TSTP Solution File: SWW353+1 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW353+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n027.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 12:26:01 EDT 2023
% Result : Theorem 48.28s 47.05s
% Output : Proof 48.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW353+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : nanocop.sh %s %d
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 18 22:40:50 EDT 2023
% 0.14/0.35 % CPUTime :
% 48.28/47.05
% 48.28/47.05 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 48.28/47.05 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.28/47.05 %-----------------------------------------------------
% 48.28/47.05 ncf(matrix, plain, [(51718 ^ _2070014) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY, v_pname))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))], !, (7971 ^ _781013) ^ [_915842, _915844, _915846, _915848] : [-(hAPP(hAPP(c_Option_Omap(_915842, _915844), _915846), hAPP(c_Option_Ooption_OSome(_915842), _915848)) = hAPP(c_Option_Ooption_OSome(_915844), hAPP(_915846, _915848)))], (44420 ^ _781013) ^ [_1666425, _1666427] : [-(_1666425 = c_List_Olist_ONil(_1666427)), -(hAPP(c_List_Ohd(_1666427), hAPP(c_List_Orev(_1666427), _1666425)) = c_List_Olast(_1666427, _1666425))], (42092 ^ _781013) ^ [_1613943, _1613945] : [-(hAPP(c_List_Oset(_1613943), hAPP(c_List_Orotate1(_1613943), _1613945)) = hAPP(c_List_Oset(_1613943), _1613945))], (35329 ^ _781013) ^ [_1449514, _1449516, _1449518] : [class_Groups_Omonoid__mult(_1449514), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1449514), _1449516), 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)))), _1449518))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1449514), _1449516), hAPP(hAPP(c_Power_Opower__class_Opower(_1449514), hAPP(hAPP(c_Power_Opower__class_Opower(_1449514), _1449516), _1449518)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (48055 ^ _781013) ^ [_1751901, _1751903, _1751905, _1751907, _1751909] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1751901, _1751901)), hAPP(hAPP(c_Product__Type_OPair(_1751901, _1751901), _1751903), _1751905)), c_Transitive__Closure_Otrancl(_1751901, _1751907))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1751901, _1751901)), hAPP(hAPP(c_Product__Type_OPair(_1751901, _1751901), _1751905), _1751909)), c_Transitive__Closure_Otrancl(_1751901, _1751907))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1751901, _1751901)), hAPP(hAPP(c_Product__Type_OPair(_1751901, _1751901), _1751903), _1751909)), c_Transitive__Closure_Otrancl(_1751901, _1751907))))], (9939 ^ _781013) ^ [_956653, _956655, _956657] : [class_Lattices_Osemilattice__inf(_956653), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956653), _956655), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956653), _956655), _956657)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956653), _956655), _956657))], (28648 ^ _781013) ^ [_1315451, _1315453, _1315455] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1315451), _1315453)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1315455), _1315453)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1315451), _1315455)), _1315453))], (27485 ^ _781013) ^ [_1293956, _1293958, _1293960] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1293956, tc_HOL_Obool)), _1293960), hAPP(c_Set_OPow(_1293956), _1293958))), -(hBOOL(hAPP(c_Predicate_OPowp(_1293956, hAPP(hAPP(c_COMBC(_1293956, tc_fun(_1293956, tc_HOL_Obool), tc_HOL_Obool), c_member(_1293956)), _1293958)), _1293960)))], (34795 ^ _781013) ^ [_1439864, _1439866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1439864)), c_Int_OBit0(_1439866))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439864), _1439866)))], (37460 ^ _781013) ^ [_1496188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1496188)), 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), _1496188)) = 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), _1496188))))))], (48499 ^ _781013) ^ [_1761532, _1761534] : [-(c_Transitive__Closure_Ortrancl(_1761532, c_Transitive__Closure_Ortrancl(_1761532, _1761534)) = c_Transitive__Closure_Ortrancl(_1761532, _1761534))], (25204 ^ _781013) ^ [_1250786, _1250788, _1250790, _1250792] : [class_Fields_Olinordered__field(_1250786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250786), _1250788), _1250790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250786), _1250792), c_Groups_Ozero__class_Ozero(_1250786))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250786), c_Groups_Ozero__class_Ozero(_1250786)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250786), _1250788), _1250790))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250786), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250786), _1250792), _1250788)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250786), _1250792), _1250790))))], (16075 ^ _781013) ^ [_1078323] : [class_Rings_Olinordered__semidom(_1078323), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078323), c_Groups_Ozero__class_Ozero(_1078323)), c_Groups_Oone__class_Oone(_1078323))))], (3440 ^ _781013) ^ [_832850, _832852] : [_832852 = _832850, -(c_List_Odrop(_832852) = c_List_Odrop(_832850))], (15107 ^ _781013) ^ [_1060494, _1060496, _1060498, _1060500] : [_1060494 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1060496, _1060498), 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)), _1060500))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1060496), _1060494)))], (31575 ^ _781013) ^ [_1376345, _1376347, _1376349, _1376351, _1376353] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376345, tc_fun(_1376347, tc_HOL_Obool)), _1376349), _1376351), _1376353))), 31576 ^ _781013 : [(31577 ^ _781013) ^ [_1376417] : [hBOOL(hAPP(hAPP(c_member(_1376345), _1376417), _1376349)), hBOOL(hAPP(hAPP(_1376351, _1376417), _1376353))]]], (29113 ^ _781013) ^ [_1324061, _1324063] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1324061), _1324063))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1324061, _1324063) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1324061), _1324063), _1324063))], (13893 ^ _781013) ^ [_1036364, _1036366, _1036368, _1036370, _1036372] : [class_Groups_Oordered__ab__semigroup__add(_1036364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036364), _1036366), _1036368)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036364), _1036370), _1036372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036364), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036364), _1036366), _1036370)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036364), _1036368), _1036372))))], (8018 ^ _781013) ^ [_917047, _917049, _917051] : [-(hAPP(hAPP(c_Set_Oinsert(_917047), _917049), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917047, tc_HOL_Obool)), _917051), hAPP(hAPP(c_Set_Oinsert(_917047), _917049), c_Orderings_Obot__class_Obot(tc_fun(_917047, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_917047), _917049), _917051))], (4070 ^ _781013) ^ [_842577, _842579, _842581, _842583] : [-(c_Relation_ORange(_842583, _842579) = c_Relation_ORange(_842581, _842577)), _842583 = _842581, _842579 = _842577], (48291 ^ _781013) ^ [_1756720, _1756722, _1756724, _1756726, _1756728, _1756730] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1756720, _1756720)), hAPP(hAPP(c_Product__Type_OPair(_1756720, _1756720), _1756722), _1756724)), c_Transitive__Closure_Ortrancl(_1756720, _1756726))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756720), tc_List_Olist(_1756720))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756720), tc_List_Olist(_1756720)), _1756728), _1756730)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1756720), c_List_Olistrel1(_1756720, _1756726)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756720), tc_List_Olist(_1756720))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756720), tc_List_Olist(_1756720)), hAPP(hAPP(c_List_Olist_OCons(_1756720), _1756722), _1756728)), hAPP(hAPP(c_List_Olist_OCons(_1756720), _1756724), _1756730))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1756720), c_List_Olistrel1(_1756720, _1756726)))))], (42264 ^ _781013) ^ [_1618168, _1618170, _1618172, _1618174] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618168) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1618170), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618168)), hAPP(hAPP(c_List_Olist_OCons(_1618170), _1618172), _1618174)) = hAPP(hAPP(c_List_Olist_OCons(_1618170), _1618172), _1618174))], (23391 ^ _781013) ^ [_1218532, _1218534] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1218532, _1218534)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1218534)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17641 ^ _781013) ^ [_1110846, _1110848] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110846), _1110848) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1110846 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1110848 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48487 ^ _781013) ^ [_1761318, _1761320] : [-(c_List_Olistrel(_1761318, c_Transitive__Closure_Ortrancl(_1761318, _1761320)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1761318), c_List_Olistrel1(_1761318, _1761320)))], (51168 ^ _781013) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (7555 ^ _781013) ^ [_907548, _907550, _907552, _907554] : [-(hBOOL(hAPP(hAPP(c_member(_907548), _907550), _907552))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907548, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_907548), _907550), _907554)), _907552) = hAPP(hAPP(c_Set_Oinsert(_907548), _907550), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907548, tc_HOL_Obool)), _907554), _907552)))], (5891 ^ _781013) ^ [_875804, _875806] : [-(c_HOL_OThe(_875804, hAPP(hAPP(c_COMBC(_875804, _875804, tc_HOL_Obool), c_fequal), _875806)) = _875806)], (2208 ^ _781013) ^ [_813542, _813544, _813546, _813548, _813550, _813552, _813554, _813556] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_813556, _813552, _813548, _813544) = c_SetInterval_Oord_OgreaterThanLessThan(_813554, _813550, _813546, _813542)), _813556 = _813554, _813552 = _813550, _813548 = _813546, _813544 = _813542], (37868 ^ _781013) ^ [_1506146, _1506148, _1506150, _1506152, _1506154] : [-(hAPP(c_Product__Type_Ofst(_1506146, _1506148), hAPP(c_Product__Type_Oapfst(_1506150, _1506146, _1506148, _1506152), _1506154)) = hAPP(_1506152, hAPP(c_Product__Type_Ofst(_1506150, _1506148), _1506154)))], (9172 ^ _781013) ^ [_943050, _943052, _943054, _943056, _943058] : [hBOOL(hAPP(hAPP(c_member(_943050), _943052), _943054)), -(hAPP(c_Map_Orestrict__map(_943050, _943056, _943058, _943054), _943052) = hAPP(_943058, _943052))], (19014 ^ _781013) ^ [_1136738, _1136740, _1136742, _1136744] : [hBOOL(hAPP(hAPP(c_member(_1136738), _1136740), c_SetInterval_Oord_OatLeast(_1136738, _1136742, _1136744))), -(hBOOL(hAPP(hAPP(_1136742, _1136744), _1136740)))], (12126 ^ _781013) ^ [_999815, _999817, _999819] : [class_Lattices_Olattice(_999815), hBOOL(hAPP(c_Finite__Set_Ofinite(_999815), _999817)), hBOOL(hAPP(hAPP(c_member(_999815), _999819), _999817)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_999815), _999819), c_Big__Operators_Olattice__class_OInf__fin(_999815, _999817)) = c_Big__Operators_Olattice__class_OInf__fin(_999815, _999817))], (10005 ^ _781013) ^ [_957894, _957896, _957898, _957900, _957902] : [class_Lattices_Olattice(_957894), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957896, _957894)), _957898), _957900), _957902) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_957894), hAPP(_957898, _957902)), hAPP(_957900, _957902)))], (1634 ^ _781013) ^ [_804180, _804182] : [-(class_Groups_Osemigroup__add(_804180)), _804182 = _804180, class_Groups_Osemigroup__add(_804182)], (41364 ^ _781013) ^ [_1596126, _1596128] : [-(_1596126 = c_List_Olist_ONil(_1596128)), hBOOL(hAPP(c_List_Odistinct(_1596128), _1596126)), -(hBOOL(hAPP(c_List_Odistinct(_1596128), c_List_Obutlast(_1596128, _1596126))))], (23471 ^ _781013) ^ [_1220167, _1220169, _1220171, _1220173] : [class_Rings_Odivision__ring(_1220167), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220167), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1220167), _1220169), _1220171)), _1220173) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1220167), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220167), _1220169), _1220173)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220167), _1220171), _1220173)))], (38409 ^ _781013) ^ [_1519231, _1519233, _1519235, _1519237, _1519239, _1519241, _1519243] : [c_Typedef_Otype__definition(_1519231, _1519233, _1519235, _1519237, _1519239), 38412 ^ _781013 : [(38419 ^ _781013) ^ [] : [_1519241 = _1519243, -(hAPP(_1519235, _1519241) = hAPP(_1519235, _1519243))], (38413 ^ _781013) ^ [] : [hAPP(_1519235, _1519241) = hAPP(_1519235, _1519243), -(_1519241 = _1519243)]]], (23180 ^ _781013) ^ [_1214597, _1214599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1214599), _1214597))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1214599), _1214597) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1214599), _1214597)), _1214597)))], (1444 ^ _781013) ^ [_801805, _801807] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_801805)), _801807 = _801805, class_Groups_Oordered__ab__semigroup__add__imp__le(_801807)], (44566 ^ _781013) ^ [_1670634, _1670636] : [-(c_List_Oconcat(tc_List_Olist(_1670634), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1670634), tc_List_Olist(tc_List_Olist(_1670634))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1670634)), _1670634, c_List_Olist_ONil(tc_List_Olist(_1670634)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1670634), tc_List_Olist(tc_List_Olist(_1670634))), _1670634), hAPP(hAPP(c_COMBC(tc_List_Olist(_1670634), tc_List_Olist(tc_List_Olist(_1670634)), tc_List_Olist(tc_List_Olist(_1670634))), c_List_Olist_OCons(tc_List_Olist(_1670634))), c_List_Olist_ONil(tc_List_Olist(_1670634)))))), _1670636)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1670634), tc_List_Olist(_1670634)), c_List_Otl(_1670634)), hAPP(c_List_Ofilter(tc_List_Olist(_1670634), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1670634)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1670634), tc_List_Olist(_1670634), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1670634)))), _1670636)))], (9156 ^ _781013) ^ [_942778, _942780, _942782, _942784] : [-(hAPP(c_Map_Orestrict__map(_942778, _942780, hAPP(c_COMBK(tc_Option_Ooption(_942780), _942778), c_Option_Ooption_ONone(_942780)), _942782), _942784) = c_Option_Ooption_ONone(_942780))], (31836 ^ _781013) ^ [_1383226, _1383228, _1383230, _1383232, _1383234, _1383236] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383226, tc_fun(_1383228, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1383230, _1383226, _1383232), _1383234)), _1383236) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383230, tc_fun(_1383228, tc_HOL_Obool)), _1383234), hAPP(hAPP(c_COMBB(_1383226, tc_fun(_1383228, tc_HOL_Obool), _1383230), _1383236), _1383232)))], (50822 ^ _781013) ^ [_1814111, _1814113, _1814115] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1814111)), c_List_Osplice(_1814111, _1814113, _1814115)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1814111)), _1814113)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1814111)), _1814115)))], (5835 ^ _781013) ^ [_874799, _874801] : [c_Com_Ocom_OWhile(_874799, _874801) = c_Com_Ocom_OSKIP], (18185 ^ _781013) ^ [_1119695, _1119697] : [18186 ^ _781013 : [(18189 ^ _781013) ^ [] : [_1119695 = _1119697], (18187 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119695), _1119697))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119695), _1119697)))], (50726 ^ _781013) ^ [_1811786] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1811786), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1811786)), c_Int_OMin)))], (25938 ^ _781013) ^ [_1263344, _1263346, _1263348, _1263350] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1263344), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1263346, tc_Int_Oint), _1263348), _1263350)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1263346, _1263344), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1263344, _1263346), c_Int_Oring__1__class_Oof__int(_1263344)), _1263348)), _1263350)), class_Groups_Ocomm__monoid__mult(_1263344), class_Rings_Oring__1(_1263344)], (14915 ^ _781013) ^ [_1057181, _1057183] : [class_Rings_Ocomm__semiring__1(_1057181), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057181), c_Groups_Ozero__class_Ozero(_1057181)), _1057183) = c_Groups_Ozero__class_Ozero(_1057181))], (32292 ^ _781013) ^ [_1393896, _1393898, _1393900] : [hBOOL(hAPP(c_Com_OWT, _1393896)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1393898, _1393900, _1393896))))], (31190 ^ _781013) ^ [_1365256, _1365258, _1365260, _1365262, _1365264] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1365256), _1365258), _1365260), _1365262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1365260), _1365264)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1365256), _1365258), _1365264), _1365262)))], (4266 ^ _781013) ^ [_845541, _845543] : [_845543 = _845541, -(c_Orderings_Otop__class_Otop(_845543) = c_Orderings_Otop__class_Otop(_845541))], (12620 ^ _781013) ^ [_1009156, _1009158] : [class_Lattices_Olattice(_1009156), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009156), _1009158)), -(_1009158 = c_Orderings_Obot__class_Obot(tc_fun(_1009156, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1009156), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1009156), 12633 ^ [_1009156, _1009158]), 12634 ^ [_1009156, _1009158])), hAPP(hAPP(c_Set_Oinsert(_1009156), 12633 ^ [_1009156, _1009158]), hAPP(hAPP(c_Set_Oinsert(_1009156), 12634 ^ [_1009156, _1009158]), c_Orderings_Obot__class_Obot(tc_fun(_1009156, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1009156), c_Big__Operators_Olattice__class_OInf__fin(_1009156, _1009158)), _1009158)))], (47122 ^ _781013) ^ [_1730005, _1730007, _1730009, _1730011] : [hBOOL(hAPP(hAPP(c_member(_1730005), _1730007), hAPP(c_Relation_ORange(_1730009, _1730005), _1730011))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730009, _1730005)), hAPP(hAPP(c_Product__Type_OPair(_1730009, _1730005), 47125 ^ [_1730005, _1730007, _1730009, _1730011]), _1730007)), _1730011)))], (44440 ^ _781013) ^ [_1666774, _1666776, _1666778, _1666780] : [-(c_List_Otranspose(_1666774, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1666774)), hAPP(hAPP(c_List_Olist_OCons(_1666774), _1666776), _1666778)), _1666780)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1666774)), hAPP(hAPP(c_List_Olist_OCons(_1666774), _1666776), c_List_Oconcat(_1666774, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1666774), tc_List_Olist(_1666774)), c_List_Olist_Olist__case(tc_List_Olist(_1666774), _1666774, c_List_Olist_ONil(_1666774), hAPP(hAPP(c_COMBB(tc_List_Olist(_1666774), tc_fun(tc_List_Olist(_1666774), tc_List_Olist(_1666774)), _1666774), c_COMBK(tc_List_Olist(_1666774), tc_List_Olist(_1666774))), hAPP(hAPP(c_COMBC(_1666774, tc_List_Olist(_1666774), tc_List_Olist(_1666774)), c_List_Olist_OCons(_1666774)), c_List_Olist_ONil(_1666774))))), _1666780)))), c_List_Otranspose(_1666774, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1666774)), _1666778), c_List_Oconcat(tc_List_Olist(_1666774), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1666774), tc_List_Olist(tc_List_Olist(_1666774))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1666774)), _1666774, c_List_Olist_ONil(tc_List_Olist(_1666774)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1666774), tc_List_Olist(tc_List_Olist(_1666774))), _1666774), hAPP(hAPP(c_COMBC(tc_List_Olist(_1666774), tc_List_Olist(tc_List_Olist(_1666774)), tc_List_Olist(tc_List_Olist(_1666774))), c_List_Olist_OCons(tc_List_Olist(_1666774))), c_List_Olist_ONil(tc_List_Olist(_1666774)))))), _1666780))))))], (51506 ^ _781013) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (38449 ^ _781013) ^ [_1519905, _1519907, _1519909, _1519911, _1519913, _1519915] : [c_Typedef_Otype__definition(_1519905, _1519907, _1519909, _1519911, _1519913), hBOOL(hAPP(hAPP(c_member(_1519907), _1519915), _1519913)), -(hAPP(_1519909, hAPP(_1519911, _1519915)) = _1519915)], (34867 ^ _781013) ^ [_1441114] : [-(c_Int_Osucc(c_Int_OBit0(_1441114)) = c_Int_OBit1(_1441114))], (11265 ^ _781013) ^ [_982151, _982153, _982155, _982157, _982159] : [c_Finite__Set_Ofolding__one(_982151, _982153, _982155), hBOOL(hAPP(c_Finite__Set_Ofinite(_982151), _982157)), hBOOL(hAPP(c_Finite__Set_Ofinite(_982151), _982159)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982151, tc_HOL_Obool)), _982157), _982159) = c_Orderings_Obot__class_Obot(tc_fun(_982151, tc_HOL_Obool))), -(hAPP(hAPP(_982153, hAPP(_982155, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982151, tc_HOL_Obool)), _982157), _982159))), hAPP(_982155, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982151, tc_HOL_Obool)), _982157), _982159))) = hAPP(hAPP(_982153, hAPP(_982155, _982157)), hAPP(_982155, _982159)))], (3948 ^ _781013) ^ [_840744, _840746, _840748, _840750] : [-(c_Random_Oselect(_840750, _840746) = c_Random_Oselect(_840748, _840744)), _840750 = _840748, _840746 = _840744], (16267 ^ _781013) ^ [_1081604, _1081606, _1081608] : [-(hAPP(hAPP(c_Set_Oinsert(_1081604), _1081606), _1081608) = hAPP(c_Set_OCollect(_1081604), hAPP(hAPP(c_COMBS(_1081604, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1081604), c_fdisj), hAPP(hAPP(c_COMBC(_1081604, _1081604, tc_HOL_Obool), c_fequal), _1081606))), hAPP(hAPP(c_COMBC(_1081604, tc_fun(_1081604, tc_HOL_Obool), tc_HOL_Obool), c_member(_1081604)), _1081608))))], (44189 ^ _781013) ^ [_1660824, _1660826, _1660828, _1660830] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1660824, tc_Nat_Onat), _1660824), c_Product__Type_Ofst(_1660824, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1660824, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1660824, 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(_1660824, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1660824, tc_Nat_Onat))), _1660826)), hAPP(hAPP(c_List_Ozip(_1660824, tc_Nat_Onat), _1660828), c_List_Oupt(_1660830, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1660830), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660824)), _1660828)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1660824, tc_Nat_Onat), _1660824), c_Product__Type_Ofst(_1660824, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1660824, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1660824, 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(_1660824, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1660824, 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(_1660824, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1660824, tc_Nat_Onat))), _1660830))), _1660826)), hAPP(hAPP(c_List_Ozip(_1660824, tc_Nat_Onat), _1660828), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660824)), _1660828))))))], (8831 ^ _781013) ^ [_935456, _935458, _935460, _935462] : [class_Lattices_Osemilattice__sup(_935456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935456), _935458), _935460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935456), _935458), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935456), _935460), _935462))))], (41314 ^ _781013) ^ [_1595283, _1595285] : [-(hAPP(c_List_OremoveAll(_1595283, _1595285), c_List_Olist_ONil(_1595283)) = c_List_Olist_ONil(_1595283))], (45556 ^ _781013) ^ [_1691298, _1691300, _1691302, _1691304] : [c_Fun_Oinj__on(_1691298, _1691300, _1691302, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1691298, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1691298), tc_fun(_1691298, tc_HOL_Obool), c_List_Oset(_1691298)), _1691304))), -(c_Fun_Oinj__on(tc_List_Olist(_1691298), tc_List_Olist(_1691300), hAPP(c_List_Omap(_1691298, _1691300), _1691302), _1691304))], (9583 ^ _781013) ^ [_950701, _950703, _950705, _950707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_950701, tc_HOL_Obool)), _950703), _950705)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_950701, tc_HOL_Obool)), _950705), _950707)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_950701, tc_HOL_Obool)), _950703), _950707)))], (31988 ^ _781013) ^ [_1387788, _1387790, _1387792, _1387794] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1387788, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387790, tc_fun(tc_fun(_1387788, tc_HOL_Obool), tc_HOL_Obool)), _1387792), hAPP(hAPP(c_COMBB(tc_fun(_1387788, tc_HOL_Obool), tc_fun(tc_fun(_1387788, tc_HOL_Obool), tc_HOL_Obool), _1387790), c_Set_OPow(_1387788)), _1387794))), hAPP(c_Set_OPow(_1387788), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387790, tc_fun(_1387788, tc_HOL_Obool)), _1387792), _1387794)))))], (29951 ^ _781013) ^ [_1339575, _1339577] : [class_Orderings_Olinorder(_1339575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339575), _1339577)), -(_1339577 = c_Orderings_Obot__class_Obot(tc_fun(_1339575, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1339575), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1339575), 29964 ^ [_1339575, _1339577]), 29965 ^ [_1339575, _1339577])), hAPP(hAPP(c_Set_Oinsert(_1339575), 29964 ^ [_1339575, _1339577]), hAPP(hAPP(c_Set_Oinsert(_1339575), 29965 ^ [_1339575, _1339577]), c_Orderings_Obot__class_Obot(tc_fun(_1339575, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1339575), c_Big__Operators_Olattice_OInf__fin(_1339575, c_Orderings_Oord__class_Omin(_1339575), _1339577)), _1339577)))], (51686 ^ _781013) ^ [_1825804, _1825806] : [-(hBOOL(_1825804)), -(hBOOL(hAPP(hAPP(c_fimplies, _1825804), _1825806)))], (12900 ^ _781013) ^ [_1015124, _1015126, _1015128, _1015130, _1015132] : [-(hAPP(c_Set_Ovimage(_1015124, _1015126, _1015128), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1015126, tc_HOL_Obool)), _1015130), _1015132)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1015124, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1015124, _1015126, _1015128), _1015130)), hAPP(c_Set_Ovimage(_1015124, _1015126, _1015128), _1015132)))], (39150 ^ _781013) ^ [_1536925, _1536927, _1536929] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1536925, tc_HOL_Obool)), hAPP(c_List_Oset(_1536925), c_List_Osublist(_1536925, _1536927, _1536929))), hAPP(c_List_Oset(_1536925), _1536927))))], (27301 ^ _781013) ^ [_1289555, _1289557, _1289559, _1289561, _1289563] : [class_Groups_Ocomm__monoid__add(_1289555), hBOOL(hAPP(c_Finite__Set_Ofinite(_1289557), _1289559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289557, tc_HOL_Obool)), _1289561), _1289559)), 27315 ^ _781013 : [(27318 ^ _781013) ^ [] : [hAPP(_1289563, 27314 ^ [_1289555, _1289557, _1289559, _1289561, _1289563]) = c_Groups_Ozero__class_Ozero(_1289555)], (27316 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1289557), 27314 ^ [_1289555, _1289557, _1289559, _1289561, _1289563]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289557, tc_HOL_Obool)), _1289559), _1289561))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289557, _1289555), _1289563), _1289559) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1289557, _1289555), _1289563), _1289561))], (20189 ^ _781013) ^ [_1158521, _1158523, _1158525] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158521)), _1158523) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158521)), _1158525), -(_1158523 = _1158525)], (38045 ^ _781013) ^ [] : [-(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)))))], (34965 ^ _781013) ^ [_1443112, _1443114] : [class_Int_Onumber__ring(_1443112), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1443112), hAPP(c_Int_Onumber__class_Onumber__of(_1443112), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1443114) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1443112), _1443114), _1443114))], (26265 ^ _781013) ^ [_1269388, _1269390, _1269392, _1269394, _1269396] : [class_Groups_Ocomm__monoid__add(_1269388), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1269388), _1269390), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1269392), _1269394), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1269396), _1269394))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1269388), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1269388, tc_Nat_Onat), _1269390), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1269394))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1269392, _1269396)))], (25242 ^ _781013) ^ [_1251501, _1251503, _1251505, _1251507] : [class_Fields_Ofield__inverse__zero(_1251501), -(_1251503 = c_Groups_Ozero__class_Ozero(_1251501)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251501), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251501), _1251505), _1251503)), _1251507) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251501), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251501), _1251505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251501), _1251507), _1251503))), _1251503))], (33870 ^ _781013) ^ [_1422574, _1422576] : [class_Int_Onumber__ring(_1422574), -(hAPP(c_Int_Onumber__class_Onumber__of(_1422574), c_Int_Opred(_1422576)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1422574), hAPP(c_Groups_Ouminus__class_Ouminus(_1422574), c_Groups_Oone__class_Oone(_1422574))), hAPP(c_Int_Onumber__class_Onumber__of(_1422574), _1422576)))], (35127 ^ _781013) ^ [_1445892, _1445894, _1445896] : [class_Rings_Olinordered__semidom(_1445892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445892), hAPP(hAPP(c_Power_Opower__class_Opower(_1445892), _1445894), 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(_1445892), _1445896), 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(_1445892), c_Groups_Ozero__class_Ozero(_1445892)), _1445896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445892), _1445894), _1445896)))], (27453 ^ _781013) ^ [_1292879, _1292881, _1292883] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1292879, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1292879, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1292879), _1292881)), hAPP(c_Set_OPow(_1292879), _1292883))), hAPP(c_Set_OPow(_1292879), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292879, tc_HOL_Obool)), _1292881), _1292883)))))], (43502 ^ _781013) ^ [_1647648, _1647650] : [-(c_List_Ofoldr(tc_List_Olist(_1647648), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1647648)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1647648))), c_List_Otranspose(_1647648, _1647650), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1647648))), hAPP(c_List_Ofilter(tc_List_Olist(_1647648), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1647648)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1647648), tc_List_Olist(_1647648), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1647648)))), _1647650)))], (1154 ^ _781013) ^ [_798180, _798182] : [-(class_Rings_Oordered__ring(_798180)), _798182 = _798180, class_Rings_Oordered__ring(_798182)], (51082 ^ _781013) ^ [_1819458, _1819460] : [class_Groups_Ouminus(_1819458), -(class_Groups_Ouminus(tc_fun(_1819460, _1819458)))], (17142 ^ _781013) ^ [_1099847, _1099849, _1099851] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1099847), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099847, tc_HOL_Obool)), _1099849), _1099851))), -(hAPP(c_Finite__Set_Ocard(_1099847), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1099847, tc_HOL_Obool)), _1099849), _1099851)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1099847), _1099849)), hAPP(c_Finite__Set_Ocard(_1099847), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099847, tc_HOL_Obool)), _1099849), _1099851))))], (50533 ^ _781013) ^ [_1808493] : [class_Nat_Osize(_1808493), -(c_FunDef_Ois__measure(_1808493, c_Nat_Osize__class_Osize(_1808493)))], (48892 ^ _781013) ^ [_1771288, _1771290, _1771292] : [-(hAPP(c_Relation_Oconverse(_1771288, _1771290), _1771292) = hAPP(c_Set_OCollect(tc_prod(_1771290, _1771288)), hAPP(c_Product__Type_Oprod_Oprod__case(_1771290, _1771288, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1771290, tc_fun(tc_prod(_1771288, _1771290), tc_HOL_Obool), tc_fun(_1771288, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1771288, tc_fun(tc_fun(tc_prod(_1771288, _1771290), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1771288, _1771290), tc_HOL_Obool), tc_fun(_1771288, tc_HOL_Obool)), _1771290), c_COMBC(_1771288, tc_fun(tc_prod(_1771288, _1771290), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1771288, tc_prod(_1771288, _1771290)), tc_fun(_1771288, tc_fun(tc_fun(tc_prod(_1771288, _1771290), tc_HOL_Obool), tc_HOL_Obool)), _1771290), hAPP(c_COMBB(tc_prod(_1771288, _1771290), tc_fun(tc_fun(tc_prod(_1771288, _1771290), tc_HOL_Obool), tc_HOL_Obool), _1771288), c_member(tc_prod(_1771288, _1771290)))), hAPP(c_COMBC(_1771288, _1771290, tc_prod(_1771288, _1771290)), c_Product__Type_OPair(_1771288, _1771290))))), _1771292))))], (36868 ^ _781013) ^ [_1484439, _1484441] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484439))), 36871 ^ _781013 : [(36878 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484441))), -(c_Divides_Odivmod__int(_1484439, _1484441) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1484439), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1484441))))], (36872 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484441)), -(c_Divides_Odivmod__int(_1484439, _1484441) = c_Divides_OnegDivAlg(_1484439, _1484441))]]], (5621 ^ _781013) ^ [_869611, _869613, _869615] : [c_Orderings_Obot__class_Obot(tc_fun(_869611, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_869611), _869613), _869615)], (23527 ^ _781013) ^ [_1221341, _1221343, _1221345, _1221347] : [class_Rings_Odivision__ring(_1221341), -(_1221343 = c_Groups_Ozero__class_Ozero(_1221341)), 23534 ^ _781013 : [(23541 ^ _781013) ^ [] : [_1221345 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221341), _1221347), _1221343), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221341), _1221345), _1221343) = _1221347)], (23535 ^ _781013) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221341), _1221345), _1221343) = _1221347, -(_1221345 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221341), _1221347), _1221343))]]], (40425 ^ _781013) ^ [_1569948, _1569950, _1569952, _1569954, _1569956, _1569958] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1569948), tc_List_Olist(_1569948))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1569948), tc_List_Olist(_1569948)), hAPP(hAPP(c_List_Olist_OCons(_1569948), _1569950), _1569952)), hAPP(hAPP(c_List_Olist_OCons(_1569948), _1569954), _1569956))), c_List_Olexord(_1569948, _1569958)))), 40426 ^ _781013 : [(40429 ^ _781013) ^ [] : [_1569950 = _1569954, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1569948), tc_List_Olist(_1569948))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1569948), tc_List_Olist(_1569948)), _1569952), _1569956)), c_List_Olexord(_1569948, _1569958)))], (40427 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569948, _1569948)), hAPP(hAPP(c_Product__Type_OPair(_1569948, _1569948), _1569950), _1569954)), _1569958))]]], (30057 ^ _781013) ^ [_1342726, _1342728, _1342730] : [class_Orderings_Olinorder(_1342726), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342726), _1342728), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342726), _1342730), _1342728))))], (462 ^ _781013) ^ [_788174, _788176] : [-(c_List_Onat__list(_788174)), _788176 = _788174, c_List_Onat__list(_788176)], (36595 ^ _781013) ^ [_1479256, _1479258, _1479260, _1479262, _1479264, _1479266] : [_1479256 = _1479258, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1479260, _1479262, _1479264), _1479266), _1479256) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1479260, _1479262, _1479264), _1479266), _1479258))], (32424 ^ _781013) ^ [_1396156, _1396158, _1396160, _1396162] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396156), hAPP(c_Int_Onumber__class_Onumber__of(_1396156), _1396158)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1396156), _1396160), _1396162)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1396156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396156), hAPP(c_Int_Onumber__class_Onumber__of(_1396156), _1396158)), _1396160)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396156), hAPP(c_Int_Onumber__class_Onumber__of(_1396156), _1396158)), _1396162))), class_Int_Onumber(_1396156), class_Rings_Osemiring(_1396156)], (29213 ^ _781013) ^ [_1326061, _1326063] : [class_Groups_Oabs__if(_1326061), 29216 ^ _781013 : [(29223 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326061), _1326063), c_Groups_Ozero__class_Ozero(_1326061)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1326061), _1326063) = _1326063)], (29217 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326061), _1326063), c_Groups_Ozero__class_Ozero(_1326061))), -(hAPP(c_Groups_Oabs__class_Oabs(_1326061), _1326063) = hAPP(c_Groups_Ouminus__class_Ouminus(_1326061), _1326063))]]], (43092 ^ _781013) ^ [_1637852, _1637854, _1637856, _1637858, _1637860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1637852, tc_HOL_Obool)), _1637854), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637856, tc_fun(_1637852, tc_HOL_Obool)), _1637858), _1637860))), 43095 ^ _781013 : [(43096 ^ _781013) ^ [_1637985] : [hBOOL(hAPP(hAPP(c_member(_1637856), _1637985), _1637858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1637852, tc_HOL_Obool)), _1637854), hAPP(_1637860, _1637985))))]]], (6557 ^ _781013) ^ [_888279, _888281] : [c_Option_Ooption_ONone(_888279) = hAPP(c_Option_Ooption_OSome(_888279), _888281)], (23945 ^ _781013) ^ [_1228049] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228049))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44488 ^ _781013) ^ [_1668545, _1668547, _1668549, _1668551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668545), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668547)), _1668549))), -(hAPP(c_List_Orev(_1668547), hAPP(hAPP(c_List_Olist__update(_1668547, _1668549), _1668545), _1668551)) = hAPP(hAPP(c_List_Olist__update(_1668547, hAPP(c_List_Orev(_1668547), _1668549)), 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(_1668547)), _1668549)), _1668545)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1668551))], (35537 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51268 ^ _781013) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (27825 ^ _781013) ^ [_1300596, _1300598, _1300600] : [class_Rings_Olinordered__idom(_1300596), -(c_Groups_Osgn__class_Osgn(_1300596, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300596), _1300598), _1300600)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300596), c_Groups_Osgn__class_Osgn(_1300596, _1300598)), c_Groups_Osgn__class_Osgn(_1300596, _1300600)))], (46507 ^ _781013) ^ [_1713478, _1713480, _1713482, _1713484] : [hBOOL(hAPP(hAPP(c_member(_1713478), _1713480), c_Wellfounded_Oacc(_1713478, _1713482))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1713478, _1713478)), hAPP(hAPP(c_Product__Type_OPair(_1713478, _1713478), _1713484), _1713480)), _1713482)), -(hBOOL(hAPP(hAPP(c_member(_1713478), _1713484), c_Wellfounded_Oacc(_1713478, _1713482))))], (38055 ^ _781013) ^ [_1510132, _1510134, _1510136] : [-(hAPP(c_Relation_OImage(_1510132, _1510132, c_Relation_OId__on(_1510132, _1510134)), _1510136) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1510132, tc_HOL_Obool)), _1510134), _1510136))], (21527 ^ _781013) ^ [] : [-(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)))], (13231 ^ _781013) ^ [_1022145, _1022147, _1022149, _1022151, _1022153, _1022155, _1022157] : [_1022145 = _1022147, -(hAPP(c_Sum__Type_Osum_Osum__case(_1022149, _1022151, _1022153, _1022155, _1022157), _1022145) = hAPP(c_Sum__Type_Osum_Osum__case(_1022149, _1022151, _1022153, _1022155, _1022157), _1022147))], (47521 ^ _781013) ^ [_1739453, _1739455, _1739457, _1739459, _1739461, _1739463] : [47524 ^ _781013 : [(47527 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1739459), _1739461), hAPP(hAPP(_1739463, 47522 ^ [_1739453, _1739455, _1739457, _1739459, _1739461, _1739463]), 47523 ^ [_1739453, _1739455, _1739457, _1739459, _1739461, _1739463])))], (47525 ^ _781013) ^ [] : [-(_1739453 = hAPP(hAPP(c_Product__Type_OPair(_1739455, _1739457), 47522 ^ [_1739453, _1739455, _1739457, _1739459, _1739461, _1739463]), 47523 ^ [_1739453, _1739455, _1739457, _1739459, _1739461, _1739463]))]], -(hBOOL(hAPP(hAPP(c_member(_1739459), _1739461), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1739455, _1739457, tc_fun(_1739459, tc_HOL_Obool)), _1739463), _1739453))))], (34825 ^ _781013) ^ [_1440414, _1440416] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1440414)), c_Int_OBit1(_1440416)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1440414), _1440416)))], (48709 ^ _781013) ^ [_1766453, _1766455, _1766457, _1766459, _1766461] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766453, _1766453)), hAPP(hAPP(c_Product__Type_OPair(_1766453, _1766453), hAPP(_1766455, hAPP(c_Nat_OSuc, 48710 ^ [_1766453, _1766455, _1766457, _1766459, _1766461]))), hAPP(_1766455, 48710 ^ [_1766453, _1766455, _1766457, _1766459, _1766461]))), c_Transitive__Closure_Ortrancl(_1766453, _1766457))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1766453, _1766453)), hAPP(hAPP(c_Product__Type_OPair(_1766453, _1766453), hAPP(_1766455, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1766459), _1766461))), hAPP(_1766455, _1766459))), c_Transitive__Closure_Ortrancl(_1766453, _1766457))))], (41306 ^ _781013) ^ [_1595144, _1595146] : [-(c_List_Oremove1(_1595144, _1595146, c_List_Olist_ONil(_1595144)) = c_List_Olist_ONil(_1595144))], (32030 ^ _781013) ^ [_1389170, _1389172, _1389174] : [_1389170 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1389172, _1389172), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1389172, _1389172), tc_HOL_Obool)), _1389170), _1389174)))], (34693 ^ _781013) ^ [_1438162] : [c_Int_OPls = _1438162, -(c_Int_OPls = c_Int_OBit0(_1438162))], (30121 ^ _781013) ^ [_1343827, _1343829, _1343831] : [class_Orderings_Olinorder(_1343827), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343827), _1343829), _1343831)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343827), _1343829), _1343831) = _1343831)], (38272 ^ _781013) ^ [_1515852, _1515854, _1515856, _1515858, _1515860, _1515862] : [-(hAPP(hAPP(c_List_Omap(_1515852, _1515854), _1515856), hAPP(hAPP(c_List_Omap(_1515858, _1515852), _1515860), _1515862)) = hAPP(hAPP(c_List_Omap(_1515858, _1515854), hAPP(c_Fun_Ocomp(_1515852, _1515854, _1515858, _1515856), _1515860)), _1515862))], (3420 ^ _781013) ^ [_832544, _832546, _832548, _832550, _832552, _832554] : [-(c_Set_Ovimage(_832554, _832550, _832546) = c_Set_Ovimage(_832552, _832548, _832544)), _832554 = _832552, _832550 = _832548, _832546 = _832544], (47449 ^ _781013) ^ [_1737357, _1737359, _1737361, _1737363, _1737365] : [47450 ^ _781013 : [(47453 ^ _781013) ^ [] : [hBOOL(hAPP(_1737365, hAPP(hAPP(c_List_Ozip(_1737357, _1737361), hAPP(hAPP(c_List_Otake(_1737357), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737357)), _1737359)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737361)), _1737363))), _1737359)), hAPP(hAPP(c_List_Otake(_1737361), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737357)), _1737359)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737361)), _1737363))), _1737363))))], (47451 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737357)), hAPP(hAPP(c_List_Otake(_1737357), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737357)), _1737359)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737361)), _1737363))), _1737359)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737361)), hAPP(hAPP(c_List_Otake(_1737361), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737357)), _1737359)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737361)), _1737363))), _1737363)))]], -(hBOOL(hAPP(_1737365, hAPP(hAPP(c_List_Ozip(_1737357, _1737361), _1737359), _1737363))))], (6619 ^ _781013) ^ [_889399, _889401, _889403, _889405, _889407, _889409, _889411] : [c_Finite__Set_Ofolding__idem(_889399, _889401, _889403, _889405), -(hAPP(c_Fun_Ocomp(_889401, _889401, _889407, hAPP(_889403, _889409)), hAPP(c_Fun_Ocomp(_889401, _889401, _889407, hAPP(_889403, _889409)), _889411)) = hAPP(c_Fun_Ocomp(_889401, _889401, _889407, hAPP(_889403, _889409)), _889411))], (17633 ^ _781013) ^ [_1110721, _1110723] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110721), _1110723) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110723), _1110721))], (48703 ^ _781013) ^ [_1766267, _1766269, _1766271] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1766267, _1766267), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1766267, _1766267), _1766269)), c_Transitive__Closure_Ortrancl(_1766267, _1766269)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1766267, _1766267), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1766267, _1766267)), hAPP(hAPP(c_Product__Type_OPair(_1766267, _1766267), _1766271), _1766271)), c_Transitive__Closure_Otrancl(_1766267, _1766269)))], (49588 ^ _781013) ^ [_1789152, _1789154, _1789156, _1789158, _1789160] : [c_Finite__Set_Ofolding__one__idem(_1789152, _1789154, _1789156), hBOOL(hAPP(c_Finite__Set_Ofinite(_1789152), _1789158)), -(hAPP(_1789156, hAPP(hAPP(c_Set_Oinsert(_1789152), _1789160), _1789158)) = hAPP(hAPP(c_Finite__Set_Ofold(_1789152, _1789152, _1789154), _1789160), _1789158))], (43635 ^ _781013) ^ [_1650689, _1650691, _1650693, _1650695, _1650697] : [class_Orderings_Olinorder(_1650689), 43638 ^ _781013 : [(43645 ^ _781013) ^ [] : [c_List_Olinorder__class_Osorted(_1650689, hAPP(hAPP(c_List_Omap(_1650691, _1650689), _1650693), _1650697)), -(c_List_Olinorder__class_Osorted(_1650689, hAPP(hAPP(c_List_Omap(_1650691, _1650689), _1650693), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1650691, _1650689, _1650693), _1650695), _1650697))))], (43639 ^ _781013) ^ [] : [c_List_Olinorder__class_Osorted(_1650689, hAPP(hAPP(c_List_Omap(_1650691, _1650689), _1650693), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1650691, _1650689, _1650693), _1650695), _1650697))), -(c_List_Olinorder__class_Osorted(_1650689, hAPP(hAPP(c_List_Omap(_1650691, _1650689), _1650693), _1650697)))]]], (49422 ^ _781013) ^ [_1785459, _1785461, _1785463] : [-(hBOOL(hAPP(hAPP(c_member(_1785459), _1785461), hAPP(c_List_Oset(_1785459), _1785463)))), 49423 ^ _781013 : [(49424 ^ _781013) ^ [_1785548, _1785550] : [_1785463 = hAPP(hAPP(c_List_Oappend(_1785459), _1785550), hAPP(hAPP(c_List_Olist_OCons(_1785459), _1785461), _1785548)), -(hBOOL(hAPP(hAPP(c_member(_1785459), _1785461), hAPP(c_List_Oset(_1785459), _1785548))))]]], (38210 ^ _781013) ^ [_1514479, _1514481, _1514483, _1514485, _1514487, _1514489, _1514491] : [c_Fun_Oinj__on(_1514479, _1514481, _1514483, c_Orderings_Otop__class_Otop(tc_fun(_1514479, tc_HOL_Obool))), hAPP(hAPP(c_Map_Omap__of(_1514479, _1514485), _1514487), _1514489) = hAPP(c_Option_Ooption_OSome(_1514485), _1514491), -(hAPP(hAPP(c_Map_Omap__of(_1514481, _1514485), hAPP(hAPP(c_List_Omap(tc_prod(_1514479, _1514485), tc_prod(_1514481, _1514485)), hAPP(c_Product__Type_Oprod_Oprod__case(_1514479, _1514485, tc_prod(_1514481, _1514485)), hAPP(hAPP(c_COMBB(_1514481, tc_fun(_1514485, tc_prod(_1514481, _1514485)), _1514479), c_Product__Type_OPair(_1514481, _1514485)), _1514483))), _1514487)), hAPP(_1514483, _1514489)) = hAPP(c_Option_Ooption_OSome(_1514485), _1514491))], (44749 ^ _781013) ^ [_1674566] : [-(c_List_Oremdups(_1674566, c_List_Olist_ONil(_1674566)) = c_List_Olist_ONil(_1674566))], (33944 ^ _781013) ^ [_1424086, _1424088] : [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(_1424088))), 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), _1424086)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1424086)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424088))))], (36569 ^ _781013) ^ [_1478779, _1478781, _1478783, _1478785, _1478787, _1478789] : [hAPP(hAPP(c_Product__Type_OPair(_1478779, _1478781), _1478783), _1478785) = hAPP(hAPP(c_Product__Type_OPair(_1478779, _1478781), _1478787), _1478789), 36572 ^ _781013 : [(36575 ^ _781013) ^ [] : [-(_1478785 = _1478789)], (36573 ^ _781013) ^ [] : [-(_1478783 = _1478787)]]], (34193 ^ _781013) ^ [_1429654] : [c_Int_OPls = c_Int_OBit1(_1429654)], (8088 ^ _781013) ^ [_918672, _918674, _918676, _918678] : [hBOOL(hAPP(hAPP(c_member(_918672), _918674), c_Map_Odom(_918672, _918676, _918678))), hAPP(_918678, _918674) = c_Option_Ooption_ONone(_918676)], (11864 ^ _781013) ^ [_994988, _994990] : [-(hBOOL(hAPP(hAPP(c_member(_994988), _994990), c_Orderings_Otop__class_Otop(tc_fun(_994988, tc_HOL_Obool)))))], (18974 ^ _781013) ^ [_1135906, _1135908, _1135910, _1135912, _1135914, _1135916] : [-(hBOOL(hAPP(hAPP(c_member(_1135906), _1135908), c_SetInterval_Oord_OgreaterThanAtMost(_1135906, _1135910, _1135912, _1135914, _1135916)))), hBOOL(hAPP(hAPP(_1135912, _1135914), _1135908)), hBOOL(hAPP(hAPP(_1135910, _1135908), _1135916))], (46043 ^ _781013) ^ [_1702490, _1702492] : [class_Orderings_Olinorder(_1702490), 46046 ^ _781013 : [(46067 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1702490, _1702492)), 46068 ^ _781013 : [(46071 ^ _781013) ^ [_1703050, _1703052] : [_1702492 = hAPP(hAPP(c_List_Olist_OCons(_1702490), _1703050), _1703052), 46077 ^ _781013 : [(46080 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1702490), _1703050), 46076 ^ [_1702490, _1702492, _1703050, _1703052]))], (46078 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1702490), 46076 ^ [_1702490, _1702492, _1703050, _1703052]), hAPP(c_List_Oset(_1702490), _1703052))))]], c_List_Olinorder__class_Osorted(_1702490, _1703052)], (46069 ^ _781013) ^ [] : [_1702492 = c_List_Olist_ONil(_1702490)]]], (46047 ^ _781013) ^ [] : [c_List_Olinorder__class_Osorted(_1702490, _1702492), -(_1702492 = c_List_Olist_ONil(_1702490)), 46056 ^ _781013 : [(46059 ^ _781013) ^ [_1702824] : [hBOOL(hAPP(hAPP(c_member(_1702490), _1702824), hAPP(c_List_Oset(_1702490), 46054 ^ [_1702490, _1702492]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1702490), 46055 ^ [_1702490, _1702492]), _1702824)))], (46065 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1702490, 46054 ^ [_1702490, _1702492]))], (46057 ^ _781013) ^ [] : [-(_1702492 = hAPP(hAPP(c_List_Olist_OCons(_1702490), 46055 ^ [_1702490, _1702492]), 46054 ^ [_1702490, _1702492]))]]]]], (47110 ^ _781013) ^ [_1729297, _1729299, _1729301, _1729303] : [hBOOL(hAPP(c_Predicate_ORangeP(_1729297, _1729299, hAPP(hAPP(c_COMBC(_1729297, tc_fun(tc_prod(_1729297, _1729299), tc_HOL_Obool), tc_fun(_1729299, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1729299, tc_fun(tc_fun(tc_prod(_1729297, _1729299), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1729297, _1729299), tc_HOL_Obool), tc_fun(_1729299, tc_HOL_Obool)), _1729297), c_COMBC(_1729299, tc_fun(tc_prod(_1729297, _1729299), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1729299, tc_prod(_1729297, _1729299)), tc_fun(_1729299, tc_fun(tc_fun(tc_prod(_1729297, _1729299), tc_HOL_Obool), tc_HOL_Obool)), _1729297), hAPP(c_COMBB(tc_prod(_1729297, _1729299), tc_fun(tc_fun(tc_prod(_1729297, _1729299), tc_HOL_Obool), tc_HOL_Obool), _1729299), c_member(tc_prod(_1729297, _1729299)))), c_Product__Type_OPair(_1729297, _1729299)))), _1729301)), _1729303)), -(hBOOL(hAPP(hAPP(c_member(_1729299), _1729303), hAPP(c_Relation_ORange(_1729297, _1729299), _1729301))))], (37542 ^ _781013) ^ [_1497818, _1497820, _1497822] : [-(hAPP(hAPP(c_Product__Type_OPair(_1497818, _1497820), hAPP(c_Product__Type_Ofst(_1497818, _1497820), _1497822)), hAPP(c_Product__Type_Osnd(_1497818, _1497820), _1497822)) = _1497822)], (49406 ^ _781013) ^ [_1785026, _1785028, _1785030] : [49407 ^ _781013 : [(49408 ^ _781013) ^ [_1785103, _1785105] : [_1785030 = hAPP(hAPP(c_List_Oappend(_1785026), _1785105), hAPP(hAPP(c_List_Olist_OCons(_1785026), _1785028), _1785103))]], -(hBOOL(hAPP(hAPP(c_member(_1785026), _1785028), hAPP(c_List_Oset(_1785026), _1785030))))], (2316 ^ _781013) ^ [_815270, _815272, _815274, _815276] : [-(c_Nat__Transfer_Otsub(_815276, _815272) = c_Nat__Transfer_Otsub(_815274, _815270)), _815276 = _815274, _815272 = _815270], (16454 ^ _781013) ^ [_1085577, _1085579, _1085581, _1085583, _1085585, _1085587, _1085589, _1085591] : [class_Groups_Ocomm__monoid__mult(_1085577), c_Fun_Oinj__on(_1085579, _1085581, _1085583, _1085585), _1085587 = hAPP(c_Set_Oimage(_1085579, _1085581, _1085583), _1085585), _1085589 = hAPP(c_Fun_Ocomp(_1085581, _1085577, _1085579, _1085591), _1085583), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1085581, _1085577), _1085591), _1085587) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1085579, _1085577), _1085589), _1085585))], (23547 ^ _781013) ^ [_1221669, _1221671, _1221673, _1221675] : [class_Rings_Odivision__ring(_1221669), -(_1221671 = c_Groups_Ozero__class_Ozero(_1221669)), 23554 ^ _781013 : [(23561 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221669), _1221673), _1221671) = _1221675, -(_1221673 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221669), _1221675), _1221671))], (23555 ^ _781013) ^ [] : [_1221673 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221669), _1221675), _1221671), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221669), _1221673), _1221671) = _1221675)]]], (31591 ^ _781013) ^ [_1376809, _1376811, _1376813, _1376815] : [hBOOL(hAPP(hAPP(c_member(_1376811), _1376815), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376809, tc_fun(_1376811, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1376809, tc_HOL_Obool))), _1376813))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376809, tc_fun(_1376811, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1376809, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1376811, tc_HOL_Obool), tc_fun(_1376811, tc_HOL_Obool), _1376809), hAPP(c_COMBC(_1376811, tc_fun(_1376811, tc_HOL_Obool), tc_HOL_Obool), c_member(_1376811))), _1376813)), _1376815)))], (19106 ^ _781013) ^ [_1138784, _1138786, _1138788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1138784), _1138786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1138784), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1138786), _1138788))))], (22200 ^ _781013) ^ [_1197345, _1197347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1197345), _1197347)), -(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)), _1197345)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1197347))))], (22182 ^ _781013) ^ [_1197048, _1197050] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1197048) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1197050), -(_1197048 = _1197050)], (30513 ^ _781013) ^ [_1351285, _1351287, _1351289] : [class_Orderings_Olinorder(_1351285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351285), _1351287)), -(_1351287 = c_Orderings_Obot__class_Obot(tc_fun(_1351285, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351285), _1351289)), -(_1351289 = c_Orderings_Obot__class_Obot(tc_fun(_1351285, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1351285, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351285, tc_HOL_Obool)), _1351287), _1351289)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351285), c_Big__Operators_Olinorder__class_OMax(_1351285, _1351287)), c_Big__Operators_Olinorder__class_OMax(_1351285, _1351289)))], (22652 ^ _781013) ^ [_1204897, _1204899, _1204901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204897)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204899), _1204901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204897), _1204901)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204897), _1204899))))], (23437 ^ _781013) ^ [_1219524, _1219526] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1219524, _1219526))))], (36148 ^ _781013) ^ [_1469455, _1469457, _1469459, _1469461, _1469463] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1469459, _1469455)), hAPP(hAPP(c_Product__Type_OPair(_1469459, _1469455), _1469463), _1469457)), _1469461)), -(hBOOL(hAPP(hAPP(c_member(_1469455), _1469457), hAPP(c_Relation_OImage(_1469459, _1469455, _1469461), hAPP(hAPP(c_Set_Oinsert(_1469459), _1469463), c_Orderings_Obot__class_Obot(tc_fun(_1469459, tc_HOL_Obool)))))))], (51570 ^ _781013) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (51250 ^ _781013) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (2988 ^ _781013) ^ [_825730, _825732, _825734, _825736] : [-(c_List_OremoveAll(_825736, _825732) = c_List_OremoveAll(_825734, _825730)), _825736 = _825734, _825732 = _825730], (47531 ^ _781013) ^ [_1739778, _1739780, _1739782, _1739784, _1739786, _1739788] : [hBOOL(hAPP(hAPP(c_member(_1739778), _1739780), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1739782, _1739784, tc_fun(_1739778, tc_HOL_Obool)), _1739786), _1739788))), 47536 ^ _781013 : [(47539 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739778), _1739780), hAPP(hAPP(_1739786, 47534 ^ [_1739778, _1739780, _1739782, _1739784, _1739786, _1739788]), 47535 ^ [_1739778, _1739780, _1739782, _1739784, _1739786, _1739788]))))], (47537 ^ _781013) ^ [] : [-(_1739788 = hAPP(hAPP(c_Product__Type_OPair(_1739782, _1739784), 47534 ^ [_1739778, _1739780, _1739782, _1739784, _1739786, _1739788]), 47535 ^ [_1739778, _1739780, _1739782, _1739784, _1739786, _1739788]))]]], (7549 ^ _781013) ^ [_907399, _907401, _907403, _907405] : [hBOOL(hAPP(hAPP(c_member(_907399), _907401), _907403)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907399, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_907399), _907401), _907405)), _907403) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907399, tc_HOL_Obool)), _907405), _907403))], (28064 ^ _781013) ^ [_1304862, _1304864, _1304866] : [-(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), _1304862), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1304864), _1304862))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304864, _1304862))), _1304866) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1304864), _1304866))], (38614 ^ _781013) ^ [_1523662] : [c_List_Onat__list(_1523662), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1523662)))], (7667 ^ _781013) ^ [_909974, _909976] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909974, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_909974, tc_HOL_Obool))), _909976) = c_Orderings_Obot__class_Obot(tc_fun(_909974, tc_HOL_Obool)))], (34829 ^ _781013) ^ [_1440500, _1440502] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1440500))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1440502))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1440500)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1440502)))], (3228 ^ _781013) ^ [_829604, _829606, _829608, _829610, _829612, _829614, _829616, _829618] : [-(c_Map_Omap__add(_829618, _829614, _829610, _829606) = c_Map_Omap__add(_829616, _829612, _829608, _829604)), _829618 = _829616, _829614 = _829612, _829610 = _829608, _829606 = _829604], (29315 ^ _781013) ^ [_1327876, _1327878, _1327880, _1327882] : [class_Orderings_Olinorder(_1327876), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327876, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1327876), _1327878)), c_SetInterval_Oord__class_OatLeastAtMost(_1327876, _1327880, _1327882)) = c_SetInterval_Oord__class_OatLeastAtMost(_1327876, _1327880, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1327876), _1327878), _1327882)))], (48547 ^ _781013) ^ [_1762702, _1762704] : [-(c_Code__Numeral_Onat__of__aux(_1762702, _1762704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1762702)), _1762704))], (51132 ^ _781013) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (12890 ^ _781013) ^ [_1014855, _1014857, _1014859, _1014861, _1014863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1014855, tc_HOL_Obool)), _1014857), _1014859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1014861, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1014861, _1014855, _1014863), _1014857)), hAPP(c_Set_Ovimage(_1014861, _1014855, _1014863), _1014859))))], (49770 ^ _781013) ^ [_1792702, _1792704, _1792706, _1792708] : [class_Complete__Lattice_Ocomplete__lattice(_1792702), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792704), _1792706)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1792704, _1792702), _1792706), _1792708) = hAPP(hAPP(c_Finite__Set_Ofold(_1792704, _1792702, hAPP(hAPP(c_COMBB(_1792702, tc_fun(_1792702, _1792702), _1792704), c_Lattices_Osemilattice__sup__class_Osup(_1792702)), _1792708)), c_Orderings_Obot__class_Obot(_1792702)), _1792706))], (10287 ^ _781013) ^ [_962997, _962999, _963001] : [hBOOL(hAPP(hAPP(c_member(_962997), _962999), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_962997, tc_HOL_Obool)), _963001))), hBOOL(hAPP(hAPP(c_member(_962997), _962999), _963001))], (2806 ^ _781013) ^ [_822863, _822865] : [_822865 = _822863, -(c_Hilbert__Choice_OGreatest(_822865) = c_Hilbert__Choice_OGreatest(_822863))], (30461 ^ _781013) ^ [_1350427] : [class_Orderings_Olinorder(_1350427), -(c_Orderings_Oord_Omin(_1350427, hAPP(c_COMBC(_1350427, _1350427, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1350427))) = c_Orderings_Oord__class_Omax(_1350427))], (38280 ^ _781013) ^ [_1516130, _1516132, _1516134, _1516136, _1516138, _1516140, _1516142] : [-(c_List_Ofoldr(_1516130, _1516132, _1516134, hAPP(hAPP(c_List_Omap(_1516136, _1516130), _1516138), _1516140), _1516142) = c_List_Ofoldr(_1516136, _1516132, hAPP(c_Fun_Ocomp(_1516130, tc_fun(_1516132, _1516132), _1516136, _1516134), _1516138), _1516140, _1516142))], (7949 ^ _781013) ^ [_915302, _915304, _915306, _915308, _915310, _915312] : [-(hAPP(hAPP(c_Option_Omap(_915302, _915304), _915306), hAPP(hAPP(c_Option_Omap(_915308, _915302), _915310), _915312)) = hAPP(hAPP(c_Option_Omap(_915308, _915304), hAPP(c_Fun_Ocomp(_915302, _915304, _915308, _915306), _915310)), _915312))], (21836 ^ _781013) ^ [_1190864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1190864)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1190864 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42422 ^ _781013) ^ [_1621231, _1621233, _1621235] : [-(hAPP(c_List_Orotate(_1621231, _1621233), _1621235) = hAPP(c_List_Orotate(_1621231, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1621233, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621231)), _1621235))), _1621235))], (26593 ^ _781013) ^ [_1276028, _1276030, _1276032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1276028)), 26599 ^ _781013 : [(26602 ^ _781013) ^ [] : [hBOOL(hAPP(_1276030, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26598 ^ [_1276028, _1276030, _1276032]), _1276028)))], (26600 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1276030, 26598 ^ [_1276028, _1276030, _1276032])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1276032)), 26607 ^ _781013 : [(26608 ^ _781013) ^ [_1276317] : [hBOOL(hAPP(_1276030, _1276317)), -(hBOOL(hAPP(_1276030, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1276317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1276032), _1276028)))))]]], (18688 ^ _781013) ^ [_1129304, _1129306, _1129308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129304), _1129306)), 18691 ^ _781013 : [(18698 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1129308), _1129304)), _1129306)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129308), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1129306), _1129304))))], (18692 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129308), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1129306), _1129304))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1129308), _1129304)), _1129306)))]]], (17314 ^ _781013) ^ [_1103926, _1103928, _1103930, _1103932, _1103934] : [class_Groups_Ocomm__monoid__add(_1103926), hBOOL(hAPP(c_Finite__Set_Ofinite(_1103928), _1103930)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1103928, _1103926), _1103932), hAPP(c_Set_OCollect(_1103928), hAPP(hAPP(c_COMBS(_1103928, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1103928), c_fconj), hAPP(hAPP(c_COMBC(_1103928, tc_fun(_1103928, tc_HOL_Obool), tc_HOL_Obool), c_member(_1103928)), _1103930))), hAPP(hAPP(c_COMBC(_1103928, tc_fun(_1103928, tc_HOL_Obool), tc_HOL_Obool), c_member(_1103928)), _1103934)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1103928, _1103926), hAPP(hAPP(c_COMBC(_1103928, _1103926, _1103926), hAPP(hAPP(c_COMBS(_1103928, _1103926, tc_fun(_1103926, _1103926)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1103926, tc_fun(_1103926, _1103926)), _1103928), c_If(_1103926)), hAPP(hAPP(c_COMBC(_1103928, tc_fun(_1103928, tc_HOL_Obool), tc_HOL_Obool), c_member(_1103928)), _1103934))), _1103932)), c_Groups_Ozero__class_Ozero(_1103926))), _1103930))], (46164 ^ _781013) ^ [_1705174, _1705176, _1705178, _1705180] : [_1705180 = c_List_Olist_ONil(_1705176), -(c_List_Olist__all2(_1705174, _1705176, _1705178, c_List_Olist_ONil(_1705174), _1705180))], (40455 ^ _781013) ^ [_1571714, _1571716, _1571718, _1571720, _1571722, _1571724, _1571726, _1571728, _1571730, _1571732, _1571734] : [-(hAPP(c_Product__Type_Omap__pair(_1571714, _1571716, _1571718, _1571720, _1571722, _1571724), hAPP(c_Product__Type_Omap__pair(_1571726, _1571714, _1571728, _1571718, _1571730, _1571732), _1571734)) = hAPP(c_Product__Type_Omap__pair(_1571726, _1571716, _1571728, _1571720, hAPP(c_Fun_Ocomp(_1571714, _1571716, _1571726, _1571722), _1571730), hAPP(c_Fun_Ocomp(_1571718, _1571720, _1571728, _1571724), _1571732)), _1571734))], (22892 ^ _781013) ^ [_1209299, _1209301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209299), _1209301)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209299), hAPP(c_Nat_OSuc, _1209301)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1209301), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209299), _1209301)))], (26635 ^ _781013) ^ [_1276860, _1276862, _1276864] : [class_Orderings_Olinorder(_1276860), 26638 ^ _781013 : [(26645 ^ _781013) ^ [] : [_1276862 = _1276864, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1276860), _1276862) = hAPP(c_SetInterval_Oord__class_OatLeast(_1276860), _1276864))], (26639 ^ _781013) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1276860), _1276862) = hAPP(c_SetInterval_Oord__class_OatLeast(_1276860), _1276864), -(_1276862 = _1276864)]]], (35827 ^ _781013) ^ [_1458223] : [-(c_Int_Oint__ge__less__than(_1458223) = 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), _1458223)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (31870 ^ _781013) ^ [_1384818, _1384820, _1384822, _1384824, _1384826, _1384828] : [-(hAPP(c_Set_Ovimage(_1384818, _1384820, _1384822), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384824, tc_fun(_1384820, tc_HOL_Obool)), _1384826), _1384828)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384824, tc_fun(_1384818, tc_HOL_Obool)), _1384826), hAPP(hAPP(c_COMBB(tc_fun(_1384820, tc_HOL_Obool), tc_fun(_1384818, tc_HOL_Obool), _1384824), c_Set_Ovimage(_1384818, _1384820, _1384822)), _1384828)))], (48303 ^ _781013) ^ [_1757099, _1757101] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1757099), _1757101) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1757099)), hAPP(c_Code__Numeral_Onat__of, _1757101))))], (41172 ^ _781013) ^ [_1592555, _1592557, _1592559, _1592561, _1592563] : [c_List_Opartition(_1592555, _1592557, _1592559) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1592555), tc_List_Olist(_1592555)), _1592561), _1592563), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1592555, tc_HOL_Obool)), hAPP(c_List_Oset(_1592555), _1592561)), hAPP(c_List_Oset(_1592555), _1592563)) = hAPP(c_List_Oset(_1592555), _1592559))], (15773 ^ _781013) ^ [_1072821, _1072823, _1072825, _1072827] : [class_Rings_Olinordered__semiring__strict(_1072821), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072821), _1072823), _1072825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072821), c_Groups_Ozero__class_Ozero(_1072821)), _1072827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072821), _1072827), _1072823)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072821), _1072827), _1072825))))], (26765 ^ _781013) ^ [_1279091, _1279093] : [class_Orderings_Olinorder(_1279091), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279091, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1279091), _1279093), c_Orderings_Obot__class_Obot(tc_fun(_1279091, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1279091), _1279093)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1279091), _1279093))], (18875 ^ _781013) ^ [_1133455, _1133457, _1133459, _1133461, _1133463] : [class_Groups_Ocomm__monoid__add(_1133455), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133457), _1133459)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133457), _1133461)), 18889 ^ _781013 : [(18892 ^ _781013) ^ [] : [hAPP(_1133463, 18888 ^ [_1133455, _1133457, _1133459, _1133461, _1133463]) = c_Groups_Ozero__class_Ozero(_1133455)], (18890 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1133457), 18888 ^ [_1133455, _1133457, _1133459, _1133461, _1133463]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1133457, tc_HOL_Obool)), _1133459), _1133461))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1133457, _1133455), _1133463), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1133457, tc_HOL_Obool)), _1133459), _1133461)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133455), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1133457, _1133455), _1133463), _1133459)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1133457, _1133455), _1133463), _1133461)))], (35311 ^ _781013) ^ [_1449038, _1449040, _1449042] : [class_Rings_Olinordered__idom(_1449038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449038), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1449038), hAPP(hAPP(c_Power_Opower__class_Opower(_1449038), _1449040), 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(_1449038), _1449042), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1449038)))], (48179 ^ _781013) ^ [_1754468, _1754470, _1754472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1754468), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754470)), _1754472))), -(hAPP(c_Random_Opick(_1754470, hAPP(hAPP(c_List_Omap(_1754470, tc_prod(tc_Code__Numeral_Ocode__numeral, _1754470)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1754470), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1754472)), hAPP(c_Code__Numeral_Oof__nat, _1754468)) = hAPP(hAPP(c_List_Onth(_1754470), _1754472), _1754468))], (23343 ^ _781013) ^ [_1217641, _1217643] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1217641, _1217643))))], (37734 ^ _781013) ^ [_1502016] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1502016)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1502016)], (45701 ^ _781013) ^ [_1694537, _1694539, _1694541] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1694537, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1694537, tc_HOL_Obool), _1694539)), _1694541) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1694537, tc_HOL_Obool), tc_fun(_1694537, tc_HOL_Obool)), _1694539), hAPP(hAPP(c_COMBC(tc_fun(_1694537, tc_HOL_Obool), tc_fun(_1694537, tc_HOL_Obool), tc_fun(_1694537, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1694537, tc_HOL_Obool))), _1694541)))], (35927 ^ _781013) ^ [_1461887, _1461889, _1461891, _1461893, _1461895, _1461897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1461887, _1461889)), hAPP(hAPP(c_Product__Type_OPair(_1461887, _1461889), _1461895), _1461897)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool)), _1461891), _1461893))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461887, tc_fun(_1461889, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1461887, tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_fun(_1461889, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461889, tc_fun(tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_fun(_1461889, tc_HOL_Obool)), _1461887), c_COMBC(_1461889, tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461889, tc_prod(_1461887, _1461889)), tc_fun(_1461889, tc_fun(tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_HOL_Obool)), _1461887), hAPP(c_COMBB(tc_prod(_1461887, _1461889), tc_fun(tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_HOL_Obool), _1461889), c_member(tc_prod(_1461887, _1461889)))), c_Product__Type_OPair(_1461887, _1461889)))), _1461891)), hAPP(hAPP(c_COMBC(_1461887, tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_fun(_1461889, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461889, tc_fun(tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_fun(_1461889, tc_HOL_Obool)), _1461887), c_COMBC(_1461889, tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461889, tc_prod(_1461887, _1461889)), tc_fun(_1461889, tc_fun(tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_HOL_Obool)), _1461887), hAPP(c_COMBB(tc_prod(_1461887, _1461889), tc_fun(tc_fun(tc_prod(_1461887, _1461889), tc_HOL_Obool), tc_HOL_Obool), _1461889), c_member(tc_prod(_1461887, _1461889)))), c_Product__Type_OPair(_1461887, _1461889)))), _1461893)), _1461895), _1461897)))], (50616 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14772 ^ _781013) ^ [_1055085, _1055087] : [-(hBOOL(hAPP(_1055087, 14773 ^ [_1055085, _1055087]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1055085, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1055085), _1055087))], (38029 ^ _781013) ^ [_1509534, _1509536, _1509538] : [-(hAPP(c_Relation_OField(_1509534), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509534, _1509534), tc_HOL_Obool)), _1509536), _1509538)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1509534, tc_HOL_Obool)), hAPP(c_Relation_OField(_1509534), _1509536)), hAPP(c_Relation_OField(_1509534), _1509538)))], (368 ^ _781013) ^ [_786737, _786739, _786741, _786743, _786745, _786747, _786749, _786751] : [-(c_Equiv__Relations_Ocongruent(_786749, _786745, _786741, _786737)), c_Equiv__Relations_Ocongruent(_786751, _786747, _786743, _786739), _786751 = _786749, _786747 = _786745, _786743 = _786741, _786739 = _786737], (41644 ^ _781013) ^ [_1603015, _1603017, _1603019] : [_1603017 = c_List_Olist_ONil(_1603015), -(hAPP(hAPP(c_List_Oappend(_1603015), _1603017), _1603019) = _1603019)], (24420 ^ _781013) ^ [_1236487, _1236489, _1236491, _1236493] : [class_Fields_Olinordered__field(_1236487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236487), c_Groups_Ozero__class_Ozero(_1236487)), _1236489)), 24427 ^ _781013 : [(24434 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236487), _1236491), _1236489)), _1236493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236487), _1236491), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1236487), _1236493), _1236489))))], (24428 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236487), _1236491), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1236487), _1236493), _1236489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236487), _1236491), _1236489)), _1236493)))]]], (19771 ^ _781013) ^ [_1151596, _1151598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151596), _1151598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1151596)), hAPP(c_Nat_OSuc, _1151598))))], (46158 ^ _781013) ^ [_1705083, _1705085, _1705087, _1705089] : [c_List_Olist__all2(_1705083, _1705085, _1705087, c_List_Olist_ONil(_1705083), _1705089), -(_1705089 = c_List_Olist_ONil(_1705085))], (50700 ^ _781013) ^ [_1811357] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1811357))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1811357)))], (31035 ^ _781013) ^ [_1362109, _1362111] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1362109), hAPP(c_Nat_OSuc, _1362111)) = 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)), _1362111)), _1362109))], (41166 ^ _781013) ^ [_1592466, _1592468, _1592470, _1592472] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1592466) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1592468), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1592466)), hAPP(hAPP(c_List_Olist_OCons(_1592468), _1592470), _1592472)) = hAPP(hAPP(c_List_Olist_OCons(_1592468), _1592470), hAPP(hAPP(c_List_Otake(_1592468), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1592466)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1592472)))], (15059 ^ _781013) ^ [_1059439, _1059441, _1059443] : [hBOOL(hAPP(hAPP(c_member(_1059439), _1059441), hAPP(c_Set_OCollect(_1059439), _1059443))), -(hBOOL(hAPP(_1059443, _1059441)))], (49932 ^ _781013) ^ [_1795731, _1795733, _1795735, _1795737, _1795739, _1795741, _1795743] : [c_Finite__Set_Ofun__left__comm(_1795731, _1795733, _1795735), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1795731, _1795733, _1795735, _1795737, _1795739), _1795741)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1795731, _1795733, _1795735, _1795737, _1795739), _1795743)), -(_1795743 = _1795741)], (39611 ^ _781013) ^ [_1547681] : [class_Orderings_Oord(_1547681), -(c_Hilbert__Choice_OGreatest(_1547681) = c_Hilbert__Choice_OGreatestM(_1547681, _1547681, c_COMBI(_1547681)))], (23493 ^ _781013) ^ [_1220698, _1220700, _1220702, _1220704, _1220706] : [class_Fields_Ofield(_1220698), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220698), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1220700, _1220698), _1220702), _1220704)), _1220706) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1220700, _1220698), hAPP(hAPP(c_COMBC(_1220700, _1220698, _1220698), hAPP(hAPP(c_COMBB(_1220698, tc_fun(_1220698, _1220698), _1220700), c_Rings_Oinverse__class_Odivide(_1220698)), _1220702)), _1220706)), _1220704))], (42282 ^ _781013) ^ [_1618593, _1618595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618593)), _1618595)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1618593), _1618595) = _1618595)], (5308 ^ _781013) ^ [_861978, _861980, _861982, _861984] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_861984, _861980) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_861982, _861978)), _861984 = _861982, _861980 = _861978], (51580 ^ _781013) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (41398 ^ _781013) ^ [_1596633, _1596635, _1596637] : [-(hAPP(hAPP(c_List_Otake(_1596633), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1596633), _1596635), _1596637)) = hAPP(hAPP(c_List_Olist_OCons(_1596633), _1596635), c_List_Olist_ONil(_1596633)))], (49720 ^ _781013) ^ [_1791646, _1791648, _1791650] : [class_Orderings_Olinorder(_1791646), hBOOL(hAPP(c_Finite__Set_Ofinite(_1791646), _1791648)), -(c_Big__Operators_Olinorder__class_OMax(_1791646, hAPP(hAPP(c_Set_Oinsert(_1791646), _1791650), _1791648)) = hAPP(hAPP(c_Finite__Set_Ofold(_1791646, _1791646, c_Orderings_Oord__class_Omax(_1791646)), _1791650), _1791648))], (4720 ^ _781013) ^ [_852410, _852412] : [_852412 = _852410, -(c_Int_OBit0(_852412) = c_Int_OBit0(_852410))], (9277 ^ _781013) ^ [_945221, _945223, _945225, _945227] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_945221, tc_HOL_Obool)), _945223), hAPP(hAPP(c_Set_Oinsert(_945221), _945225), _945227)))), 9280 ^ _781013 : [(9283 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_945221, tc_HOL_Obool)), _945223), _945227))], (9281 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_945221), _945225), _945227)))]], 9284 ^ _781013 : [(9287 ^ _781013) ^ [] : [9288 ^ _781013 : [(9291 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_945221, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_945221, tc_HOL_Obool)), _945223), hAPP(hAPP(c_Set_Oinsert(_945221), _945225), c_Orderings_Obot__class_Obot(tc_fun(_945221, tc_HOL_Obool))))), _945227))], (9289 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_945221), _945225), _945223)))]], 9292 ^ _781013 : [(9295 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945221, tc_HOL_Obool)), _945223), _945227))], (9293 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_945221), _945225), _945223))]]], (9285 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_945221), _945225), _945227))]]], (27745 ^ _781013) ^ [_1299074, _1299076] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1299074, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1299076)) = 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), _1299074), _1299076)))], (38276 ^ _781013) ^ [_1515988, _1515990, _1515992, _1515994, _1515996] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1515988), tc_List_Olist(_1515990), tc_List_Olist(_1515992), hAPP(c_List_Omap(_1515988, _1515990), _1515994)), hAPP(c_List_Omap(_1515992, _1515988), _1515996)) = hAPP(c_List_Omap(_1515992, _1515990), hAPP(c_Fun_Ocomp(_1515988, _1515990, _1515992, _1515994), _1515996)))], (43129 ^ _781013) ^ [_1638912, _1638914, _1638916, _1638918, _1638920] : [_1638912 = c_Orderings_Obot__class_Obot(tc_fun(_1638914, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638914, tc_fun(_1638916, tc_HOL_Obool)), _1638912), hAPP(hAPP(c_COMBB(tc_fun(_1638916, tc_HOL_Obool), tc_fun(_1638916, tc_HOL_Obool), _1638914), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638916, tc_HOL_Obool)), _1638918)), _1638920)) = c_Orderings_Otop__class_Otop(tc_fun(_1638916, tc_HOL_Obool)))], (29337 ^ _781013) ^ [_1328319, _1328321, _1328323, _1328325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1328319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1328321), _1328323)), -(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), _1328323), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1328325, _1328319))), _1328321)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1328323), _1328319))))], (38053 ^ _781013) ^ [_1510093] : [-(c_Relation_OId__on(_1510093, c_Orderings_Obot__class_Obot(tc_fun(_1510093, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1510093, _1510093), tc_HOL_Obool)))], (27397 ^ _781013) ^ [_1291542, _1291544] : [27398 ^ _781013 : [(27399 ^ _781013) ^ [_1291606, _1291608] : [_1291544 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1291542, _1291606), 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)), _1291608)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1291542), _1291544)))], (34633 ^ _781013) ^ [_1437130, _1437132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1437130), _1437132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1437130)), c_Int_OBit0(_1437132))))], (39574 ^ _781013) ^ [_1546748, _1546750, _1546752, _1546754] : [39576 ^ _781013 : [(39579 ^ _781013) ^ [] : [hBOOL(hAPP(_1546752, hAPP(hAPP(c_List_Onth(_1546748), _1546750), 39575 ^ [_1546748, _1546750, _1546752, _1546754])))], (39577 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39575 ^ [_1546748, _1546750, _1546752, _1546754]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1546748)), _1546750))))]], hBOOL(hAPP(hAPP(c_member(_1546748), _1546754), hAPP(c_List_Oset(_1546748), _1546750))), -(hBOOL(hAPP(_1546752, _1546754)))], (35915 ^ _781013) ^ [_1460648, _1460650, _1460652, _1460654] : [_1460652 = _1460654, -(hAPP(hAPP(c_COMBC(_1460648, tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_fun(_1460650, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460650, tc_fun(tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_fun(_1460650, tc_HOL_Obool)), _1460648), c_COMBC(_1460650, tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460650, tc_prod(_1460648, _1460650)), tc_fun(_1460650, tc_fun(tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_HOL_Obool)), _1460648), hAPP(c_COMBB(tc_prod(_1460648, _1460650), tc_fun(tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_HOL_Obool), _1460650), c_member(tc_prod(_1460648, _1460650)))), c_Product__Type_OPair(_1460648, _1460650)))), _1460652) = hAPP(hAPP(c_COMBC(_1460648, tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_fun(_1460650, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460650, tc_fun(tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_fun(_1460650, tc_HOL_Obool)), _1460648), c_COMBC(_1460650, tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460650, tc_prod(_1460648, _1460650)), tc_fun(_1460650, tc_fun(tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_HOL_Obool)), _1460648), hAPP(c_COMBB(tc_prod(_1460648, _1460650), tc_fun(tc_fun(tc_prod(_1460648, _1460650), tc_HOL_Obool), tc_HOL_Obool), _1460650), c_member(tc_prod(_1460648, _1460650)))), c_Product__Type_OPair(_1460648, _1460650)))), _1460654))], (19144 ^ _781013) ^ [_1139541, _1139543, _1139545, _1139547] : [class_Rings_Ocomm__semiring__1(_1139541), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1139541), hAPP(hAPP(c_Power_Opower__class_Opower(_1139541), _1139543), _1139545)), _1139547) = hAPP(hAPP(c_Power_Opower__class_Opower(_1139541), _1139543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1139545), _1139547)))], (32988 ^ _781013) ^ [_1406900, _1406902] : [class_Int_Onumber__ring(_1406900), class_Rings_Olinordered__idom(_1406900), 32995 ^ _781013 : [(33002 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406900), hAPP(c_Int_Onumber__class_Onumber__of(_1406900), _1406902)), c_Groups_Ozero__class_Ozero(_1406900)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1406900), hAPP(c_Int_Onumber__class_Onumber__of(_1406900), _1406902)) = hAPP(c_Int_Onumber__class_Onumber__of(_1406900), _1406902))], (32996 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406900), hAPP(c_Int_Onumber__class_Onumber__of(_1406900), _1406902)), c_Groups_Ozero__class_Ozero(_1406900))), -(hAPP(c_Groups_Oabs__class_Oabs(_1406900), hAPP(c_Int_Onumber__class_Onumber__of(_1406900), _1406902)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1406900), hAPP(c_Int_Onumber__class_Onumber__of(_1406900), _1406902)))]]], (24276 ^ _781013) ^ [_1233789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233789)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1233789)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1233789)))], (13369 ^ _781013) ^ [_1025009, _1025011, _1025013, _1025015, _1025017] : [class_Groups_Oab__group__add(_1025009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025011), _1025013)), 13376 ^ _781013 : [(13383 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1025011), _1025015), _1025013))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1025011, _1025009), _1025017), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025011, tc_HOL_Obool)), _1025013), hAPP(hAPP(c_Set_Oinsert(_1025011), _1025015), c_Orderings_Obot__class_Obot(tc_fun(_1025011, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1025011, _1025009), _1025017), _1025013))], (13377 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1025011), _1025015), _1025013)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1025011, _1025009), _1025017), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025011, tc_HOL_Obool)), _1025013), hAPP(hAPP(c_Set_Oinsert(_1025011), _1025015), c_Orderings_Obot__class_Obot(tc_fun(_1025011, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025009), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1025011, _1025009), _1025017), _1025013)), hAPP(_1025017, _1025015)))]]], (22128 ^ _781013) ^ [_1196021, _1196023, _1196025] : [-(c_Option_Ooption_Ooption__size(_1196021, _1196023, hAPP(c_Option_Ooption_OSome(_1196021), _1196025)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1196023, _1196025)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47784 ^ _781013) ^ [_1746107, _1746109, _1746111] : [47786 ^ _781013 : [(47789 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1746107), _1746111), 47785 ^ [_1746107, _1746109, _1746111]))], (47787 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1746107, tc_HOL_Obool)), 47785 ^ [_1746107, _1746109, _1746111]), _1746109)))]], -(hBOOL(hAPP(hAPP(c_member(_1746107), _1746111), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1746107, tc_HOL_Obool), _1746109))))], (32013 ^ _781013) ^ [_1388721, _1388723, _1388725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388721, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1388721, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 32014 ^ [_1388721, _1388723, _1388725])), _1388723)), _1388725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388721, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1388721, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1388723)), _1388725)))], (16828 ^ _781013) ^ [_1093057, _1093059, _1093061, _1093063] : [class_Rings_Olinordered__semiring(_1093057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093057), _1093059), _1093061)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093057), _1093059), _1093063))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093057), c_Groups_Ozero__class_Ozero(_1093057)), _1093059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093057), _1093061), _1093063)))], (18896 ^ _781013) ^ [_1133950, _1133952, _1133954, _1133956, _1133958] : [class_Groups_Ocomm__monoid__add(_1133950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133952), _1133954)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133952), _1133956)), 18910 ^ _781013 : [(18913 ^ _781013) ^ [] : [hAPP(_1133958, 18909 ^ [_1133950, _1133952, _1133954, _1133956, _1133958]) = c_Groups_Ozero__class_Ozero(_1133950)], (18911 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1133952), 18909 ^ [_1133950, _1133952, _1133954, _1133956, _1133958]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1133952, tc_HOL_Obool)), _1133954), _1133956))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1133952, _1133950), _1133958), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1133952, tc_HOL_Obool)), _1133954), _1133956)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133950), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1133952, _1133950), _1133958), _1133954)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1133952, _1133950), _1133958), _1133956)))], (25561 ^ _781013) ^ [_1256988, _1256990] : [c_Nat__Transfer_Onat__set(_1256988), c_Nat__Transfer_Onat__set(_1256990), 25568 ^ _781013 : [(25575 ^ _781013) ^ [] : [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), _1256988)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1256990))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1256988), _1256990)))], (25569 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1256988), _1256990)), -(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), _1256988)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1256990))))]]], (43229 ^ _781013) ^ [_1641563, _1641565, _1641567, _1641569, _1641571, _1641573, _1641575] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641563, tc_fun(_1641565, tc_fun(_1641567, tc_HOL_Obool))), _1641569), _1641571), _1641573), _1641575)), 43232 ^ _781013 : [(43233 ^ _781013) ^ [_1641691] : [hBOOL(hAPP(hAPP(c_member(_1641563), _1641691), _1641569)), -(hBOOL(hAPP(hAPP(hAPP(_1641571, _1641691), _1641573), _1641575)))]]], (3840 ^ _781013) ^ [_839094, _839096, _839098, _839100] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_839100, _839096) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_839098, _839094)), _839100 = _839098, _839096 = _839094], (21863 ^ _781013) ^ [_1191337, _1191339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191337)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191339)))), 21866 ^ _781013 : [(21869 ^ _781013) ^ [] : [-(_1191339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21867 ^ _781013) ^ [] : [-(_1191337 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6152 ^ _781013) ^ [_880804, _880806, _880808] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_880804, _880806, _880808))), 6155 ^ _781013 : [(6158 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _880808)))], (6156 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _880806)))]]], (7237 ^ _781013) ^ [_901811, _901813, _901815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901811, tc_HOL_Obool)), _901813), _901815)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901811, tc_HOL_Obool)), _901815), _901813) = _901815)], (48489 ^ _781013) ^ [_1761357] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1761357)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (45133 ^ _781013) ^ [_1682589] : [class_Enum_Oenum(_1682589), -(hAPP(c_List_Oset(_1682589), c_Enum_Oenum__class_Oenum(_1682589)) = c_Orderings_Otop__class_Otop(tc_fun(_1682589, tc_HOL_Obool)))], (10053 ^ _781013) ^ [_958894, _958896, _958898] : [class_Lattices_Osemilattice__inf(_958894), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958894), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_958894), _958896), _958898)), _958898)))], (40535 ^ _781013) ^ [_1574281, _1574283, _1574285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574281, _1574281), tc_HOL_Obool)), _1574283), _1574285)), c_Relation_Orefl__on(_1574281, c_Orderings_Otop__class_Otop(tc_fun(_1574281, tc_HOL_Obool)), _1574285), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1574281), tc_List_Olist(_1574281)), tc_HOL_Obool)), c_List_Olistrel1(_1574281, _1574283)), c_List_Olistrel(_1574281, _1574285))))], (31310 ^ _781013) ^ [_1367849, _1367851, _1367853, _1367855, _1367857] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1367849, _1367851)), _1367853), _1367855), _1367857)), 31315 ^ _781013 : [(31318 ^ _781013) ^ [] : [hBOOL(hAPP(_1367849, _1367853))], (31316 ^ _781013) ^ [] : [-(_1367857 = _1367853)]], 31319 ^ _781013 : [(31325 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1367849, _1367851)), 31321 ^ [_1367849, _1367851, _1367853, _1367855, _1367857]), _1367855), _1367857)))], (31323 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1367851), _1367853), _1367855), 31321 ^ [_1367849, _1367851, _1367853, _1367855, _1367857])))], (31320 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1367849, _1367853)))]]], (44767 ^ _781013) ^ [_1674831, _1674833] : [hBOOL(hAPP(c_List_Odistinct(_1674831), _1674833)), -(c_List_Oremdups(_1674831, _1674833) = _1674833)], (28490 ^ _781013) ^ [_1312646, _1312648, _1312650, _1312652] : [class_Orderings_Olinorder(_1312646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312646), _1312648), _1312650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312646), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312646), _1312652), _1312648)), _1312650)))], (41877 ^ _781013) ^ [_1608037, _1608039, _1608041, _1608043] : [-(hAPP(hAPP(c_List_Onth(_1608037), hAPP(hAPP(c_List_Oappend(_1608037), _1608039), _1608041)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608037)), _1608039)), _1608043)) = hAPP(hAPP(c_List_Onth(_1608037), _1608041), _1608043))], (3694 ^ _781013) ^ [_836853, _836855, _836857, _836859] : [-(c_Nitpick_Onorm__frac(_836859, _836855) = c_Nitpick_Onorm__frac(_836857, _836853)), _836859 = _836857, _836855 = _836853], (40397 ^ _781013) ^ [_1569178, _1569180, _1569182, _1569184] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1569178) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1569180), hAPP(hAPP(c_List_Olist_OCons(_1569180), _1569182), _1569184)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1569178)) = hAPP(hAPP(c_List_Onth(_1569180), _1569184), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1569178)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (26805 ^ _781013) ^ [_1279913, _1279915, _1279917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1279913)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1279915), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1279917)), 26812 ^ _781013 : [(26813 ^ _781013) ^ [_1280121] : [26815 ^ _781013 : [(26821 ^ _781013) ^ [] : [-(_1280121 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26817 ^ [_1279913, _1279915, _1279917, _1280121]), 26814 ^ [_1279913, _1279915, _1279917, _1280121]))], (26819 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26817 ^ [_1279913, _1279915, _1279917, _1280121]), _1279917)))], (26816 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26814 ^ [_1279913, _1279915, _1279917, _1280121]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1279913))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1280121), _1279915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1280121), _1279913)), _1279915)))]]], (11187 ^ _781013) ^ [_980408, _980410, _980412, _980414] : [-(c_Map_Odom(_980408, _980410, c_Map_Omap__add(_980408, _980410, _980412, _980414)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980408, tc_HOL_Obool)), c_Map_Odom(_980408, _980410, _980414)), c_Map_Odom(_980408, _980410, _980412)))], (45536 ^ _781013) ^ [_1690948, _1690950, _1690952, _1690954] : [class_Enum_Oenum(_1690948), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690950)), _1690952) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690948)), c_Enum_Oenum__class_Oenum(_1690948)), -(hAPP(hAPP(c_Map_Omap__of(_1690948, _1690950), hAPP(hAPP(c_List_Ozip(_1690948, _1690950), c_Enum_Oenum__class_Oenum(_1690948)), _1690952)), _1690954) = hAPP(c_Option_Ooption_OSome(_1690950), 45543 ^ [_1690948, _1690950, _1690952, _1690954]))], (37911 ^ _781013) ^ [_1507243] : [-(c_Wellfounded_Omeasure(_1507243) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1507243), c_Wellfounded_Oless__than))], (48259 ^ _781013) ^ [_1755793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1755793)), _1755793 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18229 ^ _781013) ^ [_1120358] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120358), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1120358)], (7897 ^ _781013) ^ [_914232, _914234, _914236, _914238, _914240] : [hAPP(_914232, _914234) = hAPP(c_Option_Ooption_OSome(_914236), _914238), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_914240, tc_Option_Ooption(_914236)), _914232), _914234), hAPP(c_Option_Ooption_OSome(_914236), _914238)) = _914232)], (47057 ^ _781013) ^ [_1727934, _1727936, _1727938, _1727940, _1727942] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1727934, _1727936)), hAPP(hAPP(c_Product__Type_OPair(_1727934, _1727936), _1727938), _1727940)), _1727942)), -(hBOOL(hAPP(hAPP(c_member(_1727936), _1727940), hAPP(c_Relation_ORange(_1727934, _1727936), _1727942))))], (23116 ^ _781013) ^ [_1213494, _1213496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1213494), _1213496)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213494), _1213496) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43380 ^ _781013) ^ [_1644782, _1644784] : [-(c_List_OremoveAll(_1644782, _1644784) = c_List_Ofilter(_1644782, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1644782), c_fNot), hAPP(c_fequal, _1644784))))], (28724 ^ _781013) ^ [_1317054, _1317056, _1317058, _1317060] : [class_Orderings_Olinorder(_1317054), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317054), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317054), _1317056), _1317058)), _1317060) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317054), _1317056), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317054), _1317058), _1317060)))], (37532 ^ _781013) ^ [_1497613, _1497615, _1497617, _1497619] : [-(hAPP(c_Product__Type_Ofst(_1497613, _1497615), hAPP(hAPP(c_Product__Type_OPair(_1497613, _1497615), _1497617), _1497619)) = _1497617)], (41178 ^ _781013) ^ [_1592724, _1592726] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1592724)), c_List_Olist_ONil(_1592724)), c_List_Olists(_1592724, _1592726))))], (40465 ^ _781013) ^ [_1572105, _1572107, _1572109, _1572111, _1572113, _1572115, _1572117] : [-(hAPP(c_Product__Type_Osnd(_1572105, _1572107), hAPP(c_Product__Type_Omap__pair(_1572109, _1572105, _1572111, _1572107, _1572113, _1572115), _1572117)) = hAPP(_1572115, hAPP(c_Product__Type_Osnd(_1572109, _1572111), _1572117)))], (3782 ^ _781013) ^ [_838197, _838199, _838201, _838203, _838205, _838207] : [-(c_List_OdropWhile(_838207, _838203, _838199) = c_List_OdropWhile(_838205, _838201, _838197)), _838207 = _838205, _838203 = _838201, _838199 = _838197], (6479 ^ _781013) ^ [_887050, _887052] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_887050), _887052)), -(_887052 = c_Orderings_Obot__class_Obot(tc_fun(_887050, tc_HOL_Obool))), 6488 ^ _781013 : [(6491 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_887050), 6486 ^ [_887050, _887052])))], (6489 ^ _781013) ^ [] : [-(_887052 = hAPP(hAPP(c_Set_Oinsert(_887050), 6487 ^ [_887050, _887052]), 6486 ^ [_887050, _887052]))]]], (5859 ^ _781013) ^ [_875241, _875243, _875245, _875247] : [c_Com_Ocom_OWhile(_875241, _875243) = c_Com_Ocom_OWhile(_875245, _875247), 5862 ^ _781013 : [(5865 ^ _781013) ^ [] : [-(_875243 = _875247)], (5863 ^ _781013) ^ [] : [-(_875241 = _875245)]]], (17270 ^ _781013) ^ [_1102685, _1102687, _1102689] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1102685), _1102687)), hBOOL(hAPP(hAPP(c_member(_1102685), _1102689), _1102687)), -(hAPP(c_Finite__Set_Ocard(_1102685), _1102687) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1102685), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1102685, tc_HOL_Obool)), _1102687), hAPP(hAPP(c_Set_Oinsert(_1102685), _1102689), c_Orderings_Obot__class_Obot(tc_fun(_1102685, tc_HOL_Obool)))))))], (31407 ^ _781013) ^ [_1372049, _1372051, _1372053, _1372055] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _1372049)), _1372051), hAPP(c_Nat_OSuc, _1372053)), _1372055)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1372049))), _1372051), _1372053), _1372055)))], (25348 ^ _781013) ^ [_1253496, _1253498, _1253500, _1253502] : [class_Fields_Olinordered__field(_1253496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253496), _1253498), _1253500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253496), c_Groups_Ozero__class_Ozero(_1253496)), _1253502)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253496), c_Groups_Ozero__class_Ozero(_1253496)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253496), _1253500), _1253498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253496), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253496), _1253502), _1253500)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253496), _1253502), _1253498))))], (42122 ^ _781013) ^ [_1614579, _1614581] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614579)), hAPP(c_List_Orotate1(_1614579), _1614581)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614579)), _1614581))], (28952 ^ _781013) ^ [_1321070, _1321072, _1321074, _1321076, _1321078] : [class_Rings_Olinordered__idom(_1321070), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321070), hAPP(c_Groups_Oabs__class_Oabs(_1321070), _1321072)), _1321074)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321070), hAPP(c_Groups_Oabs__class_Oabs(_1321070), _1321076)), _1321078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321070), hAPP(c_Groups_Oabs__class_Oabs(_1321070), _1321072)), hAPP(c_Groups_Oabs__class_Oabs(_1321070), _1321076))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321070), _1321074), _1321078))))], (15891 ^ _781013) ^ [_1075015, _1075017, _1075019] : [class_Rings_Olinordered__semiring__strict(_1075015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075015), c_Groups_Ozero__class_Ozero(_1075015)), _1075017)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075015), _1075019), c_Groups_Ozero__class_Ozero(_1075015))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075015), _1075017), _1075019)), c_Groups_Ozero__class_Ozero(_1075015))))], (37692 ^ _781013) ^ [_1500835, _1500837, _1500839, _1500841] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1500835, _1500837), _1500839), _1500841) = hAPP(c_Set_OCollect(tc_prod(_1500837, _1500837)), hAPP(c_Product__Type_Oprod_Oprod__case(_1500837, _1500837, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1500837, tc_fun(tc_prod(_1500835, _1500835), tc_HOL_Obool), tc_fun(_1500837, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500837, tc_fun(tc_fun(tc_prod(_1500835, _1500835), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1500835, _1500835), tc_HOL_Obool), tc_fun(_1500837, tc_HOL_Obool)), _1500837), c_COMBC(_1500837, tc_fun(tc_prod(_1500835, _1500835), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500837, tc_prod(_1500835, _1500835)), tc_fun(_1500837, tc_fun(tc_fun(tc_prod(_1500835, _1500835), tc_HOL_Obool), tc_HOL_Obool)), _1500837), hAPP(c_COMBB(tc_prod(_1500835, _1500835), tc_fun(tc_fun(tc_prod(_1500835, _1500835), tc_HOL_Obool), tc_HOL_Obool), _1500837), c_member(tc_prod(_1500835, _1500835)))), hAPP(hAPP(c_COMBC(_1500837, tc_fun(_1500837, _1500835), tc_fun(_1500837, tc_prod(_1500835, _1500835))), hAPP(hAPP(c_COMBB(tc_fun(_1500835, tc_prod(_1500835, _1500835)), tc_fun(tc_fun(_1500837, _1500835), tc_fun(_1500837, tc_prod(_1500835, _1500835))), _1500837), c_COMBB(_1500835, tc_prod(_1500835, _1500835), _1500837)), hAPP(hAPP(c_COMBB(_1500835, tc_fun(_1500835, tc_prod(_1500835, _1500835)), _1500837), c_Product__Type_OPair(_1500835, _1500835)), _1500841))), _1500841)))), _1500839))))], (11097 ^ _781013) ^ [_978445, _978447, _978449] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978445, tc_HOL_Obool)), _978447), _978449) = c_Orderings_Obot__class_Obot(tc_fun(_978445, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978445, tc_HOL_Obool)), _978447), _978449) = _978447)], (31039 ^ _781013) ^ [_1362186, _1362188, _1362190, _1362192] : [-(c_Nat_Onat_Onat__case(_1362186, _1362188, _1362190, hAPP(c_Nat_OSuc, _1362192)) = hAPP(_1362190, _1362192))], (4864 ^ _781013) ^ [_854852, _854854] : [_854854 = _854852, -(c_Lazy__Sequence_Oyield(_854854) = c_Lazy__Sequence_Oyield(_854852))], (20209 ^ _781013) ^ [_1158919, _1158921, _1158923, _1158925] : [-(c_Sum__Type_OPlus(_1158919, _1158921, _1158923, _1158925) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1158919, _1158921), tc_HOL_Obool))), _1158923 = c_Orderings_Obot__class_Obot(tc_fun(_1158919, tc_HOL_Obool)), _1158925 = c_Orderings_Obot__class_Obot(tc_fun(_1158921, tc_HOL_Obool))], (15517 ^ _781013) ^ [_1068011, _1068013, _1068015, _1068017] : [class_Rings_Oordered__semiring(_1068011), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068011), _1068013), _1068015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068011), c_Groups_Ozero__class_Ozero(_1068011)), _1068017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068011), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068011), _1068017), _1068013)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068011), _1068017), _1068015))))], (31298 ^ _781013) ^ [_1367533, _1367535, _1367537, _1367539] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1367533, _1367535)), _1367537), _1367539), _1367537))), 31299 ^ _781013 : [(31302 ^ _781013) ^ [_1367647] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1367535), _1367537), _1367539), _1367647)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1367533, _1367535)), _1367647), _1367539), _1367537))], (31300 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1367533, _1367537)))]]], (3982 ^ _781013) ^ [_841279, _841281, _841283, _841285] : [-(c_Code__Numeral_Onat__of__aux(_841285, _841281) = c_Code__Numeral_Onat__of__aux(_841283, _841279)), _841285 = _841283, _841281 = _841279], (38642 ^ _781013) ^ [_1524210, _1524212, _1524214, _1524216, _1524218] : [-(hBOOL(hAPP(hAPP(c_member(_1524210), _1524212), hAPP(c_List_Oset(_1524210), _1524214)))), -(hAPP(hAPP(c_Map_Omap__of(_1524210, _1524216), hAPP(hAPP(c_List_Ozip(_1524210, _1524216), _1524214), hAPP(hAPP(c_List_Omap(_1524210, _1524216), _1524218), _1524214))), _1524212) = c_Option_Ooption_ONone(_1524216))], (12876 ^ _781013) ^ [_1014549, _1014551, _1014553, _1014555, _1014557] : [hBOOL(hAPP(hAPP(c_member(_1014549), _1014551), hAPP(c_Set_Ovimage(_1014549, _1014553, _1014555), _1014557))), -(hBOOL(hAPP(hAPP(c_member(_1014553), hAPP(_1014555, _1014551)), _1014557)))], (32582 ^ _781013) ^ [_1399455, _1399457] : [class_Int_Onumber__ring(_1399455), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1399455), hAPP(c_Int_Onumber__class_Onumber__of(_1399455), _1399457)) = hAPP(c_Int_Onumber__class_Onumber__of(_1399455), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1399457)))], (43974 ^ _781013) ^ [_1656575, _1656577, _1656579, _1656581] : [c_List_Oupt(_1656575, _1656577) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1656579), _1656581), 43977 ^ _781013 : [(43982 ^ _781013) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656575), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1656577) = _1656581)], (43980 ^ _781013) ^ [] : [-(_1656575 = _1656579)], (43978 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656575), _1656577)))]]], (34201 ^ _781013) ^ [_1429795, _1429797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429795), _1429797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1429795)), c_Int_OBit1(_1429797))))], (20219 ^ _781013) ^ [_1159104] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1159104))], (9219 ^ _781013) ^ [_943971, _943973, _943975, _943977, _943979, _943981] : [c_Finite__Set_Ofolding(_943971, _943973, _943975, _943977), hBOOL(hAPP(c_Finite__Set_Ofinite(_943971), _943979)), hBOOL(hAPP(c_Finite__Set_Ofinite(_943971), _943981)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943971, tc_HOL_Obool)), _943979), _943981) = c_Orderings_Obot__class_Obot(tc_fun(_943971, tc_HOL_Obool)), -(hAPP(_943977, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943971, tc_HOL_Obool)), _943979), _943981)) = hAPP(c_Fun_Ocomp(_943973, _943973, _943973, hAPP(_943977, _943979)), hAPP(_943977, _943981)))], (18332 ^ _781013) ^ [_1122315, _1122317, _1122319] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122315), _1122317)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122315), _1122319)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122317), _1122319))], (19686 ^ _781013) ^ [_1149444] : [class_Power_Opower(_1149444), -(c_Power_Opower__class_Opower(_1149444) = c_Power_Opower_Opower(_1149444, c_Groups_Oone__class_Oone(_1149444), c_Groups_Otimes__class_Otimes(_1149444)))], (32434 ^ _781013) ^ [_1396399, _1396401, _1396403, _1396405] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396399), hAPP(c_Int_Onumber__class_Onumber__of(_1396399), _1396401)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1396399), _1396403), _1396405)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1396399), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396399), hAPP(c_Int_Onumber__class_Onumber__of(_1396399), _1396401)), _1396403)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396399), hAPP(c_Int_Onumber__class_Onumber__of(_1396399), _1396401)), _1396405))), class_Int_Onumber(_1396399), class_Rings_Oring(_1396399)], (36800 ^ _781013) ^ [_1483327, _1483329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1483327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1483329)), -(c_Divides_OposDivAlg(_1483327, _1483329) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1483327), _1483329)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1483327, _1483329)))], (21754 ^ _781013) ^ [_1189429, _1189431, _1189433] : [class_Rings_Osemiring__1(_1189429), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1189431), _1189433)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189429), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189429), _1189431)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189429), _1189433)))], (16253 ^ _781013) ^ [_1081309, _1081311] : [class_Groups_Ogroup__add(_1081309), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081309), _1081311), hAPP(c_Groups_Ouminus__class_Ouminus(_1081309), _1081311)) = c_Groups_Ozero__class_Ozero(_1081309))], (39195 ^ _781013) ^ [_1537987, _1537989, _1537991, _1537993, _1537995] : [class_Orderings_Olinorder(_1537987), hBOOL(hAPP(hAPP(c_member(_1537987), hAPP(_1537989, _1537991)), hAPP(c_Set_Oimage(_1537993, _1537987, _1537989), hAPP(c_List_Oset(_1537993), _1537995)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1537993, _1537987, _1537989, _1537991, _1537995) = _1537995)], (41686 ^ _781013) ^ [_1603753, _1603755, _1603757] : [_1603757 = c_List_Olist_ONil(_1603755), -(_1603753 = hAPP(hAPP(c_List_Oappend(_1603755), _1603757), _1603753))], (37540 ^ _781013) ^ [_1497770, _1497772, _1497774] : [-(_1497770 = hAPP(hAPP(c_Product__Type_OPair(_1497772, _1497774), hAPP(c_Product__Type_Ofst(_1497772, _1497774), _1497770)), hAPP(c_Product__Type_Osnd(_1497772, _1497774), _1497770)))], (20751 ^ _781013) ^ [_1168800, _1168802, _1168804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1168800), _1168802)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1168802), _1168800))), _1168804) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1168802)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1168800), _1168804)))], (31997 ^ _781013) ^ [_1388213, _1388215, _1388217, _1388219] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1388213, tc_HOL_Obool)), _1388215), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1388213), _1388217), _1388219))), 32001 ^ _781013 : [(32004 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388213), 32000 ^ [_1388213, _1388215, _1388217, _1388219]), _1388217)))], (32002 ^ _781013) ^ [] : [-(_1388215 = hAPP(c_Relation_OImage(_1388213, _1388213, _1388219), hAPP(hAPP(c_Set_Oinsert(_1388213), 32000 ^ [_1388213, _1388215, _1388217, _1388219]), c_Orderings_Obot__class_Obot(tc_fun(_1388213, tc_HOL_Obool)))))]]], (47189 ^ _781013) ^ [_1731432, _1731434] : [-(hAPP(c_Relation_ODomain(_1731432, _1731434), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1731432, _1731434), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1731432, tc_HOL_Obool)))], (26739 ^ _781013) ^ [_1278583, _1278585, _1278587] : [class_Orderings_Oorder(_1278583), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278583, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1278583, _1278585), _1278587)), hAPP(c_SetInterval_Oord__class_OatLeast(_1278583), _1278587)) = c_Orderings_Obot__class_Obot(tc_fun(_1278583, tc_HOL_Obool)))], (33968 ^ _781013) ^ [_1424672, _1424674] : [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(_1424674))), 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), _1424672)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1424672)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424674))))], (17072 ^ _781013) ^ [_1098374, _1098376, _1098378] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1098374), _1098376)), -(hAPP(c_Finite__Set_Ocard(_1098374), hAPP(hAPP(c_Set_Oinsert(_1098374), _1098378), _1098376)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1098374), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1098374, tc_HOL_Obool)), _1098376), hAPP(hAPP(c_Set_Oinsert(_1098374), _1098378), c_Orderings_Obot__class_Obot(tc_fun(_1098374, tc_HOL_Obool)))))))], (23939 ^ _781013) ^ [_1227938, _1227940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1227938)), _1227940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227938), hAPP(c_Int_Onat, _1227940))))], (49162 ^ _781013) ^ [_1778342, _1778344, _1778346, _1778348, _1778350, _1778352] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1778342, _1778342)), hAPP(hAPP(c_Product__Type_OPair(_1778342, _1778342), _1778344), _1778346)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1778342, _1778342), tc_HOL_Obool), _1778348), _1778350))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778342, _1778342)), hAPP(hAPP(c_Product__Type_OPair(_1778342, _1778342), _1778346), _1778352)), _1778350)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778342, _1778342)), hAPP(hAPP(c_Product__Type_OPair(_1778342, _1778342), _1778344), _1778352)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1778342, _1778342), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1778348)), _1778350))))], (36884 ^ _781013) ^ [_1484667, _1484669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1484667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1484667), _1484669)), -(c_Divides_Odivmod__nat(_1484669, _1484667) = 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), _1484669), _1484667)), _1484667))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1484669), _1484667), _1484667)))], (26271 ^ _781013) ^ [_1269571, _1269573] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1269571), _1269573) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1269571, _1269573))], (47872 ^ _781013) ^ [_1747960, _1747962, _1747964] : [c_List_Olist__ex(_1747960, _1747962, _1747964), 47876 ^ _781013 : [(47879 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1747962, 47875 ^ [_1747960, _1747962, _1747964])))], (47877 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747960), 47875 ^ [_1747960, _1747962, _1747964]), hAPP(c_List_Oset(_1747960), _1747964))))]]], (39360 ^ _781013) ^ [_1541823, _1541825, _1541827, _1541829] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1541823, tc_HOL_Obool)), hAPP(c_List_Oset(_1541823), hAPP(hAPP(c_List_Olist__update(_1541823, _1541825), _1541827), _1541829))), hAPP(hAPP(c_Set_Oinsert(_1541823), _1541829), hAPP(c_List_Oset(_1541823), _1541825)))))], (38748 ^ _781013) ^ [_1527506, _1527508, _1527510] : [hBOOL(hAPP(c_List_Odistinct(_1527506), _1527508)), -(hBOOL(hAPP(c_List_Odistinct(_1527506), hAPP(c_List_OremoveAll(_1527506, _1527510), _1527508))))], (42420 ^ _781013) ^ [_1621175, _1621177, _1621179] : [-(hAPP(hAPP(c_List_Otake(_1621175), _1621177), hAPP(c_List_Otl(_1621175), _1621179)) = hAPP(c_List_Otl(_1621175), hAPP(hAPP(c_List_Otake(_1621175), hAPP(c_Nat_OSuc, _1621177)), _1621179)))], (10825 ^ _781013) ^ [_972343, _972345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_972343, tc_HOL_Obool)), _972345), c_Orderings_Obot__class_Obot(tc_fun(_972343, tc_HOL_Obool))))], (42134 ^ _781013) ^ [_1614900, _1614902, _1614904, _1614906] : [-(hAPP(hAPP(c_List_Odrop(_1614900), _1614902), hAPP(hAPP(c_List_Otake(_1614900), _1614904), _1614906)) = hAPP(hAPP(c_List_Otake(_1614900), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1614904), _1614902)), hAPP(hAPP(c_List_Odrop(_1614900), _1614902), _1614906)))], (44296 ^ _781013) ^ [_1663650, _1663652] : [hBOOL(hAPP(c_List_Odistinct(_1663650), _1663652)), -(hBOOL(hAPP(c_List_Odistinct(_1663650), hAPP(c_List_Orev(_1663650), _1663652))))], (18416 ^ _781013) ^ [_1123804, _1123806] : [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), _1123804), _1123806))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1123804))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1123806)))], (20915 ^ _781013) ^ [_1171899, _1171901, _1171903, _1171905] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1171899, _1171901)), c_Sum__Type_OPlus(_1171899, _1171901, _1171903, _1171905))), 20918 ^ _781013 : [(20921 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1171901), _1171905)))], (20919 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1171899), _1171903)))]]], (14813 ^ _781013) ^ [_1055668, _1055670] : [class_Groups_Omonoid__add(_1055668), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055668), c_Groups_Ozero__class_Ozero(_1055668)), _1055670) = _1055670)], (16492 ^ _781013) ^ [_1086341, _1086343, _1086345] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1086341), _1086343)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086341), _1086345)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1086341), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086341, tc_HOL_Obool)), _1086343), _1086345))), hAPP(c_Finite__Set_Ocard(_1086341), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086341, tc_HOL_Obool)), _1086343), _1086345))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1086341), _1086343)), hAPP(c_Finite__Set_Ocard(_1086341), _1086345)))], (16371 ^ _781013) ^ [_1083817, _1083819] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1083817, tc_HOL_Obool)), _1083819) = hAPP(c_Set_OCollect(_1083817), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1083817), c_fNot), hAPP(hAPP(c_COMBC(_1083817, tc_fun(_1083817, tc_HOL_Obool), tc_HOL_Obool), c_member(_1083817)), _1083819))))], (37458 ^ _781013) ^ [_1496153, _1496155] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1496153, _1496155) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1496153, _1496155)))], (46116 ^ _781013) ^ [_1704101, _1704103, _1704105, _1704107, _1704109, _1704111, _1704113] : [c_List_Olist__all2(_1704101, _1704103, _1704105, _1704107, hAPP(hAPP(c_List_Omap(_1704109, _1704103), _1704111), _1704113)), -(c_List_Olist__all2(_1704101, _1704109, hAPP(hAPP(c_COMBC(_1704101, tc_fun(_1704109, _1704103), tc_fun(_1704109, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1704103, tc_HOL_Obool), tc_fun(tc_fun(_1704109, _1704103), tc_fun(_1704109, tc_HOL_Obool)), _1704101), c_COMBB(_1704103, tc_HOL_Obool, _1704109)), _1704105)), _1704111), _1704107, _1704113))], (51198 ^ _781013) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (47405 ^ _781013) ^ [_1736664, _1736666] : [c_Nitpick_Owf_H(_1736664, _1736666), 47408 ^ _781013 : [(47411 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1736664, _1736664)), _1736666))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (47409 ^ _781013) ^ [] : [-(c_Wellfounded_Oacyclic(_1736664, _1736666))]]], (2476 ^ _781013) ^ [_817702, _817704] : [_817704 = _817702, -(c_Int_Opred(_817704) = c_Int_Opred(_817702))], (21820 ^ _781013) ^ [_1190536, _1190538] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1190536), _1190538)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1190536)), _1190538))], (1134 ^ _781013) ^ [_797930, _797932] : [-(class_Rings_Olinordered__idom(_797930)), _797932 = _797930, class_Rings_Olinordered__idom(_797932)], (8036 ^ _781013) ^ [_917582, _917584, _917586, _917588, _917590] : [c_Finite__Set_Ofolding__one(_917582, _917584, _917586), hBOOL(hAPP(c_Finite__Set_Ofinite(_917582), _917588)), hBOOL(hAPP(hAPP(c_member(_917582), _917590), _917588)), 8047 ^ _781013 : [(8054 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917582, tc_HOL_Obool)), _917588), hAPP(hAPP(c_Set_Oinsert(_917582), _917590), c_Orderings_Obot__class_Obot(tc_fun(_917582, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_917582, tc_HOL_Obool))), -(hAPP(_917586, _917588) = hAPP(hAPP(_917584, _917590), hAPP(_917586, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917582, tc_HOL_Obool)), _917588), hAPP(hAPP(c_Set_Oinsert(_917582), _917590), c_Orderings_Obot__class_Obot(tc_fun(_917582, tc_HOL_Obool)))))))], (8048 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917582, tc_HOL_Obool)), _917588), hAPP(hAPP(c_Set_Oinsert(_917582), _917590), c_Orderings_Obot__class_Obot(tc_fun(_917582, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_917582, tc_HOL_Obool)), -(hAPP(_917586, _917588) = _917590)]]], (41095 ^ _781013) ^ [_1590750, _1590752, _1590754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1590750, _1590750), tc_HOL_Obool)), _1590752), hAPP(hAPP(c_Product__Type_OSigma(_1590750, _1590750), _1590754), hAPP(c_COMBK(tc_fun(_1590750, tc_HOL_Obool), _1590750), _1590754)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1590750), tc_List_Olist(_1590750)), tc_HOL_Obool)), c_List_Olistrel(_1590750, _1590752)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1590750), tc_List_Olist(_1590750)), c_List_Olists(_1590750, _1590754)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1590750), tc_HOL_Obool), tc_List_Olist(_1590750)), c_List_Olists(_1590750, _1590754))))))], (42691 ^ _781013) ^ [_1626836, _1626838, _1626840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1626836), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626838)), _1626840))), -(c_List_Olast(_1626838, hAPP(hAPP(c_List_Odrop(_1626838), _1626836), _1626840)) = c_List_Olast(_1626838, _1626840))], (49412 ^ _781013) ^ [_1785204, _1785206, _1785208] : [hBOOL(hAPP(hAPP(c_member(_1785204), _1785206), hAPP(c_List_Oset(_1785204), _1785208))), 49417 ^ _781013 : [(49420 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1785204), _1785206), hAPP(c_List_Oset(_1785204), 49416 ^ [_1785204, _1785206, _1785208])))], (49418 ^ _781013) ^ [] : [-(_1785208 = hAPP(hAPP(c_List_Oappend(_1785204), 49415 ^ [_1785204, _1785206, _1785208]), hAPP(hAPP(c_List_Olist_OCons(_1785204), _1785206), 49416 ^ [_1785204, _1785206, _1785208])))]]], (21686 ^ _781013) ^ [_1188267] : [class_Rings_Osemiring__1(_1188267), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188267), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1188267))], (11768 ^ _781013) ^ [_993312, _993314, _993316, _993318, _993320, _993322] : [c_Fun_Oinj__on(_993312, _993314, _993316, _993318), -(_993320 = _993322), hBOOL(hAPP(hAPP(c_member(_993312), _993320), _993318)), hBOOL(hAPP(hAPP(c_member(_993312), _993322), _993318)), hAPP(_993316, _993320) = hAPP(_993316, _993322)], (36916 ^ _781013) ^ [_1485325, _1485327, _1485329, _1485331, _1485333, _1485335, _1485337] : [-(hAPP(c_Product__Type_Oapsnd(_1485325, _1485327, _1485329, _1485331), hAPP(c_Product__Type_Oapsnd(_1485333, _1485325, _1485329, _1485335), _1485337)) = hAPP(c_Product__Type_Oapsnd(_1485333, _1485327, _1485329, hAPP(c_Fun_Ocomp(_1485325, _1485327, _1485333, _1485331), _1485335)), _1485337))], (35633 ^ _781013) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (39025 ^ _781013) ^ [_1533886, _1533888, _1533890] : [-(_1533886 = _1533888), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533890)), _1533886) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533890)), _1533888), 39031 ^ _781013 : [(39034 ^ _781013) ^ [] : [hAPP(hAPP(c_List_Onth(_1533890), _1533886), 39030 ^ [_1533886, _1533888, _1533890]) = hAPP(hAPP(c_List_Onth(_1533890), _1533888), 39030 ^ [_1533886, _1533888, _1533890])], (39032 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39030 ^ [_1533886, _1533888, _1533890]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533890)), _1533886))))]]], (4664 ^ _781013) ^ [_851602, _851604] : [_851604 = _851602, -(c_Groups_Oabs__class_Oabs(_851604) = c_Groups_Oabs__class_Oabs(_851602))], (14688 ^ _781013) ^ [_1053624, _1053626] : [hAPP(c_Finite__Set_Ocard(_1053624), _1053626) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1053626 = c_Orderings_Obot__class_Obot(tc_fun(_1053624, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053624), _1053626))], (40619 ^ _781013) ^ [_1576737, _1576739, _1576741, _1576743, _1576745] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1576737, _1576739), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1576737, tc_HOL_Obool)), _1576741), _1576743)), hAPP(c_COMBK(tc_fun(_1576739, tc_HOL_Obool), _1576737), _1576745)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1576737, _1576739), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1576737, _1576739), _1576741), hAPP(c_COMBK(tc_fun(_1576739, tc_HOL_Obool), _1576737), _1576745))), hAPP(hAPP(c_Product__Type_OSigma(_1576737, _1576739), _1576743), hAPP(c_COMBK(tc_fun(_1576739, tc_HOL_Obool), _1576737), _1576745))))], (3384 ^ _781013) ^ [_832034, _832036] : [_832036 = _832034, -(c_Option_Ooption_ONone(_832036) = c_Option_Ooption_ONone(_832034))], (4780 ^ _781013) ^ [_853470, _853472] : [_853472 = _853470, -(c_HOL_Oequal__class_Oequal(_853472) = c_HOL_Oequal__class_Oequal(_853470))], (9208 ^ _781013) ^ [_943676, _943678, _943680, _943682, _943684] : [hBOOL(hAPP(hAPP(c_member(_943676), _943678), c_Map_Oran(_943680, _943676, c_Map_Orestrict__map(_943680, _943676, _943682, _943684)))), 9212 ^ _781013 : [(9215 ^ _781013) ^ [] : [-(hAPP(_943682, 9211 ^ [_943676, _943678, _943680, _943682, _943684]) = hAPP(c_Option_Ooption_OSome(_943676), _943678))], (9213 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_943680), 9211 ^ [_943676, _943678, _943680, _943682, _943684]), _943684)))]]], (39251 ^ _781013) ^ [_1539207, _1539209, _1539211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1539207), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1539209))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1539209), _1539207), _1539211)) = 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), _1539209)), _1539211)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1539209), _1539207)))], (35053 ^ _781013) ^ [_1444574, _1444576] : [class_Rings_Olinordered__idom(_1444574), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1444574), hAPP(c_Groups_Oabs__class_Oabs(_1444574), _1444576)), 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(_1444574), _1444576), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (41632 ^ _781013) ^ [_1602803, _1602805, _1602807] : [_1602803 = _1602805, -(_1602803 = hAPP(hAPP(c_List_Oappend(_1602807), c_List_Olist_ONil(_1602807)), _1602805))], (10629 ^ _781013) ^ [_969037, _969039, _969041] : [class_Orderings_Olinorder(_969037), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969037), _969039), _969041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969037), _969041), _969039)))], (38319 ^ _781013) ^ [_1517273, _1517275, _1517277, _1517279] : [-(hAPP(c_List_Oset(_1517273), hAPP(hAPP(c_List_Omap(_1517275, _1517273), _1517277), _1517279)) = hAPP(c_Set_Oimage(_1517275, _1517273, _1517277), hAPP(c_List_Oset(_1517275), _1517279)))], (22228 ^ _781013) ^ [_1197802, _1197804] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197802)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197804)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1197802), _1197804))], (42613 ^ _781013) ^ [_1625737, _1625739, _1625741, _1625743] : [-(_1625737 = c_List_Olist_ONil(_1625739)), 42616 ^ _781013 : [(42623 ^ _781013) ^ [] : [-(_1625741 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625739)), _1625737)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1625739, hAPP(hAPP(c_List_Olist__update(_1625739, _1625737), _1625741), _1625743)) = c_List_Olast(_1625739, _1625737))], (42617 ^ _781013) ^ [] : [_1625741 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625739)), _1625737)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1625739, hAPP(hAPP(c_List_Olist__update(_1625739, _1625737), _1625741), _1625743)) = _1625743)]]], (34119 ^ _781013) ^ [_1428191] : [class_Rings_Osemiring__1(_1428191), c_Int_Oiszero(_1428191, c_Groups_Oone__class_Oone(_1428191))], (47197 ^ _781013) ^ [_1731607, _1731609, _1731611] : [_1731611 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1731607, _1731609), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1731607, _1731609), _1731611) = c_Orderings_Obot__class_Obot(tc_fun(_1731607, tc_HOL_Obool)))], (42088 ^ _781013) ^ [_1613851, _1613853] : [-(hAPP(hAPP(c_List_Odrop(_1613851), _1613853), c_List_Olist_ONil(_1613851)) = c_List_Olist_ONil(_1613851))], (8971 ^ _781013) ^ [_937919, _937921, _937923, _937925, _937927, _937929, _937931, _937933] : [c_Finite__Set_Ofolding__image__simple(_937919, _937921, _937923, _937925, _937927, _937929), hBOOL(hAPP(c_Finite__Set_Ofinite(_937921), _937931)), -(hAPP(_937929, hAPP(hAPP(c_Set_Oinsert(_937921), _937933), _937931)) = hAPP(hAPP(_937923, hAPP(_937927, _937933)), hAPP(_937929, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937921, tc_HOL_Obool)), _937931), hAPP(hAPP(c_Set_Oinsert(_937921), _937933), c_Orderings_Obot__class_Obot(tc_fun(_937921, tc_HOL_Obool)))))))], (24656 ^ _781013) ^ [_1240851, _1240853, _1240855] : [class_Fields_Olinordered__field(_1240851), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240851), c_Groups_Ozero__class_Ozero(_1240851)), _1240853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240851), c_Groups_Ozero__class_Ozero(_1240851)), _1240855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240851), c_Groups_Ozero__class_Ozero(_1240851)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240851), _1240853), _1240855))))], (8215 ^ _781013) ^ [_921308, _921310, _921312, _921314, _921316] : [-(c_Map_Omap__comp(_921308, _921310, _921312, _921314, hAPP(c_COMBK(tc_Option_Ooption(_921308), _921312), c_Option_Ooption_ONone(_921308)), _921316) = c_Option_Ooption_ONone(_921310))], (46371 ^ _781013) ^ [_1709818, _1709820, _1709822] : [hBOOL(hAPP(c_List_Odistinct(_1709818), _1709820)), -(hBOOL(hAPP(c_List_Odistinct(_1709818), c_List_Oinsert(_1709818, _1709822, _1709820))))], (38031 ^ _781013) ^ [_1509601, _1509603] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1509601, _1509601)), _1509603)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1509601), hAPP(c_Relation_OField(_1509601), _1509603))))], (6591 ^ _781013) ^ [_888875, _888877, _888879] : [_888879 = hAPP(c_COMBK(tc_Option_Ooption(_888877), _888875), c_Option_Ooption_ONone(_888877)), -(c_Map_Odom(_888875, _888877, _888879) = c_Orderings_Obot__class_Obot(tc_fun(_888875, tc_HOL_Obool)))], (10047 ^ _781013) ^ [_958787, _958789, _958791] : [class_Lattices_Olattice(_958787), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958787), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_958787), _958789), _958791)), _958791)))], (41278 ^ _781013) ^ [_1594644, _1594646, _1594648, _1594650] : [_1594646 = c_List_Olist_ONil(_1594644), -(hAPP(hAPP(c_List_Olist__update(_1594644, _1594646), _1594648), _1594650) = c_List_Olist_ONil(_1594644))], (35425 ^ _781013) ^ [_1451513, _1451515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451513)), -(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)))), _1451515)), 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)))), _1451513)) = 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, _1451515, _1451513))))], (51546 ^ _781013) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (20532 ^ _781013) ^ [_1164487, _1164489] : [20533 ^ _781013 : [(20536 ^ _781013) ^ [] : [_1164487 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20534 ^ _781013) ^ [] : [_1164489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1164487), _1164489) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33956 ^ _781013) ^ [_1424379, _1424381] : [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(_1424379))), 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)), _1424381)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424379)), hAPP(c_Nat_OSuc, _1424381))))], (1344 ^ _781013) ^ [_800555, _800557] : [-(class_Lattices_Oboolean__algebra(_800555)), _800557 = _800555, class_Lattices_Oboolean__algebra(_800557)], (16692 ^ _781013) ^ [_1090446, _1090448, _1090450, _1090452] : [class_Rings_Olinordered__ring__strict(_1090446), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090446), _1090448), c_Groups_Ozero__class_Ozero(_1090446))), 16699 ^ _781013 : [(16706 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090446), _1090452), _1090450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090446), _1090448), _1090450)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090446), _1090448), _1090452))))], (16700 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090446), _1090448), _1090450)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090446), _1090448), _1090452))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090446), _1090452), _1090450)))]]], (37594 ^ _781013) ^ [_1498967, _1498969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1498967), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1498969), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1498967), _1498969) = 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), _1498967), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1498969)))))], (16369 ^ _781013) ^ [_1083756, _1083758, _1083760] : [-(hAPP(hAPP(c_Set_Oinsert(_1083756), _1083758), _1083760) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1083756, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1083756), hAPP(hAPP(c_COMBC(_1083756, _1083756, tc_HOL_Obool), c_fequal), _1083758))), _1083760))], (39271 ^ _781013) ^ [_1539712, _1539714, _1539716, _1539718, _1539720, _1539722] : [-(hAPP(hAPP(c_List_Omap(_1539712, _1539714), _1539716), hAPP(hAPP(c_List_Olist__update(_1539712, _1539718), _1539720), _1539722)) = hAPP(hAPP(c_List_Olist__update(_1539714, hAPP(hAPP(c_List_Omap(_1539712, _1539714), _1539716), _1539718)), _1539720), hAPP(_1539716, _1539722)))], (27349 ^ _781013) ^ [_1290584, _1290586, _1290588] : [class_Fields_Olinordered__field__inverse__zero(_1290584), 27355 ^ _781013 : [(27360 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290584), 27354 ^ [_1290584, _1290586, _1290588]), _1290586)), _1290588))], (27358 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290584), 27354 ^ [_1290584, _1290586, _1290588]), c_Groups_Oone__class_Oone(_1290584))))], (27356 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290584), c_Groups_Ozero__class_Ozero(_1290584)), 27354 ^ [_1290584, _1290586, _1290588])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290584), _1290586), _1290588)))], (358 ^ _781013) ^ [_786612, _786614] : [-(c_Nat__Transfer_Onat__set(_786612)), _786614 = _786612, c_Nat__Transfer_Onat__set(_786614)], (48830 ^ _781013) ^ [_1769887, _1769889, _1769891] : [c_Relation_Orefl__on(_1769887, _1769889, _1769891), -(c_Relation_Orefl__on(_1769887, _1769889, hAPP(c_Relation_Oconverse(_1769887, _1769887), _1769891)))], (6198 ^ _781013) ^ [_881612, _881614, _881616, _881618, _881620] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_881612, _881614, _881616)), _881618), _881620))), 6199 ^ _781013 : [(6206 ^ _781013) ^ [] : [-(hBOOL(hAPP(_881612, _881618))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_881616), _881618), _881620))], (6200 ^ _781013) ^ [] : [hBOOL(hAPP(_881612, _881618)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_881614), _881618), _881620))]]], (18744 ^ _781013) ^ [_1130374, _1130376] : [class_Rings_Olinordered__idom(_1130374), 18747 ^ _781013 : [(18754 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130374), _1130376), c_Groups_Ozero__class_Ozero(_1130374))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130374), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130374), _1130376), _1130376)), c_Groups_Ozero__class_Ozero(_1130374))))], (18748 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130374), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130374), _1130376), _1130376)), c_Groups_Ozero__class_Ozero(_1130374))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130374), _1130376), c_Groups_Ozero__class_Ozero(_1130374))))]]], (16778 ^ _781013) ^ [_1092096, _1092098, _1092100, _1092102, _1092104] : [class_Rings_Olinordered__semiring__strict(_1092096), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092096), _1092098), _1092100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092096), _1092102), _1092104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092096), c_Groups_Ozero__class_Ozero(_1092096)), _1092098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092096), c_Groups_Ozero__class_Ozero(_1092096)), _1092102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092096), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092096), _1092098), _1092102)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092096), _1092100), _1092104))))], (48523 ^ _781013) ^ [_1762103, _1762105, _1762107, _1762109, _1762111] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762103), tc_List_Olist(_1762103))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762103), tc_List_Olist(_1762103)), _1762105), _1762107)), c_List_Olistrel(_1762103, c_Transitive__Closure_Ortrancl(_1762103, _1762109)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762103), tc_List_Olist(_1762103))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762103), tc_List_Olist(_1762103)), _1762107), _1762111)), c_List_Olistrel(_1762103, c_Transitive__Closure_Ortrancl(_1762103, _1762109)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762103), tc_List_Olist(_1762103))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762103), tc_List_Olist(_1762103)), _1762105), _1762111)), c_List_Olistrel(_1762103, c_Transitive__Closure_Ortrancl(_1762103, _1762109)))))], (42366 ^ _781013) ^ [_1620131, _1620133, _1620135] : [-(hAPP(hAPP(c_List_Odrop(_1620131), _1620133), hAPP(c_List_Otl(_1620131), _1620135)) = hAPP(c_List_Otl(_1620131), hAPP(hAPP(c_List_Odrop(_1620131), _1620133), _1620135)))], (42410 ^ _781013) ^ [_1621024, _1621026, _1621028] : [-(hAPP(c_List_Otl(_1621024), hAPP(hAPP(c_List_Olist_OCons(_1621024), _1621026), _1621028)) = _1621028)], (33906 ^ _781013) ^ [_1423193] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423193) = 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(_1423193)))))], (33610 ^ _781013) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (13345 ^ _781013) ^ [_1024383, _1024385, _1024387, _1024389, _1024391] : [class_Groups_Ocomm__monoid__mult(_1024383), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024385), _1024387)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024385), _1024389)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1024385, tc_HOL_Obool)), _1024387), _1024389) = c_Orderings_Obot__class_Obot(tc_fun(_1024385, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1024383, _1024385, c_Groups_Otimes__class_Otimes(_1024383)), _1024391), c_Groups_Oone__class_Oone(_1024383)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1024385, tc_HOL_Obool)), _1024387), _1024389)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024383), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1024383, _1024385, c_Groups_Otimes__class_Otimes(_1024383)), _1024391), c_Groups_Oone__class_Oone(_1024383)), _1024387)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1024383, _1024385, c_Groups_Otimes__class_Otimes(_1024383)), _1024391), c_Groups_Oone__class_Oone(_1024383)), _1024389)))], (1644 ^ _781013) ^ [_804305, _804307] : [-(class_Divides_Osemiring__div(_804305)), _804307 = _804305, class_Divides_Osemiring__div(_804307)], (25766 ^ _781013) ^ [_1260522, _1260524] : [c_Nat__Transfer_Ois__nat(_1260522), c_Nat__Transfer_Ois__nat(_1260524), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1260522), _1260524)))], (50718 ^ _781013) ^ [_1811652] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1811652)))], (38578 ^ _781013) ^ [_1523007, _1523009] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1523007, _1523009) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1523007, _1523009)))], (40187 ^ _781013) ^ [_1564566, _1564568, _1564570, _1564572] : [-(hAPP(hAPP(c_List_Otake(_1564566), hAPP(c_Nat_OSuc, _1564568)), hAPP(hAPP(c_List_Olist_OCons(_1564566), _1564570), _1564572)) = hAPP(hAPP(c_List_Olist_OCons(_1564566), _1564570), hAPP(hAPP(c_List_Otake(_1564566), _1564568), _1564572)))], (34705 ^ _781013) ^ [_1438330] : [_1438330 = c_Int_OPls, -(c_Int_OBit0(_1438330) = c_Int_OPls)], (33842 ^ _781013) ^ [_1422070, _1422072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422070), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422070)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422072)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422072))], (41508 ^ _781013) ^ [_1599401, _1599403, _1599405, _1599407, _1599409] : [-(_1599401 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1599403, _1599405, _1599407), _1599401), _1599409) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1599405), _1599403), tc_prod(_1599405, _1599403), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599405), _1599403), c_List_Olist_ONil(_1599405)), _1599409), hAPP(c_Product__Type_Oprod_Oprod__case(_1599405, _1599403, tc_prod(tc_List_Olist(_1599405), _1599403)), hAPP(hAPP(c_COMBC(_1599405, tc_fun(_1599403, tc_prod(tc_List_Olist(_1599405), _1599403)), tc_fun(_1599403, tc_prod(tc_List_Olist(_1599405), _1599403))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1599405), _1599403), tc_prod(tc_List_Olist(_1599405), _1599403)), tc_fun(tc_fun(_1599403, tc_prod(tc_List_Olist(_1599405), _1599403)), tc_fun(_1599403, tc_prod(tc_List_Olist(_1599405), _1599403))), _1599405), c_COMBB(tc_prod(tc_List_Olist(_1599405), _1599403), tc_prod(tc_List_Olist(_1599405), _1599403), _1599403)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1599405), tc_fun(_1599403, tc_prod(tc_List_Olist(_1599405), _1599403))), tc_fun(tc_prod(tc_List_Olist(_1599405), _1599403), tc_prod(tc_List_Olist(_1599405), _1599403)), _1599405), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1599405), _1599403, tc_prod(tc_List_Olist(_1599405), _1599403))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1599405), tc_List_Olist(_1599405)), tc_fun(tc_List_Olist(_1599405), tc_fun(_1599403, tc_prod(tc_List_Olist(_1599405), _1599403))), _1599405), hAPP(c_COMBB(tc_List_Olist(_1599405), tc_fun(_1599403, tc_prod(tc_List_Olist(_1599405), _1599403)), tc_List_Olist(_1599405)), c_Product__Type_OPair(tc_List_Olist(_1599405), _1599403))), c_List_Olist_OCons(_1599405))))), hAPP(c_Lazy__Sequence_Oanamorph(_1599403, _1599405, _1599407), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1599401), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1599407, _1599409)))], (29261 ^ _781013) ^ [_1326899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1326899)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1326899 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45940 ^ _781013) ^ [_1700147, _1700149, _1700151] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1700147, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1700147, tc_HOL_Obool)), _1700149), _1700151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1700147, tc_HOL_Obool)), _1700149), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1700147, tc_HOL_Obool), _1700151)))], (5849 ^ _781013) ^ [_875069, _875071, _875073, _875075] : [-(c_Com_Ocom_OSemi(_875069, _875071) = c_Com_Ocom_OSemi(_875073, _875075)), _875069 = _875073, _875071 = _875075], (36014 ^ _781013) ^ [_1466518, _1466520, _1466522] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1466518, _1466518), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1466520), _1466522))), -(_1466518 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1466522 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22538 ^ _781013) ^ [_1202943, _1202945, _1202947, _1202949, _1202951] : [class_Groups_Ocomm__monoid__add(_1202943), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1202943), _1202945), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1202947), _1202949)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1202951), _1202949))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1202943), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1202943, tc_Nat_Onat), _1202945), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1202949))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1202947), _1202951)))], (35027 ^ _781013) ^ [_1444126] : [class_Rings_Osemiring__1(_1444126), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1444126), c_Groups_Oone__class_Oone(_1444126)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1444126))], (35415 ^ _781013) ^ [_1451312, _1451314] : [class_Rings_Osemiring__1(_1451312), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451314)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1451312), 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)))), _1451314))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1451312), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1451312), hAPP(c_Int_Onat, _1451314))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1451312), hAPP(c_Int_Onat, _1451314))))], (34909 ^ _781013) ^ [_1441918, _1441920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1441918), _1441920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1441918)), c_Int_OBit1(_1441920))))], (36940 ^ _781013) ^ [_1485813, _1485815] : [36941 ^ _781013 : [(36944 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1485815), _1485813))], (36942 ^ _781013) ^ [] : [_1485813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1485815, _1485813) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1485815))], (19118 ^ _781013) ^ [_1139006, _1139008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1139006), _1139008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1139006), _1139008)))], (46685 ^ _781013) ^ [_1720148, _1720150, _1720152] : [c_Wellfounded_Owf(_1720148, _1720150), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1720148, _1720148), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1720148, _1720148, _1720148), _1720150), _1720152)), _1720150)), -(c_FunDef_Oreduction__pair(_1720148, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1720148, _1720148), tc_HOL_Obool), tc_fun(tc_prod(_1720148, _1720148), tc_HOL_Obool)), _1720150), _1720152)))], (9887 ^ _781013) ^ [_955590, _955592, _955594, _955596] : [class_Lattices_Osemilattice__inf(_955590), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955590), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955590), _955592), _955594)), _955596) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955590), _955592), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955590), _955594), _955596)))], (32324 ^ _781013) ^ [_1394387, _1394389, _1394391] : [class_Int_Onumber(_1394387), 32327 ^ _781013 : [(32334 ^ _781013) ^ [] : [_1394391 = hAPP(c_Int_Onumber__class_Onumber__of(_1394387), _1394389), -(hAPP(c_Int_Onumber__class_Onumber__of(_1394387), _1394389) = _1394391)], (32328 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1394387), _1394389) = _1394391, -(_1394391 = hAPP(c_Int_Onumber__class_Onumber__of(_1394387), _1394389))]]], (51364 ^ _781013) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (41726 ^ _781013) ^ [_1604460, _1604462, _1604464] : [_1604460 = c_List_Olist_ONil(_1604462), -(c_List_Obutlast(_1604462, hAPP(hAPP(c_List_Oappend(_1604462), _1604464), _1604460)) = c_List_Obutlast(_1604462, _1604464))], (32576 ^ _781013) ^ [_1399344, _1399346] : [class_Int_Onumber__ring(_1399344), -(hAPP(c_Int_Onumber__class_Onumber__of(_1399344), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1399346)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1399344), hAPP(c_Int_Onumber__class_Onumber__of(_1399344), _1399346)))], (19086 ^ _781013) ^ [_1138172, _1138174, _1138176, _1138178, _1138180, _1138182] : [class_Groups_Ocomm__monoid__mult(_1138172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1138174), _1138176)), 19093 ^ _781013 : [(19100 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1138174), _1138178), _1138176))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1138174, _1138172), hAPP(hAPP(c_COMBC(_1138174, _1138172, _1138172), hAPP(hAPP(c_COMBS(_1138174, _1138172, tc_fun(_1138172, _1138172)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1138172, tc_fun(_1138172, _1138172)), _1138174), c_If(_1138172)), hAPP(hAPP(c_COMBC(_1138174, _1138174, tc_HOL_Obool), c_fequal), _1138178))), _1138180)), _1138182)), _1138176) = hAPP(hAPP(c_Power_Opower__class_Opower(_1138172), _1138182), hAPP(c_Finite__Set_Ocard(_1138174), _1138176)))], (19094 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1138174), _1138178), _1138176)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1138174, _1138172), hAPP(hAPP(c_COMBC(_1138174, _1138172, _1138172), hAPP(hAPP(c_COMBS(_1138174, _1138172, tc_fun(_1138172, _1138172)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1138172, tc_fun(_1138172, _1138172)), _1138174), c_If(_1138172)), hAPP(hAPP(c_COMBC(_1138174, _1138174, tc_HOL_Obool), c_fequal), _1138178))), _1138180)), _1138182)), _1138176) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138172), hAPP(_1138180, _1138178)), hAPP(hAPP(c_Power_Opower__class_Opower(_1138172), _1138182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1138174), _1138176)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (7739 ^ _781013) ^ [_911345, _911347, _911349, _911351] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911345, tc_HOL_Obool)), _911347), hAPP(hAPP(c_Set_Oinsert(_911345), _911349), _911351)) = hAPP(hAPP(c_Set_Oinsert(_911345), _911349), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911345, tc_HOL_Obool)), _911347), _911351)))], (34042 ^ _781013) ^ [_1426822, _1426824, _1426826, _1426828] : [-(hAPP(c_Nat_Onat_Onat__rec(_1426822, _1426824, _1426826), hAPP(c_Nat_OSuc, _1426828)) = hAPP(hAPP(_1426826, _1426828), hAPP(c_Nat_Onat_Onat__rec(_1426822, _1426824, _1426826), _1426828)))], (19610 ^ _781013) ^ [_1147981, _1147983, _1147985, _1147987] : [class_Rings_Olinordered__semidom(_1147981), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147981), c_Groups_Oone__class_Oone(_1147981)), _1147983)), 19617 ^ _781013 : [(19624 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147985), _1147987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147981), hAPP(hAPP(c_Power_Opower__class_Opower(_1147981), _1147983), _1147985)), hAPP(hAPP(c_Power_Opower__class_Opower(_1147981), _1147983), _1147987))))], (19618 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147981), hAPP(hAPP(c_Power_Opower__class_Opower(_1147981), _1147983), _1147985)), hAPP(hAPP(c_Power_Opower__class_Opower(_1147981), _1147983), _1147987))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147985), _1147987)))]]], (51382 ^ _781013) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (29245 ^ _781013) ^ [_1326587, _1326589, _1326591] : [class_Fields_Olinordered__field__inverse__zero(_1326587), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326587), c_Groups_Ozero__class_Ozero(_1326587)), _1326589)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326587), hAPP(c_Groups_Oabs__class_Oabs(_1326587), _1326591)), _1326589) = hAPP(c_Groups_Oabs__class_Oabs(_1326587), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326587), _1326591), _1326589)))], (35535 ^ _781013) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (49524 ^ _781013) ^ [_1787712, _1787714, _1787716, _1787718, _1787720] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1787712, _1787714, _1787716), _1787718), _1787720) = c_HOL_OThe(_1787714, c_Finite__Set_Ofold__graph(_1787712, _1787714, _1787716, _1787718, _1787720)))], (9489 ^ _781013) ^ [_949163, _949165, _949167] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_949163, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949163, tc_HOL_Obool)), _949165), _949167)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_949163, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_949163, tc_HOL_Obool)), _949165)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_949163, tc_HOL_Obool)), _949167)))], (33598 ^ _781013) ^ [_1418272, _1418274] : [class_Int_Onumber__ring(_1418272), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1418272), hAPP(c_Int_Onumber__class_Onumber__of(_1418272), c_Int_OPls)), _1418274) = _1418274)], (14075 ^ _781013) ^ [_1040013, _1040015, _1040017] : [class_Groups_Ogroup__add(_1040013), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1040013), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040013), _1040015), _1040017)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040013), hAPP(c_Groups_Ouminus__class_Ouminus(_1040013), _1040017)), hAPP(c_Groups_Ouminus__class_Ouminus(_1040013), _1040015)))], (19883 ^ _781013) ^ [_1153463] : [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)), _1153463)), _1153463) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (14063 ^ _781013) ^ [_1039765, _1039767, _1039769] : [class_Groups_Ogroup__add(_1039765), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039765), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039765), _1039767), _1039769)), _1039769) = _1039767)], (18540 ^ _781013) ^ [_1126035, _1126037] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126035), _1126037))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1126037), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1126035), _1126037)) = _1126035)], (31866 ^ _781013) ^ [_1384625, _1384627, _1384629, _1384631, _1384633] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384625, tc_fun(_1384627, tc_HOL_Obool)), _1384629), hAPP(hAPP(c_COMBC(_1384625, tc_fun(_1384627, tc_HOL_Obool), tc_fun(_1384627, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1384627, tc_HOL_Obool), tc_fun(tc_fun(_1384627, tc_HOL_Obool), tc_fun(_1384627, tc_HOL_Obool)), _1384625), c_Groups_Ominus__class_Ominus(tc_fun(_1384627, tc_HOL_Obool))), _1384631)), _1384633)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384627, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384625, tc_fun(_1384627, tc_HOL_Obool)), _1384629), _1384631)), _1384633))], (44258 ^ _781013) ^ [_1662766, _1662768, _1662770, _1662772] : [-(hAPP(c_List_Orev(_1662766), hAPP(hAPP(c_List_Omap(_1662768, _1662766), _1662770), _1662772)) = hAPP(hAPP(c_List_Omap(_1662768, _1662766), _1662770), hAPP(c_List_Orev(_1662768), _1662772)))], (8440 ^ _781013) ^ [_926549, _926551, _926553, _926555, _926557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926549, tc_HOL_Obool)), _926551), _926553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926555, tc_HOL_Obool)), hAPP(c_Set_Oimage(_926549, _926555, _926557), _926551)), hAPP(c_Set_Oimage(_926549, _926555, _926557), _926553))))], (51150 ^ _781013) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (51626 ^ _781013) ^ [] : [hBOOL(c_fFalse)], (33980 ^ _781013) ^ [_1424965, _1424967] : [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(_1424965))), 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)), _1424967)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424965)), hAPP(c_Nat_OSuc, _1424967))))], (26031 ^ _781013) ^ [_1264964, _1264966, _1264968] : [26033 ^ _781013 : [(26036 ^ _781013) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1264968, 26032 ^ [_1264964, _1264966, _1264968]))], (26034 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1264964), 26032 ^ [_1264964, _1264966, _1264968]), _1264966)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264964, tc_Int_Oint), _1264968), _1264966) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264964, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1264964), c_Int_Onat), _1264968)), _1264966)))], (32242 ^ _781013) ^ [_1392931, _1392933, _1392935] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_1392931, _1392933, _1392935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1392935)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10823 ^ _781013) ^ [_972283, _972285, _972287] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972283, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972283, tc_HOL_Obool)), _972285), _972287)), _972285)))], (21627 ^ _781013) ^ [_1187193, _1187195] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187193)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187195)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1187193), _1187195)))], (28624 ^ _781013) ^ [_1314981, _1314983, _1314985] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314981, _1314983)), _1314985) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314981), _1314985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314983), _1314985)))], (21684 ^ _781013) ^ [_1188221, _1188223] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1188221)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1188223)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188221), _1188223)))], (5916 ^ _781013) ^ [_876293] : [5917 ^ _781013 : [(5918 ^ _781013) ^ [_876341] : [hAPP(c_Com_Obody, _876293) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _876341)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _876293))))], (32252 ^ _781013) ^ [_1393110, _1393112] : [class_Int_Onumber__ring(_1393110), 32255 ^ _781013 : [(32262 ^ _781013) ^ [] : [-(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), _1393112)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1393110), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1393112)) = c_Groups_Ozero__class_Ozero(_1393110))], (32256 ^ _781013) ^ [] : [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), _1393112))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1393110), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1393112)) = hAPP(c_Int_Onumber__class_Onumber__of(_1393110), _1393112))]]], (23369 ^ _781013) ^ [_1218091, _1218093, _1218095, _1218097] : [class_Orderings_Oorder(_1218091), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1218091, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1218091, _1218093, _1218095)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218091, _1218095), _1218097)) = c_Orderings_Obot__class_Obot(tc_fun(_1218091, tc_HOL_Obool)))], (4946 ^ _781013) ^ [_856277, _856279, _856281, _856283, _856285, _856287, _856289, _856291] : [-(c_New__Random__Sequence_Opos__empty(_856291, _856287, _856283, _856279) = c_New__Random__Sequence_Opos__empty(_856289, _856285, _856281, _856277)), _856291 = _856289, _856287 = _856285, _856283 = _856281, _856279 = _856277], (15313 ^ _781013) ^ [_1064357, _1064359, _1064361] : [class_Groups_Oordered__comm__monoid__add(_1064357), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064357), c_Groups_Ozero__class_Ozero(_1064357)), _1064359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064357), c_Groups_Ozero__class_Ozero(_1064357)), _1064361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064357), c_Groups_Ozero__class_Ozero(_1064357)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064357), _1064359), _1064361))))], (3672 ^ _781013) ^ [_836534, _836536] : [_836536 = _836534, -(c_Nitpick_Ozero__frac(_836536) = c_Nitpick_Ozero__frac(_836534))], (7585 ^ _781013) ^ [_908136, _908138, _908140, _908142] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908136, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_908136), _908138), _908140)), _908142))), hBOOL(hAPP(hAPP(c_member(_908136), _908138), _908142)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908136, tc_HOL_Obool)), _908140), _908142))], (30295 ^ _781013) ^ [_1347046] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1347046) = _1347046)], (14785 ^ _781013) ^ [_1055237, _1055239] : [class_Groups_Omonoid__add(_1055237), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055237), _1055239), c_Groups_Ozero__class_Ozero(_1055237)) = _1055239)], (9060 ^ _781013) ^ [_940453, _940455, _940457] : [-(c_Smallcheck_Oorelse(_940453, _940455, _940457) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_940453), _940453, _940457, c_Option_Ooption_OSome(_940453)), _940455))], (16265 ^ _781013) ^ [_1081519, _1081521, _1081523] : [-(hAPP(hAPP(c_Set_Oinsert(_1081519), _1081521), _1081523) = hAPP(c_Set_OCollect(_1081519), hAPP(hAPP(c_COMBS(_1081519, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1081519), c_fdisj), hAPP(hAPP(c_COMBC(_1081519, _1081519, tc_HOL_Obool), c_fequal), _1081521))), hAPP(hAPP(c_COMBC(_1081519, tc_fun(_1081519, tc_HOL_Obool), tc_HOL_Obool), c_member(_1081519)), _1081523))))], (13058 ^ _781013) ^ [_1018485, _1018487, _1018489, _1018491] : [c_Fun_Oinj__on(_1018485, _1018487, _1018489, _1018491), -(hAPP(c_Set_Oimage(_1018487, _1018485, c_Fun_Othe__inv__into(_1018485, _1018487, _1018491, _1018489)), hAPP(c_Set_Oimage(_1018485, _1018487, _1018489), _1018491)) = _1018491)], (51070 ^ _781013) ^ [_1819300, _1819302] : [class_Orderings_Oord(_1819300), -(class_Orderings_Oord(tc_fun(_1819302, _1819300)))], (10959 ^ _781013) ^ [_975309, _975311, _975313, _975315, _975317, _975319] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975309, _975311, _975313, _975315, _975317), _975319)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_975309), _975317)))], (1174 ^ _781013) ^ [_798430, _798432] : [-(class_Groups_Ogroup__add(_798430)), _798432 = _798430, class_Groups_Ogroup__add(_798432)], (42873 ^ _781013) ^ [_1631848] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631848, tc_HOL_Obool) = c_Set_OBall(_1631848))], (48253 ^ _781013) ^ [_1755761] : [-(_1755761 = 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)), _1755761)))], (42518 ^ _781013) ^ [_1623409, _1623411] : [class_Groups_Omonoid__add(_1623409), -(hAPP(c_List_Ofoldl(_1623409, _1623409, c_Groups_Oplus__class_Oplus(_1623409), c_Groups_Ozero__class_Ozero(_1623409)), _1623411) = c_List_Ofoldr(_1623409, _1623409, c_Groups_Oplus__class_Oplus(_1623409), _1623411, c_Groups_Ozero__class_Ozero(_1623409)))], (38997 ^ _781013) ^ [_1533199, _1533201, _1533203, _1533205, _1533207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1533199), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533201)), _1533203))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1533199), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533205)), _1533207))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1533201, _1533205)), hAPP(hAPP(c_List_Ozip(_1533201, _1533205), _1533203), _1533207)), _1533199) = hAPP(hAPP(c_Product__Type_OPair(_1533201, _1533205), hAPP(hAPP(c_List_Onth(_1533201), _1533203), _1533199)), hAPP(hAPP(c_List_Onth(_1533205), _1533207), _1533199)))], (25330 ^ _781013) ^ [_1253137, _1253139, _1253141, _1253143] : [class_Fields_Olinordered__field__inverse__zero(_1253137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253137), _1253139), _1253141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253137), _1253143), c_Groups_Ozero__class_Ozero(_1253137))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253137), c_Groups_Ozero__class_Ozero(_1253137)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253137), _1253139), _1253141))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253137), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253137), _1253143), _1253139)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253137), _1253143), _1253141))))], (48117 ^ _781013) ^ [_1753265, _1753267, _1753269] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1753265), _1753267))), -(c_Random_Ominus__shift(_1753269, _1753265, _1753267) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1753265), _1753267))], (33748 ^ _781013) ^ [_1420604] : [-(c_Int_Osucc(_1420604) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1420604), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5601 ^ _781013) ^ [_869201, _869203, _869205, _869207] : [c_Hoare__Mirabelle_Ohoare__derivs(_869201, _869203, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_869201)), _869205), _869207)), 5604 ^ _781013 : [(5607 ^ _781013) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_869201, _869203, _869207))], (5605 ^ _781013) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_869201, _869203, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_869201)), _869205), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_869201), tc_HOL_Obool)))))]]], (12112 ^ _781013) ^ [_999586, _999588, _999590] : [class_Lattices_Olattice(_999586), hBOOL(hAPP(c_Finite__Set_Ofinite(_999586), _999588)), hBOOL(hAPP(hAPP(c_member(_999586), _999590), _999588)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_999586), _999590), c_Big__Operators_Olattice__class_OInf__fin(_999586, _999588)) = _999590)], (21692 ^ _781013) ^ [_1188354, _1188356, _1188358] : [class_Rings_Olinordered__semidom(_1188354), 21695 ^ _781013 : [(21702 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1188356), _1188358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188354), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188354), _1188356)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188354), _1188358))))], (21696 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188354), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188354), _1188356)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188354), _1188358))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1188356), _1188358)))]]], (20484 ^ _781013) ^ [_1163579, _1163581, _1163583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1163581), _1163583)), -(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, _1163579)), _1163581)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1163579)), _1163583))))], (1514 ^ _781013) ^ [_802680, _802682] : [-(class_Rings_Oordered__cancel__semiring(_802680)), _802682 = _802680, class_Rings_Oordered__cancel__semiring(_802682)], (28322 ^ _781013) ^ [_1309672] : [_1309672 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1309672) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27801 ^ _781013) ^ [_1300232, _1300234, _1300236] : [-(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, _1300232, _1300234)), _1300236), _1300234) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1300232), _1300236), _1300234))], (608 ^ _781013) ^ [_790339, _790341, _790343, _790345] : [-(c_List_Olinorder__class_Osorted(_790343, _790339)), c_List_Olinorder__class_Osorted(_790345, _790341), _790345 = _790343, _790341 = _790339], (45003 ^ _781013) ^ [_1679976, _1679978] : [-(_1679976 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1679978, _1679976, c_List_Olist_ONil(_1679978)) = c_List_Olist_ONil(tc_List_Olist(_1679978)))], (37736 ^ _781013) ^ [_1502047, _1502049, _1502051, _1502053, _1502055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1502047, _1502049)), hAPP(_1502047, _1502051))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1502053, _1502053)), hAPP(hAPP(c_Product__Type_OPair(_1502053, _1502053), _1502049), _1502051)), c_Wellfounded_Omlex__prod(_1502053, _1502047, _1502055))))], (51280 ^ _781013) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (43339 ^ _781013) ^ [_1644085, _1644087, _1644089] : [hBOOL(hAPP(c_List_Olistsp(_1644085, _1644087), _1644089)), 43342 ^ _781013 : [(43343 ^ _781013) ^ [_1644174] : [hBOOL(hAPP(hAPP(c_member(_1644085), _1644174), hAPP(c_List_Oset(_1644085), _1644089))), -(hBOOL(hAPP(_1644087, _1644174)))]]], (8763 ^ _781013) ^ [_933871, _933873, _933875, _933877, _933879] : [c_Hoare__Mirabelle_Ohoare__valids(_933871, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_933871), tc_HOL_Obool)), _933873), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_933871), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933871)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933871))), hAPP(hAPP(c_COMBB(tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933871))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_933871)), _933875)), c_Com_Ocom_OBODY)), _933877)), _933879)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_933871), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933871)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933871))), hAPP(hAPP(c_COMBB(tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933871))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_933871)), _933875)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _933877)), _933879)), -(c_Hoare__Mirabelle_Ohoare__valids(_933871, _933873, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_933871), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933871)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933871))), hAPP(hAPP(c_COMBB(tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_933871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933871))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_933871)), _933875)), c_Com_Ocom_OBODY)), _933877)), _933879)))], (5889 ^ _781013) ^ [_875769, _875771] : [-(hAPP(c_Option_Othe(_875769), hAPP(c_Option_Ooption_OSome(_875769), _875771)) = _875771)], (33528 ^ _781013) ^ [_1417219, _1417221] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417219)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417219)), _1417221) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417219)), _1417221)))], (37554 ^ _781013) ^ [_1498181, _1498183, _1498185, _1498187, _1498189, _1498191, _1498193] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1498181, _1498183, _1498185), hAPP(c_Fun_Ocomp(_1498187, tc_fun(_1498183, _1498185), _1498181, _1498189), _1498191)), _1498193) = hAPP(hAPP(_1498189, hAPP(_1498191, hAPP(c_Product__Type_Ofst(_1498181, _1498183), _1498193))), hAPP(c_Product__Type_Osnd(_1498181, _1498183), _1498193)))], (35635 ^ _781013) ^ [_1455274] : [class_Int_Onumber__ring(_1455274), c_Int_Oiszero(_1455274, hAPP(c_Int_Onumber__class_Onumber__of(_1455274), c_Int_OMin))], (29907 ^ _781013) ^ [_1338708, _1338710, _1338712] : [class_Orderings_Olinorder(_1338708), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338708), _1338710)), -(_1338710 = c_Orderings_Obot__class_Obot(tc_fun(_1338708, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338708), _1338712)), -(_1338712 = c_Orderings_Obot__class_Obot(tc_fun(_1338708, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338708, tc_HOL_Obool)), _1338710), _1338712) = c_Orderings_Obot__class_Obot(tc_fun(_1338708, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1338708, c_Orderings_Oord__class_Omin(_1338708), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338708, tc_HOL_Obool)), _1338710), _1338712)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338708), c_Big__Operators_Olattice_OInf__fin(_1338708, c_Orderings_Oord__class_Omin(_1338708), _1338710)), c_Big__Operators_Olattice_OInf__fin(_1338708, c_Orderings_Oord__class_Omin(_1338708), _1338712)))], (33558 ^ _781013) ^ [_1417662, _1417664] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1417662)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417664)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417664))), 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), _1417662)), c_Int_Onat)))))], (25420 ^ _781013) ^ [_1254886, _1254888] : [-(c_Int_Onat__aux(_1254886, _1254888) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1254886)), _1254888))], (6088 ^ _781013) ^ [_879417, _879419, _879421] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_879417), _879419)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_879417), hAPP(hAPP(c_Set_Oinsert(_879417), _879421), _879419))))], (8517 ^ _781013) ^ [_928465, _928467, _928469, _928471] : [-(_928465 = c_Orderings_Obot__class_Obot(tc_fun(_928467, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_928467, _928469, hAPP(c_COMBK(_928469, _928467), _928471)), _928465) = hAPP(hAPP(c_Set_Oinsert(_928469), _928471), c_Orderings_Obot__class_Obot(tc_fun(_928469, tc_HOL_Obool))))], (20281 ^ _781013) ^ [_1160084, _1160086, _1160088] : [class_Rings_Ocomm__semiring__1(_1160084), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160084), hAPP(hAPP(c_Power_Opower__class_Opower(_1160084), _1160086), _1160088)), _1160086) = hAPP(hAPP(c_Power_Opower__class_Opower(_1160084), _1160086), hAPP(c_Nat_OSuc, _1160088)))], (8000 ^ _781013) ^ [_916578, _916580, _916582, _916584, _916586] : [-(_916578 = c_Option_Ooption_ONone(_916580)), -(c_Map_Odom(_916582, _916580, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_916582, tc_Option_Ooption(_916580)), _916584), _916586), _916578)) = hAPP(hAPP(c_Set_Oinsert(_916582), _916586), c_Map_Odom(_916582, _916580, _916584)))], (26921 ^ _781013) ^ [_1282108, _1282110, _1282112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1282108)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1282110), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1282112)), 26931 ^ _781013 : [(26937 ^ _781013) ^ [] : [-(_1282110 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26933 ^ [_1282108, _1282110, _1282112]), 26930 ^ [_1282108, _1282110, _1282112]))], (26935 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26933 ^ [_1282108, _1282110, _1282112]), _1282112)))], (26932 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26930 ^ [_1282108, _1282110, _1282112]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1282108))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1282110), _1282108) = _1282110)], (30387 ^ _781013) ^ [_1348832, _1348834, _1348836] : [class_Groups_Olinordered__ab__group__add(_1348832), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1348832), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348832), _1348834), _1348836)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348832), hAPP(c_Groups_Ouminus__class_Ouminus(_1348832), _1348834)), hAPP(c_Groups_Ouminus__class_Ouminus(_1348832), _1348836)))], (41793 ^ _781013) ^ [_1605993, _1605995, _1605997, _1605999] : [_1605997 = _1605999, -(hAPP(hAPP(c_List_Oappend(_1605993), _1605995), _1605997) = hAPP(hAPP(c_List_Oappend(_1605993), _1605995), _1605999))], (13707 ^ _781013) ^ [_1032635, _1032637, _1032639, _1032641, _1032643] : [class_Rings_Ocomm__semiring__1(_1032635), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032635), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032635), _1032637), _1032639)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032635), _1032641), _1032643)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032635), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032635), _1032637), _1032641)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032635), _1032639), _1032643)))], (14831 ^ _781013) ^ [_1055953, _1055955, _1055957] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1055953), 14834 ^ _781013 : [(14841 ^ _781013) ^ [] : [_1055957 = c_Groups_Ozero__class_Ozero(_1055953), -(_1055955 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055953), _1055955), _1055957))], (14835 ^ _781013) ^ [] : [_1055955 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055953), _1055955), _1055957), -(_1055957 = c_Groups_Ozero__class_Ozero(_1055953))]]], (30195 ^ _781013) ^ [_1345141, _1345143, _1345145, _1345147] : [class_Orderings_Olinorder(_1345141), 30198 ^ _781013 : [(30199 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345141), _1345143), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345141), _1345145), _1345147))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345141), _1345143), _1345145))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345141), _1345143), _1345147)))], (30209 ^ _781013) ^ [] : [30210 ^ _781013 : [(30213 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345141), _1345143), _1345147))], (30211 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345141), _1345143), _1345145))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345141), _1345143), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345141), _1345145), _1345147))))]]], (17483 ^ _781013) ^ [_1107829, _1107831, _1107833, _1107835, _1107837, _1107839] : [-(hBOOL(hAPP(hAPP(c_member(_1107829), _1107831), _1107833))), -(hAPP(c_Fun_Ooverride__on(_1107829, _1107835, _1107837, _1107839, _1107833), _1107831) = hAPP(_1107837, _1107831))], (4964 ^ _781013) ^ [_856578, _856580] : [_856580 = _856578, -(c_New__DSequence_Opos__empty(_856580) = c_New__DSequence_Opos__empty(_856578))], (34285 ^ _781013) ^ [_1431253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431253), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1431253)), c_Int_OPls)))], (8775 ^ _781013) ^ [_934499, _934501, _934503] : [class_Lattices_Osemilattice__sup(_934499), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934499), _934501), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934499), _934501), _934503))))], (41328 ^ _781013) ^ [_1595536, _1595538] : [-(c_List_Olistrelp(_1595536, _1595538, c_List_Olist_ONil(_1595536), c_List_Olist_ONil(_1595536)))], (26549 ^ _781013) ^ [_1275107, _1275109] : [class_Rings_Ocomm__semiring__1(_1275107), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1275107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1275107), c_Groups_Oone__class_Oone(_1275107)), c_Groups_Oone__class_Oone(_1275107))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1275107), c_Nat_Osemiring__1__class_Oof__nat(_1275107)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1275109))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1275107), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1275107), _1275109)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1275107), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1275107), _1275109)), c_Groups_Oone__class_Oone(_1275107))))], (51378 ^ _781013) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (44951 ^ _781013) ^ [_1678730, _1678732] : [class_Orderings_Olinorder(_1678730), 44958 ^ _781013 : [(44963 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1678730), hAPP(hAPP(c_List_Onth(_1678730), _1678732), 44956 ^ [_1678730, _1678732])), hAPP(hAPP(c_List_Onth(_1678730), _1678732), 44957 ^ [_1678730, _1678732])))], (44961 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44957 ^ [_1678730, _1678732]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678730)), _1678732))))], (44959 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 44956 ^ [_1678730, _1678732]), 44957 ^ [_1678730, _1678732])))]], -(c_List_Olinorder__class_Osorted(_1678730, _1678732))], (48239 ^ _781013) ^ [_1755478, _1755480] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1755478)), hAPP(c_Code__Numeral_Oof__nat, _1755480)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1755478), _1755480)))], (17927 ^ _781013) ^ [_1115301, _1115303, _1115305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1115301), _1115303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1115305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1115305), _1115301)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1115305), _1115303))))], (48331 ^ _781013) ^ [_1757772, _1757774, _1757776, _1757778, _1757780] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1757772, _1757772)), hAPP(hAPP(c_Product__Type_OPair(_1757772, _1757772), _1757774), _1757776)), _1757778)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1757772, _1757772)), hAPP(hAPP(c_Product__Type_OPair(_1757772, _1757772), _1757776), _1757780)), c_Transitive__Closure_Ortrancl(_1757772, _1757778))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757772, _1757772)), hAPP(hAPP(c_Product__Type_OPair(_1757772, _1757772), _1757774), _1757780)), c_Transitive__Closure_Ortrancl(_1757772, _1757778))))], (42869 ^ _781013) ^ [_1631632, _1631634, _1631636, _1631638] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1631632, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631634, tc_fun(_1631632, tc_HOL_Obool)), _1631636), _1631638)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1631634, tc_fun(_1631632, tc_HOL_Obool)), _1631636), hAPP(hAPP(c_COMBB(tc_fun(_1631632, tc_HOL_Obool), tc_fun(_1631632, tc_HOL_Obool), _1631634), c_Groups_Ouminus__class_Ouminus(tc_fun(_1631632, tc_HOL_Obool))), _1631638)))], (44438 ^ _781013) ^ [_1666701, _1666703, _1666705] : [-(hAPP(c_List_Orotate(_1666701, _1666703), hAPP(c_List_Orev(_1666701), _1666705)) = hAPP(c_List_Orev(_1666701), hAPP(c_List_Orotate(_1666701, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666701)), _1666705)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1666703, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666701)), _1666705)))), _1666705)))], (26049 ^ _781013) ^ [_1265445, _1265447, _1265449, _1265451] : [class_Groups_Oab__group__add(_1265445), 26052 ^ _781013 : [(26059 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1265447), _1265449))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1265445), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1265445, _1265445), hAPP(hAPP(c_COMBB(_1265445, tc_fun(_1265445, _1265445), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1265445)), _1265451)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1265445, tc_Nat_Onat), _1265451), 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, _1265447, _1265449)) = c_Groups_Ozero__class_Ozero(_1265445))], (26053 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1265447), _1265449)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1265445), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1265445, _1265445), hAPP(hAPP(c_COMBB(_1265445, tc_fun(_1265445, _1265445), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1265445)), _1265451)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1265445, tc_Nat_Onat), _1265451), 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, _1265447, _1265449)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265445), hAPP(_1265451, _1265447)), hAPP(_1265451, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1265449), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (41698 ^ _781013) ^ [_1603967, _1603969, _1603971] : [_1603971 = c_List_Olist_ONil(_1603969), -(_1603967 = hAPP(hAPP(c_List_Oappend(_1603969), _1603967), _1603971))], (49846 ^ _781013) ^ [_1793998, _1794000, _1794002] : [class_Orderings_Olinorder(_1793998), hBOOL(hAPP(c_Finite__Set_Ofinite(_1793998), _1794000)), -(hBOOL(hAPP(hAPP(c_member(_1793998), _1794002), _1794000))), -(c_Big__Operators_Olinorder__class_OMax(_1793998, hAPP(hAPP(c_Set_Oinsert(_1793998), _1794002), _1794000)) = hAPP(hAPP(c_Finite__Set_Ofold(_1793998, _1793998, c_Orderings_Oord__class_Omax(_1793998)), _1794002), _1794000))], (38696 ^ _781013) ^ [_1525808, _1525810, _1525812, _1525814] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1525808, _1525808)), hAPP(hAPP(c_Product__Type_OPair(_1525808, _1525808), _1525810), _1525812)), hAPP(c_List_Oset(tc_prod(_1525808, _1525808)), hAPP(hAPP(c_List_Ozip(_1525808, _1525808), _1525814), _1525814))))), hBOOL(hAPP(hAPP(c_member(_1525808), _1525810), hAPP(c_List_Oset(_1525808), _1525814))), _1525810 = _1525812], (31842 ^ _781013) ^ [_1383464, _1383466, _1383468, _1383470, _1383472] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383464, tc_fun(_1383466, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1383464, tc_HOL_Obool)), _1383468), _1383470)), _1383472) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1383466, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383464, tc_fun(_1383466, tc_HOL_Obool)), _1383468), _1383472)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383464, tc_fun(_1383466, tc_HOL_Obool)), _1383470), _1383472)))], (36651 ^ _781013) ^ [_1480806, _1480808] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1480806, _1480808) = 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), _1480806), _1480808)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1480806, _1480808)))], (51604 ^ _781013) ^ [_1824665, _1824667] : [-(hAPP(c_COMBI(_1824665), _1824667) = _1824667)], (4232 ^ _781013) ^ [_845022, _845024, _845026, _845028, _845030, _845032] : [-(c_Big__Operators_Olattice_OSup__fin(_845032, _845028, _845024) = c_Big__Operators_Olattice_OSup__fin(_845030, _845026, _845022)), _845032 = _845030, _845028 = _845026, _845024 = _845022], (22580 ^ _781013) ^ [_1203783, _1203785] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203783), _1203785) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22581 ^ _781013 : [(22590 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203783), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203785), _1203783))], (22584 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203783), _1203785))], (22582 ^ _781013) ^ [] : [_1203785 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (11740 ^ _781013) ^ [_992605, _992607, _992609, _992611, _992613] : [c_Fun_Oinj__on(_992605, _992607, _992609, c_Orderings_Otop__class_Otop(tc_fun(_992605, tc_HOL_Obool))), 11743 ^ _781013 : [(11750 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_992605, tc_HOL_Obool)), _992611), _992613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_992607, tc_HOL_Obool)), hAPP(c_Set_Oimage(_992605, _992607, _992609), _992611)), hAPP(c_Set_Oimage(_992605, _992607, _992609), _992613))))], (11744 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_992607, tc_HOL_Obool)), hAPP(c_Set_Oimage(_992605, _992607, _992609), _992611)), hAPP(c_Set_Oimage(_992605, _992607, _992609), _992613))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_992605, tc_HOL_Obool)), _992611), _992613)))]]], (15179 ^ _781013) ^ [_1061853, _1061855, _1061857] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1061853), _1061855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1061853, tc_HOL_Obool)), _1061857), _1061855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1061853), _1061855)), hAPP(c_Finite__Set_Ocard(_1061853), _1061857))), -(_1061857 = _1061855)], (25880 ^ _781013) ^ [_1262321, _1262323, _1262325] : [class_Rings_Oring__1(_1262321), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262321), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1262323), _1262325)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1262321), hAPP(c_Int_Oring__1__class_Oof__int(_1262321), _1262323)), hAPP(c_Int_Oring__1__class_Oof__int(_1262321), _1262325)))], (43293 ^ _781013) ^ [_1643130, _1643132] : [-(hAPP(c_List_Ofilter(_1643130, _1643132), c_List_Olist_ONil(_1643130)) = c_List_Olist_ONil(_1643130))], (50902 ^ _781013) ^ [_1815899, _1815901, _1815903, _1815905] : [-(c_Predicate_Oconversep(_1815899, _1815901, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1815899, tc_fun(_1815901, tc_HOL_Obool))), _1815903), _1815905)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1815901, tc_fun(_1815899, tc_HOL_Obool))), c_Predicate_Oconversep(_1815899, _1815901, _1815903)), c_Predicate_Oconversep(_1815899, _1815901, _1815905)))], (43478 ^ _781013) ^ [_1646877, _1646879, _1646881] : [hBOOL(hAPP(c_List_Odistinct(_1646877), _1646879)), -(hAPP(c_List_Ofilter(_1646877, hAPP(hAPP(c_COMBC(_1646877, tc_fun(_1646877, tc_HOL_Obool), tc_HOL_Obool), c_member(_1646877)), hAPP(c_List_Oset(_1646877), c_List_Osublist(_1646877, _1646879, _1646881)))), _1646879) = c_List_Osublist(_1646877, _1646879, _1646881))], (24188 ^ _781013) ^ [_1232131, _1232133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232133)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1232131)), hAPP(c_Int_Onat, _1232133)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232131), _1232133)))], (11145 ^ _781013) ^ [_979589, _979591, _979593, _979595, _979597] : [hBOOL(hAPP(hAPP(c_member(_979589), _979591), c_Map_Odom(_979589, _979593, _979595))), -(hAPP(c_Map_Omap__add(_979589, _979593, _979597, _979595), _979591) = hAPP(_979595, _979591))], (3120 ^ _781013) ^ [_827836, _827838, _827840, _827842, _827844, _827846] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_827846, _827842, _827838) = c_SetInterval_Oord__class_OgreaterThanLessThan(_827844, _827840, _827836)), _827846 = _827844, _827842 = _827840, _827838 = _827836], (35505 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (5284 ^ _781013) ^ [_861592, _861594] : [_861594 = _861592, -(c_Groups_Oone__class_Oone(_861594) = c_Groups_Oone__class_Oone(_861592))], (40673 ^ _781013) ^ [_1578320, _1578322, _1578324, _1578326, _1578328, _1578330] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578320, _1578322)), hAPP(hAPP(c_Product__Type_OPair(_1578320, _1578322), _1578324), _1578326)), hAPP(hAPP(c_Product__Type_OSigma(_1578320, _1578322), _1578328), _1578330))), -(hBOOL(hAPP(hAPP(c_member(_1578322), _1578326), hAPP(_1578330, _1578324))))], (31490 ^ _781013) ^ [_1374174, _1374176, _1374178] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1374174), _1374176), _1374178) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1374174, tc_HOL_Obool), tc_HOL_Obool)), -(_1374176 = c_Orderings_Obot__class_Obot(tc_fun(_1374174, tc_HOL_Obool)))], (36978 ^ _781013) ^ [_1486300, _1486302] : [-(_1486300 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36981 ^ _781013 : [(36988 ^ _781013) ^ [] : [-(_1486302 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1486300, _1486302) = 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, _1486302))), 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, _1486300)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1486302))), c_Divides_Opdivmod(_1486300, _1486302)), 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), _1486302))))), c_Divides_Opdivmod(_1486300, _1486302)))))], (36982 ^ _781013) ^ [] : [_1486302 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1486300, _1486302) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1486300))]]], (34735 ^ _781013) ^ [_1438815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1438815)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1438815), c_Int_OPls)))], (12282 ^ _781013) ^ [_1002707, _1002709, _1002711] : [class_Lattices_Olattice(_1002707), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002707), _1002709)), -(_1002711 = c_Orderings_Obot__class_Obot(tc_fun(_1002707, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002707, tc_HOL_Obool)), _1002711), _1002709)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1002707), c_Big__Operators_Olattice__class_OSup__fin(_1002707, _1002711)), c_Big__Operators_Olattice__class_OSup__fin(_1002707, _1002709)) = c_Big__Operators_Olattice__class_OSup__fin(_1002707, _1002709))], (30131 ^ _781013) ^ [_1343988, _1343990, _1343992] : [class_Orderings_Olinorder(_1343988), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343988), _1343990), _1343992)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343988), _1343992), _1343990) = _1343992)], (43615 ^ _781013) ^ [_1650398, _1650400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1650398), _1650400)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1650398, _1650400)) = _1650398)], (37907 ^ _781013) ^ [_1507143, _1507145, _1507147] : [-(c_Wellfounded_Omlex__prod(_1507143, _1507145, _1507147) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1507143), _1507143), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1507143, c_Wellfounded_Oless__than, _1507147)), hAPP(hAPP(c_COMBS(_1507143, _1507143, tc_prod(tc_Nat_Onat, _1507143)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1507143, tc_prod(tc_Nat_Onat, _1507143)), _1507143), c_Product__Type_OPair(tc_Nat_Onat, _1507143)), _1507145)), c_COMBI(_1507143))))], (37270 ^ _781013) ^ [_1492137, _1492139, _1492141] : [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), _1492137), _1492139))), -(hBOOL(hAPP(hAPP(_1492141, _1492137), _1492139))), 37277 ^ _781013 : [(37280 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1492141, 37275 ^ [_1492137, _1492139, _1492141]), 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)))), 37276 ^ [_1492137, _1492139, _1492141])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37275 ^ [_1492137, _1492139, _1492141]), 37276 ^ [_1492137, _1492139, _1492141]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 37276 ^ [_1492137, _1492139, _1492141]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37290 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1492141, 37275 ^ [_1492137, _1492139, _1492141]), 37276 ^ [_1492137, _1492139, _1492141]))], (37278 ^ _781013) ^ [] : [-(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), 37275 ^ [_1492137, _1492139, _1492141]), 37276 ^ [_1492137, _1492139, _1492141]))))]]], (34903 ^ _781013) ^ [_1441817, _1441819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1441817)), c_Int_OBit1(_1441819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1441817), _1441819)))], (28500 ^ _781013) ^ [_1312825, _1312827, _1312829] : [class_Orderings_Olinorder(_1312825), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312825), _1312827), _1312829)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312825), _1312827), _1312829) = _1312827)], (15269 ^ _781013) ^ [_1063633, _1063635, _1063637, _1063639] : [class_Groups_Oordered__comm__monoid__add(_1063633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063633), c_Groups_Ozero__class_Ozero(_1063633)), _1063635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063633), _1063637), _1063639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063633), _1063637), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063633), _1063635), _1063639))))], (4198 ^ _781013) ^ [_844503, _844505, _844507, _844509, _844511, _844513] : [-(c_Finite__Set_Ofold__image(_844513, _844509, _844505) = c_Finite__Set_Ofold__image(_844511, _844507, _844503)), _844513 = _844511, _844509 = _844507, _844505 = _844503], (37072 ^ _781013) ^ [_1488477, _1488479, _1488481, _1488483] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1488477, _1488479), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1488481), _1488483))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1488477, _1488479) = _1488483)], (17993 ^ _781013) ^ [_1116454, _1116456, _1116458] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116454), _1116456)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116458), _1116456)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1116456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116454), _1116458))], (41692 ^ _781013) ^ [_1603872, _1603874, _1603876] : [_1603872 = hAPP(hAPP(c_List_Oappend(_1603874), _1603872), _1603876), -(_1603876 = c_List_Olist_ONil(_1603874))], (48934 ^ _781013) ^ [_1772869, _1772871, _1772873] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1772869, _1772871, _1772871), _1772873), c_Relation_OId(_1772871)) = _1772873)], (26657 ^ _781013) ^ [_1277182, _1277184, _1277186] : [class_Orderings_Oord(_1277182), 26660 ^ _781013 : [(26667 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277182), _1277186), _1277184)), -(hBOOL(hAPP(hAPP(c_member(_1277182), _1277184), hAPP(c_SetInterval_Oord__class_OatLeast(_1277182), _1277186))))], (26661 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1277182), _1277184), hAPP(c_SetInterval_Oord__class_OatLeast(_1277182), _1277186))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277182), _1277186), _1277184)))]]], (10731 ^ _781013) ^ [_970475, _970477, _970479] : [class_Orderings_Olinorder(_970475), 10734 ^ _781013 : [(10741 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970475), _970479), _970477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970475), _970477), _970479))], (10735 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970475), _970477), _970479))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970475), _970479), _970477)))]]], (50830 ^ _781013) ^ [_1814302, _1814304, _1814306] : [-(c_List_Osplice(_1814302, hAPP(hAPP(c_List_Olist_OCons(_1814302), _1814304), _1814306), c_List_Olist_ONil(_1814302)) = hAPP(hAPP(c_List_Olist_OCons(_1814302), _1814304), _1814306))], (23032 ^ _781013) ^ [_1211980, _1211982] : [23034 ^ _781013 : [(23037 ^ _781013) ^ [] : [hBOOL(hAPP(_1211982, 23033 ^ [_1211980, _1211982]))], (23035 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 23033 ^ [_1211980, _1211982]), _1211980)))]], 23038 ^ _781013 : [(23039 ^ _781013) ^ [_1212130] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1212130), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211980))), -(hBOOL(hAPP(_1211982, _1212130)))]]], (51340 ^ _781013) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (20256 ^ _781013) ^ [_1159713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159713), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1159713 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11091 ^ _781013) ^ [_978242, _978244, _978246] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978242, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978242, tc_HOL_Obool)), _978244), _978246)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978242, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978242, tc_HOL_Obool)), _978244)), _978246))], (17066 ^ _781013) ^ [_1098209, _1098211, _1098213] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1098209), _1098211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1098209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1098209, tc_HOL_Obool)), _1098211), hAPP(hAPP(c_Set_Oinsert(_1098209), _1098213), c_Orderings_Obot__class_Obot(tc_fun(_1098209, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1098209), _1098211))))], (24164 ^ _781013) ^ [_1231663, _1231665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231665)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1231663)), hAPP(c_Int_Onat, _1231665)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231663), _1231665)))], (31162 ^ _781013) ^ [_1364714, _1364716, _1364718, _1364720, _1364722, _1364724] : [-(hBOOL(hAPP(_1364714, _1364716))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1364718), _1364716), _1364720), _1364722)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1364714, _1364724, _1364718)), _1364716), _1364720), _1364722)))], (7187 ^ _781013) ^ [_900900, _900902, _900904] : [_900900 = _900902, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900904, tc_HOL_Obool)), _900900), _900902)))], (29371 ^ _781013) ^ [_1328975, _1328977, _1328979] : [-(hBOOL(hAPP(_1328975, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1328977, _1328979)))), 29374 ^ _781013 : [(29377 ^ _781013) ^ [] : [hBOOL(hAPP(_1328975, _1328977))], (29375 ^ _781013) ^ [] : [-(_1328979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 29378 ^ _781013 : [(29383 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29381 ^ [_1328975, _1328977, _1328979]), _1328979)))], (29385 ^ _781013) ^ [] : [-(_1328977 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1328979), 29380 ^ [_1328975, _1328977, _1328979])), 29381 ^ [_1328975, _1328977, _1328979]))], (29387 ^ _781013) ^ [] : [hBOOL(hAPP(_1328975, 29381 ^ [_1328975, _1328977, _1328979]))], (29379 ^ _781013) ^ [] : [_1328979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (51390 ^ _781013) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (48649 ^ _781013) ^ [_1765299, _1765301] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1765299), _1765301) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1765299)), hAPP(c_Code__Numeral_Onat__of, _1765301))))], (41035 ^ _781013) ^ [_1589092, _1589094, _1589096, _1589098, _1589100, _1589102] : [class_Groups_Ocomm__monoid__add(_1589092), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589094), _1589096)), 41045 ^ _781013 : [(41048 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1589098), hAPP(_1589100, 41044 ^ [_1589092, _1589094, _1589096, _1589098, _1589100, _1589102])))], (41046 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589094), 41044 ^ [_1589092, _1589094, _1589096, _1589098, _1589100, _1589102]), _1589096)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1589094, _1589092), hAPP(hAPP(c_COMBS(_1589094, tc_fun(_1589098, tc_HOL_Obool), _1589092), hAPP(hAPP(c_COMBB(tc_fun(_1589098, _1589092), tc_fun(tc_fun(_1589098, tc_HOL_Obool), _1589092), _1589094), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1589098, _1589092)), _1589102)), _1589100)), _1589096) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1589094, _1589098), _1589092), hAPP(c_Product__Type_Oprod_Oprod__case(_1589094, _1589098, _1589092), _1589102)), hAPP(hAPP(c_Product__Type_OSigma(_1589094, _1589098), _1589096), _1589100)))], (8020 ^ _781013) ^ [_917135, _917137, _917139, _917141] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_917135), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917135, tc_HOL_Obool)), _917137), hAPP(hAPP(c_Set_Oinsert(_917135), _917139), _917141)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_917135), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917135, tc_HOL_Obool)), _917137), _917141))))], (21161 ^ _781013) ^ [_1178086, _1178088, _1178090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178086), _1178088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178088), _1178090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178086), _1178090)))], (51664 ^ _781013) ^ [_1825536, _1825538] : [hBOOL(_1825536), -(hBOOL(hAPP(hAPP(c_fdisj, _1825536), _1825538)))], (21885 ^ _781013) ^ [_1191692, _1191694, _1191696, _1191698] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1191692), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191694, tc_Nat_Onat), _1191696), _1191698)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191694, _1191692), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1191692, _1191694), c_Nat_Osemiring__1__class_Oof__nat(_1191692)), _1191696)), _1191698)), class_Groups_Ocomm__monoid__mult(_1191692), class_Rings_Osemiring__1(_1191692)], (51534 ^ _781013) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (11988 ^ _781013) ^ [_997135, _997137, _997139, _997141, _997143] : [c_Fun_Oinj__on(_997135, _997137, _997139, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_997135, tc_HOL_Obool)), _997141), _997143)), 11991 ^ _781013 : [(11998 ^ _781013) ^ [] : [_997141 = _997143, -(hAPP(c_Set_Oimage(_997135, _997137, _997139), _997141) = hAPP(c_Set_Oimage(_997135, _997137, _997139), _997143))], (11992 ^ _781013) ^ [] : [hAPP(c_Set_Oimage(_997135, _997137, _997139), _997141) = hAPP(c_Set_Oimage(_997135, _997137, _997139), _997143), -(_997141 = _997143)]]], (51318 ^ _781013) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (860 ^ _781013) ^ [_794153, _794155, _794157, _794159, _794161, _794163] : [-(c_Finite__Set_Ofun__left__comm(_794161, _794157, _794153)), c_Finite__Set_Ofun__left__comm(_794163, _794159, _794155), _794163 = _794161, _794159 = _794157, _794155 = _794153], (37425 ^ _781013) ^ [_1495487, _1495489] : [c_Relation_Oirrefl(_1495487, _1495489), 37428 ^ _781013 : [(37429 ^ _781013) ^ [_1495569] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1495487, _1495487)), hAPP(hAPP(c_Product__Type_OPair(_1495487, _1495487), _1495569), _1495569)), _1495489))]]], (21895 ^ _781013) ^ [_1191895, _1191897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1191895), _1191897)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191897)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191895)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1191897), _1191895)))], (34871 ^ _781013) ^ [_1441174] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1441174)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441174)), 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))))], (6627 ^ _781013) ^ [_889623, _889625, _889627, _889629, _889631, _889633] : [-(hAPP(hAPP(c_Fun_Ocomp(_889623, _889625, _889627, _889629), _889631), _889633) = hAPP(_889629, hAPP(_889631, _889633)))], (23092 ^ _781013) ^ [_1213103, _1213105] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213103))), -(c_SMT_Oz3div(_1213105, _1213103) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213105), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1213103))))], (35015 ^ _781013) ^ [_1443934, _1443936] : [class_Groups_Omonoid__mult(_1443934), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1443934), _1443936), 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(_1443934), _1443936), _1443936))], (738 ^ _781013) ^ [_792330, _792332, _792334, _792336, _792338, _792340] : [-(c_Relation_Osingle__valued(_792338, _792334, _792330)), c_Relation_Osingle__valued(_792340, _792336, _792332), _792340 = _792338, _792336 = _792334, _792332 = _792330], (42591 ^ _781013) ^ [_1624937, _1624939, _1624941, _1624943, _1624945] : [-(c_Map_Omap__upds(_1624937, _1624939, _1624941, _1624943, _1624945) = hAPP(c_List_Ofoldl(tc_fun(_1624937, tc_Option_Ooption(_1624939)), tc_prod(_1624937, _1624939), hAPP(hAPP(c_COMBB(tc_fun(_1624937, tc_fun(_1624939, tc_fun(_1624937, tc_Option_Ooption(_1624939)))), tc_fun(tc_prod(_1624937, _1624939), tc_fun(_1624937, tc_Option_Ooption(_1624939))), tc_fun(_1624937, tc_Option_Ooption(_1624939))), c_Product__Type_Oprod_Oprod__case(_1624937, _1624939, tc_fun(_1624937, tc_Option_Ooption(_1624939)))), hAPP(hAPP(c_COMBC(tc_fun(_1624937, tc_Option_Ooption(_1624939)), tc_fun(_1624939, tc_Option_Ooption(_1624939)), tc_fun(_1624937, tc_fun(_1624939, tc_fun(_1624937, tc_Option_Ooption(_1624939))))), hAPP(hAPP(c_COMBB(tc_fun(_1624937, tc_fun(tc_fun(_1624939, tc_Option_Ooption(_1624939)), tc_fun(_1624939, tc_fun(_1624937, tc_Option_Ooption(_1624939))))), tc_fun(tc_fun(_1624939, tc_Option_Ooption(_1624939)), tc_fun(_1624937, tc_fun(_1624939, tc_fun(_1624937, tc_Option_Ooption(_1624939))))), tc_fun(_1624937, tc_Option_Ooption(_1624939))), c_COMBC(_1624937, tc_fun(_1624939, tc_Option_Ooption(_1624939)), tc_fun(_1624939, tc_fun(_1624937, tc_Option_Ooption(_1624939))))), hAPP(hAPP(c_COMBB(tc_fun(_1624937, tc_fun(tc_Option_Ooption(_1624939), tc_fun(_1624937, tc_Option_Ooption(_1624939)))), tc_fun(_1624937, tc_fun(tc_fun(_1624939, tc_Option_Ooption(_1624939)), tc_fun(_1624939, tc_fun(_1624937, tc_Option_Ooption(_1624939))))), tc_fun(_1624937, tc_Option_Ooption(_1624939))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1624939), tc_fun(_1624937, tc_Option_Ooption(_1624939))), tc_fun(tc_fun(_1624939, tc_Option_Ooption(_1624939)), tc_fun(_1624939, tc_fun(_1624937, tc_Option_Ooption(_1624939)))), _1624937), c_COMBB(tc_Option_Ooption(_1624939), tc_fun(_1624937, tc_Option_Ooption(_1624939)), _1624939))), c_Fun_Ofun__upd(_1624937, tc_Option_Ooption(_1624939))))), c_Option_Ooption_OSome(_1624939))), _1624941), hAPP(hAPP(c_List_Ozip(_1624937, _1624939), _1624943), _1624945)))], (50580 ^ _781013) ^ [_1809317] : [class_HOL_Oequal(_1809317), -(c_fequal = c_HOL_Oequal__class_Oequal(_1809317))], (20522 ^ _781013) ^ [_1164389, _1164391] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1164389), _1164391) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1164391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1164389 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31670 ^ _781013) ^ [_1379382, _1379384, _1379386] : [-(hAPP(c_Relation_OImage(_1379382, _1379384, _1379386), c_Orderings_Obot__class_Obot(tc_fun(_1379382, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1379384, tc_HOL_Obool)))], (28424 ^ _781013) ^ [_1311478, _1311480, _1311482, _1311484] : [class_Groups_Oordered__ab__group__add__abs(_1311478), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311478), c_Groups_Ozero__class_Ozero(_1311478)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1311480, _1311478), hAPP(hAPP(c_COMBB(_1311478, _1311478, _1311480), c_Groups_Oabs__class_Oabs(_1311478)), _1311482)), _1311484))))], (41616 ^ _781013) ^ [_1602456, _1602458, _1602460, _1602462, _1602464] : [-(hAPP(hAPP(c_List_Oappend(_1602456), _1602458), _1602460) = hAPP(hAPP(c_List_Olist_OCons(_1602456), _1602462), _1602464)), 41617 ^ _781013 : [(41624 ^ _781013) ^ [_1602639] : [_1602458 = hAPP(hAPP(c_List_Olist_OCons(_1602456), _1602462), _1602639), hAPP(hAPP(c_List_Oappend(_1602456), _1602639), _1602460) = _1602464], (41618 ^ _781013) ^ [] : [_1602458 = c_List_Olist_ONil(_1602456), _1602460 = hAPP(hAPP(c_List_Olist_OCons(_1602456), _1602462), _1602464)]]], (18157 ^ _781013) ^ [_1119293, _1119295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119293), _1119295)), 18160 ^ _781013 : [(18163 ^ _781013) ^ [] : [_1119293 = _1119295], (18161 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119293), _1119295)))]]], (41272 ^ _781013) ^ [_1594541, _1594543, _1594545, _1594547] : [hAPP(hAPP(c_List_Olist__update(_1594541, _1594543), _1594545), _1594547) = c_List_Olist_ONil(_1594541), -(_1594543 = c_List_Olist_ONil(_1594541))], (27849 ^ _781013) ^ [_1301060, _1301062, _1301064, _1301066] : [class_Divides_Osemiring__div(_1301060), -(c_Divides_Odiv__class_Omod(_1301060, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1301060), _1301062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301060), _1301064), _1301066)), _1301064) = c_Divides_Odiv__class_Omod(_1301060, _1301062, _1301064))], (32758 ^ _781013) ^ [_1402393, _1402395, _1402397] : [class_Int_Onumber__ring(_1402393), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1402393), hAPP(c_Int_Onumber__class_Onumber__of(_1402393), _1402395)), hAPP(c_Int_Onumber__class_Onumber__of(_1402393), _1402397)) = hAPP(c_Int_Onumber__class_Onumber__of(_1402393), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1402395), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1402397))))], (43295 ^ _781013) ^ [_1643183, _1643185, _1643187] : [hAPP(c_List_Ofilter(_1643183, _1643185), _1643187) = c_List_Olist_ONil(_1643183), 43298 ^ _781013 : [(43299 ^ _781013) ^ [_1643280] : [hBOOL(hAPP(hAPP(c_member(_1643183), _1643280), hAPP(c_List_Oset(_1643183), _1643187))), hBOOL(hAPP(_1643185, _1643280))]]], (41346 ^ _781013) ^ [_1595867, _1595869, _1595871] : [_1595867 = c_List_Olist_ONil(_1595869), -(c_List_Obutlast(_1595869, hAPP(hAPP(c_List_Olist_OCons(_1595869), _1595871), _1595867)) = c_List_Olist_ONil(_1595869))], (15475 ^ _781013) ^ [_1067232, _1067234, _1067236] : [class_Rings_Oordered__cancel__semiring(_1067232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067232), _1067234), c_Groups_Ozero__class_Ozero(_1067232))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067232), c_Groups_Ozero__class_Ozero(_1067232)), _1067236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067232), _1067234), _1067236)), c_Groups_Ozero__class_Ozero(_1067232))))], (21251 ^ _781013) ^ [_1179624, _1179626, _1179628, _1179630, _1179632] : [c_Hoare__Mirabelle_Otriple__valid(_1179624, _1179626, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1179624), _1179628), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1179630))), _1179632)), -(c_Hoare__Mirabelle_Otriple__valid(_1179624, hAPP(c_Nat_OSuc, _1179626), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1179624), _1179628), hAPP(c_Com_Ocom_OBODY, _1179630)), _1179632)))], (3012 ^ _781013) ^ [_826100, _826102, _826104, _826106] : [-(c_List_Olistsp(_826106, _826102) = c_List_Olistsp(_826104, _826100)), _826106 = _826104, _826102 = _826100], (27922 ^ _781013) ^ [_1302271] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1302271, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1302271)], (27671 ^ _781013) ^ [_1297553, _1297555, _1297557, _1297559, _1297561, _1297563] : [class_Divides_Osemiring__div(_1297553), c_Divides_Odiv__class_Omod(_1297553, _1297555, _1297557) = c_Divides_Odiv__class_Omod(_1297553, _1297559, _1297557), c_Divides_Odiv__class_Omod(_1297553, _1297561, _1297557) = c_Divides_Odiv__class_Omod(_1297553, _1297563, _1297557), -(c_Divides_Odiv__class_Omod(_1297553, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297553), _1297555), _1297561), _1297557) = c_Divides_Odiv__class_Omod(_1297553, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297553), _1297559), _1297563), _1297557))], (44268 ^ _781013) ^ [_1663024, _1663026, _1663028] : [_1663026 = hAPP(hAPP(c_List_Olist_OCons(_1663024), _1663028), c_List_Olist_ONil(_1663024)), -(hAPP(c_List_Orev(_1663024), _1663026) = hAPP(hAPP(c_List_Olist_OCons(_1663024), _1663028), c_List_Olist_ONil(_1663024)))], (12882 ^ _781013) ^ [_1014680, _1014682, _1014684, _1014686, _1014688] : [hBOOL(hAPP(hAPP(c_member(_1014680), hAPP(_1014682, _1014684)), _1014686)), -(hBOOL(hAPP(hAPP(c_member(_1014688), _1014684), hAPP(c_Set_Ovimage(_1014688, _1014680, _1014682), _1014686))))], (40854 ^ _781013) ^ [_1583551, _1583553, _1583555, _1583557, _1583559, _1583561] : [-(hAPP(c_Set_Ovimage(_1583551, tc_prod(_1583553, _1583555), _1583557), hAPP(hAPP(c_Product__Type_OSigma(_1583553, _1583555), _1583559), hAPP(c_COMBK(tc_fun(_1583555, tc_HOL_Obool), _1583553), _1583561))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1583551, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1583551, _1583553, hAPP(c_Fun_Ocomp(tc_prod(_1583553, _1583555), _1583553, _1583551, c_Product__Type_Ofst(_1583553, _1583555)), _1583557)), _1583559)), hAPP(c_Set_Ovimage(_1583551, _1583555, hAPP(c_Fun_Ocomp(tc_prod(_1583553, _1583555), _1583555, _1583551, c_Product__Type_Osnd(_1583553, _1583555)), _1583557)), _1583561)))], (18534 ^ _781013) ^ [_1125914, _1125916, _1125918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1125914), _1125918)), _1125916)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125914), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1125916), _1125918))))], (43191 ^ _781013) ^ [_1640551, _1640553, _1640555, _1640557, _1640559] : [class_Complete__Lattice_Ocomplete__lattice(_1640551), hBOOL(hAPP(hAPP(c_member(_1640553), _1640555), _1640557)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1640551), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640553, _1640551), _1640557), _1640559)), hAPP(_1640559, _1640555))))], (3796 ^ _781013) ^ [_838418, _838420] : [_838420 = _838418, -(c_List_Odistinct(_838420) = c_List_Odistinct(_838418))], (3040 ^ _781013) ^ [_826550, _826552, _826554, _826556, _826558, _826560] : [-(c_List_Osublist(_826560, _826556, _826552) = c_List_Osublist(_826558, _826554, _826550)), _826560 = _826558, _826556 = _826554, _826552 = _826550], (40191 ^ _781013) ^ [_1564717, _1564719, _1564721, _1564723, _1564725, _1564727] : [class_Orderings_Olinorder(_1564717), 40194 ^ _781013 : [(40201 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1564717), hAPP(_1564719, _1564721)), hAPP(_1564719, _1564723)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1564725, _1564717, _1564719), _1564721), hAPP(hAPP(c_List_Olist_OCons(_1564725), _1564723), _1564727)) = hAPP(hAPP(c_List_Olist_OCons(_1564725), _1564723), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1564725, _1564717, _1564719), _1564721), _1564727)))], (40195 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1564717), hAPP(_1564719, _1564721)), hAPP(_1564719, _1564723))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1564725, _1564717, _1564719), _1564721), hAPP(hAPP(c_List_Olist_OCons(_1564725), _1564723), _1564727)) = hAPP(hAPP(c_List_Olist_OCons(_1564725), _1564721), hAPP(hAPP(c_List_Olist_OCons(_1564725), _1564723), _1564727)))]]], (1854 ^ _781013) ^ [_806930, _806932] : [-(hBOOL(_806930)), _806932 = _806930, hBOOL(_806932)], (44801 ^ _781013) ^ [_1675456] : [-(c_List_Oembed__list(_1675456) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1675456))], (22091 ^ _781013) ^ [_1195229, _1195231, _1195233] : [-(hBOOL(hAPP(_1195229, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1195231), _1195233))))), 22094 ^ _781013 : [(22097 ^ _781013) ^ [] : [hBOOL(hAPP(_1195229, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1195231)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1195233))))], (22095 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1195233), _1195231)))]], 22098 ^ _781013 : [(22101 ^ _781013) ^ [] : [hBOOL(hAPP(_1195229, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22099 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1195231), _1195233)))]]], (4302 ^ _781013) ^ [_846073, _846075, _846077, _846079] : [-(c_Big__Operators_Olinorder__class_OMin(_846079, _846075) = c_Big__Operators_Olinorder__class_OMin(_846077, _846073)), _846079 = _846077, _846075 = _846073], (47230 ^ _781013) ^ [_1732410, _1732412, _1732414, _1732416] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1732410, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1732410, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1732410, _1732412), _1732414)), hAPP(c_Relation_ODomain(_1732410, _1732412), _1732416))), hAPP(c_Relation_ODomain(_1732410, _1732412), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1732410, _1732412), tc_HOL_Obool)), _1732414), _1732416)))))], (18021 ^ _781013) ^ [_1116996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116996), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23190 ^ _781013) ^ [_1214745, _1214747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214745)), 23193 ^ _781013 : [(23200 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1214747), _1214745))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1214747), _1214745) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1214747), _1214745)), _1214745)))], (23194 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1214747), _1214745)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1214747), _1214745) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19783 ^ _781013) ^ [_1151824, _1151826, _1151828] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151824), _1151826)), _1151828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151824), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151826), _1151828)))], (15255 ^ _781013) ^ [_1063380, _1063382, _1063384, _1063386] : [class_Groups_Oordered__comm__monoid__add(_1063380), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063380), c_Groups_Ozero__class_Ozero(_1063380)), _1063382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063380), _1063384), _1063386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063380), _1063384), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063380), _1063386), _1063382))))], (13247 ^ _781013) ^ [_1022463, _1022465, _1022467, _1022469, _1022471, _1022473, _1022475] : [class_Groups_Oab__semigroup__mult(_1022463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022465), _1022467)), c_Fun_Oinj__on(_1022465, _1022469, _1022471, _1022467), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1022463, _1022469, c_Groups_Otimes__class_Otimes(_1022463)), _1022473), _1022475), hAPP(c_Set_Oimage(_1022465, _1022469, _1022471), _1022467)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1022463, _1022465, c_Groups_Otimes__class_Otimes(_1022463)), hAPP(c_Fun_Ocomp(_1022469, _1022463, _1022465, _1022473), _1022471)), _1022475), _1022467))], (19827 ^ _781013) ^ [_1152493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1152493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1152493)))], (41650 ^ _781013) ^ [_1603134, _1603136, _1603138] : [hAPP(hAPP(c_List_Oappend(_1603134), _1603136), _1603138) = _1603136, -(_1603138 = c_List_Olist_ONil(_1603134))], (21981 ^ _781013) ^ [_1193356] : [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), _1193356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193356)))], (9068 ^ _781013) ^ [_940740, _940742, _940744, _940746, _940748, _940750] : [hBOOL(hAPP(hAPP(c_member(_940740), _940742), _940744)), -(c_Map_Orestrict__map(_940740, _940746, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_940740, tc_Option_Ooption(_940746)), _940748), _940742), _940750), _940744) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_940740, tc_Option_Ooption(_940746)), c_Map_Orestrict__map(_940740, _940746, _940748, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940740, tc_HOL_Obool)), _940744), hAPP(hAPP(c_Set_Oinsert(_940740), _940742), c_Orderings_Obot__class_Obot(tc_fun(_940740, tc_HOL_Obool)))))), _940742), _940750))], (33314 ^ _781013) ^ [_1413402] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413402) = _1413402)], (48407 ^ _781013) ^ [_1759653, _1759655, _1759657, _1759659, _1759661] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1759653, _1759653)), hAPP(hAPP(c_Product__Type_OPair(_1759653, _1759653), _1759655), _1759657)), c_Transitive__Closure_Ortrancl(_1759653, _1759659))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1759653, _1759653)), hAPP(hAPP(c_Product__Type_OPair(_1759653, _1759653), _1759657), _1759661)), c_Transitive__Closure_Otrancl(_1759653, _1759659))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1759653, _1759653)), hAPP(hAPP(c_Product__Type_OPair(_1759653, _1759653), _1759655), _1759661)), c_Transitive__Closure_Otrancl(_1759653, _1759659))))], (50256 ^ _781013) ^ [_1802951] : [-(c_Nitpick_Odenom(_1802951) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1802951, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1802951)))], (28636 ^ _781013) ^ [_1315163, _1315165, _1315167, _1315169] : [class_Groups_Oordered__ab__group__add(_1315163), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1315163), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315163), _1315165), _1315167)), _1315169) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315163), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1315163), _1315165), _1315169)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1315163), _1315167), _1315169)))], (51226 ^ _781013) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (6274 ^ _781013) ^ [_882999, _883001, _883003, _883005] : [c_Com_Ocom_OCond(_882999, _883001, _883003) = hAPP(c_Com_Ocom_OBODY, _883005)], (26941 ^ _781013) ^ [_1282447, _1282449, _1282451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1282447)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1282449), _1282451)), 26948 ^ _781013 : [(26949 ^ _781013) ^ [_1282643] : [26951 ^ _781013 : [(26957 ^ _781013) ^ [] : [-(_1282643 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26953 ^ [_1282447, _1282449, _1282451, _1282643]), 26950 ^ [_1282447, _1282449, _1282451, _1282643]))], (26955 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26953 ^ [_1282447, _1282449, _1282451, _1282643]), _1282451)))], (26952 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26950 ^ [_1282447, _1282449, _1282451, _1282643]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1282447))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1282643), _1282449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1282643), _1282447)), _1282449)))]]], (35909 ^ _781013) ^ [_1460099, _1460101, _1460103, _1460105] : [hAPP(hAPP(c_COMBC(_1460099, tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_fun(_1460101, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460101, tc_fun(tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_fun(_1460101, tc_HOL_Obool)), _1460099), c_COMBC(_1460101, tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460101, tc_prod(_1460099, _1460101)), tc_fun(_1460101, tc_fun(tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_HOL_Obool)), _1460099), hAPP(c_COMBB(tc_prod(_1460099, _1460101), tc_fun(tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_HOL_Obool), _1460101), c_member(tc_prod(_1460099, _1460101)))), c_Product__Type_OPair(_1460099, _1460101)))), _1460103) = hAPP(hAPP(c_COMBC(_1460099, tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_fun(_1460101, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460101, tc_fun(tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_fun(_1460101, tc_HOL_Obool)), _1460099), c_COMBC(_1460101, tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460101, tc_prod(_1460099, _1460101)), tc_fun(_1460101, tc_fun(tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_HOL_Obool)), _1460099), hAPP(c_COMBB(tc_prod(_1460099, _1460101), tc_fun(tc_fun(tc_prod(_1460099, _1460101), tc_HOL_Obool), tc_HOL_Obool), _1460101), c_member(tc_prod(_1460099, _1460101)))), c_Product__Type_OPair(_1460099, _1460101)))), _1460105), -(_1460103 = _1460105)], (36504 ^ _781013) ^ [_1477344, _1477346, _1477348, _1477350, _1477352, _1477354, _1477356] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1477344, _1477346, tc_fun(_1477348, tc_HOL_Obool)), _1477350), hAPP(hAPP(c_Product__Type_OPair(_1477344, _1477346), _1477352), _1477354)), _1477356)), -(hBOOL(hAPP(hAPP(hAPP(_1477350, _1477352), _1477354), _1477356)))], (27164 ^ _781013) ^ [_1286753, _1286755] : [class_Orderings_Olinorder(_1286753), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1286753, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1286753), _1286755)) = hAPP(c_SetInterval_Oord__class_OatMost(_1286753), _1286755))], (688 ^ _781013) ^ [_791599, _791601, _791603, _791605, _791607, _791609] : [-(c_Equiv__Relations_Oequiv(_791607, _791603, _791599)), c_Equiv__Relations_Oequiv(_791609, _791605, _791601), _791609 = _791607, _791605 = _791603, _791601 = _791599], (5132 ^ _781013) ^ [_859256, _859258, _859260, _859262, _859264, _859266] : [-(c_List_Osplice(_859266, _859262, _859258) = c_List_Osplice(_859264, _859260, _859256)), _859266 = _859264, _859262 = _859260, _859258 = _859256], (32372 ^ _781013) ^ [_1395192, _1395194, _1395196, _1395198] : [c_Com_Ocom_OLocal(_1395192, _1395194, _1395196) = hAPP(c_Com_Ocom_OBODY, _1395198)], (44356 ^ _781013) ^ [_1664907] : [-(c_List_Oconcat(_1664907, c_List_Olist_ONil(tc_List_Olist(_1664907))) = c_List_Olist_ONil(_1664907))], (16329 ^ _781013) ^ [_1082917, _1082919, _1082921] : [-(hBOOL(hAPP(_1082917, _1082919))), -(hAPP(c_Set_OCollect(_1082921), hAPP(hAPP(c_COMBS(_1082921, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1082921), c_fconj), hAPP(hAPP(c_COMBC(_1082921, _1082921, tc_HOL_Obool), c_fequal), _1082919))), _1082917)) = c_Orderings_Obot__class_Obot(tc_fun(_1082921, tc_HOL_Obool)))], (31347 ^ _781013) ^ [_1368609, _1368611] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _1368609), _1368611), _1368609)))], (51552 ^ _781013) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (34409 ^ _781013) ^ [] : [-(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)))))], (11656 ^ _781013) ^ [_990884] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_990884), c_Orderings_Otop__class_Otop(tc_fun(_990884, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_990884)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_990884), tc_HOL_Obool)))))], (21015 ^ _781013) ^ [_1174574, _1174576, _1174578] : [class_Lattices_Odistrib__lattice(_1174574), hBOOL(hAPP(c_Finite__Set_Ofinite(_1174574), _1174576)), -(_1174576 = c_Orderings_Obot__class_Obot(tc_fun(_1174574, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1174574), _1174578), c_Big__Operators_Olattice__class_OInf__fin(_1174574, _1174576)) = c_Big__Operators_Olattice__class_OInf__fin(_1174574, hAPP(c_Set_OCollect(_1174574), hAPP(hAPP(c_COMBB(tc_fun(_1174574, tc_HOL_Obool), tc_HOL_Obool, _1174574), c_HOL_OEx(_1174574)), hAPP(hAPP(c_COMBC(_1174574, tc_fun(_1174574, tc_HOL_Obool), tc_fun(_1174574, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1174574, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1174574, tc_HOL_Obool), tc_fun(_1174574, tc_HOL_Obool)), _1174574), c_COMBS(_1174574, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1174574, tc_HOL_Obool), tc_fun(_1174574, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1174574), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1174574), c_fconj)), hAPP(hAPP(c_COMBC(_1174574, tc_fun(_1174574, _1174574), tc_fun(_1174574, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1174574, tc_HOL_Obool), tc_fun(tc_fun(_1174574, _1174574), tc_fun(_1174574, tc_HOL_Obool)), _1174574), c_COMBB(_1174574, tc_HOL_Obool, _1174574)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1174574), _1174578))))), hAPP(hAPP(c_COMBC(_1174574, tc_fun(_1174574, tc_HOL_Obool), tc_HOL_Obool), c_member(_1174574)), _1174576))))))], (2422 ^ _781013) ^ [_816877, _816879, _816881, _816883] : [-(c_Com_Ocom_OSemi(_816883, _816879) = c_Com_Ocom_OSemi(_816881, _816877)), _816883 = _816881, _816879 = _816877], (33692 ^ _781013) ^ [_1419672] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419672), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1419672), c_Int_OPls)))], (35073 ^ _781013) ^ [_1444959] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444959), _1444959)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1444959)], (49318 ^ _781013) ^ [_1782629, _1782631, _1782633, _1782635, _1782637] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1782629, _1782629)), hAPP(hAPP(c_Product__Type_OPair(_1782629, _1782629), _1782631), _1782633)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1782629, _1782629), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1782635)), _1782637))), 49322 ^ _781013 : [(49325 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782629, _1782629)), hAPP(hAPP(c_Product__Type_OPair(_1782629, _1782629), 49321 ^ [_1782629, _1782631, _1782633, _1782635, _1782637]), _1782633)), _1782637)))], (49323 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782629, _1782629)), hAPP(hAPP(c_Product__Type_OPair(_1782629, _1782629), _1782631), 49321 ^ [_1782629, _1782631, _1782633, _1782635, _1782637])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1782629, _1782629), tc_HOL_Obool), _1782635), _1782637))))]]], (34523 ^ _781013) ^ [_1435017, _1435019] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1435017, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1435019)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1435017, 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)))), _1435019)))], (41724 ^ _781013) ^ [_1604413, _1604415] : [-(hAPP(hAPP(c_List_Oappend(_1604413), c_List_Olist_ONil(_1604413)), _1604415) = _1604415)], (50539 ^ _781013) ^ [_1808570, _1808572] : [-(c_FunDef_Ois__measure(_1808570, _1808572))], (49452 ^ _781013) ^ [_1786287, _1786289, _1786291] : [class_Orderings_Olinorder(_1786287), hBOOL(hAPP(c_Finite__Set_Ofinite(_1786287), _1786289)), -(hBOOL(hAPP(hAPP(c_member(_1786287), _1786291), _1786289))), -(c_Big__Operators_Olattice_OSup__fin(_1786287, c_Orderings_Oord__class_Omax(_1786287), hAPP(hAPP(c_Set_Oinsert(_1786287), _1786291), _1786289)) = hAPP(hAPP(c_Finite__Set_Ofold(_1786287, _1786287, c_Orderings_Oord__class_Omax(_1786287)), _1786291), _1786289))], (48519 ^ _781013) ^ [_1762035, _1762037] : [-(c_Transitive__Closure_Otrancl(_1762035, c_Transitive__Closure_Ortrancl(_1762035, _1762037)) = c_Transitive__Closure_Ortrancl(_1762035, _1762037))], (18334 ^ _781013) ^ [_1122366, _1122368, _1122370] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122366), _1122368)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122370), _1122368)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122366), _1122370))], (18670 ^ _781013) ^ [_1128933, _1128935, _1128937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128933), _1128935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128937), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128935), _1128937)), _1128933))))], (46182 ^ _781013) ^ [_1705504, _1705506, _1705508, _1705510, _1705512] : [c_List_Olist__all2(_1705504, _1705506, _1705508, hAPP(c_List_Orev(_1705504), _1705510), hAPP(c_List_Orev(_1705506), _1705512)), -(c_List_Olist__all2(_1705504, _1705506, _1705508, _1705510, _1705512))], (15801 ^ _781013) ^ [_1073359, _1073361, _1073363] : [class_Rings_Olinordered__ring__strict(_1073359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073359), _1073361), c_Groups_Ozero__class_Ozero(_1073359))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073359), _1073363), c_Groups_Ozero__class_Ozero(_1073359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073359), c_Groups_Ozero__class_Ozero(_1073359)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073359), _1073361), _1073363))))], (12494 ^ _781013) ^ [_1006613, _1006615, _1006617] : [class_Lattices_Olattice(_1006613), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006613), _1006615)), -(_1006615 = c_Orderings_Obot__class_Obot(tc_fun(_1006613, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006613), _1006617)), -(_1006617 = c_Orderings_Obot__class_Obot(tc_fun(_1006613, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006613, tc_HOL_Obool)), _1006615), _1006617) = c_Orderings_Obot__class_Obot(tc_fun(_1006613, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1006613, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006613, tc_HOL_Obool)), _1006615), _1006617)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006613), c_Big__Operators_Olattice__class_OSup__fin(_1006613, _1006615)), c_Big__Operators_Olattice__class_OSup__fin(_1006613, _1006617)))], (43314 ^ _781013) ^ [_1643505, _1643507, _1643509] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1643505), tc_List_Olist(_1643505)), c_List_Opartition(_1643505, _1643507, _1643509)) = hAPP(c_List_Ofilter(_1643505, _1643507), _1643509))], (35835 ^ _781013) ^ [_1458572, _1458574] : [_1458572 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1458572, _1458574) = _1458574)], (29185 ^ _781013) ^ [_1325409, _1325411, _1325413, _1325415, _1325417] : [class_Groups_Oordered__ab__group__add__abs(_1325409), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325409), hAPP(c_Groups_Oabs__class_Oabs(_1325409), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1325409), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325409), _1325411), _1325413)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325409), _1325415), _1325417)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325409), hAPP(c_Groups_Oabs__class_Oabs(_1325409), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1325409), _1325411), _1325415))), hAPP(c_Groups_Oabs__class_Oabs(_1325409), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1325409), _1325413), _1325417))))))], (41975 ^ _781013) ^ [_1610591, _1610593, _1610595, _1610597, _1610599] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610591), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610593)), _1610595)))), -(hAPP(hAPP(c_List_Olist__update(_1610593, hAPP(hAPP(c_List_Oappend(_1610593), _1610595), _1610597)), _1610591), _1610599) = hAPP(hAPP(c_List_Oappend(_1610593), _1610595), hAPP(hAPP(c_List_Olist__update(_1610593, _1610597), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1610591), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610593)), _1610595))), _1610599)))], (50694 ^ _781013) ^ [_1811244] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1811244), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1811244)), c_Int_OPls)))], (17795 ^ _781013) ^ [_1113072, _1113074, _1113076] : [_1113074 = _1113076, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113072), _1113074) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113072), _1113076))], (20268 ^ _781013) ^ [_1159893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159893)), -(_1159893 = hAPP(c_Nat_OSuc, 20271 ^ [_1159893]))], (1936 ^ _781013) ^ [_808982, _808984, _808986, _808988] : [-(c_Option_Oset(_808988, _808984) = c_Option_Oset(_808986, _808982)), _808988 = _808986, _808984 = _808982], (7955 ^ _781013) ^ [_915509, _915511, _915513, _915515] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_915509, tc_Option_Ooption(_915511)), hAPP(c_COMBK(tc_Option_Ooption(_915511), _915509), c_Option_Ooption_ONone(_915511))), _915513), c_Option_Ooption_ONone(_915511)), _915515) = c_Option_Ooption_ONone(_915511))], (48990 ^ _781013) ^ [_1773978, _1773980, _1773982] : [c_Relation_Osingle__valued(_1773978, _1773980, _1773982), 48993 ^ _781013 : [(48994 ^ _781013) ^ [_1774099, _1774101] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773978, _1773980)), hAPP(hAPP(c_Product__Type_OPair(_1773978, _1773980), _1774101), _1774099)), _1773982)), 48997 ^ _781013 : [(48998 ^ _781013) ^ [_1774225] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773978, _1773980)), hAPP(hAPP(c_Product__Type_OPair(_1773978, _1773980), _1774101), _1774225)), _1773982)), -(_1774099 = _1774225)]]]]], (21625 ^ _781013) ^ [_1187147, _1187149] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187147)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187149)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1187147), _1187149)))], (51252 ^ _781013) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (5398 ^ _781013) ^ [_863343, _863345] : [_863345 = _863343, -(c_List_Olist_ONil(_863345) = c_List_Olist_ONil(_863343))], (33810 ^ _781013) ^ [_1421568, _1421570] : [class_Int_Onumber__ring(_1421568), class_Rings_Olinordered__idom(_1421568), 33817 ^ _781013 : [(33824 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1421570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421568), c_Groups_Ozero__class_Ozero(_1421568)), hAPP(c_Int_Onumber__class_Onumber__of(_1421568), _1421570))))], (33818 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421568), c_Groups_Ozero__class_Ozero(_1421568)), hAPP(c_Int_Onumber__class_Onumber__of(_1421568), _1421570))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1421570)))]]], (8034 ^ _781013) ^ [_917506, _917508, _917510, _917512, _917514] : [-(c_Map_Odom(_917506, _917508, hAPP(hAPP(c_COMBS(_917506, tc_Option_Ooption(_917510), tc_Option_Ooption(_917508)), hAPP(hAPP(c_COMBB(tc_fun(_917510, _917508), tc_fun(tc_Option_Ooption(_917510), tc_Option_Ooption(_917508)), _917506), c_Option_Omap(_917510, _917508)), _917512)), _917514)) = c_Map_Odom(_917506, _917510, _917514))], (40643 ^ _781013) ^ [_1577469, _1577471, _1577473, _1577475, _1577477] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1577469, _1577471), _1577473), hAPP(hAPP(c_COMBS(_1577469, tc_fun(_1577471, tc_HOL_Obool), tc_fun(_1577471, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577471, tc_HOL_Obool), tc_fun(tc_fun(_1577471, tc_HOL_Obool), tc_fun(_1577471, tc_HOL_Obool)), _1577469), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577471, tc_HOL_Obool))), _1577475)), _1577477)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1577469, _1577471), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1577469, _1577471), _1577473), _1577475)), hAPP(hAPP(c_Product__Type_OSigma(_1577469, _1577471), _1577473), _1577477)))], (22136 ^ _781013) ^ [_1196230, _1196232, _1196234] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1196230), _1196232))), 22139 ^ _781013 : [(22146 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1196234), _1196232))), -(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)), _1196230)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1196234), _1196232)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (22140 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1196234), _1196232)), -(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)), _1196230)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1196234), _1196232)) = 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))))]]], (24560 ^ _781013) ^ [_1239133, _1239135, _1239137, _1239139] : [class_Fields_Olinordered__field__inverse__zero(_1239133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239133), _1239135), _1239137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239133), c_Groups_Ozero__class_Ozero(_1239133)), _1239139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239133), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239133), _1239135), _1239139)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239133), _1239137), _1239139))))], (21229 ^ _781013) ^ [_1179276, _1179278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179278)), -(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), _1179276), _1179278))))], (11522 ^ _781013) ^ [_988184, _988186] : [class_Lattices_Oab__semigroup__idem__mult(_988184), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988184), _988186), _988186) = _988186)], (2290 ^ _781013) ^ [_814887, _814889, _814891, _814893] : [-(c_SMT_Oz3div(_814893, _814889) = c_SMT_Oz3div(_814891, _814887)), _814893 = _814891, _814889 = _814887], (35613 ^ _781013) ^ [_1455001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1455001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1455001))))], (9178 ^ _781013) ^ [_943163, _943165, _943167, _943169, _943171] : [-(hBOOL(hAPP(hAPP(c_member(_943163), _943165), _943167))), -(hAPP(c_Map_Orestrict__map(_943163, _943169, _943171, _943167), _943165) = c_Option_Ooption_ONone(_943169))], (6826 ^ _781013) ^ [_893583, _893585, _893587, _893589] : [hBOOL(hAPP(hAPP(c_member(_893583), _893585), hAPP(hAPP(c_Set_Oinsert(_893583), _893587), _893589))), -(_893585 = _893587), -(hBOOL(hAPP(hAPP(c_member(_893583), _893585), _893589)))], (46152 ^ _781013) ^ [_1704933, _1704935, _1704937, _1704939, _1704941, _1704943] : [c_List_Olist__all2(_1704933, _1704935, _1704937, _1704939, _1704941), -(c_List_Olist__all2(_1704933, _1704935, _1704937, hAPP(hAPP(c_List_Otake(_1704933), _1704943), _1704939), hAPP(hAPP(c_List_Otake(_1704935), _1704943), _1704941)))], (46377 ^ _781013) ^ [_1709921, _1709923, _1709925] : [-(c_List_Oinsert(_1709921, _1709923, c_List_Oremdups(_1709921, _1709925)) = c_List_Oremdups(_1709921, c_List_Oinsert(_1709921, _1709923, _1709925)))], (5625 ^ _781013) ^ [_869730, _869732, _869734, _869736, _869738] : [hAPP(hAPP(c_Set_Oinsert(_869730), _869732), hAPP(hAPP(c_Set_Oinsert(_869730), _869734), c_Orderings_Obot__class_Obot(tc_fun(_869730, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_869730), _869736), hAPP(hAPP(c_Set_Oinsert(_869730), _869738), c_Orderings_Obot__class_Obot(tc_fun(_869730, tc_HOL_Obool)))), 5630 ^ _781013 : [(5633 ^ _781013) ^ [] : [-(_869734 = _869738)], (5631 ^ _781013) ^ [] : [-(_869732 = _869736)]], 5634 ^ _781013 : [(5637 ^ _781013) ^ [] : [-(_869734 = _869736)], (5635 ^ _781013) ^ [] : [-(_869732 = _869738)]]], (38908 ^ _781013) ^ [_1530763, _1530765, _1530767, _1530769, _1530771] : [c_Fun_Oinj__on(_1530763, _1530765, _1530767, c_Orderings_Otop__class_Otop(tc_fun(_1530763, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1530763, _1530765), _1530767), hAPP(c_List_OremoveAll(_1530763, _1530769), _1530771)) = hAPP(c_List_OremoveAll(_1530765, hAPP(_1530767, _1530769)), hAPP(hAPP(c_List_Omap(_1530763, _1530765), _1530767), _1530771)))], (23963 ^ _781013) ^ [_1228357] : [-(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)), _1228357)) = hAPP(c_Int_Onat, _1228357))], (27785 ^ _781013) ^ [_1299966, _1299968, _1299970, _1299972] : [class_Divides_Oring__div(_1299966), -(c_Divides_Odiv__class_Omod(_1299966, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1299966), _1299968), _1299970), _1299972) = c_Divides_Odiv__class_Omod(_1299966, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1299966), _1299968), c_Divides_Odiv__class_Omod(_1299966, _1299970, _1299972)), _1299972))], (46389 ^ _781013) ^ [_1710175, _1710177, _1710179] : [hBOOL(hAPP(hAPP(c_member(_1710175), _1710177), hAPP(c_List_Oset(_1710175), _1710179))), -(c_List_Oinsert(_1710175, _1710177, _1710179) = _1710179)], (15657 ^ _781013) ^ [_1070685, _1070687, _1070689] : [class_Groups_Oordered__comm__monoid__add(_1070685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070685), _1070687), c_Groups_Ozero__class_Ozero(_1070685))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070685), _1070689), c_Groups_Ozero__class_Ozero(_1070685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070685), _1070687), _1070689)), c_Groups_Ozero__class_Ozero(_1070685))))], (11311 ^ _781013) ^ [_983229, _983231, _983233, _983235, _983237, _983239, _983241] : [-(c_Nitpick_Ofold__graph_H(_983229, _983231, _983233, _983235, _983237, hAPP(hAPP(_983233, _983239), _983241))), 11312 ^ _781013 : [(11319 ^ _781013) ^ [_983458, _983460] : [hAPP(hAPP(_983233, _983239), _983241) = hAPP(hAPP(_983233, _983460), _983458), hBOOL(hAPP(hAPP(c_member(_983229), _983460), _983237)), c_Nitpick_Ofold__graph_H(_983229, _983231, _983233, _983235, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983229, tc_HOL_Obool)), _983237), hAPP(hAPP(c_Set_Oinsert(_983229), _983460), c_Orderings_Obot__class_Obot(tc_fun(_983229, tc_HOL_Obool)))), _983458)], (11313 ^ _781013) ^ [] : [_983237 = c_Orderings_Obot__class_Obot(tc_fun(_983229, tc_HOL_Obool)), hAPP(hAPP(_983233, _983239), _983241) = _983235]]], (48806 ^ _781013) ^ [_1769401, _1769403, _1769405] : [-(hAPP(c_Relation_Oconverse(_1769401, _1769403), hAPP(c_Relation_Oconverse(_1769403, _1769401), _1769405)) = _1769405)], (51176 ^ _781013) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (7741 ^ _781013) ^ [_911412, _911414, _911416, _911418] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911412, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_911412), _911414), _911416)), _911418) = hAPP(hAPP(c_Set_Oinsert(_911412), _911414), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911412, tc_HOL_Obool)), _911416), _911418)))], (706 ^ _781013) ^ [_791868, _791870, _791872, _791874, _791876, _791878] : [-(c_Relation_Orefl__on(_791876, _791872, _791868)), c_Relation_Orefl__on(_791878, _791874, _791870), _791878 = _791876, _791874 = _791872, _791870 = _791868], (43853 ^ _781013) ^ [_1654317, _1654319] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1654317), _1654319))), -(c_List_Oupt(_1654317, _1654319) = c_List_Olist_ONil(tc_Nat_Onat))], (33706 ^ _781013) ^ [_1419885, _1419887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419885)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419887))), 33709 ^ _781013 : [(33710 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1419885), _1419887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1419887)))], (33716 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1419885), _1419887)))]]], (7001 ^ _781013) ^ [_896805, _896807, _896809] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896805, tc_HOL_Obool)), _896807), _896809) = _896809, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896805, tc_HOL_Obool)), _896807), _896809)))], (38145 ^ _781013) ^ [_1512719, _1512721, _1512723] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1512719, _1512719)), _1512721), c_Relation_OId__on(_1512719, _1512723))), 38149 ^ _781013 : [(38152 ^ _781013) ^ [] : [-(_1512721 = hAPP(hAPP(c_Product__Type_OPair(_1512719, _1512719), 38148 ^ [_1512719, _1512721, _1512723]), 38148 ^ [_1512719, _1512721, _1512723]))], (38150 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512719), 38148 ^ [_1512719, _1512721, _1512723]), _1512723)))]]], (30451 ^ _781013) ^ [_1350270, _1350272] : [class_Orderings_Olinorder(_1350270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350270), _1350272)), -(c_Big__Operators_Olinorder__class_OMax(_1350270, _1350272) = hAPP(c_Finite__Set_Ofold1(_1350270, c_Orderings_Oord__class_Omax(_1350270)), _1350272))], (8373 ^ _781013) ^ [_925095, _925097] : [-(hAPP(c_Set_Oimage(_925095, _925095, c_COMBI(_925095)), _925097) = _925097)], (41969 ^ _781013) ^ [_1610422, _1610424, _1610426, _1610428, _1610430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610422), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610424)), _1610426))), -(hAPP(hAPP(c_List_Olist__update(_1610424, hAPP(hAPP(c_List_Oappend(_1610424), _1610426), _1610428)), _1610422), _1610430) = hAPP(hAPP(c_List_Oappend(_1610424), hAPP(hAPP(c_List_Olist__update(_1610424, _1610426), _1610422), _1610430)), _1610428))], (43470 ^ _781013) ^ [_1646655, _1646657, _1646659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646655, tc_HOL_Obool)), _1646657), _1646659)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1646655), tc_HOL_Obool)), c_List_Olistsp(_1646655, _1646657)), c_List_Olistsp(_1646655, _1646659))))], (9355 ^ _781013) ^ [_946901, _946903, _946905, _946907] : [hBOOL(hAPP(hAPP(c_member(_946901), _946903), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946901, tc_HOL_Obool)), _946905), _946907))), 9358 ^ _781013 : [(9361 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_946901), _946903), _946907)))], (9359 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_946901), _946903), _946905)))]]], (13943 ^ _781013) ^ [_1037332, _1037334, _1037336, _1037338] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1037332), 13946 ^ _781013 : [(13953 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037332), _1037334), _1037338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037332), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037332), _1037334), _1037336)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037332), _1037338), _1037336))))], (13947 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037332), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037332), _1037334), _1037336)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037332), _1037338), _1037336))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037332), _1037334), _1037338)))]]], (22786 ^ _781013) ^ [_1207264, _1207266, _1207268, _1207270, _1207272] : [class_Groups_Oab__group__add(_1207264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207266), _1207268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207268), _1207270)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1207264), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207264), _1207272), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207266), _1207270))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207264), _1207272), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207266), _1207268))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207264), _1207272), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207268), _1207270)))], (49618 ^ _781013) ^ [_1789757, _1789759, _1789761, _1789763] : [class_Lattices_Osemilattice__inf(_1789757), hBOOL(hAPP(c_Finite__Set_Ofinite(_1789757), _1789759)), hBOOL(hAPP(hAPP(c_member(_1789757), _1789761), _1789759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1789757), hAPP(hAPP(c_Finite__Set_Ofold(_1789757, _1789757, c_Lattices_Osemilattice__inf__class_Oinf(_1789757)), _1789763), _1789759)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1789757), _1789761), _1789763))))], (43847 ^ _781013) ^ [_1654206, _1654208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1654206), _1654208)), -(c_List_Oupt(_1654206, _1654208) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1654206), c_List_Oupt(hAPP(c_Nat_OSuc, _1654206), _1654208)))], (9641 ^ _781013) ^ [_951656, _951658, _951660] : [class_Orderings_Oorder(_951656), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951656), _951658), _951660)), _951660 = _951658], (50214 ^ _781013) ^ [_1802064, _1802066, _1802068] : [-(c_Nitpick_Otimes__frac(_1802064, _1802066, _1802068) = hAPP(hAPP(c_Nitpick_Ofrac(_1802064), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1802064), _1802066)), hAPP(c_Nitpick_Onum(_1802064), _1802068))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1802064), _1802066)), hAPP(c_Nitpick_Odenom(_1802064), _1802068))))], (31543 ^ _781013) ^ [_1375658, _1375660, _1375662, _1375664] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1375658), _1375660)), 31546 ^ _781013 : [(31547 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1375662), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1375658, tc_fun(_1375662, tc_HOL_Obool)), _1375660), _1375664))), 31550 ^ _781013 : [(31551 ^ _781013) ^ [_1375842] : [hBOOL(hAPP(hAPP(c_member(_1375658), _1375842), _1375660)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1375662), hAPP(_1375664, _1375842))))]]], (31557 ^ _781013) ^ [] : [31559 ^ _781013 : [(31562 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1375662), hAPP(_1375664, 31558 ^ [_1375658, _1375660, _1375662, _1375664])))], (31560 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1375658), 31558 ^ [_1375658, _1375660, _1375662, _1375664]), _1375660)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1375662), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1375658, tc_fun(_1375662, tc_HOL_Obool)), _1375660), _1375664))))]]], (50824 ^ _781013) ^ [_1814169, _1814171, _1814173, _1814175, _1814177] : [-(c_List_Osplice(_1814169, hAPP(hAPP(c_List_Olist_OCons(_1814169), _1814171), _1814173), hAPP(hAPP(c_List_Olist_OCons(_1814169), _1814175), _1814177)) = hAPP(hAPP(c_List_Olist_OCons(_1814169), _1814171), hAPP(hAPP(c_List_Olist_OCons(_1814169), _1814175), c_List_Osplice(_1814169, _1814173, _1814177))))], (1804 ^ _781013) ^ [_806305, _806307] : [-(class_Groups_Ozero(_806305)), _806307 = _806305, class_Groups_Ozero(_806307)], (12606 ^ _781013) ^ [_1008867, _1008869, _1008871, _1008873, _1008875, _1008877, _1008879, _1008881] : [c_Finite__Set_Ofolding__image(_1008867, _1008869, _1008871, _1008873, _1008875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008869), _1008877)), c_Fun_Oinj__on(_1008869, _1008869, _1008879, _1008877), -(hAPP(hAPP(_1008875, _1008881), hAPP(c_Set_Oimage(_1008869, _1008869, _1008879), _1008877)) = hAPP(hAPP(_1008875, hAPP(c_Fun_Ocomp(_1008869, _1008867, _1008869, _1008881), _1008879)), _1008877))], (4 ^ _781013) ^ [_781063, _781065] : [_781065 = _781063, -(_781063 = _781065)], (19400 ^ _781013) ^ [_1144270, _1144272] : [class_Groups_Omonoid__mult(_1144270), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1144270), c_Groups_Oone__class_Oone(_1144270)), _1144272) = c_Groups_Oone__class_Oone(_1144270))], (32274 ^ _781013) ^ [_1393560, _1393562, _1393564, _1393566, _1393568] : [c_Com_Ocom_OLocal(_1393560, _1393562, _1393564) = c_Com_Ocom_OSemi(_1393566, _1393568)], (390 ^ _781013) ^ [_787090, _787092, _787094, _787096, _787098, _787100] : [-(c_Hoare__Mirabelle_Ohoare__valids(_787098, _787094, _787090)), c_Hoare__Mirabelle_Ohoare__valids(_787100, _787096, _787092), _787100 = _787098, _787096 = _787094, _787092 = _787090], (45059 ^ _781013) ^ [_1681328, _1681330] : [-(c_Enum_Oenum__class_Oenum(tc_prod(_1681328, _1681330)) = c_Enum_Oproduct(_1681328, _1681330, c_Enum_Oenum__class_Oenum(_1681328), c_Enum_Oenum__class_Oenum(_1681330))), class_Enum_Oenum(_1681328), class_Enum_Oenum(_1681330)], (6611 ^ _781013) ^ [_889245] : [-(c_Option_Oset(_889245, c_Option_Ooption_ONone(_889245)) = c_Orderings_Obot__class_Obot(tc_fun(_889245, tc_HOL_Obool)))], (17202 ^ _781013) ^ [_1101235, _1101237, _1101239, _1101241, _1101243] : [class_Groups_Ocomm__monoid__mult(_1101235), hBOOL(hAPP(c_Finite__Set_Ofinite(_1101237), _1101239)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1101237), _1101241)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1101237, tc_HOL_Obool)), _1101239), _1101241) = c_Orderings_Obot__class_Obot(tc_fun(_1101237, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1101237, _1101235), _1101243), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1101237, tc_HOL_Obool)), _1101239), _1101241)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101235), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1101237, _1101235), _1101243), _1101239)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1101237, _1101235), _1101243), _1101241)))], (19712 ^ _781013) ^ [_1149920, _1149922, _1149924, _1149926, _1149928, _1149930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1149920), _1149922)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1149924), _1149926)), 19722 ^ _781013 : [(19725 ^ _781013) ^ [] : [hAPP(c_Finite__Set_Ocard(_1149920), hAPP(c_Set_OCollect(_1149920), hAPP(hAPP(c_COMBS(_1149920, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1149920), c_fconj), hAPP(hAPP(c_COMBC(_1149920, tc_fun(_1149920, tc_HOL_Obool), tc_HOL_Obool), c_member(_1149920)), _1149922))), hAPP(hAPP(c_COMBC(_1149920, _1149924, tc_HOL_Obool), _1149928), 19721 ^ [_1149920, _1149922, _1149924, _1149926, _1149928, _1149930])))) = hAPP(_1149930, 19721 ^ [_1149920, _1149922, _1149924, _1149926, _1149928, _1149930])], (19723 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1149924), 19721 ^ [_1149920, _1149922, _1149924, _1149926, _1149928, _1149930]), _1149926)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1149920, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1149924, tc_HOL_Obool), tc_Nat_Onat, _1149920), c_Finite__Set_Ocard(_1149924)), hAPP(hAPP(c_COMBB(tc_fun(_1149924, tc_HOL_Obool), tc_fun(_1149924, tc_HOL_Obool), _1149920), c_Set_OCollect(_1149924)), hAPP(hAPP(c_COMBB(tc_fun(_1149924, tc_HOL_Obool), tc_fun(_1149924, tc_HOL_Obool), _1149920), hAPP(c_COMBS(_1149924, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1149924), c_fconj), hAPP(hAPP(c_COMBC(_1149924, tc_fun(_1149924, tc_HOL_Obool), tc_HOL_Obool), c_member(_1149924)), _1149926)))), _1149928)))), _1149922) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1149924, tc_Nat_Onat), _1149930), _1149926))], (28862 ^ _781013) ^ [_1319499] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1319499)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1319499))], (25738 ^ _781013) ^ [_1260159] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1260159)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1260159))], (11496 ^ _781013) ^ [_987749, _987751] : [-(hBOOL(hAPP(hAPP(c_member(_987749), _987751), c_Orderings_Otop__class_Otop(tc_fun(_987749, tc_HOL_Obool)))))], (23264 ^ _781013) ^ [_1216147, _1216149, _1216151] : [hBOOL(hAPP(_1216147, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1216149), _1216151))), 23269 ^ _781013 : [(23272 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1216147, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23270 ^ _781013) ^ [] : [-(_1216151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 23274 ^ _781013 : [(23279 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1216147, 23273 ^ [_1216147, _1216149, _1216151])))], (23277 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1216149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216151), hAPP(c_Nat_OSuc, 23273 ^ [_1216147, _1216149, _1216151])))))], (23275 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216151), 23273 ^ [_1216147, _1216149, _1216151])), _1216149)))]]], (50942 ^ _781013) ^ [_1817447, _1817449, _1817451] : [-(c_List_Oreplicate(_1817447, hAPP(c_Nat_OSuc, _1817449), _1817451) = hAPP(hAPP(c_List_Olist_OCons(_1817447), _1817451), c_List_Oreplicate(_1817447, _1817449, _1817451)))], (6014 ^ _781013) ^ [_878236, _878238] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_878236, _878238)))), hBOOL(hAPP(c_Com_OWT, _878236)), hBOOL(hAPP(c_Com_OWT, _878238))], (19300 ^ _781013) ^ [_1142476, _1142478, _1142480] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1142478), _1142480)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142476), _1142478)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142476), _1142480)))], (42212 ^ _781013) ^ [_1616784, _1616786, _1616788, _1616790, _1616792] : [hAPP(hAPP(c_List_Oappend(_1616784), _1616786), _1616788) = hAPP(hAPP(c_List_Oappend(_1616784), _1616790), _1616792), 42215 ^ _781013 : [(42224 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616784)), _1616786)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616784)), _1616790)))), 42227 ^ _781013 : [(42230 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1616784), hAPP(hAPP(c_List_Odrop(_1616784), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616784)), _1616790)), _1616786)), _1616788) = _1616792)], (42228 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1616784), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616784)), _1616790)), _1616786) = _1616790)]]], (42216 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616784)), _1616786)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616784)), _1616790))), 42219 ^ _781013 : [(42222 ^ _781013) ^ [] : [-(_1616788 = hAPP(hAPP(c_List_Oappend(_1616784), hAPP(hAPP(c_List_Odrop(_1616784), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616784)), _1616786)), _1616790)), _1616792))], (42220 ^ _781013) ^ [] : [-(_1616786 = hAPP(hAPP(c_List_Otake(_1616784), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616784)), _1616786)), _1616790))]]]]], (42182 ^ _781013) ^ [_1616082, _1616084, _1616086, _1616088] : [-(hAPP(hAPP(c_List_Oappend(_1616082), _1616084), _1616086) = _1616088), _1616084 = hAPP(hAPP(c_List_Otake(_1616082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616082)), _1616084)), _1616088), _1616086 = hAPP(hAPP(c_List_Odrop(_1616082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616082)), _1616084)), _1616088)], (33686 ^ _781013) ^ [_1419567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1419567), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419567) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37742 ^ _781013) ^ [_1502198] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1502198)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1502198)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10561 ^ _781013) ^ [_968022, _968024, _968026] : [class_Orderings_Olinorder(_968022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968022), _968024), _968026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968022), _968026), _968024))], (31808 ^ _781013) ^ [_1382451, _1382453, _1382455, _1382457] : [31810 ^ _781013 : [(31813 ^ _781013) ^ [] : [hAPP(_1382457, 31809 ^ [_1382451, _1382453, _1382455, _1382457]) = c_Orderings_Obot__class_Obot(tc_fun(_1382451, tc_HOL_Obool))], (31811 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382453), 31809 ^ [_1382451, _1382453, _1382455, _1382457]), _1382455)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1382451, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382453, tc_fun(_1382451, tc_HOL_Obool)), _1382455), _1382457))], (10375 ^ _781013) ^ [_964924, _964926, _964928, _964930] : [hBOOL(hAPP(hAPP(c_member(_964924), _964926), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964924, tc_HOL_Obool)), _964928), _964930))), 10378 ^ _781013 : [(10381 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_964924), _964926), _964930)))], (10379 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_964924), _964926), _964928)))]]], (14933 ^ _781013) ^ [_1057470, _1057472, _1057474] : [class_Groups_Oab__group__add(_1057470), 14936 ^ _781013 : [(14943 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057470), _1057472), _1057474) = c_Groups_Ozero__class_Ozero(_1057470), -(_1057472 = _1057474)], (14937 ^ _781013) ^ [] : [_1057472 = _1057474, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057470), _1057472), _1057474) = c_Groups_Ozero__class_Ozero(_1057470))]]], (18710 ^ _781013) ^ [_1129704, _1129706, _1129708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129704), _1129706)), 18713 ^ _781013 : [(18720 ^ _781013) ^ [] : [_1129706 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1129708), _1129704), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1129706), _1129704) = _1129708)], (18714 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1129706), _1129704) = _1129708, -(_1129706 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1129708), _1129704))]]], (41400 ^ _781013) ^ [_1596701, _1596703, _1596705] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596701), tc_List_Olist(_1596701))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596701), tc_List_Olist(_1596701)), c_List_Olist_ONil(_1596701)), _1596703)), c_List_Olistrel1(_1596701, _1596705)))], (37413 ^ _781013) ^ [_1495172, _1495174, _1495176, _1495178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1495172, _1495172)), hAPP(hAPP(c_Product__Type_OPair(_1495172, _1495172), _1495174), _1495176)), hAPP(c_Wellfounded_Omeasure(_1495172), _1495178))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1495178, _1495174)), hAPP(_1495178, _1495176))))], (29255 ^ _781013) ^ [_1326788, _1326790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1326788)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1326790, _1326788)), _1326788)))], (36669 ^ _781013) ^ [_1481140, _1481142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481140), 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)), _1481142)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1481140, _1481142), c_Divides_OnegDivAlg(_1481140, _1481142))))], (11115 ^ _781013) ^ [_978975, _978977, _978979] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978975, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978975, tc_HOL_Obool)), _978977), _978979)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978975, tc_HOL_Obool)), _978977), _978979)) = _978977)], (17290 ^ _781013) ^ [_1103235, _1103237, _1103239, _1103241] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1103235), _1103237)), hBOOL(hAPP(hAPP(c_member(_1103235), _1103239), _1103237)), -(hBOOL(hAPP(hAPP(c_member(_1103235), _1103239), _1103241))), -(hAPP(c_Finite__Set_Ocard(_1103235), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1103235, tc_HOL_Obool)), _1103237), hAPP(hAPP(c_Set_Oinsert(_1103235), _1103239), _1103241))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1103235), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1103235, tc_HOL_Obool)), _1103237), _1103241))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (4122 ^ _781013) ^ [_843351, _843353, _843355, _843357] : [-(c_List_Orotate(_843357, _843353) = c_List_Orotate(_843355, _843351)), _843357 = _843355, _843353 = _843351], (46170 ^ _781013) ^ [_1705292, _1705294, _1705296, _1705298] : [c_List_Olist__all2(_1705292, _1705294, _1705296, _1705298, c_List_Olist_ONil(_1705294)), -(_1705298 = c_List_Olist_ONil(_1705292))], (49286 ^ _781013) ^ [_1781511, _1781513, _1781515, _1781517, _1781519] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1781511, _1781511)), hAPP(hAPP(c_Product__Type_OPair(_1781511, _1781511), _1781513), _1781515)), c_Transitive__Closure_Ortrancl(_1781511, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1781511, _1781511), tc_HOL_Obool)), _1781517), _1781519)))), 49292 ^ _781013 : [(49298 ^ _781013) ^ [] : [49294 ^ [_1781511, _1781513, _1781515, _1781517, _1781519] = 49291 ^ [_1781511, _1781513, _1781515, _1781517, _1781519]], (49296 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1781511, _1781511)), hAPP(hAPP(c_Product__Type_OPair(_1781511, _1781511), 49294 ^ [_1781511, _1781513, _1781515, _1781517, _1781519]), 49291 ^ [_1781511, _1781513, _1781515, _1781517, _1781519])), _1781519)))], (49293 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1781511, _1781511)), hAPP(hAPP(c_Product__Type_OPair(_1781511, _1781511), 49291 ^ [_1781511, _1781513, _1781515, _1781517, _1781519]), _1781515)), c_Transitive__Closure_Ortrancl(_1781511, _1781517))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1781511, _1781511)), hAPP(hAPP(c_Product__Type_OPair(_1781511, _1781511), _1781513), _1781515)), c_Transitive__Closure_Ortrancl(_1781511, _1781517))))], (5960 ^ _781013) ^ [_877359, _877361, _877363, _877365, _877367] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_877359, _877361, _877363), _877365), _877367)), 5963 ^ _781013 : [(5966 ^ _781013) ^ [] : [-(hBOOL(hAPP(_877363, _877367)))], (5964 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_877361, _877365), _877367)))]]], (4870 ^ _781013) ^ [_854937, _854939, _854941, _854943] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_854943, _854939) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_854941, _854937)), _854943 = _854941, _854939 = _854937], (42567 ^ _781013) ^ [_1624367, _1624369, _1624371] : [class_Orderings_Olinorder(_1624367), -(c_Big__Operators_Olinorder__class_OMax(_1624367, hAPP(c_List_Oset(_1624367), hAPP(hAPP(c_List_Olist_OCons(_1624367), _1624369), _1624371))) = hAPP(c_List_Ofoldl(_1624367, _1624367, c_Orderings_Oord__class_Omax(_1624367), _1624369), _1624371))], (36554 ^ _781013) ^ [_1478427, _1478429, _1478431] : [hBOOL(hAPP(_1478427, 36555 ^ [_1478427, _1478429, _1478431])), 36558 ^ _781013 : [(36559 ^ _781013) ^ [_1478538, _1478540] : [-(hBOOL(hAPP(_1478427, hAPP(hAPP(c_Product__Type_OPair(_1478429, _1478431), _1478540), _1478538))))]]], (14875 ^ _781013) ^ [_1056586, _1056588, _1056590] : [class_Rings_Oring__no__zero__divisors(_1056586), 14878 ^ _781013 : [(14879 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056586), _1056588), _1056590) = c_Groups_Ozero__class_Ozero(_1056586), -(_1056588 = c_Groups_Ozero__class_Ozero(_1056586)), -(_1056590 = c_Groups_Ozero__class_Ozero(_1056586))], (14889 ^ _781013) ^ [] : [14890 ^ _781013 : [(14893 ^ _781013) ^ [] : [_1056590 = c_Groups_Ozero__class_Ozero(_1056586)], (14891 ^ _781013) ^ [] : [_1056588 = c_Groups_Ozero__class_Ozero(_1056586)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056586), _1056588), _1056590) = c_Groups_Ozero__class_Ozero(_1056586))]]], (47993 ^ _781013) ^ [_1750392, _1750394, _1750396, _1750398] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1750392, _1750392)), hAPP(hAPP(c_Product__Type_OPair(_1750392, _1750392), _1750394), _1750396)), _1750398)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1750392, _1750392)), hAPP(hAPP(c_Product__Type_OPair(_1750392, _1750392), _1750394), _1750396)), c_Transitive__Closure_Otrancl(_1750392, _1750398))))], (38608 ^ _781013) ^ [_1523515, _1523517, _1523519] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1523515, tc_HOL_Obool)), hAPP(c_List_Oset(_1523515), c_List_Oremove1(_1523515, _1523517, _1523519))), hAPP(c_List_Oset(_1523515), _1523519))))], (7613 ^ _781013) ^ [_908810, _908812, _908814, _908816] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908810, tc_HOL_Obool)), _908812), hAPP(hAPP(c_Set_Oinsert(_908810), _908814), _908816)))), 7616 ^ _781013 : [(7619 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908810, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908810, tc_HOL_Obool)), _908812), hAPP(hAPP(c_Set_Oinsert(_908810), _908814), c_Orderings_Obot__class_Obot(tc_fun(_908810, tc_HOL_Obool))))), _908816))], (7617 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_908810), _908814), _908812)))]], 7620 ^ _781013 : [(7623 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908810, tc_HOL_Obool)), _908812), _908816))], (7621 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_908810), _908814), _908812))]]], (44471 ^ _781013) ^ [_1667904, _1667906, _1667908] : [c_List_Oconcat(_1667904, _1667906) = c_List_Oconcat(_1667904, _1667908), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1667904))), _1667906) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1667904))), _1667908), 44481 ^ _781013 : [(44484 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1667904), tc_List_Olist(_1667904), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1667904), tc_fun(tc_List_Olist(_1667904), tc_Nat_Onat), tc_fun(tc_List_Olist(_1667904), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1667904), tc_Nat_Onat), tc_fun(tc_List_Olist(_1667904), tc_HOL_Obool)), tc_List_Olist(_1667904)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1667904))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1667904)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1667904))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1667904)))), 44480 ^ [_1667904, _1667906, _1667908]))], (44482 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667904), tc_List_Olist(_1667904))), 44480 ^ [_1667904, _1667906, _1667908]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1667904), tc_List_Olist(_1667904))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1667904), tc_List_Olist(_1667904)), _1667906), _1667908)))))]], -(_1667906 = _1667908)], (2326 ^ _781013) ^ [_815419, _815421, _815423, _815425] : [-(c_SMT_Oz3mod(_815425, _815421) = c_SMT_Oz3mod(_815423, _815419)), _815425 = _815423, _815421 = _815419], (11862 ^ _781013) ^ [_994932] : [-(c_Fun_Oinj__on(_994932, tc_fun(_994932, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_994932, tc_fun(_994932, tc_HOL_Obool), tc_fun(_994932, tc_HOL_Obool)), c_Set_Oinsert(_994932)), c_Orderings_Obot__class_Obot(tc_fun(_994932, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_994932, tc_HOL_Obool))))], (51114 ^ _781013) ^ [] : [-(class_HOL_Oequal(tc_Com_Ocom))], (42426 ^ _781013) ^ [_1621332, _1621334, _1621336] : [-(hAPP(c_List_Orotate(_1621332, hAPP(c_Nat_OSuc, _1621334)), _1621336) = hAPP(c_List_Orotate1(_1621332), hAPP(c_List_Orotate(_1621332, _1621334), _1621336)))], (51218 ^ _781013) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (33446 ^ _781013) ^ [_1415773] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415773))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415773)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34191 ^ _781013) ^ [_1429620] : [c_Int_OBit1(_1429620) = c_Int_OPls], (30289 ^ _781013) ^ [_1346955, _1346957] : [class_Orderings_Olinorder(_1346955), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346955), _1346957), _1346957) = _1346957)], (28670 ^ _781013) ^ [_1315979, _1315981, _1315983] : [class_Rings_Olinordered__idom(_1315979), -(hAPP(c_Groups_Oabs__class_Oabs(_1315979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315979), _1315981), _1315983)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315979), hAPP(c_Groups_Oabs__class_Oabs(_1315979), _1315981)), hAPP(c_Groups_Oabs__class_Oabs(_1315979), _1315983)))], (21503 ^ _781013) ^ [_1184961] : [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)), _1184961))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1184961)))], (1814 ^ _781013) ^ [_806430, _806432] : [-(class_Int_Onumber(_806430)), _806432 = _806430, class_Int_Onumber(_806432)], (13725 ^ _781013) ^ [_1033098, _1033100, _1033102, _1033104] : [class_Rings_Ocomm__semiring__1(_1033098), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033098), _1033100), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033098), _1033102), _1033104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033098), _1033100), _1033102)), _1033104))], (23477 ^ _781013) ^ [_1220326, _1220328, _1220330, _1220332] : [class_Rings_Odivision__ring(_1220326), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220326), _1220328), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220326), _1220330), _1220332)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220326), _1220328), _1220330)), _1220332))], (16930 ^ _781013) ^ [_1095197, _1095199, _1095201, _1095203, _1095205] : [class_Groups_Ocomm__monoid__mult(_1095197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095199), _1095201)), -(hBOOL(hAPP(hAPP(c_member(_1095199), _1095203), _1095201))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1095199, _1095197), _1095205), hAPP(hAPP(c_Set_Oinsert(_1095199), _1095203), _1095201)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095197), hAPP(_1095205, _1095203)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1095199, _1095197), _1095205), _1095201)))], (46822 ^ _781013) ^ [_1722730, _1722732, _1722734, _1722736, _1722738, _1722740, _1722742] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1722730, _1722732, _1722734, _1722736, _1722738), _1722740), _1722742)), 46826 ^ _781013 : [(46829 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1722738, 46825 ^ [_1722730, _1722732, _1722734, _1722736, _1722738, _1722740, _1722742]), _1722742)))], (46827 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1722736, _1722740), 46825 ^ [_1722730, _1722732, _1722734, _1722736, _1722738, _1722740, _1722742])))]]], (34717 ^ _781013) ^ [_1438518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1438518), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1438518)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19650 ^ _781013) ^ [_1148786, _1148788, _1148790] : [class_Rings_Olinordered__semidom(_1148786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148786), c_Groups_Ozero__class_Ozero(_1148786)), _1148788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148786), _1148788), c_Groups_Oone__class_Oone(_1148786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148786), _1148788), hAPP(hAPP(c_Power_Opower__class_Opower(_1148786), _1148788), _1148790))), hAPP(hAPP(c_Power_Opower__class_Opower(_1148786), _1148788), _1148790))))], (13991 ^ _781013) ^ [_1038253, _1038255, _1038257, _1038259] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1038253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038253), _1038255), _1038257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038253), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038253), _1038255), _1038259)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038253), _1038257), _1038259))))], (51274 ^ _781013) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (51208 ^ _781013) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (2456 ^ _781013) ^ [_817396, _817398] : [_817398 = _817396, -(c_Int_Oring__1__class_OInts(_817398) = c_Int_Oring__1__class_OInts(_817396))], (3390 ^ _781013) ^ [_832119, _832121] : [_832121 = _832119, -(c_Enum_Oenum__class_Oenum__ex(_832121) = c_Enum_Oenum__class_Oenum__ex(_832119))], (10023 ^ _781013) ^ [_958311, _958313, _958315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958311, tc_HOL_Obool)), _958313), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_958311, tc_HOL_Obool)), _958315))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958311, tc_HOL_Obool)), _958313), _958315) = c_Orderings_Obot__class_Obot(tc_fun(_958311, tc_HOL_Obool)))], (21629 ^ _781013) ^ [_1187254, _1187256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1187254), _1187256)), -(_1187256 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1187254), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21632 ^ [_1187254, _1187256])))], (41909 ^ _781013) ^ [_1608904, _1608906, _1608908] : [-(c_List_Obutlast(_1608904, hAPP(hAPP(c_List_Oappend(_1608904), _1608906), hAPP(hAPP(c_List_Olist_OCons(_1608904), _1608908), c_List_Olist_ONil(_1608904)))) = _1608906)], (226 ^ _781013) ^ [_784738, _784740] : [-(class_Rings_Odivision__ring(_784738)), _784740 = _784738, class_Rings_Odivision__ring(_784740)], (34299 ^ _781013) ^ [_1431495] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431495))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1431495)))))], (43883 ^ _781013) ^ [_1654761, _1654763, _1654765, _1654767, _1654769] : [class_Orderings_Olinorder(_1654761), -(c_List_Olinorder__class_Osorted(_1654761, hAPP(hAPP(c_List_Omap(_1654763, _1654761), _1654765), hAPP(c_List_Ofilter(_1654763, hAPP(hAPP(c_COMBC(_1654763, _1654761, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1654761, tc_fun(_1654761, tc_HOL_Obool), _1654763), c_fequal), _1654765)), hAPP(_1654767, _1654769))), _1654769))))], (51278 ^ _781013) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (21417 ^ _781013) ^ [_1183074, _1183076, _1183078] : [class_Groups_Olinordered__ab__semigroup__add(_1183074), hBOOL(hAPP(c_Finite__Set_Ofinite(_1183074), _1183076)), -(_1183076 = c_Orderings_Obot__class_Obot(tc_fun(_1183074, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183074), _1183078), c_Big__Operators_Olinorder__class_OMin(_1183074, _1183076)) = c_Big__Operators_Olinorder__class_OMin(_1183074, hAPP(c_Set_OCollect(_1183074), hAPP(hAPP(c_COMBB(tc_fun(_1183074, tc_HOL_Obool), tc_HOL_Obool, _1183074), c_HOL_OEx(_1183074)), hAPP(hAPP(c_COMBC(_1183074, tc_fun(_1183074, tc_HOL_Obool), tc_fun(_1183074, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183074, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1183074, tc_HOL_Obool), tc_fun(_1183074, tc_HOL_Obool)), _1183074), c_COMBS(_1183074, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183074, tc_HOL_Obool), tc_fun(_1183074, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1183074), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1183074), c_fconj)), hAPP(hAPP(c_COMBC(_1183074, tc_fun(_1183074, _1183074), tc_fun(_1183074, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183074, tc_HOL_Obool), tc_fun(tc_fun(_1183074, _1183074), tc_fun(_1183074, tc_HOL_Obool)), _1183074), c_COMBB(_1183074, tc_HOL_Obool, _1183074)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1183074), _1183078))))), hAPP(hAPP(c_COMBC(_1183074, tc_fun(_1183074, tc_HOL_Obool), tc_HOL_Obool), c_member(_1183074)), _1183076))))))], (25296 ^ _781013) ^ [_1252460, _1252462, _1252464, _1252466, _1252468] : [class_Fields_Ofield(_1252460), -(_1252462 = c_Groups_Ozero__class_Ozero(_1252460)), -(_1252464 = c_Groups_Ozero__class_Ozero(_1252460)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1252460), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252460), _1252466), _1252462)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252460), _1252468), _1252464)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252460), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1252460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252460), _1252466), _1252464)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252460), _1252468), _1252462))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252460), _1252462), _1252464)))], (22736 ^ _781013) ^ [_1206283, _1206285, _1206287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1206283), _1206285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206283), _1206287)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206285), _1206287))))], (582 ^ _781013) ^ [_789894, _789896, _789898, _789900, _789902, _789904, _789906, _789908, _789910, _789912] : [-(c_List_Olist__all2(_789910, _789906, _789902, _789898, _789894)), c_List_Olist__all2(_789912, _789908, _789904, _789900, _789896), _789912 = _789910, _789908 = _789906, _789904 = _789902, _789900 = _789898, _789896 = _789894], (27445 ^ _781013) ^ [_1292687] : [-(hAPP(c_Set_OPow(_1292687), c_Orderings_Otop__class_Otop(tc_fun(_1292687, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1292687, tc_HOL_Obool), tc_HOL_Obool)))], (47315 ^ _781013) ^ [_1734826, _1734828] : [c_Wellfounded_OwfP(_1734826, _1734828), 47318 ^ _781013 : [(47319 ^ _781013) ^ [_1734890] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1734826, _1734828), _1734890)))]]], (15433 ^ _781013) ^ [_1066467, _1066469, _1066471] : [class_Rings_Oordered__cancel__semiring(_1066467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066467), c_Groups_Ozero__class_Ozero(_1066467)), _1066469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066467), c_Groups_Ozero__class_Ozero(_1066467)), _1066471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066467), c_Groups_Ozero__class_Ozero(_1066467)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066467), _1066469), _1066471))))], (35885 ^ _781013) ^ [_1459542, _1459544, _1459546, _1459548, _1459550, _1459552, _1459554, _1459556, _1459558, _1459560] : [c_Equiv__Relations_Ocongruent2(_1459542, _1459544, _1459546, _1459548, _1459550, _1459552), hBOOL(hAPP(hAPP(c_member(tc_prod(_1459542, _1459542)), hAPP(hAPP(c_Product__Type_OPair(_1459542, _1459542), _1459554), _1459556)), _1459548)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1459544, _1459544)), hAPP(hAPP(c_Product__Type_OPair(_1459544, _1459544), _1459558), _1459560)), _1459550)), -(hAPP(hAPP(_1459552, _1459554), _1459558) = hAPP(hAPP(_1459552, _1459556), _1459560))], (12066 ^ _781013) ^ [_998686, _998688] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998686, tc_HOL_Obool)), _998688), c_Orderings_Otop__class_Otop(tc_fun(_998686, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_998686, tc_HOL_Obool)))], (19825 ^ _781013) ^ [] : [-(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))))], (24712 ^ _781013) ^ [_1241871, _1241873, _1241875, _1241877] : [class_Fields_Olinordered__field(_1241871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241871), _1241873), _1241875)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241871), c_Groups_Ozero__class_Ozero(_1241871)), _1241877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241871), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241871), _1241873), _1241877)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241871), _1241875), _1241877))))], (6448 ^ _781013) ^ [_886377, _886379, _886381, _886383, _886385, _886387] : [-(hAPP(hAPP(c_Fun_Ocomp(_886377, _886379, _886381, hAPP(c_COMBK(_886379, _886377), _886383)), _886385), _886387) = _886383)], (34147 ^ _781013) ^ [_1428635, _1428637, _1428639] : [class_Int_Onumber__ring(_1428635), 34150 ^ _781013 : [(34157 ^ _781013) ^ [] : [-(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), _1428637)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1428635), hAPP(c_Int_Onumber__class_Onumber__of(_1428635), _1428639)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428637))) = c_Groups_Oone__class_Oone(_1428635))], (34151 ^ _781013) ^ [] : [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), _1428637))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1428635), hAPP(c_Int_Onumber__class_Onumber__of(_1428635), _1428639)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428637))) = hAPP(hAPP(c_HOL_OLet(_1428635, _1428635), hAPP(hAPP(c_Power_Opower__class_Opower(_1428635), hAPP(c_Int_Onumber__class_Onumber__of(_1428635), _1428639)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428637))), hAPP(hAPP(c_COMBS(_1428635, _1428635, _1428635), hAPP(hAPP(c_COMBB(_1428635, tc_fun(_1428635, _1428635), _1428635), c_Groups_Otimes__class_Otimes(_1428635)), hAPP(c_Groups_Otimes__class_Otimes(_1428635), hAPP(c_Int_Onumber__class_Onumber__of(_1428635), _1428639)))), c_COMBI(_1428635))))]]], (35631 ^ _781013) ^ [_1455228] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1455228) = c_Int_Opred(_1455228))], (51188 ^ _781013) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (49126 ^ _781013) ^ [_1777370, _1777372, _1777374, _1777376] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1777370, _1777370)), _1777372), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777370, _1777370), tc_HOL_Obool), _1777374), _1777376))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777370, _1777370)), _1777372), c_Transitive__Closure_Ortrancl(_1777370, _1777376))))], (33304 ^ _781013) ^ [_1413199, _1413201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1413199), _1413201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413199)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413201))))], (9541 ^ _781013) ^ [_950030, _950032, _950034, _950036] : [class_Orderings_Opreorder(_950030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950030), _950032), _950034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950030), _950034), _950036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950030), _950032), _950036)))], (42404 ^ _781013) ^ [_1620859, _1620861, _1620863] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620859)), hAPP(c_List_Orotate(_1620859, _1620861), _1620863)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620859)), _1620863))], (47023 ^ _781013) ^ [_1727262, _1727264, _1727266, _1727268] : [47025 ^ _781013 : [(47028 ^ _781013) ^ [] : [c_Wellfounded_Owf(_1727264, hAPP(_1727266, 47024 ^ [_1727262, _1727264, _1727266, _1727268]))], (47026 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1727262, 47024 ^ [_1727262, _1727264, _1727266, _1727268])))]], -(c_Wellfounded_Owf(tc_prod(_1727268, _1727264), c_Recdef_Osame__fst(_1727268, _1727264, _1727262, _1727266)))], (41101 ^ _781013) ^ [_1590995, _1590997, _1590999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590995, tc_HOL_Obool)), _1590997), _1590999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1590995), tc_HOL_Obool)), c_List_Olists(_1590995, _1590997)), c_List_Olists(_1590995, _1590999))))], (9080 ^ _781013) ^ [_941034, _941036, _941038] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_941034), _941036)), hBOOL(hAPP(_941038, _941036)), 9091 ^ _781013 : [(9094 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_941034), 9089 ^ [_941034, _941036, _941038]), 9090 ^ [_941034, _941036, _941038])))], (9096 ^ _781013) ^ [] : [-(hBOOL(hAPP(_941038, 9090 ^ [_941034, _941036, _941038])))], (9098 ^ _781013) ^ [] : [hBOOL(hAPP(_941038, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941034, tc_HOL_Obool)), 9090 ^ [_941034, _941036, _941038]), hAPP(hAPP(c_Set_Oinsert(_941034), 9089 ^ [_941034, _941036, _941038]), c_Orderings_Obot__class_Obot(tc_fun(_941034, tc_HOL_Obool))))))], (9092 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_941034), 9090 ^ [_941034, _941036, _941038])))]], -(hBOOL(hAPP(_941038, c_Orderings_Obot__class_Obot(tc_fun(_941034, tc_HOL_Obool)))))], (51360 ^ _781013) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (36422 ^ _781013) ^ [_1475721, _1475723] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1475721), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36425 ^ _781013 : [(36434 ^ _781013) ^ [] : [-(c_Nitpick_Onorm__frac(_1475723, _1475721) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1475723), _1475721)), 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), _1475723))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1475721)))), -(_1475723 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1475721 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36426 ^ _781013) ^ [] : [36427 ^ _781013 : [(36430 ^ _781013) ^ [] : [_1475721 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36428 ^ _781013) ^ [] : [_1475723 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1475723, _1475721) = 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)))]]], (19152 ^ _781013) ^ [_1139731, _1139733] : [class_Rings_Ocomm__semiring__1(_1139731), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1139731), _1139733), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1139733)], (13142 ^ _781013) ^ [_1020540, _1020542, _1020544] : [class_Lattices_Osemilattice__inf(_1020540), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020540), _1020542)), hBOOL(hAPP(hAPP(c_member(_1020540), _1020544), _1020542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020540), hAPP(c_Finite__Set_Ofold1(_1020540, c_Lattices_Osemilattice__inf__class_Oinf(_1020540)), _1020542)), _1020544)))], (45187 ^ _781013) ^ [_1683828, _1683830, _1683832] : [class_Enum_Oenum(_1683828), 45190 ^ _781013 : [(45200 ^ _781013) ^ [] : [-(c_Enum_Oex__n__lists(_1683828, _1683830, _1683832)), 45201 ^ _781013 : [(45202 ^ _781013) ^ [_1684084] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1683828)), _1684084), hAPP(c_List_Oset(tc_List_Olist(_1683828)), c_Enum_On__lists(_1683828, _1683832, c_Enum_Oenum__class_Oenum(_1683828))))), hBOOL(hAPP(_1683830, _1684084))]]], (45191 ^ _781013) ^ [] : [c_Enum_Oex__n__lists(_1683828, _1683830, _1683832), 45195 ^ _781013 : [(45198 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1683830, 45194 ^ [_1683828, _1683830, _1683832])))], (45196 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1683828)), 45194 ^ [_1683828, _1683830, _1683832]), hAPP(c_List_Oset(tc_List_Olist(_1683828)), c_Enum_On__lists(_1683828, _1683832, c_Enum_Oenum__class_Oenum(_1683828))))))]]]]], (19793 ^ _781013) ^ [_1152043, _1152045] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1152043), _1152045)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1152043)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1152045)))], (30591 ^ _781013) ^ [_1352689, _1352691, _1352693] : [class_Orderings_Olinorder(_1352689), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352689), _1352691)), -(_1352691 = c_Orderings_Obot__class_Obot(tc_fun(_1352689, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352689), _1352693)), -(_1352693 = c_Orderings_Obot__class_Obot(tc_fun(_1352689, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1352689, tc_HOL_Obool)), _1352691), _1352693) = c_Orderings_Obot__class_Obot(tc_fun(_1352689, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1352689, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352689, tc_HOL_Obool)), _1352691), _1352693)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352689), c_Big__Operators_Olinorder__class_OMax(_1352689, _1352691)), c_Big__Operators_Olinorder__class_OMax(_1352689, _1352693)))], (3298 ^ _781013) ^ [_830679, _830681] : [_830681 = _830679, -(c_Power_Opower__class_Opower(_830681) = c_Power_Opower__class_Opower(_830679))], (11622 ^ _781013) ^ [_990185, _990187] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_990185), c_Orderings_Otop__class_Otop(tc_fun(_990185, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_990187), c_Orderings_Otop__class_Otop(tc_fun(_990187, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_990185, _990187)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_990185, _990187), tc_HOL_Obool)))))], (15919 ^ _781013) ^ [_1075525, _1075527, _1075529, _1075531] : [class_Rings_Olinordered__ring__strict(_1075525), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075525), c_Groups_Ozero__class_Ozero(_1075525)), _1075527)), 15926 ^ _781013 : [(15933 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075525), _1075529), _1075531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075525), _1075527), _1075529)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075525), _1075527), _1075531))))], (15927 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075525), _1075527), _1075529)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075525), _1075527), _1075531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075525), _1075529), _1075531)))]]], (8201 ^ _781013) ^ [_920973, _920975, _920977] : [_920977 = hAPP(c_Option_Ooption_OSome(_920973), _920975), -(hBOOL(hAPP(hAPP(c_member(_920973), _920975), c_Option_Oset(_920973, _920977))))], (39900 ^ _781013) ^ [_1557259, _1557261, _1557263, _1557265] : [39903 ^ _781013 : [(39908 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1557259, _1557259)), hAPP(hAPP(c_Product__Type_OPair(_1557259, _1557259), 39902 ^ [_1557259, _1557261, _1557263, _1557265]), 39901 ^ [_1557259, _1557261, _1557263, _1557265])), _1557261))], (39906 ^ _781013) ^ [] : [39901 ^ [_1557259, _1557261, _1557263, _1557265] = 39902 ^ [_1557259, _1557261, _1557263, _1557265]], (39904 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1557259, _1557259)), hAPP(hAPP(c_Product__Type_OPair(_1557259, _1557259), 39901 ^ [_1557259, _1557261, _1557263, _1557265]), 39902 ^ [_1557259, _1557261, _1557263, _1557265])), _1557261))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1557259), tc_List_Olist(_1557259))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1557259), tc_List_Olist(_1557259)), _1557263), _1557265)), c_List_Olexord(_1557259, _1557261)))), -(_1557263 = _1557265), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1557259), tc_List_Olist(_1557259))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1557259), tc_List_Olist(_1557259)), _1557265), _1557263)), c_List_Olexord(_1557259, _1557261))))], (16630 ^ _781013) ^ [_1089302, _1089304, _1089306, _1089308] : [class_Groups_Oordered__comm__monoid__add(_1089302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089302), c_Groups_Ozero__class_Ozero(_1089302)), _1089304)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089302), _1089306), _1089308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089302), _1089306), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089302), _1089304), _1089308))))], (47946 ^ _781013) ^ [_1749578, _1749580, _1749582, _1749584, _1749586, _1749588, _1749590] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1749578, _1749580, _1749582, _1749584), _1749586), _1749588), _1749590) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1749580, _1749582, _1749584), _1749588), hAPP(_1749586, _1749590)))], (23150 ^ _781013) ^ [_1214079, _1214081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214079)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214081), _1214079)), _1214079) = _1214081)], (50358 ^ _781013) ^ [_1805011, _1805013] : [-(c_List_Olist__all(_1805011, _1805013, c_List_Olist_ONil(_1805011)))], (11055 ^ _781013) ^ [_977510, _977512, _977514, _977516] : [hBOOL(hAPP(hAPP(c_member(_977510), _977512), _977514)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977510, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_977510), _977512), _977516)), _977514) = hAPP(hAPP(c_Set_Oinsert(_977510), _977512), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977510, tc_HOL_Obool)), _977516), _977514)))], (49023 ^ _781013) ^ [_1774834, _1774836] : [-(c_Transitive__Closure_Ortrancl(_1774834, _1774836) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774834, _1774834), tc_HOL_Obool)), c_Relation_OId(_1774834)), hAPP(hAPP(c_Relation_Orel__comp(_1774834, _1774834, _1774834), c_Transitive__Closure_Ortrancl(_1774834, _1774836)), _1774836)))], (19032 ^ _781013) ^ [_1137092, _1137094, _1137096, _1137098] : [hBOOL(hAPP(hAPP(_1137096, _1137094), _1137098)), -(hBOOL(hAPP(hAPP(c_member(_1137092), _1137094), c_SetInterval_Oord_OlessThan(_1137092, _1137096, _1137098))))], (34759 ^ _781013) ^ [_1439249, _1439251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1439249)), c_Int_OBit1(_1439251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1439249), _1439251)))], (9957 ^ _781013) ^ [_956996, _956998, _957000] : [class_Lattices_Osemilattice__inf(_956996), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956996), _956998), _957000) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956996), _957000), _956998))], (26457 ^ _781013) ^ [_1273131, _1273133, _1273135] : [class_Orderings_Oorder(_1273131), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1273131, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1273131, _1273133, _1273135)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1273131), _1273135)) = c_Orderings_Obot__class_Obot(tc_fun(_1273131, tc_HOL_Obool)))], (39158 ^ _781013) ^ [_1537137, _1537139, _1537141] : [hBOOL(hAPP(hAPP(c_member(_1537137), _1537139), hAPP(c_List_Oset(_1537137), _1537141))), 39162 ^ _781013 : [(39165 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1537137), _1537141), 39161 ^ [_1537137, _1537139, _1537141]) = _1537139)], (39163 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39161 ^ [_1537137, _1537139, _1537141]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1537137)), _1537141))))]]], (20721 ^ _781013) ^ [_1168309, _1168311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1168309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1168311), _1168309))))], (51338 ^ _781013) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (36958 ^ _781013) ^ [_1486009, _1486011] : [-(c_Divides_Opdivmod(_1486009, _1486011) = 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), _1486009)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1486011))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1486009), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1486011))))], (26877 ^ _781013) ^ [_1281297, _1281299, _1281301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281297)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1281299), _1281301)), 26884 ^ _781013 : [(26885 ^ _781013) ^ [_1281493] : [26887 ^ _781013 : [(26893 ^ _781013) ^ [] : [-(_1281493 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26889 ^ [_1281297, _1281299, _1281301, _1281493]), 26886 ^ [_1281297, _1281299, _1281301, _1281493]))], (26891 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26889 ^ [_1281297, _1281299, _1281301, _1281493]), _1281301)))], (26888 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26886 ^ [_1281297, _1281299, _1281301, _1281493]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1281297))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1281299), _1281493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1281299), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1281493), _1281297))))]]], (48341 ^ _781013) ^ [_1758060, _1758062, _1758064, _1758066] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1758060, _1758060)), hAPP(hAPP(c_Product__Type_OPair(_1758060, _1758060), _1758062), _1758064)), c_Transitive__Closure_Ortrancl(_1758060, _1758066))), -(_1758062 = _1758064), 48348 ^ _781013 : [(48351 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1758060, _1758060)), hAPP(hAPP(c_Product__Type_OPair(_1758060, _1758060), _1758062), _1758064)), c_Transitive__Closure_Otrancl(_1758060, _1758066))))], (48349 ^ _781013) ^ [] : [_1758062 = _1758064]]], (16528 ^ _781013) ^ [_1087065, _1087067, _1087069] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1087065), _1087067)), -(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(_1087065), _1087069)), hAPP(c_Finite__Set_Ocard(_1087065), _1087067))), hAPP(c_Finite__Set_Ocard(_1087065), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1087065, tc_HOL_Obool)), _1087069), _1087067)))))], (50368 ^ _781013) ^ [_1805187, _1805189, _1805191, _1805193] : [-(c_List_Olist__all(_1805187, _1805189, hAPP(hAPP(c_List_Olist_OCons(_1805187), _1805191), _1805193))), hBOOL(hAPP(_1805189, _1805191)), c_List_Olist__all(_1805187, _1805189, _1805193)], (27212 ^ _781013) ^ [_1287724, _1287726] : [class_Groups_Oordered__ab__group__add(_1287724), -(hAPP(c_Set_Oimage(_1287724, _1287724, c_Groups_Ouminus__class_Ouminus(_1287724)), hAPP(c_SetInterval_Oord__class_OatMost(_1287724), _1287726)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1287724), hAPP(c_Groups_Ouminus__class_Ouminus(_1287724), _1287726)))], (28202 ^ _781013) ^ [_1307376, _1307378, _1307380] : [hBOOL(hAPP(_1307376, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1307378, _1307380))), 28205 ^ _781013 : [(28230 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1307380), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 28233 ^ _781013 : [(28234 ^ _781013) ^ [_1307998, _1308000] : [-(hBOOL(hAPP(_1307376, _1307998))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1307380), _1307998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1307998), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1307378 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1307380), _1308000)), _1307998)]]], (28212 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307380)), 28215 ^ _781013 : [(28216 ^ _781013) ^ [_1307706, _1307708] : [-(hBOOL(hAPP(_1307376, _1307706))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307706)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1307706), _1307380)), _1307378 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1307380), _1307708)), _1307706)]]], (28206 ^ _781013) ^ [] : [_1307380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1307376, _1307378)))]]], (18486 ^ _781013) ^ [_1125052, _1125054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1125052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1125054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1125054), _1125052)), _1125054)))], (22832 ^ _781013) ^ [_1208141, _1208143, _1208145] : [class_Divides_Osemiring__div(_1208141), -(_1208143 = c_Groups_Ozero__class_Ozero(_1208141)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208141), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208141), _1208143), _1208145)), _1208143) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208141), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208141), _1208145), _1208143)), c_Groups_Oone__class_Oone(_1208141)))], (42055 ^ _781013) ^ [_1612991, _1612993, _1612995, _1612997, _1612999] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612991), tc_List_Olist(_1612991))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612991), tc_List_Olist(_1612991)), hAPP(hAPP(c_List_Oappend(_1612991), _1612993), _1612995)), hAPP(hAPP(c_List_Oappend(_1612991), _1612993), _1612997))), c_List_Olexord(_1612991, _1612999))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612991, _1612991)), hAPP(hAPP(c_Product__Type_OPair(_1612991, _1612991), 42060 ^ [_1612991, _1612993, _1612995, _1612997, _1612999]), 42060 ^ [_1612991, _1612993, _1612995, _1612997, _1612999])), _1612999))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612991), tc_List_Olist(_1612991))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612991), tc_List_Olist(_1612991)), _1612995), _1612997)), c_List_Olexord(_1612991, _1612999))))], (45594 ^ _781013) ^ [_1692207, _1692209, _1692211, _1692213] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1692207, tc_fun(_1692209, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692207, tc_HOL_Obool), _1692211)), _1692213) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1692207, tc_HOL_Obool), tc_fun(_1692209, tc_HOL_Obool)), _1692211), hAPP(hAPP(c_COMBC(tc_fun(_1692207, tc_HOL_Obool), tc_fun(_1692207, tc_fun(_1692209, tc_HOL_Obool)), tc_fun(_1692209, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1692207, tc_fun(_1692209, tc_HOL_Obool))), _1692213)))], (40555 ^ _781013) ^ [_1574733, _1574735, _1574737] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1574733, _1574735), c_Orderings_Obot__class_Obot(tc_fun(_1574733, tc_HOL_Obool))), _1574737) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1574733, _1574735), tc_HOL_Obool)))], (45081 ^ _781013) ^ [_1681701, _1681703, _1681705, _1681707] : [class_Orderings_Olinorder(_1681701), 45084 ^ _781013 : [(45091 ^ _781013) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1681703), _1681707)), -(hBOOL(hAPP(c_List_Odistinct(_1681703), c_List_Olinorder__class_Osort__key(_1681703, _1681701, _1681705, _1681707))))], (45085 ^ _781013) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1681703), c_List_Olinorder__class_Osort__key(_1681703, _1681701, _1681705, _1681707))), -(hBOOL(hAPP(c_List_Odistinct(_1681703), _1681707)))]]], (20466 ^ _781013) ^ [_1163248, _1163250] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163248), _1163250) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1163248 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1163250 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35095 ^ _781013) ^ [_1445344, _1445346] : [class_Fields_Olinordered__field__inverse__zero(_1445344), class_Int_Onumber__ring(_1445344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445344), c_Groups_Ozero__class_Ozero(_1445344)), _1445346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445344), c_Groups_Ozero__class_Ozero(_1445344)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1445344), _1445346), hAPP(c_Int_Onumber__class_Onumber__of(_1445344), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (22686 ^ _781013) ^ [_1205456, _1205458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205456), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22689 ^ _781013 : [(22696 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205458), 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), _1205458), _1205456))))], (22690 ^ _781013) ^ [] : [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), _1205458), _1205456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205458), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (44623 ^ _781013) ^ [_1672187, _1672189, _1672191] : [-(c_List_OtakeWhile(_1672187, _1672189, _1672191) = hAPP(hAPP(c_List_Otake(_1672187), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672187)), c_List_OtakeWhile(_1672187, _1672189, _1672191))), _1672191))], (34929 ^ _781013) ^ [_1442266, _1442268] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1442266)), _1442268) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1442266), _1442268))), _1442268))], (7007 ^ _781013) ^ [_896946, _896948, _896950] : [_896946 = _896948, 7010 ^ _781013 : [(7013 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896950, tc_HOL_Obool)), _896948), _896946)))], (7011 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896950, tc_HOL_Obool)), _896946), _896948)))]]], (38198 ^ _781013) ^ [_1514211, _1514213, _1514215, _1514217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1514211), _1514217)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1514215), _1514213))), -(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), _1514211), _1514213)), 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), _1514215), _1514217)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (24248 ^ _781013) ^ [_1233354] : [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, _1233354))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1233354)))], (44817 ^ _781013) ^ [_1675740, _1675742] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1675740), _1675742) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1675740)), c_List_Oembed__list(_1675742))))], (30849 ^ _781013) ^ [_1358340, _1358342, _1358344] : [class_Orderings_Olinorder(_1358340), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358340), _1358342)), -(_1358342 = c_Orderings_Obot__class_Obot(tc_fun(_1358340, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358340), _1358344)), -(_1358344 = c_Orderings_Obot__class_Obot(tc_fun(_1358340, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1358340, tc_HOL_Obool)), _1358342), _1358344) = c_Orderings_Obot__class_Obot(tc_fun(_1358340, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1358340, c_Orderings_Oord__class_Omax(_1358340), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1358340, tc_HOL_Obool)), _1358342), _1358344)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358340), c_Big__Operators_Olattice_OSup__fin(_1358340, c_Orderings_Oord__class_Omax(_1358340), _1358342)), c_Big__Operators_Olattice_OSup__fin(_1358340, c_Orderings_Oord__class_Omax(_1358340), _1358344)))], (7959 ^ _781013) ^ [_915630, _915632, _915634, _915636] : [hAPP(hAPP(c_Option_Omap(_915630, _915632), _915634), _915636) = c_Option_Ooption_ONone(_915632), -(_915636 = c_Option_Ooption_ONone(_915630))], (45145 ^ _781013) ^ [_1682789, _1682791, _1682793, _1682795] : [class_Orderings_Olinorder(_1682789), -(c_List_Olinorder__class_Osorted(_1682789, hAPP(hAPP(c_List_Omap(_1682791, _1682789), _1682793), c_List_Olinorder__class_Osort__key(_1682791, _1682789, _1682793, _1682795))))], (45968 ^ _781013) ^ [_1700694] : [class_Complete__Lattice_Ocomplete__lattice(_1700694), -(c_Complete__Lattice_OInf__class_OInf(_1700694, c_Orderings_Otop__class_Otop(tc_fun(_1700694, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1700694))], (45982 ^ _781013) ^ [_1700965, _1700967, _1700969, _1700971] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1700965, tc_fun(_1700967, tc_HOL_Obool)), _1700969), _1700971) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1700967, tc_HOL_Obool), hAPP(c_Set_Oimage(_1700965, tc_fun(_1700967, tc_HOL_Obool), _1700971), _1700969)))], (9237 ^ _781013) ^ [_944344, _944346, _944348, _944350, _944352] : [-(c_Map_Orestrict__map(_944344, _944346, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_944344, tc_Option_Ooption(_944346)), _944348), _944350), hAPP(c_Option_Ooption_OSome(_944346), _944352)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_944344, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_944344), _944350), c_Orderings_Obot__class_Obot(tc_fun(_944344, tc_HOL_Obool))))) = c_Map_Orestrict__map(_944344, _944346, _944348, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_944344, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_944344), _944350), c_Orderings_Obot__class_Obot(tc_fun(_944344, tc_HOL_Obool))))))], (12806 ^ _781013) ^ [_1012996, _1012998, _1013000, _1013002, _1013004] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1012996, _1012998, _1013000, hAPP(c_COMBK(_1012998, _1012996), _1013002), hAPP(c_COMBK(_1012998, _1013000), _1013002)), _1013004) = _1013002)], (48824 ^ _781013) ^ [_1769796, _1769798, _1769800] : [c_Relation_Orefl__on(_1769796, _1769798, hAPP(c_Relation_Oconverse(_1769796, _1769796), _1769800)), -(c_Relation_Orefl__on(_1769796, _1769798, _1769800))], (51576 ^ _781013) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (49031 ^ _781013) ^ [_1775108, _1775110, _1775112, _1775114, _1775116] : [c_Relation_Osingle__valued(_1775108, _1775108, _1775110), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775108, _1775108)), hAPP(hAPP(c_Product__Type_OPair(_1775108, _1775108), _1775112), _1775114)), c_Transitive__Closure_Ortrancl(_1775108, _1775110))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775108, _1775108)), hAPP(hAPP(c_Product__Type_OPair(_1775108, _1775108), _1775112), _1775116)), c_Transitive__Closure_Ortrancl(_1775108, _1775110))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775108, _1775108)), hAPP(hAPP(c_Product__Type_OPair(_1775108, _1775108), _1775114), _1775116)), c_Transitive__Closure_Ortrancl(_1775108, _1775110)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775108, _1775108)), hAPP(hAPP(c_Product__Type_OPair(_1775108, _1775108), _1775116), _1775114)), c_Transitive__Closure_Ortrancl(_1775108, _1775110))))], (16335 ^ _781013) ^ [_1083011, _1083013, _1083015] : [hBOOL(hAPP(_1083011, _1083013)), -(hAPP(c_Set_OCollect(_1083015), hAPP(hAPP(c_COMBS(_1083015, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1083015), c_fconj), hAPP(c_fequal, _1083013))), _1083011)) = hAPP(hAPP(c_Set_Oinsert(_1083015), _1083013), c_Orderings_Obot__class_Obot(tc_fun(_1083015, tc_HOL_Obool))))], (4050 ^ _781013) ^ [_842279, _842281, _842283, _842285] : [-(c_Relation_Oinv__image(_842285, _842281) = c_Relation_Oinv__image(_842283, _842279)), _842285 = _842283, _842281 = _842279], (18011 ^ _781013) ^ [_1116804, _1116806, _1116808] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116804), _1116806)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116804), _1116808)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1116804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116806), _1116808))], (46820 ^ _781013) ^ [_1722672] : [-(c_Wellfounded_Owf(tc_fun(_1722672, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1722672)))], (9299 ^ _781013) ^ [_945756, _945758, _945760, _945762, _945764, _945766] : [-(hBOOL(hAPP(hAPP(c_member(_945756), _945758), c_Map_Odom(_945756, _945760, _945762)))), -(c_Map_Omap__add(_945756, _945760, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_945756, tc_Option_Ooption(_945760)), _945764), _945758), hAPP(c_Option_Ooption_OSome(_945760), _945766)), _945762) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_945756, tc_Option_Ooption(_945760)), c_Map_Omap__add(_945756, _945760, _945764, _945762)), _945758), hAPP(c_Option_Ooption_OSome(_945760), _945766)))], (43248 ^ _781013) ^ [_1642094, _1642096, _1642098, _1642100, _1642102] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642094, tc_fun(_1642096, tc_HOL_Obool)), _1642098), _1642100), _1642102)), 43251 ^ _781013 : [(43252 ^ _781013) ^ [_1642203] : [hBOOL(hAPP(hAPP(c_member(_1642094), _1642203), _1642098)), -(hBOOL(hAPP(hAPP(_1642100, _1642203), _1642102)))]]], (12962 ^ _781013) ^ [_1016529, _1016531, _1016533, _1016535, _1016537] : [hAPP(_1016535, _1016531) = _1016537, -(hBOOL(hAPP(hAPP(c_member(_1016529), _1016531), hAPP(c_Set_Ovimage(_1016529, _1016533, _1016535), hAPP(hAPP(c_Set_Oinsert(_1016533), _1016537), c_Orderings_Obot__class_Obot(tc_fun(_1016533, tc_HOL_Obool)))))))], (34407 ^ _781013) ^ [] : [-(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)))], (28080 ^ _781013) ^ [_1305274, _1305276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1305274)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1305274), _1305276)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1305274, _1305276) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1305274), _1305276))], (50818 ^ _781013) ^ [_1814025, _1814027, _1814029, _1814031, _1814033] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1814025), _1814027), _1814029), _1814031), _1814033) = c_New__DSequence_Opos__single(_1814025, _1814027))], (19955 ^ _781013) ^ [_1154755, _1154757] : [19956 ^ _781013 : [(19959 ^ _781013) ^ [] : [_1154755 = _1154757], (19957 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154755), _1154757))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154755), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1154757), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (51376 ^ _781013) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (1774 ^ _781013) ^ [_805930, _805932] : [-(class_Orderings_Oord(_805930)), _805932 = _805930, class_Orderings_Oord(_805932)], (7749 ^ _781013) ^ [_911581, _911583] : [-(hBOOL(hAPP(hAPP(c_member(_911581), 7750 ^ [_911581, _911583]), _911583))), -(_911583 = c_Orderings_Obot__class_Obot(tc_fun(_911581, tc_HOL_Obool)))], (44350 ^ _781013) ^ [_1664744, _1664746, _1664748] : [-(hAPP(c_List_Orev(_1664744), hAPP(c_List_Ofilter(_1664744, _1664746), _1664748)) = hAPP(c_List_Ofilter(_1664744, _1664746), hAPP(c_List_Orev(_1664744), _1664748)))], (17873 ^ _781013) ^ [_1114481, _1114483, _1114485] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1114481), _1114483)), _1114485) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1114481), _1114485)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1114483), _1114485)))], (10059 ^ _781013) ^ [_959001, _959003, _959005] : [class_Lattices_Osemilattice__inf(_959001), 10062 ^ _781013 : [(10069 ^ _781013) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959001), _959003), _959005) = _959003, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959001), _959003), _959005)))], (10063 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959001), _959003), _959005)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959001), _959003), _959005) = _959003)]]], (34207 ^ _781013) ^ [_1429917, _1429919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1429917)), c_Int_OBit1(_1429919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429917), _1429919)))], (46551 ^ _781013) ^ [_1714656, _1714658, _1714660, _1714662, _1714664] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1714656, _1714658, _1714660), _1714662), _1714664) = hAPP(c_Set_OCollect(tc_prod(_1714656, _1714660)), hAPP(c_Product__Type_Oprod_Oprod__case(_1714656, _1714660, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1714660, tc_fun(_1714658, tc_HOL_Obool)), tc_fun(_1714660, tc_HOL_Obool), _1714656), hAPP(c_COMBB(tc_fun(_1714658, tc_HOL_Obool), tc_HOL_Obool, _1714660), c_HOL_OEx(_1714658))), hAPP(hAPP(c_COMBC(_1714656, tc_fun(_1714660, tc_fun(_1714658, tc_HOL_Obool)), tc_fun(_1714660, tc_fun(_1714658, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1714658, tc_HOL_Obool), tc_fun(_1714658, tc_HOL_Obool)), tc_fun(tc_fun(_1714660, tc_fun(_1714658, tc_HOL_Obool)), tc_fun(_1714660, tc_fun(_1714658, tc_HOL_Obool))), _1714656), c_COMBB(tc_fun(_1714658, tc_HOL_Obool), tc_fun(_1714658, tc_HOL_Obool), _1714660)), hAPP(hAPP(c_COMBB(tc_fun(_1714658, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1714658, tc_HOL_Obool), tc_fun(_1714658, tc_HOL_Obool)), _1714656), c_COMBS(_1714658, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1714658, tc_HOL_Obool), tc_fun(_1714658, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1714656), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1714658), c_fconj)), hAPP(hAPP(c_COMBC(_1714656, tc_fun(tc_prod(_1714656, _1714658), tc_HOL_Obool), tc_fun(_1714658, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1714658, tc_fun(tc_fun(tc_prod(_1714656, _1714658), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1714656, _1714658), tc_HOL_Obool), tc_fun(_1714658, tc_HOL_Obool)), _1714656), c_COMBC(_1714658, tc_fun(tc_prod(_1714656, _1714658), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1714658, tc_prod(_1714656, _1714658)), tc_fun(_1714658, tc_fun(tc_fun(tc_prod(_1714656, _1714658), tc_HOL_Obool), tc_HOL_Obool)), _1714656), hAPP(c_COMBB(tc_prod(_1714656, _1714658), tc_fun(tc_fun(tc_prod(_1714656, _1714658), tc_HOL_Obool), tc_HOL_Obool), _1714658), c_member(tc_prod(_1714656, _1714658)))), c_Product__Type_OPair(_1714656, _1714658)))), _1714662))))), hAPP(hAPP(c_COMBC(_1714660, tc_fun(tc_prod(_1714658, _1714660), tc_HOL_Obool), tc_fun(_1714658, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1714658, tc_fun(tc_fun(tc_prod(_1714658, _1714660), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1714658, _1714660), tc_HOL_Obool), tc_fun(_1714658, tc_HOL_Obool)), _1714660), c_COMBC(_1714658, tc_fun(tc_prod(_1714658, _1714660), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1714658, tc_prod(_1714658, _1714660)), tc_fun(_1714658, tc_fun(tc_fun(tc_prod(_1714658, _1714660), tc_HOL_Obool), tc_HOL_Obool)), _1714660), hAPP(c_COMBB(tc_prod(_1714658, _1714660), tc_fun(tc_fun(tc_prod(_1714658, _1714660), tc_HOL_Obool), tc_HOL_Obool), _1714658), c_member(tc_prod(_1714658, _1714660)))), hAPP(c_COMBC(_1714658, _1714660, tc_prod(_1714658, _1714660)), c_Product__Type_OPair(_1714658, _1714660))))), _1714664))))))], (24960 ^ _781013) ^ [_1246204, _1246206, _1246208] : [class_Fields_Olinordered__field(_1246204), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246204), c_Groups_Ozero__class_Ozero(_1246204)), _1246206)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246204), c_Groups_Ozero__class_Ozero(_1246204)), _1246208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246204), c_Groups_Ozero__class_Ozero(_1246204)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1246204), _1246206), _1246208))))], (33570 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (3734 ^ _781013) ^ [_837457, _837459, _837461, _837463] : [-(c_List_Ozip(_837463, _837459) = c_List_Ozip(_837461, _837457)), _837463 = _837461, _837459 = _837457], (41732 ^ _781013) ^ [_1604565, _1604567, _1604569] : [-(_1604565 = c_List_Olist_ONil(_1604567)), -(c_List_Obutlast(_1604567, hAPP(hAPP(c_List_Oappend(_1604567), _1604569), _1604565)) = hAPP(hAPP(c_List_Oappend(_1604567), _1604569), c_List_Obutlast(_1604567, _1604565)))], (19244 ^ _781013) ^ [_1141423, _1141425, _1141427, _1141429] : [class_Rings_Olinordered__semidom(_1141423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141423), c_Groups_Oone__class_Oone(_1141423)), _1141425)), 19251 ^ _781013 : [(19258 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1141427), _1141429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141423), hAPP(hAPP(c_Power_Opower__class_Opower(_1141423), _1141425), _1141427)), hAPP(hAPP(c_Power_Opower__class_Opower(_1141423), _1141425), _1141429))))], (19252 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141423), hAPP(hAPP(c_Power_Opower__class_Opower(_1141423), _1141425), _1141427)), hAPP(hAPP(c_Power_Opower__class_Opower(_1141423), _1141425), _1141429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1141427), _1141429)))]]], (16482 ^ _781013) ^ [_1086084, _1086086, _1086088] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1086084), _1086086)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086084), _1086088)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1086084), _1086086)), hAPP(c_Finite__Set_Ocard(_1086084), _1086088)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1086084), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086084, tc_HOL_Obool)), _1086086), _1086088))), hAPP(c_Finite__Set_Ocard(_1086084), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086084, tc_HOL_Obool)), _1086086), _1086088))))], (38796 ^ _781013) ^ [_1528516, _1528518, _1528520, _1528522, _1528524] : [class_Orderings_Olinorder(_1528516), -(hAPP(c_List_Oset(_1528518), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1528518, _1528516, _1528520), _1528522), _1528524)) = hAPP(hAPP(c_Set_Oinsert(_1528518), _1528522), hAPP(c_List_Oset(_1528518), _1528524)))], (7493 ^ _781013) ^ [_906291, _906293, _906295, _906297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906291, tc_HOL_Obool)), _906293), _906295)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906291, tc_HOL_Obool)), _906295), _906297)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906291, tc_HOL_Obool)), _906295), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906291, tc_HOL_Obool)), _906297), _906293)) = _906293)], (21093 ^ _781013) ^ [_1176850, _1176852, _1176854] : [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), _1176850), _1176852)), _1176854)), 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)), _1176854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176852), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11610 ^ _781013) ^ [_989941, _989943, _989945] : [class_Orderings_Otop(_989941), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_989943, _989941)), _989945) = c_Orderings_Otop__class_Otop(_989941))], (43030 ^ _781013) ^ [_1636234, _1636236, _1636238, _1636240, _1636242] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636234, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636236, tc_fun(_1636234, tc_HOL_Obool)), _1636238), _1636240)), _1636242) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636236, tc_fun(_1636234, tc_HOL_Obool)), _1636238), hAPP(hAPP(c_COMBC(_1636236, tc_fun(_1636234, tc_HOL_Obool), tc_fun(_1636234, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1636234, tc_HOL_Obool), tc_fun(tc_fun(_1636234, tc_HOL_Obool), tc_fun(_1636234, tc_HOL_Obool)), _1636236), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636234, tc_HOL_Obool))), _1636240)), _1636242)))], (28936 ^ _781013) ^ [_1320762, _1320764] : [class_Groups_Oordered__ab__group__add__abs(_1320762), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320762), c_Groups_Ozero__class_Ozero(_1320762)), _1320764)), -(hAPP(c_Groups_Oabs__class_Oabs(_1320762), _1320764) = _1320764)], (14993 ^ _781013) ^ [_1058342, _1058344] : [class_Groups_Ogroup__add(_1058342), 14996 ^ _781013 : [(15003 ^ _781013) ^ [] : [_1058344 = c_Groups_Ozero__class_Ozero(_1058342), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1058342), _1058344) = c_Groups_Ozero__class_Ozero(_1058342))], (14997 ^ _781013) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1058342), _1058344) = c_Groups_Ozero__class_Ozero(_1058342), -(_1058344 = c_Groups_Ozero__class_Ozero(_1058342))]]], (15047 ^ _781013) ^ [_1059123, _1059125, _1059127, _1059129, _1059131] : [class_Groups_Ocomm__monoid__mult(_1059123), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1059125, _1059123), hAPP(hAPP(c_COMBS(_1059125, _1059123, _1059123), hAPP(hAPP(c_COMBB(_1059123, tc_fun(_1059123, _1059123), _1059125), c_Groups_Otimes__class_Otimes(_1059123)), _1059127)), _1059129)), _1059131) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059123), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1059125, _1059123), _1059127), _1059131)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1059125, _1059123), _1059129), _1059131)))], (30745 ^ _781013) ^ [_1356535, _1356537, _1356539] : [class_Orderings_Olinorder(_1356535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356535), _1356537)), -(_1356539 = c_Orderings_Obot__class_Obot(tc_fun(_1356535, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1356535, tc_HOL_Obool)), _1356539), _1356537)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356535), c_Big__Operators_Olattice_OSup__fin(_1356535, c_Orderings_Oord__class_Omax(_1356535), _1356539)), c_Big__Operators_Olattice_OSup__fin(_1356535, c_Orderings_Oord__class_Omax(_1356535), _1356537)) = c_Big__Operators_Olattice_OSup__fin(_1356535, c_Orderings_Oord__class_Omax(_1356535), _1356537))], (42428 ^ _781013) ^ [_1621379, _1621381, _1621383] : [-(hAPP(c_List_Otl(_1621379), hAPP(hAPP(c_List_Oappend(_1621379), _1621381), _1621383)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1621379), _1621379, hAPP(c_List_Otl(_1621379), _1621383), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1621379), tc_List_Olist(_1621379)), _1621379), hAPP(hAPP(c_COMBC(tc_List_Olist(_1621379), tc_List_Olist(_1621379), tc_List_Olist(_1621379)), c_List_Oappend(_1621379)), _1621383))), _1621381))], (49176 ^ _781013) ^ [_1778781, _1778783] : [-(hAPP(hAPP(c_Nat_Ocompow(_1778781, _1778781), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1778783) = c_Fun_Oid(_1778781))], (36679 ^ _781013) ^ [_1481299, _1481301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481299), 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)), _1481301)), -(c_Divides_OnegDivAlg(_1481299, _1481301) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1481299), _1481301)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1481299, _1481301)))], (10305 ^ _781013) ^ [_963381, _963383, _963385] : [-(hBOOL(hAPP(hAPP(c_member(_963381), _963383), _963385))), -(hBOOL(hAPP(hAPP(c_member(_963381), _963383), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_963381, tc_HOL_Obool)), _963385))))], (44534 ^ _781013) ^ [_1669482, _1669484, _1669486, _1669488] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1669482)), c_List_Otranspose__rel(_1669482)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1669482)), hAPP(hAPP(c_List_Olist_OCons(_1669482), _1669484), _1669486)), _1669488))), -(c_List_Otranspose(_1669482, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1669482)), hAPP(hAPP(c_List_Olist_OCons(_1669482), _1669484), _1669486)), _1669488)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1669482)), hAPP(hAPP(c_List_Olist_OCons(_1669482), _1669484), c_List_Oconcat(_1669482, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1669482), tc_List_Olist(_1669482)), c_List_Olist_Olist__case(tc_List_Olist(_1669482), _1669482, c_List_Olist_ONil(_1669482), hAPP(hAPP(c_COMBB(tc_List_Olist(_1669482), tc_fun(tc_List_Olist(_1669482), tc_List_Olist(_1669482)), _1669482), c_COMBK(tc_List_Olist(_1669482), tc_List_Olist(_1669482))), hAPP(hAPP(c_COMBC(_1669482, tc_List_Olist(_1669482), tc_List_Olist(_1669482)), c_List_Olist_OCons(_1669482)), c_List_Olist_ONil(_1669482))))), _1669488)))), c_List_Otranspose(_1669482, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1669482)), _1669486), c_List_Oconcat(tc_List_Olist(_1669482), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1669482), tc_List_Olist(tc_List_Olist(_1669482))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1669482)), _1669482, c_List_Olist_ONil(tc_List_Olist(_1669482)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1669482), tc_List_Olist(tc_List_Olist(_1669482))), _1669482), hAPP(hAPP(c_COMBC(tc_List_Olist(_1669482), tc_List_Olist(tc_List_Olist(_1669482)), tc_List_Olist(tc_List_Olist(_1669482))), c_List_Olist_OCons(tc_List_Olist(_1669482))), c_List_Olist_ONil(tc_List_Olist(_1669482)))))), _1669488))))))], (10815 ^ _781013) ^ [_972114, _972116, _972118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972114, tc_HOL_Obool)), _972116), _972118)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972114, tc_HOL_Obool)), _972116), _972118) = _972116)], (21461 ^ _781013) ^ [] : [-(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))))], (20452 ^ _781013) ^ [_1163019, _1163021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1163019)), _1163021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1163019), _1163021)))], (17463 ^ _781013) ^ [_1107465, _1107467, _1107469, _1107471, _1107473, _1107475] : [-(hBOOL(hAPP(hAPP(c_member(_1107465), _1107467), _1107469))), -(hAPP(c_Fun_Ooverride__on(_1107465, _1107471, _1107473, _1107475, _1107469), _1107467) = hAPP(_1107473, _1107467))], (14117 ^ _781013) ^ [_1040930, _1040932, _1040934, _1040936, _1040938] : [class_Groups_Ocomm__monoid__add(_1040930), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1040932, _1040930), hAPP(hAPP(c_COMBS(_1040932, _1040930, _1040930), hAPP(hAPP(c_COMBB(_1040930, tc_fun(_1040930, _1040930), _1040932), c_Groups_Oplus__class_Oplus(_1040930)), _1040934)), _1040936)), _1040938) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040930), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1040932, _1040930), _1040934), _1040938)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1040932, _1040930), _1040936), _1040938)))], (28412 ^ _781013) ^ [_1311168, _1311170, _1311172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1311168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1311170), 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), _1311170), _1311172))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1311168))), _1311172)))], (19985 ^ _781013) ^ [_1155263] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1155263)], (18193 ^ _781013) ^ [_1119832, _1119834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119832), _1119834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119832), _1119834)))], (24236 ^ _781013) ^ [_1233122, _1233124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233124)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1233122)), hAPP(c_Int_Onat, _1233124)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1233122, _1233124)))], (50614 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47942 ^ _781013) ^ [_1749389, _1749391, _1749393, _1749395, _1749397, _1749399, _1749401, _1749403, _1749405] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1749389, _1749391, _1749393, _1749395), hAPP(hAPP(c_Product__Type_Oscomp(_1749389, _1749397, _1749399, tc_prod(_1749391, _1749393)), _1749401), _1749403)), _1749405) = hAPP(hAPP(c_Product__Type_Oscomp(_1749389, _1749397, _1749399, _1749395), _1749401), hAPP(hAPP(c_COMBC(_1749397, tc_fun(_1749391, tc_fun(_1749393, _1749395)), tc_fun(_1749399, _1749395)), hAPP(hAPP(c_COMBB(tc_fun(_1749399, tc_prod(_1749391, _1749393)), tc_fun(tc_fun(_1749391, tc_fun(_1749393, _1749395)), tc_fun(_1749399, _1749395)), _1749397), c_Product__Type_Oscomp(_1749399, _1749391, _1749393, _1749395)), _1749403)), _1749405)))], (7199 ^ _781013) ^ [_901098, _901100, _901102] : [class_Orderings_Opreorder(_901098), _901100 = _901102, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901098), _901100), _901102)))], (50514 ^ _781013) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24009 ^ _781013) ^ [_1229163, _1229165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229165)), 24016 ^ _781013 : [(24023 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229163), _1229165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229163)), hAPP(c_Int_Onat, _1229165))))], (24017 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229163)), hAPP(c_Int_Onat, _1229165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229163), _1229165)))]]], (17246 ^ _781013) ^ [_1102097, _1102099, _1102101, _1102103] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1102097), _1102099)), hBOOL(hAPP(hAPP(c_member(_1102097), _1102101), _1102099)), hBOOL(hAPP(hAPP(c_member(_1102097), _1102103), _1102099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1102097), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1102097, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1102097, tc_HOL_Obool)), _1102099), hAPP(hAPP(c_Set_Oinsert(_1102097), _1102101), c_Orderings_Obot__class_Obot(tc_fun(_1102097, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1102097), _1102103), c_Orderings_Obot__class_Obot(tc_fun(_1102097, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1102097), _1102099))))], (19757 ^ _781013) ^ [_1151110, _1151112, _1151114] : [class_Lattices_Odistrib__lattice(_1151110), hBOOL(hAPP(c_Finite__Set_Ofinite(_1151110), _1151112)), -(_1151112 = c_Orderings_Obot__class_Obot(tc_fun(_1151110, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1151110), _1151114), c_Big__Operators_Olattice__class_OSup__fin(_1151110, _1151112)) = c_Big__Operators_Olattice__class_OSup__fin(_1151110, hAPP(c_Set_OCollect(_1151110), hAPP(hAPP(c_COMBB(tc_fun(_1151110, tc_HOL_Obool), tc_HOL_Obool, _1151110), c_HOL_OEx(_1151110)), hAPP(hAPP(c_COMBC(_1151110, tc_fun(_1151110, tc_HOL_Obool), tc_fun(_1151110, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1151110, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1151110, tc_HOL_Obool), tc_fun(_1151110, tc_HOL_Obool)), _1151110), c_COMBS(_1151110, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1151110, tc_HOL_Obool), tc_fun(_1151110, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1151110), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1151110), c_fconj)), hAPP(hAPP(c_COMBC(_1151110, tc_fun(_1151110, _1151110), tc_fun(_1151110, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1151110, tc_HOL_Obool), tc_fun(tc_fun(_1151110, _1151110), tc_fun(_1151110, tc_HOL_Obool)), _1151110), c_COMBB(_1151110, tc_HOL_Obool, _1151110)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1151110), _1151114))))), hAPP(hAPP(c_COMBC(_1151110, tc_fun(_1151110, tc_HOL_Obool), tc_HOL_Obool), c_member(_1151110)), _1151112))))))], (8181 ^ _781013) ^ [_920567, _920569, _920571, _920573, _920575, _920577, _920579, _920581] : [c_Finite__Set_Ofolding__image__simple__idem(_920567, _920569, _920571, _920573, _920575, _920577), hBOOL(hAPP(c_Finite__Set_Ofinite(_920569), _920579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920569, tc_HOL_Obool)), _920581), _920579)), -(hAPP(hAPP(_920571, hAPP(_920577, _920581)), hAPP(_920577, _920579)) = hAPP(_920577, _920579))], (13652 ^ _781013) ^ [] : [-(c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))], (48587 ^ _781013) ^ [_1763550, _1763552, _1763554, _1763556] : [c_Wellfounded_Owf(_1763550, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1763550, _1763550)), hAPP(hAPP(c_Product__Type_OPair(_1763550, _1763550), _1763552), _1763554)), _1763556)), 48590 ^ _781013 : [(48593 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763550, _1763550)), hAPP(hAPP(c_Product__Type_OPair(_1763550, _1763550), _1763554), _1763552)), c_Transitive__Closure_Ortrancl(_1763550, _1763556)))], (48591 ^ _781013) ^ [] : [-(c_Wellfounded_Owf(_1763550, _1763556))]]], (11422 ^ _781013) ^ [_985999, _986001, _986003] : [class_Lattices_Olattice(_985999), hBOOL(hAPP(c_Finite__Set_Ofinite(_985999), _986001)), hBOOL(hAPP(hAPP(c_member(_985999), _986003), _986001)), 11433 ^ _781013 : [(11440 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985999, tc_HOL_Obool)), _986001), hAPP(hAPP(c_Set_Oinsert(_985999), _986003), c_Orderings_Obot__class_Obot(tc_fun(_985999, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_985999, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_985999, _986001) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_985999), _986003), c_Big__Operators_Olattice__class_OInf__fin(_985999, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985999, tc_HOL_Obool)), _986001), hAPP(hAPP(c_Set_Oinsert(_985999), _986003), c_Orderings_Obot__class_Obot(tc_fun(_985999, tc_HOL_Obool)))))))], (11434 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985999, tc_HOL_Obool)), _986001), hAPP(hAPP(c_Set_Oinsert(_985999), _986003), c_Orderings_Obot__class_Obot(tc_fun(_985999, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_985999, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_985999, _986001) = _986003)]]], (44336 ^ _781013) ^ [_1664418, _1664420] : [class_Groups_Ocomm__monoid__add(_1664418), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1664418), hAPP(c_List_Orev(_1664418), _1664420)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1664418), _1664420))], (10867 ^ _781013) ^ [_973392, _973394, _973396, _973398] : [class_Lattices_Osemilattice__sup(_973392), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973392), _973394), _973396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973392), _973394), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_973392), _973398), _973396))))], (15745 ^ _781013) ^ [_1072283, _1072285, _1072287, _1072289] : [class_Rings_Olinordered__ring__strict(_1072283), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072283), _1072285), _1072287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072283), _1072289), c_Groups_Ozero__class_Ozero(_1072283))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072283), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072283), _1072287), _1072289)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072283), _1072285), _1072289))))], (47104 ^ _781013) ^ [_1729041, _1729043, _1729045, _1729047, _1729049] : [-(hAPP(c_Relation_ORange(_1729041, _1729043), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1729041, _1729043)), hAPP(hAPP(c_Product__Type_OPair(_1729041, _1729043), _1729045), _1729047)), _1729049)) = hAPP(hAPP(c_Set_Oinsert(_1729043), _1729047), hAPP(c_Relation_ORange(_1729041, _1729043), _1729049)))], (46521 ^ _781013) ^ [_1713883, _1713885, _1713887, _1713889, _1713891] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1713883, _1713883)), hAPP(hAPP(c_Product__Type_OPair(_1713883, _1713883), _1713885), _1713887)), c_List_Omeasures(_1713883, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1713883, tc_Nat_Onat)), _1713889), _1713891)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1713889, _1713885)), hAPP(_1713889, _1713887)))), 46528 ^ _781013 : [(46531 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1713883, _1713883)), hAPP(hAPP(c_Product__Type_OPair(_1713883, _1713883), _1713885), _1713887)), c_List_Omeasures(_1713883, _1713891))))], (46529 ^ _781013) ^ [] : [-(hAPP(_1713889, _1713885) = hAPP(_1713889, _1713887))]]], (45836 ^ _781013) ^ [_1697932, _1697934] : [class_Complete__Lattice_Ocomplete__lattice(_1697932), -(c_Complete__Lattice_OInf__class_OInf(_1697932, _1697934) = c_Complete__Lattice_OSup__class_OSup(_1697932, hAPP(c_Set_OCollect(_1697932), hAPP(hAPP(c_COMBB(tc_fun(_1697932, tc_HOL_Obool), tc_HOL_Obool, _1697932), c_HOL_OAll(_1697932)), hAPP(hAPP(c_COMBB(tc_fun(_1697932, tc_HOL_Obool), tc_fun(_1697932, tc_HOL_Obool), _1697932), hAPP(c_COMBS(_1697932, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1697932), c_fimplies), hAPP(hAPP(c_COMBC(_1697932, tc_fun(_1697932, tc_HOL_Obool), tc_HOL_Obool), c_member(_1697932)), _1697934)))), c_Orderings_Oord__class_Oless__eq(_1697932))))))], (4172 ^ _781013) ^ [_844120, _844122, _844124, _844126] : [-(c_Transitive__Closure_Otrancl(_844126, _844122) = c_Transitive__Closure_Otrancl(_844124, _844120)), _844126 = _844124, _844122 = _844120], (23106 ^ _781013) ^ [_1213291, _1213293, _1213295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1213291), _1213293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213291), _1213295)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213293), _1213295))))], (46533 ^ _781013) ^ [_1714162, _1714164, _1714166, _1714168, _1714170] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1714162, _1714162)), hAPP(hAPP(c_Product__Type_OPair(_1714162, _1714162), _1714164), _1714166)), c_List_Omeasures(_1714162, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1714162, tc_Nat_Onat)), _1714168), _1714170))))), 46534 ^ _781013 : [(46537 ^ _781013) ^ [] : [hAPP(_1714168, _1714164) = hAPP(_1714168, _1714166), hBOOL(hAPP(hAPP(c_member(tc_prod(_1714162, _1714162)), hAPP(hAPP(c_Product__Type_OPair(_1714162, _1714162), _1714164), _1714166)), c_List_Omeasures(_1714162, _1714170)))], (46535 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1714168, _1714164)), hAPP(_1714168, _1714166)))]]], (19412 ^ _781013) ^ [_1144508, _1144510] : [class_Groups_Omonoid__mult(_1144508), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1144508), _1144510), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1144510)], (39546 ^ _781013) ^ [_1545845, _1545847, _1545849] : [hBOOL(hAPP(_1545845, _1545847)), -(hBOOL(hAPP(_1545845, c_Hilbert__Choice_OEps(_1545849, _1545845))))], (47065 ^ _781013) ^ [_1728153, _1728155] : [-(hAPP(c_Relation_ORange(_1728153, _1728155), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1728153, _1728155), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1728155, tc_HOL_Obool)))], (44280 ^ _781013) ^ [_1663298, _1663300, _1663302] : [_1663302 = hAPP(hAPP(c_List_Olist_OCons(_1663298), _1663300), c_List_Olist_ONil(_1663298)), -(hAPP(hAPP(c_List_Olist_OCons(_1663298), _1663300), c_List_Olist_ONil(_1663298)) = hAPP(c_List_Orev(_1663298), _1663302))], (18732 ^ _781013) ^ [_1130100, _1130102, _1130104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130100), _1130102)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130102), _1130100)), _1130104) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1130102), _1130104)), _1130100))], (16069 ^ _781013) ^ [_1078227] : [class_Rings_Olinordered__semidom(_1078227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078227), c_Groups_Oone__class_Oone(_1078227)), c_Groups_Ozero__class_Ozero(_1078227)))], (21728 ^ _781013) ^ [] : [-(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))], (3512 ^ _781013) ^ [_833992, _833994, _833996, _833998] : [-(c_List_Olists(_833998, _833994) = c_List_Olists(_833996, _833992)), _833998 = _833996, _833994 = _833992], (6286 ^ _781013) ^ [_883332, _883334, _883336] : [c_Com_Ocom_OCond(_883332, _883334, _883336) = c_Com_Ocom_OSKIP], (46597 ^ _781013) ^ [_1716038, _1716040, _1716042, _1716044, _1716046, _1716048, _1716050, _1716052] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1716038, _1716040)), hAPP(hAPP(c_Product__Type_OPair(_1716038, _1716040), _1716042), _1716044)), _1716046)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1716040, _1716048)), hAPP(hAPP(c_Product__Type_OPair(_1716040, _1716048), _1716044), _1716050)), _1716052)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1716038, _1716048)), hAPP(hAPP(c_Product__Type_OPair(_1716038, _1716048), _1716042), _1716050)), hAPP(hAPP(c_Relation_Orel__comp(_1716038, _1716040, _1716048), _1716046), _1716052))))], (44869 ^ _781013) ^ [_1676854, _1676856, _1676858] : [c_List_OdropWhile(_1676854, _1676856, _1676858) = c_List_Olist_ONil(_1676854), 44872 ^ _781013 : [(44873 ^ _781013) ^ [_1676945] : [hBOOL(hAPP(hAPP(c_member(_1676854), _1676945), hAPP(c_List_Oset(_1676854), _1676858))), -(hBOOL(hAPP(_1676856, _1676945)))]]], (23597 ^ _781013) ^ [_1222413, _1222415] : [class_Rings_Odivision__ring__inverse__zero(_1222413), 23600 ^ _781013 : [(23607 ^ _781013) ^ [] : [-(_1222415 = c_Groups_Ozero__class_Ozero(_1222413)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222413), _1222415), _1222415) = c_Groups_Oone__class_Oone(_1222413))], (23601 ^ _781013) ^ [] : [_1222415 = c_Groups_Ozero__class_Ozero(_1222413), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222413), _1222415), _1222415) = c_Groups_Ozero__class_Ozero(_1222413))]]], (51388 ^ _781013) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (24138 ^ _781013) ^ [_1231182, _1231184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231184)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231182), _1231184)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1231182)), hAPP(c_Int_Onat, _1231184)))], (45830 ^ _781013) ^ [_1697691, _1697693] : [class_Complete__Lattice_Ocomplete__lattice(_1697691), -(c_Complete__Lattice_OSup__class_OSup(_1697691, _1697693) = c_Complete__Lattice_OInf__class_OInf(_1697691, hAPP(c_Set_OCollect(_1697691), hAPP(hAPP(c_COMBB(tc_fun(_1697691, tc_HOL_Obool), tc_HOL_Obool, _1697691), c_HOL_OAll(_1697691)), hAPP(hAPP(c_COMBB(tc_fun(_1697691, tc_HOL_Obool), tc_fun(_1697691, tc_HOL_Obool), _1697691), hAPP(c_COMBS(_1697691, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1697691), c_fimplies), hAPP(hAPP(c_COMBC(_1697691, tc_fun(_1697691, tc_HOL_Obool), tc_HOL_Obool), c_member(_1697691)), _1697693)))), hAPP(c_COMBC(_1697691, _1697691, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1697691)))))))], (46263 ^ _781013) ^ [_1707305, _1707307, _1707309, _1707311, _1707313, _1707315] : [c_List_Olist__all2(_1707305, _1707307, _1707309, _1707311, _1707313), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707315), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707305)), _1707311))), -(hBOOL(hAPP(hAPP(_1707309, hAPP(hAPP(c_List_Onth(_1707305), _1707311), _1707315)), hAPP(hAPP(c_List_Onth(_1707307), _1707313), _1707315))))], (50230 ^ _781013) ^ [_1802442, _1802444, _1802446] : [c_Nitpick_Oless__frac(_1802442, _1802444, _1802446), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1802442), c_Nitpick_Oplus__frac(_1802442, _1802444, c_Nitpick_Ouminus__frac(_1802442, _1802446)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40617 ^ _781013) ^ [_1576622, _1576624, _1576626, _1576628, _1576630] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1576622, _1576624), _1576626), hAPP(hAPP(c_COMBS(_1576622, tc_fun(_1576624, tc_HOL_Obool), tc_fun(_1576624, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576624, tc_HOL_Obool), tc_fun(tc_fun(_1576624, tc_HOL_Obool), tc_fun(_1576624, tc_HOL_Obool)), _1576622), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1576624, tc_HOL_Obool))), _1576628)), _1576630)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1576622, _1576624), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1576622, _1576624), _1576626), _1576628)), hAPP(hAPP(c_Product__Type_OSigma(_1576622, _1576624), _1576626), _1576630)))], (38804 ^ _781013) ^ [_1528696, _1528698, _1528700] : [-(hBOOL(hAPP(hAPP(c_member(_1528696), _1528698), hAPP(c_List_Oset(_1528696), _1528700)))), -(hAPP(c_List_OremoveAll(_1528696, _1528698), _1528700) = _1528700)], (23168 ^ _781013) ^ [_1214420, _1214422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1214420)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1214422), _1214420)), _1214422)))], (27343 ^ _781013) ^ [_1290457, _1290459] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1290457), _1290459)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1290457, tc_HOL_Obool)), hAPP(c_Set_OPow(_1290457), _1290459)) = 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(_1290457), _1290459)))], (9651 ^ _781013) ^ [_951802, _951804, _951806] : [class_Orderings_Oorder(_951802), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951802), _951804), _951806)), _951804 = _951806], (34753 ^ _781013) ^ [_1439127, _1439129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1439127), _1439129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1439127)), c_Int_OBit1(_1439129))))], (23927 ^ _781013) ^ [_1227727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227727)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1227727)) = _1227727)], (31431 ^ _781013) ^ [_1372572, _1372574, _1372576, _1372578] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _1372572)), _1372574), _1372576), _1372578)), 31435 ^ _781013 : [(31438 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1372572))), _1372574), 31434 ^ [_1372572, _1372574, _1372576, _1372578]), _1372578)))], (31436 ^ _781013) ^ [] : [-(_1372576 = hAPP(c_Nat_OSuc, 31434 ^ [_1372572, _1372574, _1372576, _1372578]))]]], (30573 ^ _781013) ^ [_1352341, _1352343, _1352345] : [class_Orderings_Olinorder(_1352341), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352341), _1352343)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352341), _1352345)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1352341, tc_HOL_Obool)), _1352343), _1352345) = c_Orderings_Obot__class_Obot(tc_fun(_1352341, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352341), c_Big__Operators_Olinorder__class_OMax(_1352341, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352341, tc_HOL_Obool)), _1352343), _1352345))), c_Big__Operators_Olinorder__class_OMax(_1352341, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1352341, tc_HOL_Obool)), _1352343), _1352345))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352341), c_Big__Operators_Olinorder__class_OMax(_1352341, _1352343)), c_Big__Operators_Olinorder__class_OMax(_1352341, _1352345)))], (39350 ^ _781013) ^ [_1541590, _1541592, _1541594, _1541596, _1541598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1541590, tc_HOL_Obool)), hAPP(c_List_Oset(_1541590), _1541592)), _1541594)), hBOOL(hAPP(hAPP(c_member(_1541590), _1541596), _1541594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1541590, tc_HOL_Obool)), hAPP(c_List_Oset(_1541590), hAPP(hAPP(c_List_Olist__update(_1541590, _1541592), _1541598), _1541596))), _1541594)))], (22904 ^ _781013) ^ [_1209474, _1209476, _1209478, _1209480] : [class_Groups_Ocomm__monoid__add(_1209474), 22907 ^ _781013 : [(22914 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209476), _1209478))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1209474), _1209480), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209478), hAPP(c_Nat_OSuc, _1209476))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209474), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1209474), _1209480), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209478), _1209476))), hAPP(_1209480, _1209476)))], (22908 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209476), _1209478)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1209474), _1209480), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209478), hAPP(c_Nat_OSuc, _1209476))) = c_Groups_Ozero__class_Ozero(_1209474))]]], (48742 ^ _781013) ^ [_1767558, _1767560, _1767562, _1767564] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1767558), tc_List_Olist(_1767558))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1767558), tc_List_Olist(_1767558)), _1767560), _1767562)), c_List_Olistrel1(_1767558, hAPP(c_Relation_Oconverse(_1767558, _1767558), _1767564)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1767558), tc_List_Olist(_1767558))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1767558), tc_List_Olist(_1767558)), _1767560), _1767562)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1767558), tc_List_Olist(_1767558)), c_List_Olistrel1(_1767558, _1767564)))))], (10041 ^ _781013) ^ [_958680, _958682, _958684] : [class_Lattices_Osemilattice__inf(_958680), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958680), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_958680), _958682), _958684)), _958682)))], (30265 ^ _781013) ^ [_1346383, _1346385, _1346387, _1346389] : [class_Orderings_Olinorder(_1346383), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346383), _1346385), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346383), _1346387), _1346389)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346383), _1346387), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346383), _1346385), _1346389)))], (33402 ^ _781013) ^ [_1414891, _1414893] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414891) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414893)), 33405 ^ _781013 : [(33408 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414893)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33406 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414891))))]], 33409 ^ _781013 : [(33412 ^ _781013) ^ [] : [33413 ^ _781013 : [(33416 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414891) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (33414 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414893))))]], 33417 ^ _781013 : [(33420 ^ _781013) ^ [] : [_1414891 = _1414893], (33418 ^ _781013) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414893)))]]], (33410 ^ _781013) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414891)))]]], (30395 ^ _781013) ^ [_1349014] : [class_Orderings_Oord(_1349014), -(c_Orderings_Oord__class_Omax(_1349014) = c_Orderings_Oord_Omax(_1349014, c_Orderings_Oord__class_Oless__eq(_1349014)))], (49113 ^ _781013) ^ [_1777047, _1777049, _1777051] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1777047, _1777047)), _1777049), c_Transitive__Closure_Ortrancl(_1777047, _1777051))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777047, _1777047)), _1777049), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777047, _1777047), tc_HOL_Obool), 49116 ^ [_1777047, _1777049, _1777051]), _1777051))))], (34641 ^ _781013) ^ [_1437295, _1437297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1437295)), c_Int_OBit0(_1437297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437295), _1437297)))], (51326 ^ _781013) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (27563 ^ _781013) ^ [_1295555, _1295557] : [class_Groups_Osgn__if(_1295555), 27566 ^ _781013 : [(27573 ^ _781013) ^ [] : [-(_1295557 = c_Groups_Ozero__class_Ozero(_1295555)), 27576 ^ _781013 : [(27583 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295555), c_Groups_Ozero__class_Ozero(_1295555)), _1295557))), -(c_Groups_Osgn__class_Osgn(_1295555, _1295557) = hAPP(c_Groups_Ouminus__class_Ouminus(_1295555), c_Groups_Oone__class_Oone(_1295555)))], (27577 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295555), c_Groups_Ozero__class_Ozero(_1295555)), _1295557)), -(c_Groups_Osgn__class_Osgn(_1295555, _1295557) = c_Groups_Oone__class_Oone(_1295555))]]], (27567 ^ _781013) ^ [] : [_1295557 = c_Groups_Ozero__class_Ozero(_1295555), -(c_Groups_Osgn__class_Osgn(_1295555, _1295557) = c_Groups_Ozero__class_Ozero(_1295555))]]], (32130 ^ _781013) ^ [_1391035] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1391035)), -(hAPP(c_Int_Onat, _1391035) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (86 ^ _781013) ^ [_782364, _782366, _782368, _782370, _782372, _782374, _782376, _782378, _782380, _782382, _782384, _782386] : [-(c_Nitpick_Ofold__graph_H(_782384, _782380, _782376, _782372, _782368, _782364)), c_Nitpick_Ofold__graph_H(_782386, _782382, _782378, _782374, _782370, _782366), _782386 = _782384, _782382 = _782380, _782378 = _782376, _782374 = _782372, _782370 = _782368, _782366 = _782364], (12160 ^ _781013) ^ [_1000426, _1000428, _1000430, _1000432, _1000434] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1000426), hAPP(c_Set_Oimage(_1000428, _1000426, _1000430), c_Orderings_Otop__class_Otop(tc_fun(_1000428, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1000432), hAPP(c_Set_Oimage(_1000428, _1000432, hAPP(hAPP(c_COMBB(_1000426, _1000432, _1000428), _1000434), _1000430)), c_Orderings_Otop__class_Otop(tc_fun(_1000428, tc_HOL_Obool))))))], (24186 ^ _781013) ^ [_1232073, _1232075, _1232077] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1232073, tc_Nat_Onat), _1232075), _1232077) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1232073, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1232073), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1232075)), _1232077)))], (21531 ^ _781013) ^ [_1185404] : [-(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), _1185404))))], (35619 ^ _781013) ^ [] : [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)], (51482 ^ _781013) ^ [_1823486, _1823488] : [-(class_HOL_Oequal(tc_prod(_1823486, _1823488)))], (31906 ^ _781013) ^ [_1385738, _1385740, _1385742, _1385744, _1385746] : [hBOOL(hAPP(hAPP(c_member(_1385738), _1385740), _1385742)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385744, tc_HOL_Obool)), hAPP(_1385746, _1385740)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385738, tc_fun(_1385744, tc_HOL_Obool)), _1385742), _1385746)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385738, tc_fun(_1385744, tc_HOL_Obool)), _1385742), _1385746))], (43735 ^ _781013) ^ [_1652392, _1652394, _1652396] : [class_Orderings_Olinorder(_1652392), 43738 ^ _781013 : [(43745 ^ _781013) ^ [] : [c_List_Olinorder__class_Osorted(_1652392, _1652396), -(c_List_Olinorder__class_Osorted(_1652392, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1652392, _1652392, c_COMBI(_1652392)), _1652394), _1652396)))], (43739 ^ _781013) ^ [] : [c_List_Olinorder__class_Osorted(_1652392, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1652392, _1652392, c_COMBI(_1652392)), _1652394), _1652396)), -(c_List_Olinorder__class_Osorted(_1652392, _1652396))]]], (6950 ^ _781013) ^ [_895863, _895865] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895863, tc_HOL_Obool)), _895865), _895865) = _895865)], (42867 ^ _781013) ^ [_1631550, _1631552, _1631554, _1631556] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1631550, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1631552, tc_fun(_1631550, tc_HOL_Obool)), _1631554), _1631556)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631552, tc_fun(_1631550, tc_HOL_Obool)), _1631554), hAPP(hAPP(c_COMBB(tc_fun(_1631550, tc_HOL_Obool), tc_fun(_1631550, tc_HOL_Obool), _1631552), c_Groups_Ouminus__class_Ouminus(tc_fun(_1631550, tc_HOL_Obool))), _1631556)))], (10 ^ _781013) ^ [_781136, _781138, _781140] : [-(_781140 = _781136), _781140 = _781138, _781138 = _781136], (22806 ^ _781013) ^ [_1207674, _1207676, _1207678, _1207680] : [class_Rings_Osemiring__1(_1207674), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1207674, _1207676, hAPP(c_Nat_OSuc, _1207678), _1207680) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1207674, _1207676, _1207678, hAPP(_1207676, _1207680)))], (45707 ^ _781013) ^ [_1694771, _1694773, _1694775, _1694777] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1694771, tc_HOL_Obool), tc_fun(_1694773, tc_HOL_Obool)), _1694775), hAPP(hAPP(c_COMBC(tc_fun(_1694771, tc_HOL_Obool), tc_fun(_1694771, tc_fun(_1694773, tc_HOL_Obool)), tc_fun(_1694773, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1694771, tc_fun(_1694773, tc_HOL_Obool))), _1694777)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1694771, tc_fun(_1694773, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1694771, tc_HOL_Obool), _1694775)), _1694777))], (11868 ^ _781013) ^ [_995067] : [class_Finite__Set_Ofinite(_995067), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_995067), c_Orderings_Otop__class_Otop(tc_fun(_995067, tc_HOL_Obool)))))], (1314 ^ _781013) ^ [_800180, _800182] : [-(class_Lattices_Osemilattice__sup(_800180)), _800182 = _800180, class_Lattices_Osemilattice__sup(_800182)], (2488 ^ _781013) ^ [_817872, _817874, _817876, _817878, _817880, _817882, _817884, _817886] : [-(c_Nitpick_Oprod(_817886, _817882, _817878, _817874) = c_Nitpick_Oprod(_817884, _817880, _817876, _817872)), _817886 = _817884, _817882 = _817880, _817878 = _817876, _817874 = _817872], (34411 ^ _781013) ^ [_1433196, _1433198] : [class_Groups_Omonoid__mult(_1433196), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1433196), _1433198), 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(_1433196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433196), _1433198), _1433198)), _1433198))], (28688 ^ _781013) ^ [_1316300, _1316302, _1316304] : [class_Orderings_Olinorder(_1316300), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316300), _1316302), _1316304) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316300), _1316304), _1316302))], (33580 ^ _781013) ^ [_1417997] : [class_Int_Onumber__ring(_1417997), -(c_Groups_Ozero__class_Ozero(_1417997) = hAPP(c_Int_Onumber__class_Onumber__of(_1417997), c_Int_OPls))], (32746 ^ _781013) ^ [_1402079, _1402081, _1402083, _1402085] : [class_Int_Onumber__ring(_1402079), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1402079), hAPP(c_Int_Onumber__class_Onumber__of(_1402079), _1402081)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1402079), hAPP(c_Int_Onumber__class_Onumber__of(_1402079), _1402083)), _1402085)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1402079), hAPP(c_Int_Onumber__class_Onumber__of(_1402079), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1402081), _1402083))), _1402085))], (33876 ^ _781013) ^ [_1422712, _1422714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422712), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422712)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422714)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21575 ^ _781013) ^ [_1186178, _1186180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186178)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186180))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186178), _1186180)))], (13791 ^ _781013) ^ [_1034333, _1034335, _1034337, _1034339] : [class_Groups_Ocancel__ab__semigroup__add(_1034333), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034333), _1034335), _1034337) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034333), _1034335), _1034339), -(_1034337 = _1034339)], (20093 ^ _781013) ^ [_1156928, _1156930] : [20094 ^ _781013 : [(20097 ^ _781013) ^ [] : [_1156928 = _1156930], (20095 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156928), _1156930))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156928), hAPP(c_Nat_OSuc, _1156930))))], (25752 ^ _781013) ^ [_1260344] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1260344)))], (38965 ^ _781013) ^ [_1532145, _1532147, _1532149, _1532151] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1532145)), _1532147) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1532149)), _1532151), hBOOL(hAPP(c_List_Odistinct(_1532145), _1532147)), -(c_Map_Odom(_1532145, _1532149, hAPP(c_Map_Omap__of(_1532145, _1532149), hAPP(hAPP(c_List_Ozip(_1532145, _1532149), _1532147), _1532151))) = hAPP(c_List_Oset(_1532145), _1532147))], (11810 ^ _781013) ^ [_994026, _994028, _994030, _994032, _994034, _994036] : [c_Fun_Oinj__on(_994026, _994028, _994030, _994032), hAPP(_994030, _994034) = hAPP(_994030, _994036), hBOOL(hAPP(hAPP(c_member(_994026), _994034), _994032)), hBOOL(hAPP(hAPP(c_member(_994026), _994036), _994032)), -(_994034 = _994036)], (47032 ^ _781013) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (46867 ^ _781013) ^ [_1723547, _1723549, _1723551, _1723553] : [c_Wellfounded_Owf(_1723547, _1723549), hBOOL(hAPP(hAPP(c_member(tc_prod(_1723547, _1723547)), hAPP(hAPP(c_Product__Type_OPair(_1723547, _1723547), _1723551), _1723553)), _1723549)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1723547, _1723547)), hAPP(hAPP(c_Product__Type_OPair(_1723547, _1723547), _1723553), _1723551)), _1723549))], (41843 ^ _781013) ^ [_1607205, _1607207, _1607209, _1607211] : [-(hAPP(c_Map_Omap__of(_1607205, _1607207), hAPP(hAPP(c_List_Oappend(tc_prod(_1607205, _1607207)), _1607209), _1607211)) = c_Map_Omap__add(_1607205, _1607207, hAPP(c_Map_Omap__of(_1607205, _1607207), _1607211), hAPP(c_Map_Omap__of(_1607205, _1607207), _1607209)))], (6040 ^ _781013) ^ [_878671] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _878671), _878671)))], (26771 ^ _781013) ^ [_1279234, _1279236, _1279238] : [class_Orderings_Olinorder(_1279234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279234), _1279236), _1279238)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279234, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1279234, _1279236, _1279238)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1279234), _1279238)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1279234), _1279236))], (42484 ^ _781013) ^ [_1622698, _1622700, _1622702, _1622704] : [class_Groups_Osemigroup__add(_1622698), -(hAPP(c_List_Ofoldl(_1622698, _1622698, c_Groups_Oplus__class_Oplus(_1622698), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1622698), _1622700), _1622702)), _1622704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1622698), _1622700), hAPP(c_List_Ofoldl(_1622698, _1622698, c_Groups_Oplus__class_Oplus(_1622698), _1622702), _1622704)))], (1010 ^ _781013) ^ [_796362, _796364, _796366, _796368] : [-(c_Wellfounded_Oacyclic(_796366, _796362)), c_Wellfounded_Oacyclic(_796368, _796364), _796368 = _796366, _796364 = _796362], (15559 ^ _781013) ^ [_1068818, _1068820, _1068822, _1068824] : [class_Rings_Oordered__ring(_1068818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068818), _1068820), _1068822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068818), _1068824), c_Groups_Ozero__class_Ozero(_1068818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068818), _1068824), _1068822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068818), _1068824), _1068820))))], (51558 ^ _781013) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (20637 ^ _781013) ^ [_1166811, _1166813, _1166815, _1166817] : [class_Rings_Olinordered__semidom(_1166811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166811), hAPP(hAPP(c_Power_Opower__class_Opower(_1166811), _1166813), hAPP(c_Nat_OSuc, _1166815))), hAPP(hAPP(c_Power_Opower__class_Opower(_1166811), _1166817), hAPP(c_Nat_OSuc, _1166815)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166811), c_Groups_Ozero__class_Ozero(_1166811)), _1166817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166811), _1166813), _1166817)))], (18275 ^ _781013) ^ [_1121211, _1121213, _1121215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121211), _1121213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121211), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121213), _1121215))))], (17921 ^ _781013) ^ [_1115265] : [-(_1115265 = 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)), _1115265)))], (27743 ^ _781013) ^ [_1299047] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1299047, _1299047) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4012 ^ _781013) ^ [_841726, _841728] : [_841728 = _841726, -(c_Code__Numeral_OSuc__code__numeral(_841728) = c_Code__Numeral_OSuc__code__numeral(_841726))], (46887 ^ _781013) ^ [_1723975, _1723977, _1723979] : [c_Wellfounded_Owf(_1723975, _1723977), hBOOL(hAPP(hAPP(c_member(tc_prod(_1723975, _1723975)), hAPP(hAPP(c_Product__Type_OPair(_1723975, _1723975), _1723979), _1723979)), _1723977))], (20494 ^ _781013) ^ [_1163808, _1163810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1163808), _1163810)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1163810)), _1163808) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1163810), _1163808)))], (32112 ^ _781013) ^ [_1390761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390761)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1390761))], (34337 ^ _781013) ^ [_1432136] : [class_Int_Onumber__ring(_1432136), -(hAPP(c_Int_Onumber__class_Onumber__of(_1432136), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1432136))], (36474 ^ _781013) ^ [_1476624, _1476626, _1476628, _1476630, _1476632, _1476634] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476624, tc_fun(_1476626, tc_HOL_Obool))), _1476628), _1476630), _1476632), _1476634)), 36477 ^ _781013 : [(36480 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1476630, _1476632), _1476634)))], (36478 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1476628, _1476632), _1476634)))]]], (16574 ^ _781013) ^ [_1088274, _1088276, _1088278] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1088274), _1088276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1088274, tc_HOL_Obool)), _1088278), _1088276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1088274), _1088278)), hAPP(c_Finite__Set_Ocard(_1088274), _1088276))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1088274, tc_HOL_Obool)), _1088278), _1088276)))], (20957 ^ _781013) ^ [_1172672, _1172674, _1172676] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1172672), _1172674)), -(hAPP(c_Finite__Set_Ocard(_1172672), hAPP(hAPP(c_Set_Oinsert(_1172672), _1172676), _1172674)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1172672), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172672, tc_HOL_Obool)), _1172674), hAPP(hAPP(c_Set_Oinsert(_1172672), _1172676), c_Orderings_Obot__class_Obot(tc_fun(_1172672, tc_HOL_Obool)))))))], (16870 ^ _781013) ^ [_1093864, _1093866, _1093868, _1093870] : [class_Rings_Olinordered__semiring__strict(_1093864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093864), _1093866), _1093868)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093864), _1093866), _1093870))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093864), c_Groups_Ozero__class_Ozero(_1093864)), _1093866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093864), _1093868), _1093870)))], (14099 ^ _781013) ^ [_1040521, _1040523, _1040525] : [class_Rings_Ocomm__semiring__1(_1040521), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040521), _1040523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040521), _1040525), _1040523)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040521), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040521), _1040525), c_Groups_Oone__class_Oone(_1040521))), _1040523))], (19230 ^ _781013) ^ [_1141158, _1141160, _1141162, _1141164] : [class_Rings_Olinordered__semidom(_1141158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141158), c_Groups_Oone__class_Oone(_1141158)), _1141160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141158), hAPP(hAPP(c_Power_Opower__class_Opower(_1141158), _1141160), _1141162)), hAPP(hAPP(c_Power_Opower__class_Opower(_1141158), _1141160), _1141164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1141162), _1141164)))], (36932 ^ _781013) ^ [_1485643, _1485645] : [-(c_Divides_Odivmod__nat(_1485643, _1485645) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1485643), _1485645)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1485643, _1485645)))], (27182 ^ _781013) ^ [] : [-(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))))], (38282 ^ _781013) ^ [_1516197] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1516197)), c_Int_OInteg)))], (44030 ^ _781013) ^ [_1657651, _1657653, _1657655, _1657657] : [class_Groups_Ocomm__monoid__add(_1657651), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1657651), _1657653), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1657655, _1657657))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1657651), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1657651), _1657653), c_List_Oupt(_1657655, _1657657))))], (46188 ^ _781013) ^ [_1705615, _1705617, _1705619, _1705621, _1705623] : [c_List_Olist__all2(_1705615, _1705617, _1705619, _1705621, _1705623), -(c_List_Olist__all2(_1705615, _1705617, _1705619, hAPP(c_List_Orev(_1705615), _1705621), hAPP(c_List_Orev(_1705617), _1705623)))], (41430 ^ _781013) ^ [_1597595, _1597597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1597595), _1597597)), -(c_List_Oupto(_1597595, _1597597) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1597595), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1597595), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1597597)))], (20262 ^ _781013) ^ [_1159794] : [_1159794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159794), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (43476 ^ _781013) ^ [_1646790, _1646792, _1646794] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1646790, tc_HOL_Obool)), hAPP(c_List_Oset(_1646790), _1646792)), hAPP(hAPP(c_Set_Oinsert(_1646790), _1646794), c_Orderings_Obot__class_Obot(tc_fun(_1646790, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1646790), hAPP(c_List_Ofilter(_1646790, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1646790), c_fNot), hAPP(hAPP(c_COMBC(_1646790, _1646790, tc_HOL_Obool), c_fequal), _1646794))), _1646792)))], (43320 ^ _781013) ^ [_1643675, _1643677, _1643679] : [hAPP(c_List_Ofilter(_1643675, _1643677), _1643679) = _1643679, 43323 ^ _781013 : [(43324 ^ _781013) ^ [_1643766] : [hBOOL(hAPP(hAPP(c_member(_1643675), _1643766), hAPP(c_List_Oset(_1643675), _1643679))), -(hBOOL(hAPP(_1643677, _1643766)))]]], (2726 ^ _781013) ^ [_821593, _821595, _821597, _821599] : [-(c_FunDef_Orp__inv__image(_821599, _821595) = c_FunDef_Orp__inv__image(_821597, _821593)), _821599 = _821597, _821595 = _821593], (50810 ^ _781013) ^ [_1813813, _1813815, _1813817, _1813819] : [-(c_New__Random__Sequence_Oneg__map(_1813813, _1813815, _1813817, _1813819) = c_New__Random__Sequence_Oneg__bind(_1813813, _1813815, _1813819, hAPP(c_Fun_Ocomp(_1813815, 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(_1813815)))))), _1813813, c_New__Random__Sequence_Oneg__single(_1813815)), _1813817)))], (10715 ^ _781013) ^ [_970266, _970268, _970270] : [class_Orderings_Olinorder(_970266), 10718 ^ _781013 : [(10725 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970266), _970270), _970268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970266), _970268), _970270))], (10719 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970266), _970268), _970270))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970266), _970270), _970268)))]]], (25862 ^ _781013) ^ [_1261964, _1261966, _1261968] : [class_Rings_Oring__1(_1261964), -(hAPP(c_Int_Oring__1__class_Oof__int(_1261964), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1261966), _1261968)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1261964), hAPP(c_Int_Oring__1__class_Oof__int(_1261964), _1261966)), hAPP(c_Int_Oring__1__class_Oof__int(_1261964), _1261968)))], (26717 ^ _781013) ^ [_1278223, _1278225, _1278227] : [class_Orderings_Olinorder(_1278223), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278223), _1278225), _1278227)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278223, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1278223, _1278225), _1278227)), hAPP(c_SetInterval_Oord__class_OatLeast(_1278223), _1278227)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1278223), _1278225))], (5968 ^ _781013) ^ [_877496, _877498, _877500, _877502, _877504] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_877496, _877498, _877500), _877502), _877504))), hBOOL(hAPP(hAPP(_877498, _877502), _877504)), hBOOL(hAPP(_877500, _877504))], (27601 ^ _781013) ^ [_1296130, _1296132] : [class_Divides_Osemiring__div(_1296130), -(c_Divides_Odiv__class_Omod(_1296130, _1296132, _1296132) = c_Groups_Ozero__class_Ozero(_1296130))], (9763 ^ _781013) ^ [_953519, _953521, _953523] : [class_Orderings_Olinorder(_953519), 9766 ^ _781013 : [(9767 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953519), _953521), _953523))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953519), _953523), _953521))), -(_953521 = _953523)], (9777 ^ _781013) ^ [] : [9778 ^ _781013 : [(9781 ^ _781013) ^ [] : [_953521 = _953523], (9779 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953519), _953523), _953521))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953519), _953521), _953523))]]], (51154 ^ _781013) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (9074 ^ _781013) ^ [_940957, _940959, _940961, _940963, _940965, _940967] : [-(hBOOL(hAPP(hAPP(c_member(_940957), _940959), _940961))), -(c_Map_Orestrict__map(_940957, _940963, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_940957, tc_Option_Ooption(_940963)), _940965), _940959), _940967), _940961) = c_Map_Orestrict__map(_940957, _940963, _940965, _940961))], (27877 ^ _781013) ^ [_1301532, _1301534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1301532, _1301534)), _1301532)))], (29529 ^ _781013) ^ [_1331877, _1331879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1331877)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1331877), _1331879)), _1331877) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (19885 ^ _781013) ^ [_1153495, _1153497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1153495), _1153497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153495), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1153497)))], (15503 ^ _781013) ^ [_1067742, _1067744, _1067746, _1067748] : [class_Rings_Oordered__semiring(_1067742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067742), _1067744), _1067746)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067742), c_Groups_Ozero__class_Ozero(_1067742)), _1067748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067742), _1067744), _1067748)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067742), _1067746), _1067748))))], (20375 ^ _781013) ^ [_1161682, _1161684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161682), _1161684)), -(_1161684 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1161682), 20378 ^ [_1161682, _1161684])))], (41256 ^ _781013) ^ [_1594228, _1594230, _1594232, _1594234] : [hAPP(hAPP(c_List_Omap(_1594228, _1594230), _1594232), _1594234) = c_List_Olist_ONil(_1594230), -(_1594234 = c_List_Olist_ONil(_1594228))], (27653 ^ _781013) ^ [_1297132, _1297134, _1297136, _1297138] : [class_Divides_Osemiring__div(_1297132), -(c_Divides_Odiv__class_Omod(_1297132, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297132), _1297134), _1297136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297132), _1297134), _1297138)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297132), _1297134), c_Divides_Odiv__class_Omod(_1297132, _1297136, _1297138)))], (34723 ^ _781013) ^ [_1438631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1438631))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1438631)))], (35643 ^ _781013) ^ [_1455376] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1455376), c_Int_OMin) = c_Int_Osucc(_1455376))], (34445 ^ _781013) ^ [_1433713, _1433715] : [class_Int_Onumber__ring(_1433713), class_Rings_Olinordered__idom(_1433713), 34452 ^ _781013 : [(34459 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433715), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433713), hAPP(c_Int_Onumber__class_Onumber__of(_1433713), _1433715)), c_Groups_Oone__class_Oone(_1433713))))], (34453 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433713), hAPP(c_Int_Onumber__class_Onumber__of(_1433713), _1433715)), c_Groups_Oone__class_Oone(_1433713))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433715), c_Int_OBit1(c_Int_OPls))))]]], (10897 ^ _781013) ^ [_973965, _973967, _973969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_973965, tc_HOL_Obool)), _973967), _973969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973965, tc_HOL_Obool)), _973967), _973969)))], (50756 ^ _781013) ^ [_1812523] : [-(c_Lazy__Sequence_Oyieldn(_1812523) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1812523), _1812523, c_Lazy__Sequence_Oyield(_1812523)))], (5246 ^ _781013) ^ [_861031, _861033, _861035, _861037, _861039, _861041] : [-(c_Product__Type_Oprod_Oprod__case(_861041, _861037, _861033) = c_Product__Type_Oprod_Oprod__case(_861039, _861035, _861031)), _861041 = _861039, _861037 = _861035, _861033 = _861031], (11001 ^ _781013) ^ [_976322, _976324, _976326] : [-(c_Map_Omap__add(_976322, _976324, hAPP(c_COMBK(tc_Option_Ooption(_976324), _976322), c_Option_Ooption_ONone(_976324)), _976326) = _976326)], (12926 ^ _781013) ^ [_1015803, _1015805, _1015807, _1015809, _1015811, _1015813, _1015815] : [c_Finite__Set_Ofolding__image__simple(_1015803, _1015805, _1015807, _1015809, _1015811, _1015813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015805), _1015815)), -(hAPP(_1015813, _1015815) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1015803, _1015805, _1015807), _1015811), _1015809), _1015815))], (27419 ^ _781013) ^ [_1292057, _1292059, _1292061] : [-(hAPP(c_Set_OPow(_1292057), hAPP(hAPP(c_Set_Oinsert(_1292057), _1292059), _1292061)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1292057, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1292057), _1292061)), hAPP(c_Set_Oimage(tc_fun(_1292057, tc_HOL_Obool), tc_fun(_1292057, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1292057), _1292059)), hAPP(c_Set_OPow(_1292057), _1292061))))], (41208 ^ _781013) ^ [_1593391, _1593393] : [c_Orderings_Obot__class_Obot(tc_fun(_1593391, tc_HOL_Obool)) = hAPP(c_List_Oset(_1593391), _1593393), -(_1593393 = c_List_Olist_ONil(_1593391))], (37294 ^ _781013) ^ [_1492623, _1492625] : [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), _1492623), _1492625))), 37297 ^ _781013 : [(37304 ^ _781013) ^ [] : [-(_1492625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1492623, _1492625) = c_Nitpick_Onat__gcd(_1492625, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1492623, _1492625)))], (37298 ^ _781013) ^ [] : [_1492625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1492623, _1492625) = _1492623)]]], (30933 ^ _781013) ^ [_1359978, _1359980] : [class_Orderings_Olinorder(_1359978), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359978), _1359980)), -(_1359980 = c_Orderings_Obot__class_Obot(tc_fun(_1359978, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1359978), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359978), 30946 ^ [_1359978, _1359980]), 30947 ^ [_1359978, _1359980])), hAPP(hAPP(c_Set_Oinsert(_1359978), 30946 ^ [_1359978, _1359980]), hAPP(hAPP(c_Set_Oinsert(_1359978), 30947 ^ [_1359978, _1359980]), c_Orderings_Obot__class_Obot(tc_fun(_1359978, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1359978), c_Big__Operators_Olattice_OSup__fin(_1359978, c_Orderings_Oord__class_Omax(_1359978), _1359980)), _1359980)))], (12896 ^ _781013) ^ [_1015006, _1015008, _1015010] : [-(hAPP(c_Set_Ovimage(_1015006, _1015008, _1015010), c_Orderings_Otop__class_Otop(tc_fun(_1015008, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1015006, tc_HOL_Obool)))], (23707 ^ _781013) ^ [_1224127, _1224129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224129)), 23714 ^ _781013 : [(23721 ^ _781013) ^ [] : [_1224127 = _1224129, -(hAPP(c_Int_Onat, _1224127) = hAPP(c_Int_Onat, _1224129))], (23715 ^ _781013) ^ [] : [hAPP(c_Int_Onat, _1224127) = hAPP(c_Int_Onat, _1224129), -(_1224127 = _1224129)]]], (45075 ^ _781013) ^ [_1681566] : [class_Enum_Oenum(_1681566), -(c_Enum_Oenum__class_Oenum(tc_Option_Ooption(_1681566)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(_1681566)), c_Option_Ooption_ONone(_1681566)), hAPP(hAPP(c_List_Omap(_1681566, tc_Option_Ooption(_1681566)), c_Option_Ooption_OSome(_1681566)), c_Enum_Oenum__class_Oenum(_1681566))))], (16291 ^ _781013) ^ [_1082031, _1082033, _1082035, _1082037] : [class_Groups_Ocomm__monoid__add(_1082031), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1082033), _1082035))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082033, _1082031), _1082037), _1082035) = c_Groups_Ozero__class_Ozero(_1082031))], (11550 ^ _781013) ^ [_988690, _988692] : [-(c_Fun_Oinj__on(_988690, _988690, c_COMBI(_988690), _988692))], (4096 ^ _781013) ^ [_842960, _842962, _842964, _842966, _842968, _842970] : [-(c_Relation_OImage(_842970, _842966, _842962) = c_Relation_OImage(_842968, _842964, _842960)), _842970 = _842968, _842966 = _842964, _842962 = _842960], (41374 ^ _781013) ^ [_1596277, _1596279] : [-(c_List_Olist_Olist__size(_1596277, _1596279, c_List_Olist_ONil(_1596277)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42120 ^ _781013) ^ [_1614503, _1614505, _1614507, _1614509, _1614511] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1614503, _1614505)), _1614507), hAPP(hAPP(c_List_Ozip(_1614503, _1614505), _1614509), _1614511)) = hAPP(hAPP(c_List_Ozip(_1614503, _1614505), hAPP(hAPP(c_List_Odrop(_1614503), _1614507), _1614509)), hAPP(hAPP(c_List_Odrop(_1614505), _1614507), _1614511)))], (33296 ^ _781013) ^ [_1413041] : [-(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), _1413041)) = 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), _1413041))))], (35759 ^ _781013) ^ [_1457126] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1457126)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1457126)))], (3434 ^ _781013) ^ [_832765, _832767] : [_832767 = _832765, -(c_HOL_OAll(_832767) = c_HOL_OAll(_832765))], (41214 ^ _781013) ^ [_1593488, _1593490] : [_1593490 = c_List_Olist_ONil(_1593488), -(c_Orderings_Obot__class_Obot(tc_fun(_1593488, tc_HOL_Obool)) = hAPP(c_List_Oset(_1593488), _1593490))], (50840 ^ _781013) ^ [_1814628, _1814630] : [c_Wellfounded_Oacyclic(_1814628, hAPP(c_Set_OCollect(tc_prod(_1814628, _1814628)), hAPP(c_Product__Type_Oprod_Oprod__case(_1814628, _1814628, tc_HOL_Obool), _1814630))), -(c_Wellfounded_Oacyclic(_1814628, hAPP(c_Set_OCollect(tc_prod(_1814628, _1814628)), hAPP(c_Product__Type_Oprod_Oprod__case(_1814628, _1814628, tc_HOL_Obool), c_Predicate_Oconversep(_1814628, _1814628, _1814630)))))], (15399 ^ _781013) ^ [_1065877, _1065879, _1065881] : [class_Rings_Olinordered__ring__strict(_1065877), 15402 ^ _781013 : [(15417 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065877), _1065879), _1065881)), c_Groups_Ozero__class_Ozero(_1065877)))), 15418 ^ _781013 : [(15425 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065877), _1065879), c_Groups_Ozero__class_Ozero(_1065877))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065877), c_Groups_Ozero__class_Ozero(_1065877)), _1065881))], (15419 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065877), c_Groups_Ozero__class_Ozero(_1065877)), _1065879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065877), _1065881), c_Groups_Ozero__class_Ozero(_1065877)))]]], (15403 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065877), _1065879), _1065881)), c_Groups_Ozero__class_Ozero(_1065877))), 15408 ^ _781013 : [(15411 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065877), _1065881), c_Groups_Ozero__class_Ozero(_1065877))))], (15409 