30617 ^ _778495) ^ [_1337530, _1337532, _1337534, _1337536] : [class_Orderings_Olinorder(_1337530), 30620 ^ _778495 : [(30621 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337530), _1337532), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1337530), _1337534), _1337536))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337530), _1337532), _1337534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337530), _1337532), _1337536)))], (30631 ^ _778495) ^ [] : [30632 ^ _778495 : [(30635 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337530), _1337532), _1337536))], (30633 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337530), _1337532), _1337534))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337530), _1337532), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1337530), _1337534), _1337536))))]]], (23508 ^ _778495) ^ [_1199508, _1199510] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1199508, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199508, tc_HOL_Obool)), _1199510)), _1199510) = c_Orderings_Obot__class_Obot(tc_fun(_1199508, tc_HOL_Obool)))], (38148 ^ _778495) ^ [_1508137] : [-(c_Wellfounded_Ofinite__psubset(_1508137) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1508137, tc_HOL_Obool), tc_fun(_1508137, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1508137, tc_HOL_Obool), tc_fun(_1508137, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1508137, tc_HOL_Obool), tc_fun(tc_fun(_1508137, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1508137, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1508137, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1508137, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1508137, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1508137, tc_HOL_Obool)), c_COMBS(tc_fun(_1508137, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1508137, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1508137, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1508137, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1508137, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1508137, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1508137)))))], (10361 ^ _778495) ^ [_957163, _957165, _957167] : [class_Lattices_Olattice(_957163), hBOOL(hAPP(c_Finite__Set_Ofinite(_957163), _957165)), -(hBOOL(hAPP(hAPP(c_member(_957163), _957167), _957165))), -(_957165 = c_Orderings_Obot__class_Obot(tc_fun(_957163, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_957163, hAPP(hAPP(c_Set_Oinsert(_957163), _957167), _957165)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_957163), _957167), c_Big__Operators_Olattice__class_OInf__fin(_957163, _957165)))], (47912 ^ _778495) ^ [_1743747, _1743749, _1743751, _1743753] : [-(c_List_Olist__all(_1743747, _1743749, hAPP(hAPP(c_List_Olist_OCons(_1743747), _1743751), _1743753))), hBOOL(hAPP(_1743749, _1743751)), c_List_Olist__all(_1743747, _1743749, _1743753)], (6500 ^ _778495) ^ [_883980, _883982, _883984, _883986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883980, tc_HOL_Obool)), _883982), _883984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883980, tc_HOL_Obool)), _883984), _883986)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_883980, tc_HOL_Obool)), _883984), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_883980, tc_HOL_Obool)), _883986), _883982)) = _883982)], (46718 ^ _778495) ^ [_1717784, _1717786, _1717788, _1717790, _1717792] : [-(hAPP(c_List_Ofoldl(_1717784, _1717786, _1717788, _1717790), _1717792) = c_List_Ofoldr(_1717786, _1717784, hAPP(c_COMBC(_1717784, _1717786, _1717784), _1717788), hAPP(c_List_Orev(_1717786), _1717792), _1717790))], (42906 ^ _778495) ^ [_1633490, _1633492] : [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), _1633490), _1633492))), 42909 ^ _778495 : [(42916 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1633490), _1633492))), -(c_List_Oupto(_1633490, _1633492) = c_List_Olist_ONil(tc_Int_Oint))], (42910 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1633490), _1633492)), -(c_List_Oupto(_1633490, _1633492) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1633490), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1633490), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1633492)))]]], (52285 ^ _778495) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (35164 ^ _778495) ^ [_1435452, _1435454] : [c_Nat__Transfer_Onat__set(_1435452), c_Nat__Transfer_Onat__set(_1435454), 35171 ^ _778495 : [(35178 ^ _778495) ^ [] : [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), _1435452)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1435454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1435452), _1435454)))], (35172 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1435452), _1435454)), -(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), _1435452)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1435454))))]]], (4058 ^ _778495) ^ [_839979, _839981, _839983, _839985] : [-(c_Lazy__Sequence_Ohb__single(_839985, _839981) = c_Lazy__Sequence_Ohb__single(_839983, _839979)), _839985 = _839983, _839981 = _839979], (48535 ^ _778495) ^ [_1757265, _1757267, _1757269] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757265), _1757267), _1757269)), -(hBOOL(hAPP(hAPP(c_member(_1757265), _1757269), hAPP(c_List_Oset(_1757265), _1757267))))], (27233 ^ _778495) ^ [_1264807, _1264809] : [class_Rings_Oring__1(_1264807), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264809)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1264807), hAPP(c_Int_Onat, _1264809)) = hAPP(c_Int_Oring__1__class_Oof__int(_1264807), _1264809))], (52573 ^ _778495) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (50739 ^ _778495) ^ [_1805960, _1805962, _1805964, _1805966, _1805968] : [class_Rings_Ocomm__semiring__1(_1805960), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805960), hAPP(hAPP(c_Power_Opower__class_Opower(_1805960), _1805962), _1805964)), _1805966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1805968), _1805964)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805960), hAPP(hAPP(c_Power_Opower__class_Opower(_1805960), _1805962), _1805968)), _1805966)))], (1598 ^ _778495) ^ [_801498, _801500] : [-(class_Groups_Oordered__comm__monoid__add(_801498)), _801500 = _801498, class_Groups_Oordered__comm__monoid__add(_801500)], (51741 ^ _778495) ^ [_1823116, _1823118] : [51742 ^ _778495 : [(51745 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823118), _1823116))], (51743 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823116), _1823118)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1823116, _1823118))], (10809 ^ _778495) ^ [_964566, _964568, _964570] : [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, _964566)), _964568)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _964566)), _964570))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964568), _964570)))], (29428 ^ _778495) ^ [_1313736, _1313738, _1313740] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1313736, _1313738), _1313740)), 29431 ^ _778495 : [(29432 ^ _778495) ^ [_1313821] : [hBOOL(hAPP(hAPP(_1313738, _1313821), _1313740)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1313736, _1313738), _1313821)))]]], (40985 ^ _778495) ^ [_1583172, _1583174] : [-(c_Relation_Osingle__valued(_1583172, _1583172, c_Relation_OId__on(_1583172, _1583174)))], (15703 ^ _778495) ^ [_1057999, _1058001] : [-(_1057999 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1057999), _1058001) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057999), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1058001)))], (28479 ^ _778495) ^ [_1293262, _1293264, _1293266, _1293268] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1293262), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293264, tc_Nat_Onat), _1293266), _1293268)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293264, _1293262), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1293262, _1293264), c_Nat_Osemiring__1__class_Oof__nat(_1293262)), _1293266)), _1293268)), class_Groups_Ocomm__monoid__mult(_1293262), class_Rings_Osemiring__1(_1293262)], (40248 ^ _778495) ^ [_1564472, _1564474, _1564476, _1564478, _1564480] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564472, _1564472)), hAPP(hAPP(c_Product__Type_OPair(_1564472, _1564472), _1564474), _1564476)), c_Transitive__Closure_Otrancl(_1564472, _1564478))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1564472, _1564472)), hAPP(hAPP(c_Product__Type_OPair(_1564472, _1564472), _1564476), _1564480)), c_Transitive__Closure_Otrancl(_1564472, _1564478))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564472, _1564472)), hAPP(hAPP(c_Product__Type_OPair(_1564472, _1564472), _1564474), _1564480)), c_Transitive__Closure_Otrancl(_1564472, _1564478))))], (33543 ^ _778495) ^ [_1402141, _1402143, _1402145, _1402147, _1402149] : [class_Complete__Lattice_Ocomplete__lattice(_1402141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402143), _1402145)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1402141), _1402147), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402143, _1402141), _1402145), _1402149)) = hAPP(hAPP(c_Finite__Set_Ofold(_1402143, _1402141, hAPP(hAPP(c_COMBB(_1402141, tc_fun(_1402141, _1402141), _1402143), c_Lattices_Osemilattice__sup__class_Osup(_1402141)), _1402149)), _1402147), _1402145))], (41927 ^ _778495) ^ [_1610649, _1610651, _1610653] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610649, tc_HOL_Obool)), hAPP(c_List_Oset(_1610649), _1610651)), hAPP(c_List_Oset(_1610649), hAPP(hAPP(c_List_Olist_OCons(_1610649), _1610653), _1610651)))))], (6562 ^ _778495) ^ [_885209, _885211, _885213, _885215] : [hBOOL(hAPP(hAPP(c_member(_885209), _885211), _885213)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_885209, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_885209), _885211), _885215)), _885213) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_885209, tc_HOL_Obool)), _885215), _885213))], (23527 ^ _778495) ^ [_1199915, _1199917, _1199919] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199915, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1199915, tc_HOL_Obool)), _1199917), _1199919)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1199915, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199915, tc_HOL_Obool)), _1199917)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199915, tc_HOL_Obool)), _1199919)))], (26474 ^ _778495) ^ [_1252006, _1252008, _1252010] : [class_Rings_Oring__1(_1252006), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252006), hAPP(c_Groups_Ouminus__class_Ouminus(_1252006), _1252008)), _1252010) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252006), hAPP(hAPP(c_Power_Opower__class_Opower(_1252006), hAPP(c_Groups_Ouminus__class_Ouminus(_1252006), c_Groups_Oone__class_Oone(_1252006))), _1252010)), hAPP(hAPP(c_Power_Opower__class_Opower(_1252006), _1252008), _1252010)))], (1478 ^ _778495) ^ [_799998, _800000] : [-(class_Orderings_Otop(_799998)), _800000 = _799998, class_Orderings_Otop(_800000)], (44059 ^ _778495) ^ [_1660217, _1660219, _1660221, _1660223, _1660225] : [class_Orderings_Olinorder(_1660217), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660219)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660219, _1660217, _1660221), _1660223), _1660225)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660219)), _1660225)))], (20664 ^ _778495) ^ [_1148898, _1148900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1148898), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148898)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148900)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148900))], (19350 ^ _778495) ^ [_1126113, _1126115] : [class_Orderings_Olinorder(_1126113), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126113), _1126115)), -(c_Big__Operators_Olinorder__class_OMin(_1126113, _1126115) = hAPP(c_Finite__Set_Ofold1(_1126113, c_Orderings_Oord__class_Omin(_1126113)), _1126115))], (13185 ^ _778495) ^ [_1013374, _1013376, _1013378] : [class_Rings_Oring__no__zero__divisors(_1013374), 13188 ^ _778495 : [(13189 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013374), _1013376), _1013378) = c_Groups_Ozero__class_Ozero(_1013374), -(_1013376 = c_Groups_Ozero__class_Ozero(_1013374)), -(_1013378 = c_Groups_Ozero__class_Ozero(_1013374))], (13199 ^ _778495) ^ [] : [13200 ^ _778495 : [(13203 ^ _778495) ^ [] : [_1013378 = c_Groups_Ozero__class_Ozero(_1013374)], (13201 ^ _778495) ^ [] : [_1013376 = c_Groups_Ozero__class_Ozero(_1013374)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013374), _1013376), _1013378) = c_Groups_Ozero__class_Ozero(_1013374))]]], (39426 ^ _778495) ^ [_1545656, _1545658, _1545660, _1545662, _1545664, _1545666, _1545668, _1545670, _1545672, _1545674] : [-(c_Product__Type_Omap__pair(_1545656, _1545658, _1545660, _1545662, hAPP(c_Fun_Ocomp(_1545664, _1545658, _1545656, _1545666), _1545668), hAPP(c_Fun_Ocomp(_1545670, _1545662, _1545660, _1545672), _1545674)) = hAPP(c_Fun_Ocomp(tc_prod(_1545664, _1545670), tc_prod(_1545658, _1545662), tc_prod(_1545656, _1545660), c_Product__Type_Omap__pair(_1545664, _1545658, _1545670, _1545662, _1545666, _1545672)), c_Product__Type_Omap__pair(_1545656, _1545664, _1545660, _1545670, _1545668, _1545674)))], (27725 ^ _778495) ^ [_1273276, _1273278] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1273276, _1273278)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1273276, _1273278), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1273278), c_Orderings_Otop__class_Otop(tc_fun(_1273278, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1273276), c_Orderings_Otop__class_Otop(tc_fun(_1273276, tc_HOL_Obool)))))], (49039 ^ _778495) ^ [_1770211, _1770213] : [-(c_Relation_Otrans(_1770211, c_Transitive__Closure_Otrancl(_1770211, _1770213)))], (14007 ^ _778495) ^ [_1027222, _1027224] : [class_Rings_Olinordered__ring(_1027222), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027222), c_Groups_Ozero__class_Ozero(_1027222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1027222), _1027224), _1027224))))], (33254 ^ _778495) ^ [_1393228, _1393230, _1393232, _1393234] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1393228, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393230, tc_fun(tc_fun(_1393228, tc_HOL_Obool), tc_HOL_Obool)), _1393232), hAPP(hAPP(c_COMBB(tc_fun(_1393228, tc_HOL_Obool), tc_fun(tc_fun(_1393228, tc_HOL_Obool), tc_HOL_Obool), _1393230), c_Set_OPow(_1393228)), _1393234))), hAPP(c_Set_OPow(_1393228), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393230, tc_fun(_1393228, tc_HOL_Obool)), _1393232), _1393234)))))], (19136 ^ _778495) ^ [_1122488, _1122490] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122488), _1122490) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122490), _1122488))], (50172 ^ _778495) ^ [_1792994, _1792996, _1792998, _1793000, _1793002] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1792994, _1792996, tc_HOL_Obool, _1792998), _1793000), _1793002)), -(hBOOL(hAPP(_1792998, hAPP(hAPP(c_Product__Type_OPair(_1792994, _1792996), _1793000), _1793002))))], (41387 ^ _778495) ^ [_1594459, _1594461, _1594463, _1594465, _1594467] : [-(hAPP(hAPP(c_List_Olist_OCons(_1594459), _1594461), _1594463) = hAPP(hAPP(c_List_Olist_OCons(_1594459), _1594465), _1594467)), _1594461 = _1594465, _1594463 = _1594467], (31300 ^ _778495) ^ [_1350314, _1350316, _1350318] : [class_Orderings_Olinorder(_1350314), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350314, tc_HOL_Obool)), _1350316), _1350318)), -(_1350316 = c_Orderings_Obot__class_Obot(tc_fun(_1350314, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350314), _1350318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350314), c_Big__Operators_Olinorder__class_OMax(_1350314, _1350316)), c_Big__Operators_Olinorder__class_OMax(_1350314, _1350318))))], (11694 ^ _778495) ^ [_981461, _981463, _981465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981461), _981463)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981461), _981465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981463), _981465)))], (42812 ^ _778495) ^ [_1631548, _1631550] : [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(_1631548)), _1631550))), _1631550 = c_List_Olist_ONil(_1631548)], (21776 ^ _778495) ^ [_1168210, _1168212, _1168214] : [class_Groups_Oordered__ab__group__add(_1168210), 21779 ^ _778495 : [(21786 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168210), _1168214), _1168212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168210), hAPP(c_Groups_Ouminus__class_Ouminus(_1168210), _1168212)), hAPP(c_Groups_Ouminus__class_Ouminus(_1168210), _1168214))))], (21780 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168210), hAPP(c_Groups_Ouminus__class_Ouminus(_1168210), _1168212)), hAPP(c_Groups_Ouminus__class_Ouminus(_1168210), _1168214))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168210), _1168214), _1168212)))]]], (50408 ^ _778495) ^ [_1797799, _1797801, _1797803, _1797805, _1797807, _1797809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797799, tc_HOL_Obool)), _1797801), _1797803)), 50414 ^ _778495 : [(50417 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797805, tc_HOL_Obool)), hAPP(_1797807, 50413 ^ [_1797799, _1797801, _1797803, _1797805, _1797807, _1797809])), hAPP(_1797809, 50413 ^ [_1797799, _1797801, _1797803, _1797805, _1797807, _1797809])))], (50415 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797799), 50413 ^ [_1797799, _1797801, _1797803, _1797805, _1797807, _1797809]), _1797803)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797805, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797799, tc_fun(_1797805, tc_HOL_Obool)), _1797803), _1797807)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797799, tc_fun(_1797805, tc_HOL_Obool)), _1797803), _1797809))))], (42834 ^ _778495) ^ [_1632040, _1632042, _1632044] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632040), tc_List_Olist(_1632040))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632040), tc_List_Olist(_1632040)), c_List_Olist_ONil(_1632040)), _1632042)), c_List_Olex(_1632040, _1632044)))], (44893 ^ _778495) ^ [_1677805] : [-(_1677805 = 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, _1677805)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1677805))))], (33775 ^ _778495) ^ [_1407244, _1407246] : [33783 ^ _778495 : [(33786 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1407246, 33782 ^ [_1407244, _1407246])))], (33784 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 33782 ^ [_1407244, _1407246]), _1407244)))]], 33776 ^ _778495 : [(33777 ^ _778495) ^ [_1407312] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1407312), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407244))), hBOOL(hAPP(_1407246, _1407312))]]], (36186 ^ _778495) ^ [_1459456, _1459458, _1459460] : [-(c_Fun_Oinj__on(_1459456, _1459458, _1459460, c_Orderings_Obot__class_Obot(tc_fun(_1459456, tc_HOL_Obool))))], (31823 ^ _778495) ^ [_1361331, _1361333, _1361335, _1361337, _1361339, _1361341] : [class_Complete__Lattice_Ocomplete__lattice(_1361331), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361333, _1361331), _1361335), hAPP(hAPP(c_COMBB(tc_fun(_1361337, _1361331), _1361331, _1361333), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361337, _1361331), _1361339)), _1361341)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361337, _1361331), _1361339), hAPP(hAPP(c_COMBB(tc_fun(_1361333, _1361331), _1361331, _1361337), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361333, _1361331), _1361335)), hAPP(c_COMBC(_1361333, _1361337, _1361331), _1361341))))], (34249 ^ _778495) ^ [_1417164] : [-(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)), _1417164))))], (28255 ^ _778495) ^ [_1283159, _1283161, _1283163, _1283165] : [hBOOL(hAPP(hAPP(c_member(_1283159), _1283165), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283159, tc_HOL_Obool)), _1283161), _1283163))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283159, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1283159, tc_fun(_1283159, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283159)), _1283161)), hAPP(hAPP(c_COMBC(_1283159, tc_fun(_1283159, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283159)), _1283163)), _1283165)))], (52367 ^ _778495) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (52567 ^ _778495) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (5795 ^ _778495) ^ [_870428, _870430, _870432] : [-(hAPP(c_Finite__Set_Ofold1(_870428, _870430), hAPP(hAPP(c_Set_Oinsert(_870428), _870432), c_Orderings_Obot__class_Obot(tc_fun(_870428, tc_HOL_Obool)))) = _870432)], (43225 ^ _778495) ^ [_1640938, _1640940, _1640942] : [-(hAPP(hAPP(c_List_Oappend(_1640938), _1640940), _1640942) = c_List_Olist_ONil(_1640938)), _1640940 = c_List_Olist_ONil(_1640938), _1640942 = c_List_Olist_ONil(_1640938)], (8784 ^ _778495) ^ [_925744, _925746, _925748] : [class_Lattices_Olattice(_925744), hBOOL(hAPP(c_Finite__Set_Ofinite(_925744), _925746)), hBOOL(hAPP(hAPP(c_member(_925744), _925748), _925746)), 8795 ^ _778495 : [(8802 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925744, tc_HOL_Obool)), _925746), hAPP(hAPP(c_Set_Oinsert(_925744), _925748), c_Orderings_Obot__class_Obot(tc_fun(_925744, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_925744, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_925744, _925746) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925744), _925748), c_Big__Operators_Olattice__class_OSup__fin(_925744, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925744, tc_HOL_Obool)), _925746), hAPP(hAPP(c_Set_Oinsert(_925744), _925748), c_Orderings_Obot__class_Obot(tc_fun(_925744, tc_HOL_Obool)))))))], (8796 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925744, tc_HOL_Obool)), _925746), hAPP(hAPP(c_Set_Oinsert(_925744), _925748), c_Orderings_Obot__class_Obot(tc_fun(_925744, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_925744, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_925744, _925746) = _925748)]]], (26868 ^ _778495) ^ [_1258801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1258801)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1258801))))], (12166 ^ _778495) ^ [_991330, _991332, _991334, _991336] : [class_Rings_Ocomm__semiring__1(_991330), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991330), _991332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991330), _991334), _991336)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991330), _991332), _991334)), _991336))], (7686 ^ _778495) ^ [_905631, _905633, _905635, _905637, _905639, _905641] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_905631, _905633, _905635, _905637, _905639), _905641)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_905631), _905639)))], (8710 ^ _778495) ^ [_924258, _924260, _924262, _924264, _924266, _924268, _924270, _924272] : [c_Finite__Set_Ofolding__image__simple__idem(_924258, _924260, _924262, _924264, _924266, _924268), hBOOL(hAPP(c_Finite__Set_Ofinite(_924260), _924270)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_924260, tc_HOL_Obool)), _924272), _924270)), -(hAPP(hAPP(_924262, hAPP(_924268, _924272)), hAPP(_924268, _924270)) = hAPP(_924268, _924270))], (3336 ^ _778495) ^ [_828318, _828320, _828322, _828324] : [-(c_Enum_Osublists(_828324, _828320) = c_Enum_Osublists(_828322, _828318)), _828324 = _828322, _828320 = _828318], (21586 ^ _778495) ^ [] : [-(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)))], (20734 ^ _778495) ^ [_1150096, _1150098, _1150100] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150096))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150096)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150098)), _1150100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150098)), _1150100))], (33173 ^ _778495) ^ [_1391000, _1391002, _1391004, _1391006] : [-(_1391000 = c_Orderings_Obot__class_Obot(tc_fun(_1391002, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391002, tc_fun(_1391004, tc_HOL_Obool)), _1391000), hAPP(c_COMBK(tc_fun(_1391004, tc_HOL_Obool), _1391002), _1391006)) = _1391006)], (47829 ^ _778495) ^ [_1742286, _1742288] : [-(c_List_Olist__all(_1742286, _1742288, c_List_Olist_ONil(_1742286)))], (14564 ^ _778495) ^ [_1037233, _1037235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037233), hAPP(c_Nat_OSuc, _1037235))), -(_1037233 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14572 ^ _778495 : [(14575 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14571 ^ [_1037233, _1037235]), _1037235)))], (14573 ^ _778495) ^ [] : [-(_1037233 = hAPP(c_Nat_OSuc, 14571 ^ [_1037233, _1037235]))]]], (40505 ^ _778495) ^ [_1571573, _1571575, _1571577, _1571579] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571573, _1571573)), hAPP(hAPP(c_Product__Type_OPair(_1571573, _1571573), _1571575), _1571577)), c_Transitive__Closure_Ortrancl(_1571573, _1571579))), -(_1571575 = _1571577), 40512 ^ _778495 : [(40515 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571573, _1571573)), hAPP(hAPP(c_Product__Type_OPair(_1571573, _1571573), _1571575), _1571577)), c_Transitive__Closure_Otrancl(_1571573, _1571579))))], (40513 ^ _778495) ^ [] : [_1571575 = _1571577]]], (1958 ^ _778495) ^ [_805998, _806000] : [-(hBOOL(_805998)), _806000 = _805998, hBOOL(_806000)], (22140 ^ _778495) ^ [_1174525, _1174527, _1174529] : [class_Fields_Ofield__inverse__zero(_1174525), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174525), hAPP(c_Groups_Ouminus__class_Ouminus(_1174525), _1174527)), hAPP(c_Groups_Ouminus__class_Ouminus(_1174525), _1174529)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174525), _1174527), _1174529))], (1748 ^ _778495) ^ [_803373, _803375] : [-(class_Divides_Osemiring__div(_803373)), _803375 = _803373, class_Divides_Osemiring__div(_803375)], (51713 ^ _778495) ^ [_1822631, _1822633] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822631, _1822633), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822631), _1822633)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822633), _1822631)))], (19832 ^ _778495) ^ [_1134786, _1134788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134788)), -(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), _1134786), _1134788))))], (8580 ^ _778495) ^ [_921789] : [class_Lattices_Oab__semigroup__idem__mult(_921789), -(c_Finite__Set_Ofun__left__comm__idem(_921789, _921789, c_Groups_Otimes__class_Otimes(_921789)))], (28935 ^ _778495) ^ [_1303724, _1303726] : [28936 ^ _778495 : [(28939 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1303726), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (28937 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303724), _1303726))]], -(c_Divides_OposDivAlg(_1303724, _1303726) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303724))], (52479 ^ _778495) ^ [_1833650, _1833652] : [-(class_Finite__Set_Ofinite(tc_sum(_1833650, _1833652))), class_Finite__Set_Ofinite(_1833650), class_Finite__Set_Ofinite(_1833652)], (19978 ^ _778495) ^ [_1137360, _1137362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1137360), _1137362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137360)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137362))))], (18316 ^ _778495) ^ [_1106995, _1106997, _1106999, _1107001] : [class_Orderings_Olinorder(_1106995), hBOOL(hAPP(c_Finite__Set_Ofinite(_1106995), _1106997)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1106995, _1106995, c_Orderings_Oord__class_Omin(_1106995)), _1106999), hAPP(hAPP(c_Set_Oinsert(_1106995), _1107001), _1106997)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106995), _1107001), hAPP(hAPP(c_Finite__Set_Ofold(_1106995, _1106995, c_Orderings_Oord__class_Omin(_1106995)), _1106999), _1106997)))], (48772 ^ _778495) ^ [_1762984, _1762986, _1762988] : [-(c_List_Olist__ex(_1762984, _1762986, _1762988)), 48773 ^ _778495 : [(48774 ^ _778495) ^ [_1763041] : [hBOOL(hAPP(hAPP(c_member(_1762984), _1763041), hAPP(c_List_Oset(_1762984), _1762988))), hBOOL(hAPP(_1762986, _1763041))]]], (45502 ^ _778495) ^ [_1691571, _1691573] : [class_Orderings_Olinorder(_1691571), -(c_List_Olinorder__class_Osorted__list__of__set(_1691571, hAPP(c_List_Oset(_1691571), _1691573)) = c_List_Olinorder__class_Osort__key(_1691571, _1691571, c_COMBI(_1691571), c_List_Oremdups(_1691571, _1691573)))], (28745 ^ _778495) ^ [_1299761, _1299763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1299761)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1299763))), -(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(_1299763))), 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), _1299761)), c_Int_Onat))))))], (40110 ^ _778495) ^ [_1561226, _1561228, _1561230, _1561232, _1561234, _1561236, _1561238] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1561226, _1561228, _1561230, _1561232), _1561234), _1561236), _1561238) = hAPP(hAPP(_1561236, hAPP(c_Product__Type_Ofst(_1561228, _1561230), hAPP(_1561234, _1561238))), hAPP(c_Product__Type_Osnd(_1561228, _1561230), hAPP(_1561234, _1561238))))], (38546 ^ _778495) ^ [_1522890, _1522892, _1522894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522890, _1522890), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1522890, _1522890, _1522890), _1522892), _1522894)), _1522892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1522890, tc_HOL_Obool), tc_fun(_1522890, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1522890, tc_HOL_Obool), tc_fun(_1522890, tc_HOL_Obool), tc_fun(_1522890, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1522890, _1522892)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1522890, tc_HOL_Obool), tc_fun(_1522890, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1522890, _1522894)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1522890, tc_HOL_Obool), tc_fun(_1522890, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1522890, tc_HOL_Obool), tc_fun(_1522890, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1522890, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1522890, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1522890, tc_HOL_Obool), tc_fun(_1522890, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1522890, _1522892))))], (2998 ^ _778495) ^ [_823099, _823101, _823103, _823105] : [-(c_List_Olexn(_823105, _823101) = c_List_Olexn(_823103, _823099)), _823105 = _823103, _823101 = _823099], (42136 ^ _778495) ^ [_1617103, _1617105, _1617107] : [_1617103 = _1617105, 42139 ^ _778495 : [(42142 ^ _778495) ^ [_1617259] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617107, _1617107)), _1617259), hAPP(c_List_Oset(tc_prod(_1617107, _1617107)), hAPP(hAPP(c_List_Ozip(_1617107, _1617107), _1617103), _1617105)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1617107, _1617107, tc_HOL_Obool), c_fequal), _1617259)))], (42140 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617107)), _1617103) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617107)), _1617105))]]], (38381 ^ _778495) ^ [_1517838, _1517840, _1517842, _1517844] : [-(c_Product__Type_Oapfst(_1517838, _1517840, _1517842, _1517844) = c_Product__Type_Omap__pair(_1517838, _1517840, _1517842, _1517842, _1517844, c_Fun_Oid(_1517842)))], (52593 ^ _778495) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (39074 ^ _778495) ^ [_1536268, _1536270, _1536272] : [c_Wellfounded_OwfP(_1536268, _1536270), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1536268, _1536270), _1536272)))], (26324 ^ _778495) ^ [_1249234, _1249236, _1249238, _1249240] : [class_Rings_Olinordered__semidom(_1249234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249234), hAPP(hAPP(c_Power_Opower__class_Opower(_1249234), _1249236), hAPP(c_Nat_OSuc, _1249238))), hAPP(hAPP(c_Power_Opower__class_Opower(_1249234), _1249240), hAPP(c_Nat_OSuc, _1249238)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249234), c_Groups_Ozero__class_Ozero(_1249234)), _1249240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249234), _1249236), _1249240)))], (5260 ^ _778495) ^ [_858906, _858908, _858910, _858912, _858914, _858916] : [-(c_SetInterval_Oord_OatLeast(_858916, _858912, _858908) = c_SetInterval_Oord_OatLeast(_858914, _858910, _858906)), _858916 = _858914, _858912 = _858910, _858908 = _858906], (6022 ^ _778495) ^ [_874776, _874778, _874780] : [-(_874776 = _874778), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874780, tc_HOL_Obool)), _874776), _874778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874780, tc_HOL_Obool)), _874778), _874776))], (33034 ^ _778495) ^ [_1387903, _1387905, _1387907, _1387909] : [class_Orderings_Oorder(_1387903), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1387903, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1387903, _1387905, _1387907)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1387903, _1387907, _1387909)) = c_Orderings_Obot__class_Obot(tc_fun(_1387903, tc_HOL_Obool)))], (40774 ^ _778495) ^ [_1577789, _1577791, _1577793, _1577795, _1577797] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577791, _1577789)), hAPP(hAPP(c_Product__Type_OPair(_1577791, _1577789), _1577795), _1577793)), _1577797)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577789, _1577791)), hAPP(hAPP(c_Product__Type_OPair(_1577789, _1577791), _1577793), _1577795)), hAPP(c_Relation_Oconverse(_1577791, _1577789), _1577797))))], (32708 ^ _778495) ^ [_1381881, _1381883, _1381885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1381881)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1381883), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1381885)), 32718 ^ _778495 : [(32724 ^ _778495) ^ [] : [-(_1381883 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32720 ^ [_1381881, _1381883, _1381885]), 32717 ^ [_1381881, _1381883, _1381885]))], (32722 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32720 ^ [_1381881, _1381883, _1381885]), _1381885)))], (32719 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32717 ^ [_1381881, _1381883, _1381885]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1381881))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1381883), _1381881) = _1381883)], (13557 ^ _778495) ^ [_1019048, _1019050, _1019052, _1019054] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1019048), _1019050)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019052), _1019054)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1019048, _1019052)), c_Sum__Type_OPlus(_1019048, _1019052, _1019050, _1019054))))], (14271 ^ _778495) ^ [_1032019, _1032021, _1032023] : [class_Rings_Olinordered__semiring__strict(_1032019), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032019), _1032021), c_Groups_Ozero__class_Ozero(_1032019))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032019), c_Groups_Ozero__class_Ozero(_1032019)), _1032023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032019), _1032021), _1032023)), c_Groups_Ozero__class_Ozero(_1032019))))], (10425 ^ _778495) ^ [_958347, _958349, _958351] : [class_Lattices_Olattice(_958347), hBOOL(hAPP(c_Finite__Set_Ofinite(_958347), _958349)), hBOOL(hAPP(c_Finite__Set_Ofinite(_958347), _958351)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958347, tc_HOL_Obool)), _958349), _958351) = c_Orderings_Obot__class_Obot(tc_fun(_958347, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_958347), c_Big__Operators_Olattice__class_OInf__fin(_958347, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958347, tc_HOL_Obool)), _958349), _958351))), c_Big__Operators_Olattice__class_OInf__fin(_958347, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958347, tc_HOL_Obool)), _958349), _958351))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_958347), c_Big__Operators_Olattice__class_OInf__fin(_958347, _958349)), c_Big__Operators_Olattice__class_OInf__fin(_958347, _958351)))], (13066 ^ _778495) ^ [_1011494, _1011496, _1011498] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1011494), _1011496)), 13069 ^ _778495 : [(13070 ^ _778495) ^ [] : [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(_1011494, tc_Nat_Onat), _1011498), _1011496))), 13073 ^ _778495 : [(13074 ^ _778495) ^ [_1011662] : [hBOOL(hAPP(hAPP(c_member(_1011494), _1011662), _1011496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1011498, _1011662))))]]], (13080 ^ _778495) ^ [] : [13082 ^ _778495 : [(13085 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1011498, 13081 ^ [_1011494, _1011496, _1011498])))], (13083 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1011494), 13081 ^ [_1011494, _1011496, _1011498]), _1011496)))]], -(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(_1011494, tc_Nat_Onat), _1011498), _1011496))))]]], (20400 ^ _778495) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35320 ^ _778495) ^ [_1438253, _1438255, _1438257, _1438259] : [class_Orderings_Olinorder(_1438253), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438253, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1438253), _1438255)), c_SetInterval_Oord__class_OatLeastAtMost(_1438253, _1438257, _1438259)) = c_SetInterval_Oord__class_OatLeastAtMost(_1438253, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1438253), _1438255), _1438257), _1438259))], (42754 ^ _778495) ^ [_1630496, _1630498] : [_1630498 = c_List_Olist_ONil(_1630496), -(c_Orderings_Obot__class_Obot(tc_fun(_1630496, tc_HOL_Obool)) = hAPP(c_List_Oset(_1630496), _1630498))], (6926 ^ _778495) ^ [_892189, _892191, _892193, _892195] : [class_Lattices_Osemilattice__sup(_892189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892189), _892191), _892193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892189), _892195), _892193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892189), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892189), _892191), _892195)), _892193)))], (49889 ^ _778495) ^ [_1787277, _1787279, _1787281, _1787283, _1787285, _1787287] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1787277, _1787279, _1787281, _1787283), _1787285), _1787287) = hAPP(_1787283, hAPP(hAPP(c_Product__Type_OPair(_1787277, _1787279), _1787285), _1787287)))], (28315 ^ _778495) ^ [_1284944, _1284946, _1284948, _1284950] : [hAPP(hAPP(c_COMBC(_1284944, tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_fun(_1284946, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1284946, tc_fun(tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_fun(_1284946, tc_HOL_Obool)), _1284944), c_COMBC(_1284946, tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1284946, tc_prod(_1284944, _1284946)), tc_fun(_1284946, tc_fun(tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_HOL_Obool)), _1284944), hAPP(c_COMBB(tc_prod(_1284944, _1284946), tc_fun(tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_HOL_Obool), _1284946), c_member(tc_prod(_1284944, _1284946)))), c_Product__Type_OPair(_1284944, _1284946)))), _1284948) = hAPP(hAPP(c_COMBC(_1284944, tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_fun(_1284946, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1284946, tc_fun(tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_fun(_1284946, tc_HOL_Obool)), _1284944), c_COMBC(_1284946, tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1284946, tc_prod(_1284944, _1284946)), tc_fun(_1284946, tc_fun(tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_HOL_Obool)), _1284944), hAPP(c_COMBB(tc_prod(_1284944, _1284946), tc_fun(tc_fun(tc_prod(_1284944, _1284946), tc_HOL_Obool), tc_HOL_Obool), _1284946), c_member(tc_prod(_1284944, _1284946)))), c_Product__Type_OPair(_1284944, _1284946)))), _1284950), -(_1284948 = _1284950)], (52471 ^ _778495) ^ [_1833551] : [class_Lazy__Sequence_Osmall__lazy(_1833551), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1833551)))], (12787 ^ _778495) ^ [_1005391, _1005393, _1005395, _1005397, _1005399] : [class_Groups_Oab__group__add(_1005391), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005393), _1005395)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005393), _1005397)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1005393, _1005391), _1005399), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1005393, tc_HOL_Obool)), _1005395), _1005397)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1005391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1005391), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1005393, _1005391), _1005399), _1005395)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1005393, _1005391), _1005399), _1005397))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1005393, _1005391), _1005399), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1005393, tc_HOL_Obool)), _1005395), _1005397))))], (26282 ^ _778495) ^ [_1248344, _1248346, _1248348, _1248350] : [class_Groups_Omonoid__mult(_1248344), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1248344), _1248346), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1248348), _1248350)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248344), hAPP(hAPP(c_Power_Opower__class_Opower(_1248344), _1248346), _1248348)), hAPP(hAPP(c_Power_Opower__class_Opower(_1248344), _1248346), _1248350)))], (10549 ^ _778495) ^ [_960617, _960619] : [hAPP(c_Nat_OSuc, _960617) = hAPP(c_Nat_OSuc, _960619), -(_960617 = _960619)], (32038 ^ _778495) ^ [_1367720, _1367722, _1367724] : [class_Orderings_Oorder(_1367720), 32041 ^ _778495 : [(32048 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367720), _1367722), _1367724))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1367720, _1367722, _1367724) = c_Orderings_Obot__class_Obot(tc_fun(_1367720, tc_HOL_Obool)))], (32042 ^ _778495) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1367720, _1367722, _1367724) = c_Orderings_Obot__class_Obot(tc_fun(_1367720, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367720), _1367722), _1367724))]]], (41353 ^ _778495) ^ [_1592954, _1592956, _1592958] : 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hAPP(c_List_Oset(_1709896), _1709900))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709896), _1709898), _1710082)))], (46342 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709896, _1709900))]]]]], (27461 ^ _778495) ^ [_1268366, _1268368, _1268370] : [class_Lattices_Oboolean__algebra(_1268366), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1268366), _1268368), _1268370) = c_Orderings_Obot__class_Obot(_1268366), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268366), _1268368), _1268370) = c_Orderings_Otop__class_Otop(_1268366), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1268366), _1268368) = _1268370)], (28297 ^ _778495) ^ [_1284516, _1284518, _1284520, _1284522, _1284524] : [c_Finite__Set_Ofun__left__comm(_1284516, _1284518, _1284520), -(c_Finite__Set_Ofun__left__comm(_1284522, _1284518, hAPP(hAPP(c_COMBB(_1284516, tc_fun(_1284518, _1284518), _1284522), _1284520), _1284524)))], (11362 ^ _778495) ^ [_974615, _974617, _974619, _974621] : 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[(21366 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161064), _1161068), c_Groups_Ozero__class_Ozero(_1161064)))], (21364 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161064), c_Groups_Ozero__class_Ozero(_1161064)), _1161068))]]], (12154 ^ _778495) ^ [_991078, _991080, _991082] : [class_Rings_Ocomm__semiring__1(_991078), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991078), _991080), _991082) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991078), _991082), _991080))], (13404 ^ _778495) ^ [_1016648] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016648), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1016648)], (33932 ^ _778495) ^ [_1410303, _1410305, _1410307, _1410309] : [class_Orderings_Oorder(_1410303), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410303, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1410303, _1410305), _1410307)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1410303, _1410307), _1410309)) = c_Orderings_Obot__class_Obot(tc_fun(_1410303, tc_HOL_Obool)))], (19030 ^ _778495) ^ [_1120755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120755)), -(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)), _1120755))))], (3590 ^ _778495) ^ [_832303, _832305, _832307, _832309, _832311, _832313, _832315, _832317, _832319, _832321] : [-(c_List_Ofoldr(_832321, _832317, _832313, _832309, _832305) = c_List_Ofoldr(_832319, _832315, _832311, _832307, _832303)), _832321 = _832319, _832317 = _832315, _832313 = _832311, _832309 = _832307, _832305 = _832303], (21678 ^ _778495) ^ [_1166615, _1166617] : [class_Lattices_Oboolean__algebra(_1166615), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1166615), hAPP(c_Groups_Ouminus__class_Ouminus(_1166615), _1166617)) = _1166617)], (33788 ^ _778495) ^ [_1407496, _1407498] : [33790 ^ _778495 : [(33793 ^ _778495) ^ [] : [hBOOL(hAPP(_1407498, 33789 ^ [_1407496, _1407498]))], (33791 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 33789 ^ [_1407496, _1407498]), _1407496)))]], 33794 ^ _778495 : [(33795 ^ _778495) ^ [_1407646] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1407646), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407496))), -(hBOOL(hAPP(_1407498, _1407646)))]]], (40391 ^ _778495) ^ [_1568755, _1568757] : [-(c_Transitive__Closure_Ortrancl(_1568755, c_Transitive__Closure_Ortrancl(_1568755, _1568757)) = c_Transitive__Closure_Ortrancl(_1568755, _1568757))], (38901 ^ _778495) ^ [_1531836] : [class_Orderings_Owellorder(_1531836), -(c_Wellfounded_Owf(_1531836, hAPP(c_Set_OCollect(tc_prod(_1531836, _1531836)), hAPP(c_Product__Type_Oprod_Oprod__case(_1531836, _1531836, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1531836)))))], (45484 ^ _778495) ^ [_1691156, _1691158, _1691160] : [-(hBOOL(hAPP(hAPP(c_member(_1691156), _1691158), hAPP(c_List_Oset(_1691156), _1691160)))), -(c_List_Oremdups(_1691156, hAPP(hAPP(c_List_Olist_OCons(_1691156), _1691158), _1691160)) = hAPP(hAPP(c_List_Olist_OCons(_1691156), _1691158), c_List_Oremdups(_1691156, _1691160)))], (18928 ^ _778495) ^ [_1118752, _1118754, _1118756, _1118758, _1118760, _1118762] : [-(c_Nitpick_Opair__box_Opair__box__case(_1118752, _1118754, _1118756, _1118758, c_Nitpick_Opair__box_OPairBox(_1118752, _1118754, _1118760, _1118762)) = hAPP(hAPP(_1118758, _1118760), _1118762))], (22050 ^ _778495) ^ [_1172963, _1172965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1172963), _1172965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1172963)), c_Int_OBit0(_1172965))))], (34625 ^ _778495) ^ [_1426002, _1426004, _1426006] : [hAPP(c_Set_Oimage(_1426004, tc_fun(_1426004, tc_HOL_Obool), _1426002), _1426006) = hAPP(c_Set_OPow(_1426004), _1426006)], (51965 ^ _778495) ^ [_1827594, _1827596, _1827598] : [class_Rings_Ocomm__semiring__1(_1827594), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827594), _1827596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827594), _1827596), _1827598))))], (38673 ^ _778495) ^ [_1527268, _1527270] : [c_Wellfounded_Owf(_1527268, _1527270), -(c_Wellfounded_Owf(_1527268, hAPP(hAPP(c_Relation_Orel__comp(_1527268, _1527268, _1527268), _1527270), _1527270)))], (14223 ^ _778495) ^ [_1031128, _1031130, _1031132] : [class_Rings_Olinordered__semiring__strict(_1031128), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031128), c_Groups_Ozero__class_Ozero(_1031128)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031128), _1031130), _1031132))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031128), c_Groups_Ozero__class_Ozero(_1031128)), _1031130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031128), c_Groups_Ozero__class_Ozero(_1031128)), _1031132)))], (35288 ^ _778495) ^ [] : [-(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)))], (34967 ^ _778495) ^ [_1432524, _1432526] : [c_Nat__Transfer_Onat__set(_1432524), c_Nat__Transfer_Onat__set(_1432526), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1432524), _1432526) = 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), _1432524)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1432526))))], (16632 ^ _778495) ^ [_1075810, _1075812, _1075814, _1075816] : [class_Fields_Olinordered__field(_1075810), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075810), _1075812), _1075814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075810), _1075816), c_Groups_Ozero__class_Ozero(_1075810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075810), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1075810), _1075814), _1075816)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1075810), _1075812), _1075816))))], (45165 ^ _778495) ^ [_1684466, _1684468, _1684470] : [c_List_Olist__all2(_1684470, _1684470, c_fequal, _1684466, _1684468), -(_1684466 = _1684468)], (10113 ^ _778495) ^ [_952856, _952858, _952860, _952862, _952864, _952866] : [c_Finite__Set_Ofun__left__comm(_952856, _952858, _952860), -(hAPP(hAPP(_952860, _952862), hAPP(hAPP(_952860, _952864), _952866)) = hAPP(hAPP(_952860, _952864), hAPP(hAPP(_952860, _952862), _952866)))], (31764 ^ _778495) ^ [_1359726, _1359728, _1359730, _1359732] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1359726, tc_fun(_1359728, tc_HOL_Obool)), _1359730), _1359732) = c_Orderings_Otop__class_Otop(tc_fun(_1359728, tc_HOL_Obool)), 31767 ^ _778495 : [(31768 ^ _778495) ^ [_1359842] : [hBOOL(hAPP(hAPP(c_member(_1359726), _1359842), _1359730)), -(hAPP(_1359732, _1359842) = c_Orderings_Otop__class_Otop(tc_fun(_1359728, tc_HOL_Obool)))]]], (15247 ^ _778495) ^ [_1049316, _1049318, _1049320] : [class_Rings_Olinordered__idom(_1049316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049316), c_Groups_Ozero__class_Ozero(_1049316)), _1049318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049316), c_Groups_Ozero__class_Ozero(_1049316)), _1049320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049316), _1049320), c_Groups_Oone__class_Oone(_1049316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049316), _1049320), _1049318)), _1049318)))], (47237 ^ _778495) ^ [_1728709, _1728711, _1728713] : [-(c_List_Omaps(_1728709, _1728711, _1728713, c_List_Olist_ONil(_1728709)) = c_List_Olist_ONil(_1728711))], (37763 ^ _778495) ^ [_1496868, _1496870, _1496872, _1496874] : [-(hAPP(c_Set_OCollect(tc_prod(_1496868, _1496870)), hAPP(c_Product__Type_Oprod_Oprod__case(_1496868, _1496870, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1496868, tc_fun(_1496870, tc_HOL_Obool), tc_fun(_1496870, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1496870, tc_HOL_Obool), tc_fun(_1496870, tc_HOL_Obool)), _1496868), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1496870)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1496868), c_fconj), _1496872))), _1496874))) = hAPP(hAPP(c_Product__Type_OSigma(_1496868, _1496870), hAPP(c_Set_OCollect(_1496868), _1496872)), hAPP(c_COMBK(tc_fun(_1496870, tc_HOL_Obool), _1496868), hAPP(c_Set_OCollect(_1496870), _1496874))))], (49840 ^ _778495) ^ [_1786421, _1786423] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786421), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1786423, hAPP(c_Code__Numeral_Onat__of, 49845 ^ [_1786421, _1786423]))), -(hBOOL(hAPP(_1786423, _1786421)))], (6282 ^ _778495) ^ [_880143, _880145, _880147, _880149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880143, tc_HOL_Obool)), _880145), _880147)), hBOOL(hAPP(hAPP(c_member(_880143), _880149), _880145)), -(hBOOL(hAPP(hAPP(c_member(_880143), _880149), _880147)))], (30323 ^ _778495) ^ [_1330962, _1330964] : [class_Orderings_Oorder(_1330962), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330962, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1330962), _1330964), c_Orderings_Obot__class_Obot(tc_fun(_1330962, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1330962), _1330964)) = hAPP(hAPP(c_Set_Oinsert(_1330962), _1330964), c_Orderings_Obot__class_Obot(tc_fun(_1330962, tc_HOL_Obool))))], (27571 ^ _778495) ^ [_1270560, _1270562] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1270560, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1270560, tc_HOL_Obool))), _1270562) = _1270562)], (19432 ^ _778495) ^ [_1127495, _1127497, _1127499] : [class_Orderings_Olinorder(_1127495), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127495), _1127497)), -(c_Big__Operators_Olattice_OInf__fin(_1127495, c_Orderings_Oord__class_Omin(_1127495), hAPP(hAPP(c_Set_Oinsert(_1127495), _1127499), _1127497)) = hAPP(hAPP(c_Finite__Set_Ofold(_1127495, _1127495, c_Orderings_Oord__class_Omin(_1127495)), _1127499), _1127497))], (46708 ^ _778495) ^ [_1717578, _1717580] : [class_Groups_Ocomm__monoid__add(_1717578), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717578), hAPP(c_List_Orev(_1717578), _1717580)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1717578), _1717580))], (2148 ^ _778495) ^ [_809810, _809812, _809814, _809816, _809818, _809820, _809822, _809824] : [-(c_Sum__Type_OPlus(_809824, _809820, _809816, _809812) = c_Sum__Type_OPlus(_809822, _809818, _809814, _809810)), _809824 = _809822, _809820 = _809818, _809816 = _809814, _809812 = _809810], (30269 ^ _778495) ^ [_1329957, _1329959, _1329961] : [class_Orderings_Oord(_1329957), 30272 ^ _778495 : [(30279 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329957), _1329959), _1329961)), -(hBOOL(hAPP(hAPP(c_member(_1329957), _1329959), hAPP(c_SetInterval_Oord__class_OlessThan(_1329957), _1329961))))], (30273 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1329957), _1329959), hAPP(c_SetInterval_Oord__class_OlessThan(_1329957), _1329961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329957), _1329959), _1329961)))]]], (46039 ^ _778495) ^ [_1704604, _1704606, _1704608, _1704610] : [class_Groups_Ocomm__monoid__add(_1704604), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704604), _1704606), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704608, _1704610))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1704604), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704604), _1704606), c_List_Oupt(_1704608, _1704610))))], (26930 ^ _778495) ^ [_1259692, _1259694, _1259696] : [-(hAPP(c_Set_OPow(_1259692), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1259692, tc_HOL_Obool)), _1259694), _1259696)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1259692, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1259692), _1259694)), hAPP(c_Set_OPow(_1259692), _1259696)))], (22888 ^ _778495) ^ [_1187703] : [-(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, _1187703)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (94 ^ _778495) ^ [_780014, _780016, _780018, _780020, _780022, _780024, _780026, _780028, _780030, _780032, _780034, _780036] : [-(c_Finite__Set_Ofolding__image__simple__idem(_780034, _780030, _780026, _780022, _780018, _780014)), c_Finite__Set_Ofolding__image__simple__idem(_780036, _780032, _780028, _780024, _780020, _780016), _780036 = _780034, _780032 = _780030, _780028 = _780026, _780024 = _780022, _780020 = _780018, _780016 = _780014], (34367 ^ _778495) ^ [_1420131, _1420133, _1420135, _1420137, _1420139] : [hAPP(c_Set_Oimage(_1420131, _1420133, _1420135), _1420137) = _1420139, -(hAPP(c_Set_Oimage(tc_fun(_1420131, tc_HOL_Obool), tc_fun(_1420133, tc_HOL_Obool), c_Set_Oimage(_1420131, _1420133, _1420135)), hAPP(c_Set_OPow(_1420131), _1420137)) = hAPP(c_Set_OPow(_1420133), _1420139))], (12108 ^ _778495) ^ [_990250, _990252, _990254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990250), _990252)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990252), _990254)), _990250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990252), _990250)), _990254))], (27975 ^ _778495) ^ [_1277545] : [class_Complete__Lattice_Ocomplete__lattice(_1277545), -(c_Complete__Lattice_OInf__class_OInf(_1277545, c_Orderings_Obot__class_Obot(tc_fun(_1277545, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1277545))], (2580 ^ _778495) ^ [_816576, _816578] : [_816578 = _816576, -(c_Equiv__Relations_Oquotient(_816578) = c_Equiv__Relations_Oquotient(_816576))], (16618 ^ _778495) ^ [_1075541, _1075543, _1075545, _1075547] : [class_Fields_Olinordered__field__inverse__zero(_1075541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075541), _1075543), _1075545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075541), _1075547), c_Groups_Ozero__class_Ozero(_1075541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075541), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1075541), _1075545), _1075547)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1075541), _1075543), _1075547))))], (25654 ^ _778495) ^ [_1236829, _1236831] : [class_Rings_Oring__1(_1236829), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1236829), hAPP(c_Groups_Ouminus__class_Ouminus(_1236829), _1236831)), 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(_1236829), _1236831), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (40643 ^ _778495) ^ [_1574726, _1574728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1574726), _1574728)), -(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), _1574726), _1574728)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (47411 ^ _778495) ^ [_1733057, _1733059, _1733061, _1733063] : [47413 ^ _778495 : [(47416 ^ _778495) ^ [] : [hBOOL(hAPP(_1733061, 47412 ^ [_1733057, _1733059, _1733061, _1733063]))], (47414 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733057), 47412 ^ [_1733057, _1733059, _1733061, _1733063]), hAPP(c_List_Oset(_1733057), _1733059))))]], -(c_List_OdropWhile(_1733057, _1733061, hAPP(hAPP(c_List_Oappend(_1733057), _1733059), _1733063)) = c_List_OdropWhile(_1733057, _1733061, _1733063))], (10443 ^ _778495) ^ [_958695, _958697, _958699] : [class_Lattices_Olattice(_958695), hBOOL(hAPP(c_Finite__Set_Ofinite(_958695), _958697)), -(hBOOL(hAPP(hAPP(c_member(_958695), _958699), _958697))), -(c_Big__Operators_Olattice__class_OInf__fin(_958695, hAPP(hAPP(c_Set_Oinsert(_958695), _958699), _958697)) = hAPP(hAPP(c_Finite__Set_Ofold(_958695, _958695, c_Lattices_Osemilattice__inf__class_Oinf(_958695)), _958699), _958697))], (51427 ^ _778495) ^ [_1817648, _1817650, _1817652, _1817654] : [class_Divides_Osemiring__div(_1817648), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817648), _1817650), _1817652)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817648), _1817650), _1817654)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817648), _1817650), c_Divides_Odiv__class_Omod(_1817648, _1817652, _1817654))))], (47782 ^ _778495) ^ [_1741123, _1741125, _1741127] : [47783 ^ _778495 : [(47784 ^ _778495) ^ [_1741200, _1741202] : [_1741127 = hAPP(hAPP(c_List_Oappend(_1741123), _1741202), hAPP(hAPP(c_List_Olist_OCons(_1741123), _1741125), _1741200))]], -(hBOOL(hAPP(hAPP(c_member(_1741123), _1741125), hAPP(c_List_Oset(_1741123), _1741127))))], (39108 ^ _778495) ^ [_1537240, _1537242] : [c_Wellfounded_OwfP(_1537240, _1537242), -(c_Wellfounded_Oacyclic(_1537240, hAPP(c_Set_OCollect(tc_prod(_1537240, _1537240)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537240, _1537240, tc_HOL_Obool), _1537242))))], (48072 ^ _778495) ^ [_1747139, _1747141, _1747143, _1747145, _1747147] : [-(hAPP(c_New__DSequence_Opos__bind(_1747139, _1747141, _1747143, _1747145), _1747147) = hAPP(c_Lazy__Sequence_Obind(_1747139, _1747141, hAPP(_1747143, _1747147)), hAPP(hAPP(c_COMBC(_1747139, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1747141)), _1747145), _1747147)))], (190 ^ _778495) ^ [_781642, _781644, _781646, _781648, _781650, _781652, _781654, _781656, _781658, _781660] : [-(c_Big__Operators_Ocomm__monoid__big(_781658, _781654, _781650, _781646, _781642)), c_Big__Operators_Ocomm__monoid__big(_781660, _781656, _781652, _781648, _781644), _781660 = _781658, _781656 = _781654, _781652 = _781650, _781648 = _781646, _781644 = _781642], (41447 ^ _778495) ^ [_1596451, _1596453, _1596455] : [-(c_Random_Oselect__weight(_1596451, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1596451)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1596451), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1596453)), _1596455)) = c_Random_Oselect__weight(_1596451, _1596455))], (4172 ^ _778495) ^ [_841746, _841748] : [_841748 = _841746, -(c_List_Ohd(_841748) = c_List_Ohd(_841746))], (21120 ^ _778495) ^ [_1156881, _1156883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1156881)), c_Int_OBit1(_1156883))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1156881), _1156883)))], (52619 ^ _778495) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (44261 ^ _778495) ^ [_1663667, _1663669, _1663671, _1663673] : [hAPP(hAPP(c_List_Oappend(_1663667), _1663669), hAPP(hAPP(c_List_Olist_OCons(_1663667), _1663671), c_List_Olist_ONil(_1663667))) = _1663673, 44264 ^ _778495 : [(44269 ^ _778495) ^ [] : [-(c_List_Olast(_1663667, _1663673) = _1663671)], (44267 ^ _778495) ^ [] : [-(c_List_Obutlast(_1663667, _1663673) = _1663669)], (44265 ^ _778495) ^ [] : [_1663673 = c_List_Olist_ONil(_1663667)]]], (43361 ^ _778495) ^ [_1643983, _1643985, _1643987] : [-(hBOOL(hAPP(c_List_Odistinct(_1643983), hAPP(hAPP(c_List_Oappend(_1643983), _1643985), _1643987)))), hBOOL(hAPP(c_List_Odistinct(_1643983), _1643985)), hBOOL(hAPP(c_List_Odistinct(_1643983), _1643987)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643983, tc_HOL_Obool)), hAPP(c_List_Oset(_1643983), _1643985)), hAPP(c_List_Oset(_1643983), _1643987)) = c_Orderings_Obot__class_Obot(tc_fun(_1643983, tc_HOL_Obool))], (15213 ^ _778495) ^ [_1048654, _1048656, _1048658] : [class_Rings_Olinordered__ring(_1048654), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048654), c_Groups_Ozero__class_Ozero(_1048654)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048654), _1048656), _1048656)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048654), _1048658), _1048658)))))], (26942 ^ _778495) ^ [_1259940, _1259942] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1259940), hAPP(hAPP(c_Power_Opower__class_Opower(_1259940), hAPP(c_Int_Onumber__class_Onumber__of(_1259940), c_Int_OMin)), _1259942)) = c_Groups_Oone__class_Oone(_1259940)), class_Int_Onumber__ring(_1259940), class_Rings_Olinordered__idom(_1259940)], (48156 ^ _778495) ^ [_1749141, _1749143, _1749145] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749141, _1749141, hAPP(hAPP(c_COMBB(tc_fun(_1749141, tc_HOL_Obool), tc_fun(_1749141, tc_HOL_Obool), _1749141), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1749141), c_fNot)), c_fequal)), _1749143), _1749145)), _1749143 = _1749145], (34464 ^ _778495) ^ [_1422328, _1422330, _1422332, _1422334, _1422336] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1422328, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1422328, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1422330, _1422328, _1422332), _1422334)), hAPP(c_Set_Oimage(_1422330, _1422328, _1422332), _1422336))), hAPP(c_Set_Oimage(_1422330, _1422328, _1422332), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1422330, tc_HOL_Obool)), _1422334), _1422336)))))], (12178 ^ _778495) ^ [_991616, _991618, _991620, _991622] : [class_Rings_Ocomm__semiring__1(_991616), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991616), _991618), _991620)), _991622) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991616), _991618), _991622)), _991620))], (33200 ^ _778495) ^ [_1391606, _1391608, _1391610, _1391612] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1391606), _1391608)), 33203 ^ _778495 : [(33204 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1391610), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391606, tc_fun(_1391610, tc_HOL_Obool)), _1391608), _1391612))), 33207 ^ _778495 : [(33208 ^ _778495) ^ [_1391790] : [hBOOL(hAPP(hAPP(c_member(_1391606), _1391790), _1391608)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1391610), hAPP(_1391612, _1391790))))]]], (33214 ^ _778495) ^ [] : [33216 ^ _778495 : [(33219 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1391610), hAPP(_1391612, 33215 ^ [_1391606, _1391608, _1391610, _1391612])))], (33217 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391606), 33215 ^ [_1391606, _1391608, _1391610, _1391612]), _1391608)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1391610), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391606, tc_fun(_1391610, tc_HOL_Obool)), _1391608), _1391612))))]]], (30931 ^ _778495) ^ [_1343423, _1343425, _1343427, _1343429] : [class_Orderings_Olinorder(_1343423), 30934 ^ _778495 : [(30935 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343423), _1343425), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343423), _1343427), _1343429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343423), _1343425), _1343427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343423), _1343425), _1343429)))], (30945 ^ _778495) ^ [] : [30946 ^ _778495 : [(30949 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343423), _1343425), _1343429))], (30947 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343423), _1343425), _1343427))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343423), _1343425), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343423), _1343427), _1343429))))]]], (33565 ^ _778495) ^ [_1402779] : [-(hAPP(c_Int_Onat, _1402779) = 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, _1402779)), 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)))))))], (33497 ^ _778495) ^ [] : [-(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)))], (25582 ^ _778495) ^ [_1235622, _1235624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235622)), 25585 ^ _778495 : [(25592 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235622), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235624))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1235622)), _1235624)))], (25586 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1235622)), _1235624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235622), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235624))))]]], (7228 ^ _778495) ^ [_897816, _897818, _897820, _897822, _897824, _897826, _897828, _897830] : [c_Finite__Set_Ofolding__image__simple(_897816, _897818, _897820, _897822, _897824, _897826), hBOOL(hAPP(c_Finite__Set_Ofinite(_897818), _897828)), hBOOL(hAPP(hAPP(c_member(_897818), _897830), _897828)), -(hAPP(_897826, _897828) = hAPP(hAPP(_897820, hAPP(_897824, _897830)), hAPP(_897826, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897818, tc_HOL_Obool)), _897828), hAPP(hAPP(c_Set_Oinsert(_897818), _897830), c_Orderings_Obot__class_Obot(tc_fun(_897818, tc_HOL_Obool)))))))], (46198 ^ _778495) ^ [_1707492, _1707494, _1707496, _1707498] : [class_Orderings_Olinorder(_1707492), 46201 ^ _778495 : [(46210 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1707492, hAPP(hAPP(c_List_Olist_OCons(_1707492), _1707494), hAPP(hAPP(c_List_Olist_OCons(_1707492), _1707496), _1707498)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707492), _1707494), _1707496)), c_List_Olinorder__class_Osorted(_1707492, hAPP(hAPP(c_List_Olist_OCons(_1707492), _1707496), _1707498))], (46202 ^ _778495) ^ [] : [c_List_Olinorder__class_Osorted(_1707492, hAPP(hAPP(c_List_Olist_OCons(_1707492), _1707494), hAPP(hAPP(c_List_Olist_OCons(_1707492), _1707496), _1707498))), 46205 ^ _778495 : [(46208 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1707492, hAPP(hAPP(c_List_Olist_OCons(_1707492), _1707496), _1707498)))], (46206 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707492), _1707494), _1707496)))]]]]], (11688 ^ _778495) ^ [_981301, _981303] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _981301), hAPP(c_Nat_OSuc, _981303)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _981301), _981303)))], (36863 ^ _778495) ^ [_1473549, _1473551, _1473553, _1473555] : [c_Fun_Oinj__on(_1473549, _1473551, _1473553, c_Orderings_Otop__class_Otop(tc_fun(_1473549, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1473549, _1473551, c_Orderings_Otop__class_Otop(tc_fun(_1473549, tc_HOL_Obool)), _1473553), hAPP(_1473553, _1473555)) = _1473555)], (34747 ^ _778495) ^ [_1428286, _1428288, _1428290, _1428292, _1428294] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428286, tc_fun(_1428288, tc_HOL_Obool)), _1428290), hAPP(hAPP(c_COMBS(_1428286, tc_fun(_1428288, tc_HOL_Obool), tc_fun(_1428288, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428288, tc_HOL_Obool), tc_fun(tc_fun(_1428288, tc_HOL_Obool), tc_fun(_1428288, tc_HOL_Obool)), _1428286), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1428288, tc_HOL_Obool))), _1428292)), _1428294)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1428288, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1428288, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428286, tc_fun(_1428288, tc_HOL_Obool), _1428292), _1428290))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1428288, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428286, tc_fun(_1428288, tc_HOL_Obool), _1428294), _1428290))))], (42469 ^ _778495) ^ [_1624822, _1624824, _1624826] : [hBOOL(hAPP(c_List_Odistinct(_1624822), hAPP(hAPP(c_List_Olist_OCons(_1624822), _1624824), _1624826))), 42472 ^ _778495 : [(42475 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1624822), _1624826)))], (42473 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1624822), _1624824), hAPP(c_List_Oset(_1624822), _1624826)))]]], (23973 ^ _778495) ^ [_1207564, _1207566] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207564, _1207566) = 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), _1207564), _1207566) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1207566), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207564, _1207566)))], (12801 ^ _778495) ^ [_1005767, _1005769, _1005771, _1005773] : [hBOOL(hAPP(hAPP(c_member(_1005767), _1005769), _1005771)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1005767, tc_Nat_Onat), _1005773), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005767, tc_HOL_Obool)), _1005771), hAPP(hAPP(c_Set_Oinsert(_1005767), _1005769), c_Orderings_Obot__class_Obot(tc_fun(_1005767, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1005767, tc_Nat_Onat), _1005773), _1005771)), hAPP(_1005773, _1005769)))], (2370 ^ _778495) ^ [_813265, _813267, _813269, _813271, _813273, _813275, _813277, _813279, _813281, _813283] : [-(c_Product__Type_Oprod_Oprod__size(_813283, _813279, _813275, _813271, _813267) = c_Product__Type_Oprod_Oprod__size(_813281, _813277, _813273, _813269, _813265)), _813283 = _813281, _813279 = _813277, _813275 = _813273, _813271 = _813269, _813267 = _813265], (40185 ^ _778495) ^ [_1563169, _1563171] : [c_Wellfounded_Owf(_1563169, _1563171), -(c_Wellfounded_Owf(_1563169, c_Transitive__Closure_Otrancl(_1563169, _1563171)))], (42289 ^ _778495) ^ [_1620707, _1620709, _1620711, _1620713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620707)), _1620709)), _1620711)), -(hAPP(hAPP(c_List_Olist__update(_1620707, _1620709), _1620711), _1620713) = _1620709)], (314 ^ _778495) ^ [_783348, _783350, _783352, _783354, _783356, _783358] : [-(c_Finite__Set_Ofolding__one__idem(_783356, _783352, _783348)), c_Finite__Set_Ofolding__one__idem(_783358, _783354, _783350), _783358 = _783356, _783354 = _783352, _783350 = _783348], (34418 ^ _778495) ^ [_1421318, _1421320, _1421322, _1421324] : [_1421324 = c_Orderings_Obot__class_Obot(tc_fun(_1421320, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1421318, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1421320, _1421318, _1421322), _1421324))], (34695 ^ _778495) ^ [_1427267, _1427269, _1427271, _1427273] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1427267, tc_HOL_Obool), hAPP(c_Set_Oimage(_1427269, tc_fun(_1427267, tc_HOL_Obool), _1427271), _1427273)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427269, tc_fun(_1427267, tc_HOL_Obool)), _1427273), _1427271))], (39943 ^ _778495) ^ [_1557047, _1557049, _1557051] : [-(c_Hilbert__Choice_OEps(tc_prod(_1557047, _1557049), _1557051) = c_Hilbert__Choice_OEps(tc_prod(_1557047, _1557049), hAPP(c_Product__Type_Oprod_Oprod__case(_1557047, _1557049, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1557049, tc_prod(_1557047, _1557049)), tc_fun(_1557049, tc_HOL_Obool), _1557047), hAPP(c_COMBB(tc_prod(_1557047, _1557049), tc_HOL_Obool, _1557049), _1557051)), c_Product__Type_OPair(_1557047, _1557049)))))], (43776 ^ _778495) ^ [_1654085, _1654087, _1654089] : [-(hAPP(c_List_Otl(_1654085), hAPP(hAPP(c_List_Olist_OCons(_1654085), _1654087), _1654089)) = _1654089)], (37464 ^ _778495) ^ [_1488456, _1488458, _1488460, _1488462] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1488456, _1488458)), hAPP(hAPP(c_Product__Type_OSigma(_1488456, _1488458), hAPP(hAPP(c_Set_Oinsert(_1488456), _1488460), c_Orderings_Obot__class_Obot(tc_fun(_1488456, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1488458, tc_HOL_Obool), _1488456), _1488462))) = hAPP(c_Finite__Set_Ocard(_1488458), _1488462))], (12813 ^ _778495) ^ [_1006049, _1006051, _1006053, _1006055] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1006049), _1006051)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006049), _1006053)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1006049, tc_Nat_Onat), _1006055), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006049, tc_HOL_Obool)), _1006051), _1006053)) = 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(_1006049, tc_Nat_Onat), _1006055), _1006051)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1006049, tc_Nat_Onat), _1006055), _1006053))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1006049, tc_Nat_Onat), _1006055), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006049, tc_HOL_Obool)), _1006051), _1006053))))], (50599 ^ _778495) ^ [_1803510, _1803512] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803510), _1803512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1803512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1803510), _1803512)))], (24794 ^ _778495) ^ [_1222227, _1222229] : [24795 ^ _778495 : [(24796 ^ _778495) ^ [_1222276] : [_1222227 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1222229), _1222276)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1222227, _1222229) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49594 ^ _778495) ^ [_1780460, _1780462, _1780464] : [c_Fun_Oinj__on(_1780460, _1780462, _1780464, c_Orderings_Otop__class_Otop(tc_fun(_1780460, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780462, _1780460, _1780460, c_Hilbert__Choice_Oinv__into(_1780460, _1780462, c_Orderings_Otop__class_Otop(tc_fun(_1780460, tc_HOL_Obool)), _1780464)), _1780464) = c_Fun_Oid(_1780460))], (34861 ^ _778495) ^ [_1430697, _1430699, _1430701, _1430703, _1430705, _1430707] : [-(hBOOL(hAPP(hAPP(c_member(_1430697), _1430699), _1430701))), -(hAPP(c_Set_Oimage(_1430697, _1430703, c_Fun_Ofun__upd(_1430697, _1430703, _1430705, _1430699, _1430707)), _1430701) = hAPP(c_Set_Oimage(_1430697, _1430703, _1430705), _1430701))], (29035 ^ _778495) ^ [_1305613, _1305615, _1305617, _1305619, _1305621, _1305623] : [hBOOL(hAPP(hAPP(_1305613, _1305615), _1305617)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305619, tc_fun(_1305621, tc_HOL_Obool))), _1305623), _1305613), _1305615), _1305617)))], (2924 ^ _778495) ^ [_821904, _821906] : [_821906 = _821904, -(c_Nitpick_Odenom(_821906) = c_Nitpick_Odenom(_821904))], (21684 ^ _778495) ^ [_1166710, _1166712, _1166714, _1166716] : [class_Groups_Ouminus(_1166710), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1166712, _1166710)), _1166714), _1166716) = hAPP(c_Groups_Ouminus__class_Ouminus(_1166710), hAPP(_1166714, _1166716)))], (37456 ^ _778495) ^ [_1488251, _1488253, _1488255, _1488257, _1488259, _1488261] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1488251, _1488253)), hAPP(hAPP(c_Product__Type_OPair(_1488251, _1488253), _1488255), _1488257)), hAPP(hAPP(c_Product__Type_OSigma(_1488251, _1488253), _1488259), _1488261))), 37459 ^ _778495 : [(37462 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488253), _1488257), hAPP(_1488261, _1488255))))], (37460 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488251), _1488255), _1488259)))]]], (22524 ^ _778495) ^ [_1181189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181189), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1181189)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12022 ^ _778495) ^ [_988547, _988549, _988551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988547), _988549)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988551), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988549), _988547)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988551), _988547)), _988549))], (17354 ^ _778495) ^ [_1088846, _1088848, _1088850] : [class_Fields_Olinordered__field(_1088846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088846), _1088848), _1088850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088846), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1088846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088846), _1088848), _1088850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088846), c_Groups_Oone__class_Oone(_1088846)), c_Groups_Oone__class_Oone(_1088846)))), _1088850)))], (50150 ^ _778495) ^ [_1792579, _1792581, _1792583, _1792585] : [c_Fun_Obij__betw(_1792579, _1792581, _1792583, c_Orderings_Otop__class_Otop(tc_fun(_1792579, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792581, tc_HOL_Obool))), 50153 ^ _778495 : [(50160 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792581), _1792585)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1792579), hAPP(c_Set_Ovimage(_1792579, _1792581, _1792583), _1792585))))], (50154 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792579), hAPP(c_Set_Ovimage(_1792579, _1792581, _1792583), _1792585))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1792581), _1792585)))]]], (37829 ^ _778495) ^ [_1498331, _1498333, _1498335] : [hBOOL(hAPP(hAPP(c_member(_1498331), _1498333), hAPP(c_Set_OCollect(_1498331), _1498335))), -(hBOOL(hAPP(_1498335, _1498333)))], (5088 ^ _778495) ^ [_856188, _856190, _856192, _856194] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856194, _856190) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856192, _856188)), _856194 = _856192, _856190 = _856188], (37857 ^ _778495) ^ [_1498927, _1498929, _1498931] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1498927, tc_HOL_Obool)), _1498929), _1498931) = hAPP(c_Set_OCollect(_1498927), hAPP(hAPP(c_COMBS(_1498927, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498927), c_fdisj), hAPP(hAPP(c_COMBC(_1498927, tc_fun(_1498927, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498927)), _1498929))), hAPP(hAPP(c_COMBC(_1498927, tc_fun(_1498927, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498927)), _1498931))))], (43971 ^ _778495) ^ [_1658101, _1658103, _1658105] : [class_Orderings_Olinorder(_1658101), -(c_Big__Operators_Olinorder__class_OMax(_1658101, hAPP(c_List_Oset(_1658101), hAPP(hAPP(c_List_Olist_OCons(_1658101), _1658103), _1658105))) = hAPP(c_List_Ofoldl(_1658101, _1658101, c_Orderings_Oord__class_Omax(_1658101), _1658103), _1658105))], (38441 ^ _778495) ^ [_1519681, _1519683, _1519685, _1519687, _1519689, _1519691, _1519693] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1519681, _1519683, _1519685), _1519687), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519689, tc_fun(tc_prod(_1519683, _1519685), tc_HOL_Obool)), _1519691), _1519693)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519689, tc_fun(tc_prod(_1519681, _1519685), tc_HOL_Obool)), _1519691), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1519683, _1519685), tc_HOL_Obool), tc_fun(tc_prod(_1519681, _1519685), tc_HOL_Obool), _1519689), hAPP(c_Relation_Orel__comp(_1519681, _1519683, _1519685), _1519687)), _1519693)))], (13001 ^ _778495) ^ [_1010414, _1010416] : [class_Groups_Ozero(_1010414), 13004 ^ _778495 : [(13011 ^ _778495) ^ [] : [_1010416 = c_Groups_Ozero__class_Ozero(_1010414), -(c_Groups_Ozero__class_Ozero(_1010414) = _1010416)], (13005 ^ _778495) ^ [] : [c_Groups_Ozero__class_Ozero(_1010414) = _1010416, -(_1010416 = c_Groups_Ozero__class_Ozero(_1010414))]]], (21980 ^ _778495) ^ [_1171655, _1171657, _1171659] : [class_Groups_Ogroup__add(_1171655), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171655), _1171657), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171655), hAPP(c_Groups_Ouminus__class_Ouminus(_1171655), _1171657)), _1171659)) = _1171659)], (52217 ^ _778495) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (19658 ^ _778495) ^ [_1131621, _1131623, _1131625] : [class_Orderings_Olinorder(_1131621), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131621), _1131623)), -(_1131623 = c_Orderings_Obot__class_Obot(tc_fun(_1131621, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131621), _1131625)), -(_1131625 = c_Orderings_Obot__class_Obot(tc_fun(_1131621, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1131621, tc_HOL_Obool)), _1131623), _1131625) = c_Orderings_Obot__class_Obot(tc_fun(_1131621, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1131621, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1131621, tc_HOL_Obool)), _1131623), _1131625)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1131621), c_Big__Operators_Olinorder__class_OMin(_1131621, _1131623)), c_Big__Operators_Olinorder__class_OMin(_1131621, _1131625)))], (47266 ^ _778495) ^ [_1729522, _1729524, _1729526, _1729528, _1729530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1729522, _1729524)), hAPP(_1729522, _1729526))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1729528, _1729528)), hAPP(hAPP(c_Product__Type_OPair(_1729528, _1729528), _1729524), _1729526)), c_List_Omeasures(_1729528, _1729530))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729528, _1729528)), hAPP(hAPP(c_Product__Type_OPair(_1729528, _1729528), _1729524), _1729526)), c_List_Omeasures(_1729528, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729528, tc_Nat_Onat)), _1729522), _1729530)))))], (29121 ^ _778495) ^ [_1307341, _1307343] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1307341, _1307343) = 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), _1307341), _1307343)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1307341, _1307343)))], (11240 ^ _778495) ^ [_972378, _972380] : [class_Complete__Lattice_Ocomplete__lattice(_972378), hBOOL(hAPP(c_Finite__Set_Ofinite(_972378), _972380)), -(c_Complete__Lattice_OSup__class_OSup(_972378, _972380) = hAPP(hAPP(c_Finite__Set_Ofold(_972378, _972378, c_Lattices_Osemilattice__sup__class_Osup(_972378)), c_Orderings_Obot__class_Obot(_972378)), _972380))], (6386 ^ _778495) ^ [_881941, _881943, _881945, _881947] : [class_Orderings_Oord(_881941), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881941), _881943), _881945)), _881945 = _881947, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881941), _881943), _881947)))], (33944 ^ _778495) ^ [_1410538] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1410538)) = hAPP(c_Nat_OSuc, _1410538))], (1558 ^ _778495) ^ [_800998, _801000] : [-(class_Rings_Olinordered__comm__semiring__strict(_800998)), _801000 = _800998, class_Rings_Olinordered__comm__semiring__strict(_801000)], (42652 ^ _778495) ^ [_1628798, _1628800, _1628802] : [-(_1628798 = c_List_Olist_ONil(_1628800)), -(c_List_Obutlast(_1628800, hAPP(hAPP(c_List_Olist_OCons(_1628800), _1628802), _1628798)) = hAPP(hAPP(c_List_Olist_OCons(_1628800), _1628802), c_List_Obutlast(_1628800, _1628798)))], (46676 ^ _778495) ^ [_1716998, _1717000, _1717002, _1717004, _1717006] : [c_List_Olist__all2(_1716998, _1717000, _1717002, _1717004, _1717006), -(c_List_Olist__all2(_1716998, _1717000, _1717002, hAPP(c_List_Orev(_1716998), _1717004), hAPP(c_List_Orev(_1717000), _1717006)))], (20452 ^ _778495) ^ [_1145601] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1145601))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145601)))], (26792 ^ _778495) ^ [_1257511, _1257513] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1257511, tc_HOL_Obool)), hAPP(c_Set_OPow(_1257511), _1257513))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1257511), _1257513)))], (27517 ^ _778495) ^ [_1269538] : [-(hAPP(c_Set_OPow(_1269538), c_Orderings_Otop__class_Otop(tc_fun(_1269538, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1269538, tc_HOL_Obool), tc_HOL_Obool)))], (52613 ^ _778495) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (52589 ^ _778495) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (714 ^ _778495) ^ [_789316, _789318, _789320, _789322, _789324, _789326] : [-(c_List_Olist__ex1(_789324, _789320, _789316)), c_List_Olist__ex1(_789326, _789322, _789318), _789326 = _789324, _789322 = _789320, _789318 = _789316], (11089 ^ _778495) ^ [_969354, _969356] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _969354), _969356)), _969354)))], (22796 ^ _778495) ^ [_1186012, _1186014] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1186012)), _1186014) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186012), _1186014))), _1186014))], (23811 ^ _778495) ^ [_1204877, _1204879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204877)), 23814 ^ _778495 : [(23821 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204877), _1204879)), -(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), _1204879), _1204877))))], (23815 ^ _778495) ^ [] : [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), _1204879), _1204877))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204877), _1204879)))]]], (1638 ^ _778495) ^ [_801998, _802000] : [-(class_Groups_Ocancel__semigroup__add(_801998)), _802000 = _801998, class_Groups_Ocancel__semigroup__add(_802000)], (32948 ^ _778495) ^ [_1386391, _1386393, _1386395] : [class_Orderings_Oorder(_1386391), 32951 ^ _778495 : [(32958 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386391), _1386393), _1386395))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1386391, _1386393, _1386395) = c_Orderings_Obot__class_Obot(tc_fun(_1386391, tc_HOL_Obool)))], (32952 ^ _778495) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1386391, _1386393, _1386395) = c_Orderings_Obot__class_Obot(tc_fun(_1386391, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386391), _1386393), _1386395))]]], (40718 ^ _778495) ^ [_1576368, _1576370] : [-(hAPP(c_Relation_OField(_1576368), hAPP(c_Relation_Oconverse(_1576368, _1576368), _1576370)) = hAPP(c_Relation_OField(_1576368), _1576370))], (51301 ^ _778495) ^ [_1815513, _1815515] : [-(_1815513 = _1815515), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815513), _1815515)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815515), _1815513))], (31628 ^ _778495) ^ [_1356487, _1356489, _1356491, _1356493, _1356495, _1356497] : [-(hAPP(c_Product__Type_Oapfst(_1356487, _1356489, _1356491, _1356493), hAPP(hAPP(c_Product__Type_OPair(_1356487, _1356491), _1356495), _1356497)) = hAPP(hAPP(c_Product__Type_OPair(_1356489, _1356491), hAPP(_1356493, _1356495)), _1356497))], (52077 ^ _778495) ^ [_1829527, _1829529] : [class_Lattices_Obounded__lattice(_1829527), -(class_Lattices_Obounded__lattice(tc_fun(_1829529, _1829527)))], (23106 ^ _778495) ^ [_1191943, _1191945, _1191947, _1191949] : [class_Divides_Osemiring__div(_1191943), -(c_Divides_Odiv__class_Omod(_1191943, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191943), _1191945), _1191947), _1191949) = c_Divides_Odiv__class_Omod(_1191943, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191943), c_Divides_Odiv__class_Omod(_1191943, _1191945, _1191949)), _1191947), _1191949))], (27943 ^ _778495) ^ [_1276978, _1276980, _1276982] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1276978, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1276978, tc_HOL_Obool)), _1276980), _1276982)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1276978, tc_HOL_Obool)), _1276980), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1276978, tc_HOL_Obool), _1276982)))], (25716 ^ _778495) ^ [_1238022, _1238024] : [class_Rings_Olinordered__idom(_1238022), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238022), c_Groups_Ozero__class_Ozero(_1238022)), hAPP(hAPP(c_Power_Opower__class_Opower(_1238022), _1238024), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (40351 ^ _778495) ^ [_1567768, _1567770] : [-(c_Transitive__Closure_Ortrancl(_1567768, c_Transitive__Closure_Otrancl(_1567768, _1567770)) = c_Transitive__Closure_Ortrancl(_1567768, _1567770))], (10705 ^ _778495) ^ [_963001, _963003] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _963001), _963003)), _963001 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _963003 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (7870 ^ _778495) ^ [_908345, _908347, _908349] : [class_Orderings_Olinorder(_908345), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908345), _908347), _908349))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908345), _908349), _908347)))], (28679 ^ _778495) ^ [_1298209, _1298211, _1298213] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1298209), _1298211)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1298209, tc_HOL_Obool)), _1298213), _1298211) = hAPP(hAPP(c_Finite__Set_Ofold(_1298209, tc_fun(_1298209, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1298209, tc_HOL_Obool), tc_fun(tc_fun(_1298209, tc_HOL_Obool), tc_fun(_1298209, tc_HOL_Obool)), _1298209), hAPP(c_COMBC(tc_fun(_1298209, tc_HOL_Obool), tc_fun(_1298209, tc_HOL_Obool), tc_fun(_1298209, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1298209, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1298209, tc_fun(_1298209, tc_HOL_Obool), tc_fun(_1298209, tc_HOL_Obool)), c_Set_Oinsert(_1298209)), c_Orderings_Obot__class_Obot(tc_fun(_1298209, tc_HOL_Obool))))), _1298213), _1298211))], (45652 ^ _778495) ^ [_1695347, _1695349, _1695351, _1695353] : [-(c_List_Otranspose(_1695347, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695347)), hAPP(hAPP(c_List_Olist_OCons(_1695347), _1695349), _1695351)), _1695353)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695347)), hAPP(hAPP(c_List_Olist_OCons(_1695347), _1695349), c_List_Oconcat(_1695347, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695347), tc_List_Olist(_1695347)), c_List_Olist_Olist__case(tc_List_Olist(_1695347), _1695347, c_List_Olist_ONil(_1695347), hAPP(hAPP(c_COMBB(tc_List_Olist(_1695347), tc_fun(tc_List_Olist(_1695347), tc_List_Olist(_1695347)), _1695347), c_COMBK(tc_List_Olist(_1695347), tc_List_Olist(_1695347))), hAPP(hAPP(c_COMBC(_1695347, tc_List_Olist(_1695347), tc_List_Olist(_1695347)), c_List_Olist_OCons(_1695347)), c_List_Olist_ONil(_1695347))))), _1695353)))), c_List_Otranspose(_1695347, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695347)), _1695351), c_List_Oconcat(tc_List_Olist(_1695347), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695347), tc_List_Olist(tc_List_Olist(_1695347))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1695347)), _1695347, c_List_Olist_ONil(tc_List_Olist(_1695347)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1695347), tc_List_Olist(tc_List_Olist(_1695347))), _1695347), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695347), tc_List_Olist(tc_List_Olist(_1695347)), tc_List_Olist(tc_List_Olist(_1695347))), c_List_Olist_OCons(tc_List_Olist(_1695347))), c_List_Olist_ONil(tc_List_Olist(_1695347)))))), _1695353))))))], (34789 ^ _778495) ^ [] : [-(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))))], (39029 ^ _778495) ^ [_1535200, _1535202, _1535204, _1535206] : [39031 ^ _778495 : [(39034 ^ _778495) ^ [] : [c_Wellfounded_Owf(_1535202, hAPP(_1535204, 39030 ^ [_1535200, _1535202, _1535204, _1535206]))], (39032 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1535200, 39030 ^ [_1535200, _1535202, _1535204, _1535206])))]], -(c_Wellfounded_Owf(tc_prod(_1535206, _1535202), c_Recdef_Osame__fst(_1535206, _1535202, _1535200, _1535204)))], (37771 ^ _778495) ^ [_1497137, _1497139, _1497141] : [-(hAPP(c_Set_OCollect(_1497137), hAPP(hAPP(c_COMBS(_1497137, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497137), c_fdisj), _1497139)), _1497141)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1497137, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1497137), _1497139)), hAPP(c_Set_OCollect(_1497137), _1497141)))], (4692 ^ _778495) ^ [_849930, _849932, _849934, _849936] : [-(c_Complete__Lattice_OSup__class_OSup(_849936, _849932) = c_Complete__Lattice_OSup__class_OSup(_849934, _849930)), _849936 = _849934, _849932 = _849930], (34791 ^ _778495) ^ [] : [-(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))))], (41973 ^ _778495) ^ [_1611670, _1611672, _1611674, _1611676] : [-(hBOOL(hAPP(hAPP(c_member(_1611670), _1611672), hAPP(c_List_Oset(_1611670), _1611674)))), hBOOL(hAPP(hAPP(c_member(_1611670), _1611672), hAPP(c_List_Oset(_1611670), c_List_Osublist(_1611670, _1611674, _1611676))))], (36658 ^ _778495) ^ [_1468779, _1468781, _1468783] : [hBOOL(hAPP(hAPP(c_member(_1468779), _1468781), c_Wellfounded_Oacc(_1468779, _1468783))), 36661 ^ _778495 : [(36662 ^ _778495) ^ [_1468893] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1468779, _1468779)), hAPP(hAPP(c_Product__Type_OPair(_1468779, _1468779), _1468893), _1468781)), _1468783)), -(hBOOL(hAPP(hAPP(c_member(_1468779), _1468893), c_Wellfounded_Oacc(_1468779, _1468783))))]]], (43554 ^ _778495) ^ [_1649079, _1649081] : [_1649081 = c_List_Olist_ONil(_1649079), -(hAPP(c_List_Orotate1(_1649079), _1649081) = c_List_Olist_ONil(_1649079))], (34867 ^ _778495) ^ [_1430770, _1430772, _1430774] : [class_Orderings_Olinorder(_1430770), hAPP(_1430772, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1430770), 34872 ^ [_1430770, _1430772, _1430774]), 34873 ^ [_1430770, _1430772, _1430774])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1430770), hAPP(_1430772, 34872 ^ [_1430770, _1430772, _1430774])), hAPP(_1430772, 34873 ^ [_1430770, _1430772, _1430774])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430770), _1430774)), -(_1430774 = c_Orderings_Obot__class_Obot(tc_fun(_1430770, tc_HOL_Obool))), -(hAPP(_1430772, c_Big__Operators_Olattice_OSup__fin(_1430770, c_Orderings_Oord__class_Omax(_1430770), _1430774)) = c_Big__Operators_Olattice_OSup__fin(_1430770, c_Orderings_Oord__class_Omax(_1430770), hAPP(c_Set_Oimage(_1430770, _1430770, _1430772), _1430774)))], (12040 ^ _778495) ^ [_988946, _988948, _988950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988946), _988948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988950), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988948), _988950)), _988946))))], (42704 ^ _778495) ^ [_1629617, _1629619] : [-(c_List_Oremove1(_1629617, _1629619, c_List_Olist_ONil(_1629617)) = c_List_Olist_ONil(_1629617))], (42658 ^ _778495) ^ [_1628877, _1628879, _1628881, _1628883] : [_1628877 = _1628879, -(c_List_Oremove1(_1628881, _1628877, hAPP(hAPP(c_List_Olist_OCons(_1628881), _1628879), _1628883)) = _1628883)], (31978 ^ _778495) ^ [_1366462, _1366464, _1366466] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1366462, tc_fun(_1366464, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1366462, tc_HOL_Obool))), _1366466) = c_Orderings_Otop__class_Otop(tc_fun(_1366464, tc_HOL_Obool)))], (30405 ^ _778495) ^ [_1332863] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1332863) = _1332863)], (37292 ^ _778495) ^ [_1483407, _1483409, _1483411, _1483413, _1483415, _1483417] : [-(hAPP(c_Set_Oimage(_1483407, tc_prod(_1483409, _1483411), hAPP(hAPP(c_COMBS(_1483407, _1483411, tc_prod(_1483409, _1483411)), hAPP(hAPP(c_COMBB(_1483409, tc_fun(_1483411, tc_prod(_1483409, _1483411)), _1483407), c_Product__Type_OPair(_1483409, _1483411)), _1483413)), _1483415)), _1483417) = hAPP(hAPP(c_Product__Type_OSigma(_1483409, _1483411), hAPP(c_Set_Oimage(_1483407, _1483409, _1483413), _1483417)), hAPP(hAPP(c_COMBB(tc_fun(_1483407, tc_HOL_Obool), tc_fun(_1483411, tc_HOL_Obool), _1483409), c_Set_Oimage(_1483407, _1483411, _1483415)), hAPP(hAPP(c_COMBC(_1483409, tc_fun(_1483407, tc_HOL_Obool), tc_fun(_1483407, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483407, tc_HOL_Obool), tc_fun(tc_fun(_1483407, tc_HOL_Obool), tc_fun(_1483407, tc_HOL_Obool)), _1483409), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483407, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1483409, tc_HOL_Obool), tc_fun(_1483407, tc_HOL_Obool), _1483409), c_Set_Ovimage(_1483407, _1483409, _1483413)), hAPP(hAPP(c_COMBC(_1483409, tc_fun(_1483409, tc_HOL_Obool), tc_fun(_1483409, tc_HOL_Obool)), c_Set_Oinsert(_1483409)), c_Orderings_Obot__class_Obot(tc_fun(_1483409, tc_HOL_Obool)))))), _1483417))))], (30369 ^ _778495) ^ [_1331877, _1331879, _1331881, _1331883] : [class_Rings_Ocomm__semiring__1(_1331877), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1331877), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1331877), c_Groups_Oone__class_Oone(_1331877)), c_Groups_Oone__class_Oone(_1331877))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1331877), hAPP(hAPP(c_COMBB(_1331877, _1331877, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1331877), _1331879)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1331877, _1331877), hAPP(hAPP(c_COMBB(_1331877, tc_fun(_1331877, _1331877), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1331877)), c_Nat_Osemiring__1__class_Oof__nat(_1331877))), _1331881))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1331883))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1331877), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1331877), _1331883)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1331877), _1331879), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1331877), _1331879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1331877), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1331877), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1331883), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1331881)))))], (41192 ^ _778495) ^ [_1588867, _1588869, _1588871, _1588873, _1588875] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588867, _1588867)), hAPP(hAPP(c_Product__Type_OPair(_1588867, _1588867), _1588869), _1588871)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1588867, _1588867), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1588873)), _1588875))), 41196 ^ _778495 : [(41199 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588867, _1588867)), hAPP(hAPP(c_Product__Type_OPair(_1588867, _1588867), 41195 ^ [_1588867, _1588869, _1588871, _1588873, _1588875]), _1588871)), _1588875)))], (41197 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588867, _1588867)), hAPP(hAPP(c_Product__Type_OPair(_1588867, _1588867), _1588869), 41195 ^ [_1588867, _1588869, _1588871, _1588873, _1588875])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1588867, _1588867), tc_HOL_Obool), _1588873), _1588875))))]]], (11592 ^ _778495) ^ [_979439, _979441, _979443, _979445] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_979439), 11595 ^ _778495 : [(11602 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979439), _979443), _979445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979439), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979439), _979441), _979443)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979439), _979441), _979445))))], (11596 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979439), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979439), _979441), _979443)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979439), _979441), _979445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979439), _979443), _979445)))]]], (37218 ^ _778495) ^ [_1481499, _1481501, _1481503, _1481505] : [-(hAPP(c_Set_Oimage(_1481499, _1481501, _1481503), hAPP(c_Set_Ovimage(_1481499, _1481501, _1481503), _1481505)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481501, tc_HOL_Obool)), _1481505), hAPP(c_Set_Oimage(_1481499, _1481501, _1481503), c_Orderings_Otop__class_Otop(tc_fun(_1481499, tc_HOL_Obool)))))], (14709 ^ _778495) ^ [_1039367, _1039369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039369), _1039367)), -(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), _1039367), _1039369))))], (43922 ^ _778495) ^ [_1657113, _1657115] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657113), _1657115) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1657113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43928 ^ _778495 : [(43931 ^ _778495) ^ [] : [43927 ^ [_1657113, _1657115] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43929 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43927 ^ [_1657113, _1657115]), hAPP(c_List_Oset(tc_Nat_Onat), _1657115))))]]], (38487 ^ _778495) ^ [_1521062, _1521064] : [-(hAPP(c_Relation_ORange(_1521062, _1521064), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521062, _1521064), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1521064, tc_HOL_Obool)))], (51603 ^ _778495) ^ [_1820867, _1820869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1820867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1820867), _1820869)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820869), _1820867))], (39556 ^ _778495) ^ [_1548396, _1548398, _1548400, _1548402, _1548404, _1548406, _1548408] : [c_Fun_Oinj__on(_1548396, _1548398, _1548400, hAPP(c_Set_Oimage(_1548402, _1548396, _1548404), _1548406)), c_Fun_Oinj__on(_1548402, _1548396, _1548404, _1548406), hBOOL(hAPP(hAPP(c_member(_1548398), _1548408), hAPP(c_Set_Oimage(_1548396, _1548398, _1548400), hAPP(c_Set_Oimage(_1548402, _1548396, _1548404), _1548406)))), -(hAPP(c_Fun_Othe__inv__into(_1548402, _1548398, _1548406, hAPP(c_Fun_Ocomp(_1548396, _1548398, _1548402, _1548400), _1548404)), _1548408) = hAPP(hAPP(c_Fun_Ocomp(_1548396, _1548402, _1548398, c_Fun_Othe__inv__into(_1548402, _1548396, _1548406, _1548404)), c_Fun_Othe__inv__into(_1548396, _1548398, hAPP(c_Set_Oimage(_1548402, _1548396, _1548404), _1548406), _1548400)), _1548408))], (17162 ^ _778495) ^ [_1085378, _1085380, _1085382, _1085384] : [class_Fields_Olinordered__field__inverse__zero(_1085378), 17165 ^ _778495 : [(17166 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1085378), _1085380), _1085382)), _1085384)), 17169 ^ _778495 : [(17176 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), c_Groups_Ozero__class_Ozero(_1085378)), _1085382))), 17179 ^ _778495 : [(17186 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), _1085382), c_Groups_Ozero__class_Ozero(_1085378)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), c_Groups_Ozero__class_Ozero(_1085378)), _1085384)))], (17180 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), _1085382), c_Groups_Ozero__class_Ozero(_1085378))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085378), _1085384), _1085382)), _1085380)))]]], (17170 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), c_Groups_Ozero__class_Ozero(_1085378)), _1085382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), _1085380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085378), _1085384), _1085382))))]]], (17192 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1085378), _1085380), _1085382)), _1085384))), 17195 ^ _778495 : [(17198 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), _1085380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085378), _1085384), _1085382)))], (17196 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), c_Groups_Ozero__class_Ozero(_1085378)), _1085382)))]], 17199 ^ _778495 : [(17202 ^ _778495) ^ [] : [17203 ^ _778495 : [(17206 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085378), _1085384), _1085382)), _1085380))], (17204 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), _1085382), c_Groups_Ozero__class_Ozero(_1085378))))]], 17207 ^ _778495 : [(17210 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), c_Groups_Ozero__class_Ozero(_1085378)), _1085384))], (17208 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), _1085382), c_Groups_Ozero__class_Ozero(_1085378)))]]], (17200 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085378), c_Groups_Ozero__class_Ozero(_1085378)), _1085382))]]]]], (44472 ^ _778495) ^ [_1668899, _1668901] : [-(hAPP(hAPP(c_List_Omap(_1668899, _1668899), c_COMBI(_1668899)), _1668901) = _1668901)], (31911 ^ _778495) ^ [_1364820, _1364822, _1364824, _1364826, _1364828] : [class_Complete__Lattice_Ocomplete__lattice(_1364820), class_Orderings_Olinorder(_1364820), 31918 ^ _778495 : [(31928 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364820), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364822, _1364820), _1364824), _1364826)), _1364828))), 31929 ^ _778495 : [(31930 ^ _778495) ^ [_1365168] : [hBOOL(hAPP(hAPP(c_member(_1364822), _1365168), _1364824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364820), hAPP(_1364826, _1365168)), _1364828))]]], (31919 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364820), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364822, _1364820), _1364824), _1364826)), _1364828)), 31923 ^ _778495 : [(31926 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364820), hAPP(_1364826, 31922 ^ [_1364820, _1364822, _1364824, _1364826, _1364828])), _1364828)))], (31924 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364822), 31922 ^ [_1364820, _1364822, _1364824, _1364826, _1364828]), _1364824)))]]]]], (11608 ^ _778495) ^ [_979746, _979748, _979750, _979752] : [class_Groups_Oordered__cancel__ab__semigroup__add(_979746), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979746), _979748), _979750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979746), _979748), _979752)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979746), _979750), _979752))))], (30329 ^ _778495) ^ [_1331133] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1331133)), 30333 ^ _778495 : [(30334 ^ _778495) ^ [_1331213] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1331213), _1331133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1331213), 30332 ^ [_1331133])))]]], (11198 ^ _778495) ^ [_971471, _971473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _971471), _971473)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971471), _971473)))], (38121 ^ _778495) ^ [_1507341, _1507343, _1507345, _1507347] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1507341), hAPP(c_Set_OCollect(_1507341), _1507343))), 38124 ^ _778495 : [(38125 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1507345), hAPP(c_Set_OCollect(_1507345), hAPP(hAPP(c_COMBB(tc_fun(_1507341, tc_HOL_Obool), tc_HOL_Obool, _1507345), c_HOL_OEx(_1507341)), hAPP(hAPP(c_COMBB(tc_fun(_1507341, tc_HOL_Obool), tc_fun(_1507341, tc_HOL_Obool), _1507345), hAPP(c_COMBS(_1507341, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507341), c_fconj), _1507343))), _1507347))))), 38128 ^ _778495 : [(38129 ^ _778495) ^ [_1507624] : [hBOOL(hAPP(_1507343, _1507624)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1507345), hAPP(c_Set_OCollect(_1507345), hAPP(hAPP(c_COMBC(_1507345, _1507341, tc_HOL_Obool), _1507347), _1507624)))))]]], (38135 ^ _778495) ^ [] : [38137 ^ _778495 : [(38140 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1507345), hAPP(c_Set_OCollect(_1507345), hAPP(hAPP(c_COMBC(_1507345, _1507341, tc_HOL_Obool), _1507347), 38136 ^ [_1507341, _1507343, _1507345, _1507347]))))], (38138 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1507343, 38136 ^ [_1507341, _1507343, _1507345, _1507347])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1507345), hAPP(c_Set_OCollect(_1507345), hAPP(hAPP(c_COMBB(tc_fun(_1507341, tc_HOL_Obool), tc_HOL_Obool, _1507345), c_HOL_OEx(_1507341)), hAPP(hAPP(c_COMBB(tc_fun(_1507341, tc_HOL_Obool), tc_fun(_1507341, tc_HOL_Obool), _1507345), hAPP(c_COMBS(_1507341, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507341), c_fconj), _1507343))), _1507347))))))]]], (43702 ^ _778495) ^ [_1652665, _1652667, _1652669, _1652671, _1652673] : [-(hAPP(hAPP(c_List_Ozip(_1652665, _1652667), _1652669), hAPP(hAPP(c_List_Oappend(_1652667), _1652671), _1652673)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652665, _1652667)), hAPP(hAPP(c_List_Ozip(_1652665, _1652667), hAPP(hAPP(c_List_Otake(_1652665), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652667)), _1652671)), _1652669)), _1652671)), hAPP(hAPP(c_List_Ozip(_1652665, _1652667), hAPP(hAPP(c_List_Odrop(_1652665), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652667)), _1652671)), _1652669)), _1652673)))], (20309 ^ _778495) ^ [_1143425, _1143427] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1143425), _1143427))), -(c_Nat__Transfer_Otsub(_1143427, _1143425) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29256 ^ _778495) ^ [_1310416, _1310418] : [_1310416 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1310416, _1310418) = 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)))], (38685 ^ _778495) ^ [_1527460, _1527462] : [c_Wellfounded_Owf(_1527460, _1527462), -(c_Wellfounded_Owf(tc_fun(_1527460, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1527460, _1527462)))], (44891 ^ _778495) ^ [_1677767, _1677769] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1677767, _1677769) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1677767), hAPP(c_Code__Numeral_Onat__of, _1677769))))], (26338 ^ _778495) ^ [_1249515, _1249517, _1249519, _1249521] : [class_Rings_Olinordered__semidom(_1249515), hAPP(hAPP(c_Power_Opower__class_Opower(_1249515), _1249517), hAPP(c_Nat_OSuc, _1249519)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1249515), _1249521), hAPP(c_Nat_OSuc, _1249519)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249515), c_Groups_Ozero__class_Ozero(_1249515)), _1249517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249515), c_Groups_Ozero__class_Ozero(_1249515)), _1249521)), -(_1249517 = _1249521)], (9182 ^ _778495) ^ [_933612, _933614, _933616] : [class_Lattices_Olattice(_933612), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933612), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933612), _933614), _933616)), _933616)))], (48953 ^ _778495) ^ [_1768696, _1768698, _1768700, _1768702, _1768704] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1768696), tc_List_Olist(_1768696))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1768696), tc_List_Olist(_1768696)), _1768698), _1768700)), c_List_Olexord(_1768696, _1768702))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1768696), tc_List_Olist(_1768696))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1768696), tc_List_Olist(_1768696)), _1768700), _1768704)), c_List_Olexord(_1768696, _1768702))), c_Relation_Otrans(_1768696, _1768702), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1768696), tc_List_Olist(_1768696))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1768696), tc_List_Olist(_1768696)), _1768698), _1768704)), c_List_Olexord(_1768696, _1768702))))], (42246 ^ _778495) ^ [_1619774, _1619776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619774), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1619776))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1619776), _1619774)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619776))))], (26856 ^ _778495) ^ [_1258605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1258605), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1258605)), c_Int_OMin)))], (23989 ^ _778495) ^ [_1207801, _1207803, _1207805, _1207807] : [class_Divides_Osemiring__div(_1207801), -(_1207803 = c_Groups_Ozero__class_Ozero(_1207801)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207801), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207801), _1207805), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207801), _1207803), _1207807))), _1207803) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207801), _1207807), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207801), _1207805), _1207803)))], (38053 ^ _778495) ^ [_1504330, _1504332, _1504334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1504330, _1504330), tc_HOL_Obool)), _1504332), hAPP(hAPP(c_Product__Type_OSigma(_1504330, _1504330), _1504334), hAPP(c_COMBK(tc_fun(_1504330, tc_HOL_Obool), _1504330), _1504334)))), 38059 ^ _778495 : [(38062 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504330, _1504330)), hAPP(hAPP(c_Product__Type_OPair(_1504330, _1504330), 38058 ^ [_1504330, _1504332, _1504334]), 38058 ^ [_1504330, _1504332, _1504334])), _1504332))], (38060 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504330), 38058 ^ [_1504330, _1504332, _1504334]), _1504334)))]], -(c_Relation_Orefl__on(_1504330, _1504334, _1504332))], (52361 ^ _778495) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (30993 ^ _778495) ^ [_1344522, _1344524, _1344526, _1344528] : [class_Orderings_Olinorder(_1344522), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344522), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344522), _1344524), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1344522), _1344526), _1344528))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1344522), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344522), _1344524), _1344526)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344522), _1344524), _1344528)))))], (34231 ^ _778495) ^ [_1416430, _1416432, _1416434, _1416436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1416430, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1416430, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34232 ^ [_1416430, _1416432, _1416434, _1416436])), _1416432)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1416430, 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), 34232 ^ [_1416430, _1416432, _1416434, _1416436]), _1416434))), _1416436))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1416430, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1416430, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1416432)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1416430, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1416436))))], (30733 ^ _778495) ^ [_1339551, _1339553, _1339555, _1339557] : [class_Orderings_Olinorder(_1339551), 30736 ^ _778495 : [(30745 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339551), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339551), _1339553), _1339555)), _1339557))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339551), _1339553), _1339557)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339551), _1339555), _1339557))], (30737 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339551), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339551), _1339553), _1339555)), _1339557)), 30740 ^ _778495 : [(30743 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339551), _1339555), _1339557)))], (30741 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339551), _1339553), _1339557)))]]]]], (20814 ^ _778495) ^ [_1151398] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1151398), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151398)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1151398)))], (38489 ^ _778495) ^ [_1521124, _1521126, _1521128] : [hAPP(c_Relation_ORange(_1521124, _1521126), _1521128) = c_Orderings_Obot__class_Obot(tc_fun(_1521126, tc_HOL_Obool)), -(_1521128 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521124, _1521126), tc_HOL_Obool)))], (6854 ^ _778495) ^ [_890904, _890906, _890908, _890910, _890912] : [class_Groups_Ominus(_890904), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890906, _890904)), _890908), _890910), _890912) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_890904), hAPP(_890908, _890912)), hAPP(_890910, _890912)))], (13539 ^ _778495) ^ [_1018726, _1018728, _1018730, _1018732] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1018726, _1018728)), c_Sum__Type_OPlus(_1018726, _1018728, _1018730, _1018732))), 13542 ^ _778495 : [(13545 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1018728), _1018732)))], (13543 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1018726), _1018730)))]]], (42664 ^ _778495) ^ [_1628976, _1628978, _1628980, _1628982] : [-(_1628976 = _1628978), -(c_List_Oremove1(_1628980, _1628976, hAPP(hAPP(c_List_Olist_OCons(_1628980), _1628978), _1628982)) = hAPP(hAPP(c_List_Olist_OCons(_1628980), _1628978), c_List_Oremove1(_1628980, _1628976, _1628982)))], (37666 ^ _778495) ^ [_1494067, _1494069, _1494071, _1494073, _1494075, _1494077, _1494079, _1494081] : [c_Fun_Oinj__on(_1494067, _1494069, _1494071, _1494073), c_Fun_Oinj__on(_1494075, _1494077, _1494079, _1494081), -(c_Fun_Oinj__on(tc_prod(_1494067, _1494075), tc_prod(_1494069, _1494077), c_Product__Type_Omap__pair(_1494067, _1494069, _1494075, _1494077, _1494071, _1494079), hAPP(hAPP(c_Product__Type_OSigma(_1494067, _1494075), _1494073), hAPP(c_COMBK(tc_fun(_1494075, tc_HOL_Obool), _1494067), _1494081))))], (46624 ^ _778495) ^ [_1715763, _1715765, _1715767] : [_1715765 = hAPP(hAPP(c_List_Olist_OCons(_1715763), _1715767), c_List_Olist_ONil(_1715763)), -(hAPP(c_List_Orev(_1715763), _1715765) = hAPP(hAPP(c_List_Olist_OCons(_1715763), _1715767), c_List_Olist_ONil(_1715763)))], (2076 ^ _778495) ^ [_808738, _808740, _808742, _808744] : [-(c_SMT_Oz3div(_808744, _808740) = c_SMT_Oz3div(_808742, _808738)), _808744 = _808742, _808740 = _808738], (24521 ^ _778495) ^ [_1217443, _1217445] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217443)), _1217445) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1217443), _1217445)))], (34647 ^ _778495) ^ [_1426384, _1426386] : [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)), _1426384)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1426386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1426384), _1426386)))], (4246 ^ _778495) ^ [_842831, _842833, _842835, _842837, _842839, _842841] : [-(c_List_Oreplicate(_842841, _842837, _842833) = c_List_Oreplicate(_842839, _842835, _842831)), _842841 = _842839, _842837 = _842835, _842833 = _842831], (39914 ^ _778495) ^ [_1556578, _1556580] : [hBOOL(hAPP(_1556578, c_Hilbert__Choice_OEps(_1556580, _1556578))), -(hBOOL(hAPP(_1556578, 39917 ^ [_1556578, _1556580])))], (1398 ^ _778495) ^ [_798998, _799000] : [-(class_Complete__Lattice_Ocomplete__lattice(_798998)), _799000 = _798998, class_Complete__Lattice_Ocomplete__lattice(_799000)], (35044 ^ _778495) ^ [_1433733, _1433735] : [c_Nat__Transfer_Onat__set(_1433733), c_Nat__Transfer_Onat__set(_1433735), 35051 ^ _778495 : [(35058 ^ _778495) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1433733) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1433735), -(_1433733 = _1433735)], (35052 ^ _778495) ^ [] : [_1433733 = _1433735, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1433733) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1433735))]]], (48680 ^ _778495) ^ [_1760740, _1760742, _1760744] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1760740, _1760742, _1760744) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760740)], (40856 ^ _778495) ^ [_1579961, _1579963] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579961, _1579961)), _1579963)), c_Wellfounded_Oacyclic(_1579961, _1579963), -(c_Wellfounded_Owf(_1579961, hAPP(c_Relation_Oconverse(_1579961, _1579961), _1579963)))], (26698 ^ _778495) ^ [_1255897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1255897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1255897))))], (28577 ^ _778495) ^ [_1295764, _1295766, _1295768] : [class_Int_Onumber__ring(_1295764), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1295764), _1295766), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1295768))) = hAPP(hAPP(c_HOL_OLet(_1295764, _1295764), hAPP(hAPP(c_Power_Opower__class_Opower(_1295764), _1295766), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1295768))), hAPP(hAPP(c_COMBS(_1295764, _1295764, _1295764), c_Groups_Otimes__class_Otimes(_1295764)), c_COMBI(_1295764))))], (37973 ^ _778495) ^ [_1502119, _1502121, _1502123, _1502125] : [_1502119 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1502121, _1502123), 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)), _1502125))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1502121), _1502119)))], (16188 ^ _778495) ^ [_1067857, _1067859] : [class_Rings_Odivision__ring__inverse__zero(_1067857), 16191 ^ _778495 : [(16198 ^ _778495) ^ [] : [-(_1067859 = c_Groups_Ozero__class_Ozero(_1067857)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1067857), _1067859), _1067859) = c_Groups_Oone__class_Oone(_1067857))], (16192 ^ _778495) ^ [] : [_1067859 = c_Groups_Ozero__class_Ozero(_1067857), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1067857), _1067859), _1067859) = c_Groups_Ozero__class_Ozero(_1067857))]]], (37761 ^ _778495) ^ [_1496743, _1496745, _1496747, _1496749] : [-(hAPP(c_Set_OCollect(tc_prod(_1496743, _1496745)), hAPP(c_Product__Type_Oprod_Oprod__case(_1496743, _1496745, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1496743, tc_fun(_1496745, tc_HOL_Obool), tc_fun(_1496745, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1496745, tc_HOL_Obool), tc_fun(_1496745, tc_HOL_Obool)), _1496743), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1496745)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1496743), c_fconj), _1496747))), _1496749))) = hAPP(hAPP(c_Product__Type_OSigma(_1496743, _1496745), hAPP(c_Set_OCollect(_1496743), _1496747)), hAPP(hAPP(c_COMBB(tc_fun(_1496745, tc_HOL_Obool), tc_fun(_1496745, tc_HOL_Obool), _1496743), c_Set_OCollect(_1496745)), _1496749)))], (16530 ^ _778495) ^ [_1073915, _1073917, _1073919, _1073921, _1073923] : [class_Fields_Ofield__inverse__zero(_1073915), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073915), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1073915), _1073917), _1073919)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1073915), _1073921), _1073923)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1073915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073915), _1073917), _1073921)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073915), _1073919), _1073923)))], (18932 ^ _778495) ^ [_1118852] : [class_Orderings_Oord(_1118852), -(c_Orderings_Oord__class_Omin(_1118852) = c_Orderings_Oord_Omin(_1118852, c_Orderings_Oord__class_Oless__eq(_1118852)))], (1228 ^ _778495) ^ [_796873, _796875] : [-(class_Rings_Olinordered__ring(_796873)), _796875 = _796873, class_Rings_Olinordered__ring(_796875)], (44253 ^ _778495) ^ [_1663467, _1663469, _1663471] : [-(c_List_Olast(_1663467, hAPP(hAPP(c_List_Oappend(_1663467), _1663469), hAPP(hAPP(c_List_Olist_OCons(_1663467), _1663471), c_List_Olist_ONil(_1663467)))) = _1663471)], (30087 ^ _778495) ^ [_1326421] : [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), _1326421))), -(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), _1326421)) = 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), _1326421))))], (46963 ^ _778495) ^ [_1722938, _1722940] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1722938), _1722940) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1722938)), c_List_Oembed__list(_1722940))))], (1388 ^ _778495) ^ [_798873, _798875] : [-(class_Orderings_Owellorder(_798873)), _798875 = _798873, class_Orderings_Owellorder(_798875)], (32870 ^ _778495) ^ [_1384949, _1384951] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1384949, _1384951)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1384951), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1384949), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (18640 ^ _778495) ^ [_1113216, _1113218, _1113220] : [class_Orderings_Olinorder(_1113216), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113216), _1113218)), -(_1113218 = c_Orderings_Obot__class_Obot(tc_fun(_1113216, tc_HOL_Obool))), 18651 ^ _778495 : [(18661 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113216), hAPP(c_Finite__Set_Ofold1(_1113216, c_Orderings_Oord__class_Omin(_1113216)), _1113218)), _1113220))), 18662 ^ _778495 : [(18663 ^ _778495) ^ [_1113605] : [hBOOL(hAPP(hAPP(c_member(_1113216), _1113605), _1113218)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113216), _1113605), _1113220))]]], (18652 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113216), hAPP(c_Finite__Set_Ofold1(_1113216, c_Orderings_Oord__class_Omin(_1113216)), _1113218)), _1113220)), 18656 ^ _778495 : [(18659 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113216), 18655 ^ [_1113216, _1113218, _1113220]), _1113220)))], (18657 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1113216), 18655 ^ [_1113216, _1113218, _1113220]), _1113218)))]]]]], (6312 ^ _778495) ^ [_880628, _880630, _880632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880628, tc_HOL_Obool)), _880630), _880632)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880628, tc_HOL_Obool)), _880630), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_880628, tc_HOL_Obool)), _880632), _880630)) = _880632)], (846 ^ _778495) ^ [_791248, _791250, _791252, _791254] : [-(c_Relation_Osym(_791252, _791248)), c_Relation_Osym(_791254, _791250), _791254 = _791252, _791250 = _791248], (406 ^ _778495) ^ [_784674, _784676, _784678, _784680, _784682, _784684, _784686, _784688] : [-(c_Finite__Set_Ofolding__idem(_784686, _784682, _784678, _784674)), c_Finite__Set_Ofolding__idem(_784688, _784684, _784680, _784676), _784688 = _784686, _784684 = _784682, _784680 = _784678, _784676 = _784674], (28653 ^ _778495) ^ [_1297744, _1297746] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1297744)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1297746)), hAPP(c_Int_Onat, _1297744)) = hAPP(c_Int_Onat, _1297746))], (38739 ^ _778495) ^ [_1528314, _1528316, _1528318, _1528320] : [c_Wellfounded_Owf(_1528314, _1528316), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528314, _1528314)), hAPP(hAPP(c_Product__Type_OPair(_1528314, _1528314), _1528318), _1528320)), _1528316)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528314, _1528314)), hAPP(hAPP(c_Product__Type_OPair(_1528314, _1528314), _1528320), _1528318)), _1528316))], (30519 ^ _778495) ^ [_1335245, _1335247, _1335249, _1335251, _1335253, _1335255, _1335257, _1335259] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1335245, _1335247), tc_prod(_1335245, _1335247))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1335245, _1335247), tc_prod(_1335245, _1335247)), hAPP(hAPP(c_Product__Type_OPair(_1335245, _1335247), _1335249), _1335251)), hAPP(hAPP(c_Product__Type_OPair(_1335245, _1335247), _1335253), _1335255))), c_Wellfounded_Olex__prod(_1335245, _1335247, _1335257, _1335259)))), 30520 ^ _778495 : [(30523 ^ _778495) ^ [] : [_1335249 = _1335253, hBOOL(hAPP(hAPP(c_member(tc_prod(_1335247, _1335247)), hAPP(hAPP(c_Product__Type_OPair(_1335247, _1335247), _1335251), _1335255)), _1335259))], (30521 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1335245, _1335245)), hAPP(hAPP(c_Product__Type_OPair(_1335245, _1335245), _1335249), _1335253)), _1335257))]]], (48084 ^ _778495) ^ [_1747529, _1747531, _1747533, _1747535, _1747537] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1747529), _1747531), _1747533), _1747535), _1747537) = c_New__DSequence_Opos__single(_1747529, _1747531))], (14811 ^ _778495) ^ [_1041208, _1041210] : [-(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), _1041208), _1041210)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1041208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1041210))], (40067 ^ _778495) ^ [_1560201, _1560203, _1560205, _1560207, _1560209] : [_1560201 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1560203, _1560205, _1560201, _1560207), _1560209) = hAPP(c_Product__Type_OPair(_1560203, _1560205), _1560209))], (40559 ^ _778495) ^ [_1572767, _1572769, _1572771, _1572773] : [-(hBOOL(hAPP(hAPP(c_member(_1572767), _1572769), hAPP(c_Relation_ODomain(_1572767, _1572767), _1572771)))), 40562 ^ _778495 : [(40569 ^ _778495) ^ [] : [_1572769 = _1572773, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572767, _1572767)), hAPP(hAPP(c_Product__Type_OPair(_1572767, _1572767), _1572769), _1572773)), c_Transitive__Closure_Ortrancl(_1572767, _1572771))))], (40563 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572767, _1572767)), hAPP(hAPP(c_Product__Type_OPair(_1572767, _1572767), _1572769), _1572773)), c_Transitive__Closure_Ortrancl(_1572767, _1572771))), -(_1572769 = _1572773)]]], (5749 ^ _778495) ^ [_869552, _869554, _869556, _869558] : [5750 ^ _778495 : [(5753 ^ _778495) ^ [] : [hBOOL(hAPP(_869556, _869558))], (5751 ^ _778495) ^ [] : [_869554 = _869558]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_869552), _869554), _869556), _869558)))], (50080 ^ _778495) ^ [_1791171, _1791173, _1791175, _1791177, _1791179] : [-(c_Fun_Obij__betw(_1791171, _1791173, _1791175, _1791177, _1791179)), c_Fun_Oinj__on(_1791171, _1791173, _1791175, _1791177), hAPP(c_Set_Oimage(_1791171, _1791173, _1791175), _1791177) = _1791179], (8052 ^ _778495) ^ [_910994, _910996, _910998, _911000] : [class_Orderings_Oorder(_910994), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910994), _910996), _910998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910994), _911000), _910996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910994), _911000), _910998)))], (40738 ^ _778495) ^ [_1576772, _1576774, _1576776] : [c_Relation_Ototal__on(_1576772, _1576774, _1576776), -(c_Relation_Ototal__on(_1576772, _1576774, hAPP(c_Relation_Oconverse(_1576772, _1576772), _1576776)))], (51799 ^ _778495) ^ [_1824308, _1824310, _1824312, _1824314] : [class_Rings_Ocomm__ring(_1824308), class_Rings_Odvd(_1824308), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824308), _1824310), _1824312)), 51810 ^ _778495 : [(51817 ^ _778495) ^ [_1824734, _1824736] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824308), _1824310), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824308), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1824308), _1824736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824308), _1824734), _1824312))), _1824314))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824308), _1824310), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824308), _1824736), _1824314))))], (51811 ^ _778495) ^ [_1824561, _1824563] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824308), _1824310), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824308), _1824563), _1824314))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824308), _1824310), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824308), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1824308), _1824563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824308), _1824561), _1824312))), _1824314))))]]], (47011 ^ _778495) ^ [_1724047, _1724049, _1724051] : [47013 ^ _778495 : [(47016 ^ _778495) ^ [] : [hBOOL(hAPP(_1724049, 47012 ^ [_1724047, _1724049, _1724051]))], (47014 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1724047), 47012 ^ [_1724047, _1724049, _1724051]), hAPP(c_List_Oset(_1724047), _1724051))))]], -(c_List_OdropWhile(_1724047, _1724049, _1724051) = c_List_Olist_ONil(_1724047))], (5494 ^ _778495) ^ [_862581, _862583, _862585, _862587] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862587, _862583) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862585, _862581)), _862587 = _862585, _862583 = _862581], (29063 ^ _778495) ^ [_1306161, _1306163] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1306161), hAPP(c_Nat_OSuc, _1306163)) = 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)), _1306163)), _1306161))], (41985 ^ _778495) ^ [_1611972, _1611974, _1611976] : [-(hAPP(c_List_Oset(_1611972), hAPP(hAPP(c_List_Olist_OCons(_1611972), _1611974), _1611976)) = hAPP(hAPP(c_Set_Oinsert(_1611972), _1611974), hAPP(c_List_Oset(_1611972), _1611976)))], (44530 ^ _778495) ^ [_1670292, _1670294, _1670296, _1670298, _1670300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670292), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670294)), _1670296))), -(hAPP(hAPP(c_List_Onth(_1670298), hAPP(hAPP(c_List_Omap(_1670294, _1670298), _1670300), _1670296)), _1670292) = hAPP(_1670300, hAPP(hAPP(c_List_Onth(_1670294), _1670296), _1670292)))], (44007 ^ _778495) ^ [_1658951, _1658953, _1658955] : [class_Orderings_Olinorder(_1658951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1658951), _1658953)), -(c_List_Olinorder__class_Osorted__list__of__set(_1658951, hAPP(hAPP(c_Set_Oinsert(_1658951), _1658955), _1658953)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658951, _1658951, c_COMBI(_1658951)), _1658955), c_List_Olinorder__class_Osorted__list__of__set(_1658951, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1658951, tc_HOL_Obool)), _1658953), hAPP(hAPP(c_Set_Oinsert(_1658951), _1658955), c_Orderings_Obot__class_Obot(tc_fun(_1658951, tc_HOL_Obool)))))))], (38511 ^ _778495) ^ [_1521715, _1521717, _1521719, _1521721] : [-(hAPP(c_Relation_ORange(_1521715, _1521717), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521715, _1521717), tc_HOL_Obool)), _1521719), _1521721)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521717, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521715, _1521717), _1521719)), hAPP(c_Relation_ORange(_1521715, _1521717), _1521721)))], (52595 ^ _778495) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (16968 ^ _778495) ^ [_1081665, _1081667, _1081669, _1081671, _1081673] : [class_Fields_Olinordered__field(_1081665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081665), c_Groups_Ozero__class_Ozero(_1081665)), _1081667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081665), _1081667), _1081669)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081665), c_Groups_Ozero__class_Ozero(_1081665)), _1081671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081665), _1081671), _1081673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081665), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1081665), _1081667), _1081673)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1081665), _1081669), _1081671))))], (42988 ^ _778495) ^ [_1635650, _1635652, _1635654, _1635656] : [-(c_List_Osublist(_1635650, hAPP(hAPP(c_List_Olist_OCons(_1635650), _1635652), _1635654), _1635656) = hAPP(hAPP(c_List_Oappend(_1635650), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1635650)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1635656)), hAPP(hAPP(c_List_Olist_OCons(_1635650), _1635652), c_List_Olist_ONil(_1635650))), c_List_Olist_ONil(_1635650))), c_List_Osublist(_1635650, _1635654, 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)), _1635656)))))], (42858 ^ _778495) ^ [_1632571, _1632573, _1632575] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1632571))), -(c_List_Osublist(_1632573, hAPP(hAPP(c_List_Olist_OCons(_1632573), _1632575), c_List_Olist_ONil(_1632573)), _1632571) = c_List_Olist_ONil(_1632573))], (45508 ^ _778495) ^ [_1691682, _1691684] : [-(c_List_Oconcat(_1691682, _1691684) = hAPP(c_List_Ofoldl(tc_List_Olist(_1691682), tc_List_Olist(_1691682), c_List_Oappend(_1691682), c_List_Olist_ONil(_1691682)), _1691684))], (42419 ^ _778495) ^ [_1623667, _1623669, _1623671, _1623673] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623667), tc_List_Olist(_1623667))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623667), tc_List_Olist(_1623667)), _1623669), _1623671)), c_List_Olistrel1(_1623667, _1623673)))), 42420 ^ _778495 : [(42421 ^ _778495) ^ [_1623800, _1623802] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623667, _1623667)), hAPP(hAPP(c_Product__Type_OPair(_1623667, _1623667), hAPP(hAPP(c_List_Onth(_1623667), _1623669), _1623800)), _1623802)), _1623673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623800), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623667)), _1623669))), _1623671 = hAPP(hAPP(c_List_Olist__update(_1623667, _1623669), _1623800), _1623802)]]], (556 ^ _778495) ^ [_786899, _786901] : [-(class_Lattices_Oab__semigroup__idem__mult(_786899)), _786901 = _786899, class_Lattices_Oab__semigroup__idem__mult(_786901)], (34544 ^ _778495) ^ [_1424390, _1424392, _1424394, _1424396] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1424390, _1424390)), hAPP(hAPP(c_Product__Type_OPair(_1424390, _1424390), _1424392), _1424394)), c_Relation_OId__on(_1424390, _1424396))), 34547 ^ _778495 : [(34550 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1424390), _1424392), _1424396)))], (34548 ^ _778495) ^ [] : [-(_1424392 = _1424394)]]], (44514 ^ _778495) ^ [_1669967, _1669969, _1669971, _1669973, _1669975] : [c_Fun_Oinj__on(_1669967, _1669969, _1669971, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669967, tc_HOL_Obool)), hAPP(c_List_Oset(_1669967), _1669973)), hAPP(c_List_Oset(_1669967), _1669975))), 44517 ^ _778495 : [(44524 ^ _778495) ^ [] : [_1669973 = _1669975, -(hAPP(hAPP(c_List_Omap(_1669967, _1669969), _1669971), _1669973) = hAPP(hAPP(c_List_Omap(_1669967, _1669969), _1669971), _1669975))], (44518 ^ _778495) ^ [] : [hAPP(hAPP(c_List_Omap(_1669967, _1669969), _1669971), _1669973) = hAPP(hAPP(c_List_Omap(_1669967, _1669969), _1669971), _1669975), -(_1669973 = _1669975)]]], (16318 ^ _778495) ^ [_1069947, _1069949, _1069951, _1069953] : [class_Fields_Olinordered__field__inverse__zero(_1069947), 16321 ^ _778495 : [(16322 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069947), _1069949), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1069947), _1069951), _1069953))), 16325 ^ _778495 : [(16332 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069947), c_Groups_Ozero__class_Ozero(_1069947)), _1069953))), 16335 ^ _778495 : [(16342 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069947), _1069953), c_Groups_Ozero__class_Ozero(_1069947)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069947), _1069949), c_Groups_Ozero__class_Ozero(_1069947))))], (16336 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069947), _1069953), c_Groups_Ozero__class_Ozero(_1069947))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069947), _1069951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069947), _1069949), _1069953))))]]], (16326 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069947), c_Groups_Ozero__class_Ozero(_1069947)), _1069953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069947), _1069949), _1069953)), _1069951)))]]], (16348 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069947), _1069949), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1069947), _1069951), _1069953)))), 16351 ^ _778495 : [(16354 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069947), _1069949), _1069953)), _1069951))], (16352 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069947), c_Groups_Ozero__class_Ozero(_1069947)), _1069953)))]], 16355 ^ _778495 : [(16358 ^ _778495) ^ [] : [16359 ^ _778495 : [(16362 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069947), _1069951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069947), _1069949), _1069953)))], (16360 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069947), _1069953), c_Groups_Ozero__class_Ozero(_1069947))))]], 16363 ^ _778495 : [(16366 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069947), _1069949), c_Groups_Ozero__class_Ozero(_1069947)))], (16364 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069947), _1069953), c_Groups_Ozero__class_Ozero(_1069947)))]]], (16356 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069947), c_Groups_Ozero__class_Ozero(_1069947)), _1069953))]]]]], (22988 ^ _778495) ^ [_1189476, _1189478, _1189480] : [-(hBOOL(hAPP(hAPP(c_member(_1189476), _1189478), _1189480))), -(hBOOL(hAPP(hAPP(c_member(_1189476), _1189478), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1189476, tc_HOL_Obool)), _1189480))))], (46102 ^ _778495) ^ [_1706114, _1706116] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1706114, _1706116)))], (11432 ^ _778495) ^ [_976259, _976261, _976263, _976265] : [class_Rings_Ocomm__semiring__1(_976259), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976259), _976261), _976263)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976259), _976265), _976263)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976259), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976259), _976261), _976265)), _976263))], (23246 ^ _778495) ^ [_1194936, _1194938, _1194940] : [-(hBOOL(hAPP(hAPP(c_member(_1194936), _1194938), _1194940))), -(hBOOL(hAPP(hAPP(c_member(_1194936), _1194938), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1194936, tc_HOL_Obool)), _1194940))))], (24860 ^ _778495) ^ [_1223242, _1223244, _1223246] : [class_Rings_Oring__1(_1223242), hBOOL(hAPP(hAPP(c_member(_1223242), _1223244), c_Int_Oring__1__class_OInts(_1223242))), -(hBOOL(hAPP(hAPP(c_member(_1223242), hAPP(hAPP(c_Power_Opower__class_Opower(_1223242), _1223244), _1223246)), c_Int_Oring__1__class_OInts(_1223242))))], (26984 ^ _778495) ^ [] : [-(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))], (28339 ^ _778495) ^ [_1287422, _1287424, _1287426, _1287428, _1287430, _1287432] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287422, tc_fun(_1287424, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1287422, tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_fun(_1287424, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1287424, tc_fun(tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_fun(_1287424, tc_HOL_Obool)), _1287422), c_COMBC(_1287424, tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1287424, tc_prod(_1287422, _1287424)), tc_fun(_1287424, tc_fun(tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_HOL_Obool)), _1287422), hAPP(c_COMBB(tc_prod(_1287422, _1287424), tc_fun(tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_HOL_Obool), _1287424), c_member(tc_prod(_1287422, _1287424)))), c_Product__Type_OPair(_1287422, _1287424)))), _1287426)), hAPP(hAPP(c_COMBC(_1287422, tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_fun(_1287424, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1287424, tc_fun(tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_fun(_1287424, tc_HOL_Obool)), _1287422), c_COMBC(_1287424, tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1287424, tc_prod(_1287422, _1287424)), tc_fun(_1287424, tc_fun(tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_HOL_Obool)), _1287422), hAPP(c_COMBB(tc_prod(_1287422, _1287424), tc_fun(tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool), tc_HOL_Obool), _1287424), c_member(tc_prod(_1287422, _1287424)))), c_Product__Type_OPair(_1287422, _1287424)))), _1287428)), _1287430), _1287432)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1287422, _1287424)), hAPP(hAPP(c_Product__Type_OPair(_1287422, _1287424), _1287430), _1287432)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1287422, _1287424), tc_HOL_Obool)), _1287426), _1287428))))], (15191 ^ _778495) ^ [_1048258, _1048260, _1048262] : [class_Rings_Olinordered__ring__strict(_1048258), 15194 ^ _778495 : [(15203 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048258), _1048260), _1048260)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048258), _1048262), _1048262))), c_Groups_Ozero__class_Ozero(_1048258)))), _1048260 = c_Groups_Ozero__class_Ozero(_1048258), _1048262 = c_Groups_Ozero__class_Ozero(_1048258)], (15195 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048258), _1048260), _1048260)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048258), _1048262), _1048262))), c_Groups_Ozero__class_Ozero(_1048258))), 15198 ^ _778495 : [(15201 ^ _778495) ^ [] : [-(_1048262 = c_Groups_Ozero__class_Ozero(_1048258))], (15199 ^ _778495) ^ [] : [-(_1048260 = c_Groups_Ozero__class_Ozero(_1048258))]]]]], (41630 ^ _778495) ^ [_1602136, _1602138] : [-(c_List_Olistrel(_1602136, c_Transitive__Closure_Ortrancl(_1602136, _1602138)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1602136), c_List_Olistrel1(_1602136, _1602138)))], (35642 ^ _778495) ^ [_1446022, _1446024, _1446026] : [_1446024 = c_Orderings_Obot__class_Obot(tc_fun(_1446022, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446022), _1446024), _1446026) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446022, tc_HOL_Obool), tc_HOL_Obool)))], (2304 ^ _778495) ^ [_812286, _812288, _812290, _812292] : [-(c_Divides_Opdivmod(_812292, _812288) = c_Divides_Opdivmod(_812290, _812286)), _812292 = _812290, _812288 = _812286], (26746 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (22298 ^ _778495) ^ [_1177258, _1177260, _1177262] : [class_Groups_Ogroup__add(_1177258), 22301 ^ _778495 : [(22308 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177258), _1177260), _1177262) = c_Groups_Ozero__class_Ozero(_1177258), -(_1177260 = hAPP(c_Groups_Ouminus__class_Ouminus(_1177258), _1177262))], (22302 ^ _778495) ^ [] : [_1177260 = hAPP(c_Groups_Ouminus__class_Ouminus(_1177258), _1177262), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177258), _1177260), _1177262) = c_Groups_Ozero__class_Ozero(_1177258))]]], (48054 ^ _778495) ^ [_1746579, _1746581, _1746583, _1746585, _1746587] : [-(_1746579 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1746581, _1746583, _1746585, _1746587), _1746579) = hAPP(c_Lazy__Sequence_Obind(_1746581, _1746583, hAPP(_1746585, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1746579), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1746581, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746583)), _1746587), _1746579)))], (5152 ^ _778495) ^ [_857154, _857156, _857158, _857160, _857162, _857164, _857166, _857168] : [-(c_Fun_Ocomp(_857168, _857164, _857160, _857156) = c_Fun_Ocomp(_857166, _857162, _857158, _857154)), _857168 = _857166, _857164 = _857162, _857160 = _857158, _857156 = _857154], (18986 ^ _778495) ^ [_1119969, _1119971, _1119973] : [class_Orderings_Olinorder(_1119969), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119969), _1119971)), -(hBOOL(hAPP(hAPP(c_member(_1119969), _1119973), _1119971))), -(c_Big__Operators_Olinorder__class_OMin(_1119969, hAPP(hAPP(c_Set_Oinsert(_1119969), _1119973), _1119971)) = hAPP(hAPP(c_Finite__Set_Ofold(_1119969, _1119969, c_Orderings_Oord__class_Omin(_1119969)), _1119973), _1119971))], (8860 ^ _778495) ^ [_927355, _927357, _927359, _927361] : [hBOOL(hAPP(hAPP(c_member(_927355), _927357), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927355, tc_HOL_Obool)), _927359), _927361))), 8863 ^ _778495 : [(8866 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_927355), _927357), _927361)))], (8864 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_927355), _927357), _927359)))]]], (13597 ^ _778495) ^ [_1019771, _1019773] : [class_Groups_Olinordered__ab__group__add(_1019771), 13600 ^ _778495 : [(13607 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019771), c_Groups_Ozero__class_Ozero(_1019771)), _1019773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019771), c_Groups_Ozero__class_Ozero(_1019771)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019771), _1019773), _1019773))))], (13601 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019771), c_Groups_Ozero__class_Ozero(_1019771)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019771), _1019773), _1019773))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019771), c_Groups_Ozero__class_Ozero(_1019771)), _1019773)))]]], (33294 ^ _778495) ^ [_1394836, _1394838, _1394840, _1394842, _1394844] : [33296 ^ _778495 : [(33299 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1394836, tc_HOL_Obool)), hAPP(_1394842, 33295 ^ [_1394836, _1394838, _1394840, _1394842, _1394844])), _1394844))], (33297 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394838), 33295 ^ [_1394836, _1394838, _1394840, _1394842, _1394844]), _1394840)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1394836, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394838, tc_fun(_1394836, tc_HOL_Obool)), _1394840), _1394842)), _1394844)))], (9024 ^ _778495) ^ [_930735, _930737, _930739] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_930735), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930735, tc_HOL_Obool)), _930737), _930739))), -(hAPP(c_Finite__Set_Ocard(_930735), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930735, tc_HOL_Obool)), _930737), _930739)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_930735), _930737)), hAPP(c_Finite__Set_Ocard(_930735), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930735, tc_HOL_Obool)), _930737), _930739))))], (31750 ^ _778495) ^ [_1359395, _1359397, _1359399, _1359401] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1359399), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1359395, tc_fun(_1359399, tc_HOL_Obool)), _1359397), _1359401)))), 31751 ^ _778495 : [(31752 ^ _778495) ^ [_1359469] : [hBOOL(hAPP(hAPP(c_member(_1359395), _1359469), _1359397)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359399), hAPP(_1359401, _1359469)))]]], (31986 ^ _778495) ^ [_1366663, _1366665, _1366667, _1366669] : [-(_1366663 = c_Orderings_Obot__class_Obot(tc_fun(_1366665, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1366665, tc_fun(_1366667, tc_HOL_Obool)), _1366663), hAPP(c_COMBK(tc_fun(_1366667, tc_HOL_Obool), _1366665), _1366669)) = _1366669)], (15715 ^ _778495) ^ [_1058150, _1058152] : [-(_1058150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058150), _1058152) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1058150), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1058152)))], (33078 ^ _778495) ^ [_1388805, _1388807, _1388809] : [class_Orderings_Olinorder(_1388805), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388805), _1388807), _1388809)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1388805, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1388805, _1388807, _1388809)), hAPP(hAPP(c_Set_Oinsert(_1388805), _1388809), c_Orderings_Obot__class_Obot(tc_fun(_1388805, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1388805, _1388807, _1388809))], (44071 ^ _778495) ^ [_1660527] : [class_Orderings_Olinorder(_1660527), -(c_Finite__Set_Ofun__left__comm(_1660527, tc_List_Olist(_1660527), c_List_Olinorder__class_Oinsort__key(_1660527, _1660527, c_COMBI(_1660527))))], (6174 ^ _778495) ^ [_878125, _878127, _878129, _878131] : [6178 ^ _778495 : [(6181 ^ _778495) ^ [] : [hBOOL(hAPP(_878131, 6177 ^ [_878125, _878127, _878129, _878131]))], (6179 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_878125), 6177 ^ [_878125, _878127, _878129, _878131]), _878127)))]], 6183 ^ _778495 : [(6186 ^ _778495) ^ [] : [hBOOL(hAPP(_878131, 6182 ^ [_878125, _878127, _878129, _878131]))], (6184 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_878125), 6182 ^ [_878125, _878127, _878129, _878131]), _878129)))]], 6187 ^ _778495 : [(6188 ^ _778495) ^ [_878458] : [hBOOL(hAPP(hAPP(c_member(_878125), _878458), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_878125, tc_HOL_Obool)), _878127), _878129))), -(hBOOL(hAPP(_878131, _878458)))]]], (25728 ^ _778495) ^ [_1238241, _1238243] : [class_Rings_Olinordered__idom(_1238241), 25731 ^ _778495 : [(25738 ^ _778495) ^ [] : [-(_1238243 = c_Groups_Ozero__class_Ozero(_1238241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238241), c_Groups_Ozero__class_Ozero(_1238241)), hAPP(hAPP(c_Power_Opower__class_Opower(_1238241), _1238243), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25732 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238241), c_Groups_Ozero__class_Ozero(_1238241)), hAPP(hAPP(c_Power_Opower__class_Opower(_1238241), _1238243), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1238243 = c_Groups_Ozero__class_Ozero(_1238241)]]], (29541 ^ _778495) ^ [_1316081, _1316083, _1316085, _1316087] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1316081, _1316083, _1316085), hAPP(hAPP(c_COMBB(tc_fun(_1316083, tc_prod(_1316081, _1316083)), tc_fun(_1316083, _1316085), _1316081), hAPP(c_COMBB(tc_prod(_1316081, _1316083), _1316085, _1316083), _1316087)), c_Product__Type_OPair(_1316081, _1316083))) = _1316087)], (4198 ^ _778495) ^ [_842129, _842131] : [_842131 = _842129, -(c_Orderings_Oord__class_Omin(_842131) = c_Orderings_Oord__class_Omin(_842129))], (49715 ^ _778495) ^ [_1783319, _1783321, _1783323, _1783325, _1783327, _1783329] : [c_Fun_Oinj__on(_1783319, _1783321, _1783323, _1783325), hBOOL(hAPP(hAPP(c_member(_1783319), _1783327), _1783325)), hAPP(_1783323, _1783327) = _1783329, -(hAPP(c_Hilbert__Choice_Oinv__into(_1783319, _1783321, _1783325, _1783323), _1783329) = _1783327)], (10131 ^ _778495) ^ [_953181, _953183] : [class_Groups_Ocomm__monoid__mult(_953181), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953181), c_Groups_Oone__class_Oone(_953181)), _953183) = _953183)], (7368 ^ _778495) ^ [_900882, _900884] : [-(_900882 = c_Orderings_Obot__class_Obot(tc_fun(_900884, tc_HOL_Obool))), 7373 ^ _778495 : [(7376 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_900884), 7371 ^ [_900882, _900884]), 7372 ^ [_900882, _900884]))], (7374 ^ _778495) ^ [] : [-(_900882 = hAPP(hAPP(c_Set_Oinsert(_900884), 7371 ^ [_900882, _900884]), 7372 ^ [_900882, _900884]))]]], (38583 ^ _778495) ^ [_1525461, _1525463, _1525465, _1525467, _1525469, _1525471, _1525473, _1525475] : [hBOOL(hAPP(hAPP(_1525461, _1525463), _1525465)), hBOOL(hAPP(hAPP(_1525467, _1525465), _1525469)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1525471, _1525473, _1525475, _1525461, _1525467), _1525463), _1525469)))], (13320 ^ _778495) ^ [_1015508] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1015508)], (38641 ^ _778495) ^ [_1526676, _1526678, _1526680] : [-(hAPP(c_Relation_ODomain(_1526676, _1526678), hAPP(c_Set_OCollect(tc_prod(_1526676, _1526678)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526676, _1526678, tc_HOL_Obool), _1526680))) = hAPP(c_Set_OCollect(_1526676), hAPP(hAPP(c_COMBB(tc_fun(_1526678, tc_HOL_Obool), tc_HOL_Obool, _1526676), c_HOL_OEx(_1526678)), _1526680)))], (16896 ^ _778495) ^ [_1080309, _1080311, _1080313] : [class_Fields_Olinordered__field(_1080309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080309), c_Groups_Ozero__class_Ozero(_1080309)), _1080311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080309), c_Groups_Ozero__class_Ozero(_1080309)), _1080313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080309), c_Groups_Ozero__class_Ozero(_1080309)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1080309), _1080311), _1080313))))], (1208 ^ _778495) ^ [_796623, _796625] : [-(class_Groups_Oordered__ab__group__add(_796623)), _796625 = _796623, class_Groups_Oordered__ab__group__add(_796625)], (9566 ^ _778495) ^ [_941938, _941940, _941942, _941944] : [-(hBOOL(hAPP(hAPP(c_member(_941938), _941940), _941942))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941938, tc_HOL_Obool)), _941942), hAPP(hAPP(c_Set_Oinsert(_941938), _941940), _941944)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941938, tc_HOL_Obool)), _941942), _941944))], (43742 ^ _778495) ^ [_1653690, _1653692, _1653694] : [-(_1653690 = c_List_Olist_ONil(_1653692)), -(hAPP(c_List_Ohd(_1653692), hAPP(hAPP(c_List_Oappend(_1653692), _1653690), _1653694)) = hAPP(c_List_Ohd(_1653692), _1653690))], (21664 ^ _778495) ^ [_1166399] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1166399)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1166399)))], (36518 ^ _778495) ^ [_1465743, _1465745, _1465747, _1465749, _1465751] : [c_Fun_Oinj__on(_1465743, _1465745, _1465747, c_Orderings_Otop__class_Otop(tc_fun(_1465743, tc_HOL_Obool))), 36521 ^ _778495 : [(36528 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465743, tc_HOL_Obool)), _1465749), _1465751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465745, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1465743, _1465745, _1465747), _1465749)), hAPP(c_Set_Oimage(_1465743, _1465745, _1465747), _1465751))))], (36522 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465745, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1465743, _1465745, _1465747), _1465749)), hAPP(c_Set_Oimage(_1465743, _1465745, _1465747), _1465751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465743, tc_HOL_Obool)), _1465749), _1465751)))]]], (49148 ^ _778495) ^ [_1772505] : [-(c_Relation_Oantisym(_1772505, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1772505, _1772505), tc_HOL_Obool))))], (49047 ^ _778495) ^ [_1770323, _1770325, _1770327, _1770329, _1770331] : [c_Relation_Otrans(_1770323, _1770325), hBOOL(hAPP(hAPP(c_member(tc_prod(_1770323, _1770323)), hAPP(hAPP(c_Product__Type_OPair(_1770323, _1770323), _1770327), _1770329)), _1770325)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1770323, _1770323)), hAPP(hAPP(c_Product__Type_OPair(_1770323, _1770323), _1770329), _1770331)), _1770325)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1770323, _1770323)), hAPP(hAPP(c_Product__Type_OPair(_1770323, _1770323), _1770327), _1770331)), _1770325)))], (24525 ^ _778495) ^ [_1217529, _1217531, _1217533, _1217535] : [class_Rings_Ocomm__semiring__1(_1217529), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1217529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217529), _1217531), _1217533)), _1217535) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217529), hAPP(hAPP(c_Power_Opower__class_Opower(_1217529), _1217531), _1217535)), hAPP(hAPP(c_Power_Opower__class_Opower(_1217529), _1217533), _1217535)))], (9098 ^ _778495) ^ [_932189, _932191, _932193] : [class_Lattices_Osemilattice__inf(_932189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932189), _932191), _932193)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932189), _932193), _932191) = _932191)], (23999 ^ _778495) ^ [_1207979, _1207981, _1207983] : [class_Divides_Osemiring__div(_1207979), -(_1207981 = c_Groups_Ozero__class_Ozero(_1207979)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207979), _1207983), _1207981)), _1207981) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207979), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207979), _1207983), _1207981)), c_Groups_Oone__class_Oone(_1207979)))], (38150 ^ _778495) ^ [_1508297, _1508299, _1508301, _1508303] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1508297, _1508299), _1508301), _1508303) = hAPP(c_Set_OCollect(tc_prod(_1508299, _1508299)), hAPP(c_Product__Type_Oprod_Oprod__case(_1508299, _1508299, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1508299, tc_fun(tc_prod(_1508297, _1508297), tc_HOL_Obool), tc_fun(_1508299, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1508299, tc_fun(tc_fun(tc_prod(_1508297, _1508297), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1508297, _1508297), tc_HOL_Obool), tc_fun(_1508299, tc_HOL_Obool)), _1508299), c_COMBC(_1508299, tc_fun(tc_prod(_1508297, _1508297), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1508299, tc_prod(_1508297, _1508297)), tc_fun(_1508299, tc_fun(tc_fun(tc_prod(_1508297, _1508297), tc_HOL_Obool), tc_HOL_Obool)), _1508299), hAPP(c_COMBB(tc_prod(_1508297, _1508297), tc_fun(tc_fun(tc_prod(_1508297, _1508297), tc_HOL_Obool), tc_HOL_Obool), _1508299), c_member(tc_prod(_1508297, _1508297)))), hAPP(hAPP(c_COMBC(_1508299, tc_fun(_1508299, _1508297), tc_fun(_1508299, tc_prod(_1508297, _1508297))), hAPP(hAPP(c_COMBB(tc_fun(_1508297, tc_prod(_1508297, _1508297)), tc_fun(tc_fun(_1508299, _1508297), tc_fun(_1508299, tc_prod(_1508297, _1508297))), _1508299), c_COMBB(_1508297, tc_prod(_1508297, _1508297), _1508299)), hAPP(hAPP(c_COMBB(_1508297, tc_fun(_1508297, tc_prod(_1508297, _1508297)), _1508299), c_Product__Type_OPair(_1508297, _1508297)), _1508303))), _1508303)))), _1508301))))], (43327 ^ _778495) ^ [_1643017, _1643019, _1643021] : [-(c_List_Obutlast(_1643017, hAPP(hAPP(c_List_Oappend(_1643017), _1643019), hAPP(hAPP(c_List_Olist_OCons(_1643017), _1643021), c_List_Olist_ONil(_1643017)))) = _1643019)], (4148 ^ _778495) ^ [_841406, _841408] : [_841408 = _841406, -(c_List_Otl(_841408) = c_List_Otl(_841406))], (11380 ^ _778495) ^ [_975044, _975046, _975048, _975050] : [class_Rings_Ocomm__semiring__1(_975044), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975044), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975044), _975046), _975048)), _975050) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975044), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975044), _975046), _975050)), _975048))], (29835 ^ _778495) ^ [_1321072, _1321074] : [-(c_Divides_Odivmod__int__rel(_1321072, _1321074) = 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, _1321072))), 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), _1321074)))))), 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)), _1321074))), 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)), _1321074))))), 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)), _1321074)))), 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), _1321074))), 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))))))))], (26728 ^ _778495) ^ [_1256414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1256414))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1256414)))], (33250 ^ _778495) ^ [_1393010, _1393012, _1393014, _1393016, _1393018] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1393010, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393012, tc_fun(_1393010, tc_HOL_Obool)), _1393014), _1393016)), _1393018) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393012, tc_fun(_1393010, tc_HOL_Obool)), _1393014), hAPP(hAPP(c_COMBC(_1393012, tc_fun(_1393010, tc_HOL_Obool), tc_fun(_1393010, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393010, tc_HOL_Obool), tc_fun(tc_fun(_1393010, tc_HOL_Obool), tc_fun(_1393010, tc_HOL_Obool)), _1393012), c_Groups_Ominus__class_Ominus(tc_fun(_1393010, tc_HOL_Obool))), _1393016)), _1393018)))], (5446 ^ _778495) ^ [_861901, _861903] : [_861903 = _861901, -(c_Divides_Odiv__class_Odiv(_861903) = c_Divides_Odiv__class_Odiv(_861901))], (30973 ^ _778495) ^ [_1344130, _1344132, _1344134] : [class_Int_Onumber(_1344130), class_Orderings_Oord(_1344130), 30980 ^ _778495 : [(30987 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344130), hAPP(c_Int_Onumber__class_Onumber__of(_1344130), _1344132)), hAPP(c_Int_Onumber__class_Onumber__of(_1344130), _1344134)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344130), hAPP(c_Int_Onumber__class_Onumber__of(_1344130), _1344132)), hAPP(c_Int_Onumber__class_Onumber__of(_1344130), _1344134)) = hAPP(c_Int_Onumber__class_Onumber__of(_1344130), _1344132))], (30981 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344130), hAPP(c_Int_Onumber__class_Onumber__of(_1344130), _1344132)), hAPP(c_Int_Onumber__class_Onumber__of(_1344130), _1344134))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344130), hAPP(c_Int_Onumber__class_Onumber__of(_1344130), _1344132)), hAPP(c_Int_Onumber__class_Onumber__of(_1344130), _1344134)) = hAPP(c_Int_Onumber__class_Onumber__of(_1344130), _1344134))]]], (26270 ^ _778495) ^ [_1248152, _1248154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1248152)), -(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), _1248152), _1248154))))], (52207 ^ _778495) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (49166 ^ _778495) ^ [_1772848, _1772850] : [c_Relation_Oantisym(_1772848, _1772850), 49169 ^ _778495 : [(49170 ^ _778495) ^ [_1772960, _1772962] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1772848, _1772848)), hAPP(hAPP(c_Product__Type_OPair(_1772848, _1772848), _1772962), _1772960)), _1772850)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772848, _1772848)), hAPP(hAPP(c_Product__Type_OPair(_1772848, _1772848), _1772960), _1772962)), _1772850)), -(_1772962 = _1772960)]]], (43712 ^ _778495) ^ [_1653068, _1653070, _1653072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653068), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653070)), _1653072))), -(hAPP(hAPP(c_List_Oappend(_1653070), hAPP(hAPP(c_List_Otake(_1653070), _1653068), _1653072)), hAPP(hAPP(c_List_Olist_OCons(_1653070), hAPP(c_List_Ohd(_1653070), hAPP(hAPP(c_List_Odrop(_1653070), _1653068), _1653072))), c_List_Olist_ONil(_1653070))) = hAPP(hAPP(c_List_Otake(_1653070), hAPP(c_Nat_OSuc, _1653068)), _1653072))], (43548 ^ _778495) ^ [_1648988, _1648990] : [hAPP(c_List_Orotate1(_1648988), _1648990) = c_List_Olist_ONil(_1648988), -(_1648990 = c_List_Olist_ONil(_1648988))], (246 ^ _778495) ^ [_782462, _782464, _782466, _782468] : [-(c_Int_Oiszero(_782466, _782462)), c_Int_Oiszero(_782468, _782464), _782468 = _782466, _782464 = _782462], (44953 ^ _778495) ^ [_1679601, _1679603, _1679605] : [44955 ^ _778495 : [(44958 ^ _778495) ^ [] : [hBOOL(hAPP(_1679603, 44954 ^ [_1679601, _1679603, _1679605]))], (44956 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1679601), 44954 ^ [_1679601, _1679603, _1679605]), hAPP(c_List_Oset(_1679601), _1679605))))]], -(hBOOL(hAPP(c_List_Olistsp(_1679601, _1679603), _1679605)))], (48202 ^ _778495) ^ [_1750676, _1750678, _1750680, _1750682] : [-(hAPP(hAPP(c_List_Odrop(_1750676), _1750678), c_List_Oreplicate(_1750676, _1750680, _1750682)) = c_List_Oreplicate(_1750676, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1750680), _1750678), _1750682))], (41052 ^ _778495) ^ [_1585100, _1585102, _1585104, _1585106, _1585108, _1585110] : [c_Relation_Osingle__valued(_1585100, _1585102, _1585104), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585100, _1585102)), hAPP(hAPP(c_Product__Type_OPair(_1585100, _1585102), _1585106), _1585108)), _1585104)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585100, _1585102)), hAPP(hAPP(c_Product__Type_OPair(_1585100, _1585102), _1585106), _1585110)), _1585104)), -(_1585108 = _1585110)], (4388 ^ _778495) ^ [_845150, _845152, _845154, _845156, _845158, _845160, _845162, _845164, _845166, _845168] : [-(c_Option_Ooption_Ooption__case(_845168, _845164, _845160, _845156, _845152) = c_Option_Ooption_Ooption__case(_845166, _845162, _845158, _845154, _845150)), _845168 = _845166, _845164 = _845162, _845160 = _845158, _845156 = _845154, _845152 = _845150], (5990 ^ _778495) ^ [_874192, _874194, _874196] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_874192, tc_HOL_Obool)), _874194), _874196) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_874192, tc_HOL_Obool)), _874196), _874194))], (4442 ^ _778495) ^ [_846015, _846017] : [_846017 = _846015, -(c_List_Olist_OCons(_846017) = c_List_Olist_OCons(_846015))], (25373 ^ _778495) ^ [_1231880, _1231882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231882)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1231880)), hAPP(c_Int_Onat, _1231882)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231880), _1231882)))], (22584 ^ _778495) ^ [_1182223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1182223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1182223))))], (52377 ^ _778495) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (18564 ^ _778495) ^ [_1111851, _1111853, _1111855] : [class_Orderings_Olinorder(_1111851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111851), _1111853)), hBOOL(hAPP(hAPP(c_member(_1111851), _1111855), _1111853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111851), hAPP(c_Finite__Set_Ofold1(_1111851, c_Orderings_Oord__class_Omin(_1111851)), _1111853)), _1111855)))], (37971 ^ _778495) ^ [_1501971, _1501973, _1501975, _1501977, _1501979, _1501981] : [-(hAPP(c_Set_Oimage(_1501971, _1501973, hAPP(hAPP(c_COMBS(_1501971, _1501973, _1501973), hAPP(hAPP(c_COMBS(_1501971, _1501973, tc_fun(_1501973, _1501973)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1501973, tc_fun(_1501973, _1501973)), _1501971), c_If(_1501973)), _1501975)), _1501977)), _1501979)), _1501981) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501973, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1501971, _1501973, _1501977), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501971, tc_HOL_Obool)), _1501981), hAPP(c_Set_OCollect(_1501971), _1501975)))), hAPP(c_Set_Oimage(_1501971, _1501973, _1501979), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501971, tc_HOL_Obool)), _1501981), hAPP(c_Set_OCollect(_1501971), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1501971), c_fNot), _1501975))))))], (28839 ^ _778495) ^ [_1301882, _1301884, _1301886] : [class_Int_Onumber__ring(_1301882), 28842 ^ _778495 : [(28849 ^ _778495) ^ [] : [-(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), _1301884)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301882), hAPP(c_Int_Onumber__class_Onumber__of(_1301882), _1301886)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1301884))) = c_Groups_Oone__class_Oone(_1301882))], (28843 ^ _778495) ^ [] : [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), _1301884))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301882), hAPP(c_Int_Onumber__class_Onumber__of(_1301882), _1301886)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1301884))) = hAPP(hAPP(c_HOL_OLet(_1301882, _1301882), hAPP(hAPP(c_Power_Opower__class_Opower(_1301882), hAPP(c_Int_Onumber__class_Onumber__of(_1301882), _1301886)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1301884))), hAPP(hAPP(c_COMBS(_1301882, _1301882, _1301882), hAPP(hAPP(c_COMBB(_1301882, tc_fun(_1301882, _1301882), _1301882), c_Groups_Otimes__class_Otimes(_1301882)), hAPP(c_Groups_Otimes__class_Otimes(_1301882), hAPP(c_Int_Onumber__class_Onumber__of(_1301882), _1301886)))), c_COMBI(_1301882))))]]], (45650 ^ _778495) ^ [_1695227, _1695229, _1695231] : [-(c_Enum_On__lists(_1695227, hAPP(c_Nat_OSuc, _1695229), _1695231) = c_List_Oconcat(tc_List_Olist(_1695227), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695227), tc_List_Olist(tc_List_Olist(_1695227))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695227), tc_List_Olist(_1695227), tc_List_Olist(tc_List_Olist(_1695227))), hAPP(hAPP(c_COMBB(tc_fun(_1695227, tc_List_Olist(_1695227)), tc_fun(tc_List_Olist(_1695227), tc_List_Olist(tc_List_Olist(_1695227))), tc_List_Olist(_1695227)), c_List_Omap(_1695227, tc_List_Olist(_1695227))), hAPP(c_COMBC(_1695227, tc_List_Olist(_1695227), tc_List_Olist(_1695227)), c_List_Olist_OCons(_1695227)))), _1695231)), c_Enum_On__lists(_1695227, _1695229, _1695231))))], (43718 ^ _778495) ^ [_1653270, _1653272, _1653274] : [-(_1653270 = c_List_Olist_ONil(_1653272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653274), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653272)), _1653270))), -(hAPP(c_List_Ohd(_1653272), hAPP(hAPP(c_List_Odrop(_1653272), _1653274), _1653270)) = hAPP(hAPP(c_List_Onth(_1653272), _1653270), _1653274))], (52257 ^ _778495) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (13017 ^ _778495) ^ [_1010631, _1010633, _1010635, _1010637] : [class_Rings_Ocomm__semiring__1(_1010631), class_Rings_Ono__zero__divisors(_1010631), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010633), _1010635)), 13028 ^ _778495 : [(13038 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1010633, _1010631), _1010637), _1010635) = c_Groups_Ozero__class_Ozero(_1010631)), 13039 ^ _778495 : [(13040 ^ _778495) ^ [_1011009] : [hBOOL(hAPP(hAPP(c_member(_1010633), _1011009), _1010635)), hAPP(_1010637, _1011009) = c_Groups_Ozero__class_Ozero(_1010631)]]], (13029 ^ _778495) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1010633, _1010631), _1010637), _1010635) = c_Groups_Ozero__class_Ozero(_1010631), 13033 ^ _778495 : [(13036 ^ _778495) ^ [] : [-(hAPP(_1010637, 13032 ^ [_1010631, _1010633, _1010635, _1010637]) = c_Groups_Ozero__class_Ozero(_1010631))], (13034 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1010633), 13032 ^ [_1010631, _1010633, _1010635, _1010637]), _1010635)))]]]]], (49865 ^ _778495) ^ [_1786833, _1786835, _1786837, _1786839] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1786833, _1786835, _1786837, _1786839, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1786835)) = _1786837)], (24437 ^ _778495) ^ [_1215797, _1215799] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215797))), -(c_SMT_Oz3div(_1215799, _1215797) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215799), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1215797))))], (24882 ^ _778495) ^ [_1223618, _1223620] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223618))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223618), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223620)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40517 ^ _778495) ^ [_1571835, _1571837, _1571839, _1571841, _1571843] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571835, _1571835)), hAPP(hAPP(c_Product__Type_OPair(_1571835, _1571835), _1571837), _1571839)), _1571841)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571835, _1571835)), hAPP(hAPP(c_Product__Type_OPair(_1571835, _1571835), _1571839), _1571843)), c_Transitive__Closure_Ortrancl(_1571835, _1571841))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571835, _1571835)), hAPP(hAPP(c_Product__Type_OPair(_1571835, _1571835), _1571837), _1571843)), c_Transitive__Closure_Otrancl(_1571835, _1571841))))], (33894 ^ _778495) ^ [_1409361, _1409363, _1409365, _1409367] : [class_Groups_Ocomm__monoid__add(_1409361), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1409361), _1409363), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1409365)), hAPP(c_Nat_OSuc, _1409367))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1409361), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1409361, tc_Nat_Onat), _1409363), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1409365), _1409367)))], (26830 ^ _778495) ^ [_1258192] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1258192), hAPP(c_Int_Onumber__class_Onumber__of(_1258192), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1258192)), class_Int_Onumber__ring(_1258192), class_Rings_Olinordered__idom(_1258192)], (41961 ^ _778495) ^ [_1611389, _1611391, _1611393, _1611395] : [hBOOL(hAPP(hAPP(c_member(_1611389), _1611391), hAPP(c_List_Oset(_1611389), c_List_Osublist(_1611389, _1611393, _1611395)))), -(hBOOL(hAPP(hAPP(c_member(_1611389), _1611391), hAPP(c_List_Oset(_1611389), _1611393))))], (42091 ^ _778495) ^ [_1614535, _1614537, _1614539] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1614535), _1614537)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1614535)), hAPP(c_Set_OCollect(tc_List_Olist(_1614535)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1614535), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1614535)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614535), tc_fun(_1614535, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614535, tc_HOL_Obool), tc_fun(tc_fun(_1614535, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614535)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614535, tc_HOL_Obool))), c_List_Oset(_1614535))), _1614537))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614535), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1614535)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1614535)))), _1614539))))))], (19236 ^ _778495) ^ [_1124147, _1124149, _1124151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124147), _1124149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124151), _1124147)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124151), _1124149))))], (45931 ^ _778495) ^ [_1702680, _1702682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702680), _1702682)), -(c_List_Oupt(_1702682, _1702680) = c_List_Olist_ONil(tc_Nat_Onat))], (40916 ^ _778495) ^ [_1581607, _1581609, _1581611] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581607, _1581607)), _1581609), c_Transitive__Closure_Ortrancl(_1581607, _1581611))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581607, _1581607)), _1581609), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1581607, _1581607), 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(_1581607, _1581607), tc_HOL_Obool), tc_fun(tc_prod(_1581607, _1581607), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1581607, _1581607), tc_HOL_Obool)), _1581611)))))], (26874 ^ _778495) ^ [_1258890] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1258890, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43441 ^ _778495) ^ [_1646144, _1646146, _1646148, _1646150, _1646152, _1646154] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646144), tc_List_Olist(_1646144))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646144), tc_List_Olist(_1646144)), hAPP(hAPP(c_List_Oappend(_1646144), _1646146), hAPP(hAPP(c_List_Olist_OCons(_1646144), _1646148), c_List_Olist_ONil(_1646144)))), hAPP(hAPP(c_List_Oappend(_1646144), _1646150), hAPP(hAPP(c_List_Olist_OCons(_1646144), _1646152), c_List_Olist_ONil(_1646144))))), c_List_Olistrel1(_1646144, _1646154)))), 43442 ^ _778495 : [(43449 ^ _778495) ^ [] : [_1646146 = _1646150, hBOOL(hAPP(hAPP(c_member(tc_prod(_1646144, _1646144)), hAPP(hAPP(c_Product__Type_OPair(_1646144, _1646144), _1646148), _1646152)), _1646154))], (43443 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646144), tc_List_Olist(_1646144))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646144), tc_List_Olist(_1646144)), _1646146), _1646150)), c_List_Olistrel1(_1646144, _1646154))), _1646148 = _1646152]]], (2962 ^ _778495) ^ [_822465, _822467, _822469, _822471] : [-(c_List_Olenlex(_822471, _822467) = c_List_Olenlex(_822469, _822465)), _822471 = _822469, _822467 = _822465], (40995 ^ _778495) ^ [_1583443, _1583445, _1583447, _1583449] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583443, _1583443)), hAPP(hAPP(c_Product__Type_OPair(_1583443, _1583443), _1583445), _1583447)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583443, _1583443), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1583449))), -(_1583445 = _1583447)], (49947 ^ _778495) ^ [_1788666, _1788668, _1788670, _1788672] : [c_Fun_Obij__betw(_1788666, _1788668, _1788670, c_Orderings_Otop__class_Otop(tc_fun(_1788666, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788668, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1788666, _1788668, _1788670), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1788666, tc_HOL_Obool)), _1788672)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1788668, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1788666, _1788668, _1788670), _1788672)))], (45849 ^ _778495) ^ [_1700648, _1700650] : [-(c_List_Ofoldr(tc_List_Olist(_1700648), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700648)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700648))), c_List_Otranspose(_1700648, _1700650), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1700648))), hAPP(c_List_Ofilter(tc_List_Olist(_1700648), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700648)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700648), tc_List_Olist(_1700648), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700648)))), _1700650)))], (22690 ^ _778495) ^ [_1184091] : [-(c_Int_Osucc(c_Int_OBit1(_1184091)) = c_Int_OBit0(c_Int_Osucc(_1184091)))], (7794 ^ _778495) ^ [_907234, _907236, _907238] : [class_Orderings_Oorder(_907234), 7797 ^ _778495 : [(7806 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907234), _907236), _907238))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907234), _907236), _907238)), -(_907236 = _907238)], (7798 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907234), _907236), _907238)), 7801 ^ _778495 : [(7804 ^ _778495) ^ [] : [_907236 = _907238], (7802 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907234), _907236), _907238)))]]]]], (15129 ^ _778495) ^ [_1047073, _1047075, _1047077, _1047079, _1047081] : [class_Rings_Olinordered__semiring__strict(_1047073), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047073), _1047075), _1047077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047073), _1047079), _1047081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047073), c_Groups_Ozero__class_Ozero(_1047073)), _1047077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047073), c_Groups_Ozero__class_Ozero(_1047073)), _1047079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047073), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047073), _1047075), _1047079)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047073), _1047077), _1047081))))], (22832 ^ _778495) ^ [_1186584] : [-(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, _1186584))))))], (45073 ^ _778495) ^ [_1682376, _1682378, _1682380, _1682382, _1682384, _1682386, _1682388] : [c_List_Olist__all2(_1682376, _1682378, _1682380, hAPP(hAPP(c_List_Omap(_1682382, _1682376), _1682384), _1682386), _1682388), -(c_List_Olist__all2(_1682382, _1682378, hAPP(hAPP(c_COMBB(_1682376, tc_fun(_1682378, tc_HOL_Obool), _1682382), _1682380), _1682384), _1682386, _1682388))], (9554 ^ _778495) ^ [_941679, _941681, _941683, _941685] : [-(hBOOL(hAPP(hAPP(c_member(_941679), _941681), _941683))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941679, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_941679), _941681), _941685)), _941683) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941679, tc_HOL_Obool)), _941685), _941683))], (22748 ^ _778495) ^ [_1185095, _1185097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1185095), _1185097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1185095)), c_Int_OBit0(_1185097))))], (31888 ^ _778495) ^ [_1364326, _1364328, _1364330, _1364332, _1364334] : [class_Complete__Lattice_Ocomplete__lattice(_1364326), 31891 ^ _778495 : [(31892 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364326), _1364328), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364330, _1364326), _1364332), _1364334))), 31895 ^ _778495 : [(31896 ^ _778495) ^ [_1364507] : [hBOOL(hAPP(hAPP(c_member(_1364330), _1364507), _1364332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364326), _1364328), hAPP(_1364334, _1364507))))]]], (31902 ^ _778495) ^ [] : [31904 ^ _778495 : [(31907 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364326), _1364328), hAPP(_1364334, 31903 ^ [_1364326, _1364328, _1364330, _1364332, _1364334])))], (31905 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364330), 31903 ^ [_1364326, _1364328, _1364330, _1364332, _1364334]), _1364332)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364326), _1364328), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364330, _1364326), _1364332), _1364334))))]]], (41597 ^ _778495) ^ [_1601189, _1601191, _1601193] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601189, _1601189)), hAPP(hAPP(c_Product__Type_OPair(_1601189, _1601189), 41598 ^ [_1601189, _1601191, _1601193]), 41598 ^ [_1601189, _1601191, _1601193])), _1601191))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601189), tc_List_Olist(_1601189))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601189), tc_List_Olist(_1601189)), _1601193), _1601193)), c_List_Olexord(_1601189, _1601191)))], (32334 ^ _778495) ^ [_1373867, _1373869] : [32336 ^ _778495 : [(32339 ^ _778495) ^ [] : [hBOOL(hAPP(_1373869, 32335 ^ [_1373867, _1373869]))], (32337 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 32335 ^ [_1373867, _1373869]), _1373867)))]], 32340 ^ _778495 : [(32341 ^ _778495) ^ [_1374018] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1374018), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1373867))), -(hBOOL(hAPP(_1373869, _1374018)))]]], (49302 ^ _778495) ^ [_1775267, _1775269] : [49305 ^ _778495 : [(49308 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775267, _1775267)), hAPP(hAPP(c_Product__Type_OPair(_1775267, _1775267), 49304 ^ [_1775267, _1775269]), 49303 ^ [_1775267, _1775269])), _1775269))], (49306 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775267, _1775267)), hAPP(hAPP(c_Product__Type_OPair(_1775267, _1775267), 49303 ^ [_1775267, _1775269]), 49304 ^ [_1775267, _1775269])), _1775269)))]], -(c_Relation_Osym(_1775267, _1775269))], (21150 ^ _778495) ^ [_1157428, _1157430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157428), _1157430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1157428)), c_Int_OBit1(_1157430))))], (2746 ^ _778495) ^ [_819171, _819173, _819175, _819177, _819179, _819181, _819183, _819185] : [-(c_Product__Type_Oapfst(_819185, _819181, _819177, _819173) = c_Product__Type_Oapfst(_819183, _819179, _819175, _819171)), _819185 = _819183, _819181 = _819179, _819177 = _819175, _819173 = _819171], (51593 ^ _778495) ^ [_1820670, _1820672, _1820674] : [class_Divides_Oring__div(_1820670), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820670), _1820672), _1820674)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820670), _1820674), hAPP(c_Groups_Ouminus__class_Ouminus(_1820670), _1820672)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1820670), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820670), _1820674), _1820672)))], (40355 ^ _778495) ^ [_1567836, _1567838] : [-(hAPP(c_Relation_ODomain(_1567836, _1567836), c_Transitive__Closure_Ortrancl(_1567836, _1567838)) = c_Orderings_Otop__class_Otop(tc_fun(_1567836, tc_HOL_Obool)))], (12080 ^ _778495) ^ [_989717, _989719, _989721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989717), _989719)), 12083 ^ _778495 : [(12090 ^ _778495) ^ [] : [_989719 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989721), _989717), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989719), _989717) = _989721)], (12084 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989719), _989717) = _989721, -(_989719 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989721), _989717))]]], (22314 ^ _778495) ^ [_1177514, _1177516] : [class_Groups_Ogroup__add(_1177514), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177514), hAPP(c_Groups_Ouminus__class_Ouminus(_1177514), _1177516)), _1177516) = c_Groups_Ozero__class_Ozero(_1177514))], (40551 ^ _778495) ^ [_1572647] : [-(hAPP(c_Relation_ODomain(_1572647, _1572647), c_Relation_OId(_1572647)) = c_Orderings_Otop__class_Otop(tc_fun(_1572647, tc_HOL_Obool)))], (11426 ^ _778495) ^ [_976100, _976102, _976104, _976106] : [class_Rings_Ocomm__semiring__1(_976100), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976100), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976100), _976102), _976104)), _976106) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976100), _976102), _976106)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976100), _976104), _976106)))], (33487 ^ _778495) ^ [_1400342, _1400344, _1400346] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400342, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1400342, tc_HOL_Obool), _1400344)), _1400346) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1400342, tc_HOL_Obool), tc_fun(_1400342, tc_HOL_Obool)), _1400344), hAPP(hAPP(c_COMBC(tc_fun(_1400342, tc_HOL_Obool), tc_fun(_1400342, tc_HOL_Obool), tc_fun(_1400342, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400342, tc_HOL_Obool))), _1400346)))], (19100 ^ _778495) ^ [_1121859] : [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)), _1121859)), _1121859)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121859), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25142 ^ _778495) ^ [_1227927, _1227929, _1227931] : [-(hBOOL(hAPP(_1227927, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227929), _1227931)))), 25145 ^ _778495 : [(25148 ^ _778495) ^ [] : [hBOOL(hAPP(_1227927, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25146 ^ _778495) ^ [] : [-(_1227931 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25149 ^ _778495 : [(25154 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25152 ^ [_1227927, _1227929, _1227931]), _1227931)))], (25156 ^ _778495) ^ [] : [-(_1227929 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227931), 25151 ^ [_1227927, _1227929, _1227931])), 25152 ^ [_1227927, _1227929, _1227931]))], (25158 ^ _778495) ^ [] : [hBOOL(hAPP(_1227927, 25151 ^ [_1227927, _1227929, _1227931]))], (25150 ^ _778495) ^ [] : [_1227931 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43989 ^ _778495) ^ [_1658500, _1658502, _1658504, _1658506] : [class_Complete__Lattice_Ocomplete__lattice(_1658500), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1658502, _1658500), hAPP(c_List_Oset(_1658502), _1658504)), _1658506) = hAPP(c_List_Ofoldl(_1658500, _1658502, hAPP(c_COMBC(_1658502, _1658500, _1658500), hAPP(hAPP(c_COMBB(_1658500, tc_fun(_1658500, _1658500), _1658502), c_Lattices_Osemilattice__sup__class_Osup(_1658500)), _1658506)), c_Orderings_Obot__class_Obot(_1658500)), _1658504))], (38009 ^ _778495) ^ [_1502815, _1502817, _1502819, _1502821, _1502823] : [class_Groups_Ocomm__monoid__add(_1502815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502817), _1502819)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1502817, _1502815), _1502821), hAPP(c_Set_OCollect(_1502817), hAPP(hAPP(c_COMBS(_1502817, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1502817), c_fconj), hAPP(hAPP(c_COMBC(_1502817, tc_fun(_1502817, tc_HOL_Obool), tc_HOL_Obool), c_member(_1502817)), _1502819))), hAPP(hAPP(c_COMBC(_1502817, tc_fun(_1502817, tc_HOL_Obool), tc_HOL_Obool), c_member(_1502817)), _1502823)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1502817, _1502815), hAPP(hAPP(c_COMBC(_1502817, _1502815, _1502815), hAPP(hAPP(c_COMBS(_1502817, _1502815, tc_fun(_1502815, _1502815)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1502815, tc_fun(_1502815, _1502815)), _1502817), c_If(_1502815)), hAPP(hAPP(c_COMBC(_1502817, tc_fun(_1502817, tc_HOL_Obool), tc_HOL_Obool), c_member(_1502817)), _1502823))), _1502821)), c_Groups_Ozero__class_Ozero(_1502815))), _1502819))], (29318 ^ _778495) ^ [_1311575, _1311577, _1311579, _1311581] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1311575, _1311577), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1311579), _1311581))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1311575), _1311577) = _1311579)], (46913 ^ _778495) ^ [_1721907] : [-(c_List_Oreturn__list(_1721907) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1721907))], (12190 ^ _778495) ^ [_991936, _991938, _991940, _991942, _991944] : [class_Rings_Ocomm__semiring__1(_991936), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991936), _991938), _991940)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991936), _991942), _991944)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991936), _991942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991936), _991938), _991940)), _991944)))], (19620 ^ _778495) ^ [_1130803, _1130805, _1130807] : [class_Orderings_Olinorder(_1130803), hBOOL(hAPP(c_Finite__Set_Ofinite(_1130803), _1130805)), 19627 ^ _778495 : [(19634 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130803, tc_HOL_Obool)), _1130805), hAPP(hAPP(c_Set_Oinsert(_1130803), _1130807), c_Orderings_Obot__class_Obot(tc_fun(_1130803, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1130803, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1130803, hAPP(hAPP(c_Set_Oinsert(_1130803), _1130807), _1130805)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1130803), _1130807), c_Big__Operators_Olinorder__class_OMin(_1130803, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130803, tc_HOL_Obool)), _1130805), hAPP(hAPP(c_Set_Oinsert(_1130803), _1130807), c_Orderings_Obot__class_Obot(tc_fun(_1130803, tc_HOL_Obool)))))))], (19628 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130803, tc_HOL_Obool)), _1130805), hAPP(hAPP(c_Set_Oinsert(_1130803), _1130807), c_Orderings_Obot__class_Obot(tc_fun(_1130803, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1130803, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1130803, hAPP(hAPP(c_Set_Oinsert(_1130803), _1130807), _1130805)) = _1130807)]]], (35573 ^ _778495) ^ [_1443982, _1443984, _1443986] : [class_Rings_Oring__1(_1443982), -(hAPP(c_Int_Oring__1__class_Oof__int(_1443982), 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), _1443984), _1443986)), 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(_1443982), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1443982), _1443984)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1443982), _1443986)))], (49220 ^ _778495) ^ [_1773939, _1773941] : [c_Predicate_Oreflp(_1773939, _1773941), c_Predicate_Osymp(_1773939, _1773941), c_Predicate_Otransp(_1773939, _1773941), -(c_Equiv__Relations_Oequivp(_1773939, _1773941))], (37230 ^ _778495) ^ [_1481746, _1481748, _1481750, _1481752] : [c_Fun_Oinj__on(_1481746, _1481748, _1481750, c_Orderings_Otop__class_Otop(tc_fun(_1481746, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1481746, _1481748, _1481750), hAPP(c_Set_Oimage(_1481746, _1481748, _1481750), _1481752)) = _1481752)], (45725 ^ _778495) ^ [_1697179, _1697181] : [-(hAPP(c_List_Ofilter(_1697179, _1697181), c_List_Olist_ONil(_1697179)) = c_List_Olist_ONil(_1697179))], (33469 ^ _778495) ^ [_1399825, _1399827, _1399829, _1399831, _1399833] : [_1399825 = c_Orderings_Obot__class_Obot(tc_fun(_1399827, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399829, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399827, tc_fun(_1399829, tc_HOL_Obool)), _1399825), _1399831)), _1399833) = _1399833)], (14821 ^ _778495) ^ [_1041363, _1041365] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041363), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041363), _1041365)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41664 ^ _778495) ^ [_1603166, _1603168, _1603170, _1603172] : [c_List_Olistrelp(_1603166, hAPP(hAPP(c_COMBC(_1603166, tc_fun(tc_prod(_1603166, _1603166), tc_HOL_Obool), tc_fun(_1603166, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603166, tc_fun(tc_fun(tc_prod(_1603166, _1603166), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1603166, _1603166), tc_HOL_Obool), tc_fun(_1603166, tc_HOL_Obool)), _1603166), c_COMBC(_1603166, tc_fun(tc_prod(_1603166, _1603166), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603166, tc_prod(_1603166, _1603166)), tc_fun(_1603166, tc_fun(tc_fun(tc_prod(_1603166, _1603166), tc_HOL_Obool), tc_HOL_Obool)), _1603166), hAPP(c_COMBB(tc_prod(_1603166, _1603166), tc_fun(tc_fun(tc_prod(_1603166, _1603166), tc_HOL_Obool), tc_HOL_Obool), _1603166), c_member(tc_prod(_1603166, _1603166)))), c_Product__Type_OPair(_1603166, _1603166)))), _1603168), _1603170, _1603172), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603166), tc_List_Olist(_1603166))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603166), tc_List_Olist(_1603166)), _1603170), _1603172)), c_List_Olistrel(_1603166, _1603168))))], (27121 ^ _778495) ^ [_1262887, _1262889, _1262891] : [class_Rings_Oring__1(_1262887), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1262889), _1262891)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262887), hAPP(c_Int_Oring__1__class_Oof__int(_1262887), _1262889)), hAPP(c_Int_Oring__1__class_Oof__int(_1262887), _1262891)))], (13567 ^ _778495) ^ [_1019225, _1019227, _1019229, _1019231] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1019225, _1019227)), c_Sum__Type_OPlus(_1019225, _1019227, _1019229, _1019231))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1019225), _1019229)))], (42684 ^ _778495) ^ [_1629329, _1629331, _1629333] : [hAPP(hAPP(c_List_Otake(_1629329), _1629331), _1629333) = c_List_Olist_ONil(_1629329), -(_1629331 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1629333 = c_List_Olist_ONil(_1629329))], (11137 ^ _778495) ^ [_970159, _970161, _970163] : [class_Rings_Olinordered__semidom(_970159), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970159), c_Groups_Oone__class_Oone(_970159)), _970161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970159), c_Groups_Oone__class_Oone(_970159)), _970163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970159), c_Groups_Oone__class_Oone(_970159)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970159), _970161), _970163))))], (43526 ^ _778495) ^ [_1648399, _1648401, _1648403, _1648405] : [-(hAPP(hAPP(c_List_Otake(_1648399), _1648401), hAPP(hAPP(c_List_Odrop(_1648399), _1648403), _1648405)) = hAPP(hAPP(c_List_Odrop(_1648399), _1648403), hAPP(hAPP(c_List_Otake(_1648399), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1648401), _1648403)), _1648405)))], (6678 ^ _778495) ^ [_887738, _887740, _887742] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887738, tc_HOL_Obool)), _887740), _887742) = c_Orderings_Obot__class_Obot(tc_fun(_887738, tc_HOL_Obool))), _887740 = c_Orderings_Obot__class_Obot(tc_fun(_887738, tc_HOL_Obool)), _887742 = c_Orderings_Obot__class_Obot(tc_fun(_887738, tc_HOL_Obool))], (9560 ^ _778495) ^ [_941773, _941775, _941777, _941779] : [hBOOL(hAPP(hAPP(c_member(_941773), _941775), _941777)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941773, tc_HOL_Obool)), _941777), hAPP(hAPP(c_Set_Oinsert(_941773), _941775), _941779)) = hAPP(hAPP(c_Set_Oinsert(_941773), _941775), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941773, tc_HOL_Obool)), _941777), _941779)))], (47599 ^ _778495) ^ [_1737522, _1737524] : [class_Enum_Oenum(_1737522), 47602 ^ _778495 : [(47610 ^ _778495) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737522), _1737524)), 47613 ^ _778495 : [(47614 ^ _778495) ^ [_1737740] : [-(hBOOL(hAPP(_1737524, _1737740)))]]], (47603 ^ _778495) ^ [] : [hBOOL(hAPP(_1737524, 47604 ^ [_1737522, _1737524])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737522), _1737524)))]]], (37386 ^ _778495) ^ [_1486046, _1486048, _1486050, _1486052, _1486054, _1486056] : [class_Groups_Ocomm__monoid__mult(_1486046), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1486048, _1486046), hAPP(hAPP(c_COMBC(_1486048, tc_fun(_1486050, tc_HOL_Obool), _1486046), hAPP(hAPP(c_COMBB(tc_fun(_1486050, _1486046), tc_fun(tc_fun(_1486050, tc_HOL_Obool), _1486046), _1486048), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1486050, _1486046)), _1486052)), _1486054)), _1486056) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1486048, _1486050), _1486046), hAPP(c_Product__Type_Oprod_Oprod__case(_1486048, _1486050, _1486046), _1486052)), hAPP(hAPP(c_Product__Type_OSigma(_1486048, _1486050), _1486056), hAPP(c_COMBK(tc_fun(_1486050, tc_HOL_Obool), _1486048), _1486054))))], (52669 ^ _778495) ^ [] : [hBOOL(c_fFalse)], (49501 ^ _778495) ^ [_1778808, _1778810, _1778812] : [c_Relation_Orefl__on(_1778808, _1778810, _1778812), c_Relation_Osym(_1778808, _1778812), c_Relation_Otrans(_1778808, _1778812), -(c_Equiv__Relations_Oequiv(_1778808, _1778810, _1778812))], (21132 ^ _778495) ^ [_1157104, _1157106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1157104)), c_Int_OBit1(_1157106))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1157104), _1157106)))], (15958 ^ _778495) ^ [_1063321, _1063323] : [class_Rings_Olinordered__idom(_1063321), hBOOL(hAPP(hAPP(c_member(_1063321), _1063323), c_Int_Oring__1__class_OInts(_1063321))), 15965 ^ _778495 : [(15972 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063321), _1063323), c_Groups_Ozero__class_Ozero(_1063321))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063321), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063321), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063321), c_Groups_Oone__class_Oone(_1063321)), _1063323)), _1063323)), c_Groups_Ozero__class_Ozero(_1063321))))], (15966 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063321), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063321), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063321), c_Groups_Oone__class_Oone(_1063321)), _1063323)), _1063323)), c_Groups_Ozero__class_Ozero(_1063321))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063321), _1063323), c_Groups_Ozero__class_Ozero(_1063321))))]]], (36356 ^ _778495) ^ [_1462622, _1462624, _1462626, _1462628, _1462630] : [c_Fun_Oinj__on(_1462622, _1462624, _1462626, c_Orderings_Otop__class_Otop(tc_fun(_1462622, tc_HOL_Obool))), 36359 ^ _778495 : [(36366 ^ _778495) ^ [] : [_1462628 = _1462630, -(hAPP(c_Set_Oimage(_1462622, _1462624, _1462626), _1462628) = hAPP(c_Set_Oimage(_1462622, _1462624, _1462626), _1462630))], (36360 ^ _778495) ^ [] : [hAPP(c_Set_Oimage(_1462622, _1462624, _1462626), _1462628) = hAPP(c_Set_Oimage(_1462622, _1462624, _1462626), _1462630), -(_1462628 = _1462630)]]], (26044 ^ _778495) ^ [_1244178, _1244180, _1244182] : [class_Rings_Oring__1__no__zero__divisors(_1244178), -(_1244180 = c_Groups_Ozero__class_Ozero(_1244178)), hAPP(hAPP(c_Power_Opower__class_Opower(_1244178), _1244180), _1244182) = c_Groups_Ozero__class_Ozero(_1244178)], (11484 ^ _778495) ^ [_977356, _977358, _977360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977356), _977358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977356), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977360), _977358))))], (9392 ^ _778495) ^ [_938319, _938321, _938323, _938325] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938319, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938319, tc_HOL_Obool)), _938321), _938323)), _938325) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938319, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938319, tc_HOL_Obool)), _938321), _938325)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938319, tc_HOL_Obool)), _938323), _938325)))], (21382 ^ _778495) ^ [_1161833, _1161835, _1161837] : [class_Fields_Olinordered__field__inverse__zero(_1161833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161833), c_Groups_Ozero__class_Ozero(_1161833)), _1161835)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161833), hAPP(c_Groups_Oabs__class_Oabs(_1161833), _1161837)), _1161835) = hAPP(c_Groups_Oabs__class_Oabs(_1161833), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161833), _1161837), _1161835)))], (49999 ^ _778495) ^ [_1789769, _1789771, _1789773, _1789775] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1789769), _1789771)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1789773), _1789775)), 50006 ^ _778495 : [(50013 ^ _778495) ^ [] : [hAPP(c_Finite__Set_Ocard(_1789769), _1789771) = hAPP(c_Finite__Set_Ocard(_1789773), _1789775), -(c_Fun_Obij__betw(_1789769, _1789773, 50016 ^ [_1789769, _1789771, _1789773, _1789775], _1789771, _1789775))], (50007 ^ _778495) ^ [] : [50008 ^ _778495 : [(50009 ^ _778495) ^ [_1789958] : [c_Fun_Obij__betw(_1789769, _1789773, _1789958, _1789771, _1789775)]], -(hAPP(c_Finite__Set_Ocard(_1789769), _1789771) = hAPP(c_Finite__Set_Ocard(_1789773), _1789775))]]], (49612 ^ _778495) ^ [_1780875, _1780877, _1780879, _1780881, _1780883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1780875, tc_HOL_Obool)), _1780877), hAPP(c_Set_Oimage(_1780879, _1780875, _1780881), _1780883))), -(c_Fun_Oinj__on(_1780875, _1780879, c_Hilbert__Choice_Oinv__into(_1780879, _1780875, _1780883, _1780881), _1780877))], (35929 ^ _778495) ^ [_1452582, _1452584, _1452586, _1452588, _1452590, _1452592] : [c_Equiv__Relations_Oequiv(_1452582, _1452584, _1452586), c_Equiv__Relations_Ocongruent(_1452582, tc_fun(_1452588, tc_HOL_Obool), _1452586, _1452590), hBOOL(hAPP(hAPP(c_member(_1452582), _1452592), _1452584)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1452582, tc_fun(_1452588, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1452582, _1452582, _1452586), hAPP(hAPP(c_Set_Oinsert(_1452582), _1452592), c_Orderings_Obot__class_Obot(tc_fun(_1452582, tc_HOL_Obool))))), _1452590) = hAPP(_1452590, _1452592))], (8212 ^ _778495) ^ [_913939, _913941, _913943] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913939), _913941)), hBOOL(hAPP(c_Finite__Set_Ofinite(_913939), _913943)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_913939), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913939, tc_HOL_Obool)), _913941), _913943))))], (40425 ^ _778495) ^ [_1569569, _1569571, _1569573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1569569, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1569569, _1569569, _1569571), _1569573)), _1569573)), -(hAPP(c_Relation_OImage(_1569569, _1569569, c_Transitive__Closure_Ortrancl(_1569569, _1569571)), _1569573) = _1569573)], (17888 ^ _778495) ^ [_1099219, _1099221, _1099223, _1099225] : [class_Orderings_Olinorder(_1099219), 17891 ^ _778495 : [(17892 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099219), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099219), _1099221), _1099223)), _1099225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099219), _1099221), _1099225))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099219), _1099223), _1099225)))], (17902 ^ _778495) ^ [] : [17903 ^ _778495 : [(17906 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099219), _1099223), _1099225))], (17904 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099219), _1099221), _1099225))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099219), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099219), _1099221), _1099223)), _1099225)))]]], (47084 ^ _778495) ^ [_1725565, _1725567, _1725569, _1725571, _1725573] : [class_Groups_Omonoid__add(_1725565), 47090 ^ _778495 : [(47095 ^ _778495) ^ [] : [hAPP(_1725573, 47089 ^ [_1725565, _1725567, _1725569, _1725571, _1725573]) = c_Groups_Ozero__class_Ozero(_1725565)], (47093 ^ _778495) ^ [] : [hBOOL(hAPP(_1725571, 47089 ^ [_1725565, _1725567, _1725569, _1725571, _1725573]))], (47091 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725567), 47089 ^ [_1725565, _1725567, _1725569, _1725571, _1725573]), hAPP(c_List_Oset(_1725567), _1725569))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1725565), hAPP(hAPP(c_List_Omap(_1725567, _1725565), _1725573), hAPP(c_List_Ofilter(_1725567, _1725571), _1725569))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1725565), hAPP(hAPP(c_List_Omap(_1725567, _1725565), _1725573), _1725569)))], (42636 ^ _778495) ^ [_1628521] : [-(hBOOL(hAPP(c_List_Odistinct(_1628521), c_List_Olist_ONil(_1628521))))], (30651 ^ _778495) ^ [_1338102, _1338104, _1338106, _1338108, _1338110] : [class_Orderings_Olinorder(_1338102), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338102), _1338104), _1338106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338102), _1338108), _1338110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338102), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338102), _1338104), _1338108)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338102), _1338106), _1338110))))], (11001 ^ _778495) ^ [_967722, _967724, _967726] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967722)), _967724)), hAPP(c_Nat_OSuc, _967726)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967722), _967724)), _967726))], (49891 ^ _778495) ^ [_1787333, _1787335, _1787337, _1787339, _1787341] : [hBOOL(hAPP(_1787333, hAPP(hAPP(c_Product__Type_OPair(_1787335, _1787337), _1787339), _1787341))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1787335, _1787337, tc_HOL_Obool, _1787333), _1787339), _1787341)))], (5378 ^ _778495) ^ [_860737, _860739, _860741, _860743, _860745, _860747, _860749, _860751, _860753, _860755] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_860755, _860751, _860747, _860743, _860739) = c_SetInterval_Oord_OgreaterThanAtMost(_860753, _860749, _860745, _860741, _860737)), _860755 = _860753, _860751 = _860749, _860747 = _860745, _860743 = _860741, _860739 = _860737], (20173 ^ _778495) ^ [_1140856] : [_1140856 = 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), _1140856)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13111 ^ _778495) ^ [_1012266, _1012268] : [class_Rings_Ocomm__semiring__1(_1012266), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012266), c_Groups_Ozero__class_Ozero(_1012266)), _1012268) = _1012268)], (35404 ^ _778495) ^ [_1440009, _1440011, _1440013] : [class_Lattices_Olattice(_1440009), hAPP(_1440011, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1440009), 35409 ^ [_1440009, _1440011, _1440013]), 35410 ^ [_1440009, _1440011, _1440013])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1440009), hAPP(_1440011, 35409 ^ [_1440009, _1440011, _1440013])), hAPP(_1440011, 35410 ^ [_1440009, _1440011, _1440013])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440009), _1440013)), -(_1440013 = c_Orderings_Obot__class_Obot(tc_fun(_1440009, tc_HOL_Obool))), -(hAPP(_1440011, c_Big__Operators_Olattice__class_OSup__fin(_1440009, _1440013)) = c_Big__Operators_Olattice__class_OSup__fin(_1440009, hAPP(c_Set_Oimage(_1440009, _1440009, _1440011), _1440013)))], (24503 ^ _778495) ^ [_1217006, _1217008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217006)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1217006), _1217008)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1217006)), _1217008))], (34835 ^ _778495) ^ [_1430134] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1430134)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1430134)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1430134)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (27115 ^ _778495) ^ [_1262786, _1262788] : [class_Int_Onumber__ring(_1262786), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262786), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1262788)) = hAPP(c_Int_Onumber__class_Onumber__of(_1262786), _1262788))], (49879 ^ _778495) ^ [_1787012] : [-(c_Quickcheck_Obeyond(_1787012, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (49757 ^ _778495) ^ [_1784096, _1784098, _1784100, _1784102, _1784104] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1784096, _1784098, _1784100, _1784102), _1784104) = c_Hilbert__Choice_OEps(_1784096, hAPP(hAPP(c_COMBS(_1784096, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1784096), c_fconj), hAPP(hAPP(c_COMBC(_1784096, tc_fun(_1784096, tc_HOL_Obool), tc_HOL_Obool), c_member(_1784096)), _1784100))), hAPP(hAPP(c_COMBC(_1784096, _1784098, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1784098, tc_fun(_1784098, tc_HOL_Obool), _1784096), c_fequal), _1784102)), _1784104))))], (26150 ^ _778495) ^ [_1246086, _1246088, _1246090] : [class_Rings_Olinordered__semidom(_1246086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246086), c_Groups_Ozero__class_Ozero(_1246086)), _1246088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246086), c_Groups_Ozero__class_Ozero(_1246086)), hAPP(hAPP(c_Power_Opower__class_Opower(_1246086), _1246088), _1246090))))], (52741 ^ _778495) ^ [_1836706, _1836708] : [hBOOL(hAPP(hAPP(c_fimplies, _1836706), _1836708)), hBOOL(_1836706), -(hBOOL(_1836708))], (36972 ^ _778495) ^ [_1475583, _1475585, _1475587, _1475589] : [-(c_Wellfounded_Omax__extp(_1475583, _1475585, _1475587, _1475589)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475583), _1475587)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475583), _1475589)), -(_1475589 = c_Orderings_Obot__class_Obot(tc_fun(_1475583, tc_HOL_Obool))), 36986 ^ _778495 : [(36989 ^ _778495) ^ [_1475928] : [hBOOL(hAPP(hAPP(c_member(_1475583), _1475928), _1475589)), hBOOL(hAPP(hAPP(_1475585, 36985 ^ [_1475583, _1475585, _1475587, _1475589]), _1475928))], (36987 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475583), 36985 ^ [_1475583, _1475585, _1475587, _1475589]), _1475587)))]]], (28151 ^ _778495) ^ [_1280733, _1280735] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1280733), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280735)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280733)) = 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), _1280735), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1280733)))), 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)))], (29938 ^ _778495) ^ [_1323207] : [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), _1323207))), -(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), _1323207)) = 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), _1323207))))], (11767 ^ _778495) ^ [_982859, _982861, _982863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982859), _982861)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982859), _982863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _982861), _982863)))], (38365 ^ _778495) ^ [_1517548, _1517550] : [-(c_Product__Type_Oapfst(_1517548, _1517548, _1517550, c_Fun_Oid(_1517548)) = c_Fun_Oid(tc_prod(_1517548, _1517550)))], (44500 ^ _778495) ^ [_1669617, _1669619, _1669621, _1669623, _1669625] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1669617), tc_List_Olist(_1669619), tc_List_Olist(_1669621), hAPP(c_List_Omap(_1669617, _1669619), _1669623)), hAPP(c_List_Omap(_1669621, _1669617), _1669625)) = hAPP(c_List_Omap(_1669621, _1669619), hAPP(c_Fun_Ocomp(_1669617, _1669619, _1669621, _1669623), _1669625)))], (23014 ^ _778495) ^ [_1189913, _1189915, _1189917, _1189919] : [class_Divides_Osemiring__div(_1189913), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1189913), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1189913), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189913), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1189913), _1189915), _1189917)), _1189917)), c_Divides_Odiv__class_Omod(_1189913, _1189915, _1189917))), _1189919) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1189913), _1189915), _1189919))], (16674 ^ _778495) ^ [_1076603, _1076605, _1076607] : [class_Fields_Olinordered__field(_1076603), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076603), _1076605), c_Groups_Ozero__class_Ozero(_1076603))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076603), c_Groups_Ozero__class_Ozero(_1076603)), _1076607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076603), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1076603), _1076605), _1076607)), c_Groups_Ozero__class_Ozero(_1076603))))], (13350 ^ _778495) ^ [_1015848] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1015848) = _1015848)], (52641 ^ _778495) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (31023 ^ _778495) ^ [_1345285] : [class_Orderings_Oord(_1345285), -(c_Orderings_Oord__class_Omax(_1345285) = c_Orderings_Oord_Omax(_1345285, c_Orderings_Oord__class_Oless__eq(_1345285)))], (8550 ^ _778495) ^ [_921244, _921246, _921248, _921250] : [class_Groups_Oab__semigroup__mult(_921244), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921244), _921246), _921248)), _921250) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921244), _921246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921244), _921248), _921250)))], (48410 ^ _778495) ^ [_1754603, _1754605, _1754607, _1754609, _1754611] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1754603, _1754605, _1754607) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754603, _1754609, _1754611), 48413 ^ _778495 : [(48416 ^ _778495) ^ [] : [-(_1754607 = _1754611)], (48414 ^ _778495) ^ [] : [-(_1754605 = _1754609)]]], (2834 ^ _778495) ^ [_820539, _820541, _820543, _820545, _820547, _820549] : [-(c_Nitpick_Otimes__frac(_820549, _820545, _820541) = c_Nitpick_Otimes__frac(_820547, _820543, _820539)), _820549 = _820547, _820545 = _820543, _820541 = _820539], (45670 ^ _778495) ^ [_1696003, _1696005, _1696007] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696003)), hAPP(c_List_Ofilter(_1696003, _1696005), _1696007))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696003)), hAPP(c_List_Ofilter(_1696003, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1696003), c_fNot), _1696005)), _1696007))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696003)), _1696007))], (46999 ^ _778495) ^ [_1723779, _1723781, _1723783] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723779)), c_List_OdropWhile(_1723779, _1723781, _1723783))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723779)), _1723783))))], (35559 ^ _778495) ^ [_1443519, _1443521, _1443523, _1443525] : [-(hAPP(c_Relation_OImage(_1443519, _1443521, _1443523), _1443525) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1443519, tc_fun(_1443521, tc_HOL_Obool)), _1443525), hAPP(hAPP(c_COMBB(tc_fun(_1443519, tc_HOL_Obool), tc_fun(_1443521, tc_HOL_Obool), _1443519), c_Relation_OImage(_1443519, _1443521, _1443523)), hAPP(hAPP(c_COMBC(_1443519, tc_fun(_1443519, tc_HOL_Obool), tc_fun(_1443519, tc_HOL_Obool)), c_Set_Oinsert(_1443519)), c_Orderings_Obot__class_Obot(tc_fun(_1443519, tc_HOL_Obool))))))], (33274 ^ _778495) ^ [_1393953, _1393955, _1393957, _1393959, _1393961] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393953, tc_fun(_1393955, tc_HOL_Obool)), _1393957), hAPP(hAPP(c_COMBC(_1393953, tc_fun(_1393955, tc_HOL_Obool), tc_fun(_1393955, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393955, tc_HOL_Obool), tc_fun(tc_fun(_1393955, tc_HOL_Obool), tc_fun(_1393955, tc_HOL_Obool)), _1393953), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1393955, tc_HOL_Obool))), _1393959)), _1393961)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1393955, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393953, tc_fun(_1393955, tc_HOL_Obool)), _1393957), _1393959)), _1393961))], (3028 ^ _778495) ^ [_823546, _823548, _823550, _823552, _823554, _823556] : [-(c_List_Oset__Cons(_823556, _823552, _823548) = c_List_Oset__Cons(_823554, _823550, _823546)), _823556 = _823554, _823552 = _823550, _823548 = _823546], (38725 ^ _778495) ^ [_1528089, _1528091] : [c_Wellfounded_Owf(_1528089, _1528091), -(c_Wellfounded_Owf(tc_fun(_1528089, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1528089, _1528091)))], (39204 ^ _778495) ^ [_1539996, _1539998, _1540000, _1540002] : [c_Equiv__Relations_Ocongruent(_1539996, _1539998, _1540000, _1540002), 39207 ^ _778495 : [(39208 ^ _778495) ^ [_1540141] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539996, _1539996)), _1540141), _1540000)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1539996, _1539996, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1539996, tc_fun(_1539996, _1539998), tc_fun(_1539996, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1539998, tc_HOL_Obool), tc_fun(tc_fun(_1539996, _1539998), tc_fun(_1539996, tc_HOL_Obool)), _1539996), c_COMBB(_1539998, tc_HOL_Obool, _1539996)), hAPP(hAPP(c_COMBB(_1539998, tc_fun(_1539998, tc_HOL_Obool), _1539996), c_fequal), _1540002))), _1540002)), _1540141)))]]], (33090 ^ _778495) ^ [_1389117, _1389119, _1389121, _1389123] : [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), _1389117), _1389119)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1389121), _1389123))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1389117), _1389123) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1389121), _1389119))], (33317 ^ _778495) ^ [_1396149, _1396151, _1396153, _1396155, _1396157] : [class_Complete__Lattice_Ocomplete__lattice(_1396149), 33320 ^ _778495 : [(33321 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396149), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396151, _1396149), _1396153), _1396155)), _1396157)), 33324 ^ _778495 : [(33325 ^ _778495) ^ [_1396330] : [hBOOL(hAPP(hAPP(c_member(_1396151), _1396330), _1396153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396149), hAPP(_1396155, _1396330)), _1396157)))]]], (33331 ^ _778495) ^ [] : [33333 ^ _778495 : [(33336 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396149), hAPP(_1396155, 33332 ^ [_1396149, _1396151, _1396153, _1396155, _1396157])), _1396157))], (33334 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1396151), 33332 ^ [_1396149, _1396151, _1396153, _1396155, _1396157]), _1396153)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396149), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396151, _1396149), _1396153), _1396155)), _1396157)))]]], (2586 ^ _778495) ^ [_816661, _816663, _816665, _816667, _816669, _816671, _816673, _816675] : [-(c_Nitpick_Oprod(_816675, _816671, _816667, _816663) = c_Nitpick_Oprod(_816673, _816669, _816665, _816661)), _816675 = _816673, _816671 = _816669, _816667 = _816665, _816663 = _816661], (36474 ^ _778495) ^ [_1464927, _1464929, _1464931] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1464927), _1464929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1464927, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1464927, _1464927, _1464931), _1464929)), _1464929)), c_Fun_Oinj__on(_1464927, _1464927, _1464931, _1464929), -(hAPP(c_Set_Oimage(_1464927, _1464927, _1464931), _1464929) = _1464929)], (18068 ^ _778495) ^ [_1102648] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1102648) = c_Orderings_Oord__class_Omin(_1102648)), class_Lattices_Osemilattice__inf(_1102648), class_Orderings_Olinorder(_1102648)], (25562 ^ _778495) ^ [_1235251, _1235253] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1235251)))), _1235253) = 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)))), _1235251)), _1235253))], (41077 ^ _778495) ^ [_1585635, _1585637, _1585639] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585635, _1585635)), _1585637), c_Transitive__Closure_Otrancl(_1585635, _1585639)))), 41078 ^ _778495 : [(41079 ^ _778495) ^ [_1585714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1585714)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585635, _1585635)), _1585637), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585635, _1585635), tc_HOL_Obool), _1585714), _1585639)))]]], (16462 ^ _778495) ^ [_1072615, _1072617, _1072619, _1072621] : [class_Fields_Olinordered__field(_1072615), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072615), c_Groups_Ozero__class_Ozero(_1072615)), _1072617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072615), _1072619), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072615), _1072621), _1072617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072615), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1072615), _1072619), _1072617)), _1072621)))], (31762 ^ _778495) ^ [_1359654, _1359656] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1359654, tc_HOL_Obool), _1359656) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1359654, tc_HOL_Obool), tc_fun(_1359654, tc_HOL_Obool)), _1359656), c_COMBI(tc_fun(_1359654, tc_HOL_Obool))))], (48541 ^ _778495) ^ [_1757378, _1757380, _1757382] : [hBOOL(hAPP(hAPP(c_member(_1757378), _1757382), hAPP(c_List_Oset(_1757378), _1757380))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1757378), _1757380), _1757382)))], (49953 ^ _778495) ^ [_1788833, _1788835, _1788837, _1788839, _1788841, _1788843, _1788845] : [c_Fun_Obij__betw(_1788833, _1788835, _1788837, _1788839, _1788841), c_Fun_Obij__betw(_1788833, _1788835, _1788837, _1788843, _1788845), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1788835, tc_HOL_Obool)), _1788841), _1788845) = c_Orderings_Obot__class_Obot(tc_fun(_1788835, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1788833, _1788835, _1788837, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1788833, tc_HOL_Obool)), _1788839), _1788843), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1788835, tc_HOL_Obool)), _1788841), _1788845)))], (52645 ^ _778495) ^ [_1835420] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1835420)))], (36594 ^ _778495) ^ [_1467404, _1467406, _1467408, _1467410, _1467412] : [c_Fun_Oinj__on(_1467404, _1467406, _1467408, c_Orderings_Otop__class_Otop(tc_fun(_1467404, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1467404, _1467406, _1467408), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467404, tc_HOL_Obool)), _1467410), _1467412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467406, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1467404, _1467406, _1467408), _1467410)), hAPP(c_Set_Oimage(_1467404, _1467406, _1467408), _1467412)))], (38621 ^ _778495) ^ [_1526235, _1526237, _1526239, _1526241, _1526243, _1526245, _1526247] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1526235, _1526237, _1526239, _1526241, _1526243), _1526245), _1526247))), 38622 ^ _778495 : [(38623 ^ _778495) ^ [_1526306] : [hBOOL(hAPP(hAPP(_1526241, _1526245), _1526306)), hBOOL(hAPP(hAPP(_1526243, _1526306), _1526247))]]], (11420 ^ _778495) ^ [_975941, _975943, _975945, _975947] : [class_Rings_Ocomm__semiring(_975941), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975941), _975943), _975945)), _975947) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975941), _975943), _975947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975941), _975945), _975947)))], (47744 ^ _778495) ^ [_1740482, _1740484, _1740486] : [c_List_Olist__ex(_1740482, _1740484, hAPP(c_List_Orev(_1740482), _1740486)), -(c_List_Olist__ex(_1740482, _1740484, _1740486))], (13314 ^ _778495) ^ [_1015403] : [hAPP(c_Nat_OSuc, _1015403) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37550 ^ _778495) ^ [_1490694, _1490696, _1490698, _1490700] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1490694, _1490696), _1490698), _1490700) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1490694, tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool)), _1490698), hAPP(hAPP(c_COMBS(_1490694, tc_fun(_1490696, tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool)), tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490696, tc_HOL_Obool), tc_fun(tc_fun(_1490696, tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool)), tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool)), _1490694), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1490696, tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool))), _1490700)), hAPP(hAPP(c_COMBC(_1490694, tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool), tc_fun(_1490696, tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1490696, tc_fun(tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool), tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool), tc_fun(_1490696, tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool))), _1490694), c_COMBC(_1490696, tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool), tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1490696, tc_prod(_1490694, _1490696)), tc_fun(_1490696, tc_fun(tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool), tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool))), _1490694), hAPP(c_COMBB(tc_prod(_1490694, _1490696), tc_fun(tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool), tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool)), _1490696), c_Set_Oinsert(tc_prod(_1490694, _1490696)))), c_Product__Type_OPair(_1490694, _1490696)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490694, _1490696), tc_HOL_Obool))))))], (4712 ^ _778495) ^ [_850228, _850230, _850232, _850234, _850236, _850238, _850240, _850242, _850244, _850246, _850248, _850250] : [-(c_Partial__Function_Ofun__lub(_850250, _850246, _850242, _850238, _850234, _850230) = c_Partial__Function_Ofun__lub(_850248, _850244, _850240, _850236, _850232, _850228)), _850250 = _850248, _850246 = _850244, _850242 = _850240, _850238 = _850236, _850234 = _850232, _850230 = _850228], (39720 ^ _778495) ^ [_1552266, _1552268, _1552270, _1552272, _1552274, _1552276] : [c_Finite__Set_Ofolding(_1552266, _1552268, _1552270, _1552272), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552266), _1552274)), -(hAPP(hAPP(_1552272, _1552274), _1552276) = hAPP(hAPP(c_Finite__Set_Ofold(_1552266, _1552268, _1552270), _1552276), _1552274))], (48854 ^ _778495) ^ [_1764898, _1764900, _1764902, _1764904] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1764898, tc_fun(_1764900, tc_HOL_Obool)), _1764902), _1764904) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1764900, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1764900, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1764898, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1764900, tc_HOL_Obool)), c_HOL_OEx(_1764898)), hAPP(hAPP(c_COMBB(tc_fun(_1764898, tc_HOL_Obool), tc_fun(_1764898, tc_HOL_Obool), tc_fun(_1764900, tc_HOL_Obool)), hAPP(c_COMBS(_1764898, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1764898), c_fconj), hAPP(hAPP(c_COMBC(_1764898, tc_fun(_1764898, tc_HOL_Obool), tc_HOL_Obool), c_member(_1764898)), _1764902)))), hAPP(hAPP(c_COMBC(tc_fun(_1764900, tc_HOL_Obool), tc_fun(_1764898, tc_fun(_1764900, tc_HOL_Obool)), tc_fun(_1764898, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1764900, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1764898, tc_fun(_1764900, tc_HOL_Obool)), tc_fun(_1764898, tc_HOL_Obool)), tc_fun(_1764900, tc_HOL_Obool)), c_COMBB(tc_fun(_1764900, tc_HOL_Obool), tc_HOL_Obool, _1764898)), c_fequal)), _1764904))))))], (43798 ^ _778495) ^ [_1654511] : [-(c_List_Orotate(_1654511, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1654511)))], (52585 ^ _778495) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (24812 ^ _778495) ^ [_1222496, _1222498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1222496), _1222498)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1222496, _1222498) = _1222496)], (35749 ^ _778495) ^ [_1448502, _1448504, _1448506, _1448508, _1448510, _1448512, _1448514] : [c_Equiv__Relations_Oequiv(_1448502, _1448504, _1448506), hBOOL(hAPP(hAPP(c_member(tc_fun(_1448502, tc_HOL_Obool)), _1448508), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448502), _1448504), _1448506))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1448502, tc_HOL_Obool)), _1448510), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448502), _1448504), _1448506))), hBOOL(hAPP(hAPP(c_member(_1448502), _1448512), _1448508)), hBOOL(hAPP(hAPP(c_member(_1448502), _1448514), _1448510)), 35768 ^ _778495 : [(35775 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1448502, _1448502)), hAPP(hAPP(c_Product__Type_OPair(_1448502, _1448502), _1448512), _1448514)), _1448506)), -(_1448508 = _1448510)], (35769 ^ _778495) ^ [] : [_1448508 = _1448510, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1448502, _1448502)), hAPP(hAPP(c_Product__Type_OPair(_1448502, _1448502), _1448512), _1448514)), _1448506)))]]], (52603 ^ _778495) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (8912 ^ _778495) ^ [_928327, _928329, _928331] : [class_Lattices_Olattice(_928327), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928327), _928329), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928327), _928329), _928331)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928327), _928329), _928331))], (44099 ^ _778495) ^ [_1661023, _1661025, _1661027, _1661029, _1661031] : [class_Orderings_Olinorder(_1661023), 44102 ^ _778495 : [(44111 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1661025), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661025, _1661023, _1661027), _1661029), _1661031)))), -(hBOOL(hAPP(hAPP(c_member(_1661025), _1661029), hAPP(c_List_Oset(_1661025), _1661031)))), hBOOL(hAPP(c_List_Odistinct(_1661025), _1661031))], (44103 ^ _778495) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1661025), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661025, _1661023, _1661027), _1661029), _1661031))), 44106 ^ _778495 : [(44109 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1661025), _1661031)))], (44107 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1661025), _1661029), hAPP(c_List_Oset(_1661025), _1661031)))]]]]], (47276 ^ _778495) ^ [_1729795, _1729797] : [-(c_Wellfounded_Owf(_1729795, c_List_Omeasures(_1729795, _1729797)))], (38814 ^ _778495) ^ [_1529860, _1529862, _1529864] : [c_Wellfounded_Owf(_1529860, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529860, _1529860), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529860, _1529860), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1529860, _1529860, _1529860), _1529862), _1529862)), hAPP(hAPP(c_Relation_Orel__comp(_1529860, _1529860, _1529860), _1529864), _1529862))), _1529864)), -(c_Wellfounded_Owf(_1529860, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529860, _1529860), tc_HOL_Obool)), _1529862), _1529864)))], (20592 ^ _778495) ^ [_1147777, _1147779] : [class_Int_Onumber__ring(_1147777), class_Rings_Olinordered__idom(_1147777), 20599 ^ _778495 : [(20606 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1147779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147777), c_Groups_Ozero__class_Ozero(_1147777)), hAPP(c_Int_Onumber__class_Onumber__of(_1147777), _1147779))))], (20600 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147777), c_Groups_Ozero__class_Ozero(_1147777)), hAPP(c_Int_Onumber__class_Onumber__of(_1147777), _1147779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1147779)))]]], (1018 ^ _778495) ^ [_793826, _793828, _793830, _793832, _793834, _793836, _793838, _793840, _793842, _793844, _793846, _793848] : [-(c_Equiv__Relations_Ocongruent2(_793846, _793842, _793838, _793834, _793830, _793826)), c_Equiv__Relations_Ocongruent2(_793848, _793844, _793840, _793836, _793832, _793828), _793848 = _793846, _793844 = _793842, _793840 = _793838, _793836 = _793834, _793832 = _793830, _793828 = _793826], (22490 ^ _778495) ^ [_1180595, _1180597] : [class_Groups_Oordered__ab__group__add__abs(_1180595), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180595), hAPP(c_Groups_Ouminus__class_Ouminus(_1180595), _1180597)), hAPP(c_Groups_Oabs__class_Oabs(_1180595), _1180597))))], (52557 ^ _778495) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (45658 ^ _778495) ^ [_1695771, _1695773, _1695775, _1695777, _1695779] : [class_Orderings_Olinorder(_1695771), -(hAPP(c_List_Ofilter(_1695773, _1695775), c_List_Olinorder__class_Osort__key(_1695773, _1695771, _1695777, _1695779)) = c_List_Olinorder__class_Osort__key(_1695773, _1695771, _1695777, hAPP(c_List_Ofilter(_1695773, _1695775), _1695779)))], (21834 ^ _778495) ^ [_1169238, _1169240, _1169242] : [class_Lattices_Oboolean__algebra(_1169238), 21837 ^ _778495 : [(21844 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169238), _1169242), _1169240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169238), hAPP(c_Groups_Ouminus__class_Ouminus(_1169238), _1169240)), hAPP(c_Groups_Ouminus__class_Ouminus(_1169238), _1169242))))], (21838 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169238), hAPP(c_Groups_Ouminus__class_Ouminus(_1169238), _1169240)), hAPP(c_Groups_Ouminus__class_Ouminus(_1169238), _1169242))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169238), _1169242), _1169240)))]]], (9965 ^ _778495) ^ [_949757, _949759, _949761, _949763, _949765, _949767] : [c_Finite__Set_Ofun__left__comm(_949757, _949759, _949761), hBOOL(hAPP(c_Finite__Set_Ofinite(_949757), _949763)), hBOOL(hAPP(hAPP(c_member(_949757), _949765), _949763)), -(hAPP(hAPP(c_Finite__Set_Ofold(_949757, _949759, _949761), _949767), _949763) = hAPP(hAPP(_949761, _949765), hAPP(hAPP(c_Finite__Set_Ofold(_949757, _949759, _949761), _949767), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949757, tc_HOL_Obool)), _949763), hAPP(hAPP(c_Set_Oinsert(_949757), _949765), c_Orderings_Obot__class_Obot(tc_fun(_949757, tc_HOL_Obool)))))))], (30349 ^ _778495) ^ [_1331511] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1331511)), 30353 ^ _778495 : [(30354 ^ _778495) ^ [_1331591] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1331591), _1331511)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1331591), 30352 ^ [_1331511])))]]], (31570 ^ _778495) ^ [_1355223, _1355225, _1355227] : [class_Orderings_Olinorder(_1355223), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355223), _1355225)), -(hBOOL(hAPP(hAPP(c_member(_1355223), _1355227), _1355225))), -(c_Big__Operators_Olinorder__class_OMax(_1355223, hAPP(hAPP(c_Set_Oinsert(_1355223), _1355227), _1355225)) = hAPP(hAPP(c_Finite__Set_Ofold(_1355223, _1355223, c_Orderings_Oord__class_Omax(_1355223)), _1355227), _1355225))], (26396 ^ _778495) ^ [_1250526, _1250528, _1250530] : [class_Rings_Olinordered__semidom(_1250526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250526), c_Groups_Oone__class_Oone(_1250526)), _1250528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250526), c_Groups_Oone__class_Oone(_1250526)), hAPP(hAPP(c_Power_Opower__class_Opower(_1250526), _1250528), hAPP(c_Nat_OSuc, _1250530)))))], (8024 ^ _778495) ^ [_910528, _910530, _910532, _910534] : [class_Orderings_Oorder(_910528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910528), _910530), _910532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910528), _910534), _910530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910528), _910534), _910532)))], (48150 ^ _778495) ^ [_1749012, _1749014, _1749016, _1749018, _1749020] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749012, _1749014, _1749016), _1749018), _1749020)), -(hBOOL(hAPP(hAPP(_1749016, _1749020), _1749018)))], (41306 ^ _778495) ^ [_1591946, _1591948] : [-(c_Nitpick_Ouminus__frac(_1591946, _1591948) = c_Nitpick_OAbs__Frac(_1591946, 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(_1591946), _1591948))), hAPP(c_Nitpick_Odenom(_1591946), _1591948))))], (19014 ^ _778495) ^ [_1120432, _1120434] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120432)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120434)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1120432), _1120434)))], (12172 ^ _778495) ^ [_991473, _991475, _991477, _991479] : [class_Rings_Ocomm__semiring__1(_991473), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991473), _991475), _991477)), _991479) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991473), _991475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991473), _991477), _991479)))], (20337 ^ _778495) ^ [_1143842, _1143844, _1143846] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1143842), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143842)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143844)), _1143846)) = 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), _1143842), _1143844))), _1143846))], (11779 ^ _778495) ^ [_983103, _983105, _983107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983103), _983105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983105), _983107))))], (21112 ^ _778495) ^ [_1156695, _1156697, _1156699] : [class_Fields_Olinordered__field__inverse__zero(_1156695), -(hAPP(c_Groups_Oabs__class_Oabs(_1156695), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156695), _1156697), _1156699)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156695), hAPP(c_Groups_Oabs__class_Oabs(_1156695), _1156697)), hAPP(c_Groups_Oabs__class_Oabs(_1156695), _1156699)))], (34194 ^ _778495) ^ [_1415758, _1415760, _1415762] : [class_Orderings_Olinorder(_1415758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1415758), _1415760), _1415762)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415758, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1415758), _1415760)), c_SetInterval_Oord__class_OatLeastAtMost(_1415758, _1415760, _1415762)) = hAPP(c_SetInterval_Oord__class_OatMost(_1415758), _1415762))], (47099 ^ _778495) ^ [_1725956, _1725958] : [class_Orderings_Olinorder(_1725956), 47106 ^ _778495 : [(47111 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1725956), hAPP(hAPP(c_List_Onth(_1725956), _1725958), 47104 ^ [_1725956, _1725958])), hAPP(hAPP(c_List_Onth(_1725956), _1725958), 47105 ^ [_1725956, _1725958])))], (47109 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47105 ^ [_1725956, _1725958]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725956)), _1725958))))], (47107 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47104 ^ [_1725956, _1725958]), 47105 ^ [_1725956, _1725958])))]], -(c_List_Olinorder__class_Osorted(_1725956, _1725958))], (27921 ^ _778495) ^ [_1276569, _1276571] : [c_Nat__Transfer_Ois__nat(_1276569), c_Nat__Transfer_Ois__nat(_1276571), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1276569, _1276571)))], (48394 ^ _778495) ^ [_1754274, _1754276, _1754278] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1754274, _1754276), _1754278) = c_Lazy__Sequence_Oproduct(_1754274, _1754276, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1754274, _1754278), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1754276, _1754278))), class_Lazy__Sequence_Osmall__lazy(_1754274), class_Lazy__Sequence_Osmall__lazy(_1754276)], (36799 ^ _778495) ^ [_1472388, _1472390, _1472392, _1472394, _1472396, _1472398] : [c_Fun_Oinj__on(_1472388, _1472390, _1472392, _1472394), hBOOL(hAPP(hAPP(c_member(_1472390), _1472396), hAPP(c_Set_Oimage(_1472388, _1472390, _1472392), _1472394))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472388, tc_HOL_Obool)), _1472394), _1472398)), -(hBOOL(hAPP(hAPP(c_member(_1472388), hAPP(c_Fun_Othe__inv__into(_1472388, _1472390, _1472394, _1472392), _1472396)), _1472398)))], (51057 ^ _778495) ^ [_1811595, _1811597] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811595), _1811597)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811597), _1811595))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811597), _1811595)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811595), _1811597)))], (42620 ^ _778495) ^ [_1628224, _1628226, _1628228] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628224), tc_List_Olist(_1628224))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628224), tc_List_Olist(_1628224)), _1628226), c_List_Olist_ONil(_1628224))), c_List_Olistrel(_1628224, _1628228))), -(_1628226 = c_List_Olist_ONil(_1628224))], (5945 ^ _778495) ^ [_873342] : [class_Lattices_Osemilattice__sup(_873342), -(c_Finite__Set_Ofun__left__comm__idem(_873342, _873342, c_Lattices_Osemilattice__sup__class_Osup(_873342)))], (43187 ^ _778495) ^ [_1640264, _1640266, _1640268] : [_1640264 = _1640266, -(_1640264 = hAPP(hAPP(c_List_Oappend(_1640268), c_List_Olist_ONil(_1640268)), _1640266))], (9580 ^ _778495) ^ [_942225, _942227, _942229, _942231] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942225, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942225, tc_HOL_Obool)), _942227), _942229)), _942231) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942225, tc_HOL_Obool)), _942227), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942225, tc_HOL_Obool)), _942229), _942231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942225, tc_HOL_Obool)), _942231), _942227)))], (37104 ^ _778495) ^ [_1478701, _1478703, _1478705, _1478707, _1478709, _1478711] : [hAPP(_1478701, _1478703) = _1478705, hBOOL(hAPP(hAPP(c_member(_1478707), _1478705), _1478709)), -(hBOOL(hAPP(hAPP(c_member(_1478711), _1478703), hAPP(c_Set_Ovimage(_1478711, _1478707, _1478701), _1478709))))], (38334 ^ _778495) ^ [_1516623, _1516625, _1516627, _1516629, _1516631, _1516633] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1516623), _1516625)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516627), _1516629)), 38344 ^ _778495 : [(38347 ^ _778495) ^ [] : [hAPP(c_Finite__Set_Ocard(_1516623), hAPP(c_Set_OCollect(_1516623), hAPP(hAPP(c_COMBS(_1516623, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1516623), c_fconj), hAPP(hAPP(c_COMBC(_1516623, tc_fun(_1516623, tc_HOL_Obool), tc_HOL_Obool), c_member(_1516623)), _1516625))), hAPP(hAPP(c_COMBC(_1516623, _1516627, tc_HOL_Obool), _1516631), 38343 ^ [_1516623, _1516625, _1516627, _1516629, _1516631, _1516633])))) = hAPP(_1516633, 38343 ^ [_1516623, _1516625, _1516627, _1516629, _1516631, _1516633])], (38345 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1516627), 38343 ^ [_1516623, _1516625, _1516627, _1516629, _1516631, _1516633]), _1516629)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1516623, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1516627, tc_HOL_Obool), tc_Nat_Onat, _1516623), c_Finite__Set_Ocard(_1516627)), hAPP(hAPP(c_COMBB(tc_fun(_1516627, tc_HOL_Obool), tc_fun(_1516627, tc_HOL_Obool), _1516623), c_Set_OCollect(_1516627)), hAPP(hAPP(c_COMBB(tc_fun(_1516627, tc_HOL_Obool), tc_fun(_1516627, tc_HOL_Obool), _1516623), hAPP(c_COMBS(_1516627, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1516627), c_fconj), hAPP(hAPP(c_COMBC(_1516627, tc_fun(_1516627, tc_HOL_Obool), tc_HOL_Obool), c_member(_1516627)), _1516629)))), _1516631)))), _1516625) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1516627, tc_Nat_Onat), _1516633), _1516629))], (41614 ^ _778495) ^ [_1601628, _1601630, _1601632, _1601634] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601628), tc_List_Olist(_1601628))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601628), tc_List_Olist(_1601628)), _1601630), _1601632)), c_List_Olistrel(_1601628, _1601634))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601628)), _1601630) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601628)), _1601632))], (37150 ^ _778495) ^ [_1479738, _1479740, _1479742, _1479744, _1479746] : [hBOOL(hAPP(_1479744, hAPP(_1479742, _1479746))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1479738, _1479740, _1479742), _1479744), _1479746)))], (968 ^ _778495) ^ [_793087, _793089, _793091, _793093] : [-(c_Equiv__Relations_Oequivp(_793091, _793087)), c_Equiv__Relations_Oequivp(_793093, _793089), _793093 = _793091, _793089 = _793087], (30473 ^ _778495) ^ [_1334210, _1334212, _1334214, _1334216, _1334218] : [-(hBOOL(hAPP(hAPP(c_member(_1334210), _1334212), c_SetInterval_Oord_OatLeastAtMost(_1334210, _1334214, _1334216, _1334218)))), hBOOL(hAPP(hAPP(_1334214, _1334216), _1334212)), hBOOL(hAPP(hAPP(_1334214, _1334212), _1334218))], (43023 ^ _778495) ^ [_1636470, _1636472, _1636474, _1636476, _1636478] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636470), _1636472), _1636474) = hAPP(hAPP(c_List_Oappend(_1636470), _1636476), _1636478)), 43024 ^ _778495 : [(43031 ^ _778495) ^ [_1636653] : [hAPP(hAPP(c_List_Olist_OCons(_1636470), _1636472), _1636653) = _1636476, _1636474 = hAPP(hAPP(c_List_Oappend(_1636470), _1636653), _1636478)], (43025 ^ _778495) ^ [] : [_1636476 = c_List_Olist_ONil(_1636470), hAPP(hAPP(c_List_Olist_OCons(_1636470), _1636472), _1636474) = _1636478]]], (5596 ^ _778495) ^ [_864108, _864110, _864112, _864114, _864116, _864118] : [-(c_COMBS(_864118, _864114, _864110) = c_COMBS(_864116, _864112, _864108)), _864118 = _864116, _864114 = _864112, _864110 = _864108], (29761 ^ _778495) ^ [_1319646, _1319648, _1319650, _1319652, _1319654, _1319656, _1319658] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1319646, _1319648), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1319650), _1319652))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1319654, _1319648), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1319656), _1319658))), -(_1319648 = 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), _1319646), _1319654), _1319648), 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), _1319650), _1319656)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1319652), _1319658)), _1319648))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1319652), _1319658), _1319648)))))], (7442 ^ _778495) ^ [_902075, _902077, _902079] : [class_Orderings_Olinorder(_902075), 7445 ^ _778495 : [(7446 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902075), _902077), _902079))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902075), _902079), _902077))), -(_902077 = _902079)], (7456 ^ _778495) ^ [] : [7457 ^ _778495 : [(7460 ^ _778495) ^ [] : [_902077 = _902079], (7458 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902075), _902079), _902077))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902075), _902077), _902079))]]], (49664 ^ _778495) ^ [_1782074, _1782076, _1782078, _1782080] : [hAPP(c_Set_Oimage(_1782074, _1782076, _1782078), c_Orderings_Otop__class_Otop(tc_fun(_1782074, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782076, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1782074, _1782076, _1782078), hAPP(c_Set_Oimage(_1782076, _1782074, c_Hilbert__Choice_Oinv__into(_1782074, _1782076, c_Orderings_Otop__class_Otop(tc_fun(_1782074, tc_HOL_Obool)), _1782078)), _1782080)) = _1782080)], (34749 ^ _778495) ^ [_1428415, _1428417, _1428419] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1428415), _1428417), _1428419) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1428415), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1428415, tc_Int_Oint), _1428417), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1428419))), class_Groups_Ocomm__monoid__add(_1428415), class_Groups_Ocomm__monoid__mult(_1428415)], (34086 ^ _778495) ^ [_1413523, _1413525] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1413523), _1413525))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1413523), hAPP(c_Nat_OSuc, _1413525)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (2262 ^ _778495) ^ [_811615, _811617, _811619, _811621, _811623, _811625, _811627, _811629] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_811629, _811625, _811621, _811617) = c_Nat_Osemiring__1__class_Oof__nat__aux(_811627, _811623, _811619, _811615)), _811629 = _811627, _811625 = _811623, _811621 = _811619, _811617 = _811615], (6964 ^ _778495) ^ [_892866, _892868, _892870] : [hBOOL(hAPP(hAPP(c_member(_892866), _892868), hAPP(c_fequal, _892870))), -(_892868 = _892870)], (45530 ^ _778495) ^ [_1692099, _1692101, _1692103, _1692105] : [class_Orderings_Olinorder(_1692099), 45533 ^ _778495 : [(45540 ^ _778495) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1692101), _1692105)), -(hBOOL(hAPP(c_List_Odistinct(_1692101), c_List_Olinorder__class_Osort__key(_1692101, _1692099, _1692103, _1692105))))], (45534 ^ _778495) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1692101), c_List_Olinorder__class_Osort__key(_1692101, _1692099, _1692103, _1692105))), -(hBOOL(hAPP(c_List_Odistinct(_1692101), _1692105)))]]], (31392 ^ _778495) ^ [_1351867, _1351869, _1351871] : [class_Orderings_Olinorder(_1351867), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351867), _1351869)), -(hBOOL(hAPP(hAPP(c_member(_1351867), _1351871), _1351869))), -(_1351869 = c_Orderings_Obot__class_Obot(tc_fun(_1351867, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1351867, c_Orderings_Oord__class_Omax(_1351867), hAPP(hAPP(c_Set_Oinsert(_1351867), _1351871), _1351869)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351867), _1351871), c_Big__Operators_Olattice_OSup__fin(_1351867, c_Orderings_Oord__class_Omax(_1351867), _1351869)))], (39978 ^ _778495) ^ [_1558107, _1558109, _1558111, _1558113] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1558107, tc_HOL_Obool), tc_fun(_1558107, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1558107, tc_HOL_Obool), tc_fun(_1558107, tc_HOL_Obool)), _1558109), _1558111)), c_Wellfounded_Omax__ext(_1558107, _1558113))), 39981 ^ _778495 : [(39984 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1558107), _1558111)))], (39986 ^ _778495) ^ [] : [_1558111 = c_Orderings_Obot__class_Obot(tc_fun(_1558107, tc_HOL_Obool))], (39988 ^ _778495) ^ [_1558401] : [hBOOL(hAPP(hAPP(c_member(_1558107), _1558401), _1558109)), 39992 ^ _778495 : [(39995 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1558107, _1558107)), hAPP(hAPP(c_Product__Type_OPair(_1558107, _1558107), _1558401), 39991 ^ [_1558107, _1558109, _1558111, _1558113, _1558401])), _1558113)))], (39993 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558107), 39991 ^ [_1558107, _1558109, _1558111, _1558113, _1558401]), _1558111)))]]], (39982 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1558107), _1558109)))]]], (33680 ^ _778495) ^ [_1405665, _1405667, _1405669, _1405671, _1405673] : [class_Orderings_Olinorder(_1405665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405665), _1405667), _1405669)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405665), _1405671), _1405673)), 33691 ^ _778495 : [(33700 ^ _778495) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1405665, _1405667), _1405669) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1405665, _1405671), _1405673)), _1405667 = _1405671, _1405669 = _1405673], (33692 ^ _778495) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1405665, _1405667), _1405669) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1405665, _1405671), _1405673), 33695 ^ _778495 : [(33698 ^ _778495) ^ [] : [-(_1405669 = _1405673)], (33696 ^ _778495) ^ [] : [-(_1405667 = _1405671)]]]]], (50533 ^ _778495) ^ [_1802263, _1802265, _1802267] : [50535 ^ _778495 : [(50538 ^ _778495) ^ [] : [hBOOL(hAPP(_1802263, 50534 ^ [_1802263, _1802265, _1802267]))], (50536 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50534 ^ [_1802263, _1802265, _1802267]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1802265), _1802267))))]], -(c_List_Oall__interval__nat(_1802263, _1802265, _1802267))], (23054 ^ _778495) ^ [_1190935, _1190937] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1190935), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1190937), _1190935)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1190937), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190937, _1190935)))], (3426 ^ _778495) ^ [_829729, _829731, _829733, _829735] : [-(c_Random_Oselect__weight(_829735, _829731) = c_Random_Oselect__weight(_829733, _829729)), _829735 = _829733, _829731 = _829729], (10137 ^ _778495) ^ [_953276, _953278] : [class_Groups_Omonoid__mult(_953276), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953276), c_Groups_Oone__class_Oone(_953276)), _953278) = _953278)], (41696 ^ _778495) ^ [_1604499, _1604501, _1604503, _1604505, _1604507, _1604509] : [-(c_List_Olistrelp(_1604499, _1604501, hAPP(hAPP(c_List_Olist_OCons(_1604499), _1604503), _1604505), hAPP(hAPP(c_List_Olist_OCons(_1604499), _1604507), _1604509))), hBOOL(hAPP(hAPP(_1604501, _1604503), _1604507)), c_List_Olistrelp(_1604499, _1604501, _1604505, _1604509)], (41113 ^ _778495) ^ [_1586529] : [-(c_Nat_Ofunpow(_1586529) = c_Nat_Ocompow(_1586529, _1586529))], (51325 ^ _778495) ^ [_1815897, _1815899] : [class_Rings_Ocomm__semiring__1(_1815897), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815897), _1815899), _1815899)))], (49467 ^ _778495) ^ [_1778279, _1778281] : [c_Relation_Osym(_1778279, _1778281), -(c_Relation_Osym(tc_List_Olist(_1778279), c_List_Olistrel(_1778279, _1778281)))], (51757 ^ _778495) ^ [_1823415, _1823417, _1823419] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823415, _1823417) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1823419), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 51760 ^ _778495 : [(51763 ^ _778495) ^ [] : [-(_1823417 = _1823419)], (51761 ^ _778495) ^ [] : [-(_1823415 = _1823417)]]], (52223 ^ _778495) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (42970 ^ _778495) ^ [_1635122] : [class_Orderings_Olinorder(_1635122), -(c_List_Olinorder__class_Osorted__list__of__set(_1635122, c_Orderings_Obot__class_Obot(tc_fun(_1635122, tc_HOL_Obool))) = c_List_Olist_ONil(_1635122))], (48090 ^ _778495) ^ [_1747706, _1747708] : [-(c_List_Osplice(_1747706, _1747708, c_List_Olist_ONil(_1747706)) = _1747708)], (9592 ^ _778495) ^ [_942601, _942603, _942605] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_942601), _942603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942601, tc_HOL_Obool)), _942605), _942603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_942601), _942605)), hAPP(c_Finite__Set_Ocard(_942601), _942603))))], (37563 ^ _778495) ^ [_1491205, _1491207, _1491209, _1491211] : [-(c_Fun_Oinj__on(_1491205, tc_prod(_1491207, _1491205), 37561 ^ [_1491205, _1491207, _1491209, _1491211], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1491207, tc_fun(_1491205, tc_HOL_Obool)), _1491209), _1491211)))], (18164 ^ _778495) ^ [_1104585, _1104587, _1104589, _1104591] : [class_Fields_Ofield__inverse__zero(_1104585), class_Int_Onumber(_1104585), 18171 ^ _778495 : [(18172 ^ _778495) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104585), _1104587), hAPP(c_Int_Onumber__class_Onumber__of(_1104585), _1104589)) = _1104591, 18175 ^ _778495 : [(18182 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1104585), _1104589) = c_Groups_Ozero__class_Ozero(_1104585), -(_1104591 = c_Groups_Ozero__class_Ozero(_1104585))], (18176 ^ _778495) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1104585), _1104589) = c_Groups_Ozero__class_Ozero(_1104585)), -(_1104587 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104585), _1104591), hAPP(c_Int_Onumber__class_Onumber__of(_1104585), _1104589)))]]], (18188 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104585), _1104587), hAPP(c_Int_Onumber__class_Onumber__of(_1104585), _1104589)) = _1104591), 18191 ^ _778495 : [(18194 ^ _778495) ^ [] : [_1104587 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104585), _1104591), hAPP(c_Int_Onumber__class_Onumber__of(_1104585), _1104589))], (18192 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1104585), _1104589) = c_Groups_Ozero__class_Ozero(_1104585)]], 18195 ^ _778495 : [(18198 ^ _778495) ^ [] : [_1104591 = c_Groups_Ozero__class_Ozero(_1104585)], (18196 ^ _778495) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1104585), _1104589) = c_Groups_Ozero__class_Ozero(_1104585))]]]]], (22424 ^ _778495) ^ [_1179495, _1179497, _1179499] : [class_Rings_Odivision__ring(_1179495), -(_1179497 = c_Groups_Ozero__class_Ozero(_1179495)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1179495), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179495), _1179499), _1179497)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179495), _1179499), hAPP(c_Groups_Ouminus__class_Ouminus(_1179495), _1179497)))], (36420 ^ _778495) ^ [_1463839, _1463841, _1463843, _1463845] : [c_Fun_Oinj__on(_1463839, _1463841, _1463843, c_Orderings_Otop__class_Otop(tc_fun(_1463839, tc_HOL_Obool))), 36423 ^ _778495 : [(36437 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1463841), _1463845), hAPP(c_Set_Oimage(_1463839, _1463841, _1463843), c_Orderings_Otop__class_Otop(tc_fun(_1463839, tc_HOL_Obool)))))), 36438 ^ _778495 : [(36439 ^ _778495) ^ [_1464242] : [_1463845 = hAPP(_1463843, _1464242), 36443 ^ _778495 : [(36446 ^ _778495) ^ [] : [36442 ^ [_1463839, _1463841, _1463843, _1463845, _1464242] = _1464242], (36444 ^ _778495) ^ [] : [-(_1463845 = hAPP(_1463843, 36442 ^ [_1463839, _1463841, _1463843, _1463845, _1464242]))]]]]], (36424 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1463841), _1463845), hAPP(c_Set_Oimage(_1463839, _1463841, _1463843), c_Orderings_Otop__class_Otop(tc_fun(_1463839, tc_HOL_Obool))))), 36428 ^ _778495 : [(36431 ^ _778495) ^ [_1464104] : [_1463845 = hAPP(_1463843, _1464104), -(_1464104 = 36427 ^ [_1463839, _1463841, _1463843, _1463845])], (36429 ^ _778495) ^ [] : [-(_1463845 = hAPP(_1463843, 36427 ^ [_1463839, _1463841, _1463843, _1463845]))]]]]], (20046 ^ _778495) ^ [_1138592, _1138594] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138592)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138594)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1138592), _1138594)))], (30813 ^ _778495) ^ [_1340925, _1340927, _1340929, _1340931] : [class_Orderings_Olinorder(_1340925), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340925), _1340927), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340925), _1340929), _1340931)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340925), _1340929), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340925), _1340927), _1340931)))], (25026 ^ _778495) ^ [_1226062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226062)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1226062)) = _1226062)], (40798 ^ _778495) ^ [_1578362, _1578364, _1578366] : [-(hAPP(c_Relation_ODomain(_1578362, _1578364), hAPP(c_Relation_Oconverse(_1578364, _1578362), _1578366)) = hAPP(c_Relation_ORange(_1578364, _1578362), _1578366))], (27201 ^ _778495) ^ [_1264292, _1264294] : [class_Rings_Olinordered__idom(_1264292), 27204 ^ _778495 : [(27211 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264294), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264292), hAPP(c_Int_Oring__1__class_Oof__int(_1264292), _1264294)), c_Groups_Ozero__class_Ozero(_1264292))))], (27205 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264292), hAPP(c_Int_Oring__1__class_Oof__int(_1264292), _1264294)), c_Groups_Ozero__class_Ozero(_1264292))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264294), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (8434 ^ _778495) ^ [_918551, _918553, _918555, _918557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_918551), _918553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918551, tc_HOL_Obool)), _918553), _918555)), hBOOL(hAPP(_918557, c_Orderings_Obot__class_Obot(tc_fun(_918551, tc_HOL_Obool)))), 8449 ^ _778495 : [(8450 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_918551), 8448 ^ [_918551, _918553, _918555, _918557])))], (8454 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_918551), 8447 ^ [_918551, _918553, _918555, _918557]), 8448 ^ [_918551, _918553, _918555, _918557]))], (8458 ^ _778495) ^ [] : [hBOOL(hAPP(_918557, hAPP(hAPP(c_Set_Oinsert(_918551), 8447 ^ [_918551, _918553, _918555, _918557]), 8448 ^ [_918551, _918553, _918555, _918557])))], (8456 ^ _778495) ^ [] : [-(hBOOL(hAPP(_918557, 8448 ^ [_918551, _918553, _918555, _918557])))], (8452 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_918551), 8447 ^ [_918551, _918553, _918555, _918557]), _918555)))]], -(hBOOL(hAPP(_918557, _918553)))], (52381 ^ _778495) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (43247 ^ _778495) ^ [_1641333, _1641335, _1641337] : [_1641333 = hAPP(hAPP(c_List_Oappend(_1641335), _1641333), _1641337), -(_1641337 = c_List_Olist_ONil(_1641335))], (10687 ^ _778495) ^ [_962656] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962656), _962656)))], (49120 ^ _778495) ^ [_1772060] : [-(c_Relation_Oantisym(_1772060, c_Relation_OId(_1772060)))], (26742 ^ _778495) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19740 ^ _778495) ^ [_1133028, _1133030, _1133032, _1133034, _1133036] : [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), _1133028), _1133030)), _1133032)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133028), _1133034)), _1133036))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133032), _1133028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133036), _1133028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1133030), _1133034)))], (8372 ^ _778495) ^ [_917331, _917333, _917335] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_917331), _917333)), hBOOL(hAPP(_917335, _917333)), 8383 ^ _778495 : [(8386 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_917331), 8381 ^ [_917331, _917333, _917335]), 8382 ^ [_917331, _917333, _917335])))], (8388 ^ _778495) ^ [] : [-(hBOOL(hAPP(_917335, 8382 ^ [_917331, _917333, _917335])))], (8390 ^ _778495) ^ [] : [hBOOL(hAPP(_917335, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917331, tc_HOL_Obool)), 8382 ^ [_917331, _917333, _917335]), hAPP(hAPP(c_Set_Oinsert(_917331), 8381 ^ [_917331, _917333, _917335]), c_Orderings_Obot__class_Obot(tc_fun(_917331, tc_HOL_Obool))))))], (8384 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_917331), 8382 ^ [_917331, _917333, _917335])))]], -(hBOOL(hAPP(_917335, c_Orderings_Obot__class_Obot(tc_fun(_917331, tc_HOL_Obool)))))], (13673 ^ _778495) ^ [_1021063, _1021065, _1021067, _1021069] : [class_Groups_Oordered__comm__monoid__add(_1021063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021063), c_Groups_Ozero__class_Ozero(_1021063)), _1021065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021063), _1021067), _1021069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021063), _1021067), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021063), _1021065), _1021069))))], (41868 ^ _778495) ^ [_1608962, _1608964, _1608966, _1608968] : [-(_1608962 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1608964), hAPP(hAPP(c_List_Olist_OCons(_1608964), _1608966), _1608968)), _1608962) = hAPP(hAPP(c_List_Onth(_1608964), _1608968), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1608962), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (32373 ^ _778495) ^ [_1374622, _1374624] : [32381 ^ _778495 : [(32384 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1374624, 32380 ^ [_1374622, _1374624])))], (32382 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 32380 ^ [_1374622, _1374624]), _1374622)))]], 32374 ^ _778495 : [(32375 ^ _778495) ^ [_1374691] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1374691), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1374622))), hBOOL(hAPP(_1374624, _1374691))]]], (5889 ^ _778495) ^ [_872268, _872270, _872272, _872274] : [5890 ^ _778495 : [(5893 ^ _778495) ^ [] : [_872270 = _872274], (5891 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_872268), _872270), _872272))]], -(hBOOL(hAPP(hAPP(c_member(_872268), _872270), hAPP(hAPP(c_Set_Oinsert(_872268), _872274), _872272))))], (19008 ^ _778495) ^ [_1120321, _1120323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120321), _1120323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120321)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120323))))], (21314 ^ _778495) ^ [_1160407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1160407)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160407), c_Int_OPls)))], (26664 ^ _778495) ^ [_1255380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1255380)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255380), c_Int_OMin)))], (45408 ^ _778495) ^ [_1689818, _1689820] : [c_List_Oremdups(_1689818, _1689820) = _1689820, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689818)), c_List_Oremdups(_1689818, _1689820)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689818)), _1689820))], (28677 ^ _778495) ^ [_1298129, _1298131, _1298133] : [-(hAPP(c_Divides_Oadjust(_1298129), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1298131), _1298133)) = 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), _1298133), _1298129)), 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)))), _1298131)), 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)))), _1298131)), _1298133))))], (9378 ^ _778495) ^ [_937687, _937689, _937691, _937693] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937687, tc_HOL_Obool)), _937689), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937687, tc_HOL_Obool)), _937691), _937693)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937687, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937687, tc_HOL_Obool)), _937689), _937691)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937687, tc_HOL_Obool)), _937689), _937693)))], (20850 ^ _778495) ^ [_1151939, _1151941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1151939), _1151941)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1151939)), _1151941)))], (45430 ^ _778495) ^ [_1690196, _1690198] : [-(hAPP(c_List_OremoveAll(_1690196, _1690198), c_List_Olist_ONil(_1690196)) = c_List_Olist_ONil(_1690196))], (45600 ^ _778495) ^ [_1693571, _1693573, _1693575] : [-(c_List_Oconcat(_1693571, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1693571)), _1693573), _1693575)) = hAPP(hAPP(c_List_Oappend(_1693571), c_List_Oconcat(_1693571, _1693573)), c_List_Oconcat(_1693571, _1693575)))], (23500 ^ _778495) ^ [_1199354, _1199356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199354), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199354), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199356, _1199354))))], (52153 ^ _778495) ^ [_1830525, _1830527] : [class_Orderings_Otop(_1830525), -(class_Orderings_Otop(tc_fun(_1830527, _1830525)))], (33167 ^ _778495) ^ [_1390863, _1390865, _1390867, _1390869] : [_1390863 = c_Orderings_Obot__class_Obot(tc_fun(_1390865, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390865, tc_fun(_1390867, tc_HOL_Obool)), _1390863), hAPP(c_COMBK(tc_fun(_1390867, tc_HOL_Obool), _1390865), _1390869)) = c_Orderings_Obot__class_Obot(tc_fun(_1390867, tc_HOL_Obool)))], (10149 ^ _778495) ^ [_953450, _953452, _953454, _953456, _953458, _953460, _953462] : [c_Finite__Set_Ofun__left__comm(_953450, _953452, _953454), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_953450, _953452, _953454, _953456, _953458), _953460)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_953450, _953452, _953454, _953456, _953458), _953462)), -(_953462 = _953460)], (30155 ^ _778495) ^ [_1327866, _1327868, _1327870] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1327866, _1327868), _1327870)), 30158 ^ _778495 : [(30167 ^ _778495) ^ [] : [-(_1327868 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 30170 ^ _778495 : [(30179 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1327868))), 30182 ^ _778495 : [(30185 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1327870)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (30183 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1327868), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1327870))))]]], (30171 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1327868)), 30174 ^ _778495 : [(30177 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1327870)), _1327868)))], (30175 ^ _778495) ^ [] : [-(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), _1327870))))]]]]], (30161 ^ _778495) ^ [] : [_1327868 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1327870) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30159 ^ _778495) ^ [] : [-(_1327866 = 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), _1327870)), _1327868)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1327870)))]]], (51705 ^ _778495) ^ [_1822468, _1822470] : [51706 ^ _778495 : [(51709 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822470), _1822468))], (51707 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822468), _1822470)))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822468, _1822470) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (46296 ^ _778495) ^ [_1709124, _1709126, _1709128, _1709130, _1709132] : [class_Orderings_Olinorder(_1709124), 46299 ^ _778495 : [(46306 ^ _778495) ^ [] : [c_List_Olinorder__class_Osorted(_1709124, hAPP(hAPP(c_List_Omap(_1709126, _1709124), _1709128), _1709132)), -(c_List_Olinorder__class_Osorted(_1709124, hAPP(hAPP(c_List_Omap(_1709126, _1709124), _1709128), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1709126, _1709124, _1709128), _1709130), _1709132))))], (46300 ^ _778495) ^ [] : [c_List_Olinorder__class_Osorted(_1709124, hAPP(hAPP(c_List_Omap(_1709126, _1709124), _1709128), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1709126, _1709124, _1709128), _1709130), _1709132))), -(c_List_Olinorder__class_Osorted(_1709124, hAPP(hAPP(c_List_Omap(_1709126, _1709124), _1709128), _1709132)))]]], (4926 ^ _778495) ^ [_853619, _853621] : [_853621 = _853619, -(c_Fun_Oid(_853621) = c_Fun_Oid(_853619))], (35346 ^ _778495) ^ [_1438807, _1438809] : [class_Groups_Oordered__ab__group__add(_1438807), -(hAPP(c_Set_Oimage(_1438807, _1438807, c_Groups_Ouminus__class_Ouminus(_1438807)), hAPP(c_SetInterval_Oord__class_OatLeast(_1438807), _1438809)) = hAPP(c_SetInterval_Oord__class_OatMost(_1438807), hAPP(c_Groups_Ouminus__class_Ouminus(_1438807), _1438809)))], (38612 ^ _778495) ^ [_1526045, _1526047, _1526049, _1526051, _1526053, _1526055, _1526057] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1526045, _1526047, _1526049, _1526051, _1526053), _1526055), _1526057)), 38616 ^ _778495 : [(38619 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1526053, 38615 ^ [_1526045, _1526047, _1526049, _1526051, _1526053, _1526055, _1526057]), _1526057)))], (38617 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1526051, _1526055), 38615 ^ [_1526045, _1526047, _1526049, _1526051, _1526053, _1526055, _1526057])))]]], (14633 ^ _778495) ^ [_1038259, _1038261] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038259), _1038261)), 14634 ^ _778495 : [(14641 ^ _778495) ^ [] : [_1038259 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1038261 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14635 ^ _778495) ^ [] : [_1038259 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1038261 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (47215 ^ _778495) ^ [_1728268, _1728270, _1728272] : [-(c_List_Oinsert(_1728268, _1728270, c_List_Oremdups(_1728268, _1728272)) = c_List_Oremdups(_1728268, c_List_Oinsert(_1728268, _1728270, _1728272)))], (48759 ^ _778495) ^ [_1762615, _1762617, _1762619, _1762621] : [-(c_Random__Sequence_Omap(_1762615, _1762617, _1762619, _1762621) = c_Random__Sequence_Obind(_1762615, _1762617, _1762621, hAPP(c_Fun_Ocomp(_1762617, 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(_1762617)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1762615, c_Random__Sequence_Osingle(_1762617)), _1762619)))], (5236 ^ _778495) ^ [_858520, _858522, _858524, _858526, _858528, _858530, _858532, _858534] : [-(c_Lazy__Sequence_Omap(_858534, _858530, _858526, _858522) = c_Lazy__Sequence_Omap(_858532, _858528, _858524, _858520)), _858534 = _858532, _858530 = _858528, _858526 = _858524, _858522 = _858520], (4702 ^ _778495) ^ [_850079, _850081, _850083, _850085] : [-(c_Complete__Lattice_OInf__class_OInf(_850085, _850081) = c_Complete__Lattice_OInf__class_OInf(_850083, _850079)), _850085 = _850083, _850081 = _850079], (35070 ^ _778495) ^ [_1434087, _1434089] : [c_Nat__Transfer_Onat__set(_1434087), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1434089), _1434087)), -(c_Nat__Transfer_Ois__nat(_1434089))], (32360 ^ _778495) ^ [_1374392, _1374394] : [32368 ^ _778495 : [(32371 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1374394, 32367 ^ [_1374392, _1374394])))], (32369 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 32367 ^ [_1374392, _1374394]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1374392))))]], 32361 ^ _778495 : [(32362 ^ _778495) ^ [_1374461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1374461), _1374392)), hBOOL(hAPP(_1374394, _1374461))]]], (25924 ^ _778495) ^ [_1241900, _1241902] : [class_Rings_Oring__1(_1241900), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1241900), hAPP(c_Groups_Ouminus__class_Ouminus(_1241900), c_Groups_Oone__class_Oone(_1241900))), 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)))), _1241902)) = c_Groups_Oone__class_Oone(_1241900))], (14401 ^ _778495) ^ [_1034440, _1034442, _1034444, _1034446, _1034448, _1034450] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1034440), -(_1034442 = c_Groups_Ozero__class_Ozero(_1034440)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034440), _1034444), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034440), _1034442), _1034448)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034440), _1034446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034440), _1034442), _1034450)), _1034444 = _1034446, -(_1034448 = _1034450)], (40485 ^ _778495) ^ [_1571033, _1571035, _1571037, _1571039, _1571041] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571033, _1571033)), hAPP(hAPP(c_Product__Type_OPair(_1571033, _1571033), _1571035), _1571037)), c_Transitive__Closure_Otrancl(_1571033, _1571039))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571033, _1571033)), hAPP(hAPP(c_Product__Type_OPair(_1571033, _1571033), _1571037), _1571041)), c_Transitive__Closure_Ortrancl(_1571033, _1571039))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571033, _1571033)), hAPP(hAPP(c_Product__Type_OPair(_1571033, _1571033), _1571035), _1571041)), c_Transitive__Closure_Otrancl(_1571033, _1571039))))], (1368 ^ _778495) ^ [_798623, _798625] : [-(class_Rings_Oidom(_798623)), _798625 = _798623, class_Rings_Oidom(_798625)], (44578 ^ _778495) ^ [_1671345, _1671347, _1671349] : [c_Fun_Oinj__on(tc_List_Olist(_1671345), tc_List_Olist(_1671347), hAPP(c_List_Omap(_1671345, _1671347), _1671349), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671345), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1671345, _1671347, _1671349, c_Orderings_Otop__class_Otop(tc_fun(_1671345, tc_HOL_Obool))))], (23529 ^ _778495) ^ [_1199987, _1199989] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1199987), _1199989) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199987, _1199989) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (50166 ^ _778495) ^ [_1792869, _1792871, _1792873, _1792875, _1792877] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1792869, _1792871, tc_HOL_Obool, _1792873), _1792875), _1792877)), -(hBOOL(hAPP(_1792873, hAPP(hAPP(c_Product__Type_OPair(_1792869, _1792871), _1792875), _1792877))))], (40242 ^ _778495) ^ [_1564359, _1564361] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564359, _1564359)), _1564361)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564359, _1564359)), c_Transitive__Closure_Otrancl(_1564359, _1564361))))], (12721 ^ _778495) ^ [_1003796, _1003798, _1003800, _1003802, _1003804] : [class_Groups_Ocomm__monoid__add(_1003796), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003798), _1003800)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003798), _1003802)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003796), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003798, _1003796), _1003804), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003798, tc_HOL_Obool)), _1003800), _1003802))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003798, _1003796), _1003804), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1003798, tc_HOL_Obool)), _1003800), _1003802))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003796), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003798, _1003796), _1003804), _1003800)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003798, _1003796), _1003804), _1003802)))], (39023 ^ _778495) ^ [_1535089, _1535091] : [-(c_List_Olex(_1535089, _1535091) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1535089), tc_List_Olist(_1535089)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1535089, _1535091)))], (3346 ^ _778495) ^ [_828467, _828469, _828471, _828473] : [-(c_Enum_Oenum__the(_828473, _828469) = c_Enum_Oenum__the(_828471, _828467)), _828473 = _828471, _828469 = _828467], (43674 ^ _778495) ^ [_1652017, _1652019, _1652021, _1652023] : [-(hAPP(c_List_Orotate1(_1652017), c_List_Olist_ONil(_1652017)) = c_List_Olist_ONil(_1652017))], (34474 ^ _778495) ^ [_1422589, _1422591] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1422589, _1422591)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1422589), hAPP(c_Nat_OSuc, _1422591)))], (13799 ^ _778495) ^ [_1023422, _1023424, _1023426, _1023428] : [class_Rings_Oordered__ring(_1023422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023422), _1023424), _1023426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023422), _1023428), c_Groups_Ozero__class_Ozero(_1023422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023422), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023422), _1023428), _1023426)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023422), _1023428), _1023424))))], (22790 ^ _778495) ^ [_1185871, _1185873, _1185875] : [class_Int_Onumber__ring(_1185871), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185871), hAPP(c_Int_Onumber__class_Onumber__of(_1185871), _1185873)), hAPP(c_Int_Onumber__class_Onumber__of(_1185871), _1185875)) = hAPP(c_Int_Onumber__class_Onumber__of(_1185871), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1185873), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1185875))))], (42221 ^ _778495) ^ [_1619321] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619321) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42224 ^ _778495 : [(42225 ^ _778495) ^ [_1619396] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1619396), hAPP(c_List_Oset(tc_Nat_Onat), _1619321))), -(_1619396 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9422 ^ _778495) ^ [_938887, _938889, _938891] : [class_Lattices_Olattice(_938887), hBOOL(hAPP(c_Finite__Set_Ofinite(_938887), _938889)), hBOOL(hAPP(c_Finite__Set_Ofinite(_938887), _938891)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938887, tc_HOL_Obool)), _938889), _938891) = c_Orderings_Obot__class_Obot(tc_fun(_938887, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938887), c_Big__Operators_Olattice__class_OSup__fin(_938887, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938887, tc_HOL_Obool)), _938889), _938891))), c_Big__Operators_Olattice__class_OSup__fin(_938887, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938887, tc_HOL_Obool)), _938889), _938891))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938887), c_Big__Operators_Olattice__class_OSup__fin(_938887, _938889)), c_Big__Operators_Olattice__class_OSup__fin(_938887, _938891)))], (39612 ^ _778495) ^ [_1549672, _1549674, _1549676, _1549678, _1549680, _1549682] : [c_Finite__Set_Ofolding(_1549672, _1549674, _1549676, _1549678), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549672), _1549680)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549672), _1549682)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1549672, tc_HOL_Obool)), _1549680), _1549682) = c_Orderings_Obot__class_Obot(tc_fun(_1549672, tc_HOL_Obool)), -(hAPP(_1549678, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1549672, tc_HOL_Obool)), _1549680), _1549682)) = hAPP(c_Fun_Ocomp(_1549674, _1549674, _1549674, hAPP(_1549678, _1549680)), hAPP(_1549678, _1549682)))], (37548 ^ _778495) ^ [_1490420, _1490422, _1490424, _1490426, _1490428, _1490430, _1490432, _1490434] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1490420, _1490422), tc_fun(tc_prod(_1490424, _1490426), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1490420, _1490422), _1490428), hAPP(c_COMBK(tc_fun(_1490422, tc_HOL_Obool), _1490420), _1490430))), hAPP(c_Product__Type_Oprod_Oprod__case(_1490420, _1490422, tc_fun(tc_prod(_1490424, _1490426), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1490420, tc_fun(_1490422, tc_fun(_1490424, tc_fun(_1490426, tc_HOL_Obool))), tc_fun(_1490422, tc_fun(tc_prod(_1490424, _1490426), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1490424, tc_fun(_1490426, tc_HOL_Obool)), tc_fun(tc_prod(_1490424, _1490426), tc_HOL_Obool)), tc_fun(tc_fun(_1490422, tc_fun(_1490424, tc_fun(_1490426, tc_HOL_Obool))), tc_fun(_1490422, tc_fun(tc_prod(_1490424, _1490426), tc_HOL_Obool))), _1490420), c_COMBB(tc_fun(_1490424, tc_fun(_1490426, tc_HOL_Obool)), tc_fun(tc_prod(_1490424, _1490426), tc_HOL_Obool), _1490422)), hAPP(hAPP(c_COMBB(tc_fun(_1490424, tc_HOL_Obool), tc_fun(tc_fun(_1490424, tc_fun(_1490426, tc_HOL_Obool)), tc_fun(tc_prod(_1490424, _1490426), tc_HOL_Obool)), _1490420), c_Product__Type_OSigma(_1490424, _1490426)), _1490432))), hAPP(hAPP(c_COMBB(tc_fun(_1490426, tc_HOL_Obool), tc_fun(_1490424, tc_fun(_1490426, tc_HOL_Obool)), _1490422), c_COMBK(tc_fun(_1490426, tc_HOL_Obool), _1490424)), _1490434)))) = hAPP(hAPP(c_Product__Type_OSigma(_1490424, _1490426), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1490420, tc_fun(_1490424, tc_HOL_Obool)), _1490428), _1490432)), hAPP(c_COMBK(tc_fun(_1490426, tc_HOL_Obool), _1490424), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1490422, tc_fun(_1490426, tc_HOL_Obool)), _1490430), _1490434))))], (8140 ^ _778495) ^ [_912591, _912593, _912595, _912597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_912591, tc_HOL_Obool)), _912593), _912595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912591, tc_HOL_Obool)), _912595), _912597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_912591, tc_HOL_Obool)), _912593), _912597)))], (43534 ^ _778495) ^ [_1648634, _1648636] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648634)), hAPP(c_List_Orotate1(_1648634), _1648636)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648634)), _1648636))], (36997 ^ _778495) ^ [_1476096, _1476098, _1476100, _1476102] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1476096), _1476098)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476096), _1476100)), -(_1476100 = c_Orderings_Obot__class_Obot(tc_fun(_1476096, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1476096, tc_HOL_Obool), tc_fun(_1476096, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1476096, tc_HOL_Obool), tc_fun(_1476096, tc_HOL_Obool)), _1476098), _1476100)), c_Wellfounded_Omax__ext(_1476096, _1476102)))), 37011 ^ _778495 : [(37014 ^ _778495) ^ [_1476501] : [hBOOL(hAPP(hAPP(c_member(_1476096), _1476501), _1476100)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1476096, _1476096)), hAPP(hAPP(c_Product__Type_OPair(_1476096, _1476096), 37010 ^ [_1476096, _1476098, _1476100, _1476102]), _1476501)), _1476102))], (37012 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476096), 37010 ^ [_1476096, _1476098, _1476100, _1476102]), _1476098)))]]], (860 ^ _778495) ^ [_791441, _791443, _791445, _791447] : [-(c_Predicate_Osymp(_791445, _791441)), c_Predicate_Osymp(_791447, _791443), _791447 = _791445, _791443 = _791441], (48182 ^ _778495) ^ [_1750264, _1750266, _1750268] : [-(_1750264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1750266), c_List_Oreplicate(_1750266, _1750264, _1750268)) = c_List_Oreplicate(_1750266, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1750264), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1750268))], (49562 ^ _778495) ^ [_1779733, _1779735] : [-(c_Equiv__Relations_Opart__equivp(_1779733, _1779735)), 49565 ^ _778495 : [(49566 ^ _778495) ^ [_1779810] : [hBOOL(hAPP(hAPP(_1779735, _1779810), _1779810))]], c_Predicate_Osymp(_1779733, _1779735), c_Predicate_Otransp(_1779733, _1779735)], (14087 ^ _778495) ^ [_1028660, _1028662] : [class_Rings_Olinordered__ring(_1028660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028660), _1028662), _1028662)), c_Groups_Ozero__class_Ozero(_1028660)))], (13925 ^ _778495) ^ [_1025787, _1025789, _1025791] : [class_Rings_Oordered__cancel__semiring(_1025787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025787), c_Groups_Ozero__class_Ozero(_1025787)), _1025789)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025787), c_Groups_Ozero__class_Ozero(_1025787)), _1025791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025787), c_Groups_Ozero__class_Ozero(_1025787)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025787), _1025789), _1025791))))], (47233 ^ _778495) ^ [_1728613, _1728615, _1728617, _1728619] : [-(c_List_Oconcat(_1728613, hAPP(hAPP(c_List_Omap(_1728615, tc_List_Olist(_1728613)), _1728617), _1728619)) = c_List_Omaps(_1728615, _1728613, _1728617, _1728619))], (37905 ^ _778495) ^ [_1500070, _1500072] : [-(hAPP(c_Set_OCollect(_1500070), hAPP(c_fequal, _1500072)) = hAPP(hAPP(c_Set_Oinsert(_1500070), _1500072), c_Orderings_Obot__class_Obot(tc_fun(_1500070, tc_HOL_Obool))))], (44776 ^ _778495) ^ [_1675420, _1675422, _1675424, _1675426] : [class_Groups_Ocomm__monoid__add(_1675420), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1675420), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1675420), _1675422), c_List_Oupto(_1675424, _1675426))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1675420), _1675422), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1675424, _1675426))))], (42838 ^ _778495) ^ [_1632173, _1632175, _1632177, _1632179] : [-(hAPP(hAPP(c_List_Otake(_1632173), _1632175), hAPP(hAPP(c_List_Olist_OCons(_1632173), _1632177), _1632179)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1632173), c_List_Olist_ONil(_1632173), hAPP(hAPP(c_COMBB(tc_List_Olist(_1632173), tc_List_Olist(_1632173), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1632173), _1632177)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1632173), tc_List_Olist(_1632173)), c_List_Otake(_1632173)), _1632179)), _1632175))], (5978 ^ _778495) ^ [_874000, _874002, _874004] : [hBOOL(hAPP(hAPP(c_member(_874000), _874002), _874004)), -(hBOOL(hAPP(_874004, _874002)))], (41025 ^ _778495) ^ [_1584356, _1584358, _1584360] : [c_Relation_Osingle__valued(_1584356, _1584358, _1584360), 41028 ^ _778495 : [(41029 ^ _778495) ^ [_1584477, _1584479] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584356, _1584358)), hAPP(hAPP(c_Product__Type_OPair(_1584356, _1584358), _1584479), _1584477)), _1584360)), 41032 ^ _778495 : [(41033 ^ _778495) ^ [_1584603] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584356, _1584358)), hAPP(hAPP(c_Product__Type_OPair(_1584356, _1584358), _1584479), _1584603)), _1584360)), -(_1584477 = _1584603)]]]]], (40455 ^ _778495) ^ [_1570354] : [-(c_Transitive__Closure_Ortrancl(_1570354, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1570354, _1570354), tc_HOL_Obool))) = c_Relation_OId(_1570354))], (1668 ^ _778495) ^ [_802373, _802375] : [-(class_Groups_Oab__semigroup__mult(_802373)), _802375 = _802373, class_Groups_Oab__semigroup__mult(_802375)], (33148 ^ _778495) ^ [_1390389, _1390391, _1390393, _1390395] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390389, tc_fun(_1390391, tc_HOL_Obool)), _1390393), _1390395) = c_Orderings_Obot__class_Obot(tc_fun(_1390391, tc_HOL_Obool)), 33151 ^ _778495 : [(33152 ^ _778495) ^ [_1390505] : [hBOOL(hAPP(hAPP(c_member(_1390389), _1390505), _1390393)), -(hAPP(_1390395, _1390505) = c_Orderings_Obot__class_Obot(tc_fun(_1390391, tc_HOL_Obool)))]]], (13855 ^ _778495) ^ [_1024498, _1024500, _1024502, _1024504] : [class_Rings_Oordered__semiring(_1024498), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024498), _1024500), _1024502)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024498), c_Groups_Ozero__class_Ozero(_1024498)), _1024504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024498), _1024500), _1024504)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024498), _1024502), _1024504))))], (15335 ^ _778495) ^ [_1050855, _1050857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1050855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1050857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050855), _1050857))))], (610 ^ _778495) ^ [_787738, _787740, _787742, _787744, _787746, _787748] : [-(c_Finite__Set_Ofun__left__comm(_787746, _787742, _787738)), c_Finite__Set_Ofun__left__comm(_787748, _787744, _787740), _787748 = _787746, _787744 = _787742, _787740 = _787738], (52299 ^ _778495) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (48074 ^ _778495) ^ [_1747200, _1747202, _1747204, _1747206] : [-(c_New__Random__Sequence_Oneg__map(_1747200, _1747202, _1747204, _1747206) = c_New__Random__Sequence_Oneg__bind(_1747200, _1747202, _1747206, hAPP(c_Fun_Ocomp(_1747202, 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(_1747202)))))), _1747200, c_New__Random__Sequence_Oneg__single(_1747202)), _1747204)))], (23150 ^ _778495) ^ 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968674), _968676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968674), _968678)), 11058 ^ _778495 : [(11065 ^ _778495) ^ [] : [_968676 = _968678, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968676), _968674) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968678), _968674))], (11059 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968676), _968674) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968678), _968674), -(_968676 = _968678)]]], (13939 ^ _778495) ^ [_1026042, _1026044, _1026046] : [class_Rings_Olinordered__ring__strict(_1026042), 13942 ^ _778495 : [(13957 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026042), _1026044), _1026046)), c_Groups_Ozero__class_Ozero(_1026042)))), 13958 ^ _778495 : [(13965 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026042), _1026044), c_Groups_Ozero__class_Ozero(_1026042))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026042), c_Groups_Ozero__class_Ozero(_1026042)), _1026046))], (13959 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026042), c_Groups_Ozero__class_Ozero(_1026042)), _1026044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026042), _1026046), c_Groups_Ozero__class_Ozero(_1026042)))]]], (13943 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026042), _1026044), _1026046)), c_Groups_Ozero__class_Ozero(_1026042))), 13948 ^ _778495 : [(13951 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026042), _1026046), c_Groups_Ozero__class_Ozero(_1026042))))], (13949 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026042), c_Groups_Ozero__class_Ozero(_1026042)), _1026044)))]], 13952 ^ 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_778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736353), 47548 ^ [_1736353, _1736355, _1736357, _1736359, _1736361, _1736481, _1736483]), hAPP(c_List_Oset(_1736353), _1736483))))]], hBOOL(hAPP(_1736359, _1736355)), _1736357 = hAPP(c_List_Ofilter(_1736353, _1736359), _1736481)]]], (18132 ^ _778495) ^ [_1103827, _1103829, _1103831, _1103833] : [class_Int_Onumber__ring(_1103827), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103827), hAPP(c_Int_Onumber__class_Onumber__of(_1103827), _1103829)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1103827), hAPP(c_Int_Onumber__class_Onumber__of(_1103827), _1103831)), _1103833)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1103827), hAPP(c_Int_Onumber__class_Onumber__of(_1103827), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1103829), _1103831))), _1103833))], (50813 ^ _778495) ^ [_1807397, _1807399] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807397), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807399))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807397), _1807399)))], (32792 ^ _778495) ^ [_1383439, _1383441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1383439)), 32801 ^ _778495 : [(32804 ^ _778495) ^ [] : [hBOOL(hAPP(_1383441, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32797 ^ [_1383439, _1383441]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 32798 ^ [_1383439, _1383441]), _1383439))))], (32802 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1383441, 32797 ^ [_1383439, _1383441])))]], 32805 ^ _778495 : [(32808 ^ _778495) ^ [] : [hBOOL(hAPP(_1383441, 32797 ^ [_1383439, _1383441]))], (32806 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1383441, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32797 ^ [_1383439, _1383441]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 32798 ^ [_1383439, _1383441]), _1383439)))))]], 32809 ^ _778495 : [(32819 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1383441, 32826 ^ [_1383439, _1383441]))), 32820 ^ _778495 : [(32821 ^ _778495) ^ [_1383986] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1383986), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1383439))), hBOOL(hAPP(_1383441, _1383986))]]], (32810 ^ _778495) ^ [] : [32811 ^ _778495 : [(32812 ^ _778495) ^ [_1383871] : [hBOOL(hAPP(_1383441, _1383871))]], 32814 ^ _778495 : [(32817 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1383441, 32813 ^ [_1383439, _1383441])))], (32815 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32813 ^ [_1383439, _1383441]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1383439))))]]]]], (43862 ^ _778495) ^ [_1655787, _1655789, _1655791] : [-(hAPP(c_List_Orotate(_1655787, _1655789), _1655791) = hAPP(hAPP(c_List_Oappend(_1655787), hAPP(hAPP(c_List_Odrop(_1655787), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655789, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655787)), _1655791))), _1655791)), hAPP(hAPP(c_List_Otake(_1655787), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655789, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655787)), _1655791))), _1655791)))], (49142 ^ _778495) ^ [_1772414, _1772416] : [c_Relation_Oantisym(_1772414, _1772416), -(c_Relation_Oantisym(_1772414, hAPP(c_Relation_Oconverse(_1772414, _1772414), _1772416)))], (35949 ^ _778495) ^ [_1453219, _1453221] : [c_Equiv__Relations_Oequivp(_1453219, hAPP(hAPP(c_COMBC(_1453219, tc_fun(tc_prod(_1453219, _1453219), tc_HOL_Obool), tc_fun(_1453219, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453219, tc_fun(tc_fun(tc_prod(_1453219, _1453219), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1453219, _1453219), tc_HOL_Obool), tc_fun(_1453219, tc_HOL_Obool)), _1453219), c_COMBC(_1453219, tc_fun(tc_prod(_1453219, _1453219), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453219, tc_prod(_1453219, _1453219)), tc_fun(_1453219, tc_fun(tc_fun(tc_prod(_1453219, _1453219), tc_HOL_Obool), tc_HOL_Obool)), _1453219), hAPP(c_COMBB(tc_prod(_1453219, _1453219), tc_fun(tc_fun(tc_prod(_1453219, _1453219), tc_HOL_Obool), tc_HOL_Obool), _1453219), c_member(tc_prod(_1453219, _1453219)))), c_Product__Type_OPair(_1453219, _1453219)))), _1453221)), -(c_Equiv__Relations_Oequiv(_1453219, c_Orderings_Otop__class_Otop(tc_fun(_1453219, tc_HOL_Obool)), _1453221))], (5984 ^ _778495) ^ [_874093, _874095, _874097] : [hBOOL(hAPP(_874097, _874095)), -(hBOOL(hAPP(hAPP(c_member(_874093), _874095), _874097)))], (36622 ^ _778495) ^ [_1468002] : [-(c_Fun_Oinj__on(_1468002, tc_fun(_1468002, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1468002, tc_fun(_1468002, tc_HOL_Obool), tc_fun(_1468002, tc_HOL_Obool)), c_Set_Oinsert(_1468002)), c_Orderings_Obot__class_Obot(tc_fun(_1468002, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1468002, tc_HOL_Obool))))], (4288 ^ _778495) ^ [_843526, _843528, _843530, _843532, _843534, _843536, _843538, _843540] : [-(c_Lazy__Sequence_Oproduct(_843540, _843536, _843532, _843528) = c_Lazy__Sequence_Oproduct(_843538, _843534, _843530, _843526)), _843540 = _843538, _843536 = _843534, _843532 = _843530, _843528 = _843526], (9380 ^ _778495) ^ [_937771, _937773, _937775, _937777] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937771, tc_HOL_Obool)), _937773), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937771, tc_HOL_Obool)), _937775), _937777)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937771, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937771, tc_HOL_Obool)), _937773), _937775)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937771, tc_HOL_Obool)), _937773), _937777)))], (30377 ^ _778495) ^ [_1332281] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1332281)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1332281)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29138 ^ _778495) ^ [_1307748, _1307750] : [class_Rings_Oring__1(_1307748), 29141 ^ _778495 : [(29148 ^ _778495) ^ [] : [-(_1307750 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29151 ^ _778495 : [(29158 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1307750), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1307748), _1307750) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1307748), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1307748, _1307748)), tc_fun(tc_Int_Oint, _1307748)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1307748, _1307748), _1307748), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1307748, _1307748)), tc_fun(tc_Int_Oint, _1307748)), tc_Int_Oint), c_COMBB(tc_fun(_1307748, _1307748), _1307748, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1307748, tc_fun(tc_fun(_1307748, _1307748), _1307748), tc_Int_Oint), c_HOL_OLet(_1307748, _1307748)), c_Int_Oring__1__class_Oof__int(_1307748)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1307748, _1307748), tc_fun(_1307748, _1307748)), hAPP(hAPP(c_COMBB(tc_fun(_1307748, tc_fun(_1307748, _1307748)), tc_fun(tc_fun(_1307748, _1307748), tc_fun(_1307748, _1307748)), tc_Int_Oint), c_COMBS(_1307748, _1307748, _1307748)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1307748, _1307748), tc_fun(_1307748, tc_fun(_1307748, _1307748))), hAPP(hAPP(c_COMBB(tc_fun(_1307748, tc_fun(_1307748, _1307748)), tc_fun(tc_fun(_1307748, _1307748), tc_fun(_1307748, tc_fun(_1307748, _1307748))), tc_Int_Oint), c_COMBB(_1307748, tc_fun(_1307748, _1307748), _1307748)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1307748, tc_fun(_1307748, _1307748)), tc_Int_Oint), c_If(_1307748)), 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(_1307748, _1307748, _1307748), c_Groups_Oplus__class_Oplus(_1307748)), c_COMBI(_1307748))))), hAPP(hAPP(c_COMBC(_1307748, _1307748, _1307748), hAPP(hAPP(c_COMBB(_1307748, tc_fun(_1307748, _1307748), _1307748), c_Groups_Oplus__class_Oplus(_1307748)), hAPP(hAPP(c_COMBS(_1307748, _1307748, _1307748), c_Groups_Oplus__class_Oplus(_1307748)), c_COMBI(_1307748)))), c_Groups_Oone__class_Oone(_1307748))))), c_Divides_Odivmod__int(_1307750, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (29152 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1307750), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1307748), _1307750) = hAPP(c_Groups_Ouminus__class_Ouminus(_1307748), hAPP(c_Int_Oring__1__class_Oof__int(_1307748), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1307750))))]]], (29142 ^ _778495) ^ [] : [_1307750 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1307748), _1307750) = c_Groups_Ozero__class_Ozero(_1307748))]]], (29023 ^ _778495) ^ [_1305347, _1305349, _1305351, _1305353, _1305355, _1305357] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305347, tc_fun(_1305349, tc_HOL_Obool))), _1305351), _1305353), _1305355), _1305357)), -(hBOOL(hAPP(hAPP(_1305353, _1305355), _1305357)))], (39090 ^ _778495) ^ [_1536516, _1536518] : [c_Wellfounded_Owf(_1536516, _1536518), -(c_Wellfounded_OwfP(_1536516, c_FunDef_Oin__rel(_1536516, _1536516, _1536518)))], (48488 ^ _778495) ^ [_1756254] : [-(c_Lazy__Sequence_Oyieldn(_1756254) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1756254), _1756254, c_Lazy__Sequence_Oyield(_1756254)))], (45881 ^ _778495) ^ [_1701562, _1701564, _1701566] : [-(c_List_Osublist(_1701562, _1701564, _1701566) = hAPP(hAPP(c_List_Omap(tc_prod(_1701562, tc_Nat_Onat), _1701562), c_Product__Type_Ofst(_1701562, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701562, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701562, 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(_1701562, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701562, tc_Nat_Onat))), _1701566)), hAPP(hAPP(c_List_Ozip(_1701562, tc_Nat_Onat), _1701564), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701562)), _1701564))))))], (9300 ^ _778495) ^ [_936040, _936042] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936040, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_936040, tc_HOL_Obool))), _936042) = c_Orderings_Obot__class_Obot(tc_fun(_936040, tc_HOL_Obool)))], (24345 ^ _778495) ^ [_1214273, _1214275] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1214273)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1214275))) = 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), _1214273), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1214275))))], (49852 ^ _778495) ^ [_1786601] : [-(_1786601 = hAPP(c_Code__Numeral_Oof__nat, 49850 ^ [_1786601]))], (42682 ^ _778495) ^ [_1629276, _1629278] : [-(hAPP(hAPP(c_List_Otake(_1629276), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1629278) = c_List_Olist_ONil(_1629276))], (31164 ^ _778495) ^ [_1348085, _1348087, _1348089] : [class_Orderings_Olinorder(_1348085), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348085), _1348087)), hBOOL(hAPP(hAPP(c_member(_1348085), _1348089), _1348087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348085), _1348089), c_Big__Operators_Olinorder__class_OMax(_1348085, _1348087))))], (5000 ^ _778495) ^ [_854828, _854830] : [_854830 = _854828, -(c_Orderings_Otop__class_Otop(_854830) = c_Orderings_Otop__class_Otop(_854828))], (32200 ^ _778495) ^ [_1371087, _1371089] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1371087, _1371089)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1371089)), _1371087))], (10631 ^ _778495) ^ [_961738] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961738), _961738)))))], (39388 ^ _778495) ^ [_1544657, _1544659, _1544661, _1544663, _1544665, _1544667] : [-(hAPP(hAPP(c_Fun_Ocomp(_1544657, _1544659, _1544661, _1544663), _1544665), _1544667) = hAPP(_1544663, hAPP(_1544665, _1544667)))], (23543 ^ _778495) ^ [_1200233, _1200235, _1200237] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1200233, tc_HOL_Obool)), _1200235), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1200233, tc_HOL_Obool)), _1200237)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1200233, tc_HOL_Obool)), _1200235), _1200237))], (27937 ^ _778495) ^ [_1276829, _1276831, _1276833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1276829, tc_HOL_Obool), tc_HOL_Obool)), _1276831), _1276833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276829, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1276829, tc_HOL_Obool), _1276833)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1276829, tc_HOL_Obool), _1276831))))], (26634 ^ _778495) ^ [_1254940] : [c_Int_OMin = c_Int_OBit1(_1254940), -(c_Int_OMin = _1254940)], (3292 ^ _778495) ^ [_827634, _827636, _827638, _827640, _827642, _827644, _827646, _827648] : [-(c_Enum_Oproduct(_827648, _827644, _827640, _827636) = c_Enum_Oproduct(_827646, _827642, _827638, _827634)), _827648 = _827646, _827644 = _827642, _827640 = _827638, _827636 = _827634], (45715 ^ _778495) ^ [_1696910, _1696912, _1696914] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1696910), tc_List_Olist(_1696910)), c_List_Opartition(_1696910, _1696912, _1696914)) = hAPP(c_List_Ofilter(_1696910, _1696912), _1696914))], (35272 ^ _778495) ^ [_1437359, _1437361, _1437363] : [class_Orderings_Oorder(_1437359), 35275 ^ _778495 : [(35282 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437359), _1437363), _1437361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437359, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1437359), _1437361)), hAPP(c_SetInterval_Oord__class_OatLeast(_1437359), _1437363))))], (35276 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437359, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1437359), _1437361)), hAPP(c_SetInterval_Oord__class_OatLeast(_1437359), _1437363))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437359), _1437363), _1437361)))]]], (28763 ^ _778495) ^ [_1300199, _1300201] : [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(_1300199))), 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)), _1300201)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1300199)), hAPP(c_Nat_OSuc, _1300201))))], (20826 ^ _778495) ^ [_1151556] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1151556), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151556)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1151556)))], (21482 ^ _778495) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (48292 ^ _778495) ^ [_1752220, _1752222, _1752224, _1752226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752220), _1752222)), -(hAPP(hAPP(c_List_Onth(_1752224), c_List_Oreplicate(_1752224, _1752222, _1752226)), _1752220) = _1752226)], (7552 ^ _778495) ^ [_903466, _903468, _903470] : [class_Orderings_Oorder(_903466), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903466), _903468), _903470)), _903470 = _903468], (26066 ^ _778495) ^ [_1244476, _1244478] : [26067 ^ _778495 : [(26070 ^ _778495) ^ [] : [_1244476 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26068 ^ _778495) ^ [] : [_1244478 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1244476), _1244478) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27685 ^ _778495) ^ [_1272570, _1272572] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272570, tc_HOL_Obool)), _1272572), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272570, tc_HOL_Obool)), _1272572)) = c_Orderings_Otop__class_Otop(tc_fun(_1272570, tc_HOL_Obool)))], (24836 ^ _778495) ^ [_1222896] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222896)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1222896))], (45955 ^ _778495) ^ [_1703023] : [-(c_List_Oupt(_1703023, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (48138 ^ _778495) ^ [_1748788, _1748790, _1748792, _1748794, _1748796] : [hBOOL(hAPP(hAPP(_1748792, _1748796), _1748794)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748788, _1748790, _1748792), _1748794), _1748796)))], (20740 ^ _778495) ^ [_1150234, _1150236, _1150238] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150234)))), 20743 ^ _778495 : [(20750 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150236)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150234)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150236)), _1150238)) = 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), _1150234), _1150236))), _1150238))], (20744 ^ _778495) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150236))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150234)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150236)), _1150238)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150234)), _1150238))]]], (9606 ^ _778495) ^ [_942960, _942962, _942964] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942960, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942960, tc_HOL_Obool)), _942962), _942964)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942960, tc_HOL_Obool)), _942962), _942964)) = _942962)], (23603 ^ _778495) ^ [_1201233, _1201235] : [class_Divides_Osemiring__div(_1201233), -(_1201235 = c_Groups_Ozero__class_Ozero(_1201233)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1201233), _1201235), _1201235) = c_Groups_Oone__class_Oone(_1201233))], (29262 ^ _778495) ^ [_1310494, _1310496] : [-(_1310494 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29265 ^ _778495 : [(29272 ^ _778495) ^ [] : [-(_1310496 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1310494, _1310496) = 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, _1310496))), 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)), _1310496)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310494))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1310496), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1310494), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1310494, _1310496)), 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), _1310496))))), c_Divides_Opdivmod(_1310494, _1310496)))))], (29266 ^ _778495) ^ [] : [_1310496 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1310494, _1310496) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310494))]]], (22910 ^ _778495) ^ [] : [-(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))))], (17964 ^ _778495) ^ [_1100476, _1100478, _1100480, _1100482] : [class_Orderings_Olinorder(_1100476), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100476), _1100478), _1100480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100476), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100476), _1100478), _1100482)), _1100480)))], (24495 ^ _778495) ^ [_1216806, _1216808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216806)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1216806)), _1216808) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1216806), _1216808)))], (32540 ^ _778495) ^ [_1378054, _1378056] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1378054, _1378056))))], (20390 ^ _778495) ^ [_1144753, _1144755] : [_1144753 = _1144755, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144753) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144755))], (43704 ^ _778495) ^ [_1652772, _1652774, _1652776, _1652778, _1652780] : [-(hAPP(hAPP(c_List_Ozip(_1652772, _1652774), hAPP(hAPP(c_List_Oappend(_1652772), _1652776), _1652778)), _1652780) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652772, _1652774)), hAPP(hAPP(c_List_Ozip(_1652772, _1652774), _1652776), hAPP(hAPP(c_List_Otake(_1652774), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652772)), _1652776)), _1652780))), hAPP(hAPP(c_List_Ozip(_1652772, _1652774), _1652778), hAPP(hAPP(c_List_Odrop(_1652774), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652772)), _1652776)), _1652780))))], (692 ^ _778495) ^ [_788963, _788965, _788967, _788969, _788971, _788973, _788975, _788977] : [-(c_Nat__Transfer_Otransfer__morphism(_788975, _788971, _788967, _788963)), c_Nat__Transfer_Otransfer__morphism(_788977, _788973, _788969, _788965), _788977 = _788975, _788973 = _788971, _788969 = _788967, _788965 = _788963], (18062 ^ _778495) ^ [_1102513, _1102515, _1102517] : [class_Int_Onumber__ring(_1102513), -(hAPP(c_Int_Onumber__class_Onumber__of(_1102513), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1102515), _1102517)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1102513), hAPP(c_Int_Onumber__class_Onumber__of(_1102513), _1102515)), hAPP(c_Int_Onumber__class_Onumber__of(_1102513), _1102517)))], (4368 ^ _778495) ^ [_844852, _844854, _844856, _844858] : [-(c_Lazy__Sequence_Osmall__lazy_H(_844858, _844854) = c_Lazy__Sequence_Osmall__lazy_H(_844856, _844852)), _844858 = _844856, _844854 = _844852], (40966 ^ _778495) ^ [_1582680, _1582682, _1582684, _1582686] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582680, _1582680)), _1582682), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582680, _1582680), tc_HOL_Obool), _1582684), _1582686))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582680, _1582680)), _1582682), c_Transitive__Closure_Ortrancl(_1582680, _1582686))))], (15063 ^ _778495) ^ [_1045804, _1045806, _1045808, _1045810, _1045812] : [class_Rings_Olinordered__semiring__strict(_1045804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045804), _1045806), _1045808)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045804), _1045810), _1045812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045804), c_Groups_Ozero__class_Ozero(_1045804)), _1045806)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045804), c_Groups_Ozero__class_Ozero(_1045804)), _1045810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045804), _1045806), _1045810)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045804), _1045808), _1045812))))], (38423 ^ _778495) ^ [_1519115, _1519117, _1519119, _1519121, _1519123, _1519125, _1519127, _1519129] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1519115, _1519117)), hAPP(hAPP(c_Product__Type_OPair(_1519115, _1519117), _1519119), _1519121)), _1519123)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519117, _1519125)), hAPP(hAPP(c_Product__Type_OPair(_1519117, _1519125), _1519121), _1519127)), _1519129)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1519115, _1519125)), hAPP(hAPP(c_Product__Type_OPair(_1519115, _1519125), _1519119), _1519127)), hAPP(hAPP(c_Relation_Orel__comp(_1519115, _1519117, _1519125), _1519123), _1519129))))], (6510 ^ _778495) ^ [_884201, _884203, _884205] : [_884201 = _884203, 6513 ^ _778495 : [(6516 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884205, tc_HOL_Obool)), _884203), _884201)))], (6514 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884205, tc_HOL_Obool)), _884201), _884203)))]]], (14029 ^ _778495) ^ [_1027614, _1027616] : [class_Groups_Olinordered__ab__group__add(_1027614), 14032 ^ _778495 : [(14039 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027614), _1027616), c_Groups_Ozero__class_Ozero(_1027614))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027614), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027614), _1027616), _1027616)), c_Groups_Ozero__class_Ozero(_1027614))))], (14033 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027614), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027614), _1027616), _1027616)), c_Groups_Ozero__class_Ozero(_1027614))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027614), _1027616), c_Groups_Ozero__class_Ozero(_1027614))))]]], (41167 ^ _778495) ^ [_1588000, _1588002, _1588004, _1588006, _1588008] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588000, _1588000)), hAPP(hAPP(c_Product__Type_OPair(_1588000, _1588000), _1588002), _1588004)), c_Transitive__Closure_Ortrancl(_1588000, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588000, _1588000), tc_HOL_Obool)), _1588006), _1588008)))), 41173 ^ _778495 : [(41179 ^ _778495) ^ [] : [41175 ^ [_1588000, _1588002, _1588004, _1588006, _1588008] = 41172 ^ [_1588000, _1588002, _1588004, _1588006, _1588008]], (41177 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588000, _1588000)), hAPP(hAPP(c_Product__Type_OPair(_1588000, _1588000), 41175 ^ [_1588000, _1588002, _1588004, _1588006, _1588008]), 41172 ^ [_1588000, _1588002, _1588004, _1588006, _1588008])), _1588008)))], (41174 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588000, _1588000)), hAPP(hAPP(c_Product__Type_OPair(_1588000, _1588000), 41172 ^ [_1588000, _1588002, _1588004, _1588006, _1588008]), _1588004)), c_Transitive__Closure_Ortrancl(_1588000, _1588006))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588000, _1588000)), hAPP(hAPP(c_Product__Type_OPair(_1588000, _1588000), _1588002), _1588004)), c_Transitive__Closure_Ortrancl(_1588000, _1588006))))], (34731 ^ _778495) ^ [_1427994, _1427996, _1427998] : [class_Orderings_Olinorder(_1427994), 34734 ^ _778495 : [(34741 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1427994), _1427998), _1427996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427994, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1427994), _1427996)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1427994), _1427998))))], (34735 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427994, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1427994), _1427996)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1427994), _1427998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1427994), _1427998), _1427996)))]]], (29045 ^ _778495) ^ [_1305818] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1305818) = 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)))], (10253 ^ _778495) ^ [_955277, _955279, _955281] : [class_Lattices_Olattice(_955277), hBOOL(hAPP(c_Finite__Set_Ofinite(_955277), _955279)), -(_955279 = c_Orderings_Obot__class_Obot(tc_fun(_955277, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_955277, hAPP(hAPP(c_Set_Oinsert(_955277), _955281), _955279)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955277), _955281), c_Big__Operators_Olattice__class_OInf__fin(_955277, _955279)))], (9330 ^ _778495) ^ [_936625, _936627, _936629, _936631] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936625, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_936625), _936627), _936629)), hAPP(hAPP(c_Set_Oinsert(_936625), _936627), _936631)) = hAPP(hAPP(c_Set_Oinsert(_936625), _936627), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936625, tc_HOL_Obool)), _936629), _936631)))], (8248 ^ _778495) ^ [_914610, _914612, _914614, _914616] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_914610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914610, tc_HOL_Obool)), _914612), hAPP(hAPP(c_Set_Oinsert(_914610), _914614), _914616)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_914610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914610, tc_HOL_Obool)), _914612), _914616))))], (26440 ^ _778495) ^ [_1251355, _1251357, _1251359, _1251361] : [class_Rings_Olinordered__semidom(_1251355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1251357), _1251359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251355), c_Groups_Oone__class_Oone(_1251355)), _1251361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251355), hAPP(hAPP(c_Power_Opower__class_Opower(_1251355), _1251361), _1251357)), hAPP(hAPP(c_Power_Opower__class_Opower(_1251355), _1251361), _1251359))))], (22656 ^ _778495) ^ [_1183496, _1183498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183496)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183498))))], (41632 ^ _778495) ^ [_1602175, _1602177, _1602179, _1602181] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602175), tc_List_Olist(_1602175))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602175), tc_List_Olist(_1602175)), _1602177), _1602179)), c_List_Olistrel1(_1602175, _1602181))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602175), tc_List_Olist(_1602175))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602175), tc_List_Olist(_1602175)), _1602177), _1602179)), c_List_Olistrel(_1602175, c_Transitive__Closure_Ortrancl(_1602175, _1602181)))))], (42742 ^ _778495) ^ [_1630281, _1630283] : [_1630283 = c_List_Olist_ONil(_1630281), -(hAPP(c_List_Oset(_1630281), _1630283) = c_Orderings_Obot__class_Obot(tc_fun(_1630281, tc_HOL_Obool)))], (49709 ^ _778495) ^ [_1783186, _1783188, _1783190, _1783192, _1783194] : [hBOOL(hAPP(hAPP(c_member(_1783186), _1783188), hAPP(c_Set_Oimage(_1783190, _1783186, _1783192), _1783194))), -(hAPP(_1783192, hAPP(c_Hilbert__Choice_Oinv__into(_1783190, _1783186, _1783194, _1783192), _1783188)) = _1783188)], (37400 ^ _778495) ^ [_1486700, _1486702, _1486704, _1486706] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1486700), _1486702)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1486704), _1486706)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1486700, _1486704)), hAPP(hAPP(c_Product__Type_OSigma(_1486700, _1486704), _1486702), hAPP(c_COMBK(tc_fun(_1486704, tc_HOL_Obool), _1486700), _1486706)))))], (32556 ^ _778495) ^ [] : [-(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)))))], (37957 ^ _778495) ^ [_1501278, _1501280, _1501282, _1501284, _1501286, _1501288, _1501290] : [class_Groups_Ocomm__monoid__add(_1501278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1501280), _1501282)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1501284), _1501286)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1501280, _1501278), hAPP(hAPP(c_COMBS(_1501280, tc_fun(_1501284, tc_HOL_Obool), _1501278), hAPP(hAPP(c_COMBB(tc_fun(_1501284, _1501278), tc_fun(tc_fun(_1501284, tc_HOL_Obool), _1501278), _1501280), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1501284, _1501278)), _1501288)), hAPP(hAPP(c_COMBB(tc_fun(_1501284, tc_HOL_Obool), tc_fun(_1501284, tc_HOL_Obool), _1501280), c_Set_OCollect(_1501284)), hAPP(hAPP(c_COMBB(tc_fun(_1501284, tc_HOL_Obool), tc_fun(_1501284, tc_HOL_Obool), _1501280), hAPP(c_COMBS(_1501284, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1501284), c_fconj), hAPP(hAPP(c_COMBC(_1501284, tc_fun(_1501284, tc_HOL_Obool), tc_HOL_Obool), c_member(_1501284)), _1501286)))), _1501290)))), _1501282) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1501284, _1501278), hAPP(hAPP(c_COMBS(_1501284, tc_fun(_1501280, tc_HOL_Obool), _1501278), hAPP(hAPP(c_COMBB(tc_fun(_1501280, _1501278), tc_fun(tc_fun(_1501280, tc_HOL_Obool), _1501278), _1501284), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1501280, _1501278)), hAPP(c_COMBC(_1501280, _1501284, _1501278), _1501288))), hAPP(hAPP(c_COMBB(tc_fun(_1501280, tc_HOL_Obool), tc_fun(_1501280, tc_HOL_Obool), _1501284), c_Set_OCollect(_1501280)), hAPP(hAPP(c_COMBB(tc_fun(_1501280, tc_HOL_Obool), tc_fun(_1501280, tc_HOL_Obool), _1501284), hAPP(c_COMBS(_1501280, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1501280), c_fconj), hAPP(hAPP(c_COMBC(_1501280, tc_fun(_1501280, tc_HOL_Obool), tc_HOL_Obool), c_member(_1501280)), _1501282)))), hAPP(c_COMBC(_1501280, _1501284, tc_HOL_Obool), _1501290))))), _1501286))], (28645 ^ _778495) ^ [_1297595, _1297597] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1297595), _1297597))), -(hAPP(c_Finite__Set_Ocard(_1297595), _1297597) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51211 ^ _778495) ^ [_1814065, _1814067] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814065), _1814067)), 51214 ^ _778495 : [(51221 ^ _778495) ^ [] : [_1814067 = _1814065, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814067), _1814065)))], (51215 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814067), _1814065)), -(_1814067 = _1814065)]]], (38834 ^ _778495) ^ [_1530359, _1530361, _1530363, _1530365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530359, _1530361), tc_HOL_Obool)), _1530363), _1530365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1530359, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1530359, _1530361), _1530363)), hAPP(c_Relation_ODomain(_1530359, _1530361), _1530365))))], (8984 ^ _778495) ^ [_929939, _929941, _929943, _929945] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929939, tc_HOL_Obool)), _929941), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929939, tc_HOL_Obool)), _929943), _929945)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929939, tc_HOL_Obool)), _929943), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929939, tc_HOL_Obool)), _929941), _929945)))], (21032 ^ _778495) ^ [_1155267, _1155269] : [_1155267 = _1155269, -(c_Int_OBit1(_1155267) = c_Int_OBit1(_1155269))], (33964 ^ _778495) ^ [_1410879, _1410881, _1410883] : [class_Orderings_Oorder(_1410879), 33967 ^ _778495 : [(33974 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410879), _1410881), _1410883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410879, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1410879), _1410881)), hAPP(c_SetInterval_Oord__class_OatMost(_1410879), _1410883))))], (33968 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410879, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1410879), _1410881)), hAPP(c_SetInterval_Oord__class_OatMost(_1410879), _1410883))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410879), _1410881), _1410883)))]]], (16422 ^ _778495) ^ [_1071853, _1071855, _1071857, _1071859] : [class_Fields_Olinordered__field(_1071853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071853), c_Groups_Ozero__class_Ozero(_1071853)), _1071855)), 16429 ^ _778495 : [(16436 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071853), _1071857), _1071855)), _1071859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071853), _1071857), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1071853), _1071859), _1071855))))], (16430 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071853), _1071857), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1071853), _1071859), _1071855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071853), _1071857), _1071855)), _1071859)))]]], (52701 ^ _778495) ^ [_1836228, _1836230] : [hBOOL(hAPP(hAPP(c_fconj, _1836228), _1836230)), -(hBOOL(_1836230))], (48384 ^ _778495) ^ [_1753824, _1753826, _1753828] : [-(hAPP(c_List_Oset(_1753824), c_List_Oreplicate(_1753824, hAPP(c_Nat_OSuc, _1753826), _1753828)) = hAPP(hAPP(c_Set_Oinsert(_1753824), _1753828), c_Orderings_Obot__class_Obot(tc_fun(_1753824, tc_HOL_Obool))))], (34282 ^ _778495) ^ [_1417937, _1417939] : [-(c_Relation_OId__on(_1417937, _1417939) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417937, tc_fun(tc_prod(_1417937, _1417937), tc_HOL_Obool)), _1417939), hAPP(hAPP(c_COMBC(_1417937, tc_fun(tc_prod(_1417937, _1417937), tc_HOL_Obool), tc_fun(tc_prod(_1417937, _1417937), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1417937, _1417937), tc_fun(tc_fun(tc_prod(_1417937, _1417937), tc_HOL_Obool), tc_fun(tc_prod(_1417937, _1417937), tc_HOL_Obool)), _1417937), c_Set_Oinsert(tc_prod(_1417937, _1417937))), hAPP(hAPP(c_COMBS(_1417937, _1417937, tc_prod(_1417937, _1417937)), c_Product__Type_OPair(_1417937, _1417937)), c_COMBI(_1417937)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1417937, _1417937), tc_HOL_Obool)))))], (19726 ^ _778495) ^ [_1132789, _1132791, _1132793] : [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), _1132789), _1132791)), _1132793)), 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)), _1132793)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132791), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26304 ^ _778495) ^ [_1248826, _1248828, _1248830] : [class_Rings_Olinordered__idom(_1248826), -(hAPP(c_Groups_Oabs__class_Oabs(_1248826), hAPP(hAPP(c_Power_Opower__class_Opower(_1248826), hAPP(c_Groups_Ouminus__class_Ouminus(_1248826), _1248828)), _1248830)) = hAPP(c_Groups_Oabs__class_Oabs(_1248826), hAPP(hAPP(c_Power_Opower__class_Opower(_1248826), _1248828), _1248830)))], (10531 ^ _778495) ^ [_960285, _960287, _960289] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _960285)), _960287) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _960285)), _960289), -(_960287 = _960289)], (41401 ^ _778495) ^ [_1594734, _1594736, _1594738] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594734)), hAPP(hAPP(c_List_Olist_OCons(_1594734), _1594736), _1594738)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594734)), _1594738)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32584 ^ _778495) ^ [_1378775, _1378777, _1378779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1378775)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1378777), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1378779)), 32591 ^ _778495 : [(32592 ^ _778495) ^ [_1378983] : [32594 ^ _778495 : [(32600 ^ _778495) ^ [] : [-(_1378983 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32596 ^ [_1378775, _1378777, _1378779, _1378983]), 32593 ^ [_1378775, _1378777, _1378779, _1378983]))], (32598 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32596 ^ [_1378775, _1378777, _1378779, _1378983]), _1378779)))], (32595 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32593 ^ [_1378775, _1378777, _1378779, _1378983]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1378775))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1378777), _1378983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1378777), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1378983), _1378775))))]]], (38439 ^ _778495) ^ [_1519549, _1519551, _1519553, _1519555, _1519557, _1519559, _1519561] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1519549, _1519551, _1519553), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519555, tc_fun(tc_prod(_1519549, _1519551), tc_HOL_Obool)), _1519557), _1519559)), _1519561) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519555, tc_fun(tc_prod(_1519549, _1519553), tc_HOL_Obool)), _1519557), hAPP(hAPP(c_COMBC(_1519555, tc_fun(tc_prod(_1519551, _1519553), tc_HOL_Obool), tc_fun(tc_prod(_1519549, _1519553), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1519549, _1519551), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1519551, _1519553), tc_HOL_Obool), tc_fun(tc_prod(_1519549, _1519553), tc_HOL_Obool)), _1519555), c_Relation_Orel__comp(_1519549, _1519551, _1519553)), _1519559)), _1519561)))], (36715 ^ _778495) ^ [_1470273, _1470275, _1470277, _1470279, _1470281] : [-(c_Fun_Oinj__on(_1470273, _1470275, _1470277, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470273, tc_HOL_Obool)), _1470279), _1470281))), c_Fun_Oinj__on(_1470273, _1470275, _1470277, _1470279), c_Fun_Oinj__on(_1470273, _1470275, _1470277, _1470281), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470275, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470273, _1470275, _1470277), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470273, tc_HOL_Obool)), _1470279), _1470281))), hAPP(c_Set_Oimage(_1470273, _1470275, _1470277), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470273, tc_HOL_Obool)), _1470281), _1470279))) = c_Orderings_Obot__class_Obot(tc_fun(_1470275, tc_HOL_Obool))], (31855 ^ _778495) ^ [_1362388, _1362390, _1362392, _1362394, _1362396] : [31857 ^ _778495 : [(31860 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1362388), _1362390), hAPP(_1362396, 31856 ^ [_1362388, _1362390, _1362392, _1362394, _1362396])))], (31858 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1362392), 31856 ^ [_1362388, _1362390, _1362392, _1362394, _1362396]), _1362394)))]], -(hBOOL(hAPP(hAPP(c_member(_1362388), _1362390), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362392, tc_fun(_1362388, tc_HOL_Obool)), _1362394), _1362396))))], (24800 ^ _778495) ^ [_1222339, _1222341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222339)), -(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), _1222339), _1222341))))], (37827 ^ _778495) ^ [_1498268, _1498270] : [-(hAPP(c_Set_OCollect(_1498268), hAPP(hAPP(c_COMBC(_1498268, tc_fun(_1498268, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498268)), _1498270)) = _1498270)], (27563 ^ _778495) ^ [_1270391] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1270391), c_Orderings_Otop__class_Otop(tc_fun(_1270391, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1270391)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1270391), tc_HOL_Obool)))))], (9226 ^ _778495) ^ [_934390, _934392] : [class_Lattices_Obounded__lattice__bot(_934390), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934390), _934392), c_Orderings_Obot__class_Obot(_934390)) = c_Orderings_Obot__class_Obot(_934390))], (10459 ^ _778495) ^ [_958940, _958942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958940), _958942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _958940)), hAPP(c_Nat_OSuc, _958942))))], (44606 ^ _778495) ^ [_1671953, _1671955, _1671957, _1671959] : [class_Rings_Osemiring__1(_1671953), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671953), hAPP(hAPP(c_List_Omap(_1671955, _1671953), hAPP(c_COMBK(_1671953, _1671955), _1671957)), _1671959)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1671953), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1671953), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671955)), _1671959))), _1671957))], (34330 ^ _778495) ^ [_1419100, _1419102, _1419104, _1419106, _1419108] : [-(hAPP(c_Set_Oimage(_1419100, _1419102, _1419104), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1419100, tc_HOL_Obool)), _1419106), _1419108)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1419102, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1419100, _1419102, _1419104), _1419106)), hAPP(c_Set_Oimage(_1419100, _1419102, _1419104), _1419108)))], (29350 ^ _778495) ^ [_1312294, _1312296] : [-(_1312294 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1312296, _1312294) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1312296), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1312294)))], (48314 ^ _778495) ^ [_1752629, _1752631] : [-(c_List_Oconcat(_1752629, c_List_Oreplicate(tc_List_Olist(_1752629), _1752631, c_List_Olist_ONil(_1752629))) = c_List_Olist_ONil(_1752629))], (5833 ^ _778495) ^ [_871189, _871191, _871193] : [-(hAPP(hAPP(c_Set_Oinsert(_871189), _871191), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_871189, tc_HOL_Obool)), _871193), hAPP(hAPP(c_Set_Oinsert(_871189), _871191), c_Orderings_Obot__class_Obot(tc_fun(_871189, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_871189), _871191), _871193))], (31874 ^ _778495) ^ [_1363124, _1363126, _1363128, _1363130, _1363132, _1363134, _1363136] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363124, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363126, tc_fun(_1363124, tc_HOL_Obool)), _1363128), _1363130)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363132, tc_fun(_1363124, tc_HOL_Obool)), _1363134), _1363136)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363126, tc_fun(_1363124, tc_HOL_Obool)), _1363128), hAPP(hAPP(c_COMBB(tc_fun(_1363132, tc_fun(_1363124, tc_HOL_Obool)), tc_fun(_1363124, tc_HOL_Obool), _1363126), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363132, tc_fun(_1363124, tc_HOL_Obool)), _1363134)), hAPP(hAPP(c_COMBC(_1363126, tc_fun(_1363132, tc_fun(_1363124, tc_HOL_Obool)), tc_fun(_1363132, tc_fun(_1363124, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1363124, tc_HOL_Obool), tc_fun(_1363124, tc_HOL_Obool)), tc_fun(tc_fun(_1363132, tc_fun(_1363124, tc_HOL_Obool)), tc_fun(_1363132, tc_fun(_1363124, tc_HOL_Obool))), _1363126), c_COMBB(tc_fun(_1363124, tc_HOL_Obool), tc_fun(_1363124, tc_HOL_Obool), _1363132)), hAPP(hAPP(c_COMBB(tc_fun(_1363124, tc_HOL_Obool), tc_fun(tc_fun(_1363124, tc_HOL_Obool), tc_fun(_1363124, tc_HOL_Obool)), _1363126), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363124, tc_HOL_Obool))), _1363130))), _1363136))))], (40333 ^ _778495) ^ [_1567328, _1567330, _1567332] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567328, _1567328)), hAPP(hAPP(c_Product__Type_OPair(_1567328, _1567328), _1567330), _1567330)), c_Transitive__Closure_Ortrancl(_1567328, _1567332))))], (9955 ^ _778495) ^ [_949592, _949594, _949596, _949598] : [c_Big__Operators_Osemilattice__big(_949592, _949594, _949596), hBOOL(hAPP(c_Finite__Set_Ofinite(_949592), _949598)), -(hAPP(_949596, _949598) = hAPP(c_Finite__Set_Ofold1(_949592, _949594), _949598))], (18202 ^ _778495) ^ [_1105195, _1105197, _1105199, _1105201] : [class_Fields_Ofield__inverse__zero(_1105195), class_Int_Onumber(_1105195), 18209 ^ _778495 : [(18210 ^ _778495) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105195), _1105197), _1105199) = hAPP(c_Int_Onumber__class_Onumber__of(_1105195), _1105201), 18213 ^ _778495 : [(18220 ^ _778495) ^ [] : [_1105199 = c_Groups_Ozero__class_Ozero(_1105195), -(hAPP(c_Int_Onumber__class_Onumber__of(_1105195), _1105201) = c_Groups_Ozero__class_Ozero(_1105195))], (18214 ^ _778495) ^ [] : [-(_1105199 = c_Groups_Ozero__class_Ozero(_1105195)), -(_1105197 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105195), hAPP(c_Int_Onumber__class_Onumber__of(_1105195), _1105201)), _1105199))]]], (18226 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105195), _1105197), _1105199) = hAPP(c_Int_Onumber__class_Onumber__of(_1105195), _1105201)), 18229 ^ _778495 : [(18232 ^ _778495) ^ [] : [_1105197 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105195), hAPP(c_Int_Onumber__class_Onumber__of(_1105195), _1105201)), _1105199)], (18230 ^ _778495) ^ [] : [_1105199 = c_Groups_Ozero__class_Ozero(_1105195)]], 18233 ^ _778495 : [(18236 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1105195), _1105201) = c_Groups_Ozero__class_Ozero(_1105195)], (18234 ^ _778495) ^ [] : [-(_1105199 = c_Groups_Ozero__class_Ozero(_1105195))]]]]], (48094 ^ _778495) ^ [_1747768, _1747770, _1747772] : [-(c_List_Osplice(_1747768, hAPP(hAPP(c_List_Olist_OCons(_1747768), _1747770), _1747772), c_List_Olist_ONil(_1747768)) = hAPP(hAPP(c_List_Olist_OCons(_1747768), _1747770), _1747772))], (29539 ^ _778495) ^ [_1316019, _1316021, _1316023, _1316025, _1316027, _1316029] : [-(hAPP(c_Product__Type_Oapsnd(_1316019, _1316021, _1316023, _1316025), hAPP(hAPP(c_Product__Type_OPair(_1316023, _1316019), _1316027), _1316029)) = hAPP(hAPP(c_Product__Type_OPair(_1316023, _1316021), _1316027), hAPP(_1316025, _1316029)))], (19998 ^ _778495) ^ [_1137748, _1137750] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137748)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137750)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1137748), _1137750)))], (13219 ^ _778495) ^ [_1013870, _1013872] : [class_Rings_Ocomm__semiring__1(_1013870), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013870), c_Groups_Ozero__class_Ozero(_1013870)), _1013872) = c_Groups_Ozero__class_Ozero(_1013870))], (10717 ^ _778495) ^ [_963188, _963190] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _963188), _963190) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 10720 ^ _778495 : [(10723 ^ _778495) ^ [] : [-(_963190 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10721 ^ _778495) ^ [] : [-(_963188 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (11522 ^ _778495) ^ [_978081, _978083, _978085, _978087] : [class_Groups_Oordered__ab__semigroup__add(_978081), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978081), _978083), _978085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978081), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978081), _978083), _978087)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978081), _978085), _978087))))], (5769 ^ _778495) ^ [_869916, _869918, _869920, _869922] : [_869920 = _869922, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_869916, _869918, hAPP(hAPP(c_Set_Oinsert(_869916), _869920), c_Orderings_Obot__class_Obot(tc_fun(_869916, tc_HOL_Obool)))), _869922)))], (17452 ^ _778495) ^ [_1090941, _1090943, _1090945] : [class_Fields_Olinordered__field__inverse__zero(_1090941), 17458 ^ _778495 : [(17463 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090941), 17457 ^ [_1090941, _1090943, _1090945]), _1090943)), _1090945))], (17461 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090941), 17457 ^ [_1090941, _1090943, _1090945]), c_Groups_Oone__class_Oone(_1090941))))], (17459 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090941), c_Groups_Ozero__class_Ozero(_1090941)), 17457 ^ [_1090941, _1090943, _1090945])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090941), _1090943), _1090945)))], (27809 ^ _778495) ^ [_1274816] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1274816, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1274816, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1274816, tc_HOL_Obool)))], (52467 ^ _778495) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (44901 ^ _778495) ^ [_1677894, _1677896, _1677898, _1677900, _1677902] : [c_List_Opartition(_1677894, _1677896, _1677898) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1677894), tc_List_Olist(_1677894)), _1677900), _1677902), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1677894, tc_HOL_Obool)), hAPP(c_List_Oset(_1677894), _1677900)), hAPP(c_List_Oset(_1677894), _1677902)) = hAPP(c_List_Oset(_1677894), _1677898))], (43381 ^ _778495) ^ [_1644426, _1644428, _1644430, _1644432] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644426), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644428)), _1644430)))), -(hAPP(hAPP(c_List_Onth(_1644428), hAPP(hAPP(c_List_Oappend(_1644428), _1644430), _1644432)), _1644426) = hAPP(hAPP(c_List_Onth(_1644428), _1644432), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644426), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644428)), _1644430))))], (772 ^ _778495) ^ [_790207, _790209, _790211, _790213] : [-(c_Wellfounded_Oacyclic(_790211, _790207)), c_Wellfounded_Oacyclic(_790213, _790209), _790213 = _790211, _790209 = _790207], (5957 ^ _778495) ^ [_873552, _873554] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873552, tc_HOL_Obool)), _873554), _873554) = _873554)], (34839 ^ _778495) ^ [_1430217, _1430219] : [c_Nat__Transfer_Ois__nat(_1430217), c_Nat__Transfer_Ois__nat(_1430219), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1430217, _1430219) = 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, _1430217), hAPP(c_Int_Onat, _1430219))))], (38701 ^ _778495) ^ [_1527708, _1527710, _1527712] : [c_Wellfounded_Owf(_1527708, _1527710), -(c_Wellfounded_Owf(_1527708, c_Wellfounded_Omlex__prod(_1527708, _1527712, _1527710)))], (27709 ^ _778495) ^ [_1273004, _1273006] : [class_Lattices_Oboolean__algebra(_1273004), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273004), _1273006), hAPP(c_Groups_Ouminus__class_Ouminus(_1273004), _1273006)) = c_Orderings_Otop__class_Otop(_1273004))], (14965 ^ _778495) ^ [_1043935, _1043937, _1043939] : [class_Groups_Oordered__comm__monoid__add(_1043935), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043935), c_Groups_Ozero__class_Ozero(_1043935)), _1043937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043935), c_Groups_Ozero__class_Ozero(_1043935)), _1043939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043935), c_Groups_Ozero__class_Ozero(_1043935)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043935), _1043937), _1043939))))], (36238 ^ _778495) ^ [_1460569, _1460571, _1460573, _1460575, _1460577] : [c_Fun_Oinj__on(_1460569, _1460571, _1460573, _1460575), c_Fun_Oinj__on(_1460569, _1460571, _1460573, _1460577), -(c_Fun_Oinj__on(_1460569, _1460571, _1460573, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460569, tc_HOL_Obool)), _1460575), _1460577)))], (42457 ^ _778495) ^ [_1624562, _1624564, _1624566, _1624568] : [hBOOL(hAPP(c_List_Odistinct(_1624562), _1624564)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1624566, _1624562)), hAPP(hAPP(c_List_Ozip(_1624566, _1624562), _1624568), _1624564))))], (42990 ^ _778495) ^ [_1635761, _1635763, _1635765, _1635767, _1635769] : [hAPP(hAPP(c_List_Oappend(_1635761), _1635763), hAPP(hAPP(c_List_Olist_OCons(_1635761), _1635765), c_List_Olist_ONil(_1635761))) = hAPP(hAPP(c_List_Oappend(_1635761), _1635767), hAPP(hAPP(c_List_Olist_OCons(_1635761), _1635769), c_List_Olist_ONil(_1635761))), 42993 ^ _778495 : [(42996 ^ _778495) ^ [] : [-(_1635765 = _1635769)], (42994 ^ _778495) ^ [] : [-(_1635763 = _1635767)]]], (20848 ^ _778495) ^ [_1151897] : [-(c_Int_Osucc(c_Int_Opred(_1151897)) = _1151897)], (24207 ^ _778495) ^ [_1211624, _1211626, _1211628, _1211630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211626), _1211628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211628), 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), _1211626), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1211630, _1211624))), _1211628)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34284 ^ _778495) ^ [_1418073, _1418075, _1418077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1418073), _1418075)), -(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)), _1418073)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1418077), _1418075)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1418077), _1418073)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1418075), _1418073)))], (31544 ^ _778495) ^ [_1354746, _1354748, _1354750] : [class_Orderings_Olinorder(_1354746), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354746), _1354748)), -(_1354748 = c_Orderings_Obot__class_Obot(tc_fun(_1354746, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354746), _1354750)), -(_1354750 = c_Orderings_Obot__class_Obot(tc_fun(_1354746, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1354746, tc_HOL_Obool)), _1354748), _1354750) = c_Orderings_Obot__class_Obot(tc_fun(_1354746, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1354746, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1354746, tc_HOL_Obool)), _1354748), _1354750)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354746), c_Big__Operators_Olinorder__class_OMax(_1354746, _1354748)), c_Big__Operators_Olinorder__class_OMax(_1354746, _1354750)))], (14447 ^ _778495) ^ [_1035248] : [class_Rings_Olinordered__semidom(_1035248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035248), c_Groups_Oone__class_Oone(_1035248)), c_Groups_Ozero__class_Ozero(_1035248)))], (35627 ^ _778495) ^ [_1445663, _1445665, _1445667, _1445669, _1445671] : [hBOOL(hAPP(hAPP(c_member(_1445663), _1445665), hAPP(c_Relation_OImage(_1445667, _1445663, _1445669), _1445671))), 35631 ^ _778495 : [(35634 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1445667), 35630 ^ [_1445663, _1445665, _1445667, _1445669, _1445671]), _1445671)))], (35632 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1445667, _1445663)), hAPP(hAPP(c_Product__Type_OPair(_1445667, _1445663), 35630 ^ [_1445663, _1445665, _1445667, _1445669, _1445671]), _1445665)), _1445669)))]]], (41620 ^ _778495) ^ [_1601797, _1601799, _1601801, _1601803, _1601805] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601797), tc_List_Olist(_1601797))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601797), tc_List_Olist(_1601797)), _1601799), _1601801)), c_List_Olistrel(_1601797, c_Transitive__Closure_Ortrancl(_1601797, _1601803)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601797), tc_List_Olist(_1601797))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601797), tc_List_Olist(_1601797)), _1601801), _1601805)), c_List_Olistrel(_1601797, c_Transitive__Closure_Ortrancl(_1601797, _1601803)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601797), tc_List_Olist(_1601797))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601797), tc_List_Olist(_1601797)), _1601799), _1601805)), c_List_Olistrel(_1601797, c_Transitive__Closure_Ortrancl(_1601797, _1601803)))))], (33223 ^ _778495) ^ [_1392081, _1392083, _1392085, _1392087, _1392089] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392081, tc_fun(_1392083, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392081, tc_HOL_Obool)), _1392085), _1392087)), _1392089) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392083, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392081, tc_fun(_1392083, tc_HOL_Obool)), _1392085), _1392089)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392081, tc_fun(_1392083, tc_HOL_Obool)), _1392087), _1392089)))], (36687 ^ _778495) ^ [_1469511, _1469513, _1469515, _1469517, _1469519] : [c_Fun_Oinj__on(_1469511, _1469513, _1469515, hAPP(hAPP(c_Set_Oinsert(_1469511), _1469517), _1469519)), 36690 ^ _778495 : [(36693 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1469513), hAPP(_1469515, _1469517)), hAPP(c_Set_Oimage(_1469511, _1469513, _1469515), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469511, tc_HOL_Obool)), _1469519), hAPP(hAPP(c_Set_Oinsert(_1469511), _1469517), c_Orderings_Obot__class_Obot(tc_fun(_1469511, tc_HOL_Obool)))))))], (36691 ^ _778495) ^ [] : [-(c_Fun_Oinj__on(_1469511, _1469513, _1469515, _1469519))]]], (20061 ^ _778495) ^ [_1138886, _1138888] : [class_Rings_Olinordered__semidom(_1138886), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138886), c_Groups_Ozero__class_Ozero(_1138886)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1138886), _1138888))))], (1488 ^ _778495) ^ [_800123, _800125] : [-(class_Orderings_Obot(_800123)), _800125 = _800123, class_Orderings_Obot(_800125)], (40834 ^ _778495) ^ [_1579446, _1579448, _1579450, _1579452, _1579454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579448, tc_HOL_Obool)), _1579452), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579448, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579446, _1579448, hAPP(c_Relation_Oconverse(_1579448, _1579446), _1579450)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579446, tc_HOL_Obool)), _1579454))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579446, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579448, _1579446, _1579450), _1579452)), _1579454)))], (31318 ^ _778495) ^ [_1350620, _1350622, _1350624] : [class_Orderings_Olinorder(_1350620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350620), _1350622)), -(c_Big__Operators_Olattice_OSup__fin(_1350620, c_Orderings_Oord__class_Omax(_1350620), hAPP(hAPP(c_Set_Oinsert(_1350620), _1350624), _1350622)) = hAPP(hAPP(c_Finite__Set_Ofold(_1350620, _1350620, c_Orderings_Oord__class_Omax(_1350620)), _1350624), _1350622))], (36813 ^ _778495) ^ [_1472675, _1472677] : [-(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)), _1472675), _1472677))], (9879 ^ _778495) ^ [_948124, _948126, _948128, _948130, _948132] : [c_Finite__Set_Ofolding__one(_948124, _948126, _948128), hBOOL(hAPP(c_Finite__Set_Ofinite(_948124), _948130)), -(hBOOL(hAPP(hAPP(c_member(_948124), _948132), _948130))), -(hAPP(_948128, hAPP(hAPP(c_Set_Oinsert(_948124), _948132), _948130)) = hAPP(hAPP(c_Finite__Set_Ofold(_948124, _948124, _948126), _948132), _948130))], (51871 ^ _778495) ^ [_1825801, _1825803, _1825805, _1825807] : [class_Divides_Osemiring__div(_1825801), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825801), _1825803), _1825805)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825801), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825801), _1825805), _1825803)), _1825807) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825801), _1825805), _1825807)), _1825803))], (124 ^ _778495) ^ [_780559, _780561, _780563, _780565, _780567, _780569] : [-(c_Finite__Set_Ofolding__one(_780567, _780563, _780559)), c_Finite__Set_Ofolding__one(_780569, _780565, _780561), _780569 = _780567, _780565 = _780563, _780561 = _780559], (4430 ^ _778495) ^ [_845845, _845847] : [_845847 = _845845, -(c_Lazy__Sequence_Oyield(_845847) = c_Lazy__Sequence_Oyield(_845845))], (5897 ^ _778495) ^ [_872433, _872435, _872437, _872439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872433, tc_HOL_Obool)), _872435), _872437)), hBOOL(hAPP(hAPP(c_member(_872433), _872439), _872435)), -(hBOOL(hAPP(hAPP(c_member(_872433), _872439), _872437)))], (18056 ^ _778495) ^ [_1102378, _1102380, _1102382] : [class_Int_Onumber__ring(_1102378), -(hAPP(c_Int_Onumber__class_Onumber__of(_1102378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1102380), _1102382)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102378), hAPP(c_Int_Onumber__class_Onumber__of(_1102378), _1102380)), hAPP(c_Int_Onumber__class_Onumber__of(_1102378), _1102382)))], (27641 ^ _778495) ^ [_1271787, _1271789] : [class_Lattices_Obounded__lattice__top(_1271787), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1271787), _1271789), c_Orderings_Otop__class_Otop(_1271787)) = _1271789)], (37416 ^ _778495) ^ [_1487046, _1487048, _1487050, _1487052, _1487054] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1487046, _1487048), _1487050), hAPP(hAPP(c_COMBS(_1487046, tc_fun(_1487048, tc_HOL_Obool), tc_fun(_1487048, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1487048, tc_HOL_Obool), tc_fun(tc_fun(_1487048, tc_HOL_Obool), tc_fun(_1487048, tc_HOL_Obool)), _1487046), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487048, tc_HOL_Obool))), _1487052)), _1487054)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1487046, _1487048), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1487046, _1487048), _1487050), _1487052)), hAPP(hAPP(c_Product__Type_OSigma(_1487046, _1487048), _1487050), _1487054)))], (3928 ^ _778495) ^ [_837854, _837856, _837858, _837860, _837862, _837864, _837866, _837868] : [-(c_Lazy__Sequence_Ohb__bind(_837868, _837864, _837860, _837856) = c_Lazy__Sequence_Ohb__bind(_837866, _837862, _837858, _837854)), _837868 = _837866, _837864 = _837862, _837860 = _837858, _837856 = _837854], (52647 ^ _778495) ^ [_1835444, _1835446] : [-(hAPP(c_COMBI(_1835444), _1835446) = _1835446)], (48763 ^ _778495) ^ [_1762830, _1762832, _1762834] : [c_List_Olist__ex(_1762830, _1762832, _1762834), 48767 ^ _778495 : [(48770 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1762832, 48766 ^ [_1762830, _1762832, _1762834])))], (48768 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1762830), 48766 ^ [_1762830, _1762832, _1762834]), hAPP(c_List_Oset(_1762830), _1762834))))]]], (32324 ^ _778495) ^ [_1373561, _1373563, _1373565, _1373567, _1373569] : [class_Groups_Ocomm__monoid__add(_1373561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1373563), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1373565), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1373561), _1373567), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1373563, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1373565), _1373569))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373561), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1373561), _1373567), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1373563, _1373565))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1373561), _1373567), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1373565), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1373565), _1373569)))))], (3570 ^ _778495) ^ [_832005, _832007, _832009, _832011] : [-(c_List_Orotate(_832011, _832007) = c_List_Orotate(_832009, _832005)), _832011 = _832009, _832007 = _832005], (32282 ^ _778495) ^ [_1372632, _1372634, _1372636, _1372638] : [class_Groups_Ocomm__monoid__add(_1372632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1372634), _1372636)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1372632), _1372638), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1372634, _1372636)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1372632), hAPP(_1372638, _1372634)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1372632), _1372638), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1372634), _1372636))))], (13454 ^ _778495) ^ [_1017379, _1017381, _1017383] : [13455 ^ _778495 : [(13458 ^ _778495) ^ [] : [_1017379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13456 ^ _778495) ^ [] : [_1017381 = _1017383]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017379), _1017381) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017379), _1017383))], (52527 ^ _778495) ^ [_1834265, _1834267] : [-(class_Finite__Set_Ofinite(tc_prod(_1834265, _1834267))), class_Finite__Set_Ofinite(_1834265), class_Finite__Set_Ofinite(_1834267)], (23583 ^ _778495) ^ [_1200909, _1200911, _1200913, _1200915] : [class_Divides_Osemiring__div(_1200909), -(_1200911 = c_Groups_Ozero__class_Ozero(_1200909)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200909), _1200913), _1200911)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200909), _1200915), _1200911)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200909), _1200913), _1200915))], (9721 ^ _778495) ^ [_945123, _945125, _945127] : [class_Lattices_Olattice(_945123), hBOOL(hAPP(c_Finite__Set_Ofinite(_945123), _945125)), -(_945125 = c_Orderings_Obot__class_Obot(tc_fun(_945123, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_945123, hAPP(hAPP(c_Set_Oinsert(_945123), _945127), _945125)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_945123), _945127), c_Big__Operators_Olattice__class_OSup__fin(_945123, _945125)))], (48190 ^ _778495) ^ [_1750377, _1750379, _1750381] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750377)), c_List_Oreplicate(_1750377, _1750379, _1750381)) = _1750379)], (43838 ^ _778495) ^ [_1655291, _1655293, _1655295] : [-(hAPP(c_List_Otl(_1655291), hAPP(hAPP(c_List_Oappend(_1655291), _1655293), _1655295)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1655291), _1655291, hAPP(c_List_Otl(_1655291), _1655295), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1655291), tc_List_Olist(_1655291)), _1655291), hAPP(hAPP(c_COMBC(tc_List_Olist(_1655291), tc_List_Olist(_1655291), tc_List_Olist(_1655291)), c_List_Oappend(_1655291)), _1655295))), _1655293))], (11151 ^ _778495) ^ [_970414, _970416, _970418, _970420, _970422, _970424, _970426] : [c_Finite__Set_Ofun__left__comm(_970414, _970416, _970418), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_970414, _970416, _970418, _970420, _970422), _970424)), hBOOL(hAPP(hAPP(c_member(_970414), _970426), _970422)), 11163 ^ _778495 : [(11166 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_970414, _970416, _970418, _970420, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970414, tc_HOL_Obool)), _970422), hAPP(hAPP(c_Set_Oinsert(_970414), _970426), c_Orderings_Obot__class_Obot(tc_fun(_970414, tc_HOL_Obool))))), 11162 ^ [_970414, _970416, _970418, _970420, _970422, _970424, _970426])))], (11164 ^ _778495) ^ [] : [-(_970424 = hAPP(hAPP(_970418, _970426), 11162 ^ [_970414, _970416, _970418, _970420, _970422, _970424, _970426]))]]], (41399 ^ _778495) ^ [_1594699, _1594701, _1594703] : [_1594699 = hAPP(hAPP(c_List_Olist_OCons(_1594701), _1594703), _1594699)], (46021 ^ _778495) ^ [_1704240, _1704242] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1704240, _1704242) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704240, hAPP(c_Nat_OSuc, _1704242))))], (37897 ^ _778495) ^ [_1499942, _1499944, _1499946] : [-(hBOOL(hAPP(_1499942, _1499944))), -(hAPP(c_Set_OCollect(_1499946), hAPP(hAPP(c_COMBS(_1499946, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499946), c_fconj), hAPP(c_fequal, _1499944))), _1499942)) = c_Orderings_Obot__class_Obot(tc_fun(_1499946, tc_HOL_Obool)))], (14546 ^ _778495) ^ [_1036938] : [14547 ^ _778495 : [(14548 ^ _778495) ^ [_1036980] : [_1036938 = hAPP(c_Nat_OSuc, _1036980)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1036938)))], (37434 ^ _778495) ^ [_1487698, _1487700, _1487702, _1487704, _1487706, _1487708] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1487698, _1487700)), hAPP(hAPP(c_Product__Type_OPair(_1487698, _1487700), _1487702), _1487704)), hAPP(hAPP(c_Product__Type_OSigma(_1487698, _1487700), _1487706), _1487708)))), hBOOL(hAPP(hAPP(c_member(_1487698), _1487702), _1487706)), hBOOL(hAPP(hAPP(c_member(_1487700), _1487704), hAPP(_1487708, _1487702)))], (24824 ^ _778495) ^ [_1222642, _1222644, _1222646] : [-(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), _1222642), _1222644)), _1222646), _1222644) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1222646, _1222644))], (45490 ^ _778495) ^ [_1691230, _1691232] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691230)), c_List_Oremdups(_1691230, _1691232)) = hAPP(c_Finite__Set_Ocard(_1691230), hAPP(c_List_Oset(_1691230), _1691232)))], (7048 ^ _778495) ^ [_894518, _894520, _894522, _894524] : [class_Lattices_Olattice(_894518), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894518), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894518), _894520), _894522)), _894524) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894518), _894520), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894518), _894522), _894524)))], (38990 ^ _778495) ^ [_1534530, _1534532, _1534534, _1534536, _1534538] : [hBOOL(hAPP(hAPP(_1534530, _1534532), _1534534)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1534536, _1534538, _1534530), _1534532)))], (26716 ^ _778495) ^ [_1256206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1256206)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1256206), c_Int_OMin)))], (45883 ^ _778495) ^ [_1701665, _1701667, _1701669, _1701671] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1701665, tc_Nat_Onat), _1701665), c_Product__Type_Ofst(_1701665, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701665, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701665, 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(_1701665, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701665, tc_Nat_Onat))), _1701667)), hAPP(hAPP(c_List_Ozip(_1701665, tc_Nat_Onat), _1701669), c_List_Oupt(_1701671, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701671), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701665)), _1701669)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1701665, tc_Nat_Onat), _1701665), c_Product__Type_Ofst(_1701665, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701665, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701665, 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(_1701665, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1701665, 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(_1701665, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1701665, tc_Nat_Onat))), _1701671))), _1701667)), hAPP(hAPP(c_List_Ozip(_1701665, tc_Nat_Onat), _1701669), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701665)), _1701669))))))], (31730 ^ _778495) ^ [_1358945, _1358947, _1358949, _1358951, _1358953, _1358955, _1358957, _1358959] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358945, tc_fun(_1358947, tc_fun(_1358949, tc_HOL_Obool))), _1358951), _1358953), _1358955), _1358957)), hBOOL(hAPP(hAPP(c_member(_1358945), _1358959), _1358951)), -(hBOOL(hAPP(hAPP(hAPP(_1358953, _1358959), _1358955), _1358957)))], (1928 ^ _778495) ^ [_805623, _805625] : [-(class_Groups_Oone(_805623)), _805625 = _805623, class_Groups_Oone(_805625)], (20546 ^ _778495) ^ [_1147064, _1147066] : [20547 ^ _778495 : [(20550 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1147064), c_Int_OPls))], (20548 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1147064), _1147066))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147064)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147066))))], (1148 ^ _778495) ^ [_795873, _795875] : [-(class_Groups_Oordered__ab__group__add__abs(_795873)), _795875 = _795873, class_Groups_Oordered__ab__group__add__abs(_795875)], (7968 ^ _778495) ^ [_909775, _909777, _909779] : [class_Orderings_Oorder(_909775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909775), _909777), _909779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909775), _909777), _909779))), -(_909777 = _909779)], (49628 ^ _778495) ^ [_1781209, _1781211, _1781213] : [hAPP(c_Set_Oimage(_1781209, _1781211, _1781213), c_Orderings_Otop__class_Otop(tc_fun(_1781209, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781211, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1781211, _1781209, c_Hilbert__Choice_Oinv__into(_1781209, _1781211, c_Orderings_Otop__class_Otop(tc_fun(_1781209, tc_HOL_Obool)), _1781213), c_Orderings_Otop__class_Otop(tc_fun(_1781211, tc_HOL_Obool))))], (15171 ^ _778495) ^ [_1047877, _1047879, _1047881, _1047883] : [class_Rings_Olinordered__ring__strict(_1047877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047877), c_Groups_Ozero__class_Ozero(_1047877)), _1047879)), 15178 ^ _778495 : [(15185 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047877), _1047881), _1047883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047877), _1047879), _1047881)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047877), _1047879), _1047883))))], (15179 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047877), _1047879), _1047881)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047877), _1047879), _1047883))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047877), _1047881), _1047883)))]]], (5342 ^ _778495) ^ [_860181, _860183] : [_860183 = _860181, -(c_Power_Opower__class_Opower(_860183) = c_Power_Opower__class_Opower(_860181))], (31430 ^ _778495) ^ [_1352604, _1352606, _1352608] : [class_Orderings_Olinorder(_1352604), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352604), _1352606)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352604), _1352608)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1352604, tc_HOL_Obool)), _1352606), _1352608) = c_Orderings_Obot__class_Obot(tc_fun(_1352604, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352604), c_Big__Operators_Olattice_OSup__fin(_1352604, c_Orderings_Oord__class_Omax(_1352604), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352604, tc_HOL_Obool)), _1352606), _1352608))), c_Big__Operators_Olattice_OSup__fin(_1352604, c_Orderings_Oord__class_Omax(_1352604), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1352604, tc_HOL_Obool)), _1352606), _1352608))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352604), c_Big__Operators_Olattice_OSup__fin(_1352604, c_Orderings_Oord__class_Omax(_1352604), _1352606)), c_Big__Operators_Olattice_OSup__fin(_1352604, c_Orderings_Oord__class_Omax(_1352604), _1352608)))], (40469 ^ _778495) ^ [_1570637, _1570639, _1570641] : [_1570639 = _1570641, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570637, _1570637)), hAPP(hAPP(c_Product__Type_OPair(_1570637, _1570637), _1570639), _1570641)), c_Relation_OId(_1570637))))], (45656 ^ _778495) ^ [_1695716, _1695718, _1695720] : [-(hAPP(c_List_Ofilter(_1695716, _1695718), c_List_Oconcat(_1695716, _1695720)) = c_List_Oconcat(_1695716, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695716), tc_List_Olist(_1695716)), c_List_Ofilter(_1695716, _1695718)), _1695720)))], (45460 ^ _778495) ^ [_1690745, _1690747, _1690749] : [hBOOL(hAPP(c_List_Odistinct(_1690745), _1690747)), -(c_List_Oremove1(_1690745, _1690749, c_List_Oremdups(_1690745, _1690747)) = c_List_Oremdups(_1690745, c_List_Oremove1(_1690745, _1690749, _1690747)))], (47880 ^ _778495) ^ [_1743163, _1743165, _1743167] : [c_FunDef_Ois__measure(_1743163, _1743165), -(c_FunDef_Ois__measure(tc_prod(_1743163, _1743167), hAPP(hAPP(c_COMBB(_1743163, tc_Nat_Onat, tc_prod(_1743163, _1743167)), _1743165), c_Product__Type_Ofst(_1743163, _1743167))))], (21850 ^ _778495) ^ [_1169521] : [class_Groups_Ogroup__add(_1169521), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1169521), c_Groups_Ozero__class_Ozero(_1169521)) = c_Groups_Ozero__class_Ozero(_1169521))], (22872 ^ _778495) ^ [_1187392] : [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), _1187392))), 22875 ^ _778495 : [(22878 ^ _778495) ^ [] : [-(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(_1187392)))))], (22876 ^ _778495) ^ [] : [-(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(_1187392)))))]]], (32208 ^ _778495) ^ [_1371261, _1371263, _1371265, _1371267, _1371269] : [class_Complete__Lattice_Ocomplete__lattice(_1371261), hBOOL(hAPP(hAPP(c_member(_1371263), _1371265), _1371267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371261), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1371263, _1371261), _1371267), _1371269)), hAPP(_1371269, _1371265))))], (2862 ^ _778495) ^ [_820981, _820983] : [_820983 = _820981, -(c_Rings_Oinverse__class_Odivide(_820983) = c_Rings_Oinverse__class_Odivide(_820981))], (42840 ^ _778495) ^ [_1632271, _1632273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1632271), _1632273)), -(c_List_Oupto(_1632271, _1632273) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1632271), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1632271), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1632273)))], (20981 ^ _778495) ^ [_1154277, _1154279, _1154281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154279), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1154281), 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), _1154281), _1154279))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1154277)))))], (33268 ^ _778495) ^ [_1393683, _1393685, _1393687, _1393689] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393683, tc_fun(_1393685, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1393683, tc_HOL_Obool), _1393687)), _1393689) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1393683, tc_HOL_Obool), tc_fun(_1393685, tc_HOL_Obool)), _1393687), hAPP(hAPP(c_COMBC(tc_fun(_1393683, tc_HOL_Obool), tc_fun(_1393683, tc_fun(_1393685, tc_HOL_Obool)), tc_fun(_1393685, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393683, tc_fun(_1393685, tc_HOL_Obool))), _1393689)))], (41039 ^ _778495) ^ [_1584730, _1584732, _1584734] : [41042 ^ _778495 : [(41048 ^ _778495) ^ [] : [41041 ^ [_1584730, _1584732, _1584734] = 41044 ^ [_1584730, _1584732, _1584734]], (41046 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584730, _1584732)), hAPP(hAPP(c_Product__Type_OPair(_1584730, _1584732), 41040 ^ [_1584730, _1584732, _1584734]), 41044 ^ [_1584730, _1584732, _1584734])), _1584734)))], (41043 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584730, _1584732)), hAPP(hAPP(c_Product__Type_OPair(_1584730, _1584732), 41040 ^ [_1584730, _1584732, _1584734]), 41041 ^ [_1584730, _1584732, _1584734])), _1584734)))]], -(c_Relation_Osingle__valued(_1584730, _1584732, _1584734))], (8038 ^ _778495) ^ [_910761, _910763, _910765, _910767] : [class_Orderings_Opreorder(_910761), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910761), _910763), _910765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910761), _910765), _910767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910761), _910763), _910767)))], (6746 ^ _778495) ^ [_888972, _888974, _888976, _888978] : [hBOOL(hAPP(hAPP(c_member(_888972), _888974), hAPP(hAPP(c_Set_Oinsert(_888972), _888976), _888978))), -(_888974 = _888976), -(hBOOL(hAPP(hAPP(c_member(_888972), _888974), _888978)))], (27245 ^ _778495) ^ [_1265007] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1265007)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1265007)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37724 ^ _778495) ^ [_1495837, _1495839, _1495841] : [-(c_Relation_Orefl__on(_1495837, _1495839, _1495841)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1495837, _1495837), tc_HOL_Obool)), _1495841), hAPP(hAPP(c_Product__Type_OSigma(_1495837, _1495837), _1495839), hAPP(c_COMBK(tc_fun(_1495837, tc_HOL_Obool), _1495837), _1495839)))), 37730 ^ _778495 : [(37733 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1495837, _1495837)), hAPP(hAPP(c_Product__Type_OPair(_1495837, _1495837), 37729 ^ [_1495837, _1495839, _1495841]), 37729 ^ [_1495837, _1495839, _1495841])), _1495841))], (37731 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1495837), 37729 ^ [_1495837, _1495839, _1495841]), _1495839)))]]], (8770 ^ _778495) ^ [_925467, _925469, _925471, _925473, _925475, _925477, _925479, _925481] : [c_Finite__Set_Ofolding__image__simple__idem(_925467, _925469, _925471, _925473, _925475, _925477), hBOOL(hAPP(c_Finite__Set_Ofinite(_925469), _925479)), hBOOL(hAPP(hAPP(c_member(_925469), _925481), _925479)), -(hAPP(hAPP(_925471, hAPP(_925475, _925481)), hAPP(_925477, _925479)) = hAPP(_925477, _925479))], (49779 ^ _778495) ^ [_1784726, _1784728, _1784730] : [hAPP(c_Set_Oimage(_1784726, _1784728, _1784730), c_Orderings_Otop__class_Otop(tc_fun(_1784726, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784728, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1784726, _1784728, _1784728, _1784730), c_Hilbert__Choice_Oinv__into(_1784726, _1784728, c_Orderings_Otop__class_Otop(tc_fun(_1784726, tc_HOL_Obool)), _1784730)) = c_Fun_Oid(_1784728))], (22342 ^ _778495) ^ [_1177990, _1177992, _1177994] : [class_Rings_Ocomm__ring__1(_1177990), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1177990), _1177992), _1177994) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177990), _1177992), hAPP(c_Groups_Ouminus__class_Ouminus(_1177990), _1177994)))], (33994 ^ _778495) ^ [_1411494, _1411496, _1411498, _1411500, _1411502] : [class_Groups_Oab__group__add(_1411494), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1411496), _1411498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1411498), _1411500)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1411494), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411494), _1411502), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411496), _1411500))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411494), _1411502), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411496), _1411498))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411494), _1411502), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411498), _1411500)))], (6428 ^ _778495) ^ [_882592, _882594, _882596, _882598] : [class_Orderings_Opreorder(_882592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882592), _882594), _882596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882592), _882596), _882598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882592), _882594), _882598)))], (27071 ^ _778495) ^ [_1262010] : [class_Rings_Oring__1(_1262010), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262010), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1262010))], (52315 ^ _778495) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (42922 ^ _778495) ^ [_1633740, _1633742, _1633744] : [-(_1633740 = c_List_Olist_ONil(_1633742)), -(hBOOL(hAPP(hAPP(c_member(_1633742), hAPP(c_Product__Type_Ofst(_1633742, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1633742, _1633740), _1633744))), hAPP(c_List_Oset(_1633742), _1633740))))], (40750 ^ _778495) ^ [_1577020, _1577022, _1577024, _1577026] : [-(hAPP(c_Relation_Oconverse(_1577020, _1577022), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1577020, _1577022), tc_HOL_Obool)), _1577024), _1577026)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1577022, _1577020), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1577020, _1577022), _1577024)), hAPP(c_Relation_Oconverse(_1577020, _1577022), _1577026)))], (10891 ^ _778495) ^ [_966008, _966010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966008), _966010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966008), hAPP(c_Nat_OSuc, _966010))))], (34271 ^ _778495) ^ [_1417627, _1417629] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1417627), _1417629)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1417629), _1417627)))], (39856 ^ _778495) ^ [_1555304, _1555306, _1555308, _1555310, _1555312, _1555314] : [c_Finite__Set_Ofolding__idem(_1555304, _1555306, _1555308, _1555310), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555304), _1555312)), -(hAPP(_1555310, hAPP(hAPP(c_Set_Oinsert(_1555304), _1555314), _1555312)) = hAPP(c_Fun_Ocomp(_1555306, _1555306, _1555306, hAPP(_1555310, _1555312)), hAPP(_1555308, _1555314)))], (13322 ^ _778495) ^ [_1015530] : [-(_1015530 = 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)), _1015530)))], (36212 ^ _778495) ^ [_1459979, _1459981, _1459983, _1459985] : [36214 ^ _778495 : [(36218 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1459979), 36216 ^ [_1459979, _1459981, _1459983, _1459985]), _1459985)))], (36220 ^ _778495) ^ [] : [-(hAPP(_1459983, 36213 ^ [_1459979, _1459981, _1459983, _1459985]) = hAPP(_1459983, 36216 ^ [_1459979, _1459981, _1459983, _1459985]))], (36222 ^ _778495) ^ [] : [36213 ^ [_1459979, _1459981, _1459983, _1459985] = 36216 ^ [_1459979, _1459981, _1459983, _1459985]], (36215 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1459979), 36213 ^ [_1459979, _1459981, _1459983, _1459985]), _1459985)))]], -(c_Fun_Oinj__on(_1459979, _1459981, _1459983, _1459985))], (4124 ^ _778495) ^ [_841036, _841038, _841040, _841042] : [-(c_New__DSequence_Opos__single(_841042, _841038) = c_New__DSequence_Opos__single(_841040, _841036)), _841042 = _841040, _841038 = _841036], (23929 ^ _778495) ^ [_1206761, _1206763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206761)), 23932 ^ _778495 : [(23935 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206763, _1206761)), _1206761)))], (23933 ^ _778495) ^ [] : [-(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, _1206763, _1206761))))]]], (38413 ^ _778495) ^ [_1518456, _1518458] : [38414 ^ _778495 : [(38415 ^ _778495) ^ [_1518520, _1518522] : [_1518458 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1518456, _1518520), 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)), _1518522)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1518456), _1518458)))], (16063 ^ _778495) ^ [_1065536, _1065538, _1065540, _1065542, _1065544] : [class_Groups_Ocomm__monoid__add(_1065536), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065538), _1065540)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1065538, tc_HOL_Obool)), _1065542), _1065540)), 16077 ^ _778495 : [(16080 ^ _778495) ^ [] : [hAPP(_1065544, 16076 ^ [_1065536, _1065538, _1065540, _1065542, _1065544]) = c_Groups_Ozero__class_Ozero(_1065536)], (16078 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1065538), 16076 ^ [_1065536, _1065538, _1065540, _1065542, _1065544]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065538, tc_HOL_Obool)), _1065540), _1065542))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1065538, _1065536), _1065544), _1065542) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1065538, _1065536), _1065544), _1065540))], (13715 ^ _778495) ^ [_1021824, _1021826, _1021828] : [class_Rings_Oordered__cancel__semiring(_1021824), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021824), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1021824), _1021826), _1021828)), c_Groups_Ozero__class_Ozero(_1021824)))), 13720 ^ _778495 : [(13727 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021824), _1021826), c_Groups_Ozero__class_Ozero(_1021824))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021824), c_Groups_Ozero__class_Ozero(_1021824)), _1021828))], (13721 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021824), c_Groups_Ozero__class_Ozero(_1021824)), _1021826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021824), _1021828), c_Groups_Ozero__class_Ozero(_1021824)))]]], (10697 ^ _778495) ^ [_962890, _962892] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962890), _962892), 10700 ^ _778495 : [(10703 ^ _778495) ^ [] : [-(_962892 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10701 ^ _778495) ^ [] : [-(_962890 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (19943 ^ _778495) ^ [_1136731] : [19944 ^ _778495 : [(19945 ^ _778495) ^ [_1136788] : [hBOOL(hAPP(_1136731, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136788)))]], 19947 ^ _778495 : [(19950 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1136731, 19946 ^ [_1136731])))], (19948 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19946 ^ [_1136731])))]]], (9514 ^ _778495) ^ [_940788, _940790, _940792, _940794] : [class_Lattices_Osemilattice__sup(_940788), hBOOL(hAPP(c_Finite__Set_Ofinite(_940788), _940790)), -(hAPP(hAPP(c_Finite__Set_Ofold(_940788, _940788, c_Lattices_Osemilattice__sup__class_Osup(_940788)), _940792), hAPP(hAPP(c_Set_Oinsert(_940788), _940794), _940790)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_940788), _940794), hAPP(hAPP(c_Finite__Set_Ofold(_940788, _940788, c_Lattices_Osemilattice__sup__class_Osup(_940788)), _940792), _940790)))], (52327 ^ _778495) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (27957 ^ _778495) ^ [_1277203, _1277205, _1277207] : [class_Complete__Lattice_Ocomplete__lattice(_1277203), hBOOL(hAPP(hAPP(c_member(_1277203), _1277205), _1277207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277203), c_Complete__Lattice_OInf__class_OInf(_1277203, _1277207)), _1277205)))], (19952 ^ _778495) ^ [_1136892] : [19954 ^ _778495 : [(19957 ^ _778495) ^ [] : [hBOOL(hAPP(_1136892, 19953 ^ [_1136892]))], (19955 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19953 ^ [_1136892])))]], 19958 ^ _778495 : [(19959 ^ _778495) ^ [_1137019] : [-(hBOOL(hAPP(_1136892, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137019))))]]], (42351 ^ _778495) ^ [_1622118, _1622120, _1622122, _1622124] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622118, tc_HOL_Obool)), hAPP(c_List_Oset(_1622118), hAPP(hAPP(c_List_Olist__update(_1622118, _1622120), _1622122), _1622124))), hAPP(hAPP(c_Set_Oinsert(_1622118), _1622124), hAPP(c_List_Oset(_1622118), _1622120)))))], (42998 ^ _778495) ^ [_1635938, _1635940, _1635942, _1635944, _1635946] : [-(hAPP(hAPP(c_List_Oappend(_1635938), _1635940), hAPP(hAPP(c_List_Olist_OCons(_1635938), _1635942), c_List_Olist_ONil(_1635938))) = hAPP(hAPP(c_List_Oappend(_1635938), _1635944), hAPP(hAPP(c_List_Olist_OCons(_1635938), _1635946), c_List_Olist_ONil(_1635938)))), _1635940 = _1635944, _1635942 = _1635946], (49075 ^ _778495) ^ [_1771093, _1771095] : [49078 ^ _778495 : [(49084 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1771093, _1771093)), hAPP(hAPP(c_Product__Type_OPair(_1771093, _1771093), 49076 ^ [_1771093, _1771095]), 49080 ^ [_1771093, _1771095])), _1771095))], (49082 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1771093, _1771093)), hAPP(hAPP(c_Product__Type_OPair(_1771093, _1771093), 49077 ^ [_1771093, _1771095]), 49080 ^ [_1771093, _1771095])), _1771095)))], (49079 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1771093, _1771093)), hAPP(hAPP(c_Product__Type_OPair(_1771093, _1771093), 49076 ^ [_1771093, _1771095]), 49077 ^ [_1771093, _1771095])), _1771095)))]], -(c_Relation_Otrans(_1771093, _1771095))], (45907 ^ _778495) ^ [_1702254, _1702256, _1702258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702254), _1702256)), -(c_List_Oupt(_1702254, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702256), _1702258)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1702254, _1702256)), c_List_Oupt(_1702256, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702256), _1702258))))], (52655 ^ _778495) ^ [_1835616, _1835618, _1835620, _1835622, _1835624, _1835626] : [-(hAPP(hAPP(hAPP(c_COMBS(_1835616, _1835618, _1835620), _1835622), _1835624), _1835626) = hAPP(hAPP(_1835622, _1835626), hAPP(_1835624, _1835626)))], (41762 ^ _778495) ^ [_1606098, _1606100, _1606102, _1606104] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606098)), hAPP(hAPP(c_List_Olist_OCons(_1606098), _1606100), _1606102)), c_List_Olists(_1606098, _1606104)))), hBOOL(hAPP(hAPP(c_member(_1606098), _1606100), _1606104)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606098)), _1606102), c_List_Olists(_1606098, _1606104)))], (10691 ^ _778495) ^ [_962741, _962743, _962745] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962741), _962743)), _962745) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962741), _962745)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962743), _962745)))], (11077 ^ _778495) ^ [_969108, _969110, _969112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969108), _969110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _969108), _969112)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _969110), _969112))))], (6200 ^ _778495) ^ [_878688, _878690, _878692] : [_878688 = _878690, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878692, tc_HOL_Obool)), _878690), _878688)))], (27647 ^ _778495) ^ [_1271882, _1271884] : [class_Lattices_Obounded__lattice__top(_1271882), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1271882), c_Orderings_Otop__class_Otop(_1271882)), _1271884) = _1271884)], (20924 ^ _778495) ^ [_1153226] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1153226) = 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(_1153226)))))], (44093 ^ _778495) ^ [_1660917, _1660919, _1660921, _1660923, _1660925] : [class_Orderings_Olinorder(_1660917), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660919, _1660917, _1660921), _1660923), _1660925) = c_List_Olist_ONil(_1660919)], (22038 ^ _778495) ^ [_1172728, _1172730, _1172732] : [class_Groups_Oab__group__add(_1172728), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1172728), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1172728), _1172730), _1172732)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1172728), _1172732), _1172730))], (32830 ^ _778495) ^ [_1384133, _1384135, _1384137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1384133)), 32833 ^ _778495 : [(32834 ^ _778495) ^ [_1384267] : [32836 ^ _778495 : [(32842 ^ _778495) ^ [] : [-(_1384267 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32838 ^ [_1384133, _1384135, _1384137, _1384267]), 32835 ^ [_1384133, _1384135, _1384137, _1384267]))], (32840 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32838 ^ [_1384133, _1384135, _1384137, _1384267]), _1384135)))], (32837 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32835 ^ [_1384133, _1384135, _1384137, _1384267]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1384133))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384267), _1384137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1384267), _1384133)), _1384137)))]]], (24870 ^ _778495) ^ [_1223434, _1223436] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223434))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223434)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223436)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3650 ^ _778495) ^ [_833245, _833247] : [_833247 = _833245, -(c_List_Omonoid__add__class_Olistsum(_833247) = c_List_Omonoid__add__class_Olistsum(_833245))], (8994 ^ _778495) ^ [_930176, _930178, _930180, _930182] : [class_Lattices_Osemilattice__inf(_930176), hBOOL(hAPP(c_Finite__Set_Ofinite(_930176), _930178)), -(hAPP(hAPP(c_Finite__Set_Ofold(_930176, _930176, c_Lattices_Osemilattice__inf__class_Oinf(_930176)), _930180), hAPP(hAPP(c_Set_Oinsert(_930176), _930182), _930178)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930176), _930182), hAPP(hAPP(c_Finite__Set_Ofold(_930176, _930176, c_Lattices_Osemilattice__inf__class_Oinf(_930176)), _930180), _930178)))], (11576 ^ _778495) ^ [_979132, _979134, _979136, _979138] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_979132), 11579 ^ _778495 : [(11586 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979132), _979134), _979138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979132), _979134), _979136)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979132), _979138), _979136))))], (11580 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979132), _979134), _979136)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979132), _979138), _979136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979132), _979134), _979138)))]]], (45879 ^ _778495) ^ [_1701501, _1701503] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1701501))), c_List_Otranspose(_1701501, _1701503)) = c_List_Ofoldr(tc_List_Olist(_1701501), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1701501)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1701501))), _1701503, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45262 ^ _778495) ^ [_1686560, _1686562, _1686564, _1686566, _1686568, _1686570, _1686572, _1686574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686560), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686562)), _1686564))), c_List_Olist__all2(_1686562, _1686566, _1686568, _1686564, _1686570), hBOOL(hAPP(hAPP(_1686568, _1686572), _1686574)), -(c_List_Olist__all2(_1686562, _1686566, _1686568, hAPP(hAPP(c_List_Olist__update(_1686562, _1686564), _1686560), _1686572), hAPP(hAPP(c_List_Olist__update(_1686566, _1686570), _1686560), _1686574)))], (21610 ^ _778495) ^ [_1165458, _1165460] : [class_Fields_Olinordered__field__inverse__zero(_1165458), class_Int_Onumber__ring(_1165458), 21617 ^ _778495 : [(21624 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165458), c_Groups_Ozero__class_Ozero(_1165458)), _1165460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165458), c_Groups_Ozero__class_Ozero(_1165458)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165458), _1165460), hAPP(c_Int_Onumber__class_Onumber__of(_1165458), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21618 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165458), c_Groups_Ozero__class_Ozero(_1165458)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165458), _1165460), hAPP(c_Int_Onumber__class_Onumber__of(_1165458), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165458), c_Groups_Ozero__class_Ozero(_1165458)), _1165460)))]]], (14477 ^ _778495) ^ [_1035753, _1035755, _1035757, _1035759] : [class_Groups_Ocomm__monoid__add(_1035753), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035755), _1035757))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1035755, _1035753), _1035759), _1035757) = c_Groups_Ozero__class_Ozero(_1035753))], (52393 ^ _778495) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (51095 ^ _778495) ^ [_1812217, _1812219] : [_1812217 = _1812219, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812217), _1812219)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812219), _1812217)))], (38599 ^ _778495) ^ [_1525782, _1525784, _1525786, _1525788] : [hBOOL(hAPP(c_Predicate_ORangeP(_1525782, _1525784, _1525786), _1525788)), -(hBOOL(hAPP(hAPP(_1525786, 38602 ^ [_1525782, _1525784, _1525786, _1525788]), _1525788)))], (16910 ^ _778495) ^ [_1080564, _1080566, _1080568] : [class_Fields_Olinordered__field(_1080564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080564), c_Groups_Ozero__class_Ozero(_1080564)), _1080566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080564), _1080568), c_Groups_Ozero__class_Ozero(_1080564))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080564), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1080564), _1080566), _1080568)), c_Groups_Ozero__class_Ozero(_1080564))))], (48720 ^ _778495) ^ [_1761407, _1761409, _1761411] : [48722 ^ _778495 : [(48725 ^ _778495) ^ [] : [hBOOL(hAPP(_1761407, 48721 ^ [_1761407, _1761409, _1761411]))], (48723 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 48721 ^ [_1761407, _1761409, _1761411]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1761409, _1761411))))]], -(c_List_Oall__interval__int(_1761407, _1761409, _1761411))], (45971 ^ _778495) ^ [_1703322, _1703324, _1703326] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1703322), c_List_Oupt(_1703324, _1703326)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703324), _1703322), _1703326))], (26804 ^ _778495) ^ [_1257727, _1257729] : [class_Int_Onumber__ring(_1257727), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257727), _1257729), hAPP(c_Int_Onumber__class_Onumber__of(_1257727), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1257727), _1257729))], (11682 ^ _778495) ^ [_981169, _981171] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _981169)), _981171) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981169), _981171)))], (52395 ^ _778495) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (37318 ^ _778495) ^ [_1484077, _1484079, _1484081, _1484083, _1484085, _1484087] : [hBOOL(hAPP(hAPP(c_member(_1484077), _1484079), _1484081)), hBOOL(hAPP(hAPP(c_member(_1484083), _1484085), hAPP(_1484087, _1484079))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1484077, _1484083)), hAPP(hAPP(c_Product__Type_OPair(_1484077, _1484083), _1484079), _1484085)), hAPP(hAPP(c_Product__Type_OSigma(_1484077, _1484083), _1484081), _1484087))))], (47367 ^ _778495) ^ [_1732114, _1732116] : [class_Enum_Oenum(_1732114), 47370 ^ _778495 : [(47377 ^ _778495) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732114), _1732116)), -(hBOOL(hAPP(_1732116, 47380 ^ [_1732114, _1732116])))], (47371 ^ _778495) ^ [] : [47372 ^ _778495 : [(47373 ^ _778495) ^ [_1732216] : [hBOOL(hAPP(_1732116, _1732216))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732114), _1732116)))]]], (41107 ^ _778495) ^ [_1586346, _1586348, _1586350, _1586352, _1586354] : [c_Relation_Osingle__valued(_1586346, _1586348, hAPP(c_Relation_Oconverse(_1586348, _1586346), _1586350)), -(hAPP(c_Relation_OImage(_1586348, _1586346, _1586350), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1586348, tc_HOL_Obool)), _1586352), _1586354)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1586346, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1586348, _1586346, _1586350), _1586352)), hAPP(c_Relation_OImage(_1586348, _1586346, _1586350), _1586354)))], (20796 ^ _778495) ^ [_1151152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1151152), 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), _1151152)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (460 ^ _778495) ^ [_785489, _785491, _785493, _785495, _785497, _785499] : [-(c_Relation_Osingle__valued(_785497, _785493, _785489)), c_Relation_Osingle__valued(_785499, _785495, _785491), _785499 = _785497, _785495 = _785493, _785491 = _785489], (34267 ^ _778495) ^ [_1417554, _1417556] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1417554), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1417556), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1417554, _1417556))], (50381 ^ _778495) ^ [_1797094, _1797096, _1797098, _1797100, _1797102] : [hBOOL(hAPP(hAPP(c_member(_1797094), _1797096), _1797098)), -(hAPP(c_Quotient_OBabs(_1797094, _1797100, _1797098, _1797102), _1797096) = hAPP(_1797102, _1797096))], (45983 ^ _778495) ^ [_1703596, _1703598] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703596)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703598)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703596), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703598)) = c_List_Olist_ONil(tc_Nat_Onat))], (42056 ^ _778495) ^ [_1613625, _1613627, _1613629] : [hBOOL(hAPP(hAPP(c_member(_1613625), _1613627), hAPP(c_List_Oset(_1613625), _1613629))), -(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(_1613625)), _1613629))))], (52403 ^ _778495) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (51749 ^ _778495) ^ [_1823264, _1823266] : [_1823264 = _1823266, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823264, _1823266) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1823264), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (29531 ^ _778495) ^ [_1315832, _1315834, _1315836, _1315838, _1315840, _1315842] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1315832, _1315834, _1315836), _1315838), hAPP(hAPP(c_Product__Type_OPair(_1315832, _1315834), _1315840), _1315842)) = hAPP(hAPP(_1315838, _1315840), _1315842))], (24009 ^ _778495) ^ [_1208143, _1208145, _1208147] : [class_Divides_Osemiring__div(_1208143), -(_1208145 = c_Groups_Ozero__class_Ozero(_1208143)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208143), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208143), _1208145), _1208147)), _1208145) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208143), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208143), _1208147), _1208145)), c_Groups_Oone__class_Oone(_1208143)))], (32420 ^ _778495) ^ [_1375588, _1375590, _1375592, _1375594, _1375596] : [32422 ^ _778495 : [(32425 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1375594, 32421 ^ [_1375588, _1375590, _1375592, _1375594, _1375596]), _1375596))], (32423 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1375588), 32421 ^ [_1375588, _1375590, _1375592, _1375594, _1375596]), _1375592)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1375588, tc_fun(_1375590, tc_HOL_Obool)), _1375592), _1375594), _1375596)))], (21210 ^ _778495) ^ [_1158441, _1158443] : [class_Groups_Oordered__ab__group__add__abs(_1158441), 21213 ^ _778495 : [(21220 ^ _778495) ^ [] : [-(_1158443 = c_Groups_Ozero__class_Ozero(_1158441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158441), c_Groups_Ozero__class_Ozero(_1158441)), hAPP(c_Groups_Oabs__class_Oabs(_1158441), _1158443))))], (21214 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158441), c_Groups_Ozero__class_Ozero(_1158441)), hAPP(c_Groups_Oabs__class_Oabs(_1158441), _1158443))), _1158443 = c_Groups_Ozero__class_Ozero(_1158441)]]], (42315 ^ _778495) ^ [_1621162, _1621164, _1621166, _1621168] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621162)), hAPP(hAPP(c_List_Olist__update(_1621162, _1621164), _1621166), _1621168)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621162)), _1621164))], (31526 ^ _778495) ^ [_1354398, _1354400, _1354402] : [class_Orderings_Olinorder(_1354398), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354398), _1354400)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354398), _1354402)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1354398, tc_HOL_Obool)), _1354400), _1354402) = c_Orderings_Obot__class_Obot(tc_fun(_1354398, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354398), c_Big__Operators_Olinorder__class_OMax(_1354398, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1354398, tc_HOL_Obool)), _1354400), _1354402))), c_Big__Operators_Olinorder__class_OMax(_1354398, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1354398, tc_HOL_Obool)), _1354400), _1354402))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354398), c_Big__Operators_Olinorder__class_OMax(_1354398, _1354400)), c_Big__Operators_Olinorder__class_OMax(_1354398, _1354402)))], (19138 ^ _778495) ^ [_1122525, _1122527, _1122529] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122525), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122527), _1122529)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122527), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122525), _1122529)))], (11532 ^ _778495) ^ [_978276, _978278, _978280, _978282] : [class_Groups_Oordered__ab__semigroup__add(_978276), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978276), _978278), _978280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978276), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978276), _978282), _978278)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978276), _978282), _978280))))], (10193 ^ _778495) ^ [_954250, _954252, _954254] : [class_Lattices_Olattice(_954250), hBOOL(hAPP(c_Finite__Set_Ofinite(_954250), _954252)), hBOOL(hAPP(hAPP(c_member(_954250), _954254), _954252)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954250), _954254), c_Big__Operators_Olattice__class_OInf__fin(_954250, _954252)) = c_Big__Operators_Olattice__class_OInf__fin(_954250, _954252))], (40989 ^ _778495) ^ [_1583265, _1583267, _1583269, _1583271] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583265, _1583265), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1583267), _1583269)), _1583271) = hAPP(hAPP(c_Relation_Orel__comp(_1583265, _1583265, _1583265), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583265, _1583265), tc_HOL_Obool), _1583267), _1583271)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583265, _1583265), tc_HOL_Obool), _1583269), _1583271)))], (9831 ^ _778495) ^ [_947222, _947224, _947226] : [class_Lattices_Olattice(_947222), hBOOL(hAPP(c_Finite__Set_Ofinite(_947222), _947224)), -(hBOOL(hAPP(hAPP(c_member(_947222), _947226), _947224))), -(_947224 = c_Orderings_Obot__class_Obot(tc_fun(_947222, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_947222, hAPP(hAPP(c_Set_Oinsert(_947222), _947226), _947224)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_947222), _947226), c_Big__Operators_Olattice__class_OSup__fin(_947222, _947224)))], (43393 ^ _778495) ^ [_1644704, _1644706, _1644708, _1644710, _1644712] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644704), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644706)), _1644708)))), -(hAPP(hAPP(c_List_Olist__update(_1644706, hAPP(hAPP(c_List_Oappend(_1644706), _1644708), _1644710)), _1644704), _1644712) = hAPP(hAPP(c_List_Oappend(_1644706), _1644708), hAPP(hAPP(c_List_Olist__update(_1644706, _1644710), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644704), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644706)), _1644708))), _1644712)))], (21126 ^ _778495) ^ [_1156982, _1156984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1156982), _1156984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1156982)), c_Int_OBit1(_1156984))))], (49330 ^ _778495) ^ [_1775867, _1775869] : [c_Relation_Osym(_1775867, _1775869), -(c_Relation_Osym(_1775867, c_Transitive__Closure_Ortrancl(_1775867, _1775869)))], (22092 ^ _778495) ^ [] : [-(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))], (15569 ^ _778495) ^ [_1055336, _1055338, _1055340, _1055342, _1055344, _1055346] : [class_Rings_Olinordered__semiring__1(_1055336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055336), _1055338), _1055340)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055336), _1055342), _1055340)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055336), c_Groups_Ozero__class_Ozero(_1055336)), _1055344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055336), c_Groups_Ozero__class_Ozero(_1055336)), _1055346)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055336), _1055344), _1055346) = c_Groups_Oone__class_Oone(_1055336), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055336), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055336), _1055344), _1055338)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055336), _1055346), _1055342))), _1055340)))], (26138 ^ _778495) ^ [_1245866, _1245868, _1245870] : [class_Rings_Olinordered__idom(_1245866), -(hAPP(c_Groups_Oabs__class_Oabs(_1245866), hAPP(hAPP(c_Power_Opower__class_Opower(_1245866), _1245868), _1245870)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1245866), hAPP(c_Groups_Oabs__class_Oabs(_1245866), _1245868)), _1245870))], (43778 ^ _778495) ^ [_1654143, _1654145, _1654147] : [hBOOL(hAPP(c_List_Odistinct(_1654143), hAPP(c_List_Orotate(_1654143, _1654145), _1654147))), -(hBOOL(hAPP(c_List_Odistinct(_1654143), _1654147)))], (49915 ^ _778495) ^ [_1787986, _1787988, _1787990] : [c_Fun_Obij__betw(_1787986, _1787988, _1787990, c_Orderings_Otop__class_Otop(tc_fun(_1787986, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787988, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1787988, _1787986, c_Orderings_Otop__class_Otop(tc_fun(_1787988, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1787986, _1787988, c_Orderings_Otop__class_Otop(tc_fun(_1787986, tc_HOL_Obool)), _1787990)) = _1787990)], (17756 ^ _778495) ^ [_1096911, _1096913, _1096915] : [class_Orderings_Olinorder(_1096911), 17759 ^ _778495 : [(17766 ^ _778495) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096911), _1096913), _1096915) = _1096913, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096911), _1096913), _1096915)))], (17760 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096911), _1096913), _1096915)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096911), _1096913), _1096915) = _1096913)]]], (1568 ^ _778495) ^ [_801123, _801125] : [-(class_Groups_Olinordered__ab__semigroup__add(_801123)), _801125 = _801123, class_Groups_Olinordered__ab__semigroup__add(_801125)], (30245 ^ _778495) ^ [_1329603] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1329603))))], (43935 ^ _778495) ^ [_1657339, _1657341, _1657343, _1657345, _1657347] : [c_Finite__Set_Ofun__left__comm__idem(_1657339, _1657341, _1657343), -(hAPP(hAPP(c_Finite__Set_Ofold(_1657339, _1657341, _1657343), _1657345), hAPP(c_List_Oset(_1657339), _1657347)) = hAPP(c_List_Ofoldl(_1657341, _1657339, hAPP(c_COMBC(_1657339, _1657341, _1657341), _1657343), _1657345), _1657347))], (39416 ^ _778495) ^ [_1545299, _1545301, _1545303, _1545305, _1545307, _1545309, _1545311] : [-(hAPP(c_Product__Type_Oapsnd(_1545299, _1545301, _1545303, _1545305), hAPP(c_Product__Type_Oapsnd(_1545307, _1545299, _1545303, _1545309), _1545311)) = hAPP(c_Product__Type_Oapsnd(_1545307, _1545301, _1545303, hAPP(c_Fun_Ocomp(_1545299, _1545301, _1545307, _1545305), _1545309)), _1545311))], (28105 ^ _778495) ^ [_1279809, _1279811, _1279813] : [28107 ^ _778495 : [(28110 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1279809, tc_HOL_Obool)), 28106 ^ [_1279809, _1279811, _1279813]), _1279813))], (28108 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1279809, tc_HOL_Obool)), 28106 ^ [_1279809, _1279811, _1279813]), _1279811)))]], -(_1279811 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1279809, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1279809, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1279809, tc_HOL_Obool), _1279811)), _1279813)))], (5552 ^ _778495) ^ [_863432, _863434] : [_863434 = _863432, -(c_COMBI(_863434) = c_COMBI(_863432))], (23144 ^ _778495) ^ [_1192714, _1192716, _1192718, _1192720] : [class_Divides_Osemiring__div(_1192714), -(c_Divides_Odiv__class_Omod(_1192714, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192714), c_Divides_Odiv__class_Omod(_1192714, _1192716, _1192718)), _1192720), _1192718) = c_Divides_Odiv__class_Omod(_1192714, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192714), _1192716), _1192720), _1192718))], (27109 ^ _778495) ^ [_1262651, _1262653, _1262655] : [class_Rings_Oring__1(_1262651), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1262653), _1262655)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1262651), hAPP(c_Int_Oring__1__class_Oof__int(_1262651), _1262653)), hAPP(c_Int_Oring__1__class_Oof__int(_1262651), _1262655)))], (1438 ^ _778495) ^ [_799498, _799500] : [-(class_Lattices_Osemilattice__inf(_799498)), _799500 = _799498, class_Lattices_Osemilattice__inf(_799500)], (43484 ^ _778495) ^ [_1647430, _1647432, _1647434, _1647436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647430), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647432)), _1647434))), -(hAPP(hAPP(c_List_Olist__update(_1647432, _1647434), _1647430), _1647436) = hAPP(hAPP(c_List_Oappend(_1647432), hAPP(hAPP(c_List_Otake(_1647432), _1647430), _1647434)), hAPP(hAPP(c_List_Olist_OCons(_1647432), _1647436), hAPP(hAPP(c_List_Odrop(_1647432), hAPP(c_Nat_OSuc, _1647430)), _1647434))))], (26862 ^ _778495) ^ [_1258718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1258718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1258718)))], (32980 ^ _778495) ^ [_1386829, _1386831, _1386833, _1386835] : [class_Orderings_Olinorder(_1386829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386829), _1386831), _1386833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386829), _1386833), _1386835)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386829, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1386829, _1386831, _1386833)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1386829, _1386833, _1386835)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1386829, _1386831, _1386835))], (51841 ^ _778495) ^ [_1825234, _1825236, _1825238] : [class_Divides_Osemiring__div(_1825234), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825234), _1825236), _1825238)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825234), _1825236), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825234), _1825238), _1825236)) = _1825238)], (44622 ^ _778495) ^ [_1672361, _1672363, _1672365, _1672367] : [class_Groups_Ocomm__monoid__add(_1672361), 44625 ^ _778495 : [(44632 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1672363), _1672365))), -(c_Nitpick_Osetsum_H(_1672363, _1672361, _1672367, _1672365) = c_Groups_Ozero__class_Ozero(_1672361))], (44626 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1672363), _1672365)), -(c_Nitpick_Osetsum_H(_1672363, _1672361, _1672367, _1672365) = hAPP(c_List_Omonoid__add__class_Olistsum(_1672361), hAPP(hAPP(c_List_Omap(_1672363, _1672361), _1672367), c_Hilbert__Choice_OEps(tc_List_Olist(_1672363), hAPP(hAPP(c_COMBS(tc_List_Olist(_1672363), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1672363)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1672363), tc_fun(_1672363, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1672363, tc_HOL_Obool), tc_fun(tc_fun(_1672363, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1672363)), c_fequal), c_List_Oset(_1672363))), _1672365))), c_List_Odistinct(_1672363))))))]]], (10619 ^ _778495) ^ [_961529, _961531] : [10620 ^ _778495 : [(10623 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961531), _961529))], (10621 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961529), _961531))]], _961529 = _961531], (45569 ^ _778495) ^ [_1692865, _1692867] : [c_List_Oconcat(_1692865, _1692867) = c_List_Olist_ONil(_1692865), 45572 ^ _778495 : [(45573 ^ _778495) ^ [_1692956] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692865)), _1692956), hAPP(c_List_Oset(tc_List_Olist(_1692865)), _1692867))), -(_1692956 = c_List_Olist_ONil(_1692865))]]], (15319 ^ _778495) ^ [_1050587, _1050589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1050587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050587), hAPP(c_Nat_OSuc, _1050589))), _1050587)))], (39754 ^ _778495) ^ [_1552892, _1552894, _1552896, _1552898, _1552900, _1552902] : [c_Finite__Set_Ofolding(_1552892, _1552894, _1552896, _1552898), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552892), _1552900)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552892), _1552902)), -(hAPP(c_Fun_Ocomp(_1552894, _1552894, _1552894, hAPP(_1552898, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1552892, tc_HOL_Obool)), _1552900), _1552902))), hAPP(_1552898, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1552892, tc_HOL_Obool)), _1552900), _1552902))) = hAPP(c_Fun_Ocomp(_1552894, _1552894, _1552894, hAPP(_1552898, _1552900)), hAPP(_1552898, _1552902)))], (40145 ^ _778495) ^ [_1562048, _1562050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1562048), _1562050)), -(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), _1562048), _1562050)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (982 ^ _778495) ^ [_793280, _793282, _793284, _793286] : [-(c_Wellfounded_Owf(_793284, _793280)), c_Wellfounded_Owf(_793286, _793282), _793286 = _793284, _793282 = _793280], (33537 ^ _778495) ^ [_1402033, _1402035, _1402037, _1402039, _1402041] : [-(_1402033 = c_Orderings_Obot__class_Obot(tc_fun(_1402035, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1402035, tc_fun(_1402037, tc_HOL_Obool)), _1402033), hAPP(hAPP(c_COMBB(tc_fun(_1402037, tc_HOL_Obool), tc_fun(_1402037, tc_HOL_Obool), _1402035), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402037, tc_HOL_Obool)), _1402039)), _1402041)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402037, tc_HOL_Obool)), _1402039), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402035, tc_fun(_1402037, tc_HOL_Obool)), _1402033), _1402041)))], (29326 ^ _778495) ^ [_1311733, _1311735] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1311733, _1311735), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1311733), _1311735)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1311733, _1311735)))))], (37684 ^ _778495) ^ [_1494573, _1494575, _1494577] : [-(hAPP(c_Product__Type_Omap__pair(_1494573, _1494573, _1494575, _1494575, c_COMBI(_1494573), c_COMBI(_1494575)), _1494577) = _1494577)], (19248 ^ _778495) ^ [_1124390, _1124392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124390), _1124392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124390), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124392), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (7390 ^ _778495) ^ [_901337, _901339, _901341] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_901337), _901339)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_901337), hAPP(hAPP(c_Set_Oinsert(_901337), _901341), _901339))))], (13444 ^ _778495) ^ [_1017267, _1017269, _1017271] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017267), _1017269) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017267), _1017271), -(_1017269 = _1017271), -(_1017267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47141 ^ _778495) ^ [_1726852, _1726854, _1726856, _1726858] : [47143 ^ _778495 : [(47146 ^ _778495) ^ [] : [hBOOL(hAPP(_1726854, hAPP(hAPP(c_List_Onth(_1726856), _1726858), 47142 ^ [_1726852, _1726854, _1726856, _1726858])))], (47144 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47142 ^ [_1726852, _1726854, _1726856, _1726858]), _1726852)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1726852), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726856)), _1726858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1726852), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726856)), c_List_OtakeWhile(_1726856, _1726854, _1726858)))))], (5098 ^ _778495) ^ [_856337, _856339, _856341, _856343] : [-(c_Transitive__Closure_Ortrancl(_856343, _856339) = c_Transitive__Closure_Ortrancl(_856341, _856337)), _856343 = _856341, _856339 = _856337], (41326 ^ _778495) ^ [_1592371, _1592373, _1592375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592371), c_Nitpick_Oplus__frac(_1592371, _1592373, c_Nitpick_Ouminus__frac(_1592371, _1592375)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1592371, _1592373, _1592375))], (35118 ^ _778495) ^ [_1434755] : [c_Nat__Transfer_Onat__set(_1434755), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1434755) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1434755)))], (38501 ^ _778495) ^ [_1521356, _1521358, _1521360, _1521362, _1521364, _1521366, _1521368, _1521370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521356, _1521358), tc_HOL_Obool)), _1521360), hAPP(hAPP(c_Product__Type_OSigma(_1521356, _1521358), _1521362), hAPP(c_COMBK(tc_fun(_1521358, tc_HOL_Obool), _1521356), _1521364)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521358, _1521366), tc_HOL_Obool)), _1521368), hAPP(hAPP(c_Product__Type_OSigma(_1521358, _1521366), _1521364), hAPP(c_COMBK(tc_fun(_1521366, tc_HOL_Obool), _1521358), _1521370)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521356, _1521366), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1521356, _1521358, _1521366), _1521360), _1521368)), hAPP(hAPP(c_Product__Type_OSigma(_1521356, _1521366), _1521362), hAPP(c_COMBK(tc_fun(_1521366, tc_HOL_Obool), _1521356), _1521370)))))], (6662 ^ _778495) ^ [_887403, _887405] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887403, tc_HOL_Obool)), _887405), c_Orderings_Obot__class_Obot(tc_fun(_887403, tc_HOL_Obool))) = _887405)], (25363 ^ _778495) ^ [_1231675, _1231677, _1231679, _1231681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1231675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1231677), _1231679)), -(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), _1231679), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1231681, _1231675))), _1231677)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1231679), _1231675))))], (47931 ^ _778495) ^ [_1744104, _1744106, _1744108] : [c_List_Olist__all(_1744104, _1744108, _1744106), 47934 ^ _778495 : [(47935 ^ _778495) ^ [_1744185] : [hBOOL(hAPP(hAPP(c_member(_1744104), _1744185), hAPP(c_List_Oset(_1744104), _1744106))), -(hBOOL(hAPP(_1744108, _1744185)))]]], (33862 ^ _778495) ^ [_1408855, _1408857, _1408859] : [class_Orderings_Oorder(_1408855), 33865 ^ _778495 : [(33872 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408855), _1408857), _1408859))), -(c_Orderings_Obot__class_Obot(tc_fun(_1408855, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408855, _1408857), _1408859))], (33866 ^ _778495) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1408855, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408855, _1408857), _1408859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408855), _1408857), _1408859))]]], (22548 ^ _778495) ^ [_1181593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1181593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1181593))))], (47861 ^ _778495) ^ [_1742791, _1742793, _1742795] : [c_List_Olist__all(_1742791, _1742793, _1742795), 47864 ^ _778495 : [(47865 ^ _778495) ^ [_1742872] : [hBOOL(hAPP(hAPP(c_member(_1742791), _1742872), hAPP(c_List_Oset(_1742791), _1742795))), -(hBOOL(hAPP(_1742793, _1742872)))]]], (20286 ^ _778495) ^ [_1142927, _1142929, _1142931, _1142933, _1142935] : [class_Groups_Oordered__ab__semigroup__add(_1142927), class_Rings_Osemiring__1(_1142927), 20296 ^ _778495 : [(20299 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142927), hAPP(_1142933, 20295 ^ [_1142927, _1142929, _1142931, _1142933, _1142935])), _1142935))], (20297 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1142929), 20295 ^ [_1142927, _1142929, _1142931, _1142933, _1142935]), _1142931)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142927), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1142929, _1142927), _1142933), _1142931)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142927), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1142927), hAPP(c_Finite__Set_Ocard(_1142929), _1142931))), _1142935))))], (44381 ^ _778495) ^ [_1666533, _1666535, _1666537, _1666539] : [_1666539 = c_List_Olist_ONil(_1666533), -(hAPP(hAPP(c_List_Omap(_1666533, _1666535), _1666537), _1666539) = c_List_Olist_ONil(_1666535))], (14059 ^ _778495) ^ [_1028152, _1028154, _1028156] : [class_Groups_Oordered__comm__monoid__add(_1028152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028152), _1028154), c_Groups_Ozero__class_Ozero(_1028152))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028152), _1028156), c_Groups_Ozero__class_Ozero(_1028152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028152), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028152), _1028154), _1028156)), c_Groups_Ozero__class_Ozero(_1028152))))], (10747 ^ _778495) ^ [_963654, _963656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963654), hAPP(c_Nat_OSuc, _963656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963654), _963656))), -(_963654 = _963656)], (10609 ^ _778495) ^ [_961480, _961482] : [-(_961480 = _961482), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961480), _961482))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961482), _961480)))], (50573 ^ _778495) ^ [_1803050, _1803052, _1803054, _1803056, _1803058] : [-(c_Lazy__Sequence_Omap(_1803050, _1803052, _1803054, c_Lazy__Sequence_Olazy__sequence_OInsert(_1803050, _1803056, _1803058)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1803052, hAPP(_1803054, _1803056), c_Lazy__Sequence_Omap(_1803050, _1803052, _1803054, _1803058)))], (38371 ^ _778495) ^ [_1517660, _1517662] : [-(c_Product__Type_Omap__pair(_1517660, _1517660, _1517662, _1517662, c_COMBI(_1517660), c_COMBI(_1517662)) = c_Fun_Oid(tc_prod(_1517660, _1517662)))], (48036 ^ _778495) ^ [_1746287, _1746289, _1746291, _1746293, _1746295] : [_1746287 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1746289, _1746291, _1746293, _1746295), _1746287) = c_Lazy__Sequence_Ohit__bound(_1746291))], (13755 ^ _778495) ^ [_1022576, _1022578, _1022580, _1022582, _1022584] : [class_Rings_Oordered__semiring(_1022576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022576), _1022578), _1022580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022576), _1022582), _1022584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022576), c_Groups_Ozero__class_Ozero(_1022576)), _1022580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022576), c_Groups_Ozero__class_Ozero(_1022576)), _1022582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022576), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022576), _1022578), _1022582)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022576), _1022580), _1022584))))], (52399 ^ _778495) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (34855 ^ _778495) ^ [_1430500, _1430502, _1430504, _1430506, _1430508, _1430510] : [hBOOL(hAPP(hAPP(c_member(_1430500), _1430502), _1430504)), -(hAPP(c_Set_Oimage(_1430500, _1430506, c_Fun_Ofun__upd(_1430500, _1430506, _1430508, _1430502, _1430510)), _1430504) = hAPP(hAPP(c_Set_Oinsert(_1430506), _1430510), hAPP(c_Set_Oimage(_1430500, _1430506, _1430508), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430500, tc_HOL_Obool)), _1430504), hAPP(hAPP(c_Set_Oinsert(_1430500), _1430502), c_Orderings_Obot__class_Obot(tc_fun(_1430500, tc_HOL_Obool)))))))], (34432 ^ _778495) ^ [_1421611, _1421613, _1421615, _1421617] : [_1421617 = c_Orderings_Obot__class_Obot(tc_fun(_1421611, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1421611, _1421613, _1421615), _1421617) = c_Orderings_Obot__class_Obot(tc_fun(_1421613, tc_HOL_Obool)))], (5837 ^ _778495) ^ [_871339, _871341, _871343, _871345] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_871339, tc_HOL_Obool)), _871341), hAPP(hAPP(c_Set_Oinsert(_871339), _871343), _871345)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_871339, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_871339, tc_HOL_Obool)), _871341), _871345)), hAPP(hAPP(c_Set_Oinsert(_871339), _871343), c_Orderings_Obot__class_Obot(tc_fun(_871339, tc_HOL_Obool)))))], (6988 ^ _778495) ^ [_893244, _893246, _893248] : [class_Lattices_Osemilattice__sup(_893244), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893244), _893246), _893248) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893244), _893248), _893246))], (40952 ^ _778495) ^ [_1582392, _1582394, _1582396, _1582398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582392, _1582394), tc_HOL_Obool)), _1582396), _1582398)), c_Relation_Osingle__valued(_1582392, _1582394, _1582398), -(c_Relation_Osingle__valued(_1582392, _1582394, _1582396))], (36346 ^ _778495) ^ [_1462451, _1462453, _1462455, _1462457] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1462451), hAPP(c_Set_Oimage(_1462453, _1462451, _1462455), _1462457))), c_Fun_Oinj__on(_1462453, _1462451, _1462455, _1462457), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1462453), _1462457)))], (8614 ^ _778495) ^ [_922355, _922357, _922359] : [class_Lattices_Oab__semigroup__idem__mult(_922355), -(_922357 = c_Orderings_Obot__class_Obot(tc_fun(_922355, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_922355), _922357)), -(hAPP(c_Finite__Set_Ofold1(_922355, c_Groups_Otimes__class_Otimes(_922355)), hAPP(hAPP(c_Set_Oinsert(_922355), _922359), _922357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922355), _922359), hAPP(c_Finite__Set_Ofold1(_922355, c_Groups_Otimes__class_Otimes(_922355)), _922357)))], (41784 ^ _778495) ^ [_1606622, _1606624, _1606626, _1606628] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606622), tc_List_Olist(_1606622))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606622), tc_List_Olist(_1606622)), _1606624), _1606626)), c_List_Olistrel(_1606622, _1606628))), 41787 ^ _778495 : [(41790 ^ _778495) ^ [_1606851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1606851), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606622)), _1606624))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606622, _1606622)), hAPP(hAPP(c_Product__Type_OPair(_1606622, _1606622), hAPP(hAPP(c_List_Onth(_1606622), _1606624), _1606851)), hAPP(hAPP(c_List_Onth(_1606622), _1606626), _1606851))), _1606628)))], (41788 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606622)), _1606624) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606622)), _1606626))]]], (16510 ^ _778495) ^ [_1073534, _1073536, _1073538, _1073540] : [class_Fields_Olinordered__field(_1073534), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073534), _1073536), c_Groups_Ozero__class_Ozero(_1073534))), 16517 ^ _778495 : [(16524 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073534), _1073540), _1073536)), _1073538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073534), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1073534), _1073538), _1073536)), _1073540)))], (16518 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073534), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1073534), _1073538), _1073536)), _1073540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073534), _1073540), _1073536)), _1073538)))]]], (33846 ^ _778495) ^ [_1408630, _1408632, _1408634] : [class_Orderings_Oorder(_1408630), 33849 ^ _778495 : [(33856 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408630), _1408632), _1408634))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408630, _1408632), _1408634) = c_Orderings_Obot__class_Obot(tc_fun(_1408630, tc_HOL_Obool)))], (33850 ^ _778495) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408630, _1408632), _1408634) = c_Orderings_Obot__class_Obot(tc_fun(_1408630, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408630), _1408632), _1408634))]]], (27777 ^ _778495) ^ [_1274182, _1274184] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1274182), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1274182, tc_HOL_Obool), _1274184)))), 27778 ^ _778495 : [(27779 ^ _778495) ^ [_1274246] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1274182, tc_HOL_Obool)), _1274246), _1274184)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274182), _1274246))]]], (44482 ^ _778495) ^ [_1669176, _1669178, _1669180, _1669182, _1669184] : [-(hAPP(hAPP(c_List_Omap(_1669176, _1669178), _1669180), hAPP(hAPP(c_List_Oappend(_1669176), _1669182), _1669184)) = hAPP(hAPP(c_List_Oappend(_1669178), hAPP(hAPP(c_List_Omap(_1669176, _1669178), _1669180), _1669182)), hAPP(hAPP(c_List_Omap(_1669176, _1669178), _1669180), _1669184)))], (43820 ^ _778495) ^ [_1654933, _1654935, _1654937] : [-(hAPP(c_List_Orotate1(_1654933), hAPP(c_List_Orotate(_1654933, _1654935), _1654937)) = hAPP(c_List_Orotate(_1654933, _1654935), hAPP(c_List_Orotate1(_1654933), _1654937)))], (21490 ^ _778495) ^ [_1163549] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1163549))) = 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)))), _1163549))], (47892 ^ _778495) ^ [_1743415, _1743417, _1743419] : [c_List_Olist__all(_1743415, _1743417, hAPP(c_List_Orev(_1743415), _1743419)), -(c_List_Olist__all(_1743415, _1743417, _1743419))], (7692 ^ _778495) ^ [_905740, _905742, _905744] : [class_Orderings_Olinorder(_905740), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905740), _905742), _905744))), -(_905742 = _905744), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905740), _905744), _905742)))], (37174 ^ _778495) ^ [_1480406, _1480408, _1480410, _1480412] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480406, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1480408, _1480406, _1480410), hAPP(c_Set_Ovimage(_1480408, _1480406, _1480410), _1480412))), _1480412)))], (42736 ^ _778495) ^ [_1630184, _1630186] : [hAPP(c_List_Oset(_1630184), _1630186) = c_Orderings_Obot__class_Obot(tc_fun(_1630184, tc_HOL_Obool)), -(_1630186 = c_List_Olist_ONil(_1630184))], (34452 ^ _778495) ^ [_1422053, _1422055, _1422057, _1422059, _1422061] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1422053), _1422055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1422057, tc_HOL_Obool)), _1422059), hAPP(c_Set_Oimage(_1422053, _1422057, _1422061), _1422055))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1422057), _1422059)))], (11021 ^ _778495) ^ [_968120, _968122, _968124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968120), _968122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968120), _968124)), 11028 ^ _778495 : [(11035 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968122), _968124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968122), _968120)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968124), _968120))))], (11029 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968122), _968120)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968124), _968120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968122), _968124)))]]], (43205 ^ _778495) ^ [_1640595, _1640597, _1640599] : [hAPP(hAPP(c_List_Oappend(_1640595), _1640597), _1640599) = _1640597, -(_1640599 = c_List_Olist_ONil(_1640595))], (6816 ^ _778495) ^ [_890289, _890291, _890293, _890295] : [c_Hoare__Mirabelle_Ohoare__derivs(_890289, _890291, _890293), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_890289), tc_HOL_Obool)), _890295), _890293)), -(c_Hoare__Mirabelle_Ohoare__derivs(_890289, _890291, _890295))], (37567 ^ _778495) ^ [_1491345, _1491347, _1491349, _1491351, _1491353, _1491355] : [class_Groups_Ocomm__monoid__mult(_1491345), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491347), _1491349)), 37577 ^ _778495 : [(37580 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491351), hAPP(_1491353, 37576 ^ [_1491345, _1491347, _1491349, _1491351, _1491353, _1491355])))], (37578 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491347), 37576 ^ [_1491345, _1491347, _1491349, _1491351, _1491353, _1491355]), _1491349)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1491345, _1491347, c_Groups_Otimes__class_Otimes(_1491345)), hAPP(hAPP(c_COMBS(_1491347, tc_fun(_1491351, tc_HOL_Obool), _1491345), hAPP(hAPP(c_COMBC(_1491347, _1491345, tc_fun(tc_fun(_1491351, tc_HOL_Obool), _1491345)), hAPP(hAPP(c_COMBB(tc_fun(_1491351, _1491345), tc_fun(_1491345, tc_fun(tc_fun(_1491351, tc_HOL_Obool), _1491345)), _1491347), c_Finite__Set_Ofold__image(_1491345, _1491351, c_Groups_Otimes__class_Otimes(_1491345))), _1491355)), c_Groups_Oone__class_Oone(_1491345))), _1491353)), c_Groups_Oone__class_Oone(_1491345)), _1491349) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1491345, tc_prod(_1491347, _1491351), c_Groups_Otimes__class_Otimes(_1491345)), hAPP(c_Product__Type_Oprod_Oprod__case(_1491347, _1491351, _1491345), _1491355)), c_Groups_Oone__class_Oone(_1491345)), hAPP(hAPP(c_Product__Type_OSigma(_1491347, _1491351), _1491349), _1491353)))], (44833 ^ _778495) ^ [_1676734, _1676736] : [_1676734 = _1676736, -(hAPP(c_Code__Numeral_Onat__of, _1676734) = hAPP(c_Code__Numeral_Onat__of, _1676736))], (45546 ^ _778495) ^ [_1692355] : [-(c_List_Oconcat(_1692355, c_List_Olist_ONil(tc_List_Olist(_1692355))) = c_List_Olist_ONil(_1692355))], (34098 ^ _778495) ^ [] : [-(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))))], (52651 ^ _778495) ^ [_1835512, _1835514, _1835516, _1835518, _1835520, _1835522] : [-(hAPP(hAPP(hAPP(c_COMBB(_1835512, _1835514, _1835516), _1835518), _1835520), _1835522) = hAPP(_1835518, hAPP(_1835520, _1835522)))], (45999 ^ _778495) ^ [_1703848, _1703850, _1703852, _1703854] : [-(c_List_Oupt(_1703848, _1703850) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703852), _1703854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703848), _1703850)), _1703848 = _1703852, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703848), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703850) = _1703854], (24681 ^ _778495) ^ [_1220405, _1220407] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1220405, _1220407)) = _1220407), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1220405), _1220407) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1220405, _1220407)))], (32610 ^ _778495) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (48513 ^ _778495) ^ [_1756866, _1756868] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756866), c_List_Olist_ONil(_1756866)), _1756868))], (21340 ^ _778495) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (11091 ^ _778495) ^ [_969390, _969392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969390)), _969392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969390), _969392)))], (3370 ^ _778495) ^ [_828837, _828839, _828841, _828843, _828845, _828847] : [-(c_Enum_On__lists(_828847, _828843, _828839) = c_Enum_On__lists(_828845, _828841, _828837)), _828847 = _828845, _828843 = _828841, _828839 = _828837], (51573 ^ _778495) ^ [_1820244, _1820246, _1820248, _1820250] : [class_Divides_Osemiring__div(_1820244), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820244), _1820246), _1820248)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1820244), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820244), _1820248), _1820246)), _1820250) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820244), hAPP(hAPP(c_Power_Opower__class_Opower(_1820244), _1820248), _1820250)), hAPP(hAPP(c_Power_Opower__class_Opower(_1820244), _1820246), _1820250)))], (6954 ^ _778495) ^ [_892687, _892689, _892691] : [class_Lattices_Osemilattice__sup(_892687), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892687), _892689), _892691)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892687), _892691), _892689) = _892691)], (14669 ^ _778495) ^ [_1038780, _1038782] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038780), _1038782))), -(hAPP(c_Finite__Set_Ocard(_1038780), _1038782) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41638 ^ _778495) ^ [_1602382, _1602384, _1602386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602382, _1602382), tc_HOL_Obool)), _1602384), _1602386)), c_Relation_Orefl__on(_1602382, c_Orderings_Otop__class_Otop(tc_fun(_1602382, tc_HOL_Obool)), _1602386), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1602382), tc_List_Olist(_1602382)), tc_HOL_Obool)), c_List_Olistrel1(_1602382, _1602384)), c_List_Olistrel(_1602382, _1602386))))], (7408 ^ _778495) ^ [_901648, _901650] : [class_Orderings_Opreorder(_901648), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901648), _901650), _901650))], (39630 ^ _778495) ^ [_1550045, _1550047, _1550049, _1550051, _1550053, _1550055, _1550057, _1550059] : [c_Finite__Set_Ofolding(_1550045, _1550047, _1550049, _1550051), -(hAPP(c_Fun_Ocomp(_1550047, _1550047, _1550053, hAPP(_1550049, _1550055)), hAPP(c_Fun_Ocomp(_1550047, _1550047, _1550053, hAPP(_1550049, _1550057)), _1550059)) = hAPP(c_Fun_Ocomp(_1550047, _1550047, _1550053, hAPP(_1550049, _1550057)), hAPP(c_Fun_Ocomp(_1550047, _1550047, _1550053, hAPP(_1550049, _1550055)), _1550059)))], (23919 ^ _778495) ^ [_1206610, _1206612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206610), _1206612)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206610, _1206612) = _1206610)], (27581 ^ _778495) ^ [] : [-(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))], (42319 ^ _778495) ^ [_1621306, _1621308, _1621310, _1621312, _1621314, _1621316] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1621306, _1621308), hAPP(hAPP(c_List_Ozip(_1621306, _1621308), _1621310), _1621312)), _1621314), _1621316) = hAPP(hAPP(c_List_Ozip(_1621306, _1621308), hAPP(hAPP(c_List_Olist__update(_1621306, _1621310), _1621314), hAPP(c_Product__Type_Ofst(_1621306, _1621308), _1621316))), hAPP(hAPP(c_List_Olist__update(_1621308, _1621312), _1621314), hAPP(c_Product__Type_Osnd(_1621306, _1621308), _1621316))))], (9604 ^ _778495) ^ [_942876, _942878, _942880, _942882] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942876, tc_HOL_Obool)), _942878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942876, tc_HOL_Obool)), _942880), _942882)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942876, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942876, tc_HOL_Obool)), _942878), _942880)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942876, tc_HOL_Obool)), _942878), _942882)))], (4024 ^ _778495) ^ [_839444, _839446] : [_839446 = _839444, -(c_New__Random__Sequence_Oneg__single(_839446) = c_New__Random__Sequence_Oneg__single(_839444))], (41011 ^ _778495) ^ [_1583899, _1583901, _1583903, _1583905, _1583907, _1583909] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583899, _1583899)), hAPP(hAPP(c_Product__Type_OPair(_1583899, _1583899), _1583901), _1583903)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583899, _1583899), tc_HOL_Obool), _1583905), _1583907))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583899, _1583899)), hAPP(hAPP(c_Product__Type_OPair(_1583899, _1583899), _1583903), _1583909)), _1583907)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583899, _1583899)), hAPP(hAPP(c_Product__Type_OPair(_1583899, _1583899), _1583901), _1583909)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583899, _1583899), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1583905)), _1583907))))], (24565 ^ _778495) ^ [_1218395, _1218397] : [class_Rings_Ocomm__semiring__1(_1218395), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1218395), _1218397), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1218397)], (5470 ^ _778495) ^ [_862241, _862243] : [_862243 = _862241, -(c_member(_862243) = c_member(_862241))], (32429 ^ _778495) ^ [_1375841, _1375843, _1375845, _1375847, _1375849, _1375851, _1375853] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1375841, tc_fun(_1375843, tc_fun(_1375845, tc_HOL_Obool))), _1375847), _1375849), _1375851), _1375853)), 32432 ^ _778495 : [(32433 ^ _778495) ^ [_1375969] : [hBOOL(hAPP(hAPP(c_member(_1375841), _1375969), _1375847)), -(hBOOL(hAPP(hAPP(hAPP(_1375849, _1375969), _1375851), _1375853)))]]], (24553 ^ _778495) ^ [_1218123, _1218125, _1218127] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1218123, _1218125)), _1218127) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218123), _1218127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218125), _1218127)))], (38826 ^ _778495) ^ [_1530196, _1530198, _1530200] : [_1530200 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530196, _1530198), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1530196, _1530198), _1530200) = c_Orderings_Obot__class_Obot(tc_fun(_1530196, tc_HOL_Obool)))], (25906 ^ _778495) ^ [_1241531, _1241533, _1241535] : [class_Rings_Ocomm__semiring__1(_1241531), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1241531), _1241533), 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)))), _1241535))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241531), _1241533), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241531), hAPP(hAPP(c_Power_Opower__class_Opower(_1241531), _1241533), _1241535)), hAPP(hAPP(c_Power_Opower__class_Opower(_1241531), _1241533), _1241535))))], (19130 ^ _778495) ^ [_1122365, _1122367, _1122369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122365), _1122367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122365), _1122369)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122367), _1122369))))], (49654 ^ _778495) ^ [_1781857, _1781859, _1781861, _1781863, _1781865, _1781867] : [hAPP(c_Set_Oimage(_1781857, _1781859, _1781861), _1781863) = _1781865, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1781859, tc_HOL_Obool)), _1781867), _1781865)), -(hAPP(c_Set_Oimage(_1781857, _1781859, _1781861), hAPP(c_Set_Oimage(_1781859, _1781857, c_Hilbert__Choice_Oinv__into(_1781857, _1781859, _1781863, _1781861)), _1781867)) = _1781867)], (36188 ^ _778495) ^ [_1459490, _1459492] : [class_Groups_Oordered__ab__group__add(_1459490), -(c_Fun_Oinj__on(_1459490, _1459490, c_Groups_Ouminus__class_Ouminus(_1459490), _1459492))], (19698 ^ _778495) ^ [_1132327, _1132329, _1132331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132327)), _1132327 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1132329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132327), _1132331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132331), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (30227 ^ _778495) ^ [_1329118, _1329120, _1329122] : [-(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), _1329118)), 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))), _1329120))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1329122))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329122)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1329118), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1329118), 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), _1329122), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1329120)))))], (35623 ^ _778495) ^ [_1445456] : [-(_1445456 = 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), 35620 ^ [_1445456]), 35621 ^ [_1445456])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (10903 ^ _778495) ^ [_966231, _966233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966231), _966233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966231)), hAPP(c_Nat_OSuc, _966233))))], (5214 ^ _778495) ^ [_858131, _858133, _858135, _858137, _858139, _858141, _858143, _858145, _858147, _858149] : [-(c_New__DSequence_Opos__map(_858149, _858145, _858141, _858137, _858133) = c_New__DSequence_Opos__map(_858147, _858143, _858139, _858135, _858131)), _858149 = _858147, _858145 = _858143, _858141 = _858139, _858137 = _858135, _858133 = _858131], (52253 ^ _778495) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (38888 ^ _778495) ^ [_1531519, _1531521, _1531523, _1531525] : [hBOOL(hAPP(hAPP(c_member(_1531519), _1531521), hAPP(c_Relation_ODomain(_1531519, _1531523), _1531525))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531519, _1531523)), hAPP(hAPP(c_Product__Type_OPair(_1531519, _1531523), _1531521), 38891 ^ [_1531519, _1531521, _1531523, _1531525])), _1531525)))], (27163 ^ _778495) ^ [_1263684] : [class_Int_Onumber__ring(_1263684), -(hAPP(c_Int_Oring__1__class_Oof__int(_1263684), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1263684), c_Int_OMin))], (48997 ^ _778495) ^ [_1769577, _1769579, _1769581] : [c_Relation_Otrans(_1769577, _1769579), c_Relation_Otrans(_1769577, _1769581), -(c_Relation_Otrans(_1769577, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1769577, _1769577), tc_HOL_Obool)), _1769579), _1769581)))], (5781 ^ _778495) ^ [_870152, _870154, _870156, _870158] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_870152, _870154, _870156), _870158)), _870156 = c_Orderings_Obot__class_Obot(tc_fun(_870152, tc_HOL_Obool))], (35510 ^ _778495) ^ [_1442172, _1442174, _1442176, _1442178, _1442180] : [-(hAPP(c_Relation_OImage(_1442172, _1442174, _1442176), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442172, tc_HOL_Obool)), _1442178), _1442180)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442174, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442172, _1442174, _1442176), _1442178)), hAPP(c_Relation_OImage(_1442172, _1442174, _1442176), _1442180)))], (36600 ^ _778495) ^ [_1467587, _1467589, _1467591, _1467593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1467587), hAPP(c_Set_Oimage(_1467589, _1467587, _1467591), _1467593))), hAPP(c_Finite__Set_Ocard(_1467589), _1467593))), c_Fun_Oinj__on(_1467589, _1467587, _1467591, _1467593)], (36616 ^ _778495) ^ [_1467865, _1467867, _1467869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1467865, _1467865), tc_HOL_Obool)), _1467867), _1467869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467865, tc_HOL_Obool)), c_Wellfounded_Oacc(_1467865, _1467869)), c_Wellfounded_Oacc(_1467865, _1467867))))], (39235 ^ _778495) ^ [_1541055, _1541057] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1541055, _1541055)), _1541057)), 39238 ^ _778495 : [(39245 ^ _778495) ^ [] : [c_Wellfounded_Oacyclic(_1541055, _1541057), -(c_Wellfounded_Owf(_1541055, _1541057))], (39239 ^ _778495) ^ [] : [c_Wellfounded_Owf(_1541055, _1541057), -(c_Wellfounded_Oacyclic(_1541055, _1541057))]]], (27323 ^ _778495) ^ [_1266265] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1266265)], (7030 ^ _778495) ^ [_894089, _894091, _894093, _894095] : [class_Lattices_Olattice(_894089), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894089), _894091), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894089), _894093), _894095)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894089), _894093), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894089), _894091), _894095)))], (43910 ^ _778495) ^ [_1656902, _1656904] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656902), _1656904) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43913 ^ _778495 : [(43916 ^ _778495) ^ [_1657016] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1657016), hAPP(c_List_Oset(tc_Nat_Onat), _1656904))), -(_1657016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43914 ^ _778495) ^ [] : [-(_1656902 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11566 ^ _778495) ^ [_978937, _978939, _978941, _978943] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_978937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978937), _978939), _978941)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978937), _978939), _978943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978937), _978941), _978943)))], (10875 ^ _778495) ^ [_965781, _965783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965781)), _965783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965781), _965783)))], (27525 ^ _778495) ^ [_1269713] : [c_Orderings_Otop__class_Otop(tc_fun(_1269713, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1269713, tc_HOL_Obool))], (15386 ^ _778495) ^ [_1051788, _1051790, _1051792] : [hBOOL(hAPP(_1051788, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051790), _1051792))), 15389 ^ _778495 : [(15396 ^ _778495) ^ [_1051973] : [_1051790 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051792), _1051973), -(hBOOL(hAPP(_1051788, _1051973)))], (15390 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051790), _1051792)), -(hBOOL(hAPP(_1051788, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (5648 ^ _778495) ^ [_867625, _867627] : [hAPP(_867625, 5649 ^ [_867625, _867627]) = hAPP(_867627, 5649 ^ [_867625, _867627]), -(_867625 = _867627)], (4220 ^ _778495) ^ [_842448, _842450, _842452, _842454] : [-(c_List_Oconcat(_842454, _842450) = c_List_Oconcat(_842452, _842448)), _842454 = _842452, _842450 = _842448], (31059 ^ _778495) ^ [_1345963, _1345965, _1345967] : [class_Orderings_Olinorder(_1345963), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345963), _1345965)), hBOOL(hAPP(hAPP(c_member(_1345963), _1345967), _1345965)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345963), _1345967), c_Big__Operators_Olattice_OInf__fin(_1345963, c_Orderings_Oord__class_Omin(_1345963), _1345965)) = _1345967)], (24767 ^ _778495) ^ [_1221822, _1221824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221824)), 24774 ^ _778495 : [(24781 ^ _778495) ^ [] : [_1221822 = _1221824, -(hAPP(c_Int_Onat, _1221822) = hAPP(c_Int_Onat, _1221824))], (24775 ^ _778495) ^ [] : [hAPP(c_Int_Onat, _1221822) = hAPP(c_Int_Onat, _1221824), -(_1221822 = _1221824)]]], (36943 ^ _778495) ^ [_1474985, _1474987, _1474989, _1474991, _1474993, _1474995] : [c_Typedef_Otype__definition(_1474985, _1474987, _1474989, _1474991, _1474993), hBOOL(hAPP(hAPP(c_member(_1474987), _1474995), _1474993)), -(hAPP(_1474989, hAPP(_1474991, _1474995)) = _1474995)], (21488 ^ _778495) ^ [] : [-(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))))))], (41862 ^ _778495) ^ [_1608855, _1608857, _1608859, _1608861] : [_1608855 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1608857), hAPP(hAPP(c_List_Olist_OCons(_1608857), _1608859), _1608861)), _1608855) = _1608859)], (7300 ^ _778495) ^ [_899384, _899386, _899388, _899390, _899392, _899394, _899396] : [hBOOL(hAPP(hAPP(c_member(_899384), _899386), _899388)), c_Nitpick_Ofold__graph_H(_899384, _899390, _899392, _899394, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899384, tc_HOL_Obool)), _899388), hAPP(hAPP(c_Set_Oinsert(_899384), _899386), c_Orderings_Obot__class_Obot(tc_fun(_899384, tc_HOL_Obool)))), _899396), -(c_Nitpick_Ofold__graph_H(_899384, _899390, _899392, _899394, _899388, hAPP(hAPP(_899392, _899386), _899396)))], (20766 ^ _778495) ^ [_1150706, _1150708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1150706), _1150708)), -(c_Nat__Transfer_Otsub(_1150708, _1150706) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1150708), _1150706))], (11234 ^ _778495) ^ [_972201, _972203, _972205] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_972201), _972203)), -(hAPP(c_Finite__Set_Ocard(_972201), hAPP(hAPP(c_Set_Oinsert(_972201), _972205), _972203)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_972201), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972201, tc_HOL_Obool)), _972203), hAPP(hAPP(c_Set_Oinsert(_972201), _972205), c_Orderings_Obot__class_Obot(tc_fun(_972201, tc_HOL_Obool)))))))], (42499 ^ _778495) ^ [_1625421, _1625423, _1625425, _1625427] : [hBOOL(hAPP(c_List_Odistinct(_1625421), _1625423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625425), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625421)), _1625423))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625427), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625421)), _1625423))), 42510 ^ _778495 : [(42517 ^ _778495) ^ [] : [_1625425 = _1625427, -(hAPP(hAPP(c_List_Onth(_1625421), _1625423), _1625425) = hAPP(hAPP(c_List_Onth(_1625421), _1625423), _1625427))], (42511 ^ _778495) ^ [] : [hAPP(hAPP(c_List_Onth(_1625421), _1625423), _1625425) = hAPP(hAPP(c_List_Onth(_1625421), _1625423), _1625427), -(_1625425 = _1625427)]]], (29543 ^ _778495) ^ [_1316149, _1316151, _1316153, _1316155, _1316157, _1316159, _1316161, _1316163] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1316149, _1316151, _1316153), _1316155), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1316157, _1316159, tc_prod(_1316149, _1316151)), _1316161), _1316163)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1316157, _1316159, _1316153), hAPP(hAPP(c_COMBB(tc_fun(_1316159, tc_prod(_1316149, _1316151)), tc_fun(_1316159, _1316153), _1316157), hAPP(c_COMBB(tc_prod(_1316149, _1316151), _1316153, _1316159), hAPP(c_Product__Type_Oprod_Oprod__case(_1316149, _1316151, _1316153), _1316155))), _1316161)), _1316163))], (50459 ^ _778495) ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799907, _1799909), tc_prod(_1799907, _1799909))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799907, _1799909), tc_prod(_1799907, _1799909)), hAPP(hAPP(c_Product__Type_OPair(_1799907, _1799909), _1799911), _1799913)), hAPP(hAPP(c_Product__Type_OPair(_1799907, _1799909), _1799915), _1799917))), c_Transitive__Closure_Ortrancl(tc_prod(_1799907, _1799909), _1799919))), hBOOL(hAPP(hAPP(_1799921, _1799915), _1799917)), 50472 ^ _778495 : [(50475 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799907, _1799909), tc_prod(_1799907, _1799909))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799907, _1799909), tc_prod(_1799907, _1799909)), hAPP(hAPP(c_Product__Type_OPair(_1799907, _1799909), 50470 ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921]), 50471 ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921])), hAPP(hAPP(c_Product__Type_OPair(_1799907, _1799909), _1799915), _1799917))), c_Transitive__Closure_Ortrancl(tc_prod(_1799907, _1799909), _1799919))))], (50477 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1799921, 50470 ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921]), 50471 ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921])))], (50479 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1799921, 50468 ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921]), 50469 ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921]))], (50473 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799907, _1799909), tc_prod(_1799907, _1799909))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799907, _1799909), tc_prod(_1799907, _1799909)), hAPP(hAPP(c_Product__Type_OPair(_1799907, _1799909), 50468 ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921]), 50469 ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921])), hAPP(hAPP(c_Product__Type_OPair(_1799907, _1799909), 50470 ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921]), 50471 ^ [_1799907, _1799909, _1799911, _1799913, _1799915, _1799917, _1799919, _1799921]))), _1799919)))]], -(hBOOL(hAPP(hAPP(_1799921, _1799911), _1799913)))], (40762 ^ _778495) ^ [_1577427, _1577429, _1577431, _1577433, _1577435] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577427, _1577429)), hAPP(hAPP(c_Product__Type_OPair(_1577427, _1577429), _1577431), _1577433)), _1577435)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577429, _1577427)), hAPP(hAPP(c_Product__Type_OPair(_1577429, _1577427), _1577433), _1577431)), hAPP(c_Relation_Oconverse(_1577427, _1577429), _1577435))))], (16096 ^ _778495) ^ [_1066185, _1066187, _1066189, _1066191] : [class_Rings_Odivision__ring(_1066185), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066185), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066185), _1066187), _1066189)), _1066191) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066185), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066185), _1066187), _1066191)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066185), _1066189), _1066191)))], (2942 ^ _778495) ^ [_822159, _822161, _822163, _822165, _822167, _822169] : [-(c_Product__Type_Ointernal__split(_822169, _822165, _822161) = c_Product__Type_Ointernal__split(_822167, _822163, _822159)), _822169 = _822167, _822165 = _822163, _822161 = _822159], (12614 ^ _778495) ^ [_1001525, _1001527, _1001529, _1001531, _1001533, _1001535, _1001537] : [c_Finite__Set_Ofun__left__comm(_1001525, _1001527, _1001529), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1001525, _1001527, _1001529, _1001531, hAPP(hAPP(c_Set_Oinsert(_1001525), _1001533), _1001535)), _1001537)), -(hBOOL(hAPP(hAPP(c_member(_1001525), _1001533), _1001535))), 12626 ^ _778495 : [(12629 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1001525, _1001527, _1001529, _1001531, _1001535), 12625 ^ [_1001525, _1001527, _1001529, _1001531, _1001533, _1001535, _1001537])))], (12627 ^ _778495) ^ [] : [-(_1001537 = hAPP(hAPP(_1001529, _1001533), 12625 ^ [_1001525, _1001527, _1001529, _1001531, _1001533, _1001535, _1001537]))]]], (49676 ^ _778495) ^ [_1782402, _1782404, _1782406] : [hAPP(c_Set_Oimage(_1782402, _1782404, _1782406), c_Orderings_Otop__class_Otop(tc_fun(_1782402, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782404, tc_HOL_Obool)), 49679 ^ _778495 : [(49680 ^ _778495) ^ [_1782513] : [-(hAPP(_1782406, hAPP(c_Hilbert__Choice_Oinv__into(_1782402, _1782404, c_Orderings_Otop__class_Otop(tc_fun(_1782402, tc_HOL_Obool)), _1782406), _1782513)) = _1782513)]]], (16872 ^ _778495) ^ [_1079860, _1079862, _1079864, _1079866, _1079868] : [class_Fields_Ofield(_1079860), -(_1079862 = c_Groups_Ozero__class_Ozero(_1079860)), -(_1079864 = c_Groups_Ozero__class_Ozero(_1079860)), 16883 ^ _778495 : [(16890 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079860), _1079866), _1079864) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079860), _1079868), _1079862), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1079860), _1079866), _1079862) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1079860), _1079868), _1079864))], (16884 ^ _778495) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1079860), _1079866), _1079862) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1079860), _1079868), _1079864), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079860), _1079866), _1079864) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079860), _1079868), _1079862))]]], (47685 ^ _778495) ^ [_1739242, _1739244, _1739246] : [hBOOL(hAPP(hAPP(c_member(_1739242), _1739244), hAPP(c_List_Oset(_1739242), _1739246))), 47690 ^ _778495 : [(47693 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1739242), _1739244), hAPP(c_List_Oset(_1739242), 47688 ^ [_1739242, _1739244, _1739246])))], (47691 ^ _778495) ^ [] : [-(_1739246 = hAPP(hAPP(c_List_Oappend(_1739242), 47688 ^ [_1739242, _1739244, _1739246]), hAPP(hAPP(c_List_Olist_OCons(_1739242), _1739244), 47689 ^ [_1739242, _1739244, _1739246])))]]], (32054 ^ _778495) ^ [_1367939, _1367941, _1367943] : [class_Orderings_Oorder(_1367939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367939), _1367941), _1367943)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1367939, _1367943, _1367941) = c_Orderings_Obot__class_Obot(tc_fun(_1367939, tc_HOL_Obool)))], (19112 ^ _778495) ^ [_1122098, _1122100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122100), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122098), _1122100))), -(_1122098 = _1122100)], (39061 ^ _778495) ^ [_1536058, _1536060] : [c_Wellfounded_OwfP(_1536058, _1536060), 39064 ^ _778495 : [(39065 ^ _778495) ^ [_1536122] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1536058, _1536060), _1536122)))]]], (37688 ^ _778495) ^ [_1494674, _1494676, _1494678, _1494680, _1494682, _1494684, _1494686, _1494688] : [-(hAPP(c_Product__Type_Omap__pair(_1494674, _1494676, _1494678, _1494680, _1494682, _1494684), hAPP(hAPP(c_Product__Type_OPair(_1494674, _1494678), _1494686), _1494688)) = hAPP(hAPP(c_Product__Type_OPair(_1494676, _1494680), hAPP(_1494682, _1494686)), hAPP(_1494684, _1494688)))], (24597 ^ _778495) ^ [_1218911, _1218913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218913)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1218911)), hAPP(c_Int_Onat, _1218913)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1218911), _1218913)))], (50523 ^ _778495) ^ [_1802076, _1802078, _1802080] : [c_List_Oall__interval__nat(_1802076, _1802078, _1802080), 50526 ^ _778495 : [(50527 ^ _778495) ^ [_1802156] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1802156), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1802078), _1802080))), -(hBOOL(hAPP(_1802076, _1802156)))]]], (5526 ^ _778495) ^ [_863049, _863051, _863053, _863055] : [-(tc_Nitpick_Opair__box(_863055, _863051) = tc_Nitpick_Opair__box(_863053, _863049)), _863055 = _863053, _863051 = _863049], (996 ^ _778495) ^ [_793473, _793475, _793477, _793479, _793481, _793483, _793485, _793487] : [-(c_Equiv__Relations_Ocongruent(_793485, _793481, _793477, _793473)), c_Equiv__Relations_Ocongruent(_793487, _793483, _793479, _793475), _793487 = _793485, _793483 = _793481, _793479 = _793477, _793475 = _793473], (1948 ^ _778495) ^ [_805873, _805875] : [-(class_Nat_Osize(_805873)), _805875 = _805873, class_Nat_Osize(_805875)], (29059 ^ _778495) ^ [_1306071, _1306073] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1306071), hAPP(c_Nat_OSuc, _1306073)) = 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), _1306071), _1306073)))], (40463 ^ _778495) ^ [_1570520, _1570522, _1570524] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570520, _1570520)), hAPP(hAPP(c_Product__Type_OPair(_1570520, _1570520), _1570522), _1570524)), c_Relation_OId(_1570520))), -(_1570522 = _1570524)], (47750 ^ _778495) ^ [_1740571, _1740573, _1740575] : [c_List_Olist__ex(_1740571, _1740573, _1740575), -(c_List_Olist__ex(_1740571, _1740573, hAPP(c_List_Orev(_1740571), _1740575)))], (7092 ^ _778495) ^ [_895356, _895358, _895360] : [class_Lattices_Olattice(_895356), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895356), _895358), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895356), _895358), _895360))))], (16148 ^ _778495) ^ [_1067201, _1067203, _1067205, _1067207] : [class_Rings_Odivision__ring(_1067201), -(_1067203 = c_Groups_Ozero__class_Ozero(_1067201)), 16155 ^ _778495 : [(16162 ^ _778495) ^ [] : [_1067205 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067201), _1067207), _1067203), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1067201), _1067205), _1067203) = _1067207)], (16156 ^ _778495) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1067201), _1067205), _1067203) = _1067207, -(_1067205 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067201), _1067207), _1067203))]]], (6112 ^ _778495) ^ [_876702, _876704, _876706, _876708] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876702, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876702, tc_HOL_Obool)), _876704), _876706)), _876708) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876702, tc_HOL_Obool)), _876704), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876702, tc_HOL_Obool)), _876706), _876708)))], (48340 ^ _778495) ^ [_1753063, _1753065] : [-(c_List_Oreplicate(_1753063, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1753065) = c_List_Olist_ONil(_1753063))], (12352 ^ _778495) ^ [_995695, _995697, _995699, _995701, _995703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995695), _995697)), 12355 ^ _778495 : [(12362 ^ _778495) ^ [] : [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), _995697), _995695)), _995699)), _995701) = _995703, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995697), _995699)), _995701) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995695), _995699)), _995703))], (12356 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995697), _995699)), _995701) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995695), _995699)), _995703), -(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), _995697), _995695)), _995699)), _995701) = _995703)]]], (44590 ^ _778495) ^ [_1671621, _1671623, _1671625] : [c_Fun_Oinj__on(_1671621, _1671623, _1671625, c_Orderings_Otop__class_Otop(tc_fun(_1671621, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1671621), tc_List_Olist(_1671623), hAPP(c_List_Omap(_1671621, _1671623), _1671625), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671621), tc_HOL_Obool))))], (32558 ^ _778495) ^ [] : [-(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)))))], (40585 ^ _778495) ^ [_1573284, _1573286, _1573288, _1573290] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573284, _1573284)), hAPP(hAPP(c_Product__Type_OPair(_1573284, _1573284), _1573286), _1573288)), c_Transitive__Closure_Ortrancl(_1573284, _1573290))), hBOOL(hAPP(hAPP(c_member(_1573284), _1573288), c_Wellfounded_Oacc(_1573284, _1573290))), -(hBOOL(hAPP(hAPP(c_member(_1573284), _1573286), c_Wellfounded_Oacc(_1573284, _1573290))))], (32182 ^ _778495) ^ [_1370608, _1370610, _1370612, _1370614, _1370616] : [-(_1370608 = c_Orderings_Obot__class_Obot(tc_fun(_1370610, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370612, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370610, tc_fun(_1370612, tc_HOL_Obool)), _1370608), _1370614)), _1370616) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370610, tc_fun(_1370612, tc_HOL_Obool)), _1370608), hAPP(hAPP(c_COMBC(_1370610, tc_fun(_1370612, tc_HOL_Obool), tc_fun(_1370612, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370612, tc_HOL_Obool), tc_fun(tc_fun(_1370612, tc_HOL_Obool), tc_fun(_1370612, tc_HOL_Obool)), _1370610), c_Groups_Ominus__class_Ominus(tc_fun(_1370612, tc_HOL_Obool))), _1370614)), _1370616)))], (46656 ^ _778495) ^ [_1716571, _1716573] : [-(hAPP(c_List_Oset(_1716571), hAPP(c_List_Orev(_1716571), _1716573)) = hAPP(c_List_Oset(_1716571), _1716573))], (15451 ^ _778495) ^ [_1052951, _1052953, _1052955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052951), _1052953)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052955), _1052953))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1052953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052951), _1052955)))], (37176 ^ _778495) ^ [_1480459, _1480461, _1480463, _1480465] : [hAPP(c_Set_Oimage(_1480459, _1480461, _1480463), c_Orderings_Otop__class_Otop(tc_fun(_1480459, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1480461, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1480459, _1480461, _1480463), hAPP(c_Set_Ovimage(_1480459, _1480461, _1480463), _1480465)) = _1480465)], (18938 ^ _778495) ^ [_1118939, _1118941, _1118943] : [class_Orderings_Olinorder(_1118939), hBOOL(hAPP(c_Finite__Set_Ofinite(_1118939), _1118941)), hBOOL(hAPP(hAPP(c_member(_1118939), _1118943), _1118941)), 18949 ^ _778495 : [(18956 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1118939, tc_HOL_Obool)), _1118941), hAPP(hAPP(c_Set_Oinsert(_1118939), _1118943), c_Orderings_Obot__class_Obot(tc_fun(_1118939, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1118939, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1118939, _1118941) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1118939), _1118943), c_Big__Operators_Olinorder__class_OMin(_1118939, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1118939, tc_HOL_Obool)), _1118941), hAPP(hAPP(c_Set_Oinsert(_1118939), _1118943), c_Orderings_Obot__class_Obot(tc_fun(_1118939, tc_HOL_Obool)))))))], (18950 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1118939, tc_HOL_Obool)), _1118941), hAPP(hAPP(c_Set_Oinsert(_1118939), _1118943), c_Orderings_Obot__class_Obot(tc_fun(_1118939, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1118939, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1118939, _1118941) = _1118943)]]], (43139 ^ _778495) ^ [_1639124, _1639126, _1639128, _1639130] : [_1639128 = _1639130, -(hAPP(hAPP(c_List_Oappend(_1639124), _1639126), _1639128) = hAPP(hAPP(c_List_Oappend(_1639124), _1639126), _1639130))], (9292 ^ _778495) ^ [_935865, _935867, _935869, _935871] : [hBOOL(hAPP(hAPP(c_member(_935865), _935867), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_935865, tc_HOL_Obool)), _935869), _935871))), -(hBOOL(hAPP(hAPP(c_member(_935865), _935867), _935871)))], (36652 ^ _778495) ^ [_1468586, _1468588, _1468590, _1468592] : [c_Fun_Oinj__on(_1468586, _1468588, _1468590, c_Orderings_Otop__class_Otop(tc_fun(_1468586, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468588, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468586, _1468588, _1468590), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468586, tc_HOL_Obool)), _1468592))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468588, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468586, _1468588, _1468590), _1468592)))))], (22652 ^ _778495) ^ [_1183398, _1183400] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1183398)), c_Int_OBit0(_1183400)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1183398), _1183400)))], (8352 ^ _778495) ^ [_916845, _916847, _916849, _916851] : [c_Finite__Set_Ofolding__one(_916845, _916847, _916849), hBOOL(hAPP(c_Finite__Set_Ofinite(_916845), _916851)), -(_916851 = c_Orderings_Obot__class_Obot(tc_fun(_916845, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_916845), hAPP(hAPP(_916847, 8365 ^ [_916845, _916847, _916849, _916851]), 8366 ^ [_916845, _916847, _916849, _916851])), hAPP(hAPP(c_Set_Oinsert(_916845), 8365 ^ [_916845, _916847, _916849, _916851]), hAPP(hAPP(c_Set_Oinsert(_916845), 8366 ^ [_916845, _916847, _916849, _916851]), c_Orderings_Obot__class_Obot(tc_fun(_916845, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_916845), hAPP(_916849, _916851)), _916851)))], (22468 ^ _778495) ^ [_1180217, _1180219, _1180221] : [class_Groups_Oordered__ab__group__add__abs(_1180217), 22471 ^ _778495 : [(22480 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180217), hAPP(c_Groups_Oabs__class_Oabs(_1180217), _1180219)), _1180221))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180217), _1180219), _1180221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180217), hAPP(c_Groups_Ouminus__class_Ouminus(_1180217), _1180219)), _1180221))], (22472 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180217), hAPP(c_Groups_Oabs__class_Oabs(_1180217), _1180219)), _1180221)), 22475 ^ _778495 : [(22478 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180217), hAPP(c_Groups_Ouminus__class_Ouminus(_1180217), _1180219)), _1180221)))], (22476 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180217), _1180219), _1180221)))]]]]], (51417 ^ _778495) ^ [_1817475, _1817477, _1817479, _1817481] : [class_Divides_Osemiring__div(_1817475), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817475), _1817477), _1817479)), -(c_Divides_Odiv__class_Omod(_1817475, c_Divides_Odiv__class_Omod(_1817475, _1817481, _1817479), _1817477) = c_Divides_Odiv__class_Omod(_1817475, _1817481, _1817477))], (46057 ^ _778495) ^ [_1705053, _1705055, _1705057] : [46058 ^ _778495 : [(46061 ^ _778495) ^ [] : [_1705057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46059 ^ _778495) ^ [] : [-(_1705053 = c_List_Olist_ONil(tc_List_Olist(_1705055)))]], 46065 ^ _778495 : [(46068 ^ _778495) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705055)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1705055)), _1705053), 46064 ^ [_1705053, _1705055, _1705057])) = _1705057], (46066 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46064 ^ [_1705053, _1705055, _1705057]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705055))), _1705053))))]], -(c_List_Otranspose(_1705055, _1705053) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1705055)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1705055)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1705055), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1705055)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1705055)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1705055), hAPP(hAPP(c_COMBB(tc_List_Olist(_1705055), tc_fun(tc_Nat_Onat, _1705055), tc_Nat_Onat), c_List_Onth(_1705055)), hAPP(c_List_Onth(tc_List_Olist(_1705055)), _1705053))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705055))), _1705053)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1705057)))], (27967 ^ _778495) ^ [_1277368, _1277370, _1277372] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1277368, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1277368, tc_HOL_Obool), tc_HOL_Obool)), _1277370), _1277372)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1277368, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1277368, tc_HOL_Obool), _1277370)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1277368, tc_HOL_Obool), _1277372)))], (46891 ^ _778495) ^ [_1721536, _1721538, _1721540, _1721542] : [hBOOL(hAPP(_1721536, _1721538)), -(c_List_OtakeWhile(_1721540, _1721536, hAPP(hAPP(c_List_Olist_OCons(_1721540), _1721538), _1721542)) = hAPP(hAPP(c_List_Olist_OCons(_1721540), _1721538), c_List_OtakeWhile(_1721540, _1721536, _1721542)))], (24818 ^ _778495) ^ [_1222585, _1222587] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1222585), _1222587))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1222585, _1222587) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1222585), _1222587), _1222587))], (10227 ^ _778495) ^ [_954825, _954827, _954829] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_954825), _954827)), -(hBOOL(hAPP(hAPP(c_member(_954825), _954829), _954827))), -(hAPP(c_Finite__Set_Ocard(_954825), hAPP(hAPP(c_Set_Oinsert(_954825), _954829), _954827)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_954825), _954827)))], (52313 ^ _778495) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (27055 ^ _778495) ^ [_1261784, _1261786] : [class_Int_Oring__char__0(_1261784), 27058 ^ _778495 : [(27065 ^ _778495) ^ [] : [_1261786 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1261784) = hAPP(c_Int_Oring__1__class_Oof__int(_1261784), _1261786))], (27059 ^ _778495) ^ [] : [c_Groups_Ozero__class_Ozero(_1261784) = hAPP(c_Int_Oring__1__class_Oof__int(_1261784), _1261786), -(_1261786 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (6912 ^ _778495) ^ [_891918, _891920, _891922, _891924, _891926] : [class_Lattices_Osemilattice__sup(_891918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891918), _891920), _891922)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891918), _891924), _891926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891918), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891918), _891920), _891924)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891918), _891922), _891926))))], (8476 ^ _778495) ^ [_919432, _919434, _919436, _919438, _919440] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_919432, _919434, hAPP(hAPP(c_Set_Oinsert(_919432), _919436), _919438)), _919440)), 8481 ^ _778495 : [(8486 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_919432), 8479 ^ [_919432, _919434, _919436, _919438, _919440]), 8480 ^ [_919432, _919434, _919436, _919438, _919440]))], (8484 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_919432, _919432, _919434, 8479 ^ [_919432, _919434, _919436, _919438, _919440], 8480 ^ [_919432, _919434, _919436, _919438, _919440]), _919440)))], (8482 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_919432), _919436), _919438) = hAPP(hAPP(c_Set_Oinsert(_919432), 8479 ^ [_919432, _919434, _919436, _919438, _919440]), 8480 ^ [_919432, _919434, _919436, _919438, _919440]))]]], (28143 ^ _778495) ^ [_1280577] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1280577)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1280577)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50597 ^ _778495) ^ [_1803485] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1803485)))], (1628 ^ _778495) ^ [_801873, _801875] : [-(class_Rings_Oordered__comm__semiring(_801873)), _801875 = _801873, class_Rings_Oordered__comm__semiring(_801875)], (46594 ^ _778495) ^ [_1715229, _1715231] : [c_List_Olist_ONil(_1715229) = hAPP(c_List_Orev(_1715229), _1715231), -(_1715231 = c_List_Olist_ONil(_1715229))], (36564 ^ _778495) ^ [_1466785, _1466787, _1466789, _1466791] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466785), _1466787)), 36567 ^ _778495 : [(36574 ^ _778495) ^ [] : [hAPP(c_Finite__Set_Ocard(_1466789), hAPP(c_Set_Oimage(_1466785, _1466789, _1466791), _1466787)) = hAPP(c_Finite__Set_Ocard(_1466785), _1466787), -(c_Fun_Oinj__on(_1466785, _1466789, _1466791, _1466787))], (36568 ^ _778495) ^ [] : [c_Fun_Oinj__on(_1466785, _1466789, _1466791, _1466787), -(hAPP(c_Finite__Set_Ocard(_1466789), hAPP(c_Set_Oimage(_1466785, _1466789, _1466791), _1466787)) = hAPP(c_Finite__Set_Ocard(_1466785), _1466787))]]], (51731 ^ _778495) ^ [_1822955, _1822957] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822955, _1822957), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822955), _1822957)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822957), _1822955)))], (49210 ^ _778495) ^ [_1773808, _1773810] : [c_Equiv__Relations_Oequivp(_1773808, _1773810), 49213 ^ _778495 : [(49218 ^ _778495) ^ [] : [-(c_Predicate_Otransp(_1773808, _1773810))], (49216 ^ _778495) ^ [] : [-(c_Predicate_Osymp(_1773808, _1773810))], (49214 ^ _778495) ^ [] : [-(c_Predicate_Oreflp(_1773808, _1773810))]]], (3862 ^ _778495) ^ [_836663, _836665, _836667, _836669, _836671, _836673, _836675, _836677] : [-(c_New__DSequence_Oneg__decr__bind(_836677, _836673, _836669, _836665) = c_New__DSequence_Oneg__decr__bind(_836675, _836671, _836667, _836663)), _836677 = _836675, _836673 = _836671, _836669 = _836667, _836665 = _836663], (49007 ^ _778495) ^ [_1769738, _1769740] : [c_Relation_Otrans(_1769738, _1769740), -(c_Relation_Otrans(tc_List_Olist(_1769738), c_List_Olistrel(_1769738, _1769740)))], (40060 ^ _778495) ^ [_1559982, _1559984, _1559986] : [c_Wellfounded_Owf(_1559982, _1559984), hBOOL(hAPP(hAPP(c_member(tc_prod(_1559982, _1559982)), hAPP(hAPP(c_Product__Type_OPair(_1559982, _1559982), hAPP(_1559986, hAPP(c_Nat_OSuc, 40063 ^ [_1559982, _1559984, _1559986]))), hAPP(_1559986, 40063 ^ [_1559982, _1559984, _1559986]))), _1559984))], (38707 ^ _778495) ^ [_1527795] : [-(c_Wellfounded_Owf(tc_fun(_1527795, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1527795)))], (37847 ^ _778495) ^ [_1498650, _1498652, _1498654] : [hBOOL(hAPP(hAPP(c_member(_1498650), _1498652), hAPP(c_Set_OCollect(_1498650), _1498654))), -(hBOOL(hAPP(_1498654, _1498652)))], (7838 ^ _778495) ^ [_907927, _907929, _907931] : [class_Orderings_Oorder(_907927), 7841 ^ _778495 : [(7842 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907927), _907929), _907931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907927), _907929), _907931))), -(_907929 = _907931)], (7852 ^ _778495) ^ [] : [7853 ^ _778495 : [(7856 ^ _778495) ^ [] : [_907929 = _907931], (7854 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907927), _907929), _907931))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907927), _907929), _907931)))]]], (11813 ^ _778495) ^ [_983750, _983752, _983754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983750), _983752)), _983754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983750), _983754)))], (22444 ^ _778495) ^ [_1179791, _1179793, _1179795] : [class_Groups_Oordered__ab__group__add__abs(_1179791), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179791), hAPP(c_Groups_Oabs__class_Oabs(_1179791), _1179793)), _1179795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179791), hAPP(c_Groups_Ouminus__class_Ouminus(_1179791), _1179793)), _1179795)))], (43235 ^ _778495) ^ [_1641119, _1641121, _1641123] : [_1641119 = hAPP(hAPP(c_List_Oappend(_1641121), _1641123), _1641119), -(_1641123 = c_List_Olist_ONil(_1641121))], (664 ^ _778495) ^ [_788577, _788579, _788581, _788583] : [-(c_List_Olinorder__class_Osorted(_788581, _788577)), c_List_Olinorder__class_Osorted(_788583, _788579), _788583 = _788581, _788579 = _788577], (25778 ^ _778495) ^ [_1239045, _1239047] : [class_Rings_Oring__1__no__zero__divisors(_1239045), 25781 ^ _778495 : [(25782 ^ _778495) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1239045), _1239047), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1239045), -(_1239047 = c_Groups_Oone__class_Oone(_1239045)), -(_1239047 = hAPP(c_Groups_Ouminus__class_Ouminus(_1239045), c_Groups_Oone__class_Oone(_1239045)))], (25792 ^ _778495) ^ [] : [25793 ^ _778495 : [(25796 ^ _778495) ^ [] : [_1239047 = hAPP(c_Groups_Ouminus__class_Ouminus(_1239045), c_Groups_Oone__class_Oone(_1239045))], (25794 ^ _778495) ^ [] : [_1239047 = c_Groups_Oone__class_Oone(_1239045)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1239045), _1239047), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1239045))]]], (46462 ^ _778495) ^ [_1712305, _1712307, _1712309] : [class_Orderings_Olinorder(_1712305), hBOOL(hAPP(hAPP(c_member(_1712305), _1712307), hAPP(c_List_Oset(_1712305), _1712309))), c_List_Olinorder__class_Osorted(_1712305, _1712309), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712305, _1712305, c_COMBI(_1712305)), _1712307), c_List_Oremove1(_1712305, _1712307, _1712309)) = _1712309)], (26228 ^ _778495) ^ [_1247396, _1247398] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1247396), c_Groups_Ozero__class_Ozero(_1247396)), hAPP(c_Nat_OSuc, _1247398)) = c_Groups_Ozero__class_Ozero(_1247396)), class_Power_Opower(_1247396), class_Rings_Osemiring__0(_1247396)], (20842 ^ _778495) ^ [_1151770, _1151772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1151770)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1151772)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151770)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1151772), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1151770))))], (27371 ^ _778495) ^ [_1267071, _1267073] : [class_Rings_Olinordered__idom(_1267071), 27374 ^ _778495 : [(27381 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267071), c_Groups_Ozero__class_Ozero(_1267071)), _1267073)), -(c_Groups_Osgn__class_Osgn(_1267071, _1267073) = c_Groups_Oone__class_Oone(_1267071))], (27375 ^ _778495) ^ [] : [c_Groups_Osgn__class_Osgn(_1267071, _1267073) = c_Groups_Oone__class_Oone(_1267071), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267071), c_Groups_Ozero__class_Ozero(_1267071)), _1267073)))]]], (2392 ^ _778495) ^ [_813654, _813656] : [_813656 = _813654, -(c_Int_OBit0(_813656) = c_Int_OBit0(_813654))], (41267 ^ _778495) ^ [_1590874, _1590876, _1590878, _1590880, _1590882, _1590884] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590874, _1590876)), _1590878), hAPP(hAPP(c_Relation_Orel__comp(_1590874, _1590880, _1590876), _1590882), _1590884))), 41273 ^ _778495 : [(41278 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590880, _1590876)), hAPP(hAPP(c_Product__Type_OPair(_1590880, _1590876), 41271 ^ [_1590874, _1590876, _1590878, _1590880, _1590882, _1590884]), 41272 ^ [_1590874, _1590876, _1590878, _1590880, _1590882, _1590884])), _1590884)))], (41276 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590874, _1590880)), hAPP(hAPP(c_Product__Type_OPair(_1590874, _1590880), 41270 ^ [_1590874, _1590876, _1590878, _1590880, _1590882, _1590884]), 41271 ^ [_1590874, _1590876, _1590878, _1590880, _1590882, _1590884])), _1590882)))], (41274 ^ _778495) ^ [] : [-(_1590878 = hAPP(hAPP(c_Product__Type_OPair(_1590874, _1590876), 41270 ^ [_1590874, _1590876, _1590878, _1590880, _1590882, _1590884]), 41272 ^ [_1590874, _1590876, _1590878, _1590880, _1590882, _1590884]))]]], (46322 ^ _778495) ^ [_1709618, _1709620, _1709622, _1709624, _1709626] : [class_Orderings_Olinorder(_1709618), -(c_List_Olinorder__class_Osorted(_1709618, hAPP(hAPP(c_List_Omap(_1709620, _1709618), _1709622), hAPP(c_List_Ofilter(_1709620, hAPP(hAPP(c_COMBC(_1709620, _1709618, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1709618, tc_fun(_1709618, tc_HOL_Obool), _1709620), c_fequal), _1709622)), hAPP(_1709624, _1709626))), _1709626))))], (33227 ^ _778495) ^ [_1392315, _1392317, _1392319, _1392321, _1392323] : [hBOOL(hAPP(hAPP(c_member(_1392315), _1392317), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392319, tc_fun(_1392315, tc_HOL_Obool)), _1392321), _1392323))), 33231 ^ _778495 : [(33234 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1392315), _1392317), hAPP(_1392323, 33230 ^ [_1392315, _1392317, _1392319, _1392321, _1392323]))))], (33232 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1392319), 33230 ^ [_1392315, _1392317, _1392319, _1392321, _1392323]), _1392321)))]]], (8280 ^ _778495) ^ [_915300, _915302, _915304, _915306, _915308] : [class_Groups_Oab__group__add(_915300), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_915300), _915302), _915304) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_915300), _915306), _915308), 8287 ^ _778495 : [(8294 ^ _778495) ^ [] : [_915306 = _915308, -(_915302 = _915304)], (8288 ^ _778495) ^ [] : [_915302 = _915304, -(_915306 = _915308)]]], (6590 ^ _778495) ^ [_885773, _885775, _885777, _885779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885773, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_885773), _885775), _885777)), _885779)), 6593 ^ _778495 : [(6596 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885773, tc_HOL_Obool)), _885777), _885779)))], (6594 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885773), _885775), _885779)))]]], (21494 ^ _778495) ^ [_1163602, _1163604] : [class_Int_Onumber__ring(_1163602), class_Rings_Olinordered__idom(_1163602), 21501 ^ _778495 : [(21508 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1163604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163602), c_Groups_Oone__class_Oone(_1163602)), hAPP(c_Int_Onumber__class_Onumber__of(_1163602), _1163604))))], (21502 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163602), c_Groups_Oone__class_Oone(_1163602)), hAPP(c_Int_Onumber__class_Onumber__of(_1163602), _1163604))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1163604)))]]], (33495 ^ _778495) ^ [_1400656, _1400658] : [-(c_FunDef_Orp__inv__image(_1400656, _1400658) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool), tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool), tc_fun(tc_fun(_1400658, _1400656), tc_prod(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool), tc_fun(tc_fun(_1400658, _1400656), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool), tc_fun(tc_fun(_1400658, _1400656), tc_prod(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1400658, _1400656), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)), tc_fun(tc_fun(_1400658, _1400656), tc_prod(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool), tc_fun(tc_fun(_1400658, _1400656), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool), tc_fun(tc_fun(_1400658, _1400656), tc_prod(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool))))), tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1400658, _1400656), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)), tc_fun(tc_fun(_1400658, _1400656), tc_prod(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool))), tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1400658, _1400656), tc_fun(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1400658, _1400656), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)), tc_fun(tc_fun(_1400658, _1400656), tc_prod(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)))), tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool)), c_COMBS(tc_fun(_1400658, _1400656), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1400658, _1400656), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)), tc_fun(tc_fun(_1400658, _1400656), tc_fun(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)))), tc_fun(tc_prod(_1400656, _1400656), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool))), tc_fun(_1400658, _1400656)), c_Product__Type_OPair(tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool), tc_fun(tc_prod(_1400658, _1400658), tc_HOL_Obool)))), c_Relation_Oinv__image(_1400656, _1400658))))), c_Relation_Oinv__image(_1400656, _1400658))))], (28571 ^ _778495) ^ [_1295619, _1295621, _1295623, _1295625] : [class_Rings_Osemiring__1(_1295619), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1295621, _1295619), hAPP(c_COMBK(_1295619, _1295621), _1295623)), _1295625) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295619), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295619), hAPP(c_Finite__Set_Ocard(_1295621), _1295625))), _1295623))], (43538 ^ _778495) ^ [_1648733, _1648735] : [-(hAPP(c_List_Oset(_1648733), hAPP(c_List_Orotate1(_1648733), _1648735)) = hAPP(c_List_Oset(_1648733), _1648735))], (9384 ^ _778495) ^ [_937939, _937941, _937943, _937945] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937939, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937939, tc_HOL_Obool)), _937941), _937943)), _937945) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937939, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937939, tc_HOL_Obool)), _937941), _937945)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937939, tc_HOL_Obool)), _937943), _937945)))], (33463 ^ _778495) ^ [_1399699, _1399701, _1399703, _1399705, _1399707] : [-(_1399699 = c_Orderings_Obot__class_Obot(tc_fun(_1399701, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399703, tc_HOL_Obool)), _1399705), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399701, tc_fun(_1399703, tc_HOL_Obool)), _1399699), _1399707)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399701, tc_fun(_1399703, tc_HOL_Obool)), _1399699), hAPP(hAPP(c_COMBB(tc_fun(_1399703, tc_HOL_Obool), tc_fun(_1399703, tc_HOL_Obool), _1399701), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399703, tc_HOL_Obool)), _1399705)), _1399707)))], (43532 ^ _778495) ^ [_1648558, _1648560, _1648562, _1648564, _1648566] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1648558, _1648560)), _1648562), hAPP(hAPP(c_List_Ozip(_1648558, _1648560), _1648564), _1648566)) = hAPP(hAPP(c_List_Ozip(_1648558, _1648560), hAPP(hAPP(c_List_Odrop(_1648558), _1648562), _1648564)), hAPP(hAPP(c_List_Odrop(_1648560), _1648562), _1648566)))], (52371 ^ _778495) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (22926 ^ _778495) ^ [_1188305, _1188307] : [class_Int_Onumber__ring(_1188305), 22929 ^ _778495 : [(22936 ^ _778495) ^ [] : [c_Int_Oiszero(_1188305, hAPP(c_Int_Onumber__class_Onumber__of(_1188305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1188307), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1188305), _1188307) = c_Groups_Oone__class_Oone(_1188305))], (22930 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1188305), _1188307) = c_Groups_Oone__class_Oone(_1188305), -(c_Int_Oiszero(_1188305, hAPP(c_Int_Onumber__class_Onumber__of(_1188305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1188307), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (3718 ^ _778495) ^ [_834299, _834301, _834303, _834305, _834307, _834309, _834311, _834313] : [-(c_List_Ofoldl(_834313, _834309, _834305, _834301) = c_List_Ofoldl(_834311, _834307, _834303, _834299)), _834313 = _834311, _834309 = _834307, _834305 = _834303, _834301 = _834299], (42646 ^ _778495) ^ [_1628695, _1628697, _1628699] : [_1628695 = c_List_Olist_ONil(_1628697), -(c_List_Obutlast(_1628697, hAPP(hAPP(c_List_Olist_OCons(_1628697), _1628699), _1628695)) = c_List_Olist_ONil(_1628697))], (38463 ^ _778495) ^ [_1520419, _1520421] : [-(hAPP(c_Relation_ORange(_1520419, _1520419), c_Relation_OId__on(_1520419, _1520421)) = _1520421)], (3436 ^ _778495) ^ [_829878, _829880, _829882, _829884] : [-(c_Random_Opick(_829884, _829880) = c_Random_Opick(_829882, _829878)), _829884 = _829882, _829880 = _829878], (32224 ^ _778495) ^ [_1371575, _1371577, _1371579, _1371581, _1371583] : [class_Orderings_Olinorder(_1371575), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371575, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1371575, _1371577, _1371579)), c_SetInterval_Oord__class_OatLeastAtMost(_1371575, _1371581, _1371583)) = c_SetInterval_Oord__class_OatLeastAtMost(_1371575, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371575), _1371577), _1371581), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1371575), _1371579), _1371583)))], (45867 ^ _778495) ^ [_1701249, _1701251, _1701253] : [class_Groups_Omonoid__add(_1701249), -(hAPP(c_List_Ofoldl(_1701249, _1701249, c_Groups_Oplus__class_Oplus(_1701249), _1701251), _1701253) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1701249), _1701251), c_List_Ofoldr(_1701249, _1701249, c_Groups_Oplus__class_Oplus(_1701249), _1701253, c_Groups_Ozero__class_Ozero(_1701249))))], (37140 ^ _778495) ^ [_1479514, _1479516] : [-(hAPP(c_Set_Ovimage(_1479514, _1479514, c_COMBI(_1479514)), _1479516) = _1479516)], (46883 ^ _778495) ^ [_1721392, _1721394, _1721396, _1721398, _1721400] : [-(c_List_OtakeWhile(_1721392, _1721394, hAPP(hAPP(c_List_Omap(_1721396, _1721392), _1721398), _1721400)) = hAPP(hAPP(c_List_Omap(_1721396, _1721392), _1721398), c_List_OtakeWhile(_1721396, hAPP(c_Fun_Ocomp(_1721392, tc_HOL_Obool, _1721396, _1721394), _1721398), _1721400)))], (40459 ^ _778495) ^ [_1570429, _1570431, _1570433] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1570429, _1570431, _1570431), _1570433), c_Relation_OId(_1570431)) = _1570433)], (41748 ^ _778495) ^ [_1605797, _1605799, _1605801] : [c_Relation_Orefl__on(_1605797, _1605799, _1605801), -(c_Relation_Orefl__on(tc_List_Olist(_1605797), c_List_Olists(_1605797, _1605799), c_List_Olistrel(_1605797, _1605801)))], (52305 ^ _778495) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (21284 ^ _778495) ^ [_1159914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1159914)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159914), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26620 ^ _778495) ^ [] : [c_Int_OMin = c_Int_OPls], (12559 ^ _778495) ^ [_1000222, _1000224, _1000226, _1000228, _1000230] : [class_Groups_Ocomm__monoid__mult(_1000222), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000224), _1000226)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000224), _1000228)), 12573 ^ _778495 : [(12576 ^ _778495) ^ [] : [hAPP(_1000230, 12572 ^ [_1000222, _1000224, _1000226, _1000228, _1000230]) = c_Groups_Oone__class_Oone(_1000222)], (12574 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1000224), 12572 ^ [_1000222, _1000224, _1000226, _1000228, _1000230]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1000224, tc_HOL_Obool)), _1000226), _1000228))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1000222, _1000224, c_Groups_Otimes__class_Otimes(_1000222)), _1000230), c_Groups_Oone__class_Oone(_1000222)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000224, tc_HOL_Obool)), _1000226), _1000228)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000222), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1000222, _1000224, c_Groups_Otimes__class_Otimes(_1000222)), _1000230), c_Groups_Oone__class_Oone(_1000222)), _1000226)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1000222, _1000224, c_Groups_Otimes__class_Otimes(_1000222)), _1000230), c_Groups_Oone__class_Oone(_1000222)), _1000228)))], (11734 ^ _778495) ^ [_982241, _982243, _982245, _982247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982241), _982243)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982245), _982243) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982241), _982247), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982245), _982247)))], (42451 ^ _778495) ^ [_1624459, _1624461, _1624463] : [hBOOL(hAPP(c_List_Odistinct(_1624459), _1624461)), -(hBOOL(hAPP(c_List_Odistinct(_1624459), c_List_Osublist(_1624459, _1624461, _1624463))))], (9250 ^ _778495) ^ [_934966, _934968, _934970, _934972] : [class_Lattices_Odistrib__lattice(_934966), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934966), _934968), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934966), _934970), _934972)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934966), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934966), _934968), _934970)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934966), _934968), _934972)))], (21648 ^ _778495) ^ [_1166130, _1166132] : [class_Int_Onumber__ring(_1166130), -(hAPP(c_Int_Onumber__class_Onumber__of(_1166130), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1166132)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1166130), hAPP(c_Int_Onumber__class_Onumber__of(_1166130), _1166132)))], (38945 ^ _778495) ^ [_1533040, _1533042, _1533044, _1533046] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533040, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533040, _1533042), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1533040, _1533042), tc_HOL_Obool)), _1533044), _1533046))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533040, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533040, _1533042), _1533044)), hAPP(c_Relation_ODomain(_1533040, _1533042), _1533046)))))], (34849 ^ _778495) ^ [_1430376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1430376)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1430376) = 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, _1430376))))], (43856 ^ _778495) ^ [_1655710, _1655712, _1655714] : [-(_1655710 = c_List_Olist_ONil(_1655712)), -(hAPP(hAPP(c_List_Otake(_1655712), hAPP(c_Nat_OSuc, _1655714)), _1655710) = hAPP(hAPP(c_List_Olist_OCons(_1655712), hAPP(c_List_Ohd(_1655712), _1655710)), hAPP(hAPP(c_List_Otake(_1655712), _1655714), hAPP(c_List_Otl(_1655712), _1655710))))], (39390 ^ _778495) ^ [_1544707, _1544709, _1544711, _1544713, _1544715, _1544717] : [-(hAPP(hAPP(c_Fun_Ocomp(_1544707, _1544709, _1544711, hAPP(c_COMBK(_1544709, _1544707), _1544713)), _1544715), _1544717) = _1544713)], (31198 ^ _778495) ^ [_1348605, _1348607, _1348609] : [class_Orderings_Olinorder(_1348605), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348605), _1348607)), hBOOL(hAPP(hAPP(c_member(_1348605), _1348609), _1348607)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348605), _1348609), c_Big__Operators_Olinorder__class_OMax(_1348605, _1348607)) = c_Big__Operators_Olinorder__class_OMax(_1348605, _1348607))], (48991 ^ _778495) ^ [_1769454, _1769456] : [c_Relation_Otrans(_1769454, _1769456), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1769454, _1769454), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1769454, _1769454, _1769454), _1769456), _1769456)), _1769456)))], (52489 ^ _778495) ^ [_1833779, _1833781] : [-(class_Enum_Oenum(tc_sum(_1833779, _1833781))), class_Enum_Oenum(_1833779), class_Enum_Oenum(_1833781)], (6216 ^ _778495) ^ [_878932, _878934, _878936, _878938] : [hBOOL(hAPP(hAPP(c_member(_878932), _878934), _878936)), -(hBOOL(hAPP(hAPP(c_member(_878932), _878934), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_878932, tc_HOL_Obool)), _878936), _878938))))], (4862 ^ _778495) ^ [_852605, _852607, _852609, _852611] : [-(c_Quickcheck_Obeyond(_852611, _852607) = c_Quickcheck_Obeyond(_852609, _852605)), _852611 = _852609, _852607 = _852605], (23541 ^ _778495) ^ [_1200168, _1200170, _1200172] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1200168, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1200168, tc_HOL_Obool)), _1200170), _1200172)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1200168, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1200168, tc_HOL_Obool)), _1200170)), _1200172))], (44566 ^ _778495) ^ [_1671031, _1671033, _1671035, _1671037] : [class_Groups_Oab__group__add(_1671031), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1671031), hAPP(c_List_Omonoid__add__class_Olistsum(_1671031), hAPP(hAPP(c_List_Omap(_1671033, _1671031), _1671035), _1671037))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1671031), hAPP(hAPP(c_List_Omap(_1671033, _1671031), hAPP(c_Fun_Ocomp(_1671031, _1671031, _1671033, c_Groups_Ouminus__class_Ouminus(_1671031)), _1671035)), _1671037)))], (12999 ^ _778495) ^ [_1010386] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1010386))))], (4474 ^ _778495) ^ [_846483, _846485, _846487, _846489, _846491, _846493] : [-(c_FunDef_OTHE__default(_846493, _846489, _846485) = c_FunDef_OTHE__default(_846491, _846487, _846483)), _846493 = _846491, _846489 = _846487, _846485 = _846483], (3656 ^ _778495) ^ [_833330, _833332, _833334, _833336] : [-(c_List_Oremdups(_833336, _833332) = c_List_Oremdups(_833334, _833330)), _833336 = _833334, _833332 = _833330], (6414 ^ _778495) ^ [_882379, _882381, _882383] : [class_Orderings_Oorder(_882379), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882379), _882381), _882383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882379), _882383), _882381)), -(_882381 = _882383)], (31604 ^ _778495) ^ [_1355887, _1355889] : [class_Orderings_Olinorder(_1355887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355887), _1355889)), -(_1355889 = c_Orderings_Obot__class_Obot(tc_fun(_1355887, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1355887), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355887), 31617 ^ [_1355887, _1355889]), 31618 ^ [_1355887, _1355889])), hAPP(hAPP(c_Set_Oinsert(_1355887), 31617 ^ [_1355887, _1355889]), hAPP(hAPP(c_Set_Oinsert(_1355887), 31618 ^ [_1355887, _1355889]), c_Orderings_Obot__class_Obot(tc_fun(_1355887, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1355887), c_Big__Operators_Olinorder__class_OMax(_1355887, _1355889)), _1355889)))], (12593 ^ _778495) ^ [_1001024, _1001026, _1001028, _1001030, _1001032, _1001034, _1001036, _1001038] : [c_Finite__Set_Ofolding__image__simple(_1001024, _1001026, _1001028, _1001030, _1001032, _1001034), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001026), _1001036)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001026), _1001038)), 12607 ^ _778495 : [(12610 ^ _778495) ^ [] : [hAPP(_1001032, 12606 ^ [_1001024, _1001026, _1001028, _1001030, _1001032, _1001034, _1001036, _1001038]) = _1001030], (12608 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001026), 12606 ^ [_1001024, _1001026, _1001028, _1001030, _1001032, _1001034, _1001036, _1001038]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1001026, tc_HOL_Obool)), _1001036), _1001038))))]], -(hAPP(_1001034, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001026, tc_HOL_Obool)), _1001036), _1001038)) = hAPP(hAPP(_1001028, hAPP(_1001034, _1001036)), hAPP(_1001034, _1001038)))], (29188 ^ _778495) ^ [_1309266, _1309268, _1309270] : [class_Rings_Osemiring__1(_1309266), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1309266, _1309268, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1309270) = _1309270)], (226 ^ _778495) ^ [_782212, _782214] : [-(class_Fields_Olinordered__field__inverse__zero(_782212)), _782214 = _782212, class_Fields_Olinordered__field__inverse__zero(_782214)], (13390 ^ _778495) ^ [_1016441] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1016441)))], (34134 ^ _778495) ^ [_1414487, _1414489, _1414491, _1414493] : [class_Groups_Ocomm__monoid__add(_1414487), 34137 ^ _778495 : [(34144 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1414489), _1414491))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1414487), _1414493), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1414491), hAPP(c_Nat_OSuc, _1414489))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414487), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1414487), _1414493), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1414491), _1414489))), hAPP(_1414493, _1414489)))], (34138 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1414489), _1414491)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1414487), _1414493), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1414491), hAPP(c_Nat_OSuc, _1414489))) = c_Groups_Ozero__class_Ozero(_1414487))]]], (21290 ^ _778495) ^ [_1160009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160009), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1160009)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (49993 ^ _778495) ^ [_1789678, _1789680, _1789682] : [_1789680 = _1789682, -(c_Fun_Obij__betw(_1789678, _1789678, c_Fun_Oid(_1789678), _1789680, _1789682))], (25443 ^ _778495) ^ [_1233161, _1233163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1233161)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233161), _1233163)), _1233161) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34261 ^ _778495) ^ [_1417445, _1417447] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1417445, _1417445)), _1417447)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1417445), hAPP(c_Relation_OField(_1417445), _1417447))))], (52125 ^ _778495) ^ [_1830159, _1830161] : [class_Orderings_Opreorder(_1830159), -(class_Orderings_Opreorder(tc_fun(_1830161, _1830159)))], (47839 ^ _778495) ^ [_1742460, _1742462, _1742464, _1742466] : [-(c_List_Olist__all(_1742460, _1742462, hAPP(hAPP(c_List_Oappend(_1742460), _1742464), _1742466))), c_List_Olist__all(_1742460, _1742462, _1742464), c_List_Olist__all(_1742460, _1742462, _1742466)], (38369 ^ _778495) ^ [_1517619, _1517621] : [-(c_Product__Type_Omap__pair(_1517619, _1517619, _1517621, _1517621, c_Fun_Oid(_1517619), c_Fun_Oid(_1517621)) = c_Fun_Oid(tc_prod(_1517619, _1517621)))], (45424 ^ _778495) ^ [_1690103, _1690105] : [_1690105 = c_List_Olist_ONil(_1690103), -(c_List_Olist_ONil(_1690103) = c_List_Oremdups(_1690103, _1690105))], (12857 ^ _778495) ^ [_1007200, _1007202, _1007204, _1007206, _1007208] : [class_Groups_Ocomm__monoid__add(_1007200), class_Groups_Oordered__cancel__ab__semigroup__add(_1007200), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007202), _1007204)), -(_1007204 = c_Orderings_Obot__class_Obot(tc_fun(_1007202, tc_HOL_Obool))), 12875 ^ _778495 : [(12878 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007200), hAPP(_1007206, 12874 ^ [_1007200, _1007202, _1007204, _1007206, _1007208])), hAPP(_1007208, 12874 ^ [_1007200, _1007202, _1007204, _1007206, _1007208])))], (12876 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1007202), 12874 ^ [_1007200, _1007202, _1007204, _1007206, _1007208]), _1007204)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007200), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1007202, _1007200), _1007206), _1007204)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1007202, _1007200), _1007208), _1007204))))], (5953 ^ _778495) ^ [_873456, _873458, _873460] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873456, tc_HOL_Obool)), _873458), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873456, tc_HOL_Obool)), _873458), _873460))))], (16570 ^ _778495) ^ [_1074682, _1074684, _1074686] : [class_Fields_Olinordered__field__inverse__zero(_1074682), 16573 ^ _778495 : [(16588 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074682), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1074682), _1074684), _1074686)), c_Groups_Ozero__class_Ozero(_1074682)))), 16589 ^ _778495 : [(16596 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074682), _1074684), c_Groups_Ozero__class_Ozero(_1074682))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074682), c_Groups_Ozero__class_Ozero(_1074682)), _1074686))], (16590 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074682), c_Groups_Ozero__class_Ozero(_1074682)), _1074684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074682), _1074686), c_Groups_Ozero__class_Ozero(_1074682)))]]], (16574 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074682), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1074682), _1074684), _1074686)), c_Groups_Ozero__class_Ozero(_1074682))), 16579 ^ _778495 : [(16582 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074682), _1074686), c_Groups_Ozero__class_Ozero(_1074682))))], (16580 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074682), c_Groups_Ozero__class_Ozero(_1074682)), _1074684)))]], 16583 ^ _778495 : [(16586 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074682), c_Groups_Ozero__class_Ozero(_1074682)), _1074686)))], (16584 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074682), _1074684), c_Groups_Ozero__class_Ozero(_1074682))))]]]]], (8842 ^ _778495) ^ [_927009, _927011, _927013, _927015] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927009, tc_HOL_Obool)), _927011), _927013), _927015)), 8845 ^ _778495 : [(8848 ^ _778495) ^ [] : [-(hBOOL(hAPP(_927013, _927015)))], (8846 ^ _778495) ^ [] : [-(hBOOL(hAPP(_927011, _927015)))]]], (10525 ^ _778495) ^ [_960162, _960164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960162), _960164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960162), hAPP(c_Nat_OSuc, _960164))))], (14667 ^ _778495) ^ [_1038751] : [-(hAPP(c_Finite__Set_Ocard(_1038751), c_Orderings_Obot__class_Obot(tc_fun(_1038751, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36825 ^ _778495) ^ [_1472829, _1472831, _1472833] : [-(c_Fun_Oinj__on(tc_prod(_1472829, _1472831), tc_prod(_1472831, _1472829), hAPP(c_Product__Type_Oprod_Oprod__case(_1472829, _1472831, tc_prod(_1472831, _1472829)), hAPP(c_COMBC(_1472831, _1472829, tc_prod(_1472831, _1472829)), c_Product__Type_OPair(_1472831, _1472829))), _1472833))], (52015 ^ _778495) ^ [_1828417, _1828419, _1828421] : [class_Rings_Odvd(_1828417), class_Rings_Osemiring__0(_1828417), 52022 ^ _778495 : [(52032 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1828419, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828417), _1828421), 52039 ^ [_1828417, _1828419, _1828421])))), 52033 ^ _778495 : [(52034 ^ _778495) ^ [_1828746] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828417), _1828421), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1828417), _1828746), c_Groups_Ozero__class_Ozero(_1828417)))), hBOOL(hAPP(_1828419, _1828746))]]], (52023 ^ _778495) ^ [] : [52024 ^ _778495 : [(52025 ^ _778495) ^ [_1828609] : [hBOOL(hAPP(_1828419, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828417), _1828421), _1828609)))]], 52027 ^ _778495 : [(52030 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1828419, 52026 ^ [_1828417, _1828419, _1828421])))], (52028 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828417), _1828421), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1828417), 52026 ^ [_1828417, _1828419, _1828421]), c_Groups_Ozero__class_Ozero(_1828417)))))]]]]], (14045 ^ _778495) ^ [_1027897, _1027899, _1027901] : [class_Groups_Oordered__comm__monoid__add(_1027897), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027897), c_Groups_Ozero__class_Ozero(_1027897)), _1027899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027897), c_Groups_Ozero__class_Ozero(_1027897)), _1027901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027897), c_Groups_Ozero__class_Ozero(_1027897)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027897), _1027899), _1027901))))], (33252 ^ _778495) ^ [_1393119, _1393121, _1393123, _1393125, _1393127] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393119, tc_fun(_1393121, tc_HOL_Obool)), _1393123), hAPP(hAPP(c_COMBC(_1393119, tc_fun(_1393121, tc_HOL_Obool), tc_fun(_1393121, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393121, tc_HOL_Obool), tc_fun(tc_fun(_1393121, tc_HOL_Obool), tc_fun(_1393121, tc_HOL_Obool)), _1393119), c_Groups_Ominus__class_Ominus(tc_fun(_1393121, tc_HOL_Obool))), _1393125)), _1393127)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1393121, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393119, tc_fun(_1393121, tc_HOL_Obool)), _1393123), _1393125)), _1393127))], (24309 ^ _778495) ^ [_1213561, _1213563, _1213565] : [-(hBOOL(hAPP(_1213561, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213563, _1213565)))), 24312 ^ _778495 : [(24315 ^ _778495) ^ [] : [hBOOL(hAPP(_1213561, _1213563))], (24313 ^ _778495) ^ [] : [-(_1213565 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 24318 ^ _778495 : [(24319 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213565)))], (24325 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24321 ^ [_1213561, _1213563, _1213565]), _1213565)))], (24329 ^ _778495) ^ [] : [hBOOL(hAPP(_1213561, 24321 ^ [_1213561, _1213563, _1213565]))], (24327 ^ _778495) ^ [] : [-(_1213563 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1213565), 24320 ^ [_1213561, _1213563, _1213565])), 24321 ^ [_1213561, _1213563, _1213565]))], (24323 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24321 ^ [_1213561, _1213563, _1213565])))]], 24330 ^ _778495 : [(24331 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213565), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24337 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24333 ^ [_1213561, _1213563, _1213565]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24341 ^ _778495) ^ [] : [hBOOL(hAPP(_1213561, 24333 ^ [_1213561, _1213563, _1213565]))], (24339 ^ _778495) ^ [] : [-(_1213563 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1213565), 24332 ^ [_1213561, _1213563, _1213565])), 24333 ^ [_1213561, _1213563, _1213565]))], (24335 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213565), 24333 ^ [_1213561, _1213563, _1213565])))]]], (48438 ^ _778495) ^ [_1755101, _1755103] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755101), _1755103))), -(c_Lazy__Sequence_Osmall__lazy_H(_1755101, _1755103) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1755103), c_Lazy__Sequence_Osmall__lazy_H(_1755101, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1755103), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (346 ^ _778495) ^ [_783810, _783812, _783814, _783816] : [-(c_Nitpick_Owf_H(_783814, _783810)), c_Nitpick_Owf_H(_783816, _783812), _783816 = _783814, _783812 = _783810], (51441 ^ _778495) ^ [_1817889, _1817891, _1817893, _1817895] : [class_Divides_Osemiring__div(_1817889), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817889), _1817891), c_Divides_Odiv__class_Omod(_1817889, _1817893, _1817895))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817889), _1817891), _1817895)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817889), _1817891), _1817893)))], (488 ^ _778495) ^ [_785883, _785885, _785887, _785889, _785891, _785893] : [-(c_Nitpick_Oless__frac(_785891, _785887, _785883)), c_Nitpick_Oless__frac(_785893, _785889, _785885), _785893 = _785891, _785889 = _785887, _785885 = _785883], (22394 ^ _778495) ^ [_1178888, _1178890] : [class_Lattices_Oboolean__algebra(_1178888), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1178888), hAPP(c_Groups_Ouminus__class_Ouminus(_1178888), _1178890)), _1178890) = c_Orderings_Obot__class_Obot(_1178888))], (46840 ^ _778495) ^ [_1720486, _1720488, _1720490] : [class_Orderings_Olinorder(_1720486), c_List_Olinorder__class_Osorted(_1720486, _1720488), -(c_List_Olinorder__class_Osorted(_1720486, c_List_OtakeWhile(_1720486, _1720490, _1720488)))], (23979 ^ _778495) ^ [_1207623, _1207625, _1207627, _1207629] : [class_Divides_Osemiring__div(_1207623), -(_1207625 = c_Groups_Ozero__class_Ozero(_1207623)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207623), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207623), _1207627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207623), _1207629), _1207625))), _1207625) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207623), _1207629), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207623), _1207627), _1207625)))], (48985 ^ _778495) ^ [_1769355, _1769357, _1769359, _1769361] : [c_Relation_Otrans(_1769355, _1769357), -(c_Relation_Otrans(_1769359, hAPP(hAPP(c_Relation_Oinv__image(_1769355, _1769359), _1769357), _1769361)))], (23402 ^ _778495) ^ [_1197801, _1197803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197803)), -(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), _1197801), _1197803))))], (17564 ^ _778495) ^ [_1093264, _1093266, _1093268, _1093270] : [class_Rings_Olinordered__semidom(_1093264), 17570 ^ _778495 : [(17573 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093264), c_Groups_Ozero__class_Ozero(_1093264)), hAPP(_1093270, 17569 ^ [_1093264, _1093266, _1093268, _1093270])))], (17571 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1093266), 17569 ^ [_1093264, _1093266, _1093268, _1093270]), _1093268)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093264), c_Groups_Ozero__class_Ozero(_1093264)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1093266, _1093264), _1093270), _1093268))))], (36823 ^ _778495) ^ [] : [-(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))))], (27495 ^ _778495) ^ [_1269051, _1269053, _1269055] : [27497 ^ _778495 : [(27500 ^ _778495) ^ [] : [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(_1269053, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 27496 ^ [_1269051, _1269053, _1269055]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1269053, 27496 ^ [_1269051, _1269053, _1269055])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (27498 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27496 ^ [_1269051, _1269053, _1269055]), _1269051)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1269053, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1269055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1269055), hAPP(_1269053, _1269051))), 27510 ^ _778495 : [(27513 ^ _778495) ^ [] : [-(hAPP(_1269053, 27509 ^ [_1269051, _1269053, _1269055]) = _1269055)], (27511 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27509 ^ [_1269051, _1269053, _1269055]), _1269051)))]]], (51503 ^ _778495) ^ [_1818985, _1818987, _1818989, _1818991] : [class_Divides_Osemiring__div(_1818985), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818985), _1818987), _1818989)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818985), _1818987), _1818991)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1818985), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1818985), _1818989), _1818991)), _1818987) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1818985), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1818985), _1818989), _1818987)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1818985), _1818991), _1818987)))], (7116 ^ _778495) ^ [_895784, _895786, _895788] : [class_Lattices_Osemilattice__sup(_895784), 7119 ^ _778495 : [(7126 ^ _778495) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895784), _895786), _895788) = _895788, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895784), _895786), _895788)))], (7120 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895784), _895786), _895788)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895784), _895786), _895788) = _895788)]]], (52639 ^ _778495) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (21082 ^ _778495) ^ [_1156104, _1156106] : [class_Rings_Olinordered__idom(_1156104), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156104), hAPP(c_Groups_Oabs__class_Oabs(_1156104), _1156106)), hAPP(c_Groups_Oabs__class_Oabs(_1156104), _1156106)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156104), _1156106), _1156106))], (25407 ^ _778495) ^ [_1232509, _1232511] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232509) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1232511)), _1232509 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1232511)), 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), _1232511)))], (27029 ^ _778495) ^ [_1261402, _1261404] : [class_Int_Onumber__ring(_1261402), -(hAPP(c_Int_Onumber__class_Onumber__of(_1261402), _1261404) = hAPP(c_Int_Oring__1__class_Oof__int(_1261402), _1261404))], (19220 ^ _778495) ^ [_1123845, _1123847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123845), _1123847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123845), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1123847), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (13213 ^ _778495) ^ [_1013771, _1013773] : [class_Rings_Omult__zero(_1013771), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013771), _1013773), c_Groups_Ozero__class_Ozero(_1013771)) = c_Groups_Ozero__class_Ozero(_1013771))], (20402 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (3466 ^ _778495) ^ [_830333, _830335] : [_830335 = _830333, -(c_SetInterval_Oord__class_OlessThan(_830335) = c_SetInterval_Oord__class_OlessThan(_830333))], (34617 ^ _778495) ^ [_1425755, _1425757, _1425759, _1425761, _1425763, _1425765, _1425767] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1425755, _1425757)), hAPP(hAPP(c_Product__Type_OPair(_1425755, _1425757), _1425759), _1425761)), _1425763)), -(hBOOL(hAPP(hAPP(c_member(_1425765), hAPP(hAPP(_1425767, _1425759), _1425761)), hAPP(c_Set_Oimage(tc_prod(_1425755, _1425757), _1425765, hAPP(c_Product__Type_Oprod_Oprod__case(_1425755, _1425757, _1425765), _1425767)), _1425763))))], (7110 ^ _778495) ^ [_895677, _895679, _895681] : [class_Lattices_Osemilattice__sup(_895677), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895677), _895679), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895677), _895681), _895679))))], (34344 ^ _778495) ^ [_1419546, _1419548, _1419550, _1419552, _1419554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1419546, tc_HOL_Obool)), _1419548), hAPP(c_Set_Oimage(_1419550, _1419546, _1419552), _1419554))), 34348 ^ _778495 : [(34351 ^ _778495) ^ [] : [-(_1419548 = hAPP(c_Set_Oimage(_1419550, _1419546, _1419552), 34347 ^ [_1419546, _1419548, _1419550, _1419552, _1419554]))], (34349 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1419550, tc_HOL_Obool)), 34347 ^ [_1419546, _1419548, _1419550, _1419552, _1419554]), _1419554)))]]], (1986 ^ _778495) ^ [_807185, _807187, _807189, _807191, _807193, _807195, _807197, _807199, _807201, _807203] : [-(c_Nitpick_Opair__box_Opair__box__size(_807203, _807199, _807195, _807191, _807187) = c_Nitpick_Opair__box_Opair__box__size(_807201, _807197, _807193, _807189, _807185)), _807203 = _807201, _807199 = _807197, _807195 = _807193, _807191 = _807189, _807187 = _807185], (52421 ^ _778495) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (32872 ^ _778495) ^ [_1384996, _1384998] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1384996, _1384998))))], (11819 ^ _778495) ^ [_983861, _983863, _983865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983861), _983863)), _983865)), 11822 ^ _778495 : [(11825 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983863), _983865)))], (11823 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983861), _983865)))]]], (19022 ^ _778495) ^ [_1120598, _1120600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120598), _1120600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120598)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120600))))], (37356 ^ _778495) ^ [_1485183, _1485185, _1485187, _1485189, _1485191, _1485193] : [class_Groups_Ocomm__monoid__add(_1485183), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485185, _1485183), hAPP(hAPP(c_COMBC(_1485185, tc_fun(_1485187, tc_HOL_Obool), _1485183), hAPP(hAPP(c_COMBB(tc_fun(_1485187, _1485183), tc_fun(tc_fun(_1485187, tc_HOL_Obool), _1485183), _1485185), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485187, _1485183)), _1485189)), _1485191)), _1485193) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1485185, _1485187), _1485183), hAPP(c_Product__Type_Oprod_Oprod__case(_1485185, _1485187, _1485183), _1485189)), hAPP(hAPP(c_Product__Type_OSigma(_1485185, _1485187), _1485193), hAPP(c_COMBK(tc_fun(_1485187, tc_HOL_Obool), _1485185), _1485191))))], (6660 ^ _778495) ^ [_887357, _887359] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887357, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_887357, tc_HOL_Obool))), _887359) = c_Orderings_Obot__class_Obot(tc_fun(_887357, tc_HOL_Obool)))], (10675 ^ _778495) ^ [_962527, _962529] : [_962527 = _962529, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962527), _962529)))], (45097 ^ _778495) ^ [_1683090, _1683092, _1683094, _1683096, _1683098, _1683100] : [c_List_Olist__all2(_1683090, _1683092, _1683094, _1683096, _1683098), -(c_List_Olist__all2(_1683090, _1683092, _1683094, hAPP(hAPP(c_List_Odrop(_1683090), _1683100), _1683096), hAPP(hAPP(c_List_Odrop(_1683092), _1683100), _1683098)))], (44923 ^ _778495) ^ [_1678445, _1678447] : [-(c_List_Opartition(_1678445, _1678447, c_List_Olist_ONil(_1678445)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678445), tc_List_Olist(_1678445)), c_List_Olist_ONil(_1678445)), c_List_Olist_ONil(_1678445)))], (2070 ^ _778495) ^ [_808653, _808655] : [_808655 = _808653, -(c_Nat_Osemiring__1__class_ONats(_808655) = c_Nat_Osemiring__1__class_ONats(_808653))], (25666 ^ _778495) ^ [_1237087, _1237089, _1237091] : [class_Groups_Omonoid__mult(_1237087), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1237087), _1237089), 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)))), _1237091)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1237087), hAPP(hAPP(c_Power_Opower__class_Opower(_1237087), _1237089), _1237091)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (25832 ^ _778495) ^ [_1239988, _1239990, _1239992] : [class_Rings_Olinordered__idom(_1239988), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239988), c_Groups_Ozero__class_Ozero(_1239988)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1239988), hAPP(hAPP(c_Power_Opower__class_Opower(_1239988), _1239990), 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(_1239988), _1239992), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (22108 ^ _778495) ^ [_1173955] : [c_Int_OBit0(_1173955) = c_Int_OPls, -(_1173955 = c_Int_OPls)], (28455 ^ _778495) ^ [_1292688] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1292688)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1292688)), 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))))], (1338 ^ _778495) ^ [_798248, _798250] : [-(class_Groups_Oabs__if(_798248)), _798250 = _798248, class_Groups_Oabs__if(_798250)], (3106 ^ _778495) ^ [_824749, _824751, _824753, _824755] : [-(c_Big__Operators_Olattice__class_OSup__fin(_824755, _824751) = c_Big__Operators_Olattice__class_OSup__fin(_824753, _824749)), _824755 = _824753, _824751 = _824749], (29476 ^ _778495) ^ [_1314665, _1314667, _1314669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314665, tc_fun(_1314665, tc_HOL_Obool))), _1314667), _1314669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314665, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1314665, _1314669)), c_Wellfounded_Oaccp(_1314665, _1314667))))], (34933 ^ _778495) ^ [_1431975, _1431977, _1431979, _1431981, _1431983, _1431985] : [-(_1431975 = _1431977), -(hAPP(c_Fun_Ofun__upd(_1431979, _1431981, _1431983, _1431977, _1431985), _1431975) = hAPP(_1431983, _1431975))], (33577 ^ _778495) ^ [_1403012, _1403014, _1403016] : [class_Fields_Ofield(_1403012), -(_1403014 = c_Groups_Oone__class_Oone(_1403012)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1403012), hAPP(c_Power_Opower__class_Opower(_1403012), _1403014)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1403016)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1403012), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1403012), hAPP(hAPP(c_Power_Opower__class_Opower(_1403012), _1403014), _1403016)), c_Groups_Oone__class_Oone(_1403012))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1403012), _1403014), c_Groups_Oone__class_Oone(_1403012))))], (24950 ^ _778495) ^ [_1224811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224811), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1224811) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37759 ^ _778495) ^ [_1496712] : [-(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)), _1496712)))))], (8888 ^ _778495) ^ [_927875, _927877, _927879] : [class_Lattices_Osemilattice__inf(_927875), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927875), _927877), _927879) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927875), _927879), _927877))], (12016 ^ _778495) ^ [_988494, _988496] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988494), _988496))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988496), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988494), _988496)) = _988494)], (48174 ^ _778495) ^ [_1749758, _1749760, _1749762, _1749764, _1749766] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1749760, _1749758)), hAPP(hAPP(c_Product__Type_OPair(_1749760, _1749758), _1749764), _1749766)), hAPP(c_Relation_Oconverse(_1749758, _1749760), _1749762))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749758, _1749760, hAPP(hAPP(c_COMBC(_1749758, tc_fun(tc_prod(_1749758, _1749760), tc_HOL_Obool), tc_fun(_1749760, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749760, tc_fun(tc_fun(tc_prod(_1749758, _1749760), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1749758, _1749760), tc_HOL_Obool), tc_fun(_1749760, tc_HOL_Obool)), _1749758), c_COMBC(_1749760, tc_fun(tc_prod(_1749758, _1749760), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749760, tc_prod(_1749758, _1749760)), tc_fun(_1749760, 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_1701870), _1701872))], (14767 ^ _778495) ^ [_1040388, _1040390, _1040392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040388), _1040390)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040392), _1040390))), 14770 ^ _778495 : [(14773 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040388), _1040392)))], (14771 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040390)))]]], (21204 ^ _778495) ^ [_1158337, _1158339] : [class_Groups_Oordered__ab__group__add__abs(_1158337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158337), hAPP(c_Groups_Oabs__class_Oabs(_1158337), _1158339)), c_Groups_Ozero__class_Ozero(_1158337)))], (48092 ^ _778495) ^ [_1747737, _1747739] : [-(c_List_Osplice(_1747737, c_List_Olist_ONil(_1747737), _1747739) = _1747739)], (13813 ^ _778495) ^ [_1023691, _1023693, _1023695, _1023697] : [class_Rings_Oordered__ring(_1023691), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023691), _1023693), _1023695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023691), _1023697), c_Groups_Ozero__class_Ozero(_1023691))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023691), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023691), _1023695), _1023697)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023691), _1023693), _1023697))))], (41778 ^ _778495) ^ [_1606458, _1606460, _1606462] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606458)), _1606460), c_Wellfounded_Oacc(tc_List_Olist(_1606458), c_List_Olistrel1(_1606458, _1606462)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606458)), _1606460), c_List_Olists(_1606458, c_Wellfounded_Oacc(_1606458, _1606462)))))], (40993 ^ _778495) ^ [_1583385, _1583387, _1583389] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583385, _1583385)), hAPP(hAPP(c_Product__Type_OPair(_1583385, _1583385), _1583387), _1583387)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583385, _1583385), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1583389))))], (16102 ^ _778495) ^ [_1066344, _1066346, _1066348, _1066350] : [class_Rings_Odivision__ring(_1066344), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066344), _1066346), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066344), _1066348), _1066350)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066344), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066344), _1066346), _1066348)), _1066350))], (52183 ^ _778495) ^ [_1830920, _1830922] : [-(class_Enum_Oenum(tc_fun(_1830920, _1830922))), class_Enum_Oenum(_1830920), class_Enum_Oenum(_1830922)], (11909 ^ _778495) ^ [_985883, _985885, _985887, _985889, _985891] : [class_Groups_Oordered__cancel__ab__semigroup__add(_985883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985883), _985885), _985887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985883), _985889), _985891)), 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(2634 ^ _778495) ^ [_817417, _817419] : [_817419 = _817417, -(c_Int_Oint__ge__less__than(_817419) = c_Int_Oint__ge__less__than(_817417))], (5992 ^ _778495) ^ [_874241, _874243, _874245] : [class_Orderings_Olinorder(_874241), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874241), _874243), _874245))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874241), _874245), _874243)))], (47280 ^ _778495) ^ [_1729892, _1729894] : [-(c_List_Omeasures(_1729892, _1729894) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1729892), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1729892, tc_List_Olist(tc_fun(_1729892, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1729892, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1729892, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1729892), c_List_Omap(tc_fun(_1729892, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1729892, tc_Nat_Onat), _1729892, tc_Nat_Onat), c_COMBI(tc_fun(_1729892, tc_Nat_Onat))))), _1729894)))], (25566 ^ _778495) ^ [_1235355] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1235355))), 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), _1235355), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (41925 ^ _778495) ^ [_1610615, _1610617] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1610615), hAPP(c_List_Oset(_1610615), _1610617))))], (12330 ^ _778495) ^ [_995103, _995105, _995107, _995109, _995111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995103), _995105)), 12333 ^ _778495 : [(12340 ^ _778495) ^ [] : [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), _995105), _995103)), _995107)), _995109)), _995111)), -(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), _995105), _995107)), _995109)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995103), _995107)), _995111))))], (12334 ^ _778495) ^ [] : [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), _995105), _995107)), _995109)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995103), _995107)), _995111))), -(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), _995105), _995103)), _995107)), _995109)), _995111)))]]], (39830 ^ _778495) ^ [_1554761, _1554763, _1554765, _1554767, _1554769, _1554771, _1554773] : [c_Finite__Set_Ofolding__idem(_1554761, _1554763, _1554765, _1554767), -(hAPP(c_Fun_Ocomp(_1554763, _1554763, _1554769, hAPP(_1554765, _1554771)), hAPP(c_Fun_Ocomp(_1554763, _1554763, _1554769, hAPP(_1554765, _1554771)), _1554773)) = hAPP(c_Fun_Ocomp(_1554763, _1554763, _1554769, hAPP(_1554765, _1554771)), _1554773))], (25168 ^ _778495) ^ [_1228446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1228446))))], (43375 ^ _778495) ^ [_1644279, _1644281, _1644283, _1644285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644279), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644281)), _1644283))), -(hAPP(hAPP(c_List_Onth(_1644281), hAPP(hAPP(c_List_Oappend(_1644281), _1644283), _1644285)), _1644279) = hAPP(hAPP(c_List_Onth(_1644281), _1644283), _1644279))], (44867 ^ _778495) ^ [_1677321, _1677323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677321)), hAPP(c_Code__Numeral_Onat__of, _1677323))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1677321), _1677323)))], (34697 ^ _778495) ^ [_1427324, _1427326, _1427328, _1427330] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427324, tc_fun(_1427326, tc_HOL_Obool)), _1427328), _1427330) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1427326, tc_HOL_Obool), hAPP(c_Set_Oimage(_1427324, tc_fun(_1427326, tc_HOL_Obool), _1427330), _1427328)))], (10627 ^ _778495) ^ [_961676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961676), _961676))], (21534 ^ _778495) ^ [_1164221, _1164223] : [class_Int_Onumber__ring(_1164221), class_Rings_Olinordered__idom(_1164221), 21541 ^ _778495 : [(21548 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1164223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164221), c_Groups_Oone__class_Oone(_1164221)), hAPP(c_Int_Onumber__class_Onumber__of(_1164221), _1164223))))], (21542 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164221), c_Groups_Oone__class_Oone(_1164221)), hAPP(c_Int_Onumber__class_Onumber__of(_1164221), _1164223))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1164223)))]]], (33421 ^ _778495) ^ [_1398646, _1398648, _1398650, _1398652, _1398654] : [_1398646 = c_Orderings_Obot__class_Obot(tc_fun(_1398648, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1398650), _1398652), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398648, tc_fun(_1398650, tc_HOL_Obool)), _1398646), _1398654)) = hAPP(hAPP(c_Set_Oinsert(_1398650), _1398652), c_Orderings_Obot__class_Obot(tc_fun(_1398650, tc_HOL_Obool))))], (29976 ^ _778495) ^ [_1324013, _1324015, _1324017] : [29978 ^ _778495 : [(29981 ^ _778495) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1324017, 29977 ^ [_1324013, _1324015, _1324017]))], (29979 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1324013), 29977 ^ [_1324013, _1324015, _1324017]), _1324015)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1324013, tc_Int_Oint), _1324017), _1324015) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1324013, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1324013), c_Int_Onat), _1324017)), _1324015)))], (1838 ^ _778495) ^ [_804498, _804500] : [-(class_Rings_Osemiring__0(_804498)), _804500 = _804498, class_Rings_Osemiring__0(_804500)], (45873 ^ _778495) ^ [_1701382, _1701384] : [class_Groups_Omonoid__add(_1701382), -(hAPP(c_List_Ofoldl(_1701382, _1701382, c_Groups_Oplus__class_Oplus(_1701382), c_Groups_Ozero__class_Ozero(_1701382)), _1701384) = c_List_Ofoldr(_1701382, _1701382, c_Groups_Oplus__class_Oplus(_1701382), _1701384, c_Groups_Ozero__class_Ozero(_1701382)))], (45857 ^ _778495) ^ [_1701010, _1701012, _1701014, _1701016, _1701018, _1701020] : [-(c_List_Ofoldr(_1701010, _1701012, _1701014, hAPP(hAPP(c_List_Oappend(_1701010), _1701016), _1701018), _1701020) = c_List_Ofoldr(_1701010, _1701012, _1701014, _1701016, c_List_Ofoldr(_1701010, _1701012, _1701014, _1701018, _1701020)))], (11829 ^ _778495) ^ [_984049, _984051] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _984049), _984051)), _984049) = _984051)], (14093 ^ _778495) ^ [_1028770, _1028772, _1028774, _1028776] : [class_Rings_Olinordered__ring__strict(_1028770), 14096 ^ _778495 : [(14111 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028770), _1028772), _1028774)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028770), _1028776), _1028774)))), 14112 ^ _778495 : [(14119 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028770), _1028774), c_Groups_Ozero__class_Ozero(_1028770))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028770), _1028776), _1028772))], (14113 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028770), c_Groups_Ozero__class_Ozero(_1028770)), _1028774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028770), _1028772), _1028776))]]], (14097 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028770), _1028772), _1028774)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028770), _1028776), _1028774))), 14102 ^ _778495 : [(14105 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028770), _1028772), _1028776)))], (14103 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028770), c_Groups_Ozero__class_Ozero(_1028770)), _1028774)))]], 14106 ^ _778495 : [(14109 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028770), _1028776), _1028772)))], (14107 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028770), _1028774), c_Groups_Ozero__class_Ozero(_1028770))))]]]]], (45989 ^ _778495) ^ [_1703675, _1703677, _1703679, _1703681] : [c_List_Oupt(_1703675, _1703677) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703679), _1703681), 45992 ^ _778495 : [(45997 ^ _778495) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703675), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703677) = _1703681)], (45995 ^ _778495) ^ [] : [-(_1703675 = _1703679)], (45993 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703675), _1703677)))]]], (48344 ^ _778495) ^ [_1753166, _1753168, _1753170, _1753172] : [hBOOL(hAPP(hAPP(c_member(_1753166), _1753168), hAPP(c_List_Oset(_1753166), c_List_Oreplicate(_1753166, _1753170, _1753172)))), 48347 ^ _778495 : [(48350 ^ _778495) ^ [] : [_1753170 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48348 ^ _778495) ^ [] : [-(_1753168 = _1753172)]]], (2132 ^ _778495) ^ [_809576, _809578, _809580, _809582] : [-(c_Nitpick_Onat__lcm(_809582, _809578) = c_Nitpick_Onat__lcm(_809580, _809576)), _809582 = _809580, _809578 = _809576], (16862 ^ _778495) ^ [_1079698, _1079700, _1079702, _1079704] : [class_Fields_Ofield__inverse__zero(_1079698), -(_1079700 = c_Groups_Ozero__class_Ozero(_1079698)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1079698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079698), _1079700), _1079702)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079698), _1079700), _1079704)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1079698), _1079702), _1079704))], (33553 ^ _778495) ^ [_1402399, _1402401, _1402403, _1402405, _1402407, _1402409] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1402399, _1402399)), hAPP(hAPP(c_Product__Type_OPair(_1402399, _1402399), _1402401), _1402403)), hAPP(hAPP(c_Relation_Oinv__image(_1402405, _1402399), _1402407), _1402409))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1402405, _1402405)), hAPP(hAPP(c_Product__Type_OPair(_1402405, _1402405), hAPP(_1402409, _1402401)), hAPP(_1402409, _1402403))), _1402407)))], (29065 ^ _778495) ^ [_1306206, _1306208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1306206)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1306208)), -(c_Divides_OposDivAlg(_1306206, _1306208) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1306206), _1306208)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1306206, _1306208)))], (47115 ^ _778495) ^ [_1726327, _1726329, _1726331] : [47117 ^ _778495 : [(47120 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1726329, 47116 ^ [_1726327, _1726329, _1726331])))], (47118 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726327), 47116 ^ [_1726327, _1726329, _1726331]), hAPP(c_List_Oset(_1726327), c_List_OdropWhile(_1726327, _1726329, _1726331)))))]], -(c_List_OtakeWhile(_1726327, _1726329, _1726331) = hAPP(c_List_Ofilter(_1726327, _1726329), _1726331))], (6098 ^ _778495) ^ [_876293, _876295, _876297] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876293, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_876293, tc_HOL_Obool)), _876295), _876297)), _876297) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876293, tc_HOL_Obool)), _876295), _876297))], (28345 ^ _778495) ^ [_1288079, _1288081, _1288083, _1288085, _1288087, _1288089] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1288079, _1288081)), hAPP(hAPP(c_Product__Type_OPair(_1288079, _1288081), _1288087), _1288089)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool)), _1288083), _1288085))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288079, tc_fun(_1288081, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1288079, tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_fun(_1288081, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1288081, tc_fun(tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_fun(_1288081, tc_HOL_Obool)), _1288079), c_COMBC(_1288081, tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1288081, tc_prod(_1288079, _1288081)), tc_fun(_1288081, tc_fun(tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_HOL_Obool)), _1288079), hAPP(c_COMBB(tc_prod(_1288079, _1288081), tc_fun(tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_HOL_Obool), _1288081), c_member(tc_prod(_1288079, _1288081)))), c_Product__Type_OPair(_1288079, _1288081)))), _1288083)), hAPP(hAPP(c_COMBC(_1288079, tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_fun(_1288081, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1288081, tc_fun(tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_fun(_1288081, tc_HOL_Obool)), _1288079), c_COMBC(_1288081, tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1288081, tc_prod(_1288079, _1288081)), tc_fun(_1288081, tc_fun(tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_HOL_Obool)), _1288079), hAPP(c_COMBB(tc_prod(_1288079, _1288081), tc_fun(tc_fun(tc_prod(_1288079, _1288081), tc_HOL_Obool), tc_HOL_Obool), _1288081), c_member(tc_prod(_1288079, _1288081)))), c_Product__Type_OPair(_1288079, _1288081)))), _1288085)), _1288087), _1288089)))], (9466 ^ _778495) ^ [_939712, _939714, _939716, _939718] : [class_Lattices_Olattice(_939712), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939712), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939712), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939712), _939714), _939716)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939712), _939714), _939718))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939712), _939714), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939712), _939716), _939718)))))], (6976 ^ _778495) ^ [_893062, _893064] : [class_Lattices_Osemilattice__sup(_893062), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893062), _893064), _893064) = _893064)], (44025 ^ _778495) ^ [_1659391, _1659393, _1659395] : [44026 ^ _778495 : [(44027 ^ _778495) ^ [_1659480, _1659482] : [_1659393 = hAPP(hAPP(c_List_Olist_OCons(_1659391), _1659482), _1659480)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659391), tc_List_Olist(_1659391))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659391), tc_List_Olist(_1659391)), c_List_Olist_ONil(_1659391)), _1659393)), c_List_Olexord(_1659391, _1659395))))], (10479 ^ _778495) ^ [_959314, _959316, _959318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959314), _959316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959314), _959318)), 10486 ^ _778495 : [(10493 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _959316), _959318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959316), _959314)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959318), _959314))))], (10487 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959316), _959314)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959318), _959314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _959316), _959318)))]]], (46750 ^ _778495) ^ [_1718424, _1718426, _1718428] : [-(hAPP(c_List_Orev(_1718424), hAPP(hAPP(c_List_Otake(_1718424), _1718426), _1718428)) = hAPP(hAPP(c_List_Odrop(_1718424), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718424)), _1718428)), _1718426)), hAPP(c_List_Orev(_1718424), _1718428)))], (25024 ^ _778495) ^ [_1226003, _1226005, _1226007] : [-(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), _1226003), _1226005)), _1226007)), _1226005) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1226007), _1226005))], (22818 ^ _778495) ^ [_1186394, _1186396] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1186394)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1186396)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186394), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186396))))], (43211 ^ _778495) ^ [_1640690, _1640692, _1640694] : [_1640694 = c_List_Olist_ONil(_1640690), -(hAPP(hAPP(c_List_Oappend(_1640690), _1640692), _1640694) = _1640692)], (34060 ^ _778495) ^ [_1412969, _1412971, _1412973] : [class_Groups_Ocomm__monoid__add(_1412969), hAPP(_1412971, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1412969), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1412969), _1412971), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1412973)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1412969), _1412971), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1412973)))], (19094 ^ _778495) ^ [_1121751] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121751), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1121751)], (9869 ^ _778495) ^ [_947929, _947931, _947933] : [class_Lattices_Oab__semigroup__idem__mult(_947929), hBOOL(hAPP(c_Finite__Set_Ofinite(_947929), _947931)), -(hAPP(c_Finite__Set_Ofold1(_947929, c_Groups_Otimes__class_Otimes(_947929)), hAPP(hAPP(c_Set_Oinsert(_947929), _947933), _947931)) = hAPP(hAPP(c_Finite__Set_Ofold(_947929, _947929, c_Groups_Otimes__class_Otimes(_947929)), _947933), _947931))], (15721 ^ _778495) ^ [_1058212, _1058214] : [class_Rings_Olinordered__idom(_1058212), 15724 ^ _778495 : [(15731 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058212), _1058214), c_Groups_Ozero__class_Ozero(_1058212))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058212), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058212), _1058214), _1058214)), c_Groups_Ozero__class_Ozero(_1058212))))], (15725 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058212), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058212), _1058214), _1058214)), c_Groups_Ozero__class_Ozero(_1058212))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058212), _1058214), c_Groups_Ozero__class_Ozero(_1058212))))]]], (48082 ^ _778495) ^ [_1747466, _1747468, _1747470, _1747472] : [-(c_New__Random__Sequence_Opos__map(_1747466, _1747468, _1747470, _1747472) = c_New__Random__Sequence_Opos__bind(_1747466, _1747468, _1747472, hAPP(c_Fun_Ocomp(_1747468, 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(_1747468))))), _1747466, c_New__Random__Sequence_Opos__single(_1747468)), _1747470)))], (35589 ^ _778495) ^ [_1444395] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1444395) = 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), _1444395), 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))))))], (19990 ^ _778495) ^ [_1137591, _1137593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1137591), _1137593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137591)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137593))))], (48741 ^ _778495) ^ [_1762108, _1762110, _1762112, _1762114, _1762116, _1762118, _1762120] : [hBOOL(hAPP(hAPP(_1762108, hAPP(c_Product__Type_Osnd(_1762110, _1762112), _1762114)), hAPP(c_Product__Type_Ofst(_1762110, _1762112), _1762114))), 48748 ^ _778495 : [(48751 ^ _778495) ^ [] : [hBOOL(hAPP(_1762116, hAPP(hAPP(_1762118, 48746 ^ [_1762108, _1762110, _1762112, _1762114, _1762116, _1762118, _1762120]), 48747 ^ [_1762108, _1762110, _1762112, _1762114, _1762116, _1762118, _1762120])))], (48749 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1762108, 48747 ^ [_1762108, _1762110, _1762112, _1762114, _1762116, _1762118, _1762120]), 48746 ^ [_1762108, _1762110, _1762112, _1762114, _1762116, _1762118, _1762120])))]], -(hBOOL(hAPP(_1762116, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1762110, _1762112, _1762120), _1762118), _1762114))))], (10337 ^ _778495) ^ [_956696, _956698, _956700, _956702, _956704] : [c_Finite__Set_Ofun__left__comm(_956696, _956698, _956700), hBOOL(hAPP(c_Finite__Set_Ofinite(_956696), _956702)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_956696, _956698, _956700, _956704, _956702), hAPP(hAPP(c_Finite__Set_Ofold(_956696, _956698, _956700), _956704), _956702))))], (20872 ^ _778495) ^ [_1152296, _1152298, _1152300] : [class_Rings_Osemiring__1(_1152296), hBOOL(hAPP(hAPP(c_member(_1152296), _1152298), c_Nat_Osemiring__1__class_ONats(_1152296))), hBOOL(hAPP(hAPP(c_member(_1152296), _1152300), c_Nat_Osemiring__1__class_ONats(_1152296))), -(hBOOL(hAPP(hAPP(c_member(_1152296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152296), _1152298), _1152300)), c_Nat_Osemiring__1__class_ONats(_1152296))))], (32142 ^ _778495) ^ [_1369569, _1369571, _1369573, _1369575, _1369577] : [class_Complete__Lattice_Ocomplete__lattice(_1369569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1369571, tc_HOL_Obool)), _1369573), _1369575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369569), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1369571, _1369569), _1369575), _1369577)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1369571, _1369569), _1369573), _1369577))))], (26622 ^ _778495) ^ [_1254772] : [c_Int_OBit1(_1254772) = c_Int_OMin, -(_1254772 = c_Int_OMin)], (31674 ^ _778495) ^ [_1357693, _1357695] : [class_Rings_Ocomm__semiring__1(_1357693), 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c_Big__Operators_Olattice__class_OSup__fin(_945645, _945649)))], (16604 ^ _778495) ^ [_1075272, _1075274, _1075276, _1075278] : [class_Fields_Olinordered__field__inverse__zero(_1075272), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075272), _1075274), _1075276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075272), c_Groups_Ozero__class_Ozero(_1075272)), _1075278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075272), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1075272), _1075274), _1075278)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1075272), _1075276), _1075278))))], (6540 ^ _778495) ^ [_884798, _884800, _884802] : [class_Orderings_Olinorder(_884798), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884798), _884800), _884802))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884798), _884802), _884800)))], (52735 ^ _778495) ^ [_1836623, _1836625] : [hBOOL(_1836623), -(hBOOL(hAPP(hAPP(c_fimplies, _1836625), _1836623)))], (36388 ^ _778495) ^ 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[hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814996), _1814994))], (51275 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814994), _1814996)))]], -(_1814994 = _1814996)], (25984 ^ _778495) ^ [_1243059, _1243061, _1243063, _1243065] : [class_Rings_Olinordered__semidom(_1243059), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243059), _1243061), _1243063)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243059), c_Groups_Ozero__class_Ozero(_1243059)), _1243061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1243065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243059), hAPP(hAPP(c_Power_Opower__class_Opower(_1243059), _1243061), _1243065)), hAPP(hAPP(c_Power_Opower__class_Opower(_1243059), _1243063), _1243065))))], (33102 ^ _778495) ^ [_1389417, _1389419, _1389421, _1389423] : [c_FunDef_Oreduction__pair(_1389417, _1389419), -(c_FunDef_Oreduction__pair(_1389421, 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_1715525] : [_1715525 = c_List_Olist_ONil(_1715523), -(hAPP(c_List_Orev(_1715523), _1715525) = c_List_Olist_ONil(_1715523))], (49652 ^ _778495) ^ [_1781789, _1781791, _1781793, _1781795] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1781789, _1781791, c_Orderings_Otop__class_Otop(tc_fun(_1781789, tc_HOL_Obool)), _1781793), _1781795) = c_Hilbert__Choice_OEps(_1781789, hAPP(hAPP(c_COMBC(_1781789, _1781791, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1781791, tc_fun(_1781791, tc_HOL_Obool), _1781789), c_fequal), _1781793)), _1781795)))], (35200 ^ _778495) ^ [_1436044, _1436046, _1436048] : [class_Orderings_Olinorder(_1436044), hAPP(_1436046, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1436044), 35205 ^ [_1436044, _1436046, _1436048]), 35206 ^ [_1436044, _1436046, _1436048])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1436044), hAPP(_1436046, 35205 ^ [_1436044, _1436046, _1436048])), hAPP(_1436046, 35206 ^ [_1436044, _1436046, _1436048])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1436044), _1436048)), -(_1436048 = c_Orderings_Obot__class_Obot(tc_fun(_1436044, tc_HOL_Obool))), -(hAPP(_1436046, c_Big__Operators_Olinorder__class_OMax(_1436044, _1436048)) = c_Big__Operators_Olinorder__class_OMax(_1436044, hAPP(c_Set_Oimage(_1436044, _1436044, _1436046), _1436048)))], (33521 ^ _778495) ^ [_1401655, _1401657, _1401659, _1401661, _1401663] : [class_Complete__Lattice_Ocomplete__lattice(_1401655), hBOOL(hAPP(hAPP(c_member(_1401657), _1401659), _1401661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401655), hAPP(_1401663, _1401659)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401657, _1401655), _1401661), _1401663))))], (45693 ^ _778495) ^ [_1696542, _1696544, _1696546] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696542)), hAPP(c_List_Ofilter(_1696542, _1696544), _1696546))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696542)), _1696546))))], (51971 ^ _778495) ^ [_1827701, _1827703, _1827705, _1827707] : [class_Rings_Oidom(_1827701), 51974 ^ _778495 : [(51975 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827701), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827701), _1827703), _1827705)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827701), _1827707), _1827705))), -(_1827705 = c_Groups_Ozero__class_Ozero(_1827701)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827701), _1827703), _1827707)))], (51985 ^ _778495) ^ [] : [51986 ^ _778495 : [(51989 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827701), _1827703), _1827707))], (51987 ^ _778495) ^ [] : [_1827705 = c_Groups_Ozero__class_Ozero(_1827701)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827701), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827701), _1827703), _1827705)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827701), _1827707), _1827705))))]]], (23348 ^ _778495) ^ [_1196966, _1196968] : [-(_1196966 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23351 ^ _778495 : [(23358 ^ _778495) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1196968, _1196966) = 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), _1196968)), _1196966) = 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), _1196968), _1196966))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23352 ^ _778495) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1196968, _1196966) = 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), _1196968)), _1196966) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1196968), _1196966)))]]], (20032 ^ _778495) ^ [_1138316, _1138318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138316)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138318))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1138316), _1138318)))], (33666 ^ _778495) ^ [_1405355, _1405357, _1405359, _1405361, _1405363, _1405365] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405355, tc_fun(_1405357, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405359, tc_fun(_1405355, tc_HOL_Obool)), _1405361), _1405363)), _1405365) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405359, tc_fun(_1405357, tc_HOL_Obool)), _1405361), hAPP(hAPP(c_COMBC(_1405359, tc_fun(_1405355, tc_fun(_1405357, tc_HOL_Obool)), tc_fun(_1405357, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405355, tc_HOL_Obool), tc_fun(tc_fun(_1405355, tc_fun(_1405357, tc_HOL_Obool)), tc_fun(_1405357, tc_HOL_Obool)), _1405359), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405355, tc_fun(_1405357, tc_HOL_Obool))), _1405363)), _1405365)))], (41987 ^ _778495) ^ [_1612025, _1612027, _1612029] : [-(c_List_Osublist(_1612025, _1612027, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1612029)) = hAPP(hAPP(c_List_Otake(_1612025), _1612029), _1612027))], (21630 ^ _778495) ^ [_1165808, _1165810] : [class_Fields_Olinordered__field__inverse__zero(_1165808), class_Int_Onumber__ring(_1165808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165808), c_Groups_Ozero__class_Ozero(_1165808)), _1165810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165808), c_Groups_Ozero__class_Ozero(_1165808)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165808), _1165810), hAPP(c_Int_Onumber__class_Onumber__of(_1165808), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (52685 ^ _778495) ^ [_1836002, _1836004] : [hBOOL(_1836002), hBOOL(_1836004), -(hBOOL(hAPP(hAPP(c_fconj, _1836002), _1836004)))], (36075 ^ _778495) ^ [_1455900, _1455902, _1455904, _1455906, _1455908, _1455910, _1455912] : [c_Equiv__Relations_Oequiv(_1455900, _1455902, _1455904), c_Equiv__Relations_Ocongruent(_1455900, tc_fun(_1455906, tc_HOL_Obool), _1455904, _1455908), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1455900, tc_fun(_1455906, tc_HOL_Obool)), _1455910), _1455908) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1455900, tc_fun(_1455906, tc_HOL_Obool)), _1455912), _1455908), hBOOL(hAPP(hAPP(c_member(tc_fun(_1455900, tc_HOL_Obool)), _1455910), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1455900), _1455902), _1455904))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1455900, tc_HOL_Obool)), _1455912), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1455900), _1455902), _1455904))), 36097 ^ _778495 : [(36101 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1455900), 36099 ^ [_1455900, _1455902, _1455904, _1455906, _1455908, _1455910, _1455912]), _1455902)))], (36103 ^ _778495) ^ [] : [-(hAPP(_1455908, 36096 ^ [_1455900, _1455902, _1455904, _1455906, _1455908, _1455910, _1455912]) = hAPP(_1455908, 36099 ^ [_1455900, _1455902, _1455904, _1455906, _1455908, _1455910, _1455912]))], (36105 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1455900, _1455900)), hAPP(hAPP(c_Product__Type_OPair(_1455900, _1455900), 36096 ^ [_1455900, _1455902, _1455904, _1455906, _1455908, _1455910, _1455912]), 36099 ^ [_1455900, _1455902, _1455904, _1455906, _1455908, _1455910, _1455912])), _1455904))], (36098 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1455900), 36096 ^ [_1455900, _1455902, _1455904, _1455906, _1455908, _1455910, _1455912]), _1455902)))]], -(_1455910 = _1455912)], (19000 ^ _778495) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (19166 ^ _778495) ^ [_1123018] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123018), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1123018)], (6206 ^ _778495) ^ [_878787, _878789, _878791] : [class_Orderings_Opreorder(_878787), _878789 = _878791, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878787), _878789), _878791)))], (7572 ^ _778495) ^ [_903772, _903774, _903776] : [class_Orderings_Oorder(_903772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903772), _903774), _903776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903772), _903776), _903774))], (9632 ^ _778495) ^ [_943412, _943414, _943416, _943418] : [class_Lattices_Osemilattice__sup(_943412), hBOOL(hAPP(c_Finite__Set_Ofinite(_943412), _943414)), hBOOL(hAPP(hAPP(c_member(_943412), _943416), _943414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943412), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_943412), _943416), _943418)), hAPP(hAPP(c_Finite__Set_Ofold(_943412, _943412, c_Lattices_Osemilattice__sup__class_Osup(_943412)), _943418), _943414))))], (25912 ^ _778495) ^ [_1241712] : [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, _1241712, 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, _1241712, 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))], (37362 ^ _778495) ^ [_1485428, _1485430, _1485432] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1485428, _1485430), _1485432), hAPP(c_COMBK(tc_fun(_1485430, tc_HOL_Obool), _1485428), c_Orderings_Obot__class_Obot(tc_fun(_1485430, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1485428, _1485430), tc_HOL_Obool)))], (9118 ^ _778495) ^ [_932511, _932513, _932515, _932517] : [class_Lattices_Osemilattice__inf(_932511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932511), _932513), _932515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932511), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932511), _932517), _932513)), _932515)))], (20378 ^ _778495) ^ [_1144562, _1144564] : [_1144562 = _1144564, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144562) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144564))], (48386 ^ _778495) ^ [_1753876, _1753878] : [class_Lazy__Sequence_Osmall__lazy(_1753876), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1753876), _1753878) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1753876), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1753876)), c_List_Olist_ONil(_1753876)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753876))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1753878)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1753876, tc_List_Olist(_1753876)), tc_List_Olist(_1753876), c_Lazy__Sequence_Oproduct(_1753876, tc_List_Olist(_1753876), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753876, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1753878), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1753876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1753878), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1753876, tc_List_Olist(_1753876), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753876))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1753876), tc_List_Olist(_1753876)), tc_fun(tc_List_Olist(_1753876), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753876))), _1753876), hAPP(c_COMBB(tc_List_Olist(_1753876), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753876)), tc_List_Olist(_1753876)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1753876)))), c_List_Olist_OCons(_1753876))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1753876)))))], (35561 ^ _778495) ^ [_1443634, _1443636, _1443638, _1443640, _1443642] : [hBOOL(hAPP(hAPP(c_member(_1443634), _1443636), hAPP(c_Relation_OImage(_1443638, _1443634, _1443640), hAPP(hAPP(c_Set_Oinsert(_1443638), _1443642), c_Orderings_Obot__class_Obot(tc_fun(_1443638, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1443638, _1443634)), hAPP(hAPP(c_Product__Type_OPair(_1443638, _1443634), _1443642), _1443636)), _1443640)))], (36919 ^ _778495) ^ [_1474572, _1474574, _1474576, _1474578, _1474580, _1474582, _1474584] : [c_Typedef_Otype__definition(_1474572, _1474574, _1474576, _1474578, _1474580), hBOOL(hAPP(hAPP(c_member(_1474574), _1474582), _1474580)), hBOOL(hAPP(hAPP(c_member(_1474574), _1474584), _1474580)), 36930 ^ _778495 : [(36937 ^ _778495) ^ [] : [_1474582 = _1474584, -(hAPP(_1474578, _1474582) = hAPP(_1474578, _1474584))], (36931 ^ _778495) ^ [] : [hAPP(_1474578, _1474582) = hAPP(_1474578, _1474584), -(_1474582 = _1474584)]]], (48907 ^ _778495) ^ [_1767570, _1767572, _1767574, _1767576] : [c_Wellfounded_Omax__extp(_1767570, _1767572, _1767574, _1767576), 48910 ^ _778495 : [(48913 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1767570), _1767576)))], (48915 ^ _778495) ^ [] : [_1767576 = c_Orderings_Obot__class_Obot(tc_fun(_1767570, tc_HOL_Obool))], (48917 ^ _778495) ^ [_1767786] : [hBOOL(hAPP(hAPP(c_member(_1767570), _1767786), _1767574)), 48921 ^ _778495 : [(48924 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1767572, _1767786), 48920 ^ [_1767570, _1767572, _1767574, _1767576, _1767786])))], (48922 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767570), 48920 ^ [_1767570, _1767572, _1767574, _1767576, _1767786]), _1767576)))]]], (48911 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1767570), _1767574)))]]], (40744 ^ _778495) ^ [_1576869, _1576871, _1576873] : [-(hAPP(c_Relation_Oconverse(_1576869, _1576871), hAPP(c_Relation_Oconverse(_1576871, _1576869), _1576873)) = _1576873)], (25108 ^ _778495) ^ [_1227324, _1227326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227324)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227326), _1227324))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227326), _1227324) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1227326), _1227324)), _1227324)))], (37410 ^ _778495) ^ [_1486903, _1486905, _1486907] : [c_Equiv__Relations_Oequiv(_1486903, _1486905, _1486907), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1486903, _1486903), tc_HOL_Obool)), _1486907), hAPP(hAPP(c_Product__Type_OSigma(_1486903, _1486903), _1486905), hAPP(c_COMBK(tc_fun(_1486903, tc_HOL_Obool), _1486903), _1486905)))))], (30285 ^ _778495) ^ [_1330225, _1330227, _1330229] : [class_Orderings_Olinorder(_1330225), 30288 ^ _778495 : [(30295 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330225), _1330227), _1330229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1330225, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1330225), _1330227)), hAPP(c_SetInterval_Oord__class_OlessThan(_1330225), _1330229))))], (30289 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1330225, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1330225), _1330227)), hAPP(c_SetInterval_Oord__class_OlessThan(_1330225), _1330229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330225), _1330227), _1330229)))]]], (2468 ^ _778495) ^ [_814830, _814832] : [_814832 = _814830, -(c_Nitpick_Ozero__frac(_814832) = c_Nitpick_Ozero__frac(_814830))], (26084 ^ _778495) ^ [_1244726, _1244728] : [26085 ^ _778495 : [(26088 ^ _778495) ^ [] : [_1244728 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26086 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1244726))]], -(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), _1244726), _1244728))))], (37396 ^ _778495) ^ [_1486484, _1486486, _1486488, _1486490, _1486492] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1486484, _1486486), _1486488), hAPP(hAPP(c_COMBS(_1486484, tc_fun(_1486486, tc_HOL_Obool), tc_fun(_1486486, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1486486, tc_HOL_Obool), tc_fun(tc_fun(_1486486, tc_HOL_Obool), tc_fun(_1486486, tc_HOL_Obool)), _1486484), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1486486, tc_HOL_Obool))), _1486490)), _1486492)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1486484, _1486486), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486484, _1486486), _1486488), _1486490)), hAPP(hAPP(c_Product__Type_OSigma(_1486484, _1486486), _1486488), _1486492)))], (34961 ^ _778495) ^ [_1432466, _1432468, _1432470, _1432472, _1432474, _1432476] : [-(_1432466 = _1432468), -(hAPP(c_Fun_Ofun__upd(_1432470, _1432472, _1432474, _1432468, _1432476), _1432466) = hAPP(_1432474, _1432466))], (35184 ^ _778495) ^ [_1435755, _1435757, _1435759] : [class_Groups_Ocomm__monoid__add(_1435755), class_Groups_Ocomm__monoid__mult(_1435755), c_Nat__Transfer_Onat__set(_1435757), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1435755), _1435759), _1435757) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1435755), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1435755, tc_Nat_Onat), _1435759), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1435757)))], (3880 ^ _778495) ^ [_836964, _836966, _836968, _836970, _836972, _836974, _836976, _836978, _836980, _836982, _836984, _836986, _836988, _836990] : [-(c_New__Random__Sequence_Opos__decr__bind(_836990, _836986, _836982, _836978, _836974, _836970, _836966) = c_New__Random__Sequence_Opos__decr__bind(_836988, _836984, _836980, _836976, _836972, _836968, _836964)), _836990 = _836988, _836986 = _836984, _836982 = _836980, _836978 = _836976, _836974 = _836972, _836970 = _836968, _836966 = _836964], (49600 ^ _778495) ^ [_1780611, _1780613, _1780615] : [c_Fun_Oinj__on(_1780611, _1780613, _1780615, c_Orderings_Otop__class_Otop(tc_fun(_1780611, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780613, _1780611, _1780611, c_Hilbert__Choice_Oinv__into(_1780611, _1780613, c_Orderings_Otop__class_Otop(tc_fun(_1780611, tc_HOL_Obool)), _1780615)), _1780615) = c_Fun_Oid(_1780611))], (36254 ^ _778495) ^ [_1460857, _1460859, _1460861, _1460863, _1460865, _1460867] : [c_Fun_Oinj__on(_1460857, _1460859, _1460861, _1460863), hAPP(_1460861, _1460865) = hAPP(_1460861, _1460867), hBOOL(hAPP(hAPP(c_member(_1460857), _1460865), _1460863)), hBOOL(hAPP(hAPP(c_member(_1460857), _1460867), _1460863)), -(_1460865 = _1460867)], (20055 ^ _778495) ^ [_1138766, _1138768] : [20056 ^ _778495 : [(20057 ^ _778495) ^ [_1138819] : [_1138768 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1138766), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138819))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1138766), _1138768)))], (21824 ^ _778495) ^ [_1169059, _1169061, _1169063] : [class_Lattices_Oboolean__algebra(_1169059), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169059), _1169061), _1169063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169059), hAPP(c_Groups_Ouminus__class_Ouminus(_1169059), _1169063)), hAPP(c_Groups_Ouminus__class_Ouminus(_1169059), _1169061))))], (26132 ^ _778495) ^ [_1245707, _1245709, _1245711, _1245713] : [class_Fields_Ofield__inverse__zero(_1245707), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1245707), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245707), _1245709), _1245711)), _1245713) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245707), hAPP(hAPP(c_Power_Opower__class_Opower(_1245707), _1245709), _1245713)), hAPP(hAPP(c_Power_Opower__class_Opower(_1245707), _1245711), _1245713)))], (32130 ^ _778495) ^ [_1369223, _1369225, _1369227, _1369229] : [class_Groups_Ocomm__monoid__add(_1369223), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369223), _1369225), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1369227), hAPP(c_Nat_OSuc, _1369229))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369223), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1369223, tc_Nat_Onat), _1369225), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1369227, _1369229)))], (45839 ^ _778495) ^ [_1700395, _1700397] : [-(c_Random_Oselect__weight(_1700395, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1700395), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1700395, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1700395, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1700395)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1700397)) = c_Random_Oselect__weight(_1700395, _1700397))], (4416 ^ _778495) ^ [_845624, _845626, _845628, _845630, _845632, _845634] : [-(c_Lazy__Sequence_Oanamorph(_845634, _845630, _845626) = c_Lazy__Sequence_Oanamorph(_845632, _845628, _845624)), _845634 = _845632, _845630 = _845628, _845626 = _845624], (4030 ^ _778495) ^ [_839529, _839531, _839533, _839535, _839537, _839539, _839541, _839543] : [-(c_New__DSequence_Opos__bind(_839543, _839539, _839535, _839531) = c_New__DSequence_Opos__bind(_839541, _839537, _839533, _839529)), _839543 = _839541, _839539 = _839537, _839535 = _839533, _839531 = _839529], (24541 ^ _778495) ^ [_1217890, _1217892, _1217894] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217890), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1217892), _1217894)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217890), _1217892)), _1217894))], (52335 ^ _778495) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (30133 ^ _778495) ^ [_1327389, _1327391, _1327393] : [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), _1327389), _1327391))), -(hBOOL(hAPP(hAPP(_1327393, _1327389), _1327391))), 30140 ^ _778495 : [(30143 ^ _778495) ^ [] : [-(30139 ^ [_1327389, _1327391, _1327393] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1327393, 30139 ^ [_1327389, _1327391, _1327393]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 30138 ^ [_1327389, _1327391, _1327393], 30139 ^ [_1327389, _1327391, _1327393]))))], (30149 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1327393, 30138 ^ [_1327389, _1327391, _1327393]), 30139 ^ [_1327389, _1327391, _1327393]))], (30141 ^ _778495) ^ [] : [-(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), 30138 ^ [_1327389, _1327391, _1327393]), 30139 ^ [_1327389, _1327391, _1327393]))))]]], (26670 ^ _778495) ^ [_1255475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255475), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1255475)), c_Int_OMin)))], (17094 ^ _778495) ^ [_1084078, _1084080, _1084082, _1084084] : [class_Fields_Olinordered__field(_1084078), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084078), c_Groups_Ozero__class_Ozero(_1084078)), _1084080)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084078), _1084082), _1084080)), _1084084)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084078), _1084082), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1084078), _1084084), _1084080))))], (45314 ^ _778495) ^ [_1687864, _1687866] : [_1687864 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1687866, _1687864, c_List_Olist_ONil(_1687866)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687866)), c_List_Olist_ONil(_1687866)), c_List_Olist_ONil(tc_List_Olist(_1687866))))], (38395 ^ _778495) ^ [_1518117, _1518119, _1518121, _1518123] : [class_Groups_Ocomm__monoid__mult(_1518117), c_Fun_Oinj__on(_1518119, _1518117, _1518121, _1518123), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1518119, _1518117), _1518121), _1518123) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1518117, _1518117), c_Fun_Oid(_1518117)), hAPP(c_Set_Oimage(_1518119, _1518117, _1518121), _1518123)))], (42614 ^ _778495) ^ [_1628077, _1628079, _1628081] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628077), tc_List_Olist(_1628077))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628077), tc_List_Olist(_1628077)), c_List_Olist_ONil(_1628077)), _1628079)), c_List_Olistrel(_1628077, _1628081))), -(_1628079 = c_List_Olist_ONil(_1628077))], (49856 ^ _778495) ^ [_1786664, _1786666] : [49858 ^ _778495 : [(49861 ^ _778495) ^ [] : [hBOOL(hAPP(_1786664, hAPP(c_Code__Numeral_Oof__nat, 49857 ^ [_1786664, _1786666])))], (49859 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49857 ^ [_1786664, _1786666]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1786664, _1786666)))], (52599 ^ _778495) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (50375 ^ _778495) ^ [_1796997, _1796999, _1797001, _1797003] : [c_Equiv__Relations_Oequivp(_1796997, _1796999), -(c_Quotient_OBabs(_1796997, _1797001, c_Quotient_ORespects(_1796997, _1796999), _1797003) = _1797003)], (11994 ^ _778495) ^ [_988038, _988040] : [11995 ^ _778495 : [(11996 ^ _778495) ^ [_988091] : [_988040 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988038), _988091))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988038), _988040)))], (19806 ^ _778495) ^ [_1134281, _1134283, _1134285, _1134287, _1134289, _1134291] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1134281), _1134283)), _1134285) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1134287), _1134289)), _1134291), 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), _1134287), _1134289)), _1134291)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1134285), _1134281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1134287), _1134281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1134289), _1134283)))], (39410 ^ _778495) ^ [_1545178, _1545180, _1545182, _1545184, _1545186, _1545188, _1545190] : [hAPP(c_Fun_Ocomp(_1545178, _1545180, _1545182, _1545184), _1545186) = _1545188, -(hAPP(_1545184, hAPP(_1545186, _1545190)) = hAPP(_1545188, _1545190))], (22096 ^ _778495) ^ [_1173787] : [c_Int_OPls = c_Int_OBit0(_1173787), -(c_Int_OPls = _1173787)], (5763 ^ _778495) ^ [_869801, _869803, _869805, _869807] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_869801, _869803, hAPP(hAPP(c_Set_Oinsert(_869801), _869805), c_Orderings_Obot__class_Obot(tc_fun(_869801, tc_HOL_Obool)))), _869807)), -(_869805 = _869807)], (22454 ^ _778495) ^ [_1179970, _1179972, _1179974] : [class_Groups_Oordered__ab__group__add__abs(_1179970), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179970), _1179972), _1179974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179970), hAPP(c_Groups_Ouminus__class_Ouminus(_1179970), _1179972)), _1179974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179970), hAPP(c_Groups_Oabs__class_Oabs(_1179970), _1179972)), _1179974)))], (31506 ^ _778495) ^ [_1353928, _1353930, _1353932] : [class_Orderings_Olinorder(_1353928), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353928), _1353930)), 31513 ^ _778495 : [(31520 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353928, tc_HOL_Obool)), _1353930), hAPP(hAPP(c_Set_Oinsert(_1353928), _1353932), c_Orderings_Obot__class_Obot(tc_fun(_1353928, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353928, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1353928, hAPP(hAPP(c_Set_Oinsert(_1353928), _1353932), _1353930)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353928), _1353932), c_Big__Operators_Olinorder__class_OMax(_1353928, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353928, tc_HOL_Obool)), _1353930), hAPP(hAPP(c_Set_Oinsert(_1353928), _1353932), c_Orderings_Obot__class_Obot(tc_fun(_1353928, tc_HOL_Obool)))))))], (31514 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353928, tc_HOL_Obool)), _1353930), hAPP(hAPP(c_Set_Oinsert(_1353928), _1353932), c_Orderings_Obot__class_Obot(tc_fun(_1353928, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353928, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1353928, hAPP(hAPP(c_Set_Oinsert(_1353928), _1353932), _1353930)) = _1353932)]]], (42353 ^ _778495) ^ [_1622184, _1622186, _1622188, _1622190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622184), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622186)), _1622188))), -(hAPP(hAPP(c_List_Onth(_1622186), hAPP(hAPP(c_List_Olist__update(_1622186, _1622188), _1622184), _1622190)), _1622184) = _1622190)], (7420 ^ _778495) ^ [_901821, _901823, _901825] : [class_Orderings_Olinorder(_901821), 7423 ^ _778495 : [(7424 ^ _778495) ^ [] : [-(_901823 = _901825), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901821), _901823), _901825))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901821), _901825), _901823)))], (7434 ^ _778495) ^ [] : [7435 ^ _778495 : [(7438 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901821), _901825), _901823))], (7436 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901821), _901823), _901825))]], _901823 = _901825]]], (27077 ^ _778495) ^ [_1262097, _1262099, _1262101] : [class_Rings_Olinordered__idom(_1262097), 27080 ^ _778495 : [(27087 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1262099), _1262101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262097), hAPP(c_Int_Oring__1__class_Oof__int(_1262097), _1262099)), hAPP(c_Int_Oring__1__class_Oof__int(_1262097), _1262101))))], (27081 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262097), hAPP(c_Int_Oring__1__class_Oof__int(_1262097), _1262099)), hAPP(c_Int_Oring__1__class_Oof__int(_1262097), _1262101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1262099), _1262101)))]]], (9286 ^ _778495) ^ [_935734, _935736, _935738, _935740] : [hBOOL(hAPP(hAPP(c_member(_935734), _935736), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_935734, tc_HOL_Obool)), _935738), _935740))), -(hBOOL(hAPP(hAPP(c_member(_935734), _935736), _935738)))], (30005 ^ _778495) ^ [_1324716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1324716)), 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), _1324716)) = 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), _1324716))))))], (28639 ^ _778495) ^ [_1297468, _1297470] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1297468), _1297470)), -(hAPP(c_Finite__Set_Ocard(_1297468), _1297470) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1297468, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1297468), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1297470))], (34426 ^ _778495) ^ [_1421500, _1421502, _1421504, _1421506] : [hAPP(c_Set_Oimage(_1421500, _1421502, _1421504), _1421506) = c_Orderings_Obot__class_Obot(tc_fun(_1421502, tc_HOL_Obool)), -(_1421506 = c_Orderings_Obot__class_Obot(tc_fun(_1421500, tc_HOL_Obool)))], (1678 ^ _778495) ^ [_802498, _802500] : [-(class_Groups_Ocomm__monoid__mult(_802498)), _802500 = _802498, class_Groups_Ocomm__monoid__mult(_802500)], (51517 ^ _778495) ^ [_1819284, _1819286, _1819288] : [class_Rings_Ocomm__ring__1(_1819284), 51520 ^ _778495 : [(51527 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819284), _1819286), _1819288)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819284), hAPP(c_Groups_Ouminus__class_Ouminus(_1819284), _1819286)), _1819288)))], (51521 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819284), hAPP(c_Groups_Ouminus__class_Ouminus(_1819284), _1819286)), _1819288)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819284), _1819286), _1819288)))]]], (32612 ^ _778495) ^ [_1379301, _1379303, _1379305, _1379307, _1379309, _1379311] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1379301, tc_HOL_Obool), tc_fun(_1379301, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1379301, tc_HOL_Obool), tc_fun(_1379301, tc_HOL_Obool)), _1379303), _1379305)), c_Wellfounded_Omax__ext(_1379301, _1379307))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1379301, tc_HOL_Obool), tc_fun(_1379301, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1379301, tc_HOL_Obool), tc_fun(_1379301, tc_HOL_Obool)), _1379309), _1379311)), c_Wellfounded_Omax__ext(_1379301, _1379307))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1379301, tc_HOL_Obool), tc_fun(_1379301, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1379301, tc_HOL_Obool), tc_fun(_1379301, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379301, tc_HOL_Obool)), _1379303), _1379309)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379301, tc_HOL_Obool)), _1379305), _1379311))), c_Wellfounded_Omax__ext(_1379301, _1379307))))], (360 ^ _778495) ^ [_784003, _784005] : [-(c_Nitpick_Ounknown(_784003)), _784005 = _784003, c_Nitpick_Ounknown(_784005)], (9352 ^ _778495) ^ [_937102, _937104, _937106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937102, tc_HOL_Obool)), _937104), _937106)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937102, tc_HOL_Obool)), _937106), _937104) = _937104)], (27945 ^ _778495) ^ [_1277051] : [c_Nat__Transfer_Ois__nat(_1277051), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277051)))], (34943 ^ _778495) ^ [_1432148, _1432150, _1432152, _1432154, _1432156] : [c_Fun_Ofun__upd(_1432148, _1432150, _1432152, _1432154, _1432156) = _1432152, -(hAPP(_1432152, _1432154) = _1432156)], (44790 ^ _778495) ^ [_1675844, _1675846] : [-(c_Random_Oselect(_1675844, _1675846) = 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(_1675844, 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(_1675844)), _1675846)))), hAPP(hAPP(c_COMBB(_1675844, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675844, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1675844, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1675844, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1675844), _1675846)), c_Code__Numeral_Onat__of))))], (49019 ^ _778495) ^ [_1769925, _1769927] : [c_Relation_Otrans(_1769925, _1769927), -(c_Relation_Otrans(_1769925, hAPP(c_Relation_Oconverse(_1769925, _1769925), _1769927)))], (47857 ^ _778495) ^ [_1742723, _1742725] : [-(c_FunDef_Ois__measure(_1742723, _1742725))], (12823 ^ _778495) ^ [_1006342, _1006344, _1006346, _1006348, _1006350, _1006352, _1006354] : [c_Big__Operators_Ocomm__monoid__big(_1006342, _1006344, _1006346, _1006348, _1006350), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1006344), _1006352))), -(hAPP(hAPP(_1006350, _1006354), _1006352) = _1006348)], (11889 ^ _778495) ^ [_985481, _985483] : [class_Rings_Ocomm__semiring__1(_985481), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985481), _985483), _985483) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985481), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985481), c_Groups_Oone__class_Oone(_985481)), c_Groups_Oone__class_Oone(_985481))), _985483))], (9004 ^ _778495) ^ [_930399, _930401, _930403, _930405, _930407, _930409, _930411] : [c_Finite__Set_Ofolding__image__simple__idem(_930399, _930401, _930403, _930405, _930407, _930409), -(hAPP(hAPP(_930403, _930411), _930411) = _930411)], (5839 ^ _778495) ^ [_871422, _871424, _871426, _871428, _871430, _871432] : [c_Finite__Set_Ofolding__image__idem(_871422, _871424, _871426, _871428, _871430), -(hAPP(hAPP(_871426, _871432), _871432) = _871432)], (42900 ^ _778495) ^ [_1633420, _1633422, _1633424] : [-(hBOOL(hAPP(hAPP(c_member(_1633420), _1633422), hAPP(c_List_Oset(_1633420), _1633424)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633420)), c_List_Oremove1(_1633420, _1633422, _1633424)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633420)), _1633424))], (35668 ^ _778495) ^ [_1446620, _1446622, _1446624] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446620), hAPP(hAPP(c_Set_Oinsert(_1446620), _1446622), c_Orderings_Obot__class_Obot(tc_fun(_1446620, tc_HOL_Obool)))), _1446624) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1446620, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446620, _1446620, _1446624), hAPP(hAPP(c_Set_Oinsert(_1446620), _1446622), c_Orderings_Obot__class_Obot(tc_fun(_1446620, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446620, tc_HOL_Obool), tc_HOL_Obool))))], (37520 ^ _778495) ^ [_1489725, _1489727, _1489729, _1489731] : [_1489725 = c_Orderings_Obot__class_Obot(tc_fun(_1489727, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1489727, _1489729), _1489729, c_Product__Type_Osnd(_1489727, _1489729)), hAPP(hAPP(c_Product__Type_OSigma(_1489727, _1489729), _1489725), hAPP(c_COMBK(tc_fun(_1489729, tc_HOL_Obool), _1489727), _1489731))) = c_Orderings_Obot__class_Obot(tc_fun(_1489729, tc_HOL_Obool)))], (10975 ^ _778495) ^ [_967289, _967291] : [10976 ^ _778495 : [(10979 ^ _778495) ^ [] : [_967289 = _967291], (10977 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967289), _967291))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967289), _967291)))], (23318 ^ _778495) ^ [_1196362, _1196364, _1196366] : [class_Divides_Osemiring__div(_1196362), -(c_Divides_Odiv__class_Omod(_1196362, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196362), _1196364), _1196366), _1196364) = c_Groups_Ozero__class_Ozero(_1196362))], (5464 ^ _778495) ^ [_862156, _862158] : [_862158 = _862156, -(c_Groups_Ozero__class_Ozero(_862158) = c_Groups_Ozero__class_Ozero(_862156))], (33118 ^ _778495) ^ [_1389731, _1389733, _1389735, _1389737, _1389739, _1389741] : [hBOOL(hAPP(hAPP(c_member(_1389731), _1389733), _1389735)), hBOOL(hAPP(hAPP(c_member(_1389737), _1389739), hAPP(_1389741, _1389733))), -(hBOOL(hAPP(hAPP(c_member(_1389737), _1389739), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389731, tc_fun(_1389737, tc_HOL_Obool)), _1389735), _1389741))))], (52261 ^ _778495) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (304 ^ _778495) ^ [_783223, _783225] : [-(c_Nat__Transfer_Ois__nat(_783223)), _783225 = _783223, c_Nat__Transfer_Ois__nat(_783225)], (44728 ^ _778495) ^ [_1674462, _1674464, _1674466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1674462), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674464), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1674464)), _1674466)))), -(hBOOL(hAPP(hAPP(c_member(_1674464), hAPP(c_Random_Opick(_1674464, _1674466), _1674462)), hAPP(c_List_Oset(_1674464), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674464), _1674464), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1674464)), _1674466)))))], (28785 ^ _778495) ^ [_1300690, _1300692, _1300694, _1300696, _1300698, _1300700] : [class_Groups_Ocomm__monoid__mult(_1300690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300692), _1300694)), 28792 ^ _778495 : [(28799 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1300692), _1300696), _1300694))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1300692, _1300690), hAPP(hAPP(c_COMBC(_1300692, _1300690, _1300690), hAPP(hAPP(c_COMBS(_1300692, _1300690, tc_fun(_1300690, _1300690)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1300690, tc_fun(_1300690, _1300690)), _1300692), c_If(_1300690)), hAPP(hAPP(c_COMBC(_1300692, _1300692, tc_HOL_Obool), c_fequal), _1300696))), _1300698)), _1300700)), _1300694) = hAPP(hAPP(c_Power_Opower__class_Opower(_1300690), _1300700), hAPP(c_Finite__Set_Ocard(_1300692), _1300694)))], (28793 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1300692), _1300696), _1300694)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1300692, _1300690), hAPP(hAPP(c_COMBC(_1300692, _1300690, _1300690), hAPP(hAPP(c_COMBS(_1300692, _1300690, tc_fun(_1300690, _1300690)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1300690, tc_fun(_1300690, _1300690)), _1300692), c_If(_1300690)), hAPP(hAPP(c_COMBC(_1300692, _1300692, tc_HOL_Obool), c_fequal), _1300696))), _1300698)), _1300700)), _1300694) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300690), hAPP(_1300698, _1300696)), hAPP(hAPP(c_Power_Opower__class_Opower(_1300690), _1300700), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1300692), _1300694)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (38731 ^ _778495) ^ [] : [-(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)))))], (52445 ^ _778495) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (44087 ^ _778495) ^ [_1660808, _1660810, _1660812] : [class_Orderings_Olinorder(_1660808), -(c_List_Oremove1(_1660808, _1660810, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660808, _1660808, c_COMBI(_1660808)), _1660810), _1660812)) = _1660812)], (33278 ^ _778495) ^ [_1394152, _1394154, _1394156, _1394158, _1394160] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394152, tc_HOL_Obool)), _1394154), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394156, tc_fun(_1394152, tc_HOL_Obool)), _1394158), _1394160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394156, tc_fun(_1394152, tc_HOL_Obool)), _1394158), hAPP(hAPP(c_COMBB(tc_fun(_1394152, tc_HOL_Obool), tc_fun(_1394152, tc_HOL_Obool), _1394156), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394152, tc_HOL_Obool)), _1394154)), _1394160)))], (49759 ^ _778495) ^ [_1784196, _1784198, _1784200, _1784202, _1784204] : [c_Fun_Oinj__on(_1784196, _1784198, _1784200, c_Orderings_Otop__class_Otop(tc_fun(_1784196, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1784198, _1784202, _1784196, hAPP(c_Fun_Ocomp(_1784196, _1784202, _1784198, _1784204), c_Hilbert__Choice_Oinv__into(_1784196, _1784198, c_Orderings_Otop__class_Otop(tc_fun(_1784196, tc_HOL_Obool)), _1784200))), _1784200) = _1784204)], (45695 ^ _778495) ^ [_1696594, _1696596, _1696598, _1696600] : [-(hAPP(c_List_Ofilter(_1696594, _1696596), hAPP(c_List_Ofilter(_1696594, _1696598), _1696600)) = hAPP(c_List_Ofilter(_1696594, hAPP(hAPP(c_COMBS(_1696594, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1696594), c_fconj), _1696598)), _1696596)), _1696600))], (2184 ^ _778495) ^ [_810412, _810414, _810416, _810418] : [-(c_Nat__Transfer_Otsub(_810418, _810414) = c_Nat__Transfer_Otsub(_810416, _810412)), _810418 = _810416, _810414 = _810412], (22628 ^ _778495) ^ [_1183009, _1183011] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1183009)), c_Int_OBit1(_1183011)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1183009), _1183011)))], (1408 ^ _778495) ^ [_799123, _799125] : [-(class_Lattices_Obounded__lattice__top(_799123)), _799125 = _799123, class_Lattices_Obounded__lattice__top(_799125)], (46937 ^ _778495) ^ [_1722413, _1722415] : [-(_1722413 = c_List_Olist_ONil(_1722415)), hBOOL(hAPP(c_List_Odistinct(_1722415), _1722413)), -(c_List_OtakeWhile(_1722415, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722415), c_fNot), hAPP(hAPP(c_COMBC(_1722415, _1722415, tc_HOL_Obool), c_fequal), c_List_Olast(_1722415, _1722413))), _1722413) = c_List_Obutlast(_1722415, _1722413))], (35296 ^ _778495) ^ [_1437780, _1437782] : [class_Orderings_Olinorder(_1437780), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1437780, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1437780), _1437782)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1437780), _1437782))], (52245 ^ _778495) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (44813 ^ _778495) ^ [_1676414] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1676414)) = _1676414)], (4982 ^ _778495) ^ [_854527, _854529, _854531, _854533, _854535, _854537, _854539, _854541] : [-(c_Hilbert__Choice_Oinv__into(_854541, _854537, _854533, _854529) = c_Hilbert__Choice_Oinv__into(_854539, _854535, _854531, _854527)), _854541 = _854539, _854537 = _854535, _854533 = _854531, _854529 = _854527], (5687 ^ _778495) ^ [_868339, _868341, _868343] : [c_Orderings_Obot__class_Obot(tc_fun(_868339, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_868339), _868341), _868343)], (44560 ^ _778495) ^ [_1670890, _1670892] : [class_Groups_Oordered__ab__group__add__abs(_1670890), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670890), hAPP(c_Groups_Oabs__class_Oabs(_1670890), hAPP(c_List_Omonoid__add__class_Olistsum(_1670890), _1670892))), hAPP(c_List_Omonoid__add__class_Olistsum(_1670890), hAPP(hAPP(c_List_Omap(_1670890, _1670890), c_Groups_Oabs__class_Oabs(_1670890)), _1670892)))))], (31950 ^ _778495) ^ [_1365711, _1365713, _1365715, _1365717] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365711, tc_fun(_1365713, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1365711, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1365713, tc_HOL_Obool), tc_fun(_1365713, tc_HOL_Obool), _1365711), hAPP(c_COMBC(_1365713, tc_fun(_1365713, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365713))), _1365715)), _1365717)), -(hBOOL(hAPP(hAPP(c_member(_1365713), _1365717), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365711, tc_fun(_1365713, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1365711, tc_HOL_Obool))), _1365715))))], (22148 ^ _778495) ^ [_1174695, _1174697] : [class_Groups_Oordered__ab__group__add__abs(_1174695), -(hAPP(c_Groups_Oabs__class_Oabs(_1174695), hAPP(c_Groups_Ouminus__class_Ouminus(_1174695), _1174697)) = hAPP(c_Groups_Oabs__class_Oabs(_1174695), _1174697))], (28489 ^ _778495) ^ [_1293465, _1293467, _1293469] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293465, tc_Nat_Onat), _1293467), _1293469) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293465, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1293465), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1293467)), _1293469)))], (52569 ^ _778495) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (950 ^ _778495) ^ [_792818, _792820, _792822, _792824, _792826, _792828] : [-(c_Relation_Orefl__on(_792826, _792822, _792818)), c_Relation_Orefl__on(_792828, _792824, _792820), _792828 = _792826, _792824 = _792822, _792820 = _792818], (44811 ^ _778495) ^ [_1676385] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1676385)) = _1676385)], (43482 ^ _778495) ^ [_1647336, _1647338] : [-(hAPP(c_List_Orotate1(_1647336), _1647338) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1647336), _1647336, c_List_Olist_ONil(_1647336), hAPP(hAPP(c_COMBB(tc_List_Olist(_1647336), tc_fun(tc_List_Olist(_1647336), tc_List_Olist(_1647336)), _1647336), hAPP(c_COMBC(tc_List_Olist(_1647336), tc_List_Olist(_1647336), tc_List_Olist(_1647336)), c_List_Oappend(_1647336))), hAPP(hAPP(c_COMBC(_1647336, tc_List_Olist(_1647336), tc_List_Olist(_1647336)), c_List_Olist_OCons(_1647336)), c_List_Olist_ONil(_1647336)))), _1647338))], (44873 ^ _778495) ^ [_1677432] : [-(hAPP(c_Code__Numeral_Onat__of, _1677432) = c_Code__Numeral_Onat__of__aux(_1677432, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29186 ^ _778495) ^ [_1309237] : [-(c_Divides_Odivmod__nat(_1309237, 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)), _1309237))], (52643 ^ _778495) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (18438 ^ _778495) ^ [_1109401, _1109403, _1109405, _1109407] : [class_Fields_Olinordered__field__inverse__zero(_1109401), class_Int_Onumber(_1109401), 18445 ^ _778495 : [(18446 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109401), _1109403), _1109405)), hAPP(c_Int_Onumber__class_Onumber__of(_1109401), _1109407))), 18449 ^ _778495 : [(18456 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), c_Groups_Ozero__class_Ozero(_1109401)), _1109405))), 18459 ^ _778495 : [(18466 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), _1109405), c_Groups_Ozero__class_Ozero(_1109401)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), c_Groups_Ozero__class_Ozero(_1109401)), hAPP(c_Int_Onumber__class_Onumber__of(_1109401), _1109407))))], (18460 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), _1109405), c_Groups_Ozero__class_Ozero(_1109401))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109401), hAPP(c_Int_Onumber__class_Onumber__of(_1109401), _1109407)), _1109405)), _1109403)))]]], (18450 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), c_Groups_Ozero__class_Ozero(_1109401)), _1109405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), _1109403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109401), hAPP(c_Int_Onumber__class_Onumber__of(_1109401), _1109407)), _1109405))))]]], (18472 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109401), _1109403), _1109405)), hAPP(c_Int_Onumber__class_Onumber__of(_1109401), _1109407)))), 18475 ^ _778495 : [(18478 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), _1109403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109401), hAPP(c_Int_Onumber__class_Onumber__of(_1109401), _1109407)), _1109405)))], (18476 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), c_Groups_Ozero__class_Ozero(_1109401)), _1109405)))]], 18479 ^ _778495 : [(18482 ^ _778495) ^ [] : [18483 ^ _778495 : [(18486 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109401), hAPP(c_Int_Onumber__class_Onumber__of(_1109401), _1109407)), _1109405)), _1109403))], (18484 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), _1109405), c_Groups_Ozero__class_Ozero(_1109401))))]], 18487 ^ _778495 : [(18490 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), c_Groups_Ozero__class_Ozero(_1109401)), hAPP(c_Int_Onumber__class_Onumber__of(_1109401), _1109407)))], (18488 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), _1109405), c_Groups_Ozero__class_Ozero(_1109401)))]]], (18480 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109401), c_Groups_Ozero__class_Ozero(_1109401)), _1109405))]]]]], (37134 ^ _778495) ^ [_1479381, _1479383, _1479385, _1479387, _1479389] : [hBOOL(hAPP(hAPP(c_member(_1479385), hAPP(_1479387, _1479383)), _1479389)), -(hBOOL(hAPP(hAPP(c_member(_1479381), _1479383), hAPP(c_Set_Ovimage(_1479381, _1479385, _1479387), _1479389))))], (43427 ^ _778495) ^ [_1645734, _1645736, _1645738, _1645740, _1645742, _1645744] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645734), tc_List_Olist(_1645734))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645734), tc_List_Olist(_1645734)), hAPP(hAPP(c_List_Oappend(_1645734), _1645736), hAPP(hAPP(c_List_Olist_OCons(_1645734), _1645738), c_List_Olist_ONil(_1645734)))), hAPP(hAPP(c_List_Oappend(_1645734), _1645740), hAPP(hAPP(c_List_Olist_OCons(_1645734), _1645742), c_List_Olist_ONil(_1645734))))), c_List_Olistrel1(_1645734, _1645744))), 43432 ^ _778495 : [(43435 ^ _778495) ^ [] : [-(_1645738 = _1645742)], (43433 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645734), tc_List_Olist(_1645734))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645734), tc_List_Olist(_1645734)), _1645736), _1645740)), c_List_Olistrel1(_1645734, _1645744))))]], 43436 ^ _778495 : [(43439 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1645734, _1645734)), hAPP(hAPP(c_Product__Type_OPair(_1645734, _1645734), _1645738), _1645742)), _1645744)))], (43437 ^ _778495) ^ [] : [-(_1645736 = _1645740)]]], (34683 ^ _778495) ^ [_1427013, _1427015] : [-(hAPP(c_Relation_OField(_1427013), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1427013, _1427013), tc_HOL_Obool), _1427015)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1427013, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1427013, _1427013), tc_HOL_Obool), tc_fun(_1427013, tc_HOL_Obool), c_Relation_OField(_1427013)), _1427015)))], (21236 ^ _778495) ^ [_1158811, _1158813, _1158815] : [class_Groups_Oordered__ab__group__add__abs(_1158811), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158811), hAPP(c_Groups_Oabs__class_Oabs(_1158811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158811), _1158813), _1158815))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158811), hAPP(c_Groups_Oabs__class_Oabs(_1158811), _1158813)), hAPP(c_Groups_Oabs__class_Oabs(_1158811), _1158815)))))], (25032 ^ _778495) ^ [_1226147] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226147))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1226147)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28531 ^ _778495) ^ [_1294571, _1294573, _1294575, _1294577, _1294579] : [class_Groups_Ocomm__monoid__mult(_1294571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294573), _1294575)), 28538 ^ _778495 : [(28545 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1294573), _1294577), _1294575))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294573, _1294571), hAPP(hAPP(c_COMBC(_1294573, _1294571, _1294571), hAPP(hAPP(c_COMBS(_1294573, _1294571, tc_fun(_1294571, _1294571)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1294571, tc_fun(_1294571, _1294571)), _1294573), c_If(_1294571)), hAPP(hAPP(c_COMBC(_1294573, _1294573, tc_HOL_Obool), c_fequal), _1294577))), _1294579)), c_Groups_Oone__class_Oone(_1294571))), _1294575) = c_Groups_Oone__class_Oone(_1294571))], (28539 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1294573), _1294577), _1294575)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294573, _1294571), hAPP(hAPP(c_COMBC(_1294573, _1294571, _1294571), hAPP(hAPP(c_COMBS(_1294573, _1294571, tc_fun(_1294571, _1294571)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1294571, tc_fun(_1294571, _1294571)), _1294573), c_If(_1294571)), hAPP(hAPP(c_COMBC(_1294573, _1294573, tc_HOL_Obool), c_fequal), _1294577))), _1294579)), c_Groups_Oone__class_Oone(_1294571))), _1294575) = hAPP(_1294579, _1294577))]]], (13105 ^ _778495) ^ [_1012171, _1012173] : [class_Rings_Ocomm__semiring__1(_1012171), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012171), _1012173), c_Groups_Ozero__class_Ozero(_1012171)) = _1012173)], (37903 ^ _778495) ^ [_1500017, _1500019] : [-(hAPP(c_Set_OCollect(_1500017), hAPP(hAPP(c_COMBC(_1500017, _1500017, tc_HOL_Obool), c_fequal), _1500019)) = hAPP(hAPP(c_Set_Oinsert(_1500017), _1500019), c_Orderings_Obot__class_Obot(tc_fun(_1500017, tc_HOL_Obool))))], (25062 ^ _778495) ^ [_1226574, _1226576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1226574), hAPP(c_Int_Onat, _1226576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1226574)), _1226576)))], (22518 ^ _778495) ^ [_1181094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1181094)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181094), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52235 ^ _778495) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (7512 ^ _778495) ^ [_902854, _902856, _902858] : [class_Orderings_Oorder(_902854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902854), _902856), _902858)), _902856 = _902858], (9276 ^ _778495) ^ [_935531, _935533, _935535, _935537] : [-(hBOOL(hAPP(hAPP(c_member(_935531), _935533), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_935531, tc_HOL_Obool)), _935535), _935537)))), hBOOL(hAPP(hAPP(c_member(_935531), _935533), _935535)), hBOOL(hAPP(hAPP(c_member(_935531), _935533), _935537))], (36180 ^ _778495) ^ [_1459109, _1459111, _1459113] : [hBOOL(hAPP(hAPP(c_member(_1459109), _1459113), c_Wellfounded_Oacc(_1459109, _1459111))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1459109, hAPP(hAPP(c_COMBC(_1459109, tc_fun(tc_prod(_1459109, _1459109), tc_HOL_Obool), tc_fun(_1459109, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459109, tc_fun(tc_fun(tc_prod(_1459109, _1459109), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1459109, _1459109), tc_HOL_Obool), tc_fun(_1459109, tc_HOL_Obool)), _1459109), c_COMBC(_1459109, tc_fun(tc_prod(_1459109, _1459109), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459109, tc_prod(_1459109, _1459109)), tc_fun(_1459109, tc_fun(tc_fun(tc_prod(_1459109, _1459109), tc_HOL_Obool), tc_HOL_Obool)), _1459109), hAPP(c_COMBB(tc_prod(_1459109, _1459109), tc_fun(tc_fun(tc_prod(_1459109, _1459109), tc_HOL_Obool), tc_HOL_Obool), _1459109), c_member(tc_prod(_1459109, _1459109)))), c_Product__Type_OPair(_1459109, _1459109)))), _1459111)), _1459113)))], (13354 ^ _778495) ^ [_1015918, _1015920] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015918), _1015920) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 13357 ^ _778495 : [(13360 ^ _778495) ^ [] : [-(_1015920 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13358 ^ _778495) ^ [] : [-(_1015918 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (33280 ^ _778495) ^ [_1394242, _1394244, _1394246, _1394248, _1394250] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394242, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394244, tc_fun(_1394242, tc_HOL_Obool)), _1394246), _1394248)), _1394250) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394244, tc_fun(_1394242, tc_HOL_Obool)), _1394246), hAPP(hAPP(c_COMBC(_1394244, tc_fun(_1394242, tc_HOL_Obool), tc_fun(_1394242, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1394242, tc_HOL_Obool), tc_fun(tc_fun(_1394242, tc_HOL_Obool), tc_fun(_1394242, tc_HOL_Obool)), _1394244), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394242, tc_HOL_Obool))), _1394248)), _1394250)))], (4832 ^ _778495) ^ [_852150, _852152] : [_852152 = _852150, -(c_HOL_OEx(_852152) = c_HOL_OEx(_852150))], (25900 ^ _778495) ^ [_1241378, _1241380, _1241382] : [class_Groups_Omonoid__mult(_1241378), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1241378), _1241380), 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)))), _1241382))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241378), _1241380), hAPP(hAPP(c_Power_Opower__class_Opower(_1241378), hAPP(hAPP(c_Power_Opower__class_Opower(_1241378), _1241380), _1241382)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (31246 ^ _778495) ^ [_1349380, _1349382, _1349384] : [class_Orderings_Olinorder(_1349380), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349380), _1349382)), -(_1349384 = c_Orderings_Obot__class_Obot(tc_fun(_1349380, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1349380, tc_HOL_Obool)), _1349384), _1349382)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349380), c_Big__Operators_Olattice_OSup__fin(_1349380, c_Orderings_Oord__class_Omax(_1349380), _1349384)), c_Big__Operators_Olattice_OSup__fin(_1349380, c_Orderings_Oord__class_Omax(_1349380), _1349382)) = c_Big__Operators_Olattice_OSup__fin(_1349380, c_Orderings_Oord__class_Omax(_1349380), _1349382))], (31837 ^ _778495) ^ [_1361781, _1361783, _1361785, _1361787] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1361781, tc_HOL_Obool), tc_fun(_1361783, tc_HOL_Obool)), _1361785), hAPP(hAPP(c_COMBC(tc_fun(_1361781, tc_HOL_Obool), tc_fun(_1361781, tc_fun(_1361783, tc_HOL_Obool)), tc_fun(_1361783, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361781, tc_fun(_1361783, tc_HOL_Obool))), _1361787)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361781, tc_fun(_1361783, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1361781, tc_HOL_Obool), _1361785)), _1361787))], (42878 ^ _778495) ^ [_1632894, _1632896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632894)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632896))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632894), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632896)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632894)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632894)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632896))))], (36780 ^ _778495) ^ [_1471881, _1471883, _1471885, _1471887, _1471889, _1471891, _1471893, _1471895] : [c_Fun_Oinj__on(_1471881, _1471883, _1471885, _1471887), 36786 ^ _778495 : [(36789 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471881, tc_HOL_Obool)), hAPP(_1471893, 36785 ^ [_1471881, _1471883, _1471885, _1471887, _1471889, _1471891, _1471893, _1471895])), _1471887))], (36787 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471889), 36785 ^ [_1471881, _1471883, _1471885, _1471887, _1471889, _1471891, _1471893, _1471895]), _1471891)))]], hBOOL(hAPP(hAPP(c_member(_1471889), _1471895), _1471891)), -(hAPP(c_Set_Oimage(_1471881, _1471883, _1471885), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1471889, tc_fun(_1471881, tc_HOL_Obool)), _1471891), _1471893)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1471889, tc_fun(_1471883, tc_HOL_Obool)), _1471891), hAPP(hAPP(c_COMBB(tc_fun(_1471881, tc_HOL_Obool), tc_fun(_1471883, tc_HOL_Obool), _1471889), c_Set_Oimage(_1471881, _1471883, _1471885)), _1471893)))], (49515 ^ _778495) ^ [_1779017, _1779019, _1779021] : [c_Equiv__Relations_Oequiv(_1779017, _1779019, _1779021), 49518 ^ _778495 : [(49523 ^ _778495) ^ [] : [-(c_Relation_Otrans(_1779017, _1779021))], (49521 ^ _778495) ^ [] : [-(c_Relation_Osym(_1779017, _1779021))], (49519 ^ _778495) ^ [] : [-(c_Relation_Orefl__on(_1779017, _1779019, _1779021))]]], (40726 ^ _778495) ^ [_1576542, _1576544, _1576546] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576544, _1576542)), _1576546)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576542, _1576544)), hAPP(c_Relation_Oconverse(_1576544, _1576542), _1576546))))], (27862 ^ _778495) ^ [_1275665, _1275667, _1275669] : [class_Complete__Lattice_Ocomplete__lattice(_1275665), class_Orderings_Olinorder(_1275665), 27869 ^ _778495 : [(27879 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275665), c_Complete__Lattice_OInf__class_OInf(_1275665, _1275667)), _1275669))), 27880 ^ _778495 : [(27881 ^ _778495) ^ [_1275971] : [hBOOL(hAPP(hAPP(c_member(_1275665), _1275971), _1275667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275665), _1275971), _1275669))]]], (27870 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275665), c_Complete__Lattice_OInf__class_OInf(_1275665, _1275667)), _1275669)), 27874 ^ _778495 : [(27877 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275665), 27873 ^ [_1275665, _1275667, _1275669]), _1275669)))], (27875 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1275665), 27873 ^ [_1275665, _1275667, _1275669]), _1275667)))]]]]], (29214 ^ _778495) ^ [_1309809, _1309811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309809)), 29217 ^ _778495 : [(29224 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309811))), 29227 ^ _778495 : [(29234 ^ _778495) ^ [] : [-(_1309809 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1309809, _1309811) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1309809), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1309811))))], (29228 ^ _778495) ^ [] : [_1309809 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1309809, _1309811) = 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)))]]], (29218 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309811)), -(c_Divides_Odivmod__int(_1309809, _1309811) = c_Divides_OposDivAlg(_1309809, _1309811))]]], (29523 ^ _778495) ^ [_1315649, _1315651, _1315653, _1315655, _1315657, _1315659] : [_1315649 = _1315651, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1315653, _1315655, _1315657), _1315659), _1315649) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1315653, _1315655, _1315657), _1315659), _1315651))], (26798 ^ _778495) ^ [_1257616, _1257618] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1257616), _1257618)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1257616, tc_HOL_Obool)), hAPP(c_Set_OPow(_1257616), _1257618))))], (31962 ^ _778495) ^ [_1366155, _1366157, _1366159, _1366161, _1366163] : [hBOOL(hAPP(hAPP(c_member(_1366155), _1366157), _1366159)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366161, tc_HOL_Obool)), hAPP(_1366163, _1366157)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1366155, tc_fun(_1366161, tc_HOL_Obool)), _1366159), _1366163)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1366155, tc_fun(_1366161, tc_HOL_Obool)), _1366159), _1366163))], (43287 ^ _778495) ^ [_1642026, _1642028, _1642030] : [-(_1642026 = c_List_Olist_ONil(_1642028)), -(c_List_Obutlast(_1642028, hAPP(hAPP(c_List_Oappend(_1642028), _1642030), _1642026)) = hAPP(hAPP(c_List_Oappend(_1642028), _1642030), c_List_Obutlast(_1642028, _1642026)))], (44031 ^ _778495) ^ [_1659575, _1659577, _1659579, _1659581] : [class_Orderings_Olinorder(_1659575), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659577, _1659575, _1659579), _1659581), c_List_Olist_ONil(_1659577)) = hAPP(hAPP(c_List_Olist_OCons(_1659577), _1659581), c_List_Olist_ONil(_1659577)))], (52465 ^ _778495) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (43822 ^ _778495) ^ [_1654982, _1654984] : [-(c_List_Orotate(_1654982, _1654984) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1654982), tc_List_Olist(_1654982)), _1654984), c_List_Orotate1(_1654982)))], (48782 ^ _778495) ^ [_1763198, _1763200, _1763202] : [-(c_List_Olist__ex(_1763198, _1763202, _1763200)), 48783 ^ _778495 : [(48784 ^ _778495) ^ [_1763255] : [hBOOL(hAPP(hAPP(c_member(_1763198), _1763255), hAPP(c_List_Oset(_1763198), _1763200))), hBOOL(hAPP(_1763202, _1763255))]]], (6068 ^ _778495) ^ [_875667, _875669, _875671, _875673] : [-(hBOOL(hAPP(hAPP(c_member(_875667), _875669), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_875667, tc_HOL_Obool)), _875671), _875673)))), hBOOL(hAPP(hAPP(c_member(_875667), _875669), _875671)), -(hBOOL(hAPP(hAPP(c_member(_875667), _875669), _875673)))], (41648 ^ _778495) ^ [_1602599, _1602601, _1602603, _1602605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602599), tc_List_Olist(_1602599))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602599), tc_List_Olist(_1602599)), _1602601), _1602603)), c_List_Olistrel(_1602599, _1602605))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602599), tc_List_Olist(_1602599))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602599), tc_List_Olist(_1602599)), _1602601), _1602603)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1602599), c_List_Olistrel1(_1602599, _1602605)))))], (4686 ^ _778495) ^ [_849845, _849847] : [_849847 = _849845, -(c_Set_OBex(_849847) = c_Set_OBex(_849845))], (5520 ^ _778495) ^ [_862964, _862966] : [_862966 = _862964, -(tc_Option_Ooption(_862966) = tc_Option_Ooption(_862964))], (28659 ^ _778495) ^ [_1297849, _1297851] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1297849))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1297851)), hAPP(c_Int_Onat, _1297849)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1297851), _1297849)), 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)))], (38643 ^ _778495) ^ [_1526744, _1526746] : [-(c_HOL_OThe(_1526744, hAPP(c_fequal, _1526746)) = _1526746)], (37909 ^ _778495) ^ [_1500219, _1500221] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1500219), hAPP(c_Set_OCollect(_1500219), _1500221))), 37912 ^ _778495 : [(37919 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1500219), c_Orderings_Otop__class_Otop(tc_fun(_1500219, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1500219), hAPP(c_Set_OCollect(_1500219), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1500219), c_fNot), _1500221)))))], (37913 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1500219), hAPP(c_Set_OCollect(_1500219), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1500219), c_fNot), _1500221)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1500219), c_Orderings_Otop__class_Otop(tc_fun(_1500219, tc_HOL_Obool)))))]]], (26744 ^ _778495) ^ [_1256628] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1256628) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1256628))], (47904 ^ _778495) ^ [_1743620, _1743622, _1743624, _1743626] : [c_List_Olist__all(_1743620, _1743622, hAPP(hAPP(c_List_Olist_OCons(_1743620), _1743624), _1743626)), 47907 ^ _778495 : [(47910 ^ _778495) ^ [] : [-(c_List_Olist__all(_1743620, _1743622, _1743626))], (47908 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1743622, _1743624)))]]], (37424 ^ _778495) ^ [_1487413, _1487415] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1487413, _1487415), c_Orderings_Otop__class_Otop(tc_fun(_1487413, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1487415, tc_HOL_Obool), _1487413), c_Orderings_Otop__class_Otop(tc_fun(_1487415, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1487413, _1487415), tc_HOL_Obool)))], (35102 ^ _778495) ^ [_1434535] : [c_Nat__Transfer_Onat__set(_1434535), 35105 ^ _778495 : [(35112 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1434535))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1434535)))], (35106 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1434535)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1434535))))]]], (8076 ^ _778495) ^ [_911424, _911426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_911424, tc_HOL_Obool)), _911426), c_Orderings_Obot__class_Obot(tc_fun(_911424, tc_HOL_Obool))))], (24509 ^ _778495) ^ [_1217123, _1217125, _1217127] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1217123), _1217125)), _1217127) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1217123), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217125), _1217127))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1217123), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1217125, _1217127))), _1217127)))], (31690 ^ _778495) ^ [_1358109, _1358111, _1358113, _1358115, _1358117, _1358119] : [hBOOL(hAPP(hAPP(c_member(_1358109), _1358111), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358113, tc_fun(_1358109, tc_HOL_Obool)), _1358115), _1358117))), hBOOL(hAPP(hAPP(c_member(_1358113), _1358119), _1358115)), -(hBOOL(hAPP(hAPP(c_member(_1358109), _1358111), hAPP(_1358117, _1358119))))], (37686 ^ _778495) ^ [_1494614, _1494616, _1494618, _1494620, _1494622, _1494624, _1494626] : [-(hAPP(c_Product__Type_Ofst(_1494614, _1494616), hAPP(c_Product__Type_Omap__pair(_1494618, _1494614, _1494620, _1494616, _1494622, _1494624), _1494626)) = hAPP(_1494622, hAPP(c_Product__Type_Ofst(_1494618, _1494620), _1494626)))], (33433 ^ _778495) ^ [_1398919, _1398921, _1398923, _1398925, _1398927] : [_1398919 = c_Orderings_Obot__class_Obot(tc_fun(_1398921, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398921, tc_fun(_1398923, tc_HOL_Obool)), _1398919), hAPP(hAPP(c_COMBB(tc_fun(_1398923, tc_HOL_Obool), tc_fun(_1398923, tc_HOL_Obool), _1398921), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398923, tc_HOL_Obool)), _1398925)), _1398927)) = c_Orderings_Obot__class_Obot(tc_fun(_1398923, tc_HOL_Obool)))], (48064 ^ _778495) ^ [_1746887, _1746889, _1746891, _1746893, _1746895] : [-(hAPP(c_New__DSequence_Oneg__bind(_1746887, _1746889, _1746891, _1746893), _1746895) = c_Lazy__Sequence_Ohb__bind(_1746887, _1746889, hAPP(_1746891, _1746895), hAPP(hAPP(c_COMBC(_1746887, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746889))), _1746893), _1746895)))], (43902 ^ _778495) ^ [_1656727, _1656729, _1656731, _1656733, _1656735, _1656737] : [-(hAPP(c_List_Ofoldl(_1656727, _1656729, _1656731, _1656733), hAPP(hAPP(c_List_Oappend(_1656729), _1656735), _1656737)) = hAPP(c_List_Ofoldl(_1656727, _1656729, _1656731, hAPP(c_List_Ofoldl(_1656727, _1656729, _1656731, _1656733), _1656735)), _1656737))], (50130 ^ _778495) ^ [_1792163, _1792165, _1792167] : [-(c_Fun_Obij__betw(_1792163, _1792165, _1792167, c_Orderings_Otop__class_Otop(tc_fun(_1792163, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792165, tc_HOL_Obool)))), c_Fun_Oinj__on(_1792163, _1792165, _1792167, c_Orderings_Otop__class_Otop(tc_fun(_1792163, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1792163, _1792165, _1792167), c_Orderings_Otop__class_Otop(tc_fun(_1792163, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792165, tc_HOL_Obool))], (14313 ^ _778495) ^ [_1032798, _1032800, _1032802, _1032804] : [class_Rings_Olinordered__semiring__strict(_1032798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032798), _1032800), _1032802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032798), c_Groups_Ozero__class_Ozero(_1032798)), _1032804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032798), _1032804), _1032800)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032798), _1032804), _1032802))))], (1348 ^ _778495) ^ [_798373, _798375] : [-(class_Rings_Oring__1(_798373)), _798375 = _798373, class_Rings_Oring__1(_798375)], (52355 ^ _778495) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (28377 ^ _778495) ^ [_1289634, _1289636, _1289638, _1289640] : [class_Groups_Oordered__ab__group__add__abs(_1289634), -(hAPP(c_Groups_Oabs__class_Oabs(_1289634), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289636, _1289634), hAPP(hAPP(c_COMBB(_1289634, _1289634, _1289636), c_Groups_Oabs__class_Oabs(_1289634)), _1289638)), _1289640)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289636, _1289634), hAPP(hAPP(c_COMBB(_1289634, _1289634, _1289636), c_Groups_Oabs__class_Oabs(_1289634)), _1289638)), _1289640))], (2126 ^ _778495) ^ [_809491, _809493] : [_809493 = _809491, -(c_Int_Oring__1__class_OInts(_809493) = c_Int_Oring__1__class_OInts(_809491))], (50102 ^ _778495) ^ [_1791574, _1791576, _1791578] : [c_Fun_Obij__betw(_1791574, _1791576, _1791578, c_Orderings_Otop__class_Otop(tc_fun(_1791574, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1791576, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1791574, _1791576, _1791578), c_Orderings_Otop__class_Otop(tc_fun(_1791574, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1791576, tc_HOL_Obool)))], (44494 ^ _778495) ^ [_1669410, _1669412, _1669414, _1669416, _1669418, _1669420] : [-(hAPP(hAPP(c_List_Omap(_1669410, _1669412), _1669414), hAPP(hAPP(c_List_Omap(_1669416, _1669410), _1669418), _1669420)) = hAPP(hAPP(c_List_Omap(_1669416, _1669412), hAPP(c_Fun_Ocomp(_1669410, _1669412, _1669416, _1669414), _1669418)), _1669420))], (42714 ^ _778495) ^ [_1629800, _1629802, _1629804] : [-(hAPP(hAPP(c_List_Ozip(_1629800, _1629802), c_List_Olist_ONil(_1629800)), _1629804) = c_List_Olist_ONil(tc_prod(_1629800, _1629802)))], (35636 ^ _778495) ^ [_1445905, _1445907, _1445909] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1445905), _1445907), _1445909) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1445905, tc_HOL_Obool), tc_HOL_Obool)), -(_1445907 = c_Orderings_Obot__class_Obot(tc_fun(_1445905, tc_HOL_Obool)))], (39778 ^ _778495) ^ [_1553472, _1553474, _1553476, _1553478, _1553480, _1553482] : [class_Groups_Ocomm__monoid__add(_1553472), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553474), _1553476)), 39788 ^ _778495 : [(39789 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553474), 39787 ^ [_1553472, _1553474, _1553476, _1553478, _1553480, _1553482]), _1553476)))], (39794 ^ _778495) ^ [] : [39787 ^ [_1553472, _1553474, _1553476, _1553478, _1553480, _1553482] = 39790 ^ [_1553472, _1553474, _1553476, _1553478, _1553480, _1553482]], (39798 ^ _778495) ^ [] : [hAPP(_1553480, hAPP(_1553478, 39787 ^ [_1553472, _1553474, _1553476, _1553478, _1553480, _1553482])) = c_Groups_Ozero__class_Ozero(_1553472)], (39796 ^ _778495) ^ [] : [-(hAPP(_1553478, 39787 ^ [_1553472, _1553474, _1553476, _1553478, _1553480, _1553482]) = hAPP(_1553478, 39790 ^ [_1553472, _1553474, _1553476, _1553478, _1553480, _1553482]))], (39792 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553474), 39790 ^ [_1553472, _1553474, _1553476, _1553478, _1553480, _1553482]), _1553476)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1553482, _1553472), _1553480), hAPP(c_Set_Oimage(_1553474, _1553482, _1553478), _1553476)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1553474, _1553472), hAPP(c_Fun_Ocomp(_1553482, _1553472, _1553474, _1553480), _1553478)), _1553476))], (48432 ^ _778495) ^ [_1755014, _1755016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755014), _1755016)), -(c_Lazy__Sequence_Osmall__lazy_H(_1755014, _1755016) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (38552 ^ _778495) ^ [_1523282, _1523284, _1523286, _1523288] : [hBOOL(hAPP(c_Predicate_ORangeP(_1523282, _1523284, hAPP(hAPP(c_COMBC(_1523282, tc_fun(tc_prod(_1523282, _1523284), tc_HOL_Obool), tc_fun(_1523284, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523284, tc_fun(tc_fun(tc_prod(_1523282, _1523284), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1523282, _1523284), tc_HOL_Obool), tc_fun(_1523284, tc_HOL_Obool)), _1523282), c_COMBC(_1523284, tc_fun(tc_prod(_1523282, _1523284), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523284, tc_prod(_1523282, _1523284)), tc_fun(_1523284, tc_fun(tc_fun(tc_prod(_1523282, _1523284), tc_HOL_Obool), tc_HOL_Obool)), _1523282), hAPP(c_COMBB(tc_prod(_1523282, _1523284), tc_fun(tc_fun(tc_prod(_1523282, _1523284), tc_HOL_Obool), tc_HOL_Obool), _1523284), c_member(tc_prod(_1523282, _1523284)))), c_Product__Type_OPair(_1523282, _1523284)))), _1523286)), _1523288)), -(hBOOL(hAPP(hAPP(c_member(_1523284), _1523288), hAPP(c_Relation_ORange(_1523282, _1523284), _1523286))))], (52301 ^ _778495) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (47433 ^ _778495) ^ [_1733633, _1733635] : [class_Orderings_Olinorder(_1733633), hBOOL(hAPP(c_Finite__Set_Ofinite(_1733633), _1733635)), 47441 ^ _778495 : [(47444 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1733633, 47440 ^ [_1733633, _1733635]))], (47446 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1733633), 47440 ^ [_1733633, _1733635])))], (47448 ^ _778495) ^ [_1733959] : [-(_1733959 = 47440 ^ [_1733633, _1733635]), hAPP(c_List_Oset(_1733633), _1733959) = _1733635, c_List_Olinorder__class_Osorted(_1733633, _1733959), hBOOL(hAPP(c_List_Odistinct(_1733633), _1733959))], (47442 ^ _778495) ^ [] : [-(hAPP(c_List_Oset(_1733633), 47440 ^ [_1733633, _1733635]) = _1733635)]]], (18122 ^ _778495) ^ [_1103584, _1103586, _1103588, _1103590] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103584), hAPP(c_Int_Onumber__class_Onumber__of(_1103584), _1103586)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103584), _1103588), _1103590)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103584), hAPP(c_Int_Onumber__class_Onumber__of(_1103584), _1103586)), _1103588)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103584), hAPP(c_Int_Onumber__class_Onumber__of(_1103584), _1103586)), _1103590))), class_Int_Onumber(_1103584), class_Rings_Osemiring(_1103584)], (7728 ^ _778495) ^ [_906268, _906270, _906272, _906274] : [-(c_Nitpick_Ofold__graph_H(_906268, _906270, _906272, _906274, c_Orderings_Obot__class_Obot(tc_fun(_906268, tc_HOL_Obool)), _906274))], (35662 ^ _778495) ^ [_1446449, _1446451, _1446453, _1446455] : [hBOOL(hAPP(hAPP(c_member(_1446449), _1446451), _1446453)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1446449, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446449, _1446449, _1446455), hAPP(hAPP(c_Set_Oinsert(_1446449), _1446451), c_Orderings_Obot__class_Obot(tc_fun(_1446449, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446449), _1446453), _1446455))))], (35526 ^ _778495) ^ [_1442646, _1442648, _1442650] : [-(hAPP(c_Relation_OImage(_1442646, _1442646, c_Relation_OId__on(_1442646, _1442648)), _1442650) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442646, tc_HOL_Obool)), _1442648), _1442650))], (49945 ^ _778495) ^ [_1788625, _1788627, _1788629, _1788631] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1788625, _1788627, _1788629), c_Product__Type_Ocurry(_1788625, _1788627, _1788629, _1788631)) = _1788631)], (25074 ^ _778495) ^ [_1226790] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1226790))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42826 ^ _778495) ^ [_1631759, _1631761, _1631763] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631759), tc_List_Olist(_1631759))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631759), tc_List_Olist(_1631759)), c_List_Olist_ONil(_1631759)), _1631761)), c_List_Olistrel1(_1631759, _1631763)))], (13312 ^ _778495) ^ [_1015368] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1015368)], (41670 ^ _778495) ^ [_1603543, _1603545, _1603547, _1603549] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603543), tc_List_Olist(_1603543))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603543), tc_List_Olist(_1603543)), _1603547), _1603549)), c_List_Olistrel(_1603543, _1603545))), -(c_List_Olistrelp(_1603543, hAPP(hAPP(c_COMBC(_1603543, tc_fun(tc_prod(_1603543, _1603543), tc_HOL_Obool), tc_fun(_1603543, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603543, tc_fun(tc_fun(tc_prod(_1603543, _1603543), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1603543, _1603543), tc_HOL_Obool), tc_fun(_1603543, tc_HOL_Obool)), _1603543), c_COMBC(_1603543, tc_fun(tc_prod(_1603543, _1603543), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603543, tc_prod(_1603543, _1603543)), tc_fun(_1603543, tc_fun(tc_fun(tc_prod(_1603543, _1603543), tc_HOL_Obool), tc_HOL_Obool)), _1603543), hAPP(c_COMBB(tc_prod(_1603543, _1603543), tc_fun(tc_fun(tc_prod(_1603543, _1603543), tc_HOL_Obool), tc_HOL_Obool), _1603543), c_member(tc_prod(_1603543, _1603543)))), c_Product__Type_OPair(_1603543, _1603543)))), _1603545), _1603547, _1603549))], (2936 ^ _778495) ^ [_822074, _822076] : [_822076 = _822074, -(c_Nitpick_ORep__Frac(_822076) = c_Nitpick_ORep__Frac(_822074))], (40810 ^ _778495) ^ [_1578664, _1578666, _1578668, _1578670] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578664, _1578664)), hAPP(hAPP(c_Product__Type_OPair(_1578664, _1578664), _1578666), _1578668)), c_Transitive__Closure_Ortrancl(_1578664, hAPP(c_Relation_Oconverse(_1578664, _1578664), _1578670)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578664, _1578664)), hAPP(hAPP(c_Product__Type_OPair(_1578664, _1578664), _1578668), _1578666)), c_Transitive__Closure_Ortrancl(_1578664, _1578670))))], (13129 ^ _778495) ^ [_1012551, _1012553] : [class_Groups_Olinordered__ab__group__add(_1012551), 13132 ^ _778495 : [(13139 ^ _778495) ^ [] : [_1012553 = c_Groups_Ozero__class_Ozero(_1012551), -(c_Groups_Ozero__class_Ozero(_1012551) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012551), _1012553), _1012553))], (13133 ^ _778495) ^ [] : [c_Groups_Ozero__class_Ozero(_1012551) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012551), _1012553), _1012553), -(_1012553 = c_Groups_Ozero__class_Ozero(_1012551))]]], (33762 ^ _778495) ^ [_1407016, _1407018] : [33770 ^ _778495 : [(33773 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1407018, 33769 ^ [_1407016, _1407018])))], (33771 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 33769 ^ [_1407016, _1407018]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407016))))]], 33763 ^ _778495 : [(33764 ^ _778495) ^ [_1407084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1407084), _1407016)), hBOOL(hAPP(_1407018, _1407084))]]], (832 ^ _778495) ^ [_791055, _791057, _791059, _791061] : [-(c_Relation_Otrans(_791059, _791055)), c_Relation_Otrans(_791061, _791057), _791061 = _791059, _791057 = _791055], (7388 ^ _778495) ^ [_901305] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_901305), c_Orderings_Obot__class_Obot(tc_fun(_901305, tc_HOL_Obool)))))], (31812 ^ _778495) ^ [_1360947, _1360949, _1360951, _1360953, _1360955] : [31814 ^ _778495 : [(31817 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360947, tc_HOL_Obool)), _1360949), hAPP(_1360955, 31813 ^ [_1360947, _1360949, _1360951, _1360953, _1360955])))], (31815 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1360951), 31813 ^ [_1360947, _1360949, _1360951, _1360953, _1360955]), _1360953)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360947, tc_HOL_Obool)), _1360949), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1360951, tc_fun(_1360947, tc_HOL_Obool)), _1360953), _1360955))))], (34164 ^ _778495) ^ [_1415086, _1415088, _1415090] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1415086, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1415088)), _1415090) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415086, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1415086, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1415088)), _1415090)), hAPP(_1415090, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (30429 ^ _778495) ^ [_1333331, _1333333, _1333335, _1333337, _1333339, _1333341] : [hBOOL(hAPP(hAPP(c_member(_1333331), _1333333), c_SetInterval_Oord_OatLeastLessThan(_1333331, _1333335, _1333337, _1333339, _1333341))), 30432 ^ _778495 : [(30435 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1333337, _1333333), _1333341)))], (30433 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1333335, _1333339), _1333333)))]]], (22244 ^ _778495) ^ [_1176337, _1176339] : [class_Groups_Oordered__ab__group__add(_1176337), 22247 ^ _778495 : [(22254 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176337), _1176339), c_Groups_Ozero__class_Ozero(_1176337))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176337), c_Groups_Ozero__class_Ozero(_1176337)), hAPP(c_Groups_Ouminus__class_Ouminus(_1176337), _1176339))))], (22248 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176337), c_Groups_Ozero__class_Ozero(_1176337)), hAPP(c_Groups_Ouminus__class_Ouminus(_1176337), _1176339))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176337), _1176339), c_Groups_Ozero__class_Ozero(_1176337))))]]], (28079 ^ _778495) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (25481 ^ _778495) ^ [_1233740, _1233742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233742)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1233740)), hAPP(c_Int_Onat, _1233742)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1233740, _1233742)))], (10777 ^ _778495) ^ [_964065, _964067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964065), _964067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964065), hAPP(c_Nat_OSuc, _964067))))], (10927 ^ _778495) ^ [_966633, _966635] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966633), _966635))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966635)), _966633)))], (40539 ^ _778495) ^ [_1572381, _1572383, _1572385, _1572387] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572381, _1572381)), hAPP(hAPP(c_Product__Type_OPair(_1572381, _1572381), _1572383), _1572385)), c_Transitive__Closure_Ortrancl(_1572381, _1572387)))), 40540 ^ _778495 : [(40543 ^ _778495) ^ [] : [-(_1572383 = _1572385), hBOOL(hAPP(hAPP(c_member(tc_prod(_1572381, _1572381)), hAPP(hAPP(c_Product__Type_OPair(_1572381, _1572381), _1572383), _1572385)), c_Transitive__Closure_Otrancl(_1572381, _1572387)))], (40541 ^ _778495) ^ [] : [_1572383 = _1572385]]], (6194 ^ _778495) ^ [_878589, _878591, _878593] : [_878589 = _878591, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878593, tc_HOL_Obool)), _878589), _878591)))], (1138 ^ _778495) ^ [_795748, _795750] : [-(class_Rings_Olinordered__semiring__1__strict(_795748)), _795750 = _795748, class_Rings_Olinordered__semiring__1__strict(_795750)], (638 ^ _778495) ^ [_788132, _788134, _788136, _788138, _788140, _788142, _788144, _788146, _788148, _788150] : [-(c_List_Olist__all2(_788148, _788144, _788140, _788136, _788132)), c_List_Olist__all2(_788150, _788146, _788142, _788138, _788134), _788150 = _788148, _788146 = _788144, _788142 = _788140, _788138 = _788136, _788134 = _788132], (10815 ^ _778495) ^ [_964697, _964699, _964701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964699), _964701)), -(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, _964697)), _964699)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _964697)), _964701))))], (22044 ^ _778495) ^ [_1172862, _1172864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1172862)), c_Int_OBit0(_1172864))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1172862), _1172864)))], (47666 ^ _778495) ^ [_1738834, _1738836, _1738838] : [c_List_Olist__ex(_1738834, _1738836, _1738838), 47670 ^ _778495 : [(47673 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1738836, hAPP(hAPP(c_List_Onth(_1738834), _1738838), 47669 ^ [_1738834, _1738836, _1738838]))))], (47671 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47669 ^ [_1738834, _1738836, _1738838]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738834)), _1738838))))]]], (48280 ^ _778495) ^ [_1752021, _1752023, _1752025, _1752027, _1752029] : [-(c_List_Oreplicate(_1752021, _1752023, _1752025) = c_List_Oreplicate(_1752021, _1752027, _1752029)), _1752023 = _1752027, 48285 ^ _778495 : [(48288 ^ _778495) ^ [] : [_1752025 = _1752029], (48286 ^ _778495) ^ [] : [_1752023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (8242 ^ _778495) ^ [_914480, _914482, _914484, _914486, _914488] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_914480, _914482, _914484, _914486, c_Orderings_Obot__class_Obot(tc_fun(_914480, tc_HOL_Obool))), _914488)), -(_914488 = _914486)], (46506 ^ _778495) ^ [_1713270, _1713272, _1713274, _1713276] : [class_Orderings_Olinorder(_1713270), c_List_Olinorder__class_Osorted(_1713270, _1713272), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713274), _1713276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713276), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713270)), _1713272))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713270), hAPP(hAPP(c_List_Onth(_1713270), _1713272), _1713274)), hAPP(hAPP(c_List_Onth(_1713270), _1713272), _1713276))))], (20038 ^ _778495) ^ [_1138421, _1138423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1138421), _1138423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138421)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138423))))], (37853 ^ _778495) ^ [_1498757, _1498759, _1498761] : [-(hAPP(hAPP(c_Set_Oinsert(_1498757), _1498759), _1498761) = hAPP(c_Set_OCollect(_1498757), hAPP(hAPP(c_COMBS(_1498757, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498757), c_fdisj), hAPP(hAPP(c_COMBC(_1498757, _1498757, tc_HOL_Obool), c_fequal), _1498759))), hAPP(hAPP(c_COMBC(_1498757, tc_fun(_1498757, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498757)), _1498761))))], (44496 ^ _778495) ^ [_1669478, _1669480, _1669482, _1669484, _1669486, _1669488] : [-(hAPP(hAPP(c_List_Omap(_1669478, _1669480), _1669482), hAPP(hAPP(c_List_Omap(_1669484, _1669478), _1669486), _1669488)) = hAPP(hAPP(c_List_Omap(_1669484, _1669480), hAPP(c_Fun_Ocomp(_1669478, _1669480, _1669484, _1669482), _1669486)), _1669488))], (17814 ^ _778495) ^ [_1097905, _1097907, _1097909] : [class_Orderings_Olinorder(_1097905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097905), _1097907), _1097909)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1097905), _1097907), _1097909) = _1097907)], (6518 ^ _778495) ^ [_884350, _884352, _884354, _884356, _884358] : [class_Orderings_Oord(_884350), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884352, _884350)), _884354), _884356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884350), hAPP(_884354, _884358)), hAPP(_884356, _884358))))], (28403 ^ _778495) ^ [_1290318, _1290320, _1290322, _1290324, _1290326] : [class_Groups_Ocomm__monoid__add(_1290318), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1290320, _1290318), hAPP(hAPP(c_COMBS(_1290320, _1290318, _1290318), hAPP(hAPP(c_COMBB(_1290318, tc_fun(_1290318, _1290318), _1290320), c_Groups_Oplus__class_Oplus(_1290318)), _1290322)), _1290324)), _1290326) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1290318), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1290320, _1290318), _1290322), _1290326)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1290320, _1290318), _1290324), _1290326)))], (41219 ^ _778495) ^ [_1589751, _1589753, _1589755, _1589757] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589751, _1589751)), hAPP(hAPP(c_Product__Type_OPair(_1589751, _1589751), _1589753), _1589755)), c_Transitive__Closure_Otrancl(_1589751, _1589757))), 41223 ^ _778495 : [(41226 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589751, _1589751)), hAPP(hAPP(c_Product__Type_OPair(_1589751, _1589751), 41222 ^ [_1589751, _1589753, _1589755, _1589757]), _1589755)), _1589757)))], (41224 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589751, _1589751)), hAPP(hAPP(c_Product__Type_OPair(_1589751, _1589751), _1589753), 41222 ^ [_1589751, _1589753, _1589755, _1589757])), c_Transitive__Closure_Ortrancl(_1589751, _1589757))))]]], (7620 ^ _778495) ^ [_904567, _904569, _904571, _904573] : [class_Orderings_Oord(_904567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904567), _904569), _904571)), _904571 = _904573, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904567), _904569), _904573)))], (43840 ^ _778495) ^ [_1655377, _1655379, _1655381] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655377, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655379)), _1655381)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1655379, _1655377), _1655381) = _1655381)], (29356 ^ _778495) ^ [_1312353, _1312355] : [_1312353 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1312353, _1312355) = 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)))], (35001 ^ _778495) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (29886 ^ _778495) ^ [_1322121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1322121)), 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), _1322121)) = 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), _1322121))))))], (26962 ^ _778495) ^ [_1260327, _1260329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1260327), _1260329)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1260327), _1260329) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (19326 ^ _778495) ^ [_1125715, _1125717, _1125719] : [class_Orderings_Olinorder(_1125715), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125715), _1125717)), hBOOL(hAPP(hAPP(c_member(_1125715), _1125719), _1125717)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1125715), _1125719), c_Big__Operators_Olinorder__class_OMin(_1125715, _1125717)) = c_Big__Operators_Olinorder__class_OMin(_1125715, _1125717))], (6442 ^ _778495) ^ [_882825, _882827, _882829] : [class_Orderings_Oorder(_882825), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882825), _882827), _882829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882825), _882829), _882827)), -(_882829 = _882827)], (9210 ^ _778495) ^ [_934112, _934114, _934116, _934118] : [class_Lattices_Osemilattice__inf(_934112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934112), _934114), _934116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934112), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934112), _934118), _934114)), _934116)))], (47058 ^ _778495) ^ [_1724933, _1724935, _1724937, _1724939, _1724941] : [c_List_OdropWhile(_1724933, _1724935, _1724937) = hAPP(hAPP(c_List_Olist_OCons(_1724933), _1724939), _1724941), 47061 ^ _778495 : [(47064 ^ _778495) ^ [] : [hBOOL(hAPP(_1724935, _1724939))], (47062 ^ _778495) ^ [] : [-(_1724937 = hAPP(hAPP(c_List_Oappend(_1724933), c_List_OtakeWhile(_1724933, _1724935, _1724937)), hAPP(hAPP(c_List_Olist_OCons(_1724933), _1724939), _1724941)))]]], (25399 ^ _778495) ^ [_1232376, _1232378] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232376) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1232378), 25402 ^ _778495 : [(25405 ^ _778495) ^ [] : [-(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), _1232378))))], (25403 ^ _778495) ^ [] : [-(_1232376 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1232378)))]]], (42932 ^ _778495) ^ [_1634055, _1634057, _1634059, _1634061, _1634063, _1634065] : [-(hAPP(c_List_Olist_Olist__case(_1634055, _1634057, _1634059, _1634061), hAPP(hAPP(c_List_Olist_OCons(_1634057), _1634063), _1634065)) = hAPP(hAPP(_1634061, _1634063), _1634065))], (26878 ^ _778495) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (4104 ^ _778495) ^ [_840730, _840732] : [_840732 = _840730, -(c_New__Random__Sequence_Opos__single(_840732) = c_New__Random__Sequence_Opos__single(_840730))], (30360 ^ _778495) ^ [_1331698] : [30362 ^ _778495 : [(30365 ^ _778495) ^ [_1331808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 30361 ^ [_1331698, _1331808]), _1331808))], (30363 ^ _778495) ^ [_1331774] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30361 ^ [_1331698, _1331774]), _1331698)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1331698)))], (45947 ^ _778495) ^ [_1702890, _1702892] : [45948 ^ _778495 : [(45951 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702892), _1702890))], (45949 ^ _778495) ^ [] : [_1702892 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1702890, _1702892) = c_List_Olist_ONil(tc_Nat_Onat))], (30891 ^ _778495) ^ [_1342624, _1342626] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1342624)), hAPP(c_Nat_OSuc, _1342626)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1342624), _1342626)))], (50507 ^ _778495) ^ [_1801789, _1801791, _1801793] : [-(c_Lazy__Sequence_Oflat(_1801789, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1801789), _1801791, _1801793)) = c_Lazy__Sequence_Oappend(_1801789, _1801791, c_Lazy__Sequence_Oflat(_1801789, _1801793)))], (52547 ^ _778495) ^ [_1834523, _1834525] : [-(class_Nat_Osize(tc_prod(_1834523, _1834525)))], (24673 ^ _778495) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23949 ^ _778495) ^ [_1207152, _1207154, _1207156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1207152, tc_HOL_Obool)), _1207154), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1207152, tc_HOL_Obool)), _1207156))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1207152, tc_HOL_Obool)), _1207154), _1207156) = c_Orderings_Obot__class_Obot(tc_fun(_1207152, tc_HOL_Obool)))], (51455 ^ _778495) ^ [_1818130, _1818132, _1818134, _1818136] : [class_Rings_Ocomm__semiring__1(_1818130), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818130), _1818132), _1818134)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818130), hAPP(hAPP(c_Power_Opower__class_Opower(_1818130), _1818132), _1818136)), hAPP(hAPP(c_Power_Opower__class_Opower(_1818130), _1818134), _1818136))))], (44927 ^ _778495) ^ [_1678912, _1678914, _1678916, _1678918] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1678912)), _1678914), c_List_Olists(_1678912, _1678916))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1678912)), _1678914), c_List_Olists(_1678912, _1678918))), -(hBOOL(hAPP(c_List_Olistsp(_1678912, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1678912, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1678912, tc_fun(_1678912, tc_HOL_Obool), tc_HOL_Obool), c_member(_1678912)), _1678916)), hAPP(hAPP(c_COMBC(_1678912, tc_fun(_1678912, tc_HOL_Obool), tc_HOL_Obool), c_member(_1678912)), _1678918))), _1678914)))], (27721 ^ _778495) ^ [] : [-(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))))], (20652 ^ _778495) ^ [_1148713] : [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), _1148713))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1148713)))], (51833 ^ _778495) ^ [_1825071, _1825073, _1825075] : [51834 ^ _778495 : [(51837 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825073), _1825075))], (51835 ^ _778495) ^ [] : [_1825071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1825071), _1825073)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1825071), _1825075))))], (35220 ^ _778495) ^ [_1436447, _1436449, _1436451] : [class_Orderings_Olinorder(_1436447), hAPP(_1436449, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1436447), 35225 ^ [_1436447, _1436449, _1436451]), 35226 ^ [_1436447, _1436449, _1436451])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1436447), hAPP(_1436449, 35225 ^ [_1436447, _1436449, _1436451])), hAPP(_1436449, 35226 ^ [_1436447, _1436449, _1436451])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1436447), _1436451)), -(_1436451 = c_Orderings_Obot__class_Obot(tc_fun(_1436447, tc_HOL_Obool))), -(hAPP(_1436449, c_Big__Operators_Olinorder__class_OMin(_1436447, _1436451)) = c_Big__Operators_Olinorder__class_OMin(_1436447, hAPP(c_Set_Oimage(_1436447, _1436447, _1436449), _1436451)))], (23012 ^ _778495) ^ [_1189830, _1189832, _1189834] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1189830), _1189832)), _1189834) = 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), _1189830), _1189834)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1189832), _1189834))), 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, _1189830, _1189834)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189832, _1189834))), _1189834)))], (26144 ^ _778495) ^ [_1245995, _1245997] : [class_Groups_Omonoid__mult(_1245995), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1245995), _1245997), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1245997)], (21308 ^ _778495) ^ [_1160306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1160306)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1160306))))], (48501 ^ _778495) ^ [_1756622, _1756624, _1756626] : [hBOOL(hAPP(hAPP(c_member(_1756622), _1756624), hAPP(c_List_Oset(_1756622), _1756626))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756622), _1756626), _1756624)))], (41880 ^ _778495) ^ [_1609168, _1609170, _1609172, _1609174] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609168) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1609170), hAPP(hAPP(c_List_Olist_OCons(_1609170), _1609172), _1609174)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609168)) = hAPP(hAPP(c_List_Onth(_1609170), _1609174), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609168)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (8116 ^ _778495) ^ [_912185, _912187, _912189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912185, tc_HOL_Obool)), _912187), _912189)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_912185, tc_HOL_Obool)), _912187), _912189))), -(_912187 = _912189)], (30489 ^ _778495) ^ [_1334527, _1334529, _1334531, _1334533] : [hBOOL(hAPP(hAPP(_1334531, _1334529), _1334533)), -(hBOOL(hAPP(hAPP(c_member(_1334527), _1334529), c_SetInterval_Oord_OlessThan(_1334527, _1334531, _1334533))))], (3260 ^ _778495) ^ [_827166, _827168] : [_827168 = _827166, -(c_Lazy__Sequence_Ohb__not__seq(_827168) = c_Lazy__Sequence_Ohb__not__seq(_827166))], (21468 ^ _778495) ^ [_1163290, _1163292] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163290), _1163292), hAPP(c_Int_Onumber__class_Onumber__of(_1163290), c_Int_OBit1(c_Int_OPls))) = _1163292), class_Fields_Ofield(_1163290), class_Int_Onumber__ring(_1163290)], (29344 ^ _778495) ^ [_1312205, _1312207] : [_1312205 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1312207, _1312205) = 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), _1312207)))], (48352 ^ _778495) ^ [_1753309, _1753311, _1753313, _1753315] : [-(hBOOL(hAPP(hAPP(c_member(_1753309), _1753311), hAPP(c_List_Oset(_1753309), c_List_Oreplicate(_1753309, _1753313, _1753315))))), _1753311 = _1753315, -(_1753313 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (888 ^ _778495) ^ [_791827, _791829, _791831, _791833] : [-(c_Equiv__Relations_Opart__equivp(_791831, _791827)), c_Equiv__Relations_Opart__equivp(_791833, _791829), _791833 = _791831, _791829 = _791827], (49013 ^ _778495) ^ [_1769840, _1769842] : [c_Relation_Otrans(_1769840, hAPP(c_Relation_Oconverse(_1769840, _1769840), _1769842)), -(c_Relation_Otrans(_1769840, _1769842))], (22820 ^ _778495) ^ [_1186449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1186449), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1186449) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186449))], (48692 ^ _778495) ^ [_1760961, _1760963, _1760965] : [c_List_Oall__interval__int(_1760961, _1760963, _1760965), -(c_List_Olist__all(tc_Int_Oint, _1760961, c_List_Oupto(_1760963, _1760965)))], (36953 ^ _778495) ^ [_1475183, _1475185, _1475187, _1475189] : [c_Wellfounded_Omax__extp(_1475183, _1475185, _1475187, _1475189), 36956 ^ _778495 : [(36959 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1475183), _1475189)))], (36961 ^ _778495) ^ [] : [_1475189 = c_Orderings_Obot__class_Obot(tc_fun(_1475183, tc_HOL_Obool))], (36963 ^ _778495) ^ [_1475399] : [hBOOL(hAPP(hAPP(c_member(_1475183), _1475399), _1475187)), 36967 ^ _778495 : [(36970 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1475185, _1475399), 36966 ^ [_1475183, _1475185, _1475187, _1475189, _1475399])))], (36968 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475183), 36966 ^ [_1475183, _1475185, _1475187, _1475189, _1475399]), _1475189)))]]], (36957 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1475183), _1475187)))]]], (36450 ^ _778495) ^ [_1464469, _1464471, _1464473, _1464475] : [-(_1464469 = c_Orderings_Obot__class_Obot(tc_fun(_1464471, tc_HOL_Obool))), 36453 ^ _778495 : [(36454 ^ _778495) ^ [] : [-(hAPP(c_Set_Oimage(_1464473, _1464471, 36461 ^ [_1464469, _1464471, _1464473, _1464475]), _1464475) = _1464469), 36455 ^ _778495 : [(36456 ^ _778495) ^ [_1464610] : [c_Fun_Oinj__on(_1464471, _1464473, _1464610, _1464469), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1464473, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1464471, _1464473, _1464610), _1464469)), _1464475))]]], (36465 ^ _778495) ^ [] : [36466 ^ _778495 : [(36467 ^ _778495) ^ [_1464802] : [hAPP(c_Set_Oimage(_1464473, _1464471, _1464802), _1464475) = _1464469]], 36469 ^ _778495 : [(36472 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1464473, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1464471, _1464473, 36468 ^ [_1464469, _1464471, _1464473, _1464475]), _1464469)), _1464475)))], (36470 ^ _778495) ^ [] : [-(c_Fun_Oinj__on(_1464471, _1464473, 36468 ^ [_1464469, _1464471, _1464473, _1464475], _1464469))]]]]], (38421 ^ _778495) ^ [_1519040, _1519042, _1519044] : [-(hAPP(c_Relation_ORange(_1519040, _1519042), hAPP(c_Set_OCollect(tc_prod(_1519040, _1519042)), hAPP(c_Product__Type_Oprod_Oprod__case(_1519040, _1519042, tc_HOL_Obool), _1519044))) = hAPP(c_Set_OCollect(_1519042), hAPP(hAPP(c_COMBB(tc_fun(_1519040, tc_HOL_Obool), tc_HOL_Obool, _1519042), c_HOL_OEx(_1519040)), hAPP(c_COMBC(_1519040, _1519042, tc_HOL_Obool), _1519044))))], (44881 ^ _778495) ^ [_1677578] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1677578), 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, _1677578)) = _1677578)], (25538 ^ _778495) ^ [_1234818, _1234820, _1234822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1234818)), 25541 ^ _778495 : [(25542 ^ _778495) ^ [] : [-(_1234820 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1234822), _1234818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1234818), _1234820)), _1234822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1234822), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1234818), hAPP(c_Nat_OSuc, _1234820))))], (25552 ^ _778495) ^ [] : [_1234820 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1234822), _1234818), 25555 ^ _778495 : [(25558 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1234822), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1234818), hAPP(c_Nat_OSuc, _1234820)))))], (25556 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1234818), _1234820)), _1234822)))]]]]], (25684 ^ _778495) ^ [_1237452, _1237454, _1237456] : [class_Rings_Olinordered__semidom(_1237452), hAPP(hAPP(c_Power_Opower__class_Opower(_1237452), _1237454), 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(_1237452), _1237456), 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(_1237452), c_Groups_Ozero__class_Ozero(_1237452)), _1237454)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237452), c_Groups_Ozero__class_Ozero(_1237452)), _1237456)), -(_1237454 = _1237456)], (6136 ^ _778495) ^ [_877279, _877281, _877283, _877285] : [6150 ^ _778495 : [(6153 ^ _778495) ^ [] : [-(hBOOL(hAPP(_877285, 6149 ^ [_877279, _877281, _877283, _877285])))], (6151 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877279), 6149 ^ [_877279, _877281, _877283, _877285]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_877279, tc_HOL_Obool)), _877281), _877283))))]], 6137 ^ _778495 : [(6144 ^ _778495) ^ [_877488] : [hBOOL(hAPP(hAPP(c_member(_877279), _877488), _877283)), hBOOL(hAPP(_877285, _877488))], (6138 ^ _778495) ^ [_877392] : [hBOOL(hAPP(hAPP(c_member(_877279), _877392), _877281)), hBOOL(hAPP(_877285, _877392))]]], (23913 ^ _778495) ^ [_1206505, _1206507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206505), 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, _1206507, _1206505)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47312 ^ _778495) ^ [_1730786, _1730788, _1730790, _1730792, _1730794, _1730796, _1730798, _1730800] : [47314 ^ _778495 : [(47317 ^ _778495) ^ [] : [hAPP(c_Fun_Ocomp(_1730790, _1730790, _1730792, hAPP(_1730794, 47313 ^ [_1730786, _1730788, _1730790, _1730792, _1730794, _1730796, _1730798, _1730800])), _1730796) = hAPP(c_Fun_Ocomp(_1730792, _1730790, _1730792, _1730796), hAPP(_1730798, 47313 ^ [_1730786, _1730788, _1730790, _1730792, _1730794, _1730796, _1730798, _1730800]))], (47315 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730786), 47313 ^ [_1730786, _1730788, _1730790, _1730792, _1730794, _1730796, _1730798, _1730800]), hAPP(c_List_Oset(_1730786), _1730788))))]], -(hAPP(c_List_Ofoldl(_1730790, _1730786, hAPP(c_COMBC(_1730786, _1730790, _1730790), _1730794), hAPP(_1730796, _1730800)), _1730788) = hAPP(_1730796, hAPP(c_List_Ofoldl(_1730792, _1730786, hAPP(c_COMBC(_1730786, _1730792, _1730792), _1730798), _1730800), _1730788)))], (34801 ^ _778495) ^ [_1429439, _1429441, _1429443] : [class_Orderings_Oorder(_1429439), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429439, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1429439, _1429441, _1429443)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1429439), _1429443)) = c_Orderings_Obot__class_Obot(tc_fun(_1429439, tc_HOL_Obool)))], (32684 ^ _778495) ^ [_1381409, _1381411, _1381413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1381409)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1381411), _1381413)), 32691 ^ _778495 : [(32692 ^ _778495) ^ [_1381605] : [32694 ^ _778495 : [(32700 ^ _778495) ^ [] : [-(_1381605 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32696 ^ [_1381409, _1381411, _1381413, _1381605]), 32693 ^ [_1381409, _1381411, _1381413, _1381605]))], (32698 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32696 ^ [_1381409, _1381411, _1381413, _1381605]), _1381413)))], (32695 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32693 ^ [_1381409, _1381411, _1381413, _1381605]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1381409))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1381411), _1381605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1381411), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1381605), _1381409))))]]], (52425 ^ _778495) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (11252 ^ _778495) ^ [_972584, _972586, _972588] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972584), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972586), _972588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972584), _972586)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972584), _972588)))], (3116 ^ _778495) ^ [_824898, _824900, _824902, _824904] : [-(c_Big__Operators_Olattice__class_OInf__fin(_824904, _824900) = c_Big__Operators_Olattice__class_OInf__fin(_824902, _824898)), _824904 = _824902, _824900 = _824898], (42796 ^ _778495) ^ [_1631277, _1631279, _1631281, _1631283] : [-(hBOOL(hAPP(hAPP(c_member(_1631277), _1631279), hAPP(c_List_Oset(_1631277), _1631281)))), hBOOL(hAPP(hAPP(c_member(_1631277), _1631279), hAPP(c_List_Oset(_1631277), c_List_Oremove1(_1631277, _1631283, _1631281))))], (52663 ^ _778495) ^ [_1835760, _1835762] : [_1835760 = _1835762, -(hBOOL(hAPP(hAPP(c_fequal, _1835760), _1835762)))], (10519 ^ _778495) ^ [_960063, _960065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960063), hAPP(c_Nat_OSuc, _960065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960063), _960065)))], (40784 ^ _778495) ^ [_1578097, _1578099] : [c_Wellfounded_Owf(_1578097, hAPP(c_Relation_Oconverse(_1578097, _1578097), _1578099)), -(c_Wellfounded_Owf(_1578097, hAPP(c_Relation_Oconverse(_1578097, _1578097), c_Transitive__Closure_Otrancl(_1578097, _1578099))))], (20044 ^ _778495) ^ [_1138532, _1138534, _1138536] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138532)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138534)), _1138536)) = 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), _1138532), _1138534))), _1138536))], (28118 ^ _778495) ^ [_1280071, _1280073, _1280075] : [28120 ^ _778495 : [(28123 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1280071), _1280075), 28119 ^ [_1280071, _1280073, _1280075]))], (28121 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1280071, tc_HOL_Obool)), 28119 ^ [_1280071, _1280073, _1280075]), _1280073)))]], -(hBOOL(hAPP(hAPP(c_member(_1280071), _1280075), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1280071, tc_HOL_Obool), _1280073))))], (39686 ^ _778495) ^ [_1551555, _1551557, _1551559, _1551561, _1551563, _1551565] : [c_Finite__Set_Ofolding(_1551555, _1551557, _1551559, _1551561), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551555), _1551563)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551555), _1551565)), -(hAPP(c_Fun_Ocomp(_1551557, _1551557, _1551557, hAPP(_1551561, _1551565)), hAPP(_1551561, _1551563)) = hAPP(c_Fun_Ocomp(_1551557, _1551557, _1551557, hAPP(_1551561, _1551563)), hAPP(_1551561, _1551565)))], (33900 ^ _778495) ^ [_1409532, _1409534, _1409536, _1409538] : [class_Orderings_Olinorder(_1409532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409532), _1409534), _1409536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409532), _1409536), _1409538)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409532, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409532, _1409534), _1409536)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409532, _1409536), _1409538)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409532, _1409534), _1409538))], (11254 ^ _778495) ^ [_972641, _972643, _972645] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972641), _972643)), _972645) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972641), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972643), _972645)))], (29599 ^ _778495) ^ [_1317070, _1317072, _1317074] : [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), _1317070), _1317072))), -(hBOOL(hAPP(hAPP(_1317074, _1317070), _1317072))), 29606 ^ _778495 : [(29609 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1317074, 29604 ^ [_1317070, _1317072, _1317074]), 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)))), 29605 ^ [_1317070, _1317072, _1317074])))), -(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), 29604 ^ [_1317070, _1317072, _1317074]), 29605 ^ [_1317070, _1317072, _1317074])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 29605 ^ [_1317070, _1317072, _1317074]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29619 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1317074, 29604 ^ [_1317070, _1317072, _1317074]), 29605 ^ [_1317070, _1317072, _1317074]))], (29607 ^ _778495) ^ [] : [-(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), 29604 ^ [_1317070, _1317072, _1317074]), 29605 ^ [_1317070, _1317072, _1317074]))))]]], (51167 ^ _778495) ^ [_1813369, _1813371, _1813373] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813369), _1813371)), _1813371 = _1813373, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813369), _1813373)))], (26530 ^ _778495) ^ [_1253090, _1253092, _1253094, _1253096] : [class_Rings_Olinordered__semidom(_1253090), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1253092), _1253094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253090), c_Groups_Ozero__class_Ozero(_1253090)), _1253096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253090), _1253096), c_Groups_Oone__class_Oone(_1253090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253090), hAPP(hAPP(c_Power_Opower__class_Opower(_1253090), _1253096), _1253094)), hAPP(hAPP(c_Power_Opower__class_Opower(_1253090), _1253096), _1253092))))], (29053 ^ _778495) ^ [_1305962, _1305964] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1305962), _1305964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1305962)), _1305964)))], (43824 ^ _778495) ^ [_1655021, _1655023, _1655025] : [-(_1655021 = c_List_Olist_ONil(_1655023)), -(hAPP(c_List_Otl(_1655023), hAPP(hAPP(c_List_Oappend(_1655023), _1655021), _1655025)) = hAPP(hAPP(c_List_Oappend(_1655023), hAPP(c_List_Otl(_1655023), _1655021)), _1655025))], (41280 ^ _778495) ^ [_1591252, _1591254, _1591256, _1591258] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591252, _1591254)), _1591256), hAPP(c_Relation_Oconverse(_1591254, _1591252), _1591258))), 41285 ^ _778495 : [(41288 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591254, _1591252)), hAPP(hAPP(c_Product__Type_OPair(_1591254, _1591252), 41283 ^ [_1591252, _1591254, _1591256, _1591258]), 41284 ^ [_1591252, _1591254, _1591256, _1591258])), _1591258)))], (41286 ^ _778495) ^ [] : [-(_1591256 = hAPP(hAPP(c_Product__Type_OPair(_1591252, _1591254), 41284 ^ [_1591252, _1591254, _1591256, _1591258]), 41283 ^ [_1591252, _1591254, _1591256, _1591258]))]]], (43888 ^ _778495) ^ [_1656376, _1656378, _1656380] : [class_Groups_Omonoid__add(_1656376), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656376), _1656378), hAPP(c_List_Ofoldl(_1656376, _1656376, c_Groups_Oplus__class_Oplus(_1656376), c_Groups_Ozero__class_Ozero(_1656376)), _1656380)) = hAPP(c_List_Ofoldl(_1656376, _1656376, c_Groups_Oplus__class_Oplus(_1656376), _1656378), _1656380))], (46142 ^ _778495) ^ [_1706700, _1706702, _1706704] : [class_Orderings_Olinorder(_1706700), c_List_Olinorder__class_Osorted(_1706700, _1706702), -(c_List_Olinorder__class_Osorted(_1706700, c_List_Oremove1(_1706700, _1706704, _1706702)))], (2052 ^ _778495) ^ [_808352, _808354, _808356, _808358, _808360, _808362, _808364, _808366] : [-(c_Nitpick_Opair__box_OPairBox(_808366, _808362, _808358, _808354) = c_Nitpick_Opair__box_OPairBox(_808364, _808360, _808356, _808352)), _808366 = _808364, _808362 = _808360, _808358 = _808356, _808354 = _808352], (35042 ^ _778495) ^ [_1433708] : [-(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)), _1433708)))], (27915 ^ _778495) ^ [_1276484, _1276486] : [c_Nat__Transfer_Ois__nat(_1276484), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1276484), _1276486)))], (11754 ^ _778495) ^ [_982620, _982622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _982620), _982622)), -(_982622 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982620), 11757 ^ [_982620, _982622]))], (12951 ^ _778495) ^ [_1009367, _1009369, _1009371, _1009373] : [class_Groups_Ocomm__monoid__mult(_1009367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009369), _1009371)), 12961 ^ _778495 : [(12964 ^ _778495) ^ [] : [hAPP(_1009373, 12960 ^ [_1009367, _1009369, _1009371, _1009373]) = c_Groups_Oone__class_Oone(_1009367)], (12962 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1009369), 12960 ^ [_1009367, _1009369, _1009371, _1009373]), _1009371)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1009367, _1009369, c_Groups_Otimes__class_Otimes(_1009367)), _1009373), c_Groups_Oone__class_Oone(_1009367)), _1009371) = c_Groups_Oone__class_Oone(_1009367))], (38353 ^ _778495) ^ [_1517362, _1517364] : [-(hAPP(c_Fun_Oid(_1517362), _1517364) = _1517364)], (40495 ^ _778495) ^ [_1571306, _1571308, _1571310, _1571312, _1571314] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571306, _1571306)), hAPP(hAPP(c_Product__Type_OPair(_1571306, _1571306), _1571308), _1571310)), c_Transitive__Closure_Ortrancl(_1571306, _1571312))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571306, _1571306)), hAPP(hAPP(c_Product__Type_OPair(_1571306, _1571306), _1571310), _1571314)), _1571312)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571306, _1571306)), hAPP(hAPP(c_Product__Type_OPair(_1571306, _1571306), _1571308), _1571314)), c_Transitive__Closure_Otrancl(_1571306, _1571312))))], (50725 ^ _778495) ^ [_1805721, _1805723, _1805725] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1805721), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1805723), _1805725))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1805721), _1805723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1805725), _1805723)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1805721), _1805725)))], (4848 ^ _778495) ^ [_852384, _852386, _852388, _852390, _852392, _852394] : [-(c_Finite__Set_Ofold__image(_852394, _852390, _852386) = c_Finite__Set_Ofold__image(_852392, _852388, _852384)), _852394 = _852392, _852390 = _852388, _852386 = _852384], (10741 ^ _778495) ^ [_963551, _963553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963551)), _963553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963551), _963553)))], (3500 ^ _778495) ^ [_830860, _830862] : [_830862 = _830860, -(c_SetInterval_Oord__class_OatMost(_830862) = c_SetInterval_Oord__class_OatMost(_830860))], (7706 ^ _778495) ^ [_905875, _905877, _905879, _905881, _905883] : [class_Groups_Oordered__ab__group__add(_905875), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_905875), _905877), _905879) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_905875), _905881), _905883), 7713 ^ _778495 : [(7720 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905875), _905881), _905883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905875), _905877), _905879)))], (7714 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905875), _905877), _905879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905875), _905881), _905883)))]]], (37929 ^ _778495) ^ [_1500652, _1500654, _1500656, _1500658] : [-(hAPP(c_Set_Ovimage(_1500652, _1500654, _1500656), _1500658) = hAPP(c_Set_OCollect(_1500652), hAPP(hAPP(c_COMBC(_1500652, tc_fun(_1500654, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1500654, tc_fun(tc_fun(_1500654, tc_HOL_Obool), tc_HOL_Obool), _1500652), c_member(_1500654)), _1500656)), _1500658)))], (10695 ^ _778495) ^ [_962849] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _962849) = _962849)], (29908 ^ _778495) ^ [_1322643, _1322645, _1322647, _1322649, _1322651, _1322653] : [hAPP(_1322649, hAPP(c_Product__Type_Osnd(_1322647, _1322643), _1322651)) = hAPP(_1322653, hAPP(c_Product__Type_Osnd(_1322647, _1322643), _1322651)), -(hAPP(c_Product__Type_Oapsnd(_1322643, _1322645, _1322647, _1322649), _1322651) = hAPP(c_Product__Type_Oapsnd(_1322643, _1322645, _1322647, _1322653), _1322651))], (23336 ^ _778495) ^ [_1196749, _1196751, _1196753, _1196755] : [class_Divides_Osemiring__div(_1196749), -(c_Divides_Odiv__class_Omod(_1196749, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1196749), _1196751), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196749), _1196753), _1196755)), _1196753) = c_Divides_Odiv__class_Omod(_1196749, _1196751, _1196753))], (43846 ^ _778495) ^ [_1655490, _1655492, _1655494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655490)), _1655492)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1655490, _1655494), _1655492) = _1655492)], (39366 ^ _778495) ^ [_1544098, _1544100, _1544102, _1544104, _1544106, _1544108, _1544110] : [hAPP(c_Fun_Ocomp(_1544098, _1544100, _1544102, _1544104), _1544106) = hAPP(c_Fun_Ocomp(_1544100, _1544100, _1544102, c_Fun_Oid(_1544100)), _1544108), -(hAPP(_1544104, hAPP(_1544106, _1544110)) = hAPP(_1544108, _1544110))], (34506 ^ _778495) ^ [_1423350, _1423352, _1423354, _1423356] : [-(hAPP(c_Set_Oimage(_1423350, _1423352, _1423354), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1423350, tc_HOL_Obool), _1423356)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1423350, tc_HOL_Obool), tc_fun(_1423352, tc_HOL_Obool)), _1423356), c_Set_Oimage(_1423350, _1423352, _1423354)))], (10665 ^ _778495) ^ [_962364, _962366, _962368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962364), _962366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962366), _962368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962364), _962368)))], (10919 ^ _778495) ^ [_966475, _966477] : [10920 ^ _778495 : [(10923 ^ _778495) ^ [] : [_966475 = hAPP(c_Nat_OSuc, _966477)], (10921 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966475), _966477))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966475), hAPP(c_Nat_OSuc, _966477))))], (25652 ^ _778495) ^ [] : [-(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)))))], (3618 ^ _778495) ^ [_832777, _832779, _832781, _832783] : [-(c_List_Otranspose(_832783, _832779) = c_List_Otranspose(_832781, _832777)), _832783 = _832781, _832779 = _832777], (8960 ^ _778495) ^ [_929435, _929437, _929439, _929441, _929443] : [class_Lattices_Olattice(_929435), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929437, _929435)), _929439), _929441), _929443) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929435), hAPP(_929439, _929443)), hAPP(_929441, _929443)))], (31073 ^ _778495) ^ [_1346198, _1346200] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1346198)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1346200)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1346200))), 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, _1346198))), 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), _1346198)), c_Int_Onat)))))], (11288 ^ _778495) ^ [_973332, _973334, _973336, _973338] : [class_Groups_Ocancel__semigroup__add(_973332), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973332), _973334), _973336) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973332), _973338), _973336), -(_973334 = _973338)], (43387 ^ _778495) ^ [_1644535, _1644537, _1644539, _1644541, _1644543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644535), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644537)), _1644539))), -(hAPP(hAPP(c_List_Olist__update(_1644537, hAPP(hAPP(c_List_Oappend(_1644537), _1644539), _1644541)), _1644535), _1644543) = hAPP(hAPP(c_List_Oappend(_1644537), hAPP(hAPP(c_List_Olist__update(_1644537, _1644539), _1644535), _1644543)), _1644541))], (28727 ^ _778495) ^ [_1299320, _1299322] : [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(_1299322))), 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), _1299320)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1299320)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1299322))))], (31184 ^ _778495) ^ [_1348425, _1348427] : [class_Orderings_Olinorder(_1348425), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348425), _1348427)), -(_1348427 = c_Orderings_Obot__class_Obot(tc_fun(_1348425, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1348425), c_Big__Operators_Olinorder__class_OMax(_1348425, _1348427)), _1348427)))], (8462 ^ _778495) ^ [_919216, _919218, _919220, _919222, _919224] : [c_Finite__Set_Ofolding__one__idem(_919216, _919218, _919220), hBOOL(hAPP(c_Finite__Set_Ofinite(_919216), _919222)), -(_919222 = c_Orderings_Obot__class_Obot(tc_fun(_919216, tc_HOL_Obool))), -(hAPP(_919220, hAPP(hAPP(c_Set_Oinsert(_919216), _919224), _919222)) = hAPP(hAPP(_919218, _919224), hAPP(_919220, _919222)))], (9368 ^ _778495) ^ [_937442, _937444, _937446, _937448, _937450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937442, tc_HOL_Obool)), _937444), _937446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937442, tc_HOL_Obool)), _937448), _937450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937442, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937442, tc_HOL_Obool)), _937444), _937448)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937442, tc_HOL_Obool)), _937446), _937450))))], (44782 ^ _778495) ^ [_1675563, _1675565, _1675567] : [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, _1675563), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1675563)), _1675565)))), -(hBOOL(hAPP(hAPP(c_member(_1675563), hAPP(c_Product__Type_Ofst(_1675563, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1675563, _1675565), _1675567))), hAPP(c_List_Oset(_1675563), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1675563), _1675563), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1675563)), _1675565)))))], (43736 ^ _778495) ^ [_1653634, _1653636, _1653638] : [-(_1653634 = c_List_Olist_ONil(_1653636)), -(hAPP(c_List_Ohd(_1653636), hAPP(hAPP(c_List_Oappend(_1653636), _1653634), _1653638)) = hAPP(c_List_Ohd(_1653636), _1653634))], (42333 ^ _778495) ^ [_1621698, _1621700, _1621702, _1621704] : [-(hAPP(hAPP(c_List_Olist__update(_1621698, hAPP(hAPP(c_List_Olist_OCons(_1621698), _1621700), _1621702)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1621704) = hAPP(hAPP(c_List_Olist_OCons(_1621698), _1621704), _1621702))], (32896 ^ _778495) ^ [_1385444, _1385446, _1385448, _1385450, _1385452] : [class_Orderings_Olinorder(_1385444), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385444, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1385444, _1385446, _1385448)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1385444, _1385450, _1385452)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1385444, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1385444), _1385446), _1385450), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1385444), _1385448), _1385452)))], (34653 ^ _778495) ^ [_1426495, _1426497, _1426499] : [class_Orderings_Olinorder(_1426495), 34656 ^ _778495 : [(34663 ^ _778495) ^ [] : [_1426497 = _1426499, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1426495), _1426497) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1426495), _1426499))], (34657 ^ _778495) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1426495), _1426497) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1426495), _1426499), -(_1426497 = _1426499)]]], (42866 ^ _778495) ^ [_1632694, _1632696, _1632698, _1632700] : [_1632694 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1632696), _1632694), hAPP(hAPP(c_List_Olist_OCons(_1632696), _1632698), _1632700)) = c_List_Olist_ONil(_1632696))], (17664 ^ _778495) ^ [_1095335, _1095337, _1095339] : [class_Orderings_Olinorder(_1095335), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095335), _1095337), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095335), _1095337), _1095339)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095335), _1095337), _1095339))], (4464 ^ _778495) ^ [_846334, _846336, _846338, _846340] : [-(c_HOL_OThe(_846340, _846336) = c_HOL_OThe(_846338, _846334)), _846340 = _846338, _846336 = _846334], (33499 ^ _778495) ^ [_1401187, _1401189, _1401191, _1401193, _1401195] : [class_Complete__Lattice_Ocomplete__lattice(_1401187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401189, tc_HOL_Obool)), _1401191), _1401193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401187), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401189, _1401187), _1401191), _1401195)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401189, _1401187), _1401193), _1401195))))], (42930 ^ _778495) ^ [_1633854, _1633856, _1633858, _1633860, _1633862] : [-(hAPP(hAPP(c_List_Ozip(_1633854, _1633856), hAPP(hAPP(c_List_Olist_OCons(_1633854), _1633858), _1633860)), _1633862) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1633854, _1633856)), _1633856, c_List_Olist_ONil(tc_prod(_1633854, _1633856)), hAPP(hAPP(c_COMBC(_1633856, tc_fun(tc_List_Olist(_1633856), tc_List_Olist(tc_prod(_1633854, _1633856))), tc_fun(tc_List_Olist(_1633856), tc_List_Olist(tc_prod(_1633854, _1633856)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1633854, _1633856)), tc_List_Olist(tc_prod(_1633854, _1633856))), tc_fun(tc_fun(tc_List_Olist(_1633856), tc_List_Olist(tc_prod(_1633854, _1633856))), tc_fun(tc_List_Olist(_1633856), tc_List_Olist(tc_prod(_1633854, _1633856)))), _1633856), c_COMBB(tc_List_Olist(tc_prod(_1633854, _1633856)), tc_List_Olist(tc_prod(_1633854, _1633856)), tc_List_Olist(_1633856))), hAPP(hAPP(c_COMBB(tc_prod(_1633854, _1633856), tc_fun(tc_List_Olist(tc_prod(_1633854, _1633856)), tc_List_Olist(tc_prod(_1633854, _1633856))), _1633856), c_List_Olist_OCons(tc_prod(_1633854, _1633856))), hAPP(c_Product__Type_OPair(_1633854, _1633856), _1633858)))), hAPP(c_List_Ozip(_1633854, _1633856), _1633860))), _1633862))], (31382 ^ _778495) ^ [_1351682, _1351684, _1351686] : [class_Orderings_Olinorder(_1351682), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351682), _1351684)), -(c_Big__Operators_Olinorder__class_OMax(_1351682, hAPP(hAPP(c_Set_Oinsert(_1351682), _1351686), _1351684)) = hAPP(hAPP(c_Finite__Set_Ofold(_1351682, _1351682, c_Orderings_Oord__class_Omax(_1351682)), _1351686), _1351684))], (8394 ^ _778495) ^ [_917856, _917858, _917860, _917862, _917864] : [c_Finite__Set_Ofolding__one__idem(_917856, _917858, _917860), hBOOL(hAPP(c_Finite__Set_Ofinite(_917856), _917862)), -(_917862 = c_Orderings_Obot__class_Obot(tc_fun(_917856, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_917856), _917864)), -(_917864 = c_Orderings_Obot__class_Obot(tc_fun(_917856, tc_HOL_Obool))), -(hAPP(_917860, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917856, tc_HOL_Obool)), _917862), _917864)) = hAPP(hAPP(_917858, hAPP(_917860, _917862)), hAPP(_917860, _917864)))], (16490 ^ _778495) ^ [_1073153, _1073155, _1073157, _1073159] : [class_Fields_Olinordered__field(_1073153), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073153), _1073155), c_Groups_Ozero__class_Ozero(_1073153))), 16497 ^ _778495 : [(16504 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073153), _1073159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073153), _1073157), _1073155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073153), _1073157), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1073153), _1073159), _1073155))))], (16498 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073153), _1073157), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1073153), _1073159), _1073155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073153), _1073159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073153), _1073157), _1073155))))]]], (46762 ^ _778495) ^ [_1718806, _1718808, _1718810, _1718812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718806), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718808)), _1718810))), -(hAPP(c_List_Orev(_1718808), hAPP(hAPP(c_List_Olist__update(_1718808, _1718810), _1718806), _1718812)) = hAPP(hAPP(c_List_Olist__update(_1718808, hAPP(c_List_Orev(_1718808), _1718810)), 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(_1718808)), _1718810)), _1718806)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1718812))], (32520 ^ _778495) ^ [_1377646, _1377648, _1377650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1377646)), 32523 ^ _778495 : [(32524 ^ _778495) ^ [_1377780] : [32526 ^ _778495 : [(32532 ^ _778495) ^ [] : [-(_1377780 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32528 ^ [_1377646, _1377648, _1377650, _1377780]), 32525 ^ [_1377646, _1377648, _1377650, _1377780]))], (32530 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32528 ^ [_1377646, _1377648, _1377650, _1377780]), _1377648)))], (32527 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32525 ^ [_1377646, _1377648, _1377650, _1377780]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1377646))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1377650), _1377780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1377650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1377780), _1377646))))]]], (2664 ^ _778495) ^ [_817888, _817890, _817892, _817894, _817896, _817898] : [-(c_FunDef_Oin__rel(_817898, _817894, _817890) = c_FunDef_Oin__rel(_817896, _817892, _817888)), _817898 = _817896, _817894 = _817892, _817890 = _817888], (4 ^ _778495) ^ [_778545, _778547] : [_778547 = _778545, -(_778545 = _778547)], (40443 ^ _778495) ^ [_1570022, _1570024, _1570026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570022, _1570022), tc_HOL_Obool)), c_Relation_OId(_1570022)), _1570024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570022, _1570022), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1570022, _1570022, _1570022), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1570022, _1570022), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1570022, _1570026)), _1570024)), _1570026)), _1570024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570022, _1570022), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1570022, _1570026)), _1570024)))], (47898 ^ _778495) ^ [_1743504, _1743506, _1743508] : [c_List_Olist__all(_1743504, _1743506, _1743508), -(c_List_Olist__all(_1743504, _1743506, hAPP(c_List_Orev(_1743504), _1743508)))], (49881 ^ _778495) ^ [_1787038, _1787040, _1787042, _1787044, _1787046, _1787048] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1787038, _1787040, _1787042, _1787044, c_Lazy__Sequence_Olazy__sequence_OInsert(_1787040, _1787046, _1787048)) = hAPP(hAPP(hAPP(_1787044, _1787046), _1787048), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1787038, _1787040, _1787042, _1787044, _1787048)))], (13480 ^ _778495) ^ [_1017764] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017764), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9194 ^ _778495) ^ [_933826, _933828, _933830] : [class_Lattices_Olattice(_933826), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933826), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933826), _933828), _933830)), _933828)))], (40298 ^ _778495) ^ [_1565755, _1565757] : [-(c_Transitive__Closure_Otrancl(_1565755, _1565757) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565755, _1565755), tc_HOL_Obool)), _1565757), hAPP(hAPP(c_Relation_Orel__comp(_1565755, _1565755, _1565755), c_Transitive__Closure_Otrancl(_1565755, _1565757)), _1565757)))], (42103 ^ _778495) ^ [_1615162, _1615164, _1615166, _1615168] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615162), tc_List_Olist(_1615162))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615162), tc_List_Olist(_1615162)), _1615164), _1615166)), c_List_Olistrel(_1615162, _1615168))), 42106 ^ _778495 : [(42109 ^ _778495) ^ [_1615498] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615162, _1615162)), _1615498), hAPP(c_List_Oset(tc_prod(_1615162, _1615162)), hAPP(hAPP(c_List_Ozip(_1615162, _1615162), _1615164), _1615166)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1615162, _1615162, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1615162, tc_fun(tc_prod(_1615162, _1615162), tc_HOL_Obool), tc_fun(_1615162, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615162, tc_fun(tc_fun(tc_prod(_1615162, _1615162), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1615162, _1615162), tc_HOL_Obool), tc_fun(_1615162, tc_HOL_Obool)), _1615162), c_COMBC(_1615162, tc_fun(tc_prod(_1615162, _1615162), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615162, tc_prod(_1615162, _1615162)), tc_fun(_1615162, tc_fun(tc_fun(tc_prod(_1615162, _1615162), tc_HOL_Obool), tc_HOL_Obool)), _1615162), hAPP(c_COMBB(tc_prod(_1615162, _1615162), tc_fun(tc_fun(tc_prod(_1615162, _1615162), tc_HOL_Obool), tc_HOL_Obool), _1615162), c_member(tc_prod(_1615162, _1615162)))), c_Product__Type_OPair(_1615162, _1615162)))), _1615168)), _1615498)))], (42107 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615162)), _1615164) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615162)), _1615166))]]], (41612 ^ _778495) ^ [_1601575, _1601577] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1601575), tc_List_Olist(_1601575)), tc_HOL_Obool)), c_List_Olistrel(_1601575, _1601577)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1601575), c_List_Olistrel1(_1601575, _1601577)))))], (40306 ^ _778495) ^ [_1566019, _1566021, _1566023, _1566025] : [-(c_Transitive__Closure_Otrancl(_1566019, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1566019, _1566019)), hAPP(hAPP(c_Product__Type_OPair(_1566019, _1566019), _1566021), _1566023)), _1566025)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566019, _1566019), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1566019, _1566025)), hAPP(c_Set_OCollect(tc_prod(_1566019, _1566019)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566019, _1566019, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1566019, tc_fun(_1566019, tc_HOL_Obool), tc_fun(_1566019, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1566019, tc_HOL_Obool), tc_fun(_1566019, tc_HOL_Obool)), _1566019), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1566019)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566019), c_fconj), hAPP(hAPP(c_COMBC(_1566019, tc_fun(tc_prod(_1566019, _1566019), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1566019, _1566019), tc_fun(tc_fun(tc_prod(_1566019, _1566019), tc_HOL_Obool), tc_HOL_Obool), _1566019), c_member(tc_prod(_1566019, _1566019))), hAPP(hAPP(c_COMBC(_1566019, _1566019, tc_prod(_1566019, _1566019)), c_Product__Type_OPair(_1566019, _1566019)), _1566021))), c_Transitive__Closure_Ortrancl(_1566019, _1566025))))), hAPP(hAPP(c_COMBC(_1566019, tc_fun(tc_prod(_1566019, _1566019), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1566019, _1566019), tc_fun(tc_fun(tc_prod(_1566019, _1566019), tc_HOL_Obool), tc_HOL_Obool), _1566019), c_member(tc_prod(_1566019, _1566019))), hAPP(c_Product__Type_OPair(_1566019, _1566019), _1566023))), c_Transitive__Closure_Ortrancl(_1566019, _1566025)))))))], (44329 ^ _778495) ^ [_1664889, _1664891, _1664893] : [c_Fun_Oinj__on(_1664889, _1664891, _1664893, c_Orderings_Otop__class_Otop(tc_fun(_1664889, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1664889), tc_List_Olist(_1664891), hAPP(c_List_Omap(_1664889, _1664891), _1664893), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1664889), tc_HOL_Obool))))], (19506 ^ _778495) ^ [_1128742, _1128744, _1128746] : [class_Orderings_Olinorder(_1128742), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128742), _1128744)), -(hBOOL(hAPP(hAPP(c_member(_1128742), _1128746), _1128744))), -(_1128744 = c_Orderings_Obot__class_Obot(tc_fun(_1128742, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1128742, c_Orderings_Oord__class_Omin(_1128742), hAPP(hAPP(c_Set_Oinsert(_1128742), _1128746), _1128744)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1128742), _1128746), c_Big__Operators_Olattice_OInf__fin(_1128742, c_Orderings_Oord__class_Omin(_1128742), _1128744)))], (25449 ^ _778495) ^ [] : [-(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)))))], (29649 ^ _778495) ^ [_1318189] : [-(_1318189 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1318189), 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)))))], (11761 ^ _778495) ^ [_982727, _982729] : [11762 ^ _778495 : [(11763 ^ _778495) ^ [_982777] : [_982729 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982727), _982777)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _982727), _982729)))], (10599 ^ _778495) ^ [_961418, _961420] : [-(_961418 = _961420), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961418), _961420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961420), _961418)))], (10331 ^ _778495) ^ [_956519, _956521, _956523] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_956519), _956521)), -(hAPP(c_Finite__Set_Ocard(_956519), hAPP(hAPP(c_Set_Oinsert(_956519), _956523), _956521)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_956519), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_956519, tc_HOL_Obool)), _956521), hAPP(hAPP(c_Set_Oinsert(_956519), _956523), c_Orderings_Obot__class_Obot(tc_fun(_956519, tc_HOL_Obool)))))))], (17744 ^ _778495) ^ [_1096697, _1096699, _1096701] : [class_Orderings_Olinorder(_1096697), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096697), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096697), _1096699), _1096701)), _1096699)))], (5632 ^ _778495) ^ [_864648, _864650, _864652, _864654] : [-(tc_fun(_864654, _864650) = tc_fun(_864652, _864648)), _864654 = _864652, _864650 = _864648], (33389 ^ _778495) ^ [_1397668, _1397670, _1397672, _1397674] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397668, tc_fun(_1397670, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397668, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1397670, tc_HOL_Obool), tc_fun(_1397670, tc_HOL_Obool), _1397668), hAPP(c_COMBC(_1397670, tc_fun(_1397670, tc_HOL_Obool), tc_HOL_Obool), c_member(_1397670))), _1397672)), _1397674)), -(hBOOL(hAPP(hAPP(c_member(_1397670), _1397674), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397668, tc_fun(_1397670, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397668, tc_HOL_Obool))), _1397672))))], (11131 ^ _778495) ^ [_970054, _970056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970054), _970056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _970054)), _970056)))], (26310 ^ _778495) ^ [_1248965, _1248967, _1248969, _1248971] : [class_Rings_Olinordered__semidom(_1248965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248965), hAPP(hAPP(c_Power_Opower__class_Opower(_1248965), _1248967), _1248969)), hAPP(hAPP(c_Power_Opower__class_Opower(_1248965), _1248971), _1248969))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248965), c_Groups_Ozero__class_Ozero(_1248965)), _1248971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248965), _1248967), _1248971)))], (30693 ^ _778495) ^ [_1338871, _1338873, _1338875] : [class_Orderings_Olinorder(_1338871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338871), _1338873), _1338875)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338871), _1338875), _1338873) = _1338875)], (26764 ^ _778495) ^ [_1256872] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1256872), c_Int_OMin) = c_Int_Osucc(_1256872))], (11113 ^ _778495) ^ [_969734, _969736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969734), _969736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969734)), _969736)))], (26676 ^ _778495) ^ [_1255588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1255588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1255588)))], (41183 ^ _778495) ^ [_1588559, _1588561, _1588563, _1588565, _1588567] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588559, _1588559)), hAPP(hAPP(c_Product__Type_OPair(_1588559, _1588559), _1588561), _1588563)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1588559, _1588559), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1588565)), _1588567))), 41187 ^ _778495 : [(41190 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588559, _1588559)), hAPP(hAPP(c_Product__Type_OPair(_1588559, _1588559), 41186 ^ [_1588559, _1588561, _1588563, _1588565, _1588567]), _1588563)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1588559, _1588559), tc_HOL_Obool), _1588565), _1588567))))], (41188 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588559, _1588559)), hAPP(hAPP(c_Product__Type_OPair(_1588559, _1588559), _1588561), 41186 ^ [_1588559, _1588561, _1588563, _1588565, _1588567])), _1588567)))]]], (33483 ^ _778495) ^ [_1400162, _1400164, _1400166, _1400168, _1400170] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400162, tc_fun(_1400164, tc_HOL_Obool)), _1400166), hAPP(hAPP(c_COMBB(tc_fun(_1400164, tc_HOL_Obool), tc_fun(_1400164, tc_HOL_Obool), _1400162), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400164, tc_HOL_Obool)), _1400168)), _1400170)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400164, tc_HOL_Obool)), _1400168), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1400162, tc_fun(_1400164, tc_HOL_Obool)), _1400166), _1400170)))], (16818 ^ _778495) ^ [_1079042, _1079044, _1079046, _1079048] : [class_Fields_Ofield__inverse__zero(_1079042), 16821 ^ _778495 : [(16822 ^ _778495) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1079042), _1079044), _1079046) = _1079048, 16825 ^ _778495 : [(16832 ^ _778495) ^ [] : [_1079046 = c_Groups_Ozero__class_Ozero(_1079042), -(_1079048 = c_Groups_Ozero__class_Ozero(_1079042))], (16826 ^ _778495) ^ [] : [-(_1079046 = c_Groups_Ozero__class_Ozero(_1079042)), -(_1079044 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079042), _1079048), _1079046))]]], (16838 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1079042), _1079044), _1079046) = _1079048), 16841 ^ _778495 : [(16844 ^ _778495) ^ [] : [_1079044 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079042), _1079048), _1079046)], (16842 ^ _778495) ^ [] : [_1079046 = c_Groups_Ozero__class_Ozero(_1079042)]], 16845 ^ _778495 : [(16848 ^ _778495) ^ [] : [_1079048 = c_Groups_Ozero__class_Ozero(_1079042)], (16846 ^ _778495) ^ [] : [-(_1079046 = c_Groups_Ozero__class_Ozero(_1079042))]]]]], (44939 ^ _778495) ^ [_1679321, _1679323] : [-(hBOOL(hAPP(c_List_Olistsp(_1679321, _1679323), c_List_Olist_ONil(_1679321))))], (52281 ^ _778495) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (19712 ^ _778495) ^ [_1132556, _1132558, _1132560] : [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), _1132556), _1132558)), _1132560))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132560), _1132556)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132558)))], (24716 ^ _778495) ^ [_1220995] : [-(hBOOL(hAPP(_1220995, 24723 ^ [_1220995]))), 24717 ^ _778495 : [(24718 ^ _778495) ^ [_1221047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221047)), hBOOL(hAPP(_1220995, hAPP(c_Int_Onat, _1221047)))]]], (11955 ^ _778495) ^ [_987032, _987034, _987036, _987038, _987040, _987042] : [class_Rings_Oordered__ring(_987032), 11958 ^ _778495 : [(11965 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987032), _987038), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987032), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_987032), _987040), _987034)), _987036)), _987042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987032), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987032), _987034), _987036)), _987038)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987032), _987040), _987036)), _987042))))], (11959 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987032), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987032), _987034), _987036)), _987038)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987032), _987040), _987036)), _987042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987032), _987038), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987032), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_987032), _987040), _987034)), _987036)), _987042))))]]], (42399 ^ _778495) ^ [_1623102, _1623104, _1623106, _1623108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623102), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623104)), _1623106))), -(hBOOL(hAPP(hAPP(c_member(_1623104), _1623108), hAPP(c_List_Oset(_1623104), hAPP(hAPP(c_List_Olist__update(_1623104, _1623106), _1623102), _1623108)))))], (28071 ^ _778495) ^ [_1279306, _1279308, _1279310] : [class_Divides_Osemiring__div(_1279306), -(_1279308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279306), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1279306), _1279308), _1279310)), _1279310)), c_Divides_Odiv__class_Omod(_1279306, _1279308, _1279310)))], (52203 ^ _778495) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (52601 ^ _778495) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (40603 ^ _778495) ^ [_1573721, _1573723, _1573725, _1573727] : [-(c_Wellfounded_Owf(_1573721, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1573721, _1573721)), hAPP(hAPP(c_Product__Type_OPair(_1573721, _1573721), _1573723), _1573725)), _1573727))), c_Wellfounded_Owf(_1573721, _1573727), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573721, _1573721)), hAPP(hAPP(c_Product__Type_OPair(_1573721, _1573721), _1573725), _1573723)), c_Transitive__Closure_Ortrancl(_1573721, _1573727))))], (8562 ^ _778495) ^ [_921512, _921514] : [class_Lattices_Oab__semigroup__idem__mult(_921512), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921512), _921514), _921514) = _921514)], (10169 ^ _778495) ^ [_953802, _953804, _953806, _953808, _953810, _953812] : [c_Finite__Set_Ofun__left__comm(_953802, _953804, _953806), hBOOL(hAPP(c_Finite__Set_Ofinite(_953802), _953808)), -(hAPP(hAPP(_953806, _953810), hAPP(hAPP(c_Finite__Set_Ofold(_953802, _953804, _953806), _953812), _953808)) = hAPP(hAPP(c_Finite__Set_Ofold(_953802, _953804, _953806), hAPP(hAPP(_953806, _953810), _953812)), _953808))], (28159 ^ _778495) ^ [_1280853, _1280855, _1280857, _1280859] : [class_Groups_Oordered__ab__group__add__abs(_1280853), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280853), hAPP(c_Groups_Oabs__class_Oabs(_1280853), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1280855, _1280853), _1280857), _1280859))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1280855, _1280853), hAPP(hAPP(c_COMBB(_1280853, _1280853, _1280855), c_Groups_Oabs__class_Oabs(_1280853)), _1280857)), _1280859))))], (48070 ^ _778495) ^ [_1747016, _1747018, _1747020, _1747022, _1747024, _1747026, _1747028] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1747016, _1747018, _1747020, _1747022), _1747024), _1747026), _1747028) = c_New__DSequence_Oneg__bind(_1747016, _1747018, hAPP(hAPP(hAPP(_1747020, _1747024), _1747026), _1747028), hAPP(hAPP(c_COMBC(_1747016, 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(_1747018)))), hAPP(hAPP(c_COMBC(_1747016, 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(_1747018))))), hAPP(hAPP(c_COMBC(_1747016, 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(_1747018)))))), _1747022), _1747024)), _1747026)), _1747028)))], (22678 ^ _778495) ^ [_1183895] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1183895))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1183895)))))], (24563 ^ _778495) ^ [_1218344, _1218346, _1218348] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1218344), _1218346)), _1218348) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1218344), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218346), _1218348)))], (52563 ^ _778495) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (40987 ^ _778495) ^ [_1583201, _1583203, _1583205] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583201, _1583201), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1583203)), _1583205) = hAPP(hAPP(c_Relation_Orel__comp(_1583201, _1583201, _1583201), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583201, _1583201), tc_HOL_Obool), _1583203), _1583205)), _1583205))], (28991 ^ _778495) ^ [_1304711, _1304713, _1304715, _1304717, _1304719, _1304721] : [hBOOL(hAPP(hAPP(_1304711, _1304713), _1304715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304717, tc_fun(_1304719, tc_HOL_Obool))), _1304711), _1304721)), -(hBOOL(hAPP(hAPP(_1304721, _1304713), _1304715)))], (46580 ^ _778495) ^ [_1714978, _1714980] : [hBOOL(hAPP(c_List_Odistinct(_1714978), hAPP(c_List_Orev(_1714978), _1714980))), -(hBOOL(hAPP(c_List_Odistinct(_1714978), _1714980)))], (3946 ^ _778495) ^ [_838155, _838157, _838159, _838161, _838163, _838165, _838167, _838169] : [-(c_New__Random__Sequence_Opos__empty(_838169, _838165, _838161, _838157) = c_New__Random__Sequence_Opos__empty(_838167, _838163, _838159, _838155)), _838169 = _838167, _838165 = _838163, _838161 = _838159, _838157 = _838155], (7768 ^ _778495) ^ [_906907, _906909, _906911] : [class_Orderings_Olinorder(_906907), 7771 ^ _778495 : [(7778 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906907), _906911), _906909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906907), _906909), _906911))], (7772 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906907), _906909), _906911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906907), _906911), _906909)))]]], (10061 ^ _778495) ^ [_951811, _951813, _951815] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_951811), _951813)), 10064 ^ _778495 : [(10071 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_951811), _951815), _951813))), -(hAPP(c_Finite__Set_Ocard(_951811), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_951811, tc_HOL_Obool)), _951813), hAPP(hAPP(c_Set_Oinsert(_951811), _951815), c_Orderings_Obot__class_Obot(tc_fun(_951811, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_951811), _951813))], (10065 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_951811), _951815), _951813)), -(hAPP(c_Finite__Set_Ocard(_951811), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_951811, tc_HOL_Obool)), _951813), hAPP(hAPP(c_Set_Oinsert(_951811), _951815), c_Orderings_Obot__class_Obot(tc_fun(_951811, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_951811), _951813)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (12116 ^ _778495) ^ [_990416] : [-(hAPP(c_Nat_OSuc, _990416) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990416), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (21398 ^ _778495) ^ [_1162191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1162191)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1162191 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42892 ^ _778495) ^ [_1633188, _1633190] : [-(c_List_Oset__Cons(_1633188, _1633190, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633188)), c_List_Olist_ONil(_1633188)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633188), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1633188, tc_List_Olist(_1633188), hAPP(hAPP(c_COMBC(_1633188, tc_List_Olist(_1633188), tc_List_Olist(_1633188)), c_List_Olist_OCons(_1633188)), c_List_Olist_ONil(_1633188))), _1633190))], (4266 ^ _778495) ^ [_843137, _843139, _843141, _843143, _843145, _843147, _843149, _843151, _843153, _843155] : [-(c_Predicate_Opred__comp(_843155, _843151, _843147, _843143, _843139) = c_Predicate_Opred__comp(_843153, _843149, _843145, _843141, _843137)), _843155 = _843153, _843151 = _843149, _843147 = _843145, _843143 = _843141, _843139 = _843137], (41736 ^ _778495) ^ [_1605563, _1605565, _1605567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605563, tc_HOL_Obool)), _1605565), _1605567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1605563), tc_HOL_Obool)), c_List_Olists(_1605563, _1605565)), c_List_Olists(_1605563, _1605567))))], (38965 ^ _778495) ^ [_1533570, _1533572, _1533574, _1533576] : [hBOOL(hAPP(c_Predicate_ODomainP(_1533570, _1533572, hAPP(hAPP(c_COMBC(_1533570, tc_fun(tc_prod(_1533570, _1533572), tc_HOL_Obool), tc_fun(_1533572, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533572, tc_fun(tc_fun(tc_prod(_1533570, _1533572), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1533570, _1533572), tc_HOL_Obool), tc_fun(_1533572, tc_HOL_Obool)), _1533570), c_COMBC(_1533572, tc_fun(tc_prod(_1533570, _1533572), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533572, tc_prod(_1533570, _1533572)), tc_fun(_1533572, tc_fun(tc_fun(tc_prod(_1533570, _1533572), tc_HOL_Obool), tc_HOL_Obool)), _1533570), hAPP(c_COMBB(tc_prod(_1533570, _1533572), tc_fun(tc_fun(tc_prod(_1533570, _1533572), tc_HOL_Obool), tc_HOL_Obool), _1533572), c_member(tc_prod(_1533570, _1533572)))), c_Product__Type_OPair(_1533570, _1533572)))), _1533574)), _1533576)), -(hBOOL(hAPP(hAPP(c_member(_1533570), _1533576), hAPP(c_Relation_ODomain(_1533570, _1533572), _1533574))))], (9524 ^ _778495) ^ [_941011, _941013, _941015, _941017] : [hBOOL(hAPP(hAPP(c_member(_941011), _941013), _941015)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941011, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_941011), _941013), _941017)), _941015) = hAPP(hAPP(c_Set_Oinsert(_941011), _941013), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941011, tc_HOL_Obool)), _941017), _941015)))], (39386 ^ _778495) ^ [_1544590, _1544592, _1544594, _1544596, _1544598, _1544600, _1544602] : [-(hAPP(c_Fun_Ocomp(_1544590, _1544592, _1544594, _1544596), hAPP(c_Fun_Ocomp(_1544598, _1544590, _1544594, _1544600), _1544602)) = hAPP(c_Fun_Ocomp(_1544598, _1544592, _1544594, hAPP(c_Fun_Ocomp(_1544590, _1544592, _1544598, _1544596), _1544600)), _1544602))], (39009 ^ _778495) ^ [] : [-(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))))], (34166 ^ _778495) ^ [_1415158] : [-(c_Wellfounded_Omeasure(_1415158) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1415158), c_Wellfounded_Oless__than))], (24369 ^ _778495) ^ [_1214701, _1214703] : [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), _1214701))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1214703))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1214701))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1214703)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1214701)))], (48328 ^ _778495) ^ [_1752883, _1752885, _1752887] : [c_List_Olist_ONil(_1752883) = c_List_Oreplicate(_1752883, _1752885, _1752887), -(_1752885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47774 ^ _778495) ^ [_1740964, _1740966, _1740968] : [hBOOL(hAPP(hAPP(c_member(_1740964), _1740966), hAPP(c_List_Oset(_1740964), _1740968))), -(_1740968 = hAPP(hAPP(c_List_Oappend(_1740964), 47777 ^ [_1740964, _1740966, _1740968]), hAPP(hAPP(c_List_Olist_OCons(_1740964), _1740966), 47778 ^ [_1740964, _1740966, _1740968])))], (50180 ^ _778495) ^ [_1793175, _1793177, _1793179, _1793181, _1793183, _1793185, _1793187, _1793189] : [c_Fun_Obij__betw(_1793175, _1793177, _1793179, _1793181, _1793183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1793175, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1793185, _1793175, _1793187), _1793189)), _1793181)), 50187 ^ _778495 : [(50194 ^ _778495) ^ [] : [c_Fun_Obij__betw(_1793185, _1793177, hAPP(c_Fun_Ocomp(_1793175, _1793177, _1793185, _1793179), _1793187), _1793189, _1793183), -(c_Fun_Obij__betw(_1793185, _1793175, _1793187, _1793189, _1793181))], (50188 ^ _778495) ^ [] : [c_Fun_Obij__betw(_1793185, _1793175, _1793187, _1793189, _1793181), -(c_Fun_Obij__betw(_1793185, _1793177, hAPP(c_Fun_Ocomp(_1793175, _1793177, _1793185, _1793179), _1793187), _1793189, _1793183))]]], (9304 ^ _778495) ^ [_936150, _936152, _936154] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936150, tc_HOL_Obool)), _936152), _936154) = c_Orderings_Obot__class_Obot(tc_fun(_936150, tc_HOL_Obool)), 9307 ^ _778495 : [(9308 ^ _778495) ^ [_936274] : [hBOOL(hAPP(hAPP(c_member(_936150), _936274), _936152)), 9311 ^ _778495 : [(9312 ^ _778495) ^ [_936364] : [hBOOL(hAPP(hAPP(c_member(_936150), _936364), _936154)), _936274 = _936364]]]]], (17728 ^ _778495) ^ [_1096456, _1096458, _1096460] : [class_Int_Onumber(_1096456), 17731 ^ _778495 : [(17738 ^ _778495) ^ [] : [_1096460 = hAPP(c_Int_Onumber__class_Onumber__of(_1096456), _1096458), -(hAPP(c_Int_Onumber__class_Onumber__of(_1096456), _1096458) = _1096460)], (17732 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1096456), _1096458) = _1096460, -(_1096460 = hAPP(c_Int_Onumber__class_Onumber__of(_1096456), _1096458))]]], (5669 ^ _778495) ^ [_867960, _867962, _867964, _867966] : [c_Hoare__Mirabelle_Ohoare__derivs(_867960, _867962, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867960)), _867964), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867960), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_867960, _867962, _867966), -(c_Hoare__Mirabelle_Ohoare__derivs(_867960, _867962, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867960)), _867964), _867966)))], (43502 ^ _778495) ^ [_1647919, _1647921] : [hBOOL(hAPP(c_List_Odistinct(_1647919), hAPP(c_List_Orotate1(_1647919), _1647921))), -(hBOOL(hAPP(c_List_Odistinct(_1647919), _1647921)))], (44861 ^ _778495) ^ [_1677216, _1677218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1677216), _1677218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677216)), hAPP(c_Code__Numeral_Onat__of, _1677218))))], (28093 ^ _778495) ^ [_1279685, _1279687] : [_1279685 = _1279687, -(c_Random_Oinc__shift(_1279685, _1279687) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (45288 ^ _778495) ^ [_1687106, _1687108] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1687106), tc_fun(_1687106, tc_HOL_Obool), c_List_Oset(_1687106)), hAPP(c_List_Oset(tc_List_Olist(_1687106)), c_Enum_Osublists(_1687106, _1687108))) = hAPP(c_Set_OPow(_1687106), hAPP(c_List_Oset(_1687106), _1687108)))], (52391 ^ _778495) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (52365 ^ _778495) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (8106 ^ _778495) ^ [_911989, _911991, _911993] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_911989, tc_HOL_Obool)), _911991), _911993))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911989, tc_HOL_Obool)), _911991), _911993)), -(_911991 = _911993)], (27519 ^ _778495) ^ [_1269579, _1269581] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1269579, _1269581)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1269579, _1269581), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1269581), c_Orderings_Otop__class_Otop(tc_fun(_1269581, tc_HOL_Obool)))))], (1048 ^ _778495) ^ [_794371, _794373, _794375, _794377, _794379, _794381] : [-(c_List_Olist__all(_794379, _794375, _794371)), c_List_Olist__all(_794381, _794377, _794373), _794381 = _794379, _794377 = _794375, _794373 = _794371], (13973 ^ _778495) ^ [_1026632, _1026634, _1026636] : [class_Rings_Olinordered__ring__strict(_1026632), 13976 ^ _778495 : [(13991 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026632), c_Groups_Ozero__class_Ozero(_1026632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026632), _1026634), _1026636)))), 13992 ^ _778495 : [(13999 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026632), _1026634), c_Groups_Ozero__class_Ozero(_1026632))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026632), _1026636), c_Groups_Ozero__class_Ozero(_1026632)))], (13993 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026632), c_Groups_Ozero__class_Ozero(_1026632)), _1026634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026632), c_Groups_Ozero__class_Ozero(_1026632)), _1026636))]]], (13977 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026632), c_Groups_Ozero__class_Ozero(_1026632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026632), _1026634), _1026636))), 13982 ^ _778495 : [(13985 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026632), c_Groups_Ozero__class_Ozero(_1026632)), _1026636)))], (13983 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026632), c_Groups_Ozero__class_Ozero(_1026632)), _1026634)))]], 13986 ^ _778495 : [(13989 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026632), _1026636), c_Groups_Ozero__class_Ozero(_1026632))))], (13987 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026632), _1026634), c_Groups_Ozero__class_Ozero(_1026632))))]]]]], (26922 ^ _778495) ^ [_1259528] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1259528)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1259528)))], (5142 ^ _778495) ^ [_857005, _857007, _857009, _857011] : [-(c_List_Oupt(_857011, _857007) = c_List_Oupt(_857009, _857005)), _857011 = _857009, _857007 = _857005], (20987 ^ _778495) ^ [_1154424, _1154426, _1154428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1154426), 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), _1154426), _1154428))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1154424))), _1154428)))], (23324 ^ _778495) ^ [_1196467, _1196469, _1196471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196467)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1196469, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1196471), _1196467)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1196471), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1196469), _1196471), _1196467))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1196469, _1196471)))], (36226 ^ _778495) ^ [_1460371, _1460373] : [-(c_Fun_Oinj__on(_1460371, _1460371, c_COMBI(_1460371), _1460373))], (28457 ^ _778495) ^ [_1292725, _1292727, _1292729, _1292731, _1292733] : [class_Fields_Ofield__inverse__zero(_1292725), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292727), _1292729)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292727, _1292725), hAPP(hAPP(c_COMBS(_1292727, _1292725, _1292725), hAPP(hAPP(c_COMBB(_1292725, tc_fun(_1292725, _1292725), _1292727), c_Rings_Oinverse__class_Odivide(_1292725)), _1292731)), _1292733)), _1292729) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292725), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292727, _1292725), _1292731), _1292729)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292727, _1292725), _1292733), _1292729)))], (19842 ^ _778495) ^ [] : [-(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))))], (41579 ^ _778495) ^ [_1600639, _1600641, _1600643, _1600645, _1600647, _1600649] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600639), tc_List_Olist(_1600639))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600639), tc_List_Olist(_1600639)), hAPP(hAPP(c_List_Olist_OCons(_1600639), _1600641), _1600643)), hAPP(hAPP(c_List_Olist_OCons(_1600639), _1600645), _1600647))), c_List_Olistrel1(_1600639, _1600649)))), 41580 ^ _778495 : [(41587 ^ _778495) ^ [] : [_1600641 = _1600645, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600639), tc_List_Olist(_1600639))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600639), tc_List_Olist(_1600639)), _1600643), _1600647)), c_List_Olistrel1(_1600639, _1600649)))], (41581 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600639, _1600639)), hAPP(hAPP(c_Product__Type_OPair(_1600639, _1600639), _1600641), _1600645)), _1600649)), _1600643 = _1600647]]], (27811 ^ _778495) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21760 ^ _778495) ^ [_1167886, _1167888, _1167890] : [class_Int_Onumber__ring(_1167886), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167886), hAPP(c_Groups_Ouminus__class_Ouminus(_1167886), hAPP(c_Int_Onumber__class_Onumber__of(_1167886), _1167888))), _1167890) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167886), hAPP(c_Int_Onumber__class_Onumber__of(_1167886), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1167888))), _1167890))], (20002 ^ _778495) ^ [] : [-(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))], (23026 ^ _778495) ^ [_1190247, _1190249, _1190251] : [class_Divides_Osemiring__div(_1190247), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190247), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190247), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190247), _1190249), _1190251)), _1190251)), c_Divides_Odiv__class_Omod(_1190247, _1190249, _1190251)) = _1190249)], (7174 ^ _778495) ^ [_896778, _896780, _896782] : [class_Lattices_Osemilattice__sup(_896778), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896778), _896780), _896782)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896778), _896780), _896782) = _896782)], (52577 ^ _778495) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (52241 ^ _778495) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (26654 ^ _778495) ^ [_1255222, _1255224] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1255222, tc_HOL_Obool), hAPP(c_Set_OPow(_1255222), _1255224)) = _1255224)], (36001 ^ _778495) ^ [_1454334, _1454336] : [-(c_Equiv__Relations_Oequivp(_1454334, _1454336)), 36006 ^ _778495 : [(36009 ^ _778495) ^ [] : [hAPP(_1454336, 36002 ^ [_1454334, _1454336]) = hAPP(_1454336, 36003 ^ [_1454334, _1454336])], (36007 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1454336, 36002 ^ [_1454334, _1454336]), 36003 ^ [_1454334, _1454336])))]], 36010 ^ _778495 : [(36013 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1454336, 36002 ^ [_1454334, _1454336]), 36003 ^ [_1454334, _1454336]))], (36011 ^ _778495) ^ [] : [-(hAPP(_1454336, 36002 ^ [_1454334, _1454336]) = hAPP(_1454336, 36003 ^ [_1454334, _1454336]))]]], (39303 ^ _778495) ^ [_1542414, _1542416, _1542418, _1542420] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542414), _1542416)), 39309 ^ _778495 : [(39312 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542418), hAPP(_1542420, 39308 ^ [_1542414, _1542416, _1542418, _1542420])))], (39310 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542414), 39308 ^ [_1542414, _1542416, _1542418, _1542420]), _1542416)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1542418), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542414, tc_fun(_1542418, tc_HOL_Obool)), _1542416), _1542420))))], (4642 ^ _778495) ^ [_849153, _849155, _849157, _849159, _849161, _849163, _849165, _849167] : [-(c_Random__Sequence_Obind(_849167, _849163, _849159, _849155) = c_Random__Sequence_Obind(_849165, _849161, _849157, _849153)), _849167 = _849165, _849163 = _849161, _849159 = _849157, _849155 = _849153], (22542 ^ _778495) ^ [_1181510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1181510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1181510)))], (52411 ^ _778495) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (6982 ^ _778495) ^ [_893153, _893155] : [class_Lattices_Osemilattice__sup(_893153), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893153), _893155), _893155) = _893155)], (44492 ^ _778495) ^ [_1669375] : [-(hAPP(c_List_Omap(_1669375, _1669375), c_COMBI(_1669375)) = c_Fun_Oid(tc_List_Olist(_1669375)))], (6756 ^ _778495) ^ [_889106, _889108, _889110, _889112] : [6757 ^ _778495 : [(6760 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889106), _889108), _889112))], (6758 ^ _778495) ^ [] : [_889108 = _889110]], -(hBOOL(hAPP(hAPP(c_member(_889106), _889108), hAPP(hAPP(c_Set_Oinsert(_889106), _889110), _889112))))], (29324 ^ _778495) ^ [_1311690, _1311692] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1311690), _1311692)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1311690), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1311692)))], (38367 ^ _778495) ^ [_1517585, _1517587] : [-(hAPP(c_Set_Ovimage(_1517585, _1517585, c_Fun_Oid(_1517585)), _1517587) = _1517587)], (52243 ^ _778495) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (49525 ^ _778495) ^ [_1779146, _1779148, _1779150] : [-(c_Equiv__Relations_Oequiv(_1779146, _1779148, _1779150)), c_Relation_Orefl__on(_1779146, _1779148, _1779150), c_Relation_Osym(_1779146, _1779150), c_Relation_Otrans(_1779146, _1779150)], (27039 ^ _778495) ^ [_1261558, _1261560] : [class_Int_Oring__char__0(_1261558), 27042 ^ _778495 : [(27049 ^ _778495) ^ [] : [_1261560 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1261558), _1261560) = c_Groups_Ozero__class_Ozero(_1261558))], (27043 ^ _778495) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1261558), _1261560) = c_Groups_Ozero__class_Ozero(_1261558), -(_1261560 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (8568 ^ _778495) ^ [_921603, _921605] : [class_Lattices_Oab__semigroup__idem__mult(_921603), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921603), _921605), _921605) = _921605)], (20670 ^ _778495) ^ [_1149010, _1149012] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149010), c_Int_OPls))), 20673 ^ _778495 : [(20680 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149012), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149010)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149012)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149010), _1149012)))], (20674 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149012), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149010)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149012)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149010))]]], (36372 ^ _778495) ^ [_1462903, _1462905, _1462907, _1462909, _1462911] : [c_Fun_Oinj__on(_1462903, _1462905, _1462907, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1462903, tc_HOL_Obool)), _1462909), _1462911)), 36375 ^ _778495 : [(36382 ^ _778495) ^ [] : [_1462909 = _1462911, -(hAPP(c_Set_Oimage(_1462903, _1462905, _1462907), _1462909) = hAPP(c_Set_Oimage(_1462903, _1462905, _1462907), _1462911))], (36376 ^ _778495) ^ [] : [hAPP(c_Set_Oimage(_1462903, _1462905, _1462907), _1462909) = hAPP(c_Set_Oimage(_1462903, _1462905, _1462907), _1462911), -(_1462909 = _1462911)]]], (6970 ^ _778495) ^ [_892961, _892963, _892965] : [_892963 = _892965, -(hBOOL(hAPP(hAPP(c_member(_892961), _892963), hAPP(c_fequal, _892965))))], (46178 ^ _778495) ^ [_1707223, _1707225] : [class_Orderings_Olinorder(_1707223), -(_1707225 = c_List_Olist_ONil(_1707223)), c_List_Olinorder__class_Osorted(_1707223, _1707225), -(c_List_Olinorder__class_Osorted(_1707223, c_List_Obutlast(_1707223, _1707225)))], (34600 ^ _778495) ^ [_1425343, _1425345, _1425347, _1425349] : [hAPP(c_Set_Oimage(_1425343, _1425345, _1425347), c_Orderings_Otop__class_Otop(tc_fun(_1425343, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1425345, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1425345, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1425345, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1425343, _1425345, _1425347), _1425349))), hAPP(c_Set_Oimage(_1425343, _1425345, _1425347), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1425343, tc_HOL_Obool)), _1425349)))))], (43760 ^ _778495) ^ [_1653842, _1653844] : [-(_1653842 = c_List_Olist_ONil(_1653844)), -(hAPP(c_List_Orotate1(_1653844), _1653842) = hAPP(hAPP(c_List_Oappend(_1653844), hAPP(c_List_Otl(_1653844), _1653842)), hAPP(hAPP(c_List_Olist_OCons(_1653844), hAPP(c_List_Ohd(_1653844), _1653842)), c_List_Olist_ONil(_1653844))))], (23020 ^ _778495) ^ [_1190080, _1190082, _1190084, _1190086] : [class_Divides_Osemiring__div(_1190080), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190080), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190080), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190080), _1190082), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190080), _1190084), _1190082))), c_Divides_Odiv__class_Omod(_1190080, _1190084, _1190082))), _1190086) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190080), _1190084), _1190086))], (43145 ^ _778495) ^ [_1639260, _1639262, _1639264, _1639266] : [hAPP(hAPP(c_List_Oappend(_1639260), _1639262), _1639264) = hAPP(hAPP(c_List_Oappend(_1639260), _1639266), _1639264), -(_1639262 = _1639266)], (45887 ^ _778495) ^ [_1701907, _1701909] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1701907), _1701909) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701907, _1701909)))], (34759 ^ _778495) ^ [_1428606, _1428608, _1428610, _1428612, _1428614] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428606, tc_fun(_1428608, tc_HOL_Obool)), _1428610), hAPP(hAPP(c_COMBS(_1428606, tc_fun(_1428608, tc_HOL_Obool), tc_fun(_1428608, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428608, tc_HOL_Obool), tc_fun(tc_fun(_1428608, tc_HOL_Obool), tc_fun(_1428608, tc_HOL_Obool)), _1428606), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428608, tc_HOL_Obool))), _1428612)), _1428614)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428608, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1428608, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428606, tc_fun(_1428608, tc_HOL_Obool), _1428612), _1428610))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1428608, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428606, tc_fun(_1428608, tc_HOL_Obool), _1428614), _1428610))))], (38996 ^ _778495) ^ [_1534656, _1534658, _1534660, _1534662] : [hBOOL(hAPP(c_Predicate_ODomainP(_1534656, _1534658, _1534660), _1534662)), -(hBOOL(hAPP(hAPP(_1534660, _1534662), 38999 ^ [_1534656, _1534658, _1534660, _1534662])))], (42680 ^ _778495) ^ [_1629239, _1629241] : [-(hAPP(hAPP(c_List_Otake(_1629239), _1629241), c_List_Olist_ONil(_1629239)) = c_List_Olist_ONil(_1629239))], (16268 ^ _778495) ^ [_1069100, _1069102, _1069104] : [class_Rings_Oring__1(_1069100), hBOOL(hAPP(hAPP(c_member(_1069100), _1069102), c_Int_Oring__1__class_OInts(_1069100))), hBOOL(hAPP(hAPP(c_member(_1069100), _1069104), c_Int_Oring__1__class_OInts(_1069100))), -(hBOOL(hAPP(hAPP(c_member(_1069100), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1069100), _1069102), _1069104)), c_Int_Oring__1__class_OInts(_1069100))))], (43754 ^ _778495) ^ [_1653795, _1653797] : [-(_1653795 = c_List_Olist_ONil(_1653797)), -(hAPP(c_List_Ohd(_1653797), _1653795) = hAPP(hAPP(c_List_Onth(_1653797), _1653795), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (40475 ^ _778495) ^ [_1570760, _1570762, _1570764, _1570766, _1570768] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570760, _1570760)), hAPP(hAPP(c_Product__Type_OPair(_1570760, _1570760), _1570762), _1570764)), c_Transitive__Closure_Ortrancl(_1570760, _1570766))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570760, _1570760)), hAPP(hAPP(c_Product__Type_OPair(_1570760, _1570760), _1570764), _1570768)), c_Transitive__Closure_Otrancl(_1570760, _1570766))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570760, _1570760)), hAPP(hAPP(c_Product__Type_OPair(_1570760, _1570760), _1570762), _1570768)), c_Transitive__Closure_Otrancl(_1570760, _1570766))))], (40258 ^ _778495) ^ [_1564745, _1564747, _1564749, _1564751, _1564753] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564745, _1564745)), hAPP(hAPP(c_Product__Type_OPair(_1564745, _1564745), _1564747), _1564749)), c_Transitive__Closure_Otrancl(_1564745, _1564751))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1564745, _1564745)), hAPP(hAPP(c_Product__Type_OPair(_1564745, _1564745), _1564749), _1564753)), _1564751)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564745, _1564745)), hAPP(hAPP(c_Product__Type_OPair(_1564745, _1564745), _1564747), _1564753)), c_Transitive__Closure_Otrancl(_1564745, _1564751))))], (50521 ^ _778495) ^ [_1802026] : [-(c_Lazy__Sequence_Oflat(_1802026, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1802026))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802026))], (52083 ^ _778495) ^ [_1829606, _1829608] : [class_Complete__Lattice_Ocomplete__lattice(_1829606), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1829608, _1829606)))], (3238 ^ _778495) ^ [_826847, _826849] : [_826849 = _826847, -(c_Random_Orange(_826849) = c_Random_Orange(_826847))], (32874 ^ _778495) ^ [_1385027, _1385029, _1385031] : [class_Orderings_Oorder(_1385027), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385027), _1385029), _1385031)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1385027, _1385031, _1385029) = c_Orderings_Obot__class_Obot(tc_fun(_1385027, tc_HOL_Obool)))], (45143 ^ _778495) ^ [_1684033, _1684035, _1684037, _1684039, _1684041, _1684043, _1684045] : [-(c_List_Olist__all2(_1684033, _1684035, _1684037, hAPP(hAPP(c_List_Olist_OCons(_1684033), _1684039), _1684041), hAPP(hAPP(c_List_Olist_OCons(_1684035), _1684043), _1684045))), hBOOL(hAPP(hAPP(_1684037, _1684039), _1684043)), c_List_Olist__all2(_1684033, _1684035, _1684037, _1684041, _1684045)], (37198 ^ _778495) ^ [_1481055, _1481057, _1481059, _1481061] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1481055), hAPP(c_Set_Ovimage(_1481055, _1481057, _1481059), _1481061))), hAPP(c_Set_Oimage(_1481055, _1481057, _1481059), c_Orderings_Otop__class_Otop(tc_fun(_1481055, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1481057, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1481057), _1481061)))], (51905 ^ _778495) ^ [_1826514, _1826516, _1826518, _1826520] : [class_Rings_Ocomm__semiring__1(_1826514), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826514), _1826516), _1826518)), _1826520)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826514), _1826516), _1826520)))], (8184 ^ _778495) ^ [_913424, _913426, _913428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913424, tc_HOL_Obool)), _913426), _913428)), hBOOL(hAPP(c_Finite__Set_Ofinite(_913424), _913428)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_913424), _913426)))], (22766 ^ _778495) ^ [_1185440, _1185442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1185440)), c_Int_OBit1(_1185442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185440), _1185442)))], (39418 ^ _778495) ^ [_1545366, _1545368, _1545370, _1545372, _1545374, _1545376, _1545378] : [-(hAPP(c_Product__Type_Oapfst(_1545366, _1545368, _1545370, _1545372), hAPP(c_Product__Type_Oapfst(_1545374, _1545366, _1545370, _1545376), _1545378)) = hAPP(c_Product__Type_Oapfst(_1545374, _1545368, _1545370, hAPP(c_Fun_Ocomp(_1545366, _1545368, _1545374, _1545372), _1545376)), _1545378))], (50210 ^ _778495) ^ [_1793799, _1793801, _1793803, _1793805, _1793807, _1793809, _1793811, _1793813] : [c_Fun_Obij__betw(_1793799, _1793801, _1793803, _1793805, _1793807), c_Fun_Obij__betw(_1793801, _1793809, _1793811, _1793807, _1793813), -(c_Fun_Obij__betw(_1793799, _1793809, hAPP(c_Fun_Ocomp(_1793801, _1793809, _1793799, _1793811), _1793803), _1793805, _1793813))], (32016 ^ _778495) ^ [_1367268, _1367270, _1367272, _1367274, _1367276] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367268, tc_fun(_1367270, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1367268), _1367272), _1367274)), _1367276) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367270, tc_HOL_Obool)), hAPP(_1367276, _1367272)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367268, tc_fun(_1367270, tc_HOL_Obool)), _1367274), _1367276)))], (28551 ^ _778495) ^ [_1295109, _1295111, _1295113, _1295115, _1295117] : [class_Groups_Ocomm__monoid__mult(_1295109), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295111), _1295113)), 28558 ^ _778495 : [(28565 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1295111), _1295115), _1295113))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295111, _1295109), hAPP(hAPP(c_COMBC(_1295111, _1295109, _1295109), hAPP(hAPP(c_COMBS(_1295111, _1295109, tc_fun(_1295109, _1295109)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1295109, tc_fun(_1295109, _1295109)), _1295111), c_If(_1295109)), hAPP(c_fequal, _1295115))), _1295117)), c_Groups_Oone__class_Oone(_1295109))), _1295113) = c_Groups_Oone__class_Oone(_1295109))], (28559 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1295111), _1295115), _1295113)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295111, _1295109), hAPP(hAPP(c_COMBC(_1295111, _1295109, _1295109), hAPP(hAPP(c_COMBS(_1295111, _1295109, tc_fun(_1295109, _1295109)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1295109, tc_fun(_1295109, _1295109)), _1295111), c_If(_1295109)), hAPP(c_fequal, _1295115))), _1295117)), c_Groups_Oone__class_Oone(_1295109))), _1295113) = hAPP(_1295117, _1295115))]]], (7320 ^ _778495) ^ [_899878, _899880, _899882, _899884, _899886] : [c_Finite__Set_Ofolding__one(_899878, _899880, _899882), hBOOL(hAPP(c_Finite__Set_Ofinite(_899878), _899884)), 7327 ^ _778495 : [(7334 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899878, tc_HOL_Obool)), _899884), hAPP(hAPP(c_Set_Oinsert(_899878), _899886), c_Orderings_Obot__class_Obot(tc_fun(_899878, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_899878, tc_HOL_Obool))), -(hAPP(_899882, hAPP(hAPP(c_Set_Oinsert(_899878), _899886), _899884)) = hAPP(hAPP(_899880, _899886), hAPP(_899882, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899878, tc_HOL_Obool)), _899884), hAPP(hAPP(c_Set_Oinsert(_899878), _899886), c_Orderings_Obot__class_Obot(tc_fun(_899878, tc_HOL_Obool)))))))], (7328 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899878, tc_HOL_Obool)), _899884), hAPP(hAPP(c_Set_Oinsert(_899878), _899886), c_Orderings_Obot__class_Obot(tc_fun(_899878, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_899878, tc_HOL_Obool)), -(hAPP(_899882, hAPP(hAPP(c_Set_Oinsert(_899878), _899886), _899884)) = _899886)]]], (29182 ^ _778495) ^ [_1309151, _1309153, _1309155] : [-(hAPP(c_Nat_Onat_Onat__rec(_1309151, _1309153, _1309155), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1309153)], (39889 ^ _778495) ^ [_1556100, _1556102] : [39891 ^ _778495 : [(39894 ^ _778495) ^ [] : [39890 ^ [_1556100, _1556102] = c_Orderings_Obot__class_Obot(tc_fun(_1556100, tc_HOL_Obool))], (39892 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1556100, tc_HOL_Obool)), 39890 ^ [_1556100, _1556102]), hAPP(c_Relation_OImage(_1556100, _1556100, _1556102), 39890 ^ [_1556100, _1556102]))))]], -(c_Wellfounded_Owf(_1556100, _1556102))], (24956 ^ _778495) ^ [_1224904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224904), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1224904) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34365 ^ _778495) ^ [_1420067, _1420069, _1420071, _1420073, _1420075, _1420077] : [-(hAPP(c_Set_Oimage(_1420067, _1420069, _1420071), hAPP(c_Set_Oimage(_1420073, _1420067, _1420075), _1420077)) = hAPP(c_Set_Oimage(_1420073, _1420069, hAPP(hAPP(c_COMBB(_1420067, _1420069, _1420073), _1420071), _1420075)), _1420077))], (50777 ^ _778495) ^ [_1806706, _1806708, _1806710, _1806712] : [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), _1806706, _1806708)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806710, _1806712))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806706), _1806708)), 50784 ^ _778495 : [(50787 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806708), _1806712)))], (50785 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806710), _1806706)))]]], (3546 ^ _778495) ^ [_831635, _831637, _831639, _831641] : [-(c_List_Olinorder__class_Osorted__list__of__set(_831641, _831637) = c_List_Olinorder__class_Osorted__list__of__set(_831639, _831635)), _831641 = _831639, _831637 = _831635], (26904 ^ _778495) ^ [_1259269, _1259271] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1259269), _1259271) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 26905 ^ _778495 : [(26912 ^ _778495) ^ [] : [_1259269 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1259271 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (26906 ^ _778495) ^ [] : [_1259269 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1259271 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (48192 ^ _778495) ^ [_1750415, _1750417, _1750419, _1750421] : [-(hAPP(hAPP(c_List_Omap(_1750415, _1750417), hAPP(c_COMBK(_1750417, _1750415), _1750419)), _1750421) = c_List_Oreplicate(_1750417, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750415)), _1750421), _1750419))], (37236 ^ _778495) ^ [_1481884, _1481886, _1481888, _1481890] : [hBOOL(hAPP(hAPP(c_member(_1481884), _1481886), _1481888)), -(hAPP(c_Set_Ovimage(_1481890, _1481884, hAPP(c_COMBK(_1481884, _1481890), _1481886)), _1481888) = c_Orderings_Otop__class_Otop(tc_fun(_1481890, tc_HOL_Obool)))], (44879 ^ _778495) ^ [_1677532, _1677534] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1677532), _1677534) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677532)), hAPP(c_Code__Numeral_Onat__of, _1677534))))], (1358 ^ _778495) ^ [_798498, _798500] : [-(class_Rings_Oring(_798498)), _798500 = _798498, class_Rings_Oring(_798500)], (48792 ^ _778495) ^ [_1763388, _1763390, _1763392] : [c_List_Olist__ex(_1763388, _1763392, _1763390), 48796 ^ _778495 : [(48799 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1763392, 48795 ^ [_1763388, _1763390, _1763392])))], (48797 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763388), 48795 ^ [_1763388, _1763390, _1763392]), hAPP(c_List_Oset(_1763388), _1763390))))]]], (43882 ^ _778495) ^ [_1656261, _1656263, _1656265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656261), _1656263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656261), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656263), _1656265))))], (33457 ^ _778495) ^ [_1399566, _1399568, _1399570, _1399572, _1399574] : [_1399566 = c_Orderings_Obot__class_Obot(tc_fun(_1399568, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399570, tc_HOL_Obool)), _1399572), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399568, tc_fun(_1399570, tc_HOL_Obool)), _1399566), _1399574)) = _1399572)], (39011 ^ _778495) ^ [_1534907, _1534909] : [c_Wellfounded_Owf(_1534907, _1534909), -(c_Wellfounded_Owf(tc_List_Olist(_1534907), c_List_Olex(_1534907, _1534909)))], (31624 ^ _778495) ^ [_1356331, _1356333, _1356335, _1356337, _1356339, _1356341, _1356343] : [-(hAPP(c_Product__Type_Oapfst(_1356331, _1356333, _1356335, _1356337), hAPP(c_Product__Type_Oapsnd(_1356339, _1356335, _1356331, _1356341), _1356343)) = hAPP(hAPP(c_Product__Type_OPair(_1356333, _1356335), hAPP(_1356337, hAPP(c_Product__Type_Ofst(_1356331, _1356339), _1356343))), hAPP(_1356341, hAPP(c_Product__Type_Osnd(_1356331, _1356339), _1356343))))], (33367 ^ _778495) ^ [_1397161, _1397163, _1397165, _1397167] : [class_Complete__Lattice_Ocomplete__lattice(_1397161), -(_1397163 = c_Orderings_Obot__class_Obot(tc_fun(_1397165, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397165, _1397161), _1397163), hAPP(c_COMBK(_1397161, _1397165), _1397167)) = _1397167)], (40991 ^ _778495) ^ [_1583346, _1583348] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583346, _1583346), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1583348) = c_Relation_OId(_1583346))], (41294 ^ _778495) ^ [_1591707, _1591709, _1591711] : [-(c_Nitpick_Oof__frac(_1591709, _1591707, _1591711) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1591707), hAPP(c_Int_Oring__1__class_Oof__int(_1591707), hAPP(c_Nitpick_Onum(_1591709), _1591711))), hAPP(c_Int_Oring__1__class_Oof__int(_1591707), hAPP(c_Nitpick_Odenom(_1591709), _1591711)))), class_Rings_Oinverse(_1591707), class_Rings_Oring__1(_1591707)], (26658 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33256 ^ _778495) ^ [_1393323, _1393325, _1393327, _1393329, _1393331, _1393333] : [class_Complete__Lattice_Ocomplete__lattice(_1393323), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393325, _1393323), _1393327), hAPP(hAPP(c_COMBB(tc_fun(_1393329, _1393323), _1393323, _1393325), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393329, _1393323), _1393331)), _1393333)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393329, _1393323), _1393331), hAPP(hAPP(c_COMBB(tc_fun(_1393325, _1393323), _1393323, _1393329), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393325, _1393323), _1393327)), hAPP(c_COMBC(_1393325, _1393329, _1393323), _1393333))))], (22694 ^ _778495) ^ [_1184151, _1184153] : [class_Int_Onumber__ring(_1184151), -(hAPP(c_Int_Onumber__class_Onumber__of(_1184151), c_Int_OBit0(_1184153)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184151), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184151), c_Groups_Ozero__class_Ozero(_1184151)), hAPP(c_Int_Onumber__class_Onumber__of(_1184151), _1184153))), hAPP(c_Int_Onumber__class_Onumber__of(_1184151), _1184153)))], (42672 ^ _778495) ^ [_1629109, _1629111, _1629113] : [c_List_Olist_ONil(_1629109) = hAPP(hAPP(c_List_Olist_OCons(_1629109), _1629111), _1629113)], (39017 ^ _778495) ^ [_1534994, _1534996, _1534998] : [c_Wellfounded_Owf(_1534994, _1534996), -(c_Wellfounded_Owf(tc_List_Olist(_1534994), hAPP(c_List_Olexn(_1534994, _1534996), _1534998)))], (45223 ^ _778495) ^ [_1685585, _1685587, _1685589, _1685591, _1685593] : [c_List_Olist__all2(_1685585, _1685587, _1685589, _1685591, _1685593), 45226 ^ _778495 : [(45229 ^ _778495) ^ [_1685748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685748), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685585)), _1685591))), -(hBOOL(hAPP(hAPP(_1685589, hAPP(hAPP(c_List_Onth(_1685585), _1685591), _1685748)), hAPP(hAPP(c_List_Onth(_1685587), _1685593), _1685748))))], (45227 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685585)), _1685591) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685587)), _1685593))]]], (2956 ^ _778495) ^ [_822380, _822382] : [_822382 = _822380, -(c_HOL_Obool_Obool__size(_822382) = c_HOL_Obool_Obool__size(_822380))], (7982 ^ _778495) ^ [_909947, _909949, _909951] : [class_Orderings_Oorder(_909947), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909947), _909949), _909951)), -(_909949 = _909951), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909947), _909949), _909951)))], (35240 ^ _778495) ^ [_1436850, _1436852, _1436854] : [class_Orderings_Olinorder(_1436850), 35243 ^ _778495 : [(35250 ^ _778495) ^ [] : [_1436852 = _1436854, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1436850), _1436852) = hAPP(c_SetInterval_Oord__class_OatLeast(_1436850), _1436854))], (35244 ^ _778495) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1436850), _1436852) = hAPP(c_SetInterval_Oord__class_OatLeast(_1436850), _1436854), -(_1436852 = _1436854)]]], (44474 ^ _778495) ^ [_1668935, _1668937, _1668939, _1668941, _1668943] : [-(hAPP(hAPP(c_List_Otake(_1668935), _1668937), hAPP(hAPP(c_List_Omap(_1668939, _1668935), _1668941), _1668943)) = hAPP(hAPP(c_List_Omap(_1668939, _1668935), _1668941), hAPP(hAPP(c_List_Otake(_1668939), _1668937), _1668943)))], (20161 ^ _778495) ^ [_1140654, _1140656] : [class_Rings_Oring__1(_1140654), -(hBOOL(hAPP(hAPP(c_member(_1140654), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140654), _1140656)), c_Int_Oring__1__class_OInts(_1140654))))], (34412 ^ _778495) ^ [_1421207, _1421209, _1421211, _1421213] : [c_Orderings_Obot__class_Obot(tc_fun(_1421207, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1421209, _1421207, _1421211), _1421213), -(_1421213 = c_Orderings_Obot__class_Obot(tc_fun(_1421209, tc_HOL_Obool)))], (2532 ^ _778495) ^ [_815836, _815838, _815840, _815842] : [-(c_Divides_Odivmod__nat(_815842, _815838) = c_Divides_Odivmod__nat(_815840, _815836)), _815842 = _815840, _815838 = _815836], (35450 ^ _778495) ^ [_1440981, _1440983] : [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)), _1440981), _1440983)), 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)), _1440981), 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)), _1440983), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (46234 ^ _778495) ^ [_1708131, _1708133] : [class_Orderings_Olinorder(_1708131), c_List_Olinorder__class_Osorted(_1708131, _1708133), -(c_List_Olinorder__class_Osorted(_1708131, c_List_Oremdups(_1708131, _1708133)))], (8696 ^ _778495) ^ [_923965, _923967, _923969, _923971, _923973, _923975, _923977, _923979] : [c_Finite__Set_Ofolding__image__simple__idem(_923965, _923967, _923969, _923971, _923973, _923975), hBOOL(hAPP(c_Finite__Set_Ofinite(_923967), _923977)), hBOOL(hAPP(c_Finite__Set_Ofinite(_923967), _923979)), -(hAPP(_923975, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923967, tc_HOL_Obool)), _923977), _923979)) = hAPP(hAPP(_923969, hAPP(_923975, _923977)), hAPP(_923975, _923979)))], (3244 ^ _778495) ^ [_826932, _826934, _826936, _826938] : [-(c_Code__Numeral_Onat__of__aux(_826938, _826934) = c_Code__Numeral_Onat__of__aux(_826936, _826932)), _826938 = _826936, _826934 = _826932], (15283 ^ _778495) ^ [_1049962] : [class_Rings_Olinordered__semidom(_1049962), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049962), c_Groups_Ozero__class_Ozero(_1049962)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049962), c_Groups_Oone__class_Oone(_1049962)), c_Groups_Oone__class_Oone(_1049962)))))], (28201 ^ _778495) ^ [_1281826, _1281828, _1281830, _1281832, _1281834] : [class_Lattices_Olattice(_1281826), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281828, _1281826)), _1281830), _1281832), _1281834) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281826), hAPP(_1281830, _1281834)), hAPP(_1281832, _1281834)))], (1588 ^ _778495) ^ [_801373, _801375] : [-(class_Groups_Oordered__ab__semigroup__add(_801373)), _801375 = _801373, class_Groups_Oordered__ab__semigroup__add(_801375)], (19972 ^ _778495) ^ [_1137255, _1137257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137255)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137257))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1137255), _1137257)))], (29900 ^ _778495) ^ [_1322413, _1322415, _1322417, _1322419, _1322421] : [-(hAPP(c_Product__Type_Osnd(_1322413, _1322415), hAPP(c_Product__Type_Oapsnd(_1322417, _1322415, _1322413, _1322419), _1322421)) = hAPP(_1322419, hAPP(c_Product__Type_Osnd(_1322413, _1322417), _1322421)))], (22700 ^ _778495) ^ [_1184296, _1184298] : [class_Groups_Oordered__ab__group__add__abs(_1184296), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184296), _1184298), c_Groups_Ozero__class_Ozero(_1184296))), -(hAPP(c_Groups_Oabs__class_Oabs(_1184296), _1184298) = hAPP(c_Groups_Ouminus__class_Ouminus(_1184296), _1184298))], (12424 ^ _778495) ^ [_997389, _997391, _997393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_997389, tc_HOL_Obool), tc_HOL_Obool)), _997391), _997393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997389, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_997389, tc_HOL_Obool), _997391)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_997389, tc_HOL_Obool), _997393))))], (26762 ^ _778495) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (49854 ^ _778495) ^ [_1786629] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49850 ^ [_1786629]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (6638 ^ _778495) ^ [_886872, _886874, _886876, _886878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886872, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886872, tc_HOL_Obool)), _886874), hAPP(hAPP(c_Set_Oinsert(_886872), _886876), c_Orderings_Obot__class_Obot(tc_fun(_886872, tc_HOL_Obool))))), _886878)), hBOOL(hAPP(hAPP(c_member(_886872), _886876), _886874)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886872, tc_HOL_Obool)), _886874), hAPP(hAPP(c_Set_Oinsert(_886872), _886876), _886878))))], (28583 ^ _778495) ^ [_1295935, _1295937, _1295939, _1295941, _1295943] : [class_Groups_Ocomm__monoid__mult(_1295935), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295937), _1295939)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1295935, _1295937, c_Groups_Otimes__class_Otimes(_1295935)), hAPP(hAPP(c_COMBS(_1295937, _1295935, _1295935), hAPP(hAPP(c_COMBB(_1295935, tc_fun(_1295935, _1295935), _1295937), c_Groups_Otimes__class_Otimes(_1295935)), _1295941)), _1295943)), c_Groups_Oone__class_Oone(_1295935)), _1295939) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295935), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1295935, _1295937, c_Groups_Otimes__class_Otimes(_1295935)), _1295941), c_Groups_Oone__class_Oone(_1295935)), _1295939)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1295935, _1295937, c_Groups_Otimes__class_Otimes(_1295935)), _1295943), c_Groups_Oone__class_Oone(_1295935)), _1295939)))], (44399 ^ _778495) ^ [_1666982, _1666984, _1666986, _1666988, _1666990] : [44401 ^ _778495 : [(44404 ^ _778495) ^ [] : [hAPP(_1666986, 44400 ^ [_1666982, _1666984, _1666986, _1666988, _1666990]) = hAPP(_1666990, 44400 ^ [_1666982, _1666984, _1666986, _1666988, _1666990])], (44402 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1666982), 44400 ^ [_1666982, _1666984, _1666986, _1666988, _1666990]), hAPP(c_List_Oset(_1666982), _1666988))))]], -(hAPP(hAPP(c_List_Omap(_1666982, _1666984), _1666986), _1666988) = hAPP(hAPP(c_List_Omap(_1666982, _1666984), _1666990), _1666988))], (20756 ^ _778495) ^ [_1150559, _1150561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1150559, _1150561))))], (6726 ^ _778495) ^ [_888558, _888560, _888562] : [_888558 = c_Orderings_Obot__class_Obot(tc_fun(_888560, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_888560), _888562), _888558))], (25473 ^ _778495) ^ [_1233604, _1233606] : [25474 ^ _778495 : [(25477 ^ _778495) ^ [] : [_1233606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25475 ^ _778495) ^ [] : [-(_1233604 = 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), _1233604)), _1233606))))], (49324 ^ _778495) ^ [_1775790, _1775792] : [c_Equiv__Relations_Oequivp(_1775790, _1775792), -(c_Equiv__Relations_Opart__equivp(_1775790, _1775792))], (37156 ^ _778495) ^ [_1479851, _1479853, _1479855] : [-(hAPP(c_Set_Ovimage(_1479851, _1479853, _1479855), c_Orderings_Obot__class_Obot(tc_fun(_1479853, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1479851, tc_HOL_Obool)))], (49539 ^ _778495) ^ [_1779354, _1779356] : [c_Predicate_Osymp(_1779354, _1779356), -(c_Relation_Osym(_1779354, hAPP(c_Set_OCollect(tc_prod(_1779354, _1779354)), hAPP(c_Product__Type_Oprod_Oprod__case(_1779354, _1779354, tc_HOL_Obool), _1779356))))], (29292 ^ _778495) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (28981 ^ _778495) ^ [_1304478, _1304480, _1304482, _1304484, _1304486, _1304488] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304478, tc_fun(_1304480, tc_HOL_Obool))), _1304482), _1304484), _1304486), _1304488)), 28984 ^ _778495 : [(28987 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1304484, _1304486), _1304488)))], (28985 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1304482, _1304486), _1304488)))]]], (26656 ^ _778495) ^ [_1255270, _1255272] : [hAPP(c_Set_OPow(_1255270), _1255272) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1255270, tc_HOL_Obool), tc_HOL_Obool))], (52631 ^ _778495) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (17772 ^ _778495) ^ [_1097167, _1097169, _1097171, _1097173] : [class_Orderings_Olinorder(_1097167), 17775 ^ _778495 : [(17784 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097167), _1097169), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1097167), _1097171), _1097173)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097167), _1097169), _1097171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097167), _1097169), _1097173))], (17776 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097167), _1097169), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1097167), _1097171), _1097173))), 17779 ^ _778495 : [(17782 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097167), _1097169), _1097173)))], (17780 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097167), _1097169), _1097171)))]]]]], (38031 ^ _778495) ^ [_1503738, _1503740, _1503742, _1503744, _1503746, _1503748] : [class_Groups_Ocomm__monoid__add(_1503738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503740), _1503742)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503740, _1503738), hAPP(hAPP(c_COMBS(_1503740, _1503738, _1503738), hAPP(hAPP(c_COMBS(_1503740, _1503738, tc_fun(_1503738, _1503738)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1503738, tc_fun(_1503738, _1503738)), _1503740), c_If(_1503738)), _1503744)), _1503746)), _1503748)), _1503742) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1503738), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503740, _1503738), _1503746), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1503740, tc_HOL_Obool)), _1503742), hAPP(c_Set_OCollect(_1503740), _1503744)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503740, _1503738), _1503748), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1503740, tc_HOL_Obool)), _1503742), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1503740, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1503740), _1503744))))))], (48632 ^ _778495) ^ [_1759644, _1759646, _1759648] : [-(c_FunDef_OTHE__default(_1759646, _1759648, _1759644) = _1759648), 48634 ^ _778495 : [(48637 ^ _778495) ^ [_1759766] : [hBOOL(hAPP(_1759644, _1759766)), -(_1759766 = 48633 ^ [_1759644, _1759646, _1759648])], (48635 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1759644, 48633 ^ [_1759644, _1759646, _1759648])))]]], (47616 ^ _778495) ^ [_1737775, _1737777, _1737779] : [class_Enum_Oenum(_1737775), class_Enum_Oenum(_1737777), 47623 ^ _778495 : [(47630 ^ _778495) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737777), hAPP(hAPP(c_COMBB(tc_fun(_1737775, tc_HOL_Obool), tc_HOL_Obool, _1737777), c_Enum_Oenum__class_Oenum__all(_1737775)), hAPP(hAPP(c_COMBB(tc_fun(_1737775, tc_prod(_1737777, _1737775)), tc_fun(_1737775, tc_HOL_Obool), _1737777), hAPP(c_COMBB(tc_prod(_1737777, _1737775), tc_HOL_Obool, _1737775), _1737779)), c_Product__Type_OPair(_1737777, _1737775))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1737777, _1737775)), _1737779)))], (47624 ^ _778495) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1737777, _1737775)), _1737779)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737777), hAPP(hAPP(c_COMBB(tc_fun(_1737775, tc_HOL_Obool), tc_HOL_Obool, _1737777), c_Enum_Oenum__class_Oenum__all(_1737775)), hAPP(hAPP(c_COMBB(tc_fun(_1737775, tc_prod(_1737777, _1737775)), tc_fun(_1737775, tc_HOL_Obool), _1737777), hAPP(c_COMBB(tc_prod(_1737777, _1737775), tc_HOL_Obool, _1737775), _1737779)), c_Product__Type_OPair(_1737777, _1737775))))))]]], (7532 ^ _778495) ^ [_903160, _903162, _903164] : [class_Orderings_Opreorder(_903160), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903160), _903162), _903164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903160), _903164), _903162))], (39664 ^ _778495) ^ [_1551012, _1551014, _1551016, _1551018, _1551020, _1551022, _1551024] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1551012, _1551014, _1551016), hAPP(c_Fun_Ocomp(_1551018, tc_fun(_1551014, _1551016), _1551012, _1551020), _1551022)), _1551024) = hAPP(hAPP(_1551020, hAPP(_1551022, hAPP(c_Product__Type_Ofst(_1551012, _1551014), _1551024))), hAPP(c_Product__Type_Osnd(_1551012, _1551014), _1551024)))], (38041 ^ _778495) ^ [_1504117, _1504119] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1504117))), -(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)), _1504117))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1504119)))) = 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)), _1504117))), 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, _1504119))))))], (23094 ^ _778495) ^ [_1191665, _1191667, _1191669, _1191671] : [class_Divides_Osemiring__div(_1191665), -(c_Divides_Odiv__class_Omod(_1191665, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191665), _1191667), c_Divides_Odiv__class_Omod(_1191665, _1191669, _1191671)), _1191671) = c_Divides_Odiv__class_Omod(_1191665, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191665), _1191667), _1191669), _1191671))], (11718 ^ _778495) ^ [_981927, _981929, _981931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981927), _981929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981927), _981931)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981929), _981931))))], (12968 ^ _778495) ^ [_1009708, _1009710, _1009712, _1009714] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1009708), _1009710)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009712), _1009714)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1009708, _1009712)), c_Sum__Type_OPlus(_1009708, _1009712, _1009710, _1009714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1009708), _1009710)), hAPP(c_Finite__Set_Ocard(_1009712), _1009714)))], (48430 ^ _778495) ^ [_1754945, _1754947, _1754949, _1754951] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1754945, _1754947), c_Lazy__Sequence_Olazy__sequence_OInsert(_1754945, _1754949, _1754951)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1754947, _1754949)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1754945, _1754947), _1754951))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12922 ^ _778495) ^ [_1008585, _1008587, _1008589] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1008585, tc_HOL_Obool)), _1008587)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008585), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1008585, tc_HOL_Obool), _1008587))), 12932 ^ _778495 : [(12935 ^ _778495) ^ [] : [hAPP(c_Finite__Set_Ocard(_1008585), 12931 ^ [_1008585, _1008587, _1008589]) = _1008589], (12933 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1008585, tc_HOL_Obool)), 12931 ^ [_1008585, _1008587, _1008589]), _1008587)))]], 12939 ^ _778495 : [(12943 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1008585, tc_HOL_Obool)), 12941 ^ [_1008585, _1008587, _1008589]), _1008587)))], (12945 ^ _778495) ^ [] : [12938 ^ [_1008585, _1008587, _1008589] = 12941 ^ [_1008585, _1008587, _1008589]], (12947 ^ _778495) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1008585, tc_HOL_Obool)), 12938 ^ [_1008585, _1008587, _1008589]), 12941 ^ [_1008585, _1008587, _1008589]) = c_Orderings_Obot__class_Obot(tc_fun(_1008585, tc_HOL_Obool))], (12940 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1008585, tc_HOL_Obool)), 12938 ^ [_1008585, _1008587, _1008589]), _1008587)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1008589), hAPP(c_Finite__Set_Ocard(tc_fun(_1008585, tc_HOL_Obool)), _1008587)) = hAPP(c_Finite__Set_Ocard(_1008585), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1008585, tc_HOL_Obool), _1008587)))], (30307 ^ _778495) ^ [_1330670, _1330672, _1330674] : [class_Orderings_Olinorder(_1330670), 30310 ^ _778495 : [(30317 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330670), _1330672), _1330674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1330670, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1330670), _1330672)), hAPP(c_SetInterval_Oord__class_OlessThan(_1330670), _1330674))))], (30311 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1330670, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1330670), _1330672)), hAPP(c_SetInterval_Oord__class_OlessThan(_1330670), _1330674))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330670), _1330672), _1330674)))]]], (52581 ^ _778495) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (27573 ^ _778495) ^ [_1270601, _1270603] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1270601, tc_HOL_Obool)), _1270603), c_Orderings_Otop__class_Otop(tc_fun(_1270601, tc_HOL_Obool))) = _1270603)], (43802 ^ _778495) ^ [_1654597, _1654599, _1654601] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654597)), hAPP(c_List_Orotate(_1654597, _1654599), _1654601)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654597)), _1654601))], (11791 ^ _778495) ^ [_983325, _983327, _983329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983325), _983327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983325), _983329)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983327), _983329))))], (33710 ^ _778495) ^ [_1406146, _1406148, _1406150, _1406152, _1406154] : [class_Orderings_Olinorder(_1406146), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1406146, _1406148), _1406150) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1406146, _1406152), _1406154), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406146), _1406148), _1406150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406146), _1406152), _1406154)), -(_1406148 = _1406152)], (38373 ^ _778495) ^ [_1517701, _1517703] : [-(hAPP(c_Set_Oimage(_1517701, _1517701, c_Fun_Oid(_1517701)), _1517703) = _1517703)], (43728 ^ _778495) ^ [_1653469, _1653471, _1653473] : [-(hAPP(c_List_Ohd(_1653469), hAPP(hAPP(c_List_Olist_OCons(_1653469), _1653471), _1653473)) = _1653471)], (30584 ^ _778495) ^ [_1336887, _1336889, _1336891, _1336893, _1336895] : [class_Groups_Oordered__ab__group__add(_1336887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336889), _1336891)), 30594 ^ _778495 : [(30597 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336887), c_Groups_Ozero__class_Ozero(_1336887)), hAPP(_1336893, 30593 ^ [_1336887, _1336889, _1336891, _1336893, _1336895])))], (30595 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1336889), 30593 ^ [_1336887, _1336889, _1336891, _1336893, _1336895]), _1336891)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1336889, _1336887), _1336893), _1336891) = c_Groups_Ozero__class_Ozero(_1336887), hBOOL(hAPP(hAPP(c_member(_1336889), _1336895), _1336891)), -(hAPP(_1336893, _1336895) = c_Groups_Ozero__class_Ozero(_1336887))], (42115 ^ _778495) ^ [_1615891, _1615893, _1615895, _1615897] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615891), tc_List_Olist(_1615891))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615891), tc_List_Olist(_1615891)), _1615893), _1615895)), c_List_Olistrel(_1615891, _1615897)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615891)), _1615893) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615891)), _1615895), 42121 ^ _778495 : [(42124 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1615891, _1615891, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1615891, tc_fun(tc_prod(_1615891, _1615891), tc_HOL_Obool), tc_fun(_1615891, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615891, tc_fun(tc_fun(tc_prod(_1615891, _1615891), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1615891, _1615891), tc_HOL_Obool), tc_fun(_1615891, tc_HOL_Obool)), _1615891), c_COMBC(_1615891, tc_fun(tc_prod(_1615891, _1615891), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615891, tc_prod(_1615891, _1615891)), tc_fun(_1615891, tc_fun(tc_fun(tc_prod(_1615891, _1615891), tc_HOL_Obool), tc_HOL_Obool)), _1615891), hAPP(c_COMBB(tc_prod(_1615891, _1615891), tc_fun(tc_fun(tc_prod(_1615891, _1615891), tc_HOL_Obool), tc_HOL_Obool), _1615891), c_member(tc_prod(_1615891, _1615891)))), c_Product__Type_OPair(_1615891, _1615891)))), _1615897)), 42120 ^ [_1615891, _1615893, _1615895, _1615897]))], (42122 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615891, _1615891)), 42120 ^ [_1615891, _1615893, _1615895, _1615897]), hAPP(c_List_Oset(tc_prod(_1615891, _1615891)), hAPP(hAPP(c_List_Ozip(_1615891, _1615891), _1615893), _1615895)))))]]], (43784 ^ _778495) ^ [_1654246, _1654248, _1654250] : [hBOOL(hAPP(c_List_Odistinct(_1654246), _1654250)), -(hBOOL(hAPP(c_List_Odistinct(_1654246), hAPP(c_List_Orotate(_1654246, _1654248), _1654250))))], (23276 ^ _778495) ^ [_1195547, _1195549] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195547)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195549)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195547), _1195549))], (34606 ^ _778495) ^ [_1425538, _1425540, _1425542] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1425538, _1425538)), _1425540), c_Relation_OId__on(_1425538, _1425542))), 34610 ^ _778495 : [(34613 ^ _778495) ^ [] : [-(_1425540 = hAPP(hAPP(c_Product__Type_OPair(_1425538, _1425538), 34609 ^ [_1425538, _1425540, _1425542]), 34609 ^ [_1425538, _1425540, _1425542]))], (34611 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425538), 34609 ^ [_1425538, _1425540, _1425542]), _1425542)))]]], (27309 ^ _778495) ^ [_1266008] : [class_Groups_Osgn__if(_1266008), -(c_Groups_Osgn__class_Osgn(_1266008, c_Groups_Ozero__class_Ozero(_1266008)) = c_Groups_Ozero__class_Ozero(_1266008))], (3970 ^ _778495) ^ [_838541, _838543, _838545, _838547, _838549, _838551, _838553, _838555] : [-(c_New__DSequence_Oneg__bind(_838555, _838551, _838547, _838543) = c_New__DSequence_Oneg__bind(_838553, _838549, _838545, _838541)), _838555 = _838553, _838551 = _838549, _838547 = _838545, _838543 = _838541], (38 ^ _778495) ^ [_779024, _779026, _779028, _779030, _779032, _779034, _779036, _779038, _779040, _779042] : [-(c_Finite__Set_Ofolding__image__idem(_779040, _779036, _779032, _779028, _779024)), c_Finite__Set_Ofolding__image__idem(_779042, _779038, _779034, _779030, _779026), _779042 = _779040, _779038 = _779036, _779034 = _779032, _779030 = _779028, _779026 = _779024], (26264 ^ _778495) ^ [_1248021, _1248023, _1248025] : [class_Power_Opower(_1248021), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1248021), _1248023), hAPP(c_Nat_OSuc, _1248025)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248021), _1248023), hAPP(hAPP(c_Power_Opower__class_Opower(_1248021), _1248023), _1248025)))], (12438 ^ _778495) ^ [_997730, _997732, _997734] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_997730, tc_HOL_Obool)), _997732), _997734) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_997730, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_997730, tc_HOL_Obool)), _997732), hAPP(hAPP(c_Set_Oinsert(tc_fun(_997730, tc_HOL_Obool)), _997734), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_997730, tc_HOL_Obool), tc_HOL_Obool))))))], (31720 ^ _778495) ^ [_1358744, _1358746, _1358748, _1358750, _1358752, _1358754] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358744, tc_fun(_1358746, tc_HOL_Obool)), _1358748), _1358750), _1358752)), -(hBOOL(hAPP(hAPP(_1358750, _1358754), _1358752))), hBOOL(hAPP(hAPP(c_member(_1358744), _1358754), _1358748))], (24826 ^ _778495) ^ [_1222689, _1222691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1222689), _1222691)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1222691, _1222689) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1222691), _1222689), _1222689))], (41754 ^ _778495) ^ [_1605917, _1605919, _1605921, _1605923] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605917)), hAPP(hAPP(c_List_Olist_OCons(_1605917), _1605919), _1605921)), c_List_Olists(_1605917, _1605923))), 41757 ^ _778495 : [(41760 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605917)), _1605921), c_List_Olists(_1605917, _1605923))))], (41758 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605917), _1605919), _1605923)))]]], (45382 ^ _778495) ^ [_1689361, _1689363] : [hBOOL(hAPP(c_List_Odistinct(_1689361), _1689363)), -(c_List_Oremdups(_1689361, _1689363) = _1689363)], (9484 ^ _778495) ^ [_940191, _940193, _940195] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_940191), _940193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940191, tc_HOL_Obool)), _940195), _940193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_940191), _940193)), hAPP(c_Finite__Set_Ocard(_940191), _940195))), -(_940195 = _940193)], (22400 ^ _778495) ^ [_1178993, _1178995] : [class_Lattices_Oboolean__algebra(_1178993), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1178993), _1178995), hAPP(c_Groups_Ouminus__class_Ouminus(_1178993), _1178995)) = c_Orderings_Obot__class_Obot(_1178993))], (24249 ^ _778495) ^ [_1212419, _1212421, _1212423, _1212425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212419)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212421), _1212423)), -(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), _1212423), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212425, _1212419))), _1212421))))], (44353 ^ _778495) ^ [_1665654, _1665656, _1665658, _1665660, _1665662, _1665664, _1665666, _1665668] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1665654, _1665656), _1665658), _1665660), hAPP(hAPP(c_List_Ozip(_1665654, _1665656), hAPP(hAPP(c_List_Omap(_1665662, _1665654), _1665664), _1665666)), _1665668)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665662, _1665656), _1665658), hAPP(c_Product__Type_Oprod_Oprod__case(_1665662, _1665656, _1665658), hAPP(hAPP(c_COMBB(tc_fun(_1665656, tc_prod(_1665654, _1665656)), tc_fun(_1665656, _1665658), _1665662), hAPP(c_COMBB(tc_prod(_1665654, _1665656), _1665658, _1665656), _1665660)), hAPP(hAPP(c_COMBB(_1665654, tc_fun(_1665656, tc_prod(_1665654, _1665656)), _1665662), c_Product__Type_OPair(_1665654, _1665656)), _1665664)))), hAPP(hAPP(c_List_Ozip(_1665662, _1665656), _1665666), _1665668)))], (38909 ^ _778495) ^ [_1532029, _1532031] : [c_FunDef_Oreduction__pair(_1532029, _1532031), 38912 ^ _778495 : [(38915 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532029, _1532029), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1532029, _1532029, _1532029), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532029, _1532029), tc_HOL_Obool), tc_fun(tc_prod(_1532029, _1532029), tc_HOL_Obool)), _1532031)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1532029, _1532029), tc_HOL_Obool), tc_fun(tc_prod(_1532029, _1532029), tc_HOL_Obool)), _1532031))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532029, _1532029), tc_HOL_Obool), tc_fun(tc_prod(_1532029, _1532029), tc_HOL_Obool)), _1532031))))], (38913 ^ _778495) ^ [] : [-(c_Wellfounded_Owf(_1532029, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532029, _1532029), tc_HOL_Obool), tc_fun(tc_prod(_1532029, _1532029), tc_HOL_Obool)), _1532031)))]]], (43082 ^ _778495) ^ [_1637772, _1637774, _1637776, _1637778] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637772)), hAPP(hAPP(c_List_Oappend(_1637772), _1637774), _1637776)), c_List_Olists(_1637772, _1637778))), 43085 ^ _778495 : [(43088 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637772)), _1637776), c_List_Olists(_1637772, _1637778))))], (43086 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637772)), _1637774), c_List_Olists(_1637772, _1637778))))]]], (43646 ^ _778495) ^ [_1651258, _1651260, _1651262, _1651264, _1651266] : [-(hAPP(hAPP(c_List_Oappend(_1651258), _1651260), _1651262) = hAPP(hAPP(c_List_Oappend(_1651258), _1651264), _1651266)), 43649 ^ _778495 : [(43652 ^ _778495) ^ [] : [_1651260 = hAPP(hAPP(c_List_Otake(_1651258), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651258)), _1651260)), _1651264), _1651262 = hAPP(hAPP(c_List_Oappend(_1651258), hAPP(hAPP(c_List_Odrop(_1651258), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651258)), _1651260)), _1651264)), _1651266)], (43650 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651258)), _1651260)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651258)), _1651264))))]], 43657 ^ _778495 : [(43660 ^ _778495) ^ [] : [hAPP(hAPP(c_List_Otake(_1651258), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651258)), _1651264)), _1651260) = _1651264, hAPP(hAPP(c_List_Oappend(_1651258), hAPP(hAPP(c_List_Odrop(_1651258), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651258)), _1651264)), _1651260)), _1651262) = _1651266], (43658 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651258)), _1651260)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651258)), _1651264)))]]], (45286 ^ _778495) ^ [_1687036, _1687038, _1687040, _1687042] : [-(hAPP(c_List_Oset(tc_prod(_1687036, _1687038)), c_Enum_Oproduct(_1687036, _1687038, _1687040, _1687042)) = hAPP(hAPP(c_Product__Type_OSigma(_1687036, _1687038), hAPP(c_List_Oset(_1687036), _1687040)), hAPP(c_COMBK(tc_fun(_1687038, tc_HOL_Obool), _1687036), hAPP(c_List_Oset(_1687038), _1687042))))], (15007 ^ _778495) ^ [_1044728, _1044730, _1044732, _1044734] : [class_Rings_Olinordered__semiring__strict(_1044728), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044728), _1044730), _1044732)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044728), _1044730), _1044734))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044728), c_Groups_Ozero__class_Ozero(_1044728)), _1044730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044728), _1044732), _1044734)))], (38111 ^ _778495) ^ [_1506641, _1506643] : [-(hAPP(c_Set_OPow(_1506641), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1506641, tc_HOL_Obool)), _1506643)) = hAPP(c_Set_OCollect(tc_fun(_1506641, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1506641, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1506641, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1506641, tc_HOL_Obool), tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1506641, tc_HOL_Obool)), c_COMBS(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1506641, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1506641, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1506641, tc_HOL_Obool), tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_fun(_1506641, tc_HOL_Obool)), tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_fun(_1506641, tc_HOL_Obool)), tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1506641, tc_HOL_Obool)), c_COMBB(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1506641, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1506641, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506641, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1506641, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1506641, tc_HOL_Obool)), _1506643)), c_Set_OPow(_1506641))))))], (40979 ^ _778495) ^ [_1583008, _1583010, _1583012] : [40980 ^ _778495 : [(40981 ^ _778495) ^ [_1583084] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583008, _1583008)), _1583010), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583008, _1583008), tc_HOL_Obool), _1583084), _1583012)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583008, _1583008)), _1583010), c_Transitive__Closure_Ortrancl(_1583008, _1583012))))], (3910 ^ _778495) ^ [_837553, _837555, _837557, _837559, _837561, _837563, _837565, _837567] : [-(c_New__DSequence_Opos__decr__bind(_837567, _837563, _837559, _837555) = c_New__DSequence_Opos__decr__bind(_837565, _837561, _837557, _837553)), _837567 = _837565, _837563 = _837561, _837559 = _837557, _837555 = _837553], (33088 ^ _778495) ^ [_1389014, _1389016, _1389018] : [-(c_Wellfounded_Omlex__prod(_1389014, _1389016, _1389018) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1389014), _1389014), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1389014, c_Wellfounded_Oless__than, _1389018)), hAPP(hAPP(c_COMBS(_1389014, _1389014, tc_prod(tc_Nat_Onat, _1389014)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1389014, tc_prod(tc_Nat_Onat, _1389014)), _1389014), c_Product__Type_OPair(tc_Nat_Onat, _1389014)), _1389016)), c_COMBI(_1389014))))], (11318 ^ _778495) ^ [_973833, _973835, _973837, _973839] : [class_Groups_Ocancel__semigroup__add(_973833), 11321 ^ _778495 : [(11328 ^ _778495) ^ [] : [_973835 = _973839, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973833), _973835), _973837) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973833), _973839), _973837))], (11322 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973833), _973835), _973837) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973833), _973839), _973837), -(_973835 = _973839)]]], (2234 ^ _778495) ^ [_811165, _811167, _811169, _811171, _811173, _811175, _811177, _811179] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_811179, _811175, _811171, _811167) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_811177, _811173, _811169, _811165)), _811179 = _811177, _811175 = _811173, _811171 = _811169, _811167 = _811165], (51939 ^ _778495) ^ [_1827129, _1827131, _1827133, _1827135] : [class_Rings_Ocomm__semiring__1(_1827129), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827129), _1827131), _1827133)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827129), _1827131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827129), _1827135), _1827133))))], (43626 ^ _778495) ^ [_1650745, _1650747, _1650749, _1650751, _1650753] : [hAPP(hAPP(c_List_Oappend(_1650745), _1650747), _1650749) = hAPP(hAPP(c_List_Oappend(_1650745), _1650751), _1650753), 43629 ^ _778495 : [(43638 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650745)), _1650747)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650745)), _1650751)))), 43641 ^ _778495 : [(43644 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1650745), hAPP(hAPP(c_List_Odrop(_1650745), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650745)), _1650751)), _1650747)), _1650749) = _1650753)], (43642 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1650745), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650745)), _1650751)), _1650747) = _1650751)]]], (43630 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650745)), _1650747)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650745)), _1650751))), 43633 ^ _778495 : [(43636 ^ _778495) ^ [] : [-(_1650749 = hAPP(hAPP(c_List_Oappend(_1650745), hAPP(hAPP(c_List_Odrop(_1650745), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650745)), _1650747)), _1650751)), _1650753))], (43634 ^ _778495) ^ [] : [-(_1650747 = hAPP(hAPP(c_List_Otake(_1650745), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650745)), _1650747)), _1650751))]]]]], (43959 ^ _778495) ^ [_1657843, _1657845, _1657847] : [class_Lattices_Olattice(_1657843), -(c_Big__Operators_Olattice__class_OInf__fin(_1657843, hAPP(c_List_Oset(_1657843), hAPP(hAPP(c_List_Olist_OCons(_1657843), _1657845), _1657847))) = hAPP(c_List_Ofoldl(_1657843, _1657843, c_Lattices_Osemilattice__inf__class_Oinf(_1657843), _1657845), _1657847))], (48200 ^ _778495) ^ [_1750625, _1750627, _1750629, _1750631] : [-(hAPP(hAPP(c_List_Otake(_1750625), _1750627), c_List_Oreplicate(_1750625, _1750629, _1750631)) = c_List_Oreplicate(_1750625, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750627), _1750629), _1750631))], (52383 ^ _778495) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (42240 ^ _778495) ^ [_1619645, _1619647, _1619649] : [class_Groups_Omonoid__add(_1619645), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1619645), hAPP(hAPP(c_List_Olist_OCons(_1619645), _1619647), _1619649)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1619645), _1619647), hAPP(c_List_Omonoid__add__class_Olistsum(_1619645), _1619649)))], (37488 ^ _778495) ^ [_1489132, _1489134, _1489136, _1489138] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1489132, _1489134)), hAPP(hAPP(c_Product__Type_OSigma(_1489132, _1489134), _1489136), hAPP(c_COMBK(tc_fun(_1489134, tc_HOL_Obool), _1489132), _1489138)))), -(_1489136 = c_Orderings_Obot__class_Obot(tc_fun(_1489132, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1489134), _1489138)))], (9346 ^ _778495) ^ [_936981, _936983, _936985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936981, tc_HOL_Obool)), _936983), _936985)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936981, tc_HOL_Obool)), _936983), _936985) = _936983)], (43806 ^ _778495) ^ [_1654705, _1654707, _1654709] : [hAPP(c_List_Orotate(_1654705, _1654707), _1654709) = c_List_Olist_ONil(_1654705), -(_1654709 = c_List_Olist_ONil(_1654705))], (4624 ^ _778495) ^ [_848852, _848854, _848856, _848858, _848860, _848862, _848864, _848866] : [-(c_Random__Sequence_Omap(_848866, _848862, _848858, _848854) = c_Random__Sequence_Omap(_848864, _848860, _848856, _848852)), _848866 = _848864, _848862 = _848860, _848858 = _848856, _848854 = _848852], (11444 ^ _778495) ^ [_976611, _976613, _976615, _976617, _976619] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_976611), 11447 ^ _778495 : [(11448 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976611), _976613), _976615)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976611), _976617), _976619)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976611), _976613), _976619)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976611), _976617), _976615)), -(_976613 = _976617), -(_976615 = _976619)], (11458 ^ _778495) ^ [] : [11459 ^ _778495 : [(11462 ^ _778495) ^ [] : [_976615 = _976619], (11460 ^ _778495) ^ [] : [_976613 = _976617]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976611), _976613), _976615)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976611), _976617), _976619)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976611), _976613), _976619)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976611), _976617), _976615)))]]], (49425 ^ _778495) ^ [_1777628, _1777630] : [c_Relation_Osym(_1777628, _1777630), -(c_Relation_Osym(_1777628, c_Transitive__Closure_Otrancl(_1777628, _1777630)))], (32636 ^ _778495) ^ [_1380509, _1380511, _1380513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380509)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1380511), _1380513)), 32643 ^ _778495 : [(32644 ^ _778495) ^ [_1380699] : [32646 ^ _778495 : [(32652 ^ _778495) ^ [] : [-(_1380699 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32648 ^ [_1380509, _1380511, _1380513, _1380699]), 32645 ^ [_1380509, _1380511, _1380513, _1380699]))], (32650 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32648 ^ [_1380509, _1380511, _1380513, _1380699]), _1380513)))], (32647 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32645 ^ [_1380509, _1380511, _1380513, _1380699]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1380509))))]], -(_1380699 = _1380511), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1380699), _1380509) = _1380511]]], (25968 ^ _778495) ^ [_1242799] : [-(_1242799 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 25971 ^ _778495 : [(25978 ^ _778495) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1242799, 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, _1242799) = 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), _1242799), 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)))], (25972 ^ _778495) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1242799, 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, _1242799) = 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), _1242799), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (27357 ^ _778495) ^ [_1266826, _1266828] : [class_Rings_Olinordered__idom(_1266826), -(hAPP(c_Groups_Oabs__class_Oabs(_1266826), _1266828) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266826), _1266828), c_Groups_Osgn__class_Osgn(_1266826, _1266828)))], (30093 ^ _778495) ^ [_1326536, _1326538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1326536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1326538), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1326536), _1326538) = 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), _1326536), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1326538)))))], (42612 ^ _778495) ^ [_1628038, _1628040] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1628038)), c_List_Olist_ONil(_1628038)), c_List_Olists(_1628038, _1628040))))], (43772 ^ _778495) ^ [_1653979, _1653981, _1653983] : [-(hAPP(c_List_Otl(_1653979), hAPP(hAPP(c_List_Odrop(_1653979), _1653981), _1653983)) = hAPP(hAPP(c_List_Odrop(_1653979), _1653981), hAPP(c_List_Otl(_1653979), _1653983)))], (10561 ^ _778495) ^ [_960802] : [hAPP(c_Nat_OSuc, _960802) = _960802], (35086 ^ _778495) ^ [_1434309, _1434311] : [c_Nat__Transfer_Onat__set(_1434309), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1434311), _1434309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1434311)))], (41935 ^ _778495) ^ [_1610823, _1610825, _1610827, _1610829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1610823), _1610825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610827, tc_HOL_Obool)), hAPP(c_List_Oset(_1610827), hAPP(hAPP(c_List_Otake(_1610827), _1610823), _1610829))), hAPP(c_List_Oset(_1610827), hAPP(hAPP(c_List_Otake(_1610827), _1610825), _1610829)))))], (38536 ^ _778495) ^ [_1522355, _1522357, _1522359, _1522361] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522355, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1522357, _1522355), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1522357, _1522355), tc_HOL_Obool)), _1522359), _1522361))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522355, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1522357, _1522355), _1522359)), hAPP(c_Relation_ORange(_1522357, _1522355), _1522361)))))], (16234 ^ _778495) ^ [_1068495] : [class_Rings_Oring__1(_1068495), -(hBOOL(hAPP(hAPP(c_member(_1068495), c_Groups_Ozero__class_Ozero(_1068495)), c_Int_Oring__1__class_OInts(_1068495))))], (31636 ^ _778495) ^ [_1356725, _1356727, _1356729, _1356731, _1356733, _1356735] : [hAPP(_1356731, hAPP(c_Product__Type_Ofst(_1356725, _1356729), _1356733)) = hAPP(_1356735, hAPP(c_Product__Type_Ofst(_1356725, _1356729), _1356733)), -(hAPP(c_Product__Type_Oapfst(_1356725, _1356727, _1356729, _1356731), _1356733) = hAPP(c_Product__Type_Oapfst(_1356725, _1356727, _1356729, _1356735), _1356733))], (37170 ^ _778495) ^ [_1480278, _1480280, _1480282, _1480284, _1480286, _1480288] : [-(hAPP(c_Set_Ovimage(_1480278, _1480280, _1480282), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480284, tc_fun(_1480280, tc_HOL_Obool)), _1480286), _1480288)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480284, tc_fun(_1480278, tc_HOL_Obool)), _1480286), hAPP(hAPP(c_COMBB(tc_fun(_1480280, tc_HOL_Obool), tc_fun(_1480278, tc_HOL_Obool), _1480284), c_Set_Ovimage(_1480278, _1480280, _1480282)), _1480288)))], (28963 ^ _778495) ^ [_1304092, _1304094, _1304096, _1304098, _1304100, _1304102] : [28964 ^ _778495 : [(28967 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1304098, _1304094), _1304096))], (28965 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1304092, _1304094), _1304096))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304100, tc_fun(_1304102, tc_HOL_Obool))), _1304098), _1304092), _1304094), _1304096)))], (30879 ^ _778495) ^ [_1342306, _1342308, _1342310, _1342312] : [class_Orderings_Olinorder(_1342306), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342306), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342306), _1342308), _1342310)), _1342312) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342306), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342306), _1342308), _1342312)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342306), _1342310), _1342312)))], (4756 ^ _778495) ^ [_851014, _851016, _851018, _851020] : [-(c_List_Olexord(_851020, _851016) = c_List_Olexord(_851018, _851014)), _851020 = _851018, _851016 = _851014], (10505 ^ _778495) ^ [_959790, _959792] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959790), _959792)), hAPP(c_Nat_OSuc, _959790))))], (43080 ^ _778495) ^ [_1637690, _1637692, _1637694, _1637696] : [-(hAPP(hAPP(c_List_Oappend(_1637690), hAPP(hAPP(c_List_Olist_OCons(_1637690), _1637692), _1637694)), _1637696) = hAPP(hAPP(c_List_Olist_OCons(_1637690), _1637692), hAPP(hAPP(c_List_Oappend(_1637690), _1637694), _1637696)))], (50042 ^ _778495) ^ [_1790485, _1790487, _1790489, _1790491] : [c_Fun_Obij__betw(_1790485, _1790487, _1790489, _1790491, c_Orderings_Obot__class_Obot(tc_fun(_1790487, tc_HOL_Obool))), -(_1790491 = c_Orderings_Obot__class_Obot(tc_fun(_1790485, tc_HOL_Obool)))], (22196 ^ _778495) ^ [_1175527, _1175529] : [class_Groups_Oordered__ab__group__add(_1175527), 22199 ^ _778495 : [(22206 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175527), c_Groups_Ozero__class_Ozero(_1175527)), _1175529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175527), hAPP(c_Groups_Ouminus__class_Ouminus(_1175527), _1175529)), c_Groups_Ozero__class_Ozero(_1175527))))], (22200 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175527), hAPP(c_Groups_Ouminus__class_Ouminus(_1175527), _1175529)), c_Groups_Ozero__class_Ozero(_1175527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175527), c_Groups_Ozero__class_Ozero(_1175527)), _1175529)))]]], (45560 ^ _778495) ^ [_1692659, _1692661] : [45562 ^ _778495 : [(45565 ^ _778495) ^ [] : [45561 ^ [_1692659, _1692661] = c_List_Olist_ONil(_1692659)], (45563 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692659)), 45561 ^ [_1692659, _1692661]), hAPP(c_List_Oset(tc_List_Olist(_1692659)), _1692661))))]], -(c_List_Olist_ONil(_1692659) = c_List_Oconcat(_1692659, _1692661))], (25644 ^ _778495) ^ [_1236677] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1236677)), 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, _1236677, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (46630 ^ _778495) ^ [_1715912, _1715914, _1715916] : [hAPP(hAPP(c_List_Olist_OCons(_1715912), _1715914), c_List_Olist_ONil(_1715912)) = hAPP(c_List_Orev(_1715912), _1715916), -(_1715916 = hAPP(hAPP(c_List_Olist_OCons(_1715912), _1715914), c_List_Olist_ONil(_1715912)))], (12735 ^ _778495) ^ [_1004157, _1004159, _1004161, _1004163, _1004165] : [class_Groups_Oab__group__add(_1004157), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004159), _1004161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1004159, tc_HOL_Obool)), _1004163), _1004161)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004159, _1004157), _1004165), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1004159, tc_HOL_Obool)), _1004161), _1004163)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1004157), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004159, _1004157), _1004165), _1004161)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004159, _1004157), _1004165), _1004163)))], (1848 ^ _778495) ^ [_804623, _804625] : [-(class_Rings_Omult__zero(_804623)), _804625 = _804623, class_Rings_Omult__zero(_804625)], (31710 ^ _778495) ^ [_1358547, _1358549, _1358551, _1358553, _1358555, _1358557] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358547, tc_fun(_1358549, tc_HOL_Obool)), _1358551), _1358553), _1358555)), hBOOL(hAPP(hAPP(c_member(_1358547), _1358557), _1358551)), -(hBOOL(hAPP(hAPP(_1358553, _1358557), _1358555)))], (42047 ^ _778495) ^ [_1613405, _1613407, _1613409] : [42049 ^ _778495 : [(42052 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1613405), 42048 ^ [_1613405, _1613407, _1613409]), _1613409))], (42050 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613405), 42048 ^ [_1613405, _1613407, _1613409]), hAPP(c_List_Oset(_1613405), _1613407))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1613405)), _1613407), c_List_Olists(_1613405, _1613409))))], (37937 ^ _778495) ^ [_1500884, _1500886, _1500888, _1500890, _1500892] : [c_Relation_Orefl__on(_1500884, _1500886, _1500888), c_Relation_Orefl__on(_1500884, _1500890, _1500892), -(c_Relation_Orefl__on(_1500884, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1500884, tc_HOL_Obool)), _1500886), _1500890), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1500884, _1500884), tc_HOL_Obool)), _1500888), _1500892)))], (38983 ^ _778495) ^ [_1534365, _1534367, _1534369, _1534371] : [hBOOL(hAPP(hAPP(c_member(_1534365), _1534367), hAPP(c_Relation_ODomain(_1534365, _1534369), _1534371))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534365, _1534369)), hAPP(hAPP(c_Product__Type_OPair(_1534365, _1534369), _1534367), 38986 ^ [_1534365, _1534367, _1534369, _1534371])), _1534371)))], (30849 ^ _778495) ^ [_1341679, _1341681] : [class_Orderings_Olinorder(_1341679), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341679), _1341681), _1341681) = _1341681)], (42716 ^ _778495) ^ [_1629843] : [class_Groups_Omonoid__add(_1629843), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1629843), c_List_Olist_ONil(_1629843)) = c_Groups_Ozero__class_Ozero(_1629843))], (42161 ^ _778495) ^ [_1617749, _1617751, _1617753, _1617755] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617749, _1617749)), hAPP(hAPP(c_Product__Type_OPair(_1617749, _1617749), _1617751), _1617753)), hAPP(c_List_Oset(tc_prod(_1617749, _1617749)), hAPP(hAPP(c_List_Ozip(_1617749, _1617749), _1617755), _1617755)))), 42164 ^ _778495 : [(42167 ^ _778495) ^ [] : [-(_1617751 = _1617753)], (42165 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617749), _1617751), hAPP(c_List_Oset(_1617749), _1617755))))]]], (49703 ^ _778495) ^ [_1783045, _1783047, _1783049, _1783051, _1783053] : [hBOOL(hAPP(hAPP(c_member(_1783045), _1783047), hAPP(c_Set_Oimage(_1783049, _1783045, _1783051), _1783053))), -(hBOOL(hAPP(hAPP(c_member(_1783049), hAPP(c_Hilbert__Choice_Oinv__into(_1783049, _1783045, _1783053, _1783051), _1783047)), _1783053)))], (19086 ^ _778495) ^ [_1121622, _1121624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1121622), _1121624)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121622), _1121624)))], (35705 ^ _778495) ^ [_1447607, _1447609, _1447611] : [c_Equiv__Relations_Oequiv(_1447607, _1447609, _1447611), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1447607, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447607), _1447609), _1447611)) = _1447609)], (38528 ^ _778495) ^ [_1522124, _1522126, _1522128, _1522130] : [38529 ^ _778495 : [(38530 ^ _778495) ^ [_1522199] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522128, _1522124)), hAPP(hAPP(c_Product__Type_OPair(_1522128, _1522124), _1522199), _1522126)), _1522130))]], -(hBOOL(hAPP(hAPP(c_member(_1522124), _1522126), hAPP(c_Relation_ORange(_1522128, _1522124), _1522130))))], (1578 ^ _778495) ^ [_801248, _801250] : [-(class_Rings_Olinordered__semiring__strict(_801248)), _801250 = _801248, class_Rings_Olinordered__semiring__strict(_801250)], (41553 ^ _778495) ^ [_1599794, _1599796, _1599798, _1599800] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599794), tc_List_Olist(_1599794))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599794), tc_List_Olist(_1599794)), _1599796), _1599798)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1599794), tc_List_Olist(_1599794)), c_List_Olistrel1(_1599794, _1599800)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599794), tc_List_Olist(_1599794))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599794), tc_List_Olist(_1599794)), _1599796), _1599798)), c_List_Olistrel1(_1599794, hAPP(c_Relation_Oconverse(_1599794, _1599794), _1599800)))))], (46448 ^ _778495) ^ [_1712084, _1712086] : [class_Orderings_Olinorder(_1712084), hBOOL(hAPP(c_Finite__Set_Ofinite(_1712084), _1712086)), 46455 ^ _778495 : [(46460 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1712084), c_List_Olinorder__class_Osorted__list__of__set(_1712084, _1712086))))], (46458 ^ _778495) ^ [] : [-(c_List_Olinorder__class_Osorted(_1712084, c_List_Olinorder__class_Osorted__list__of__set(_1712084, _1712086)))], (46456 ^ _778495) ^ [] : [-(hAPP(c_List_Oset(_1712084), c_List_Olinorder__class_Osorted__list__of__set(_1712084, _1712086)) = _1712086)]]], (1278 ^ _778495) ^ [_797498, _797500] : [-(class_Groups_Ogroup__add(_797498)), _797500 = _797498, class_Groups_Ogroup__add(_797500)], (4448 ^ _778495) ^ [_846100, _846102] : [_846102 = _846100, -(c_List_Omember(_846102) = c_List_Omember(_846100))], (30665 ^ _778495) ^ [_1338373, _1338375, _1338377, _1338379] : [class_Orderings_Olinorder(_1338373), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338373), _1338375), _1338377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338373), _1338379), _1338377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338373), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338373), _1338375), _1338379)), _1338377)))], (32136 ^ _778495) ^ [_1369386, _1369388, _1369390, _1369392, _1369394] : [class_Groups_Ocomm__monoid__add(_1369386), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369386), _1369388), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1369390), _1369392), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1369394), _1369392))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369386), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1369386, tc_Nat_Onat), _1369388), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1369392))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1369390, _1369394)))], (1878 ^ _778495) ^ [_804998, _805000] : [-(class_Orderings_Oord(_804998)), _805000 = _804998, class_Orderings_Oord(_805000)], (12412 ^ _778495) ^ [_997150, _997152, _997154, _997156] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_997150, tc_HOL_Obool)), _997152), _997154)), hBOOL(hAPP(hAPP(c_member(_997150), _997156), _997152)), -(hBOOL(hAPP(hAPP(c_member(_997150), _997156), c_Complete__Lattice_OSup__class_OSup(tc_fun(_997150, tc_HOL_Obool), _997154))))], (2884 ^ _778495) ^ [_821300, _821302] : [_821302 = _821300, -(c_Nitpick_Ofrac(_821302) = c_Nitpick_Ofrac(_821300))], (25417 ^ _778495) ^ [_1232674, _1232676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232676)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1232674)), hAPP(c_Int_Onat, _1232676)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232674), _1232676)))], (44345 ^ _778495) ^ [_1665213, _1665215, _1665217, _1665219] : [-(hAPP(hAPP(c_List_Omap(_1665213, _1665215), _1665217), hAPP(c_List_Otl(_1665213), _1665219)) = hAPP(c_List_Otl(_1665215), hAPP(hAPP(c_List_Omap(_1665213, _1665215), _1665217), _1665219)))], (42317 ^ _778495) ^ [_1621214, _1621216, _1621218, _1621220, _1621222, _1621224, _1621226] : [-(hAPP(hAPP(c_List_Ozip(_1621214, _1621216), hAPP(hAPP(c_List_Olist__update(_1621214, _1621218), _1621220), _1621222)), hAPP(hAPP(c_List_Olist__update(_1621216, _1621224), _1621220), _1621226)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1621214, _1621216), hAPP(hAPP(c_List_Ozip(_1621214, _1621216), _1621218), _1621224)), _1621220), hAPP(hAPP(c_Product__Type_OPair(_1621214, _1621216), _1621222), _1621226)))], (33236 ^ _778495) ^ [_1392523, _1392525, _1392527, _1392529, _1392531] : [-(hBOOL(hAPP(hAPP(c_member(_1392523), _1392525), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392527, tc_fun(_1392523, tc_HOL_Obool)), _1392529), _1392531)))), 33237 ^ _778495 : [(33238 ^ _778495) ^ [_1392605] : [hBOOL(hAPP(hAPP(c_member(_1392527), _1392605), _1392529)), hBOOL(hAPP(hAPP(c_member(_1392523), _1392525), hAPP(_1392531, _1392605)))]]], (11368 ^ _778495) ^ [_974758, _974760, _974762, _974764] : [class_Rings_Ocomm__semiring__1(_974758), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974758), _974760), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974758), _974762), _974764)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974758), _974760), _974762)), _974764))], (52629 ^ _778495) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (19996 ^ _778495) ^ [_1137702, _1137704] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137702)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1137704)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1137702), _1137704)))], (42776 ^ _778495) ^ [_1630907, _1630909, _1630911] : [-(hAPP(hAPP(c_List_Olist__update(_1630907, c_List_Olist_ONil(_1630907)), _1630909), _1630911) = c_List_Olist_ONil(_1630907))], (1868 ^ _778495) ^ [_804873, _804875] : [-(class_Rings_Osemiring(_804873)), _804875 = _804873, class_Rings_Osemiring(_804875)], (29643 ^ _778495) ^ [_1318042, _1318044, _1318046, _1318048, _1318050, _1318052, _1318054] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1318042, _1318044, tc_fun(_1318046, tc_HOL_Obool)), _1318048), hAPP(hAPP(c_Product__Type_OPair(_1318042, _1318044), _1318050), _1318052)), _1318054)), -(hBOOL(hAPP(hAPP(hAPP(_1318048, _1318050), _1318052), _1318054)))], (45010 ^ _778495) ^ [_1680807, _1680809, _1680811, _1680813] : [hBOOL(hAPP(c_List_Olistsp(_1680807, _1680809), hAPP(hAPP(c_List_Oappend(_1680807), _1680811), _1680813))), 45013 ^ _778495 : [(45016 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1680807, _1680809), _1680813)))], (45014 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1680807, _1680809), _1680811)))]]], (3310 ^ _778495) ^ [_827935, _827937, _827939, _827941] : [-(c_Product__Type_OSigma(_827941, _827937) = c_Product__Type_OSigma(_827939, _827935)), _827941 = _827939, _827937 = _827935], (3398 ^ _778495) ^ [_829279, _829281, _829283, _829285] : [-(c_List_OremoveAll(_829285, _829281) = c_List_OremoveAll(_829283, _829279)), _829285 = _829283, _829281 = _829279], (30465 ^ _778495) ^ [_1334061, _1334063, _1334065, _1334067, _1334069] : [hBOOL(hAPP(hAPP(c_member(_1334061), _1334063), c_SetInterval_Oord_OatLeastAtMost(_1334061, _1334065, _1334067, _1334069))), 30468 ^ _778495 : [(30471 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1334065, _1334063), _1334069)))], (30469 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1334065, _1334067), _1334063)))]]], (22912 ^ _778495) ^ [] : [-(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))))))], (44542 ^ _778495) ^ [_1670552, _1670554, _1670556, _1670558] : [hBOOL(hAPP(c_List_Odistinct(_1670552), hAPP(hAPP(c_List_Omap(_1670554, _1670552), _1670556), _1670558))), 44545 ^ _778495 : [(44548 ^ _778495) ^ [] : [-(c_Fun_Oinj__on(_1670554, _1670552, _1670556, hAPP(c_List_Oset(_1670554), _1670558)))], (44546 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1670554), _1670558)))]]], (12463 ^ _778495) ^ [_998503, _998505, _998507] : [class_Complete__Lattice_Ocomplete__lattice(_998503), 12466 ^ _778495 : [(12467 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998503), c_Complete__Lattice_OSup__class_OSup(_998503, _998505)), _998507)), 12470 ^ _778495 : [(12471 ^ _778495) ^ [_998661] : [hBOOL(hAPP(hAPP(c_member(_998503), _998661), _998505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998503), _998661), _998507)))]]], (12477 ^ _778495) ^ [] : [12479 ^ _778495 : [(12482 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998503), 12478 ^ [_998503, _998505, _998507]), _998507))], (12480 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_998503), 12478 ^ [_998503, _998505, _998507]), _998505)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998503), c_Complete__Lattice_OSup__class_OSup(_998503, _998505)), _998507)))]]], (38927 ^ _778495) ^ [_1532639, _1532641, _1532643, _1532645] : [c_FunDef_Oreduction__pair(_1532639, _1532641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532639, _1532639), tc_HOL_Obool)), _1532643), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532639, _1532639), tc_HOL_Obool), tc_fun(tc_prod(_1532639, _1532639), tc_HOL_Obool)), _1532641))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532639, _1532639), tc_HOL_Obool)), _1532645), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1532639, _1532639), tc_HOL_Obool), tc_fun(tc_prod(_1532639, _1532639), tc_HOL_Obool)), _1532641))), c_Wellfounded_Owf(_1532639, _1532645), -(c_Wellfounded_Owf(_1532639, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1532639, _1532639), tc_HOL_Obool)), _1532643), _1532645)))], (48255 ^ _778495) ^ [_1751626, _1751628, _1751630, _1751632] : [48263 ^ _778495 : [(48266 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1751632, 48262 ^ [_1751626, _1751628, _1751630, _1751632])))], (48264 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751626), 48262 ^ [_1751626, _1751628, _1751630, _1751632]), hAPP(c_List_Oset(_1751626), c_List_Oreplicate(_1751626, _1751628, _1751630)))))]], hBOOL(hAPP(_1751632, _1751630)), -(_1751628 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43528 ^ _778495) ^ [_1648466, _1648468] : [-(hAPP(hAPP(c_List_Odrop(_1648466), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1648468) = _1648468)], (42277 ^ _778495) ^ [_1620393, _1620395, _1620397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1620393), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1620395))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1620395), _1620393), _1620397)) = 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), _1620395)), _1620397)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1620395), _1620393)))], (22798 ^ _778495) ^ [_1186074, _1186076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186074)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186076)))), 22801 ^ _778495 : [(22804 ^ _778495) ^ [] : [-(_1186076 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22802 ^ _778495) ^ [] : [-(_1186074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3196 ^ _778495) ^ [_826176, _826178, _826180, _826182, _826184, _826186, _826188, _826190] : [-(c_Nitpick_Osetsum_H(_826190, _826186, _826182, _826178) = c_Nitpick_Osetsum_H(_826188, _826184, _826180, _826176)), _826190 = _826188, _826186 = _826184, _826182 = _826180, _826178 = _826176], (49755 ^ _778495) ^ [_1784059] : [-(c_Hilbert__Choice_Oinv__into(_1784059, _1784059, c_Orderings_Otop__class_Otop(tc_fun(_1784059, tc_HOL_Obool)), c_Fun_Oid(_1784059)) = c_Fun_Oid(_1784059))], (49483 ^ _778495) ^ [_1778527, _1778529, _1778531, _1778533] : [c_Relation_Osym(_1778527, _1778529), -(c_Relation_Osym(_1778531, hAPP(hAPP(c_Relation_Oinv__image(_1778527, _1778531), _1778529), _1778533)))], (4786 ^ _778495) ^ [_851469, _851471, _851473, _851475] : [-(c_Relation_OId__on(_851475, _851471) = c_Relation_OId__on(_851473, _851469)), _851475 = _851473, _851471 = _851469], (21392 ^ _778495) ^ [_1162034, _1162036] : [class_Int_Onumber__ring(_1162034), -(hAPP(c_Int_Onumber__class_Onumber__of(_1162034), c_Int_OBit1(_1162036)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162034), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162034), c_Groups_Oone__class_Oone(_1162034)), hAPP(c_Int_Onumber__class_Onumber__of(_1162034), _1162036))), hAPP(c_Int_Onumber__class_Onumber__of(_1162034), _1162036)))], (28243 ^ _778495) ^ [_1282842, _1282844, _1282846] : [class_Orderings_Obot(_1282842), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1282844, _1282842)), _1282846) = c_Orderings_Obot__class_Obot(_1282842))], (45091 ^ _778495) ^ [_1682887, _1682889, _1682891, _1682893, _1682895, _1682897, _1682899] : [c_List_Olist__all2(_1682887, _1682895, hAPP(hAPP(c_COMBC(_1682887, tc_fun(_1682895, _1682889), tc_fun(_1682895, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682889, tc_HOL_Obool), tc_fun(tc_fun(_1682895, _1682889), tc_fun(_1682895, tc_HOL_Obool)), _1682887), c_COMBB(_1682889, tc_HOL_Obool, _1682895)), _1682891)), _1682897), _1682893, _1682899), -(c_List_Olist__all2(_1682887, _1682889, _1682891, _1682893, hAPP(hAPP(c_List_Omap(_1682895, _1682889), _1682897), _1682899)))], (14785 ^ _778495) ^ [_1040738, _1040740, _1040742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040738), _1040740)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040738), _1040742))), 14788 ^ _778495 : [(14791 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040740), _1040742)))], (14789 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040738)))]]], (1066 ^ _778495) ^ [_794640, _794642, _794644, _794646, _794648, _794650] : [-(c_List_Olist__ex(_794648, _794644, _794640)), c_List_Olist__ex(_794650, _794646, _794642), _794650 = _794648, _794646 = _794644, _794642 = _794640], (32276 ^ _778495) ^ [_1372505, _1372507, _1372509] : [class_Orderings_Oorder(_1372505), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372505, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1372505), _1372507)), c_SetInterval_Oord__class_OatLeastAtMost(_1372505, _1372507, _1372509)) = c_Orderings_Obot__class_Obot(tc_fun(_1372505, tc_HOL_Obool)))], (23967 ^ _778495) ^ [_1207471, _1207473] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207471, _1207473) = 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), _1207471), _1207473) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16688 ^ _778495) ^ [_1076858, _1076860, _1076862] : [class_Fields_Olinordered__field(_1076858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076858), c_Groups_Ozero__class_Ozero(_1076858)), _1076860)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076858), _1076862), c_Groups_Ozero__class_Ozero(_1076858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076858), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1076858), _1076860), _1076862)), c_Groups_Ozero__class_Ozero(_1076858))))], (42670 ^ _778495) ^ [_1629057, _1629059, _1629061] : [hAPP(hAPP(c_List_Olist_OCons(_1629057), _1629059), _1629061) = c_List_Olist_ONil(_1629057)], (28889 ^ _778495) ^ [_1302933, _1302935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1302933), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1302935, _1302933) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1302935), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1302933)))], (30953 ^ _778495) ^ [_1343772, _1343774, _1343776, _1343778] : [class_Orderings_Olinorder(_1343772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343772), _1343774), _1343776)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343772), _1343774), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343772), _1343778), _1343776))))], (28285 ^ _778495) ^ [_1284130, _1284132, _1284134, _1284136, _1284138, _1284140] : [class_Groups_Ocomm__monoid__add(_1284130), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1284132, _1284130), hAPP(hAPP(c_COMBC(_1284132, tc_fun(_1284134, tc_HOL_Obool), _1284130), hAPP(hAPP(c_COMBB(tc_fun(_1284134, _1284130), tc_fun(tc_fun(_1284134, tc_HOL_Obool), _1284130), _1284132), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1284134, _1284130)), _1284136)), _1284138)), _1284140) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1284134, _1284130), hAPP(hAPP(c_COMBC(_1284134, tc_fun(_1284132, tc_HOL_Obool), _1284130), hAPP(hAPP(c_COMBB(tc_fun(_1284132, _1284130), tc_fun(tc_fun(_1284132, tc_HOL_Obool), _1284130), _1284134), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1284132, _1284130)), hAPP(c_COMBC(_1284132, _1284134, _1284130), _1284136))), _1284140)), _1284138))], (13378 ^ _778495) ^ [_1016273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016273), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1016273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41856 ^ _778495) ^ [_1608686, _1608688, _1608690, _1608692] : [-(hAPP(hAPP(c_List_Onth(_1608686), hAPP(hAPP(c_List_Olist_OCons(_1608686), _1608688), _1608690)), hAPP(c_Nat_OSuc, _1608692)) = hAPP(hAPP(c_List_Onth(_1608686), _1608690), _1608692))], (44235 ^ _778495) ^ [_1663257, _1663259, _1663261] : [_1663257 = c_List_Olist_ONil(_1663259), -(c_List_Olast(_1663259, hAPP(hAPP(c_List_Oappend(_1663259), _1663261), _1663257)) = c_List_Olast(_1663259, _1663261))], (27909 ^ _778495) ^ [_1276391] : [class_Complete__Lattice_Ocomplete__lattice(_1276391), -(c_Complete__Lattice_OInf__class_OInf(_1276391, c_Orderings_Otop__class_Otop(tc_fun(_1276391, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1276391))], (45782 ^ _778495) ^ [_1698409, _1698411, _1698413] : [-(hAPP(c_List_Oset(_1698409), hAPP(c_List_Ofilter(_1698409, _1698411), _1698413)) = hAPP(c_Set_OCollect(_1698409), hAPP(hAPP(c_COMBS(_1698409, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1698409), c_fconj), hAPP(hAPP(c_COMBC(_1698409, tc_fun(_1698409, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698409)), hAPP(c_List_Oset(_1698409), _1698413)))), _1698411)))], (51233 ^ _778495) ^ [_1814383, _1814385] : [-(_1814383 = _1814385), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814383), _1814385)), 51240 ^ _778495 : [(51243 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814385), _1814383))], (51241 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814383), _1814385)))]]], (37184 ^ _778495) ^ [_1480687, _1480689, _1480691, _1480693, _1480695] : [hBOOL(hAPP(hAPP(c_member(_1480687), _1480689), hAPP(c_Set_Ovimage(_1480687, _1480691, _1480693), hAPP(hAPP(c_Set_Oinsert(_1480691), _1480695), c_Orderings_Obot__class_Obot(tc_fun(_1480691, tc_HOL_Obool)))))), -(hAPP(_1480693, _1480689) = _1480695)], (40768 ^ _778495) ^ [_1577622, _1577624, _1577626, _1577628, _1577630] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577622, _1577624)), hAPP(hAPP(c_Product__Type_OPair(_1577622, _1577624), _1577626), _1577628)), hAPP(c_Relation_Oconverse(_1577624, _1577622), _1577630))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577624, _1577622)), hAPP(hAPP(c_Product__Type_OPair(_1577624, _1577622), _1577628), _1577626)), _1577630)))], (33643 ^ _778495) ^ [_1404646, _1404648, _1404650, _1404652, _1404654, _1404656, _1404658] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404646, tc_fun(_1404648, tc_fun(_1404650, tc_HOL_Obool))), _1404652), _1404654), _1404656), _1404658)), 33647 ^ _778495 : [(33650 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1404654, 33646 ^ [_1404646, _1404648, _1404650, _1404652, _1404654, _1404656, _1404658]), _1404656), _1404658)))], (33648 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404646), 33646 ^ [_1404646, _1404648, _1404650, _1404652, _1404654, _1404656, _1404658]), _1404652)))]]], (22412 ^ _778495) ^ [_1179217, _1179219, _1179221] : [class_Lattices_Oboolean__algebra(_1179217), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1179217), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1179217), _1179219), _1179221)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1179217), hAPP(c_Groups_Ouminus__class_Ouminus(_1179217), _1179219)), hAPP(c_Groups_Ouminus__class_Ouminus(_1179217), _1179221)))], (45195 ^ _778495) ^ [_1684991, _1684993, _1684995, _1684997] : [_1684997 = c_List_Olist_ONil(_1684993), -(c_List_Olist__all2(_1684991, _1684993, _1684995, c_List_Olist_ONil(_1684991), _1684997))], (40401 ^ _778495) ^ [_1568997, _1568999, _1569001] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568997, _1568997), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568997, _1568997), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568997, _1568999)), c_Transitive__Closure_Ortrancl(_1568997, _1569001))), c_Transitive__Closure_Ortrancl(_1568997, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568997, _1568997), tc_HOL_Obool)), _1568999), _1569001)))))], (40457 ^ _778495) ^ [_1570390, _1570392, _1570394] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1570390, _1570390, _1570392), c_Relation_OId(_1570390)), _1570394) = _1570394)], (29394 ^ _778495) ^ [_1313141, _1313143, _1313145, _1313147, _1313149] : [hBOOL(hAPP(hAPP(_1313141, _1313143), _1313145)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1313147, _1313149, tc_HOL_Obool), _1313141), hAPP(hAPP(c_Product__Type_OPair(_1313147, _1313149), _1313143), _1313145))))], (43900 ^ _778495) ^ [_1656664, _1656666, _1656668, _1656670, _1656672, _1656674] : [-(hAPP(c_List_Ofoldl(_1656664, _1656666, _1656668, _1656670), hAPP(hAPP(c_List_Olist_OCons(_1656666), _1656672), _1656674)) = hAPP(c_List_Ofoldl(_1656664, _1656666, _1656668, hAPP(hAPP(_1656668, _1656670), _1656672)), _1656674))], (44478 ^ _778495) ^ [_1669053, _1669055, _1669057, _1669059] : [-(hAPP(c_List_Oset(_1669053), hAPP(hAPP(c_List_Omap(_1669055, _1669053), _1669057), _1669059)) = hAPP(c_Set_Oimage(_1669055, _1669053, _1669057), hAPP(c_List_Oset(_1669055), _1669059)))], (24353 ^ _778495) ^ [_1214409, _1214411, _1214413] : [class_Int_Onumber__ring(_1214409), 24356 ^ _778495 : [(24363 ^ _778495) ^ [] : [c_Int_Oiszero(_1214409, hAPP(c_Int_Onumber__class_Onumber__of(_1214409), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214411), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214413)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1214409), _1214411) = hAPP(c_Int_Onumber__class_Onumber__of(_1214409), _1214413))], (24357 ^ _778495) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1214409), _1214411) = hAPP(c_Int_Onumber__class_Onumber__of(_1214409), _1214413), -(c_Int_Oiszero(_1214409, hAPP(c_Int_Onumber__class_Onumber__of(_1214409), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214411), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214413)))))]]], (12096 ^ _778495) ^ [_989976, _989978, _989980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989976), _989978)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989980), _989978)), _989976) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989980), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989978), _989976)))], (23186 ^ _778495) ^ [_1193683, _1193685, _1193687, _1193689] : [class_Divides_Oring__div(_1193683), -(c_Divides_Odiv__class_Omod(_1193683, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1193683), _1193685), _1193687), _1193689) = c_Divides_Odiv__class_Omod(_1193683, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1193683), c_Divides_Odiv__class_Omod(_1193683, _1193685, _1193689)), _1193687), _1193689))], (46564 ^ _778495) ^ [_1714507, _1714509, _1714511, _1714513] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714507), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1714507))), _1714509))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714511), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714507))), c_List_Otranspose(_1714507, _1714509)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714513), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714507))), hAPP(c_List_Ofilter(tc_List_Olist(_1714507), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714507)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714511)), c_Nat_Osize__class_Osize(tc_List_Olist(_1714507)))), _1714509)))), -(hAPP(hAPP(c_List_Onth(_1714507), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714507)), c_List_Otranspose(_1714507, _1714509)), _1714511)), _1714513) = hAPP(hAPP(c_List_Onth(_1714507), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714507)), _1714509), _1714513)), _1714511))], (50220 ^ _778495) ^ [_1793986, _1793988, _1793990, _1793992, _1793994, _1793996, _1793998, _1794000] : [c_Fun_Obij__betw(_1793986, _1793988, _1793990, _1793992, _1793994), 50223 ^ _778495 : [(50230 ^ _778495) ^ [] : [c_Fun_Obij__betw(_1793986, _1793996, hAPP(c_Fun_Ocomp(_1793988, _1793996, _1793986, _1793998), _1793990), _1793992, _1794000), -(c_Fun_Obij__betw(_1793988, _1793996, _1793998, _1793994, _1794000))], (50224 ^ _778495) ^ [] : [c_Fun_Obij__betw(_1793988, _1793996, _1793998, _1793994, _1794000), -(c_Fun_Obij__betw(_1793986, _1793996, hAPP(c_Fun_Ocomp(_1793988, _1793996, _1793986, _1793998), _1793990), _1793992, _1794000))]]], (28395 ^ _778495) ^ [_1290059, _1290061, _1290063, _1290065, _1290067] : [class_Groups_Oab__group__add(_1290059), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1290061, _1290059), hAPP(hAPP(c_COMBS(_1290061, _1290059, _1290059), hAPP(hAPP(c_COMBB(_1290059, tc_fun(_1290059, _1290059), _1290061), c_Groups_Ominus__class_Ominus(_1290059)), _1290063)), _1290065)), _1290067) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1290059), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1290061, _1290059), _1290063), _1290067)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1290061, _1290059), _1290065), _1290067)))], (40800 ^ _778495) ^ [_1578407, _1578409, _1578411] : [-(hAPP(c_Relation_ORange(_1578407, _1578409), _1578411) = hAPP(c_Relation_ODomain(_1578409, _1578407), hAPP(c_Relation_Oconverse(_1578407, _1578409), _1578411)))], (22056 ^ _778495) ^ [_1173085, _1173087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1173085)), c_Int_OBit0(_1173087))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1173085), _1173087)))], (9200 ^ _778495) ^ [_933933, _933935, _933937, _933939] : [class_Lattices_Osemilattice__inf(_933933), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933933), _933935), _933937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933933), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933933), _933935), _933939)), _933937)))], (43983 ^ _778495) ^ [_1658365, _1658367, _1658369] : [class_Orderings_Olinorder(_1658365), -(c_Big__Operators_Olattice_OSup__fin(_1658365, c_Orderings_Oord__class_Omax(_1658365), hAPP(c_List_Oset(_1658365), hAPP(hAPP(c_List_Olist_OCons(_1658365), _1658367), _1658369))) = hAPP(c_List_Ofoldl(_1658365, _1658365, c_Orderings_Oord__class_Omax(_1658365), _1658367), _1658369))], (22260 ^ _778495) ^ [_1176611, _1176613] : [class_Groups_Oordered__ab__group__add(_1176611), 22263 ^ _778495 : [(22270 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176611), c_Groups_Ozero__class_Ozero(_1176611)), _1176613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176611), hAPP(c_Groups_Ouminus__class_Ouminus(_1176611), _1176613)), c_Groups_Ozero__class_Ozero(_1176611))))], (22264 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176611), hAPP(c_Groups_Ouminus__class_Ouminus(_1176611), _1176613)), c_Groups_Ozero__class_Ozero(_1176611))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176611), c_Groups_Ozero__class_Ozero(_1176611)), _1176613)))]]], (22572 ^ _778495) ^ [_1182021, _1182023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182021), _1182023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1182021)), c_Int_OBit1(_1182023))))], (27217 ^ _778495) ^ [_1264554, _1264556] : [class_Rings_Olinordered__idom(_1264554), 27220 ^ _778495 : [(27227 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264554), c_Groups_Ozero__class_Ozero(_1264554)), hAPP(c_Int_Oring__1__class_Oof__int(_1264554), _1264556))))], (27221 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264554), c_Groups_Ozero__class_Ozero(_1264554)), hAPP(c_Int_Oring__1__class_Oof__int(_1264554), _1264556))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264556)))]]], (28077 ^ _778495) ^ [_1279439, _1279441] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1279439), _1279441) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1279439), _1279441))], (46130 ^ _778495) ^ [_1706525, _1706527] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1706525, _1706527)))], (47066 ^ _778495) ^ [_1725114, _1725116, _1725118, _1725120, _1725122] : [-(c_List_OdropWhile(_1725114, _1725116, _1725118) = hAPP(hAPP(c_List_Olist_OCons(_1725114), _1725120), _1725122)), _1725118 = hAPP(hAPP(c_List_Oappend(_1725114), c_List_OtakeWhile(_1725114, _1725116, _1725118)), hAPP(hAPP(c_List_Olist_OCons(_1725114), _1725120), _1725122)), -(hBOOL(hAPP(_1725116, _1725120)))], (39945 ^ _778495) ^ [_1557125, _1557127, _1557129, _1557131] : [-(c_Hilbert__Choice_OEps(tc_prod(_1557125, _1557127), hAPP(c_Product__Type_Oprod_Oprod__case(_1557125, _1557127, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1557125, tc_fun(_1557127, tc_HOL_Obool), tc_fun(_1557127, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1557127, tc_HOL_Obool), tc_fun(_1557127, tc_HOL_Obool)), _1557125), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1557127)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1557125), c_fconj), hAPP(c_fequal, _1557129)))), hAPP(c_fequal, _1557131)))) = hAPP(hAPP(c_Product__Type_OPair(_1557125, _1557127), _1557129), _1557131))], (32064 ^ _778495) ^ [_1368102, _1368104, _1368106, _1368108, _1368110] : [class_Orderings_Oorder(_1368102), 32067 ^ _778495 : [(32080 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1368102, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1368102, _1368104, _1368106)), c_SetInterval_Oord__class_OatLeastAtMost(_1368102, _1368108, _1368110)))), 32081 ^ _778495 : [(32084 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368102), _1368108), _1368104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368102), _1368106), _1368110))], (32082 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368102), _1368104), _1368106)))]]], (32068 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1368102, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1368102, _1368104, _1368106)), c_SetInterval_Oord__class_OatLeastAtMost(_1368102, _1368108, _1368110))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368102), _1368104), _1368106)), 32075 ^ _778495 : [(32078 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368102), _1368106), _1368110)))], (32076 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368102), _1368108), _1368104)))]]]]], (29637 ^ _778495) ^ [_1317871, _1317873, _1317875, _1317877, _1317879, _1317881, _1317883] : [hBOOL(hAPP(hAPP(c_member(_1317871), _1317873), hAPP(hAPP(_1317875, _1317877), _1317879))), -(hBOOL(hAPP(hAPP(c_member(_1317871), _1317873), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1317881, _1317883, tc_fun(_1317871, tc_HOL_Obool)), _1317875), hAPP(hAPP(c_Product__Type_OPair(_1317881, _1317883), _1317877), _1317879)))))], (52337 ^ _778495) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (38306 ^ _778495) ^ [_1514875, _1514877, _1514879, _1514881] : [-(c_Nitpick_Oprod(_1514875, _1514877, _1514879, _1514881) = hAPP(c_Set_OCollect(tc_prod(_1514875, _1514877)), hAPP(c_Product__Type_Oprod_Oprod__case(_1514875, _1514877, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1514875, tc_fun(_1514877, tc_HOL_Obool), tc_fun(_1514877, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1514877, tc_HOL_Obool), tc_fun(_1514877, tc_HOL_Obool)), _1514875), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1514877)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1514875), c_fconj), hAPP(hAPP(c_COMBC(_1514875, tc_fun(_1514875, tc_HOL_Obool), tc_HOL_Obool), c_member(_1514875)), _1514879)))), hAPP(hAPP(c_COMBC(_1514877, tc_fun(_1514877, tc_HOL_Obool), tc_HOL_Obool), c_member(_1514877)), _1514881)))))], (10863 ^ _778495) ^ [_965513, _965515, _965517] : [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, _965513)), _965515)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965513)), _965517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965515), _965517)))], (20331 ^ _778495) ^ [_1143723, _1143725, _1143727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1143723), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143723)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143725)), _1143727)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30019 ^ _778495) ^ [_1325021, _1325023, _1325025, _1325027] : [-(_1325021 = _1325023), hAPP(c_Product__Type_Ofst(_1325025, _1325027), _1325021) = hAPP(c_Product__Type_Ofst(_1325025, _1325027), _1325023), hAPP(c_Product__Type_Osnd(_1325025, _1325027), _1325021) = hAPP(c_Product__Type_Osnd(_1325025, _1325027), _1325023)], (41979 ^ _778495) ^ [_1611794, _1611796, _1611798, _1611800] : [-(hAPP(hAPP(c_List_Otake(_1611794), hAPP(c_Nat_OSuc, _1611796)), hAPP(hAPP(c_List_Olist_OCons(_1611794), _1611798), _1611800)) = hAPP(hAPP(c_List_Olist_OCons(_1611794), _1611798), hAPP(hAPP(c_List_Otake(_1611794), _1611796), _1611800)))], (48116 ^ _778495) ^ [_1748351] : [-(c_Predicate_Oconversep(_1748351, _1748351, c_fequal) = c_fequal)], (34793 ^ _778495) ^ [] : [-(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)))], (9408 ^ _778495) ^ [_938673, _938675, _938677] : [class_Lattices_Olattice(_938673), hBOOL(hAPP(c_Finite__Set_Ofinite(_938673), _938675)), -(hBOOL(hAPP(hAPP(c_member(_938673), _938677), _938675))), -(c_Big__Operators_Olattice__class_OSup__fin(_938673, hAPP(hAPP(c_Set_Oinsert(_938673), _938677), _938675)) = hAPP(hAPP(c_Finite__Set_Ofold(_938673, _938673, c_Lattices_Osemilattice__sup__class_Osup(_938673)), _938677), _938675))], (43830 ^ _778495) ^ [_1655087, _1655089, _1655091] : [-(hAPP(hAPP(c_List_Otake(_1655087), _1655089), hAPP(c_List_Otl(_1655087), _1655091)) = hAPP(c_List_Otl(_1655087), hAPP(hAPP(c_List_Otake(_1655087), hAPP(c_Nat_OSuc, _1655089)), _1655091)))], (29781 ^ _778495) ^ [_1320192, _1320194] : [29782 ^ _778495 : [(29785 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1320194), _1320192))], (29783 ^ _778495) ^ [] : [_1320192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1320194, _1320192) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1320194))], (41843 ^ _778495) ^ [_1608371, _1608373, _1608375] : [-(_1608371 = _1608373), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608375)), _1608371) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608375)), _1608373), 41849 ^ _778495 : [(41852 ^ _778495) ^ [] : [hAPP(hAPP(c_List_Onth(_1608375), _1608371), 41848 ^ [_1608371, _1608373, _1608375]) = hAPP(hAPP(c_List_Onth(_1608375), _1608373), 41848 ^ [_1608371, _1608373, _1608375])], (41850 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41848 ^ [_1608371, _1608373, _1608375]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608375)), _1608371))))]]], (45853 ^ _778495) ^ [_1700914, _1700916, _1700918, _1700920] : [-(c_List_Ofoldr(_1700914, _1700916, _1700918, c_List_Olist_ONil(_1700914), _1700920) = _1700920)], (14285 ^ _778495) ^ [_1032274, _1032276, _1032278] : [class_Rings_Olinordered__ring__strict(_1032274), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032274), _1032276), c_Groups_Ozero__class_Ozero(_1032274))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032274), _1032278), c_Groups_Ozero__class_Ozero(_1032274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032274), c_Groups_Ozero__class_Ozero(_1032274)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032274), _1032276), _1032278))))], (14589 ^ _778495) ^ [_1037650, _1037652] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037650), _1037652) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14594 ^ _778495 : [(14597 ^ _778495) ^ [] : [-(_1037652 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14595 ^ _778495) ^ [] : [-(_1037650 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 14598 ^ _778495 : [(14601 ^ _778495) ^ [] : [-(_1037652 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14599 ^ _778495) ^ [] : [-(_1037650 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6608 ^ _778495) ^ [_886176, _886178, _886180, _886182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886176, tc_HOL_Obool)), _886178), hAPP(hAPP(c_Set_Oinsert(_886176), _886180), _886182))), 6611 ^ _778495 : [(6618 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886176), _886180), _886178))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886176, tc_HOL_Obool)), _886178), _886182)))], (6612 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886176), _886180), _886178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886176, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886176, tc_HOL_Obool)), _886178), hAPP(hAPP(c_Set_Oinsert(_886176), _886180), c_Orderings_Obot__class_Obot(tc_fun(_886176, tc_HOL_Obool))))), _886182)))]]], (26120 ^ _778495) ^ [_1245443, _1245445, _1245447] : [class_Rings_Osemiring__1(_1245443), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1245443), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1245445), _1245447)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1245443), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1245443), _1245445)), _1245447))], (40613 ^ _778495) ^ [_1573968, _1573970, _1573972, _1573974] : [c_Wellfounded_Oacyclic(_1573968, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1573968, _1573968)), hAPP(hAPP(c_Product__Type_OPair(_1573968, _1573968), _1573970), _1573972)), _1573974)), 40616 ^ _778495 : [(40619 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573968, _1573968)), hAPP(hAPP(c_Product__Type_OPair(_1573968, _1573968), _1573972), _1573970)), c_Transitive__Closure_Ortrancl(_1573968, _1573974)))], (40617 ^ _778495) ^ [] : [-(c_Wellfounded_Oacyclic(_1573968, _1573974))]]], (45189 ^ _778495) ^ [_1684900, _1684902, _1684904, _1684906] : [c_List_Olist__all2(_1684900, _1684902, _1684904, c_List_Olist_ONil(_1684900), _1684906), -(_1684906 = c_List_Olist_ONil(_1684902))], (43574 ^ _778495) ^ [_1649517, _1649519, _1649521] : [hAPP(hAPP(c_List_Odrop(_1649517), _1649519), _1649521) = c_List_Olist_ONil(_1649517), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649517)), _1649521)), _1649519)))], (30061 ^ _778495) ^ [_1325874, _1325876, _1325878, _1325880, _1325882, _1325884] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1325874, _1325876), _1325876, _1325878), hAPP(hAPP(c_COMBB(_1325880, tc_fun(_1325876, _1325878), tc_prod(_1325874, _1325876)), _1325882), hAPP(hAPP(c_COMBB(_1325874, _1325880, tc_prod(_1325874, _1325876)), _1325884), c_Product__Type_Ofst(_1325874, _1325876)))), c_Product__Type_Osnd(_1325874, _1325876)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1325874, _1325876, _1325878), hAPP(hAPP(c_COMBB(_1325880, tc_fun(_1325876, _1325878), _1325874), _1325882), _1325884)))], (41874 ^ _778495) ^ [_1609049, _1609051, _1609053, _1609055] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609049) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1609051), hAPP(hAPP(c_List_Olist_OCons(_1609051), _1609053), _1609055)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609049)) = _1609053)], (43492 ^ _778495) ^ [_1647674, _1647676, _1647678, _1647680] : [-(hAPP(hAPP(c_List_Odrop(_1647674), hAPP(c_Nat_OSuc, _1647676)), hAPP(hAPP(c_List_Olist_OCons(_1647674), _1647678), _1647680)) = hAPP(hAPP(c_List_Odrop(_1647674), _1647676), _1647680))], (40710 ^ _778495) ^ [_1576212, _1576214, _1576216] : [c_Relation_Orefl__on(_1576212, _1576214, _1576216), -(c_Relation_Orefl__on(_1576212, _1576214, hAPP(c_Relation_Oconverse(_1576212, _1576212), _1576216)))], (15879 ^ _778495) ^ [_1061678, _1061680] : [class_Groups_Olinordered__ab__group__add(_1061678), 15882 ^ _778495 : [(15889 ^ _778495) ^ [] : [_1061680 = c_Groups_Ozero__class_Ozero(_1061678), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061678), _1061680), _1061680) = c_Groups_Ozero__class_Ozero(_1061678))], (15883 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061678), _1061680), _1061680) = c_Groups_Ozero__class_Ozero(_1061678), -(_1061680 = c_Groups_Ozero__class_Ozero(_1061678))]]], (8906 ^ _778495) ^ [_928202, _928204, _928206] : [class_Lattices_Osemilattice__inf(_928202), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928202), _928204), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928202), _928204), _928206)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928202), _928204), _928206))], (1258 ^ _778495) ^ [_797248, _797250] : [-(class_Rings_Oordered__ring(_797248)), _797250 = _797248, class_Rings_Oordered__ring(_797250)], (1688 ^ _778495) ^ [_802623, _802625] : [-(class_Groups_Oab__semigroup__add(_802623)), _802625 = _802623, class_Groups_Oab__semigroup__add(_802625)], (52575 ^ _778495) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (26734 ^ _778495) ^ [_1256497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1256497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1256497))))], (43217 ^ _778495) ^ [_1640809, _1640811, _1640813] : [hAPP(hAPP(c_List_Oappend(_1640809), _1640811), _1640813) = c_List_Olist_ONil(_1640809), 43220 ^ _778495 : [(43223 ^ _778495) ^ [] : [-(_1640813 = c_List_Olist_ONil(_1640809))], (43221 ^ _778495) ^ [] : [-(_1640811 = c_List_Olist_ONil(_1640809))]]], (45774 ^ _778495) ^ [_1698093, _1698095, _1698097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1698093), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1698095))), c_List_Otranspose(_1698095, _1698097)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1698095)), c_List_Otranspose(_1698095, _1698097)), _1698093) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698095), _1698095), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698095), tc_Nat_Onat, _1698095), c_List_Onth(_1698095)), _1698093)), hAPP(c_List_Ofilter(tc_List_Olist(_1698095), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1698095)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1698093)), c_Nat_Osize__class_Osize(tc_List_Olist(_1698095)))), _1698097)))], (20048 ^ _778495) ^ [_1138653, _1138655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1138653), _1138655)), -(_1138655 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1138653), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20051 ^ [_1138653, _1138655])))], (9691 ^ _778495) ^ [_944494, _944496, _944498] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_944494), _944496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944494, tc_HOL_Obool)), _944496), _944498)), -(hAPP(c_Finite__Set_Ocard(_944494), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_944494, tc_HOL_Obool)), _944498), _944496)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_944494), _944498)), hAPP(c_Finite__Set_Ocard(_944494), _944496)))], (15895 ^ _778495) ^ [_1061937, _1061939, _1061941] : [hAPP(c_Finite__Set_Ocard(_1061937), _1061939) = hAPP(c_Nat_OSuc, _1061941), 15900 ^ _778495 : [(15903 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1061937), 15898 ^ [_1061937, _1061939, _1061941]), 15899 ^ [_1061937, _1061939, _1061941]))], (15905 ^ _778495) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1061937), 15899 ^ [_1061937, _1061939, _1061941]) = _1061941)], (15907 ^ _778495) ^ [] : [_1061941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(15899 ^ [_1061937, _1061939, _1061941] = c_Orderings_Obot__class_Obot(tc_fun(_1061937, tc_HOL_Obool)))], (15901 ^ _778495) ^ [] : [-(_1061939 = hAPP(hAPP(c_Set_Oinsert(_1061937), 15898 ^ [_1061937, _1061939, _1061941]), 15899 ^ [_1061937, _1061939, _1061941]))]]], (21872 ^ _778495) ^ [_1169844, _1169846] : [class_Groups_Olinordered__ab__group__add(_1169844), 21875 ^ _778495 : [(21882 ^ _778495) ^ [] : [_1169846 = c_Groups_Ozero__class_Ozero(_1169844), -(_1169846 = hAPP(c_Groups_Ouminus__class_Ouminus(_1169844), _1169846))], (21876 ^ _778495) ^ [] : [_1169846 = hAPP(c_Groups_Ouminus__class_Ouminus(_1169844), _1169846), -(_1169846 = c_Groups_Ozero__class_Ozero(_1169844))]]], (17310 ^ _778495) ^ [_1088065, _1088067, _1088069, _1088071] : [class_Fields_Ofield__inverse__zero(_1088065), -(_1088067 = c_Groups_Ozero__class_Ozero(_1088065)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088065), _1088069), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1088065), _1088071), _1088067)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1088065), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088065), _1088071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088065), _1088069), _1088067))), _1088067))], (35096 ^ _778495) ^ [_1434450] : [c_Nat__Transfer_Onat__set(_1434450), -(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), _1434450)) = _1434450)], (20188 ^ _778495) ^ [_1141101, _1141103] : [20189 ^ _778495 : [(20190 ^ _778495) ^ [_1141157] : [_1141103 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141101), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1141157)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141101), _1141103)))], (45334 ^ _778495) ^ [_1688215, _1688217, _1688219, _1688221, _1688223] : [45336 ^ _778495 : [(45339 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1688215, _1688217, tc_HOL_Obool), _1688223), 45335 ^ [_1688215, _1688217, _1688219, _1688221, _1688223]))], (45337 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1688215, _1688217)), 45335 ^ [_1688215, _1688217, _1688219, _1688221, _1688223]), hAPP(c_List_Oset(tc_prod(_1688215, _1688217)), hAPP(hAPP(c_List_Ozip(_1688215, _1688217), _1688219), _1688221)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688215)), _1688219) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688217)), _1688221), -(c_List_Olist__all2(_1688215, _1688217, _1688223, _1688219, _1688221))], (4914 ^ _778495) ^ [_853449, _853451] : [_853451 = _853449, -(c_Lattices_Osemilattice__inf__class_Oinf(_853451) = c_Lattices_Osemilattice__inf__class_Oinf(_853449))], (13589 ^ _778495) ^ [_1019671, _1019673, _1019675, _1019677] : [13590 ^ _778495 : [(13593 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1019675), _1019677)))], (13591 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1019671), _1019673)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1019671, _1019675)), c_Sum__Type_OPlus(_1019671, _1019675, _1019673, _1019677)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2798 ^ _778495) ^ [_820007, _820009, _820011, _820013] : [-(c_Relation_ORange(_820013, _820009) = c_Relation_ORange(_820011, _820007)), _820013 = _820011, _820009 = _820007], (2640 ^ _778495) ^ [_817502, _817504] : [_817504 = _817502, -(c_Int_Oint__ge__less__than2(_817504) = c_Int_Oint__ge__less__than2(_817502))], (34615 ^ _778495) ^ [] : [-(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))))], (51199 ^ _778495) ^ [_1813871, _1813873] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813871), _1813873)), 51204 ^ _778495 : [(51207 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813873), _1813871))], (51205 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813871), _1813873)))]], -(_1813871 = _1813873)], (52537 ^ _778495) ^ [_1834394, _1834396] : [-(class_Enum_Oenum(tc_prod(_1834394, _1834396))), class_Enum_Oenum(_1834394), class_Enum_Oenum(_1834396)], (47046 ^ _778495) ^ [_1724670, _1724672, _1724674, _1724676, _1724678] : [-(c_List_OdropWhile(_1724670, _1724672, hAPP(hAPP(c_List_Omap(_1724674, _1724670), _1724676), _1724678)) = hAPP(hAPP(c_List_Omap(_1724674, _1724670), _1724676), c_List_OdropWhile(_1724674, hAPP(c_Fun_Ocomp(_1724670, tc_HOL_Obool, _1724674, _1724672), _1724676), _1724678)))], (35314 ^ _778495) ^ [_1438122, _1438124, _1438126] : [class_Orderings_Oorder(_1438122), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438122, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1438122, _1438124), _1438126)), hAPP(c_SetInterval_Oord__class_OatLeast(_1438122), _1438126)) = c_Orderings_Obot__class_Obot(tc_fun(_1438122, tc_HOL_Obool)))], (50200 ^ _778495) ^ [_1793564, _1793566, _1793568, _1793570, _1793572] : [c_Fun_Obij__betw(_1793564, _1793566, _1793568, c_Orderings_Otop__class_Otop(tc_fun(_1793564, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793566, tc_HOL_Obool))), c_Fun_Obij__betw(_1793566, _1793570, _1793572, c_Orderings_Otop__class_Otop(tc_fun(_1793566, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793570, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1793564, _1793570, hAPP(c_Fun_Ocomp(_1793566, _1793570, _1793564, _1793572), _1793568), c_Orderings_Otop__class_Otop(tc_fun(_1793564, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793570, tc_HOL_Obool))))], (2320 ^ _778495) ^ [_812520, _812522, _812524, _812526] : [-(c_Divides_Odivmod__int__rel(_812526, _812522) = c_Divides_Odivmod__int__rel(_812524, _812520)), _812526 = _812524, _812522 = _812520], (32347 ^ _778495) ^ [_1374121, _1374123] : [32349 ^ _778495 : [(32352 ^ _778495) ^ [] : [hBOOL(hAPP(_1374123, 32348 ^ [_1374121, _1374123]))], (32350 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 32348 ^ [_1374121, _1374123]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1374121))))]], 32353 ^ _778495 : [(32354 ^ _778495) ^ [_1374276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1374276), _1374121)), -(hBOOL(hAPP(_1374123, _1374276)))]]], (47229 ^ _778495) ^ [_1728523, _1728525, _1728527] : [-(hAPP(c_List_Oset(_1728523), c_List_Oinsert(_1728523, _1728525, _1728527)) = hAPP(hAPP(c_Set_Oinsert(_1728523), _1728525), hAPP(c_List_Oset(_1728523), _1728527)))], (23198 ^ _778495) ^ [_1193961, _1193963, _1193965, _1193967, _1193969, _1193971] : [class_Divides_Oring__div(_1193961), c_Divides_Odiv__class_Omod(_1193961, _1193963, _1193965) = c_Divides_Odiv__class_Omod(_1193961, _1193967, _1193965), c_Divides_Odiv__class_Omod(_1193961, _1193969, _1193965) = c_Divides_Odiv__class_Omod(_1193961, _1193971, _1193965), -(c_Divides_Odiv__class_Omod(_1193961, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1193961), _1193963), _1193969), _1193965) = c_Divides_Odiv__class_Omod(_1193961, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1193961), _1193967), _1193971), _1193965))], (25427 ^ _778495) ^ [_1232853, _1232855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232853)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232853), _1232855)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1232853)), hAPP(c_Int_Onat, _1232855)))], (39297 ^ _778495) ^ [_1542223] : [-(_1542223 = hAPP(c_Int_OAbs__Integ, 39295 ^ [_1542223]))], (52385 ^ _778495) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (46045 ^ _778495) ^ [_1704747, _1704749, _1704751, _1704753] : [class_Groups_Ocomm__monoid__add(_1704747), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704747), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704747), _1704749), c_List_Oupt(_1704751, _1704753))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704747), _1704749), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704751, _1704753))))], (37075 ^ _778495) ^ [_1477994, _1477996, _1477998] : [-(hAPP(c_Finite__Set_Ofold1(_1477994, _1477996), _1477998) = c_HOL_OThe(_1477994, c_Finite__Set_Ofold1Set(_1477994, _1477996, _1477998)))], (24481 ^ _778495) ^ [_1216527, _1216529] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1216527, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1216527, tc_HOL_Obool)), _1216529)) = _1216529)], (38443 ^ _778495) ^ [_1519785, _1519787, _1519789, _1519791, _1519793, _1519795, _1519797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519785, _1519787), tc_HOL_Obool)), _1519789), _1519791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519787, _1519793), tc_HOL_Obool)), _1519795), _1519797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519785, _1519793), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1519785, _1519787, _1519793), _1519789), _1519795)), hAPP(hAPP(c_Relation_Orel__comp(_1519785, _1519787, _1519793), _1519791), _1519797))))], (18962 ^ _778495) ^ [_1119445, _1119447, _1119449] : [class_Orderings_Olinorder(_1119445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119445), _1119447)), hBOOL(hAPP(hAPP(c_member(_1119445), _1119449), _1119447)), 18973 ^ _778495 : [(18980 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1119445, tc_HOL_Obool)), _1119447), hAPP(hAPP(c_Set_Oinsert(_1119445), _1119449), c_Orderings_Obot__class_Obot(tc_fun(_1119445, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1119445, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1119445, c_Orderings_Oord__class_Omin(_1119445), _1119447) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1119445), _1119449), c_Big__Operators_Olattice_OInf__fin(_1119445, c_Orderings_Oord__class_Omin(_1119445), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1119445, tc_HOL_Obool)), _1119447), hAPP(hAPP(c_Set_Oinsert(_1119445), _1119449), c_Orderings_Obot__class_Obot(tc_fun(_1119445, tc_HOL_Obool)))))))], (18974 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1119445, tc_HOL_Obool)), _1119447), hAPP(hAPP(c_Set_Oinsert(_1119445), _1119449), c_Orderings_Obot__class_Obot(tc_fun(_1119445, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1119445, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1119445, c_Orderings_Oord__class_Omin(_1119445), _1119447) = _1119449)]]], (44654 ^ _778495) ^ [_1673086, _1673088] : [_1673086 = _1673088, -(hAPP(c_Code__Numeral_Oof__nat, _1673086) = hAPP(c_Code__Numeral_Oof__nat, _1673088))], (50951 ^ _778495) ^ [_1809851, _1809853] : [class_Rings_Ocomm__semiring__1(_1809851), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809851), c_Groups_Oone__class_Oone(_1809851)), _1809853)))], (13310 ^ _778495) ^ [_1015333] : [hAPP(c_Nat_OSuc, _1015333) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27002 ^ _778495) ^ [_1260984, _1260986] : [-(c_Nitpick_Oint__lcm(_1260984, _1260986) = 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), _1260984)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1260986)))))], (46931 ^ _778495) ^ [_1722261, _1722263, _1722265, _1722267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722261), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722263)), c_List_OtakeWhile(_1722263, _1722265, _1722267)))), -(hAPP(hAPP(c_List_Onth(_1722263), c_List_OtakeWhile(_1722263, _1722265, _1722267)), _1722261) = hAPP(hAPP(c_List_Onth(_1722263), _1722267), _1722261))], (22688 ^ _778495) ^ [_1184056] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1184056)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1184056))))], (35514 ^ _778495) ^ [_1442330, _1442332, _1442334, _1442336, _1442338, _1442340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1442330, _1442332), tc_HOL_Obool)), _1442334), _1442336)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1442330, tc_HOL_Obool)), _1442338), _1442340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1442332, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442330, _1442332, _1442334), _1442338)), hAPP(c_Relation_OImage(_1442330, _1442332, _1442336), _1442340))))], (40790 ^ _778495) ^ [_1578204, _1578206, _1578208] : [c_Equiv__Relations_Oequiv(_1578204, _1578206, _1578208), -(hAPP(hAPP(c_Relation_Orel__comp(_1578204, _1578204, _1578204), hAPP(c_Relation_Oconverse(_1578204, _1578204), _1578208)), _1578208) = _1578208)], (23068 ^ _778495) ^ [_1191160, _1191162] : [class_Divides_Osemiring__div(_1191160), -(c_Divides_Odiv__class_Omod(_1191160, _1191162, _1191162) = c_Groups_Ozero__class_Ozero(_1191160))], (46096 ^ _778495) ^ [_1706019, _1706021] : [class_Orderings_Olinorder(_1706019), -(c_List_Olinorder__class_Osorted(_1706019, hAPP(hAPP(c_List_Olist_OCons(_1706019), _1706021), c_List_Olist_ONil(_1706019))))], (40212 ^ _778495) ^ [_1563650, _1563652] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1563650, _1563650), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1563650, _1563652)), hAPP(hAPP(c_Product__Type_OSigma(_1563650, _1563650), hAPP(c_Relation_OField(_1563650), _1563652)), hAPP(c_COMBK(tc_fun(_1563650, tc_HOL_Obool), _1563650), hAPP(c_Relation_OField(_1563650), _1563652))))))], (29041 ^ _778495) ^ [_1305746, _1305748, _1305750] : [-(c_Nat_Onat_Onat__case(_1305746, _1305748, _1305750, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1305748)], (19894 ^ _778495) ^ [] : [-(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))))], (33914 ^ _778495) ^ [_1409809, _1409811, _1409813, _1409815, _1409817] : [class_Groups_Ocomm__monoid__add(_1409809), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1409809), _1409811), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1409813), _1409815)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1409817), _1409815))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1409809), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1409809, tc_Nat_Onat), _1409811), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1409815))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1409813), _1409817)))], (12759 ^ _778495) ^ [_1004727, _1004729, _1004731, _1004733, _1004735] : [class_Groups_Ocomm__monoid__add(_1004727), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004729), _1004731)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004729, _1004727), _1004733), hAPP(hAPP(c_Set_Oinsert(_1004729), _1004735), _1004731)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004727), hAPP(_1004733, _1004735)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004729, _1004727), _1004733), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1004729, tc_HOL_Obool)), _1004731), hAPP(hAPP(c_Set_Oinsert(_1004729), _1004735), c_Orderings_Obot__class_Obot(tc_fun(_1004729, tc_HOL_Obool)))))))], (13362 ^ _778495) ^ [_1016029, _1016031] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016029), _1016031) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1016029 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1016031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23284 ^ _778495) ^ [_1195735, _1195737, _1195739] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1195735), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195737, _1195739)), _1195739) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1195735), _1195737), _1195739))], (37631 ^ _778495) ^ [_1493143, _1493145, _1493147, _1493149] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1493143), _1493145)), 37637 ^ _778495 : [(37640 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1493147), hAPP(_1493149, 37636 ^ [_1493143, _1493145, _1493147, _1493149])))], (37638 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493143), 37636 ^ [_1493143, _1493145, _1493147, _1493149]), _1493145)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1493143, _1493147)), hAPP(hAPP(c_Product__Type_OSigma(_1493143, _1493147), _1493145), _1493149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493143, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1493147, tc_HOL_Obool), tc_Nat_Onat, _1493143), c_Finite__Set_Ocard(_1493147)), _1493149)), _1493145))], (39730 ^ _778495) ^ [_1552455, _1552457, _1552459, _1552461, _1552463, _1552465, _1552467] : [c_Finite__Set_Ofolding__image(_1552455, _1552457, _1552459, _1552461, _1552463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552457), _1552465)), -(hAPP(hAPP(_1552463, _1552467), _1552465) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1552455, _1552457, _1552459), _1552467), _1552461), _1552465))], (19932 ^ _778495) ^ [_1136561] : [-(hBOOL(hAPP(_1136561, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 19939 ^ [_1136561])))), 19933 ^ _778495 : [(19934 ^ _778495) ^ [_1136613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136613)), hBOOL(hAPP(_1136561, _1136613))]]], (28363 ^ _778495) ^ [_1289088, _1289090, _1289092, _1289094, _1289096, _1289098, _1289100] : [class_Rings_Osemiring__0(_1289088), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289088), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289090, _1289088), _1289092), _1289094)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289096, _1289088), _1289098), _1289100)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289090, _1289088), hAPP(hAPP(c_COMBC(_1289090, tc_fun(_1289096, tc_HOL_Obool), _1289088), hAPP(hAPP(c_COMBB(tc_fun(_1289096, _1289088), tc_fun(tc_fun(_1289096, tc_HOL_Obool), _1289088), _1289090), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289096, _1289088)), hAPP(hAPP(c_COMBC(_1289090, tc_fun(_1289096, _1289088), tc_fun(_1289096, _1289088)), hAPP(hAPP(c_COMBB(tc_fun(_1289088, _1289088), tc_fun(tc_fun(_1289096, _1289088), tc_fun(_1289096, _1289088)), _1289090), c_COMBB(_1289088, _1289088, _1289096)), hAPP(hAPP(c_COMBB(_1289088, tc_fun(_1289088, _1289088), _1289090), c_Groups_Otimes__class_Otimes(_1289088)), _1289092))), _1289098))), _1289100)), _1289094))], (17266 ^ _778495) ^ [_1087284, _1087286, _1087288, _1087290, _1087292] : [class_Fields_Ofield(_1087284), -(_1087286 = c_Groups_Ozero__class_Ozero(_1087284)), -(_1087288 = c_Groups_Ozero__class_Ozero(_1087284)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087284), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1087284), _1087290), _1087286)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1087284), _1087292), _1087288)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1087284), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087284), _1087290), _1087288)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087284), _1087292), _1087286))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087284), _1087286), _1087288)))], (37841 ^ _778495) ^ [_1498543, _1498545, _1498547] : [hBOOL(hAPP(hAPP(c_member(_1498543), _1498545), hAPP(c_Set_OCollect(_1498543), _1498547))), -(hBOOL(hAPP(_1498547, _1498545)))], (35587 ^ _778495) ^ [] : [-(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))))))], (30409 ^ _778495) ^ [] : [-(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))], (35873 ^ _778495) ^ [_1451164, _1451166, _1451168, _1451170, _1451172] : [c_Equiv__Relations_Oequiv(_1451164, _1451166, _1451168), hBOOL(hAPP(hAPP(c_member(tc_prod(_1451164, _1451164)), hAPP(hAPP(c_Product__Type_OPair(_1451164, _1451164), _1451170), _1451172)), _1451168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1451164, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1451164, _1451164, _1451168), hAPP(hAPP(c_Set_Oinsert(_1451164), _1451170), c_Orderings_Obot__class_Obot(tc_fun(_1451164, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1451164, _1451164, _1451168), hAPP(hAPP(c_Set_Oinsert(_1451164), _1451172), c_Orderings_Obot__class_Obot(tc_fun(_1451164, tc_HOL_Obool)))))))], (45717 ^ _778495) ^ [_1696957, _1696959, _1696961] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1696957), tc_List_Olist(_1696957)), c_List_Opartition(_1696957, _1696959, _1696961)) = hAPP(c_List_Ofilter(_1696957, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1696957, c_fNot), _1696959)), _1696961))], (22160 ^ _778495) ^ [_1174899, _1174901] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1174899)), c_Int_OBit0(_1174901)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1174899), _1174901)))], (24906 ^ _778495) ^ [_1224031, _1224033, _1224035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1224031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1224031), _1224033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1224035), _1224033)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1224035), _1224031))))], (20404 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (3228 ^ _778495) ^ [_826698, _826700, _826702, _826704] : [-(c_Random_Oselect(_826704, _826700) = c_Random_Oselect(_826702, _826698)), _826704 = _826702, _826700 = _826698], (28409 ^ _778495) ^ [_1290540, _1290542, _1290544, _1290546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290540, tc_fun(_1290542, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1290540, tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_fun(_1290542, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1290542, tc_fun(tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_fun(_1290542, tc_HOL_Obool)), _1290540), c_COMBC(_1290542, tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1290542, tc_prod(_1290540, _1290542)), tc_fun(_1290542, tc_fun(tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_HOL_Obool)), _1290540), hAPP(c_COMBB(tc_prod(_1290540, _1290542), tc_fun(tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_HOL_Obool), _1290542), c_member(tc_prod(_1290540, _1290542)))), c_Product__Type_OPair(_1290540, _1290542)))), _1290544)), hAPP(hAPP(c_COMBC(_1290540, tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_fun(_1290542, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1290542, tc_fun(tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_fun(_1290542, tc_HOL_Obool)), _1290540), c_COMBC(_1290542, tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1290542, tc_prod(_1290540, _1290542)), tc_fun(_1290542, tc_fun(tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_HOL_Obool)), _1290540), hAPP(c_COMBB(tc_prod(_1290540, _1290542), tc_fun(tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool), tc_HOL_Obool), _1290542), c_member(tc_prod(_1290540, _1290542)))), c_Product__Type_OPair(_1290540, _1290542)))), _1290546))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1290540, _1290542), tc_HOL_Obool)), _1290544), _1290546)))], (52379 ^ _778495) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (35444 ^ _778495) ^ [_1440850, _1440852] : [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)), _1440850), 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)), _1440852), 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)), _1440850), _1440852)), c_Int_Ointrel)))], (52719 ^ _778495) ^ [_1836489, _1836491] : [hBOOL(hAPP(hAPP(c_fdisj, _1836489), _1836491)), -(hBOOL(_1836489)), -(hBOOL(_1836491))], (12807 ^ _778495) ^ [_1005958, _1005960, _1005962, _1005964] : [-(hBOOL(hAPP(hAPP(c_member(_1005958), _1005960), _1005962))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1005958, tc_Nat_Onat), _1005964), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005958, tc_HOL_Obool)), _1005962), hAPP(hAPP(c_Set_Oinsert(_1005958), _1005960), c_Orderings_Obot__class_Obot(tc_fun(_1005958, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1005958, tc_Nat_Onat), _1005964), _1005962))], (40631 ^ _778495) ^ [_1574389, _1574391] : [-(c_Relation_Orefl__on(_1574389, c_Orderings_Otop__class_Otop(tc_fun(_1574389, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574389, _1574389), tc_HOL_Obool)), _1574391), c_Relation_OId(_1574389))))], (21054 ^ _778495) ^ [_1155622, _1155624] : [class_Groups_Oordered__ab__group__add__abs(_1155622), 21057 ^ _778495 : [(21064 ^ _778495) ^ [] : [_1155624 = c_Groups_Ozero__class_Ozero(_1155622), -(hAPP(c_Groups_Oabs__class_Oabs(_1155622), _1155624) = c_Groups_Ozero__class_Ozero(_1155622))], (21058 ^ _778495) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1155622), _1155624) = c_Groups_Ozero__class_Ozero(_1155622), -(_1155624 = c_Groups_Ozero__class_Ozero(_1155622))]]], (34761 ^ _778495) ^ [_1428735, _1428737, _1428739] : [-(hAPP(c_Set_OPow(_1428735), hAPP(hAPP(c_Set_Oinsert(_1428735), _1428737), _1428739)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1428735, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1428735), _1428739)), hAPP(c_Set_Oimage(tc_fun(_1428735, tc_HOL_Obool), tc_fun(_1428735, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1428735), _1428737)), hAPP(c_Set_OPow(_1428735), _1428739))))], (2096 ^ _778495) ^ [_809036, _809038, _809040, _809042] : [-(c_Int_Onat__aux(_809042, _809038) = c_Int_Onat__aux(_809040, _809036)), _809042 = _809040, _809038 = _809036], (42712 ^ _778495) ^ [_1629757, _1629759, _1629761] : [-(hAPP(hAPP(c_List_Ozip(_1629757, _1629759), _1629761), c_List_Olist_ONil(_1629759)) = c_List_Olist_ONil(tc_prod(_1629757, _1629759)))], (42217 ^ _778495) ^ [_1619239, _1619241] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1619239, _1619241) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619239, _1619241)))], (40828 ^ _778495) ^ [_1579255, _1579257, _1579259, _1579261, _1579263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579255, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579257, _1579255, _1579259), _1579261)), _1579263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579257, tc_HOL_Obool)), _1579261), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579257, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579255, _1579257, hAPP(c_Relation_Oconverse(_1579257, _1579255), _1579259)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579255, tc_HOL_Obool)), _1579263))))))], (48698 ^ _778495) ^ [_1761070, _1761072, _1761074] : [c_List_Olist__ex(tc_Int_Oint, _1761070, c_List_Oupto(_1761072, _1761074)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1761070), _1761072, _1761074)], (5440 ^ _778495) ^ [_861816, _861818] : [_861818 = _861816, -(c_Groups_Ominus__class_Ominus(_861818) = c_Groups_Ominus__class_Ominus(_861816))], (31264 ^ _778495) ^ [_1349712, _1349714, _1349716] : [class_Orderings_Olinorder(_1349712), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349712), _1349714)), hBOOL(hAPP(hAPP(c_member(_1349712), _1349716), _1349714)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349712), _1349716), c_Big__Operators_Olattice_OSup__fin(_1349712, c_Orderings_Oord__class_Omax(_1349712), _1349714)) = _1349716)], (22074 ^ _778495) ^ [_1173409, _1173411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1173409), _1173411)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1173409)), c_Int_OBit0(_1173411))))], (4766 ^ _778495) ^ [_851163, _851165] : [_851165 = _851163, -(c_Wellfounded_Ofinite__psubset(_851165) = c_Wellfounded_Ofinite__psubset(_851163))], (42068 ^ _778495) ^ [_1613907, _1613909, _1613911] : [hBOOL(hAPP(hAPP(c_member(_1613907), _1613909), hAPP(c_List_Oset(_1613907), _1613911))), 42072 ^ _778495 : [(42075 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1613907), _1613911), 42071 ^ [_1613907, _1613909, _1613911]) = _1613909)], (42073 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42071 ^ [_1613907, _1613909, _1613911]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613907)), _1613911))))]]], (1168 ^ _778495) ^ [_796123, _796125] : [-(class_Rings_Oring__1__no__zero__divisors(_796123)), _796125 = _796123, class_Rings_Oring__1__no__zero__divisors(_796125)], (4680 ^ _778495) ^ [_849760, _849762] : [_849762 = _849760, -(c_List_Oset(_849762) = c_List_Oset(_849760))], (42062 ^ _778495) ^ [_1613746, _1613748, _1613750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613746), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613748)), _1613750))), -(hBOOL(hAPP(hAPP(c_member(_1613748), hAPP(hAPP(c_List_Onth(_1613748), _1613750), _1613746)), hAPP(c_List_Oset(_1613748), _1613750))))], (48308 ^ _778495) ^ [_1752573, _1752575, _1752577, _1752579] : [-(hBOOL(hAPP(_1752573, _1752575))), -(hAPP(c_List_Ofilter(_1752577, _1752573), c_List_Oreplicate(_1752577, _1752579, _1752575)) = c_List_Olist_ONil(_1752577))], (34777 ^ _778495) ^ [_1429037, _1429039] : [class_Orderings_Olinorder(_1429037), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1429037, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1429037), _1429039)) = hAPP(c_SetInterval_Oord__class_OatMost(_1429037), _1429039))], (31017 ^ _778495) ^ [_1345146, _1345148] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1345146), _1345148)), _1345148) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1345146), _1345148))], (50515 ^ _778495) ^ [_1801935, _1801937, _1801939] : [c_List_Oall__interval__nat(_1801935, _1801937, _1801939), -(c_List_Olist__all(tc_Nat_Onat, _1801935, c_List_Oupt(_1801937, _1801939)))], (49899 ^ _778495) ^ [_1787488, _1787490, _1787492, _1787494, _1787496, _1787498] : [c_Fun_Obij__betw(_1787488, _1787490, _1787492, c_Orderings_Otop__class_Otop(tc_fun(_1787488, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787490, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1787488, _1787490, _1787492), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1787494, tc_fun(_1787488, tc_HOL_Obool)), _1787496), _1787498)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1787494, tc_fun(_1787490, tc_HOL_Obool)), _1787496), hAPP(hAPP(c_COMBB(tc_fun(_1787488, tc_HOL_Obool), tc_fun(_1787490, tc_HOL_Obool), _1787494), c_Set_Oimage(_1787488, _1787490, _1787492)), _1787498)))], (17628 ^ _778495) ^ [_1094547, _1094549] : [class_Orderings_Olinorder(_1094547), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094547), _1094549), _1094549) = _1094549)], (45802 ^ _778495) ^ [_1698923, _1698925] : [c_List_Otranspose(_1698923, _1698925) = c_List_Olist_ONil(tc_List_Olist(_1698923)), 45805 ^ _778495 : [(45806 ^ _778495) ^ [_1699018] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698923)), _1699018), hAPP(c_List_Oset(tc_List_Olist(_1698923)), _1698925))), -(_1699018 = c_List_Olist_ONil(_1698923))]]], (19278 ^ _778495) ^ [_1124948, _1124950, _1124952] : [class_Orderings_Olinorder(_1124948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1124948), _1124950)), hBOOL(hAPP(hAPP(c_member(_1124948), _1124952), _1124950)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1124948), _1124952), c_Big__Operators_Olattice_OInf__fin(_1124948, c_Orderings_Oord__class_Omin(_1124948), _1124950)) = c_Big__Operators_Olattice_OInf__fin(_1124948, c_Orderings_Oord__class_Omin(_1124948), _1124950))], (45705 ^ _778495) ^ [_1696764, _1696766, _1696768, _1696770, _1696772, _1696774] : [class_Orderings_Olinorder(_1696764), -(hBOOL(hAPP(_1696766, _1696768))), -(hAPP(c_List_Ofilter(_1696770, _1696766), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696770, _1696764, _1696772), _1696768), _1696774)) = hAPP(c_List_Ofilter(_1696770, _1696766), _1696774))], (28611 ^ _778495) ^ [_1296663, _1296665, _1296667] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1296663, tc_HOL_Obool)), _1296667), hAPP(c_Set_OPow(_1296663), _1296665))), -(hBOOL(hAPP(c_Predicate_OPowp(_1296663, hAPP(hAPP(c_COMBC(_1296663, tc_fun(_1296663, tc_HOL_Obool), tc_HOL_Obool), c_member(_1296663)), _1296665)), _1296667)))], (22914 ^ _778495) ^ [_1188135] : [-(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)))), _1188135) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1188135)))], (32772 ^ _778495) ^ [_1383031, _1383033, _1383035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1383031)), 32775 ^ _778495 : [(32776 ^ _778495) ^ [_1383165] : [32778 ^ _778495 : [(32784 ^ _778495) ^ [] : [-(_1383165 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32780 ^ [_1383031, _1383033, _1383035, _1383165]), 32777 ^ [_1383031, _1383033, _1383035, _1383165]))], (32782 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32780 ^ [_1383031, _1383033, _1383035, _1383165]), _1383033)))], (32779 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32777 ^ [_1383031, _1383033, _1383035, _1383165]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1383031))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383165), _1383035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1383165), _1383031)), _1383035)))]]], (34829 ^ _778495) ^ [_1430007, _1430009, _1430011] : [class_Orderings_Oorder(_1430007), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430007, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1430007, _1430009, _1430011)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1430007), _1430011)) = c_Orderings_Obot__class_Obot(tc_fun(_1430007, tc_HOL_Obool)))], (48408 ^ _778495) ^ [_1754534, _1754536, _1754538, _1754540] : [-(c_Lazy__Sequence_Oappend(_1754534, c_Lazy__Sequence_Olazy__sequence_OInsert(_1754534, _1754536, _1754538), _1754540) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754534, _1754536, c_Lazy__Sequence_Oappend(_1754534, _1754538, _1754540)))], (39768 ^ _778495) ^ [_1553217, _1553219, _1553221, _1553223, _1553225, _1553227] : [c_Finite__Set_Ofolding(_1553217, _1553219, _1553221, _1553223), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553217), _1553225)), -(hAPP(_1553223, hAPP(hAPP(c_Set_Oinsert(_1553217), _1553227), _1553225)) = hAPP(c_Fun_Ocomp(_1553219, _1553219, _1553219, hAPP(_1553223, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1553217, tc_HOL_Obool)), _1553225), hAPP(hAPP(c_Set_Oinsert(_1553217), _1553227), c_Orderings_Obot__class_Obot(tc_fun(_1553217, tc_HOL_Obool)))))), hAPP(_1553221, _1553227)))], (37482 ^ _778495) ^ [_1488951, _1488953, _1488955, _1488957, _1488959, _1488961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1488951, _1488953), tc_HOL_Obool)), _1488955), hAPP(hAPP(c_Product__Type_OSigma(_1488951, _1488953), _1488957), hAPP(c_COMBK(tc_fun(_1488953, tc_HOL_Obool), _1488951), _1488959)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488953, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1488951, _1488953, _1488955), _1488961)), _1488959)))], (42830 ^ _778495) ^ [_1631892, _1631894] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631892), tc_List_Olist(_1631892))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631892), tc_List_Olist(_1631892)), c_List_Olist_ONil(_1631892)), c_List_Olist_ONil(_1631892))), c_List_Olistrel(_1631892, _1631894))))], (9256 ^ _778495) ^ [_935125, _935127, _935129] : [class_Lattices_Olattice(_935125), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935125), _935127), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935125), _935127), _935129)) = _935127)], (48243 ^ _778495) ^ [_1751384, _1751386, _1751388, _1751390] : [48250 ^ _778495 : [(48253 ^ _778495) ^ [] : [_1751386 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48251 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1751390, _1751388)))]], 48244 ^ _778495 : [(48245 ^ _778495) ^ [_1751456] : [hBOOL(hAPP(hAPP(c_member(_1751384), _1751456), hAPP(c_List_Oset(_1751384), c_List_Oreplicate(_1751384, _1751386, _1751388)))), hBOOL(hAPP(_1751390, _1751456))]]], (47203 ^ _778495) ^ [_1728099, _1728101, _1728103] : [hBOOL(hAPP(hAPP(c_member(_1728099), _1728101), hAPP(c_List_Oset(_1728099), _1728103))), -(c_List_Oinsert(_1728099, _1728101, _1728103) = _1728103)], (45374 ^ _778495) ^ [_1689212, _1689214] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689212)), c_List_Oremdups(_1689212, _1689214))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689212)), _1689214))))], (33427 ^ _778495) ^ [_1398799, _1398801, _1398803, _1398805, _1398807] : [-(_1398799 = c_Orderings_Obot__class_Obot(tc_fun(_1398801, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1398803), _1398805), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398801, tc_fun(_1398803, tc_HOL_Obool)), _1398799), _1398807)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398801, tc_fun(_1398803, tc_HOL_Obool)), _1398799), hAPP(hAPP(c_COMBB(tc_fun(_1398803, tc_HOL_Obool), tc_fun(_1398803, tc_HOL_Obool), _1398801), hAPP(c_Set_Oinsert(_1398803), _1398805)), _1398807)))], (31680 ^ _778495) ^ [_1357894, _1357896, _1357898, _1357900] : [class_Complete__Lattice_Ocomplete__lattice(_1357894), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357896), _1357898)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357896, _1357894), _1357898), _1357900) = hAPP(hAPP(c_Finite__Set_Ofold(_1357896, _1357894, hAPP(hAPP(c_COMBB(_1357894, tc_fun(_1357894, _1357894), _1357896), c_Lattices_Osemilattice__inf__class_Oinf(_1357894)), _1357900)), c_Orderings_Otop__class_Otop(_1357894)), _1357898))], (20398 ^ _778495) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (41943 ^ _778495) ^ [_1611041, _1611043, _1611045] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611041, tc_HOL_Obool)), hAPP(c_List_Oset(_1611041), c_List_Osublist(_1611041, _1611043, _1611045))), hAPP(c_List_Oset(_1611041), _1611043))))], (28703 ^ _778495) ^ [_1298881, _1298883] : [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(_1298883))), 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)), _1298881))))), -(hAPP(c_Nat_OSuc, _1298881) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1298883))], (9388 ^ _778495) ^ [_938162, _938164, _938166, _938168] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938162, tc_HOL_Obool)), _938164), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938162, tc_HOL_Obool)), _938166), _938168)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938162, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938162, tc_HOL_Obool)), _938164), _938166)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938162, tc_HOL_Obool)), _938164), _938168)))], (34703 ^ _778495) ^ [_1427510, _1427512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1427510), _1427512)), -(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)), _1427510)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1427512))))], (16288 ^ _778495) ^ [_1069450, _1069452] : [class_Int_Oring__char__0(_1069450), hBOOL(hAPP(hAPP(c_member(_1069450), _1069452), c_Int_Oring__1__class_OInts(_1069450))), 16295 ^ _778495 : [(16302 ^ _778495) ^ [] : [_1069452 = c_Groups_Ozero__class_Ozero(_1069450), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069450), _1069452), _1069452) = c_Groups_Ozero__class_Ozero(_1069450))], (16296 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069450), _1069452), _1069452) = c_Groups_Ozero__class_Ozero(_1069450), -(_1069452 = c_Groups_Ozero__class_Ozero(_1069450))]]], (43586 ^ _778495) ^ [_1649761, _1649763, _1649765, _1649767] : [-(hAPP(hAPP(c_List_Odrop(_1649761), _1649763), hAPP(hAPP(c_List_Oappend(_1649761), _1649765), _1649767)) = hAPP(hAPP(c_List_Oappend(_1649761), hAPP(hAPP(c_List_Odrop(_1649761), _1649763), _1649765)), hAPP(hAPP(c_List_Odrop(_1649761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1649763), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649761)), _1649765))), _1649767)))], (34635 ^ _778495) ^ [_1426173, _1426175] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1426173) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1426175), -(_1426173 = _1426175)], (37091 ^ _778495) ^ [_1478363, _1478365, _1478367, _1478369] : [c_Fun_Oinj__on(_1478363, _1478365, _1478367, c_Orderings_Otop__class_Otop(tc_fun(_1478363, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478363, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1478363, _1478365, _1478367), hAPP(hAPP(c_Set_Oinsert(_1478365), _1478369), c_Orderings_Obot__class_Obot(tc_fun(_1478365, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1478363), c_HOL_OThe(_1478363, hAPP(hAPP(c_COMBC(_1478363, _1478365, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1478365, tc_fun(_1478365, tc_HOL_Obool), _1478363), c_fequal), _1478367)), _1478369))), c_Orderings_Obot__class_Obot(tc_fun(_1478363, tc_HOL_Obool))))))], (7610 ^ _778495) ^ [_904370, _904372, _904374, _904376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_904370, tc_HOL_Obool)), _904372), _904374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_904370, tc_HOL_Obool)), _904374), _904376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_904370, tc_HOL_Obool)), _904372), _904376)))], (39080 ^ _778495) ^ [_1536357, _1536359, _1536361] : [c_Wellfounded_OwfP(_1536357, _1536359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1536357, tc_fun(_1536357, tc_HOL_Obool))), _1536361), _1536359)), -(c_Wellfounded_OwfP(_1536357, _1536361))], (38377 ^ _778495) ^ [_1517753] : [-(hAPP(c_Set_Oimage(_1517753, _1517753, c_Fun_Oid(_1517753)), c_Orderings_Otop__class_Otop(tc_fun(_1517753, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1517753, tc_HOL_Obool)))], (31700 ^ _778495) ^ [_1358326, _1358328, _1358330, _1358332, _1358334, _1358336] : [hBOOL(hAPP(hAPP(c_member(_1358326), _1358328), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358330, tc_fun(_1358326, tc_HOL_Obool)), _1358332), _1358334))), -(hBOOL(hAPP(hAPP(c_member(_1358326), _1358328), hAPP(_1358334, _1358336)))), hBOOL(hAPP(hAPP(c_member(_1358330), _1358336), _1358332))], (11334 ^ _778495) ^ [_974098, _974100, _974102, _974104] : [class_Groups_Ocancel__semigroup__add(_974098), 11337 ^ _778495 : [(11344 ^ _778495) ^ [] : [_974102 = _974104, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974098), _974100), _974102) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974098), _974100), _974104))], (11338 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974098), _974100), _974102) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974098), _974100), _974104), -(_974102 = _974104)]]], (46035 ^ _778495) ^ [_1704520] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1704520) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1704520))))], (13506 ^ _778495) ^ [_1018161, _1018163, _1018165, _1018167] : [class_Groups_Ocomm__monoid__mult(_1018161), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1018163), _1018165))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1018163, _1018161), _1018167), _1018165) = c_Groups_Oone__class_Oone(_1018161))], (14619 ^ _778495) ^ [_1038075, _1038077] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038075), _1038077), 14624 ^ _778495 : [(14627 ^ _778495) ^ [] : [-(_1038077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14625 ^ _778495) ^ [] : [-(_1038075 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 14628 ^ _778495 : [(14631 ^ _778495) ^ [] : [-(_1038077 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14629 ^ _778495) ^ [] : [-(_1038075 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (24840 ^ _778495) ^ [_1222960, _1222962, _1222964] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1222960), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1222962), _1222964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1222960), _1222962)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1222960), _1222964)))], (39299 ^ _778495) ^ [_1542251] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39295 ^ [_1542251]), c_Int_OInteg)))], (25226 ^ _778495) ^ [_1229318, _1229320] : [-(hAPP(c_Int_Onat, _1229318) = _1229320), 25229 ^ _778495 : [(25232 ^ _778495) ^ [] : [_1229318 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229320)], (25230 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229318)))]], 25233 ^ _778495 : [(25236 ^ _778495) ^ [] : [_1229320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25234 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229318))]]], (28357 ^ _778495) ^ [_1288905, _1288907, _1288909, _1288911, _1288913] : [class_Rings_Osemiring__0(_1288905), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288905), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1288907, _1288905), _1288909), _1288911)), _1288913) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1288907, _1288905), hAPP(hAPP(c_COMBC(_1288907, _1288905, _1288905), hAPP(hAPP(c_COMBB(_1288905, tc_fun(_1288905, _1288905), _1288907), c_Groups_Otimes__class_Otimes(_1288905)), _1288909)), _1288913)), _1288911))], (26786 ^ _778495) ^ [_1257351, _1257353, _1257355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257351, tc_HOL_Obool)), _1257353), _1257355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1257351, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1257351), _1257353)), hAPP(c_Set_OPow(_1257351), _1257355))))], (19122 ^ _778495) ^ [_1122216, _1122218] : [19123 ^ _778495 : [(19126 ^ _778495) ^ [] : [_1122216 = _1122218], (19124 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122216), _1122218))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122216), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122218), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (28665 ^ _778495) ^ [_1297913, _1297915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1297913), 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)), _1297915)), -(c_Divides_OnegDivAlg(_1297913, _1297915) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1297913), _1297915)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1297913, _1297915)))], (52579 ^ _778495) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (28811 ^ _778495) ^ [_1301468, _1301470] : [-(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), _1301468)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1301470), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1301468))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (38679 ^ _778495) ^ [_1527361, _1527363] : [c_Wellfounded_Owf(_1527361, hAPP(hAPP(c_Relation_Orel__comp(_1527361, _1527361, _1527361), _1527363), _1527363)), -(c_Wellfounded_Owf(_1527361, _1527363))], (23294 ^ _778495) ^ [_1195964, _1195966] : [class_Divides_Osemiring__div(_1195964), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1195964), c_Groups_Ozero__class_Ozero(_1195964)), _1195966) = c_Groups_Ozero__class_Ozero(_1195964))], (28261 ^ _778495) ^ [_1283385, _1283387, _1283389, _1283391] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1283385, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1283385, tc_fun(_1283385, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283385)), _1283387)), hAPP(hAPP(c_COMBC(_1283385, tc_fun(_1283385, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283385)), _1283389)), _1283391)), -(hBOOL(hAPP(hAPP(c_member(_1283385), _1283391), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1283385, tc_HOL_Obool)), _1283387), _1283389))))], (38767 ^ _778495) ^ [_1528885] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1528885)))], (49682 ^ _778495) ^ [_1782552, _1782554, _1782556] : [hAPP(_1782556, hAPP(c_Hilbert__Choice_Oinv__into(_1782552, _1782554, c_Orderings_Otop__class_Otop(tc_fun(_1782552, tc_HOL_Obool)), _1782556), 49683 ^ [_1782552, _1782554, _1782556])) = 49683 ^ [_1782552, _1782554, _1782556], -(hAPP(c_Set_Oimage(_1782552, _1782554, _1782556), c_Orderings_Otop__class_Otop(tc_fun(_1782552, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782554, tc_HOL_Obool)))], (48619 ^ _778495) ^ [_1759386, _1759388, _1759390] : [-(c_FunDef_OTHE__default(_1759388, _1759390, _1759386) = c_HOL_OThe(_1759388, _1759386)), 48620 ^ _778495 : [(48621 ^ _778495) ^ [_1759450] : [hBOOL(hAPP(_1759386, _1759450)), 48625 ^ _778495 : [(48628 ^ _778495) ^ [] : [48624 ^ [_1759386, _1759388, _1759390, _1759450] = _1759450], (48626 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1759386, 48624 ^ [_1759386, _1759388, _1759390, _1759450])))]]]]], (15641 ^ _778495) ^ [_1056939, _1056941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1056939), _1056941))), 15644 ^ _778495 : [(15647 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1056939), _1056941)))], (15645 ^ _778495) ^ [] : [_1056941 = c_Orderings_Obot__class_Obot(tc_fun(_1056939, tc_HOL_Obool))]]], (23292 ^ _778495) ^ [_1195922, _1195924] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195922, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195924)) = 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), _1195922), _1195924)))], (24375 ^ _778495) ^ [_1214838, _1214840] : [-(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), _1214838)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1214840))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1214838))) = 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), _1214840)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1214838)))], (6810 ^ _778495) ^ [_890184, _890186, _890188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_890184), tc_HOL_Obool)), _890186), _890188)), -(c_Hoare__Mirabelle_Ohoare__derivs(_890184, _890188, _890186))], (21672 ^ _778495) ^ [_1166528, _1166530] : [_1166528 = _1166530, -(c_Int_OBit0(_1166528) = c_Int_OBit0(_1166530))], (29529 ^ _778495) ^ [_1315774, _1315776, _1315778, _1315780, _1315782, _1315784] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1315774, _1315776, _1315778), _1315780), hAPP(hAPP(c_Product__Type_OPair(_1315774, _1315776), _1315782), _1315784)) = hAPP(hAPP(_1315780, _1315782), _1315784))], (5789 ^ _778495) ^ [_870309, _870311, _870313, _870315] : [_870309 = c_Finite__Set_Ofold1(_870311, _870313), -(hAPP(_870309, hAPP(hAPP(c_Set_Oinsert(_870311), _870315), c_Orderings_Obot__class_Obot(tc_fun(_870311, tc_HOL_Obool)))) = _870315)], (19874 ^ _778495) ^ [_1135560, _1135562] : [class_Orderings_Olinorder(_1135560), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135560), _1135562)), -(_1135562 = c_Orderings_Obot__class_Obot(tc_fun(_1135560, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1135560), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1135560), 19887 ^ [_1135560, _1135562]), 19888 ^ [_1135560, _1135562])), hAPP(hAPP(c_Set_Oinsert(_1135560), 19887 ^ [_1135560, _1135562]), hAPP(hAPP(c_Set_Oinsert(_1135560), 19888 ^ [_1135560, _1135562]), c_Orderings_Obot__class_Obot(tc_fun(_1135560, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1135560), c_Big__Operators_Olinorder__class_OMin(_1135560, _1135562)), _1135562)))], (29176 ^ _778495) ^ [_1309024, _1309026] : [class_Rings_Osemiring__1(_1309024), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1309024), _1309026) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1309024, hAPP(hAPP(c_COMBC(_1309024, _1309024, _1309024), c_Groups_Oplus__class_Oplus(_1309024)), c_Groups_Oone__class_Oone(_1309024)), _1309026, c_Groups_Ozero__class_Ozero(_1309024)))], (14923 ^ _778495) ^ [_1043174, _1043176, _1043178, _1043180] : [class_Groups_Oordered__comm__monoid__add(_1043174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043174), c_Groups_Ozero__class_Ozero(_1043174)), _1043176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043174), _1043178), _1043180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043174), _1043178), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043174), _1043176), _1043180))))], (6002 ^ _778495) ^ [_874377, _874379, _874381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874377, tc_HOL_Obool)), _874379), _874381)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_874377, tc_HOL_Obool)), _874379), _874381) = _874381)], (38951 ^ _778495) ^ [_1533257, _1533259, _1533261, _1533263] : [c_Wellfounded_Owf(_1533257, _1533259), c_Fun_Oinj__on(_1533257, _1533261, _1533263, c_Orderings_Otop__class_Otop(tc_fun(_1533257, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1533261, hAPP(c_Set_Oimage(tc_prod(_1533257, _1533257), tc_prod(_1533261, _1533261), c_Product__Type_Omap__pair(_1533257, _1533261, _1533257, _1533261, _1533263, _1533263)), _1533259)))], (23270 ^ _778495) ^ [_1195394, _1195396, _1195398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195394, tc_HOL_Obool)), _1195398), _1195396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195394, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1195394, tc_HOL_Obool)), _1195396)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1195394, tc_HOL_Obool)), _1195398))))], (37260 ^ _778495) ^ [_1482411, _1482413, _1482415, _1482417, _1482419, _1482421] : [hBOOL(hAPP(hAPP(c_member(_1482411), _1482413), _1482415)), 37263 ^ _778495 : [(37270 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482411), _1482417), _1482415))), -(hAPP(c_Set_Ovimage(_1482419, _1482411, hAPP(hAPP(c_COMBC(_1482419, _1482411, _1482411), hAPP(hAPP(c_COMBC(_1482419, _1482411, tc_fun(_1482411, _1482411)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1482411, tc_fun(_1482411, _1482411)), _1482419), c_If(_1482411)), hAPP(hAPP(c_COMBC(_1482419, tc_fun(_1482419, tc_HOL_Obool), tc_HOL_Obool), c_member(_1482419)), _1482421))), _1482413)), _1482417)), _1482415) = _1482421)], (37264 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1482411), _1482417), _1482415)), -(hAPP(c_Set_Ovimage(_1482419, _1482411, hAPP(hAPP(c_COMBC(_1482419, _1482411, _1482411), hAPP(hAPP(c_COMBC(_1482419, _1482411, tc_fun(_1482411, _1482411)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1482411, tc_fun(_1482411, _1482411)), _1482419), c_If(_1482411)), hAPP(hAPP(c_COMBC(_1482419, tc_fun(_1482419, tc_HOL_Obool), tc_HOL_Obool), c_member(_1482419)), _1482421))), _1482413)), _1482417)), _1482415) = c_Orderings_Otop__class_Otop(tc_fun(_1482419, tc_HOL_Obool)))]]], (13841 ^ _778495) ^ [_1024229, _1024231, _1024233, _1024235] : [class_Rings_Oordered__semiring(_1024229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024229), _1024231), _1024233)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024229), c_Groups_Ozero__class_Ozero(_1024229)), _1024235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024229), _1024235), _1024231)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024229), _1024235), _1024233))))], (18026 ^ _778495) ^ [_1101635, _1101637, _1101639] : [class_Int_Onumber__ring(_1101635), -(hAPP(c_Int_Onumber__class_Onumber__of(_1101635), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1101637), _1101639)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101635), hAPP(c_Int_Onumber__class_Onumber__of(_1101635), _1101637)), hAPP(c_Int_Onumber__class_Onumber__of(_1101635), _1101639)))], (294 ^ _778495) ^ [_783098, _783100] : [-(class_Fields_Ofield(_783098)), _783100 = _783098, class_Fields_Ofield(_783100)], (43173 ^ _778495) ^ [_1639832, _1639834, _1639836] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639832)), hAPP(hAPP(c_List_Oappend(_1639832), _1639834), _1639836)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639832)), _1639834)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639832)), _1639836)))], (42600 ^ _778495) ^ [_1627826, _1627828, _1627830, _1627832] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627826) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1627828), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627826)), hAPP(hAPP(c_List_Olist_OCons(_1627828), _1627830), _1627832)) = c_List_Olist_ONil(_1627828))], (41565 ^ _778495) ^ [_1600269, _1600271, _1600273, _1600275, _1600277, _1600279] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600269), tc_List_Olist(_1600269))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600269), tc_List_Olist(_1600269)), hAPP(hAPP(c_List_Olist_OCons(_1600269), _1600271), _1600273)), hAPP(hAPP(c_List_Olist_OCons(_1600269), _1600275), _1600277))), c_List_Olistrel1(_1600269, _1600279))), 41570 ^ _778495 : [(41573 ^ _778495) ^ [] : [-(_1600273 = _1600277)], (41571 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600269, _1600269)), hAPP(hAPP(c_Product__Type_OPair(_1600269, _1600269), _1600271), _1600275)), _1600279)))]], 41574 ^ _778495 : [(41577 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600269), tc_List_Olist(_1600269))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600269), tc_List_Olist(_1600269)), _1600273), _1600277)), c_List_Olistrel1(_1600269, _1600279))))], (41575 ^ _778495) ^ [] : [-(_1600271 = _1600275)]]], (33493 ^ _778495) ^ [_1400574, _1400576, _1400578, _1400580] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1400574, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400576, tc_fun(_1400574, tc_HOL_Obool)), _1400578), _1400580)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1400576, tc_fun(_1400574, tc_HOL_Obool)), _1400578), hAPP(hAPP(c_COMBB(tc_fun(_1400574, tc_HOL_Obool), tc_fun(_1400574, tc_HOL_Obool), _1400576), c_Groups_Ouminus__class_Ouminus(tc_fun(_1400574, tc_HOL_Obool))), _1400580)))], (25078 ^ _778495) ^ [_1226858, _1226860] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226858), _1226860))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1226858))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1226860))))], (50343 ^ _778495) ^ [_1796409, _1796411, _1796413] : [hBOOL(hAPP(hAPP(c_member(_1796409), _1796411), c_Quotient_ORespects(_1796409, _1796413))), -(hBOOL(hAPP(hAPP(_1796413, _1796411), _1796411)))], (17595 ^ _778495) ^ [_1093886, _1093888, _1093890] : [class_Fields_Olinordered__field(_1093886), 17601 ^ _778495 : [(17604 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093886), _1093888), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093886), _1093890), 17600 ^ [_1093886, _1093888, _1093890])))], (17602 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093886), c_Groups_Ozero__class_Ozero(_1093886)), 17600 ^ [_1093886, _1093888, _1093890])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093886), _1093888), _1093890)))], (29208 ^ _778495) ^ [_1309607, _1309609] : [-(c_Divides_Odivmod__int(_1309607, _1309609) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1309607), _1309609)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1309607, _1309609)))], (2166 ^ _778495) ^ [_810111, _810113, _810115, _810117, _810119, _810121, _810123, _810125] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_810125, _810121, _810117, _810113) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_810123, _810119, _810115, _810111)), _810125 = _810123, _810121 = _810119, _810117 = _810115, _810113 = _810111], (45048 ^ _778495) ^ [_1681680, _1681682, _1681684, _1681686, _1681688] : [c_List_Olist__all2(_1681680, _1681682, _1681684, _1681686, _1681688), 45051 ^ _778495 : [(45054 ^ _778495) ^ [_1681846] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681680, _1681682)), _1681846), hAPP(c_List_Oset(tc_prod(_1681680, _1681682)), hAPP(hAPP(c_List_Ozip(_1681680, _1681682), _1681686), _1681688)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1681680, _1681682, tc_HOL_Obool), _1681684), _1681846)))], (45052 ^ _778495) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681680)), _1681686) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681682)), _1681688))]]], (14909 ^ _778495) ^ [_1042919, _1042921, _1042923] : [class_Groups_Oordered__comm__monoid__add(_1042919), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042919), _1042921), c_Groups_Ozero__class_Ozero(_1042919))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042919), _1042923), c_Groups_Ozero__class_Ozero(_1042919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042919), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042919), _1042921), _1042923)), c_Groups_Ozero__class_Ozero(_1042919))))], (11386 ^ _778495) ^ [_975187, _975189, _975191, _975193, _975195] : [class_Rings_Ocomm__semiring__1(_975187), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975187), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975187), _975189), _975191)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975187), _975193), _975195)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975187), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975187), _975189), _975193)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975187), _975191), _975195)))], (23004 ^ _778495) ^ [_1189700] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189700, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1189700)], (23282 ^ _778495) ^ [_1195684, _1195686, _1195688] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195684), _1195686), _1195688) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195684), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195686, _1195688)), _1195688))], (9108 ^ _778495) ^ [_932350, _932352, _932354] : [class_Lattices_Osemilattice__inf(_932350), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932350), _932352), _932354)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932350), _932352), _932354) = _932352)], (24501 ^ _778495) ^ [_1216923, _1216925, _1216927] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1216923), _1216925)), _1216927) = 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), _1216923), _1216927)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1216925), _1216927))), 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, _1216923, _1216927)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1216925, _1216927))), _1216927)))], (25806 ^ _778495) ^ [_1239499, _1239501, _1239503] : [class_Rings_Oring__1(_1239499), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1239499), hAPP(c_Groups_Ouminus__class_Ouminus(_1239499), _1239501)), 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)))), _1239503)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1239499), _1239501), 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)))), _1239503)))], (31278 ^ _778495) ^ [_1349947, _1349949, _1349951] : [class_Orderings_Olinorder(_1349947), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349947), _1349949)), -(_1349949 = c_Orderings_Obot__class_Obot(tc_fun(_1349947, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349947), _1349951)), -(_1349951 = c_Orderings_Obot__class_Obot(tc_fun(_1349947, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1349947, c_Orderings_Oord__class_Omax(_1349947), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1349947, tc_HOL_Obool)), _1349949), _1349951)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349947), c_Big__Operators_Olattice_OSup__fin(_1349947, c_Orderings_Oord__class_Omax(_1349947), _1349949)), c_Big__Operators_Olattice_OSup__fin(_1349947, c_Orderings_Oord__class_Omax(_1349947), _1349951)))], (23192 ^ _778495) ^ [_1193818, _1193820, _1193822, _1193824] : [class_Divides_Oring__div(_1193818), -(c_Divides_Odiv__class_Omod(_1193818, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1193818), _1193820), _1193822), _1193824) = c_Divides_Odiv__class_Omod(_1193818, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1193818), c_Divides_Odiv__class_Omod(_1193818, _1193820, _1193824)), c_Divides_Odiv__class_Omod(_1193818, _1193822, _1193824)), _1193824))], (43193 ^ _778495) ^ [_1640381, _1640383, _1640385] : [hAPP(hAPP(c_List_Oappend(_1640381), _1640383), _1640385) = _1640385, -(_1640383 = c_List_Olist_ONil(_1640381))], (11628 ^ _778495) ^ [_980136, _980138, _980140, _980142, _980144] : [class_Groups_Oordered__cancel__ab__semigroup__add(_980136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980136), _980138), _980140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980136), _980142), _980144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980136), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980136), _980138), _980142)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980136), _980140), _980144))))], (52591 ^ _778495) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (40361 ^ _778495) ^ [_1567948, _1567950, _1567952, _1567954, _1567956] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567948, _1567948)), hAPP(hAPP(c_Product__Type_OPair(_1567948, _1567948), _1567950), _1567952)), c_Transitive__Closure_Ortrancl(_1567948, _1567954))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567948, _1567948)), hAPP(hAPP(c_Product__Type_OPair(_1567948, _1567948), _1567952), _1567956)), c_Transitive__Closure_Ortrancl(_1567948, _1567954))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567948, _1567948)), hAPP(hAPP(c_Product__Type_OPair(_1567948, _1567948), _1567950), _1567956)), c_Transitive__Closure_Ortrancl(_1567948, _1567954))))], (5847 ^ _778495) ^ [_871554, _871556] : [class_Orderings_Opreorder(_871554), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871554), _871556), _871556)))], (22760 ^ _778495) ^ [_1185318, _1185320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1185318), _1185320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1185318)), c_Int_OBit0(_1185320))))], (27655 ^ _778495) ^ [_1272023, _1272025] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272023), c_Orderings_Otop__class_Otop(tc_fun(_1272023, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1272023), _1272025) = hAPP(c_Finite__Set_Ocard(_1272023), c_Orderings_Otop__class_Otop(tc_fun(_1272023, tc_HOL_Obool))), -(_1272025 = c_Orderings_Otop__class_Otop(tc_fun(_1272023, tc_HOL_Obool)))], (26608 ^ _778495) ^ [_1254541, _1254543, _1254545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254541, tc_HOL_Obool)), _1254543), _1254545)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1254541, tc_HOL_Obool)), _1254543), hAPP(c_Set_OPow(_1254541), _1254545))))], (39969 ^ _778495) ^ [_1557848, _1557850, _1557852] : [39971 ^ _778495 : [(39974 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1557848), 39970 ^ [_1557848, _1557850, _1557852]), c_Wellfounded_Oacc(_1557848, _1557852)))], (39972 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1557848, _1557848)), hAPP(hAPP(c_Product__Type_OPair(_1557848, _1557848), 39970 ^ [_1557848, _1557850, _1557852]), _1557850)), _1557852)))]], -(hBOOL(hAPP(hAPP(c_member(_1557848), _1557850), c_Wellfounded_Oacc(_1557848, _1557852))))], (9302 ^ _778495) ^ [_936086, _936088] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936086, tc_HOL_Obool)), _936088), c_Orderings_Obot__class_Obot(tc_fun(_936086, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_936086, tc_HOL_Obool)))], (6692 ^ _778495) ^ [_888059, _888061] : [class_Orderings_Obot(_888059), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888059), c_Orderings_Obot__class_Obot(_888059)), _888061)))], (13328 ^ _778495) ^ [_1015566, _1015568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015566), _1015568)), _1015568 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22536 ^ _778495) ^ [_1181397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181397), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1181397)), c_Int_OPls)))], (49041 ^ _778495) ^ [_1770239, _1770241] : [-(c_Relation_Otrans(_1770239, c_Relation_OId__on(_1770239, _1770241)))], (30855 ^ _778495) ^ [_1341770, _1341772, _1341774] : [class_Orderings_Olinorder(_1341770), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341770), _1341772), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1341770), _1341772), _1341774)) = _1341772)], (21076 ^ _778495) ^ [_1155945, _1155947, _1155949] : [class_Groups_Oordered__ab__group__add__abs(_1155945), -(hAPP(c_Groups_Oabs__class_Oabs(_1155945), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155945), hAPP(c_Groups_Oabs__class_Oabs(_1155945), _1155947)), hAPP(c_Groups_Oabs__class_Oabs(_1155945), _1155949))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155945), hAPP(c_Groups_Oabs__class_Oabs(_1155945), _1155947)), hAPP(c_Groups_Oabs__class_Oabs(_1155945), _1155949)))], (20506 ^ _778495) ^ [_1146398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146398), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146398))], (10833 ^ _778495) ^ [_965080, _965082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965080), hAPP(c_Nat_OSuc, _965082))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965080), _965082))), -(_965080 = _965082)], (7948 ^ _778495) ^ [_909519, _909521, _909523] : [class_Orderings_Olinorder(_909519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909519), _909521), _909523)), 7955 ^ _778495 : [(7962 ^ _778495) ^ [] : [_909521 = _909523, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909519), _909521), _909523))], (7956 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909519), _909521), _909523))), -(_909521 = _909523)]]], (9084 ^ _778495) ^ [_931940, _931942, _931944, _931946] : [class_Lattices_Osemilattice__inf(_931940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931940), _931942), _931944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931940), _931942), _931946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931940), _931942), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931940), _931944), _931946))))], (8532 ^ _778495) ^ [_920945, _920947, _920949] : [class_Groups_Oab__semigroup__mult(_920945), -(_920947 = c_Orderings_Obot__class_Obot(tc_fun(_920945, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_920945), _920947)), -(hBOOL(hAPP(hAPP(c_member(_920945), _920949), _920947))), -(hAPP(c_Finite__Set_Ofold1(_920945, c_Groups_Otimes__class_Otimes(_920945)), hAPP(hAPP(c_Set_Oinsert(_920945), _920949), _920947)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920945), _920949), hAPP(c_Finite__Set_Ofold1(_920945, c_Groups_Otimes__class_Otimes(_920945)), _920947)))], (41513 ^ _778495) ^ [_1598452, _1598454] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1598452), tc_List_Olist(_1598452)), tc_HOL_Obool)), c_List_Olistrel1(_1598452, c_Transitive__Closure_Ortrancl(_1598452, _1598454))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598452), c_List_Olistrel1(_1598452, _1598454)))))], (30611 ^ _778495) ^ [_1337451] : [class_Orderings_Olinorder(_1337451), -(c_Finite__Set_Ofun__left__comm__idem(_1337451, _1337451, c_Orderings_Oord__class_Omax(_1337451)))], (4812 ^ _778495) ^ [_851852, _851854, _851856, _851858] : [-(c_Relation_Oinv__image(_851858, _851854) = c_Relation_Oinv__image(_851856, _851852)), _851858 = _851856, _851854 = _851852], (47649 ^ _778495) ^ [_1738500, _1738502, _1738504] : [class_Orderings_Olinorder(_1738500), 47655 ^ _778495 : [(47658 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1738500), _1738504), 47654 ^ [_1738500, _1738502, _1738504]))], (47656 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738500), 47654 ^ [_1738500, _1738502, _1738504]), hAPP(c_List_Oset(_1738500), _1738502))))]], c_List_Olinorder__class_Osorted(_1738500, _1738502), -(c_List_Olinorder__class_Osorted(_1738500, hAPP(hAPP(c_List_Olist_OCons(_1738500), _1738504), _1738502)))], (3826 ^ _778495) ^ [_835989, _835991] : [_835991 = _835989, -(c_Lazy__Sequence_Ohit__bound(_835991) = c_Lazy__Sequence_Ohit__bound(_835989))], (4436 ^ _778495) ^ [_845930, _845932] : [_845932 = _845930, -(c_List_Olist_ONil(_845932) = c_List_Olist_ONil(_845930))], (30153 ^ _778495) ^ [_1327811, _1327813] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1327811), _1327813) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1327811, _1327813)))], (37712 ^ _778495) ^ [_1495520, _1495522, _1495524] : [c_Relation_Orefl__on(_1495520, _1495522, _1495524), 37715 ^ _778495 : [(37718 ^ _778495) ^ [_1495702] : [hBOOL(hAPP(hAPP(c_member(_1495520), _1495702), _1495522)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1495520, _1495520)), hAPP(hAPP(c_Product__Type_OPair(_1495520, _1495520), _1495702), _1495702)), _1495524)))], (37716 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1495520, _1495520), tc_HOL_Obool)), _1495524), hAPP(hAPP(c_Product__Type_OSigma(_1495520, _1495520), _1495522), hAPP(c_COMBK(tc_fun(_1495520, tc_HOL_Obool), _1495520), _1495522)))))]]], (22726 ^ _778495) ^ [_1184739, _1184741] : [class_Groups_Oabs__if(_1184739), 22729 ^ _778495 : [(22736 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184739), _1184741), c_Groups_Ozero__class_Ozero(_1184739)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1184739), _1184741) = _1184741)], (22730 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184739), _1184741), c_Groups_Ozero__class_Ozero(_1184739))), -(hAPP(c_Groups_Oabs__class_Oabs(_1184739), _1184741) = hAPP(c_Groups_Ouminus__class_Ouminus(_1184739), _1184741))]]], (52219 ^ _778495) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (2678 ^ _778495) ^ [_818109, _818111, _818113, _818115] : [-(c_Predicate_OPowp(_818115, _818111) = c_Predicate_OPowp(_818113, _818109)), _818115 = _818113, _818111 = _818109], (49234 ^ _778495) ^ [_1774120, _1774122, _1774124, _1774126] : [c_Predicate_Osymp(_1774120, _1774122), hBOOL(hAPP(hAPP(_1774122, _1774124), _1774126)), -(hBOOL(hAPP(hAPP(_1774122, _1774126), _1774124)))], (50178 ^ _778495) ^ [_1793119, _1793121, _1793123, _1793125, _1793127, _1793129] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1793119, _1793121, _1793123, _1793125), _1793127), _1793129) = hAPP(_1793125, hAPP(hAPP(c_Product__Type_OPair(_1793119, _1793121), _1793127), _1793129)))], (27575 ^ _778495) ^ [_1270642, _1270644] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270642, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1270642, tc_HOL_Obool))), _1270644) = c_Orderings_Otop__class_Otop(tc_fun(_1270642, tc_HOL_Obool)))], (49897 ^ _778495) ^ [_1787458, _1787460] : [-(c_Fun_Obij__betw(_1787458, _1787458, c_Fun_Oid(_1787458), _1787460, _1787460))], (38156 ^ _778495) ^ [_1508620, _1508622, _1508624] : [class_Groups_Olinordered__ab__semigroup__add(_1508620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508620), _1508622)), -(_1508622 = c_Orderings_Obot__class_Obot(tc_fun(_1508620, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1508620), _1508624), c_Big__Operators_Olinorder__class_OMin(_1508620, _1508622)) = c_Big__Operators_Olinorder__class_OMin(_1508620, hAPP(c_Set_OCollect(_1508620), hAPP(hAPP(c_COMBB(tc_fun(_1508620, tc_HOL_Obool), tc_HOL_Obool, _1508620), c_HOL_OEx(_1508620)), hAPP(hAPP(c_COMBC(_1508620, tc_fun(_1508620, tc_HOL_Obool), tc_fun(_1508620, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1508620, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1508620, tc_HOL_Obool), tc_fun(_1508620, tc_HOL_Obool)), _1508620), c_COMBS(_1508620, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1508620, tc_HOL_Obool), tc_fun(_1508620, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1508620), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508620), c_fconj)), hAPP(hAPP(c_COMBC(_1508620, tc_fun(_1508620, _1508620), tc_fun(_1508620, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1508620, tc_HOL_Obool), tc_fun(tc_fun(_1508620, _1508620), tc_fun(_1508620, tc_HOL_Obool)), _1508620), c_COMBB(_1508620, tc_HOL_Obool, _1508620)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1508620), _1508624))))), hAPP(hAPP(c_COMBC(_1508620, tc_fun(_1508620, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508620)), _1508622))))))], (38715 ^ _778495) ^ [_1527930, _1527932, _1527934] : [c_Wellfounded_Owf(_1527930, _1527932), -(c_Wellfounded_Owf(_1527930, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1527930, _1527930), tc_HOL_Obool)), _1527934), _1527932)))], (37534 ^ _778495) ^ [_1490113, _1490115, _1490117, _1490119] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490113), _1490115)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1490113, _1490113), tc_HOL_Obool)), _1490117), hAPP(hAPP(c_Product__Type_OSigma(_1490113, _1490113), _1490115), hAPP(c_COMBK(tc_fun(_1490113, tc_HOL_Obool), _1490113), _1490115)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1490113, tc_HOL_Obool)), _1490119), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490113), _1490115), _1490117))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1490113), _1490119)))], (52415 ^ _778495) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (38206 ^ _778495) ^ [_1510691, _1510693, _1510695] : [class_Lattices_Odistrib__lattice(_1510691), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510691), _1510693)), -(_1510693 = c_Orderings_Obot__class_Obot(tc_fun(_1510691, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1510691), _1510695), c_Big__Operators_Olattice__class_OInf__fin(_1510691, _1510693)) = c_Big__Operators_Olattice__class_OInf__fin(_1510691, hAPP(c_Set_OCollect(_1510691), hAPP(hAPP(c_COMBB(tc_fun(_1510691, tc_HOL_Obool), tc_HOL_Obool, _1510691), c_HOL_OEx(_1510691)), hAPP(hAPP(c_COMBC(_1510691, tc_fun(_1510691, tc_HOL_Obool), tc_fun(_1510691, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1510691, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1510691, tc_HOL_Obool), tc_fun(_1510691, tc_HOL_Obool)), _1510691), c_COMBS(_1510691, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1510691, tc_HOL_Obool), tc_fun(_1510691, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1510691), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510691), c_fconj)), hAPP(hAPP(c_COMBC(_1510691, tc_fun(_1510691, _1510691), tc_fun(_1510691, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1510691, tc_HOL_Obool), tc_fun(tc_fun(_1510691, _1510691), tc_fun(_1510691, tc_HOL_Obool)), _1510691), c_COMBB(_1510691, tc_HOL_Obool, _1510691)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1510691), _1510695))))), hAPP(hAPP(c_COMBC(_1510691, tc_fun(_1510691, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510691)), _1510693))))))], (43494 ^ _778495) ^ [_1647730, _1647732, _1647734] : [-(hAPP(hAPP(c_List_Odrop(_1647730), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1647730), _1647732), _1647734)) = _1647734)], (48735 ^ _778495) ^ [_1761729, _1761731, _1761733, _1761735] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761729), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1761731, _1761733, _1761729, _1761735) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1761731, 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(_1761731)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1761733, _1761735)), 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(_1761731)))), 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(_1761731)))), 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(_1761731)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1761731, 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(_1761731)))), 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(_1761731)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1761731, _1761733, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1761729), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1761735))), 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(_1761731)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761731))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761731)))), 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(_1761731)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1761731, 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(_1761731)))), 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(_1761731)))), 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(_1761731))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761731)))), 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(_1761731)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761731)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761731))))), tc_prod(_1761731, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1761731)), hAPP(hAPP(c_COMBB(_1761731, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761731)))), tc_prod(_1761731, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1761731)), c_Product__Type_Ofst(_1761731, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (9244 ^ _778495) ^ [_934807, _934809, _934811, _934813] : [class_Lattices_Odistrib__lattice(_934807), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934807), _934809), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934807), _934811), _934813)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934807), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934807), _934809), _934811)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934807), _934809), _934813)))], (35883 ^ _778495) ^ [_1451445, _1451447, _1451449, _1451451, _1451453] : [c_Equiv__Relations_Oequiv(_1451445, _1451447, _1451449), hBOOL(hAPP(hAPP(c_member(_1451445), _1451451), _1451447)), hBOOL(hAPP(hAPP(c_member(_1451445), _1451453), _1451447)), 35894 ^ _778495 : [(35901 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1451445, _1451445)), hAPP(hAPP(c_Product__Type_OPair(_1451445, _1451445), _1451451), _1451453)), _1451449)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1451445), hAPP(hAPP(c_Set_Oinsert(_1451445), _1451451), c_Orderings_Obot__class_Obot(tc_fun(_1451445, tc_HOL_Obool)))), _1451449) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1451445), hAPP(hAPP(c_Set_Oinsert(_1451445), _1451453), c_Orderings_Obot__class_Obot(tc_fun(_1451445, tc_HOL_Obool)))), _1451449))], (35895 ^ _778495) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1451445), hAPP(hAPP(c_Set_Oinsert(_1451445), _1451451), c_Orderings_Obot__class_Obot(tc_fun(_1451445, tc_HOL_Obool)))), _1451449) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1451445), hAPP(hAPP(c_Set_Oinsert(_1451445), _1451453), c_Orderings_Obot__class_Obot(tc_fun(_1451445, tc_HOL_Obool)))), _1451449), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1451445, _1451445)), hAPP(hAPP(c_Product__Type_OPair(_1451445, _1451445), _1451451), _1451453)), _1451449)))]]], (8088 ^ _778495) ^ [_911643, _911645, _911647, _911649] : [class_Lattices_Osemilattice__sup(_911643), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911643), _911645), _911647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911643), _911645), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911643), _911647), _911649))))], (3486 ^ _778495) ^ [_830639, _830641, _830643, _830645, _830647, _830649] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_830649, _830645, _830641) = c_SetInterval_Oord__class_OgreaterThanLessThan(_830647, _830643, _830639)), _830649 = _830647, _830645 = _830643, _830641 = _830639], (28835 ^ _778495) ^ [_1301762, _1301764] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1301762)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1301764)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1301764))), 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), _1301762)), c_Int_Onat)))))], (6717 ^ _778495) ^ [_888452, _888454] : [-(_888454 = c_Orderings_Obot__class_Obot(tc_fun(_888452, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_888452), 6720 ^ [_888452, _888454]), _888454)))], (52249 ^ _778495) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (38495 ^ _778495) ^ [_1521237, _1521239, _1521241] : [_1521241 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521237, _1521239), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1521237, _1521239), _1521241) = c_Orderings_Obot__class_Obot(tc_fun(_1521239, tc_HOL_Obool)))], (50020 ^ _778495) ^ [_1790123, _1790125, _1790127, _1790129, _1790131] : [c_Fun_Obij__betw(_1790123, _1790125, _1790127, _1790129, _1790131), 50023 ^ _778495 : [(50030 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1790125), _1790131)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1790123), _1790129)))], (50024 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1790123), _1790129)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1790125), _1790131)))]]], (20554 ^ _778495) ^ [_1147225] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147225))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147225) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44355 ^ _778495) ^ [_1665797, _1665799, _1665801, _1665803, _1665805, _1665807] : [-(hAPP(hAPP(c_List_Ozip(_1665797, _1665799), hAPP(hAPP(c_List_Omap(_1665801, _1665797), _1665803), _1665805)), _1665807) = hAPP(hAPP(c_List_Omap(tc_prod(_1665801, _1665799), tc_prod(_1665797, _1665799)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665801, _1665799, tc_prod(_1665797, _1665799)), hAPP(hAPP(c_COMBB(_1665797, tc_fun(_1665799, tc_prod(_1665797, _1665799)), _1665801), c_Product__Type_OPair(_1665797, _1665799)), _1665803))), hAPP(hAPP(c_List_Ozip(_1665801, _1665799), _1665805), _1665807)))], (22920 ^ _778495) ^ [_1188234] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188234), 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), _1188234), _1188234))], (4306 ^ _778495) ^ [_843827, _843829, _843831, _843833, _843835, _843837, _843839, _843841, _843843, _843845, _843847, _843849] : [-(c_New__Random__Sequence_Opos__union(_843849, _843845, _843841, _843837, _843833, _843829) = c_New__Random__Sequence_Opos__union(_843847, _843843, _843839, _843835, _843831, _843827)), _843849 = _843847, _843845 = _843843, _843841 = _843839, _843837 = _843835, _843833 = _843831, _843829 = _843827], (44343 ^ _778495) ^ [_1665111, _1665113, _1665115, _1665117, _1665119, _1665121, _1665123] : [-(hAPP(c_List_Ofoldl(_1665111, _1665113, _1665115, _1665117), hAPP(hAPP(c_List_Omap(_1665119, _1665113), _1665121), _1665123)) = hAPP(c_List_Ofoldl(_1665111, _1665119, hAPP(hAPP(c_COMBC(_1665111, tc_fun(_1665119, _1665113), tc_fun(_1665119, _1665111)), hAPP(hAPP(c_COMBB(tc_fun(_1665113, _1665111), tc_fun(tc_fun(_1665119, _1665113), tc_fun(_1665119, _1665111)), _1665111), c_COMBB(_1665113, _1665111, _1665119)), _1665115)), _1665121), _1665117), _1665123))], (24177 ^ _778495) ^ [_1211159, _1211161, _1211163, _1211165] : [_1211159 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1211161), _1211163)), _1211165), -(_1211161 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1211159, _1211161) = _1211165), 24184 ^ _778495 : [(24187 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211165)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211165), _1211161))], (24185 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211161)))]], 24192 ^ _778495 : [(24195 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211161), _1211165)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211165), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24193 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211161))]]], (3096 ^ _778495) ^ [_824600, _824602, _824604, _824606] : [-(c_Finite__Set_Ofold1(_824606, _824602) = c_Finite__Set_Ofold1(_824604, _824600)), _824606 = _824604, _824602 = _824600], (21920 ^ _778495) ^ [_1170528, _1170530, _1170532] : [class_Groups_Oordered__ab__group__add(_1170528), 21923 ^ _778495 : [(21930 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170528), _1170532), _1170530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170528), hAPP(c_Groups_Ouminus__class_Ouminus(_1170528), _1170530)), hAPP(c_Groups_Ouminus__class_Ouminus(_1170528), _1170532))))], (21924 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170528), hAPP(c_Groups_Ouminus__class_Ouminus(_1170528), _1170530)), hAPP(c_Groups_Ouminus__class_Ouminus(_1170528), _1170532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170528), _1170532), _1170530)))]]], (43401 ^ _778495) ^ [_1644886, _1644888, _1644890, _1644892, _1644894, _1644896, _1644898, _1644900] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644886, _1644886)), hAPP(hAPP(c_Product__Type_OPair(_1644886, _1644886), _1644888), _1644890)), _1644892)), _1644894 = hAPP(hAPP(c_List_Oappend(_1644886), _1644896), hAPP(hAPP(c_List_Olist_OCons(_1644886), _1644888), _1644898)), _1644900 = hAPP(hAPP(c_List_Oappend(_1644886), _1644896), hAPP(hAPP(c_List_Olist_OCons(_1644886), _1644890), _1644898)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644886), tc_List_Olist(_1644886))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644886), tc_List_Olist(_1644886)), _1644894), _1644900)), c_List_Olistrel1(_1644886, _1644892))))], (46967 ^ _778495) ^ [_1723009, _1723011, _1723013] : [hBOOL(hAPP(c_List_Odistinct(_1723009), _1723011)), hBOOL(hAPP(hAPP(c_member(_1723009), _1723013), hAPP(c_List_Oset(_1723009), _1723011))), -(c_List_OtakeWhile(_1723009, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723009), c_fNot), hAPP(hAPP(c_COMBC(_1723009, _1723009, tc_HOL_Obool), c_fequal), _1723013)), hAPP(c_List_Orev(_1723009), _1723011)) = hAPP(c_List_Orev(_1723009), hAPP(c_List_Otl(_1723009), c_List_OdropWhile(_1723009, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723009), c_fNot), hAPP(hAPP(c_COMBC(_1723009, _1723009, tc_HOL_Obool), c_fequal), _1723013)), _1723011))))], (41503 ^ _778495) ^ [_1598211, _1598213, _1598215, _1598217] : [hBOOL(hAPP(hAPP(c_member(_1598211), _1598213), c_Wellfounded_Oacc(_1598211, _1598215))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1598211)), _1598217), c_Wellfounded_Oacc(tc_List_Olist(_1598211), c_List_Olistrel1(_1598211, _1598215)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1598211)), hAPP(hAPP(c_List_Olist_OCons(_1598211), _1598213), _1598217)), c_Wellfounded_Oacc(tc_List_Olist(_1598211), c_List_Olistrel1(_1598211, _1598215)))))], (19042 ^ _778495) ^ [_1120935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1120935)))], (6738 ^ _778495) ^ [_888790, _888792] : [_888792 = c_Orderings_Obot__class_Obot(tc_fun(_888790, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888790, tc_HOL_Obool)), _888792), c_Orderings_Obot__class_Obot(tc_fun(_888790, tc_HOL_Obool)))))], (24235 ^ _778495) ^ [_1212154, _1212156, _1212158, _1212160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212156), _1212158)), -(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), _1212158), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212160, _1212154))), _1212156)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1212158), _1212154))))], (28857 ^ _778495) ^ [_1302312, _1302314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302312)), 28860 ^ _778495 : [(28867 ^ _778495) ^ [] : [-(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), _1302314), _1302312)))), -(c_Divides_OnegDivAlg(_1302314, _1302312) = hAPP(c_Divides_Oadjust(_1302312), c_Divides_OnegDivAlg(_1302314, 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)))), _1302312))))], (28861 ^ _778495) ^ [] : [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), _1302314), _1302312))), -(c_Divides_OnegDivAlg(_1302314, _1302312) = 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), _1302314), _1302312)))]]], (45739 ^ _778495) ^ [_1697428, _1697430, _1697432, _1697434] : [-(hAPP(c_List_Ofilter(_1697428, _1697430), hAPP(hAPP(c_List_Oappend(_1697428), _1697432), _1697434)) = hAPP(hAPP(c_List_Oappend(_1697428), hAPP(c_List_Ofilter(_1697428, _1697430), _1697432)), hAPP(c_List_Ofilter(_1697428, _1697430), _1697434)))], (42341 ^ _778495) ^ [_1621885, _1621887, _1621889, _1621891, _1621893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621885, tc_HOL_Obool)), hAPP(c_List_Oset(_1621885), _1621887)), _1621889)), hBOOL(hAPP(hAPP(c_member(_1621885), _1621891), _1621889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621885, tc_HOL_Obool)), hAPP(c_List_Oset(_1621885), hAPP(hAPP(c_List_Olist__update(_1621885, _1621887), _1621893), _1621891))), _1621889)))], (35591 ^ _778495) ^ [_1444439, _1444441, _1444443, _1444445] : [-(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), _1444439), _1444441)), 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), _1444443), _1444445)), 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), _1444439), _1444443)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444441), _1444445))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (10591 ^ _778495) ^ [_961297, _961299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961297), _961299)), _961299 = _961297], (37398 ^ _778495) ^ [_1486599, _1486601, _1486603, _1486605] : [-(hAPP(c_Set_Oimage(tc_prod(_1486599, _1486601), tc_prod(_1486601, _1486599), hAPP(c_Product__Type_Oprod_Oprod__case(_1486599, _1486601, tc_prod(_1486601, _1486599)), hAPP(c_COMBC(_1486601, _1486599, tc_prod(_1486601, _1486599)), c_Product__Type_OPair(_1486601, _1486599)))), hAPP(hAPP(c_Product__Type_OSigma(_1486599, _1486601), _1486603), hAPP(c_COMBK(tc_fun(_1486601, tc_HOL_Obool), _1486599), _1486605))) = hAPP(hAPP(c_Product__Type_OSigma(_1486601, _1486599), _1486605), hAPP(c_COMBK(tc_fun(_1486599, tc_HOL_Obool), _1486601), _1486603)))], (28593 ^ _778495) ^ [_1296250, _1296252, _1296254, _1296256] : [class_Groups_Ocomm__monoid__mult(_1296250), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296252), _1296254)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296252, _1296250), hAPP(c_COMBK(_1296250, _1296252), _1296256)), _1296254) = hAPP(hAPP(c_Power_Opower__class_Opower(_1296250), _1296256), hAPP(c_Finite__Set_Ocard(_1296252), _1296254)))], (12034 ^ _778495) ^ [_988821, _988823, _988825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988821), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988825), _988823))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988821), _988823)), _988825)))], (32728 ^ _778495) ^ [_1382220, _1382222, _1382224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1382220)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382222), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1382224)), 32738 ^ _778495 : [(32744 ^ _778495) ^ [] : [-(_1382222 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32740 ^ [_1382220, _1382222, _1382224]), 32737 ^ [_1382220, _1382222, _1382224]))], (32742 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32740 ^ [_1382220, _1382222, _1382224]), _1382224)))], (32739 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32737 ^ [_1382220, _1382222, _1382224]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1382220))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382222), _1382220) = _1382222)], (18038 ^ _778495) ^ [_1101905, _1101907, _1101909, _1101911] : [class_Int_Onumber__ring(_1101905), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101905), hAPP(c_Int_Onumber__class_Onumber__of(_1101905), _1101907)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101905), hAPP(c_Int_Onumber__class_Onumber__of(_1101905), _1101909)), _1101911)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101905), hAPP(c_Int_Onumber__class_Onumber__of(_1101905), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1101907), _1101909))), _1101911))], (19804 ^ _778495) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (36336 ^ _778495) ^ [_1462284, _1462286, _1462288, _1462290, _1462292] : [c_Fun_Oinj__on(_1462284, _1462286, _1462288, c_Orderings_Otop__class_Otop(tc_fun(_1462284, tc_HOL_Obool))), hAPP(_1462288, _1462290) = hAPP(_1462288, _1462292), -(_1462290 = _1462292)], (33377 ^ _778495) ^ [_1397295, _1397297, _1397299, _1397301, _1397303, _1397305] : [hBOOL(hAPP(hAPP(c_member(_1397295), _1397297), _1397299)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397295, tc_fun(_1397301, tc_HOL_Obool)), _1397299), hAPP(hAPP(c_COMBB(tc_fun(_1397301, tc_HOL_Obool), tc_fun(_1397301, tc_HOL_Obool), _1397295), hAPP(c_Set_Oinsert(_1397301), _1397303)), _1397305)) = hAPP(hAPP(c_Set_Oinsert(_1397301), _1397303), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397295, tc_fun(_1397301, tc_HOL_Obool)), _1397299), _1397305)))], (47922 ^ _778495) ^ [_1743928, _1743930, _1743932] : [47924 ^ _778495 : [(47927 ^ _778495) ^ [] : [hBOOL(hAPP(_1743932, 47923 ^ [_1743928, _1743930, _1743932]))], (47925 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743928), 47923 ^ [_1743928, _1743930, _1743932]), hAPP(c_List_Oset(_1743928), _1743930))))]], -(c_List_Olist__all(_1743928, _1743932, _1743930))], (13869 ^ _778495) ^ [_1024767, _1024769, _1024771] : [class_Rings_Oordered__ring(_1024767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024767), _1024769), c_Groups_Ozero__class_Ozero(_1024767))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024767), _1024771), c_Groups_Ozero__class_Ozero(_1024767))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024767), c_Groups_Ozero__class_Ozero(_1024767)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024767), _1024769), _1024771))))], (14209 ^ _778495) ^ [_1030873, _1030875, _1030877] : [class_Rings_Olinordered__semiring__strict(_1030873), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030873), c_Groups_Ozero__class_Ozero(_1030873)), _1030875)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030873), _1030877), c_Groups_Ozero__class_Ozero(_1030873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030873), _1030877), _1030875)), c_Groups_Ozero__class_Ozero(_1030873))))], (30549 ^ _778495) ^ [_1336062, _1336064, _1336066, _1336068, _1336070, _1336072, _1336074] : [hBOOL(hAPP(_1336062, _1336064)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1336066, _1336066)), hAPP(hAPP(c_Product__Type_OPair(_1336066, _1336066), _1336068), _1336070)), hAPP(_1336072, _1336064))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1336074, _1336066), tc_prod(_1336074, _1336066))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1336074, _1336066), tc_prod(_1336074, _1336066)), hAPP(hAPP(c_Product__Type_OPair(_1336074, _1336066), _1336064), _1336068)), hAPP(hAPP(c_Product__Type_OPair(_1336074, _1336066), _1336064), _1336070))), c_Recdef_Osame__fst(_1336074, _1336066, _1336062, _1336072))))], (1238 ^ _778495) ^ [_796998, _797000] : [-(class_Rings_Olinordered__idom(_796998)), _797000 = _796998, class_Rings_Olinordered__idom(_797000)], (40575 ^ _778495) ^ [_1573063, _1573065, _1573067, _1573069] : [hBOOL(hAPP(hAPP(c_member(_1573063), _1573065), c_Wellfounded_Oacc(_1573063, _1573067))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1573063, _1573063)), hAPP(hAPP(c_Product__Type_OPair(_1573063, _1573063), _1573069), _1573065)), c_Transitive__Closure_Ortrancl(_1573063, _1573067))), -(hBOOL(hAPP(hAPP(c_member(_1573063), _1573069), c_Wellfounded_Oacc(_1573063, _1573067))))], (14747 ^ _778495) ^ [_1040008, _1040010, _1040012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040008), _1040010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040012), _1040008)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040012), _1040010))))], (26494 ^ _778495) ^ [_1252454, _1252456, _1252458, _1252460] : [class_Rings_Olinordered__semidom(_1252454), hAPP(hAPP(c_Power_Opower__class_Opower(_1252454), _1252456), _1252458) = hAPP(hAPP(c_Power_Opower__class_Opower(_1252454), _1252460), _1252458), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252454), c_Groups_Ozero__class_Ozero(_1252454)), _1252456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252454), c_Groups_Ozero__class_Ozero(_1252454)), _1252460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1252458)), -(_1252456 = _1252460)], (19168 ^ _778495) ^ [_1123062, _1123064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123062), _1123064)), 19171 ^ _778495 : [(19174 ^ _778495) ^ [] : [_1123062 = _1123064], (19172 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123062), _1123064)))]]], (2604 ^ _778495) ^ [_816962, _816964] : [_816964 = _816962, -(c_Wellfounded_Omeasure(_816964) = c_Wellfounded_Omeasure(_816962))], (51851 ^ _778495) ^ [_1825411, _1825413, _1825415, _1825417] : [class_Divides_Osemiring__div(_1825411), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825411), _1825413), _1825415)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825411), _1825417), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825411), _1825415), _1825413)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825411), _1825417), _1825415)), _1825413))], (40555 ^ _778495) ^ [_1572719] : [-(c_Relation_Orefl__on(_1572719, c_Orderings_Otop__class_Otop(tc_fun(_1572719, tc_HOL_Obool)), c_Relation_OId(_1572719)))], (50635 ^ _778495) ^ [_1804127, _1804129, _1804131] : [class_Divides_Osemiring__div(_1804127), class_Int_Onumber(_1804127), 50642 ^ _778495 : [(50649 ^ _778495) ^ [] : [c_Divides_Odiv__class_Omod(_1804127, hAPP(c_Int_Onumber__class_Onumber__of(_1804127), _1804131), hAPP(c_Int_Onumber__class_Onumber__of(_1804127), _1804129)) = c_Groups_Ozero__class_Ozero(_1804127), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804127), hAPP(c_Int_Onumber__class_Onumber__of(_1804127), _1804129)), hAPP(c_Int_Onumber__class_Onumber__of(_1804127), _1804131))))], (50643 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804127), hAPP(c_Int_Onumber__class_Onumber__of(_1804127), _1804129)), hAPP(c_Int_Onumber__class_Onumber__of(_1804127), _1804131))), -(c_Divides_Odiv__class_Omod(_1804127, hAPP(c_Int_Onumber__class_Onumber__of(_1804127), _1804131), hAPP(c_Int_Onumber__class_Onumber__of(_1804127), _1804129)) = c_Groups_Ozero__class_Ozero(_1804127))]]], (5558 ^ _778495) ^ [_863517, _863519, _863521, _863523] : [-(c_COMBK(_863523, _863519) = c_COMBK(_863521, _863517)), _863523 = _863521, _863519 = _863517], (36554 ^ _778495) ^ [_1466602, _1466604, _1466606, _1466608] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466602), _1466604)), hAPP(c_Finite__Set_Ocard(_1466606), hAPP(c_Set_Oimage(_1466602, _1466606, _1466608), _1466604)) = hAPP(c_Finite__Set_Ocard(_1466602), _1466604), -(c_Fun_Oinj__on(_1466602, _1466606, _1466608, _1466604))], (6698 ^ _778495) ^ [_888161, _888163] : [-(hBOOL(hAPP(hAPP(c_member(_888161), 6699 ^ [_888161, _888163]), _888163))), -(_888163 = c_Orderings_Obot__class_Obot(tc_fun(_888161, tc_HOL_Obool)))], (39528 ^ _778495) ^ [_1547846, _1547848, _1547850, _1547852, _1547854] : [class_Groups_Ocomm__monoid__add(_1547846), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547848), _1547850)), c_Fun_Oinj__on(_1547848, _1547848, _1547852, _1547850), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1547848, _1547846), _1547854), hAPP(c_Set_Oimage(_1547848, _1547848, _1547852), _1547850)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1547848, _1547846), hAPP(c_Fun_Ocomp(_1547848, _1547846, _1547848, _1547854), _1547852)), _1547850))], (28817 ^ _778495) ^ [_1301531, _1301533] : [28818 ^ _778495 : [(28821 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1301533), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (28819 ^ _778495) ^ [] : [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), _1301531), _1301533)))]], -(c_Divides_OnegDivAlg(_1301531, _1301533) = 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), _1301531), _1301533)))], (33305 ^ _778495) ^ [_1395177, _1395179, _1395181, _1395183, _1395185, _1395187] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395177, tc_fun(_1395179, tc_fun(_1395181, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1395177, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1395179, _1395181), tc_HOL_Obool), tc_fun(_1395179, tc_fun(_1395181, tc_HOL_Obool)), _1395177), hAPP(c_COMBC(_1395179, tc_fun(tc_prod(_1395179, _1395181), tc_HOL_Obool), tc_fun(_1395181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395181, tc_fun(tc_fun(tc_prod(_1395179, _1395181), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1395179, _1395181), tc_HOL_Obool), tc_fun(_1395181, tc_HOL_Obool)), _1395179), c_COMBC(_1395181, tc_fun(tc_prod(_1395179, _1395181), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395181, tc_prod(_1395179, _1395181)), tc_fun(_1395181, tc_fun(tc_fun(tc_prod(_1395179, _1395181), tc_HOL_Obool), tc_HOL_Obool)), _1395179), hAPP(c_COMBB(tc_prod(_1395179, _1395181), tc_fun(tc_fun(tc_prod(_1395179, _1395181), tc_HOL_Obool), tc_HOL_Obool), _1395181), c_member(tc_prod(_1395179, _1395181)))), c_Product__Type_OPair(_1395179, _1395181))))), _1395183)), _1395185), _1395187)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1395179, _1395181)), hAPP(hAPP(c_Product__Type_OPair(_1395179, _1395181), _1395185), _1395187)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395177, tc_fun(tc_prod(_1395179, _1395181), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1395177, tc_HOL_Obool))), _1395183))))], (16090 ^ _778495) ^ [_1066086, _1066088] : [class_Rings_Odivision__ring__inverse__zero(_1066086), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066086), _1066088), c_Groups_Ozero__class_Ozero(_1066086)) = c_Groups_Ozero__class_Ozero(_1066086))], (44387 ^ _778495) ^ [_1666642, _1666644, _1666646, _1666648, _1666650, _1666652] : [-(hAPP(hAPP(c_List_Omap(_1666642, _1666644), _1666646), hAPP(hAPP(c_List_Olist__update(_1666642, _1666648), _1666650), _1666652)) = hAPP(hAPP(c_List_Olist__update(_1666644, hAPP(hAPP(c_List_Omap(_1666642, _1666644), _1666646), _1666648)), _1666650), hAPP(_1666646, _1666652)))], (27287 ^ _778495) ^ [_1265695, _1265697] : [_1265695 = _1265697, -(c_Code__Numeral_OSuc__code__numeral(_1265695) = c_Code__Numeral_OSuc__code__numeral(_1265697))], (37026 ^ _778495) ^ [_1476783, _1476785] : [-(c_Nitpick_Onumber__of__frac(_1476783, _1476785) = c_Nitpick_OAbs__Frac(_1476783, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1476785), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (45388 ^ _778495) ^ [_1689454, _1689456, _1689458] : [hBOOL(hAPP(c_List_Odistinct(_1689454), _1689456)), -(hBOOL(hAPP(c_List_Odistinct(_1689454), hAPP(c_List_OremoveAll(_1689454, _1689458), _1689456))))], (23290 ^ _778495) ^ [_1195880, _1195882] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195880), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195882)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195880, _1195882)))], (18494 ^ _778495) ^ [_1110470, _1110472, _1110474, _1110476] : [class_Fields_Olinordered__field__inverse__zero(_1110470), class_Int_Onumber(_1110470), 18501 ^ _778495 : [(18502 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110470), _1110472), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474))), _1110476)), 18505 ^ _778495 : [(18512 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), c_Groups_Ozero__class_Ozero(_1110470)), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474)))), 18515 ^ _778495 : [(18522 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474)), c_Groups_Ozero__class_Ozero(_1110470)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), c_Groups_Ozero__class_Ozero(_1110470)), _1110476)))], (18516 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474)), c_Groups_Ozero__class_Ozero(_1110470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110470), _1110476), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474))), _1110472)))]]], (18506 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), c_Groups_Ozero__class_Ozero(_1110470)), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), _1110472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110470), _1110476), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474)))))]]], (18528 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110470), _1110472), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474))), _1110476))), 18531 ^ _778495 : [(18534 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), _1110472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110470), _1110476), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474))))], (18532 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), c_Groups_Ozero__class_Ozero(_1110470)), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474))))]], 18535 ^ _778495 : [(18538 ^ _778495) ^ [] : [18539 ^ _778495 : [(18542 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110470), _1110476), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474))), _1110472))], (18540 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474)), c_Groups_Ozero__class_Ozero(_1110470))))]], 18543 ^ _778495 : [(18546 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), c_Groups_Ozero__class_Ozero(_1110470)), _1110476))], (18544 