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065877), c_Groups_Ozero__class_Ozero(_1065877)), _1065879)))]], 15412 ^ _781013 : [(15415 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065877), c_Groups_Ozero__class_Ozero(_1065877)), _1065881)))], (15413 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065877), _1065879), c_Groups_Ozero__class_Ozero(_1065877))))]]]]], (27741 ^ _781013) ^ [_1299020] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1299020) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30699 ^ _781013) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (35393 ^ _781013) ^ [_1450879, _1450881, _1450883] : [class_Rings_Olinordered__idom(_1450879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450879), _1450881), c_Groups_Ozero__class_Ozero(_1450879))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450879), hAPP(hAPP(c_Power_Opower__class_Opower(_1450879), _1450881), 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)))), _1450883)))), c_Groups_Ozero__class_Ozero(_1450879))))], (47297 ^ _781013) ^ [_1734525] : [-(c_Wellfounded_OwfP(_1734525, hAPP(c_COMBK(tc_fun(_1734525, tc_HOL_Obool), _1734525), hAPP(c_COMBK(tc_HOL_Obool, _1734525), c_fFalse))))], (1754 ^ _781013) ^ [_805680, _805682] : [-(class_Orderings_Oorder(_805680)), _805682 = _805680, class_Orderings_Oorder(_805682)], (8219 ^ _781013) ^ [_921408, _921410, _921412, _921414, _921416] : [c_Finite__Set_Ofolding__one__idem(_921408, _921410, _921412), hBOOL(hAPP(c_Finite__Set_Ofinite(_921408), _921414)), -(_921414 = c_Orderings_Obot__class_Obot(tc_fun(_921408, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_921408), _921416)), -(_921416 = c_Orderings_Obot__class_Obot(tc_fun(_921408, tc_HOL_Obool))), -(hAPP(_921412, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921408, tc_HOL_Obool)), _921414), _921416)) = hAPP(hAPP(_921410, hAPP(_921412, _921414)), hAPP(_921412, _921416)))], (39675 ^ _781013) ^ [_1549193, _1549195, _1549197, _1549199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1549193), _1549195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1549197, tc_HOL_Obool)), hAPP(c_List_Oset(_1549197), hAPP(hAPP(c_List_Otake(_1549197), _1549193), _1549199))), hAPP(c_List_Oset(_1549197), hAPP(hAPP(c_List_Otake(_1549197), _1549195), _1549199)))))], (51560 ^ _781013) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (6985 ^ _781013) ^ [_896552, _896554, _896556] : [class_Orderings_Olinorder(_896552), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896552), _896554), _896556))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896552), _896556), _896554)))], (4350 ^ _781013) ^ [_846813, _846815, _846817, _846819, _846821, _846823, _846825, _846827] : [-(c_List_Ofoldl(_846827, _846823, _846819, _846815) = c_List_Ofoldl(_846825, _846821, _846817, _846813)), _846827 = _846825, _846823 = _846821, _846819 = _846817, _846815 = _846813], (9691 ^ _781013) ^ [_952414, _952416, _952418] : [class_Orderings_Olinorder(_952414), -(_952416 = _952418), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952414), _952416), _952418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952414), _952418), _952416)))], (17365 ^ _781013) ^ [_1105555, _1105557, _1105559, _1105561, _1105563] : [-(c_Map_Odom(_1105555, _1105557, c_Fun_Ooverride__on(_1105555, tc_Option_Ooption(_1105557), _1105559, _1105561, _1105563)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1105555, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1105555, tc_HOL_Obool)), c_Map_Odom(_1105555, _1105557, _1105559)), hAPP(c_Set_OCollect(_1105555), hAPP(hAPP(c_COMBC(_1105555, tc_fun(_1105555, tc_HOL_Obool), tc_HOL_Obool), c_member(_1105555)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1105555, tc_HOL_Obool)), _1105563), c_Map_Odom(_1105555, _1105557, _1105561)))))), hAPP(c_Set_OCollect(_1105555), hAPP(hAPP(c_COMBC(_1105555, tc_fun(_1105555, tc_HOL_Obool), tc_HOL_Obool), c_member(_1105555)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1105555, tc_HOL_Obool)), _1105563), c_Map_Odom(_1105555, _1105557, _1105561))))))], (34747 ^ _781013) ^ [_1439026, _1439028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1439026)), c_Int_OBit1(_1439028))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1439026), _1439028)))], (39257 ^ _781013) ^ [_1539368, _1539370, _1539372, _1539374] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1539368)), hAPP(hAPP(c_List_Olist__update(_1539368, _1539370), _1539372), _1539374)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1539368)), _1539370))], (44995 ^ _781013) ^ [_1679807, _1679809] : [-(c_Enum_On__lists(_1679807, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1679809) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1679807)), c_List_Olist_ONil(_1679807)), c_List_Olist_ONil(tc_List_Olist(_1679807))))], (27433 ^ _781013) ^ [_1292413, _1292415, _1292417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1292413, tc_HOL_Obool)), _1292415), _1292417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1292413, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1292413), _1292415)), hAPP(c_Set_OPow(_1292413), _1292417))))], (50212 ^ _781013) ^ [_1801933, _1801935, _1801937] : [-(c_Nitpick_Oplus__frac(_1801933, _1801935, _1801937) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1801933), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1801933), _1801935), hAPP(c_Nitpick_Odenom(_1801933), _1801937))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1801933), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1801933), tc_Int_Oint), c_Nitpick_Ofrac(_1801933)), 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(_1801933), _1801935))), 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(_1801933), _1801935))))), 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(_1801933), _1801937))), 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(_1801933), _1801937)))))), c_COMBI(tc_Int_Oint))))], (12318 ^ _781013) ^ [_1003335, _1003337, _1003339] : [class_Lattices_Olattice(_1003335), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003335), _1003337)), -(_1003337 = c_Orderings_Obot__class_Obot(tc_fun(_1003335, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003335), _1003339)), -(_1003339 = c_Orderings_Obot__class_Obot(tc_fun(_1003335, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1003335, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003335, tc_HOL_Obool)), _1003337), _1003339)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1003335), c_Big__Operators_Olattice__class_OSup__fin(_1003335, _1003337)), c_Big__Operators_Olattice__class_OSup__fin(_1003335, _1003339)))], (2336 ^ _781013) ^ [_815568, _815570, _815572, _815574] : [-(c_Orderings_Oord_Omax(_815574, _815570) = c_Orderings_Oord_Omax(_815572, _815568)), _815574 = _815572, _815570 = _815568], (39693 ^ _781013) ^ [_1549631, _1549633, _1549635, _1549637, _1549639] : [hBOOL(hAPP(hAPP(c_member(_1549631), _1549633), hAPP(c_List_Oset(_1549631), _1549635))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1549637), hAPP(_1549639, _1549633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1549637), c_List_Olist_Olist__size(_1549631, _1549639, _1549635))))], (28820 ^ _781013) ^ [_1318761, _1318763, _1318765, _1318767] : [class_Orderings_Olinorder(_1318761), 28823 ^ _781013 : [(28832 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318761), _1318763), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318761), _1318765), _1318767)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318761), _1318763), _1318765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318761), _1318763), _1318767))], (28824 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318761), _1318763), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318761), _1318765), _1318767))), 28827 ^ _781013 : [(28830 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318761), _1318763), _1318767)))], (28828 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318761), _1318763), _1318765)))]]]]], (48533 ^ _781013) ^ [_1762457, _1762459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1762457), _1762459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1762457)), hAPP(c_Code__Numeral_Onat__of, _1762459))))], (38168 ^ _781013) ^ [_1513267, _1513269] : [-(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), _1513267), _1513269)), 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), _1513269), _1513267)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (42446 ^ _781013) ^ [_1621779, _1621781] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621779)), hAPP(c_List_Otl(_1621779), _1621781)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621779)), _1621781)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (46517 ^ _781013) ^ [_1713708, _1713710, _1713712] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1713708, _1713708)), hAPP(hAPP(c_Product__Type_OPair(_1713708, _1713708), _1713710), _1713712)), c_List_Omeasures(_1713708, c_List_Olist_ONil(tc_fun(_1713708, tc_Nat_Onat)))))], (22384 ^ _781013) ^ [_1200364, _1200366, _1200368, _1200370] : [class_Divides_Osemiring__div(_1200364), -(_1200366 = c_Groups_Ozero__class_Ozero(_1200364)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200364), _1200366), _1200368)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200364), _1200366), _1200370)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200364), _1200368), _1200370))], (7973 ^ _781013) ^ [_915917, _915919, _915921, _915923, _915925] : [hAPP(hAPP(c_Option_Omap(_915917, _915919), _915921), _915923) = hAPP(c_Option_Ooption_OSome(_915919), _915925), 7977 ^ _781013 : [(7980 ^ _781013) ^ [] : [-(hAPP(_915921, 7976 ^ [_915917, _915919, _915921, _915923, _915925]) = _915925)], (7978 ^ _781013) ^ [] : [-(_915923 = hAPP(c_Option_Ooption_OSome(_915917), 7976 ^ [_915917, _915919, _915921, _915923, _915925]))]]], (13014 ^ _781013) ^ [_1017712, _1017714, _1017716, _1017718] : [-(hBOOL(hAPP(hAPP(c_member(_1017712), _1017714), _1017716))), -(hAPP(c_Set_Ovimage(_1017718, _1017712, hAPP(c_COMBK(_1017712, _1017718), _1017714)), _1017716) = c_Orderings_Obot__class_Obot(tc_fun(_1017718, tc_HOL_Obool)))], (38740 ^ _781013) ^ [_1527259, _1527261, _1527263, _1527265, _1527267] : [c_Fun_Oinj__on(_1527259, _1527261, _1527263, hAPP(hAPP(c_Set_Oinsert(_1527259), _1527265), hAPP(c_List_Oset(_1527259), _1527267))), -(hAPP(hAPP(c_List_Omap(_1527259, _1527261), _1527263), hAPP(c_List_OremoveAll(_1527259, _1527265), _1527267)) = hAPP(c_List_OremoveAll(_1527261, hAPP(_1527263, _1527265)), hAPP(hAPP(c_List_Omap(_1527259, _1527261), _1527263), _1527267)))], (9014 ^ _781013) ^ [_939535, _939537, _939539, _939541, _939543] : [-(hBOOL(hAPP(hAPP(c_member(_939535), _939537), _939539))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_939535, tc_Option_Ooption(_939541)), c_Map_Orestrict__map(_939535, _939541, _939543, _939539)), _939537), c_Option_Ooption_ONone(_939541)) = c_Map_Orestrict__map(_939535, _939541, _939543, _939539))], (330 ^ _781013) ^ [_786226, _786228, _786230, _786232] : [-(c_Nitpick_Orefl_H(_786230, _786226)), c_Nitpick_Orefl_H(_786232, _786228), _786232 = _786230, _786228 = _786226], (42432 ^ _781013) ^ [_1621495, _1621497, _1621499] : [-(c_List_Orotate(_1621495, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1621497), _1621499)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1621495), tc_List_Olist(_1621495), tc_List_Olist(_1621495), c_List_Orotate(_1621495, _1621497)), c_List_Orotate(_1621495, _1621499)))], (30421 ^ _781013) ^ [_1349495, _1349497, _1349499, _1349501, _1349503] : [class_Orderings_Olinorder(_1349495), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349495, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349495, _1349497), _1349499)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349495, _1349501), _1349503)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349495, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349495), _1349497), _1349501)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349495), _1349499), _1349503)))], (46128 ^ _781013) ^ [_1704519, _1704521, _1704523] : [_1704519 = _1704521, -(c_List_Olist__all2(_1704523, _1704523, c_fequal, _1704519, _1704521))], (4412 ^ _781013) ^ [_847822, _847824, _847826, _847828, _847830, _847832] : [-(c_Finite__Set_Ofold(_847832, _847828, _847824) = c_Finite__Set_Ofold(_847830, _847826, _847822)), _847832 = _847830, _847828 = _847826, _847824 = _847822], (49136 ^ _781013) ^ [_1777633, _1777635, _1777637, _1777639] : [-(hAPP(_1777633, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1777635, _1777635), _1777637), _1777633), _1777639)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1777635, _1777635), _1777637), _1777633), hAPP(_1777633, _1777639)))], (20311 ^ _781013) ^ [_1160754, _1160756] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160754), _1160756), 20316 ^ _781013 : [(20319 ^ _781013) ^ [] : [-(_1160756 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20317 ^ _781013) ^ [] : [-(_1160754 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20320 ^ _781013 : [(20323 ^ _781013) ^ [] : [-(_1160756 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20321 ^ _781013) ^ [] : [-(_1160754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (26309 ^ _781013) ^ [_1270265, _1270267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1270265), hAPP(c_Nat_OSuc, _1270267))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1270265, hAPP(c_Nat_OSuc, _1270267)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1270267)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1270265, _1270267)))], (48772 ^ _781013) ^ [_1768557, _1768559, _1768561, _1768563, _1768565] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768557, _1768559)), hAPP(hAPP(c_Product__Type_OPair(_1768557, _1768559), _1768561), _1768563)), hAPP(c_Relation_Oconverse(_1768559, _1768557), _1768565))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1768559, _1768557)), hAPP(hAPP(c_Product__Type_OPair(_1768559, _1768557), _1768563), _1768561)), _1768565)))], (14927 ^ _781013) ^ [_1057375, _1057377] : [class_Groups_Ogroup__add(_1057375), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057375), _1057377), _1057377) = c_Groups_Ozero__class_Ozero(_1057375))], (34231 ^ _781013) ^ [_1430323, _1430325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1430323)), c_Int_OBit1(_1430325))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430323), _1430325)))], (38274 ^ _781013) ^ [_1515920, _1515922, _1515924, _1515926, _1515928, _1515930] : [-(hAPP(hAPP(c_List_Omap(_1515920, _1515922), _1515924), hAPP(hAPP(c_List_Omap(_1515926, _1515920), _1515928), _1515930)) = hAPP(hAPP(c_List_Omap(_1515926, _1515922), hAPP(c_Fun_Ocomp(_1515920, _1515922, _1515926, _1515924), _1515928)), _1515930))], (42468 ^ _781013) ^ [_1622200, _1622202, _1622204, _1622206] : [42469 ^ _781013 : [(42470 ^ _781013) ^ [_1622297, _1622299] : [_1622200 = hAPP(hAPP(c_List_Olist_OCons(_1622202), _1622299), _1622297)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622202), tc_List_Olist(_1622202))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622202), tc_List_Olist(_1622202)), _1622204), hAPP(hAPP(c_List_Oappend(_1622202), _1622204), _1622200))), c_List_Olexord(_1622202, _1622206))))], (25098 ^ _781013) ^ [_1248746, _1248748, _1248750, _1248752] : [class_Fields_Olinordered__field(_1248746), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248746), c_Groups_Ozero__class_Ozero(_1248746)), _1248748)), 25105 ^ _781013 : [(25112 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248746), _1248750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248746), _1248752), _1248748))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248746), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248746), _1248750), _1248748)), _1248752)))], (25106 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248746), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248746), _1248750), _1248748)), _1248752)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248746), _1248750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248746), _1248752), _1248748))))]]], (41520 ^ _781013) ^ [_1600003, _1600005, _1600007, _1600009] : [-(hAPP(c_List_Olist_Olist__case(_1600003, _1600005, _1600007, _1600009), c_List_Olist_ONil(_1600005)) = _1600007)], (27685 ^ _781013) ^ [_1297836, _1297838, _1297840] : [class_Divides_Osemiring__div(_1297836), -(c_Divides_Odiv__class_Omod(_1297836, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1297836), _1297838), _1297840), _1297840) = c_Divides_Odiv__class_Omod(_1297836, _1297838, _1297840))], (14598 ^ _781013) ^ [_1052089] : [-(hAPP(c_Finite__Set_Ocard(_1052089), c_Orderings_Obot__class_Obot(tc_fun(_1052089, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51024 ^ _781013) ^ [_1818697, _1818699] : [class_Lattices_Odistrib__lattice(_1818697), -(class_Lattices_Odistrib__lattice(tc_fun(_1818699, _1818697)))], (25444 ^ _781013) ^ [_1255275, _1255277, _1255279] : [class_Groups_Ocomm__monoid__add(_1255275), class_Groups_Ocomm__monoid__mult(_1255275), c_Nat__Transfer_Onat__set(_1255277), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1255275), _1255279), _1255277) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1255275), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1255275, tc_Nat_Onat), _1255279), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1255277)))], (9020 ^ _781013) ^ [_939612, _939614, _939616, _939618, _939620] : [class_Groups_Oordered__ab__group__add(_939612), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_939612), _939614), _939616) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_939612), _939618), _939620), 9027 ^ _781013 : [(9034 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939612), _939618), _939620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939612), _939614), _939616)))], (9028 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939612), _939614), _939616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939612), _939618), _939620)))]]], (51156 ^ _781013) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (24852 ^ _781013) ^ [_1244170, _1244172, _1244174] : [class_Fields_Olinordered__field(_1244170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244170), _1244172), c_Groups_Ozero__class_Ozero(_1244170))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244170), _1244174), c_Groups_Ozero__class_Ozero(_1244170))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244170), c_Groups_Ozero__class_Ozero(_1244170)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1244170), _1244172), _1244174))))], (13917 ^ _781013) ^ [_1036830, _1036832, _1036834, _1036836] : [class_Groups_Oordered__ab__semigroup__add(_1036830), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036830), _1036832), _1036834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036830), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036830), _1036832), _1036836)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036830), _1036834), _1036836))))], (36400 ^ _781013) ^ [_1475199, _1475201, _1475203, _1475205, _1475207] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1475199, _1475201), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1475203), _1475205))), -(_1475201 = 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), _1475207), _1475199), _1475201), 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), _1475207), _1475203)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1475207), _1475205)), _1475201))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1475207), _1475205), _1475201)))))], (19038 ^ _781013) ^ [_1137228, _1137230, _1137232, _1137234] : [hBOOL(hAPP(hAPP(c_member(_1137228), _1137230), c_SetInterval_Oord_OgreaterThan(_1137228, _1137232, _1137234))), -(hBOOL(hAPP(hAPP(_1137232, _1137234), _1137230)))], (25792 ^ _781013) ^ [_1260871] : [class_Rings_Oring__1(_1260871), -(hAPP(c_Int_Oring__1__class_Oof__int(_1260871), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1260871))], (23785 ^ _781013) ^ [_1225494, _1225496, _1225498] : [class_Orderings_Oorder(_1225494), 23788 ^ _781013 : [(23795 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225494), _1225496), _1225498))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1225494, _1225496, _1225498) = c_Orderings_Obot__class_Obot(tc_fun(_1225494, tc_HOL_Obool)))], (23789 ^ _781013) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1225494, _1225496, _1225498) = c_Orderings_Obot__class_Obot(tc_fun(_1225494, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225494), _1225496), _1225498))]]], (41115 ^ _781013) ^ [_1591267, _1591269, _1591271] : [c_Relation_Orefl__on(_1591267, _1591269, _1591271), -(c_Relation_Orefl__on(tc_List_Olist(_1591267), c_List_Olists(_1591267, _1591269), c_List_Olistrel(_1591267, _1591271)))], (14281 ^ _781013) ^ [_1044956, _1044958, _1044960, _1044962] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044956), _1044958)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1044956), _1044960)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1044956, tc_Nat_Onat), _1044962), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1044956, tc_HOL_Obool)), _1044958), _1044960)) = 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(_1044956, tc_Nat_Onat), _1044962), _1044958)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1044956, tc_Nat_Onat), _1044962), _1044960))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1044956, tc_Nat_Onat), _1044962), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1044956, tc_HOL_Obool)), _1044958), _1044960))))], (34397 ^ _781013) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (50148 ^ _781013) ^ [_1800389, _1800391] : [-(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)))), _1800389)) = 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)))), _1800391))), 50150 ^ _781013 : [(50153 ^ _781013) ^ [] : [50154 ^ _781013 : [(50157 ^ _781013) ^ [] : [hBOOL(hAPP(_1800391, 50149 ^ [_1800389, _1800391]))], (50155 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1800389, 50149 ^ [_1800389, _1800391])))]], 50158 ^ _781013 : [(50161 ^ _781013) ^ [] : [hBOOL(hAPP(_1800389, 50149 ^ [_1800389, _1800391]))], (50159 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1800391, 50149 ^ [_1800389, _1800391])))]]], (50151 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 50149 ^ [_1800389, _1800391])))]]], (27908 ^ _781013) ^ [_1302066, _1302068] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1302066, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1302068)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1302066, _1302068) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (29287 ^ _781013) ^ [_1327273, _1327275] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1327273), _1327275))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1327273))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1327275))))], (23903 ^ _781013) ^ [_1227406] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227406))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1227406)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (46621 ^ _781013) ^ [_1716834, _1716836, _1716838, _1716840] : [hAPP(hAPP(c_Relation_Orel__comp(_1716834, _1716834, _1716834), _1716836), _1716838) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1716834, _1716834), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1716834, _1716834, _1716834), _1716840), _1716838) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1716834, _1716834), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1716834, _1716834, _1716834), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1716834, _1716834), tc_HOL_Obool)), _1716836), _1716840)), _1716838) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1716834, _1716834), tc_HOL_Obool)))], (28614 ^ _781013) ^ [_1314799, _1314801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1314799), _1314801)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314799, _1314801) = _1314799)], (6641 ^ _781013) ^ [_889962, _889964, _889966, _889968] : [c_Map_Odom(_889962, _889964, _889966) = hAPP(hAPP(c_Set_Oinsert(_889962), _889968), c_Orderings_Obot__class_Obot(tc_fun(_889962, tc_HOL_Obool))), -(_889966 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_889962, tc_Option_Ooption(_889964)), hAPP(c_COMBK(tc_Option_Ooption(_889964), _889962), c_Option_Ooption_ONone(_889964))), _889968), hAPP(c_Option_Ooption_OSome(_889964), 6644 ^ [_889962, _889964, _889966, _889968])))], (36520 ^ _781013) ^ [_1477686, _1477688, _1477690, _1477692, _1477694, _1477696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477686, tc_fun(_1477688, tc_HOL_Obool))), _1477690), _1477692)), hBOOL(hAPP(hAPP(_1477690, _1477694), _1477696)), -(hBOOL(hAPP(hAPP(_1477692, _1477694), _1477696)))], (7903 ^ _781013) ^ [_914369, _914371, _914373, _914375, _914377, _914379, _914381] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_914369, tc_Option_Ooption(_914371)), _914373), _914375), hAPP(c_Option_Ooption_OSome(_914371), _914377)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_914369, tc_Option_Ooption(_914371)), _914379), _914375), hAPP(c_Option_Ooption_OSome(_914371), _914381)), -(_914377 = _914381)], (17805 ^ _781013) ^ [_1113279, _1113281] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113279), _1113281) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113281), _1113279))], (41981 ^ _781013) ^ [_1610694, _1610696, _1610698, _1610700] : [-(c_List_Osublist(_1610694, hAPP(hAPP(c_List_Oappend(_1610694), _1610696), _1610698), _1610700) = hAPP(hAPP(c_List_Oappend(_1610694), c_List_Osublist(_1610694, _1610696, _1610700)), c_List_Osublist(_1610694, _1610698, 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(_1610694)), _1610696)))), _1610700)))))], (44540 ^ _781013) ^ [_1670015, _1670017] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1670015), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1670015))), _1670017))), 44543 ^ _781013 : [(44550 ^ _781013) ^ [] : [-(_1670017 = c_List_Olist_ONil(tc_List_Olist(_1670015))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1670015))), c_List_Otranspose(_1670015, _1670017)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670015)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1670015)), _1670017), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44544 ^ _781013) ^ [] : [_1670017 = c_List_Olist_ONil(tc_List_Olist(_1670015)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1670015))), c_List_Otranspose(_1670015, _1670017)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20125 ^ _781013) ^ [_1157463, _1157465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157463), hAPP(c_Nat_OSuc, _1157465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157463), _1157465))), -(_1157463 = hAPP(c_Nat_OSuc, _1157465))], (49670 ^ _781013) ^ [_1790727, _1790729] : [class_Complete__Lattice_Ocomplete__lattice(_1790727), hBOOL(hAPP(c_Finite__Set_Ofinite(_1790727), _1790729)), -(c_Complete__Lattice_OInf__class_OInf(_1790727, _1790729) = hAPP(hAPP(c_Finite__Set_Ofold(_1790727, _1790727, c_Lattices_Osemilattice__inf__class_Oinf(_1790727)), c_Orderings_Otop__class_Otop(_1790727)), _1790729))], (16323 ^ _781013) ^ [_1082744, _1082746, _1082748] : [hBOOL(hAPP(_1082744, _1082746)), -(hAPP(c_Set_OCollect(_1082748), hAPP(hAPP(c_COMBS(_1082748, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1082748), c_fconj), hAPP(hAPP(c_COMBC(_1082748, _1082748, tc_HOL_Obool), c_fequal), _1082746))), _1082744)) = hAPP(hAPP(c_Set_Oinsert(_1082748), _1082746), c_Orderings_Obot__class_Obot(tc_fun(_1082748, tc_HOL_Obool))))], (44892 ^ _781013) ^ [_1677338, _1677340, _1677342] : [-(c_List_OdropWhile(_1677338, _1677340, _1677342) = c_List_Olist_ONil(_1677338)), hBOOL(hAPP(_1677340, hAPP(c_List_Ohd(_1677338), c_List_OdropWhile(_1677338, _1677340, _1677342))))], (42859 ^ _781013) ^ [_1631167, _1631169, _1631171, _1631173, _1631175, _1631177] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631167, tc_fun(_1631169, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1631171, tc_fun(_1631167, tc_HOL_Obool)), _1631173), _1631175)), _1631177) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631171, tc_fun(_1631169, tc_HOL_Obool)), _1631173), hAPP(hAPP(c_COMBC(_1631171, tc_fun(_1631167, tc_fun(_1631169, tc_HOL_Obool)), tc_fun(_1631169, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1631167, tc_HOL_Obool), tc_fun(tc_fun(_1631167, tc_fun(_1631169, tc_HOL_Obool)), tc_fun(_1631169, tc_HOL_Obool)), _1631171), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631167, tc_fun(_1631169, tc_HOL_Obool))), _1631175)), _1631177)))], (32534 ^ _781013) ^ [_1398331, _1398333, _1398335] : [class_Int_Onumber__ring(_1398331), -(hAPP(c_Int_Onumber__class_Onumber__of(_1398331), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1398333), _1398335)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1398331), hAPP(c_Int_Onumber__class_Onumber__of(_1398331), _1398333)), hAPP(c_Int_Onumber__class_Onumber__of(_1398331), _1398335)))], (51346 ^ _781013) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (47334 ^ _781013) ^ [_1735136, _1735138] : [c_Wellfounded_OwfP(_1735136, hAPP(hAPP(c_COMBC(_1735136, tc_fun(tc_prod(_1735136, _1735136), tc_HOL_Obool), tc_fun(_1735136, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1735136, tc_fun(tc_fun(tc_prod(_1735136, _1735136), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1735136, _1735136), tc_HOL_Obool), tc_fun(_1735136, tc_HOL_Obool)), _1735136), c_COMBC(_1735136, tc_fun(tc_prod(_1735136, _1735136), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1735136, tc_prod(_1735136, _1735136)), tc_fun(_1735136, tc_fun(tc_fun(tc_prod(_1735136, _1735136), tc_HOL_Obool), tc_HOL_Obool)), _1735136), hAPP(c_COMBB(tc_prod(_1735136, _1735136), tc_fun(tc_fun(tc_prod(_1735136, _1735136), tc_HOL_Obool), tc_HOL_Obool), _1735136), c_member(tc_prod(_1735136, _1735136)))), c_Product__Type_OPair(_1735136, _1735136)))), _1735138)), -(c_Wellfounded_Owf(_1735136, _1735138))], (40060 ^ _781013) ^ [_1561638, _1561640, _1561642, _1561644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1561638), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1561640)), _1561642))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1561638), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1561640)), _1561644))), 40070 ^ _781013 : [(40073 ^ _781013) ^ [] : [hAPP(hAPP(c_List_Onth(_1561640), _1561642), 40069 ^ [_1561638, _1561640, _1561642, _1561644]) = hAPP(hAPP(c_List_Onth(_1561640), _1561644), 40069 ^ [_1561638, _1561640, _1561642, _1561644])], (40071 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40069 ^ [_1561638, _1561640, _1561642, _1561644]), _1561638)))]], -(hAPP(hAPP(c_List_Otake(_1561640), _1561638), _1561642) = hAPP(hAPP(c_List_Otake(_1561640), _1561638), _1561644))], (18061 ^ _781013) ^ [_1117578, _1117580] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117578), _1117580) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 18064 ^ _781013 : [(18067 ^ _781013) ^ [] : [-(_1117580 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18065 ^ _781013) ^ [] : [-(_1117578 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20077 ^ _781013) ^ [_1156690, _1156692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156690), _1156692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1156690)), hAPP(c_Nat_OSuc, _1156692))))], (42260 ^ _781013) ^ [_1618056, _1618058, _1618060, _1618062] : [-(hAPP(c_List_Orotate1(_1618056), c_List_Olist_ONil(_1618056)) = c_List_Olist_ONil(_1618056))], (47658 ^ _781013) ^ [_1742964, _1742966, _1742968, _1742970, _1742972] : [-(hAPP(c_List_Ofilter(_1742964, _1742966), _1742968) = hAPP(hAPP(c_List_Olist_OCons(_1742964), _1742970), _1742972)), 47659 ^ _781013 : [(47660 ^ _781013) ^ [_1743092, _1743094] : [_1742968 = hAPP(hAPP(c_List_Oappend(_1742964), _1743094), hAPP(hAPP(c_List_Olist_OCons(_1742964), _1742970), _1743092)), 47666 ^ _781013 : [(47669 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1742966, 47665 ^ [_1742964, _1742966, _1742968, _1742970, _1742972, _1743092, _1743094])))], (47667 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742964), 47665 ^ [_1742964, _1742966, _1742968, _1742970, _1742972, _1743092, _1743094]), hAPP(c_List_Oset(_1742964), _1743094))))]], hBOOL(hAPP(_1742966, _1742970)), _1742972 = hAPP(c_List_Ofilter(_1742964, _1742966), _1743092)]]], (34319 ^ _781013) ^ [_1431789, _1431791] : [class_Int_Onumber__ring(_1431789), -(hAPP(c_Int_Onumber__class_Onumber__of(_1431789), c_Int_OBit1(_1431791)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431789), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431789), c_Groups_Oone__class_Oone(_1431789)), hAPP(c_Int_Onumber__class_Onumber__of(_1431789), _1431791))), hAPP(c_Int_Onumber__class_Onumber__of(_1431789), _1431791)))], (10275 ^ _781013) ^ [_962799, _962801] : [class_Lattices_Obounded__lattice__bot(_962799), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_962799), _962801), c_Orderings_Obot__class_Obot(_962799)) = c_Orderings_Obot__class_Obot(_962799))], (31864 ^ _781013) ^ [_1384516, _1384518, _1384520, _1384522, _1384524] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384516, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384518, tc_fun(_1384516, tc_HOL_Obool)), _1384520), _1384522)), _1384524) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384518, tc_fun(_1384516, tc_HOL_Obool)), _1384520), hAPP(hAPP(c_COMBC(_1384518, tc_fun(_1384516, tc_HOL_Obool), tc_fun(_1384516, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1384516, tc_HOL_Obool), tc_fun(tc_fun(_1384516, tc_HOL_Obool), tc_fun(_1384516, tc_HOL_Obool)), _1384518), c_Groups_Ominus__class_Ominus(tc_fun(_1384516, tc_HOL_Obool))), _1384522)), _1384524)))], (42128 ^ _781013) ^ [_1614755, _1614757, _1614759, _1614761] : [hBOOL(hAPP(hAPP(c_member(_1614755), _1614757), hAPP(c_List_Oset(_1614755), hAPP(hAPP(c_List_Odrop(_1614755), _1614759), _1614761)))), -(hBOOL(hAPP(hAPP(c_member(_1614755), _1614757), hAPP(c_List_Oset(_1614755), _1614761))))], (18817 ^ _781013) ^ [_1132224, _1132226, _1132228, _1132230, _1132232] : [class_Groups_Ocomm__monoid__mult(_1132224), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132226), _1132228)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132226), _1132230)), 18831 ^ _781013 : [(18834 ^ _781013) ^ [] : [hAPP(_1132232, 18830 ^ [_1132224, _1132226, _1132228, _1132230, _1132232]) = c_Groups_Oone__class_Oone(_1132224)], (18832 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1132226), 18830 ^ [_1132224, _1132226, _1132228, _1132230, _1132232]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1132226, tc_HOL_Obool)), _1132228), _1132230))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1132226, _1132224), _1132232), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1132226, tc_HOL_Obool)), _1132228), _1132230)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132224), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1132226, _1132224), _1132232), _1132228)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1132226, _1132224), _1132232), _1132230)))], (51264 ^ _781013) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (50986 ^ _781013) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (14965 ^ _781013) ^ [_1057952] : [class_Rings_Ozero__neq__one(_1057952), c_Groups_Ozero__class_Ozero(_1057952) = c_Groups_Oone__class_Oone(_1057952)], (43316 ^ _781013) ^ [_1643552, _1643554, _1643556] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643552)), hAPP(c_List_Ofilter(_1643552, _1643554), _1643556))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643552)), _1643556))))], (39562 ^ _781013) ^ [_1546098, _1546100, _1546102, _1546104] : [class_Orderings_Oord(_1546098), -(c_Hilbert__Choice_OLeastM(_1546100, _1546098, _1546102, _1546104) = c_Hilbert__Choice_OEps(_1546100, hAPP(hAPP(c_COMBS(_1546100, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546100), c_fconj), _1546104)), hAPP(hAPP(c_COMBB(tc_fun(_1546100, tc_HOL_Obool), tc_HOL_Obool, _1546100), c_HOL_OAll(_1546100)), hAPP(hAPP(c_COMBB(tc_fun(_1546100, tc_HOL_Obool), tc_fun(_1546100, tc_HOL_Obool), _1546100), hAPP(c_COMBS(_1546100, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546100), c_fimplies), _1546104))), hAPP(hAPP(c_COMBC(_1546100, tc_fun(_1546100, _1546098), tc_fun(_1546100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546098, tc_HOL_Obool), tc_fun(tc_fun(_1546100, _1546098), tc_fun(_1546100, tc_HOL_Obool)), _1546100), c_COMBB(_1546098, tc_HOL_Obool, _1546100)), hAPP(hAPP(c_COMBB(_1546098, tc_fun(_1546098, tc_HOL_Obool), _1546100), c_Orderings_Oord__class_Oless__eq(_1546098)), _1546102))), _1546102))))))], (45598 ^ _781013) ^ [_1692346, _1692348, _1692350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1692346, tc_HOL_Obool), tc_HOL_Obool)), _1692348), _1692350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1692346, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692346, tc_HOL_Obool), _1692348)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692346, tc_HOL_Obool), _1692350))))], (41638 ^ _781013) ^ [_1602920, _1602922, _1602924] : [hAPP(hAPP(c_List_Oappend(_1602920), _1602922), _1602924) = _1602924, -(_1602922 = c_List_Olist_ONil(_1602920))], (39609 ^ _781013) ^ [_1547600, _1547602, _1547604] : [-(c_Hilbert__Choice_OEps(tc_prod(_1547600, _1547602), hAPP(c_Product__Type_Oprod_Oprod__case(_1547600, _1547602, tc_HOL_Obool), _1547604)) = c_Hilbert__Choice_OEps(tc_prod(_1547600, _1547602), hAPP(hAPP(c_COMBS(tc_prod(_1547600, _1547602), _1547602, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1547600, tc_fun(_1547602, tc_HOL_Obool), tc_prod(_1547600, _1547602)), _1547604), c_Product__Type_Ofst(_1547600, _1547602))), c_Product__Type_Osnd(_1547600, _1547602))))], (48035 ^ _781013) ^ [_1751367, _1751369, _1751371, _1751373, _1751375] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1751367, _1751367)), hAPP(hAPP(c_Product__Type_OPair(_1751367, _1751367), _1751369), _1751371)), _1751373)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1751367, _1751367)), hAPP(hAPP(c_Product__Type_OPair(_1751367, _1751367), _1751371), _1751375)), c_Transitive__Closure_Otrancl(_1751367, _1751373))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1751367, _1751367)), hAPP(hAPP(c_Product__Type_OPair(_1751367, _1751367), _1751369), _1751375)), c_Transitive__Closure_Otrancl(_1751367, _1751373))))], (28626 ^ _781013) ^ [_1315034] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1315034) = c_Orderings_Oord__class_Omin(_1315034)), class_Lattices_Osemilattice__inf(_1315034), class_Orderings_Olinorder(_1315034)], (49027 ^ _781013) ^ [_1774938] : [-(c_Relation_OId(_1774938) = hAPP(c_Set_OCollect(tc_prod(_1774938, _1774938)), hAPP(hAPP(c_COMBB(tc_fun(_1774938, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1774938, _1774938)), c_HOL_OEx(_1774938)), hAPP(hAPP(c_COMBC(tc_prod(_1774938, _1774938), tc_fun(_1774938, tc_prod(_1774938, _1774938)), tc_fun(_1774938, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1774938, _1774938), tc_HOL_Obool), tc_fun(tc_fun(_1774938, tc_prod(_1774938, _1774938)), tc_fun(_1774938, tc_HOL_Obool)), tc_prod(_1774938, _1774938)), c_COMBB(tc_prod(_1774938, _1774938), tc_HOL_Obool, _1774938)), c_fequal)), hAPP(hAPP(c_COMBS(_1774938, _1774938, tc_prod(_1774938, _1774938)), c_Product__Type_OPair(_1774938, _1774938)), c_COMBI(_1774938))))))], (43468 ^ _781013) ^ [_1646591, _1646593, _1646595] : [-(c_List_Opartition(_1646591, _1646593, _1646595) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646591), tc_List_Olist(_1646591)), hAPP(c_List_Ofilter(_1646591, _1646593), _1646595)), hAPP(c_List_Ofilter(_1646591, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1646591, c_fNot), _1646593)), _1646595)))], (44290 ^ _781013) ^ [_1663551, _1663553] : [hBOOL(hAPP(c_List_Odistinct(_1663551), hAPP(c_List_Orev(_1663551), _1663553))), -(hBOOL(hAPP(c_List_Odistinct(_1663551), _1663553)))], (27292 ^ _781013) ^ [_1289425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1289425)), 27296 ^ _781013 : [(27299 ^ _781013) ^ [] : [-(_1289425 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 27295 ^ [_1289425]))], (27297 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 27295 ^ [_1289425])))]]], (18376 ^ _781013) ^ [_1123133, _1123135, _1123137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123133), _1123135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123133), _1123137)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1123135), _1123133)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1123137), _1123133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1123135), _1123137))], (21451 ^ _781013) ^ [_1184154, _1184156] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1184154), _1184156))), -(c_Nat__Transfer_Otsub(_1184156, _1184154) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15905 ^ _781013) ^ [_1075270, _1075272, _1075274] : [class_Rings_Olinordered__semiring__strict(_1075270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075270), c_Groups_Ozero__class_Ozero(_1075270)), _1075272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075270), c_Groups_Ozero__class_Ozero(_1075270)), _1075274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075270), c_Groups_Ozero__class_Ozero(_1075270)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075270), _1075272), _1075274))))], (10929 ^ _781013) ^ [_974556, _974558, _974560] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_974556, tc_HOL_Obool)), _974558), _974560))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974556, tc_HOL_Obool)), _974558), _974560)), -(_974558 = _974560)], (40117 ^ _781013) ^ [_1563268, _1563270, _1563272] : [-(hAPP(c_List_Oset(_1563268), hAPP(hAPP(c_List_Olist_OCons(_1563268), _1563270), _1563272)) = hAPP(hAPP(c_Set_Oinsert(_1563268), _1563270), hAPP(c_List_Oset(_1563268), _1563272)))], (42915 ^ _781013) ^ [_1632699, _1632701, _1632703, _1632705] : [-(_1632699 = c_Orderings_Obot__class_Obot(tc_fun(_1632701, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632701, tc_fun(_1632703, tc_HOL_Obool)), _1632699), hAPP(c_COMBK(tc_fun(_1632703, tc_HOL_Obool), _1632701), _1632705)) = _1632705)], (26586 ^ _781013) ^ [_1275915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275915), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1275915 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 26589 ^ [_1275915]))))], (51380 ^ _781013) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (51298 ^ _781013) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (30375 ^ _781013) ^ [_1348520, _1348522, _1348524, _1348526] : [class_Orderings_Olinorder(_1348520), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348520), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348520), _1348522), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348520), _1348524), _1348526))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348520), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348520), _1348522), _1348524)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348520), _1348522), _1348526)))))], (31986 ^ _781013) ^ [_1387711, _1387713, _1387715, _1387717, _1387719] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387711, tc_fun(_1387713, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1387711), _1387715), _1387717)), _1387719) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387713, tc_HOL_Obool)), hAPP(_1387719, _1387715)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387711, tc_fun(_1387713, tc_HOL_Obool)), _1387717), _1387719)))], (14706 ^ _781013) ^ [_1053938, _1053940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1053938), _1053940))), 14709 ^ _781013 : [(14712 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1053938), _1053940)))], (14710 ^ _781013) ^ [] : [_1053940 = c_Orderings_Obot__class_Obot(tc_fun(_1053938, tc_HOL_Obool))]]], (50242 ^ _781013) ^ [_1802688, _1802690, _1802692] : [c_Nitpick_Oless__eq__frac(_1802688, _1802690, _1802692), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1802688), c_Nitpick_Oplus__frac(_1802688, _1802690, c_Nitpick_Ouminus__frac(_1802688, _1802692)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37985 ^ _781013) ^ [_1508558, _1508560, _1508562, _1508564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1508558), _1508560)), -(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), _1508558), _1508562)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1508560), _1508564))), c_FunDef_Opair__leq)))], (37626 ^ _781013) ^ [_1499690, _1499692, _1499694] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1499690, _1499692), _1499694)), 37629 ^ _781013 : [(37638 ^ _781013) ^ [] : [-(_1499692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37641 ^ _781013 : [(37650 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1499692))), 37653 ^ _781013 : [(37656 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1499694)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37654 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1499692), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1499694))))]]], (37642 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1499692)), 37645 ^ _781013 : [(37648 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1499694)), _1499692)))], (37646 ^ _781013) ^ [] : [-(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), _1499694))))]]]]], (37632 ^ _781013) ^ [] : [_1499692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1499694) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37630 ^ _781013) ^ [] : [-(_1499690 = 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), _1499694)), _1499692)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1499694)))]]], (50834 ^ _781013) ^ [_1814487, _1814489] : [c_Wellfounded_Oacyclic(_1814487, hAPP(c_Set_OCollect(tc_prod(_1814487, _1814487)), hAPP(c_Product__Type_Oprod_Oprod__case(_1814487, _1814487, tc_HOL_Obool), c_Predicate_Oconversep(_1814487, _1814487, _1814489)))), -(c_Wellfounded_Oacyclic(_1814487, hAPP(c_Set_OCollect(tc_prod(_1814487, _1814487)), hAPP(c_Product__Type_Oprod_Oprod__case(_1814487, _1814487, tc_HOL_Obool), _1814489))))], (12936 ^ _781013) ^ [_1016000, _1016002, _1016004, _1016006, _1016008, _1016010, _1016012] : [c_Finite__Set_Ofolding__image(_1016000, _1016002, _1016004, _1016006, _1016008), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016002), _1016010)), -(hAPP(hAPP(_1016008, _1016012), _1016010) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1016000, _1016002, _1016004), _1016012), _1016006), _1016010))], (40115 ^ _781013) ^ [_1563212, _1563214, _1563216, _1563218] : [-(hAPP(hAPP(c_List_Onth(_1563212), hAPP(hAPP(c_List_Olist_OCons(_1563212), _1563214), _1563216)), hAPP(c_Nat_OSuc, _1563218)) = hAPP(hAPP(c_List_Onth(_1563212), _1563216), _1563218))], (37866 ^ _781013) ^ [_1506084, _1506086, _1506088, _1506090, _1506092, _1506094] : [-(hAPP(c_Product__Type_Oapfst(_1506084, _1506086, _1506088, _1506090), hAPP(hAPP(c_Product__Type_OPair(_1506084, _1506088), _1506092), _1506094)) = hAPP(hAPP(c_Product__Type_OPair(_1506086, _1506088), hAPP(_1506090, _1506092)), _1506094))], (48760 ^ _781013) ^ [_1768213, _1768215, _1768217, _1768219, _1768221] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768215, _1768213)), hAPP(hAPP(c_Product__Type_OPair(_1768215, _1768213), _1768219), _1768217)), _1768221)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1768213, _1768215)), hAPP(hAPP(c_Product__Type_OPair(_1768213, _1768215), _1768217), _1768219)), hAPP(c_Relation_Oconverse(_1768215, _1768213), _1768221))))], (16215 ^ _781013) ^ [_1080682, _1080684, _1080686] : [class_Groups_Ogroup__add(_1080682), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080682), _1080684), _1080686) = c_Groups_Ozero__class_Ozero(_1080682), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1080682), _1080684) = _1080686)], (16281 ^ _781013) ^ [_1081907, _1081909, _1081911, _1081913] : [class_Groups_Ocomm__monoid__add(_1081907), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1081909), _1081911))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081909, _1081907), _1081913), _1081911) = c_Groups_Ozero__class_Ozero(_1081907))], (44408 ^ _781013) ^ [_1666102, _1666104, _1666106, _1666108] : [_1666104 = hAPP(hAPP(c_List_Oappend(_1666102), hAPP(c_List_Orev(_1666102), _1666108)), hAPP(hAPP(c_List_Olist_OCons(_1666102), _1666106), c_List_Olist_ONil(_1666102))), -(hAPP(c_List_Orev(_1666102), _1666104) = hAPP(hAPP(c_List_Olist_OCons(_1666102), _1666106), _1666108))], (33366 ^ _781013) ^ [_1414326, _1414328] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1414326) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414328)), _1414326 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414328)), 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), _1414328)))], (33680 ^ _781013) ^ [_1419480] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419480) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1419480), c_Int_OPls)))], (5685 ^ _781013) ^ [_870897, _870899] : [_870897 = _870899, -(hAPP(c_Com_Ocom_OBODY, _870897) = hAPP(c_Com_Ocom_OBODY, _870899))], (5922 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (26419 ^ _781013) ^ [_1272338, _1272340, _1272342, _1272344] : [class_Orderings_Oorder(_1272338), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1272338, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1272338, _1272340, _1272342)), c_SetInterval_Oord__class_OatLeastAtMost(_1272338, _1272342, _1272344)) = c_Orderings_Obot__class_Obot(tc_fun(_1272338, tc_HOL_Obool)))], (48111 ^ _781013) ^ [_1753150, _1753152, _1753154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1753150), _1753152)), -(c_Random_Ominus__shift(_1753154, _1753150, _1753152) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1753154), _1753150)), _1753152))], (23337 ^ _781013) ^ [_1217515, _1217517] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_1217515, _1217517)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1217515)), c_Com_Ocom_Ocom__size(_1217517))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20669 ^ _781013) ^ [_1167419, _1167421, _1167423] : [class_Rings_Oring__1(_1167419), hBOOL(hAPP(hAPP(c_member(_1167419), _1167421), c_Int_Oring__1__class_OInts(_1167419))), -(hBOOL(hAPP(hAPP(c_member(_1167419), hAPP(hAPP(c_Power_Opower__class_Opower(_1167419), _1167421), _1167423)), c_Int_Oring__1__class_OInts(_1167419))))], (34847 ^ _781013) ^ [_1440821, _1440823] : [class_Int_Onumber__ring(_1440821), class_Int_Oring__char__0(_1440821), 34854 ^ _781013 : [(34861 ^ _781013) ^ [] : [c_Int_Oiszero(_1440821, hAPP(c_Int_Onumber__class_Onumber__of(_1440821), _1440823)), -(c_Int_Oiszero(_1440821, hAPP(c_Int_Onumber__class_Onumber__of(_1440821), c_Int_OBit0(_1440823))))], (34855 ^ _781013) ^ [] : [c_Int_Oiszero(_1440821, hAPP(c_Int_Onumber__class_Onumber__of(_1440821), c_Int_OBit0(_1440823))), -(c_Int_Oiszero(_1440821, hAPP(c_Int_Onumber__class_Onumber__of(_1440821), _1440823)))]]], (8329 ^ _781013) ^ [_923908, _923910, _923912] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_923908, tc_HOL_Obool)), _923910), hAPP(hAPP(c_Set_Oinsert(_923908), _923912), c_Orderings_Obot__class_Obot(tc_fun(_923908, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_923908, _923912, _923910) = c_HOL_OThe(_923908, hAPP(hAPP(c_COMBC(_923908, tc_fun(_923908, tc_HOL_Obool), tc_HOL_Obool), c_member(_923908)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923908, tc_HOL_Obool)), _923910), hAPP(hAPP(c_Set_Oinsert(_923908), _923912), c_Orderings_Obot__class_Obot(tc_fun(_923908, tc_HOL_Obool)))))))], (49284 ^ _781013) ^ [_1781466, _1781468, _1781470, _1781472] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1781466, _1781468, _1781470, _1781472) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1781466, _1781468), _1781470), _1781472)))], (12204 ^ _781013) ^ [_1001354, _1001356, _1001358] : [-(c_Map_Odom(_1001354, _1001356, hAPP(hAPP(c_COMBB(_1001356, tc_Option_Ooption(_1001356), _1001354), c_Option_Ooption_OSome(_1001356)), _1001358)) = c_Orderings_Otop__class_Otop(tc_fun(_1001354, tc_HOL_Obool)))], (5785 ^ _781013) ^ [_873258, _873260, _873262] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_873258, _873260, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873258)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873258), _873262), c_Com_Ocom_OSKIP), _873262)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873258), tc_HOL_Obool)))))], (35825 ^ _781013) ^ [_1458179, _1458181] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1458179), _1458181) = c_Smallcheck_Osmall_H(_1458179, hAPP(c_Code__Numeral_Oint__of, _1458181), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1458181))))], (11534 ^ _781013) ^ [_988366, _988368, _988370] : [class_Lattices_Oab__semigroup__idem__mult(_988366), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988366), _988368), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988366), _988368), _988370)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988366), _988368), _988370))], (42843 ^ _781013) ^ [_1629972, _1629974, _1629976, _1629978, _1629980, _1629982] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629972, tc_fun(_1629974, tc_HOL_Obool)), _1629976), hAPP(hAPP(c_COMBB(_1629978, tc_fun(_1629974, tc_HOL_Obool), _1629972), _1629980), _1629982)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629978, tc_fun(_1629974, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1629972, _1629978, _1629982), _1629976)), _1629980))], (1204 ^ _781013) ^ [_798805, _798807] : [-(class_Int_Onumber__ring(_798805)), _798807 = _798805, class_Int_Onumber__ring(_798807)], (48810 ^ _781013) ^ [_1769495, _1769497, _1769499] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1769495, _1769497)), hAPP(c_Relation_Oconverse(_1769497, _1769495), _1769499))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1769497, _1769495)), _1769499)))], (7805 ^ _781013) ^ [_912498, _912500, _912502] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_912498), _912500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912498, tc_HOL_Obool)), _912502), _912500)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_912498), _912502)))], (50340 ^ _781013) ^ [_1804725, _1804727, _1804729, _1804731] : [c_List_Olist__all(_1804725, _1804727, hAPP(hAPP(c_List_Oappend(_1804725), _1804729), _1804731)), 50343 ^ _781013 : [(50346 ^ _781013) ^ [] : [-(c_List_Olist__all(_1804725, _1804727, _1804731))], (50344 ^ _781013) ^ [] : [-(c_List_Olist__all(_1804725, _1804727, _1804729))]]], (21848 ^ _781013) ^ [] : [-(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))], (4842 ^ _781013) ^ [_854463, _854465, _854467, _854469, _854471, _854473, _854475, _854477, _854479, _854481] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_854481, _854477, _854473, _854469, _854465) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_854479, _854475, _854471, _854467, _854463)), _854481 = _854479, _854477 = _854475, _854473 = _854471, _854469 = _854467, _854465 = _854463], (10849 ^ _781013) ^ [_972877, _972879, _972881, _972883] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972877, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972877, tc_HOL_Obool)), _972879), _972881)), _972883) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972877, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972877, tc_HOL_Obool)), _972879), _972883)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972877, tc_HOL_Obool)), _972881), _972883)))], (12640 ^ _781013) ^ [_1009600, _1009602] : [class_Lattices_Olattice(_1009600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009600), _1009602)), -(_1009602 = c_Orderings_Obot__class_Obot(tc_fun(_1009600, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1009600), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009600), 12653 ^ [_1009600, _1009602]), 12654 ^ [_1009600, _1009602])), hAPP(hAPP(c_Set_Oinsert(_1009600), 12653 ^ [_1009600, _1009602]), hAPP(hAPP(c_Set_Oinsert(_1009600), 12654 ^ [_1009600, _1009602]), c_Orderings_Obot__class_Obot(tc_fun(_1009600, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1009600), c_Big__Operators_Olattice__class_OSup__fin(_1009600, _1009602)), _1009602)))], (1454 ^ _781013) ^ [_801930, _801932] : [-(class_Rings_Olinordered__comm__semiring__strict(_801930)), _801932 = _801930, class_Rings_Olinordered__comm__semiring__strict(_801932)], (47640 ^ _781013) ^ [_1742446, _1742448, _1742450, _1742452, _1742454] : [hAPP(c_List_Ofilter(_1742446, _1742448), _1742450) = hAPP(hAPP(c_List_Olist_OCons(_1742446), _1742452), _1742454), 47645 ^ _781013 : [(47654 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1742448, _1742452)))], (47656 ^ _781013) ^ [] : [-(_1742454 = hAPP(c_List_Ofilter(_1742446, _1742448), 47644 ^ [_1742446, _1742448, _1742450, _1742452, _1742454]))], (47648 ^ _781013) ^ [_1742760] : [hBOOL(hAPP(hAPP(c_member(_1742446), _1742760), hAPP(c_List_Oset(_1742446), 47643 ^ [_1742446, _1742448, _1742450, _1742452, _1742454]))), hBOOL(hAPP(_1742448, _1742760))], (47646 ^ _781013) ^ [] : [-(_1742450 = hAPP(hAPP(c_List_Oappend(_1742446), 47643 ^ [_1742446, _1742448, _1742450, _1742452, _1742454]), hAPP(hAPP(c_List_Olist_OCons(_1742446), _1742452), 47644 ^ [_1742446, _1742448, _1742450, _1742452, _1742454])))]]], (11472 ^ _781013) ^ [_987143, _987145, _987147, _987149, _987151] : [c_Fun_Oinj__on(_987143, _987145, _987147, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987143, tc_HOL_Obool)), _987149), _987151)), 11475 ^ _781013 : [(11480 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_987145, tc_HOL_Obool)), hAPP(c_Set_Oimage(_987143, _987145, _987147), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987143, tc_HOL_Obool)), _987149), _987151))), hAPP(c_Set_Oimage(_987143, _987145, _987147), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987143, tc_HOL_Obool)), _987151), _987149))) = c_Orderings_Obot__class_Obot(tc_fun(_987145, tc_HOL_Obool)))], (11478 ^ _781013) ^ [] : [-(c_Fun_Oinj__on(_987143, _987145, _987147, _987151))], (11476 ^ _781013) ^ [] : [-(c_Fun_Oinj__on(_987143, _987145, _987147, _987149))]]], (35021 ^ _781013) ^ [] : [-(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))))))], (26185 ^ _781013) ^ [_1267931, _1267933, _1267935, _1267937, _1267939] : [class_Orderings_Oorder(_1267931), 26188 ^ _781013 : [(26201 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267931, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1267931, _1267933, _1267935)), c_SetInterval_Oord__class_OatLeastAtMost(_1267931, _1267937, _1267939)))), 26202 ^ _781013 : [(26205 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267931), _1267937), _1267933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267931), _1267935), _1267939))], (26203 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267931), _1267933), _1267935)))]]], (26189 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267931, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1267931, _1267933, _1267935)), c_SetInterval_Oord__class_OatLeastAtMost(_1267931, _1267937, _1267939))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267931), _1267933), _1267935)), 26196 ^ _781013 : [(26199 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267931), _1267935), _1267939)))], (26197 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267931), _1267937), _1267933)))]]]]], (21611 ^ _781013) ^ [_1186871, _1186873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186871)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186871), _1186873)))], (18199 ^ _781013) ^ [_1119929, _1119931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119929), _1119931)), -(_1119929 = _1119931), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119929), _1119931)))], (50006 ^ _781013) ^ [_1797080, _1797082, _1797084, _1797086, _1797088, _1797090, _1797092] : [c_Finite__Set_Ofun__left__comm(_1797080, _1797082, _1797084), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1797080, _1797082, _1797084, _1797086, _1797088), _1797090)), hBOOL(hAPP(hAPP(c_member(_1797080), _1797092), _1797088)), 50018 ^ _781013 : [(50021 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1797080, _1797082, _1797084, _1797086, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1797080, tc_HOL_Obool)), _1797088), hAPP(hAPP(c_Set_Oinsert(_1797080), _1797092), c_Orderings_Obot__class_Obot(tc_fun(_1797080, tc_HOL_Obool))))), 50017 ^ [_1797080, _1797082, _1797084, _1797086, _1797088, _1797090, _1797092])))], (50019 ^ _781013) ^ [] : [-(_1797090 = hAPP(hAPP(_1797084, _1797092), 50017 ^ [_1797080, _1797082, _1797084, _1797086, _1797088, _1797090, _1797092]))]]], (34243 ^ _781013) ^ [_1430546, _1430548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1430546)), c_Int_OBit1(_1430548))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430546), _1430548)))], (31585 ^ _781013) ^ [_1376590, _1376592, _1376594, _1376596] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376590, tc_fun(_1376592, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1376590, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1376592, tc_HOL_Obool), tc_fun(_1376592, tc_HOL_Obool), _1376590), hAPP(c_COMBC(_1376592, tc_fun(_1376592, tc_HOL_Obool), tc_HOL_Obool), c_member(_1376592))), _1376594)), _1376596)), -(hBOOL(hAPP(hAPP(c_member(_1376592), _1376596), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376590, tc_fun(_1376592, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1376590, tc_HOL_Obool))), _1376594))))], (43529 ^ _781013) ^ [_1648317] : [-(c_List_Otranspose(_1648317, c_List_Olist_ONil(tc_List_Olist(_1648317))) = c_List_Olist_ONil(tc_List_Olist(_1648317)))], (6244 ^ _781013) ^ [_882498, _882500, _882502] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_882498, _882500, _882502))), 6247 ^ _781013 : [(6250 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _882502)))], (6248 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _882500)))]]], (9345 ^ _781013) ^ [_946730, _946732, _946734, _946736] : [hBOOL(hAPP(_946730, _946732)), hBOOL(hAPP(_946734, _946732)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946736, tc_HOL_Obool)), _946730), _946734), _946732)))], (26425 ^ _781013) ^ [_1272465, _1272467, _1272469, _1272471] : [class_Groups_Ocomm__monoid__add(_1272465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1272467), _1272469)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1272465), _1272471), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1272467, _1272469)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272465), hAPP(_1272471, _1272467)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1272465), _1272471), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1272467), _1272469))))], (18306 ^ _781013) ^ [_1121820, _1121822] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121820), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121820), _1121822))))], (25366 ^ _781013) ^ [_1253855, _1253857, _1253859, _1253861] : [class_Fields_Olinordered__field(_1253855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253855), _1253857), c_Groups_Ozero__class_Ozero(_1253855))), 25373 ^ _781013 : [(25380 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253855), _1253861), _1253857)), _1253859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253855), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253855), _1253859), _1253857)), _1253861)))], (25374 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253855), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253855), _1253859), _1253857)), _1253861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253855), _1253861), _1253857)), _1253859)))]]], (24440 ^ _781013) ^ [_1236868, _1236870, _1236872, _1236874] : [class_Fields_Olinordered__field(_1236868), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236868), c_Groups_Ozero__class_Ozero(_1236868)), _1236870)), 24447 ^ _781013 : [(24454 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236868), _1236872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236868), _1236874), _1236870))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236868), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1236868), _1236872), _1236870)), _1236874)))], (24448 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236868), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1236868), _1236872), _1236870)), _1236874)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236868), _1236872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236868), _1236874), _1236870))))]]], (36410 ^ _781013) ^ [_1475421, _1475423, _1475425, _1475427, _1475429, _1475431, _1475433] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1475421, _1475423)), hAPP(hAPP(c_Product__Type_OPair(_1475421, _1475423), _1475425), _1475427)), _1475429)), -(hBOOL(hAPP(hAPP(c_member(_1475431), hAPP(hAPP(_1475433, _1475425), _1475427)), hAPP(c_Set_Oimage(tc_prod(_1475421, _1475423), _1475431, hAPP(c_Product__Type_Oprod_Oprod__case(_1475421, _1475423, _1475431), _1475433)), _1475429))))], (20550 ^ _781013) ^ [_1165035, _1165037, _1165039, _1165041] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1165035), hAPP(c_Set_OCollect(_1165035), _1165037))), 20553 ^ _781013 : [(20554 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1165039), hAPP(c_Set_OCollect(_1165039), hAPP(hAPP(c_COMBB(tc_fun(_1165035, tc_HOL_Obool), tc_HOL_Obool, _1165039), c_HOL_OEx(_1165035)), hAPP(hAPP(c_COMBB(tc_fun(_1165035, tc_HOL_Obool), tc_fun(_1165035, tc_HOL_Obool), _1165039), hAPP(c_COMBS(_1165035, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1165035), c_fconj), _1165037))), _1165041))))), 20557 ^ _781013 : [(20558 ^ _781013) ^ [_1165318] : [hBOOL(hAPP(_1165037, _1165318)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1165039), hAPP(c_Set_OCollect(_1165039), hAPP(hAPP(c_COMBC(_1165039, _1165035, tc_HOL_Obool), _1165041), _1165318)))))]]], (20564 ^ _781013) ^ [] : [20566 ^ _781013 : [(20569 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1165039), hAPP(c_Set_OCollect(_1165039), hAPP(hAPP(c_COMBC(_1165039, _1165035, tc_HOL_Obool), _1165041), 20565 ^ [_1165035, _1165037, _1165039, _1165041]))))], (20567 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1165037, 20565 ^ [_1165035, _1165037, _1165039, _1165041])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1165039), hAPP(c_Set_OCollect(_1165039), hAPP(hAPP(c_COMBB(tc_fun(_1165035, tc_HOL_Obool), tc_HOL_Obool, _1165039), c_HOL_OEx(_1165035)), hAPP(hAPP(c_COMBB(tc_fun(_1165035, tc_HOL_Obool), tc_fun(_1165035, tc_HOL_Obool), _1165039), hAPP(c_COMBS(_1165035, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1165035), c_fconj), _1165037))), _1165041))))))]]], (48794 ^ _781013) ^ [_1769080, _1769082, _1769084] : [c_Equiv__Relations_Oequiv(_1769080, _1769082, _1769084), -(hAPP(hAPP(c_Relation_Orel__comp(_1769080, _1769080, _1769080), hAPP(c_Relation_Oconverse(_1769080, _1769080), _1769084)), _1769084) = _1769084)], (34131 ^ _781013) ^ [_1428352, _1428354, _1428356] : [class_Int_Onumber__ring(_1428352), 34134 ^ _781013 : [(34141 ^ _781013) ^ [] : [c_Int_Oiszero(_1428352, hAPP(c_Int_Onumber__class_Onumber__of(_1428352), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428354), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1428356)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1428352), _1428354) = hAPP(c_Int_Onumber__class_Onumber__of(_1428352), _1428356))], (34135 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1428352), _1428354) = hAPP(c_Int_Onumber__class_Onumber__of(_1428352), _1428356), -(c_Int_Oiszero(_1428352, hAPP(c_Int_Onumber__class_Onumber__of(_1428352), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428354), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1428356)))))]]], (48936 ^ _781013) ^ [_1772908, _1772910, _1772912, _1772914, _1772916] : [c_Relation_Osingle__valued(_1772908, _1772910, _1772912), c_Relation_Osingle__valued(_1772910, _1772914, _1772916), -(c_Relation_Osingle__valued(_1772908, _1772914, hAPP(hAPP(c_Relation_Orel__comp(_1772908, _1772910, _1772914), _1772912), _1772916)))], (4732 ^ _781013) ^ [_852580, _852582, _852584, _852586, _852588, _852590, _852592, _852594, _852596, _852598, _852600, _852602, _852604, _852606] : [-(c_New__Random__Sequence_Oneg__decr__bind(_852606, _852602, _852598, _852594, _852590, _852586, _852582) = c_New__Random__Sequence_Oneg__decr__bind(_852604, _852600, _852596, _852592, _852588, _852584, _852580)), _852606 = _852604, _852602 = _852600, _852598 = _852596, _852594 = _852592, _852590 = _852588, _852586 = _852584, _852582 = _852580], (13425 ^ _781013) ^ [_1026294, _1026296] : [class_Groups_Ocomm__monoid__mult(_1026294), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026294), _1026296), c_Groups_Oone__class_Oone(_1026294)) = _1026296)], (45635 ^ _781013) ^ [_1693033, _1693035, _1693037] : [class_Complete__Lattice_Ocomplete__lattice(_1693033), 45638 ^ _781013 : [(45639 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1693033), c_Complete__Lattice_OSup__class_OSup(_1693033, _1693035)), _1693037)), 45642 ^ _781013 : [(45643 ^ _781013) ^ [_1693191] : [hBOOL(hAPP(hAPP(c_member(_1693033), _1693191), _1693035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1693033), _1693191), _1693037)))]]], (45649 ^ _781013) ^ [] : [45651 ^ _781013 : [(45654 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1693033), 45650 ^ [_1693033, _1693035, _1693037]), _1693037))], (45652 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1693033), 45650 ^ [_1693033, _1693035, _1693037]), _1693035)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1693033), c_Complete__Lattice_OSup__class_OSup(_1693033, _1693035)), _1693037)))]]], (43330 ^ _781013) ^ [_1643875, _1643877, _1643879] : [43332 ^ _781013 : [(43335 ^ _781013) ^ [] : [hBOOL(hAPP(_1643877, 43331 ^ [_1643875, _1643877, _1643879]))], (43333 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1643875), 43331 ^ [_1643875, _1643877, _1643879]), hAPP(c_List_Oset(_1643875), _1643879))))]], -(hAPP(c_List_Ofilter(_1643875, _1643877), _1643879) = _1643879)], (23491 ^ _781013) ^ [_1220657, _1220659] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1220657, _1220659)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1220659), _1220657)))], (12732 ^ _781013) ^ [_1011307, _1011309, _1011311, _1011313, _1011315, _1011317, _1011319] : [c_Fun_Oinj__on(_1011307, _1011309, _1011311, hAPP(c_Set_Oimage(_1011313, _1011307, _1011315), _1011317)), c_Fun_Oinj__on(_1011313, _1011307, _1011315, _1011317), hBOOL(hAPP(hAPP(c_member(_1011309), _1011319), hAPP(c_Set_Oimage(_1011307, _1011309, _1011311), hAPP(c_Set_Oimage(_1011313, _1011307, _1011315), _1011317)))), -(hAPP(c_Fun_Othe__inv__into(_1011313, _1011309, _1011317, hAPP(c_Fun_Ocomp(_1011307, _1011309, _1011313, _1011311), _1011315)), _1011319) = hAPP(hAPP(c_Fun_Ocomp(_1011307, _1011313, _1011309, c_Fun_Othe__inv__into(_1011313, _1011307, _1011317, _1011315)), c_Fun_Othe__inv__into(_1011307, _1011309, hAPP(c_Set_Oimage(_1011313, _1011307, _1011315), _1011317), _1011311)), _1011319))], (1434 ^ _781013) ^ [_801680, _801682] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_801680)), _801682 = _801680, class_Groups_Oordered__cancel__ab__semigroup__add(_801682)], (44793 ^ _781013) ^ [_1675296, _1675298, _1675300] : [-(c_List_Oremdups(_1675296, hAPP(c_List_Ofilter(_1675296, _1675298), _1675300)) = hAPP(c_List_Ofilter(_1675296, _1675298), c_List_Oremdups(_1675296, _1675300)))], (14861 ^ _781013) ^ [_1056366, _1056368, _1056370] : [class_Rings_Ono__zero__divisors(_1056366), -(_1056368 = c_Groups_Ozero__class_Ozero(_1056366)), -(_1056370 = c_Groups_Ozero__class_Ozero(_1056366)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056366), _1056368), _1056370) = c_Groups_Ozero__class_Ozero(_1056366)], (11978 ^ _781013) ^ [_996964, _996966, _996968, _996970] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_996964), hAPP(c_Set_Oimage(_996966, _996964, _996968), _996970))), c_Fun_Oinj__on(_996966, _996964, _996968, _996970), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_996966), _996970)))], (26291 ^ _781013) ^ [_1269932, _1269934, _1269936] : [class_Orderings_Olinorder(_1269932), 26294 ^ _781013 : [(26301 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269932), _1269936), _1269934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269932, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1269932), _1269934)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1269932), _1269936))))], (26295 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269932, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1269932), _1269934)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1269932), _1269936))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269932), _1269936), _1269934)))]]], (18153 ^ _781013) ^ [_1119194, _1119196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119194), _1119196)), _1119196))], (7655 ^ _781013) ^ [_909740, _909742, _909744] : [-(hBOOL(hAPP(hAPP(c_member(_909740), _909742), _909744))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909740, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_909740), _909742), _909744)), hAPP(hAPP(c_Set_Oinsert(_909740), _909742), c_Orderings_Obot__class_Obot(tc_fun(_909740, tc_HOL_Obool)))) = _909744)], (48441 ^ _781013) ^ [_1760488, _1760490, _1760492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1760488, _1760488), tc_HOL_Obool)), _1760490), _1760492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1760488, _1760488), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1760488, _1760490)), c_Transitive__Closure_Ortrancl(_1760488, _1760492))))], (10017 ^ _781013) ^ [_958168, _958170, _958172] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958168, tc_HOL_Obool)), _958170), _958172) = c_Orderings_Obot__class_Obot(tc_fun(_958168, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958168, tc_HOL_Obool)), _958170), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_958168, tc_HOL_Obool)), _958172))))], (48491 ^ _781013) ^ [_1761388] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1761388)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1761388))], (15025 ^ _781013) ^ [_1058800, _1058802] : [class_Groups_Ogroup__add(_1058800), 15028 ^ _781013 : [(15035 ^ _781013) ^ [] : [c_Groups_Ozero__class_Ozero(_1058800) = _1058802, -(c_Groups_Ozero__class_Ozero(_1058800) = hAPP(c_Groups_Ouminus__class_Ouminus(_1058800), _1058802))], (15029 ^ _781013) ^ [] : [c_Groups_Ozero__class_Ozero(_1058800) = hAPP(c_Groups_Ouminus__class_Ouminus(_1058800), _1058802), -(c_Groups_Ozero__class_Ozero(_1058800) = _1058802)]]], (42096 ^ _781013) ^ [_1614032, _1614034, _1614036] : [-(c_List_Obutlast(_1614032, hAPP(hAPP(c_List_Odrop(_1614032), _1614034), _1614036)) = hAPP(hAPP(c_List_Odrop(_1614032), _1614034), c_List_Obutlast(_1614032, _1614036)))], (16842 ^ _781013) ^ [_1093326, _1093328, _1093330, _1093332] : [class_Rings_Olinordered__semiring__strict(_1093326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093326), _1093328), _1093330)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093326), _1093328), _1093332))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093326), c_Groups_Ozero__class_Ozero(_1093326)), _1093328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093326), _1093330), _1093332)))], (24260 ^ _781013) ^ [_1233530, _1233532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233530)), 24263 ^ _781013 : [(24270 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233530), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1233530)), _1233532)))], (24264 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1233530)), _1233532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233530), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233532))))]]], (18426 ^ _781013) ^ [_1123914, _1123916] : [18427 ^ _781013 : [(18430 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1123916))], (18428 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1123914))]], -(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), _1123914), _1123916))))], (31045 ^ _781013) ^ [_1362322, _1362324] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1362322), hAPP(c_Nat_OSuc, _1362324)) = 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), _1362322), _1362324)))], (28056 ^ _781013) ^ [_1304742, _1304744] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304742, _1304744) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304742, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1304744)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304742, _1304744)), _1304744))], (6160 ^ _781013) ^ [_880960, _880962, _880964, _880966, _880968, _880970] : [c_Com_Ocom_OCond(_880960, _880962, _880964) = c_Com_Ocom_OCond(_880966, _880968, _880970), 6163 ^ _781013 : [(6168 ^ _781013) ^ [] : [-(_880964 = _880970)], (6166 ^ _781013) ^ [] : [-(_880962 = _880968)], (6164 ^ _781013) ^ [] : [-(_880960 = _880966)]]], (11942 ^ _781013) ^ [_996389, _996391] : [class_Lattices_Obounded__lattice__top(_996389), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_996389), c_Orderings_Otop__class_Otop(_996389)), _996391) = _996391)], (40603 ^ _781013) ^ [_1575998, _1576000, _1576002, _1576004, _1576006, _1576008] : [class_Groups_Ocomm__monoid__mult(_1575998), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1576000, _1575998), hAPP(hAPP(c_COMBC(_1576000, tc_fun(_1576002, tc_HOL_Obool), _1575998), hAPP(hAPP(c_COMBB(tc_fun(_1576002, _1575998), tc_fun(tc_fun(_1576002, tc_HOL_Obool), _1575998), _1576000), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1576002, _1575998)), _1576004)), _1576006)), _1576008) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1576000, _1576002), _1575998), hAPP(c_Product__Type_Oprod_Oprod__case(_1576000, _1576002, _1575998), _1576004)), hAPP(hAPP(c_Product__Type_OSigma(_1576000, _1576002), _1576008), hAPP(c_COMBK(tc_fun(_1576002, tc_HOL_Obool), _1576000), _1576006))))], (51512 ^ _781013) ^ [_1823813] : [-(class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(_1823813)))], (20514 ^ _781013) ^ [_1164235] : [-(hAPP(c_Nat_OSuc, _1164235) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1164235))], (22212 ^ _781013) ^ [_1197576, _1197578] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197576) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197578), -(_1197576 = _1197578)], (40737 ^ _781013) ^ [_1579841, _1579843, _1579845, _1579847] : [-(hAPP(c_Set_OCollect(tc_prod(_1579841, _1579843)), hAPP(c_Product__Type_Oprod_Oprod__case(_1579841, _1579843, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1579841, tc_fun(_1579843, tc_HOL_Obool), tc_fun(_1579843, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1579843, tc_HOL_Obool), tc_fun(_1579843, tc_HOL_Obool)), _1579841), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1579843)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1579841), c_fconj), _1579845))), _1579847))) = hAPP(hAPP(c_Product__Type_OSigma(_1579841, _1579843), hAPP(c_Set_OCollect(_1579841), _1579845)), hAPP(hAPP(c_COMBB(tc_fun(_1579843, tc_HOL_Obool), tc_fun(_1579843, tc_HOL_Obool), _1579841), c_Set_OCollect(_1579843)), _1579847)))], (44647 ^ _781013) ^ [_1672543, _1672545] : [-(c_List_OtakeWhile(_1672543, _1672545, c_List_Olist_ONil(_1672543)) = c_List_Olist_ONil(_1672543))], (13187 ^ _781013) ^ [_1021355, _1021357, _1021359] : [class_Lattices_Oab__semigroup__idem__mult(_1021355), -(_1021357 = c_Orderings_Obot__class_Obot(tc_fun(_1021355, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021355), _1021357)), -(hAPP(c_Finite__Set_Ofold1(_1021355, c_Groups_Otimes__class_Otimes(_1021355)), hAPP(hAPP(c_Set_Oinsert(_1021355), _1021359), _1021357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1021355), _1021359), hAPP(c_Finite__Set_Ofold1(_1021355, c_Groups_Otimes__class_Otimes(_1021355)), _1021357)))], (33008 ^ _781013) ^ [_1407252, _1407254, _1407256, _1407258] : [class_Int_Onumber__ring(_1407252), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1407252), hAPP(c_Int_Onumber__class_Onumber__of(_1407252), _1407254)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1407252), _1407256), hAPP(c_Int_Onumber__class_Onumber__of(_1407252), _1407258))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1407252), hAPP(c_Int_Onumber__class_Onumber__of(_1407252), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1407254), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1407258)))), _1407256))], (42288 ^ _781013) ^ [_1618704, _1618706, _1618708, _1618710, _1618712] : [-(hAPP(hAPP(c_List_Ozip(_1618704, _1618706), _1618708), hAPP(hAPP(c_List_Oappend(_1618706), _1618710), _1618712)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1618704, _1618706)), hAPP(hAPP(c_List_Ozip(_1618704, _1618706), hAPP(hAPP(c_List_Otake(_1618704), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618706)), _1618710)), _1618708)), _1618710)), hAPP(hAPP(c_List_Ozip(_1618704, _1618706), hAPP(hAPP(c_List_Odrop(_1618704), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618706)), _1618710)), _1618708)), _1618712)))], (32036 ^ _781013) ^ [_1389291, _1389293, _1389295, _1389297] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1389291), _1389293)), 32042 ^ _781013 : [(32045 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1389295), hAPP(_1389297, 32041 ^ [_1389291, _1389293, _1389295, _1389297])))], (32043 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389291), 32041 ^ [_1389291, _1389293, _1389295, _1389297]), _1389293)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1389295), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389291, tc_fun(_1389295, tc_HOL_Obool)), _1389293), _1389297))))], (41911 ^ _781013) ^ [_1608952, _1608954, _1608956, _1608958, _1608960, _1608962] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608952), tc_List_Olist(_1608952))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608952), tc_List_Olist(_1608952)), hAPP(hAPP(c_List_Oappend(_1608952), _1608954), _1608960)), hAPP(hAPP(c_List_Oappend(_1608952), _1608956), _1608962))), c_List_Olistrel1(_1608952, _1608958)))), 41912 ^ _781013 : [(41919 ^ _781013) ^ [] : [_1608954 = _1608956, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608952), tc_List_Olist(_1608952))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608952), tc_List_Olist(_1608952)), _1608960), _1608962)), c_List_Olistrel1(_1608952, _1608958)))], (41913 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608952), tc_List_Olist(_1608952))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608952), tc_List_Olist(_1608952)), _1608954), _1608956)), c_List_Olistrel1(_1608952, _1608958))), _1608960 = _1608962]]], (9387 ^ _781013) ^ [_947496, _947498, _947500] : [class_Groups_Oordered__ab__group__add(_947496), 9390 ^ _781013 : [(9397 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947496), _947500), _947498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947496), hAPP(c_Groups_Ouminus__class_Ouminus(_947496), _947498)), hAPP(c_Groups_Ouminus__class_Ouminus(_947496), _947500))))], (9391 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947496), hAPP(c_Groups_Ouminus__class_Ouminus(_947496), _947498)), hAPP(c_Groups_Ouminus__class_Ouminus(_947496), _947500))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947496), _947500), _947498)))]]], (6184 ^ _781013) ^ [_881354, _881356, _881358, _881360, _881362] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_881354, _881356, _881358)), _881360), _881362)), 6189 ^ _781013 : [(6192 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_881356), _881360), _881362)))], (6190 ^ _781013) ^ [] : [-(hBOOL(hAPP(_881354, _881360)))]], 6193 ^ _781013 : [(6196 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_881358), _881360), _881362)))], (6194 ^ _781013) ^ [] : [hBOOL(hAPP(_881354, _881360))]]], (34 ^ _781013) ^ [_781466, _781468, _781470, _781472, _781474, _781476, _781478, _781480] : [-(c_Finite__Set_Ofolding__idem(_781478, _781474, _781470, _781466)), c_Finite__Set_Ofolding__idem(_781480, _781476, _781472, _781468), _781480 = _781478, _781476 = _781474, _781472 = _781470, _781468 = _781466], (38936 ^ _781013) ^ [_1531534, _1531536, _1531538, _1531540, _1531542] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1531534)), _1531536) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1531538)), _1531540), 38939 ^ _781013 : [(38947 ^ _781013) ^ [] : [38948 ^ _781013 : [(38949 ^ _781013) ^ [_1531826] : [hAPP(hAPP(c_Map_Omap__of(_1531534, _1531538), hAPP(hAPP(c_List_Ozip(_1531534, _1531538), _1531536), _1531540)), _1531542) = hAPP(c_Option_Ooption_OSome(_1531538), _1531826)]], -(hBOOL(hAPP(hAPP(c_member(_1531534), _1531542), hAPP(c_List_Oset(_1531534), _1531536))))], (38940 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1531534), _1531542), hAPP(c_List_Oset(_1531534), _1531536))), -(hAPP(hAPP(c_Map_Omap__of(_1531534, _1531538), hAPP(hAPP(c_List_Ozip(_1531534, _1531538), _1531536), _1531540)), _1531542) = hAPP(c_Option_Ooption_OSome(_1531538), 38943 ^ [_1531534, _1531536, _1531538, _1531540, _1531542]))]]], (38176 ^ _781013) ^ [_1513494, _1513496] : [-(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), _1513494), _1513496)), 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), _1513494), _1513496))], (31884 ^ _781013) ^ [_1385195, _1385197, _1385199, _1385201, _1385203] : [class_Complete__Lattice_Ocomplete__lattice(_1385195), hBOOL(hAPP(hAPP(c_member(_1385197), _1385199), _1385201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385195), hAPP(_1385203, _1385199)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385197, _1385195), _1385201), _1385203))))], (50618 ^ _781013) ^ [_1809828, _1809830] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1809828)), _1809830) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1809828, tc_Lazy__Sequence_Olazy__sequence(_1809828)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1809828, tc_Lazy__Sequence_Olazy__sequence(_1809828), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809828), tc_Nat_Onat), _1809828), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1809828), 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(_1809828)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1809828)))), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), hAPP(c_Lazy__Sequence_Oyield(_1809828), _1809830)))], (11528 ^ _781013) ^ [_988275, _988277] : [class_Lattices_Oab__semigroup__idem__mult(_988275), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988275), _988277), _988277) = _988277)], (33534 ^ _781013) ^ [_1417292, _1417294] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417292))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417292)), _1417294)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1417294))], (23865 ^ _781013) ^ [_1226815, _1226817] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1226815)), hAPP(c_Int_Onat, _1226817)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226815), _1226817))], (8412 ^ _781013) ^ [_925964, _925966, _925968, _925970] : [hAPP(c_Set_Oimage(_925964, _925966, _925968), _925970) = c_Orderings_Obot__class_Obot(tc_fun(_925966, tc_HOL_Obool)), -(_925970 = c_Orderings_Obot__class_Obot(tc_fun(_925964, tc_HOL_Obool)))], (5066 ^ _781013) ^ [_858253, _858255, _858257, _858259, _858261, _858263, _858265, _858267] : [-(c_Fun_Ocomp(_858267, _858263, _858259, _858255) = c_Fun_Ocomp(_858265, _858261, _858257, _858253)), _858267 = _858265, _858263 = _858261, _858259 = _858257, _858255 = _858253], (35773 ^ _781013) ^ [_1457335, _1457337] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1457335), hAPP(c_Int_Onumber__class_Onumber__of(_1457335), c_Int_OMin)), _1457337) = hAPP(c_Groups_Ouminus__class_Ouminus(_1457335), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1457335), c_Groups_Oone__class_Oone(_1457335)), _1457337))), class_Fields_Ofield__inverse__zero(_1457335), class_Int_Onumber__ring(_1457335)], (45980 ^ _781013) ^ [_1700908, _1700910, _1700912, _1700914] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1700908, tc_HOL_Obool), hAPP(c_Set_Oimage(_1700910, tc_fun(_1700908, tc_HOL_Obool), _1700912), _1700914)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1700910, tc_fun(_1700908, tc_HOL_Obool)), _1700914), _1700912))], (40679 ^ _781013) ^ [_1578481, _1578483, _1578485, _1578487, _1578489, _1578491] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578481, _1578483)), hAPP(hAPP(c_Product__Type_OPair(_1578481, _1578483), _1578485), _1578487)), hAPP(hAPP(c_Product__Type_OSigma(_1578481, _1578483), _1578489), _1578491))), 40682 ^ _781013 : [(40685 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578483), _1578487), hAPP(_1578491, _1578485))))], (40683 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578481), _1578485), _1578489)))]]], (6094 ^ _781013) ^ [_879528] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_879528), c_Orderings_Obot__class_Obot(tc_fun(_879528, tc_HOL_Obool)))))], (45800 ^ _781013) ^ [_1696979, _1696981, _1696983, _1696985] : [45802 ^ _781013 : [(45807 ^ _781013) ^ [] : [hBOOL(hAPP(_1696985, hAPP(hAPP(c_List_Onth(_1696981), _1696983), 45801 ^ [_1696979, _1696981, _1696983, _1696985])))], (45805 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45801 ^ [_1696979, _1696981, _1696983, _1696985]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696981)), _1696983))))], (45803 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45801 ^ [_1696979, _1696981, _1696983, _1696985]), _1696979)))]], 45810 ^ _781013 : [(45813 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1696985, hAPP(hAPP(c_List_Onth(_1696981), _1696983), _1696979))))], (45811 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1696979), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696981)), _1696983))))]], -(c_List_OtakeWhile(_1696981, _1696985, _1696983) = hAPP(hAPP(c_List_Otake(_1696981), _1696979), _1696983))], (42380 ^ _781013) ^ [_1620398] : [-(hAPP(c_List_Otl(_1620398), c_List_Olist_ONil(_1620398)) = c_List_Olist_ONil(_1620398))], (38574 ^ _781013) ^ [_1522927, _1522929, _1522931, _1522933] : [-(c_List_Oremove1(_1522927, _1522929, c_List_Oremove1(_1522927, _1522931, _1522933)) = c_List_Oremove1(_1522927, _1522931, c_List_Oremove1(_1522927, _1522929, _1522933)))], (45876 ^ _781013) ^ [_1698931, _1698933, _1698935] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1698931, tc_HOL_Obool)), _1698933), _1698935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1698931, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1698931, tc_HOL_Obool), _1698935)), _1698933)))], (40759 ^ _781013) ^ [_1580509, _1580511, _1580513, _1580515] : [-(_1580509 = c_Orderings_Obot__class_Obot(tc_fun(_1580511, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1580511, _1580513), _1580513, c_Product__Type_Osnd(_1580511, _1580513)), hAPP(hAPP(c_Product__Type_OSigma(_1580511, _1580513), _1580509), hAPP(c_COMBK(tc_fun(_1580513, tc_HOL_Obool), _1580511), _1580515))) = _1580515)], (27629 ^ _781013) ^ [_1296598, _1296600, _1296602] : [class_Divides_Oring__div(_1296598), -(c_Divides_Odiv__class_Omod(_1296598, hAPP(c_Groups_Ouminus__class_Ouminus(_1296598), _1296600), _1296602) = c_Divides_Odiv__class_Omod(_1296598, hAPP(c_Groups_Ouminus__class_Ouminus(_1296598), c_Divides_Odiv__class_Omod(_1296598, _1296600, _1296602)), _1296602))], (17839 ^ _781013) ^ [_1114012] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114012), _1114012)))], (48675 ^ _781013) ^ [_1765807, _1765809, _1765811, _1765813, _1765815] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765807, _1765807)), hAPP(hAPP(c_Product__Type_OPair(_1765807, _1765807), _1765809), _1765811)), c_Transitive__Closure_Ortrancl(_1765807, _1765813))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1765807, _1765807), tc_HOL_Obool)), _1765813), hAPP(hAPP(c_Product__Type_OSigma(_1765807, _1765807), _1765815), hAPP(c_COMBK(tc_fun(_1765807, tc_HOL_Obool), _1765807), _1765815)))), -(_1765809 = _1765811), -(hBOOL(hAPP(hAPP(c_member(_1765807), _1765809), _1765815)))], (34525 ^ _781013) ^ [_1435062, _1435064] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1435062))), _1435064) = 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)))), _1435062), _1435064))], (9927 ^ _781013) ^ [_956403, _956405, _956407] : [class_Lattices_Osemilattice__inf(_956403), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956403), _956405), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956403), _956405), _956407)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956403), _956405), _956407))], (38321 ^ _781013) ^ [_1517328, _1517330, _1517332, _1517334, _1517336] : [c_Fun_Oinj__on(_1517328, _1517330, _1517332, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517328, tc_HOL_Obool)), hAPP(c_List_Oset(_1517328), _1517334)), hAPP(c_List_Oset(_1517328), _1517336))), 38324 ^ _781013 : [(38331 ^ _781013) ^ [] : [_1517334 = _1517336, -(hAPP(hAPP(c_List_Omap(_1517328, _1517330), _1517332), _1517334) = hAPP(hAPP(c_List_Omap(_1517328, _1517330), _1517332), _1517336))], (38325 ^ _781013) ^ [] : [hAPP(hAPP(c_List_Omap(_1517328, _1517330), _1517332), _1517334) = hAPP(hAPP(c_List_Omap(_1517328, _1517330), _1517332), _1517336), -(_1517334 = _1517336)]]], (40942 ^ _781013) ^ [_1587081, _1587083, _1587085] : [-(hAPP(c_Fun_Ocomp(_1587081, _1587083, _1587081, _1587085), c_Fun_Oid(_1587081)) = _1587085)], (43452 ^ _781013) ^ [_1646205, _1646207, _1646209] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1646205), tc_List_Olist(_1646205)), c_List_Opartition(_1646205, _1646207, _1646209)) = hAPP(c_List_Ofilter(_1646205, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1646205, c_fNot), _1646207)), _1646209))], (17469 ^ _781013) ^ [_1107528, _1107530, _1107532, _1107534, _1107536, _1107538] : [hBOOL(hAPP(hAPP(c_member(_1107528), _1107530), _1107532)), -(hAPP(c_Fun_Ooverride__on(_1107528, _1107534, _1107536, _1107538, _1107532), _1107530) = hAPP(_1107538, _1107530))], (44418 ^ _781013) ^ [_1666373, _1666375] : [-(hAPP(c_List_Oset(_1666373), c_List_Oconcat(_1666373, _1666375)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1666373), tc_fun(_1666373, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1666373)), _1666375)), c_List_Oset(_1666373)))], (43036 ^ _781013) ^ [_1636523, _1636525, _1636527, _1636529, _1636531] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636523, tc_fun(_1636525, tc_HOL_Obool)), _1636527), hAPP(hAPP(c_COMBC(_1636523, tc_fun(_1636525, tc_HOL_Obool), tc_fun(_1636525, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1636525, tc_HOL_Obool), tc_fun(tc_fun(_1636525, tc_HOL_Obool), tc_fun(_1636525, tc_HOL_Obool)), _1636523), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636525, tc_HOL_Obool))), _1636529)), _1636531)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636525, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636523, tc_fun(_1636525, tc_HOL_Obool)), _1636527), _1636529)), _1636531))], (24474 ^ _781013) ^ [_1237518, _1237520, _1237522, _1237524, _1237526] : [class_Fields_Ofield__inverse__zero(_1237518), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237518), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237518), _1237520), _1237522)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237518), _1237524), _1237526)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237518), _1237520), _1237524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237518), _1237522), _1237526)))], (41052 ^ _781013) ^ [_1589569, _1589571, _1589573, _1589575, _1589577, _1589579] : [class_Groups_Ocomm__monoid__mult(_1589569), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589571), _1589573)), 41062 ^ _781013 : [(41065 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1589575), hAPP(_1589577, 41061 ^ [_1589569, _1589571, _1589573, _1589575, _1589577, _1589579])))], (41063 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589571), 41061 ^ [_1589569, _1589571, _1589573, _1589575, _1589577, _1589579]), _1589573)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1589569, _1589571, c_Groups_Otimes__class_Otimes(_1589569)), hAPP(hAPP(c_COMBS(_1589571, tc_fun(_1589575, tc_HOL_Obool), _1589569), hAPP(hAPP(c_COMBC(_1589571, _1589569, tc_fun(tc_fun(_1589575, tc_HOL_Obool), _1589569)), hAPP(hAPP(c_COMBB(tc_fun(_1589575, _1589569), tc_fun(_1589569, tc_fun(tc_fun(_1589575, tc_HOL_Obool), _1589569)), _1589571), c_Finite__Set_Ofold__image(_1589569, _1589575, c_Groups_Otimes__class_Otimes(_1589569))), _1589579)), c_Groups_Oone__class_Oone(_1589569))), _1589577)), c_Groups_Oone__class_Oone(_1589569)), _1589573) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1589569, tc_prod(_1589571, _1589575), c_Groups_Otimes__class_Otimes(_1589569)), hAPP(c_Product__Type_Oprod_Oprod__case(_1589571, _1589575, _1589569), _1589579)), c_Groups_Oone__class_Oone(_1589569)), hAPP(hAPP(c_Product__Type_OSigma(_1589571, _1589575), _1589573), _1589577)))], (48659 ^ _781013) ^ [_1765488, _1765490] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1765488), _1765490) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1765488)), hAPP(c_Code__Numeral_Onat__of, _1765490))))], (16119 ^ _781013) ^ [_1079056, _1079058] : [class_Groups_Olinordered__ab__group__add(_1079056), 16122 ^ _781013 : [(16129 