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474)), c_Groups_Ozero__class_Ozero(_1110470)))]]], (18536 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110470), c_Groups_Ozero__class_Ozero(_1110470)), hAPP(c_Int_Onumber__class_Onumber__of(_1110470), _1110474)))]]]]], (52459 ^ _778495) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (14539 ^ _778495) ^ [_1036847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1036847)), -(_1036847 = hAPP(c_Nat_OSuc, 14542 ^ [_1036847]))], (51281 ^ _778495) ^ [_1815184, _1815186] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815184), _1815186))), 51282 ^ _778495 : [(51283 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815184), _1815186)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815186), _1815184)))], (51289 ^ _778495) ^ [] : [_1815184 = _1815186]]], (52517 ^ _778495) ^ [_1834136, _1834138] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1834136, _1834138))), class_Lazy__Sequence_Osmall__lazy(_1834136), class_Lazy__Sequence_Osmall__lazy(_1834138)], (37614 ^ _778495) ^ [_1492666, _1492668, _1492670, _1492672, _1492674, _1492676] : [class_Groups_Ocomm__monoid__add(_1492666), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492668), _1492670)), 37624 ^ _778495 : [(37627 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492672), hAPP(_1492674, 37623 ^ [_1492666, _1492668, _1492670, _1492672, _1492674, _1492676])))], (37625 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492668), 37623 ^ [_1492666, _1492668, _1492670, _1492672, _1492674, _1492676]), _1492670)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492668, _1492666), hAPP(hAPP(c_COMBS(_1492668, tc_fun(_1492672, tc_HOL_Obool), _1492666), hAPP(hAPP(c_COMBB(tc_fun(_1492672, _1492666), tc_fun(tc_fun(_1492672, tc_HOL_Obool), _1492666), _1492668), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492672, _1492666)), _1492676)), _1492674)), _1492670) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1492668, _1492672), _1492666), hAPP(c_Product__Type_Oprod_Oprod__case(_1492668, _1492672, _1492666), _1492676)), hAPP(hAPP(c_Product__Type_OSigma(_1492668, _1492672), _1492670), _1492674)))], (20303 ^ _778495) ^ [_1143326, _1143328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1143326), _1143328)), -(c_Nat__Transfer_Otsub(_1143328, _1143326) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1143328), _1143326))], (18044 ^ _778495) ^ [_1102074, _1102076, _1102078, _1102080] : [class_Int_Onumber__ring(_1102074), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102074), hAPP(c_Int_Onumber__class_Onumber__of(_1102074), _1102076)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102074), hAPP(c_Int_Onumber__class_Onumber__of(_1102074), _1102078)), _1102080)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102074), hAPP(c_Int_Onumber__class_Onumber__of(_1102074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1102076), _1102078))), _1102080))], (5118 ^ _778495) ^ [_856635, _856637, _856639, _856641, _856643, _856645] : [-(c_Lazy__Sequence_Oappend(_856645, _856641, _856637) = c_Lazy__Sequence_Oappend(_856643, _856639, _856635)), _856645 = _856643, _856641 = _856639, _856637 = _856635], (24533 ^ _778495) ^ [_1217724, _1217726, _1217728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1217724), _1217726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217724), _1217728)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217726), _1217728))))], (8748 ^ _778495) ^ [_924980, _924982, _924984] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_924980), _924982)), hBOOL(hAPP(_924984, c_Orderings_Obot__class_Obot(tc_fun(_924980, tc_HOL_Obool)))), 8759 ^ _778495 : [(8762 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_924980), 8757 ^ [_924980, _924982, _924984]), 8758 ^ [_924980, _924982, _924984]))], (8764 ^ _778495) ^ [] : [-(hBOOL(hAPP(_924984, 8758 ^ [_924980, _924982, _924984])))], (8766 ^ _778495) ^ [] : [hBOOL(hAPP(_924984, hAPP(hAPP(c_Set_Oinsert(_924980), 8757 ^ [_924980, _924982, _924984]), 8758 ^ [_924980, _924982, _924984])))], (8760 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_924980), 8758 ^ [_924980, _924982, _924984])))]], -(hBOOL(hAPP(_924984, _924982)))], (49061 ^ _778495) ^ [_1770651, _1770653] : [c_Relation_Otrans(_1770651, _1770653), 49064 ^ _778495 : [(49065 ^ _778495) ^ [_1770787, _1770789] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1770651, _1770651)), hAPP(hAPP(c_Product__Type_OPair(_1770651, _1770651), _1770789), _1770787)), _1770653)), 49068 ^ _778495 : [(49069 ^ _778495) ^ [_1770930] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1770651, _1770651)), hAPP(hAPP(c_Product__Type_OPair(_1770651, _1770651), _1770787), _1770930)), _1770653)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1770651, _1770651)), hAPP(hAPP(c_Product__Type_OPair(_1770651, _1770651), _1770789), _1770930)), _1770653)))]]]]], (35003 ^ _778495) ^ [_1433121, _1433123] : [c_Nat__Transfer_Onat__set(_1433121), c_Nat__Transfer_Onat__set(_1433123), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1433121), _1433123)))], (43522 ^ _778495) ^ [_1648283, _1648285, _1648287] : [-(c_List_Obutlast(_1648283, hAPP(hAPP(c_List_Odrop(_1648283), _1648285), _1648287)) = hAPP(hAPP(c_List_Odrop(_1648283), _1648285), c_List_Obutlast(_1648283, _1648287)))], (27839 ^ _778495) ^ [_1275231, _1275233, _1275235] : [class_Complete__Lattice_Ocomplete__lattice(_1275231), 27842 ^ _778495 : [(27843 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275231), _1275233), c_Complete__Lattice_OInf__class_OInf(_1275231, _1275235))), 27846 ^ _778495 : [(27847 ^ _778495) ^ [_1275389] : [hBOOL(hAPP(hAPP(c_member(_1275231), _1275389), _1275235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275231), _1275233), _1275389)))]]], (27853 ^ _778495) ^ [] : [27855 ^ _778495 : [(27858 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275231), _1275233), 27854 ^ [_1275231, _1275233, _1275235]))], (27856 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1275231), 27854 ^ [_1275231, _1275233, _1275235]), _1275235)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275231), _1275233), c_Complete__Lattice_OInf__class_OInf(_1275231, _1275235))))]]], (19160 ^ _778495) ^ [_1122904, _1122906] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122904), _1122906) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122906), _1122904))], (43259 ^ _778495) ^ [_1641529, _1641531] : [-(hAPP(hAPP(c_List_Oappend(_1641529), _1641531), c_List_Olist_ONil(_1641529)) = _1641531)], (41379 ^ _778495) ^ [_1594322, _1594324, _1594326, _1594328, _1594330] : [hAPP(hAPP(c_List_Olist_OCons(_1594322), _1594324), _1594326) = hAPP(hAPP(c_List_Olist_OCons(_1594322), _1594328), _1594330), 41382 ^ _778495 : [(41385 ^ _778495) ^ [] : [-(_1594326 = _1594330)], (41383 ^ _778495) ^ [] : [-(_1594324 = _1594328)]]], (51227 ^ _778495) ^ [_1814297, _1814299] : [_1814297 = _1814299, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814297), _1814299)))], (19226 ^ _778495) ^ [_1123956, _1123958, _1123960, _1123962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123956), _1123958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123960), _1123962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123956), _1123960)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123958), _1123962))))], (33000 ^ _778495) ^ [_1387221, _1387223] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1387221), _1387223) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1387221, _1387223))], (11392 ^ _778495) ^ [_975364, _975366, _975368, _975370] : [class_Rings_Ocomm__semiring__1(_975364), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975364), _975366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975364), _975368), _975370)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975364), _975366), _975368)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975364), _975366), _975370)))], (43800 ^ _778495) ^ [_1654541, _1654543, _1654545] : [-(c_List_Orotate(_1654541, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1654543), _1654545)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1654541), tc_List_Olist(_1654541), tc_List_Olist(_1654541), c_List_Orotate(_1654541, _1654543)), c_List_Orotate(_1654541, _1654545)))], (29508 ^ _778495) ^ [_1315324, _1315326, _1315328] : [hBOOL(hAPP(_1315324, 29509 ^ [_1315324, _1315326, _1315328])), 29512 ^ _778495 : [(29513 ^ _778495) ^ [_1315435, _1315437] : [-(hBOOL(hAPP(_1315324, hAPP(hAPP(c_Product__Type_OPair(_1315326, _1315328), _1315437), _1315435))))]]], (45648 ^ _778495) ^ [_1695140, _1695142, _1695144, _1695146] : [-(c_List_Oconcat(_1695140, hAPP(hAPP(c_List_Omap(_1695142, tc_List_Olist(_1695140)), hAPP(hAPP(c_COMBC(_1695142, tc_List_Olist(_1695140), tc_List_Olist(_1695140)), hAPP(hAPP(c_COMBB(_1695140, tc_fun(tc_List_Olist(_1695140), tc_List_Olist(_1695140)), _1695142), c_List_Olist_OCons(_1695140)), _1695144)), c_List_Olist_ONil(_1695140))), _1695146)) = hAPP(hAPP(c_List_Omap(_1695142, _1695140), _1695144), _1695146))], (49905 ^ _778495) ^ [_1787701, _1787703, _1787705, _1787707, _1787709] : [c_Fun_Obij__betw(_1787701, _1787703, _1787705, c_Orderings_Otop__class_Otop(tc_fun(_1787701, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787703, tc_HOL_Obool))), c_Fun_Obij__betw(_1787707, _1787701, _1787709, c_Orderings_Otop__class_Otop(tc_fun(_1787707, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787701, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1787707, _1787703, c_Orderings_Otop__class_Otop(tc_fun(_1787707, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1787701, _1787703, _1787707, _1787705), _1787709)) = hAPP(c_Fun_Ocomp(_1787701, _1787707, _1787703, c_Hilbert__Choice_Oinv__into(_1787707, _1787701, c_Orderings_Otop__class_Otop(tc_fun(_1787707, tc_HOL_Obool)), _1787709)), c_Hilbert__Choice_Oinv__into(_1787701, _1787703, c_Orderings_Otop__class_Otop(tc_fun(_1787701, tc_HOL_Obool)), _1787705)))], (52319 ^ _778495) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (19758 ^ _778495) ^ [_1133377, _1133379, _1133381, _1133383, _1133385, _1133387] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133377), _1133379)), _1133381) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133383), _1133385)), _1133387), 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), _1133383), _1133385)), _1133387))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133387), _1133383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133381)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1133383), _1133377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1133379), _1133385)))], (28421 ^ _778495) ^ [_1291766, _1291768, _1291770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291766, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1291766, tc_fun(_1291766, tc_HOL_Obool), tc_HOL_Obool), c_member(_1291766)), _1291768)), hAPP(hAPP(c_COMBC(_1291766, tc_fun(_1291766, tc_HOL_Obool), tc_HOL_Obool), c_member(_1291766)), _1291770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291766, tc_HOL_Obool)), _1291768), _1291770)))], (41397 ^ _778495) ^ [_1594649, _1594651, _1594653] : [hAPP(hAPP(c_List_Olist_OCons(_1594649), _1594651), _1594653) = _1594653], (37692 ^ _778495) ^ [_1494868, _1494870, _1494872, _1494874, _1494876, _1494878, _1494880, _1494882, _1494884, _1494886] : [hAPP(c_Set_Oimage(_1494868, _1494870, _1494872), _1494874) = _1494876, hAPP(c_Set_Oimage(_1494878, _1494880, _1494882), _1494884) = _1494886, -(hAPP(c_Set_Oimage(tc_prod(_1494868, _1494878), tc_prod(_1494870, _1494880), c_Product__Type_Omap__pair(_1494868, _1494870, _1494878, _1494880, _1494872, _1494882)), hAPP(hAPP(c_Product__Type_OSigma(_1494868, _1494878), _1494874), hAPP(c_COMBK(tc_fun(_1494878, tc_HOL_Obool), _1494868), _1494884))) = hAPP(hAPP(c_Product__Type_OSigma(_1494870, _1494880), _1494876), hAPP(c_COMBK(tc_fun(_1494880, tc_HOL_Obool), _1494870), _1494886)))], (47990 ^ _778495) ^ [] : [-(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)))], (49393 ^ _778495) ^ [_1776960, _1776962] : [-(c_Equiv__Relations_Opart__equivp(_1776960, _1776962)), 49396 ^ _778495 : [(49397 ^ _778495) ^ [_1777080] : [hBOOL(hAPP(hAPP(_1776962, _1777080), _1777080))]], 49414 ^ _778495 : [(49417 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1776962, 49399 ^ [_1776960, _1776962]), 49399 ^ [_1776960, _1776962])))], (49419 ^ _778495) ^ [] : [-(hAPP(_1776962, 49398 ^ [_1776960, _1776962]) = hAPP(_1776962, 49399 ^ [_1776960, _1776962]))], (49421 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1776962, 49398 ^ [_1776960, _1776962]), 49399 ^ [_1776960, _1776962]))], (49415 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1776962, 49398 ^ [_1776960, _1776962]), 49398 ^ [_1776960, _1776962])))]], 49402 ^ _778495 : [(49405 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1776962, 49398 ^ [_1776960, _1776962]), 49398 ^ [_1776960, _1776962])), hBOOL(hAPP(hAPP(_1776962, 49399 ^ [_1776960, _1776962]), 49399 ^ [_1776960, _1776962])), hAPP(_1776962, 49398 ^ [_1776960, _1776962]) = hAPP(_1776962, 49399 ^ [_1776960, _1776962])], (49403 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1776962, 49398 ^ [_1776960, _1776962]), 49399 ^ [_1776960, _1776962])))]]], (49312 ^ _778495) ^ [_1775532, _1775534, _1775536, _1775538] : [c_Relation_Osym(_1775532, _1775534), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775532, _1775532)), hAPP(hAPP(c_Product__Type_OPair(_1775532, _1775532), _1775536), _1775538)), _1775534)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775532, _1775532)), hAPP(hAPP(c_Product__Type_OPair(_1775532, _1775532), _1775538), _1775536)), _1775534)))], (44664 ^ _778495) ^ [_1673228, _1673230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673228)), hAPP(c_Code__Numeral_Oof__nat, _1673230))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673228), _1673230)))], (51881 ^ _778495) ^ [_1826014, _1826016, _1826018, _1826020, _1826022] : [class_Divides_Osemiring__div(_1826014), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826014), _1826016), _1826018)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826014), _1826020), _1826022)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826014), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826014), _1826018), _1826016)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826014), _1826022), _1826020)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826014), _1826018), _1826022)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826014), _1826016), _1826020)))], (12102 ^ _778495) ^ [_990113, _990115, _990117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990113), _990115)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990115), _990113)), _990117) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990115), _990117)), _990113))], (36668 ^ _778495) ^ [_1469032, _1469034, _1469036] : [36670 ^ _778495 : [(36673 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1469032), 36669 ^ [_1469032, _1469034, _1469036]), c_Wellfounded_Oacc(_1469032, _1469036)))], (36671 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1469032, _1469032)), hAPP(hAPP(c_Product__Type_OPair(_1469032, _1469032), 36669 ^ [_1469032, _1469034, _1469036]), _1469034)), _1469036)))]], -(hBOOL(hAPP(hAPP(c_member(_1469032), _1469034), c_Wellfounded_Oacc(_1469032, _1469036))))], (16021 ^ _778495) ^ [_1064634, _1064636, _1064638, _1064640, _1064642] : [class_Groups_Ocomm__monoid__mult(_1064634), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064636), _1064638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1064636, tc_HOL_Obool)), _1064640), _1064638)), 16035 ^ _778495 : [(16038 ^ _778495) ^ [] : [hAPP(_1064642, 16034 ^ [_1064634, _1064636, _1064638, _1064640, _1064642]) = c_Groups_Oone__class_Oone(_1064634)], (16036 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1064636), 16034 ^ [_1064634, _1064636, _1064638, _1064640, _1064642]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064636, tc_HOL_Obool)), _1064638), _1064640))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1064636, _1064634), _1064642), _1064640) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1064636, _1064634), _1064642), _1064638))], (14951 ^ _778495) ^ [_1043680, _1043682, _1043684] : [class_Groups_Oordered__comm__monoid__add(_1043680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043680), c_Groups_Ozero__class_Ozero(_1043680)), _1043682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043680), c_Groups_Ozero__class_Ozero(_1043680)), _1043684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043680), c_Groups_Ozero__class_Ozero(_1043680)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043680), _1043682), _1043684))))], (11883 ^ _778495) ^ [_985336, _985338, _985340] : [class_Rings_Ocomm__semiring__1(_985336), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985336), _985338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985336), _985340), _985338)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985336), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985336), _985340), c_Groups_Oone__class_Oone(_985336))), _985338))], (39842 ^ _778495) ^ [_1555039, _1555041, _1555043, _1555045, _1555047, _1555049] : [c_Finite__Set_Ofolding__idem(_1555039, _1555041, _1555043, _1555045), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555039), _1555047)), hBOOL(hAPP(hAPP(c_member(_1555039), _1555049), _1555047)), -(hAPP(c_Fun_Ocomp(_1555041, _1555041, _1555041, hAPP(_1555045, _1555047)), hAPP(_1555043, _1555049)) = hAPP(_1555045, _1555047))], (50851 ^ _778495) ^ [_1808097, _1808099] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1808097), 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)))), _1808099)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808099), _1808097)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808097), _1808099)))], (10783 ^ _778495) ^ [_964167, _964169] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964167), _964169))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964167), hAPP(c_Nat_OSuc, _964169))), -(_964169 = _964167)], (39912 ^ _778495) ^ [_1556525, _1556527] : [-(c_Hilbert__Choice_OEps(_1556525, hAPP(hAPP(c_COMBC(_1556525, _1556525, tc_HOL_Obool), c_fequal), _1556527)) = _1556527)], (20067 ^ _778495) ^ [_1138989, _1138991] : [class_Rings_Olinordered__semidom(_1138989), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138989), c_Groups_Ozero__class_Ozero(_1138989)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1138989), _1138991))))], (51949 ^ _778495) ^ [_1827308, _1827310, _1827312, _1827314] : [class_Rings_Ocomm__semiring__1(_1827308), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827308), _1827310), _1827312)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827308), _1827310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827308), _1827312), _1827314))))], (17834 ^ _778495) ^ [_1098227, _1098229, _1098231, _1098233] : [class_Orderings_Olinorder(_1098227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098227), _1098229), _1098231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098227), _1098229), _1098233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098227), _1098229), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1098227), _1098231), _1098233))))], (11724 ^ _778495) ^ [_982050, _982052, _982054, _982056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982050), _982052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982054), _982056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982050), _982054)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982052), _982056))))], (42128 ^ _778495) ^ [_1616629, _1616631, _1616633, _1616635] : [-(hAPP(c_List_Oset(tc_prod(_1616629, _1616631)), hAPP(hAPP(c_List_Ozip(_1616629, _1616631), _1616633), _1616635)) = hAPP(c_Set_OCollect(tc_prod(_1616629, _1616631)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1616629, _1616631)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1616629, _1616631), 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(_1616629, _1616631)), 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(_1616629, _1616631)), 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(_1616629, _1616631), tc_fun(tc_Nat_Onat, tc_prod(_1616629, _1616631)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1616629, _1616631), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1616629, _1616631)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1616629, _1616631)), c_COMBB(tc_prod(_1616629, _1616631), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1616631, tc_prod(_1616629, _1616631)), hAPP(hAPP(c_COMBB(_1616629, tc_fun(_1616631, tc_prod(_1616629, _1616631)), tc_Nat_Onat), c_Product__Type_OPair(_1616629, _1616631)), hAPP(c_List_Onth(_1616629), _1616633))), hAPP(c_List_Onth(_1616631), _1616635)))))), 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(_1616629)), _1616633)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616631)), _1616635)))))))], (10689 ^ _778495) ^ [_962684, _962686, _962688] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962684), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962686), _962688)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962684), _962686)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962684), _962688)))], (10237 ^ _778495) ^ [_954983, _954985, _954987] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_954983), _954985)), 10240 ^ _778495 : [(10247 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_954983), _954987), _954985))), -(hAPP(c_Finite__Set_Ocard(_954983), hAPP(hAPP(c_Set_Oinsert(_954983), _954987), _954985)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_954983), _954985)))], (10241 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_954983), _954987), _954985)), -(hAPP(c_Finite__Set_Ocard(_954983), hAPP(hAPP(c_Set_Oinsert(_954983), _954987), _954985)) = hAPP(c_Finite__Set_Ocard(_954983), _954985))]]], (14803 ^ _778495) ^ [_1041085, _1041087] : [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), _1041085), _1041087))), 14806 ^ _778495 : [(14809 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1041087)))], (14807 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1041085)))]]], (23048 ^ _778495) ^ [_1190766, _1190768, _1190770] : [-(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), _1190766), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1190768), _1190766))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190768, _1190766))), _1190770) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190768), _1190770))], (10285 ^ _778495) ^ [_955799, _955801, _955803] : [class_Lattices_Olattice(_955799), hBOOL(hAPP(c_Finite__Set_Ofinite(_955799), _955801)), -(_955801 = c_Orderings_Obot__class_Obot(tc_fun(_955799, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_955799), _955803)), -(_955803 = c_Orderings_Obot__class_Obot(tc_fun(_955799, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_955799, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_955799, tc_HOL_Obool)), _955801), _955803)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955799), c_Big__Operators_Olattice__class_OInf__fin(_955799, _955801)), c_Big__Operators_Olattice__class_OInf__fin(_955799, _955803)))], (11204 ^ _778495) ^ [_971568, _971570] : [class_Rings_Ocomm__semiring__1(_971568), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971568), _971570), c_Groups_Oone__class_Oone(_971568)) = _971570)], (22626 ^ _778495) ^ [_1182966, _1182968] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1182966)), c_Int_OBit0(_1182968)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1182966), _1182968)))], (27547 ^ _778495) ^ [_1270069, _1270071] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1270069), c_Orderings_Otop__class_Otop(tc_fun(_1270069, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270071), c_Orderings_Otop__class_Otop(tc_fun(_1270071, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1270069, _1270071)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1270069, _1270071), tc_HOL_Obool)))))], (10087 ^ _778495) ^ [_952410, _952412, _952414] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_952410), _952412)), hBOOL(hAPP(hAPP(c_member(_952410), _952414), _952412)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_952410), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952410, tc_HOL_Obool)), _952412), hAPP(hAPP(c_Set_Oinsert(_952410), _952414), c_Orderings_Obot__class_Obot(tc_fun(_952410, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_952410), _952412))], (22158 ^ _778495) ^ [_1174864] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1174864)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1174864)))], (33068 ^ _778495) ^ [_1388596, _1388598, _1388600] : [class_Orderings_Olinorder(_1388596), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388596), _1388598), _1388600)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1388596, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1388596), _1388598), c_Orderings_Obot__class_Obot(tc_fun(_1388596, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1388596, _1388598, _1388600)) = c_SetInterval_Oord__class_OatLeastAtMost(_1388596, _1388598, _1388600))], (38355 ^ _778495) ^ [_1517392, _1517394] : [-(hAPP(c_Fun_Oid(_1517392), _1517394) = _1517394)], (20408 ^ _778495) ^ [_1144994] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1144994) = _1144994)], (30723 ^ _778495) ^ [_1339372, _1339374, _1339376, _1339378] : [class_Orderings_Olinorder(_1339372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339372), _1339374), _1339376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339372), _1339374), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339372), _1339376), _1339378))))], (47076 ^ _778495) ^ [_1725328, _1725330, _1725332] : [-(c_List_OdropWhile(_1725328, _1725330, _1725332) = hAPP(hAPP(c_List_Odrop(_1725328), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725328)), c_List_OtakeWhile(_1725328, _1725330, _1725332))), _1725332))], (20026 ^ _778495) ^ [_1138190, _1138192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1138190), _1138192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138190)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1138192))))], (25056 ^ _778495) ^ [_1226468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226468)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1226468)) = _1226468)], (6490 ^ _778495) ^ [_883735, _883737, _883739, _883741, _883743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883735, tc_HOL_Obool)), _883737), _883739)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883735, tc_HOL_Obool)), _883741), _883743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883735, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_883735, tc_HOL_Obool)), _883737), _883743)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_883735, tc_HOL_Obool)), _883739), _883741))))], (31872 ^ _778495) ^ [_1363015, _1363017, _1363019, _1363021, _1363023] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363015, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363017, tc_fun(_1363015, tc_HOL_Obool)), _1363019), _1363021)), _1363023) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363017, tc_fun(_1363015, tc_HOL_Obool)), _1363019), hAPP(hAPP(c_COMBC(_1363017, tc_fun(_1363015, tc_HOL_Obool), tc_fun(_1363015, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363015, tc_HOL_Obool), tc_fun(tc_fun(_1363015, tc_HOL_Obool), tc_fun(_1363015, tc_HOL_Obool)), _1363017), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363015, tc_HOL_Obool))), _1363021)), _1363023)))], (3214 ^ _778495) ^ [_826477, _826479, _826481, _826483, _826485, _826487] : [-(c_List_Olist_Olist__size(_826487, _826483, _826479) = c_List_Olist_Olist__size(_826485, _826481, _826477)), _826487 = _826485, _826483 = _826481, _826479 = _826477], (7018 ^ _778495) ^ [_893821, _893823, _893825] : [class_Lattices_Osemilattice__sup(_893821), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893821), _893823), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893821), _893823), _893825)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893821), _893823), _893825))], (34332 ^ _778495) ^ [_1419174, _1419176, _1419178, _1419180, _1419182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1419174, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1419176, _1419174, _1419178), _1419180)), _1419182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1419174, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1419176, tc_HOL_Obool), tc_fun(_1419174, tc_HOL_Obool), c_Set_Oimage(_1419176, _1419174, _1419178)), hAPP(c_Set_OPow(_1419176), _1419180))), hAPP(c_Set_OPow(_1419174), _1419182))))], (52653 ^ _778495) ^ [_1835564, _1835566, _1835568, _1835570, _1835572, _1835574] : [-(hAPP(hAPP(hAPP(c_COMBC(_1835564, _1835566, _1835568), _1835570), _1835572), _1835574) = hAPP(hAPP(_1835570, _1835574), _1835572))], (19092 ^ _778495) ^ [] : [-(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))))], (24025 ^ _778495) ^ [_1208390, _1208392] : [c_Int_Oiszero(_1208390, hAPP(c_Int_Onumber__class_Onumber__of(_1208390), c_Int_OBit1(_1208392))), class_Int_Onumber__ring(_1208390), class_Int_Oring__char__0(_1208390)], (32506 ^ _778495) ^ [_1377365, _1377367, _1377369, _1377371] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1377365), _1377367)), 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)), _1377365), _1377369)), 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)), _1377367), _1377371)), 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)), _1377367), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1377369), _1377371))), c_FunDef_Omin__strict)))], (24573 ^ _778495) ^ [_1218546, _1218548] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1218546))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1218546)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1218548)) = 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), _1218548)))], (48484 ^ _778495) ^ [_1755999, _1756001, _1756003] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755999, _1756001), _1756003) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1755999, tc_Lazy__Sequence_Olazy__sequence(_1755999)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1755999, tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1755999, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_Nat_Onat)), _1755999), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1755999), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1755999)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1755999, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755999), tc_Nat_Onat)), _1755999), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1755999))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1755999), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1756001))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755999, _1756001))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1755999), _1756003)))], (49491 ^ _778495) ^ [_1778671, _1778673, _1778675] : [c_Equiv__Relations_Oequiv(_1778671, _1778673, _1778675), 49494 ^ _778495 : [(49499 ^ _778495) ^ [] : [-(c_Relation_Otrans(_1778671, _1778675))], (49497 ^ _778495) ^ [] : [-(c_Relation_Osym(_1778671, _1778675))], (49495 ^ _778495) ^ [] : [-(c_Relation_Orefl__on(_1778671, _1778673, _1778675))]]], (45963 ^ _778495) ^ [_1703186, _1703188] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1703186), _1703188)) = c_List_Oupt(_1703186, _1703188))], (18671 ^ _778495) ^ [_1113766, _1113768, _1113770] : [class_Orderings_Olinorder(_1113766), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113766), _1113768)), -(_1113768 = c_Orderings_Obot__class_Obot(tc_fun(_1113766, tc_HOL_Obool))), 18682 ^ _778495 : [(18683 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113766), _1113770), hAPP(c_Finite__Set_Ofold1(_1113766, c_Orderings_Oord__class_Omin(_1113766)), _1113768))), 18686 ^ _778495 : [(18687 ^ _778495) ^ [_1114059] : [hBOOL(hAPP(hAPP(c_member(_1113766), _1114059), _1113768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113766), _1113770), _1114059)))]]], (18693 ^ _778495) ^ [] : [18695 ^ _778495 : [(18698 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113766), _1113770), 18694 ^ [_1113766, _1113768, _1113770]))], (18696 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1113766), 18694 ^ [_1113766, _1113768, _1113770]), _1113768)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113766), _1113770), hAPP(c_Finite__Set_Ofold1(_1113766, c_Orderings_Oord__class_Omin(_1113766)), _1113768))))]]], (37162 ^ _778495) ^ [_1480053, _1480055, _1480057, _1480059, _1480061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480053, tc_HOL_Obool)), _1480055), _1480057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480059, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1480059, _1480053, _1480061), _1480055)), hAPP(c_Set_Ovimage(_1480059, _1480053, _1480061), _1480057))))], (34837 ^ _778495) ^ [_1430181] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1430181) = 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), _1430181))))], (44199 ^ _778495) ^ [_1662762, _1662764, _1662766] : [_1662762 = c_List_Olist_ONil(_1662764), -(c_List_Olast(_1662764, hAPP(hAPP(c_List_Olist_OCons(_1662764), _1662766), _1662762)) = _1662766)], (22406 ^ _778495) ^ [_1179098, _1179100, _1179102] : [class_Lattices_Oboolean__algebra(_1179098), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1179098), _1179100), _1179102) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1179098), _1179100), hAPP(c_Groups_Ouminus__class_Ouminus(_1179098), _1179102)))], (52353 ^ _778495) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (44941 ^ _778495) ^ [_1679353, _1679355] : [-(hBOOL(hAPP(c_List_Olistsp(_1679353, _1679355), c_List_Olist_ONil(_1679353))))], (37305 ^ _778495) ^ [_1483785, _1483787, _1483789, _1483791, _1483793, _1483795] : [-(_1483785 = c_Orderings_Obot__class_Obot(tc_fun(_1483787, tc_HOL_Obool))), 37311 ^ _778495 : [(37314 ^ _778495) ^ [] : [c_Fun_Oinj__on(_1483789, _1483791, _1483793, hAPP(_1483795, 37310 ^ [_1483785, _1483787, _1483789, _1483791, _1483793, _1483795]))], (37312 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1483787), 37310 ^ [_1483785, _1483787, _1483789, _1483791, _1483793, _1483795]), _1483785)))]], -(c_Fun_Oinj__on(_1483789, _1483791, _1483793, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483787, tc_fun(_1483789, tc_HOL_Obool)), _1483785), _1483795)))], (6550 ^ _778495) ^ [_884918, _884920, _884922, _884924, _884926] : [c_Finite__Set_Ofun__left__comm__idem(_884918, _884920, _884922), -(hAPP(hAPP(_884922, _884924), hAPP(hAPP(_884922, _884924), _884926)) = hAPP(hAPP(_884922, _884924), _884926))], (30507 ^ _778495) ^ [_1334920, _1334922, _1334924, _1334926, _1334928, _1334930, _1334932, _1334934] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1334920, _1334922), tc_prod(_1334920, _1334922))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1334920, _1334922), tc_prod(_1334920, _1334922)), hAPP(hAPP(c_Product__Type_OPair(_1334920, _1334922), _1334924), _1334926)), hAPP(hAPP(c_Product__Type_OPair(_1334920, _1334922), _1334928), _1334930))), c_Wellfounded_Olex__prod(_1334920, _1334922, _1334932, _1334934))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1334920, _1334920)), hAPP(hAPP(c_Product__Type_OPair(_1334920, _1334920), _1334924), _1334928)), _1334932))), 30514 ^ _778495 : [(30517 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1334922, _1334922)), hAPP(hAPP(c_Product__Type_OPair(_1334922, _1334922), _1334926), _1334930)), _1334934)))], (30515 ^ _778495) ^ [] : [-(_1334924 = _1334928)]]], (22128 ^ _778495) ^ [_1174267, _1174269, _1174271] : [class_Rings_Odivision__ring(_1174267), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1174267), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174267), _1174269), _1174271)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174267), hAPP(c_Groups_Ouminus__class_Ouminus(_1174267), _1174269)), _1174271))], (6878 ^ _778495) ^ [_891368, _891370, _891372] : [class_Lattices_Obounded__lattice__bot(_891368), 6881 ^ _778495 : [(6890 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891368), _891370), _891372) = c_Orderings_Obot__class_Obot(_891368)), _891370 = c_Orderings_Obot__class_Obot(_891368), _891372 = c_Orderings_Obot__class_Obot(_891368)], (6882 ^ _778495) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891368), _891370), _891372) = c_Orderings_Obot__class_Obot(_891368), 6885 ^ _778495 : [(6888 ^ _778495) ^ [] : [-(_891372 = c_Orderings_Obot__class_Obot(_891368))], (6886 ^ _778495) ^ [] : [-(_891370 = c_Orderings_Obot__class_Obot(_891368))]]]]], (52075 ^ _778495) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (11839 ^ _778495) ^ [_984288, _984290] : [class_Rings_Olinordered__semidom(_984288), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984288), _984290), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984288), _984290), c_Groups_Oone__class_Oone(_984288)))))], (22754 ^ _778495) ^ [_1185217, _1185219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1185217)), c_Int_OBit0(_1185219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1185217), _1185219)))], (37514 ^ _778495) ^ [_1489632, _1489634, _1489636, _1489638] : [-(_1489632 = c_Orderings_Obot__class_Obot(tc_fun(_1489634, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1489636, _1489634), _1489636, c_Product__Type_Ofst(_1489636, _1489634)), hAPP(hAPP(c_Product__Type_OSigma(_1489636, _1489634), _1489638), hAPP(c_COMBK(tc_fun(_1489634, tc_HOL_Obool), _1489636), _1489632))) = _1489638)], (24944 ^ _778495) ^ [_1224724] : [hAPP(c_Int_Onat, _1224724) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224724), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8174 ^ _778495) ^ [_913255, _913257, _913259] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913255), _913257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913255, tc_HOL_Obool)), _913259), _913257)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_913255), _913259)))], (29294 ^ _778495) ^ [_1311179, _1311181, _1311183, _1311185] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1311179, _1311181), _1311183)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1311179, _1311181), _1311185)), -(_1311183 = _1311185)], (49987 ^ _778495) ^ [_1789593, _1789595, _1789597] : [c_Fun_Obij__betw(_1789593, _1789593, c_Fun_Oid(_1789593), _1789595, _1789597), -(_1789595 = _1789597)], (52341 ^ _778495) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (40453 ^ _778495) ^ [_1570297, _1570299] : [-(c_Transitive__Closure_Ortrancl(_1570297, _1570299) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570297, _1570297), tc_HOL_Obool)), c_Relation_OId(_1570297)), hAPP(hAPP(c_Relation_Orel__comp(_1570297, _1570297, _1570297), c_Transitive__Closure_Ortrancl(_1570297, _1570299)), _1570299)))], (16168 ^ _778495) ^ [_1067529, _1067531, _1067533, _1067535] : [class_Rings_Odivision__ring(_1067529), -(_1067531 = c_Groups_Ozero__class_Ozero(_1067529)), 16175 ^ _778495 : [(16182 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067529), _1067533), _1067531) = _1067535, -(_1067533 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1067529), _1067535), _1067531))], (16176 ^ _778495) ^ [] : [_1067533 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1067529), _1067535), _1067531), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067529), _1067533), _1067531) = _1067535)]]], (40168 ^ _778495) ^ [_1562693, _1562695] : [-(c_Wellfounded_Owf(_1562693, _1562695)), 40171 ^ _778495 : [(40174 ^ _778495) ^ [_1562913] : [hBOOL(hAPP(hAPP(c_member(_1562693), _1562913), 40169 ^ [_1562693, _1562695])), 40178 ^ _778495 : [(40181 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562693), 40177 ^ [_1562693, _1562695, _1562913]), 40169 ^ [_1562693, _1562695])))], (40179 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562693, _1562693)), hAPP(hAPP(c_Product__Type_OPair(_1562693, _1562693), 40177 ^ [_1562693, _1562695, _1562913]), _1562913)), _1562695)))]]], (40172 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562693), 40170 ^ [_1562693, _1562695]), 40169 ^ [_1562693, _1562695])))]]], (22840 ^ _778495) ^ [_1186726, _1186728] : [class_Int_Onumber__ring(_1186726), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186726), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186726), c_Groups_Oone__class_Oone(_1186726)), c_Groups_Oone__class_Oone(_1186726))), hAPP(c_Int_Onumber__class_Onumber__of(_1186726), _1186728)) = hAPP(c_Int_Onumber__class_Onumber__of(_1186726), c_Int_OBit0(_1186728)))], (35979 ^ _778495) ^ [_1453932, _1453934, _1453936] : [c_Equiv__Relations_Oequivp(_1453932, _1453934), -(hBOOL(hAPP(hAPP(_1453934, _1453936), _1453936)))], (52649 ^ _778495) ^ [_1835474, _1835476, _1835478, _1835480] : [-(hAPP(hAPP(c_COMBK(_1835474, _1835476), _1835478), _1835480) = _1835478)], (40214 ^ _778495) ^ [_1563719, _1563721, _1563723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1563719, _1563719), tc_HOL_Obool)), _1563721), _1563723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1563719, _1563719), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1563719, _1563719, _1563719), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1563719, _1563719), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1563719, _1563721)), _1563723)), _1563721)), _1563723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1563719, _1563719), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1563719, _1563721)), _1563723)))], (11250 ^ _778495) ^ [_972547, _972549] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972547), _972549) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972549), _972547))], (27249 ^ _778495) ^ [_1265079, _1265081] : [class_Rings_Olinordered__idom(_1265079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265079), _1265081), c_Groups_Ozero__class_Ozero(_1265079))), -(c_Groups_Osgn__class_Osgn(_1265079, _1265081) = hAPP(c_Groups_Ouminus__class_Ouminus(_1265079), c_Groups_Oone__class_Oone(_1265079)))], (44476 ^ _778495) ^ [_1669000, _1669002, _1669004, _1669006] : [-(hAPP(hAPP(c_List_Omap(_1669000, _1669002), _1669004), c_List_Obutlast(_1669000, _1669006)) = c_List_Obutlast(_1669002, hAPP(hAPP(c_List_Omap(_1669000, _1669002), _1669004), _1669006)))], (26692 ^ _778495) ^ [_1255814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1255814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1255814)))], (7060 ^ _778495) ^ [_894804, _894806, _894808, _894810] : [hBOOL(hAPP(_894804, _894806)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894808, tc_HOL_Obool)), _894804), _894810)), -(hBOOL(hAPP(_894810, _894806)))], (49551 ^ _778495) ^ [_1779581, _1779583] : [c_Equiv__Relations_Opart__equivp(_1779581, _1779583), 49555 ^ _778495 : [(49560 ^ _778495) ^ [] : [-(c_Predicate_Otransp(_1779581, _1779583))], (49558 ^ _778495) ^ [] : [-(c_Predicate_Osymp(_1779581, _1779583))], (49556 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1779583, 49554 ^ [_1779581, _1779583]), 49554 ^ [_1779581, _1779583])))]]], (37565 ^ _778495) ^ [_1491259, _1491261, _1491263, _1491265] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1491261, _1491259), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491259, tc_prod(_1491261, _1491259), 37561 ^ [_1491259, _1491261, _1491263, _1491265]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1491261, tc_fun(_1491259, tc_HOL_Obool)), _1491263), _1491265))), hAPP(hAPP(c_Product__Type_OSigma(_1491261, _1491259), _1491263), _1491265))))], (9602 ^ _778495) ^ [_942792, _942794, _942796, _942798] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942792, tc_HOL_Obool)), _942794), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942792, tc_HOL_Obool)), _942796), _942798)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942792, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942792, tc_HOL_Obool)), _942794), _942796)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942792, tc_HOL_Obool)), _942794), _942798)))], (22640 ^ _778495) ^ [_1183216, _1183218] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183216)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183218)), _1183216 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1183218 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10047 ^ _778495) ^ [_951559, _951561, _951563, _951565, _951567, _951569] : [c_Finite__Set_Ofun__left__comm(_951559, _951561, _951563), hBOOL(hAPP(c_Finite__Set_Ofinite(_951559), _951565)), -(hBOOL(hAPP(hAPP(c_member(_951559), _951567), _951565))), -(hAPP(hAPP(c_Finite__Set_Ofold(_951559, _951561, _951563), _951569), hAPP(hAPP(c_Set_Oinsert(_951559), _951567), _951565)) = hAPP(hAPP(c_Finite__Set_Ofold(_951559, _951561, _951563), hAPP(hAPP(_951563, _951567), _951569)), _951565))], (36580 ^ _778495) ^ [_1467069, _1467071, _1467073, _1467075, _1467077, _1467079] : [c_Fun_Oinj__on(_1467069, _1467071, _1467073, _1467075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467069, tc_HOL_Obool)), _1467077), _1467075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467069, tc_HOL_Obool)), _1467079), _1467075)), -(hAPP(c_Set_Oimage(_1467069, _1467071, _1467073), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467069, tc_HOL_Obool)), _1467077), _1467079)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467071, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1467069, _1467071, _1467073), _1467077)), hAPP(c_Set_Oimage(_1467069, _1467071, _1467073), _1467079)))], (36498 ^ _778495) ^ [_1465353, _1465355] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465353), c_Orderings_Otop__class_Otop(tc_fun(_1465353, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1465353, _1465353, _1465355), c_Orderings_Otop__class_Otop(tc_fun(_1465353, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1465353, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1465353, _1465353, _1465355, c_Orderings_Otop__class_Otop(tc_fun(_1465353, tc_HOL_Obool))))], (38850 ^ _778495) ^ [_1530756, _1530758] : [c_Wellfounded_Owf(_1530756, _1530758), 38854 ^ _778495 : [(38855 ^ _778495) ^ [_1530892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530756, _1530756)), hAPP(hAPP(c_Product__Type_OPair(_1530756, _1530756), hAPP(_1530892, hAPP(c_Nat_OSuc, 38853 ^ [_1530756, _1530758, _1530892]))), hAPP(_1530892, 38853 ^ [_1530756, _1530758, _1530892]))), _1530758))]]], (48104 ^ _778495) ^ [_1748011, _1748013] : [c_Wellfounded_Oacyclic(_1748011, hAPP(c_Set_OCollect(tc_prod(_1748011, _1748011)), hAPP(c_Product__Type_Oprod_Oprod__case(_1748011, _1748011, tc_HOL_Obool), _1748013))), -(c_Wellfounded_Oacyclic(_1748011, hAPP(c_Set_OCollect(tc_prod(_1748011, _1748011)), hAPP(c_Product__Type_Oprod_Oprod__case(_1748011, _1748011, tc_HOL_Obool), c_Predicate_Oconversep(_1748011, _1748011, _1748013)))))], (22826 ^ _778495) ^ [_1186540] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1186540), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1186540) = _1186540)], (20951 ^ _778495) ^ [_1153735, _1153737, _1153739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153735)), 20957 ^ _778495 : [(20960 ^ _778495) ^ [] : [hBOOL(hAPP(_1153737, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 20956 ^ [_1153735, _1153737, _1153739]), _1153735)))], (20958 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1153737, 20956 ^ [_1153735, _1153737, _1153739])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153739)), 20965 ^ _778495 : [(20966 ^ _778495) ^ [_1154024] : [hBOOL(hAPP(_1153737, _1154024)), -(hBOOL(hAPP(_1153737, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1154024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1153739), _1153735)))))]]], (46989 ^ _778495) ^ [_1723640, _1723642, _1723644] : [class_Orderings_Olinorder(_1723640), c_List_Olinorder__class_Osorted(_1723640, _1723642), -(c_List_Olinorder__class_Osorted(_1723640, c_List_OdropWhile(_1723640, _1723644, _1723642)))], (44498 ^ _778495) ^ [_1669546, _1669548, _1669550, _1669552, _1669554] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1669546), tc_List_Olist(_1669548), tc_List_Olist(_1669550), hAPP(c_List_Omap(_1669546, _1669548), _1669552)), hAPP(c_List_Omap(_1669550, _1669546), _1669554)) = hAPP(c_List_Omap(_1669550, _1669548), hAPP(c_Fun_Ocomp(_1669546, _1669548, _1669550, _1669552), _1669554)))], (51187 ^ _778495) ^ [_1813675, _1813677] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813675), _1813677)), -(_1813675 = _1813677), 51194 ^ _778495 : [(51197 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813677), _1813675))], (51195 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813675), _1813677)))]]], (22632 ^ _778495) ^ [_1183099, _1183101] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183099)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183101), 22635 ^ _778495 : [(22638 ^ _778495) ^ [] : [-(_1183101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22636 ^ _778495) ^ [] : [-(_1183099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44255 ^ _778495) ^ [_1663515, _1663517, _1663519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663515), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663517)), _1663519))), -(c_List_Olast(_1663517, hAPP(hAPP(c_List_Odrop(_1663517), _1663515), _1663519)) = c_List_Olast(_1663517, _1663519))], (52359 ^ _778495) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (34054 ^ _778495) ^ [_1412838, _1412840, _1412842, _1412844] : [class_Orderings_Oorder(_1412838), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412838, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1412838, _1412840, _1412842)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1412838, _1412842), _1412844)) = c_Orderings_Obot__class_Obot(tc_fun(_1412838, tc_HOL_Obool)))], (8488 ^ _778495) ^ [_919849, _919851, _919853, _919855, _919857] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_919849, _919851, hAPP(hAPP(c_Set_Oinsert(_919849), _919853), _919855)), _919857)), 8493 ^ _778495 : [(8498 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_919849), 8491 ^ [_919849, _919851, _919853, _919855, _919857]), 8492 ^ [_919849, _919851, _919853, _919855, _919857]))], (8496 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_919849, _919849, _919851, 8491 ^ [_919849, _919851, _919853, _919855, _919857], 8492 ^ [_919849, _919851, _919853, _919855, _919857]), _919857)))], (8494 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_919849), _919853), _919855) = hAPP(hAPP(c_Set_Oinsert(_919849), 8491 ^ [_919849, _919851, _919853, _919855, _919857]), 8492 ^ [_919849, _919851, _919853, _919855, _919857]))]]], (48428 ^ _778495) ^ [_1754883, _1754885, _1754887, _1754889, _1754891, _1754893] : [-(c_New__Random__Sequence_Opos__union(_1754883, _1754885, _1754887, _1754889, _1754891, _1754893) = c_New__DSequence_Opos__union(_1754883, hAPP(hAPP(hAPP(_1754885, _1754889), _1754891), _1754893), hAPP(hAPP(hAPP(_1754887, _1754889), _1754891), _1754893)))], (25570 ^ _778495) ^ [_1235446] : [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, _1235446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1235446)))], (42541 ^ _778495) ^ [_1626331, _1626333] : [42543 ^ _778495 : [(42547 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42545 ^ [_1626331, _1626333]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626331)), _1626333))))], (42549 ^ _778495) ^ [] : [42542 ^ [_1626331, _1626333] = 42545 ^ [_1626331, _1626333]], (42551 ^ _778495) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1626331), _1626333), 42542 ^ [_1626331, _1626333]) = hAPP(hAPP(c_List_Onth(_1626331), _1626333), 42545 ^ [_1626331, _1626333]))], (42544 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42542 ^ [_1626331, _1626333]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626331)), _1626333))))]], -(hBOOL(hAPP(c_List_Odistinct(_1626331), _1626333)))], (44462 ^ _778495) ^ [_1668708, _1668710, _1668712, _1668714, _1668716] : [hAPP(hAPP(c_List_Omap(_1668708, _1668710), _1668712), _1668714) = hAPP(hAPP(c_List_Omap(_1668708, _1668710), _1668712), _1668716), c_Fun_Oinj__on(_1668708, _1668710, _1668712, c_Orderings_Otop__class_Otop(tc_fun(_1668708, tc_HOL_Obool))), -(_1668714 = _1668716)], (44857 ^ _778495) ^ [_1677151] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1677151)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1677151))], (24483 ^ _778495) ^ [_1216586, _1216588, _1216590] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1216586, tc_HOL_Obool)), _1216588) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1216586, tc_HOL_Obool)), _1216590), -(_1216588 = _1216590)], (28249 ^ _778495) ^ [_1282960, _1282962, _1282964, _1282966] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282960, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1282960, tc_fun(_1282960, tc_HOL_Obool), tc_HOL_Obool), c_member(_1282960)), _1282962)), hAPP(hAPP(c_COMBC(_1282960, tc_fun(_1282960, tc_HOL_Obool), tc_HOL_Obool), c_member(_1282960)), _1282964)), _1282966)), -(hBOOL(hAPP(hAPP(c_member(_1282960), _1282966), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282960, tc_HOL_Obool)), _1282962), _1282964))))], (24585 ^ _778495) ^ [_1218742, _1218744] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1218742))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1218742)), _1218744) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218744))], (13613 ^ _778495) ^ [_1020054, _1020056] : [class_Groups_Olinordered__ab__group__add(_1020054), 13616 ^ _778495 : [(13623 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020054), _1020056), c_Groups_Ozero__class_Ozero(_1020054))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020054), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020054), _1020056), _1020056)), c_Groups_Ozero__class_Ozero(_1020054))))], (13617 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020054), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020054), _1020056), _1020056)), c_Groups_Ozero__class_Ozero(_1020054))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020054), _1020056), c_Groups_Ozero__class_Ozero(_1020054))))]]], (30065 ^ _778495) ^ [_1326034, _1326036, _1326038, _1326040, _1326042] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1326034, _1326036, _1326038), _1326040), _1326042) = hAPP(hAPP(_1326040, hAPP(c_Product__Type_Ofst(_1326034, _1326036), _1326042)), hAPP(c_Product__Type_Osnd(_1326034, _1326036), _1326042)))], (38513 ^ _778495) ^ [_1521787, _1521789, _1521791] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1521787, _1521789)), _1521791)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521789), hAPP(c_Relation_ORange(_1521787, _1521789), _1521791))))], (44676 ^ _778495) ^ [_1673444, _1673446] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1673444), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1673446), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 44683 ^ _778495 : [(44690 ^ _778495) ^ [] : [_1673444 = _1673446, -(hAPP(c_Code__Numeral_Oof__nat, _1673444) = hAPP(c_Code__Numeral_Oof__nat, _1673446))], (44684 ^ _778495) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1673444) = hAPP(c_Code__Numeral_Oof__nat, _1673446), -(_1673444 = _1673446)]]], (14823 ^ _778495) ^ [_1041400, _1041402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041400), _1041402)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041400), _1041402) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10077 ^ _778495) ^ [_952175, _952177, _952179] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_952175), _952177)), hBOOL(hAPP(hAPP(c_member(_952175), _952179), _952177)), -(hAPP(c_Finite__Set_Ocard(_952175), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952175, tc_HOL_Obool)), _952177), hAPP(hAPP(c_Set_Oinsert(_952175), _952179), c_Orderings_Obot__class_Obot(tc_fun(_952175, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_952175), _952177)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (6096 ^ _778495) ^ [_876233, _876235, _876237] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_876233, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_876233, tc_HOL_Obool)), _876235), _876237)), _876237) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_876233, tc_HOL_Obool)), _876235), _876237))], (38465 ^ _778495) ^ [_1520453, _1520455, _1520457, _1520459] : [hAPP(hAPP(c_Relation_Orel__comp(_1520453, _1520453, _1520453), _1520455), _1520457) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520453, _1520453), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1520453, _1520453, _1520453), _1520455), _1520459) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520453, _1520453), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1520453, _1520453, _1520453), _1520455), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520453, _1520453), tc_HOL_Obool)), _1520457), _1520459)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520453, _1520453), tc_HOL_Obool)))], (37785 ^ _778495) ^ [_1497535, _1497537, _1497539] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1497535), hAPP(c_Set_OCollect(_1497535), hAPP(hAPP(c_COMBS(_1497535, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497535), c_fdisj), _1497537)), _1497539))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497535), hAPP(c_Set_OCollect(_1497535), _1497537))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497535), hAPP(c_Set_OCollect(_1497535), _1497539)))], (23739 ^ _778495) ^ [_1203734, _1203736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203734), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23742 ^ _778495 : [(23749 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203736), 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), _1203736), _1203734))))], (23743 ^ _778495) ^ [] : [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), _1203736), _1203734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203736), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (34373 ^ _778495) ^ [_1420282, _1420284, _1420286, _1420288, _1420290, _1420292] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1420282, tc_fun(_1420284, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1420286, _1420282, _1420288), _1420290)), _1420292) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1420286, tc_fun(_1420284, tc_HOL_Obool)), _1420290), hAPP(hAPP(c_COMBB(_1420282, tc_fun(_1420284, tc_HOL_Obool), _1420286), _1420292), _1420288)))], (42262 ^ _778495) ^ [_1620064] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1620064)), -(c_List_Onat__list(_1620064))], (12314 ^ _778495) ^ [_994712, _994714, _994716, _994718, _994720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994712), _994714)), 12317 ^ _778495 : [(12324 ^ _778495) ^ [] : [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), _994714), _994712)), _994716)), _994718)), _994720)), -(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), _994714), _994716)), _994718)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994712), _994716)), _994720))))], (12318 ^ _778495) ^ [] : [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), _994714), _994716)), _994718)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994712), _994716)), _994720))), -(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), _994714), _994712)), _994716)), _994718)), _994720)))]]], (52373 ^ _778495) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (3174 ^ _778495) ^ [_825787, _825789, _825791, _825793, _825795, _825797, _825799, _825801, _825803, _825805] : [-(c_Fun_Ofun__upd(_825805, _825801, _825797, _825793, _825789) = c_Fun_Ofun__upd(_825803, _825799, _825795, _825791, _825787)), _825805 = _825803, _825801 = _825799, _825797 = _825795, _825793 = _825791, _825789 = _825787], (30387 ^ _778495) ^ [_1332503, _1332505, _1332507, _1332509] : [hBOOL(hAPP(hAPP(_1332507, _1332505), _1332509)), -(hBOOL(hAPP(hAPP(c_member(_1332503), _1332505), c_SetInterval_Oord_OatMost(_1332503, _1332507, _1332509))))], (44347 ^ _778495) ^ [_1665270, _1665272, _1665274, _1665276, _1665278] : [-(hAPP(c_List_Orotate(_1665270, _1665272), hAPP(hAPP(c_List_Omap(_1665274, _1665270), _1665276), _1665278)) = hAPP(hAPP(c_List_Omap(_1665274, _1665270), _1665276), hAPP(c_List_Orotate(_1665274, _1665272), _1665278)))], (34542 ^ _778495) ^ [_1424331] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1424331)) = 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), _1424331))))], (42130 ^ _778495) ^ [_1616854, _1616856, _1616858, _1616860, _1616862] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1616854, _1616856)), _1616858), hAPP(hAPP(c_List_Ozip(_1616854, _1616856), _1616860), _1616862)) = hAPP(hAPP(c_List_Ozip(_1616854, _1616856), hAPP(hAPP(c_List_Otake(_1616854), _1616858), _1616860)), hAPP(hAPP(c_List_Otake(_1616856), _1616858), _1616862)))], (3820 ^ _778495) ^ [_835904, _835906] : [_835906 = _835904, -(c_Nat_Osemiring__1__class_Oof__nat(_835906) = c_Nat_Osemiring__1__class_Oof__nat(_835904))], (750 ^ _778495) ^ [_789854, _789856, _789858, _789860, _789862, _789864, _789866, _789868] : [-(c_Wellfounded_Omax__extp(_789866, _789862, _789858, _789854)), c_Wellfounded_Omax__extp(_789868, _789864, _789860, _789856), _789868 = _789866, _789864 = _789862, _789860 = _789858, _789856 = _789854], (50789 ^ _778495) ^ [_1806927, _1806929, _1806931, _1806933] : [-(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), _1806927, _1806929)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806931, _1806933)))), 50790 ^ _778495 : [(50793 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806931), _1806927)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806929), _1806933))], (50791 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806927), _1806929)))]]], (12298 ^ _778495) ^ [_994321, _994323, _994325, _994327, _994329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994321), _994323)), 12301 ^ _778495 : [(12308 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994327), 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), _994323), _994321)), _994325)), _994329))), -(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), _994321), _994325)), _994327)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994323), _994325)), _994329))))], (12302 ^ _778495) ^ [] : [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), _994321), _994325)), _994327)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994323), _994325)), _994329))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994327), 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), _994323), _994321)), _994325)), _994329))))]]], (25606 ^ _778495) ^ [_1236029, _1236031] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1236029))), _1236031) = 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)))), _1236029), _1236031))], (17688 ^ _778495) ^ [_1095769, _1095771, _1095773] : [class_Int_Onumber(_1095769), class_Orderings_Oord(_1095769), 17695 ^ _778495 : [(17702 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095769), hAPP(c_Int_Onumber__class_Onumber__of(_1095769), _1095771)), hAPP(c_Int_Onumber__class_Onumber__of(_1095769), _1095773)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095769), hAPP(c_Int_Onumber__class_Onumber__of(_1095769), _1095771)), hAPP(c_Int_Onumber__class_Onumber__of(_1095769), _1095773)) = hAPP(c_Int_Onumber__class_Onumber__of(_1095769), _1095773))], (17696 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095769), hAPP(c_Int_Onumber__class_Onumber__of(_1095769), _1095771)), hAPP(c_Int_Onumber__class_Onumber__of(_1095769), _1095773))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095769), hAPP(c_Int_Onumber__class_Onumber__of(_1095769), _1095771)), hAPP(c_Int_Onumber__class_Onumber__of(_1095769), _1095773)) = hAPP(c_Int_Onumber__class_Onumber__of(_1095769), _1095771))]]], (44821 ^ _778495) ^ [_1676543, _1676545] : [_1676543 = _1676545, -(hAPP(c_Code__Numeral_Onat__of, _1676543) = hAPP(c_Code__Numeral_Onat__of, _1676545))], (50236 ^ _778495) ^ [_1794277, _1794279, _1794281, _1794283, _1794285] : [c_Fun_Obij__betw(_1794277, _1794279, _1794281, c_Orderings_Otop__class_Otop(tc_fun(_1794277, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794279, tc_HOL_Obool))), 50239 ^ _778495 : [(50246 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794279, tc_HOL_Obool)), _1794283), hAPP(c_Set_Oimage(_1794277, _1794279, _1794281), _1794285))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794277, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1794277, _1794279, _1794281), _1794283)), _1794285)))], (50240 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794277, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1794277, _1794279, _1794281), _1794283)), _1794285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794279, tc_HOL_Obool)), _1794283), hAPP(c_Set_Oimage(_1794277, _1794279, _1794281), _1794285))))]]], (38864 ^ _778495) ^ [_1531060, _1531062, _1531064] : [c_Wellfounded_Owf(_1531060, _1531062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531060, tc_HOL_Obool)), _1531064), hAPP(c_Relation_OImage(_1531060, _1531060, _1531062), _1531064))), -(_1531064 = c_Orderings_Obot__class_Obot(tc_fun(_1531060, tc_HOL_Obool)))], (14459 ^ _778495) ^ [_1035440] : [class_Rings_Olinordered__semidom(_1035440), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1035440), c_Groups_Ozero__class_Ozero(_1035440)), c_Groups_Oone__class_Oone(_1035440))))], (19312 ^ _778495) ^ [_1125535, _1125537] : [class_Orderings_Olinorder(_1125535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125535), _1125537)), -(_1125537 = c_Orderings_Obot__class_Obot(tc_fun(_1125535, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1125535), c_Big__Operators_Olinorder__class_OMin(_1125535, _1125537)), _1125537)))], (41491 ^ _778495) ^ [_1597790, _1597792, _1597794, _1597796, _1597798, _1597800] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597790, _1597790)), hAPP(hAPP(c_Product__Type_OPair(_1597790, _1597790), _1597792), _1597794)), c_Transitive__Closure_Ortrancl(_1597790, _1597796))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597790), tc_List_Olist(_1597790))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597790), tc_List_Olist(_1597790)), _1597798), _1597800)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597790), c_List_Olistrel1(_1597790, _1597796)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597790), tc_List_Olist(_1597790))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597790), tc_List_Olist(_1597790)), hAPP(hAPP(c_List_Olist_OCons(_1597790), _1597792), _1597798)), hAPP(hAPP(c_List_Olist_OCons(_1597790), _1597794), _1597800))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597790), c_List_Olistrel1(_1597790, _1597796)))))], (45366 ^ _778495) ^ [_1689001, _1689003, _1689005, _1689007, _1689009] : [c_Fun_Oinj__on(_1689001, _1689003, _1689005, hAPP(hAPP(c_Set_Oinsert(_1689001), _1689007), hAPP(c_List_Oset(_1689001), _1689009))), -(hAPP(hAPP(c_List_Omap(_1689001, _1689003), _1689005), hAPP(c_List_OremoveAll(_1689001, _1689007), _1689009)) = hAPP(c_List_OremoveAll(_1689003, hAPP(_1689005, _1689007)), hAPP(hAPP(c_List_Omap(_1689001, _1689003), _1689005), _1689009)))], (40906 ^ _778495) ^ [_1581381, _1581383, _1581385, _1581387, _1581389, _1581391] : [c_Relation_Osingle__valued(_1581381, _1581383, hAPP(c_Relation_Oconverse(_1581383, _1581381), _1581385)), -(_1581387 = c_Orderings_Obot__class_Obot(tc_fun(_1581389, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1581383, _1581381, _1581385), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581389, tc_fun(_1581383, tc_HOL_Obool)), _1581387), _1581391)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581389, tc_fun(_1581381, tc_HOL_Obool)), _1581387), hAPP(hAPP(c_COMBB(tc_fun(_1581383, tc_HOL_Obool), tc_fun(_1581381, tc_HOL_Obool), _1581389), c_Relation_OImage(_1581383, _1581381, _1581385)), _1581391)))], (31212 ^ _778495) ^ [_1348840, _1348842] : [class_Orderings_Olinorder(_1348840), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348840), _1348842)), -(c_Big__Operators_Olattice_OSup__fin(_1348840, c_Orderings_Oord__class_Omax(_1348840), _1348842) = hAPP(c_Finite__Set_Ofold1(_1348840, c_Orderings_Oord__class_Omax(_1348840)), _1348842))], (874 ^ _778495) ^ [_791634, _791636, _791638, _791640] : [-(c_Predicate_Otransp(_791638, _791634)), c_Predicate_Otransp(_791640, _791636), _791640 = _791638, _791636 = _791634], (23545 ^ _778495) ^ [_1200290, _1200292, _1200294] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1200290, tc_HOL_Obool)), _1200292), _1200294) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1200290, tc_HOL_Obool)), _1200292), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1200290, tc_HOL_Obool)), _1200294)))], (38691 ^ _778495) ^ [_1527549, _1527551, _1527553] : [c_Wellfounded_Owf(_1527549, _1527551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527549, _1527549), tc_HOL_Obool)), _1527553), _1527551)), -(c_Wellfounded_Owf(_1527549, _1527553))], (4950 ^ _778495) ^ [_854005, _854007, _854009, _854011, _854013, _854015, _854017, _854019] : [-(c_Product__Type_Ocurry(_854019, _854015, _854011, _854007) = c_Product__Type_Ocurry(_854017, _854013, _854009, _854005)), _854019 = _854017, _854015 = _854013, _854011 = _854009, _854007 = _854005], (33419 ^ _778495) ^ [_1398568, _1398570] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398568, tc_fun(_1398568, tc_HOL_Obool)), _1398570), hAPP(hAPP(c_COMBC(_1398568, tc_fun(_1398568, tc_HOL_Obool), tc_fun(_1398568, tc_HOL_Obool)), c_Set_Oinsert(_1398568)), c_Orderings_Obot__class_Obot(tc_fun(_1398568, tc_HOL_Obool)))) = _1398570)], (43568 ^ _778495) ^ [_1649376, _1649378, _1649380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649376)), _1649378)), _1649380)), -(hAPP(hAPP(c_List_Odrop(_1649376), _1649380), _1649378) = c_List_Olist_ONil(_1649376))], (52413 ^ _778495) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (3760 ^ _778495) ^ [_834986, _834988] : [_834988 = _834986, -(c_New__DSequence_Opos__not__seq(_834988) = c_New__DSequence_Opos__not__seq(_834986))], (24675 ^ _778495) ^ [_1220306, _1220308] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1220306, _1220308)) = _1220308, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1220306), _1220308) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26850 ^ _778495) ^ [_1258510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1258510)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1258510), c_Int_OMin)))], (37350 ^ _778495) ^ [_1484948, _1484950, _1484952, _1484954, _1484956] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1484948, _1484950), _1484952), hAPP(hAPP(c_COMBS(_1484948, tc_fun(_1484950, tc_HOL_Obool), tc_fun(_1484950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484950, tc_HOL_Obool), tc_fun(tc_fun(_1484950, tc_HOL_Obool), tc_fun(_1484950, tc_HOL_Obool)), _1484948), c_Groups_Ominus__class_Ominus(tc_fun(_1484950, tc_HOL_Obool))), _1484954)), _1484956)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1484948, _1484950), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1484948, _1484950), _1484952), _1484954)), hAPP(hAPP(c_Product__Type_OSigma(_1484948, _1484950), _1484952), _1484956)))], (50767 ^ _778495) ^ [_1806494, _1806496, _1806498, _1806500] : [class_Rings_Ocomm__semiring__1(_1806494), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1806496), _1806498)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806494), hAPP(hAPP(c_Power_Opower__class_Opower(_1806494), _1806500), _1806496)), hAPP(hAPP(c_Power_Opower__class_Opower(_1806494), _1806500), _1806498))))], (30057 ^ _778495) ^ [_1325802, _1325804] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1325802), _1325804) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1325802, _1325804)))], (5316 ^ _778495) ^ [_859790, _859792] : [_859792 = _859790, -(c_Groups_Oabs__class_Oabs(_859792) = c_Groups_Oabs__class_Oabs(_859790))], (6690 ^ _778495) ^ [_887992, _887994, _887996, _887998] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887992, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_887992), _887994), _887996)), _887998) = hAPP(hAPP(c_Set_Oinsert(_887992), _887994), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887992, tc_HOL_Obool)), _887996), _887998)))], (23002 ^ _778495) ^ [_1189674] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1189674), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28603 ^ _778495) ^ [_1296449, _1296451] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1296449), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1296451))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1296449), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1296451))), 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))))], (34552 ^ _778495) ^ [_1424551, _1424553, _1424555, _1424557] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1424551, _1424551)), hAPP(hAPP(c_Product__Type_OPair(_1424551, _1424551), _1424553), _1424555)), c_Relation_OId__on(_1424551, _1424557)))), _1424553 = _1424555, hBOOL(hAPP(hAPP(c_member(_1424551), _1424553), _1424557))], (20572 ^ _778495) ^ [_1147463, _1147465] : [class_Int_Onumber__ring(_1147463), class_Rings_Olinordered__idom(_1147463), 20579 ^ _778495 : [(20586 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1147465), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147463), hAPP(c_Int_Onumber__class_Onumber__of(_1147463), _1147465)), c_Groups_Ozero__class_Ozero(_1147463))))], (20580 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147463), hAPP(c_Int_Onumber__class_Onumber__of(_1147463), _1147465)), c_Groups_Ozero__class_Ozero(_1147463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1147465), c_Int_OPls)))]]], (8850 ^ _778495) ^ [_927154, _927156, _927158, _927160] : [hBOOL(hAPP(hAPP(c_member(_927154), _927156), _927158)), hBOOL(hAPP(hAPP(c_member(_927154), _927156), _927160)), -(hBOOL(hAPP(hAPP(c_member(_927154), _927156), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927154, tc_HOL_Obool)), _927158), _927160))))], (44351 ^ _778495) ^ [_1665473, _1665475, _1665477, _1665479, _1665481, _1665483, _1665485, _1665487] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1665473, _1665475), _1665477), _1665479), hAPP(hAPP(c_List_Ozip(_1665473, _1665475), _1665481), hAPP(hAPP(c_List_Omap(_1665483, _1665475), _1665485), _1665487))) = hAPP(hAPP(c_List_Omap(tc_prod(_1665473, _1665483), _1665477), hAPP(c_Product__Type_Oprod_Oprod__case(_1665473, _1665483, _1665477), hAPP(hAPP(c_COMBB(tc_fun(_1665483, tc_prod(_1665473, _1665475)), tc_fun(_1665483, _1665477), _1665473), hAPP(c_COMBB(tc_prod(_1665473, _1665475), _1665477, _1665483), _1665479)), hAPP(hAPP(c_COMBC(_1665473, tc_fun(_1665483, _1665475), tc_fun(_1665483, tc_prod(_1665473, _1665475))), hAPP(hAPP(c_COMBB(tc_fun(_1665475, tc_prod(_1665473, _1665475)), tc_fun(tc_fun(_1665483, _1665475), tc_fun(_1665483, tc_prod(_1665473, _1665475))), _1665473), c_COMBB(_1665475, tc_prod(_1665473, _1665475), _1665483)), c_Product__Type_OPair(_1665473, _1665475))), _1665485)))), hAPP(hAPP(c_List_Ozip(_1665473, _1665483), _1665481), _1665487)))], (17646 ^ _778495) ^ [_1094924, _1094926, _1094928, _1094930] : [class_Orderings_Olinorder(_1094924), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094924), _1094926), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094924), _1094928), _1094930)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094924), _1094928), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094924), _1094926), _1094930)))], (8260 ^ _778495) ^ [_914921, _914923, _914925, _914927, _914929, _914931, _914933] : [-(hBOOL(hAPP(hAPP(c_member(_914921), _914923), _914925))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_914921, _914927, _914929, _914931, _914925), _914933)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_914921, _914927, _914929, _914931, hAPP(hAPP(c_Set_Oinsert(_914921), _914923), _914925)), hAPP(hAPP(_914929, _914923), _914933))))], (50548 ^ _778495) ^ [_1802551, _1802553, _1802555] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1802551), _1802553, _1802555)), -(c_List_Olist__ex(tc_Nat_Onat, _1802551, c_List_Oupt(_1802553, _1802555)))], (19188 ^ _778495) ^ [_1123367, _1123369] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123367), _1123369))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123369), _1123367)))], (11712 ^ _778495) ^ [_981816, _981818, _981820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981816), _981818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981820), _981818))))], (11097 ^ _778495) ^ [_969493, _969495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969493), _969495)), 11100 ^ _778495 : [(11107 ^ _778495) ^ [] : [_969495 = _969493, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969495), hAPP(c_Nat_OSuc, _969493))))], (11101 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969495), hAPP(c_Nat_OSuc, _969493))), -(_969495 = _969493)]]], (38066 ^ _778495) ^ [_1504677, _1504679, _1504681, _1504683, _1504685, _1504687] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1504677), _1504679)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1504681), _1504683)), 38076 ^ _778495 : [(38079 ^ _778495) ^ [] : [hAPP(c_Finite__Set_Ocard(_1504677), hAPP(c_Set_OCollect(_1504677), hAPP(hAPP(c_COMBS(_1504677, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1504677), c_fconj), hAPP(hAPP(c_COMBC(_1504677, tc_fun(_1504677, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504677)), _1504679))), hAPP(hAPP(c_COMBC(_1504677, _1504681, tc_HOL_Obool), _1504685), 38075 ^ [_1504677, _1504679, _1504681, _1504683, _1504685, _1504687])))) = _1504687], (38077 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504681), 38075 ^ [_1504677, _1504679, _1504681, _1504683, _1504685, _1504687]), _1504683)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1504677, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1504681, tc_HOL_Obool), tc_Nat_Onat, _1504677), c_Finite__Set_Ocard(_1504681)), hAPP(hAPP(c_COMBB(tc_fun(_1504681, tc_HOL_Obool), tc_fun(_1504681, tc_HOL_Obool), _1504677), c_Set_OCollect(_1504681)), hAPP(hAPP(c_COMBB(tc_fun(_1504681, tc_HOL_Obool), tc_fun(_1504681, tc_HOL_Obool), _1504677), hAPP(c_COMBS(_1504681, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1504681), c_fconj), hAPP(hAPP(c_COMBC(_1504681, tc_fun(_1504681, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504681)), _1504683)))), _1504685)))), _1504679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1504687), hAPP(c_Finite__Set_Ocard(_1504681), _1504683)))], (33559 ^ _778495) ^ [_1402586, _1402588, _1402590, _1402592, _1402594, _1402596] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1402592, _1402592)), hAPP(hAPP(c_Product__Type_OPair(_1402592, _1402592), hAPP(_1402596, _1402588)), hAPP(_1402596, _1402590))), _1402594)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1402586, _1402586)), hAPP(hAPP(c_Product__Type_OPair(_1402586, _1402586), _1402588), _1402590)), hAPP(hAPP(c_Relation_Oinv__image(_1402592, _1402586), _1402594), _1402596))))], (4160 ^ _778495) ^ [_841576, _841578] : [_841578 = _841576, -(c_List_Otake(_841578) = c_List_Otake(_841576))], (11642 ^ _778495) ^ [_980407, _980409, _980411, _980413] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_980407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980407), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980407), _980409), _980411)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980407), _980413), _980411))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980407), _980409), _980413)))], (21182 ^ _778495) ^ [_1157981, _1157983] : [class_Groups_Oordered__ab__group__add__abs(_1157981), 21185 ^ _778495 : [(21192 ^ _778495) ^ [] : [_1157983 = c_Groups_Ozero__class_Ozero(_1157981), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157981), hAPP(c_Groups_Oabs__class_Oabs(_1157981), _1157983)), c_Groups_Ozero__class_Ozero(_1157981))))], (21186 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157981), hAPP(c_Groups_Oabs__class_Oabs(_1157981), _1157983)), c_Groups_Ozero__class_Ozero(_1157981))), -(_1157983 = c_Groups_Ozero__class_Ozero(_1157981))]]], (11827 ^ _778495) ^ [_984012, _984014] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _984012), _984014)), _984014) = _984012)], (50349 ^ _778495) ^ [_1796514, _1796516, _1796518] : [hBOOL(hAPP(hAPP(_1796518, _1796516), _1796516)), -(hBOOL(hAPP(hAPP(c_member(_1796514), _1796516), c_Quotient_ORespects(_1796514, _1796518))))], (38310 ^ _778495) ^ [_1515049] : [-(c_Int_Oint__ge__less__than(_1515049) = 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), _1515049)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (48096 ^ _778495) ^ [_1747817, _1747819, _1747821] : [-(hAPP(c_New__DSequence_Opos__single(_1747817, _1747819), _1747821) = hAPP(c_Lazy__Sequence_Osingle(_1747817), _1747819))], (52553 ^ _778495) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (42884 ^ _778495) ^ [_1633053, _1633055] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633053)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633055)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633053), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633055)) = c_List_Olist_ONil(tc_Int_Oint))], (34627 ^ _778495) ^ [_1426044] : [-(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)), _1426044)) = _1426044)], (27745 ^ _778495) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (23547 ^ _778495) ^ [_1200347, _1200349, _1200351, _1200353] : [class_Divides_Osemiring__div(_1200347), 23550 ^ _778495 : [(23557 ^ _778495) ^ [] : [-(_1200349 = c_Groups_Ozero__class_Ozero(_1200347)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200347), _1200349), _1200351)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200347), _1200349), _1200353)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200347), _1200351), _1200353))], (23551 ^ _778495) ^ [] : [_1200349 = c_Groups_Ozero__class_Ozero(_1200347), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200347), _1200349), _1200351)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200347), _1200349), _1200353)) = c_Groups_Ozero__class_Ozero(_1200347))]]], (41021 ^ _778495) ^ [_1584212, _1584214, _1584216] : [-(hAPP(hAPP(c_Nat_Ocompow(_1584212, _1584212), hAPP(c_Nat_OSuc, _1584214)), _1584216) = hAPP(c_Fun_Ocomp(_1584212, _1584212, _1584212, _1584216), hAPP(hAPP(c_Nat_Ocompow(_1584212, _1584212), _1584214), _1584216)))], (34488 ^ _778495) ^ [_1422898, _1422900, _1422902, _1422904] : [-(_1422898 = c_Orderings_Obot__class_Obot(tc_fun(_1422900, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1422900, _1422902, hAPP(c_COMBK(_1422902, _1422900), _1422904)), _1422898) = hAPP(hAPP(c_Set_Oinsert(_1422902), _1422904), c_Orderings_Obot__class_Obot(tc_fun(_1422902, tc_HOL_Obool))))], (25918 ^ _778495) ^ [_1241803] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1241803, 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, _1241803, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25162 ^ _778495) ^ [_1228361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1228361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228361)))], (1698 ^ _778495) ^ [_802748, _802750] : [-(class_Rings_Oordered__semiring(_802748)), _802750 = _802748, class_Rings_Oordered__semiring(_802750)], (5194 ^ _778495) ^ [_857825, _857827, _857829, _857831, _857833, _857835] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_857835, _857831, _857827) = c_Lazy__Sequence_Olazy__sequence_OInsert(_857833, _857829, _857825)), _857835 = _857833, _857831 = _857829, _857827 = _857825], (47241 ^ _778495) ^ [_1728805, _1728807] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1728805)), _1728807)), 47247 ^ _778495 : [(47250 ^ _778495) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1728805), 47246 ^ [_1728805, _1728807]))], (47248 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728805)), 47246 ^ [_1728805, _1728807]), hAPP(c_List_Oset(tc_List_Olist(_1728805)), _1728807))))]], 47254 ^ _778495 : [(47258 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728805)), 47256 ^ [_1728805, _1728807]), hAPP(c_List_Oset(tc_List_Olist(_1728805)), _1728807))))], (47260 ^ _778495) ^ [] : [47253 ^ [_1728805, _1728807] = 47256 ^ [_1728805, _1728807]], (47262 ^ _778495) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1728805, tc_HOL_Obool)), hAPP(c_List_Oset(_1728805), 47253 ^ [_1728805, _1728807])), hAPP(c_List_Oset(_1728805), 47256 ^ [_1728805, _1728807])) = c_Orderings_Obot__class_Obot(tc_fun(_1728805, tc_HOL_Obool))], (47255 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728805)), 47253 ^ [_1728805, _1728807]), hAPP(c_List_Oset(tc_List_Olist(_1728805)), _1728807))))]], -(hBOOL(hAPP(c_List_Odistinct(_1728805), c_List_Oconcat(_1728805, _1728807))))], (50054 ^ _778495) ^ [_1790701, _1790703, _1790705, _1790707, _1790709] : [c_Fun_Obij__betw(_1790701, _1790703, _1790705, _1790707, _1790709), -(c_Fun_Obij__betw(_1790703, _1790701, c_Fun_Othe__inv__into(_1790701, _1790703, _1790707, _1790705), _1790709, _1790707))], (39301 ^ _778495) ^ [_1542286, _1542288] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1542286, tc_HOL_Obool), _1542288) = hAPP(c_Set_OCollect(_1542286), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542286, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1542286), c_HOL_OAll(tc_fun(_1542286, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542286, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1542286, tc_HOL_Obool), tc_HOL_Obool), _1542286), hAPP(c_COMBS(tc_fun(_1542286, 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(_1542286, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1542286, tc_HOL_Obool), tc_fun(tc_fun(_1542286, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1542286, tc_HOL_Obool))), _1542288)))), c_member(_1542286)))))], (1798 ^ _778495) ^ [_803998, _804000] : [-(class_Orderings_Olinorder(_803998)), _804000 = _803998, class_Orderings_Olinorder(_804000)], (50577 ^ _778495) ^ [_1803138, _1803140, _1803142, _1803144, _1803146] : [-(c_New__DSequence_Opos__map(_1803138, _1803140, _1803142, _1803144, _1803146) = c_Lazy__Sequence_Omap(_1803138, _1803140, _1803142, hAPP(_1803144, _1803146)))], (29174 ^ _778495) ^ [_1308872, _1308874, _1308876, _1308878, _1308880] : [-(hAPP(c_Nat_Onat_Onat__rec(_1308872, _1308874, _1308876), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1308878)), _1308880)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1308872), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1308878))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1308872, _1308872), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1308872, tc_fun(_1308872, _1308872)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1308872, tc_fun(_1308872, _1308872)), tc_Int_Oint), c_If(_1308872)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1308872, _1308874, _1308876), _1308880))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1308872, _1308872), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1308872, _1308872), tc_Int_Oint), _1308876), 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)), _1308880))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1308872, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1308872, _1308874, _1308876)), 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)), _1308880))))))], (12196 ^ _778495) ^ [_992113, _992115, _992117, _992119, _992121] : [class_Rings_Ocomm__semiring__1(_992113), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992113), _992115), _992117)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992113), _992119), _992121)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992113), _992115), _992119)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992113), _992117), _992121)))], (6376 ^ _778495) ^ [_881744, _881746, _881748, _881750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881744, tc_HOL_Obool)), _881746), _881748)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881744, tc_HOL_Obool)), _881748), _881750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881744, tc_HOL_Obool)), _881746), _881750)))], (45684 ^ _778495) ^ [_1696350, _1696352, _1696354] : [45686 ^ _778495 : [(45689 ^ _778495) ^ [] : [hBOOL(hAPP(_1696352, 45685 ^ [_1696350, _1696352, _1696354]))], (45687 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1696350), 45685 ^ [_1696350, _1696352, _1696354]), hAPP(c_List_Oset(_1696350), _1696354))))]], -(hAPP(c_List_Ofilter(_1696350, _1696352), _1696354) = _1696354)], (47471 ^ _778495) ^ [_1734424, _1734426, _1734428, _1734430, _1734432] : [class_Orderings_Olinorder(_1734424), 47477 ^ _778495 : [(47480 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1734424), hAPP(_1734430, _1734432)), hAPP(_1734430, 47476 ^ [_1734424, _1734426, _1734428, _1734430, _1734432])))], (47478 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734426), 47476 ^ [_1734424, _1734426, _1734428, _1734430, _1734432]), hAPP(c_List_Oset(_1734426), _1734428))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1734426, _1734424, _1734430), _1734432), _1734428) = hAPP(hAPP(c_List_Olist_OCons(_1734426), _1734432), _1734428))], (48585 ^ 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[_1758377, _1758379, _1758381, _1758383]), 48601 ^ [_1758377, _1758379, _1758381, _1758383])))], (48613 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758379), 48609 ^ [_1758377, _1758379, _1758381, _1758383]), 48604 ^ [_1758377, _1758379, _1758381, _1758383])))], (48608 ^ _778495) ^ [] : [48601 ^ [_1758377, _1758379, _1758381, _1758383] = 48604 ^ [_1758377, _1758379, _1758381, _1758383]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1758379, _1758377), _1758383), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1758379, tc_HOL_Obool), _1758381)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1758379, tc_HOL_Obool), _1758377), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1758379, _1758377), _1758383)), _1758381))], (5006 ^ _778495) ^ [_854913, _854915, _854917, _854919, _854921, _854923] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_854923, _854919, _854915) = c_SetInterval_Oord__class_OatLeastAtMost(_854921, _854917, _854913)), _854923 = _854921, _854919 = _854917, _854915 = _854913], (18702 ^ _778495) ^ [_1114344, _1114346, _1114348, _1114350] : [class_Fields_Olinordered__field__inverse__zero(_1114344), class_Int_Onumber(_1114344), 18709 ^ _778495 : [(18710 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114344), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114344), _1114346), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348))), _1114350)), 18713 ^ _778495 : [(18720 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114344), c_Groups_Ozero__class_Ozero(_1114344)), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348)))), 18723 ^ _778495 : [(18730 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114344), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348)), c_Groups_Ozero__class_Ozero(_1114344)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114344), c_Groups_Ozero__class_Ozero(_1114344)), _1114350)))], (18724 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114344), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348)), c_Groups_Ozero__class_Ozero(_1114344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114344), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114344), _1114350), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348))), _1114346)))]]], (18714 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114344), c_Groups_Ozero__class_Ozero(_1114344)), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114344), _1114346), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114344), _1114350), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348)))))]]], (18736 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114344), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114344), _1114346), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348))), _1114350))), 18739 ^ _778495 : [(18742 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114344), _1114346), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114344), _1114350), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348))))], (18740 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114344), c_Groups_Ozero__class_Ozero(_1114344)), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348))))]], 18743 ^ _778495 : [(18746 ^ _778495) ^ [] : [18747 ^ _778495 : [(18750 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114344), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114344), _1114350), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348))), _1114346))], (18748 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114344), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348)), c_Groups_Ozero__class_Ozero(_1114344))))]], 18751 ^ _778495 : [(18754 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114344), c_Groups_Ozero__class_Ozero(_1114344)), _1114350))], (18752 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114344), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348)), c_Groups_Ozero__class_Ozero(_1114344)))]]], (18744 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114344), c_Groups_Ozero__class_Ozero(_1114344)), hAPP(c_Int_Onumber__class_Onumber__of(_1114344), _1114348)))]]]]], (16042 ^ _778495) ^ [_1065085, _1065087, _1065089, _1065091, _1065093] : [class_Groups_Ocomm__monoid__mult(_1065085), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065087), _1065089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1065087, tc_HOL_Obool)), _1065091), _1065089)), 16056 ^ _778495 : [(16059 ^ _778495) ^ [] : [hAPP(_1065093, 16055 ^ [_1065085, _1065087, _1065089, _1065091, _1065093]) = c_Groups_Oone__class_Oone(_1065085)], (16057 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1065087), 16055 ^ [_1065085, _1065087, _1065089, _1065091, _1065093]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065087, tc_HOL_Obool)), _1065089), _1065091))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1065087, _1065085), _1065093), _1065089) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1065087, _1065085), _1065093), _1065091))], (1378 ^ _778495) ^ [_798748, _798750] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_798748)), _798750 = _798748, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_798750)], (6528 ^ _778495) ^ [_884535, _884537, _884539, _884541] : [hBOOL(hAPP(hAPP(c_member(_884535), _884537), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_884535, tc_HOL_Obool)), _884539), _884541))), -(hBOOL(hAPP(hAPP(c_member(_884535), _884537), _884539)))], (37142 ^ _778495) ^ [_1479548, _1479550, _1479552, _1479554] : [-(hAPP(c_Set_Ovimage(_1479548, _1479550, _1479552), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1479550, tc_HOL_Obool)), _1479554)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1479548, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1479548, _1479550, _1479552), _1479554)))], (45498 ^ _778495) ^ [_1691438, _1691440, _1691442] : [-(hAPP(c_List_Oset(_1691438), hAPP(c_List_OremoveAll(_1691438, _1691440), _1691442)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1691438, tc_HOL_Obool)), hAPP(c_List_Oset(_1691438), _1691442)), hAPP(hAPP(c_Set_Oinsert(_1691438), _1691440), c_Orderings_Obot__class_Obot(tc_fun(_1691438, tc_HOL_Obool)))))], (22964 ^ _778495) ^ [_1188983, _1188985] : [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), _1188983))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1188985)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1188983))) = 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), _1188985), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1188983)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30115 ^ _778495) ^ [_1326979, _1326981, _1326983, _1326985, _1326987, _1326989] : [hBOOL(hAPP(_1326979, _1326981)), hBOOL(hAPP(_1326983, _1326985)), 30122 ^ _778495 : [(30125 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1326983, hAPP(c_Product__Type_Osnd(_1326987, _1326989), hAPP(hAPP(c_Product__Type_OPair(_1326987, _1326989), _1326981), _1326985)))))], (30123 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1326979, hAPP(c_Product__Type_Ofst(_1326987, _1326989), hAPP(hAPP(c_Product__Type_OPair(_1326987, _1326989), _1326981), _1326985)))))]]], (15313 ^ _778495) ^ [_1050490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1050490)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050490), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1050490)], (33826 ^ _778495) ^ [_1408247] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1408247) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1408247))], (23306 ^ _778495) ^ [_1196162, _1196164] : [class_Divides_Osemiring__div(_1196162), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1196162), _1196164), c_Groups_Oone__class_Oone(_1196162)) = _1196164)], (34290 ^ _778495) ^ [_1418225, _1418227, _1418229] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1418225), _1418227))), 34293 ^ _778495 : [(34300 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1418229), _1418227))), -(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)), _1418225)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1418229), _1418227)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34294 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1418229), _1418227)), -(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)), _1418225)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1418229), _1418227)) = 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))))]]], (42169 ^ _778495) ^ [_1617948, _1617950, _1617952, _1617954] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617948, _1617948)), hAPP(hAPP(c_Product__Type_OPair(_1617948, _1617948), _1617950), _1617952)), hAPP(c_List_Oset(tc_prod(_1617948, _1617948)), hAPP(hAPP(c_List_Ozip(_1617948, _1617948), _1617954), _1617954))))), hBOOL(hAPP(hAPP(c_member(_1617948), _1617950), hAPP(c_List_Oset(_1617948), _1617954))), _1617950 = _1617952], (8978 ^ _778495) ^ [_929794, _929796] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929794, tc_HOL_Obool)), _929796), _929796) = _929796)], (17122 ^ _778495) ^ [_1084616, _1084618, _1084620, _1084622] : [class_Fields_Olinordered__field(_1084616), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084616), c_Groups_Ozero__class_Ozero(_1084616)), _1084618)), 17129 ^ _778495 : [(17136 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084616), _1084620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084616), _1084622), _1084618))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084616), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1084616), _1084620), _1084618)), _1084622)))], (17130 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084616), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1084616), _1084620), _1084618)), _1084622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084616), _1084620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084616), _1084622), _1084618))))]]], (15307 ^ _778495) ^ [_1050391, _1050393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1050391), _1050393))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050391), _1050393)))], (26690 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (49646 ^ _778495) ^ [_1781642, _1781644, _1781646] : [c_Fun_Oinj__on(_1781642, _1781644, _1781646, c_Orderings_Otop__class_Otop(tc_fun(_1781642, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781644, _1781642, c_Hilbert__Choice_Oinv__into(_1781642, _1781644, c_Orderings_Otop__class_Otop(tc_fun(_1781642, tc_HOL_Obool)), _1781646)), c_Orderings_Otop__class_Otop(tc_fun(_1781644, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781642, tc_HOL_Obool)))], (7054 ^ _778495) ^ [_894661, _894663, _894665, _894667] : [class_Lattices_Osemilattice__sup(_894661), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894661), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894661), _894663), _894665)), _894667) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894661), _894663), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894661), _894665), _894667)))], (23174 ^ _778495) ^ [_1193413, _1193415, _1193417, _1193419] : [class_Divides_Osemiring__div(_1193413), -(c_Divides_Odiv__class_Omod(_1193413, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193413), _1193415), _1193417), _1193419) = c_Divides_Odiv__class_Omod(_1193413, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193413), _1193415), c_Divides_Odiv__class_Omod(_1193413, _1193417, _1193419)), _1193419))], (46031 ^ _778495) ^ [_1704441, _1704443] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1704441, _1704443) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1704441), hAPP(c_Nat_OSuc, _1704443))))], (7252 ^ _778495) ^ [_898318, _898320, _898322, _898324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898318, tc_HOL_Obool)), _898320), hAPP(hAPP(c_Set_Oinsert(_898318), _898322), _898324))), 7255 ^ _778495 : [(7262 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898318), _898322), _898324))), 7265 ^ _778495 : [(7272 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898318), _898322), _898320))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898318, tc_HOL_Obool)), _898320), _898324)))], (7266 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898318), _898322), _898320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898318, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898318, tc_HOL_Obool)), _898320), hAPP(hAPP(c_Set_Oinsert(_898318), _898322), c_Orderings_Obot__class_Obot(tc_fun(_898318, tc_HOL_Obool))))), _898324)))]]], (7256 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898318), _898322), _898324)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898318, tc_HOL_Obool)), _898320), _898324)))]]], (34150 ^ _778495) ^ [_1414817, _1414819, _1414821, _1414823] : [class_Orderings_Olinorder(_1414817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1414817), _1414819), _1414821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414817), _1414821), _1414823)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414817, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1414817, _1414819, _1414821)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1414817, _1414821), _1414823)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1414817, _1414819, _1414823))], (25068 ^ _778495) ^ [_1226679, _1226681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1226679)), _1226681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1226679), hAPP(c_Int_Onat, _1226681))))], (8942 ^ _778495) ^ [_929006, _929008, _929010, _929012] : [class_Lattices_Osemilattice__inf(_929006), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929006), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929006), _929008), _929010)), _929012) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929006), _929008), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_929006), _929010), _929012)))], (37114 ^ _778495) ^ [_1478894, _1478896, _1478898, _1478900, _1478902] : [-(hAPP(c_Set_Ovimage(_1478894, _1478896, _1478898), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1478896, tc_HOL_Obool)), _1478900), _1478902)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1478894, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1478894, _1478896, _1478898), _1478900)), hAPP(c_Set_Ovimage(_1478894, _1478896, _1478898), _1478902)))], (37861 ^ _778495) ^ [_1499134, _1499136, _1499138, _1499140] : [hBOOL(hAPP(hAPP(c_member(_1499134), _1499136), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499134, tc_HOL_Obool)), _1499138), hAPP(c_Set_OCollect(_1499134), _1499140)))), 37864 ^ _778495 : [(37867 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1499140, _1499136)))], (37865 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1499134), _1499136), _1499138)))]]], (37294 ^ _778495) ^ [_1483604, _1483606] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1483604), c_Int_OInteg)), hBOOL(hAPP(_1483606, hAPP(c_Int_ORep__Integ, 37299 ^ [_1483604, _1483606]))), -(hBOOL(hAPP(_1483606, _1483604)))], (23312 ^ _778495) ^ [_1196257, _1196259, _1196261] : [class_Divides_Osemiring__div(_1196257), -(c_Divides_Odiv__class_Omod(_1196257, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196257), _1196259), _1196261), _1196261) = c_Groups_Ozero__class_Ozero(_1196257))], (45594 ^ _778495) ^ [_1693434, _1693436, _1693438, _1693440, _1693442] : [class_Orderings_Olinorder(_1693434), -(c_List_Olinorder__class_Osort__key(_1693436, _1693434, _1693438, hAPP(hAPP(c_List_Olist_OCons(_1693436), _1693440), _1693442)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1693436, _1693434, _1693438), _1693440), c_List_Olinorder__class_Osort__key(_1693436, _1693434, _1693438, _1693442)))], (7402 ^ _778495) ^ [_901565, _901567] : [class_Finite__Set_Ofinite(_901565), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_901565), _901567)))], (37869 ^ _778495) ^ [_1499301, _1499303, _1499305, _1499307] : [-(hBOOL(hAPP(hAPP(c_member(_1499301), _1499303), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499301, tc_HOL_Obool)), _1499305), hAPP(c_Set_OCollect(_1499301), _1499307))))), hBOOL(hAPP(hAPP(c_member(_1499301), _1499303), _1499305)), hBOOL(hAPP(_1499307, _1499303))], (25463 ^ _778495) ^ [_1233455, _1233457] : [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), _1233455)), _1233457))), _1233455 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1233457 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17536 ^ _778495) ^ [_1092661] : [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), _1092661))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092661) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092661)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (32120 ^ _778495) ^ [_1369058, _1369060, _1369062] : [class_Orderings_Oorder(_1369058), _1369060 = _1369062, -(c_SetInterval_Oord__class_OatLeastAtMost(_1369058, _1369060, _1369062) = hAPP(hAPP(c_Set_Oinsert(_1369058), _1369060), c_Orderings_Obot__class_Obot(tc_fun(_1369058, tc_HOL_Obool))))], (4378 ^ _778495) ^ [_845001, _845003, _845005, _845007] : [-(c_Wellfounded_Oaccp(_845007, _845003) = c_Wellfounded_Oaccp(_845005, _845001)), _845007 = _845005, _845003 = _845001], (44422 ^ _778495) ^ [_1667673, _1667675, _1667677] : [class_Groups_Omonoid__add(_1667673), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667673), hAPP(hAPP(c_List_Omap(_1667675, _1667673), hAPP(c_COMBK(_1667673, _1667675), c_Groups_Ozero__class_Ozero(_1667673))), _1667677)) = c_Groups_Ozero__class_Ozero(_1667673))], (25501 ^ _778495) ^ [_1234116, _1234118, _1234120] : [hBOOL(hAPP(_1234116, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1234118), _1234120))), 25506 ^ _778495 : [(25509 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1234116, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25507 ^ _778495) ^ [] : [-(_1234120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25511 ^ _778495 : [(25516 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1234116, 25510 ^ [_1234116, _1234118, _1234120])))], (25514 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1234118), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1234120), hAPP(c_Nat_OSuc, 25510 ^ [_1234116, _1234118, _1234120])))))], (25512 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1234120), 25510 ^ [_1234116, _1234118, _1234120])), _1234118)))]]], (35660 ^ _778495) ^ [_1446403, _1446405] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446403), c_Orderings_Obot__class_Obot(tc_fun(_1446403, tc_HOL_Obool))), _1446405) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446403, tc_HOL_Obool), tc_HOL_Obool)))], (28475 ^ _778495) ^ [_1293159, _1293161, _1293163] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293159, tc_Nat_Onat), _1293161), _1293163) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293159, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1293159), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1293161)), _1293163)))], (52057 ^ _778495) ^ [_1829176, _1829178, _1829180, _1829182, _1829184] : [class_Groups_Ocomm__monoid__mult(_1829176), class_Rings_Odvd(_1829176), hBOOL(hAPP(c_Finite__Set_Ofinite(_1829178), _1829180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1829178, tc_HOL_Obool)), _1829182), _1829180)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829176), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1829178, _1829176), _1829184), _1829182)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1829178, _1829176), _1829184), _1829180))))], (5797 ^ _778495) ^ [_870474, _870476, _870478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870474, tc_HOL_Obool)), _870476), hAPP(hAPP(c_Set_Oinsert(_870474), _870478), c_Orderings_Obot__class_Obot(tc_fun(_870474, tc_HOL_Obool))))), -(_870476 = c_Orderings_Obot__class_Obot(tc_fun(_870474, tc_HOL_Obool))), -(_870476 = hAPP(hAPP(c_Set_Oinsert(_870474), _870478), c_Orderings_Obot__class_Obot(tc_fun(_870474, tc_HOL_Obool))))], (37364 ^ _778495) ^ [_1485507, _1485509, _1485511, _1485513] : [hAPP(hAPP(c_Product__Type_OSigma(_1485507, _1485509), _1485511), hAPP(c_COMBK(tc_fun(_1485509, tc_HOL_Obool), _1485507), _1485513)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1485507, _1485509), tc_HOL_Obool)), -(_1485511 = c_Orderings_Obot__class_Obot(tc_fun(_1485507, tc_HOL_Obool))), -(_1485513 = c_Orderings_Obot__class_Obot(tc_fun(_1485509, tc_HOL_Obool)))], (45865 ^ _778495) ^ [_1701182, _1701184, _1701186, _1701188, _1701190, _1701192, _1701194] : [-(c_List_Ofoldr(_1701182, _1701184, _1701186, hAPP(hAPP(c_List_Omap(_1701188, _1701182), _1701190), _1701192), _1701194) = c_List_Ofoldr(_1701188, _1701184, hAPP(c_Fun_Ocomp(_1701182, tc_fun(_1701184, _1701184), _1701188, _1701186), _1701190), _1701192, _1701194))], (21594 ^ _778495) ^ [_1165233, _1165235] : [class_Int_Onumber__ring(_1165233), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1165233), c_Groups_Oone__class_Oone(_1165233)), hAPP(c_Int_Onumber__class_Onumber__of(_1165233), _1165235)) = hAPP(c_Int_Onumber__class_Onumber__of(_1165233), 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), _1165235))))], (37532 ^ _778495) ^ [_1489960, _1489962, _1489964, _1489966, _1489968, _1489970] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1489960, _1489962), hAPP(hAPP(c_Set_Oinsert(_1489960), _1489964), _1489966)), hAPP(c_COMBK(tc_fun(_1489962, tc_HOL_Obool), _1489960), hAPP(hAPP(c_Set_Oinsert(_1489962), _1489968), _1489970))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1489960, _1489962)), hAPP(hAPP(c_Product__Type_OPair(_1489960, _1489962), _1489964), _1489968)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1489960, _1489962), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1489960, _1489962), _1489966), hAPP(c_COMBK(tc_fun(_1489962, tc_HOL_Obool), _1489960), hAPP(hAPP(c_Set_Oinsert(_1489962), _1489968), _1489970)))), hAPP(hAPP(c_Product__Type_OSigma(_1489960, _1489962), hAPP(hAPP(c_Set_Oinsert(_1489960), _1489964), _1489966)), hAPP(c_COMBK(tc_fun(_1489962, tc_HOL_Obool), _1489960), _1489970)))))], (50291 ^ _778495) ^ [_1795392, _1795394] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795392), _1795394)), -(c_Fun_Obij__betw(_1795392, tc_Nat_Onat, 50294 ^ [_1795392, _1795394], _1795394, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1795392), _1795394))))], (51823 ^ _778495) ^ [_1824939, _1824941, _1824943] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1824939), _1824941)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1824939), _1824943))), -(_1824939 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824941), _1824943)))], (21888 ^ _778495) ^ [_1170070, _1170072] : [class_Groups_Ogroup__add(_1170070), 21891 ^ _778495 : [(21898 ^ _778495) ^ [] : [_1170072 = c_Groups_Ozero__class_Ozero(_1170070), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1170070), _1170072) = c_Groups_Ozero__class_Ozero(_1170070))], (21892 ^ _778495) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1170070), _1170072) = c_Groups_Ozero__class_Ozero(_1170070), -(_1170072 = c_Groups_Ozero__class_Ozero(_1170070))]]], (22566 ^ _778495) ^ [_1181920, _1181922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1181920)), c_Int_OBit1(_1181922))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181920), _1181922)))], (36857 ^ _778495) ^ [_1473426, _1473428, _1473430, _1473432] : [c_Fun_Oinj__on(_1473426, _1473428, _1473430, _1473432), -(hAPP(c_Set_Oimage(_1473428, _1473426, c_Fun_Othe__inv__into(_1473426, _1473428, _1473432, _1473430)), hAPP(c_Set_Oimage(_1473426, _1473428, _1473430), _1473432)) = _1473432)], (46885 ^ _778495) ^ [_1721453, _1721455, _1721457, _1721459, _1721461] : [-(hBOOL(hAPP(_1721453, _1721455))), -(c_List_OtakeWhile(_1721457, _1721453, hAPP(hAPP(c_List_Oappend(_1721457), _1721459), hAPP(hAPP(c_List_Olist_OCons(_1721457), _1721455), _1721461))) = c_List_OtakeWhile(_1721457, _1721453, _1721459))], (39960 ^ _778495) ^ [_1557621, _1557623, _1557625] : [-(hBOOL(hAPP(hAPP(c_member(_1557621), _1557623), c_Wellfounded_Oacc(_1557621, _1557625)))), 39964 ^ _778495 : [(39967 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1557621), 39963 ^ [_1557621, _1557623, _1557625]), c_Wellfounded_Oacc(_1557621, _1557625)))], (39965 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1557621, _1557621)), hAPP(hAPP(c_Product__Type_OPair(_1557621, _1557621), 39963 ^ [_1557621, _1557623, _1557625]), _1557623)), _1557625)))]]], (26780 ^ _778495) ^ [_1257222, _1257224, _1257226] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1257222, tc_HOL_Obool)), _1257224), hAPP(c_Set_OPow(_1257222), _1257226))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257222, tc_HOL_Obool)), _1257224), _1257226)))], (24916 ^ _778495) ^ [_1224212, _1224214, _1224216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1224212)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1224212), _1224214)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1224212), _1224216)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1224214), _1224216))], (25174 ^ _778495) ^ [_1228537, _1228539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228539)), 25181 ^ _778495 : [(25188 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228537), _1228539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1228537)), hAPP(c_Int_Onat, _1228539))))], (25182 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1228537)), hAPP(c_Int_Onat, _1228539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228537), _1228539)))]]], (47756 ^ _778495) ^ [_1740687, _1740689, _1740691, _1740693] : [c_List_Olist__ex(_1740687, _1740689, hAPP(hAPP(c_List_Olist_OCons(_1740687), _1740691), _1740693)), -(hBOOL(hAPP(_1740689, _1740691))), -(c_List_Olist__ex(_1740687, _1740689, _1740693))], (37067 ^ _778495) ^ [_1477732, _1477734, _1477736] : [-(c_HOL_OThe(tc_prod(_1477732, _1477734), _1477736) = c_HOL_OThe(tc_prod(_1477732, _1477734), hAPP(c_Product__Type_Oprod_Oprod__case(_1477732, _1477734, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1477734, tc_prod(_1477732, _1477734)), tc_fun(_1477734, tc_HOL_Obool), _1477732), hAPP(c_COMBB(tc_prod(_1477732, _1477734), tc_HOL_Obool, _1477734), _1477736)), c_Product__Type_OPair(_1477732, _1477734)))))], (42577 ^ _778495) ^ [_1627231, _1627233, _1627235, _1627237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1627231), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627233)), _1627235))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1627231), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627233)), _1627237))), 42587 ^ _778495 : [(42590 ^ _778495) ^ [] : [hAPP(hAPP(c_List_Onth(_1627233), _1627235), 42586 ^ [_1627231, _1627233, _1627235, _1627237]) = hAPP(hAPP(c_List_Onth(_1627233), _1627237), 42586 ^ [_1627231, _1627233, _1627235, _1627237])], (42588 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42586 ^ [_1627231, _1627233, _1627235, _1627237]), _1627231)))]], -(hAPP(hAPP(c_List_Otake(_1627233), _1627231), _1627235) = hAPP(hAPP(c_List_Otake(_1627233), _1627231), _1627237))], (14577 ^ _778495) ^ [_1037413, _1037415] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037413), hAPP(c_Nat_OSuc, _1037415)))), 14578 ^ _778495 : [(14581 ^ _778495) ^ [_1037501] : [_1037413 = hAPP(c_Nat_OSuc, _1037501), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037501), _1037415))], (14579 ^ _778495) ^ [] : [_1037413 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43313 ^ _778495) ^ [_1642714, _1642716, _1642718, _1642720] : [-(hBOOL(hAPP(hAPP(c_member(_1642714), _1642716), hAPP(c_List_Oset(_1642714), _1642718)))), -(c_List_Oremove1(_1642714, _1642716, hAPP(hAPP(c_List_Oappend(_1642714), _1642718), _1642720)) = hAPP(hAPP(c_List_Oappend(_1642714), _1642718), c_List_Oremove1(_1642714, _1642716, _1642720)))], (4588 ^ _778495) ^ [_848312, _848314, _848316, _848318] : [-(c_Product__Type_Ofst(_848318, _848314) = c_Product__Type_Ofst(_848316, _848312)), _848318 = _848316, _848314 = _848312], (29378 ^ _778495) ^ [_1312743, _1312745, _1312747, _1312749, _1312751] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1312743, _1312745), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1312747), _1312749))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1312745)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1312751), _1312743), _1312745), 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), _1312751), _1312747)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1312751), _1312749)), _1312745))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1312751), _1312749), _1312745)))))], (24549 ^ _778495) ^ [_1218036, _1218038] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1218036, _1218038)), _1218036)))], (15345 ^ _778495) ^ [_1051014, _1051016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1051014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1051016)), -(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), _1051016), _1051014))))], (47818 ^ _778495) ^ [_1742060, _1742062, _1742064] : [47820 ^ _778495 : [(47823 ^ _778495) ^ [] : [hBOOL(hAPP(_1742062, hAPP(hAPP(c_List_Onth(_1742060), _1742064), 47819 ^ [_1742060, _1742062, _1742064])))], (47821 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47819 ^ [_1742060, _1742062, _1742064]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742060)), _1742064))))]], -(c_List_Olist__all(_1742060, _1742062, _1742064))], (22660 ^ _778495) ^ [_1183575, _1183577] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1183575), _1183577) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1183575), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183577)))], (37498 ^ _778495) ^ [_1489296, _1489298, _1489300, _1489302] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1489296, _1489298)), hAPP(hAPP(c_Product__Type_OSigma(_1489296, _1489298), _1489300), hAPP(c_COMBK(tc_fun(_1489298, tc_HOL_Obool), _1489296), _1489302)))), -(_1489302 = c_Orderings_Obot__class_Obot(tc_fun(_1489298, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1489296), _1489300)))], (44247 ^ _778495) ^ [_1663414, _1663416] : [-(_1663414 = c_List_Olist_ONil(_1663416)), -(hBOOL(hAPP(hAPP(c_member(_1663416), c_List_Olast(_1663416, _1663414)), hAPP(c_List_Oset(_1663416), _1663414))))], (51619 ^ _778495) ^ [_1821114] : [_1821114 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821114), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (43730 ^ _778495) ^ [_1653521, _1653523, _1653525] : [_1653521 = c_List_Olist_ONil(_1653523), -(hAPP(c_List_Ohd(_1653523), hAPP(hAPP(c_List_Oappend(_1653523), _1653521), _1653525)) = hAPP(c_List_Ohd(_1653523), _1653525))], (47798 ^ _778495) ^ [_1741556, _1741558, _1741560] : [-(hBOOL(hAPP(hAPP(c_member(_1741556), _1741558), hAPP(c_List_Oset(_1741556), _1741560)))), 47799 ^ _778495 : [(47800 ^ _778495) ^ [_1741645, _1741647] : [_1741560 = hAPP(hAPP(c_List_Oappend(_1741556), _1741647), hAPP(hAPP(c_List_Olist_OCons(_1741556), _1741558), _1741645)), -(hBOOL(hAPP(hAPP(c_member(_1741556), _1741558), hAPP(c_List_Oset(_1741556), _1741645))))]]], (27541 ^ _778495) ^ [_1269976] : [class_Complete__Lattice_Ocomplete__lattice(_1269976), -(c_Complete__Lattice_OSup__class_OSup(_1269976, c_Orderings_Otop__class_Otop(tc_fun(_1269976, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1269976))], (50971 ^ _778495) ^ [_1810174, _1810176, _1810178] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810174), _1810176)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810176), _1810174))), 50986 ^ _778495 : [(50989 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810178), _1810174))], (50987 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810174), _1810178)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810176), _1810178)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810178), _1810176)))], (39165 ^ _778495) ^ [_1539196, _1539198] : [c_Wellfounded_Owf(_1539196, _1539198), -(c_Wellfounded_Oacyclic(_1539196, _1539198))], (1498 ^ _778495) ^ [_800248, _800250] : [-(class_Groups_Ouminus(_800248)), _800250 = _800248, class_Groups_Ouminus(_800250)], (33282 ^ _778495) ^ [_1394351, _1394353, _1394355, _1394357, _1394359, _1394361, _1394363] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394351, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394353, tc_fun(_1394351, tc_HOL_Obool)), _1394355), _1394357)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394359, tc_fun(_1394351, tc_HOL_Obool)), _1394361), _1394363)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394353, tc_fun(_1394351, tc_HOL_Obool)), _1394355), hAPP(hAPP(c_COMBB(tc_fun(_1394359, tc_fun(_1394351, tc_HOL_Obool)), tc_fun(_1394351, tc_HOL_Obool), _1394353), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394359, tc_fun(_1394351, tc_HOL_Obool)), _1394361)), hAPP(hAPP(c_COMBC(_1394353, tc_fun(_1394359, tc_fun(_1394351, tc_HOL_Obool)), tc_fun(_1394359, tc_fun(_1394351, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1394351, tc_HOL_Obool), tc_fun(_1394351, tc_HOL_Obool)), tc_fun(tc_fun(_1394359, tc_fun(_1394351, tc_HOL_Obool)), tc_fun(_1394359, tc_fun(_1394351, tc_HOL_Obool))), _1394353), c_COMBB(tc_fun(_1394351, tc_HOL_Obool), tc_fun(_1394351, tc_HOL_Obool), _1394359)), hAPP(hAPP(c_COMBB(tc_fun(_1394351, tc_HOL_Obool), tc_fun(tc_fun(_1394351, tc_HOL_Obool), tc_fun(_1394351, tc_HOL_Obool)), _1394353), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394351, tc_HOL_Obool))), _1394357))), _1394363))))], (5452 ^ _778495) ^ [_861986, _861988] : [_861988 = _861986, -(c_Groups_Otimes__class_Otimes(_861988) = c_Groups_Otimes__class_Otimes(_861986))], (1708 ^ _778495) ^ [_802873, _802875] : [-(class_Rings_Ono__zero__divisors(_802873)), _802875 = _802873, class_Rings_Ono__zero__divisors(_802875)], (5819 ^ _778495) ^ [_870900, _870902, _870904] : [_870902 = _870904, -(hBOOL(hAPP(hAPP(c_member(_870900), _870902), hAPP(hAPP(c_Set_Oinsert(_870900), _870904), c_Orderings_Obot__class_Obot(tc_fun(_870900, tc_HOL_Obool))))))], (26824 ^ _778495) ^ [_1258095] : [class_Int_Onumber__ring(_1258095), -(hAPP(c_Int_Onumber__class_Onumber__of(_1258095), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1258095), c_Groups_Oone__class_Oone(_1258095)))], (23380 ^ _778495) ^ [_1197513] : [class_Rings_Osemiring__1(_1197513), -(c_Int_Oiszero(_1197513, c_Groups_Ozero__class_Ozero(_1197513)))], (22292 ^ _778495) ^ [_1177153, _1177155] : [class_Groups_Ogroup__add(_1177153), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177153), _1177155), hAPP(c_Groups_Ouminus__class_Ouminus(_1177153), _1177155)) = c_Groups_Ozero__class_Ozero(_1177153))], (38461 ^ _778495) ^ [_1520364, _1520366, _1520368, _1520370] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1520364, _1520366, _1520368), _1520370), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520366, _1520368), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520364, _1520368), tc_HOL_Obool)))], (20410 ^ _778495) ^ [_1145020] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1145020) = c_Int_OPls)], (9508 ^ _778495) ^ [_940627, _940629, _940631] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_940627), _940629)), -(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(_940627), _940631)), hAPP(c_Finite__Set_Ocard(_940627), _940629))), hAPP(c_Finite__Set_Ocard(_940627), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940627, tc_HOL_Obool)), _940631), _940629)))))], (33801 ^ _778495) ^ [_1407747, _1407749] : [33803 ^ _778495 : [(33806 ^ _778495) ^ [] : [hBOOL(hAPP(_1407749, 33802 ^ [_1407747, _1407749]))], (33804 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 33802 ^ [_1407747, _1407749]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407747))))]], 33807 ^ _778495 : [(33808 ^ _778495) ^ [_1407900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1407900), _1407747)), -(hBOOL(hAPP(_1407749, _1407900)))]]], (23300 ^ _778495) ^ [_1196063, _1196065] : [class_Divides_Osemiring__div(_1196063), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1196063), _1196065), c_Groups_Ozero__class_Ozero(_1196063)) = c_Groups_Ozero__class_Ozero(_1196063))], (49867 ^ _778495) ^ [_1786879, _1786881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1786879), _1786881)), -(c_Quickcheck_Obeyond(_1786879, _1786881) = _1786881)], (11168 ^ _778495) ^ [_970798, _970800] : [class_Lattices_Olattice(_970798), hBOOL(hAPP(c_Finite__Set_Ofinite(_970798), _970800)), -(_970800 = c_Orderings_Obot__class_Obot(tc_fun(_970798, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_970798), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970798), 11181 ^ [_970798, _970800]), 11182 ^ [_970798, _970800])), hAPP(hAPP(c_Set_Oinsert(_970798), 11181 ^ [_970798, _970800]), hAPP(hAPP(c_Set_Oinsert(_970798), 11182 ^ [_970798, _970800]), c_Orderings_Obot__class_Obot(tc_fun(_970798, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_970798), c_Big__Operators_Olattice__class_OInf__fin(_970798, _970800)), _970800)))], (47871 ^ _778495) ^ [_1742981, _1742983, _1742985] : [47873 ^ _778495 : [(47876 ^ _778495) ^ [] : [hBOOL(hAPP(_1742983, 47872 ^ [_1742981, _1742983, _1742985]))], (47874 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742981), 47872 ^ [_1742981, _1742983, _1742985]), hAPP(c_List_Oset(_1742981), _1742985))))]], -(c_List_Olist__all(_1742981, _1742983, _1742985))], (29206 ^ _778495) ^ [_1309563, _1309565] : [-(c_Divides_Odivmod__nat(_1309563, _1309565) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1309563), _1309565)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1309563, _1309565)))], (42708 ^ _778495) ^ [_1629695, _1629697] : [-(c_List_Olistrelp(_1629695, _1629697, c_List_Olist_ONil(_1629695), c_List_Olist_ONil(_1629695)))], (36897 ^ _778495) ^ [_1474208, _1474210, _1474212, _1474214, _1474216, _1474218] : [c_Typedef_Otype__definition(_1474208, _1474210, _1474212, _1474214, _1474216), -(hAPP(_1474214, hAPP(_1474212, _1474218)) = _1474218)], (13048 ^ _778495) ^ [_1011164, _1011166, _1011168, _1011170] : [class_Rings_Ocomm__semiring__1(_1011164), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011166), _1011168)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011166, _1011164), _1011170), _1011168) = c_Groups_Ozero__class_Ozero(_1011164)), 13057 ^ _778495 : [(13058 ^ _778495) ^ [_1011345] : [hBOOL(hAPP(hAPP(c_member(_1011166), _1011345), _1011168)), hAPP(_1011170, _1011345) = c_Groups_Ozero__class_Ozero(_1011164)]]], (44357 ^ _778495) ^ [_1665901, _1665903, _1665905, _1665907, _1665909, _1665911, _1665913, _1665915] : [-(hAPP(hAPP(c_List_Ozip(_1665901, _1665903), hAPP(hAPP(c_List_Omap(_1665905, _1665901), _1665907), _1665909)), hAPP(hAPP(c_List_Omap(_1665911, _1665903), _1665913), _1665915)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665905, _1665911), tc_prod(_1665901, _1665903)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665905, _1665911, tc_prod(_1665901, _1665903)), hAPP(hAPP(c_COMBC(_1665905, tc_fun(_1665911, _1665903), tc_fun(_1665911, tc_prod(_1665901, _1665903))), hAPP(hAPP(c_COMBB(tc_fun(_1665903, tc_prod(_1665901, _1665903)), tc_fun(tc_fun(_1665911, _1665903), tc_fun(_1665911, tc_prod(_1665901, _1665903))), _1665905), c_COMBB(_1665903, tc_prod(_1665901, _1665903), _1665911)), hAPP(hAPP(c_COMBB(_1665901, tc_fun(_1665903, tc_prod(_1665901, _1665903)), _1665905), c_Product__Type_OPair(_1665901, _1665903)), _1665907))), _1665913))), hAPP(hAPP(c_List_Ozip(_1665905, _1665911), _1665909), _1665915)))], (27321 ^ _778495) ^ [_1266231] : [c_Code__Numeral_OSuc__code__numeral(_1266231) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (47239 ^ _778495) ^ [_1728745, _1728747, _1728749, _1728751, _1728753] : [-(c_List_Omaps(_1728745, _1728747, _1728749, hAPP(hAPP(c_List_Olist_OCons(_1728745), _1728751), _1728753)) = hAPP(hAPP(c_List_Oappend(_1728747), hAPP(_1728749, _1728751)), c_List_Omaps(_1728745, _1728747, _1728749, _1728753)))], (35585 ^ _778495) ^ [_1444313, _1444315] : [-(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), _1444313), _1444315)), 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), _1444315), _1444313)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (23234 ^ _778495) ^ [_1194676, _1194678, _1194680] : [hBOOL(hAPP(hAPP(c_member(_1194676), _1194678), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1194676, tc_HOL_Obool)), _1194680))), hBOOL(hAPP(hAPP(c_member(_1194676), _1194678), _1194680))], (28605 ^ _778495) ^ [_1296518, _1296520, _1296522] : [hBOOL(hAPP(c_Predicate_OPowp(_1296518, hAPP(hAPP(c_COMBC(_1296518, tc_fun(_1296518, tc_HOL_Obool), tc_HOL_Obool), c_member(_1296518)), _1296520)), _1296522)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1296518, tc_HOL_Obool)), _1296522), hAPP(c_Set_OPow(_1296518), _1296520))))], (37348 ^ _778495) ^ [_1484838, _1484840, _1484842, _1484844, _1484846] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1484838, _1484840), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1484838, tc_HOL_Obool)), _1484842), _1484844)), hAPP(c_COMBK(tc_fun(_1484840, tc_HOL_Obool), _1484838), _1484846)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1484838, _1484840), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1484838, _1484840), _1484842), hAPP(c_COMBK(tc_fun(_1484840, tc_HOL_Obool), _1484838), _1484846))), hAPP(hAPP(c_Product__Type_OSigma(_1484838, _1484840), _1484844), hAPP(c_COMBK(tc_fun(_1484840, tc_HOL_Obool), _1484838), _1484846))))], (19254 ^ _778495) ^ [_1124516, _1124518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124516), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1124518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124516), _1124518)))], (48048 ^ _778495) ^ [_1746482, _1746484, _1746486, _1746488, _1746490] : [_1746482 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1746484, _1746486, _1746488, _1746490), _1746482) = c_Lazy__Sequence_Oempty(_1746486))], (22976 ^ _778495) ^ [_1189212, _1189214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189212)), -(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)))), _1189214)), 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)))), _1189212)) = 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, _1189214, _1189212))))], (35530 ^ _778495) ^ [_1442812, _1442814, _1442816, _1442818, _1442820] : [hBOOL(hAPP(hAPP(c_member(_1442812), _1442814), hAPP(c_Relation_OImage(_1442816, _1442812, _1442818), _1442820))), 35534 ^ _778495 : [(35537 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1442816, _1442812)), hAPP(hAPP(c_Product__Type_OPair(_1442816, _1442812), 35533 ^ [_1442812, _1442814, _1442816, _1442818, _1442820]), _1442814)), _1442818)))], (35535 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442816), 35533 ^ [_1442812, _1442814, _1442816, _1442818, _1442820]), _1442820)))]]], (13516 ^ _778495) ^ [_1018285, _1018287, _1018289] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018285), _1018287)), 13519 ^ _778495 : [(13520 ^ _778495) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1018285, tc_Nat_Onat), _1018289), _1018287) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 13523 ^ _778495 : [(13524 ^ _778495) ^ [_1018447] : [hBOOL(hAPP(hAPP(c_member(_1018285), _1018447), _1018287)), -(hAPP(_1018289, _1018447) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (13530 ^ _778495) ^ [] : [13532 ^ _778495 : [(13535 ^ _778495) ^ [] : [hAPP(_1018289, 13531 ^ [_1018285, _1018287, _1018289]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (13533 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1018285), 13531 ^ [_1018285, _1018287, _1018289]), _1018287)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1018285, tc_Nat_Onat), _1018289), _1018287) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (45518 ^ _778495) ^ [_1691873, _1691875, _1691877, _1691879] : [class_Orderings_Olinorder(_1691873), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691875)), c_List_Olinorder__class_Osort__key(_1691875, _1691873, _1691877, _1691879)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691875)), _1691879))], (12896 ^ _778495) ^ [_1008056, _1008058, _1008060, _1008062, _1008064, _1008066] : [class_Rings_Olinordered__semiring__1__strict(_1008056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008056), _1008058), _1008060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008056), _1008062), _1008060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008056), c_Groups_Ozero__class_Ozero(_1008056)), _1008064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008056), c_Groups_Ozero__class_Ozero(_1008056)), _1008066)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008056), _1008064), _1008066) = c_Groups_Oone__class_Oone(_1008056), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008056), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008056), _1008064), _1008058)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008056), _1008066), _1008062))), _1008060)))], (1508 ^ _778495) ^ [_800373, _800375] : [-(class_Lazy__Sequence_Osmall__lazy(_800373)), _800375 = _800373, class_Lazy__Sequence_Osmall__lazy(_800375)], (40191 ^ _778495) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (48858 ^ _778495) ^ [_1765266, _1765268, _1765270, _1765272] : [class_Complete__Lattice_Ocomplete__lattice(_1765266), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1765268, _1765266), _1765270), _1765272) = c_Complete__Lattice_OSup__class_OSup(_1765266, hAPP(c_Set_OCollect(_1765266), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1765268, _1765266), tc_HOL_Obool), tc_HOL_Obool, _1765266), c_HOL_OEx(tc_fun(_1765268, _1765266))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1765268, _1765266), tc_HOL_Obool), tc_fun(tc_fun(_1765268, _1765266), tc_HOL_Obool), _1765266), hAPP(c_COMBS(tc_fun(_1765268, _1765266), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1765268, _1765266)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1765268, _1765266), tc_fun(tc_fun(_1765268, _1765266), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1765268, _1765266))), _1765270)))), hAPP(hAPP(c_COMBC(_1765266, tc_fun(tc_fun(_1765268, _1765266), _1765266), tc_fun(tc_fun(_1765268, _1765266), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1765266, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1765268, _1765266), _1765266), tc_fun(tc_fun(_1765268, _1765266), tc_HOL_Obool)), _1765266), c_COMBB(_1765266, tc_HOL_Obool, tc_fun(_1765268, _1765266))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1765268, _1765266), _1765268, _1765266), c_COMBI(tc_fun(_1765268, _1765266))), _1765272)))))))], (43295 ^ _778495) ^ [_1642150, _1642152, _1642154, _1642156] : [-(hAPP(hAPP(c_List_Onth(_1642150), hAPP(hAPP(c_List_Oappend(_1642150), _1642152), _1642154)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642150)), _1642152)), _1642156)) = hAPP(hAPP(c_List_Onth(_1642150), _1642154), _1642156))], (52131 ^ _778495) ^ [_1830238, _1830240] : [-(class_Finite__Set_Ofinite(tc_fun(_1830238, _1830240))), class_Finite__Set_Ofinite(_1830238), class_Finite__Set_Ofinite(_1830240)], (39997 ^ _778495) ^ [_1558613, _1558615, _1558617, _1558619] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1558613, tc_HOL_Obool), tc_fun(_1558613, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1558613, tc_HOL_Obool), tc_fun(_1558613, tc_HOL_Obool)), _1558615), _1558617)), c_Wellfounded_Omax__ext(_1558613, _1558619)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558613), _1558615)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558613), _1558617)), -(_1558617 = c_Orderings_Obot__class_Obot(tc_fun(_1558613, tc_HOL_Obool))), 40011 ^ _778495 : [(40014 ^ _778495) ^ [_1559018] : [hBOOL(hAPP(hAPP(c_member(_1558613), _1559018), _1558617)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1558613, _1558613)), hAPP(hAPP(c_Product__Type_OPair(_1558613, _1558613), 40010 ^ [_1558613, _1558615, _1558617, _1558619]), _1559018)), _1558619))], (40012 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558613), 40010 ^ [_1558613, _1558615, _1558617, _1558619]), _1558615)))]]], (20127 ^ _778495) ^ [_1140020, _1140022, _1140024] : [class_Rings_Olinordered__semidom(_1140020), 20130 ^ _778495 : [(20137 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1140022), _1140024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140020), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140020), _1140022)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140020), _1140024))))], (20131 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140020), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140020), _1140022)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1140020), _1140024))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1140022), _1140024)))]]], (48486 ^ _778495) ^ [_1756192, _1756194, _1756196, _1756198, _1756200] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1756192, _1756194, _1756196, _1756198, _1756200) = c_Option_Ooption_Ooption__case(_1756192, tc_prod(_1756194, tc_Lazy__Sequence_Olazy__sequence(_1756194)), _1756196, hAPP(c_Product__Type_Oprod_Oprod__case(_1756194, tc_Lazy__Sequence_Olazy__sequence(_1756194), _1756192), _1756198), hAPP(c_Lazy__Sequence_Oyield(_1756194), _1756200)))], (43690 ^ _778495) ^ [_1652345, _1652347, _1652349, _1652351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1652345), _1652347)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652349)), _1652351))), -(hAPP(hAPP(c_List_Otake(_1652349), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1652345), _1652347)), _1652351) = hAPP(hAPP(c_List_Oappend(_1652349), hAPP(hAPP(c_List_Otake(_1652349), _1652345), _1652351)), hAPP(hAPP(c_List_Otake(_1652349), _1652347), hAPP(hAPP(c_List_Odrop(_1652349), _1652345), _1652351))))], (42097 ^ _778495) ^ [_1614838, _1614840, _1614842] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1614838), _1614840)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1614838)), hAPP(c_Set_OCollect(tc_List_Olist(_1614838)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1614838), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1614838)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614838), tc_fun(_1614838, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614838, tc_HOL_Obool), tc_fun(tc_fun(_1614838, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614838)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614838, tc_HOL_Obool))), c_List_Oset(_1614838))), _1614840))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614838), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1614838)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1614838)))), _1614842))))))], (18082 ^ _778495) ^ [_1102832, _1102834] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1102832)), hAPP(c_Nat_OSuc, _1102834)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1102832), _1102834)))], (34240 ^ _778495) ^ [_1416851, _1416853, _1416855, _1416857] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1416851, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34241 ^ [_1416851, _1416853, _1416855, _1416857])), _1416853) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1416851, 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), 34241 ^ [_1416851, _1416853, _1416855, _1416857]), _1416855))), _1416857), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1416851, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1416853) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1416851, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1416857))], (41344 ^ _778495) ^ [_1592687, _1592689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41345 ^ [_1592687, _1592689]), hAPP(_1592687, 41345 ^ [_1592687, _1592689]))), -(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)), _1592687)), _1592689)))))], (27403 ^ _778495) ^ [_1267559, _1267561] : [-(_1267559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1267561, _1267559) = c_Nitpick_Onat__gcd(_1267559, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1267561, _1267559)))], (25076 ^ _778495) ^ [_1226822, _1226824] : [-(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), _1226822)), _1226824))))], (44937 ^ _778495) ^ [_1679189, _1679191, _1679193] : [-(c_List_Olistsp(_1679189, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1679189, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1679189, tc_fun(_1679189, tc_HOL_Obool), tc_HOL_Obool), c_member(_1679189)), _1679191)), hAPP(hAPP(c_COMBC(_1679189, tc_fun(_1679189, tc_HOL_Obool), tc_HOL_Obool), c_member(_1679189)), _1679193))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1679189), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1679189), tc_fun(tc_List_Olist(_1679189), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1679189))), c_List_Olists(_1679189, _1679191))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1679189), tc_fun(tc_List_Olist(_1679189), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1679189))), c_List_Olists(_1679189, _1679193))))], (40022 ^ _778495) ^ [_1559246, _1559248, _1559250, _1559252] : [class_Orderings_Olinorder(_1559246), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559246), _1559248)), 40032 ^ _778495 : [(40035 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1559246), 40031 ^ [_1559246, _1559248, _1559250, _1559252]), _1559250))], (40033 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559246), 40031 ^ [_1559246, _1559248, _1559250, _1559252]), _1559248)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1559246), hAPP(hAPP(c_Finite__Set_Ofold(_1559246, _1559246, c_Orderings_Oord__class_Omax(_1559246)), _1559252), _1559248)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1559246), _1559250), _1559252))))], (22114 ^ _778495) ^ [_1174030] : [_1174030 = c_Int_OPls, -(c_Int_OBit0(_1174030) = c_Int_OPls)], (52215 ^ _778495) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (52369 ^ _778495) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (33591 ^ _778495) ^ [_1403299, _1403301, _1403303, _1403305, _1403307] : [33593 ^ _778495 : [(33596 ^ _778495) ^ [] : [hBOOL(hAPP(_1403307, 33592 ^ [_1403299, _1403301, _1403303, _1403305, _1403307]))], (33594 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403299), 33592 ^ [_1403299, _1403301, _1403303, _1403305, _1403307]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403301, tc_fun(_1403299, tc_HOL_Obool)), _1403303), _1403305))))]], 33597 ^ _778495 : [(33598 ^ _778495) ^ [_1403521] : [hBOOL(hAPP(hAPP(c_member(_1403301), _1403521), _1403303)), 33601 ^ _778495 : [(33602 ^ _778495) ^ [_1403618] : [hBOOL(hAPP(hAPP(c_member(_1403299), _1403618), hAPP(_1403305, _1403521))), -(hBOOL(hAPP(_1403307, _1403618)))]]]]], (10939 ^ _778495) ^ [_966793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966793)), _966793))], (13472 ^ _778495) ^ [_1017635, _1017637] : [13473 ^ _778495 : [(13476 ^ _778495) ^ [] : [_1017637 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13474 ^ _778495) ^ [] : [_1017635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017635), _1017637) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32470 ^ _778495) ^ [_1376619, _1376621] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1376619, _1376621)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1376621), _1376619)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (27991 ^ _778495) ^ [_1277851, _1277853, _1277855] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277851, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277851, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1277851, tc_HOL_Obool), _1277853)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1277851, tc_HOL_Obool), _1277855))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1277851, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1277851, tc_HOL_Obool), tc_HOL_Obool)), _1277853), _1277855)))))], (42523 ^ _778495) ^ [_1625871, _1625873] : [hBOOL(hAPP(c_List_Odistinct(_1625871), _1625873)), 42526 ^ _778495 : [(42527 ^ _778495) ^ [_1626003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1626003), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625871)), _1625873))), 42530 ^ _778495 : [(42531 ^ _778495) ^ [_1626130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1626130), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625871)), _1625873))), -(_1626003 = _1626130), hAPP(hAPP(c_List_Onth(_1625871), _1625873), _1626003) = hAPP(hAPP(c_List_Onth(_1625871), _1625873), _1626130)]]]]], (34472 ^ _778495) ^ [_1422543, _1422545] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1422543), _1422545)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1422543)), hAPP(c_Nat_OSuc, _1422545)))], (50753 ^ _778495) ^ [_1806227, _1806229, _1806231, _1806233, _1806235] : [class_Rings_Ocomm__semiring__1(_1806227), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806227), _1806229), _1806231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1806233), _1806235)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806227), hAPP(hAPP(c_Power_Opower__class_Opower(_1806227), _1806229), _1806233)), hAPP(hAPP(c_Power_Opower__class_Opower(_1806227), _1806231), _1806235))))], (2474 ^ _778495) ^ [_814915, _814917] : [_814917 = _814915, -(c_Nitpick_Oone__frac(_814917) = c_Nitpick_Oone__frac(_814915))], (23905 ^ _778495) ^ [_1206356, _1206358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206356), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23908 ^ _778495 : [(23911 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206356), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206358, _1206356))))], (23909 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206358, _1206356)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (33531 ^ _778495) ^ [_1401864, _1401866, _1401868, _1401870, _1401872] : [_1401864 = c_Orderings_Obot__class_Obot(tc_fun(_1401866, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401866, tc_fun(_1401868, tc_HOL_Obool)), _1401864), hAPP(hAPP(c_COMBB(tc_fun(_1401868, tc_HOL_Obool), tc_fun(_1401868, tc_HOL_Obool), _1401866), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401868, tc_HOL_Obool)), _1401870)), _1401872)) = c_Orderings_Otop__class_Otop(tc_fun(_1401868, tc_HOL_Obool)))], (34322 ^ _778495) ^ [_1418798, _1418800, _1418802, _1418804, _1418806, _1418808] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418798, tc_fun(_1418800, tc_HOL_Obool)), _1418802), hAPP(hAPP(c_COMBB(_1418804, tc_fun(_1418800, tc_HOL_Obool), _1418798), _1418806), _1418808)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418804, tc_fun(_1418800, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1418798, _1418804, _1418808), _1418802)), _1418806))], (8982 ^ _778495) ^ [_929879, _929881, _929883] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929879, tc_HOL_Obool)), _929881), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929879, tc_HOL_Obool)), _929881), _929883)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929879, tc_HOL_Obool)), _929881), _929883))], (15877 ^ _778495) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24557 ^ _778495) ^ [_1218205, _1218207, _1218209, _1218211] : [class_Rings_Ocomm__semiring__1(_1218205), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1218205), hAPP(hAPP(c_Power_Opower__class_Opower(_1218205), _1218207), _1218209)), _1218211) = hAPP(hAPP(c_Power_Opower__class_Opower(_1218205), _1218207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218209), _1218211)))], (15649 ^ _778495) ^ [_1057080, _1057082] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1057080), _1057082)))), -(_1057082 = c_Orderings_Obot__class_Obot(tc_fun(_1057080, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057080), _1057082))], (18080 ^ _778495) ^ [_1102803] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1102803), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20906 ^ _778495) ^ [_1152901, _1152903] : [class_Rings_Osemiring__1(_1152901), -(hBOOL(hAPP(hAPP(c_member(_1152901), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1152901), _1152903)), c_Nat_Osemiring__1__class_ONats(_1152901))))], (12222 ^ _778495) ^ [_992804, _992806, _992808, _992810, _992812, _992814] : [class_Groups_Oab__semigroup__mult(_992804), hBOOL(hAPP(c_Finite__Set_Ofinite(_992806), _992808)), -(hBOOL(hAPP(hAPP(c_member(_992806), _992810), _992808))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_992804, _992806, c_Groups_Otimes__class_Otimes(_992804)), _992812), _992814), hAPP(hAPP(c_Set_Oinsert(_992806), _992810), _992808)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992804), hAPP(_992812, _992810)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_992804, _992806, c_Groups_Otimes__class_Otimes(_992804)), _992812), _992814), _992808)))], (40932 ^ _778495) ^ [_1581988, _1581990, _1581992] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1581988, _1581988, _1581988), _1581990), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581988, _1581988), tc_HOL_Obool), _1581992), _1581990)) = hAPP(hAPP(c_Relation_Orel__comp(_1581988, _1581988, _1581988), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581988, _1581988), tc_HOL_Obool), _1581992), _1581990)), _1581990))], (5825 ^ _778495) ^ [_871021, _871023, _871025, _871027, _871029, _871031] : [c_Finite__Set_Ofolding__image__simple(_871021, _871023, _871025, _871027, _871029, _871031), -(hAPP(_871031, c_Orderings_Obot__class_Obot(tc_fun(_871023, tc_HOL_Obool))) = _871027)], (11125 ^ _778495) ^ [_969955, _969957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969955)), _969957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969955), _969957)))], (52291 ^ _778495) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (13334 ^ _778495) ^ [_1015663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015663), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50284 ^ _778495) ^ [_1795273, _1795275] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795273), _1795275)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1795273, 50287 ^ [_1795273, _1795275], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1795273), _1795275)), _1795275))], (24787 ^ _778495) ^ [_1222122, _1222124] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1222122, _1222124) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1222122 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1222124), 24790 ^ [_1222122, _1222124]))], (11700 ^ _778495) ^ [_981580, _981582, _981584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981582), _981584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981580), _981582)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981580), _981584))))], (21038 ^ _778495) ^ [_1155354, _1155356] : [class_Groups_Oordered__ab__group__add__abs(_1155354), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155354), _1155356), hAPP(c_Groups_Oabs__class_Oabs(_1155354), _1155356))))], (32439 ^ _778495) ^ [_1376088, _1376090, _1376092, _1376094, _1376096, _1376098, _1376100] : [32441 ^ _778495 : [(32444 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1376096, 32440 ^ [_1376088, _1376090, _1376092, _1376094, _1376096, _1376098, _1376100]), _1376098), _1376100))], (32442 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376088), 32440 ^ [_1376088, _1376090, _1376092, _1376094, _1376096, _1376098, _1376100]), _1376094)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1376088, tc_fun(_1376090, tc_fun(_1376092, tc_HOL_Obool))), _1376094), _1376096), _1376098), _1376100)))], (17610 ^ _778495) ^ [_1094253, _1094255, _1094257, _1094259, _1094261, _1094263] : [c_Nitpick_Opair__box_OPairBox(_1094253, _1094255, _1094257, _1094259) = c_Nitpick_Opair__box_OPairBox(_1094253, _1094255, _1094261, _1094263), 17613 ^ _778495 : [(17616 ^ _778495) ^ [] : [-(_1094259 = _1094263)], (17614 ^ _778495) ^ [] : [-(_1094257 = _1094261)]]], (43606 ^ _778495) ^ [_1650258, _1650260, _1650262, _1650264] : [-(hAPP(hAPP(c_List_Odrop(_1650258), _1650260), hAPP(hAPP(c_List_Olist_OCons(_1650258), _1650262), _1650264)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1650258), hAPP(hAPP(c_List_Olist_OCons(_1650258), _1650262), _1650264), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1650258), tc_List_Olist(_1650258)), c_List_Odrop(_1650258)), _1650264), _1650260))], (40381 ^ _778495) ^ [_1568488, _1568490, _1568492, _1568494, _1568496] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568488, _1568488)), hAPP(hAPP(c_Product__Type_OPair(_1568488, _1568488), _1568490), _1568492)), _1568494)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568488, _1568488)), hAPP(hAPP(c_Product__Type_OPair(_1568488, _1568488), _1568492), _1568496)), c_Transitive__Closure_Ortrancl(_1568488, _1568494))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568488, _1568488)), hAPP(hAPP(c_Product__Type_OPair(_1568488, _1568488), _1568490), _1568496)), c_Transitive__Closure_Ortrancl(_1568488, _1568494))))], (14683 ^ _778495) ^ [_1038951, _1038953] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1038951), _1038953) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1038951 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1038953 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18092 ^ _778495) ^ [_1103014, _1103016, _1103018] : [class_Int_Onumber(_1103014), class_Orderings_Olinorder(_1103014), 18099 ^ _778495 : [(18106 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103014), hAPP(c_Int_Onumber__class_Onumber__of(_1103014), _1103018)), hAPP(c_Int_Onumber__class_Onumber__of(_1103014), _1103016)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103014), hAPP(c_Int_Onumber__class_Onumber__of(_1103014), _1103016)), hAPP(c_Int_Onumber__class_Onumber__of(_1103014), _1103018))))], (18100 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103014), hAPP(c_Int_Onumber__class_Onumber__of(_1103014), _1103016)), hAPP(c_Int_Onumber__class_Onumber__of(_1103014), _1103018))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103014), hAPP(c_Int_Onumber__class_Onumber__of(_1103014), _1103018)), hAPP(c_Int_Onumber__class_Onumber__of(_1103014), _1103016)))]]], (18148 ^ _778495) ^ [_1104239, _1104241, _1104243, _1104245] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104239), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1104239), _1104241), _1104243)), hAPP(c_Int_Onumber__class_Onumber__of(_1104239), _1104245)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1104239), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104239), _1104241), hAPP(c_Int_Onumber__class_Onumber__of(_1104239), _1104245))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104239), _1104243), hAPP(c_Int_Onumber__class_Onumber__of(_1104239), _1104245)))), class_Int_Onumber(_1104239), class_Rings_Oring(_1104239)], (2646 ^ _778495) ^ [_817587, _817589, _817591, _817593, _817595, _817597, _817599, _817601] : [-(c_Recdef_Osame__fst(_817601, _817597, _817593, _817589) = c_Recdef_Osame__fst(_817599, _817595, _817591, _817587)), _817601 = _817599, _817597 = _817595, _817593 = _817591, _817589 = _817587], (20218 ^ _778495) ^ [_1141723] : [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), _1141723))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1141723)))], (24806 ^ _778495) ^ [_1222432, _1222434] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1222432), _1222434))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1222432, _1222434) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1222432), _1222434), _1222434))], (45770 ^ _778495) ^ [_1698006, _1698008] : [-(c_List_OremoveAll(_1698006, _1698008) = c_List_Ofilter(_1698006, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698006), c_fNot), hAPP(c_fequal, _1698008))))], (44943 ^ _778495) ^ [_1679403, _1679405, _1679407] : [hBOOL(hAPP(c_List_Olistsp(_1679403, _1679405), _1679407)), 44946 ^ _778495 : [(44947 ^ _778495) ^ [_1679492] : [hBOOL(hAPP(hAPP(c_member(_1679403), _1679492), hAPP(c_List_Oset(_1679403), _1679407))), -(hBOOL(hAPP(_1679405, _1679492)))]]], (15325 ^ _778495) ^ [_1050696, _1050698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1050696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1050698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050698), _1050696))))], (13643 ^ _778495) ^ [_1020592, _1020594, _1020596] : [class_Groups_Oordered__comm__monoid__add(_1020592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020592), c_Groups_Ozero__class_Ozero(_1020592)), _1020594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020592), c_Groups_Ozero__class_Ozero(_1020592)), _1020596)), 13654 ^ _778495 : [(13663 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020592), _1020594), _1020596) = c_Groups_Ozero__class_Ozero(_1020592)), _1020594 = c_Groups_Ozero__class_Ozero(_1020592), _1020596 = c_Groups_Ozero__class_Ozero(_1020592)], (13655 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020592), _1020594), _1020596) = c_Groups_Ozero__class_Ozero(_1020592), 13658 ^ _778495 : [(13661 ^ _778495) ^ [] : [-(_1020596 = c_Groups_Ozero__class_Ozero(_1020592))], (13659 ^ _778495) ^ [] : [-(_1020594 = c_Groups_Ozero__class_Ozero(_1020592))]]]]], (38655 ^ _778495) ^ [_1526923, _1526925, _1526927, _1526929] : [c_Wellfounded_Owf(_1526923, _1526925), c_Wellfounded_Owf(_1526927, _1526929), -(c_Wellfounded_Owf(tc_prod(_1526923, _1526927), c_Wellfounded_Olex__prod(_1526923, _1526927, _1526925, _1526929)))], (30221 ^ _778495) ^ [_1329011, _1329013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1329011)), -(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(_1329011), _1329013))), _1329011)))], (10681 ^ _778495) ^ [_962610, _962612] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962610), _962612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962612), _962610)))], (22846 ^ _778495) ^ [_1186865, _1186867] : [class_Int_Onumber__ring(_1186865), class_Rings_Olinordered__idom(_1186865), 22853 ^ _778495 : [(22860 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186865), hAPP(c_Int_Onumber__class_Onumber__of(_1186865), _1186867)), c_Groups_Ozero__class_Ozero(_1186865)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1186865), hAPP(c_Int_Onumber__class_Onumber__of(_1186865), _1186867)) = hAPP(c_Int_Onumber__class_Onumber__of(_1186865), _1186867))], (22854 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186865), hAPP(c_Int_Onumber__class_Onumber__of(_1186865), _1186867)), c_Groups_Ozero__class_Ozero(_1186865))), -(hAPP(c_Groups_Oabs__class_Oabs(_1186865), hAPP(c_Int_Onumber__class_Onumber__of(_1186865), _1186867)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1186865), hAPP(c_Int_Onumber__class_Onumber__of(_1186865), _1186867)))]]], (10757 ^ _778495) ^ [_963772, _963774, _963776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963772), _963774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963774), _963776)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963772)), _963776)))], (13484 ^ _778495) ^ [_1017819, _1017821, _1017823] : [class_Groups_Ocomm__monoid__mult(_1017819), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1017821, _1017819), _1017823), c_Orderings_Obot__class_Obot(tc_fun(_1017821, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1017819))], (19442 ^ _778495) ^ [_1127686, _1127688, _1127690] : [class_Orderings_Olinorder(_1127686), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127686), _1127688)), -(_1127688 = c_Orderings_Obot__class_Obot(tc_fun(_1127686, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1127686, hAPP(hAPP(c_Set_Oinsert(_1127686), _1127690), _1127688)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1127686), _1127690), c_Big__Operators_Olinorder__class_OMin(_1127686, _1127688)))], (40139 ^ _778495) ^ [_1561943, _1561945] : [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), _1561943), _1561945)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1561943), _1561945)))], (45478 ^ _778495) ^ [_1691031, _1691033, _1691035] : [hBOOL(hAPP(hAPP(c_member(_1691031), _1691033), hAPP(c_List_Oset(_1691031), _1691035))), -(c_List_Oremdups(_1691031, hAPP(hAPP(c_List_Olist_OCons(_1691031), _1691033), _1691035)) = c_List_Oremdups(_1691031, _1691035))], (14693 ^ _778495) ^ [_1039094, _1039096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1039094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1039096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039096), _1039094)), _1039096)))], (8160 ^ _778495) ^ [_912985] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_912985), c_Orderings_Obot__class_Obot(tc_fun(_912985, tc_HOL_Obool)))))], (6100 ^ _778495) ^ [_876374, _876376, _876378, _876380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876374, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_876374, tc_HOL_Obool)), _876376), _876378)), _876380)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876374, tc_HOL_Obool)), _876376), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876374, tc_HOL_Obool)), _876378), _876380))))], (22918 ^ _778495) ^ [_1188202] : [-(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)))), _1188202) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1188202), _1188202))], (41604 ^ _778495) ^ [_1601364, _1601366, _1601368] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601364), tc_List_Olist(_1601364))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601364), tc_List_Olist(_1601364)), _1601366), _1601366)), c_List_Olistrel(_1601364, c_Transitive__Closure_Ortrancl(_1601364, _1601368)))))], (25768 ^ _778495) ^ [_1238858, _1238860] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1238858), hAPP(c_Int_Onumber__class_Onumber__of(_1238858), _1238860)), 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(_1238858), hAPP(c_Int_Onumber__class_Onumber__of(_1238858), _1238860)), hAPP(c_Int_Onumber__class_Onumber__of(_1238858), _1238860))), class_Groups_Omonoid__mult(_1238858), class_Int_Onumber(_1238858)], (26662 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (45276 ^ _778495) ^ [_1686859, _1686861, _1686863, _1686865] : [hBOOL(hAPP(c_List_Odistinct(_1686859), _1686861)), hBOOL(hAPP(c_List_Odistinct(_1686863), _1686865)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1686859, _1686863)), c_Enum_Oproduct(_1686859, _1686863, _1686861, _1686865))))], (52211 ^ _778495) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (26926 ^ _778495) ^ [_1259600, _1259602, _1259604, _1259606, _1259608] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1259600, _1259602, _1259604), _1259606), hAPP(c_Nat_OSuc, _1259608)) = hAPP(hAPP(_1259604, _1259606), hAPP(hAPP(c_Power_Opower_Opower(_1259600, _1259602, _1259604), _1259606), _1259608)))], (51563 ^ _778495) ^ [_1820069, _1820071, _1820073] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820069), _1820071)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820069), _1820073)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820069), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1820071), _1820073))))], (12128 ^ _778495) ^ [_990645, _990647, _990649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990645), _990647)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990649), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990647), _990645))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990649), _990645)), hAPP(c_Nat_OSuc, _990647)))], (31845 ^ _778495) ^ [_1362145, _1362147, _1362149, _1362151, _1362153] : [hBOOL(hAPP(hAPP(c_member(_1362145), _1362147), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1362149, tc_fun(_1362145, tc_HOL_Obool)), _1362151), _1362153))), 31848 ^ _778495 : [(31849 ^ _778495) ^ [_1362269] : [hBOOL(hAPP(hAPP(c_member(_1362149), _1362269), _1362151)), -(hBOOL(hAPP(hAPP(c_member(_1362145), _1362147), hAPP(_1362153, _1362269))))]]], (36141 ^ _778495) ^ [_1457872, _1457874, _1457876, _1457878, _1457880, _1457882, _1457884] : [c_Equiv__Relations_Oequiv(_1457872, _1457874, _1457876), c_Equiv__Relations_Ocongruent(_1457872, tc_fun(_1457878, tc_HOL_Obool), _1457876, _1457880), hBOOL(hAPP(hAPP(c_member(tc_fun(_1457872, tc_HOL_Obool)), _1457882), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457872), _1457874), _1457876))), 36155 ^ _778495 : [(36158 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1457878, tc_HOL_Obool)), hAPP(_1457880, 36154 ^ [_1457872, _1457874, _1457876, _1457878, _1457880, _1457882, _1457884])), _1457884))], (36156 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457872), 36154 ^ [_1457872, _1457874, _1457876, _1457878, _1457880, _1457882, _1457884]), _1457874)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1457878, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1457872, tc_fun(_1457878, tc_HOL_Obool)), _1457882), _1457880)), _1457884)))], (15933 ^ _778495) ^ [_1062777, _1062779, _1062781, _1062783, _1062785] : [class_Groups_Ocomm__monoid__add(_1062777), class_Groups_Oordered__ab__semigroup__add(_1062777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062779), _1062781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1062779, tc_HOL_Obool)), _1062783), _1062781)), 15951 ^ _778495 : [(15954 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062777), c_Groups_Ozero__class_Ozero(_1062777)), hAPP(_1062785, 15950 ^ [_1062777, _1062779, _1062781, _1062783, _1062785])))], (15952 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062779), 15950 ^ [_1062777, _1062779, _1062781, _1062783, _1062785]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1062779, tc_HOL_Obool)), _1062781), _1062783))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062777), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1062779, _1062777), _1062785), _1062783)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1062779, _1062777), _1062785), _1062781))))], (27669 ^ _778495) ^ [_1272292, _1272294] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272292), _1272294)), 27672 ^ _778495 : [(27679 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272292), c_Orderings_Otop__class_Otop(tc_fun(_1272292, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1272292), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272292, tc_HOL_Obool)), _1272294))))], (27673 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272292), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272292, tc_HOL_Obool)), _1272294))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1272292), c_Orderings_Otop__class_Otop(tc_fun(_1272292, tc_HOL_Obool)))))]]], (12651 ^ _778495) ^ [_1002321, _1002323, _1002325, _1002327, _1002329] : [class_Rings_Oring(_1002321), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002323), _1002325)), hBOOL(hAPP(hAPP(c_member(_1002323), _1002327), _1002325)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1002323, _1002321), _1002329), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002323, tc_HOL_Obool)), _1002325), hAPP(hAPP(c_Set_Oinsert(_1002323), _1002327), c_Orderings_Obot__class_Obot(tc_fun(_1002323, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1002321), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1002323, _1002321), _1002329), _1002325)), hAPP(_1002329, _1002327)))], (30885 ^ _778495) ^ [_1342465, _1342467, _1342469, _1342471] : [class_Orderings_Olinorder(_1342465), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342465), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342465), _1342467), _1342469)), _1342471) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342465), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342465), _1342467), _1342471)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342465), _1342469), _1342471)))], (6764 ^ _778495) ^ [_889270, _889272, _889274, _889276] : [-(hBOOL(hAPP(hAPP(c_member(_889270), _889272), _889274))), -(hBOOL(hAPP(hAPP(c_member(_889270), _889272), _889276))), 6771 ^ _778495 : [(6778 ^ _778495) ^ [] : [_889274 = _889276, -(hAPP(hAPP(c_Set_Oinsert(_889270), _889272), _889274) = hAPP(hAPP(c_Set_Oinsert(_889270), _889272), _889276))], (6772 ^ _778495) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_889270), _889272), _889274) = hAPP(hAPP(c_Set_Oinsert(_889270), _889272), _889276), -(_889274 = _889276)]]], (28769 ^ _778495) ^ [_1300332, _1300334, _1300336] : [class_Int_Onumber__ring(_1300332), 28772 ^ _778495 : [(28779 ^ _778495) ^ [] : [-(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), _1300334)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1300332), _1300336), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1300334))) = c_Groups_Oone__class_Oone(_1300332))], (28773 ^ _778495) ^ [] : [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), _1300334))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1300332), _1300336), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1300334))) = hAPP(hAPP(c_HOL_OLet(_1300332, _1300332), hAPP(hAPP(c_Power_Opower__class_Opower(_1300332), _1300336), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1300334))), hAPP(hAPP(c_COMBS(_1300332, _1300332, _1300332), hAPP(hAPP(c_COMBB(_1300332, tc_fun(_1300332, _1300332), _1300332), c_Groups_Otimes__class_Otimes(_1300332)), hAPP(c_Groups_Otimes__class_Otimes(_1300332), _1300336))), c_COMBI(_1300332))))]]], (28207 ^ _778495) ^ [_1281963, _1281965, _1281967, _1281969, _1281971] : [class_Lattices_Olattice(_1281963), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1281965, _1281963)), _1281967), _1281969), _1281971) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1281963), hAPP(_1281967, _1281971)), hAPP(_1281969, _1281971)))], (47278 ^ _778495) ^ [_1729838, _1729840, _1729842] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729838, _1729838)), hAPP(hAPP(c_Product__Type_OPair(_1729838, _1729838), _1729840), _1729842)), c_List_Omeasures(_1729838, c_List_Olist_ONil(tc_fun(_1729838, tc_Nat_Onat)))))], (5078 ^ _778495) ^ [_856039, _856041, _856043, _856045] : [-(c_Transitive__Closure_Otrancl(_856045, _856041) = c_Transitive__Closure_Otrancl(_856043, _856039)), _856045 = _856043, _856041 = _856039], (33948 ^ _778495) ^ [_1410611, _1410613, _1410615] : [class_Orderings_Oord(_1410611), 33951 ^ _778495 : [(33958 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410611), _1410613), _1410615)), -(hBOOL(hAPP(hAPP(c_member(_1410611), _1410613), hAPP(c_SetInterval_Oord__class_OatMost(_1410611), _1410615))))], (33952 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1410611), _1410613), hAPP(c_SetInterval_Oord__class_OatMost(_1410611), _1410615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410611), _1410613), _1410615)))]]], (26596 ^ _778495) ^ [_1254325] : [class_Power_Opower(_1254325), -(c_Power_Opower__class_Opower(_1254325) = c_Power_Opower_Opower(_1254325, c_Groups_Oone__class_Oone(_1254325), c_Groups_Otimes__class_Otimes(_1254325)))], (12160 ^ _778495) ^ [_991187, _991189, _991191, _991193] : [class_Rings_Ocomm__semiring__1(_991187), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991187), _991189), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991187), _991191), _991193)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991187), _991191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991187), _991189), _991193)))], (37374 ^ _778495) ^ [_1485669, _1485671, _1485673, _1485675] : [37375 ^ _778495 : [(37378 ^ _778495) ^ [] : [_1485675 = c_Orderings_Obot__class_Obot(tc_fun(_1485671, tc_HOL_Obool))], (37376 ^ _778495) ^ [] : [_1485673 = c_Orderings_Obot__class_Obot(tc_fun(_1485669, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1485669, _1485671), _1485673), hAPP(c_COMBK(tc_fun(_1485671, tc_HOL_Obool), _1485669), _1485675)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1485669, _1485671), tc_HOL_Obool)))], (31998 ^ _778495) ^ [_1366882, _1366884, _1366886, _1366888, _1366890] : [-(_1366882 = c_Orderings_Obot__class_Obot(tc_fun(_1366884, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366886, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1366884, tc_fun(_1366886, tc_HOL_Obool)), _1366882), _1366888)), _1366890) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1366884, tc_fun(_1366886, tc_HOL_Obool)), _1366882), hAPP(hAPP(c_COMBC(_1366884, tc_fun(_1366886, tc_HOL_Obool), tc_fun(_1366886, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366886, tc_HOL_Obool), tc_fun(tc_fun(_1366886, tc_HOL_Obool), tc_fun(_1366886, tc_HOL_Obool)), _1366884), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366886, tc_HOL_Obool))), _1366888)), _1366890)))], (1768 ^ _778495) ^ [_803623, _803625] : [-(class_Nat_Osemiring__char__0(_803623)), _803625 = _803623, class_Nat_Osemiring__char__0(_803625)], (21428 ^ _778495) ^ [_1162660] : [class_Int_Onumber__ring(_1162660), -(hAPP(c_Int_Onumber__class_Onumber__of(_1162660), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1162660))], (9138 ^ _778495) ^ [_932869, _932871, _932873, _932875] : [class_Lattices_Osemilattice__inf(_932869), 9141 ^ _778495 : [(9150 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932869), _932871), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932869), _932873), _932875)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932869), _932871), _932873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932869), _932871), _932875))], (9142 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932869), _932871), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932869), _932873), _932875))), 9145 ^ _778495 : [(9148 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932869), _932871), _932875)))], (9146 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932869), _932871), _932873)))]]]]], (50307 ^ _778495) ^ [_1795779, _1795781, _1795783] : [c_Equiv__Relations_Oequivp(_1795779, _1795781), 50310 ^ _778495 : [(50311 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1795783, 50318 ^ [_1795779, _1795781, _1795783]))), 50312 ^ _778495 : [(50313 ^ _778495) ^ [_1795901] : [hBOOL(hAPP(hAPP(c_member(_1795779), _1795901), c_Quotient_ORespects(_1795779, _1795781))), hBOOL(hAPP(_1795783, _1795901))]]], (50322 ^ _778495) ^ [] : [50323 ^ _778495 : [(50324 ^ _778495) ^ [_1796068] : [hBOOL(hAPP(_1795783, _1796068))]], 50326 ^ _778495 : [(50329 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1795783, 50325 ^ [_1795779, _1795781, _1795783])))], (50327 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795779), 50325 ^ [_1795779, _1795781, _1795783]), c_Quotient_ORespects(_1795779, _1795781))))]]]]], (38606 ^ _778495) ^ [_1525897, _1525899, _1525901, _1525903] : [38607 ^ _778495 : [(38608 ^ _778495) ^ [_1525951] : [hBOOL(hAPP(hAPP(_1525901, _1525951), _1525903))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1525897, _1525899, _1525901), _1525903)))], (8600 ^ _778495) ^ [_922108, _922110, _922112, _922114, _922116] : [c_Finite__Set_Ofolding__one__idem(_922108, _922110, _922112), hBOOL(hAPP(c_Finite__Set_Ofinite(_922108), _922114)), hBOOL(hAPP(hAPP(c_member(_922108), _922116), _922114)), -(hAPP(hAPP(_922110, _922116), hAPP(_922112, _922114)) = hAPP(_922112, _922114))], (50298 ^ _778495) ^ [_1795511, _1795513, _1795515, _1795517, _1795519] : [50300 ^ _778495 : [(50303 ^ _778495) ^ [] : [c_Relation_Orefl__on(_1795515, hAPP(_1795517, 50299 ^ [_1795511, _1795513, _1795515, _1795517, _1795519]), hAPP(_1795519, 50299 ^ [_1795511, _1795513, _1795515, _1795517, _1795519]))], (50301 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795511), 50299 ^ [_1795511, _1795513, _1795515, _1795517, _1795519]), _1795513)))]], -(c_Relation_Orefl__on(_1795515, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1795511, tc_fun(_1795515, tc_HOL_Obool)), _1795513), _1795517), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1795511, tc_fun(tc_prod(_1795515, _1795515), tc_HOL_Obool)), _1795513), _1795519)))], (52195 ^ _778495) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (49618 ^ _778495) ^ [_1781006, _1781008, _1781010, _1781012, _1781014] : [c_Fun_Oinj__on(_1781006, _1781008, _1781010, _1781012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1781006, tc_HOL_Obool)), _1781014), _1781012)), -(hAPP(c_Set_Oimage(_1781008, _1781006, c_Hilbert__Choice_Oinv__into(_1781006, _1781008, _1781012, _1781010)), hAPP(c_Set_Oimage(_1781006, _1781008, _1781010), _1781014)) = _1781014)], (4110 ^ _778495) ^ [_840815, _840817, _840819, _840821, _840823, _840825] : [-(c_List_Osplice(_840825, _840821, _840817) = c_List_Osplice(_840823, _840819, _840815)), _840825 = _840823, _840821 = _840819, _840817 = _840815], (38802 ^ _778495) ^ [_1529530, _1529532] : [hAPP(hAPP(c_Relation_Orel__comp(_1529530, _1529530, _1529530), _1529532), _1529532) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529530, _1529530), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1529530, _1529532))], (30559 ^ _778495) ^ [_1336367, _1336369, _1336371, _1336373, _1336375, _1336377] : [class_Groups_Oordered__ab__group__add(_1336367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336369), _1336371)), 30569 ^ _778495 : [(30572 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336367), c_Groups_Ozero__class_Ozero(_1336367)), hAPP(_1336373, 30568 ^ [_1336367, _1336369, _1336371, _1336373, _1336375, _1336377])))], (30570 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1336369), 30568 ^ [_1336367, _1336369, _1336371, _1336373, _1336375, _1336377]), _1336371)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1336369, _1336367), _1336373), _1336371) = _1336375, hBOOL(hAPP(hAPP(c_member(_1336369), _1336377), _1336371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336367), hAPP(_1336373, _1336377)), _1336375)))], (5961 ^ _778495) ^ [_873636, _873638, _873640, _873642] : [class_Orderings_Oord(_873636), 5964 ^ _778495 : [(5971 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873636), hAPP(_873640, 5972 ^ [_873636, _873638, _873640, _873642])), hAPP(_873642, 5972 ^ [_873636, _873638, _873640, _873642]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873638, _873636)), _873640), _873642)))], (5965 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873638, _873636)), _873640), _873642)), 5968 ^ _778495 : [(5969 ^ _778495) ^ [_873793] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873636), hAPP(_873640, _873793)), hAPP(_873642, _873793))))]]]]], (11438 ^ _778495) ^ [_976418, _976420, _976422, _976424, _976426] : [class_Rings_Osemiring(_976418), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976418), _976420), _976422)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976418), _976424), _976422)), _976426)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976418), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976418), _976420), _976424)), _976422)), _976426))], (52349 ^ _778495) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (25818 ^ _778495) ^ [_1239725, _1239727, _1239729] : [class_Rings_Olinordered__semidom(_1239725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239725), hAPP(hAPP(c_Power_Opower__class_Opower(_1239725), _1239727), 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(_1239725), _1239729), 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(_1239725), c_Groups_Ozero__class_Ozero(_1239725)), _1239729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239725), _1239727), _1239729)))], (33248 ^ _778495) ^ [_1392891, _1392893, _1392895, _1392897, _1392899, _1392901] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392891, tc_fun(_1392893, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392895, tc_fun(_1392891, tc_HOL_Obool)), _1392897), _1392899)), _1392901) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392895, tc_fun(_1392893, tc_HOL_Obool)), _1392897), hAPP(hAPP(c_COMBC(_1392895, tc_fun(_1392891, tc_fun(_1392893, tc_HOL_Obool)), tc_fun(_1392893, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392891, tc_HOL_Obool), tc_fun(tc_fun(_1392891, tc_fun(_1392893, tc_HOL_Obool)), tc_fun(_1392893, tc_HOL_Obool)), _1392895), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392891, tc_fun(_1392893, tc_HOL_Obool))), _1392899)), _1392901)))], (28231 ^ _778495) ^ [_1282614, _1282616] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1282614, tc_HOL_Obool)), _1282616)), -(hBOOL(hAPP(hAPP(c_member(_1282614), _1282616), c_Orderings_Obot__class_Obot(tc_fun(_1282614, tc_HOL_Obool)))))], (40268 ^ _778495) ^ [_1565012, _1565014, _1565016, _1565018, _1565020] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565012, _1565012)), hAPP(hAPP(c_Product__Type_OPair(_1565012, _1565012), _1565014), _1565016)), _1565018)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565012, _1565012)), hAPP(hAPP(c_Product__Type_OPair(_1565012, _1565012), _1565016), _1565020)), c_Transitive__Closure_Otrancl(_1565012, _1565018))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565012, _1565012)), hAPP(hAPP(c_Product__Type_OPair(_1565012, _1565012), _1565014), _1565020)), c_Transitive__Closure_Otrancl(_1565012, _1565018))))], (11662 ^ _778495) ^ [_980797, _980799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_980797), c_Complete__Lattice_OSup__class_OSup(tc_fun(_980797, tc_HOL_Obool), _980799))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_980797, tc_HOL_Obool)), _980799)))], (38419 ^ _778495) ^ [_1518592, _1518594, _1518596, _1518598, _1518600] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1518592, _1518594, _1518596), _1518598), _1518600) = hAPP(c_Set_OCollect(tc_prod(_1518592, _1518596)), hAPP(c_Product__Type_Oprod_Oprod__case(_1518592, _1518596, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1518596, tc_fun(_1518594, tc_HOL_Obool)), tc_fun(_1518596, tc_HOL_Obool), _1518592), hAPP(c_COMBB(tc_fun(_1518594, tc_HOL_Obool), tc_HOL_Obool, _1518596), c_HOL_OEx(_1518594))), hAPP(hAPP(c_COMBC(_1518592, tc_fun(_1518596, tc_fun(_1518594, tc_HOL_Obool)), tc_fun(_1518596, tc_fun(_1518594, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1518594, tc_HOL_Obool), tc_fun(_1518594, tc_HOL_Obool)), tc_fun(tc_fun(_1518596, tc_fun(_1518594, tc_HOL_Obool)), tc_fun(_1518596, tc_fun(_1518594, tc_HOL_Obool))), _1518592), c_COMBB(tc_fun(_1518594, tc_HOL_Obool), tc_fun(_1518594, tc_HOL_Obool), _1518596)), hAPP(hAPP(c_COMBB(tc_fun(_1518594, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1518594, tc_HOL_Obool), tc_fun(_1518594, tc_HOL_Obool)), _1518592), c_COMBS(_1518594, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518594, tc_HOL_Obool), tc_fun(_1518594, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1518592), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518594), c_fconj)), hAPP(hAPP(c_COMBC(_1518592, tc_fun(tc_prod(_1518592, _1518594), tc_HOL_Obool), tc_fun(_1518594, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518594, tc_fun(tc_fun(tc_prod(_1518592, _1518594), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1518592, _1518594), tc_HOL_Obool), tc_fun(_1518594, tc_HOL_Obool)), _1518592), c_COMBC(_1518594, tc_fun(tc_prod(_1518592, _1518594), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518594, tc_prod(_1518592, _1518594)), tc_fun(_1518594, tc_fun(tc_fun(tc_prod(_1518592, _1518594), tc_HOL_Obool), tc_HOL_Obool)), _1518592), hAPP(c_COMBB(tc_prod(_1518592, _1518594), tc_fun(tc_fun(tc_prod(_1518592, _1518594), tc_HOL_Obool), tc_HOL_Obool), _1518594), c_member(tc_prod(_1518592, _1518594)))), c_Product__Type_OPair(_1518592, _1518594)))), _1518598))))), hAPP(hAPP(c_COMBC(_1518596, tc_fun(tc_prod(_1518594, _1518596), tc_HOL_Obool), tc_fun(_1518594, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518594, tc_fun(tc_fun(tc_prod(_1518594, _1518596), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1518594, _1518596), tc_HOL_Obool), tc_fun(_1518594, tc_HOL_Obool)), _1518596), c_COMBC(_1518594, tc_fun(tc_prod(_1518594, _1518596), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518594, tc_prod(_1518594, _1518596)), tc_fun(_1518594, tc_fun(tc_fun(tc_prod(_1518594, _1518596), tc_HOL_Obool), tc_HOL_Obool)), _1518596), hAPP(c_COMBB(tc_prod(_1518594, _1518596), tc_fun(tc_fun(tc_prod(_1518594, _1518596), tc_HOL_Obool), tc_HOL_Obool), _1518594), c_member(tc_prod(_1518594, _1518596)))), hAPP(c_COMBC(_1518594, _1518596, tc_prod(_1518594, _1518596)), c_Product__Type_OPair(_1518594, _1518596))))), _1518600))))))], (12631 ^ _778495) ^ [_1001851, _1001853, _1001855, _1001857, _1001859] : [class_Groups_Oab__group__add(_1001851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001853), _1001855)), 12638 ^ _778495 : [(12645 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001853), _1001857), _1001855))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1001853, _1001851), _1001859), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1001853, tc_HOL_Obool)), _1001855), hAPP(hAPP(c_Set_Oinsert(_1001853), _1001857), c_Orderings_Obot__class_Obot(tc_fun(_1001853, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1001853, _1001851), _1001859), _1001855))], (12639 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1001853), _1001857), _1001855)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1001853, _1001851), _1001859), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1001853, tc_HOL_Obool)), _1001855), hAPP(hAPP(c_Set_Oinsert(_1001853), _1001857), c_Orderings_Obot__class_Obot(tc_fun(_1001853, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1001851), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1001853, _1001851), _1001859), _1001855)), hAPP(_1001859, _1001857)))]]], (31075 ^ _778495) ^ [_1346270, _1346272, _1346274] : [class_Orderings_Olinorder(_1346270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346270), _1346272)), hBOOL(hAPP(hAPP(c_member(_1346270), _1346274), _1346272)), 31086 ^ _778495 : [(31093 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346270, tc_HOL_Obool)), _1346272), hAPP(hAPP(c_Set_Oinsert(_1346270), _1346274), c_Orderings_Obot__class_Obot(tc_fun(_1346270, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1346270, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1346270, _1346272) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346270), _1346274), c_Big__Operators_Olinorder__class_OMax(_1346270, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346270, tc_HOL_Obool)), _1346272), hAPP(hAPP(c_Set_Oinsert(_1346270), _1346274), c_Orderings_Obot__class_Obot(tc_fun(_1346270, tc_HOL_Obool)))))))], (31087 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346270, tc_HOL_Obool)), _1346272), hAPP(hAPP(c_Set_Oinsert(_1346270), _1346274), c_Orderings_Obot__class_Obot(tc_fun(_1346270, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1346270, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1346270, _1346272) = _1346274)]]], (37777 ^ _778495) ^ [_1497340, _1497342, _1497344] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497340), hAPP(c_Set_OCollect(_1497340), hAPP(hAPP(c_COMBS(_1497340, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497340), c_fdisj), _1497342)), _1497344)))), 37780 ^ _778495 : [(37783 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1497340), hAPP(c_Set_OCollect(_1497340), _1497344))))], (37781 ^ _778495) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1497340), hAPP(c_Set_OCollect(_1497340), _1497342))))]]], (14195 ^ _778495) ^ [_1030618, _1030620, _1030622] : [class_Rings_Olinordered__semiring__strict(_1030618), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), c_Groups_Ozero__class_Ozero(_1030618)), _1030620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), _1030622), c_Groups_Ozero__class_Ozero(_1030618))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030618), _1030620), _1030622)), c_Groups_Ozero__class_Ozero(_1030618))))], (21014 ^ _778495) ^ [_1154943, _1154945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1154943)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1154945)), _1154943) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1154945), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1154943), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (7582 ^ _778495) ^ [_903932, _903934, _903936, _903938] : [class_Orderings_Oord(_903932), _903934 = _903936, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903932), _903936), _903938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903932), _903934), _903938)))], (12442 ^ _778495) ^ [_997892, _997894, _997896] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_997892, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_997892, tc_HOL_Obool), _997894)), _997896) = c_Orderings_Obot__class_Obot(tc_fun(_997892, tc_HOL_Obool)), 12445 ^ _778495 : [(12446 ^ _778495) ^ [_998027] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_997892, tc_HOL_Obool)), _998027), _997894)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_997892, tc_HOL_Obool)), _998027), _997896) = c_Orderings_Obot__class_Obot(tc_fun(_997892, tc_HOL_Obool)))]]], (45400 ^ _778495) ^ [_1689652, _1689654] : [-(hAPP(c_List_Oset(_1689652), c_List_Oremdups(_1689652, _1689654)) = hAPP(c_List_Oset(_1689652), _1689654))], (42463 ^ _778495) ^ [_1624683, _1624685, _1624687, _1624689] : [hBOOL(hAPP(c_List_Odistinct(_1624683), _1624685)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1624683, _1624687)), hAPP(hAPP(c_List_Ozip(_1624683, _1624687), _1624685), _1624689))))], (5488 ^ _778495) ^ [_862496, _862498] : [_862498 = _862496, -(c_Rings_Odvd__class_Odvd(_862498) = c_Rings_Odvd__class_Odvd(_862496))], (7938 ^ _778495) ^ [_909360, _909362, _909364] : [class_Orderings_Opreorder(_909360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909360), _909362), _909364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909360), _909362), _909364)))], (9268 ^ _778495) ^ [_935364, _935366, _935368, _935370] : [hBOOL(hAPP(hAPP(c_member(_935364), _935366), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_935364, tc_HOL_Obool)), _935368), _935370))), 9271 ^ _778495 : [(9274 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_935364), _935366), _935370)))], (9272 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_935364), _935366), _935368)))]]], (5336 ^ _778495) ^ [_860096, _860098] : [_860098 = _860096, -(c_Groups_Oone__class_Oone(_860098) = c_Groups_Oone__class_Oone(_860096))], (5655 ^ _778495) ^ [_867751, _867753] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_867751, _867753, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867751), tc_HOL_Obool))))], (216 ^ _778495) ^ [_782087, _782089] : [-(class_Rings_Odivision__ring__inverse__zero(_782087)), _782089 = _782087, class_Rings_Odivision__ring__inverse__zero(_782089)], (36885 ^ _778495) ^ [_1473984, _1473986, _1473988, _1473990, _1473992] : [c_Typedef_Otype__definition(_1473984, _1473986, _1473988, _1473990, _1473992), -(hAPP(c_Set_Oimage(_1473984, _1473986, _1473988), c_Orderings_Otop__class_Otop(tc_fun(_1473984, tc_HOL_Obool))) = _1473992)], (39500 ^ _778495) ^ [_1547284, _1547286, _1547288, _1547290, _1547292, _1547294, _1547296, _1547298] : [class_Groups_Ocomm__monoid__mult(_1547284), c_Fun_Oinj__on(_1547286, _1547288, _1547290, _1547292), _1547294 = hAPP(c_Set_Oimage(_1547286, _1547288, _1547290), _1547292), _1547296 = hAPP(c_Fun_Ocomp(_1547288, _1547284, _1547286, _1547298), _1547290), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1547288, _1547284), _1547298), _1547294) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1547286, _1547284), _1547296), _1547292))], (40716 ^ _778495) ^ [_1576309, _1576311, _1576313, _1576315] : [-(hAPP(c_Relation_Oconverse(_1576309, _1576309), hAPP(hAPP(c_Relation_Oinv__image(_1576311, _1576309), _1576313), _1576315)) = hAPP(hAPP(c_Relation_Oinv__image(_1576311, _1576309), hAPP(c_Relation_Oconverse(_1576311, _1576311), _1576313)), _1576315))], (44241 ^ _778495) ^ [_1663362, _1663364, _1663366] : [-(_1663362 = c_List_Olist_ONil(_1663364)), -(c_List_Olast(_1663364, hAPP(hAPP(c_List_Oappend(_1663364), _1663366), _1663362)) = c_List_Olast(_1663364, _1663362))], (49431 ^ _778495) ^ [_1777711, _1777713, _1777715] : [c_Relation_Osym(_1777711, _1777713), c_Relation_Osym(_1777711, _1777715), -(c_Relation_Osym(_1777711, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1777711, _1777711), tc_HOL_Obool)), _1777713), _1777715)))], (51483 ^ _778495) ^ [_1818625, _1818627] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818625), _1818627)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1818627), _1818625))))], (11773 ^ _778495) ^ [_982978, _982980, _982982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _982980), _982982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982978), _982980)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982978), _982982))))], (34586 ^ _778495) ^ [_1425143, _1425145] : [class_Groups_Olinordered__ab__group__add(_1425143), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425143), _1425145)), -(_1425145 = c_Orderings_Obot__class_Obot(tc_fun(_1425143, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1425143), c_Big__Operators_Olinorder__class_OMax(_1425143, _1425145)) = c_Big__Operators_Olinorder__class_OMin(_1425143, hAPP(c_Set_Oimage(_1425143, _1425143, c_Groups_Ouminus__class_Ouminus(_1425143)), _1425145)))], (13402 ^ _778495) ^ [_1016619] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016619), _1016619) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11861 ^ _778495) ^ [_984794, _984796, _984798, _984800, _984802, _984804] : [class_Rings_Oring(_984794), 11864 ^ _778495 : [(11871 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984794), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_984794), _984796), _984802)), _984798)), _984800) = _984804, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984794), _984796), _984798)), _984800) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984794), _984802), _984798)), _984804))], (11865 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984794), _984796), _984798)), _984800) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984794), _984802), _984798)), _984804), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984794), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_984794), _984796), _984802)), _984798)), _984800) = _984804)]]], (31021 ^ _778495) ^ [_1345237, _1345239] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1345237), hAPP(c_Nat_OSuc, _1345239)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1345239), 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)), _1345239)), _1345237))], (44490 ^ _778495) ^ [_1669310, _1669312, _1669314, _1669316, _1669318] : [-(hAPP(hAPP(c_List_Odrop(_1669310), _1669312), hAPP(hAPP(c_List_Omap(_1669314, _1669310), _1669316), _1669318)) = hAPP(hAPP(c_List_Omap(_1669314, _1669310), _1669316), hAPP(hAPP(c_List_Odrop(_1669314), _1669312), _1669318)))], (40431 ^ _778495) ^ [_1569702, _1569704, _1569706, _1569708] : [40432 ^ _778495 : [(40435 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569702, _1569702)), _1569704), c_Transitive__Closure_Ortrancl(_1569702, _1569708)))], (40433 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569702, _1569702)), _1569704), c_Transitive__Closure_Ortrancl(_1569702, _1569706)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569702, _1569702)), _1569704), c_Transitive__Closure_Ortrancl(_1569702, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569702, _1569702), tc_HOL_Obool)), _1569706), _1569708)))))], (3452 ^ _778495) ^ [_830112, _830114, _830116, _830118, _830120, _830122] : [-(c_List_Osublist(_830122, _830118, _830114) = c_List_Osublist(_830120, _830116, _830112)), _830122 = _830120, _830118 = _830116, _830114 = _830112], (34100 ^ _778495) ^ [_1413752, _1413754, _1413756, _1413758] : [class_Orderings_Olinorder(_1413752), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413752, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1413752), _1413754)), c_SetInterval_Oord__class_OatLeastAtMost(_1413752, _1413756, _1413758)) = c_SetInterval_Oord__class_OatLeastAtMost(_1413752, _1413756, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1413752), _1413754), _1413758)))], (43977 ^ _778495) ^ [_1658230, _1658232, _1658234] : [class_Orderings_Olinorder(_1658230), -(c_Big__Operators_Olattice_OInf__fin(_1658230, c_Orderings_Oord__class_Omin(_1658230), hAPP(c_List_Oset(_1658230), hAPP(hAPP(c_List_Olist_OCons(_1658230), _1658232), _1658234))) = hAPP(c_List_Ofoldl(_1658230, _1658230, c_Orderings_Oord__class_Omin(_1658230), _1658232), _1658234))], (48060 ^ _778495) ^ [_1746659, _1746661, _1746663, _1746665, _1746667, _1746669, _1746671] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1746659, _1746661, _1746663, _1746665, _1746667, _1746669, _1746671) = c_New__DSequence_Oneg__decr__bind(_1746659, _1746661, hAPP(hAPP(hAPP(_1746663, _1746667), _1746669), _1746671), hAPP(hAPP(c_COMBC(_1746659, 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(_1746661)))), hAPP(hAPP(c_COMBC(_1746659, 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(_1746661))))), hAPP(hAPP(c_COMBC(_1746659, 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(_1746661)))))), _1746665), _1746667)), _1746669)), _1746671)))], (36404 ^ _778495) ^ [_1463528, _1463530, _1463532, _1463534, _1463536] : [c_Fun_Oinj__on(_1463528, _1463530, _1463532, c_Orderings_Otop__class_Otop(tc_fun(_1463528, tc_HOL_Obool))), 36407 ^ _778495 : [(36414 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1463528), _1463534), _1463536)), -(hBOOL(hAPP(hAPP(c_member(_1463530), hAPP(_1463532, _1463534)), hAPP(c_Set_Oimage(_1463528, _1463530, _1463532), _1463536))))], (36408 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1463530), hAPP(_1463532, _1463534)), hAPP(c_Set_Oimage(_1463528, _1463530, _1463532), _1463536))), -(hBOOL(hAPP(hAPP(c_member(_1463528), _1463534), _1463536)))]]], (13547 ^ _778495) ^ [_1018869, _1018871, _1018873, _1018875] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1018869, _1018871)), c_Sum__Type_OPlus(_1018869, _1018871, _1018873, _1018875)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018869), _1018873)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018871), _1018875))], (21478 ^ _778495) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (27127 ^ _778495) ^ [_1263022] : [class_Rings_Oring__1(_1263022), -(hAPP(c_Int_Oring__1__class_Oof__int(_1263022), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1263022))], (8514 ^ _778495) ^ [_920601, _920603, _920605, _920607, _920609] : [class_Groups_Oab__semigroup__mult(_920601), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_920601, _920601, c_Groups_Otimes__class_Otimes(_920601), _920603, _920605), _920607)), hBOOL(hAPP(hAPP(c_member(_920601), _920609), _920605)), -(hBOOL(hAPP(hAPP(c_member(_920601), _920603), _920605))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_920601, _920601, c_Groups_Otimes__class_Otimes(_920601), _920609, hAPP(hAPP(c_Set_Oinsert(_920601), _920603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920601, tc_HOL_Obool)), _920605), hAPP(hAPP(c_Set_Oinsert(_920601), _920609), c_Orderings_Obot__class_Obot(tc_fun(_920601, tc_HOL_Obool)))))), _920607)))], (48114 ^ _778495) ^ [_1748296, _1748298, _1748300, _1748302, _1748304] : [-(c_Predicate_Oconversep(_1748296, _1748298, c_Predicate_Opred__comp(_1748296, _1748300, _1748298, _1748302, _1748304)) = c_Predicate_Opred__comp(_1748298, _1748300, _1748296, c_Predicate_Oconversep(_1748300, _1748298, _1748304), c_Predicate_Oconversep(_1748296, _1748300, _1748302)))], (4178 ^ _778495) ^ [_841831, _841833, _841835, _841837] : [-(c_List_Olast(_841837, _841833) = c_List_Olast(_841835, _841831)), _841837 = _841835, _841833 = _841831], (38485 ^ _778495) ^ [_1520999, _1521001, _1521003] : [-(hAPP(c_Relation_ORange(_1520999, _1521001), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1520999, _1521001), tc_HOL_Obool), _1521003)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1520999, _1521001), tc_HOL_Obool), tc_fun(_1521001, tc_HOL_Obool)), _1521003), c_Relation_ORange(_1520999, _1521001)))], (24633 ^ _778495) ^ [_1219555] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1219555), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1219555)], (29567 ^ _778495) ^ [_1316578, _1316580] : [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), _1316578), _1316580))), 29570 ^ _778495 : [(29577 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1316580), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 29580 ^ _778495 : [(29589 ^ _778495) ^ [] : [-(c_Nitpick_Onorm__frac(_1316578, _1316580) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1316578), _1316580)), 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), _1316578))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1316580)))), -(_1316578 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1316580 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29581 ^ _778495) ^ [] : [29582 ^ _778495 : [(29585 ^ _778495) ^ [] : [_1316580 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (29583 ^ _778495) ^ [] : [_1316578 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1316578, _1316580) = 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)))]]], (29571 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1316580), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1316578, _1316580) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1316578), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1316580)))]]], (14757 ^ _778495) ^ [_1040189, _1040191, _1040193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040189), _1040191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040189), _1040193)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040191), _1040193))))], (26016 ^ _778495) ^ [_1243672, _1243674, _1243676] : [class_Rings_Olinordered__semidom(_1243672), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243672), c_Groups_Oone__class_Oone(_1243672)), _1243674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1243676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243672), c_Groups_Oone__class_Oone(_1243672)), hAPP(hAPP(c_Power_Opower__class_Opower(_1243672), _1243674), _1243676))))], (45450 ^ _778495) ^ [_1690556, _1690558, _1690560, _1690562] : [-(_1690556 = _1690558), -(hAPP(c_List_OremoveAll(_1690560, _1690556), hAPP(hAPP(c_List_Olist_OCons(_1690560), _1690558), _1690562)) = hAPP(hAPP(c_List_Olist_OCons(_1690560), _1690558), hAPP(c_List_OremoveAll(_1690560, _1690556), _1690562)))], (12995 ^ _778495) ^ [_1010333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1010333), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (38152 ^ _778495) ^ [_1508538] : [-(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)))), _1508538)) = 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), _1508538), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (44612 ^ _778495) ^ [_1672112, _1672114, _1672116, _1672118, _1672120] : [class_Groups_Ocomm__monoid__add(_1672112), hBOOL(hAPP(hAPP(c_member(_1672114), _1672116), hAPP(c_List_Oset(_1672114), _1672118))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672112), hAPP(hAPP(c_List_Omap(_1672114, _1672112), _1672120), _1672118)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1672112), hAPP(_1672120, _1672116)), hAPP(c_List_Omonoid__add__class_Olistsum(_1672112), hAPP(hAPP(c_List_Omap(_1672114, _1672112), _1672120), c_List_Oremove1(_1672114, _1672116, _1672118)))))], (15501 ^ _778495) ^ [_1053897, _1053899, _1053901, _1053903, _1053905] : [class_Groups_Ocomm__monoid__mult(_1053897), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053899), _1053901)), -(hBOOL(hAPP(hAPP(c_member(_1053899), _1053903), _1053901))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1053899, _1053897), _1053905), hAPP(hAPP(c_Set_Oinsert(_1053899), _1053903), _1053901)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053897), hAPP(_1053905, _1053903)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1053899, _1053897), _1053905), _1053901)))], (46276 ^ _778495) ^ [_1708754, _1708756, _1708758, _1708760, _1708762] : [class_Orderings_Olinorder(_1708754), c_List_Olinorder__class_Osorted(_1708754, hAPP(hAPP(c_List_Omap(_1708756, _1708754), _1708758), _1708760)), -(c_List_Olinorder__class_Osorted(_1708754, hAPP(hAPP(c_List_Omap(_1708756, _1708754), _1708758), c_List_Olinorder__class_Oinsort__insert__key(_1708756, _1708754, _1708758, _1708762, _1708760))))], (37418 ^ _778495) ^ [_1487161, _1487163, _1487165, _1487167, _1487169] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1487161, _1487163), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487161, tc_HOL_Obool)), _1487165), _1487167)), hAPP(c_COMBK(tc_fun(_1487163, tc_HOL_Obool), _1487161), _1487169)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1487161, _1487163), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1487161, _1487163), _1487165), hAPP(c_COMBK(tc_fun(_1487163, tc_HOL_Obool), _1487161), _1487169))), hAPP(hAPP(c_Product__Type_OSigma(_1487161, _1487163), _1487167), hAPP(c_COMBK(tc_fun(_1487163, tc_HOL_Obool), _1487161), _1487169))))], (30375 ^ _778495) ^ [_1332200, _1332202, _1332204] : [-(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), _1332200)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1332202))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1332204))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1332204), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1332200), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1332200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1332204), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1332202)))))], (24465 ^ _778495) ^ [_1216201, _1216203] : [class_Rings_Oring__1(_1216201), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1216201), hAPP(c_Groups_Ouminus__class_Ouminus(_1216201), c_Groups_Oone__class_Oone(_1216201))), 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)))), _1216203))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1216201), c_Groups_Oone__class_Oone(_1216201)))], (27989 ^ _778495) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (27037 ^ _778495) ^ [_1261526] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1261526)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1261526))], (22684 ^ _778495) ^ [_1183996] : [-(c_Int_Opred(c_Int_OBit0(_1183996)) = c_Int_OBit1(c_Int_Opred(_1183996)))], (13157 ^ _778495) ^ [_1012982, _1012984, _1012986] : [class_Rings_Ono__zero__divisors(_1012982), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012982), _1012984), _1012986) = c_Groups_Ozero__class_Ozero(_1012982), -(_1012984 = c_Groups_Ozero__class_Ozero(_1012982)), -(_1012986 = c_Groups_Ozero__class_Ozero(_1012982))], (5288 ^ _778495) ^ [_859348, _859350, _859352, _859354, _859356, _859358] : [-(c_SetInterval_Oord_OlessThan(_859358, _859354, _859350) = c_SetInterval_Oord_OlessThan(_859356, _859352, _859348)), _859358 = _859356, _859354 = _859352, _859350 = _859348], (46013 ^ _778495) ^ [_1704089, _1704091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704089), _1704091)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1704089, _1704091)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1704091), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (6732 ^ _778495) ^ [_888677, _888679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888677, tc_HOL_Obool)), _888679), c_Orderings_Obot__class_Obot(tc_fun(_888677, tc_HOL_Obool)))), -(_888679 = c_Orderings_Obot__class_Obot(tc_fun(_888677, tc_HOL_Obool)))], (10507 ^ _778495) ^ [_959844, _959846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _959844), _959846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _959844)), _959846)))], (39714 ^ _778495) ^ [_1552161, _1552163, _1552165, _1552167] : [c_Finite__Set_Ofolding(_1552161, _1552163, _1552165, _1552167), -(hAPP(_1552167, c_Orderings_Obot__class_Obot(tc_fun(_1552161, tc_HOL_Obool))) = c_Fun_Oid(_1552163))], (39223 ^ _778495) ^ [_1540747, _1540749, _1540751, _1540753] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1540747, tc_fun(_1540749, tc_HOL_Obool)), _1540751), _1540753) = hAPP(c_Set_OCollect(_1540749), hAPP(hAPP(c_COMBB(tc_fun(_1540747, tc_HOL_Obool), tc_HOL_Obool, _1540749), c_HOL_OAll(_1540747)), hAPP(hAPP(c_COMBB(tc_fun(_1540747, tc_HOL_Obool), tc_fun(_1540747, tc_HOL_Obool), _1540749), hAPP(c_COMBS(_1540747, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540747), c_fimplies), hAPP(hAPP(c_COMBC(_1540747, tc_fun(_1540747, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540747)), _1540751)))), hAPP(hAPP(c_COMBC(_1540749, tc_fun(_1540747, tc_fun(_1540749, tc_HOL_Obool)), tc_fun(_1540747, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1540749, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1540747, tc_fun(_1540749, tc_HOL_Obool)), tc_fun(_1540747, tc_HOL_Obool)), _1540749), c_COMBB(tc_fun(_1540749, tc_HOL_Obool), tc_HOL_Obool, _1540747)), c_member(_1540749))), _1540753)))))], (44660 ^ _778495) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (32608 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (47725 ^ _778495) ^ [_1740114, _1740116, _1740118] : [c_List_Olist__ex(_1740114, _1740116, _1740118), 47729 ^ _778495 : [(47732 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1740116, 47728 ^ [_1740114, _1740116, _1740118])))], (47730 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740114), 47728 ^ [_1740114, _1740116, _1740118]), hAPP(c_List_Oset(_1740114), _1740118))))]]], (22086 ^ _778495) ^ [_1173632, _1173634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1173632), _1173634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1173632)), c_Int_OBit0(_1173634))))], (30113 ^ _778495) ^ [_1326912, _1326914, _1326916, _1326918, _1326920] : [-(c_Product__Type_Oprod_Oprod__size(_1326912, _1326914, _1326916, _1326918, _1326920) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1326916, hAPP(c_Product__Type_Ofst(_1326912, _1326914), _1326920))), hAPP(_1326918, hAPP(c_Product__Type_Osnd(_1326912, _1326914), _1326920)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28837 ^ _778495) ^ [_1301825, _1301827] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1301825)), hAPP(c_Nat_OSuc, _1301827)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1301825))), 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)), _1301827)))))], (12004 ^ _778495) ^ [_988254, _988256, _988258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988254), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988256), _988258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988254), _988258)), _988256)))], (10 ^ _778495) ^ [_778618, _778620, _778622] : [-(_778622 = _778618), _778622 = _778620, _778620 = _778618], (18078 ^ _778495) ^ [_1102777] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102777) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3090 ^ _778495) ^ [_824515, _824517] : [_824517 = _824515, -(c_List_Orotate1(_824517) = c_List_Orotate1(_824515))], (43832 ^ _778495) ^ [_1655143, _1655145, _1655147] : [-(hAPP(c_List_Orotate(_1655143, _1655145), _1655147) = hAPP(c_List_Orotate(_1655143, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655145, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655143)), _1655147))), _1655147))], (13171 ^ _778495) ^ [_1013154, _1013156, _1013158] : [class_Rings_Ono__zero__divisors(_1013154), -(_1013156 = c_Groups_Ozero__class_Ozero(_1013154)), -(_1013158 = c_Groups_Ozero__class_Ozero(_1013154)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013154), _1013156), _1013158) = c_Groups_Ozero__class_Ozero(_1013154)], (41529 ^ _778495) ^ [_1598941, _1598943, _1598945, _1598947, _1598949] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598941), tc_List_Olist(_1598941))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598941), tc_List_Olist(_1598941)), _1598943), _1598945)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598941), c_List_Olistrel1(_1598941, _1598947)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598941), tc_List_Olist(_1598941))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598941), tc_List_Olist(_1598941)), hAPP(hAPP(c_List_Olist_OCons(_1598941), _1598949), _1598943)), hAPP(hAPP(c_List_Olist_OCons(_1598941), _1598949), _1598945))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598941), c_List_Olistrel1(_1598941, _1598947)))))], (42397 ^ _778495) ^ [_1623054, _1623056] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623054)), c_List_Obutlast(_1623054, _1623056)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623054)), _1623056)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (31992 ^ _778495) ^ [_1366749, _1366751, _1366753, _1366755, _1366757] : [_1366749 = c_Orderings_Obot__class_Obot(tc_fun(_1366751, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366753, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1366751, tc_fun(_1366753, tc_HOL_Obool)), _1366749), _1366755)), _1366757) = _1366757)], (4920 ^ _778495) ^ [_853534, _853536] : [_853536 = _853534, -(c_Lattices_Osemilattice__sup__class_Osup(_853536) = c_Lattices_Osemilattice__sup__class_Osup(_853534))], (8936 ^ _778495) ^ [_928863, _928865, _928867, _928869] : [class_Lattices_Osemilattice__inf(_928863), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928863), _928865), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928863), _928867), _928869)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928863), _928867), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928863), _928865), _928869)))], (31626 ^ _778495) ^ [_1356409, _1356411, _1356413, _1356415, _1356417, _1356419, _1356421] : [-(hAPP(c_Product__Type_Oapsnd(_1356409, _1356411, _1356413, _1356415), hAPP(c_Product__Type_Oapfst(_1356417, _1356413, _1356409, _1356419), _1356421)) = hAPP(hAPP(c_Product__Type_OPair(_1356413, _1356411), hAPP(_1356419, hAPP(c_Product__Type_Ofst(_1356417, _1356409), _1356421))), hAPP(_1356415, hAPP(c_Product__Type_Osnd(_1356417, _1356409), _1356421))))], (20406 ^ _778495) ^ [_1144965] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1144965), c_Int_OPls) = _1144965)], (35694 ^ _778495) ^ [_1447361, _1447363, _1447365, _1447367] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1447361, tc_HOL_Obool)), _1447363), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447361), _1447365), _1447367))), 35698 ^ _778495 : [(35701 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1447361), 35697 ^ [_1447361, _1447363, _1447365, _1447367]), _1447365)))], (35699 ^ _778495) ^ [] : [-(_1447363 = hAPP(c_Relation_OImage(_1447361, _1447361, _1447367), hAPP(hAPP(c_Set_Oinsert(_1447361), 35697 ^ [_1447361, _1447363, _1447365, _1447367]), c_Orderings_Obot__class_Obot(tc_fun(_1447361, tc_HOL_Obool)))))]]], (49244 ^ _778495) ^ [_1774292, _1774294] : [c_Equiv__Relations_Oequivp(_1774292, _1774294), 49247 ^ _778495 : [(49252 ^ _778495) ^ [] : [-(c_Predicate_Otransp(_1774292, _1774294))], (49250 ^ _778495) ^ [] : [-(c_Predicate_Osymp(_1774292, _1774294))], (49248 ^ _778495) ^ [] : [-(c_Predicate_Oreflp(_1774292, _1774294))]]], (50877 ^ _778495) ^ [_1808519, _1808521, _1808523] : [class_Divides_Osemiring__div(_1808519), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808519), _1808521), _1808523)), -(c_Divides_Odiv__class_Omod(_1808519, _1808523, _1808521) = c_Groups_Ozero__class_Ozero(_1808519))], (43070 ^ _778495) ^ [_1637481, _1637483, _1637485, _1637487, _1637489, _1637491] : [hAPP(hAPP(c_List_Olist_OCons(_1637481), _1637483), _1637485) = _1637487, _1637489 = hAPP(hAPP(c_List_Oappend(_1637481), _1637485), _1637491), -(hAPP(hAPP(c_List_Olist_OCons(_1637481), _1637483), _1637489) = hAPP(hAPP(c_List_Oappend(_1637481), _1637487), _1637491))], (24687 ^ _778495) ^ [_1220464] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1220464, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20524 ^ _778495) ^ [_1146709, _1146711] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146709)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146711)))), 20527 ^ _778495 : [(20530 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1146711))], (20528 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1146709), _1146711)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1146709), _1146711))], (10827 ^ _778495) ^ [_964954, _964956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964954), _964956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _964954)), hAPP(c_Nat_OSuc, _964956))))], (28389 ^ _778495) ^ [_1289922, _1289924, _1289926, _1289928, _1289930] : [class_Groups_Ominus(_1289922), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289924, _1289922)), _1289926), _1289928), _1289930) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1289922), hAPP(_1289926, _1289930)), hAPP(_1289928, _1289930)))], (31410 ^ _778495) ^ [_1352116, _1352118, _1352120] : [class_Orderings_Olinorder(_1352116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352116), _1352118)), 31417 ^ _778495 : [(31424 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352116, tc_HOL_Obool)), _1352118), hAPP(hAPP(c_Set_Oinsert(_1352116), _1352120), c_Orderings_Obot__class_Obot(tc_fun(_1352116, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1352116, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1352116, c_Orderings_Oord__class_Omax(_1352116), hAPP(hAPP(c_Set_Oinsert(_1352116), _1352120), _1352118)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352116), _1352120), c_Big__Operators_Olattice_OSup__fin(_1352116, c_Orderings_Oord__class_Omax(_1352116), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352116, tc_HOL_Obool)), _1352118), hAPP(hAPP(c_Set_Oinsert(_1352116), _1352120), c_Orderings_Obot__class_Obot(tc_fun(_1352116, tc_HOL_Obool)))))))], (31418 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352116, tc_HOL_Obool)), _1352118), hAPP(hAPP(c_Set_Oinsert(_1352116), _1352120), c_Orderings_Obot__class_Obot(tc_fun(_1352116, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1352116, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1352116, c_Orderings_Oord__class_Omax(_1352116), hAPP(hAPP(c_Set_Oinsert(_1352116), _1352120), _1352118)) = _1352120)]]], (52303 ^ _778495) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (34466 ^ _778495) ^ [_1422412, _1422414, _1422416] : [class_Groups_Oordered__ab__group__add(_1422412), -(hAPP(c_Set_Oimage(_1422412, _1422412, c_Groups_Ouminus__class_Ouminus(_1422412)), c_SetInterval_Oord__class_OatLeastAtMost(_1422412, _1422414, _1422416)) = c_SetInterval_Oord__class_OatLeastAtMost(_1422412, hAPP(c_Groups_Ouminus__class_Ouminus(_1422412), _1422416), hAPP(c_Groups_Ouminus__class_Ouminus(_1422412), _1422414)))], (11797 ^ _778495) ^ [_983448, _983450, _983452, _983454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983448), _983450)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983452), _983454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983448), _983452)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983450), _983454))))], (26752 ^ _778495) ^ [_1256724] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1256724) = c_Int_Opred(_1256724))], (46740 ^ _778495) ^ [_1718272, _1718274] : [-(_1718272 = c_List_Olist_ONil(_1718274)), -(hAPP(c_List_Ohd(_1718274), hAPP(c_List_Orev(_1718274), _1718272)) = c_List_Olast(_1718274, _1718272))], (45741 ^ _778495) ^ [_1697509, _1697511, _1697513] : [hAPP(c_List_Ofilter(_1697509, _1697511), _1697513) = c_List_Olist_ONil(_1697509), 45744 ^ _778495 : [(45745 ^ _778495) ^ [_1697606] : [hBOOL(hAPP(hAPP(c_member(_1697509), _1697606), hAPP(c_List_Oset(_1697509), _1697513))), hBOOL(hAPP(_1697511, _1697606))]]], (34572 ^ _778495) ^ [_1424943, _1424945] : [class_Groups_Olinordered__ab__group__add(_1424943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424943), _1424945)), -(_1424945 = c_Orderings_Obot__class_Obot(tc_fun(_1424943, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1424943), c_Big__Operators_Olinorder__class_OMin(_1424943, _1424945)) = c_Big__Operators_Olinorder__class_OMax(_1424943, hAPP(c_Set_Oimage(_1424943, _1424943, c_Groups_Ouminus__class_Ouminus(_1424943)), _1424945)))], (21268 ^ _778495) ^ [_1159591, _1159593, _1159595] : [class_Groups_Oordered__ab__group__add__abs(_1159591), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159591), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1159591), hAPP(c_Groups_Oabs__class_Oabs(_1159591), _1159593)), hAPP(c_Groups_Oabs__class_Oabs(_1159591), _1159595))), hAPP(c_Groups_Oabs__class_Oabs(_1159591), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1159591), _1159595), _1159593)))))], (26972 ^ _778495) ^ [_1260494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260494)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1260494) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1260494), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34629 ^ _778495) ^ [_1426088, _1426090] : [_1426088 = _1426090, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1426088) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1426090))], (17290 ^ _778495) ^ [_1087709, _1087711, _1087713, _1087715] : [class_Fields_Ofield__inverse__zero(_1087709), -(_1087711 = c_Groups_Ozero__class_Ozero(_1087709)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087709), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1087709), _1087713), _1087711)), _1087715) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1087709), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087709), _1087713), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087709), _1087715), _1087711))), _1087711))], (30755 ^ _778495) ^ [_1339931, _1339933, _1339935] : [class_Orderings_Olinorder(_1339931), 30758 ^ _778495 : [(30765 ^ _778495) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339931), _1339933), _1339935) = _1339935, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339931), _1339933), _1339935)))], (30759 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339931), _1339933), _1339935)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339931), _1339933), _1339935) = _1339935)]]], (18014 ^ _778495) ^ [_1101317, _1101319, _1101321, _1101323] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1101317), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101317), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1101317), _1101319), _1101321)), _1101323) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1101317), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101317), _1101319), _1101323)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101317), _1101321), _1101323)))], (39114 ^ _778495) ^ [_1537346, _1537348, _1537350, _1537352] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1537346), _1537348))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537350), hAPP(c_Set_Oimage(_1537346, _1537350, _1537352), _1537348))), 39122 ^ _778495 : [(39125 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1537346), hAPP(c_Set_OCollect(_1537346), hAPP(hAPP(c_COMBS(_1537346, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1537346), c_fconj), hAPP(hAPP(c_COMBC(_1537346, tc_fun(_1537346, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537346)), _1537348))), hAPP(hAPP(c_COMBC(_1537346, _1537350, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1537350, tc_fun(_1537350, tc_HOL_Obool), _1537346), c_fequal), _1537352)), hAPP(_1537352, 39121 ^ [_1537346, _1537348, _1537350, _1537352]))))))], (39123 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537346), 39121 ^ [_1537346, _1537348, _1537350, _1537352]), _1537348)))]]], (8882 ^ _778495) ^ [_927784, _927786] : [class_Lattices_Osemilattice__inf(_927784), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927784), _927786), _927786) = _927786)], (24986 ^ _778495) ^ [_1225404, _1225406] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1225404)), hAPP(c_Int_Onat, _1225406)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225406)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225404), _1225406))], (10207 ^ _778495) ^ [_954485, _954487, _954489, _954491, _954493, _954495] : [c_Finite__Set_Ofun__left__comm(_954485, _954487, _954489), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_954485, _954487, _954489, _954491, _954493), _954495)), -(hAPP(hAPP(c_Finite__Set_Ofold(_954485, _954487, _954489), _954491), _954493) = _954495)], (11831 ^ _778495) ^ [_984086, _984088, _984090] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984086), _984088)), _984090) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _984088), _984090)))], (49640 ^ _778495) ^ [_1781499, _1781501, _1781503, _1781505] : [c_Fun_Oinj__on(_1781499, _1781501, _1781503, c_Orderings_Otop__class_Otop(tc_fun(_1781499, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781501, _1781499, c_Hilbert__Choice_Oinv__into(_1781499, _1781501, c_Orderings_Otop__class_Otop(tc_fun(_1781499, tc_HOL_Obool)), _1781503)), hAPP(c_Set_Oimage(_1781499, _1781501, _1781503), _1781505)) = _1781505)], (8222 ^ _778495) ^ [_914118, _914120, _914122] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_914118), _914120)), 8225 ^ _778495 : [(8232 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_914118), _914122)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_914118), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914118, tc_HOL_Obool)), _914122), _914120))))], (8226 ^ _778495) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_914118), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914118, tc_HOL_Obool)), _914122), _914120))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_914118), _914122)))]]], (36019 ^ _778495) ^ [_1454686, _1454688, _1454690, _1454692, _1454694, _1454696, _1454698, _1454700] : [c_Equiv__Relations_Oequiv(_1454686, _1454688, _1454690), c_Equiv__Relations_Ocongruent2(_1454686, _1454692, _1454694, _1454690, _1454696, _1454698), hBOOL(hAPP(hAPP(c_member(_1454686), _1454700), _1454688)), -(c_Equiv__Relations_Ocongruent(_1454692, _1454694, _1454696, hAPP(_1454698, _1454700)))], (50625 ^ _778495) ^ [_1803946, _1803948, _1803950] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803946), _1803948)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803946), _1803950))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1803946)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803948), _1803950)))], (1308 ^ _778495) ^ [_797873, _797875] : [-(class_Int_Oring__char__0(_797873)), _797875 = _797873, class_Int_Oring__char__0(_797875)], (51347 ^ _778495) ^ [_1816254, _1816256, _1816258] : [class_Rings_Olinordered__idom(_1816254), 51350 ^ _778495 : [(51357 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816254), _1816256), _1816258)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816254), hAPP(c_Groups_Oabs__class_Oabs(_1816254), _1816256)), _1816258)))], (51351 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816254), hAPP(c_Groups_Oabs__class_Oabs(_1816254), _1816256)), _1816258)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816254), _1816256), _1816258)))]]], (524 ^ _778495) ^ [_786421, _786423] : [-(c_Nat__Transfer_Onat__set(_786421)), _786423 = _786421, c_Nat__Transfer_Onat__set(_786423)], (3708 ^ _778495) ^ [_834150, _834152, _834154, _834156] : [-(c_List_Omeasures(_834156, _834152) = c_List_Omeasures(_834154, _834150)), _834156 = _834154, _834152 = _834150], (38709 ^ _778495) ^ [_1527823, _1527825, _1527827] : [c_Wellfounded_Owf(_1527823, _1527825), -(c_Wellfounded_Owf(_1527823, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1527823, _1527823), tc_HOL_Obool)), _1527825), _1527827)))], (52457 ^ _778495) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (17676 ^ _778495) ^ [_1095569, _1095571, _1095573] : [class_Orderings_Olinorder(_1095569), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095569), _1095571), _1095573) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095569), _1095573), _1095571))], (2142 ^ _778495) ^ [_809725, _809727] : [_809727 = _809725, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_809727) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_809725))], (42606 ^ _778495) ^ [_1627949, _1627951, _1627953, _1627955] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627949) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1627951), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627949)), hAPP(hAPP(c_List_Olist_OCons(_1627951), _1627953), _1627955)) = hAPP(hAPP(c_List_Olist_OCons(_1627951), _1627953), hAPP(hAPP(c_List_Otake(_1627951), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627949)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1627955)))], (26480 ^ _778495) ^ [_1252171, _1252173, _1252175] : [class_Rings_Olinordered__semidom(_1252171), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252171), c_Groups_Ozero__class_Ozero(_1252171)), _1252173)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252171), _1252173), c_Groups_Oone__class_Oone(_1252171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252171), _1252173), hAPP(hAPP(c_Power_Opower__class_Opower(_1252171), _1252173), _1252175))), hAPP(hAPP(c_Power_Opower__class_Opower(_1252171), _1252173), _1252175))))], (13490 ^ _778495) ^ [_1017928, _1017930, _1017932] : [class_Groups_Ocomm__monoid__mult(_1017928), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1017930, _1017928), _1017932), c_Orderings_Obot__class_Obot(tc_fun(_1017930, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1017928))], (10379 ^ _778495) ^ [_957400, _957402, _957404] : [class_Lattices_Olattice(_957400), hBOOL(hAPP(c_Finite__Set_Ofinite(_957400), _957402)), 10386 ^ _778495 : [(10393 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_957400, tc_HOL_Obool)), _957402), hAPP(hAPP(c_Set_Oinsert(_957400), _957404), c_Orderings_Obot__class_Obot(tc_fun(_957400, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_957400, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_957400, hAPP(hAPP(c_Set_Oinsert(_957400), _957404), _957402)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_957400), _957404), c_Big__Operators_Olattice__class_OInf__fin(_957400, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_957400, tc_HOL_Obool)), _957402), hAPP(hAPP(c_Set_Oinsert(_957400), _957404), c_Orderings_Obot__class_Obot(tc_fun(_957400, tc_HOL_Obool)))))))], (10387 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_957400, tc_HOL_Obool)), _957402), hAPP(hAPP(c_Set_Oinsert(_957400), _957404), c_Orderings_Obot__class_Obot(tc_fun(_957400, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_957400, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_957400, hAPP(hAPP(c_Set_Oinsert(_957400), _957404), _957402)) = _957404)]]], (39202 ^ _778495) ^ [_1539841, _1539843, _1539845, _1539847] : [-(hAPP(c_Set_OCollect(_1539841), hAPP(hAPP(c_COMBB(tc_fun(_1539843, tc_HOL_Obool), tc_HOL_Obool, _1539841), c_HOL_OAll(_1539843)), hAPP(hAPP(c_COMBB(tc_fun(_1539843, tc_HOL_Obool), tc_fun(_1539843, tc_HOL_Obool), _1539841), hAPP(c_COMBS(_1539843, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539843), c_fimplies), hAPP(hAPP(c_COMBC(_1539843, tc_fun(_1539843, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539843)), _1539845)))), _1539847))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1539843, tc_fun(_1539841, tc_HOL_Obool)), _1539845), hAPP(hAPP(c_COMBB(tc_fun(_1539841, tc_HOL_Obool), tc_fun(_1539841, tc_HOL_Obool), _1539843), c_Set_OCollect(_1539841)), hAPP(c_COMBC(_1539841, _1539843, tc_HOL_Obool), _1539847))))], (23180 ^ _778495) ^ [_1193548, _1193550, _1193552, _1193554] : [class_Divides_Oring__div(_1193548), -(c_Divides_Odiv__class_Omod(_1193548, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1193548), _1193550), _1193552), _1193554) = c_Divides_Odiv__class_Omod(_1193548, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1193548), _1193550), c_Divides_Odiv__class_Omod(_1193548, _1193552, _1193554)), _1193554))], (30895 ^ _778495) ^ [_1342699] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1342699) = _1342699)], (38115 ^ _778495) ^ [_1506980, _1506982, _1506984, _1506986] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506980), hAPP(c_Set_OCollect(_1506980), _1506982))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506984), hAPP(c_Set_OCollect(_1506984), hAPP(hAPP(c_COMBB(tc_fun(_1506980, tc_HOL_Obool), tc_HOL_Obool, _1506984), c_HOL_OEx(_1506980)), hAPP(hAPP(c_COMBC(_1506984, tc_fun(_1506980, tc_HOL_Obool), tc_fun(_1506980, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506980, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1506980, tc_HOL_Obool), tc_fun(_1506980, tc_HOL_Obool)), _1506984), c_COMBS(_1506980, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506980, tc_HOL_Obool), tc_fun(_1506980, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1506984), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506980), c_fconj)), hAPP(hAPP(c_COMBC(_1506984, tc_fun(_1506980, _1506984), tc_fun(_1506980, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506984, tc_HOL_Obool), tc_fun(tc_fun(_1506980, _1506984), tc_fun(_1506980, tc_HOL_Obool)), _1506984), c_COMBB(_1506984, tc_HOL_Obool, _1506980)), c_fequal)), _1506986)))), _1506982))))))], (47223 ^ _778495) ^ [_1728412, _1728414, _1728416] : [hBOOL(hAPP(hAPP(c_member(_1728412), _1728414), hAPP(c_List_Oset(_1728412), _1728416))), -(c_List_Oinsert(_1728412, _1728414, _1728416) = _1728416)], (45046 ^ _778495) ^ [_1681578, _1681580, _1681582, _1681584, _1681586] : [-(c_Enum_Oproduct(_1681578, _1681580, hAPP(hAPP(c_List_Olist_OCons(_1681578), _1681582), _1681584), _1681586) = hAPP(hAPP(c_List_Oappend(tc_prod(_1681578, _1681580)), hAPP(hAPP(c_List_Omap(_1681580, tc_prod(_1681578, _1681580)), hAPP(c_Product__Type_OPair(_1681578, _1681580), _1681582)), _1681586)), c_Enum_Oproduct(_1681578, _1681580, _1681584, _1681586)))], (48086 ^ _778495) ^ [_1747577, _1747579, _1747581] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747577)), c_List_Osplice(_1747577, _1747579, _1747581)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747577)), _1747579)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747577)), _1747581)))], (17018 ^ _778495) ^ [_1082598, _1082600, _1082602, _1082604] : [class_Fields_Olinordered__field(_1082598), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082598), _1082600), _1082602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082598), _1082604), c_Groups_Ozero__class_Ozero(_1082598))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082598), c_Groups_Ozero__class_Ozero(_1082598)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082598), _1082600), _1082602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082598), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1082598), _1082604), _1082600)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1082598), _1082604), _1082602))))], (20418 ^ _778495) ^ [_1145123] : [class_Int_Onumber__ring(_1145123), -(c_Groups_Ozero__class_Ozero(_1145123) = hAPP(c_Int_Onumber__class_Onumber__of(_1145123), c_Int_OPls))], (46578 ^ _778495) ^ [_1714930, _1714932] : [-(c_Fun_Oinj__on(tc_List_Olist(_1714930), tc_List_Olist(_1714930), c_List_Orev(_1714930), _1714932))], (16114 ^ _778495) ^ [_1066646, _1066648] : [class_Rings_Odivision__ring(_1066646), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066646), _1066648), c_Groups_Oone__class_Oone(_1066646)) = _1066648)], (39316 ^ _778495) ^ [_1542701, _1542703] : [39318 ^ _778495 : [(39321 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1542703), 39317 ^ [_1542701, _1542703]))], (39319 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 39317 ^ [_1542701, _1542703]), _1542701)))]], -(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)), _1542703), _1542701))], (43774 ^ _778495) ^ [_1654032, _1654034, _1654036] : [-(hAPP(hAPP(c_List_Odrop(_1654032), _1654034), hAPP(c_List_Otl(_1654032), _1654036)) = hAPP(c_List_Otl(_1654032), hAPP(hAPP(c_List_Odrop(_1654032), _1654034), _1654036)))], (39474 ^ _778495) ^ [_1546779, _1546781, _1546783, _1546785, _1546787, _1546789] : [c_Fun_Oinj__on(_1546779, _1546781, _1546783, _1546785), 39477 ^ _778495 : [(39484 ^ _778495) ^ [] : [c_Fun_Oinj__on(_1546779, _1546787, hAPP(c_Fun_Ocomp(_1546781, _1546787, _1546779, _1546789), _1546783), _1546785), -(c_Fun_Oinj__on(_1546781, _1546787, _1546789, hAPP(c_Set_Oimage(_1546779, _1546781, _1546783), _1546785)))], (39478 ^ _778495) ^ [] : [c_Fun_Oinj__on(_1546781, _1546787, _1546789, hAPP(c_Set_Oimage(_1546779, _1546781, _1546783), _1546785)), -(c_Fun_Oinj__on(_1546779, _1546787, hAPP(c_Fun_Ocomp(_1546781, _1546787, _1546779, _1546789), _1546783), _1546785))]]], (10267 ^ _778495) ^ [_955485, _955487, _955489] : [class_Lattices_Olattice(_955485), hBOOL(hAPP(c_Finite__Set_Ofinite(_955485), _955487)), -(_955489 = c_Orderings_Obot__class_Obot(tc_fun(_955485, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_955485, tc_HOL_Obool)), _955489), _955487)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955485), c_Big__Operators_Olattice__class_OInf__fin(_955485, _955489)), c_Big__Operators_Olattice__class_OInf__fin(_955485, _955487)) = c_Big__Operators_Olattice__class_OInf__fin(_955485, _955487))], (37526 ^ _778495) ^ [_1489882, _1489884, _1489886, _1489888] : [-(_1489882 = c_Orderings_Obot__class_Obot(tc_fun(_1489884, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1489884, _1489886), _1489886, c_Product__Type_Osnd(_1489884, _1489886)), hAPP(hAPP(c_Product__Type_OSigma(_1489884, _1489886), _1489882), hAPP(c_COMBK(tc_fun(_1489886, tc_HOL_Obool), _1489884), _1489888))) = _1489888)], (35583 ^ _778495) ^ [_1444284] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1444284)) = _1444284)], (40395 ^ _778495) ^ [_1568836, _1568838] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568836, _1568836), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568836, _1568838)), c_Relation_OId(_1568836)) = c_Transitive__Closure_Ortrancl(_1568836, _1568838))], (46706 ^ _778495) ^ [_1717543, _1717545] : [-(hAPP(c_List_Orev(_1717543), hAPP(c_List_Orev(_1717543), _1717545)) = _1717545)], (5504 ^ _778495) ^ [_862730, _862732] : [_862732 = _862730, -(tc_List_Olist(_862732) = tc_List_Olist(_862730))], (32176 ^ _778495) ^ [_1370443, _1370445, _1370447, _1370449, _1370451] : [_1370443 = c_Orderings_Obot__class_Obot(tc_fun(_1370445, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370447, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370445, tc_fun(_1370447, tc_HOL_Obool)), _1370443), _1370449)), _1370451) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370447, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1370447, tc_HOL_Obool))), _1370451))], (25838 ^ _778495) ^ [_1240131, _1240133, _1240135] : [class_Rings_Olinordered__idom(_1240131), 25841 ^ _778495 : [(25850 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240131), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1240131), hAPP(hAPP(c_Power_Opower__class_Opower(_1240131), _1240133), 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(_1240131), _1240135), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1240131)))), _1240133 = c_Groups_Ozero__class_Ozero(_1240131), _1240135 = c_Groups_Ozero__class_Ozero(_1240131)], (25842 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240131), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1240131), hAPP(hAPP(c_Power_Opower__class_Opower(_1240131), _1240133), 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(_1240131), _1240135), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1240131))), 25845 ^ _778495 : [(25848 ^ _778495) ^ [] : [-(_1240135 = c_Groups_Ozero__class_Ozero(_1240131))], (25846 ^ _778495) ^ [] : [-(_1240133 = c_Groups_Ozero__class_Ozero(_1240131))]]]]], (23775 ^ _778495) ^ [_1204310, _1204312, _1204314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204312)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204312), _1204314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204310), _1204314)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204310), _1204312))))], (41449 ^ _778495) ^ [_1596531, _1596533, _1596535, _1596537, _1596539, _1596541] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596531), tc_List_Olist(_1596531))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596531), tc_List_Olist(_1596531)), hAPP(hAPP(c_List_Olist_OCons(_1596531), _1596533), _1596535)), hAPP(hAPP(c_List_Olist_OCons(_1596531), _1596537), _1596539))), c_List_Olexord(_1596531, _1596541))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596531, _1596531)), hAPP(hAPP(c_Product__Type_OPair(_1596531, _1596531), _1596533), _1596537)), _1596541))), 41456 ^ _778495 : [(41459 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596531), tc_List_Olist(_1596531))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596531), tc_List_Olist(_1596531)), _1596535), _1596539)), c_List_Olexord(_1596531, _1596541))))], (41457 ^ _778495) ^ [] : [-(_1596533 = _1596537)]]], (17489 ^ _778495) ^ [_1091733, _1091735] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1091733), _1091735)), 17495 ^ _778495 : [(17498 ^ _778495) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17496 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1091733), 17494 ^ [_1091733, _1091735]), _1091735)))]], -(hAPP(c_Finite__Set_Ocard(_1091733), _1091735) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25930 ^ _778495) ^ [_1242015, _1242017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242017)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1242017), _1242015)), _1242017) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1242017), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1242015), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (46132 ^ _778495) ^ [_1706553, _1706555, _1706557] : [class_Orderings_Olinorder(_1706553), c_List_Olinorder__class_Osorted(_1706553, _1706555), -(c_List_Olinorder__class_Osorted(_1706553, hAPP(hAPP(c_List_Otake(_1706553), _1706557), _1706555)))], (30047 ^ _778495) ^ [_1325550, _1325552, _1325554, _1325556, _1325558] : [-(hAPP(c_Product__Type_Ofst(_1325550, _1325552), hAPP(c_Product__Type_Oapsnd(_1325554, _1325552, _1325550, _1325556), _1325558)) = hAPP(c_Product__Type_Ofst(_1325550, _1325554), _1325558))], (30807 ^ _778495) ^ [_1340782, _1340784, _1340786, _1340788] : [class_Orderings_Olinorder(_1340782), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340782), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340782), _1340784), _1340786)), _1340788) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340782), _1340784), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340782), _1340786), _1340788)))], (22530 ^ _778495) ^ [_1181302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1181302)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181302), c_Int_OPls)))], (4188 ^ _778495) ^ [_841980, _841982, _841984, _841986] : [-(c_List_Ozip(_841986, _841982) = c_List_Ozip(_841984, _841980)), _841986 = _841984, _841982 = _841980], (33489 ^ _778495) ^ [_1400425, _1400427, _1400429] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400425, tc_HOL_Obool)), _1400427), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1400425, tc_HOL_Obool), _1400429)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1400425, tc_HOL_Obool), tc_fun(_1400425, tc_HOL_Obool)), _1400429), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400425, tc_HOL_Obool)), _1400427)))], (40102 ^ _778495) ^ [_1561005, _1561007, _1561009, _1561011] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1561005, _1561007, _1561009, tc_prod(_1561007, _1561009)), _1561011), c_Product__Type_OPair(_1561007, _1561009)) = _1561011)], (52283 ^ _778495) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (2848 ^ _778495) ^ [_820760, _820762, _820764, _820766, _820768, _820770] : [-(c_Nitpick_Oof__frac(_820770, _820766, _820762) = c_Nitpick_Oof__frac(_820768, _820764, _820760)), _820770 = _820768, _820766 = _820764, _820762 = _820760], (8574 ^ _778495) ^ [_921694, _921696, _921698, _921700] : [c_Finite__Set_Ofolding__one__idem(_921694, _921696, _921698), -(hAPP(hAPP(_921696, _921700), _921700) = _921700)], (52265 ^ _778495) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (3742 ^ _778495) ^ [_834685, _834687, _834689, _834691, _834693, _834695, _834697, _834699] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_834699, _834695, _834691, _834687) = c_New__Random__Sequence_Opos__not__random__dseq(_834697, _834693, _834689, _834685)), _834699 = _834697, _834695 = _834693, _834691 = _834689, _834687 = _834685], (43199 ^ _778495) ^ [_1640476, _1640478, _1640480] : [_1640478 = c_List_Olist_ONil(_1640476), -(hAPP(hAPP(c_List_Oappend(_1640476), _1640478), _1640480) = _1640480)], (22838 ^ _778495) ^ [] : [-(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))], (23955 ^ _778495) ^ [_1207310, _1207312] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207310, _1207312) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207310, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1207312)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27397 ^ _778495) ^ [_1267482, _1267484] : [_1267482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1267484, _1267482) = _1267484)], (9342 ^ _778495) ^ [_936885, _936887, _936889] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936885, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936885, tc_HOL_Obool)), _936887), _936889)), _936887)))], (39190 ^ _778495) ^ [_1539654, _1539656, _1539658] : [c_Wellfounded_Oacyclic(_1539654, _1539656), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1539654, _1539654), tc_HOL_Obool)), _1539658), _1539656)), -(c_Wellfounded_Oacyclic(_1539654, _1539658))], (21492 ^ _778495) ^ [] : [-(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)))))], (51005 ^ _778495) ^ [_1810747, _1810749, _1810751] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810747), _1810749)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810749), _1810747))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810749), _1810751)), 51016 ^ _778495 : [(51019 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810751), _1810747))], (51017 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810747), _1810751)))]]], (38308 ^ _778495) ^ [_1515003] : [-(c_Int_Oint__ge__less__than2(_1515003) = 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), _1515003)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (45290 ^ _778495) ^ [_1687165, _1687167] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1687165))), c_Enum_Osublists(_1687165, _1687167)) = 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(_1687165)), _1687167)))], (44646 ^ _778495) ^ [_1672940, _1672942] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1672940)), hAPP(c_Code__Numeral_Oof__nat, _1672942)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1672940), _1672942)))], (5254 ^ _778495) ^ [_858821, _858823] : [_858823 = _858821, -(c_Int_Onumber__class_Onumber__of(_858823) = c_Int_Onumber__class_Onumber__of(_858821))], (38667 ^ _778495) ^ [_1527106, _1527108, _1527110, _1527112, _1527114] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527106, _1527108)), hAPP(hAPP(c_Product__Type_OPair(_1527106, _1527108), _1527110), _1527112)), _1527114)), -(hBOOL(hAPP(hAPP(c_member(_1527106), _1527110), hAPP(c_Relation_ODomain(_1527106, _1527108), _1527114))))], (9572 ^ _778495) ^ [_942017, _942019, _942021] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942017, tc_HOL_Obool)), _942019), _942021) = c_Orderings_Obot__class_Obot(tc_fun(_942017, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942017, tc_HOL_Obool)), _942019), _942021) = _942019)], (41517 ^ _778495) ^ [_1598555, _1598557, _1598559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598555, _1598555), tc_HOL_Obool)), _1598557), _1598559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1598555), tc_List_Olist(_1598555)), tc_HOL_Obool)), c_List_Olistrel1(_1598555, _1598557)), c_List_Olistrel1(_1598555, _1598559))))], (7414 ^ _778495) ^ [_901738, _901740] : [class_Finite__Set_Ofinite(_901738), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_901738), _901740)))], (42762 ^ _778495) ^ [_1630655, _1630657, _1630659, _1630661] : [hAPP(hAPP(c_List_Olist__update(_1630655, _1630657), _1630659), _1630661) = c_List_Olist_ONil(_1630655), -(_1630657 = c_List_Olist_ONil(_1630655))], (34375 ^ _778495) ^ [_1420359, _1420361, _1420363, _1420365, _1420367, _1420369] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1420359, tc_fun(_1420361, tc_HOL_Obool)), _1420363), hAPP(hAPP(c_COMBB(_1420365, tc_fun(_1420361, tc_HOL_Obool), _1420359), _1420367), _1420369)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1420365, tc_fun(_1420361, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1420359, _1420365, _1420369), _1420363)), _1420367))], (42295 ^ _778495) ^ [_1620830, _1620832, _1620834] : [-(hAPP(hAPP(c_List_Olist__update(_1620830, _1620832), _1620834), hAPP(hAPP(c_List_Onth(_1620830), _1620832), _1620834)) = _1620832)], (2610 ^ _778495) ^ [_817047, _817049, _817051, _817053] : [-(c_Wellfounded_Omin__ext(_817053, _817049) = c_Wellfounded_Omin__ext(_817051, _817047)), _817053 = _817051, _817049 = _817047], (31144 ^ _778495) ^ [_1347731, _1347733] : [class_Orderings_Olinorder(_1347731), -(c_Big__Operators_Olinorder__class_OMax(_1347731, hAPP(hAPP(c_Set_Oinsert(_1347731), _1347733), c_Orderings_Obot__class_Obot(tc_fun(_1347731, tc_HOL_Obool)))) = _1347733)], (40108 ^ _778495) ^ [_1561164, _1561166, _1561168, _1561170, _1561172, _1561174, _1561176] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1561164, _1561166, _1561168, _1561170), _1561172), _1561174), _1561176) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1561166, _1561168, _1561170), _1561174), hAPP(_1561172, _1561176)))], (42802 ^ _778495) ^ [_1631397, _1631399, _1631401] : [-(hBOOL(hAPP(hAPP(c_member(_1631397), _1631399), hAPP(c_List_Oset(_1631397), _1631401)))), -(c_List_Oremove1(_1631397, _1631399, _1631401) = _1631401)], (28453 ^ _778495) ^ [_1292656] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1292656) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1292656)))], (42555 ^ _778495) ^ [_1626763, _1626765] : [class_Groups_Ocomm__monoid__add(_1626763), hBOOL(hAPP(c_List_Odistinct(_1626763), _1626765)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1626763), _1626765) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1626763, _1626763), c_COMBI(_1626763)), hAPP(c_List_Oset(_1626763), _1626765)))], (44167 ^ _778495) ^ [_1662220, _1662222, _1662224, _1662226, _1662228] : [class_Orderings_Olinorder(_1662220), hBOOL(hAPP(hAPP(c_member(_1662220), hAPP(_1662222, _1662224)), hAPP(c_Set_Oimage(_1662226, _1662220, _1662222), hAPP(c_List_Oset(_1662226), _1662228)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1662226, _1662220, _1662222, _1662224, _1662228) = _1662228)], (9849 ^ _778495) ^ [_947459, _947461, _947463] : [class_Lattices_Olattice(_947459), hBOOL(hAPP(c_Finite__Set_Ofinite(_947459), _947461)), 9856 ^ _778495 : [(9863 ^ _778495) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947459, tc_HOL_Obool)), _947461), hAPP(hAPP(c_Set_Oinsert(_947459), _947463), c_Orderings_Obot__class_Obot(tc_fun(_947459, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_947459, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_947459, hAPP(hAPP(c_Set_Oinsert(_947459), _947463), _947461)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_947459), _947463), c_Big__Operators_Olattice__class_OSup__fin(_947459, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947459, tc_HOL_Obool)), _947461), hAPP(hAPP(c_Set_Oinsert(_947459), _947463), c_Orderings_Obot__class_Obot(tc_fun(_947459, tc_HOL_Obool)))))))], (9857 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947459, tc_HOL_Obool)), _947461), hAPP(hAPP(c_Set_Oinsert(_947459), _947463), c_Orderings_Obot__class_Obot(tc_fun(_947459, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_947459, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_947459, hAPP(hAPP(c_Set_Oinsert(_947459), _947463), _947461)) = _947463)]]], (31150 ^ _778495) ^ [_1347838, _1347840, _1347842] : [class_Orderings_Olinorder(_1347838), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347838), _1347840)), hBOOL(hAPP(hAPP(c_member(_1347838), _1347842), _1347840)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347838), _1347842), c_Big__Operators_Olattice_OSup__fin(_1347838, c_Orderings_Oord__class_Omax(_1347838), _1347840)) = c_Big__Operators_Olattice_OSup__fin(_1347838, c_Orderings_Oord__class_Omax(_1347838), _1347840))], (5835 ^ _778495) ^ [_871256, _871258, _871260, _871262] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_871256, tc_HOL_Obool)), _871258), hAPP(hAPP(c_Set_Oinsert(_871256), _871260), _871262)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_871256, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_871256, tc_HOL_Obool)), _871258), hAPP(hAPP(c_Set_Oinsert(_871256), _871260), c_Orderings_Obot__class_Obot(tc_fun(_871256, tc_HOL_Obool))))), _871262))], (30127 ^ _778495) ^ [_1327226, _1327228, _1327230, _1327232, _1327234] : [hBOOL(hAPP(hAPP(_1327226, _1327228), _1327230)), -(hBOOL(hAPP(hAPP(_1327226, hAPP(c_Product__Type_Osnd(_1327232, _1327234), hAPP(hAPP(c_Product__Type_OPair(_1327232, _1327234), _1327230), _1327228))), hAPP(c_Product__Type_Ofst(_1327232, _1327234), hAPP(hAPP(c_Product__Type_OPair(_1327232, _1327234), _1327230), _1327228)))))], (42780 ^ _778495) ^ [_1630977, _1630979, _1630981, _1630983] : [-(_1630977 = _1630979), 42783 ^ _778495 : [(42790 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630981), _1630977), hAPP(c_List_Oset(_1630981), _1630983))), -(hBOOL(hAPP(hAPP(c_member(_1630981), _1630977), hAPP(c_List_Oset(_1630981), c_List_Oremove1(_1630981, _1630979, _1630983)))))], (42784 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630981), _1630977), hAPP(c_List_Oset(_1630981), c_List_Oremove1(_1630981, _1630979, _1630983)))), -(hBOOL(hAPP(hAPP(c_member(_1630981), _1630977), hAPP(c_List_Oset(_1630981), _1630983))))]]], (45060 ^ _778495) ^ [_1682005, _1682007, _1682009, _1682011, _1682013] : [-(c_List_Olist__all2(_1682005, _1682007, _1682009, _1682011, _1682013)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682005)), _1682011) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682007)), _1682013), 45066 ^ _778495 : [(45069 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1682005, _1682007, tc_HOL_Obool), _1682009), 45065 ^ [_1682005, _1682007, _1682009, _1682011, _1682013]))], (45067 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682005, _1682007)), 45065 ^ [_1682005, _1682007, _1682009, _1682011, _1682013]), hAPP(c_List_Oset(tc_prod(_1682005, _1682007)), hAPP(hAPP(c_List_Ozip(_1682005, _1682007), _1682011), _1682013)))))]]], (43496 ^ _778495) ^ [_1647773, _1647775, _1647777, _1647779, _1647781] : [hAPP(hAPP(c_List_Odrop(_1647773), _1647775), _1647777) = hAPP(hAPP(c_List_Olist_OCons(_1647773), _1647779), _1647781), -(hAPP(hAPP(c_List_Onth(_1647773), _1647777), _1647775) = _1647779)], (42774 ^ _778495) ^ [_1630867, _1630869, _1630871] : [-(hAPP(hAPP(c_List_Olist__update(_1630867, c_List_Olist_ONil(_1630867)), _1630869), _1630871) = c_List_Olist_ONil(_1630867))], (46023 ^ _778495) ^ [_1704278] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1704278) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1704278)))], (52317 ^ _778495) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (27169 ^ _778495) ^ [_1263777, _1263779] : [class_Rings_Olinordered__idom(_1263777), 27172 ^ _778495 : [(27179 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263777), c_Groups_Ozero__class_Ozero(_1263777)), hAPP(c_Int_Oring__1__class_Oof__int(_1263777), _1263779))))], (27173 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263777), c_Groups_Ozero__class_Ozero(_1263777)), hAPP(c_Int_Oring__1__class_Oof__int(_1263777), _1263779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263779)))]]], (31956 ^ _778495) ^ [_1365930, _1365932, _1365934, _1365936] : [hBOOL(hAPP(hAPP(c_member(_1365932), _1365936), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365930, tc_fun(_1365932, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1365930, tc_HOL_Obool))), _1365934))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365930, tc_fun(_1365932, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1365930, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1365932, tc_HOL_Obool), tc_fun(_1365932, tc_HOL_Obool), _1365930), hAPP(c_COMBC(_1365932, tc_fun(_1365932, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365932))), _1365934)), _1365936)))], (41595 ^ _778495) ^ [_1601067, _1601069, _1601071, _1601073] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1601067), tc_List_Olist(_1601067), c_List_Olistrel(_1601067, _1601069)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1601067)), hAPP(hAPP(c_List_Olist_OCons(_1601067), _1601071), _1601073)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1601067), tc_HOL_Obool)))) = c_List_Oset__Cons(_1601067, hAPP(c_Relation_OImage(_1601067, _1601067, _1601069), hAPP(hAPP(c_Set_Oinsert(_1601067), _1601071), c_Orderings_Obot__class_Obot(tc_fun(_1601067, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1601067), tc_List_Olist(_1601067), c_List_Olistrel(_1601067, _1601069)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1601067)), _1601073), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1601067), tc_HOL_Obool))))))], (13336 ^ _778495) ^ [_1015697] : [-(_1015697 = 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)), _1015697)))], (23168 ^ _778495) ^ [_1193278, _1193280, _1193282, _1193284] : [class_Divides_Osemiring__div(_1193278), -(c_Divides_Odiv__class_Omod(_1193278, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193278), _1193280), _1193282), _1193284) = c_Divides_Odiv__class_Omod(_1193278, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193278), c_Divides_Odiv__class_Omod(_1193278, _1193280, _1193284)), _1193282), _1193284))], (33413 ^ _778495) ^ [_1398466, _1398468, _1398470, _1398472, _1398474] : [-(_1398466 = c_Orderings_Obot__class_Obot(tc_fun(_1398468, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398468, tc_fun(_1398470, tc_HOL_Obool)), _1398466), hAPP(hAPP(c_COMBB(tc_fun(_1398470, tc_HOL_Obool), tc_fun(_1398470, tc_HOL_Obool), _1398468), hAPP(c_Set_Oinsert(_1398470), _1398472)), _1398474)) = hAPP(hAPP(c_Set_Oinsert(_1398470), _1398472), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398468, tc_fun(_1398470, tc_HOL_Obool)), _1398466), _1398474)))], (30039 ^ _778495) ^ [_1325393, _1325395, _1325397, _1325399, _1325401] : [hAPP(c_Product__Type_Ofst(_1325393, _1325395), hAPP(hAPP(c_Product__Type_OPair(_1325393, _1325395), _1325397), _1325399)) = _1325401, -(_1325397 = _1325401)], (33451 ^ _778495) ^ [_1399421, _1399423, _1399425, _1399427, _1399429] : [-(_1399421 = c_Orderings_Obot__class_Obot(tc_fun(_1399423, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399423, tc_fun(_1399425, tc_HOL_Obool)), _1399421), hAPP(hAPP(c_COMBC(_1399423, tc_fun(_1399425, tc_HOL_Obool), tc_fun(_1399425, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1399425, tc_HOL_Obool), tc_fun(tc_fun(_1399425, tc_HOL_Obool), tc_fun(_1399425, tc_HOL_Obool)), _1399423), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399425, tc_HOL_Obool))), _1399427)), _1399429)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399425, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399423, tc_fun(_1399425, tc_HOL_Obool)), _1399421), _1399427)), _1399429))], (2930 ^ _778495) ^ [_821989, _821991] : [_821991 = _821989, -(c_Nitpick_Onum(_821991) = c_Nitpick_Onum(_821989))], (17374 ^ _778495) ^ [_1089276, _1089278, _1089280, _1089282] : [class_Fields_Olinordered__field__inverse__zero(_1089276), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089276), _1089278), _1089280)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089276), _1089282), c_Groups_Ozero__class_Ozero(_1089276))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089276), c_Groups_Ozero__class_Ozero(_1089276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089276), _1089278), _1089280))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089276), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1089276), _1089282), _1089278)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1089276), _1089282), _1089280))))], (52513 ^ _778495) ^ [_1834085] : [-(class_Nat_Osize(tc_Option_Ooption(_1834085)))], (34797 ^ _778495) ^ [_1429355, _1429357] : [-(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)), _1429355)), 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), _1429357), _1429355))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1429355), _1429357))], (44714 ^ _778495) ^ [_1674200, _1674202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1674200)), hAPP(c_Code__Numeral_Oof__nat, _1674202))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1674200), _1674202)))], (44504 ^ _778495) ^ [_1669744, _1669746, _1669748, _1669750, _1669752] : [hAPP(hAPP(c_List_Omap(_1669744, _1669746), _1669748), _1669750) = hAPP(hAPP(c_List_Omap(_1669744, _1669746), _1669748), _1669752), c_Fun_Oinj__on(_1669744, _1669746, _1669748, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669744, tc_HOL_Obool)), hAPP(c_List_Oset(_1669744), _1669750)), hAPP(c_List_Oset(_1669744), _1669752))), -(_1669750 = _1669752)], (10715 ^ _778495) ^ [_963144] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _963144), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _963144)], (3356 ^ _778495) ^ [_828616, _828618, _828620, _828622, _828624, _828626] : [-(c_Finite__Set_Ofold(_828626, _828622, _828618) = c_Finite__Set_Ofold(_828624, _828620, _828616)), _828626 = _828624, _828622 = _828620, _828618 = _828616], (25304 ^ _778495) ^ [_1230552, _1230554] : [-(hBOOL(hAPP(_1230552, hAPP(c_Int_Onat, _1230554)))), 25308 ^ _778495 : [(25311 ^ _778495) ^ [] : [hBOOL(hAPP(_1230552, 25307 ^ [_1230552, _1230554]))], (25309 ^ _778495) ^ [] : [-(_1230554 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 25307 ^ [_1230552, _1230554]))]], 25312 ^ _778495 : [(25315 ^ _778495) ^ [] : [hBOOL(hAPP(_1230552, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25313 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230554), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (50140 ^ _778495) ^ [_1792372, _1792374, _1792376] : [c_Fun_Oinj__on(_1792372, _1792374, _1792376, c_Orderings_Otop__class_Otop(tc_fun(_1792372, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1792372, _1792374, _1792376), c_Orderings_Otop__class_Otop(tc_fun(_1792372, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792374, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1792372, _1792374, _1792376, c_Orderings_Otop__class_Otop(tc_fun(_1792372, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792374, tc_HOL_Obool))))], (45438 ^ _778495) ^ [_1690333, _1690335] : [_1690335 = c_List_Olist_ONil(_1690333), -(c_List_Oremdups(_1690333, _1690335) = c_List_Olist_ONil(_1690333))], (48846 ^ _778495) ^ [_1764664, _1764666, _1764668] : [hBOOL(hAPP(hAPP(c_member(_1764666), _1764664), c_Orderings_Obot__class_Obot(tc_fun(_1764666, tc_HOL_Obool)))), hBOOL(hAPP(_1764668, _1764664))], (29457 ^ _778495) ^ [_1314312, _1314314, _1314316] : [29459 ^ _778495 : [(29462 ^ _778495) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1314312, _1314314), 29458 ^ [_1314312, _1314314, _1314316]))], (29460 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(_1314314, 29458 ^ [_1314312, _1314314, _1314316]), _1314316)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1314312, _1314314), _1314316)))], (39398 ^ _778495) ^ [_1544874, _1544876, _1544878, _1544880, _1544882, _1544884, _1544886, _1544888, _1544890, _1544892, _1544894] : [hAPP(_1544874, hAPP(_1544876, _1544878)) = hAPP(_1544880, hAPP(_1544882, _1544884)), -(hAPP(hAPP(c_Fun_Ocomp(_1544886, _1544888, _1544890, _1544874), _1544876), _1544878) = hAPP(hAPP(c_Fun_Ocomp(_1544892, _1544888, _1544894, _1544880), _1544882), _1544884))], (27533 ^ _778495) ^ [_1269837] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1269837, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1269837, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1269837, tc_HOL_Obool)))], (13777 ^ _778495) ^ [_1022999, _1023001, _1023003, _1023005, _1023007] : [class_Rings_Oordered__semiring(_1022999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022999), _1023001), _1023003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022999), _1023005), _1023007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022999), c_Groups_Ozero__class_Ozero(_1022999)), _1023001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022999), c_Groups_Ozero__class_Ozero(_1022999)), _1023005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022999), _1023001), _1023005)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022999), _1023003), _1023007))))], (32920 ^ _778495) ^ [_1385919, _1385921] : [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), _1385919), _1385921)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1385919), _1385921)))], (49943 ^ _778495) ^ [_1788584, _1788586, _1788588, _1788590] : [-(c_Product__Type_Ocurry(_1788584, _1788586, _1788588, hAPP(c_Product__Type_Oprod_Oprod__case(_1788584, _1788586, _1788588), _1788590)) = _1788590)], (11083 ^ _778495) ^ [_969231, _969233, _969235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969231), _969233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _969235), _969233)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _969235), _969231))))], (17142 ^ _778495) ^ [_1084997, _1084999, _1085001, _1085003] : [class_Fields_Olinordered__field(_1084997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084997), c_Groups_Ozero__class_Ozero(_1084997)), _1084999)), 17149 ^ _778495 : [(17156 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084997), _1085001), _1084999)), _1085003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084997), _1085001), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1084997), _1085003), _1084999))))], (17150 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084997), _1085001), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1084997), _1085003), _1084999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084997), _1085001), _1084999)), _1085003)))]]], (23032 ^ _778495) ^ [_1190380, _1190382, _1190384] : [class_Divides_Osemiring__div(_1190380), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190380), _1190382), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190380), _1190384), _1190382))), c_Divides_Odiv__class_Omod(_1190380, _1190384, _1190382)) = _1190384)], (14649 ^ _778495) ^ [_1038500, _1038502] : [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), _1038500), _1038502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1038500))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1038502)))], (34532 ^ _778495) ^ [_1423963, _1423965, _1423967, _1423969] : [-(hAPP(c_Set_Oimage(_1423963, _1423965, _1423967), _1423969) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1423963, tc_fun(_1423965, tc_HOL_Obool)), _1423969), hAPP(hAPP(c_COMBC(_1423963, tc_fun(_1423965, tc_HOL_Obool), tc_fun(_1423965, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1423965, tc_fun(tc_fun(_1423965, tc_HOL_Obool), tc_fun(_1423965, tc_HOL_Obool)), _1423963), c_Set_Oinsert(_1423965)), _1423967)), c_Orderings_Obot__class_Obot(tc_fun(_1423965, tc_HOL_Obool)))))], (4154 ^ _778495) ^ [_841491, _841493] : [_841493 = _841491, -(c_List_Orev(_841493) = c_List_Orev(_841491))], (27387 ^ _778495) ^ [_1267318, _1267320] : [class_Rings_Olinordered__idom(_1267318), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267318), c_Groups_Ozero__class_Ozero(_1267318)), _1267320)), -(c_Groups_Osgn__class_Osgn(_1267318, _1267320) = c_Groups_Oone__class_Oone(_1267318))], (35528 ^ _778495) ^ [_1442694, _1442696, _1442698, _1442700, _1442702, _1442704] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1442694, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442696, _1442694, _1442698), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1442700, tc_fun(_1442696, tc_HOL_Obool)), _1442702), _1442704))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1442700, tc_fun(_1442694, tc_HOL_Obool)), _1442702), hAPP(hAPP(c_COMBB(tc_fun(_1442696, tc_HOL_Obool), tc_fun(_1442694, tc_HOL_Obool), _1442700), c_Relation_OImage(_1442696, _1442694, _1442698)), _1442704)))))], (23038 ^ _778495) ^ [_1190513, _1190515, _1190517] : [class_Divides_Osemiring__div(_1190513), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190513), c_Divides_Odiv__class_Omod(_1190513, _1190515, _1190517)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190513), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190513), _1190515), _1190517)), _1190517)) = _1190515)], (39648 ^ _778495) ^ [_1550534, _1550536, _1550538, _1550540, _1550542, _1550544] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1550534, tc_fun(_1550536, tc_HOL_Obool)), _1550538), hAPP(c_Fun_Ocomp(_1550540, tc_fun(_1550536, tc_HOL_Obool), _1550534, _1550542), _1550544)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1550540, tc_fun(_1550536, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1550534, _1550540, _1550544), _1550538)), _1550542))], (23488 ^ _778495) ^ [_1199156, _1199158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199156, _1199158)), _1199156)))], (41290 ^ _778495) ^ [_1591505, _1591507, _1591509] : [-(c_Nitpick_Oplus__frac(_1591505, _1591507, _1591509) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1591505), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1591505), _1591507), hAPP(c_Nitpick_Odenom(_1591505), _1591509))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1591505), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1591505), tc_Int_Oint), c_Nitpick_Ofrac(_1591505)), 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(_1591505), _1591507))), 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(_1591505), _1591507))))), 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(_1591505), _1591509))), 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(_1591505), _1591509)))))), c_COMBI(tc_Int_Oint))))], (45723 ^ _778495) ^ [_1697145] : [-(c_List_Otranspose(_1697145, c_List_Olist_ONil(tc_List_Olist(_1697145))) = c_List_Olist_ONil(tc_List_Olist(_1697145)))], (29043 ^ _778495) ^ [_1305778, _1305780, _1305782, _1305784] : [-(c_Nat_Onat_Onat__case(_1305778, _1305780, _1305782, hAPP(c_Nat_OSuc, _1305784)) = hAPP(_1305782, _1305784))], (6598 ^ _778495) ^ [_885946, _885948, _885950, _885952] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885946, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_885946), _885948), _885950)), _885952))), hBOOL(hAPP(hAPP(c_member(_885946), _885948), _885952)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885946, tc_HOL_Obool)), _885950), _885952))], (4210 ^ _778495) ^ [_842299, _842301, _842303, _842305] : [-(c_List_Ofilter(_842305, _842301) = c_List_Ofilter(_842303, _842299)), _842305 = _842303, _842301 = _842299], (12274 ^ _778495) ^ [_993738, _993740, _993742] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_993738), _993740)), -(hBOOL(hAPP(hAPP(c_member(_993738), _993742), _993740))), -(hAPP(c_Finite__Set_Ocard(_993738), hAPP(hAPP(c_Set_Oinsert(_993738), _993742), _993740)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_993738), _993740)))], (20632 ^ _778495) ^ [_1148387, _1148389] : [class_Int_Onumber__ring(_1148387), class_Rings_Olinordered__idom(_1148387), 20639 ^ _778495 : [(20646 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1148389), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148387), hAPP(c_Int_Onumber__class_Onumber__of(_1148387), _1148389)), c_Groups_Ozero__class_Ozero(_1148387))))], (20640 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148387), hAPP(c_Int_Onumber__class_Onumber__of(_1148387), _1148389)), c_Groups_Ozero__class_Ozero(_1148387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1148389), c_Int_OPls)))]]], (38832 ^ _778495) ^ [_1530315, _1530317] : [-(hAPP(c_Relation_ODomain(_1530315, _1530317), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530315, _1530317), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1530315, tc_HOL_Obool)))], (9498 ^ _778495) ^ [_940436, _940438, _940440] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_940436), _940438)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940436, tc_HOL_Obool)), _940440), _940438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_940436), _940440)), hAPP(c_Finite__Set_Ocard(_940436), _940438))))], (1548 ^ _778495) ^ [_800873, _800875] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_800873)), _800875 = _800873, class_Groups_Oordered__ab__semigroup__add__imp__le(_800875)], (37907 ^ _778495) ^ [_1500116, _1500118, _1500120] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1500116, tc_HOL_Obool)), _1500118), _1500120) = hAPP(c_Set_OCollect(_1500116), hAPP(hAPP(c_COMBS(_1500116, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1500116), c_fconj), hAPP(hAPP(c_COMBC(_1500116, tc_fun(_1500116, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500116)), _1500118))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1500116), c_fNot), hAPP(hAPP(c_COMBC(_1500116, tc_fun(_1500116, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500116)), _1500120)))))], (22686 ^ _778495) ^ [_1184027] : [-(c_Int_Opred(c_Int_OBit1(_1184027)) = c_Int_OBit0(_1184027))], (15793 ^ _778495) ^ [_1059680, _1059682, _1059684, _1059686, _1059688] : [class_Groups_Ocomm__monoid__mult(_1059680), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059682), _1059684)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059682), _1059686)), 15807 ^ _778495 : [(15810 ^ _778495) ^ [] : [hAPP(_1059688, 15806 ^ [_1059680, _1059682, _1059684, _1059686, _1059688]) = c_Groups_Oone__class_Oone(_1059680)], (15808 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1059682), 15806 ^ [_1059680, _1059682, _1059684, _1059686, _1059688]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1059682, tc_HOL_Obool)), _1059684), _1059686))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1059682, _1059680), _1059688), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1059682, tc_HOL_Obool)), _1059684), _1059686)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059680), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1059682, _1059680), _1059688), _1059684)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1059682, _1059680), _1059688), _1059686)))], (32884 ^ _778495) ^ [_1385190, _1385192, _1385194, _1385196] : [class_Orderings_Oorder(_1385190), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385190, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1385190, _1385192, _1385194)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1385190, _1385194, _1385196)) = c_Orderings_Obot__class_Obot(tc_fun(_1385190, tc_HOL_Obool)))], (29861 ^ _778495) ^ [_1321673, _1321675] : [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), _1321673), _1321675))), 29864 ^ _778495 : [(29871 ^ _778495) ^ [] : [-(_1321675 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1321673, _1321675) = c_Nitpick_Onat__gcd(_1321675, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1321673, _1321675)))], (29865 ^ _778495) ^ [] : [_1321675 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1321673, _1321675) = _1321673)]]], (26276 ^ _778495) ^ [_1248249, _1248251] : [class_Power_Opower(_1248249), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1248249), _1248251), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1248249))], (39127 ^ _778495) ^ [_1537829, _1537831, _1537833] : [c_Relation_Orefl__on(_1537829, _1537831, _1537833), 39130 ^ _778495 : [(39137 ^ _778495) ^ [_1538313] : [hBOOL(hAPP(hAPP(c_member(_1537829), _1538313), _1537831)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1537829, _1537829)), hAPP(hAPP(c_Product__Type_OPair(_1537829, _1537829), _1538313), _1538313)), _1537833)))], (39131 ^ _778495) ^ [_1538040] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537829, _1537829)), _1538040), _1537833)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1537829, _1537829, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1537829, tc_fun(_1537829, tc_HOL_Obool), tc_fun(_1537829, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1537829, tc_HOL_Obool), tc_fun(_1537829, tc_HOL_Obool)), _1537829), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1537829)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1537829), c_fconj), hAPP(hAPP(c_COMBC(_1537829, tc_fun(_1537829, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537829)), _1537831)))), hAPP(hAPP(c_COMBC(_1537829, tc_fun(_1537829, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537829)), _1537831))), _1538040)))]]], (50679 ^ _778495) ^ [_1804889, _1804891, _1804893, _1804895, _1804897] : [class_Divides_Osemiring__div(_1804889), -(_1804891 = c_Groups_Ozero__class_Ozero(_1804889)), -(_1804893 = c_Groups_Ozero__class_Ozero(_1804889)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804889), _1804891), _1804895)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804889), _1804893), _1804897)), 50698 ^ _778495 : [(50705 ^ _778495) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804889), _1804895), _1804893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804889), _1804891), _1804897), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1804889), _1804895), _1804891) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1804889), _1804897), _1804893))], (50699 ^ _778495) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1804889), _1804895), _1804891) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1804889), _1804897), _1804893), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804889), _1804895), _1804893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804889), _1804891), _1804897))]]], (29515 ^ _778495) ^ [_1315471, _1315473, _1315475] : [hBOOL(hAPP(_1315471, hAPP(hAPP(c_Product__Type_OPair(_1315473, _1315475), 29516 ^ [_1315471, _1315473, _1315475]), 29517 ^ [_1315471, _1315473, _1315475]))), 29520 ^ _778495 : [(29521 ^ _778495) ^ [_1315618] : [-(hBOOL(hAPP(_1315471, _1315618)))]]], (40403 ^ _778495) ^ [_1569074, _1569076, _1569078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569074, _1569074), tc_HOL_Obool)), _1569076), _1569078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569074, _1569074), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1569074, _1569076)), c_Transitive__Closure_Ortrancl(_1569074, _1569078))))], (15021 ^ _778495) ^ [_1044997, _1044999, _1045001, _1045003] : [class_Rings_Olinordered__semiring(_1044997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044997), _1044999), _1045001)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044997), _1044999), _1045003))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044997), c_Groups_Ozero__class_Ozero(_1044997)), _1044999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044997), _1045001), _1045003)))], (5737 ^ _778495) ^ [_869356, _869358, _869360, _869362] : [-(hAPP(hAPP(c_Set_Oinsert(_869356), _869358), hAPP(hAPP(c_Set_Oinsert(_869356), _869360), _869362)) = hAPP(hAPP(c_Set_Oinsert(_869356), _869360), hAPP(hAPP(c_Set_Oinsert(_869356), _869358), _869362)))], (42268 ^ _778495) ^ [_1620143, _1620145, _1620147, _1620149] : [42270 ^ _778495 : [(42273 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1620147, 42269 ^ [_1620143, _1620145, _1620147, _1620149])), hAPP(_1620149, 42269 ^ [_1620143, _1620145, _1620147, _1620149])))], (42271 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620143), 42269 ^ [_1620143, _1620145, _1620147, _1620149]), hAPP(c_List_Oset(_1620143), _1620145))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1620143, _1620147, _1620145)), c_List_Olist_Olist__size(_1620143, _1620149, _1620145))))], (30399 ^ _778495) ^ [_1332748, _1332750, _1332752, _1332754] : [hBOOL(hAPP(hAPP(_1332752, _1332754), _1332750)), -(hBOOL(hAPP(hAPP(c_member(_1332748), _1332750), c_SetInterval_Oord_OatLeast(_1332748, _1332752, _1332754))))], (28145 ^ _778495) ^ [_1280622, _1280624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1280622), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280624)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280622)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280624))], (48196 ^ _778495) ^ [_1750539, _1750541, _1750543] : [-(c_List_Oreplicate(_1750539, hAPP(c_Nat_OSuc, _1750541), _1750543) = hAPP(hAPP(c_List_Olist_OCons(_1750539), _1750543), c_List_Oreplicate(_1750539, _1750541, _1750543)))], (18138 ^ _778495) ^ [_1103996, _1103998, _1104000, _1104002] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103996), hAPP(c_Int_Onumber__class_Onumber__of(_1103996), _1103998)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1103996), _1104000), _1104002)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1103996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103996), hAPP(c_Int_Onumber__class_Onumber__of(_1103996), _1103998)), _1104000)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103996), hAPP(c_Int_Onumber__class_Onumber__of(_1103996), _1103998)), _1104002))), class_Int_Onumber(_1103996), class_Rings_Oring(_1103996)], (49152 ^ _778495) ^ [_1772564, _1772566, _1772568, _1772570] : [c_Relation_Oantisym(_1772564, _1772566), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772564, _1772564)), hAPP(hAPP(c_Product__Type_OPair(_1772564, _1772564), _1772568), _1772570)), _1772566)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772564, _1772564)), hAPP(hAPP(c_Product__Type_OPair(_1772564, _1772564), _1772570), _1772568)), _1772566)), -(_1772568 = _1772570)], (15435 ^ _778495) ^ [_1052650, _1052652, _1052654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1052650)), 15438 ^ _778495 : [(15445 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052652), _1052654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052650), _1052652)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052650), _1052654))))], (15439 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052650), _1052652)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052650), _1052654))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052652), _1052654)))]]], (22816 ^ _778495) ^ [_1186360] : [-(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), _1186360))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34393 ^ _778495) ^ [_1420784, _1420786, _1420788, _1420790, _1420792] : [hBOOL(hAPP(hAPP(c_member(_1420784), _1420786), hAPP(c_Set_Oimage(_1420788, _1420784, _1420790), _1420792))), 34397 ^ _778495 : [(34400 ^ _778495) ^ [] : [-(_1420786 = hAPP(_1420790, 34396 ^ [_1420784, _1420786, _1420788, _1420790, _1420792]))], (34398 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1420788), 34396 ^ [_1420784, _1420786, _1420788, _1420790, _1420792]), _1420792)))]]], (40151 ^ _778495) ^ [_1562174, _1562176] : [c_Wellfounded_Owf(_1562174, _1562176), 40154 ^ _778495 : [(40155 ^ _778495) ^ [_1562306] : [40156 ^ _778495 : [(40157 ^ _778495) ^ [_1562411] : [hBOOL(hAPP(hAPP(c_member(_1562174), _1562411), _1562306))]], 40159 ^ _778495 : [(40162 ^ _778495) ^ [_1562533] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562174, _1562174)), hAPP(hAPP(c_Product__Type_OPair(_1562174, _1562174), _1562533), 40158 ^ [_1562174, _1562176, _1562306])), _1562176)), hBOOL(hAPP(hAPP(c_member(_1562174), _1562533), _1562306))], (40160 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562174), 40158 ^ [_1562174, _1562176, _1562306]), _1562306)))]]]]], (20083 ^ _778495) ^ [_1139288] : [class_Rings_Osemiring__1(_1139288), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1139288), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1139288))], (13436 ^ _778495) ^ [_1017106, _1017108, _1017110] : [13437 ^ _778495 : [(13440 ^ _778495) ^ [] : [_1017108 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13438 ^ _778495) ^ [] : [_1017106 = _1017110]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017106), _1017108) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017110), _1017108))], (50509 ^ _778495) ^ [_1801850, _1801852, _1801854] : [c_List_Olist__all(tc_Nat_Onat, _1801850, c_List_Oupt(_1801852, _1801854)), -(c_List_Oall__interval__nat(_1801850, _1801852, _1801854))], (52637 ^ _778495) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (34476 ^ _778495) ^ [_1422631, _1422633, _1422635] : [class_Groups_Oordered__ab__group__add(_1422631), -(hAPP(c_Set_Oimage(_1422631, _1422631, c_Groups_Ouminus__class_Ouminus(_1422631)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1422631, _1422633, _1422635)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1422631, hAPP(c_Groups_Ouminus__class_Ouminus(_1422631), _1422635), hAPP(c_Groups_Ouminus__class_Ouminus(_1422631), _1422633)))], (35033 ^ _778495) ^ [_1433560] : [35035 ^ _778495 : [(35038 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35034 ^ [_1433560]))], (35036 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35034 ^ [_1433560]), _1433560)))]], -(c_Nat__Transfer_Onat__set(_1433560))], (8628 ^ _778495) ^ [_922625, _922627, _922629] : [class_Lattices_Oab__semigroup__idem__mult(_922625), hBOOL(hAPP(c_Finite__Set_Ofinite(_922625), _922627)), -(_922627 = c_Orderings_Obot__class_Obot(tc_fun(_922625, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_922625), _922629)), -(_922629 = c_Orderings_Obot__class_Obot(tc_fun(_922625, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_922625, c_Groups_Otimes__class_Otimes(_922625)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922625, tc_HOL_Obool)), _922627), _922629)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922625), hAPP(c_Finite__Set_Ofold1(_922625, c_Groups_Otimes__class_Otimes(_922625)), _922627)), hAPP(c_Finite__Set_Ofold1(_922625, c_Groups_Otimes__class_Otimes(_922625)), _922629)))], (38170 ^ _778495) ^ [_1509106, _1509108, _1509110] : [class_Groups_Olinordered__ab__semigroup__add(_1509106), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509106), _1509108)), -(_1509108 = c_Orderings_Obot__class_Obot(tc_fun(_1509106, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1509106), _1509110), c_Big__Operators_Olinorder__class_OMax(_1509106, _1509108)) = c_Big__Operators_Olinorder__class_OMax(_1509106, hAPP(c_Set_OCollect(_1509106), hAPP(hAPP(c_COMBB(tc_fun(_1509106, tc_HOL_Obool), tc_HOL_Obool, _1509106), c_HOL_OEx(_1509106)), hAPP(hAPP(c_COMBC(_1509106, tc_fun(_1509106, tc_HOL_Obool), tc_fun(_1509106, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509106, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1509106, tc_HOL_Obool), tc_fun(_1509106, tc_HOL_Obool)), _1509106), c_COMBS(_1509106, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509106, tc_HOL_Obool), tc_fun(_1509106, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1509106), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509106), c_fconj)), hAPP(hAPP(c_COMBC(_1509106, tc_fun(_1509106, _1509106), tc_fun(_1509106, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509106, tc_HOL_Obool), tc_fun(tc_fun(_1509106, _1509106), tc_fun(_1509106, tc_HOL_Obool)), _1509106), c_COMBB(_1509106, tc_HOL_Obool, _1509106)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1509106), _1509110))))), hAPP(hAPP(c_COMBC(_1509106, tc_fun(_1509106, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509106)), _1509108))))))], (1898 ^ _778495) ^ [_805248, _805250] : [-(class_Power_Opower(_805248)), _805250 = _805248, class_Power_Opower(_805250)], (31835 ^ _778495) ^ [_1361691, _1361693, _1361695, _1361697] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361691, tc_fun(_1361693, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1361691, tc_HOL_Obool), _1361695)), _1361697) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1361691, tc_HOL_Obool), tc_fun(_1361693, tc_HOL_Obool)), _1361695), hAPP(hAPP(c_COMBC(tc_fun(_1361691, tc_HOL_Obool), tc_fun(_1361691, tc_fun(_1361693, tc_HOL_Obool)), tc_fun(_1361693, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1361691, tc_fun(_1361693, tc_HOL_Obool))), _1361697)))], (5060 ^ _778495) ^ [_855738, _855740, _855742, _855744, _855746, _855748, _855750, _855752] : [-(c_Quotient_OBabs(_855752, _855748, _855744, _855740) = c_Quotient_OBabs(_855750, _855746, _855742, _855738)), _855752 = _855750, _855748 = _855746, _855744 = _855742, _855740 = _855738], (22590 ^ _778495) ^ [_1182324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1182324)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182324), c_Int_OPls)))], (32934 ^ _778495) ^ [_1386166, _1386168] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1386166, _1386168))))], (39458 ^ _778495) ^ [_1546469, _1546471, _1546473, _1546475, _1546477, _1546479] : [c_Fun_Oinj__on(_1546469, _1546471, hAPP(c_Fun_Ocomp(_1546473, _1546471, _1546469, _1546475), _1546477), _1546479), -(c_Fun_Oinj__on(_1546473, _1546471, _1546475, hAPP(c_Set_Oimage(_1546469, _1546473, _1546477), _1546479)))], (21666 ^ _778495) ^ [_1166447, _1166449] : [c_Int_OBit0(_1166447) = c_Int_OBit0(_1166449), -(_1166447 = _1166449)], (48684 ^ _778495) ^ [_1760821, _1760823, _1760825, _1760827] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1760821, _1760823, _1760825, _1760827, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760823)) = _1760825)], (45965 ^ _778495) ^ [_1703223, _1703225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703223), _1703225)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1703223, _1703225)) = _1703223)], (51723 ^ _778495) ^ [_1822792, _1822794] : [51724 ^ _778495 : [(51727 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822794), _1822792))], (51725 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822792), _1822794)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822792, _1822794))], (41941 ^ _778495) ^ [_1610986, _1610988, _1610990] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610986, tc_HOL_Obool)), hAPP(c_List_Oset(_1610986), hAPP(hAPP(c_List_Otake(_1610986), _1610988), _1610990))), hAPP(c_List_Oset(_1610986), _1610990))))], (24854 ^ _778495) ^ [_1223200] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1223200))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1223200)) = _1223200)], (34775 ^ _778495) ^ [_1429005] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1429005) = 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)), _1429005)))], (37116 ^ _778495) ^ [_1478968, _1478970, _1478972, _1478974, _1478976] : [hBOOL(hAPP(hAPP(c_member(_1478968), hAPP(_1478970, _1478972)), _1478974)), -(hBOOL(hAPP(hAPP(c_member(_1478976), _1478972), hAPP(c_Set_Ovimage(_1478976, _1478968, _1478970), _1478974))))], (24647 ^ _778495) ^ [_1219804, _1219806, _1219808] : [-(_1219804 = 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), _1219804), _1219806)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1219804), _1219808)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1219806), _1219808))], (3052 ^ _778495) ^ [_823916, _823918, _823920, _823922] : [-(c_List_Olistrel1(_823922, _823918) = c_List_Olistrel1(_823920, _823916)), _823922 = _823920, _823918 = _823916], (41023 ^ _778495) ^ [_1584268, _1584270, _1584272, _1584274] : [-(hAPP(hAPP(c_Nat_Ocompow(_1584268, _1584268), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1584270), _1584272)), _1584274) = hAPP(c_Fun_Ocomp(_1584268, _1584268, _1584268, hAPP(hAPP(c_Nat_Ocompow(_1584268, _1584268), _1584270), _1584274)), hAPP(hAPP(c_Nat_Ocompow(_1584268, _1584268), _1584272), _1584274)))], (4932 ^ _778495) ^ [_853704, _853706, _853708, _853710, _853712, _853714, _853716, _853718] : [-(c_Fun_Othe__inv__into(_853718, _853714, _853710, _853706) = c_Fun_Othe__inv__into(_853716, _853712, _853708, _853704)), _853718 = _853716, _853714 = _853712, _853710 = _853708, _853706 = _853704], (4872 ^ _778495) ^ [_852754, _852756, _852758, _852760, _852762, _852764, _852766, _852768, _852770, _852772] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_852772, _852768, _852764, _852760, _852756) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_852770, _852766, _852762, _852758, _852754)), _852772 = _852770, _852768 = _852766, _852764 = _852762, _852760 = _852758, _852756 = _852754], (51659 ^ _778495) ^ [_1821673, _1821675] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821673), _1821675)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821675, _1821673) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (35256 ^ _778495) ^ [_1437091, _1437093, _1437095] : [class_Orderings_Oord(_1437091), 35259 ^ _778495 : [(35266 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437091), _1437095), _1437093)), -(hBOOL(hAPP(hAPP(c_member(_1437091), _1437093), hAPP(c_SetInterval_Oord__class_OatLeast(_1437091), _1437095))))], (35260 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1437091), _1437093), hAPP(c_SetInterval_Oord__class_OatLeast(_1437091), _1437095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437091), _1437095), _1437093)))]]], (44788 ^ _778495) ^ [_1675760, _1675762] : [-(c_Random_Oselect__weight(_1675760, _1675762) = 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(_1675760, 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, _1675760), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1675760)), _1675762)))), hAPP(hAPP(c_COMBB(_1675760, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675760, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1675760, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1675760, _1675762))))], (25812 ^ _778495) ^ [_1239630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1239630)), -(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), _1239630), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (2440 ^ _778495) ^ [_814426, _814428] : [_814428 = _814426, -(c_Int_Opred(_814428) = c_Int_Opred(_814426))], (37891 ^ _778495) ^ [_1499783, _1499785, _1499787] : [hBOOL(hAPP(_1499783, _1499785)), -(hAPP(c_Set_OCollect(_1499787), hAPP(hAPP(c_COMBS(_1499787, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499787), c_fconj), hAPP(c_fequal, _1499785))), _1499783)) = hAPP(hAPP(c_Set_Oinsert(_1499787), _1499785), c_Orderings_Obot__class_Obot(tc_fun(_1499787, tc_HOL_Obool))))], (29109 ^ _778495) ^ [_1307065, _1307067, _1307069, _1307071, _1307073] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1307065, _1307067, _1307069), _1307071), _1307073)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1307065, _1307067)), hAPP(hAPP(c_Product__Type_OPair(_1307065, _1307067), _1307071), _1307073)), _1307069)))], (46694 ^ _778495) ^ [_1717347, _1717349, _1717351] : [hAPP(c_List_Orev(_1717347), _1717349) = _1717351, -(_1717349 = hAPP(c_List_Orev(_1717347), _1717351))], (18326 ^ _778495) ^ [_1107218, _1107220, _1107222, _1107224] : [class_Fields_Olinordered__field__inverse__zero(_1107218), class_Int_Onumber(_1107218), 18333 ^ _778495 : [(18334 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), _1107220), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107218), _1107222), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224)))), 18337 ^ _778495 : [(18344 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), c_Groups_Ozero__class_Ozero(_1107218)), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224)))), 18347 ^ _778495 : [(18354 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224)), c_Groups_Ozero__class_Ozero(_1107218)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), _1107220), c_Groups_Ozero__class_Ozero(_1107218))))], (18348 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224)), c_Groups_Ozero__class_Ozero(_1107218))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), _1107222), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107218), _1107220), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224)))))]]], (18338 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), c_Groups_Ozero__class_Ozero(_1107218)), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107218), _1107220), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224))), _1107222)))]]], (18360 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), _1107220), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107218), _1107222), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224))))), 18363 ^ _778495 : [(18366 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107218), _1107220), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224))), _1107222))], (18364 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), c_Groups_Ozero__class_Ozero(_1107218)), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224))))]], 18367 ^ _778495 : [(18370 ^ _778495) ^ [] : [18371 ^ _778495 : [(18374 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), _1107222), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107218), _1107220), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224))))], (18372 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224)), c_Groups_Ozero__class_Ozero(_1107218))))]], 18375 ^ _778495 : [(18378 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), _1107220), c_Groups_Ozero__class_Ozero(_1107218)))], (18376 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224)), c_Groups_Ozero__class_Ozero(_1107218)))]]], (18368 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107218), c_Groups_Ozero__class_Ozero(_1107218)), hAPP(c_Int_Onumber__class_Onumber__of(_1107218), _1107224)))]]]]], (33179 ^ _778495) ^ [_1391068, _1391070, _1391072] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391068, tc_fun(_1391070, tc_HOL_Obool)), _1391072), hAPP(c_COMBK(tc_fun(_1391070, tc_HOL_Obool), _1391068), c_Orderings_Obot__class_Obot(tc_fun(_1391070, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1391070, tc_HOL_Obool)))], (40936 ^ _778495) ^ [_1582122, _1582124, _1582126, _1582128, _1582130] : [c_Relation_Osingle__valued(_1582122, _1582124, _1582126), c_Relation_Osingle__valued(_1582124, _1582128, _1582130), -(c_Relation_Osingle__valued(_1582122, _1582128, hAPP(hAPP(c_Relation_Orel__comp(_1582122, _1582124, _1582128), _1582126), _1582130)))], (50355 ^ _778495) ^ [_1796625, _1796627, _1796629, _1796631] : [c_Equiv__Relations_Oequivp(_1796625, _1796627), 50361 ^ _778495 : [(50364 ^ _778495) ^ [] : [hBOOL(hAPP(_1796631, 50360 ^ [_1796625, _1796627, _1796629, _1796631]))], (50362 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1796629, 50360 ^ [_1796625, _1796627, _1796629, _1796631])))]], 50367 ^ _778495 : [(50368 ^ _778495) ^ [_1796884] : [hBOOL(hAPP(_1796629, _1796884))]], 50370 ^ _778495 : [(50373 ^ _778495) ^ [] : [-(hBOOL(hAPP(_1796631, 50369 ^ [_1796625, _1796627, _1796629, _1796631])))], (50371 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796625), 50369 ^ [_1796625, _1796627, _1796629, _1796631]), c_Quotient_ORespects(_1796625, _1796627))))]]], (14355 ^ _778495) ^ [_1033605, _1033607, _1033609, _1033611] : [class_Rings_Olinordered__ring__strict(_1033605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033605), _1033607), _1033609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033605), _1033611), c_Groups_Ozero__class_Ozero(_1033605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033605), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033605), _1033611), _1033609)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033605), _1033611), _1033607))))], (3786 ^ _778495) ^ [_835377, _835379, _835381, _835383, _835385, _835387] : [-(c_List_OtakeWhile(_835387, _835383, _835379) = c_List_OtakeWhile(_835385, _835381, _835377)), _835387 = _835385, _835383 = _835381, _835379 = _835377], (48852 ^ _778495) ^ [_1764770, _1764772] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1764770, tc_HOL_Obool), _1764772) = hAPP(c_Set_OCollect(_1764770), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1764770, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1764770), c_HOL_OEx(tc_fun(_1764770, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1764770, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1764770, tc_HOL_Obool), tc_HOL_Obool), _1764770), hAPP(c_COMBS(tc_fun(_1764770, 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(_1764770, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1764770, tc_HOL_Obool), tc_fun(tc_fun(_1764770, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1764770, tc_HOL_Obool))), _1764772)))), c_member(_1764770)))))], (39422 ^ _778495) ^ [_1545499, _1545501, _1545503, _1545505, _1545507, _1545509] : [-(hAPP(c_Set_Ovimage(_1545499, _1545501, hAPP(c_Fun_Ocomp(_1545503, _1545501, _1545499, _1545505), _1545507)), _1545509) = hAPP(c_Set_Ovimage(_1545499, _1545503, _1545507), hAPP(c_Set_Ovimage(_1545503, _1545501, _1545505), _1545509)))], (43530 ^ _778495) ^ [_1648499, _1648501, _1648503, _1648505] : [-(hAPP(hAPP(c_List_Odrop(_1648499), _1648501), hAPP(hAPP(c_List_Odrop(_1648499), _1648503), _1648505)) = hAPP(hAPP(c_List_Odrop(_1648499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1648501), _1648503)), _1648505))], (48462 ^ _778495) ^ [_1755451, _1755453, _1755455] : [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), _1755451), _1755453))), -(hBOOL(hAPP(hAPP(_1755455, _1755451), _1755453))), 48469 ^ _778495 : [(48472 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48467 ^ [_1755451, _1755453, _1755455]), 48468 ^ [_1755451, _1755453, _1755455]))), -(hBOOL(hAPP(hAPP(_1755455, 48467 ^ [_1755451, _1755453, _1755455]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48468 ^ [_1755451, _1755453, _1755455]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48478 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(_1755455, 48467 ^ [_1755451, _1755453, _1755455]), 48468 ^ [_1755451, _1755453, _1755455]))], (48470 ^ _778495) ^ [] : [-(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), 48467 ^ [_1755451, _1755453, _1755455]), 48468 ^ [_1755451, _1755453, _1755455]))))]]], (43706 ^ _778495) ^ [_1652879, _1652881, _1652883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652879), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652881)), _1652883))), -(_1652883 = hAPP(hAPP(c_List_Oappend(_1652881), hAPP(hAPP(c_List_Otake(_1652881), _1652879), _1652883)), hAPP(hAPP(c_List_Olist_OCons(_1652881), hAPP(hAPP(c_List_Onth(_1652881), _1652883), _1652879)), hAPP(hAPP(c_List_Odrop(_1652881), hAPP(c_Nat_OSuc, _1652879)), _1652883))))], (45631 ^ _778495) ^ [_1694499, _1694501, _1694503] : [c_List_Oconcat(_1694499, _1694501) = c_List_Oconcat(_1694499, _1694503), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694499))), _1694501) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694499))), _1694503), 45641 ^ _778495 : [(45644 ^ _778495) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1694499), tc_List_Olist(_1694499), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694499), tc_fun(tc_List_Olist(_1694499), tc_Nat_Onat), tc_fun(tc_List_Olist(_1694499), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1694499), tc_Nat_Onat), tc_fun(tc_List_Olist(_1694499), tc_HOL_Obool)), tc_List_Olist(_1694499)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1694499))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1694499)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1694499))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1694499)))), 45640 ^ [_1694499, _1694501, _1694503]))], (45642 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694499), tc_List_Olist(_1694499))), 45640 ^ [_1694499, _1694501, _1694503]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1694499), tc_List_Olist(_1694499))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1694499), tc_List_Olist(_1694499)), _1694501), _1694503)))))]], -(_1694501 = _1694503)], (22880 ^ _778495) ^ [_1187531, _1187533] : [class_Int_Onumber__ring(_1187531), -(hAPP(c_Int_Onumber__class_Onumber__of(_1187531), c_Int_Opred(_1187533)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187531), hAPP(c_Groups_Ouminus__class_Ouminus(_1187531), c_Groups_Oone__class_Oone(_1187531))), hAPP(c_Int_Onumber__class_Onumber__of(_1187531), _1187533)))], (34508 ^ _778495) ^ [_1423411, _1423413, _1423415, _1423417] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1423411), _1423413)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1423415), hAPP(c_Set_Oimage(_1423411, _1423415, _1423417), _1423413))), hAPP(c_Finite__Set_Ocard(_1423411), _1423413))))], (29775 ^ _778495) ^ [_1319956, _1319958, _1319960, _1319962] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1319956, _1319958), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1319960), _1319962))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1319956), _1319958), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1319962), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1319960)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1319960)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1319962), 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), _1319958), _1319962))))))], (46664 ^ _778495) ^ [_1716746, _1716748, _1716750, _1716752, _1716754] : [c_List_Olist__all2(_1716746, _1716748, _1716750, _1716752, hAPP(c_List_Orev(_1716748), _1716754)), -(c_List_Olist__all2(_1716746, _1716748, _1716750, hAPP(c_List_Orev(_1716746), _1716752), _1716754))], (6900 ^ _778495) ^ [_891695, _891697, _891699, _891701] : [class_Lattices_Osemilattice__sup(_891695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891695), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891695), _891697), _891699)), _891701)), 6907 ^ _778495 : [(6910 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891695), _891699), _891701)))], (6908 ^ _778495) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891695), _891697), _891701)))]]], (50331 ^ _778495) ^ [_1796195, _1796197, _1796199] : [hBOOL(hAPP(c_Quotient_ORespects(_1796195, _1796197), _1796199)), -(hBOOL(hAPP(hAPP(_1796197, _1796199), _1796199)))], (21484 ^ _778495) ^ [] : [-(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)))], (46947 ^ _778495) ^ [_1722610, _1722612, _1722614, _1722616, _1722618] : [class_Orderings_Olinorder(_1722610), c_List_Olinorder__class_Osorted(_1722610, hAPP(c_List_Orev(_1722610), hAPP(hAPP(c_List_Omap(_1722612, _1722610), _1722614), _1722616))), -(hAPP(c_List_Ofilter(_1722612, hAPP(hAPP(c_COMBB(_1722610, tc_HOL_Obool, _1722612), hAPP(c_Orderings_Oord__class_Oless(_1722610), _1722618)), _1722614)), _1722616) = c_List_OtakeWhile(_1722612, hAPP(hAPP(c_COMBB(_1722610, tc_HOL_Obool, _1722612), hAPP(c_Orderings_Oord__class_Oless(_1722610), _1722618)), _1722614), _1722616))], (48316 ^ _778495) ^ [_1752685, _1752687, _1752689] : [c_List_Oreplicate(_1752685, _1752687, _1752689) = c_List_Olist_ONil(_1752685), -(_1752687 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44710 ^ _778495) ^ [_1674073, _1674075, _1674077] : [-(hAPP(hAPP(c_List_Ozip(_1674073, _1674075), hAPP(hAPP(c_List_Omap(tc_prod(_1674073, _1674075), _1674073), c_Product__Type_Ofst(_1674073, _1674075)), _1674077)), hAPP(hAPP(c_List_Omap(tc_prod(_1674073, _1674075), _1674075), c_Product__Type_Osnd(_1674073, _1674075)), _1674077)) = _1674077)], (16120 ^ _778495) ^ [_1066741, _1066743, _1066745, _1066747] : [class_Rings_Odivision__ring(_1066741), -(_1066743 = c_Groups_Ozero__class_Ozero(_1066741)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066741), _1066745), _1066743) = _1066747, -(_1066745 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066741), _1066747), _1066743))], (36891 ^ _778495) ^ [_1474097, _1474099, _1474101, _1474103, _1474105, _1474107] : [c_Typedef_Otype__definition(_1474097, _1474099, _1474101, _1474103, _1474105), -(hBOOL(hAPP(hAPP(c_member(_1474099), hAPP(_1474101, _1474107)), _1474105)))], (44726 ^ _778495) ^ [_1674416, _1674418] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1674416)), hAPP(c_Code__Numeral_Oof__nat, _1674418)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1674416), _1674418)))], (47808 ^ _778495) ^ [_1741846, _1741848, _1741850] : [c_List_Olist__all(_1741846, _1741848, _1741850), 47811 ^ _778495 : [(47812 ^ _778495) ^ [_1741935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741935), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741846)), _1741850))), -(hBOOL(hAPP(_1741848, hAPP(hAPP(c_List_Onth(_1741846), _1741850), _1741935))))]]], (37795 ^ _778495) ^ [_1497779, _1497781] : [hAPP(c_Set_OCollect(_1497779), _1497781) = c_Orderings_Obot__class_Obot(tc_fun(_1497779, tc_HOL_Obool)), 37798 ^ _778495 : [(37799 ^ _778495) ^ [_1497864] : [hBOOL(hAPP(_1497781, _1497864))]]], (6556 ^ _778495) ^ [_885039, _885041, _885043, _885045] : [hBOOL(hAPP(hAPP(c_member(_885039), _885041), _885043)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_885039, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_885039), _885041), _885045)), _885043) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_885039, tc_HOL_Obool)), _885045), _885043))], (42982 ^ _778495) ^ [_1635356, _1635358, _1635360, _1635362, _1635364] : [-(_1635356 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1635358, _1635360, _1635362), _1635356), _1635364) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1635360), _1635358), tc_prod(_1635360, _1635358), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635360), _1635358), c_List_Olist_ONil(_1635360)), _1635364), hAPP(c_Product__Type_Oprod_Oprod__case(_1635360, _1635358, tc_prod(tc_List_Olist(_1635360), _1635358)), hAPP(hAPP(c_COMBC(_1635360, tc_fun(_1635358, tc_prod(tc_List_Olist(_1635360), _1635358)), tc_fun(_1635358, tc_prod(tc_List_Olist(_1635360), _1635358))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1635360), _1635358), tc_prod(tc_List_Olist(_1635360), _1635358)), tc_fun(tc_fun(_1635358, tc_prod(tc_List_Olist(_1635360), _1635358)), tc_fun(_1635358, tc_prod(tc_List_Olist(_1635360), _1635358))), _1635360), c_COMBB(tc_prod(tc_List_Olist(_1635360), _1635358), tc_prod(tc_List_Olist(_1635360), _1635358), _1635358)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1635360), tc_fun(_1635358, tc_prod(tc_List_Olist(_1635360), _1635358))), tc_fun(tc_prod(tc_List_Olist(_1635360), _1635358), tc_prod(tc_List_Olist(_1635360), _1635358)), _1635360), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1635360), _1635358, tc_prod(tc_List_Olist(_1635360), _1635358))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1635360), tc_List_Olist(_1635360)), tc_fun(tc_List_Olist(_1635360), tc_fun(_1635358, tc_prod(tc_List_Olist(_1635360), _1635358))), _1635360), hAPP(c_COMBB(tc_List_Olist(_1635360), tc_fun(_1635358, tc_prod(tc_List_Olist(_1635360), _1635358)), tc_List_Olist(_1635360)), c_Product__Type_OPair(tc_List_Olist(_1635360), _1635358))), c_List_Olist_OCons(_1635360))))), hAPP(c_Lazy__Sequence_Oanamorph(_1635358, _1635360, _1635362), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1635356), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1635362, _1635364)))], (50991 ^ _778495) ^ [_1810517, _1810519] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810517), _1810519)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810519), _1810517))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810519), _1810517)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810517), _1810519)))], (1608 ^ _778495) ^ [_801623, _801625] : [-(class_Groups_Ocancel__ab__semigroup__add(_801623)), _801625 = _801623, class_Groups_Ocancel__ab__semigroup__add(_801625)], (46728 ^ _778495) ^ [_1718074, _1718076, _1718078, _1718080] : [_1718076 = hAPP(hAPP(c_List_Oappend(_1718074), hAPP(c_List_Orev(_1718074), _1718080)), hAPP(hAPP(c_List_Olist_OCons(_1718074), _1718078), c_List_Olist_ONil(_1718074))), -(hAPP(c_List_Orev(_1718074), _1718076) = hAPP(hAPP(c_List_Olist_OCons(_1718074), _1718078), _1718080))], (40754 ^ _778495) ^ [_1577164, _1577166, _1577168, _1577170, _1577172] : [-(hAPP(c_Relation_Oconverse(_1577164, _1577166), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577168, tc_fun(tc_prod(_1577164, _1577166), tc_HOL_Obool)), _1577170), _1577172)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577168, tc_fun(tc_prod(_1577166, _1577164), tc_HOL_Obool)), _1577170), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1577164, _1577166), tc_HOL_Obool), tc_fun(tc_prod(_1577166, _1577164), tc_HOL_Obool), _1577168), c_Relation_Oconverse(_1577164, _1577166)), _1577172)))], (31137 ^ _778495) ^ [_1347498, _1347500, _1347502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1347498, 31138 ^ [_1347498, _1347500, _1347502])), hAPP(_1347500, 31138 ^ [_1347498, _1347500, _1347502]))), -(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), _1347500), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1347502))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1347498), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1347502))) = 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)), _1347500)), _1347498)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1347502)))], (7996 ^ _778495) ^ [_910121, _910123, _910125] : [class_Orderings_Oorder(_910121), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910121), _910123), _910125)), -(_910125 = _910123), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910121), _910123), _910125)))], (21100 ^ _778495) ^ [_1156499] : [class_Rings_Olinordered__idom(_1156499), -(hAPP(c_Groups_Oabs__class_Oabs(_1156499), c_Groups_Oone__class_Oone(_1156499)) = c_Groups_Oone__class_Oone(_1156499))]], input).
% 47.22/46.15  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))],start(52751 ^ 0)).
% 47.22/46.15  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))))],extension(6810 ^ 1,bind([[_890184, _890186, _890188], [t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))]]))).
% 47.22/46.15  ncf('1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))))],extension(5951 ^ 2,bind([[_873421, _873423], [tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))]]))).
% 47.22/46.15  %-----------------------------------------------------
% 47.22/46.15  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------