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079056), _1079058), c_Groups_Ozero__class_Ozero(_1079056))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079056), _1079058), hAPP(c_Groups_Ouminus__class_Ouminus(_1079056), _1079058))))], (16123 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079056), _1079058), hAPP(c_Groups_Ouminus__class_Ouminus(_1079056), _1079058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079056), _1079058), c_Groups_Ozero__class_Ozero(_1079056))))]]], (36924 ^ _781013) ^ [_1485501, _1485503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1485501), _1485503)), -(c_Divides_Odivmod__nat(_1485501, _1485503) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1485501))], (42861 ^ _781013) ^ [_1631286, _1631288, _1631290, _1631292, _1631294, _1631296] : [-(hAPP(c_Set_Ovimage(_1631286, _1631288, _1631290), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631292, tc_fun(_1631288, tc_HOL_Obool)), _1631294), _1631296)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631292, tc_fun(_1631286, tc_HOL_Obool)), _1631294), hAPP(hAPP(c_COMBB(tc_fun(_1631288, tc_HOL_Obool), tc_fun(_1631286, tc_HOL_Obool), _1631292), c_Set_Ovimage(_1631286, _1631288, _1631290)), _1631296)))], (5924 ^ _781013) ^ [_876435, _876437] : [c_Option_Ois__none(_876435, hAPP(c_Option_Ooption_OSome(_876435), _876437))], (16341 ^ _781013) ^ [_1083170, _1083172, _1083174] : [-(hBOOL(hAPP(_1083170, _1083172))), -(hAPP(c_Set_OCollect(_1083174), hAPP(hAPP(c_COMBS(_1083174, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1083174), c_fconj), hAPP(c_fequal, _1083172))), _1083170)) = c_Orderings_Obot__class_Obot(tc_fun(_1083174, tc_HOL_Obool)))], (51258 ^ _781013) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (38353 ^ _781013) ^ [_1517958, _1517960, _1517962, _1517964] : [hAPP(c_Map_Omap__of(_1517958, _1517960), _1517962) = hAPP(c_Map_Omap__of(_1517958, _1517960), _1517964), -(hAPP(c_Set_Oimage(tc_prod(_1517958, _1517960), _1517958, c_Product__Type_Ofst(_1517958, _1517960)), hAPP(c_List_Oset(tc_prod(_1517958, _1517960)), _1517962)) = hAPP(c_Set_Oimage(tc_prod(_1517958, _1517960), _1517958, c_Product__Type_Ofst(_1517958, _1517960)), hAPP(c_List_Oset(tc_prod(_1517958, _1517960)), _1517964)))], (26387 ^ _781013) ^ [_1271692, _1271694, _1271696, _1271698] : [class_Orderings_Olinorder(_1271692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271692), _1271694), _1271696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271692), _1271696), _1271698)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271692, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1271692, _1271694, _1271696)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1271692, _1271696, _1271698)) = c_SetInterval_Oord__class_OatLeastAtMost(_1271692, _1271694, _1271698))], (28050 ^ _781013) ^ [_1304649, _1304651] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304649, _1304651) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304649, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1304651)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43703 ^ _781013) ^ [_1651852, _1651854] : [43704 ^ _781013 : [(43707 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651854), _1651852))], (43705 ^ _781013) ^ [] : [_1651854 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1651852, _1651854) = c_List_Olist_ONil(tc_Nat_Onat))], (37838 ^ _781013) ^ [_1505394, _1505396, _1505398, _1505400, _1505402] : [c_Equiv__Relations_Oequivp(_1505394, _1505396), hBOOL(hAPP(hAPP(_1505396, _1505398), _1505400)), hBOOL(hAPP(hAPP(_1505396, _1505400), _1505402)), -(hBOOL(hAPP(hAPP(_1505396, _1505398), _1505402)))], (43531 ^ _781013) ^ [_1648351, _1648353, _1648355, _1648357, _1648359, _1648361] : [hAPP(hAPP(c_Map_Omap__of(_1648351, _1648353), _1648355), _1648357) = hAPP(c_Option_Ooption_OSome(_1648353), _1648359), hBOOL(hAPP(hAPP(_1648361, _1648357), _1648359)), -(hAPP(hAPP(c_Map_Omap__of(_1648351, _1648353), hAPP(c_List_Ofilter(tc_prod(_1648351, _1648353), hAPP(c_Product__Type_Oprod_Oprod__case(_1648351, _1648353, tc_HOL_Obool), _1648361)), _1648355)), _1648357) = hAPP(c_Option_Ooption_OSome(_1648353), _1648359))], (50832 ^ _781013) ^ [_1814351, _1814353, _1814355, _1814357] : [-(c_Lazy__Sequence_Oproduct(_1814351, _1814353, _1814355, _1814357) = hAPP(c_Lazy__Sequence_Obind(_1814351, tc_prod(_1814351, _1814353), _1814355), hAPP(hAPP(c_COMBB(tc_fun(_1814353, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1814351, _1814353))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1814351, _1814353)), _1814351), c_Lazy__Sequence_Obind(_1814353, tc_prod(_1814351, _1814353), _1814357)), hAPP(hAPP(c_COMBB(tc_fun(_1814353, tc_prod(_1814351, _1814353)), tc_fun(_1814353, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1814351, _1814353))), _1814351), hAPP(c_COMBB(tc_prod(_1814351, _1814353), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1814351, _1814353)), _1814353), c_Lazy__Sequence_Osingle(tc_prod(_1814351, _1814353)))), c_Product__Type_OPair(_1814351, _1814353)))))], (30007 ^ _781013) ^ [_1341640, _1341642] : [-(c_Nitpick_Oint__lcm(_1341640, _1341642) = 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), _1341640)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1341642)))))], (21525 ^ _781013) ^ [] : [-(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))], (6493 ^ _781013) ^ [_887252, _887254] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_887252), _887254))), 6494 ^ _781013 : [(6497 ^ _781013) ^ [_887355] : [6498 ^ _781013 : [(6499 ^ _781013) ^ [_887408] : [_887254 = hAPP(hAPP(c_Set_Oinsert(_887252), _887408), _887355)]], hBOOL(hAPP(c_Finite__Set_Ofinite(_887252), _887355))], (6495 ^ _781013) ^ [] : [_887254 = c_Orderings_Obot__class_Obot(tc_fun(_887252, tc_HOL_Obool))]]], (45103 ^ _781013) ^ [_1682082, _1682084, _1682086, _1682088] : [class_Orderings_Olinorder(_1682082), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682084)), c_List_Olinorder__class_Osort__key(_1682084, _1682082, _1682086, _1682088)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682084)), _1682088))], (41933 ^ _781013) ^ [_1609653, _1609655, _1609657] : [hBOOL(hAPP(c_List_Odistinct(_1609653), hAPP(hAPP(c_List_Oappend(_1609653), _1609655), _1609657))), 41936 ^ _781013 : [(41941 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1609653, tc_HOL_Obool)), hAPP(c_List_Oset(_1609653), _1609655)), hAPP(c_List_Oset(_1609653), _1609657)) = c_Orderings_Obot__class_Obot(tc_fun(_1609653, tc_HOL_Obool)))], (41939 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1609653), _1609657)))], (41937 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1609653), _1609655)))]]], (38258 ^ _781013) ^ [_1515556, _1515558, _1515560] : [c_Fun_Oinj__on(tc_List_Olist(_1515556), tc_List_Olist(_1515558), hAPP(c_List_Omap(_1515556, _1515558), _1515560), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1515556), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1515556, _1515558, _1515560, c_Orderings_Otop__class_Otop(tc_fun(_1515556, tc_HOL_Obool))))], (51386 ^ _781013) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (41560 ^ _781013) ^ [_1601260, _1601262, _1601264, _1601266, _1601268] : [-(hAPP(hAPP(c_List_Oappend(_1601260), _1601262), hAPP(hAPP(c_List_Olist_OCons(_1601260), _1601264), c_List_Olist_ONil(_1601260))) = hAPP(hAPP(c_List_Oappend(_1601260), _1601266), hAPP(hAPP(c_List_Olist_OCons(_1601260), _1601268), c_List_Olist_ONil(_1601260)))), _1601262 = _1601266, _1601264 = _1601268], (2372 ^ _781013) ^ [_816100, _816102] : [_816102 = _816100, -(c_Hoare__Mirabelle_Otriple_Otriple(_816102) = c_Hoare__Mirabelle_Otriple_Otriple(_816100))], (38722 ^ _781013) ^ [_1526699, _1526701, _1526703, _1526705, _1526707, _1526709, _1526711, _1526713] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1526699)), _1526701) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1526703)), _1526705), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1526699)), _1526707) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1526703)), _1526705), -(hBOOL(hAPP(hAPP(c_member(_1526703), _1526709), hAPP(c_List_Oset(_1526703), _1526705)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1526703, tc_Option_Ooption(_1526699)), hAPP(c_Map_Omap__of(_1526703, _1526699), hAPP(hAPP(c_List_Ozip(_1526703, _1526699), _1526705), _1526701))), _1526709), hAPP(c_Option_Ooption_OSome(_1526699), _1526711)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1526703, tc_Option_Ooption(_1526699)), hAPP(c_Map_Omap__of(_1526703, _1526699), hAPP(hAPP(c_List_Ozip(_1526703, _1526699), _1526705), _1526707))), _1526709), hAPP(c_Option_Ooption_OSome(_1526699), _1526713)), -(hAPP(c_Map_Omap__of(_1526703, _1526699), hAPP(hAPP(c_List_Ozip(_1526703, _1526699), _1526705), _1526701)) = hAPP(c_Map_Omap__of(_1526703, _1526699), hAPP(hAPP(c_List_Ozip(_1526703, _1526699), _1526705), _1526707)))], (13654 ^ _781013) ^ [_1031454, _1031456, _1031458, _1031460, _1031462] : [class_Groups_Ocomm__monoid__add(_1031454), class_Groups_Oordered__cancel__ab__semigroup__add(_1031454), hBOOL(hAPP(c_Finite__Set_Ofinite(_1031456), _1031458)), -(_1031458 = c_Orderings_Obot__class_Obot(tc_fun(_1031456, tc_HOL_Obool))), 13672 ^ _781013 : [(13675 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031454), hAPP(_1031460, 13671 ^ [_1031454, _1031456, _1031458, _1031460, _1031462])), hAPP(_1031462, 13671 ^ [_1031454, _1031456, _1031458, _1031460, _1031462])))], (13673 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1031456), 13671 ^ [_1031454, _1031456, _1031458, _1031460, _1031462]), _1031458)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031454), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1031456, _1031454), _1031460), _1031458)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1031456, _1031454), _1031462), _1031458))))], (17639 ^ _781013) ^ [_1110802] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110802), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6597 ^ _781013) ^ [_888994, _888996] : [-(c_Map_Odom(_888994, _888996, hAPP(c_COMBK(tc_Option_Ooption(_888996), _888994), c_Option_Ooption_ONone(_888996))) = c_Orderings_Obot__class_Obot(tc_fun(_888994, tc_HOL_Obool)))], (19841 ^ _781013) ^ [] : [-(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))], (21445 ^ _781013) ^ [_1184055, _1184057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1184055), _1184057)), -(c_Nat__Transfer_Otsub(_1184057, _1184055) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1184057), _1184055))], (38754 ^ _781013) ^ [_1527613, _1527615, _1527617, _1527619] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1527613)), hAPP(hAPP(c_List_Omap(_1527615, _1527613), _1527617), _1527619)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1527615)), _1527619))], (28306 ^ _781013) ^ [_1309392, _1309394] : [-(_1309392 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 28309 ^ _781013 : [(28316 ^ _781013) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1309394, _1309392) = 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), _1309394)), _1309392) = 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), _1309394), _1309392))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28310 ^ _781013) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1309394, _1309392) = 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), _1309394)), _1309392) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1309394), _1309392)))]]], (38706 ^ _781013) ^ [_1526043, _1526045, _1526047, _1526049, _1526051, _1526053, _1526055, _1526057] : [-(hAPP(hAPP(c_List_Ozip(_1526043, _1526045), hAPP(hAPP(c_List_Omap(_1526047, _1526043), _1526049), _1526051)), hAPP(hAPP(c_List_Omap(_1526053, _1526045), _1526055), _1526057)) = hAPP(hAPP(c_List_Omap(tc_prod(_1526047, _1526053), tc_prod(_1526043, _1526045)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526047, _1526053, tc_prod(_1526043, _1526045)), hAPP(hAPP(c_COMBC(_1526047, tc_fun(_1526053, _1526045), tc_fun(_1526053, tc_prod(_1526043, _1526045))), hAPP(hAPP(c_COMBB(tc_fun(_1526045, tc_prod(_1526043, _1526045)), tc_fun(tc_fun(_1526053, _1526045), tc_fun(_1526053, tc_prod(_1526043, _1526045))), _1526047), c_COMBB(_1526045, tc_prod(_1526043, _1526045), _1526053)), hAPP(hAPP(c_COMBB(_1526043, tc_fun(_1526045, tc_prod(_1526043, _1526045)), _1526047), c_Product__Type_OPair(_1526043, _1526045)), _1526049))), _1526055))), hAPP(hAPP(c_List_Ozip(_1526047, _1526053), _1526051), _1526057)))], (43984 ^ _781013) ^ [_1656748, _1656750, _1656752, _1656754] : [-(c_List_Oupt(_1656748, _1656750) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1656752), _1656754)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656748), _1656750)), _1656748 = _1656752, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656748), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1656750) = _1656754], (27709 ^ _781013) ^ [_1298324, _1298326, _1298328, _1298330] : [class_Divides_Osemiring__div(_1298324), -(c_Divides_Odiv__class_Omod(_1298324, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298324), _1298326), _1298328), _1298330) = c_Divides_Odiv__class_Omod(_1298324, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298324), c_Divides_Odiv__class_Omod(_1298324, _1298326, _1298330)), c_Divides_Odiv__class_Omod(_1298324, _1298328, _1298330)), _1298330))], (39703 ^ _781013) ^ [_1549851, _1549853, _1549855, _1549857] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1549851), tc_List_Olist(_1549851))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1549851), tc_List_Olist(_1549851)), _1549853), _1549855)), c_List_Olexord(_1549851, _1549857))), 39708 ^ _781013 : [(39711 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1549851), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549851)), _1549853)), _1549855) = _1549853)], (39709 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549851)), _1549853)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549851)), _1549855))))]], 39713 ^ _781013 : [(39718 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549851, _1549851)), hAPP(hAPP(c_Product__Type_OPair(_1549851, _1549851), hAPP(hAPP(c_List_Onth(_1549851), _1549853), 39712 ^ [_1549851, _1549853, _1549855, _1549857])), hAPP(hAPP(c_List_Onth(_1549851), _1549855), 39712 ^ [_1549851, _1549853, _1549855, _1549857]))), _1549857)))], (39716 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1549851), 39712 ^ [_1549851, _1549853, _1549855, _1549857]), _1549853) = hAPP(hAPP(c_List_Otake(_1549851), 39712 ^ [_1549851, _1549853, _1549855, _1549857]), _1549855))], (39714 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39712 ^ [_1549851, _1549853, _1549855, _1549857]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549851)), _1549853)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549851)), _1549855)))))]]], (43869 ^ _781013) ^ [_1654500, _1654502, _1654504, _1654506, _1654508] : [class_Orderings_Olinorder(_1654500), c_List_Olinorder__class_Osorted(_1654500, hAPP(hAPP(c_List_Omap(_1654502, _1654500), _1654504), _1654506)), -(c_List_Olinorder__class_Osorted(_1654500, hAPP(hAPP(c_List_Omap(_1654502, _1654500), _1654504), c_List_Olinorder__class_Oinsort__insert__key(_1654502, _1654500, _1654504, _1654508, _1654506))))], (18917 ^ _781013) ^ [_1134445, _1134447, _1134449, _1134451, _1134453] : [class_Groups_Ocomm__monoid__add(_1134445), class_Groups_Oordered__ab__semigroup__add(_1134445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134447), _1134449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1134447, tc_HOL_Obool)), _1134451), _1134449)), 18935 ^ _781013 : [(18938 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134445), c_Groups_Ozero__class_Ozero(_1134445)), hAPP(_1134453, 18934 ^ [_1134445, _1134447, _1134449, _1134451, _1134453])))], (18936 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1134447), 18934 ^ [_1134445, _1134447, _1134449, _1134451, _1134453]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1134447, tc_HOL_Obool)), _1134449), _1134451))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134445), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1134447, _1134445), _1134453), _1134451)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1134447, _1134445), _1134453), _1134449))))], (38959 ^ _781013) ^ [_1532075, _1532077, _1532079] : [-(hBOOL(hAPP(hAPP(c_member(_1532075), _1532077), hAPP(c_List_Oset(_1532075), _1532079)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1532075)), c_List_Oremove1(_1532075, _1532077, _1532079)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1532075)), _1532079))], (41408 ^ _781013) ^ [_1596982, _1596984, _1596986] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596982), tc_List_Olist(_1596982))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596982), tc_List_Olist(_1596982)), c_List_Olist_ONil(_1596982)), _1596984)), c_List_Olex(_1596982, _1596986)))], (35347 ^ _781013) ^ [_1449960, _1449962] : [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), _1449960))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1449962))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1449960))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1449962)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1449960)))], (9993 ^ _781013) ^ [_957616, _957618, _957620] : [class_Lattices_Oboolean__algebra(_957616), -(hAPP(c_Groups_Ouminus__class_Ouminus(_957616), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_957616), _957618), _957620)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_957616), hAPP(c_Groups_Ouminus__class_Ouminus(_957616), _957618)), hAPP(c_Groups_Ouminus__class_Ouminus(_957616), _957620)))], (48800 ^ _781013) ^ [_1769193, _1769195, _1769197, _1769199] : [-(hAPP(c_Relation_Oconverse(_1769193, _1769195), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1769193, _1769195), tc_HOL_Obool)), _1769197), _1769199)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1769195, _1769193), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1769193, _1769195), _1769197)), hAPP(c_Relation_Oconverse(_1769193, _1769195), _1769199)))], (50854 ^ _781013) ^ [_1814941, _1814943, _1814945, _1814947, _1814949] : [hBOOL(hAPP(hAPP(_1814941, _1814943), _1814945)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1814947, _1814949, _1814941), _1814945), _1814943)))], (30063 ^ _781013) ^ [_1342833, _1342835, _1342837] : [class_Orderings_Olinorder(_1342833), 30066 ^ _781013 : [(30073 ^ _781013) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342833), _1342835), _1342837) = _1342837, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342833), _1342835), _1342837)))], (30067 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342833), _1342835), _1342837)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342833), _1342835), _1342837) = _1342837)]]], (27883 ^ _781013) ^ [_1301631, _1301633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1301633, _1301631)), _1301631)))], (40044 ^ _781013) ^ [_1560997, _1560999, _1561001] : [-(c_Relation_Orefl__on(_1560997, _1560999, _1561001)), 40048 ^ _781013 : [(40051 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1560997, _1560997, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1560997, tc_fun(_1560997, tc_HOL_Obool), tc_fun(_1560997, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1560997, tc_HOL_Obool), tc_fun(_1560997, tc_HOL_Obool)), _1560997), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1560997)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560997), c_fconj), hAPP(hAPP(c_COMBC(_1560997, tc_fun(_1560997, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560997)), _1560999)))), hAPP(hAPP(c_COMBC(_1560997, tc_fun(_1560997, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560997)), _1560999))), 40047 ^ [_1560997, _1560999, _1561001]))], (40049 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560997, _1560997)), 40047 ^ [_1560997, _1560999, _1561001]), _1561001)))]], 40053 ^ _781013 : [(40056 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560997, _1560997)), hAPP(hAPP(c_Product__Type_OPair(_1560997, _1560997), 40052 ^ [_1560997, _1560999, _1561001]), 40052 ^ [_1560997, _1560999, _1561001])), _1561001))], (40054 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560997), 40052 ^ [_1560997, _1560999, _1561001]), _1560999)))]]], (43805 ^ _781013) ^ [_1653441, _1653443, _1653445, _1653447] : [class_Orderings_Olinorder(_1653441), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1653441), _1653443), _1653445)), c_List_Olinorder__class_Osorted(_1653441, hAPP(hAPP(c_List_Olist_OCons(_1653441), _1653445), _1653447)), -(c_List_Olinorder__class_Osorted(_1653441, hAPP(hAPP(c_List_Olist_OCons(_1653441), _1653443), hAPP(hAPP(c_List_Olist_OCons(_1653441), _1653445), _1653447))))], (21959 ^ _781013) ^ [_1192978, _1192980] : [class_Orderings_Olinorder(_1192978), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192978), _1192980)), -(_1192980 = c_Orderings_Obot__class_Obot(tc_fun(_1192978, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1192978), c_Big__Operators_Olinorder__class_OMin(_1192978, _1192980)), _1192980)))], (2626 ^ _781013) ^ [_819985, _819987, _819989, _819991] : [-(c_Divides_Odivmod__int(_819991, _819987) = c_Divides_Odivmod__int(_819989, _819985)), _819991 = _819989, _819987 = _819985], (10347 ^ _781013) ^ [_964297, _964299, _964301] : [class_Groups_Oab__group__add(_964297), -(hAPP(c_Groups_Ouminus__class_Ouminus(_964297), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_964297), _964299), _964301)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_964297), _964301), _964299))], (11924 ^ _781013) ^ [_996098, _996100] : [class_Orderings_Otop(_996098), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996098), _996100), c_Orderings_Otop__class_Otop(_996098))))], (38746 ^ _781013) ^ [_1527438, _1527440, _1527442, _1527444] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1527438, _1527440))), hAPP(hAPP(c_List_Ozip(_1527438, _1527440), _1527442), _1527444)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1527438)), _1527442)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1527440)), _1527444)))], (12080 ^ _781013) ^ [_999032] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_999032, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_999032, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_999032, tc_HOL_Obool)))], (35815 ^ _781013) ^ [] : [-(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)))], (9741 ^ _781013) ^ [_953170, _953172, _953174, _953176] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953170, tc_HOL_Obool)), _953172), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953170, tc_HOL_Obool)), _953174), _953176)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953170, tc_HOL_Obool)), _953174), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953170, tc_HOL_Obool)), _953172), _953176)))], (44621 ^ _781013) ^ [_1672137, _1672139, _1672141] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672137)), c_List_OtakeWhile(_1672137, _1672139, _1672141))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672137)), _1672141))))], (9555 ^ _781013) ^ [_950263, _950265, _950267, _950269] : [class_Orderings_Oorder(_950263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950263), _950265), _950267)), _950265 = _950269, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950263), _950269), _950267)))], (49578 ^ _781013) ^ [_1788921, _1788923, _1788925, _1788927, _1788929] : [class_Complete__Lattice_Ocomplete__lattice(_1788921), hBOOL(hAPP(c_Finite__Set_Ofinite(_1788923), _1788925)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1788921), _1788927), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1788923, _1788921), _1788925), _1788929)) = hAPP(hAPP(c_Finite__Set_Ofold(_1788923, _1788921, hAPP(hAPP(c_COMBB(_1788921, tc_fun(_1788921, _1788921), _1788923), c_Lattices_Osemilattice__sup__class_Osup(_1788921)), _1788929)), _1788927), _1788925))], (45017 ^ _781013) ^ [_1680412, _1680414, _1680416] : [-(c_Enum_Oproduct(_1680412, _1680414, c_List_Olist_ONil(_1680412), _1680416) = c_List_Olist_ONil(tc_prod(_1680412, _1680414)))], (40830 ^ _781013) ^ [_1582537, _1582539, _1582541, _1582543, _1582545, _1582547, _1582549, _1582551] : [c_Fun_Oinj__on(_1582537, _1582539, _1582541, _1582543), c_Fun_Oinj__on(_1582545, _1582547, _1582549, _1582551), -(c_Fun_Oinj__on(tc_prod(_1582537, _1582545), tc_prod(_1582539, _1582547), c_Product__Type_Omap__pair(_1582537, _1582539, _1582545, _1582547, _1582541, _1582549), hAPP(hAPP(c_Product__Type_OSigma(_1582537, _1582545), _1582543), hAPP(c_COMBK(tc_fun(_1582545, tc_HOL_Obool), _1582537), _1582551))))], (116 ^ _781013) ^ [_782909, _782911, _782913, _782915, _782917, _782919, _782921, _782923, _782925, _782927, _782929, _782931] : [-(c_Finite__Set_Ofolding__image__simple(_782929, _782925, _782921, _782917, _782913, _782909)), c_Finite__Set_Ofolding__image__simple(_782931, _782927, _782923, _782919, _782915, _782911), _782931 = _782929, _782927 = _782925, _782923 = _782921, _782919 = _782917, _782915 = _782913, _782911 = _782909], (4988 ^ _781013) ^ [_856964, _856966, _856968, _856970, _856972, _856974, _856976, _856978] : [-(c_New__Random__Sequence_Oneg__map(_856978, _856974, _856970, _856966) = c_New__Random__Sequence_Oneg__map(_856976, _856972, _856968, _856964)), _856978 = _856976, _856974 = _856972, _856970 = _856968, _856966 = _856964], (44723 ^ _781013) ^ [_1674138, _1674140] : [-(hAPP(c_List_Oset(_1674138), c_List_Oremdups(_1674138, _1674140)) = hAPP(c_List_Oset(_1674138), _1674140))], (47232 ^ _781013) ^ [_1732492, _1732494] : [-(hAPP(c_Relation_OField(_1732492), _1732494) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1732492, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1732492, _1732492), _1732494)), hAPP(c_Relation_ORange(_1732492, _1732492), _1732494)))], (41139 ^ _781013) ^ [_1591803, _1591805, _1591807] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1591803)), _1591805), c_List_Olists(_1591803, _1591807))), 41142 ^ _781013 : [(41143 ^ _781013) ^ [_1591911] : [hBOOL(hAPP(hAPP(c_member(_1591803), _1591911), hAPP(c_List_Oset(_1591803), _1591805))), -(hBOOL(hAPP(hAPP(c_member(_1591803), _1591911), _1591807)))]]], (39472 ^ _781013) ^ [_1544245, _1544247, _1544249, _1544251] : [class_Groups_Ocomm__monoid__add(_1544245), 39475 ^ _781013 : [(39482 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544247), _1544249))), -(c_Nitpick_Osetsum_H(_1544247, _1544245, _1544251, _1544249) = c_Groups_Ozero__class_Ozero(_1544245))], (39476 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544247), _1544249)), -(c_Nitpick_Osetsum_H(_1544247, _1544245, _1544251, _1544249) = hAPP(c_List_Omonoid__add__class_Olistsum(_1544245), hAPP(hAPP(c_List_Omap(_1544247, _1544245), _1544251), c_Hilbert__Choice_OEps(tc_List_Olist(_1544247), hAPP(hAPP(c_COMBS(tc_List_Olist(_1544247), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1544247)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1544247), tc_fun(_1544247, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1544247, tc_HOL_Obool), tc_fun(tc_fun(_1544247, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1544247)), c_fequal), c_List_Oset(_1544247))), _1544249))), c_List_Odistinct(_1544247))))))]]], (38236 ^ _781013) ^ [_1515114, _1515116, _1515118] : [c_Fun_Oinj__on(tc_List_Olist(_1515114), tc_List_Olist(_1515116), hAPP(c_List_Omap(_1515114, _1515116), _1515118), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1515114), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1515114, _1515116, _1515118, c_Orderings_Otop__class_Otop(tc_fun(_1515114, tc_HOL_Obool))))], (2796 ^ _781013) ^ [_822714, _822716, _822718, _822720] : [-(c_Hilbert__Choice_OEps(_822720, _822716) = c_Hilbert__Choice_OEps(_822718, _822714)), _822720 = _822718, _822716 = _822714], (23357 ^ _781013) ^ [_1217876, _1217878] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1217876)), _1217878) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1217876, _1217878))], (3414 ^ _781013) ^ [_832459, _832461] : [_832461 = _832459, -(c_Equiv__Relations_Oquotient(_832461) = c_Equiv__Relations_Oquotient(_832459))], (17533 ^ _781013) ^ [_1108628, _1108630, _1108632, _1108634, _1108636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1108628), _1108630)), 17536 ^ _781013 : [(17543 ^ _781013) ^ [] : [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), _1108630), _1108628)), _1108632)), _1108634)), _1108636)), -(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), _1108630), _1108632)), _1108634)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108628), _1108632)), _1108636))))], (17537 ^ _781013) ^ [] : [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), _1108630), _1108632)), _1108634)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108628), _1108632)), _1108636))), -(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), _1108630), _1108628)), _1108632)), _1108634)), _1108636)))]]], (2546 ^ _781013) ^ [_818785, _818787, _818789, _818791] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_818791, _818787) = c_Code__Numeral_Odiv__mod__code__numeral(_818789, _818785)), _818791 = _818789, _818787 = _818785], (43593 ^ _781013) ^ [_1650019, _1650021, _1650023, _1650025, _1650027] : [class_Orderings_Olinorder(_1650019), c_List_Olinorder__class_Osorted(_1650019, hAPP(hAPP(c_List_Omap(_1650021, _1650019), _1650023), _1650025)), -(c_List_Olinorder__class_Osorted(_1650019, hAPP(hAPP(c_List_Omap(_1650021, _1650019), _1650023), hAPP(c_List_Ofilter(_1650021, _1650027), _1650025))))], (22170 ^ _781013) ^ [_1196837, _1196839] : [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)), _1196837)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1196839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1196837), _1196839)))], (38127 ^ _781013) ^ [_1512261, _1512263] : [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)), _1512261), _1512263)), 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)), _1512261), 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)), _1512263), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (4616 ^ _781013) ^ [_850892, _850894] : [_850894 = _850892, -(c_List_Orev(_850894) = c_List_Orev(_850892))], (38121 ^ _781013) ^ [_1512130, _1512132] : [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)), _1512130), 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)), _1512132), 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)), _1512130), _1512132)), c_Int_Ointrel)))], (9403 ^ _781013) ^ [_947779, _947781, _947783] : [class_Groups_Ogroup__add(_947779), 9406 ^ _781013 : [(9413 ^ _781013) ^ [] : [_947781 = _947783, -(hAPP(c_Groups_Ouminus__class_Ouminus(_947779), _947781) = hAPP(c_Groups_Ouminus__class_Ouminus(_947779), _947783))], (9407 ^ _781013) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_947779), _947781) = hAPP(c_Groups_Ouminus__class_Ouminus(_947779), _947783), -(_947781 = _947783)]]], (42136 ^ _781013) ^ [_1614967, _1614969, _1614971] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614967)), hAPP(hAPP(c_List_Odrop(_1614967), _1614969), _1614971)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614967)), _1614971)), _1614969))], (20147 ^ _781013) ^ [_1157810, _1157812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157810), _1157812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1157810)), hAPP(c_Nat_OSuc, _1157812))))], (22152 ^ _781013) ^ [_1196499, _1196501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1196499)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196501)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1196501), _1196499)), _1196501) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1196501), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1196499), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (51422 ^ _781013) ^ [_1822718, _1822720] : [-(class_HOL_Oequal(tc_sum(_1822718, _1822720)))], (39536 ^ _781013) ^ [_1545672, _1545674] : [-(c_Hilbert__Choice_OEps(_1545672, hAPP(hAPP(c_COMBC(_1545672, _1545672, tc_HOL_Obool), c_fequal), _1545674)) = _1545674)], (33924 ^ _781013) ^ [_1423572, _1423574] : [hAPP(c_Nat_OSuc, _1423572) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423574), -(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(_1423574))), 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)), _1423572))))))], (37377 ^ _781013) ^ [_1494509, _1494511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1494509)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1494511)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1494509, _1494511) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1494509, _1494511)))], (1734 ^ _781013) ^ [_805430, _805432] : [-(class_Rings_Osemiring__0(_805430)), _805432 = _805430, class_Rings_Osemiring__0(_805432)], (14909 ^ _781013) ^ [_1057082, _1057084] : [class_Rings_Ocomm__semiring__1(_1057082), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057082), _1057084), c_Groups_Ozero__class_Ozero(_1057082)) = c_Groups_Ozero__class_Ozero(_1057082))], (39179 ^ _781013) ^ [_1537687, _1537689, _1537691] : [class_Orderings_Olinorder(_1537687), hBOOL(hAPP(hAPP(c_member(_1537687), _1537689), hAPP(c_List_Oset(_1537687), _1537691))), -(c_List_Olinorder__class_Oinsort__insert__key(_1537687, _1537687, c_COMBI(_1537687), _1537689, _1537691) = _1537691)], (50226 ^ _781013) ^ [_1802328, _1802330] : [-(c_Nitpick_Oinverse__frac(_1802328, _1802330) = hAPP(hAPP(c_Nitpick_Ofrac(_1802328), hAPP(c_Nitpick_Odenom(_1802328), _1802330)), hAPP(c_Nitpick_Onum(_1802328), _1802330)))], (45273 ^ _781013) ^ [_1685782, _1685784] : [class_Enum_Oenum(_1685782), 45276 ^ _781013 : [(45285 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1685782)), _1685784))), hBOOL(hAPP(_1685784, c_Option_Ooption_ONone(_1685782))), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1685782), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1685782), tc_HOL_Obool, _1685782), _1685784), c_Option_Ooption_OSome(_1685782))))], (45277 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1685782)), _1685784)), 45280 ^ _781013 : [(45283 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1685782), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1685782), tc_HOL_Obool, _1685782), _1685784), c_Option_Ooption_OSome(_1685782)))))], (45281 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1685784, c_Option_Ooption_ONone(_1685782))))]]]]], (25232 ^ _781013) ^ [_1251323, _1251325, _1251327, _1251329] : [class_Fields_Ofield(_1251323), -(_1251325 = c_Groups_Ozero__class_Ozero(_1251323)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251323), _1251327), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251323), _1251329), _1251325)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251323), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251323), _1251325), _1251327)), _1251329)), _1251325))], (11037 ^ _781013) ^ [_977119, _977121, _977123, _977125] : [c_Finite__Set_Ofun__left__comm__idem(_977119, _977121, _977123), -(hAPP(c_Fun_Ocomp(_977121, _977121, _977121, hAPP(_977123, _977125)), hAPP(_977123, _977125)) = hAPP(_977123, _977125))], (40258 ^ _781013) ^ [_1566201] : [-(c_Relation_Orefl__on(_1566201, c_Orderings_Obot__class_Obot(tc_fun(_1566201, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1566201, _1566201), tc_HOL_Obool))))], (16658 ^ _781013) ^ [_1089810, _1089812, _1089814] : [class_Groups_Oordered__comm__monoid__add(_1089810), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089810), c_Groups_Ozero__class_Ozero(_1089810)), _1089812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089810), c_Groups_Ozero__class_Ozero(_1089810)), _1089814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089810), c_Groups_Ozero__class_Ozero(_1089810)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089810), _1089812), _1089814))))], (48305 ^ _781013) ^ [_1757145] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1757145)) = _1757145)], (42482 ^ _781013) ^ [_1622596, _1622598, _1622600, _1622602, _1622604, _1622606, _1622608] : [-(hAPP(c_List_Ofoldl(_1622596, _1622598, _1622600, _1622602), hAPP(hAPP(c_List_Omap(_1622604, _1622598), _1622606), _1622608)) = hAPP(c_List_Ofoldl(_1622596, _1622604, hAPP(hAPP(c_COMBC(_1622596, tc_fun(_1622604, _1622598), tc_fun(_1622604, _1622596)), hAPP(hAPP(c_COMBB(tc_fun(_1622598, _1622596), tc_fun(tc_fun(_1622604, _1622598), tc_fun(_1622604, _1622596)), _1622596), c_COMBB(_1622598, _1622596, _1622604)), _1622600)), _1622606), _1622602), _1622608))], (38186 ^ _781013) ^ [_1513798, _1513800, _1513802, _1513804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1513798), _1513804)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1513802), _1513800))), -(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), _1513798), _1513800)), 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), _1513802), _1513804)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (35005 ^ _781013) ^ [] : [-(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))))], (37955 ^ _781013) ^ [_1508126, _1508128, _1508130, _1508132] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1508126), _1508128)), 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)), _1508130), _1508126)), 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)), _1508132), _1508128)), 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)), _1508130), _1508132)), _1508128)), c_FunDef_Omax__strict)))], (48515 ^ _781013) ^ [_1761953, _1761955] : [-(c_Transitive__Closure_Otrancl(_1761953, _1761955) = hAPP(hAPP(c_Relation_Orel__comp(_1761953, _1761953, _1761953), _1761955), c_Transitive__Closure_Ortrancl(_1761953, _1761955)))], (44324 ^ _781013) ^ [_1664222, _1664224, _1664226] : [hAPP(c_List_Orev(_1664222), _1664224) = hAPP(c_List_Orev(_1664222), _1664226), -(_1664224 = _1664226)], (10217 ^ _781013) ^ [_961771, _961773, _961775] : [class_Groups_Oordered__ab__group__add(_961771), 10220 ^ _781013 : [(10227 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961771), _961775), hAPP(c_Groups_Ouminus__class_Ouminus(_961771), _961773))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961771), _961773), hAPP(c_Groups_Ouminus__class_Ouminus(_961771), _961775))))], (10221 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961771), _961773), hAPP(c_Groups_Ouminus__class_Ouminus(_961771), _961775))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961771), _961775), hAPP(c_Groups_Ouminus__class_Ouminus(_961771), _961773))))]]], (19282 ^ _781013) ^ [_1142137, _1142139, _1142141, _1142143] : [class_Rings_Olinordered__semidom(_1142137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1142139), _1142141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142137), c_Groups_Ozero__class_Ozero(_1142137)), _1142143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142137), _1142143), c_Groups_Oone__class_Oone(_1142137))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142137), hAPP(hAPP(c_Power_Opower__class_Opower(_1142137), _1142143), _1142141)), hAPP(hAPP(c_Power_Opower__class_Opower(_1142137), _1142143), _1142139))))], (50023 ^ _781013) ^ [_1797464, _1797466, _1797468, _1797470, _1797472, _1797474, _1797476] : [c_Finite__Set_Ofun__left__comm(_1797464, _1797466, _1797468), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1797464, _1797466, _1797468, _1797470, hAPP(hAPP(c_Set_Oinsert(_1797464), _1797472), _1797474)), _1797476)), -(hBOOL(hAPP(hAPP(c_member(_1797464), _1797472), _1797474))), 50035 ^ _781013 : [(50038 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1797464, _1797466, _1797468, _1797470, _1797474), 50034 ^ [_1797464, _1797466, _1797468, _1797470, _1797472, _1797474, _1797476])))], (50036 ^ _781013) ^ [] : [-(_1797476 = hAPP(hAPP(_1797468, _1797472), 50034 ^ [_1797464, _1797466, _1797468, _1797470, _1797472, _1797474, _1797476]))]]], (34671 ^ _781013) ^ [_1437822, _1437824] : [_1437822 = _1437824, -(c_Int_OBit0(_1437822) = c_Int_OBit0(_1437824))], (12020 ^ _781013) ^ [_997720, _997722, _997724, _997726, _997728, _997730] : [c_Fun_Oinj__on(_997720, _997722, _997724, _997726), c_Fun_Oinj__on(_997722, _997728, _997730, hAPP(c_Set_Oimage(_997720, _997722, _997724), _997726)), -(c_Fun_Oinj__on(_997720, _997728, hAPP(c_Fun_Ocomp(_997722, _997728, _997720, _997730), _997724), _997726))], (41841 ^ _781013) ^ [_1607131, _1607133, _1607135, _1607137, _1607139] : [-(hAPP(hAPP(c_List_Omap(_1607131, _1607133), _1607135), hAPP(hAPP(c_List_Oappend(_1607131), _1607137), _1607139)) = hAPP(hAPP(c_List_Oappend(_1607133), hAPP(hAPP(c_List_Omap(_1607131, _1607133), _1607135), _1607137)), hAPP(hAPP(c_List_Omap(_1607131, _1607133), _1607135), _1607139)))], (48509 ^ _781013) ^ [_1761791, _1761793, _1761795] : [-(c_Transitive__Closure_Ortrancl(_1761791, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1761791, _1761791), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1761791, _1761793)), c_Transitive__Closure_Ortrancl(_1761791, _1761795))) = c_Transitive__Closure_Ortrancl(_1761791, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1761791, _1761791), tc_HOL_Obool)), _1761793), _1761795)))], (42172 ^ _781013) ^ [_1615800, _1615802, _1615804, _1615806] : [-(hAPP(hAPP(c_List_Odrop(_1615800), _1615802), hAPP(hAPP(c_List_Oappend(_1615800), _1615804), _1615806)) = hAPP(hAPP(c_List_Oappend(_1615800), hAPP(hAPP(c_List_Odrop(_1615800), _1615802), _1615804)), hAPP(hAPP(c_List_Odrop(_1615800), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1615802), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615800)), _1615804))), _1615806)))], (30277 ^ _781013) ^ [_1346669, _1346671, _1346673, _1346675] : [class_Orderings_Olinorder(_1346669), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346669), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346669), _1346671), _1346673)), _1346675) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346669), _1346671), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346669), _1346673), _1346675)))], (13679 ^ _781013) ^ [_1031985, _1031987, _1031989, _1031991, _1031993] : [class_Groups_Ocomm__monoid__add(_1031985), hBOOL(hAPP(c_Finite__Set_Ofinite(_1031987), _1031989)), hBOOL(hAPP(hAPP(c_member(_1031987), _1031991), _1031989)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1031987, _1031985), _1031993), _1031989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031985), hAPP(_1031993, _1031991)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1031987, _1031985), _1031993), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031987, tc_HOL_Obool)), _1031989), hAPP(hAPP(c_Set_Oinsert(_1031987), _1031991), c_Orderings_Obot__class_Obot(tc_fun(_1031987, tc_HOL_Obool)))))))], (49144 ^ _781013) ^ [_1777795, _1777797] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777795, _1777795), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1777797) = _1777797)], (3054 ^ _781013) ^ [_826771, _826773, _826775, _826777] : [-(c_List_Oupto(_826777, _826773) = c_List_Oupto(_826775, _826771)), _826777 = _826775, _826773 = _826771], (42811 ^ _781013) ^ [_1629217, _1629219, _1629221, _1629223, _1629225, _1629227, _1629229, _1629231] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629217, tc_fun(_1629219, tc_fun(_1629221, tc_HOL_Obool))), _1629223), _1629225), _1629227), _1629229)), -(hBOOL(hAPP(hAPP(hAPP(_1629225, _1629231), _1629227), _1629229))), hBOOL(hAPP(hAPP(c_member(_1629217), _1629231), _1629223))], (46831 ^ _781013) ^ [_1722920, _1722922, _1722924, _1722926, _1722928, _1722930, _1722932] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1722920, _1722922, _1722924, _1722926, _1722928), _1722930), _1722932))), 46832 ^ _781013 : [(46833 ^ _781013) ^ [_1722991] : [hBOOL(hAPP(hAPP(_1722926, _1722930), _1722991)), hBOOL(hAPP(hAPP(_1722928, _1722991), _1722932))]]], (2134 ^ _781013) ^ [_812357, _812359, _812361, _812363, _812365, _812367] : [-(c_SetInterval_Oord_OatMost(_812367, _812363, _812359) = c_SetInterval_Oord_OatMost(_812365, _812361, _812357)), _812367 = _812365, _812363 = _812361, _812359 = _812357], (28596 ^ _781013) ^ [_1314488, _1314490] : [class_Groups_Oordered__ab__group__add__abs(_1314488), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314488), _1314490), hAPP(c_Groups_Oabs__class_Oabs(_1314488), _1314490))))], (31425 ^ _781013) ^ [_1372463, _1372465] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1372463), _1372465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1372463)), _1372465)))], (36609 ^ _781013) ^ [_1479594, _1479596, _1479598] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1479594, tc_HOL_Obool), tc_fun(_1479594, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1479594, tc_HOL_Obool), tc_fun(_1479594, tc_HOL_Obool)), _1479596), _1479598)), c_Wellfounded_Ofinite__psubset(_1479594)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1479594, tc_HOL_Obool)), _1479596), _1479598)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479594), _1479598))], (10531 ^ _781013) ^ [_967607, _967609, _967611] : [class_Orderings_Olinorder(_967607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967607), _967609), _967611)), 10538 ^ _781013 : [(10545 ^ _781013) ^ [] : [_967609 = _967611, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967607), _967609), _967611))], (10539 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967607), _967609), _967611))), -(_967609 = _967611)]]], (44851 ^ _781013) ^ [_1676600, _1676602, _1676604, _1676606] : [-(hBOOL(hAPP(_1676600, _1676602))), -(c_List_OdropWhile(_1676604, _1676600, hAPP(hAPP(c_List_Olist_OCons(_1676604), _1676602), _1676606)) = hAPP(hAPP(c_List_Olist_OCons(_1676604), _1676602), _1676606))], (14759 ^ _781013) ^ [_1054905, _1054907] : [-(hBOOL(hAPP(_1054907, 14760 ^ [_1054905, _1054907]))), -(hAPP(c_Set_OCollect(_1054905), _1054907) = c_Orderings_Obot__class_Obot(tc_fun(_1054905, tc_HOL_Obool)))], (42474 ^ _781013) ^ [_1622396, _1622398, _1622400, _1622402, _1622404, _1622406] : [-(hAPP(c_List_Ofoldl(_1622396, _1622398, _1622400, _1622402), hAPP(hAPP(c_List_Olist_OCons(_1622398), _1622404), _1622406)) = hAPP(c_List_Ofoldl(_1622396, _1622398, _1622400, hAPP(hAPP(_1622400, _1622402), _1622404)), _1622406))], (10789 ^ _781013) ^ [_971529, _971531, _971533, _971535, _971537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971529, tc_HOL_Obool)), _971531), _971533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971529, tc_HOL_Obool)), _971535), _971537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971529, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971529, tc_HOL_Obool)), _971531), _971535)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971529, tc_HOL_Obool)), _971533), _971537))))], (27831 ^ _781013) ^ [_1300723, _1300725, _1300727] : [class_Divides_Osemiring__div(_1300723), -(c_Divides_Odiv__class_Omod(_1300723, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300723), _1300725), _1300727), _1300725) = c_Groups_Ozero__class_Ozero(_1300723))], (6778 ^ _781013) ^ [_892684, _892686, _892688, _892690, _892692, _892694] : [c_Finite__Set_Ofolding__idem(_892684, _892686, _892688, _892690), hBOOL(hAPP(c_Finite__Set_Ofinite(_892684), _892692)), hBOOL(hAPP(c_Finite__Set_Ofinite(_892684), _892694)), -(hAPP(_892690, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892684, tc_HOL_Obool)), _892692), _892694)) = hAPP(c_Fun_Ocomp(_892686, _892686, _892686, hAPP(_892690, _892692)), hAPP(_892690, _892694)))], (12992 ^ _781013) ^ [_1017268, _1017270, _1017272, _1017274] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1017268), _1017270)), c_Fun_Oinj__on(_1017272, _1017268, _1017274, c_Orderings_Otop__class_Otop(tc_fun(_1017272, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1017272), hAPP(c_Set_Ovimage(_1017272, _1017268, _1017274), _1017270))))], (20540 ^ _781013) ^ [_1164616] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1164616) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3802 ^ _781013) ^ [_838503, _838505, _838507, _838509, _838511, _838513] : [-(c_List_OtakeWhile(_838513, _838509, _838505) = c_List_OtakeWhile(_838511, _838507, _838503)), _838513 = _838511, _838509 = _838507, _838505 = _838503], (12242 ^ _781013) ^ [_1002081, _1002083] : [class_Lattices_Oboolean__algebra(_1002081), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1002081), _1002083), hAPP(c_Groups_Ouminus__class_Ouminus(_1002081), _1002083)) = c_Orderings_Otop__class_Otop(_1002081))], (51308 ^ _781013) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (1284 ^ _781013) ^ [_799805, _799807] : [-(class_Complete__Lattice_Ocomplete__lattice(_799805)), _799807 = _799805, class_Complete__Lattice_Ocomplete__lattice(_799807)], (9102 ^ _781013) ^ [_941559, _941561, _941563, _941565] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_941559), _941561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941559, tc_HOL_Obool)), _941561), _941563)), hBOOL(hAPP(_941565, c_Orderings_Obot__class_Obot(tc_fun(_941559, tc_HOL_Obool)))), 9117 ^ _781013 : [(9118 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_941559), 9116 ^ [_941559, _941561, _941563, _941565])))], (9122 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_941559), 9115 ^ [_941559, _941561, _941563, _941565]), 9116 ^ [_941559, _941561, _941563, _941565]))], (9126 ^ _781013) ^ [] : [hBOOL(hAPP(_941565, hAPP(hAPP(c_Set_Oinsert(_941559), 9115 ^ [_941559, _941561, _941563, _941565]), 9116 ^ [_941559, _941561, _941563, _941565])))], (9124 ^ _781013) ^ [] : [-(hBOOL(hAPP(_941565, 9116 ^ [_941559, _941561, _941563, _941565])))], (9120 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_941559), 9115 ^ [_941559, _941561, _941563, _941565]), _941563)))]], -(hBOOL(hAPP(_941565, _941561)))], (12068 ^ _781013) ^ [_998732, _998734, _998736, _998738, _998740] : [hAPP(c_Set_Oimage(_998732, _998734, _998736), c_Orderings_Otop__class_Otop(tc_fun(_998732, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_998734, tc_HOL_Obool)), hAPP(c_Set_Oimage(_998734, _998738, _998740), c_Orderings_Otop__class_Otop(tc_fun(_998734, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_998738, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_998732, _998738, hAPP(c_Fun_Ocomp(_998734, _998738, _998732, _998740), _998736)), c_Orderings_Otop__class_Otop(tc_fun(_998732, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_998738, tc_HOL_Obool)))], (774 ^ _781013) ^ [_792868, _792870, _792872, _792874, _792876, _792878, _792880, _792882] : [-(c_Finite__Set_Ofolding(_792880, _792876, _792872, _792868)), c_Finite__Set_Ofolding(_792882, _792878, _792874, _792870), _792882 = _792880, _792878 = _792876, _792874 = _792872, _792870 = _792868], (48397 ^ _781013) ^ [_1759380, _1759382, _1759384, _1759386, _1759388] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1759380, _1759380)), hAPP(hAPP(c_Product__Type_OPair(_1759380, _1759380), _1759382), _1759384)), c_Transitive__Closure_Otrancl(_1759380, _1759386))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1759380, _1759380)), hAPP(hAPP(c_Product__Type_OPair(_1759380, _1759380), _1759384), _1759388)), c_Transitive__Closure_Ortrancl(_1759380, _1759386))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1759380, _1759380)), hAPP(hAPP(c_Product__Type_OPair(_1759380, _1759380), _1759382), _1759388)), c_Transitive__Closure_Otrancl(_1759380, _1759386))))], (33894 ^ _781013) ^ [_1423012, _1423014, _1423016] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1423012), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423012)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423014)), _1423016)) = 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), _1423012), _1423014))), _1423016))], (22812 ^ _781013) ^ [_1207785, _1207787, _1207789, _1207791] : [class_Divides_Osemiring__div(_1207785), -(_1207787 = c_Groups_Ozero__class_Ozero(_1207785)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207785), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207785), _1207789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207785), _1207791), _1207787))), _1207787) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207785), _1207791), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207785), _1207789), _1207787)))], (37516 ^ _781013) ^ [_1497325, _1497327, _1497329, _1497331, _1497333] : [-(hAPP(c_Product__Type_Ofst(_1497325, _1497327), hAPP(c_Product__Type_Oapsnd(_1497329, _1497327, _1497325, _1497331), _1497333)) = hAPP(c_Product__Type_Ofst(_1497325, _1497329), _1497333))], (39936 ^ _781013) ^ [_1558114, _1558116, _1558118] : [39938 ^ _781013 : [(39941 ^ _781013) ^ [] : [hBOOL(hAPP(_1558116, 39937 ^ [_1558114, _1558116, _1558118]))], (39939 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558114), 39937 ^ [_1558114, _1558116, _1558118]), _1558118)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1558114, _1558116), _1558118)))], (51502 ^ _781013) ^ [] : [-(class_HOL_Oequal(tc_Product__Type_Ounit))], (20871 ^ _781013) ^ [_1171222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171222)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171222), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1171222)], (19302 ^ _781013) ^ [_1142533, _1142535, _1142537] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1142533), _1142535)), _1142537) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142533), _1142537)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142535), _1142537)))], (51248 ^ _781013) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (23979 ^ _781013) ^ [_1228620, _1228622, _1228624, _1228626] : [class_Fields_Ofield(_1228620), -(_1228622 = c_Groups_Ozero__class_Ozero(_1228620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1228624), _1228626)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1228620), _1228622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1228626), _1228624)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1228620), hAPP(hAPP(c_Power_Opower__class_Opower(_1228620), _1228622), _1228626)), hAPP(hAPP(c_Power_Opower__class_Opower(_1228620), _1228622), _1228624)))], (15121 ^ _781013) ^ [_1060847, _1060849, _1060851, _1060853] : [-(hAPP(c_Set_Ovimage(_1060847, _1060849, _1060851), hAPP(c_Set_OCollect(_1060849), _1060853)) = hAPP(c_Set_OCollect(_1060847), hAPP(hAPP(c_COMBB(_1060849, tc_HOL_Obool, _1060847), _1060853), _1060851)))], (39852 ^ _781013) ^ [_1554152, _1554154] : [-(c_List_Olenlex(_1554152, _1554154) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1554152), tc_List_Olist(_1554152))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1554152), tc_List_Olist(_1554152), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1554152), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1554152), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool)), tc_List_Olist(_1554152)), c_COMBS(tc_List_Olist(_1554152), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool), tc_fun(tc_List_Olist(_1554152), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1554152)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1554152)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1554152), tc_fun(tc_List_Olist(_1554152), tc_Nat_Onat), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1554152), tc_Nat_Onat), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool)), tc_List_Olist(_1554152)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1554152))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1554152)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1554152))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1554152)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1554152), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1554152), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool)), tc_List_Olist(_1554152)), c_COMBS(tc_List_Olist(_1554152), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool), tc_fun(tc_List_Olist(_1554152), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1554152)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1554152)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1554152), tc_fun(tc_List_Olist(_1554152), tc_Nat_Onat), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1554152), tc_Nat_Onat), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool)), tc_List_Olist(_1554152)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1554152))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1554152)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1554152))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1554152)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1554152), tc_fun(tc_prod(tc_List_Olist(_1554152), tc_List_Olist(_1554152)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1554152), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1554152), tc_List_Olist(_1554152)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1554152), tc_List_Olist(_1554152)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1554152), tc_HOL_Obool)), tc_List_Olist(_1554152)), c_COMBC(tc_List_Olist(_1554152), tc_fun(tc_prod(tc_List_Olist(_1554152), tc_List_Olist(_1554152)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1554152), tc_prod(tc_List_Olist(_1554152), tc_List_Olist(_1554152))), tc_fun(tc_List_Olist(_1554152), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1554152), tc_List_Olist(_1554152)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1554152)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1554152), tc_List_Olist(_1554152)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1554152), tc_List_Olist(_1554152)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1554152)), c_member(tc_prod(tc_List_Olist(_1554152), tc_List_Olist(_1554152))))), c_Product__Type_OPair(tc_List_Olist(_1554152), tc_List_Olist(_1554152))))), c_List_Olex(_1554152, _1554154)))))))], (38021 ^ _781013) ^ [_1509348] : [-(hAPP(c_Relation_OField(_1509348), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509348, _1509348), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1509348, tc_HOL_Obool)))], (42863 ^ _781013) ^ [_1631370, _1631372, _1631374, _1631376, _1631378] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1631370, tc_fun(_1631372, tc_HOL_Obool)), _1631374), hAPP(hAPP(c_COMBB(tc_fun(_1631372, tc_HOL_Obool), tc_fun(_1631372, tc_HOL_Obool), _1631370), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1631372, tc_HOL_Obool)), _1631376)), _1631378)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1631372, tc_HOL_Obool)), _1631376), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631370, tc_fun(_1631372, tc_HOL_Obool)), _1631374), _1631378)))], (37028 ^ _781013) ^ [_1487582, _1487584, _1487586, _1487588, _1487590] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1487582, _1487584), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1487586), _1487588))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1487584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1487590)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1487582, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1487584), _1487590)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1487586), _1487590)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1487584), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1487586, _1487590))), _1487588)))))], (28798 ^ _781013) ^ [_1318412, _1318414, _1318416, _1318418] : [class_Orderings_Olinorder(_1318412), 28801 ^ _781013 : [(28802 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318412), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318412), _1318414), _1318416)), _1318418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318412), _1318414), _1318418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318412), _1318416), _1318418)))], (28812 ^ _781013) ^ [] : [28813 ^ _781013 : [(28816 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318412), _1318416), _1318418))], (28814 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318412), _1318414), _1318418))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318412), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318412), _1318414), _1318416)), _1318418)))]]], (49568 ^ _781013) ^ [_1788698, _1788700, _1788702, _1788704, _1788706, _1788708] : [c_Finite__Set_Ofun__left__comm__idem(_1788698, _1788700, _1788702), hBOOL(hAPP(c_Finite__Set_Ofinite(_1788698), _1788704)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1788698, _1788700, _1788702), _1788706), hAPP(hAPP(c_Set_Oinsert(_1788698), _1788708), _1788704)) = hAPP(hAPP(_1788702, _1788708), hAPP(hAPP(c_Finite__Set_Ofold(_1788698, _1788700, _1788702), _1788706), _1788704)))], (34249 ^ _781013) ^ [_1430647, _1430649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430647), _1430649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1430647)), c_Int_OBit1(_1430649))))], (51178 ^ _781013) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (48728 ^ _781013) ^ [_1767108, _1767110] : [-(c_Transitive__Closure_Ortrancl(_1767108, hAPP(c_Relation_Oconverse(_1767108, _1767108), _1767110)) = hAPP(c_Relation_Oconverse(_1767108, _1767108), c_Transitive__Closure_Ortrancl(_1767108, _1767110)))], (18966 ^ _781013) ^ [_1135753, _1135755, _1135757, _1135759, _1135761, _1135763] : [hBOOL(hAPP(hAPP(c_member(_1135753), _1135755), c_SetInterval_Oord_OgreaterThanAtMost(_1135753, _1135757, _1135759, _1135761, _1135763))), 18969 ^ _781013 : [(18972 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1135757, _1135755), _1135763)))], (18970 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1135759, _1135761), _1135755)))]]], (46094 ^ _781013) ^ [_1703552, _1703554, _1703556, _1703558, _1703560, _1703562, _1703564] : [-(c_List_Olist__all2(_1703552, _1703554, _1703556, hAPP(hAPP(c_List_Olist_OCons(_1703552), _1703558), _1703560), hAPP(hAPP(c_List_Olist_OCons(_1703554), _1703562), _1703564))), hBOOL(hAPP(hAPP(_1703556, _1703558), _1703562)), c_List_Olist__all2(_1703552, _1703554, _1703556, _1703560, _1703564)], (42412 ^ _781013) ^ [_1621064, _1621066, _1621068] : [-(hAPP(c_List_Orotate1(_1621064), hAPP(c_List_Orotate(_1621064, _1621066), _1621068)) = hAPP(c_List_Orotate(_1621064, _1621066), hAPP(c_List_Orotate1(_1621064), _1621068)))], (18209 ^ _781013) ^ [_1120041, _1120043] : [18210 ^ _781013 : [(18213 ^ _781013) ^ [] : [_1120041 = _1120043], (18211 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120041), _1120043))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120041), _1120043)))], (31541 ^ _781013) ^ [_1375583, _1375585, _1375587, _1375589, _1375591, _1375593] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1375583, tc_fun(_1375585, tc_HOL_Obool)), _1375587), hAPP(c_Fun_Ocomp(_1375589, tc_fun(_1375585, tc_HOL_Obool), _1375583, _1375591), _1375593)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1375589, tc_fun(_1375585, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1375583, _1375589, _1375593), _1375587)), _1375591))], (34831 ^ _781013) ^ [_1440565] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1440565)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1440565))))], (8793 ^ _781013) ^ [_934820, _934822, _934824] : [class_Lattices_Osemilattice__sup(_934820), 8796 ^ _781013 : [(8803 ^ _781013) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934820), _934822), _934824) = _934824, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934820), _934822), _934824)))], (8797 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934820), _934822), _934824)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934820), _934822), _934824) = _934824)]]], (23100 ^ _781013) ^ [_1213196, _1213198] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1213196), _1213198))))], (49097 ^ _781013) ^ [_1776658, _1776660, _1776662] : [c_Relation_Osingle__valued(_1776658, _1776658, _1776660), -(c_Relation_Osingle__valued(_1776658, _1776658, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1776658, _1776658), tc_HOL_Obool), _1776662), _1776660)))], (7463 ^ _781013) ^ [_905582, _905584, _905586, _905588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905582, tc_HOL_Obool)), _905584), _905586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905582, tc_HOL_Obool)), _905588), _905586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905582, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905582, tc_HOL_Obool)), _905584), _905588)), _905586)))], (10249 ^ _781013) ^ [_962337, _962339, _962341] : [class_Groups_Oordered__ab__group__add(_962337), 10252 ^ _781013 : [(10259 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962337), _962341), _962339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962337), hAPP(c_Groups_Ouminus__class_Ouminus(_962337), _962339)), hAPP(c_Groups_Ouminus__class_Ouminus(_962337), _962341))))], (10253 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962337), hAPP(c_Groups_Ouminus__class_Ouminus(_962337), _962339)), hAPP(c_Groups_Ouminus__class_Ouminus(_962337), _962341))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962337), _962341), _962339)))]]], (51350 ^ _781013) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (50688 ^ _781013) ^ [_1811149] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1811149)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1811149), c_Int_OPls)))], (38612 ^ _781013) ^ [_1523609, _1523611] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1523609, _1523611) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1523609), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1523611)))], (35875 ^ _781013) ^ [_1459383, _1459385] : [class_Int_Onumber__ring(_1459383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1459385)), -(hBOOL(hAPP(hAPP(c_member(_1459383), hAPP(c_Int_Onumber__class_Onumber__of(_1459383), _1459385)), c_Nat_Osemiring__1__class_ONats(_1459383))))], (40177 ^ _781013) ^ [_1564408, _1564410, _1564412, _1564414] : [hBOOL(hAPP(hAPP(c_member(_1564408), _1564410), hAPP(c_List_Oset(_1564408), hAPP(hAPP(c_List_Olist_OCons(_1564408), _1564412), _1564414)))), -(_1564410 = _1564412), -(hBOOL(hAPP(hAPP(c_member(_1564408), _1564410), hAPP(c_List_Oset(_1564408), _1564414))))], (33322 ^ _781013) ^ [_1413548, _1413550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413548), _1413550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413548)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413550))))], (4484 ^ _781013) ^ [_848932, _848934] : [_848934 = _848932, -(c_Divides_Odiv__class_Odiv(_848934) = c_Divides_Odiv__class_Odiv(_848932))], (35817 ^ _781013) ^ [_1458050, _1458052] : [class_Int_Onumber__ring(_1458050), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1458050), hAPP(c_Int_Onumber__class_Onumber__of(_1458050), 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)))), _1458052)) = c_Groups_Oone__class_Oone(_1458050))], (31858 ^ _781013) ^ [_1384365, _1384367, _1384369, _1384371, _1384373, _1384375] : [class_Complete__Lattice_Ocomplete__lattice(_1384365), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384367, tc_fun(_1384369, _1384365)), _1384371), _1384373), _1384375) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384367, _1384365), _1384371), hAPP(hAPP(c_COMBC(_1384367, _1384369, _1384365), _1384373), _1384375)))], (25286 ^ _781013) ^ [_1252282, _1252284, _1252286, _1252288] : [class_Fields_Ofield(_1252282), -(_1252284 = c_Groups_Ozero__class_Ozero(_1252282)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1252282), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252282), _1252286), _1252284)), _1252288) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252282), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1252282), _1252286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252282), _1252284), _1252288))), _1252284))], (23749 ^ _781013) ^ [_1224921, _1224923, _1224925] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1224921), _1224923), _1224925) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1224921), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1224921, tc_Int_Oint), _1224923), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1224925))), class_Groups_Ocomm__monoid__add(_1224921), class_Groups_Ocomm__monoid__mult(_1224921)], (7917 ^ _781013) ^ [_914714, _914716, _914718, _914720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914714, tc_HOL_Obool)), _914716), _914718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914714, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_914714), _914720), _914716)), hAPP(hAPP(c_Set_Oinsert(_914714), _914720), _914718))))], (41382 ^ _781013) ^ [_1596401, _1596403] : [-(c_List_Osublist(_1596401, _1596403, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1596401))], (33864 ^ _781013) ^ [_1422455, _1422457] : [class_Int_Onumber__ring(_1422455), -(hAPP(c_Int_Onumber__class_Onumber__of(_1422455), c_Int_Osucc(_1422457)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1422455), c_Groups_Oone__class_Oone(_1422455)), hAPP(c_Int_Onumber__class_Onumber__of(_1422455), _1422457)))], (6844 ^ _781013) ^ [_893888, _893890, _893892, _893894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893888, tc_HOL_Obool)), _893890), _893892)), hBOOL(hAPP(hAPP(c_member(_893888), _893894), _893890)), -(hBOOL(hAPP(hAPP(c_member(_893888), _893894), _893892)))], (51496 ^ _781013) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (41302 ^ _781013) ^ [_1595064, _1595066, _1595068] : [-(hAPP(hAPP(c_List_Ozip(_1595064, _1595066), _1595068), c_List_Olist_ONil(_1595066)) = c_List_Olist_ONil(tc_prod(_1595064, _1595066)))], (32090 ^ _781013) ^ [_1390383, _1390385, _1390387, _1390389, _1390391, _1390393, _1390395] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390383, tc_fun(_1390385, tc_fun(_1390387, tc_HOL_Obool))), _1390389), _1390391), _1390393), _1390395))), 32091 ^ _781013 : [(32092 ^ _781013) ^ [_1390468] : [hBOOL(hAPP(hAPP(c_member(_1390383), _1390468), _1390389)), hBOOL(hAPP(hAPP(hAPP(_1390391, _1390468), _1390393), _1390395))]]], (35341 ^ _781013) ^ [_1449836, _1449838] : [class_Rings_Oring__1(_1449836), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1449836), hAPP(c_Groups_Ouminus__class_Ouminus(_1449836), c_Groups_Oone__class_Oone(_1449836))), 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)))), _1449838)) = c_Groups_Oone__class_Oone(_1449836))], (51374 ^ _781013) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (5006 ^ _781013) ^ [_857265, _857267, _857269, _857271, _857273, _857275, _857277, _857279] : [-(c_New__Random__Sequence_Oneg__bind(_857279, _857275, _857271, _857267) = c_New__Random__Sequence_Oneg__bind(_857277, _857273, _857269, _857265)), _857279 = _857277, _857275 = _857273, _857271 = _857269, _857267 = _857265], (13743 ^ _781013) ^ [_1033493, _1033495, _1033497, _1033499] : [class_Groups_Oab__semigroup__add(_1033493), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033493), _1033495), _1033497)), _1033499) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033493), _1033495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033493), _1033497), _1033499)))], (51636 ^ _781013) ^ [_1825188] : [-(hBOOL(_1825188)), -(hBOOL(hAPP(c_fNot, _1825188)))], (49502 ^ _781013) ^ [_1787285, _1787287, _1787289] : [class_Complete__Lattice_Ocomplete__lattice(_1787285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1787285), _1787287)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1787285), _1787289), c_Complete__Lattice_OInf__class_OInf(_1787285, _1787287)) = hAPP(hAPP(c_Finite__Set_Ofold(_1787285, _1787285, c_Lattices_Osemilattice__inf__class_Oinf(_1787285)), _1787289), _1787287))], (39344 ^ _781013) ^ [_1541359, _1541361, _1541363, _1541365, _1541367] : [class_Groups_Oab__group__add(_1541359), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1541359), hAPP(hAPP(c_List_Omap(_1541361, _1541359), hAPP(hAPP(c_COMBS(_1541361, _1541359, _1541359), hAPP(hAPP(c_COMBB(_1541359, tc_fun(_1541359, _1541359), _1541361), c_Groups_Ominus__class_Ominus(_1541359)), _1541363)), _1541365)), _1541367)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1541359), hAPP(c_List_Omonoid__add__class_Olistsum(_1541359), hAPP(hAPP(c_List_Omap(_1541361, _1541359), _1541363), _1541367))), hAPP(c_List_Omonoid__add__class_Olistsum(_1541359), hAPP(hAPP(c_List_Omap(_1541361, _1541359), _1541365), _1541367))))], (37788 ^ _781013) ^ [_1504483] : [-(c_Equiv__Relations_Oequivp(_1504483, c_fequal))], (51124 ^ _781013) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (50397 ^ _781013) ^ [_1805761, _1805763, _1805765, _1805767] : [c_List_Olist__ex1(_1805761, _1805763, hAPP(hAPP(c_List_Olist_OCons(_1805761), _1805765), _1805767)), 50400 ^ _781013 : [(50407 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1805763, _1805765))), -(c_List_Olist__ex1(_1805761, _1805763, _1805767))], (50401 ^ _781013) ^ [] : [hBOOL(hAPP(_1805763, _1805765)), -(c_List_Olist__all(_1805761, hAPP(hAPP(c_COMBS(_1805761, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805761), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1805761), c_fNot), _1805763))), hAPP(c_fequal, _1805765)), _1805767))]]], (37438 ^ _781013) ^ [_1495680, _1495682, _1495684] : [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), _1495680), _1495682))), -(hBOOL(hAPP(hAPP(_1495684, _1495680), _1495682))), 37445 ^ _781013 : [(37448 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37444 ^ [_1495680, _1495682, _1495684]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1495684, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37443 ^ [_1495680, _1495682, _1495684])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37444 ^ [_1495680, _1495682, _1495684]))))], (37454 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1495684, 37443 ^ [_1495680, _1495682, _1495684]), 37444 ^ [_1495680, _1495682, _1495684]))], (37446 ^ _781013) ^ [] : [-(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), 37443 ^ [_1495680, _1495682, _1495684]), 37444 ^ [_1495680, _1495682, _1495684]))))]]], (8167 ^ _781013) ^ [_920290, _920292, _920294, _920296, _920298, _920300, _920302, _920304] : [c_Finite__Set_Ofolding__image__simple__idem(_920290, _920292, _920294, _920296, _920298, _920300), hBOOL(hAPP(c_Finite__Set_Ofinite(_920292), _920302)), hBOOL(hAPP(hAPP(c_member(_920292), _920304), _920302)), -(hAPP(hAPP(_920294, hAPP(_920298, _920304)), hAPP(_920300, _920302)) = hAPP(_920300, _920302))], (27250 ^ _781013) ^ [_1288523, _1288525, _1288527, _1288529, _1288531] : [class_Groups_Ocomm__monoid__mult(_1288523), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288525), _1288527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288525, tc_HOL_Obool)), _1288529), _1288527)), 27264 ^ _781013 : [(27267 ^ _781013) ^ [] : [hAPP(_1288531, 27263 ^ [_1288523, _1288525, _1288527, _1288529, _1288531]) = c_Groups_Oone__class_Oone(_1288523)], (27265 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1288525), 27263 ^ [_1288523, _1288525, _1288527, _1288529, _1288531]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288525, tc_HOL_Obool)), _1288527), _1288529))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1288525, _1288523), _1288531), _1288527) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1288525, _1288523), _1288531), _1288529))], (51372 ^ _781013) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (25460 ^ _781013) ^ [_1255538, _1255540] : [c_Nat__Transfer_Onat__set(_1255538), c_Nat__Transfer_Onat__set(_1255540), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1255538), _1255540)))], (39136 ^ _781013) ^ [_1536521, _1536523, _1536525] : [-(hAPP(c_List_Oset(_1536521), c_List_Osublist(_1536521, _1536523, _1536525)) = hAPP(c_Set_OCollect(_1536521), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1536521), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1536521, 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)), _1536521), 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)), _1536521), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1536521, tc_fun(tc_Nat_Onat, _1536521), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536521, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1536521), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1536521), c_COMBB(_1536521, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1536521), _1536523))))), 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(_1536521)), _1536523)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1536525))))))], (42316 ^ _781013) ^ [_1619544, _1619546, _1619548, _1619550] : [-(_1619544 = c_List_Olist_ONil(_1619546)), -(hAPP(c_List_Ohd(_1619548), hAPP(hAPP(c_List_Omap(_1619546, _1619548), _1619550), _1619544)) = hAPP(_1619550, hAPP(c_List_Ohd(_1619546), _1619544)))], (20949 ^ _781013) ^ [_1172511, _1172513, _1172515, _1172517] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1172511, _1172513)), c_Sum__Type_OPlus(_1172511, _1172513, _1172515, _1172517))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1172513), _1172517)))], (2162 ^ _781013) ^ [_812799, _812801, _812803, _812805, _812807, _812809] : [-(c_SetInterval_Oord_OlessThan(_812809, _812805, _812801) = c_SetInterval_Oord_OlessThan(_812807, _812803, _812799)), _812809 = _812807, _812805 = _812803, _812801 = _812799], (38296 ^ _781013) ^ [_1516669, _1516671] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1516669), hAPP(c_List_Oset(_1516669), _1516671))))], (7671 ^ _781013) ^ [_910061, _910063] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910061, tc_HOL_Obool)), _910063), _910063) = c_Orderings_Obot__class_Obot(tc_fun(_910061, tc_HOL_Obool)))], (38610 ^ _781013) ^ [_1523566, _1523568] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1523566), _1523568) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1523566, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1523568), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (14173 ^ _781013) ^ [_1042179, _1042181, _1042183, _1042185, _1042187, _1042189] : [class_Rings_Oring(_1042179), 14176 ^ _781013 : [(14183 ^ _781013) ^ [] : [_1042185 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042179), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042179), _1042187), _1042181)), _1042183)), _1042189), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042179), _1042181), _1042183)), _1042185) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042179), _1042187), _1042183)), _1042189))], (14177 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042179), _1042181), _1042183)), _1042185) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042179), _1042187), _1042183)), _1042189), -(_1042185 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042179), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042179), _1042187), _1042181)), _1042183)), _1042189))]]], (49556 ^ _781013) ^ [_1788431, _1788433, _1788435, _1788437] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1788431, _1788433, _1788435), _1788437), c_Orderings_Obot__class_Obot(tc_fun(_1788431, tc_HOL_Obool))) = _1788437)], (44699 ^ _781013) ^ [_1673609, _1673611, _1673613, _1673615, _1673617] : [class_Orderings_Olinorder(_1673609), c_List_Olinorder__class_Osorted(_1673609, hAPP(c_List_Orev(_1673609), hAPP(hAPP(c_List_Omap(_1673611, _1673609), _1673613), _1673615))), -(hAPP(c_List_Ofilter(_1673611, hAPP(hAPP(c_COMBB(_1673609, tc_HOL_Obool, _1673611), hAPP(c_Orderings_Oord__class_Oless(_1673609), _1673617)), _1673613)), _1673615) = c_List_OtakeWhile(_1673611, hAPP(hAPP(c_COMBB(_1673609, tc_HOL_Obool, _1673611), hAPP(c_Orderings_Oord__class_Oless(_1673609), _1673617)), _1673613), _1673615))], (43685 ^ _781013) ^ [_1651632] : [-(c_List_Oupt(_1651632, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (51122 ^ _781013) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (44159 ^ _781013) ^ [_1660241, _1660243, _1660245, _1660247, _1660249] : [class_Orderings_Olinorder(_1660241), c_Fun_Oinj__on(_1660243, _1660241, _1660245, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1660243, tc_HOL_Obool)), hAPP(c_List_Oset(_1660243), _1660247)), hAPP(c_List_Oset(_1660243), _1660249))), c_List_Olinorder__class_Osorted(_1660241, hAPP(hAPP(c_List_Omap(_1660243, _1660241), _1660245), _1660247)), hBOOL(hAPP(c_List_Odistinct(_1660241), hAPP(hAPP(c_List_Omap(_1660243, _1660241), _1660245), _1660247))), c_List_Olinorder__class_Osorted(_1660241, hAPP(hAPP(c_List_Omap(_1660243, _1660241), _1660245), _1660249)), hBOOL(hAPP(c_List_Odistinct(_1660241), hAPP(hAPP(c_List_Omap(_1660243, _1660241), _1660245), _1660249))), hAPP(c_List_Oset(_1660243), _1660247) = hAPP(c_List_Oset(_1660243), _1660249), -(_1660247 = _1660249)], (12906 ^ _781013) ^ [_1015334, _1015336, _1015338, _1015340] : [-(hAPP(c_Set_Ovimage(_1015334, _1015336, _1015338), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1015336, tc_HOL_Obool)), _1015340)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1015334, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1015334, _1015336, _1015338), _1015340)))], (28430 ^ _781013) ^ [_1311617, _1311619, _1311621] : [class_Orderings_Olinorder(_1311617), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311617), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311617), _1311619), _1311621)), _1311619)))], (44791 ^ _781013) ^ [_1675262, _1675264] : [-(c_List_Oremdups(_1675262, c_List_Oremdups(_1675262, _1675264)) = c_List_Oremdups(_1675262, _1675264))], (47226 ^ _781013) ^ [_1732257, _1732259, _1732261, _1732263, _1732265] : [-(hAPP(c_Relation_ODomain(_1732257, _1732259), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1732257, _1732259)), hAPP(hAPP(c_Product__Type_OPair(_1732257, _1732259), _1732261), _1732263)), _1732265)) = hAPP(hAPP(c_Set_Oinsert(_1732257), _1732261), hAPP(c_Relation_ODomain(_1732257, _1732259), _1732265)))], (19170 ^ _781013) ^ [_1140072, _1140074, _1140076, _1140078] : [class_Groups_Ocomm__monoid__mult(_1140072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1140074), _1140076)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1140074, _1140072), hAPP(c_COMBK(_1140072, _1140074), _1140078)), _1140076) = hAPP(hAPP(c_Power_Opower__class_Opower(_1140072), _1140078), hAPP(c_Finite__Set_Ocard(_1140074), _1140076)))], (34305 ^ _781013) ^ [_1431596] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1431596)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1431596))))], (48790 ^ _781013) ^ [_1768919, _1768921, _1768923, _1768925, _1768927] : [-(hAPP(c_Relation_Oconverse(_1768919, _1768921), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1768923, tc_fun(tc_prod(_1768919, _1768921), tc_HOL_Obool)), _1768925), _1768927)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1768923, tc_fun(tc_prod(_1768921, _1768919), tc_HOL_Obool)), _1768925), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1768919, _1768921), tc_HOL_Obool), tc_fun(tc_prod(_1768921, _1768919), tc_HOL_Obool), _1768923), c_Relation_Oconverse(_1768919, _1768921)), _1768927)))], (40741 ^ _781013) ^ [_1580102, _1580104, _1580106, _1580108] : [_1580102 = c_Orderings_Obot__class_Obot(tc_fun(_1580104, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1580106, _1580104), _1580106, c_Product__Type_Ofst(_1580106, _1580104)), hAPP(hAPP(c_Product__Type_OSigma(_1580106, _1580104), _1580108), hAPP(c_COMBK(tc_fun(_1580104, tc_HOL_Obool), _1580106), _1580102))) = c_Orderings_Obot__class_Obot(tc_fun(_1580106, tc_HOL_Obool)))], (13110 ^ _781013) ^ [_1019544, _1019546, _1019548, _1019550, _1019552, _1019554] : [hBOOL(hAPP(hAPP(c_member(_1019544), _1019546), _1019548)), 13113 ^ _781013 : [(13120 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1019544), _1019550), _1019548))), -(hAPP(c_Set_Ovimage(_1019552, _1019544, hAPP(hAPP(c_COMBC(_1019552, _1019544, _1019544), hAPP(hAPP(c_COMBC(_1019552, _1019544, tc_fun(_1019544, _1019544)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1019544, tc_fun(_1019544, _1019544)), _1019552), c_If(_1019544)), hAPP(hAPP(c_COMBC(_1019552, tc_fun(_1019552, tc_HOL_Obool), tc_HOL_Obool), c_member(_1019552)), _1019554))), _1019546)), _1019550)), _1019548) = _1019554)], (13114 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1019544), _1019550), _1019548)), -(hAPP(c_Set_Ovimage(_1019552, _1019544, hAPP(hAPP(c_COMBC(_1019552, _1019544, _1019544), hAPP(hAPP(c_COMBC(_1019552, _1019544, tc_fun(_1019544, _1019544)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1019544, tc_fun(_1019544, _1019544)), _1019552), c_If(_1019544)), hAPP(hAPP(c_COMBC(_1019552, tc_fun(_1019552, tc_HOL_Obool), tc_HOL_Obool), c_member(_1019552)), _1019554))), _1019546)), _1019550)), _1019548) = c_Orderings_Otop__class_Otop(tc_fun(_1019552, tc_HOL_Obool)))]]], (21678 ^ _781013) ^ [_1188090, _1188092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1188090)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1188092))))], (19304 ^ _781013) ^ [_1142590] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1142590) = _1142590)], (14137 ^ _781013) ^ [_1041402, _1041404, _1041406, _1041408, _1041410] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1041402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041402), _1041404), _1041406)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041402), _1041408), _1041410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041402), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041402), _1041404), _1041408)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041402), _1041406), _1041410))))], (40667 ^ _781013) ^ [_1578165, _1578167, _1578169, _1578171, _1578173, _1578175] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578165, _1578167)), hAPP(hAPP(c_Product__Type_OPair(_1578165, _1578167), _1578169), _1578171)), hAPP(hAPP(c_Product__Type_OSigma(_1578165, _1578167), _1578173), _1578175))), -(hBOOL(hAPP(hAPP(c_member(_1578165), _1578169), _1578173)))], (44230 ^ _781013) ^ [_1662295, _1662297] : [-(c_Fun_Oinj__on(tc_List_Olist(_1662295), tc_List_Olist(_1662295), c_List_Orev(_1662295), _1662297))], (48657 ^ _781013) ^ [_1765442, _1765444] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1765442), _1765444) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1765442)), hAPP(c_Code__Numeral_Onat__of, _1765444))))], (45210 ^ _781013) ^ [_1684247, _1684249, _1684251] : [class_Enum_Oenum(_1684247), 45213 ^ _781013 : [(45214 ^ _781013) ^ [] : [c_Enum_Oall__n__lists(_1684247, _1684249, _1684251), 45217 ^ _781013 : [(45218 ^ _781013) ^ [_1684397] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1684247)), _1684397), hAPP(c_List_Oset(tc_List_Olist(_1684247)), c_Enum_On__lists(_1684247, _1684251, c_Enum_Oenum__class_Oenum(_1684247))))), -(hBOOL(hAPP(_1684249, _1684397)))]]], (45224 ^ _781013) ^ [] : [45226 ^ _781013 : [(45229 ^ _781013) ^ [] : [hBOOL(hAPP(_1684249, 45225 ^ [_1684247, _1684249, _1684251]))], (45227 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1684247)), 45225 ^ [_1684247, _1684249, _1684251]), hAPP(c_List_Oset(tc_List_Olist(_1684247)), c_Enum_On__lists(_1684247, _1684251, c_Enum_Oenum__class_Oenum(_1684247))))))]], -(c_Enum_Oall__n__lists(_1684247, _1684249, _1684251))]]], (46812 ^ _781013) ^ [_1722558] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1722558)))], (44779 ^ _781013) ^ [_1675030, _1675032] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675030)), c_List_Oremdups(_1675030, _1675032)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675030)), _1675032), -(c_List_Oremdups(_1675030, _1675032) = _1675032)], (28682 ^ _781013) ^ [_1316209, _1316211] : [class_Orderings_Olinorder(_1316209), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316209), _1316211), _1316211) = _1316211)], (9969 ^ _781013) ^ [_957222, _957224] : [class_Lattices_Osemilattice__inf(_957222), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_957222), _957224), _957224) = _957224)], (27126 ^ _781013) ^ [_1286088] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1286088)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1286088))], (35509 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (48667 ^ _781013) ^ [_1765654, _1765656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1765654), _1765656)), -(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), _1765654), _1765656)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (51300 ^ _781013) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (31358 ^ _781013) ^ [_1368874, _1368876, _1368878, _1368880, _1368882] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_1368874, _1368876)), _1368878), _1368880), _1368882))), 31359 ^ _781013 : [(31360 ^ _781013) ^ [_1368956] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1368874), _1368878), _1368880), _1368956)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1368876), _1368956), _1368880), _1368882))]]], (40950 ^ _781013) ^ [_1587210, _1587212] : [-(c_Product__Type_Oapsnd(_1587210, _1587210, _1587212, c_Fun_Oid(_1587210)) = c_Fun_Oid(tc_prod(_1587212, _1587210)))], (14087 ^ _781013) ^ [_1040271, _1040273, _1040275] : [class_Groups_Ogroup__add(_1040271), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040271), hAPP(c_Groups_Ouminus__class_Ouminus(_1040271), _1040273)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040271), _1040273), _1040275)) = _1040275)], (6583 ^ _781013) ^ [_888707, _888709, _888711, _888713] : [-(c_Option_Ooption_Ooption__rec(_888707, _888709, _888711, _888713, c_Option_Ooption_ONone(_888709)) = _888711)], (17627 ^ _781013) ^ [_1110600, _1110602, _1110604, _1110606, _1110608] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_1110600, _1110602, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1110600), _1110604), _1110606), _1110608)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20305 ^ _781013) ^ [_1160608, _1160610, _1160612] : [class_Groups_Omonoid__mult(_1160608), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1160608), _1160610), hAPP(c_Nat_OSuc, _1160612)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160608), hAPP(hAPP(c_Power_Opower__class_Opower(_1160608), _1160610), _1160612)), _1160610))], (6108 ^ _781013) ^ [_879826, _879828, _879830, _879832, _879834, _879836, _879838] : [c_Hoare__Mirabelle_Ohoare__derivs(_879826, _879828, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_879826)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_879826), c_Hoare__Mirabelle_Opeek__and(_879826, _879830, _879832)), _879834), _879836)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_879826), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_879826, _879828, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_879826)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_879826), c_Hoare__Mirabelle_Opeek__and(_879826, _879830, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _879832))), _879838), _879836)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_879826), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_879826, _879828, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_879826)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_879826), _879830), c_Com_Ocom_OCond(_879832, _879834, _879838)), _879836)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_879826), tc_HOL_Obool)))))], (38712 ^ _781013) ^ [_1526460, _1526462, _1526464] : [class_Orderings_Olinorder(_1526460), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526460), _1526462)), -(c_List_Olinorder__class_Osorted__list__of__set(_1526460, hAPP(hAPP(c_Set_Oinsert(_1526460), _1526464), _1526462)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1526460, _1526460, c_COMBI(_1526460)), _1526464), c_List_Olinorder__class_Osorted__list__of__set(_1526460, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1526460, tc_HOL_Obool)), _1526462), hAPP(hAPP(c_Set_Oinsert(_1526460), _1526464), c_Orderings_Obot__class_Obot(tc_fun(_1526460, tc_HOL_Obool)))))))], (6812 ^ _781013) ^ [_893317, _893319, _893321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893317, tc_HOL_Obool)), _893319), _893321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893317, tc_HOL_Obool)), _893321), _893319)), -(_893319 = _893321)], (38373 ^ _781013) ^ [_1518556, _1518558, _1518560, _1518562] : [hAPP(hAPP(c_Map_Omap__of(_1518556, _1518558), _1518560), _1518562) = c_Option_Ooption_ONone(_1518558), hBOOL(hAPP(hAPP(c_member(_1518556), _1518562), hAPP(c_Set_Oimage(tc_prod(_1518556, _1518558), _1518556, c_Product__Type_Ofst(_1518556, _1518558)), hAPP(c_List_Oset(tc_prod(_1518556, _1518558)), _1518560))))], (27665 ^ _781013) ^ [_1297418, _1297420, _1297422, _1297424] : [class_Divides_Osemiring__div(_1297418), -(c_Divides_Odiv__class_Omod(_1297418, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297418), c_Divides_Odiv__class_Omod(_1297418, _1297420, _1297422)), _1297424), _1297422) = c_Divides_Odiv__class_Omod(_1297418, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297418), _1297420), _1297424), _1297422))], (44900 ^ _781013) ^ [_1677509, _1677511, _1677513, _1677515, _1677517] : [hBOOL(hAPP(hAPP(c_member(_1677509), _1677511), hAPP(c_List_Oset(_1677509), _1677513))), -(hBOOL(hAPP(_1677515, _1677511))), -(c_List_OdropWhile(_1677509, _1677515, hAPP(hAPP(c_List_Oappend(_1677509), _1677513), _1677517)) = hAPP(hAPP(c_List_Oappend(_1677509), c_List_OdropWhile(_1677509, _1677515, _1677513)), _1677517))], (16151 ^ _781013) ^ [_1079598, _1079600] : [class_Rings_Olinordered__idom(_1079598), 16154 ^ _781013 : [(16161 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079598), _1079600), c_Groups_Ozero__class_Ozero(_1079598))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079598), _1079600), hAPP(c_Groups_Ouminus__class_Ouminus(_1079598), _1079600))))], (16155 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079598), _1079600), hAPP(c_Groups_Ouminus__class_Ouminus(_1079598), _1079600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079598), _1079600), c_Groups_Ozero__class_Ozero(_1079598))))]]], (23993 ^ _781013) ^ [_1228904, _1228906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228904)), 23996 ^ _781013 : [(24003 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228904), _1228906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1228904)), hAPP(c_Int_Onat, _1228906))))], (23997 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1228904)), hAPP(c_Int_Onat, _1228906))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228904), _1228906)))]]], (41338 ^ _781013) ^ [_1595689, _1595691, _1595693, _1595695] : [class_Orderings_Olinorder(_1595689), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1595691, _1595689, _1595693), _1595695), c_List_Olist_ONil(_1595691)) = hAPP(hAPP(c_List_Olist_OCons(_1595691), _1595695), c_List_Olist_ONil(_1595691)))], (51240 ^ _781013) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (36542 ^ _781013) ^ [_1478143, _1478145, _1478147, _1478149, _1478151, _1478153] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478143, tc_fun(_1478145, tc_HOL_Obool))), _1478147), _1478149), _1478151), _1478153)), -(hBOOL(hAPP(hAPP(_1478147, _1478151), _1478153)))], (19969 ^ _781013) ^ [_1155008, _1155010] : [hAPP(c_Nat_OSuc, _1155008) = hAPP(c_Nat_OSuc, _1155010), -(_1155008 = _1155010)], (40439 ^ _781013) ^ [_1570404, _1570406, _1570408, _1570410] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1570404), tc_List_Olist(_1570404), c_List_Olistrel(_1570404, _1570406)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1570404)), hAPP(hAPP(c_List_Olist_OCons(_1570404), _1570408), _1570410)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1570404), tc_HOL_Obool)))) = c_List_Oset__Cons(_1570404, hAPP(c_Relation_OImage(_1570404, _1570404, _1570406), hAPP(hAPP(c_Set_Oinsert(_1570404), _1570408), c_Orderings_Obot__class_Obot(tc_fun(_1570404, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1570404), tc_List_Olist(_1570404), c_List_Olistrel(_1570404, _1570406)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1570404)), _1570410), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1570404), tc_HOL_Obool))))))], (12814 ^ _781013) ^ [_1013287, _1013289, _1013291] : [class_Groups_Oab__semigroup__mult(_1013287), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013287), _1013289)), -(_1013289 = c_Orderings_Obot__class_Obot(tc_fun(_1013287, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013287), _1013291)), -(_1013291 = c_Orderings_Obot__class_Obot(tc_fun(_1013287, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013287, tc_HOL_Obool)), _1013289), _1013291) = c_Orderings_Obot__class_Obot(tc_fun(_1013287, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1013287, c_Groups_Otimes__class_Otimes(_1013287)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013287, tc_HOL_Obool)), _1013289), _1013291)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013287), hAPP(c_Finite__Set_Ofold1(_1013287, c_Groups_Otimes__class_Otimes(_1013287)), _1013289)), hAPP(c_Finite__Set_Ofold1(_1013287, c_Groups_Otimes__class_Otimes(_1013287)), _1013291)))], (33698 ^ _781013) ^ [_1419759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1419759), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419759))], (11874 ^ _781013) ^ [_995158, _995160] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_995158, tc_HOL_Obool)), _995160), c_Orderings_Otop__class_Otop(tc_fun(_995158, tc_HOL_Obool)))))], (40451 ^ _781013) ^ [_1571572, _1571574, _1571576, _1571578, _1571580, _1571582, _1571584, _1571586] : [-(hAPP(c_Product__Type_Omap__pair(_1571572, _1571574, _1571576, _1571578, _1571580, _1571582), hAPP(hAPP(c_Product__Type_OPair(_1571572, _1571576), _1571584), _1571586)) = hAPP(hAPP(c_Product__Type_OPair(_1571574, _1571578), hAPP(_1571580, _1571584)), hAPP(_1571582, _1571586)))], (44969 ^ _781013) ^ [_1679225, _1679227] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1679225))), c_Enum_Osublists(_1679225, _1679227)) = 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(_1679225)), _1679227)))], (18652 ^ _781013) ^ [_1128534, _1128536, _1128538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128534), _1128536)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128538), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128536), _1128534)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128538), _1128534)), _1128536))], (43291 ^ _781013) ^ [_1643098, _1643100] : [-(hBOOL(hAPP(c_List_Olistsp(_1643098, _1643100), c_List_Olist_ONil(_1643098))))], (23341 ^ _781013) ^ [_1217610, _1217612] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1217610, _1217612))))], (20933 ^ _781013) ^ [_1172221, _1172223, _1172225, _1172227] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1172221), _1172223)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172225), _1172227)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1172221, _1172225)), c_Sum__Type_OPlus(_1172221, _1172225, _1172223, _1172227))))], (51204 ^ _781013) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (39523 ^ _781013) ^ [_1545467, _1545469] : [hBOOL(hAPP(_1545467, c_Hilbert__Choice_OEps(_1545469, _1545467))), -(hBOOL(hAPP(_1545467, 39526 ^ [_1545467, _1545469])))], (23071 ^ _781013) ^ [_1212728, _1212730] : [23079 ^ _781013 : [(23082 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1212730, 23078 ^ [_1212728, _1212730])))], (23080 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 23078 ^ [_1212728, _1212730]), _1212728)))]], 23072 ^ _781013 : [(23073 ^ _781013) ^ [_1212796] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1212796), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212728))), hBOOL(hAPP(_1212730, _1212796))]]], (35979 ^ _781013) ^ [_1465752, _1465754, _1465756, _1465758, _1465760, _1465762] : [hBOOL(hAPP(hAPP(c_member(_1465752), _1465754), _1465756)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1465752, _1465758)), hAPP(hAPP(c_Product__Type_OPair(_1465752, _1465758), _1465754), _1465760)), _1465762)), -(hBOOL(hAPP(hAPP(c_member(_1465758), _1465760), hAPP(c_Relation_OImage(_1465752, _1465758, _1465762), _1465756))))], (48289 ^ _781013) ^ [_1756660, _1756662, _1756664] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756660), tc_List_Olist(_1756660))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756660), tc_List_Olist(_1756660)), _1756662), _1756662)), c_List_Olistrel(_1756660, c_Transitive__Closure_Ortrancl(_1756660, _1756664)))))], (12436 ^ _781013) ^ [_1005325, _1005327, _1005329] : [class_Lattices_Olattice(_1005325), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005325), _1005327)), 12443 ^ _781013 : [(12450 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005325, tc_HOL_Obool)), _1005327), hAPP(hAPP(c_Set_Oinsert(_1005325), _1005329), c_Orderings_Obot__class_Obot(tc_fun(_1005325, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1005325, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1005325, hAPP(hAPP(c_Set_Oinsert(_1005325), _1005329), _1005327)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005325), _1005329), c_Big__Operators_Olattice__class_OSup__fin(_1005325, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005325, tc_HOL_Obool)), _1005327), hAPP(hAPP(c_Set_Oinsert(_1005325), _1005329), c_Orderings_Obot__class_Obot(tc_fun(_1005325, tc_HOL_Obool)))))))], (12444 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005325, tc_HOL_Obool)), _1005327), hAPP(hAPP(c_Set_Oinsert(_1005325), _1005329), c_Orderings_Obot__class_Obot(tc_fun(_1005325, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1005325, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1005325, hAPP(hAPP(c_Set_Oinsert(_1005325), _1005329), _1005327)) = _1005329)]]], (42408 ^ _781013) ^ [_1620967, _1620969, _1620971, _1620973] : [-(hAPP(hAPP(c_List_Omap(_1620967, _1620969), _1620971), hAPP(c_List_Otl(_1620967), _1620973)) = hAPP(c_List_Otl(_1620969), hAPP(hAPP(c_List_Omap(_1620967, _1620969), _1620971), _1620973)))], (41160 ^ _781013) ^ [_1592343, _1592345, _1592347, _1592349] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1592343) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1592345), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1592343)), hAPP(hAPP(c_List_Olist_OCons(_1592345), _1592347), _1592349)) = c_List_Olist_ONil(_1592345))], (19562 ^ _781013) ^ [_1147177, _1147179] : [class_Power_Opower(_1147177), class_Rings_Osemiring__0(_1147177), 19569 ^ _781013 : [(19576 ^ _781013) ^ [] : [-(_1147179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1147177), c_Groups_Ozero__class_Ozero(_1147177)), _1147179) = c_Groups_Ozero__class_Ozero(_1147177))], (19570 ^ _781013) ^ [] : [_1147179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1147177), c_Groups_Ozero__class_Ozero(_1147177)), _1147179) = c_Groups_Oone__class_Oone(_1147177))]]], (21065 ^ _781013) ^ [_1176388, _1176390, _1176392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176388)), _1176388 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1176388), _1176392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176392), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (6954 ^ _781013) ^ [_895947, _895949, _895951, _895953] : [class_Orderings_Oord(_895947), 6957 ^ _781013 : [(6964 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895947), hAPP(_895951, 6965 ^ [_895947, _895949, _895951, _895953])), hAPP(_895953, 6965 ^ [_895947, _895949, _895951, _895953]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895949, _895947)), _895951), _895953)))], (6958 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895949, _895947)), _895951), _895953)), 6961 ^ _781013 : [(6962 ^ _781013) ^ [_896104] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895947), hAPP(_895951, _896104)), hAPP(_895953, _896104))))]]]]], (48641 ^ _781013) ^ [_1765054, _1765056, _1765058, _1765060] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1765054), tc_List_Olist(_1765054))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1765054), tc_List_Olist(_1765054)), _1765056), _1765058)), c_List_Olistrel(_1765054, _1765060))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1765054), tc_List_Olist(_1765054))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1765054), tc_List_Olist(_1765054)), _1765056), _1765058)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1765054), c_List_Olistrel1(_1765054, _1765060)))))], (51368 ^ _781013) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (34002 ^ _781013) ^ [_1425385, _1425387, _1425389, _1425391, _1425393] : [-(c_Nat_Onat_Onat__case(_1425385, _1425387, _1425389, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425391)), _1425393)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1425385), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1425391))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1425385, _1425385), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1425385, tc_fun(_1425385, _1425385)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1425385, tc_fun(_1425385, _1425385)), tc_Int_Oint), c_If(_1425385)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1425385, _1425387, _1425389, _1425393))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1425385, tc_Int_Oint), _1425389), 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)), _1425393)))))], (50216 ^ _781013) ^ [_1802135, _1802137, _1802139] : [-(c_Nitpick_Oof__frac(_1802137, _1802135, _1802139) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1802135), hAPP(c_Int_Oring__1__class_Oof__int(_1802135), hAPP(c_Nitpick_Onum(_1802137), _1802139))), hAPP(c_Int_Oring__1__class_Oof__int(_1802135), hAPP(c_Nitpick_Odenom(_1802137), _1802139)))), class_Rings_Oinverse(_1802135), class_Rings_Oring__1(_1802135)], (45743 ^ _781013) ^ [_1695699, _1695701, _1695703] : [class_Complete__Lattice_Ocomplete__lattice(_1695699), -(c_Complete__Lattice_OSup__class_OSup(_1695699, hAPP(hAPP(c_Set_Oinsert(_1695699), _1695701), hAPP(hAPP(c_Set_Oinsert(_1695699), _1695703), c_Orderings_Obot__class_Obot(tc_fun(_1695699, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1695699), _1695701), _1695703))], (1094 ^ _781013) ^ [_797430, _797432] : [-(class_Rings_Olinordered__semiring__1(_797430)), _797432 = _797430, class_Rings_Olinordered__semiring__1(_797432)], (36074 ^ _781013) ^ [_1468157, _1468159, _1468161, _1468163] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468157, _1468159), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1468161), _1468163))), -(_1468159 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1468157, _1468159) = _1468163)], (39625 ^ _781013) ^ [_1548047, _1548049, _1548051, _1548053, _1548055, _1548057, _1548059] : [-(hBOOL(hAPP(hAPP(c_member(_1548047), _1548049), hAPP(c_List_Oset(_1548047), hAPP(hAPP(c_List_Otake(_1548047), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1548051)), _1548053)), _1548055))))), -(c_Map_Omap__upds(_1548047, _1548051, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1548047, tc_Option_Ooption(_1548051)), _1548057), _1548049), hAPP(c_Option_Ooption_OSome(_1548051), _1548059)), _1548055, _1548053) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1548047, tc_Option_Ooption(_1548051)), c_Map_Omap__upds(_1548047, _1548051, _1548057, _1548055, _1548053)), _1548049), hAPP(c_Option_Ooption_OSome(_1548051), _1548059)))], (18508 ^ _781013) ^ [_1125430, _1125432] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1125430), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1125430), _1125432)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46661 ^ _781013) ^ [_1718100, _1718102, _1718104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1718100, _1718100), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1718100, _1718100, _1718100), _1718102), _1718104)), _1718102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1718100, tc_HOL_Obool), tc_fun(_1718100, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1718100, tc_HOL_Obool), tc_fun(_1718100, tc_HOL_Obool), tc_fun(_1718100, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1718100, _1718102)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1718100, tc_HOL_Obool), tc_fun(_1718100, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1718100, _1718104)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1718100, tc_HOL_Obool), tc_fun(_1718100, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1718100, tc_HOL_Obool), tc_fun(_1718100, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1718100, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1718100, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1718100, tc_HOL_Obool), tc_fun(_1718100, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1718100, _1718102))))], (10571 ^ _781013) ^ [_968182, _968184, _968186] : [class_Orderings_Oorder(_968182), -(_968184 = _968186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968182), _968186), _968184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968182), _968186), _968184)))], (12004 ^ _781013) ^ [_997428, _997430, _997432, _997434, _997436, _997438] : [c_Fun_Oinj__on(_997428, _997430, _997432, _997434), 12007 ^ _781013 : [(12014 ^ _781013) ^ [] : [c_Fun_Oinj__on(_997428, _997436, hAPP(c_Fun_Ocomp(_997430, _997436, _997428, _997438), _997432), _997434), -(c_Fun_Oinj__on(_997430, _997436, _997438, hAPP(c_Set_Oimage(_997428, _997430, _997432), _997434)))], (12008 ^ _781013) ^ [] : [c_Fun_Oinj__on(_997430, _997436, _997438, hAPP(c_Set_Oimage(_997428, _997430, _997432), _997434)), -(c_Fun_Oinj__on(_997428, _997436, hAPP(c_Fun_Ocomp(_997430, _997436, _997428, _997438), _997432), _997434))]]], (47263 ^ _781013) ^ [_1733696, _1733698, _1733700, _1733702] : [hBOOL(hAPP(c_Predicate_ODomainP(_1733696, _1733698, _1733700), _1733702)), -(hBOOL(hAPP(hAPP(_1733700, _1733702), 47266 ^ [_1733696, _1733698, _1733700, _1733702])))], (50678 ^ _781013) ^ [_1810944, _1810946] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1810944), _1810946) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1810944), _1810946)))], (3560 ^ _781013) ^ [_834740, _834742] : [_834742 = _834740, -(c_Wellfounded_Omeasure(_834742) = c_Wellfounded_Omeasure(_834740))], (48611 ^ _781013) ^ [_1764226, _1764228, _1764230, _1764232] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1764226), tc_List_Olist(_1764226))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1764226), tc_List_Olist(_1764226)), _1764228), _1764230)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1764226), c_List_Olistrel1(_1764226, _1764232)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764226)), _1764228) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764226)), _1764230))], (27982 ^ _781013) ^ [_1303532, _1303534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303532), 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, _1303534, _1303532)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47484 ^ _781013) ^ [_1738437, _1738439, _1738441] : [c_Wellfounded_OwfP(_1738437, hAPP(_1738439, 47485 ^ [_1738437, _1738439, _1738441])), 47492 ^ _781013 : [(47495 ^ _781013) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1738437, tc_HOL_Obool)), c_Predicate_ODomainP(_1738437, _1738437, hAPP(_1738439, 47490 ^ [_1738437, _1738439, _1738441]))), c_Predicate_ORangeP(_1738437, _1738437, hAPP(_1738439, 47491 ^ [_1738437, _1738439, _1738441]))) = c_Orderings_Obot__class_Obot(tc_fun(_1738437, tc_HOL_Obool))], (47493 ^ _781013) ^ [] : [hAPP(_1738439, 47490 ^ [_1738437, _1738439, _1738441]) = hAPP(_1738439, 47491 ^ [_1738437, _1738439, _1738441])]], -(c_Wellfounded_OwfP(_1738437, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1738441, tc_fun(_1738437, tc_fun(_1738437, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1738441, tc_HOL_Obool))), _1738439)))], (6048 ^ _781013) ^ [_878786, _878788, _878790, _878792, _878794] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_878786), _878788), _878790)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_878792), _878790), _878794)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_878786, _878792)), _878788), _878794)))], (4524 ^ _781013) ^ [_849544, _849546] : [_849546 = _849544, -(c_Rings_Oinverse__class_Odivide(_849546) = c_Rings_Oinverse__class_Odivide(_849544))], (10107 ^ _781013) ^ [_959816, _959818, _959820, _959822] : [class_Lattices_Osemilattice__inf(_959816), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959816), _959818), _959820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959816), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959816), _959822), _959818)), _959820)))], (17901 ^ _781013) ^ [_1114985, _1114987] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1114985), _1114987) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 17904 ^ _781013 : [(17907 ^ _781013) ^ [] : [-(_1114987 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17905 ^ _781013) ^ [] : [-(_1114985 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (30247 ^ _781013) ^ [_1346024, _1346026, _1346028] : [class_Orderings_Olinorder(_1346024), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346024), _1346026), _1346028) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346024), _1346028), _1346026))], (18516 ^ _781013) ^ [_1125581, _1125583] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1125581), _1125583) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1125581), _1125583)))], (47244 ^ _781013) ^ [_1733048, _1733050, _1733052, _1733054] : [hBOOL(hAPP(hAPP(c_member(_1733048), _1733054), hAPP(c_Relation_ODomain(_1733048, _1733050), _1733052))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1733048, _1733050, hAPP(hAPP(c_COMBC(_1733048, tc_fun(tc_prod(_1733048, _1733050), tc_HOL_Obool), tc_fun(_1733050, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1733050, tc_fun(tc_fun(tc_prod(_1733048, _1733050), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1733048, _1733050), tc_HOL_Obool), tc_fun(_1733050, tc_HOL_Obool)), _1733048), c_COMBC(_1733050, tc_fun(tc_prod(_1733048, _1733050), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1733050, tc_prod(_1733048, _1733050)), tc_fun(_1733050, tc_fun(tc_fun(tc_prod(_1733048, _1733050), tc_HOL_Obool), tc_HOL_Obool)), _1733048), hAPP(c_COMBB(tc_prod(_1733048, _1733050), tc_fun(tc_fun(tc_prod(_1733048, _1733050), tc_HOL_Obool), tc_HOL_Obool), _1733050), c_member(tc_prod(_1733048, _1733050)))), c_Product__Type_OPair(_1733048, _1733050)))), _1733052)), _1733054)))], (34065 ^ _781013) ^ [_1427385, _1427387] : [class_Int_Onumber__ring(_1427385), 34068 ^ _781013 : [(34075 ^ _781013) ^ [] : [c_Int_Oiszero(_1427385, hAPP(c_Int_Onumber__class_Onumber__of(_1427385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427387)))), -(c_Groups_Ozero__class_Ozero(_1427385) = hAPP(c_Int_Onumber__class_Onumber__of(_1427385), _1427387))], (34069 ^ _781013) ^ [] : [c_Groups_Ozero__class_Ozero(_1427385) = hAPP(c_Int_Onumber__class_Onumber__of(_1427385), _1427387), -(c_Int_Oiszero(_1427385, hAPP(c_Int_Onumber__class_Onumber__of(_1427385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427387)))))]]], (10955 ^ _781013) ^ [_975225, _975227, _975229, _975231] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975225, _975227, _975229, _975231, c_Orderings_Obot__class_Obot(tc_fun(_975225, tc_HOL_Obool))), _975231)))], (51104 ^ _781013) ^ [_1819745, _1819747] : [-(class_Enum_Oenum(tc_fun(_1819745, _1819747))), class_Enum_Oenum(_1819745), class_Enum_Oenum(_1819747)], (10165 ^ _781013) ^ [_960815, _960817, _960819, _960821, _960823] : [class_Lattices_Osemilattice__inf(_960815), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960815), _960817), _960819)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960815), _960821), _960823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960815), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960815), _960817), _960821)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960815), _960819), _960823))))], (45019 ^ _781013) ^ [_1680451, _1680453, _1680455, _1680457] : [hBOOL(hAPP(c_List_Odistinct(_1680451), _1680453)), hBOOL(hAPP(c_List_Odistinct(_1680455), _1680457)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1680451, _1680455)), c_Enum_Oproduct(_1680451, _1680455, _1680453, _1680457))))], (14051 ^ _781013) ^ [_1039463, _1039465, _1039467, _1039469, _1039471] : [class_Rings_Osemiring(_1039463), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039463), _1039465), _1039467)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039463), _1039469), _1039467)), _1039471)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039463), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039463), _1039465), _1039469)), _1039467)), _1039471))], (26275 ^ _781013) ^ [_1269664, _1269666, _1269668] : [class_Orderings_Oord(_1269664), 26278 ^ _781013 : [(26285 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269664), _1269668), _1269666)), -(hBOOL(hAPP(hAPP(c_member(_1269664), _1269666), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1269664), _1269668))))], (26279 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1269664), _1269666), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1269664), _1269668))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269664), _1269668), _1269666)))]]], (34729 ^ _781013) ^ [_1438714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1438714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1438714))))], (8133 ^ _781013) ^ [_919627, _919629, _919631, _919633, _919635, _919637, _919639] : [hAPP(_919627, _919629) = hAPP(c_Option_Ooption_OSome(_919631), _919633), -(c_Map_Omap__comp(_919631, _919635, _919637, _919639, _919627, _919629) = hAPP(_919639, _919633))], (30931 ^ _781013) ^ [_1359929, _1359931] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1359929), _1359931) = 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), _1359929)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1359931)))))], (36972 ^ _781013) ^ [_1486222, _1486224] : [_1486222 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1486222, _1486224) = 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)))], (48077 ^ _781013) ^ [_1752444, _1752446, _1752448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1752444, _1752444), tc_HOL_Obool)), _1752446), hAPP(hAPP(c_Product__Type_OSigma(_1752444, _1752444), _1752448), hAPP(c_COMBK(tc_fun(_1752444, tc_HOL_Obool), _1752444), _1752448)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1752444, _1752444), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1752444, _1752446)), hAPP(hAPP(c_Product__Type_OSigma(_1752444, _1752444), _1752448), hAPP(c_COMBK(tc_fun(_1752444, tc_HOL_Obool), _1752444), _1752448)))))], (34935 ^ _781013) ^ [_1442403, _1442405, _1442407] : [class_Int_Onumber__ring(_1442403), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1442403), _1442405), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1442407))) = hAPP(hAPP(c_HOL_OLet(_1442403, _1442403), hAPP(hAPP(c_Power_Opower__class_Opower(_1442403), _1442405), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442407))), hAPP(hAPP(c_COMBS(_1442403, _1442403, _1442403), c_Groups_Otimes__class_Otimes(_1442403)), c_COMBI(_1442403))))], (47363 ^ _781013) ^ [_1736049, _1736051] : [c_Wellfounded_Owf(_1736049, _1736051), -(c_Wellfounded_Oacyclic(_1736049, _1736051))], (1074 ^ _781013) ^ [_797180, _797182] : [-(class_Rings_Olinordered__ring__strict(_797180)), _797182 = _797180, class_Rings_Olinordered__ring__strict(_797182)], (38784 ^ _781013) ^ [_1528272, _1528274, _1528276, _1528278, _1528280] : [class_Orderings_Olinorder(_1528272), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528274)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1528274, _1528272, _1528276), _1528278), _1528280)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528274)), _1528280)))], (40511 ^ _781013) ^ [_1573362, _1573364, _1573366, _1573368, _1573370] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1573362), tc_List_Olist(_1573362))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1573362), tc_List_Olist(_1573362)), _1573364), hAPP(hAPP(c_List_Olist_OCons(_1573362), _1573366), _1573368))), c_List_Olistrel(_1573362, _1573370))), 40516 ^ _781013 : [(40521 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1573362), tc_List_Olist(_1573362))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1573362), tc_List_Olist(_1573362)), 40515 ^ [_1573362, _1573364, _1573366, _1573368, _1573370]), _1573368)), c_List_Olistrel(_1573362, _1573370))))], (40519 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573362, _1573362)), hAPP(hAPP(c_Product__Type_OPair(_1573362, _1573362), 40514 ^ [_1573362, _1573364, _1573366, _1573368, _1573370]), _1573366)), _1573370)))], (40517 ^ _781013) ^ [] : [-(_1573364 = hAPP(hAPP(c_List_Olist_OCons(_1573362), 40514 ^ [_1573362, _1573364, _1573366, _1573368, _1573370]), 40515 ^ [_1573362, _1573364, _1573366, _1573368, _1573370]))]]], (7957 ^ _781013) ^ [_915569, _915571, _915573] : [-(hAPP(hAPP(c_Option_Omap(_915569, _915571), _915573), c_Option_Ooption_ONone(_915569)) = c_Option_Ooption_ONone(_915571))], (38471 ^ _781013) ^ [_1520574, _1520576, _1520578, _1520580, _1520582] : [hBOOL(hAPP(c_List_Odistinct(_1520574), hAPP(hAPP(c_List_Omap(tc_prod(_1520574, _1520576), _1520574), c_Product__Type_Ofst(_1520574, _1520576)), _1520578))), 38474 ^ _781013 : [(38481 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1520574, _1520576)), hAPP(hAPP(c_Product__Type_OPair(_1520574, _1520576), _1520582), _1520580)), hAPP(c_List_Oset(tc_prod(_1520574, _1520576)), _1520578))), -(hAPP(c_Option_Ooption_OSome(_1520576), _1520580) = hAPP(hAPP(c_Map_Omap__of(_1520574, _1520576), _1520578), _1520582))], (38475 ^ _781013) ^ [] : [hAPP(c_Option_Ooption_OSome(_1520576), _1520580) = hAPP(hAPP(c_Map_Omap__of(_1520574, _1520576), _1520578), _1520582), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1520574, _1520576)), hAPP(hAPP(c_Product__Type_OPair(_1520574, _1520576), _1520582), _1520580)), hAPP(c_List_Oset(tc_prod(_1520574, _1520576)), _1520578))))]]], (39013 ^ _781013) ^ [_1533599, _1533601, _1533603] : [_1533599 = _1533601, 39016 ^ _781013 : [(39019 ^ _781013) ^ [_1533747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1533747), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533603)), _1533599))), -(hAPP(hAPP(c_List_Onth(_1533603), _1533599), _1533747) = hAPP(hAPP(c_List_Onth(_1533603), _1533601), _1533747))], (39017 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533603)), _1533599) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533603)), _1533601))]]], (6324 ^ _781013) ^ [_883985, _883987, _883989, _883991] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_883985, _883987)), _883989), _883991)), 6329 ^ _781013 : [(6332 ^ _781013) ^ [] : [hBOOL(hAPP(_883985, _883989))], (6330 ^ _781013) ^ [] : [-(_883991 = _883989)]], 6333 ^ _781013 : [(6339 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_883985, _883987)), 6335 ^ [_883985, _883987, _883989, _883991]), _883991)))], (6337 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_883987), _883989), 6335 ^ [_883985, _883987, _883989, _883991])))], (6334 ^ _781013) ^ [] : [-(hBOOL(hAPP(_883985, _883989)))]]], (31273 ^ _781013) ^ [_1366996, _1366998, _1367000, _1367002] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1366996), _1366998), _1367000), _1367002)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1366996), _1366998), _1367002)))], (51676 ^ _781013) ^ [_1825710, _1825712] : [hBOOL(hAPP(hAPP(c_fdisj, _1825710), _1825712)), -(hBOOL(_1825710)), -(hBOOL(_1825712))], (42937 ^ _781013) ^ [_1633370, _1633372, _1633374, _1633376, _1633378] : [hBOOL(hAPP(hAPP(c_member(_1633370), _1633372), _1633374)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1633376, tc_HOL_Obool)), hAPP(_1633378, _1633372)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633370, tc_fun(_1633376, tc_HOL_Obool)), _1633374), _1633378)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633370, tc_fun(_1633376, tc_HOL_Obool)), _1633374), _1633378))], (14791 ^ _781013) ^ [_1055332, _1055334] : [class_Groups_Olinordered__ab__group__add(_1055332), 14794 ^ _781013 : [(14801 ^ _781013) ^ [] : [_1055334 = c_Groups_Ozero__class_Ozero(_1055332), -(c_Groups_Ozero__class_Ozero(_1055332) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055332), _1055334), _1055334))], (14795 ^ _781013) ^ [] : [c_Groups_Ozero__class_Ozero(_1055332) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055332), _1055334), _1055334), -(_1055334 = c_Groups_Ozero__class_Ozero(_1055332))]]], (42094 ^ _781013) ^ [_1613983, _1613985, _1613987] : [-(hAPP(hAPP(c_List_Odrop(_1613983), _1613985), c_List_Obutlast(_1613983, _1613987)) = c_List_Obutlast(_1613983, hAPP(hAPP(c_List_Odrop(_1613983), _1613985), _1613987)))], (8213 ^ _781013) ^ [_921253, _921255, _921257, _921259, _921261, _921263] : [-(c_Map_Omap__comp(_921253, _921255, _921257, _921259, _921261, _921263) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_921255), _921253, c_Option_Ooption_ONone(_921255), _921259), hAPP(_921261, _921263)))], (42262 ^ _781013) ^ [_1618091, _1618093, _1618095, _1618097] : [-(hAPP(c_List_Orotate1(_1618093), hAPP(hAPP(c_List_Olist_OCons(_1618093), _1618095), _1618097)) = hAPP(hAPP(c_List_Oappend(_1618093), _1618097), hAPP(hAPP(c_List_Olist_OCons(_1618093), _1618095), c_List_Olist_ONil(_1618093))))], (10783 ^ _781013) ^ [_971362, _971364] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971362, tc_HOL_Obool)), _971364), c_Orderings_Obot__class_Obot(tc_fun(_971362, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_971362, tc_HOL_Obool)))], (40775 ^ _781013) ^ [_1580888, _1580890, _1580892, _1580894] : [-(hAPP(c_Set_Oimage(tc_prod(_1580888, _1580890), tc_prod(_1580890, _1580888), hAPP(c_Product__Type_Oprod_Oprod__case(_1580888, _1580890, tc_prod(_1580890, _1580888)), hAPP(c_COMBC(_1580890, _1580888, tc_prod(_1580890, _1580888)), c_Product__Type_OPair(_1580890, _1580888)))), hAPP(hAPP(c_Product__Type_OSigma(_1580888, _1580890), _1580892), hAPP(c_COMBK(tc_fun(_1580890, tc_HOL_Obool), _1580888), _1580894))) = hAPP(hAPP(c_Product__Type_OSigma(_1580890, _1580888), _1580894), hAPP(c_COMBK(tc_fun(_1580888, tc_HOL_Obool), _1580890), _1580892)))], (30259 ^ _781013) ^ [_1346258, _1346260, _1346262] : [class_Orderings_Olinorder(_1346258), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346258), _1346260), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346258), _1346260), _1346262)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346258), _1346260), _1346262))], (45737 ^ _781013) ^ [_1695416, _1695418, _1695420] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1695416, tc_HOL_Obool)), _1695418), _1695420) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1695416, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1695416, tc_HOL_Obool)), _1695418), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1695416, tc_HOL_Obool)), _1695420), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1695416, tc_HOL_Obool), tc_HOL_Obool))))))], (11828 ^ _781013) ^ [_994335, _994337, _994339, _994341, _994343] : [c_Fun_Oinj__on(_994335, _994337, _994339, _994341), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_994335, tc_HOL_Obool)), _994343), _994341)), -(c_Fun_Oinj__on(_994335, _994337, _994339, _994343))], (39797 ^ _781013) ^ [_1552533, _1552535, _1552537, _1552539] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1552533), tc_List_Olist(_1552533))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1552533), tc_List_Olist(_1552533)), _1552535), _1552537)), c_List_Olistrel(_1552533, _1552539)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552533)), _1552535) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552533)), _1552537), 39803 ^ _781013 : [(39806 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1552533, _1552533)), hAPP(hAPP(c_Product__Type_OPair(_1552533, _1552533), hAPP(hAPP(c_List_Onth(_1552533), _1552535), 39802 ^ [_1552533, _1552535, _1552537, _1552539])), hAPP(hAPP(c_List_Onth(_1552533), _1552537), 39802 ^ [_1552533, _1552535, _1552537, _1552539]))), _1552539))], (39804 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39802 ^ [_1552533, _1552535, _1552537, _1552539]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552533)), _1552535))))]]], (5591 ^ _781013) ^ [_869004, _869006, _869008, _869010] : [c_Hoare__Mirabelle_Ohoare__derivs(_869004, _869006, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_869004)), _869008), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_869004), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_869004, _869006, _869010), -(c_Hoare__Mirabelle_Ohoare__derivs(_869004, _869006, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_869004)), _869008), _869010)))], (11762 ^ _781013) ^ [_993129, _993131, _993133, _993135, _993137] : [c_Fun_Oinj__on(_993129, _993131, _993133, c_Orderings_Otop__class_Otop(tc_fun(_993129, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_993129, _993131, _993133), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_993129, tc_HOL_Obool)), _993135), _993137)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_993131, tc_HOL_Obool)), hAPP(c_Set_Oimage(_993129, _993131, _993133), _993135)), hAPP(c_Set_Oimage(_993129, _993131, _993133), _993137)))], (51352 ^ _781013) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (39511 ^ _781013) ^ [_1545303, _1545305] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1545303), _1545305))), -(c_Nitpick_Ocard_H(_1545303, _1545305) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30829 ^ _781013) ^ [_1357852, _1357854, _1357856] : [class_Orderings_Olinorder(_1357852), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357852), _1357854)), 30836 ^ _781013 : [(30843 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357852, tc_HOL_Obool)), _1357854), hAPP(hAPP(c_Set_Oinsert(_1357852), _1357856), c_Orderings_Obot__class_Obot(tc_fun(_1357852, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1357852, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1357852, c_Orderings_Oord__class_Omax(_1357852), hAPP(hAPP(c_Set_Oinsert(_1357852), _1357856), _1357854)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357852), _1357856), c_Big__Operators_Olattice_OSup__fin(_1357852, c_Orderings_Oord__class_Omax(_1357852), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357852, tc_HOL_Obool)), _1357854), hAPP(hAPP(c_Set_Oinsert(_1357852), _1357856), c_Orderings_Obot__class_Obot(tc_fun(_1357852, tc_HOL_Obool)))))))], (30837 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357852, tc_HOL_Obool)), _1357854), hAPP(hAPP(c_Set_Oinsert(_1357852), _1357856), c_Orderings_Obot__class_Obot(tc_fun(_1357852, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1357852, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1357852, c_Orderings_Oord__class_Omax(_1357852), hAPP(hAPP(c_Set_Oinsert(_1357852), _1357856), _1357854)) = _1357856)]]], (51036 ^ _781013) ^ [_1818855, _1818857] : [class_Orderings_Opreorder(_1818855), -(class_Orderings_Opreorder(tc_fun(_1818857, _1818855)))], (31926 ^ _781013) ^ [_1386272, _1386274, _1386276, _1386278, _1386280] : [_1386272 = c_Orderings_Obot__class_Obot(tc_fun(_1386274, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1386276), _1386278), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386274, tc_fun(_1386276, tc_HOL_Obool)), _1386272), _1386280)) = hAPP(hAPP(c_Set_Oinsert(_1386276), _1386278), c_Orderings_Obot__class_Obot(tc_fun(_1386276, tc_HOL_Obool))))], (49025 ^ _781013) ^ [_1774891, _1774893] : [-(c_Relation_Orefl__on(_1774891, c_Orderings_Otop__class_Otop(tc_fun(_1774891, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774891, _1774891), tc_HOL_Obool)), _1774893), c_Relation_OId(_1774891))))], (14449 ^ _781013) ^ [_1048946, _1048948, _1048950] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048946), c_Map_Odom(_1048946, _1048948, _1048950))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048946), c_Orderings_Otop__class_Otop(tc_fun(_1048946, tc_HOL_Obool))))), -(hAPP(_1048950, 14456 ^ [_1048946, _1048948, _1048950]) = c_Option_Ooption_ONone(_1048948))], (28068 ^ _781013) ^ [_1304996, _1304998] : [-(_1304996 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1304998), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1304996), _1304998))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304996, _1304998)))], (49277 ^ _781013) ^ [_1781394, _1781396] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1781394, _1781394)), hAPP(hAPP(c_Product__Type_OPair(_1781394, _1781394), 49278 ^ [_1781394, _1781396]), 49278 ^ [_1781394, _1781396])), c_Transitive__Closure_Otrancl(_1781394, _1781396)))), -(c_Wellfounded_Oacyclic(_1781394, _1781396))], (22232 ^ _781013) ^ [_1197888, _1197890] : [class_Divides_Osemiring__div(_1197888), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1197888), _1197890), c_Groups_Ozero__class_Ozero(_1197888)) = c_Groups_Ozero__class_Ozero(_1197888))], (9743 ^ _781013) ^ [_953243, _953245, _953247] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953243, tc_HOL_Obool)), _953245), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953243, tc_HOL_Obool)), _953245), _953247)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953243, tc_HOL_Obool)), _953245), _953247))], (51332 ^ _781013) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (26465 ^ _781013) ^ [_1273305, _1273307, _1273309, _1273311] : [class_Groups_Ocomm__monoid__add(_1273305), 26468 ^ _781013 : [(26475 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1273307)), _1273309))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1273305), _1273311), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1273309, hAPP(c_Nat_OSuc, _1273307))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273305), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1273305), _1273311), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1273309, _1273307))), hAPP(_1273311, hAPP(c_Nat_OSuc, _1273307))))], (26469 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1273307)), _1273309)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1273305), _1273311), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1273309, hAPP(c_Nat_OSuc, _1273307))) = c_Groups_Ozero__class_Ozero(_1273305))]]], (16275 ^ _781013) ^ [_1081798, _1081800, _1081802] : [class_Groups_Ocomm__monoid__add(_1081798), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081800, _1081798), _1081802), c_Orderings_Obot__class_Obot(tc_fun(_1081800, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1081798))], (5609 ^ _781013) ^ [_869368, _869370, _869372, _869374, _869376] : [hAPP(_869368, _869370) = hAPP(c_Option_Ooption_OSome(_869372), _869374), -(hAPP(hAPP(c_Set_Oinsert(_869376), _869370), c_Map_Odom(_869376, _869372, _869368)) = c_Map_Odom(_869376, _869372, _869368))], (37042 ^ _781013) ^ [_1487889, _1487891, _1487893, _1487895, _1487897] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1487889, _1487891), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1487893), _1487895))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1487891)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1487897), _1487889), _1487891), 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), _1487897), _1487893)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1487897), _1487895)), _1487891))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1487897), _1487895), _1487891)))))], (13719 ^ _781013) ^ [_1032955, _1032957, _1032959, _1032961] : [class_Rings_Ocomm__semiring__1(_1032955), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032955), _1032957), _1032959)), _1032961) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032955), _1032957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032955), _1032959), _1032961)))], (34307 ^ _781013) ^ [_1431631, _1431633] : [c_Int_Oiszero(_1431631, hAPP(c_Int_Onumber__class_Onumber__of(_1431631), c_Int_OBit1(_1431633))), class_Int_Onumber__ring(_1431631), class_Int_Oring__char__0(_1431631)], (8637 ^ _781013) ^ [_930857, _930859, _930861, _930863] : [class_Lattices_Osemilattice__sup(_930857), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930857), _930859), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930857), _930861), _930863)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930857), _930861), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930857), _930859), _930863)))], (35651 ^ _781013) ^ [_1455518, _1455520] : [class_Int_Onumber__ring(_1455518), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1455518), _1455520), hAPP(c_Int_Onumber__class_Onumber__of(_1455518), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1455518), _1455520))], (17581 ^ _781013) ^ [_1109720, _1109722, _1109724] : [-(hBOOL(hAPP(_1109720, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109722), _1109724)))), 17584 ^ _781013 : [(17587 ^ _781013) ^ [] : [hBOOL(hAPP(_1109720, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17585 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109722), _1109724)))]], 17589 ^ _781013 : [(17592 ^ _781013) ^ [] : [hBOOL(hAPP(_1109720, 17588 ^ [_1109720, _1109722, _1109724]))], (17590 ^ _781013) ^ [] : [-(_1109722 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109724), 17588 ^ [_1109720, _1109722, _1109724]))]]], (8595 ^ _781013) ^ [_930064, _930066] : [class_Lattices_Osemilattice__sup(_930064), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930064), _930066), _930066) = _930066)], (50828 ^ _781013) ^ [_1814271, _1814273] : [-(c_List_Osplice(_1814271, _1814273, c_List_Olist_ONil(_1814271)) = _1814273)], (22822 ^ _781013) ^ [_1207963, _1207965, _1207967, _1207969] : [class_Divides_Osemiring__div(_1207963), -(_1207965 = c_Groups_Ozero__class_Ozero(_1207963)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207963), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207963), _1207967), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207963), _1207965), _1207969))), _1207965) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207963), _1207969), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207963), _1207967), _1207965)))], (27043 ^ _781013) ^ [_1284429, _1284431, _1284433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284429)), 27046 ^ _781013 : [(27047 ^ _781013) ^ [_1284563] : [27049 ^ _781013 : [(27055 ^ _781013) ^ [] : [-(_1284563 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27051 ^ [_1284429, _1284431, _1284433, _1284563]), 27048 ^ [_1284429, _1284431, _1284433, _1284563]))], (27053 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27051 ^ [_1284429, _1284431, _1284433, _1284563]), _1284431)))], (27050 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27048 ^ [_1284429, _1284431, _1284433, _1284563]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1284429))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284433), _1284563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284433), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1284563), _1284429))))]]], (15863 ^ _781013) ^ [_1074505, _1074507, _1074509] : [class_Rings_Olinordered__semiring__strict(_1074505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074505), c_Groups_Ozero__class_Ozero(_1074505)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074505), _1074507), _1074509))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074505), c_Groups_Ozero__class_Ozero(_1074505)), _1074507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074505), c_Groups_Ozero__class_Ozero(_1074505)), _1074509)))], (38810 ^ _781013) ^ [_1528752, _1528754] : [hBOOL(hAPP(c_List_Odistinct(_1528752), _1528754)), -(hAPP(c_Finite__Set_Ocard(_1528752), hAPP(c_List_Oset(_1528752), _1528754)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528752)), _1528754))], (50878 ^ _781013) ^ [_1815427, _1815429, _1815431, _1815433, _1815435] : [hBOOL(hAPP(hAPP(_1815431, _1815435), _1815433)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815427, _1815429, _1815431), _1815433), _1815435)))], (41706 ^ _781013) ^ [_1604121, _1604123, _1604125] : [c_List_Olist_ONil(_1604121) = hAPP(hAPP(c_List_Oappend(_1604121), _1604123), _1604125), 41709 ^ _781013 : [(41712 ^ _781013) ^ [] : [-(_1604125 = c_List_Olist_ONil(_1604121))], (41710 ^ _781013) ^ [] : [-(_1604123 = c_List_Olist_ONil(_1604121))]]], (7053 ^ _781013) ^ [_897803, _897805, _897807, _897809] : [hBOOL(hAPP(hAPP(c_member(_897803), _897805), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897803, tc_HOL_Obool)), _897807), _897809))), 7056 ^ _781013 : [(7059 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_897803), _897805), _897809))], (7057 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_897803), _897805), _897807)))]]], (32552 ^ _781013) ^ [_1398770, _1398772, _1398774] : [class_Int_Onumber__ring(_1398770), -(hAPP(c_Int_Onumber__class_Onumber__of(_1398770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1398772), _1398774)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398770), hAPP(c_Int_Onumber__class_Onumber__of(_1398770), _1398772)), hAPP(c_Int_Onumber__class_Onumber__of(_1398770), _1398774)))], (9040 ^ _781013) ^ [_939967, _939969, _939971, _939973] : [c_Finite__Set_Ofolding__one(_939967, _939969, _939971), hBOOL(hAPP(c_Finite__Set_Ofinite(_939967), _939973)), -(_939973 = c_Orderings_Obot__class_Obot(tc_fun(_939967, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_939967), hAPP(hAPP(_939969, 9053 ^ [_939967, _939969, _939971, _939973]), 9054 ^ [_939967, _939969, _939971, _939973])), hAPP(hAPP(c_Set_Oinsert(_939967), 9053 ^ [_939967, _939969, _939971, _939973]), hAPP(hAPP(c_Set_Oinsert(_939967), 9054 ^ [_939967, _939969, _939971, _939973]), c_Orderings_Obot__class_Obot(tc_fun(_939967, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_939967), hAPP(_939971, _939973)), _939973)))], (51224 ^ _781013) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (35141 ^ _781013) ^ [_1446155, _1446157] : [class_Rings_Olinordered__idom(_1446155), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446155), c_Groups_Ozero__class_Ozero(_1446155)), hAPP(hAPP(c_Power_Opower__class_Opower(_1446155), _1446157), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (27759 ^ _781013) ^ [_1299405, _1299407, _1299409, _1299411, _1299413, _1299415] : [class_Divides_Oring__div(_1299405), c_Divides_Odiv__class_Omod(_1299405, _1299407, _1299409) = c_Divides_Odiv__class_Omod(_1299405, _1299411, _1299409), c_Divides_Odiv__class_Omod(_1299405, _1299413, _1299409) = c_Divides_Odiv__class_Omod(_1299405, _1299415, _1299409), -(c_Divides_Odiv__class_Omod(_1299405, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1299405), _1299407), _1299413), _1299409) = c_Divides_Odiv__class_Omod(_1299405, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1299405), _1299411), _1299415), _1299409))], (41402 ^ _781013) ^ [_1596775, _1596777, _1596779] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596775), tc_List_Olist(_1596775))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596775), tc_List_Olist(_1596775)), _1596777), c_List_Olist_ONil(_1596775))), c_List_Olistrel1(_1596775, _1596779)))], (40801 ^ _781013) ^ [_1581728, _1581730, _1581732] : [-(c_Relation_Orefl__on(_1581728, _1581730, _1581732)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581728, _1581728), tc_HOL_Obool)), _1581732), hAPP(hAPP(c_Product__Type_OSigma(_1581728, _1581728), _1581730), hAPP(c_COMBK(tc_fun(_1581728, tc_HOL_Obool), _1581728), _1581730)))), 40807 ^ _781013 : [(40810 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581728, _1581728)), hAPP(hAPP(c_Product__Type_OPair(_1581728, _1581728), 40806 ^ [_1581728, _1581730, _1581732]), 40806 ^ [_1581728, _1581730, _1581732])), _1581732))], (40808 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1581728), 40806 ^ [_1581728, _1581730, _1581732]), _1581730)))]]], (20621 ^ _781013) ^ [_1166543] : [class_Rings_Oring__1(_1166543), -(hBOOL(hAPP(hAPP(c_member(_1166543), c_Groups_Oone__class_Oone(_1166543)), c_Int_Oring__1__class_OInts(_1166543))))], (19664 ^ _781013) ^ [_1149069, _1149071, _1149073, _1149075] : [class_Rings_Olinordered__semidom(_1149069), hAPP(hAPP(c_Power_Opower__class_Opower(_1149069), _1149071), _1149073) = hAPP(hAPP(c_Power_Opower__class_Opower(_1149069), _1149075), _1149073), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149069), c_Groups_Ozero__class_Ozero(_1149069)), _1149071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149069), c_Groups_Ozero__class_Ozero(_1149069)), _1149075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1149073)), -(_1149071 = _1149075)], (33608 ^ _781013) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (25996 ^ _781013) ^ [_1264315, _1264317] : [class_Rings_Olinordered__idom(_1264315), 25999 ^ _781013 : [(26006 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264317), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264315), hAPP(c_Int_Oring__1__class_Oof__int(_1264315), _1264317)), c_Groups_Ozero__class_Ozero(_1264315))))], (26000 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264315), hAPP(c_Int_Oring__1__class_Oof__int(_1264315), _1264317)), c_Groups_Ozero__class_Ozero(_1264315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264317), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (44044 ^ _781013) ^ [_1657966, _1657968, _1657970] : [class_Orderings_Olinorder(_1657966), 44047 ^ _781013 : [(44060 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1657966, hAPP(hAPP(c_List_Olist_OCons(_1657966), _1657968), _1657970))), 44064 ^ _781013 : [(44067 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1657966), _1657968), 44063 ^ [_1657966, _1657968, _1657970]))], (44065 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1657966), 44063 ^ [_1657966, _1657968, _1657970]), hAPP(c_List_Oset(_1657966), _1657970))))]], c_List_Olinorder__class_Osorted(_1657966, _1657970)], (44048 ^ _781013) ^ [] : [c_List_Olinorder__class_Osorted(_1657966, hAPP(hAPP(c_List_Olist_OCons(_1657966), _1657968), _1657970)), 44051 ^ _781013 : [(44052 ^ _781013) ^ [_1658134] : [hBOOL(hAPP(hAPP(c_member(_1657966), _1658134), hAPP(c_List_Oset(_1657966), _1657970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1657966), _1657968), _1658134)))], (44058 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1657966, _1657970))]]]]], (5084 ^ _781013) ^ [_858554, _858556, _858558, _858560] : [-(c_New__DSequence_Oneg__single(_858560, _858556) = c_New__DSequence_Oneg__single(_858558, _858554)), _858560 = _858558, _858556 = _858554], (11880 ^ _781013) ^ [_995290, _995292] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_995290, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_995290, tc_HOL_Obool))), _995292) = _995292)], (4622 ^ _781013) ^ [_850977, _850979, _850981, _850983, _850985, _850987] : [-(c_Product__Type_Ointernal__split(_850987, _850983, _850979) = c_Product__Type_Ointernal__split(_850985, _850981, _850977)), _850987 = _850985, _850983 = _850981, _850979 = _850977], (32376 ^ _781013) ^ [_1395308, _1395310, _1395312, _1395314, _1395316] : [c_Com_Ocom_OLocal(_1395308, _1395310, _1395312) = c_Com_Ocom_OWhile(_1395314, _1395316)], (46444 ^ _781013) ^ [_1711683, _1711685, _1711687] : [hBOOL(hAPP(hAPP(c_member(_1711683), _1711687), c_Wellfounded_Oacc(_1711683, _1711685))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1711683, hAPP(hAPP(c_COMBC(_1711683, tc_fun(tc_prod(_1711683, _1711683), tc_HOL_Obool), tc_fun(_1711683, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711683, tc_fun(tc_fun(tc_prod(_1711683, _1711683), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1711683, _1711683), tc_HOL_Obool), tc_fun(_1711683, tc_HOL_Obool)), _1711683), c_COMBC(_1711683, tc_fun(tc_prod(_1711683, _1711683), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711683, tc_prod(_1711683, _1711683)), tc_fun(_1711683, tc_fun(tc_fun(tc_prod(_1711683, _1711683), tc_HOL_Obool), tc_HOL_Obool)), _1711683), hAPP(c_COMBB(tc_prod(_1711683, _1711683), tc_fun(tc_fun(tc_prod(_1711683, _1711683), tc_HOL_Obool), tc_HOL_Obool), _1711683), c_member(tc_prod(_1711683, _1711683)))), c_Product__Type_OPair(_1711683, _1711683)))), _1711685)), _1711687)))], (6798 ^ _781013) ^ [_893054, _893056, _893058, _893060] : [_893054 = _893056, 6803 ^ _781013 : [(6806 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893058), _893060), _893056)))], (6804 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893058), _893060), _893054)))]], 6807 ^ _781013 : [(6810 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_893058), _893060), _893056))], (6808 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_893058), _893060), _893054))]]], (34527 ^ _781013) ^ [_1435107, _1435109] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1435107))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435109)) = 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)))), _1435107), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435109)))], (30169 ^ _781013) ^ [_1344647, _1344649, _1344651, _1344653, _1344655] : [class_Orderings_Olinorder(_1344647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344647), _1344649), _1344651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344647), _1344653), _1344655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344647), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344647), _1344649), _1344653)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344647), _1344651), _1344655))))], (1504 ^ _781013) ^ [_802555, _802557] : [-(class_Groups_Ocancel__ab__semigroup__add(_802555)), _802557 = _802555, class_Groups_Ocancel__ab__semigroup__add(_802557)], (39785 ^ _781013) ^ [_1552125, _1552127, _1552129, _1552131] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1552125), tc_List_Olist(_1552125))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1552125), tc_List_Olist(_1552125)), _1552127), _1552129)), c_List_Olistrel(_1552125, _1552131))), 39788 ^ _781013 : [(39791 ^ _781013) ^ [_1552354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1552354), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552125)), _1552127))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1552125, _1552125)), hAPP(hAPP(c_Product__Type_OPair(_1552125, _1552125), hAPP(hAPP(c_List_Onth(_1552125), _1552127), _1552354)), hAPP(hAPP(c_List_Onth(_1552125), _1552129), _1552354))), _1552131)))], (39789 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552125)), _1552127) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552125)), _1552129))]]], (30701 ^ _781013) ^ [_1355792, _1355794, _1355796] : [class_Orderings_Olinorder(_1355792), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355792), _1355794)), hBOOL(hAPP(hAPP(c_member(_1355792), _1355796), _1355794)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355792), _1355796), c_Big__Operators_Olattice_OSup__fin(_1355792, c_Orderings_Oord__class_Omax(_1355792), _1355794)) = c_Big__Operators_Olattice_OSup__fin(_1355792, c_Orderings_Oord__class_Omax(_1355792), _1355794))], (38278 ^ _781013) ^ [_1516059, _1516061, _1516063, _1516065, _1516067] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1516059), tc_List_Olist(_1516061), tc_List_Olist(_1516063), hAPP(c_List_Omap(_1516059, _1516061), _1516065)), hAPP(c_List_Omap(_1516063, _1516059), _1516067)) = hAPP(c_List_Omap(_1516063, _1516061), hAPP(c_Fun_Ocomp(_1516059, _1516061, _1516063, _1516065), _1516067)))], (47328 ^ _781013) ^ [_1735036, _1735038] : [c_Wellfounded_Owf(_1735036, _1735038), -(c_Wellfounded_OwfP(_1735036, c_FunDef_Oin__rel(_1735036, _1735036, _1735038)))], (4568 ^ _781013) ^ [_850182, _850184, _850186, _850188, _850190, _850192] : [-(c_Nitpick_Oplus__frac(_850192, _850188, _850184) = c_Nitpick_Oplus__frac(_850190, _850186, _850182)), _850192 = _850190, _850188 = _850186, _850184 = _850182], (35371 ^ _781013) ^ [_1450374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1450374)), -(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), _1450374), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (33620 ^ _781013) ^ [_1418608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1418608), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1418608)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (30445 ^ _781013) ^ [_1350127, _1350129, _1350131, _1350133] : [class_Orderings_Olinorder(_1350127), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1350127, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1350127, _1350129, _1350131)), hAPP(c_SetInterval_Oord__class_OatLeast(_1350127), _1350133)) = c_SetInterval_Oord__class_OatLeastAtMost(_1350127, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350127), _1350129), _1350133), _1350131))], (15939 ^ _781013) ^ [_1075906, _1075908, _1075910, _1075912] : [class_Rings_Olinordered__ring__strict(_1075906), 15942 ^ _781013 : [(15957 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075906), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075906), _1075908), _1075910)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075906), _1075908), _1075912)))), 15958 ^ _781013 : [(15965 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075906), _1075908), c_Groups_Ozero__class_Ozero(_1075906))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075906), _1075912), _1075910))], (15959 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075906), c_Groups_Ozero__class_Ozero(_1075906)), _1075908)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075906), _1075910), _1075912))]]], (15943 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075906), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075906), _1075908), _1075910)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075906), _1075908), _1075912))), 15948 ^ _781013 : [(15951 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075906), _1075910), _1075912)))], (15949 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075906), c_Groups_Ozero__class_Ozero(_1075906)), _1075908)))]], 15952 ^ _781013 : [(15955 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075906), _1075912), _1075910)))], (15953 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075906), _1075908), c_Groups_Ozero__class_Ozero(_1075906))))]]]]], (13731 ^ _781013) ^ [_1033241, _1033243, _1033245, _1033247] : [class_Rings_Ocomm__semiring__1(_1033241), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033241), _1033243), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033241), _1033245), _1033247)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033241), _1033245), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033241), _1033243), _1033247)))], (38666 ^ _781013) ^ [_1524810, _1524812, _1524814, _1524816, _1524818, _1524820, _1524822, _1524824] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1524810, _1524812), _1524814), _1524816), hAPP(hAPP(c_List_Ozip(_1524810, _1524812), _1524818), hAPP(hAPP(c_List_Omap(_1524820, _1524812), _1524822), _1524824))) = hAPP(hAPP(c_List_Omap(tc_prod(_1524810, _1524820), _1524814), hAPP(c_Product__Type_Oprod_Oprod__case(_1524810, _1524820, _1524814), hAPP(hAPP(c_COMBB(tc_fun(_1524820, tc_prod(_1524810, _1524812)), tc_fun(_1524820, _1524814), _1524810), hAPP(c_COMBB(tc_prod(_1524810, _1524812), _1524814, _1524820), _1524816)), hAPP(hAPP(c_COMBC(_1524810, tc_fun(_1524820, _1524812), tc_fun(_1524820, tc_prod(_1524810, _1524812))), hAPP(hAPP(c_COMBB(tc_fun(_1524812, tc_prod(_1524810, _1524812)), tc_fun(tc_fun(_1524820, _1524812), tc_fun(_1524820, tc_prod(_1524810, _1524812))), _1524810), c_COMBB(_1524812, tc_prod(_1524810, _1524812), _1524820)), c_Product__Type_OPair(_1524810, _1524812))), _1524822)))), hAPP(hAPP(c_List_Ozip(_1524810, _1524820), _1524818), _1524824)))], (42599 ^ _781013) ^ [_1625371, _1625373, _1625375] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625371), tc_List_Olist(_1625371))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625371), tc_List_Olist(_1625371)), c_List_Olist_ONil(_1625371)), _1625373)), c_List_Olexord(_1625371, _1625375))), -(_1625373 = hAPP(hAPP(c_List_Olist_OCons(_1625371), 42602 ^ [_1625371, _1625373, _1625375]), 42603 ^ [_1625371, _1625373, _1625375]))], (24946 ^ _781013) ^ [_1245949, _1245951, _1245953] : [class_Fields_Olinordered__field(_1245949), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245949), c_Groups_Ozero__class_Ozero(_1245949)), _1245951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245949), _1245953), c_Groups_Ozero__class_Ozero(_1245949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245949), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245949), _1245951), _1245953)), c_Groups_Ozero__class_Ozero(_1245949))))], (37393 ^ _781013) ^ [_1494783, _1494785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1494783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494785), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1494783, _1494785) = 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), _1494783), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1494785)))))], (44993 ^ _781013) ^ [_1679763] : [-(c_Enum_Osublists(_1679763, c_List_Olist_ONil(_1679763)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1679763)), c_List_Olist_ONil(_1679763)), c_List_Olist_ONil(tc_List_Olist(_1679763))))], (24222 ^ _781013) ^ [_1232820, _1232822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232820)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1232820), _1232822)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1232820)), _1232822))], (256 ^ _781013) ^ [_785113, _785115] : [-(c_Nat__Transfer_Ois__nat(_785113)), _785115 = _785113, c_Nat__Transfer_Ois__nat(_785115)], (27914 ^ _781013) ^ [_1302156, _1302158] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1302156), _1302158) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1302156, _1302158) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (12082 ^ _781013) ^ [_999073, _999075] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_999073), _999075)), 12085 ^ _781013 : [(12092 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_999073), c_Orderings_Otop__class_Otop(tc_fun(_999073, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_999073), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_999073, tc_HOL_Obool)), _999075))))], (12086 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_999073), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_999073, tc_HOL_Obool)), _999075))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_999073), c_Orderings_Otop__class_Otop(tc_fun(_999073, tc_HOL_Obool)))))]]], (22712 ^ _781013) ^ [_1205877, _1205879, _1205881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205877), 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)), _1205879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205879), _1205881)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205877), _1205879)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205877), _1205881))))], (38075 ^ _781013) ^ [_1510559, _1510561, _1510563, _1510565] : [_1510559 = _1510561, hBOOL(hAPP(hAPP(c_member(_1510563), _1510559), _1510565)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1510563, _1510563)), hAPP(hAPP(c_Product__Type_OPair(_1510563, _1510563), _1510559), _1510561)), c_Relation_OId__on(_1510563, _1510565))))], (40471 ^ _781013) ^ [_1572348, _1572350, _1572352, _1572354, _1572356, _1572358] : [hAPP(c_Set_Oimage(_1572348, _1572350, _1572352), c_Orderings_Otop__class_Otop(tc_fun(_1572348, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1572350, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1572354, _1572356, _1572358), c_Orderings_Otop__class_Otop(tc_fun(_1572354, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1572356, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1572348, _1572354), tc_prod(_1572350, _1572356), c_Product__Type_Omap__pair(_1572348, _1572350, _1572354, _1572356, _1572352, _1572358)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1572348, _1572354), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1572350, _1572356), tc_HOL_Obool)))], (8375 ^ _781013) ^ [_925129, _925131, _925133, _925135, _925137, _925139] : [-(hAPP(c_Set_Oimage(_925129, _925131, _925133), hAPP(c_Set_Oimage(_925135, _925129, _925137), _925139)) = hAPP(c_Set_Oimage(_925135, _925131, hAPP(hAPP(c_COMBB(_925129, _925131, _925135), _925133), _925137)), _925139))], (21788 ^ _781013) ^ [_1189964] : [class_Rings_Osemiring__1(_1189964), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189964), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1189964))], (43889 ^ _781013) ^ [_1654924, _1654926] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1654924, _1654926)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1654926), _1654924))], (37310 ^ _781013) ^ [_1492841, _1492843, _1492845, _1492847] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1492841), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1492843), _1492845)))), -(hBOOL(hAPP(hAPP(hAPP(_1492847, _1492841), _1492843), _1492845))), 37318 ^ _781013 : [(37321 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37316 ^ [_1492841, _1492843, _1492845, _1492847]), 37317 ^ [_1492841, _1492843, _1492845, _1492847]))), hAPP(37315 ^ [_1492841, _1492843, _1492845, _1492847], 37317 ^ [_1492841, _1492843, _1492845, _1492847]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1492847, 37315 ^ [_1492841, _1492843, _1492845, _1492847]), 37316 ^ [_1492841, _1492843, _1492845, _1492847]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 37317 ^ [_1492841, _1492843, _1492845, _1492847]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (37331 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1492847, 37315 ^ [_1492841, _1492843, _1492845, _1492847]), 37316 ^ [_1492841, _1492843, _1492845, _1492847]), 37317 ^ [_1492841, _1492843, _1492845, _1492847]))], (37319 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), 37315 ^ [_1492841, _1492843, _1492845, _1492847]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 37316 ^ [_1492841, _1492843, _1492845, _1492847]), 37317 ^ [_1492841, _1492843, _1492845, _1492847])))))]]], (42254 ^ _781013) ^ [_1617885, _1617887, _1617889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1617885), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617887)), _1617889))), -(hAPP(hAPP(c_List_Olist_OCons(_1617887), hAPP(hAPP(c_List_Onth(_1617887), _1617889), _1617885)), hAPP(hAPP(c_List_Odrop(_1617887), hAPP(c_Nat_OSuc, _1617885)), _1617889)) = hAPP(hAPP(c_List_Odrop(_1617887), _1617885), _1617889))], (27527 ^ _781013) ^ [_1294822, _1294824, _1294826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294822), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 27530 ^ _781013 : [(27531 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1294824, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1294826), _1294822)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1294826, _1294822))), 27534 ^ _781013 : [(27535 ^ _781013) ^ [_1295032, _1295034] : [-(hBOOL(hAPP(hAPP(_1294824, _1295034), _1295032))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294822), _1295032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295032), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1294826 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1294822), _1295034)), _1295032)]]], (27549 ^ _781013) ^ [] : [27552 ^ _781013 : [(27555 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 27551 ^ [_1294822, _1294824, _1294826]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27557 ^ _781013) ^ [] : [-(_1294826 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1294822), 27550 ^ [_1294822, _1294824, _1294826])), 27551 ^ [_1294822, _1294824, _1294826]))], (27559 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1294824, 27550 ^ [_1294822, _1294824, _1294826]), 27551 ^ [_1294822, _1294824, _1294826]))], (27553 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294822), 27551 ^ [_1294822, _1294824, _1294826])))]], -(hBOOL(hAPP(hAPP(_1294824, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1294826), _1294822)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1294826, _1294822))))]]], (38772 ^ _781013) ^ [_1528006, _1528008, _1528010, _1528012] : [class_Orderings_Olinorder(_1528006), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1528006, _1528006, c_COMBI(_1528006)), _1528008), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1528006, _1528006, c_COMBI(_1528006)), _1528010), _1528012)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1528006, _1528006, c_COMBI(_1528006)), _1528010), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1528006, _1528006, c_COMBI(_1528006)), _1528008), _1528012)))], (48673 ^ _781013) ^ [_1765765, _1765767] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1765765, _1765767) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1765765), hAPP(c_Code__Numeral_Onat__of, _1765767))))], (44250 ^ _781013) ^ [_1662637, _1662639] : [_1662639 = c_List_Olist_ONil(_1662637), -(c_List_Olist_ONil(_1662637) = hAPP(c_List_Orev(_1662637), _1662639))], (6284 ^ _781013) ^ [_883286, _883288, _883290] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_883286, _883288, _883290)], (47940 ^ _781013) ^ [_1749343, _1749345, _1749347, _1749349] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1749343, _1749345, _1749347, tc_prod(_1749345, _1749347)), _1749349), c_Product__Type_OPair(_1749345, _1749347)) = _1749349)], (29309 ^ _781013) ^ [_1327735, _1327737] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1327735, _1327737) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1327735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1327735), _1327737)), _1327737)))], (20394 ^ _781013) ^ [_1162029, _1162031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1162029)), _1162031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162029), _1162031)))], (35201 ^ _781013) ^ [_1447160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1447160), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1447160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1447160 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7939 ^ _781013) ^ [_915137, _915139, _915141, _915143] : [c_Hoare__Mirabelle_Ohoare__derivs(_915137, _915139, _915141), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_915137), tc_HOL_Obool)), _915139), _915143)), -(c_Hoare__Mirabelle_Ohoare__derivs(_915137, _915143, _915141))], (30283 ^ _781013) ^ [_1346812, _1346814, _1346816, _1346818] : [class_Orderings_Olinorder(_1346812), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346812), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346812), _1346814), _1346816)), _1346818) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346812), _1346814), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346812), _1346816), _1346818)))], (28864 ^ _781013) ^ [_1319531] : [class_Orderings_Olinorder(_1319531), -(c_Finite__Set_Ofun__left__comm__idem(_1319531, _1319531, c_Orderings_Oord__class_Omin(_1319531)))], (9807 ^ _781013) ^ [_954027, _954029] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_954027, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_954027, tc_HOL_Obool)), _954029)) = _954029)], (47291 ^ _781013) ^ [_1734416, _1734418] : [c_Wellfounded_Owf(_1734416, hAPP(c_Set_OCollect(tc_prod(_1734416, _1734416)), hAPP(c_Product__Type_Oprod_Oprod__case(_1734416, _1734416, tc_HOL_Obool), _1734418))), -(c_Wellfounded_OwfP(_1734416, _1734418))], (8947 ^ _781013) ^ [_937455, _937457] : [class_Lattices_Obounded__lattice__bot(_937455), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_937455), _937457), c_Orderings_Obot__class_Obot(_937455)) = _937457)], (32081 ^ _781013) ^ [_1390165, _1390167, _1390169, _1390171, _1390173, _1390175, _1390177] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390165, tc_fun(_1390167, tc_fun(_1390169, tc_HOL_Obool))), _1390171), _1390173), _1390175), _1390177)), 32085 ^ _781013 : [(32088 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1390173, 32084 ^ [_1390165, _1390167, _1390169, _1390171, _1390173, _1390175, _1390177]), _1390175), _1390177)))], (32086 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1390165), 32084 ^ [_1390165, _1390167, _1390169, _1390171, _1390173, _1390175, _1390177]), _1390171)))]]], (11221 ^ _781013) ^ [_981261, _981263, _981265, _981267, _981269, _981271, _981273, _981275] : [c_Finite__Set_Ofolding__image__simple(_981261, _981263, _981265, _981267, _981269, _981271), hBOOL(hAPP(c_Finite__Set_Ofinite(_981263), _981273)), hBOOL(hAPP(c_Finite__Set_Ofinite(_981263), _981275)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981263, tc_HOL_Obool)), _981273), _981275) = c_Orderings_Obot__class_Obot(tc_fun(_981263, tc_HOL_Obool)), -(hAPP(_981271, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_981263, tc_HOL_Obool)), _981273), _981275)) = hAPP(hAPP(_981265, hAPP(_981271, _981273)), hAPP(_981271, _981275)))], (34823 ^ _781013) ^ [_1440381] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1440381)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1440381)))], (35409 ^ _781013) ^ [_1451205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1451205)), -(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), _1451205), 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)))))))], (48101 ^ _781013) ^ [_1753068, _1753070] : [-(c_Random_Olog(_1753068, _1753070) = 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(_1753068, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1753070), _1753068)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1753068), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1753070), _1753068)))], (8743 ^ _781013) ^ [_933114, _933116, _933118, _933120, _933122] : [c_Hoare__Mirabelle_Ohoare__derivs(_933114, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_933114), tc_HOL_Obool)), _933116), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_933114), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933114)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933114))), hAPP(hAPP(c_COMBB(tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933114))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_933114)), _933118)), c_Com_Ocom_OBODY)), _933120)), _933122)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_933114), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933114)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933114))), hAPP(hAPP(c_COMBB(tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933114))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_933114)), _933118)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _933120)), _933122)), -(c_Hoare__Mirabelle_Ohoare__derivs(_933114, _933116, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_933114), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933114)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933114))), hAPP(hAPP(c_COMBB(tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_933114, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_933114))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_933114)), _933118)), c_Com_Ocom_OBODY)), _933120)), _933122)))], (47191 ^ _781013) ^ [_1731494, _1731496, _1731498] : [hAPP(c_Relation_ODomain(_1731494, _1731496), _1731498) = c_Orderings_Obot__class_Obot(tc_fun(_1731494, tc_HOL_Obool)), -(_1731498 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1731494, _1731496), tc_HOL_Obool)))], (47321 ^ _781013) ^ [_1734918, _1734920] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1734918, _1734920), 47322 ^ [_1734918, _1734920])), -(c_Wellfounded_OwfP(_1734918, _1734920))], (39975 ^ _781013) ^ [_1559105, _1559107, _1559109, _1559111] : [39977 ^ _781013 : [(39980 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1559105, _1559105, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1559105, tc_fun(_1559105, _1559107), tc_fun(_1559105, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559107, tc_HOL_Obool), tc_fun(tc_fun(_1559105, _1559107), tc_fun(_1559105, tc_HOL_Obool)), _1559105), c_COMBB(_1559107, tc_HOL_Obool, _1559105)), hAPP(hAPP(c_COMBB(_1559107, tc_fun(_1559107, tc_HOL_Obool), _1559105), c_fequal), _1559111))), _1559111)), 39976 ^ [_1559105, _1559107, _1559109, _1559111]))], (39978 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559105, _1559105)), 39976 ^ [_1559105, _1559107, _1559109, _1559111]), _1559109)))]], -(c_Equiv__Relations_Ocongruent(_1559105, _1559107, _1559109, _1559111))], (6932 ^ _781013) ^ [_895557, _895559, _895561, _895563, _895565, _895567] : [-(_895557 = _895559), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895561, _895563), _895565), _895559), _895567), _895557) = hAPP(_895565, _895557))], (5520 ^ _781013) ^ [_865184, _865186] : [_865186 = _865184, -(c_Option_Ooption_OSome(_865186) = c_Option_Ooption_OSome(_865184))], (45109 ^ _781013) ^ [_1682199, _1682201] : [class_Orderings_Olinorder(_1682199), -(c_List_Olinorder__class_Osorted(_1682199, c_List_Olinorder__class_Osort__key(_1682199, _1682199, c_COMBI(_1682199), _1682201)))], (12046 ^ _781013) ^ [_998243, _998245, _998247, _998249] : [-(hBOOL(hAPP(hAPP(c_member(_998243), hAPP(_998245, _998247)), hAPP(c_Set_Oimage(_998249, _998243, _998245), c_Orderings_Otop__class_Otop(tc_fun(_998249, tc_HOL_Obool))))))], (47091 ^ _781013) ^ [_1728724, _1728726, _1728728, _1728730] : [hBOOL(hAPP(hAPP(c_member(_1728724), _1728726), hAPP(c_Relation_ORange(_1728728, _1728724), _1728730))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1728728, _1728724)), hAPP(hAPP(c_Product__Type_OPair(_1728728, _1728724), 47094 ^ [_1728724, _1728726, _1728728, _1728730]), _1728726)), _1728730)))], (34677 ^ _781013) ^ [_1437909] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1437909)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1437909)))], (47480 ^ _781013) ^ [_1738374] : [-(_1738374 = hAPP(c_Int_OAbs__Integ, 47478 ^ [_1738374]))], (39038 ^ _781013) ^ [_1534201, _1534203, _1534205, _1534207, _1534209] : [class_Orderings_Olinorder(_1534201), hBOOL(hAPP(c_List_Odistinct(_1534203), _1534205)), -(hBOOL(hAPP(c_List_Odistinct(_1534203), c_List_Olinorder__class_Oinsort__insert__key(_1534203, _1534201, _1534207, _1534209, _1534205))))], (41482 ^ _781013) ^ [_1598854, _1598856] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1598854), tc_List_Olist(_1598854), c_List_Olistrel(_1598854, _1598856)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1598854)), c_List_Olist_ONil(_1598854)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1598854), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1598854)), c_List_Olist_ONil(_1598854)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1598854), tc_HOL_Obool))))], (27837 ^ _781013) ^ [_1300828, _1300830, _1300832] : [class_Divides_Osemiring__div(_1300828), -(c_Divides_Odiv__class_Omod(_1300828, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300828), _1300830), _1300832), _1300832) = c_Groups_Ozero__class_Ozero(_1300828))], (41270 ^ _781013) ^ [_1594480, _1594482, _1594484] : [-(hAPP(hAPP(c_List_Olist__update(_1594480, c_List_Olist_ONil(_1594480)), _1594482), _1594484) = c_List_Olist_ONil(_1594480))], (51578 ^ _781013) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (37546 ^ _781013) ^ [_1497925, _1497927] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1497925), _1497927) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1497925, _1497927)))], (44568 ^ _781013) ^ [_1670786, _1670788, _1670790, _1670792] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1670786), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1670786))), _1670788))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670790), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1670786))), c_List_Otranspose(_1670786, _1670788)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670792), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1670786))), hAPP(c_List_Ofilter(tc_List_Olist(_1670786), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1670786)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670790)), c_Nat_Osize__class_Osize(tc_List_Olist(_1670786)))), _1670788)))), -(hAPP(hAPP(c_List_Onth(_1670786), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1670786)), c_List_Otranspose(_1670786, _1670788)), _1670790)), _1670792) = hAPP(hAPP(c_List_Onth(_1670786), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1670786)), _1670788), _1670792)), _1670790))], (28146 ^ _781013) ^ [_1306316, _1306318, _1306320, _1306322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1306316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306318), _1306320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1306320), 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), _1306318), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1306322, _1306316))), _1306320)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8432 ^ _781013) ^ [_926368, _926370, _926372, _926374] : [_926374 = c_Orderings_Obot__class_Obot(tc_fun(_926370, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_926368, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_926370, _926368, _926372), _926374))], (23339 ^ _781013) ^ [_1217561, _1217563, _1217565] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_1217561, _1217563, _1217565)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1217563)), c_Com_Ocom_Ocom__size(_1217565))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9727 ^ _781013) ^ [_952899, _952901, _952903] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952899, tc_HOL_Obool)), _952901) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952899, tc_HOL_Obool)), _952903), -(_952901 = _952903)], (19002 ^ _781013) ^ [_1136493, _1136495, _1136497, _1136499] : [hBOOL(hAPP(hAPP(c_member(_1136493), _1136495), c_SetInterval_Oord_OatMost(_1136493, _1136497, _1136499))), -(hBOOL(hAPP(hAPP(_1136497, _1136495), _1136499)))], (51142 ^ _781013) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (19310 ^ _781013) ^ [_1142682, _1142684, _1142686] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142682), _1142684)), _1142686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142684), _1142686)))], (49077 ^ _781013) ^ [_1776202, _1776204, _1776206] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776202, _1776202)), _1776204), c_Transitive__Closure_Ortrancl(_1776202, _1776206))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776202, _1776202)), _1776204), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1776202, _1776202), 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(_1776202, _1776202), tc_HOL_Obool), tc_fun(tc_prod(_1776202, _1776202), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1776202, _1776202), tc_HOL_Obool)), _1776206)))))], (36810 ^ _781013) ^ [_1483502, _1483504] : [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), _1483502))), 36813 ^ _781013 : [(36820 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1483504)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1483502)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1483504), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1483502)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1483502)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1483504), 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), _1483502)))))], (36814 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1483504)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1483502))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1483504), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1483502)) = 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), _1483504)))]]], (48808 ^ _781013) ^ [_1769440, _1769442] : [-(hAPP(c_Relation_Oconverse(_1769440, _1769440), c_Relation_OId__on(_1769440, _1769442)) = c_Relation_OId__on(_1769440, _1769442))], (37556 ^ _781013) ^ [_1498258, _1498260, _1498262] : [-(c_HOL_OThe(tc_prod(_1498258, _1498260), hAPP(c_Product__Type_Oprod_Oprod__case(_1498258, _1498260, tc_HOL_Obool), _1498262)) = c_HOL_OThe(tc_prod(_1498258, _1498260), hAPP(hAPP(c_COMBS(tc_prod(_1498258, _1498260), _1498260, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1498258, tc_fun(_1498260, tc_HOL_Obool), tc_prod(_1498258, _1498260)), _1498262), c_Product__Type_Ofst(_1498258, _1498260))), c_Product__Type_Osnd(_1498258, _1498260))))], (15545 ^ _781013) ^ [_1068549, _1068551, _1068553, _1068555] : [class_Rings_Oordered__ring(_1068549), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068549), _1068551), _1068553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068549), _1068555), c_Groups_Ozero__class_Ozero(_1068549))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068549), _1068553), _1068555)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068549), _1068551), _1068555))))], (22164 ^ _781013) ^ [_1196732, _1196734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1196732), _1196734)), -(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)), _1196732)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1196734))))], (11922 ^ _781013) ^ [_996026, _996028, _996030, _996032, _996034] : [-(hAPP(c_Set_Oimage(_996026, _996028, hAPP(hAPP(c_COMBB(_996030, _996028, _996026), _996032), _996034)), c_Orderings_Otop__class_Otop(tc_fun(_996026, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_996030, _996028, _996032), hAPP(c_Set_Oimage(_996026, _996030, _996034), c_Orderings_Otop__class_Otop(tc_fun(_996026, tc_HOL_Obool)))))], (51296 ^ _781013) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (27364 ^ _781013) ^ [_1290933, _1290935, _1290937, _1290939, _1290941] : [class_Groups_Ocomm__monoid__add(_1290933), class_Groups_Ocomm__monoid__mult(_1290933), _1290935 = _1290937, c_Nat__Transfer_Onat__set(_1290937), 27382 ^ _781013 : [(27385 ^ _781013) ^ [] : [hAPP(_1290939, 27381 ^ [_1290933, _1290935, _1290937, _1290939, _1290941]) = hAPP(_1290941, 27381 ^ [_1290933, _1290935, _1290937, _1290939, _1290941])], (27383 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27381 ^ [_1290933, _1290935, _1290937, _1290939, _1290941])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1290933), _1290939), _1290935) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1290933), _1290941), _1290937))], (13431 ^ _781013) ^ [_1026389, _1026391] : [class_Groups_Omonoid__mult(_1026389), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026389), _1026391), c_Groups_Oone__class_Oone(_1026389)) = _1026391)], (39552 ^ _781013) ^ [_1545938, _1545940, _1545942] : [39553 ^ _781013 : [(39554 ^ _781013) ^ [_1545992] : [hBOOL(hAPP(_1545938, _1545992))]], _1545940 = c_Hilbert__Choice_OEps(_1545942, _1545938), -(hBOOL(hAPP(_1545938, _1545940)))], (19496 ^ _781013) ^ [_1145909, _1145911, _1145913, _1145915] : [class_Rings_Olinordered__semidom(_1145909), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145909), c_Groups_Oone__class_Oone(_1145909)), _1145911)), 19503 ^ _781013 : [(19510 ^ _781013) ^ [] : [_1145913 = _1145915, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1145909), _1145911), _1145913) = hAPP(hAPP(c_Power_Opower__class_Opower(_1145909), _1145911), _1145915))], (19504 ^ _781013) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1145909), _1145911), _1145913) = hAPP(hAPP(c_Power_Opower__class_Opower(_1145909), _1145911), _1145915), -(_1145913 = _1145915)]]], (43767 ^ _781013) ^ [_1652871, _1652873, _1652875] : [class_Orderings_Olinorder(_1652871), c_List_Olinorder__class_Osorted(_1652871, _1652873), -(c_List_Olinorder__class_Osorted(_1652871, c_List_Olinorder__class_Oinsort__insert__key(_1652871, _1652871, c_COMBI(_1652871), _1652875, _1652873)))], (44398 ^ _781013) ^ [_1665814, _1665816, _1665818, _1665820] : [-(hAPP(hAPP(c_List_Omap(_1665814, _1665816), _1665818), c_List_Oconcat(_1665814, _1665820)) = c_List_Oconcat(_1665816, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1665814), tc_List_Olist(_1665816)), hAPP(c_List_Omap(_1665814, _1665816), _1665818)), _1665820)))], (51312 ^ _781013) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (48247 ^ _781013) ^ [_1755644, _1755646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755644), _1755646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1755644)), hAPP(c_Code__Numeral_Oof__nat, _1755646))))], (42962 ^ _781013) ^ [_1634058, _1634060, _1634062, _1634064, _1634066, _1634068] : [hBOOL(hAPP(hAPP(c_member(_1634058), _1634060), _1634062)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634058, tc_fun(_1634064, tc_HOL_Obool)), _1634062), hAPP(hAPP(c_COMBB(tc_fun(_1634064, tc_HOL_Obool), tc_fun(_1634064, tc_HOL_Obool), _1634058), hAPP(c_Set_Oinsert(_1634064), _1634066)), _1634068)) = hAPP(hAPP(c_Set_Oinsert(_1634064), _1634066), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634058, tc_fun(_1634064, tc_HOL_Obool)), _1634062), _1634068)))], (23687 ^ _781013) ^ [_1223776] : [hBOOL(hAPP(_1223776, 23688 ^ [_1223776])), 23691 ^ _781013 : [(23692 ^ _781013) ^ [_1223870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223870)), -(hBOOL(hAPP(_1223776, hAPP(c_Int_Onat, _1223870))))]]], (8255 ^ _781013) ^ [_922086, _922088, _922090, _922092] : [8256 ^ _781013 : [(8259 ^ _781013) ^ [] : [hBOOL(hAPP(_922090, _922088))], (8257 ^ _781013) ^ [] : [hBOOL(hAPP(_922086, _922088))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922092, tc_HOL_Obool)), _922090), _922086), _922088)))], (22326 ^ _781013) ^ [_1199429, _1199431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199429)), 22329 ^ _781013 : [(22336 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199431), 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), _1199431), _1199429)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22330 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1199431), _1199429)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199431), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (27779 ^ _781013) ^ [_1299831, _1299833, _1299835, _1299837] : [class_Divides_Oring__div(_1299831), -(c_Divides_Odiv__class_Omod(_1299831, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1299831), _1299833), _1299835), _1299837) = c_Divides_Odiv__class_Omod(_1299831, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1299831), c_Divides_Odiv__class_Omod(_1299831, _1299833, _1299837)), _1299835), _1299837))], (7321 ^ _781013) ^ [_903247, _903249, _903251, _903253] : [class_Orderings_Oord(_903247), _903249 = _903251, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903247), _903251), _903253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903247), _903249), _903253)))], (22382 ^ _781013) ^ [_1200335] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1200335) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1200335))], (50319 ^ _781013) ^ [_1804320, _1804322, _1804324] : [50321 ^ _781013 : [(50324 ^ _781013) ^ [] : [hBOOL(hAPP(_1804322, 50320 ^ [_1804320, _1804322, _1804324]))], (50322 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804320), 50320 ^ [_1804320, _1804322, _1804324]), hAPP(c_List_Oset(_1804320), _1804324))))]], -(c_List_Olist__all(_1804320, _1804322, _1804324))], (5771 ^ _781013) ^ [_872722, _872724, _872726, _872728, _872730, _872732] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_872722, _872724, _872726, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872722), _872728), _872730), _872732)) = hAPP(hAPP(hAPP(_872726, _872728), _872730), _872732))], (8347 ^ _781013) ^ [_924260, _924262, _924264, _924266, _924268, _924270] : [c_Hoare__Mirabelle_Ohoare__derivs(_924260, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_924260), tc_HOL_Obool)), _924262), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_924260), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_924260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_924260)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_924260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_924260))), hAPP(hAPP(c_COMBB(tc_fun(_924260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_924260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_924260))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_924260)), _924264)), c_Com_Ocom_OBODY)), _924266)), _924268)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_924260), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_924260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_924260)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_924260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_924260))), hAPP(hAPP(c_COMBB(tc_fun(_924260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_924260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_924260))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_924260)), _924264)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _924266)), _924268)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _924270), _924268)), -(c_Hoare__Mirabelle_Ohoare__derivs(_924260, _924262, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_924260)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_924260), hAPP(_924264, _924270)), hAPP(c_Com_Ocom_OBODY, _924270)), hAPP(_924266, _924270))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_924260), tc_HOL_Obool)))))], (34533 ^ _781013) ^ [_1435256, _1435258] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1435256)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435258)) = 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)))), _1435256)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435258)))], (41442 ^ _781013) ^ [_1597770, _1597772, _1597774] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1597770)), -(c_List_Osublist(_1597772, hAPP(hAPP(c_List_Olist_OCons(_1597772), _1597774), c_List_Olist_ONil(_1597772)), _1597770) = hAPP(hAPP(c_List_Olist_OCons(_1597772), _1597774), c_List_Olist_ONil(_1597772)))], (21283 ^ _781013) ^ [] : [-(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)))], (37704 ^ _781013) ^ [_1501323] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1501323)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1501323)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (39779 ^ _781013) ^ [_1552025, _1552027, _1552029, _1552031] : [-(_1552025 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552027)), _1552029)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1552027, hAPP(hAPP(c_List_Olist__update(_1552027, _1552029), _1552025), _1552031)) = hAPP(hAPP(c_List_Olist__update(_1552027, c_List_Obutlast(_1552027, _1552029)), _1552025), _1552031))], (45986 ^ _781013) ^ [_1701089, _1701091, _1701093] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1701089, tc_HOL_Obool)), _1701091), _1701093) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1701089, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1701089, tc_HOL_Obool)), _1701091), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1701089, tc_HOL_Obool)), _1701093), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1701089, tc_HOL_Obool), tc_HOL_Obool))))))], (30347 ^ _781013) ^ [_1347967, _1347969, _1347971, _1347973] : [class_Orderings_Olinorder(_1347967), 30350 ^ _781013 : [(30359 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347967), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347967), _1347969), _1347971)), _1347973))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347967), _1347969), _1347973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347967), _1347971), _1347973))], (30351 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347967), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347967), _1347969), _1347971)), _1347973)), 30354 ^ _781013 : [(30357 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347967), _1347971), _1347973)))], (30355 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347967), _1347969), _1347973)))]]]]], (47499 ^ _781013) ^ [_1738877, _1738879, _1738881, _1738883] : [47501 ^ _781013 : [(47504 ^ _781013) ^ [] : [hBOOL(hAPP(_1738881, 47500 ^ [_1738877, _1738879, _1738881, _1738883]))], (47502 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738877), 47500 ^ [_1738877, _1738879, _1738881, _1738883]), hAPP(c_List_Oset(_1738877), _1738879))))]], -(c_List_OdropWhile(_1738877, _1738881, hAPP(hAPP(c_List_Oappend(_1738877), _1738879), _1738883)) = c_List_OdropWhile(_1738877, _1738881, _1738883))], (36548 ^ _781013) ^ [_1478276, _1478278, _1478280, _1478282, _1478284, _1478286] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478276, tc_fun(_1478278, tc_HOL_Obool))), _1478280), _1478282), _1478284), _1478286)), -(hBOOL(hAPP(hAPP(_1478282, _1478284), _1478286)))], (47053 ^ _781013) ^ [_1727818, _1727820, _1727822] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1727818), _1727820), _1727822) = c_Nitpick_OAbs__Frac(_1727818, c_Nitpick_Onorm__frac(_1727820, _1727822)))], (35335 ^ _781013) ^ [_1449667, _1449669, _1449671] : [class_Rings_Ocomm__semiring__1(_1449667), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1449667), _1449669), 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)))), _1449671))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1449667), _1449669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1449667), hAPP(hAPP(c_Power_Opower__class_Opower(_1449667), _1449669), _1449671)), hAPP(hAPP(c_Power_Opower__class_Opower(_1449667), _1449669), _1449671))))], (1744 ^ _781013) ^ [_805555, _805557] : [-(class_Rings_Omult__zero(_805555)), _805557 = _805555, class_Rings_Omult__zero(_805557)], (38284 ^ _781013) ^ [_1516228, _1516230, _1516232, _1516234, _1516236] : [-(hAPP(c_Map_Omap__of(_1516228, _1516230), hAPP(hAPP(c_List_Omap(tc_prod(_1516228, _1516232), tc_prod(_1516228, _1516230)), hAPP(c_Product__Type_Oprod_Oprod__case(_1516228, _1516232, tc_prod(_1516228, _1516230)), hAPP(hAPP(c_COMBC(_1516228, tc_fun(_1516232, _1516230), tc_fun(_1516232, tc_prod(_1516228, _1516230))), hAPP(hAPP(c_COMBB(tc_fun(_1516230, tc_prod(_1516228, _1516230)), tc_fun(tc_fun(_1516232, _1516230), tc_fun(_1516232, tc_prod(_1516228, _1516230))), _1516228), c_COMBB(_1516230, tc_prod(_1516228, _1516230), _1516232)), c_Product__Type_OPair(_1516228, _1516230))), _1516234))), _1516236)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1516232), tc_Option_Ooption(_1516230), _1516228, hAPP(c_Option_Omap(_1516232, _1516230), _1516234)), hAPP(c_Map_Omap__of(_1516228, _1516232), _1516236)))], (7789 ^ _781013) ^ [_912210, _912212] : [_912212 = c_Orderings_Obot__class_Obot(tc_fun(_912210, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912210, tc_HOL_Obool)), _912212), c_Orderings_Obot__class_Obot(tc_fun(_912210, tc_HOL_Obool)))))], (22882 ^ _781013) ^ [_1209057, _1209059, _1209061, _1209063] : [class_Groups_Ocomm__monoid__add(_1209057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209059), _1209061)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1209057), _1209063), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209059), _1209061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209057), hAPP(_1209063, _1209059)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1209057), _1209063), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1209059)), _1209061))))], (45954 ^ _781013) ^ [_1700443, _1700445] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1700443, tc_HOL_Obool), _1700445) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1700443, tc_HOL_Obool), tc_fun(_1700443, tc_HOL_Obool)), _1700445), c_COMBI(tc_fun(_1700443, tc_HOL_Obool))))], (46572 ^ _781013) ^ [_1715525, _1715527, _1715529, _1715531] : [-(c_Wellfounded_Omax__extp(_1715525, _1715527, _1715529, _1715531)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1715525), _1715529)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1715525), _1715531)), -(_1715531 = c_Orderings_Obot__class_Obot(tc_fun(_1715525, tc_HOL_Obool))), 46586 ^ _781013 : [(46589 ^ _781013) ^ [_1715870] : [hBOOL(hAPP(hAPP(c_member(_1715525), _1715870), _1715531)), hBOOL(hAPP(hAPP(_1715527, 46585 ^ [_1715525, _1715527, _1715529, _1715531]), _1715870))], (46587 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715525), 46585 ^ [_1715525, _1715527, _1715529, _1715531]), _1715529)))]]], (48689 ^ _781013) ^ [_1766077] : [-(_1766077 = 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, _1766077)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1766077))))], (33330 ^ _781013) ^ [_1413694] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413694) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1413694))], (12048 ^ _781013) ^ [_998294, _998296, _998298, _998300, _998302] : [_998294 = hAPP(_998296, _998298), -(hBOOL(hAPP(hAPP(c_member(_998300), _998294), hAPP(c_Set_Oimage(_998302, _998300, _998296), c_Orderings_Otop__class_Otop(tc_fun(_998302, tc_HOL_Obool))))))], (31260 ^ _781013) ^ [_1366741, _1366743, _1366745] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1366741), _1366743), _1366745)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1366741), _1366743), 31263 ^ [_1366741, _1366743, _1366745]), _1366745)))], (41412 ^ _781013) ^ [_1597115, _1597117, _1597119, _1597121, _1597123] : [c_List_Opartition(_1597115, _1597117, _1597119) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597115), tc_List_Olist(_1597115)), _1597121), _1597123), 41415 ^ _781013 : [(41422 ^ _781013) ^ [_1597377] : [hBOOL(hAPP(hAPP(c_member(_1597115), _1597377), hAPP(c_List_Oset(_1597115), _1597123))), hBOOL(hAPP(_1597117, _1597377))], (41416 ^ _781013) ^ [_1597268] : [hBOOL(hAPP(hAPP(c_member(_1597115), _1597268), hAPP(c_List_Oset(_1597115), _1597121))), -(hBOOL(hAPP(_1597117, _1597268)))]]], (23156 ^ _781013) ^ [_1214184, _1214186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214184)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214184), _1214186)), _1214184) = _1214186)], (44262 ^ _781013) ^ [_1662899, _1662901, _1662903] : [hAPP(c_List_Orev(_1662899), _1662901) = hAPP(hAPP(c_List_Olist_OCons(_1662899), _1662903), c_List_Olist_ONil(_1662899)), -(_1662901 = hAPP(hAPP(c_List_Olist_OCons(_1662899), _1662903), c_List_Olist_ONil(_1662899)))], (4132 ^ _781013) ^ [_843500, _843502] : [_843502 = _843500, -(c_List_Orotate1(_843502) = c_List_Orotate1(_843500))], (15077 ^ _781013) ^ [_1059774, _1059776, _1059778] : [hBOOL(hAPP(_1059778, _1059776)), -(hBOOL(hAPP(hAPP(c_member(_1059774), _1059776), hAPP(c_Set_OCollect(_1059774), _1059778))))], (24198 ^ _781013) ^ [_1232310, _1232312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232310)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232310), _1232312)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1232310)), hAPP(c_Int_Onat, _1232312)))], (14766 ^ _781013) ^ [_1054977, _1054979] : [c_Orderings_Obot__class_Obot(tc_fun(_1054977, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1054977), _1054979), 14769 ^ _781013 : [(14770 ^ _781013) ^ [_1055062] : [hBOOL(hAPP(_1054979, _1055062))]]], (7049 ^ _781013) ^ [_897649, _897651, _897653] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897649, tc_HOL_Obool)), _897651), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897649, tc_HOL_Obool)), _897651), _897653)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897649, tc_HOL_Obool)), _897651), _897653))], (9987 ^ _781013) ^ [_957499, _957501, _957503, _957505] : [class_Groups_Ouminus(_957499), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957501, _957499)), _957503), _957505) = hAPP(c_Groups_Ouminus__class_Ouminus(_957499), hAPP(_957503, _957505)))], (2402 ^ _781013) ^ [_816571, _816573] : [_816573 = _816571, -(c_Com_Ocom_Ocom__size(_816573) = c_Com_Ocom_Ocom__size(_816571))], (3408 ^ _781013) ^ [_832374, _832376] : [_832376 = _832374, -(c_Set_OPow(_832376) = c_Set_OPow(_832374))], (4552 ^ _781013) ^ [_849948, _849950, _849952, _849954] : [-(c_Nitpick_OAbs__Frac(_849954, _849950) = c_Nitpick_OAbs__Frac(_849952, _849948)), _849954 = _849952, _849950 = _849948], (22996 ^ _781013) ^ [_1211251, _1211253, _1211255] : [-(hBOOL(hAPP(_1211251, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211253), _1211255)))), 22999 ^ _781013 : [(23002 ^ _781013) ^ [] : [hBOOL(hAPP(_1211251, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23000 ^ _781013) ^ [] : [-(_1211255 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 23005 ^ _781013 : [(23006 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211255)))], (23012 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23008 ^ [_1211251, _1211253, _1211255]), _1211255)))], (23016 ^ _781013) ^ [] : [hBOOL(hAPP(_1211251, 23007 ^ [_1211251, _1211253, _1211255]))], (23014 ^ _781013) ^ [] : [-(_1211253 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1211255), 23007 ^ [_1211251, _1211253, _1211255])), 23008 ^ [_1211251, _1211253, _1211255]))], (23010 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23008 ^ [_1211251, _1211253, _1211255])))]], 23017 ^ _781013 : [(23018 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211255), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23024 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23020 ^ [_1211251, _1211253, _1211255]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23028 ^ _781013) ^ [] : [hBOOL(hAPP(_1211251, 23019 ^ [_1211251, _1211253, _1211255]))], (23026 ^ _781013) ^ [] : [-(_1211253 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1211255), 23019 ^ [_1211251, _1211253, _1211255])), 23020 ^ [_1211251, _1211253, _1211255]))], (23022 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211255), 23020 ^ [_1211251, _1211253, _1211255])))]]], (25886 ^ _781013) ^ [_1262456, _1262458] : [class_Rings_Oring__1(_1262456), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262456), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1262458)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1262456), _1262458))], (11446 ^ _781013) ^ [_986505, _986507, _986509] : [class_Lattices_Olattice(_986505), hBOOL(hAPP(c_Finite__Set_Ofinite(_986505), _986507)), hBOOL(hAPP(hAPP(c_member(_986505), _986509), _986507)), 11457 ^ _781013 : [(11464 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_986505, tc_HOL_Obool)), _986507), hAPP(hAPP(c_Set_Oinsert(_986505), _986509), c_Orderings_Obot__class_Obot(tc_fun(_986505, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_986505, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_986505, _986507) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_986505), _986509), c_Big__Operators_Olattice__class_OSup__fin(_986505, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_986505, tc_HOL_Obool)), _986507), hAPP(hAPP(c_Set_Oinsert(_986505), _986509), c_Orderings_Obot__class_Obot(tc_fun(_986505, tc_HOL_Obool)))))))], (11458 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_986505, tc_HOL_Obool)), _986507), hAPP(hAPP(c_Set_Oinsert(_986505), _986509), c_Orderings_Obot__class_Obot(tc_fun(_986505, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_986505, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_986505, _986507) = _986509)]]], (21871 ^ _781013) ^ [_1191464, _1191466] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191464)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191466))))), _1191464 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1191466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14698 ^ _781013) ^ [_1053779, _1053781] : [14699 ^ _781013 : [(14702 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1053779), _1053781)))], (14700 ^ _781013) ^ [] : [_1053781 = c_Orderings_Obot__class_Obot(tc_fun(_1053779, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1053779), _1053781) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49354 ^ _781013) ^ [_1783821, _1783823, _1783825, _1783827] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1783821, _1783821)), hAPP(hAPP(c_Product__Type_OPair(_1783821, _1783821), _1783823), _1783825)), c_Transitive__Closure_Otrancl(_1783821, _1783827))), 49358 ^ _781013 : [(49361 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783821, _1783821)), hAPP(hAPP(c_Product__Type_OPair(_1783821, _1783821), 49357 ^ [_1783821, _1783823, _1783825, _1783827]), _1783825)), c_Transitive__Closure_Ortrancl(_1783821, _1783827))))], (49359 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783821, _1783821)), hAPP(hAPP(c_Product__Type_OPair(_1783821, _1783821), _1783823), 49357 ^ [_1783821, _1783823, _1783825, _1783827])), _1783827)))]]], (3958 ^ _781013) ^ [_840893, _840895, _840897, _840899, _840901, _840903, _840905, _840907] : [-(c_Product__Type_Oscomp(_840907, _840903, _840899, _840895) = c_Product__Type_Oscomp(_840905, _840901, _840897, _840893)), _840907 = _840905, _840903 = _840901, _840899 = _840897, _840895 = _840893], (20520 ^ _781013) ^ [_1164328, _1164330] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1164328), hAPP(c_Nat_OSuc, _1164330)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1164328), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1164330))], (11043 ^ _781013) ^ [_977251, _977253, _977255, _977257] : [hBOOL(hAPP(hAPP(c_member(_977251), _977253), _977255)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977251, tc_HOL_Obool)), _977255), hAPP(hAPP(c_Set_Oinsert(_977251), _977253), _977257)) = hAPP(hAPP(c_Set_Oinsert(_977251), _977253), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977251, tc_HOL_Obool)), _977255), _977257)))], (3860 ^ _781013) ^ [_839392, _839394, _839396, _839398, _839400, _839402, _839404, _839406] : [-(c_Random_Oiterate(_839406, _839402, _839398, _839394) = c_Random_Oiterate(_839404, _839400, _839396, _839392)), _839406 = _839404, _839402 = _839400, _839398 = _839396, _839394 = _839392], (37343 ^ _781013) ^ [_1493796, _1493798, _1493800, _1493802, _1493804, _1493806] : [hAPP(c_Product__Type_Oapsnd(_1493796, _1493798, _1493800, _1493802), _1493804) = hAPP(c_Product__Type_Oapsnd(_1493796, _1493798, _1493800, _1493806), _1493804), -(hAPP(_1493802, hAPP(c_Product__Type_Osnd(_1493800, _1493796), _1493804)) = hAPP(_1493806, hAPP(c_Product__Type_Osnd(_1493800, _1493796), _1493804)))], (46758 ^ _781013) ^ [_1721418, _1721420] : [hAPP(hAPP(c_Relation_Orel__comp(_1721418, _1721418, _1721418), _1721420), _1721420) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1721418, _1721418), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1721418, _1721420))], (41352 ^ _781013) ^ [_1595970, _1595972, _1595974] : [-(_1595970 = c_List_Olist_ONil(_1595972)), -(c_List_Obutlast(_1595972, hAPP(hAPP(c_List_Olist_OCons(_1595972), _1595974), _1595970)) = hAPP(hAPP(c_List_Olist_OCons(_1595972), _1595974), c_List_Obutlast(_1595972, _1595970)))], (41771 ^ _781013) ^ [_1605475, _1605477, _1605479, _1605481, _1605483] : [-(hAPP(hAPP(c_List_Oappend(_1605475), _1605477), _1605479) = hAPP(hAPP(c_List_Oappend(_1605475), _1605481), _1605483)), 41772 ^ _781013 : [(41779 ^ _781013) ^ [_1605699] : [hAPP(hAPP(c_List_Oappend(_1605475), _1605477), _1605699) = _1605481, _1605479 = hAPP(hAPP(c_List_Oappend(_1605475), _1605699), _1605483)], (41773 ^ _781013) ^ [_1605587] : [_1605477 = hAPP(hAPP(c_List_Oappend(_1605475), _1605481), _1605587), hAPP(hAPP(c_List_Oappend(_1605475), _1605587), _1605479) = _1605483]]], (23857 ^ _781013) ^ [_1226680, _1226682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1226680)), hAPP(c_Int_Onat, _1226682))), 23860 ^ _781013 : [(23863 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226680), _1226682)))], (23861 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226682)))]]], (50463 ^ _781013) ^ [_1807004, _1807006, _1807008] : [c_List_Olist__ex1(_1807004, _1807006, _1807008), 50467 ^ _781013 : [(50472 ^ _781013) ^ [_1807250] : [-(_1807250 = 50466 ^ [_1807004, _1807006, _1807008]), hBOOL(hAPP(hAPP(c_member(_1807004), _1807250), hAPP(c_List_Oset(_1807004), _1807008))), hBOOL(hAPP(_1807006, _1807250))], (50470 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1807006, 50466 ^ [_1807004, _1807006, _1807008])))], (50468 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1807004), 50466 ^ [_1807004, _1807006, _1807008]), hAPP(c_List_Oset(_1807004), _1807008))))]]], (31466 ^ _781013) ^ [_1373503, _1373505, _1373507] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1373503), _1373505)), c_Fun_Oinj__on(_1373503, tc_fun(tc_fun(_1373503, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1373503, tc_fun(tc_prod(_1373503, _1373503), tc_HOL_Obool), tc_fun(tc_fun(_1373503, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373503, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1373503, _1373503), tc_HOL_Obool), tc_fun(tc_fun(_1373503, tc_HOL_Obool), tc_HOL_Obool)), _1373503), c_Equiv__Relations_Oquotient(_1373503)), hAPP(hAPP(c_COMBC(_1373503, tc_fun(_1373503, tc_HOL_Obool), tc_fun(_1373503, tc_HOL_Obool)), c_Set_Oinsert(_1373503)), c_Orderings_Obot__class_Obot(tc_fun(_1373503, tc_HOL_Obool))))), _1373507), _1373505), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1373503, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1373503), _1373505), _1373507)) = hAPP(c_Finite__Set_Ocard(_1373503), _1373505))], (48215 ^ _781013) ^ [_1755102, _1755104] : [_1755102 = _1755104, -(hAPP(c_Code__Numeral_Oof__nat, _1755102) = hAPP(c_Code__Numeral_Oof__nat, _1755104))], (42887 ^ _781013) ^ [_1632153, _1632155, _1632157, _1632159, _1632161] : [_1632153 = c_Orderings_Obot__class_Obot(tc_fun(_1632155, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1632157, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632155, tc_fun(_1632157, tc_HOL_Obool)), _1632153), _1632159)), _1632161) = _1632161)], (36922 ^ _781013) ^ [_1485472] : [-(c_Divides_Odivmod__nat(_1485472, 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)), _1485472))], (36052 ^ _781013) ^ [_1467069, _1467071, _1467073, _1467075, _1467077, _1467079] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1467069, tc_fun(_1467071, tc_fun(_1467073, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1467069, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1467071, _1467073), tc_HOL_Obool), tc_fun(_1467071, tc_fun(_1467073, tc_HOL_Obool)), _1467069), hAPP(c_COMBC(_1467071, tc_fun(tc_prod(_1467071, _1467073), tc_HOL_Obool), tc_fun(_1467073, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467073, tc_fun(tc_fun(tc_prod(_1467071, _1467073), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1467071, _1467073), tc_HOL_Obool), tc_fun(_1467073, tc_HOL_Obool)), _1467071), c_COMBC(_1467073, tc_fun(tc_prod(_1467071, _1467073), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467073, tc_prod(_1467071, _1467073)), tc_fun(_1467073, tc_fun(tc_fun(tc_prod(_1467071, _1467073), tc_HOL_Obool), tc_HOL_Obool)), _1467071), hAPP(c_COMBB(tc_prod(_1467071, _1467073), tc_fun(tc_fun(tc_prod(_1467071, _1467073), tc_HOL_Obool), tc_HOL_Obool), _1467073), c_member(tc_prod(_1467071, _1467073)))), c_Product__Type_OPair(_1467071, _1467073))))), _1467075)), _1467077), _1467079)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1467071, _1467073)), hAPP(hAPP(c_Product__Type_OPair(_1467071, _1467073), _1467077), _1467079)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1467069, tc_fun(tc_prod(_1467071, _1467073), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1467069, tc_HOL_Obool))), _1467075))))], (45582 ^ _781013) ^ [_1691809, _1691811, _1691813, _1691815] : [-(hAPP(c_Set_Oimage(_1691809, _1691811, _1691813), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1691809, tc_HOL_Obool), _1691815)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1691809, tc_HOL_Obool), tc_fun(_1691811, tc_HOL_Obool)), _1691815), c_Set_Oimage(_1691809, _1691811, _1691813)))], (51216 ^ _781013) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (49327 ^ _781013) ^ [_1782941, _1782943, _1782945, _1782947, _1782949] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1782941, _1782941)), hAPP(hAPP(c_Product__Type_OPair(_1782941, _1782941), _1782943), _1782945)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1782941, _1782941), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1782947)), _1782949))), 49331 ^ _781013 : [(49334 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782941, _1782941)), hAPP(hAPP(c_Product__Type_OPair(_1782941, _1782941), 49330 ^ [_1782941, _1782943, _1782945, _1782947, _1782949]), _1782945)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1782941, _1782941), tc_HOL_Obool), _1782947), _1782949))))], (49332 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782941, _1782941)), hAPP(hAPP(c_Product__Type_OPair(_1782941, _1782941), _1782943), 49330 ^ [_1782941, _1782943, _1782945, _1782947, _1782949])), _1782949)))]]], (37468 ^ _781013) ^ [_1496359, _1496361, _1496363] : [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), _1496359), _1496361))), -(hBOOL(hAPP(hAPP(_1496363, _1496359), _1496361))), 37475 ^ _781013 : [(37478 ^ _781013) ^ [] : [-(37474 ^ [_1496359, _1496361, _1496363] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1496363, 37474 ^ [_1496359, _1496361, _1496363]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 37473 ^ [_1496359, _1496361, _1496363], 37474 ^ [_1496359, _1496361, _1496363]))))], (37484 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1496363, 37473 ^ [_1496359, _1496361, _1496363]), 37474 ^ [_1496359, _1496361, _1496363]))], (37476 ^ _781013) ^ [] : [-(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), 37473 ^ [_1496359, _1496361, _1496363]), 37474 ^ [_1496359, _1496361, _1496363]))))]]], (7025 ^ _781013) ^ [_897262, _897264, _897266] : [class_Orderings_Oorder(_897262), 7028 ^ _781013 : [(7037 ^ _781013) ^ [] : [-(_897264 = _897266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897262), _897264), _897266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897262), _897266), _897264))], (7029 ^ _781013) ^ [] : [_897264 = _897266, 7032 ^ _781013 : [(7035 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897262), _897266), _897264)))], (7033 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897262), _897264), _897266)))]]]]], (39241 ^ _781013) ^ [_1538968, _1538970, _1538972, _1538974, _1538976, _1538978, _1538980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1538968)), _1538970)), _1538972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1538972), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1538974)), _1538976))), -(c_Map_Omap__upds(_1538968, _1538974, _1538978, _1538970, hAPP(hAPP(c_List_Olist__update(_1538974, _1538976), _1538972), _1538980)) = c_Map_Omap__upds(_1538968, _1538974, _1538978, _1538970, _1538976))], (5729 ^ _781013) ^ [_871707, _871709, _871711] : [c_Hoare__Mirabelle_Ohoare__derivs(_871707, _871709, _871711), -(c_Hoare__Mirabelle_Ohoare__valids(_871707, _871709, _871711))], (30315 ^ _781013) ^ [_1347439, _1347441, _1347443, _1347445] : [class_Orderings_Olinorder(_1347439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347439), _1347441), _1347443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347439), _1347441), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347439), _1347445), _1347443))))], (21529 ^ _781013) ^ [_1185376] : [-(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), _1185376))))], (7047 ^ _781013) ^ [_897589, _897591, _897593] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897589, tc_HOL_Obool)), _897591), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897589, tc_HOL_Obool)), _897593), _897591)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897589, tc_HOL_Obool)), _897591), _897593))], (19991 ^ _781013) ^ [_1155368] : [hAPP(c_Nat_OSuc, _1155368) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51164 ^ _781013) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (39965 ^ _781013) ^ [_1558729, _1558731, _1558733, _1558735] : [c_Equiv__Relations_Ocongruent(_1558729, _1558731, _1558733, _1558735), 39968 ^ _781013 : [(39969 ^ _781013) ^ [_1558874] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1558729, _1558729)), _1558874), _1558733)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1558729, _1558729, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1558729, tc_fun(_1558729, _1558731), tc_fun(_1558729, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558731, tc_HOL_Obool), tc_fun(tc_fun(_1558729, _1558731), tc_fun(_1558729, tc_HOL_Obool)), _1558729), c_COMBB(_1558731, tc_HOL_Obool, _1558729)), hAPP(hAPP(c_COMBB(_1558731, tc_fun(_1558731, tc_HOL_Obool), _1558729), c_fequal), _1558735))), _1558735)), _1558874)))]]], (49239 ^ _781013) ^ [_1780471, _1780473, _1780475, _1780477, _1780479] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780471, _1780471)), hAPP(hAPP(c_Product__Type_OPair(_1780471, _1780471), _1780473), _1780475)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1780471, _1780471), tc_HOL_Obool), _1780477), _1780479))), 49244 ^ _781013 : [(49247 ^ _781013) ^ [] : [-(_1780473 = _1780475)], (49245 ^ _781013) ^ [] : [-(_1780477 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 49250 ^ _781013 : [(49255 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780471, _1780471)), hAPP(hAPP(c_Product__Type_OPair(_1780471, _1780471), 49248 ^ [_1780471, _1780473, _1780475, _1780477, _1780479]), _1780475)), _1780479)))], (49253 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780471, _1780471)), hAPP(hAPP(c_Product__Type_OPair(_1780471, _1780471), _1780473), 49248 ^ [_1780471, _1780473, _1780475, _1780477, _1780479])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1780471, _1780471), tc_HOL_Obool), 49249 ^ [_1780471, _1780473, _1780475, _1780477, _1780479]), _1780479))))], (49251 ^ _781013) ^ [] : [-(_1780477 = hAPP(c_Nat_OSuc, 49249 ^ [_1780471, _1780473, _1780475, _1780477, _1780479]))]]], (50794 ^ _781013) ^ [_1813376, _1813378, _1813380, _1813382, _1813384] : [-(_1813376 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1813378, _1813380, _1813382, _1813384), _1813376) = hAPP(c_Lazy__Sequence_Obind(_1813378, _1813380, hAPP(_1813382, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1813376), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1813378, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1813380)), _1813384), _1813376)))], (14189 ^ _781013) ^ [_1042576, _1042578, _1042580] : [class_Groups_Ogroup__add(_1042576), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042576), _1042578), _1042580) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042576), _1042578), hAPP(c_Groups_Ouminus__class_Ouminus(_1042576), _1042580)))], (51158 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (13044 ^ _781013) ^ [_1018205, _1018207, _1018209] : [-(hAPP(c_Finite__Set_Ofold1(_1018205, _1018207), _1018209) = c_HOL_OThe(_1018205, c_Finite__Set_Ofold1Set(_1018205, _1018207, _1018209)))], (20883 ^ _781013) ^ [_1171425, _1171427] : [_1171425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1171425), _1171427) = _1171427)], (34008 ^ _781013) ^ [_1425786, _1425788, _1425790, _1425792, _1425794, _1425796, _1425798, _1425800, _1425802, _1425804, _1425806] : [c_Equiv__Relations_Oequiv(_1425786, _1425788, _1425790), c_Equiv__Relations_Oequiv(_1425792, _1425794, _1425796), c_Equiv__Relations_Ocongruent2(_1425786, _1425792, tc_fun(_1425798, tc_HOL_Obool), _1425790, _1425796, _1425800), hBOOL(hAPP(hAPP(c_member(tc_fun(_1425786, tc_HOL_Obool)), _1425802), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1425786), _1425788), _1425790))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1425792, tc_HOL_Obool)), _1425804), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1425792), _1425794), _1425796))), 34030 ^ _781013 : [(34036 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1425798, tc_HOL_Obool)), hAPP(hAPP(_1425800, 34029 ^ [_1425786, _1425788, _1425790, _1425792, _1425794, _1425796, _1425798, _1425800, _1425802, _1425804, _1425806]), 34032 ^ [_1425786, _1425788, _1425790, _1425792, _1425794, _1425796, _1425798, _1425800, _1425802, _1425804, _1425806])), _1425806))], (34034 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425792), 34032 ^ [_1425786, _1425788, _1425790, _1425792, _1425794, _1425796, _1425798, _1425800, _1425802, _1425804, _1425806]), _1425794)))], (34031 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425786), 34029 ^ [_1425786, _1425788, _1425790, _1425792, _1425794, _1425796, _1425798, _1425800, _1425802, _1425804, _1425806]), _1425788)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1425798, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425786, tc_fun(_1425798, tc_HOL_Obool)), _1425802), hAPP(hAPP(c_COMBB(tc_fun(_1425792, tc_fun(_1425798, tc_HOL_Obool)), tc_fun(_1425798, tc_HOL_Obool), _1425786), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425792, tc_fun(_1425798, tc_HOL_Obool)), _1425804)), _1425800))), _1425806)))], (35191 ^ _781013) ^ [_1446973, _1446975] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1446973), hAPP(c_Int_Onumber__class_Onumber__of(_1446973), _1446975)), 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(_1446973), hAPP(c_Int_Onumber__class_Onumber__of(_1446973), _1446975)), hAPP(c_Int_Onumber__class_Onumber__of(_1446973), _1446975))), class_Groups_Omonoid__mult(_1446973), class_Int_Onumber(_1446973)], (44206 ^ _781013) ^ [_1661539, _1661541] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1661539)), c_List_Otranspose__rel(_1661539)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1661539)), c_List_Olist_ONil(_1661539)), _1661541))), -(c_List_Otranspose(_1661539, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1661539)), c_List_Olist_ONil(_1661539)), _1661541)) = c_List_Otranspose(_1661539, _1661541))], (5564 ^ _781013) ^ [_865818, _865820] : [_865820 = _865818, -(tc_Hoare__Mirabelle_Otriple(_865820) = tc_Hoare__Mirabelle_Otriple(_865818))], (26733 ^ _781013) ^ [_1278520, _1278522] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1278520), _1278522))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1278522, _1278520) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1278522), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1278522), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1278520)))], (11500 ^ _781013) ^ [_987820, _987822] : [class_Groups_Oordered__ab__group__add(_987820), -(c_Fun_Oinj__on(_987820, _987820, c_Groups_Ouminus__class_Ouminus(_987820), _987822))], (47369 ^ _781013) ^ [_1736126, _1736128, _1736130] : [c_Wellfounded_Oacyclic(_1736126, _1736128), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1736126, _1736126), tc_HOL_Obool)), _1736130), _1736128)), -(c_Wellfounded_Oacyclic(_1736126, _1736130))], (38139 ^ _781013) ^ [_1512566, _1512568, _1512570, _1512572] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1512566), _1512572) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1512570), _1512568), -(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), _1512566), _1512568)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1512570), _1512572))), c_Int_Ointrel)))], (43279 ^ _781013) ^ [_1642844, _1642846, _1642848, _1642850] : [-(hBOOL(hAPP(c_List_Olistsp(_1642844, _1642846), hAPP(hAPP(c_List_Oappend(_1642844), _1642848), _1642850)))), hBOOL(hAPP(c_List_Olistsp(_1642844, _1642846), _1642848)), hBOOL(hAPP(c_List_Olistsp(_1642844, _1642846), _1642850))], (30101 ^ _781013) ^ [_1343469, _1343471, _1343473, _1343475] : [class_Orderings_Olinorder(_1343469), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343469), _1343471), _1343473)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343469), _1343471), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343469), _1343473), _1343475))))], (51266 ^ _781013) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (31368 ^ _781013) ^ [_1369152, _1369154, _1369156, _1369158, _1369160] : [c_Hoare__Mirabelle_Otriple__valid(_1369152, _1369154, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1369152), _1369156), _1369158), _1369160)), 31371 ^ _781013 : [(31372 ^ _781013) ^ [_1369282, _1369284] : [hBOOL(hAPP(hAPP(_1369156, _1369284), _1369282)), 31375 ^ _781013 : [(31376 ^ _781013) ^ [_1369381] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1369158), _1369282), _1369154), _1369381)), -(hBOOL(hAPP(hAPP(_1369160, _1369284), _1369381)))]]]]], (33606 ^ _781013) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50413 ^ _781013) ^ [_1806037, _1806039, _1806041, _1806043] : [-(c_List_Olist__ex1(_1806037, _1806039, hAPP(hAPP(c_List_Olist_OCons(_1806037), _1806041), _1806043))), 50416 ^ _781013 : [(50419 ^ _781013) ^ [] : [c_List_Olist__all(_1806037, hAPP(hAPP(c_COMBS(_1806037, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1806037), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1806037), c_fNot), _1806039))), hAPP(c_fequal, _1806041)), _1806043)], (50417 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1806039, _1806041)))]], 50420 ^ _781013 : [(50423 ^ _781013) ^ [] : [c_List_Olist__ex1(_1806037, _1806039, _1806043)], (50421 ^ _781013) ^ [] : [hBOOL(hAPP(_1806039, _1806041))]]], (43723 ^ _781013) ^ [_1652215, _1652217, _1652219] : [class_Orderings_Olinorder(_1652215), c_List_Olinorder__class_Osorted(_1652215, _1652217), -(c_List_Olinorder__class_Osorted(_1652215, hAPP(hAPP(c_List_Otake(_1652215), _1652219), _1652217)))], (43410 ^ _781013) ^ [_1645399, _1645401, _1645403, _1645405] : [hBOOL(hAPP(c_List_Olistsp(_1645399, _1645401), _1645403)), hBOOL(hAPP(c_List_Olistsp(_1645399, _1645405), _1645403)), -(hBOOL(hAPP(c_List_Olistsp(_1645399, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1645399, tc_HOL_Obool)), _1645401), _1645405)), _1645403)))], (8561 ^ _781013) ^ [_929367, _929369, _929371, _929373, _929375, _929377] : [c_Finite__Set_Ofolding(_929367, _929369, _929371, _929373), hBOOL(hAPP(c_Finite__Set_Ofinite(_929367), _929375)), hBOOL(hAPP(c_Finite__Set_Ofinite(_929367), _929377)), -(hAPP(c_Fun_Ocomp(_929369, _929369, _929369, hAPP(_929373, _929377)), hAPP(_929373, _929375)) = hAPP(c_Fun_Ocomp(_929369, _929369, _929369, hAPP(_929373, _929375)), hAPP(_929373, _929377)))], (43661 ^ _781013) ^ [_1651188, _1651190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651188), _1651190)), -(c_List_Oupt(_1651188, hAPP(c_Nat_OSuc, _1651190)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1651188, _1651190)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1651190), c_List_Olist_ONil(tc_Nat_Onat))))], (28328 ^ _781013) ^ [_1309748] : [-(_1309748 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 28331 ^ _781013 : [(28338 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309748))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1309748) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28332 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309748)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1309748) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (50684 ^ _781013) ^ [_1811057, _1811059] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1811057)), c_Int_OBit0(_1811059)))], (28786 ^ _781013) ^ [_1318148, _1318150, _1318152, _1318154] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1318148), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1318148), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318148), _1318150), _1318152)), _1318154) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318148), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1318148), _1318150), _1318154)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1318148), _1318152), _1318154)))], (9809 ^ _781013) ^ [_954068, _954070] : [class_Orderings_Opreorder(_954068), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954068), _954070), _954070))], (35951 ^ _781013) ^ [_1463513, _1463515, _1463517, _1463519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool)), _1463517), _1463519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1463513, tc_fun(_1463515, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1463513, tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_fun(_1463515, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1463515, tc_fun(tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_fun(_1463515, tc_HOL_Obool)), _1463513), c_COMBC(_1463515, tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1463515, tc_prod(_1463513, _1463515)), tc_fun(_1463515, tc_fun(tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_HOL_Obool)), _1463513), hAPP(c_COMBB(tc_prod(_1463513, _1463515), tc_fun(tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_HOL_Obool), _1463515), c_member(tc_prod(_1463513, _1463515)))), c_Product__Type_OPair(_1463513, _1463515)))), _1463517)), hAPP(hAPP(c_COMBC(_1463513, tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_fun(_1463515, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1463515, tc_fun(tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_fun(_1463515, tc_HOL_Obool)), _1463513), c_COMBC(_1463515, tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1463515, tc_prod(_1463513, _1463515)), tc_fun(_1463515, tc_fun(tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_HOL_Obool)), _1463513), hAPP(c_COMBB(tc_prod(_1463513, _1463515), tc_fun(tc_fun(tc_prod(_1463513, _1463515), tc_HOL_Obool), tc_HOL_Obool), _1463515), c_member(tc_prod(_1463513, _1463515)))), c_Product__Type_OPair(_1463513, _1463515)))), _1463519))))], (26781 ^ _781013) ^ [_1279429, _1279431, _1279433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1279429)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1279431), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1279433)), 26788 ^ _781013 : [(26789 ^ _781013) ^ [_1279637] : [26791 ^ _781013 : [(26797 ^ _781013) ^ [] : [-(_1279637 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26793 ^ [_1279429, _1279431, _1279433, _1279637]), 26790 ^ [_1279429, _1279431, _1279433, _1279637]))], (26795 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26793 ^ [_1279429, _1279431, _1279433, _1279637]), _1279433)))], (26792 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26790 ^ [_1279429, _1279431, _1279433, _1279637]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1279429))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1279431), _1279637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1279431), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1279637), _1279429))))]]], (4406 ^ _781013) ^ [_847737, _847739] : [_847739 = _847737, -(c_Orderings_Oord__class_Omin(_847739) = c_Orderings_Oord__class_Omin(_847737))], (17669 ^ _781013) ^ [_1111203, _1111205, _1111207] : [17670 ^ _781013 : [(17673 ^ _781013) ^ [] : [_1111205 = _1111207], (17671 ^ _781013) ^ [] : [_1111203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111203), _1111205) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111203), _1111207))], (3100 ^ _781013) ^ [_827530, _827532] : [_827532 = _827530, -(c_SetInterval_Oord__class_OlessThan(_827532) = c_SetInterval_Oord__class_OlessThan(_827530))], (19442 ^ _781013) ^ [_1145051, _1145053, _1145055] : [class_Rings_Olinordered__semidom(_1145051), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145051), c_Groups_Ozero__class_Ozero(_1145051)), _1145053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145051), c_Groups_Ozero__class_Ozero(_1145051)), hAPP(hAPP(c_Power_Opower__class_Opower(_1145051), _1145053), _1145055))))], (39428 ^ _781013) ^ [_1543248, _1543250, _1543252, _1543254] : [class_Groups_Ocomm__monoid__add(_1543248), hBOOL(hAPP(c_List_Odistinct(_1543250), _1543252)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1543248), hAPP(hAPP(c_List_Omap(_1543250, _1543248), _1543254), _1543252)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543250, _1543248), _1543254), hAPP(c_List_Oset(_1543250), _1543252)))], (50940 ^ _781013) ^ [_1817386, _1817388, _1817390] : [-(hAPP(hAPP(c_List_Oappend(_1817386), c_List_Oreplicate(_1817386, _1817388, _1817390)), hAPP(hAPP(c_List_Olist_OCons(_1817386), _1817390), c_List_Olist_ONil(_1817386))) = hAPP(hAPP(c_List_Olist_OCons(_1817386), _1817390), c_List_Oreplicate(_1817386, _1817388, _1817390)))], (41845 ^ _781013) ^ [_1607289, _1607291, _1607293, _1607295] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607289)), hAPP(hAPP(c_List_Oappend(_1607289), _1607291), _1607293)), c_List_Olists(_1607289, _1607295))), 41848 ^ _781013 : [(41851 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607289)), _1607293), c_List_Olists(_1607289, _1607295))))], (41849 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607289)), _1607291), c_List_Olists(_1607289, _1607295))))]]], (15877 ^ _781013) ^ [_1074760, _1074762, _1074764] : [class_Rings_Olinordered__semiring__strict(_1074760), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074760), c_Groups_Ozero__class_Ozero(_1074760)), _1074762)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074760), _1074764), c_Groups_Ozero__class_Ozero(_1074760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074760), _1074764), _1074762)), c_Groups_Ozero__class_Ozero(_1074760))))], (31944 ^ _781013) ^ [_1386678, _1386680, _1386682, _1386684, _1386686] : [-(_1386678 = c_Orderings_Obot__class_Obot(tc_fun(_1386680, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386682, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386680, tc_fun(_1386682, tc_HOL_Obool)), _1386678), _1386684)), _1386686) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386680, tc_fun(_1386682, tc_HOL_Obool)), _1386678), hAPP(hAPP(c_COMBC(_1386680, tc_fun(_1386682, tc_HOL_Obool), tc_fun(_1386682, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1386682, tc_HOL_Obool), tc_fun(tc_fun(_1386682, tc_HOL_Obool), tc_fun(_1386682, tc_HOL_Obool)), _1386680), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386682, tc_HOL_Obool))), _1386684)), _1386686)))], (40932 ^ _781013) ^ [_1586858, _1586860] : [-(c_Product__Type_Omap__pair(_1586858, _1586858, _1586860, _1586860, c_COMBI(_1586858), c_COMBI(_1586860)) = c_Fun_Oid(tc_prod(_1586858, _1586860)))], (19833 ^ _781013) ^ [_1152572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1152572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1152572)))], (10619 ^ _781013) ^ [_968917, _968919, _968921] : [class_Orderings_Olinorder(_968917), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968917), _968919), _968921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968917), _968921), _968919)))], (31182 ^ _781013) ^ [_1365128, _1365130, _1365132] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _1365128), _1365130), _1365132)), -(_1365132 = _1365128)], (10475 ^ _781013) ^ [_966854, _966856, _966858, _966860] : [class_Orderings_Opreorder(_966854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966854), _966856), _966858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966854), _966858), _966860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966854), _966856), _966860)))], (11119 ^ _781013) ^ [_979119, _979121, _979123, _979125] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979119, tc_HOL_Obool)), _979121), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979119, tc_HOL_Obool)), _979123), _979125)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979119, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979119, tc_HOL_Obool)), _979121), _979123)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979119, tc_HOL_Obool)), _979121), _979125)))], (1604 ^ _781013) ^ [_803805, _803807] : [-(class_Rings_Ono__zero__divisors(_803805)), _803807 = _803805, class_Rings_Ono__zero__divisors(_803807)], (49095 ^ _781013) ^ [_1776619, _1776621] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1776619, _1776619), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1776621) = c_Relation_OId(_1776619))], (50074 ^ _781013) ^ [_1798518, _1798520, _1798522, _1798524] : [class_Lattices_Osemilattice__inf(_1798518), hBOOL(hAPP(c_Finite__Set_Ofinite(_1798518), _1798520)), 50084 ^ _781013 : [(50087 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1798518), _1798522), 50083 ^ [_1798518, _1798520, _1798522, _1798524]))], (50085 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798518), 50083 ^ [_1798518, _1798520, _1798522, _1798524]), _1798520)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1798518), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1798518), _1798522), _1798524)), hAPP(hAPP(c_Finite__Set_Ofold(_1798518, _1798518, c_Lattices_Osemilattice__inf__class_Oinf(_1798518)), _1798524), _1798520))))], (49536 ^ _781013) ^ [_1787985, _1787987, _1787989, _1787991] : [class_Orderings_Olinorder(_1787985), hBOOL(hAPP(c_Finite__Set_Ofinite(_1787985), _1787987)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1787985, _1787985, c_Orderings_Oord__class_Omin(_1787985)), _1787989), hAPP(hAPP(c_Set_Oinsert(_1787985), _1787991), _1787987)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1787985), _1787991), hAPP(hAPP(c_Finite__Set_Ofold(_1787985, _1787985, c_Orderings_Oord__class_Omin(_1787985)), _1787989), _1787987)))], (38688 ^ _781013) ^ [_1525609, _1525611, _1525613, _1525615] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1525609, _1525609)), hAPP(hAPP(c_Product__Type_OPair(_1525609, _1525609), _1525611), _1525613)), hAPP(c_List_Oset(tc_prod(_1525609, _1525609)), hAPP(hAPP(c_List_Ozip(_1525609, _1525609), _1525615), _1525615)))), 38691 ^ _781013 : [(38694 ^ _781013) ^ [] : [-(_1525611 = _1525613)], (38692 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525609), _1525611), hAPP(c_List_Oset(_1525609), _1525615))))]]], (47986 ^ _781013) ^ [_1750318, _1750320] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1750318, _1750318)), hAPP(hAPP(c_Product__Type_OPair(_1750318, _1750318), 47987 ^ [_1750318, _1750320]), 47987 ^ [_1750318, _1750320])), c_Transitive__Closure_Otrancl(_1750318, _1750320)))), -(c_Wellfounded_Oacyclic(_1750318, _1750320))], (49818 ^ _781013) ^ [_1793570, _1793572, _1793574] : [class_Lattices_Olattice(_1793570), hBOOL(hAPP(c_Finite__Set_Ofinite(_1793570), _1793572)), -(hBOOL(hAPP(hAPP(c_member(_1793570), _1793574), _1793572))), -(c_Big__Operators_Olattice__class_OInf__fin(_1793570, hAPP(hAPP(c_Set_Oinsert(_1793570), _1793574), _1793572)) = hAPP(hAPP(c_Finite__Set_Ofold(_1793570, _1793570, c_Lattices_Osemilattice__inf__class_Oinf(_1793570)), _1793574), _1793572))], (20055 ^ _781013) ^ [_1156336, _1156338] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156336), _1156338))), 20058 ^ _781013 : [(20065 ^ _781013) ^ [] : [_1156336 = _1156338, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156336), hAPP(c_Nat_OSuc, _1156338))))], (20059 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156336), hAPP(c_Nat_OSuc, _1156338))), -(_1156336 = _1156338)]]], (46273 ^ _781013) ^ [_1707522, _1707524, _1707526, _1707528, _1707530, _1707532] : [c_List_Olist__all2(_1707522, _1707524, _1707526, _1707528, _1707530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707532), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707524)), _1707530))), -(hBOOL(hAPP(hAPP(_1707526, hAPP(hAPP(c_List_Onth(_1707522), _1707528), _1707532)), hAPP(hAPP(c_List_Onth(_1707524), _1707530), _1707532))))], (40487 ^ _781013) ^ [_1572763, _1572765] : [c_Relation_Orefl__on(_1572763, c_Orderings_Otop__class_Otop(tc_fun(_1572763, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1572763, _1572763)), hAPP(c_Product__Type_Oprod_Oprod__case(_1572763, _1572763, tc_HOL_Obool), _1572765))), -(c_Predicate_Oreflp(_1572763, _1572765))], (51152 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (44426 ^ _781013) ^ [_1666472, _1666474] : [-(_1666472 = c_List_Olist_ONil(_1666474)), -(c_List_Olast(_1666474, hAPP(c_List_Orev(_1666474), _1666472)) = hAPP(c_List_Ohd(_1666474), _1666472))], (42066 ^ _781013) ^ [_1613310, _1613312] : [-(hAPP(c_List_Orotate1(_1613310), _1613312) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1613310), _1613310, c_List_Olist_ONil(_1613310), hAPP(hAPP(c_COMBB(tc_List_Olist(_1613310), tc_fun(tc_List_Olist(_1613310), tc_List_Olist(_1613310)), _1613310), hAPP(c_COMBC(tc_List_Olist(_1613310), tc_List_Olist(_1613310), tc_List_Olist(_1613310)), c_List_Oappend(_1613310))), hAPP(hAPP(c_COMBC(_1613310, tc_List_Olist(_1613310), tc_List_Olist(_1613310)), c_List_Olist_OCons(_1613310)), c_List_Olist_ONil(_1613310)))), _1613312))], (11331 ^ _781013) ^ [_983750, _983752, _983754] : [class_Lattices_Oboolean__algebra(_983750), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_983750), _983752), _983754) = c_Orderings_Obot__class_Obot(_983750), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_983750), _983752), _983754) = c_Orderings_Otop__class_Otop(_983750), -(hAPP(c_Groups_Ouminus__class_Ouminus(_983750), _983752) = _983754)], (42148 ^ _781013) ^ [_1615252, _1615254, _1615256, _1615258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1615252), _1615254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1615256, tc_HOL_Obool)), hAPP(c_List_Oset(_1615256), hAPP(hAPP(c_List_Odrop(_1615256), _1615254), _1615258))), hAPP(c_List_Oset(_1615256), hAPP(hAPP(c_List_Odrop(_1615256), _1615252), _1615258)))))], (14971 ^ _781013) ^ [_1058034] : [class_Rings_Ozero__neq__one(_1058034), c_Groups_Oone__class_Oone(_1058034) = c_Groups_Ozero__class_Ozero(_1058034)], (10265 ^ _781013) ^ [_962620, _962622, _962624] : [class_Groups_Oordered__ab__group__add(_962620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962620), _962622), _962624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962620), hAPP(c_Groups_Ouminus__class_Ouminus(_962620), _962624)), hAPP(c_Groups_Ouminus__class_Ouminus(_962620), _962622))))], (45666 ^ _781013) ^ [_1693659, _1693661, _1693663] : [c_Equiv__Relations_Oequiv(_1693659, _1693661, _1693663), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1693659, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1693659), _1693661), _1693663)) = _1693661)], (38242 ^ _781013) ^ [_1515245, _1515247, _1515249, _1515251, _1515253] : [c_Fun_Oinj__on(_1515245, _1515247, _1515249, c_Orderings_Otop__class_Otop(tc_fun(_1515245, tc_HOL_Obool))), 38245 ^ _781013 : [(38252 ^ _781013) ^ [] : [_1515251 = _1515253, -(hAPP(hAPP(c_List_Omap(_1515245, _1515247), _1515249), _1515251) = hAPP(hAPP(c_List_Omap(_1515245, _1515247), _1515249), _1515253))], (38246 ^ _781013) ^ [] : [hAPP(hAPP(c_List_Omap(_1515245, _1515247), _1515249), _1515251) = hAPP(hAPP(c_List_Omap(_1515245, _1515247), _1515249), _1515253), -(_1515251 = _1515253)]]], (18800 ^ _781013) ^ [_1131534, _1131536, _1131538, _1131540, _1131542, _1131544] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1131534), _1131536)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131538), _1131540)), 18810 ^ _781013 : [(18813 ^ _781013) ^ [] : [hAPP(c_Finite__Set_Ocard(_1131534), hAPP(c_Set_OCollect(_1131534), hAPP(hAPP(c_COMBS(_1131534, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1131534), c_fconj), hAPP(hAPP(c_COMBC(_1131534, tc_fun(_1131534, tc_HOL_Obool), tc_HOL_Obool), c_member(_1131534)), _1131536))), hAPP(hAPP(c_COMBC(_1131534, _1131538, tc_HOL_Obool), _1131542), 18809 ^ [_1131534, _1131536, _1131538, _1131540, _1131542, _1131544])))) = _1131544], (18811 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1131538), 18809 ^ [_1131534, _1131536, _1131538, _1131540, _1131542, _1131544]), _1131540)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131534, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1131538, tc_HOL_Obool), tc_Nat_Onat, _1131534), c_Finite__Set_Ocard(_1131538)), hAPP(hAPP(c_COMBB(tc_fun(_1131538, tc_HOL_Obool), tc_fun(_1131538, tc_HOL_Obool), _1131534), c_Set_OCollect(_1131538)), hAPP(hAPP(c_COMBB(tc_fun(_1131538, tc_HOL_Obool), tc_fun(_1131538, tc_HOL_Obool), _1131534), hAPP(c_COMBS(_1131538, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1131538), c_fconj), hAPP(hAPP(c_COMBC(_1131538, tc_fun(_1131538, tc_HOL_Obool), tc_HOL_Obool), c_member(_1131538)), _1131540)))), _1131542)))), _1131536) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1131544), hAPP(c_Finite__Set_Ocard(_1131538), _1131540)))], (29663 ^ _781013) ^ [_1334060, _1334062, _1334064] : [class_Orderings_Olinorder(_1334060), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334060), _1334062)), 29670 ^ _781013 : [(29677 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334060, tc_HOL_Obool)), _1334062), hAPP(hAPP(c_Set_Oinsert(_1334060), _1334064), c_Orderings_Obot__class_Obot(tc_fun(_1334060, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1334060, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1334060, hAPP(hAPP(c_Set_Oinsert(_1334060), _1334064), _1334062)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334060), _1334064), c_Big__Operators_Olinorder__class_OMin(_1334060, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334060, tc_HOL_Obool)), _1334062), hAPP(hAPP(c_Set_Oinsert(_1334060), _1334064), c_Orderings_Obot__class_Obot(tc_fun(_1334060, tc_HOL_Obool)))))))], (29671 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334060, tc_HOL_Obool)), _1334062), hAPP(hAPP(c_Set_Oinsert(_1334060), _1334064), c_Orderings_Obot__class_Obot(tc_fun(_1334060, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1334060, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1334060, hAPP(hAPP(c_Set_Oinsert(_1334060), _1334064), _1334062)) = _1334064)]]], (50758 ^ _781013) ^ [_1812556, _1812558, _1812560, _1812562, _1812564] : [-(hAPP(c_New__DSequence_Oneg__bind(_1812556, _1812558, _1812560, _1812562), _1812564) = c_Lazy__Sequence_Ohb__bind(_1812556, _1812558, hAPP(_1812560, _1812564), hAPP(hAPP(c_COMBC(_1812556, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1812558))), _1812562), _1812564)))], (19308 ^ _781013) ^ [_1142645, _1142647] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142645), _1142647) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142647), _1142645))], (17637 ^ _781013) ^ [_1110776] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1110776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48539 ^ _781013) ^ [_1762562, _1762564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1762562)), hAPP(c_Code__Numeral_Onat__of, _1762564))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1762562), _1762564)))], (41300 ^ _781013) ^ [_1595021, _1595023, _1595025] : [-(hAPP(hAPP(c_List_Ozip(_1595021, _1595023), c_List_Olist_ONil(_1595021)), _1595025) = c_List_Olist_ONil(tc_prod(_1595021, _1595023)))], (27455 ^ _781013) ^ [_1292959, _1292961, _1292963] : [-(hAPP(c_Set_OPow(_1292959), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1292959, tc_HOL_Obool)), _1292961), _1292963)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1292959, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1292959), _1292961)), hAPP(c_Set_OPow(_1292959), _1292963)))], (22524 ^ _781013) ^ [_1202666, _1202668, _1202670, _1202672] : [class_Orderings_Olinorder(_1202666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202666), _1202668), _1202670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202666), _1202670), _1202672)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1202666, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1202666, _1202668), _1202670)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1202666, _1202670), _1202672)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1202666, _1202668), _1202672))], (28852 ^ _781013) ^ [_1319320, _1319322, _1319324, _1319326] : [class_Orderings_Olinorder(_1319320), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319320), _1319322), _1319324)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319320), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319320), _1319322), _1319326)), _1319324)))], (51500 ^ _781013) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (18227 ^ _781013) ^ [_1120329] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120329), _1120329) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44306 ^ _781013) ^ [_1663867, _1663869] : [-(c_List_Oconcat(_1663867, _1663869) = hAPP(c_List_Ofoldl(tc_List_Olist(_1663867), tc_List_Olist(_1663867), c_List_Oappend(_1663867), c_List_Olist_ONil(_1663867)), _1663869))], (38192 ^ _781013) ^ [_1514018, _1514020, _1514022, _1514024] : [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), _1514018), _1514020)), 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), _1514022), _1514024)), 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), _1514018), _1514024)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1514022), _1514020))))], (43026 ^ _781013) ^ [_1635949, _1635951, _1635953, _1635955] : [-(hAPP(c_Set_OPow(_1635949), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635951, tc_fun(_1635949, tc_HOL_Obool)), _1635953), _1635955)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635951, tc_fun(tc_fun(_1635949, tc_HOL_Obool), tc_HOL_Obool)), _1635953), hAPP(hAPP(c_COMBB(tc_fun(_1635949, tc_HOL_Obool), tc_fun(tc_fun(_1635949, tc_HOL_Obool), tc_HOL_Obool), _1635951), c_Set_OPow(_1635949)), _1635955)))], (18269 ^ _781013) ^ [_1121100, _1121102, _1121104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121100), _1121102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121100), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121104), _1121102))))], (11383 ^ _781013) ^ [_985154, _985156, _985158, _985160, _985162, _985164, _985166, _985168] : [c_Finite__Set_Ofolding__image__simple(_985154, _985156, _985158, _985160, _985162, _985164), hBOOL(hAPP(c_Finite__Set_Ofinite(_985156), _985166)), hBOOL(hAPP(c_Finite__Set_Ofinite(_985156), _985168)), 11397 ^ _781013 : [(11400 ^ _781013) ^ [] : [hAPP(_985162, 11396 ^ [_985154, _985156, _985158, _985160, _985162, _985164, _985166, _985168]) = _985160], (11398 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_985156), 11396 ^ [_985154, _985156, _985158, _985160, _985162, _985164, _985166, _985168]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_985156, tc_HOL_Obool)), _985166), _985168))))]], -(hAPP(_985164, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_985156, tc_HOL_Obool)), _985166), _985168)) = hAPP(hAPP(_985158, hAPP(_985164, _985166)), hAPP(_985164, _985168)))], (18478 ^ _781013) ^ [_1124890, _1124892, _1124894] : [18479 ^ _781013 : [(18482 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124892), _1124894))], (18480 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1124890)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124890), _1124892)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124890), _1124894))))], (34219 ^ _781013) ^ [_1430140, _1430142] : [c_Int_OBit1(_1430140) = c_Int_OBit1(_1430142), -(_1430140 = _1430142)], (17612 ^ _781013) ^ [_1110315, _1110317, _1110319] : [-(hBOOL(hAPP(_1110315, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110317), _1110319)))), 17615 ^ _781013 : [(17618 ^ _781013) ^ [] : [hBOOL(hAPP(_1110315, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17616 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110317), _1110319)))]], 17620 ^ _781013 : [(17623 ^ _781013) ^ [] : [hBOOL(hAPP(_1110315, 17619 ^ [_1110315, _1110317, _1110319]))], (17621 ^ _781013) ^ [] : [-(_1110317 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110319), 17619 ^ [_1110315, _1110317, _1110319]))]]], (10941 ^ _781013) ^ [_974818, _974820, _974822, _974824] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974818, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974818, tc_HOL_Obool)), _974820), _974822)), _974824) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974818, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974818, tc_HOL_Obool)), _974820), _974824)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974818, tc_HOL_Obool)), _974822), _974824)))], (32514 ^ _781013) ^ [_1397939, _1397941, _1397943] : [class_Int_Onumber(_1397939), class_Orderings_Oord(_1397939), 32521 ^ _781013 : [(32528 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397939), hAPP(c_Int_Onumber__class_Onumber__of(_1397939), _1397941)), hAPP(c_Int_Onumber__class_Onumber__of(_1397939), _1397943)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1397939), hAPP(c_Int_Onumber__class_Onumber__of(_1397939), _1397941)), hAPP(c_Int_Onumber__class_Onumber__of(_1397939), _1397943)) = hAPP(c_Int_Onumber__class_Onumber__of(_1397939), _1397941))], (32522 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397939), hAPP(c_Int_Onumber__class_Onumber__of(_1397939), _1397941)), hAPP(c_Int_Onumber__class_Onumber__of(_1397939), _1397943))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1397939), hAPP(c_Int_Onumber__class_Onumber__of(_1397939), _1397941)), hAPP(c_Int_Onumber__class_Onumber__of(_1397939), _1397943)) = hAPP(c_Int_Onumber__class_Onumber__of(_1397939), _1397943))]]], (8655 ^ _781013) ^ [_931286, _931288, _931290, _931292] : [class_Lattices_Osemilattice__sup(_931286), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931286), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931286), _931288), _931290)), _931292) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931286), _931288), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931286), _931290), _931292)))], (35499 ^ _781013) ^ [_1453325] : [c_Int_OMin = c_Int_OBit0(_1453325)], (6824 ^ _781013) ^ [_893546, _893548] : [hBOOL(hAPP(hAPP(c_member(_893546), _893548), c_Orderings_Obot__class_Obot(tc_fun(_893546, tc_HOL_Obool))))], (19997 ^ _781013) ^ [_1155464, _1155466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1155464)), hAPP(c_Nat_OSuc, _1155466))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155464), _1155466)))], (37578 ^ _781013) ^ [_1498667] : [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), _1498667))), -(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), _1498667)) = 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), _1498667))))], (41458 ^ _781013) ^ [_1598437, _1598439, _1598441, _1598443] : [_1598437 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1598439), _1598437), hAPP(hAPP(c_List_Olist_OCons(_1598439), _1598441), _1598443)) = c_List_Olist_ONil(_1598439))], (45604 ^ _781013) ^ [_1692495, _1692497, _1692499] : [class_Complete__Lattice_Ocomplete__lattice(_1692495), class_Orderings_Olinorder(_1692495), 45611 ^ _781013 : [(45621 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1692495), _1692497), c_Complete__Lattice_OSup__class_OSup(_1692495, _1692499)))), 45622 ^ _781013 : [(45623 ^ _781013) ^ [_1692801] : [hBOOL(hAPP(hAPP(c_member(_1692495), _1692801), _1692499)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1692495), _1692497), _1692801))]]], (45612 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1692495), _1692497), c_Complete__Lattice_OSup__class_OSup(_1692495, _1692499))), 45616 ^ _781013 : [(45619 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1692495), _1692497), 45615 ^ [_1692495, _1692497, _1692499])))], (45617 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1692495), 45615 ^ [_1692495, _1692497, _1692499]), _1692499)))]]]]], (24902 ^ _781013) ^ [_1245103, _1245105, _1245107, _1245109, _1245111] : [class_Fields_Olinordered__field(_1245103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245103), c_Groups_Ozero__class_Ozero(_1245103)), _1245105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245103), _1245105), _1245107)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245103), c_Groups_Ozero__class_Ozero(_1245103)), _1245109)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245103), _1245109), _1245111)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245103), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245103), _1245105), _1245111)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245103), _1245107), _1245109))))], (10383 ^ _781013) ^ [_965091, _965093, _965095, _965097] : [-(hBOOL(hAPP(hAPP(c_member(_965091), _965093), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965091, tc_HOL_Obool)), _965095), _965097)))), hBOOL(hAPP(hAPP(c_member(_965091), _965093), _965095)), hBOOL(hAPP(hAPP(c_member(_965091), _965093), _965097))], (3826 ^ _781013) ^ [_838873, _838875, _838877, _838879, _838881, _838883] : [-(c_Set_Oimage(_838883, _838879, _838875) = c_Set_Oimage(_838881, _838877, _838873)), _838883 = _838881, _838879 = _838877, _838875 = _838873], (48431 ^ _781013) ^ [_1760285, _1760287, _1760289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1760285, _1760285), tc_HOL_Obool)), _1760287), _1760289)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1760285, _1760285), tc_HOL_Obool)), _1760289), c_Transitive__Closure_Ortrancl(_1760285, _1760287))), -(c_Transitive__Closure_Ortrancl(_1760285, _1760289) = c_Transitive__Closure_Ortrancl(_1760285, _1760287))], (10355 ^ _781013) ^ [_964454, _964456, _964458, _964460] : [-(c_Nitpick_Ofold__graph_H(_964454, _964456, _964458, _964460, c_Orderings_Obot__class_Obot(tc_fun(_964454, tc_HOL_Obool)), _964460))], (4810 ^ _781013) ^ [_853941, _853943, _853945, _853947, _853949, _853951] : [-(c_Lazy__Sequence_Oanamorph(_853951, _853947, _853943) = c_Lazy__Sequence_Oanamorph(_853949, _853945, _853941)), _853951 = _853949, _853947 = _853945, _853943 = _853941], (31382 ^ _781013) ^ [_1369506, _1369508, _1369510, _1369512, _1369514] : [31385 ^ _781013 : [(31391 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1369514, 31383 ^ [_1369506, _1369508, _1369510, _1369512, _1369514]), 31387 ^ [_1369506, _1369508, _1369510, _1369512, _1369514]))], (31389 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1369512), 31384 ^ [_1369506, _1369508, _1369510, _1369512, _1369514]), _1369508), 31387 ^ [_1369506, _1369508, _1369510, _1369512, _1369514])))], (31386 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1369510, 31383 ^ [_1369506, _1369508, _1369510, _1369512, _1369514]), 31384 ^ [_1369506, _1369508, _1369510, _1369512, _1369514])))]], -(c_Hoare__Mirabelle_Otriple__valid(_1369506, _1369508, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1369506), _1369510), _1369512), _1369514)))], (11005 ^ _781013) ^ [_976406] : [-(c_Finite__Set_Ofun__left__comm__idem(_976406, tc_fun(_976406, tc_HOL_Obool), c_Set_Oinsert(_976406)))], (15143 ^ _781013) ^ [_1061281, _1061283, _1061285, _1061287] : [class_Groups_Ocomm__monoid__mult(_1061281), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1061283), _1061285))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1061283, _1061281), _1061287), _1061285) = c_Groups_Oone__class_Oone(_1061281))], (43201 ^ _781013) ^ [] : [-(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)))], (24588 ^ _781013) ^ [_1239671, _1239673, _1239675] : [class_Fields_Olinordered__field__inverse__zero(_1239671), 24591 ^ _781013 : [(24606 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239671), c_Groups_Ozero__class_Ozero(_1239671)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239671), _1239673), _1239675)))), 24607 ^ _781013 : [(24614 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239671), _1239673), c_Groups_Ozero__class_Ozero(_1239671))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239671), _1239675), c_Groups_Ozero__class_Ozero(_1239671)))], (24608 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239671), c_Groups_Ozero__class_Ozero(_1239671)), _1239673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239671), c_Groups_Ozero__class_Ozero(_1239671)), _1239675))]]], (24592 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239671), c_Groups_Ozero__class_Ozero(_1239671)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239671), _1239673), _1239675))), 24597 ^ _781013 : [(24600 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239671), c_Groups_Ozero__class_Ozero(_1239671)), _1239675)))], (24598 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239671), c_Groups_Ozero__class_Ozero(_1239671)), _1239673)))]], 24601 ^ _781013 : [(24604 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239671), _1239675), c_Groups_Ozero__class_Ozero(_1239671))))], (24602 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239671), _1239673), c_Groups_Ozero__class_Ozero(_1239671))))]]]]], (50826 ^ _781013) ^ [_1814240, _1814242] : [-(c_List_Osplice(_1814240, c_List_Olist_ONil(_1814240), _1814242) = _1814242)], (39538 ^ _781013) ^ [_1545710, _1545712] : [-(c_Hilbert__Choice_OEps(_1545710, hAPP(c_fequal, _1545712)) = _1545712)], (44971 ^ _781013) ^ [_1679272, _1679274, _1679276] : [hBOOL(hAPP(c_List_Odistinct(_1679272), _1679274)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1679272)), c_Enum_On__lists(_1679272, _1679276, _1679274))))], (1834 ^ _781013) ^ [_806680, _806682] : [-(class_HOL_Oequal(_806680)), _806682 = _806680, class_HOL_Oequal(_806682)], (44717 ^ _781013) ^ [_1674003, _1674005] : [-(hBOOL(hAPP(c_List_Odistinct(_1674003), c_List_Oremdups(_1674003, _1674005))))], (51392 ^ _781013) ^ [] : [-(class_HOL_Oequal(tc_HOL_Obool))], (32286 ^ _781013) ^ [_1393799, _1393801, _1393803] : [hBOOL(hAPP(c_Com_OWT, _1393803)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1393799, _1393801, _1393803))))], (38985 ^ _781013) ^ [_1532802, _1532804, _1532806, _1532808, _1532810] : [class_Orderings_Olinorder(_1532802), -(hBOOL(hAPP(hAPP(c_member(_1532802), hAPP(_1532804, _1532806)), hAPP(c_Set_Oimage(_1532808, _1532802, _1532804), hAPP(c_List_Oset(_1532808), _1532810))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1532808, _1532802, _1532804, _1532806, _1532810) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1532808, _1532802, _1532804), _1532806), _1532810))], (46709 ^ _781013) ^ [_1720613, _1720615, _1720617, _1720619] : [c_Wellfounded_Owf(_1720613, _1720615), -(c_Wellfounded_Owf(_1720617, hAPP(hAPP(c_Relation_Oinv__image(_1720613, _1720617), _1720615), _1720619)))], (45334 ^ _781013) ^ [_1686730, _1686732] : [class_Enum_Oenum(_1686730), 45337 ^ _781013 : [(45344 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1686730), _1686732)), -(hBOOL(hAPP(_1686732, 45347 ^ [_1686730, _1686732])))], (45338 ^ _781013) ^ [] : [45339 ^ _781013 : [(45340 ^ _781013) ^ [_1686832] : [hBOOL(hAPP(_1686732, _1686832))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1686730), _1686732)))]]], (27635 ^ _781013) ^ [_1296719, _1296721, _1296723, _1296725] : [class_Divides_Osemiring__div(_1296719), -(c_Divides_Odiv__class_Omod(_1296719, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296719), _1296721), _1296723), _1296725) = c_Divides_Odiv__class_Omod(_1296719, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296719), _1296721), c_Divides_Odiv__class_Omod(_1296719, _1296723, _1296725)), _1296725))], (15595 ^ _781013) ^ [_1069510, _1069512, _1069514, _1069516, _1069518] : [class_Rings_Oordered__semiring(_1069510), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069510), _1069512), _1069514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069510), _1069516), _1069518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069510), c_Groups_Ozero__class_Ozero(_1069510)), _1069514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069510), c_Groups_Ozero__class_Ozero(_1069510)), _1069516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069510), _1069512), _1069516)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069510), _1069514), _1069518))))], (31872 ^ _781013) ^ [_1384902, _1384904, _1384906, _1384908, _1384910] : [class_Complete__Lattice_Ocomplete__lattice(_1384902), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1384904, tc_HOL_Obool)), _1384906), _1384908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384902), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384904, _1384902), _1384906), _1384910)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384904, _1384902), _1384908), _1384910))))], (6262 ^ _781013) ^ [_882774, _882776, _882778] : [hBOOL(hAPP(c_Com_OWT, _882774)), hBOOL(hAPP(c_Com_OWT, _882776)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_882778, _882774, _882776))))], (45956 ^ _781013) ^ [_1700494, _1700496] : [class_Complete__Lattice_Ocomplete__lattice(_1700494), -(c_Complete__Lattice_OInf__class_OInf(_1700494, hAPP(hAPP(c_Set_Oinsert(_1700494), _1700496), c_Orderings_Obot__class_Obot(tc_fun(_1700494, tc_HOL_Obool)))) = _1700496)], (44582 ^ _781013) ^ [_1671209, _1671211] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1671209), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1671209))), _1671211))), -(c_List_Otranspose(_1671209, c_List_Otranspose(_1671209, _1671211)) = c_List_OtakeWhile(tc_List_Olist(_1671209), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1671209)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1671209), tc_List_Olist(_1671209), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1671209))), _1671211))], (21774 ^ _781013) ^ [_1189764, _1189766] : [class_Groups_Olinordered__ab__group__add(_1189764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1189764), _1189766)), -(_1189766 = c_Orderings_Obot__class_Obot(tc_fun(_1189764, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1189764), c_Big__Operators_Olinorder__class_OMin(_1189764, _1189766)) = c_Big__Operators_Olinorder__class_OMax(_1189764, hAPP(c_Set_Oimage(_1189764, _1189764, c_Groups_Ouminus__class_Ouminus(_1189764)), _1189766)))], (22226 ^ _781013) ^ [_1197776] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197776) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (39763 ^ _781013) ^ [_1551641, _1551643, _1551645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1551641), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551643)), _1551645))), -(hAPP(hAPP(c_List_Otake(_1551643), _1551641), c_List_Obutlast(_1551643, _1551645)) = hAPP(hAPP(c_List_Otake(_1551643), _1551641), _1551645))], (2534 ^ _781013) ^ [_818615, _818617] : [_818617 = _818615, -(c_Smallcheck_Osmall__class_Osmall(_818617) = c_Smallcheck_Osmall__class_Osmall(_818615))], (43506 ^ _781013) ^ [_1647781, _1647783] : [-(c_List_Otranspose(_1647781, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1647781)), c_List_Olist_ONil(_1647781)), _1647783)) = c_List_Otranspose(_1647781, _1647783))], (20406 ^ _781013) ^ [_1162248, _1162250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162248), _1162250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162248), hAPP(c_Nat_OSuc, _1162250))))], (1254 ^ _781013) ^ [_799430, _799432] : [-(class_Rings_Oidom(_799430)), _799432 = _799430, class_Rings_Oidom(_799432)], (48001 ^ _781013) ^ [_1750624, _1750626, _1750628] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1750624, _1750624)), _1750626), _1750628)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1750624, _1750624)), _1750626), c_Transitive__Closure_Otrancl(_1750624, _1750628))))], (22460 ^ _781013) ^ [_1201597, _1201599, _1201601] : [class_Orderings_Oorder(_1201597), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201597), _1201599), _1201601)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1201597, _1201601), _1201599) = c_Orderings_Obot__class_Obot(tc_fun(_1201597, tc_HOL_Obool)))], (45988 ^ _781013) ^ [_1701163, _1701165, _1701167, _1701169, _1701171] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1701163, tc_fun(_1701165, tc_HOL_Obool)), _1701167), hAPP(hAPP(c_COMBS(_1701163, tc_fun(_1701165, tc_HOL_Obool), tc_fun(_1701165, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1701165, tc_HOL_Obool), tc_fun(tc_fun(_1701165, tc_HOL_Obool), tc_fun(_1701165, tc_HOL_Obool)), _1701163), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1701165, tc_HOL_Obool))), _1701169)), _1701171)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1701165, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1701165, tc_HOL_Obool), hAPP(c_Set_Oimage(_1701163, tc_fun(_1701165, tc_HOL_Obool), _1701169), _1701167))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1701165, tc_HOL_Obool), hAPP(c_Set_Oimage(_1701163, tc_fun(_1701165, tc_HOL_Obool), _1701171), _1701167))))], (23345 ^ _781013) ^ [_1217672, _1217674, _1217676] : [class_Orderings_Oorder(_1217672), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217672), _1217674), _1217676)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1217672, _1217676, _1217674) = c_Orderings_Obot__class_Obot(tc_fun(_1217672, tc_HOL_Obool)))], (10939 ^ _781013) ^ [_974734, _974736, _974738, _974740] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974734, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974734, tc_HOL_Obool)), _974736), _974738)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974734, tc_HOL_Obool)), _974740), _974738)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974734, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974734, tc_HOL_Obool)), _974736), _974738)), _974740))], (9945 ^ _781013) ^ [_956778, _956780, _956782] : [class_Lattices_Osemilattice__inf(_956778), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956778), _956780), _956782) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956778), _956782), _956780))], (38359 ^ _781013) ^ [_1518147, _1518149, _1518151, _1518153, _1518155] : [hAPP(hAPP(c_Map_Omap__of(_1518147, _1518149), _1518151), _1518153) = hAPP(c_Option_Ooption_OSome(_1518149), _1518155), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1518147, _1518149)), hAPP(hAPP(c_Product__Type_OPair(_1518147, _1518149), _1518153), _1518155)), hAPP(c_List_Oset(tc_prod(_1518147, _1518149)), _1518151))))], (27920 ^ _781013) ^ [_1302245] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1302245), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23633 ^ _781013) ^ [_1222931, _1222933, _1222935, _1222937] : [class_Fields_Ofield(_1222931), -(_1222933 = c_Groups_Ozero__class_Ozero(_1222931)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1222931), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222931), _1222935), _1222933)), _1222937) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222931), hAPP(hAPP(c_Power_Opower__class_Opower(_1222931), _1222935), _1222937)), hAPP(hAPP(c_Power_Opower__class_Opower(_1222931), _1222933), _1222937)))], (35517 ^ _781013) ^ [_1453545] : [_1453545 = c_Int_OMin, -(c_Int_OBit1(_1453545) = c_Int_OMin)], (3572 ^ _781013) ^ [_834910, _834912] : [_834912 = _834910, -(c_Int_Oint__ge__less__than2(_834912) = c_Int_Oint__ge__less__than2(_834910))], (11884 ^ _781013) ^ [_995372, _995374] : [class_Lattices_Olattice(_995372), hBOOL(hAPP(c_Finite__Set_Ofinite(_995372), _995374)), -(_995374 = c_Orderings_Obot__class_Obot(tc_fun(_995372, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995372), c_Big__Operators_Olattice__class_OInf__fin(_995372, _995374)), c_Big__Operators_Olattice__class_OSup__fin(_995372, _995374))))], (16958 ^ _781013) ^ [_1095697, _1095699, _1095701, _1095703, _1095705] : [class_Groups_Ocomm__monoid__mult(_1095697), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095699), _1095701)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095699), _1095703)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095697), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1095699, _1095697), _1095705), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1095699, tc_HOL_Obool)), _1095701), _1095703))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1095699, _1095697), _1095705), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095699, tc_HOL_Obool)), _1095701), _1095703))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095697), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1095699, _1095697), _1095705), _1095701)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1095699, _1095697), _1095705), _1095703)))], (32124 ^ _781013) ^ [_1390944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390944), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1390944)))], (44890 ^ _781013) ^ [_1677296, _1677298, _1677300] : [-(hAPP(hAPP(c_List_Oappend(_1677296), c_List_OtakeWhile(_1677296, _1677298, _1677300)), c_List_OdropWhile(_1677296, _1677298, _1677300)) = _1677300)], (19136 ^ _781013) ^ [_1139325, _1139327, _1139329, _1139331] : [class_Rings_Ocomm__semiring__1(_1139325), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1139325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139325), _1139327), _1139329)), _1139331) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139325), hAPP(hAPP(c_Power_Opower__class_Opower(_1139325), _1139327), _1139331)), hAPP(hAPP(c_Power_Opower__class_Opower(_1139325), _1139329), _1139331)))], (42953 ^ _781013) ^ [_1633810, _1633812, _1633814, _1633816, _1633818] : [42955 ^ _781013 : [(42958 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1633810), _1633812), hAPP(_1633818, 42954 ^ [_1633810, _1633812, _1633814, _1633816, _1633818])))], (42956 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633814), 42954 ^ [_1633810, _1633812, _1633814, _1633816, _1633818]), _1633816)))]], -(hBOOL(hAPP(hAPP(c_member(_1633810), _1633812), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633814, tc_fun(_1633810, tc_HOL_Obool)), _1633816), _1633818))))], (10415 ^ _781013) ^ [_965686, _965688, _965690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965686, tc_HOL_Obool)), _965688), _965690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965686, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_965686, tc_HOL_Obool)), _965690)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_965686, tc_HOL_Obool)), _965688))))], (51260 ^ _781013) ^ [] : [-(class_HOL_Oequal(tc_Int_Oint))], (28116 ^ _781013) ^ [_1305851, _1305853, _1305855, _1305857] : [_1305851 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1305853), _1305855)), _1305857), -(_1305853 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1305851, _1305853) = _1305857), 28123 ^ _781013 : [(28126 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1305857)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1305857), _1305853))], (28124 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1305853)))]], 28131 ^ _781013 : [(28134 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1305853), _1305857)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1305857), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (28132 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1305853))]]], (39261 ^ _781013) ^ [_1539460, _1539462, _1539464, _1539466, _1539468] : [-(_1539460 = _1539462), -(hAPP(hAPP(c_List_Onth(_1539464), hAPP(hAPP(c_List_Olist__update(_1539464, _1539466), _1539460), _1539468)), _1539462) = hAPP(hAPP(c_List_Onth(_1539464), _1539466), _1539462))], (15731 ^ _781013) ^ [_1072014, _1072016, _1072018, _1072020] : [class_Rings_Olinordered__ring__strict(_1072014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072014), _1072016), _1072018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072014), _1072020), c_Groups_Ozero__class_Ozero(_1072014))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072014), _1072020), _1072018)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072014), _1072020), _1072016))))], (47852 ^ _781013) ^ [_1747597, _1747599, _1747601, _1747603] : [47853 ^ _781013 : [(47856 ^ _781013) ^ [] : [c_List_Olist__ex(_1747597, _1747599, _1747603)], (47854 ^ _781013) ^ [] : [c_List_Olist__ex(_1747597, _1747599, _1747601)]], -(c_List_Olist__ex(_1747597, _1747599, hAPP(hAPP(c_List_Oappend(_1747597), _1747601), _1747603)))], (51314 ^ _781013) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (2090 ^ _781013) ^ [_811579, _811581, _811583, _811585, _811587, _811589, _811591, _811593, _811595, _811597] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_811597, _811593, _811589, _811585, _811581) = c_SetInterval_Oord_OgreaterThanAtMost(_811595, _811591, _811587, _811583, _811579)), _811597 = _811595, _811593 = _811591, _811589 = _811587, _811585 = _811583, _811581 = _811579], (46651 ^ _781013) ^ [_1717741, _1717743, _1717745, _1717747, _1717749, _1717751, _1717753, _1717755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1717741, _1717743), tc_HOL_Obool)), _1717745), hAPP(hAPP(c_Product__Type_OSigma(_1717741, _1717743), _1717747), hAPP(c_COMBK(tc_fun(_1717743, tc_HOL_Obool), _1717741), _1717749)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1717743, _1717751), tc_HOL_Obool)), _1717753), hAPP(hAPP(c_Product__Type_OSigma(_1717743, _1717751), _1717749), hAPP(c_COMBK(tc_fun(_1717751, tc_HOL_Obool), _1717743), _1717755)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1717741, _1717751), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1717741, _1717743, _1717751), _1717745), _1717753)), hAPP(hAPP(c_Product__Type_OSigma(_1717741, _1717751), _1717747), hAPP(c_COMBK(tc_fun(_1717751, tc_HOL_Obool), _1717741), _1717755)))))], (9158 ^ _781013) ^ [_942823, _942825, _942827, _942829, _942831] : [-(hBOOL(hAPP(hAPP(c_member(_942823), _942825), _942827))), -(hAPP(c_Map_Orestrict__map(_942823, _942829, _942831, _942827), _942825) = c_Option_Ooption_ONone(_942829))], (20355 ^ _781013) ^ [_1161363, _1161365] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1161363), _1161365) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 20356 ^ _781013 : [(20363 ^ _781013) ^ [] : [_1161363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1161365 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20357 ^ _781013) ^ [] : [_1161363 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (12520 ^ _781013) ^ [_1007090, _1007092, _1007094] : [class_Lattices_Olattice(_1007090), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007090), _1007092)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007090), _1007094)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1007090, tc_HOL_Obool)), _1007092), _1007094) = c_Orderings_Obot__class_Obot(tc_fun(_1007090, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1007090), c_Big__Operators_Olattice__class_OInf__fin(_1007090, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1007090, tc_HOL_Obool)), _1007092), _1007094))), c_Big__Operators_Olattice__class_OInf__fin(_1007090, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1007090, tc_HOL_Obool)), _1007092), _1007094))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1007090), c_Big__Operators_Olattice__class_OInf__fin(_1007090, _1007092)), c_Big__Operators_Olattice__class_OInf__fin(_1007090, _1007094)))], (51254 ^ _781013) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (27940 ^ _781013) ^ [_1302752, _1302754, _1302756] : [class_Divides_Osemiring__div(_1302752), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1302752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302752), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1302752), _1302754), _1302756)), _1302756)), c_Divides_Odiv__class_Omod(_1302752, _1302754, _1302756)) = _1302754)], (46633 ^ _781013) ^ [_1717162, _1717164, _1717166, _1717168] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1717162, _1717164, _1717166), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1717162, _1717164), tc_HOL_Obool))), _1717168) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1717162, _1717166), tc_HOL_Obool)))], (42629 ^ _781013) ^ [_1626039, _1626041, _1626043] : [_1626039 = c_List_Olist_ONil(_1626041), -(c_List_Olast(_1626041, hAPP(hAPP(c_List_Olist_OCons(_1626041), _1626043), _1626039)) = _1626043)], (48475 ^ _781013) ^ [_1761142, _1761144] : [hAPP(c_Code__Numeral_Onat__of, _1761142) = hAPP(c_Code__Numeral_Onat__of, _1761144), -(_1761142 = _1761144)], (12382 ^ _781013) ^ [_1004468, _1004470] : [class_Lattices_Olattice(_1004468), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004468), _1004470), _1004470) = _1004470)], (34687 ^ _781013) ^ [_1438087] : [c_Int_OPls = c_Int_OBit0(_1438087), -(c_Int_OPls = _1438087)], (30045 ^ _781013) ^ [_1342540] : [class_Orderings_Olinorder(_1342540), -(c_Finite__Set_Ofun__left__comm__idem(_1342540, _1342540, c_Orderings_Oord__class_Omax(_1342540)))], (35289 ^ _781013) ^ [_1448663, _1448665, _1448667] : [class_Rings_Olinordered__idom(_1448663), 35292 ^ _781013 : [(35293 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448663), c_Groups_Ozero__class_Ozero(_1448663)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1448663), hAPP(hAPP(c_Power_Opower__class_Opower(_1448663), _1448665), 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(_1448663), _1448667), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1448665 = c_Groups_Ozero__class_Ozero(_1448663), _1448667 = c_Groups_Ozero__class_Ozero(_1448663)], (35303 ^ _781013) ^ [] : [35304 ^ _781013 : [(35307 ^ _781013) ^ [] : [-(_1448667 = c_Groups_Ozero__class_Ozero(_1448663))], (35305 ^ _781013) ^ [] : [-(_1448665 = c_Groups_Ozero__class_Ozero(_1448663))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448663), c_Groups_Ozero__class_Ozero(_1448663)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1448663), hAPP(hAPP(c_Power_Opower__class_Opower(_1448663), _1448665), 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(_1448663), _1448667), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (9130 ^ _781013) ^ [_942224, _942226, _942228, _942230, _942232] : [c_Finite__Set_Ofolding__one__idem(_942224, _942226, _942228), hAPP(_942230, hAPP(hAPP(_942226, 9135 ^ [_942224, _942226, _942228, _942230, _942232]), 9136 ^ [_942224, _942226, _942228, _942230, _942232])) = hAPP(hAPP(_942226, hAPP(_942230, 9135 ^ [_942224, _942226, _942228, _942230, _942232])), hAPP(_942230, 9136 ^ [_942224, _942226, _942228, _942230, _942232])), hBOOL(hAPP(c_Finite__Set_Ofinite(_942224), _942232)), -(_942232 = c_Orderings_Obot__class_Obot(tc_fun(_942224, tc_HOL_Obool))), -(hAPP(_942230, hAPP(_942228, _942232)) = hAPP(_942228, hAPP(c_Set_Oimage(_942224, _942224, _942230), _942232)))], (20341 ^ _781013) ^ [_1161179, _1161181] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1161179), _1161181) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20346 ^ _781013 : [(20349 ^ _781013) ^ [] : [-(_1161181 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20347 ^ _781013) ^ [] : [-(_1161179 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20350 ^ _781013 : [(20353 ^ _781013) ^ [] : [-(_1161181 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20351 ^ _781013) ^ [] : [-(_1161179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (36038 ^ _781013) ^ [_1466838, _1466840, _1466842, _1466844, _1466846, _1466848] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1466838, _1466840), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1466842), _1466844))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1466838, _1466840), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1466846), _1466848))), -(_1466840 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1466844 = _1466848)], (14367 ^ _781013) ^ [_1046961, _1046963, _1046965, _1046967, _1046969] : [class_Groups_Ocomm__monoid__add(_1046961), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046963), _1046965)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046963), _1046967)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046961), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046963, _1046961), _1046969), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1046963, tc_HOL_Obool)), _1046965), _1046967))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046963, _1046961), _1046969), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1046963, tc_HOL_Obool)), _1046965), _1046967))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046961), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046963, _1046961), _1046969), _1046965)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046963, _1046961), _1046969), _1046967)))], (32280 ^ _781013) ^ [_1393708, _1393710, _1393712] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1393708, _1393710, _1393712))), -(hBOOL(hAPP(c_Com_OWT, _1393712)))], (22342 ^ _781013) ^ [_1199688, _1199690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199688), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22345 ^ _781013 : [(22352 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1199690), _1199688)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22346 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1199690), _1199688)), 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)), _1199690)))]]], (37884 ^ _781013) ^ [_1506582, _1506584, _1506586, _1506588, _1506590, _1506592, _1506594] : [-(hAPP(c_Product__Type_Oapfst(_1506582, _1506584, _1506586, _1506588), hAPP(c_Product__Type_Oapfst(_1506590, _1506582, _1506586, _1506592), _1506594)) = hAPP(c_Product__Type_Oapfst(_1506590, _1506584, _1506586, hAPP(c_Fun_Ocomp(_1506582, _1506584, _1506590, _1506588), _1506592)), _1506594))], (51444 ^ _781013) ^ [_1823000] : [class_Enum_Oenum(_1823000), -(class_Enum_Oenum(tc_Option_Ooption(_1823000)))], (50620 ^ _781013) ^ [_1809944, _1809946, _1809948, _1809950, _1809952] : [_1809944 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1809946, _1809948, _1809950, _1809952), _1809944) = c_Lazy__Sequence_Ohit__bound(_1809948))], (38580 ^ _781013) ^ [_1523038, _1523040, _1523042] : [-(hBOOL(hAPP(hAPP(c_member(_1523038), _1523040), hAPP(c_List_Oset(_1523038), _1523042)))), -(c_List_Oremove1(_1523038, _1523040, _1523042) = _1523042)], (36164 ^ _781013) ^ [_1469893, _1469895, _1469897, _1469899, _1469901, _1469903, _1469905] : [c_Equiv__Relations_Oequiv(_1469893, _1469895, _1469897), hBOOL(hAPP(hAPP(c_member(tc_fun(_1469893, tc_HOL_Obool)), _1469899), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1469893), _1469895), _1469897))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1469893, tc_HOL_Obool)), _1469901), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1469893), _1469895), _1469897))), hBOOL(hAPP(hAPP(c_member(_1469893), _1469903), _1469899)), hBOOL(hAPP(hAPP(c_member(_1469893), _1469905), _1469901)), 36183 ^ _781013 : [(36190 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1469893, _1469893)), hAPP(hAPP(c_Product__Type_OPair(_1469893, _1469893), _1469903), _1469905)), _1469897)), -(_1469899 = _1469901)], (36184 ^ _781013) ^ [] : [_1469899 = _1469901, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1469893, _1469893)), hAPP(hAPP(c_Product__Type_OPair(_1469893, _1469893), _1469903), _1469905)), _1469897)))]]], (40225 ^ _781013) ^ [_1565480, _1565482, _1565484, _1565486, _1565488, _1565490] : [hBOOL(hAPP(hAPP(_1565480, _1565482), _1565484)), c_List_Olistrelp(_1565486, _1565480, _1565488, _1565490), -(c_List_Olistrelp(_1565486, _1565480, hAPP(hAPP(c_List_Olist_OCons(_1565486), _1565482), _1565488), hAPP(hAPP(c_List_Olist_OCons(_1565486), _1565484), _1565490)))], (30657 ^ _781013) ^ [_1354213, _1354215, _1354217] : [class_Orderings_Olinorder(_1354213), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354213), _1354215)), -(_1354215 = c_Orderings_Obot__class_Obot(tc_fun(_1354213, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354213), _1354217)), -(_1354217 = c_Orderings_Obot__class_Obot(tc_fun(_1354213, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1354213), c_Big__Operators_Olattice_OSup__fin(_1354213, c_Orderings_Oord__class_Omax(_1354213), _1354215)), c_Big__Operators_Olattice_OSup__fin(_1354213, c_Orderings_Oord__class_Omax(_1354213), _1354217)) = c_Big__Operators_Olattice_OSup__fin(_1354213, c_Orderings_Oord__class_Omax(_1354213), hAPP(c_Set_OCollect(_1354213), hAPP(hAPP(c_COMBB(tc_fun(_1354213, tc_HOL_Obool), tc_HOL_Obool, _1354213), c_HOL_OEx(_1354213)), hAPP(hAPP(c_COMBB(tc_fun(_1354213, tc_fun(_1354213, tc_HOL_Obool)), tc_fun(_1354213, tc_HOL_Obool), _1354213), hAPP(c_COMBB(tc_fun(_1354213, tc_HOL_Obool), tc_HOL_Obool, _1354213), c_HOL_OEx(_1354213))), hAPP(hAPP(c_COMBC(_1354213, tc_fun(_1354213, tc_fun(_1354213, tc_HOL_Obool)), tc_fun(_1354213, tc_fun(_1354213, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1354213, tc_fun(tc_fun(_1354213, tc_HOL_Obool), tc_fun(_1354213, tc_HOL_Obool))), tc_fun(tc_fun(_1354213, tc_fun(_1354213, tc_HOL_Obool)), tc_fun(_1354213, tc_fun(_1354213, tc_HOL_Obool))), _1354213), c_COMBS(_1354213, tc_fun(_1354213, tc_HOL_Obool), tc_fun(_1354213, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1354213, tc_fun(_1354213, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1354213, tc_fun(tc_fun(_1354213, tc_HOL_Obool), tc_fun(_1354213, tc_HOL_Obool))), _1354213), hAPP(c_COMBB(tc_fun(_1354213, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1354213, tc_HOL_Obool), tc_fun(_1354213, tc_HOL_Obool)), _1354213), c_COMBS(_1354213, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1354213, tc_fun(_1354213, tc_HOL_Obool)), tc_fun(_1354213, tc_fun(_1354213, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1354213), hAPP(c_COMBB(tc_fun(_1354213, tc_HOL_Obool), tc_fun(_1354213, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1354213), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1354213), c_fconj))), hAPP(hAPP(c_COMBC(_1354213, tc_fun(_1354213, tc_fun(_1354213, _1354213)), tc_fun(_1354213, tc_fun(_1354213, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1354213, _1354213), tc_fun(_1354213, tc_HOL_Obool)), tc_fun(tc_fun(_1354213, tc_fun(_1354213, _1354213)), tc_fun(_1354213, tc_fun(_1354213, tc_HOL_Obool))), _1354213), c_COMBB(tc_fun(_1354213, _1354213), tc_fun(_1354213, tc_HOL_Obool), _1354213)), hAPP(hAPP(c_COMBB(tc_fun(_1354213, tc_HOL_Obool), tc_fun(tc_fun(_1354213, _1354213), tc_fun(_1354213, tc_HOL_Obool)), _1354213), c_COMBB(_1354213, tc_HOL_Obool, _1354213)), c_fequal))), c_Orderings_Oord__class_Omin(_1354213)))))), hAPP(hAPP(c_COMBC(_1354213, tc_fun(_1354213, tc_HOL_Obool), tc_fun(_1354213, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1354213, tc_HOL_Obool), tc_fun(_1354213, tc_HOL_Obool)), _1354213), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1354213)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1354213), c_fconj), hAPP(hAPP(c_COMBC(_1354213, tc_fun(_1354213, tc_HOL_Obool), tc_HOL_Obool), c_member(_1354213)), _1354215)))), hAPP(hAPP(c_COMBC(_1354213, tc_fun(_1354213, tc_HOL_Obool), tc_HOL_Obool), c_member(_1354213)), _1354217))))))))], (34869 ^ _781013) ^ [_1441143] : [-(c_Int_Osucc(c_Int_OBit1(_1441143)) = c_Int_OBit0(c_Int_Osucc(_1441143)))], (31736 ^ _781013) ^ [_1380852, _1380854, _1380856, _1380858, _1380860] : [hBOOL(hAPP(hAPP(c_member(_1380852), _1380854), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380856, tc_fun(_1380852, tc_HOL_Obool)), _1380858), _1380860))), 31740 ^ _781013 : [(31743 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1380852), _1380854), hAPP(_1380860, 31739 ^ [_1380852, _1380854, _1380856, _1380858, _1380860]))))], (31741 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1380856), 31739 ^ [_1380852, _1380854, _1380856, _1380858, _1380860]), _1380858)))]]], (9733 ^ _781013) ^ [_953006, _953008, _953010] : [_953008 = _953010, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_953006, tc_HOL_Obool)), _953008) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_953006, tc_HOL_Obool)), _953010))], (2276 ^ _781013) ^ [_814666, _814668, _814670, _814672, _814674, _814676] : [-(c_Option_Ooption_Ooption__size(_814676, _814672, _814668) = c_Option_Ooption_Ooption__size(_814674, _814670, _814666)), _814676 = _814674, _814672 = _814670, _814668 = _814666], (48974 ^ _781013) ^ [_1773630, _1773632] : [-(c_Transitive__Closure_Ortrancl(_1773630, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1773630, _1773630), tc_HOL_Obool)), _1773632), c_Relation_OId(_1773630))) = c_Transitive__Closure_Ortrancl(_1773630, _1773632))], (8841 ^ _781013) ^ [_935635, _935637, _935639, _935641] : [class_Lattices_Osemilattice__sup(_935635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935635), _935637), _935639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935635), _935637), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935635), _935641), _935639))))], (21824 ^ _781013) ^ [_1190622, _1190624, _1190626, _1190628] : [class_Rings_Osemiring__1(_1190622), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1190622), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1190624, tc_Nat_Onat), _1190626), _1190628)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1190624, _1190622), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1190622, _1190624), c_Nat_Osemiring__1__class_Oof__nat(_1190622)), _1190626)), _1190628))], (42943 ^ _781013) ^ [_1633567, _1633569, _1633571, _1633573, _1633575] : [hBOOL(hAPP(hAPP(c_member(_1633567), _1633569), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633571, tc_fun(_1633567, tc_HOL_Obool)), _1633573), _1633575))), 42946 ^ _781013 : [(42947 ^ _781013) ^ [_1633691] : [hBOOL(hAPP(hAPP(c_member(_1633571), _1633691), _1633573)), -(hBOOL(hAPP(hAPP(c_member(_1633567), _1633569), hAPP(_1633575, _1633691))))]]], (20009 ^ _781013) ^ [_1155676, _1155678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155676), hAPP(c_Nat_OSuc, _1155678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155676), _1155678))), -(_1155676 = _1155678)], (28706 ^ _781013) ^ [_1316643, _1316645, _1316647] : [class_Orderings_Olinorder(_1316643), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316643), _1316645), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316643), _1316645), _1316647)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316643), _1316645), _1316647))], (51310 ^ _781013) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (12864 ^ _781013) ^ [_1014289, _1014291, _1014293, _1014295, _1014297] : [hBOOL(hAPP(hAPP(c_member(_1014289), _1014291), hAPP(c_Set_Ovimage(_1014289, _1014293, _1014295), _1014297))), -(hBOOL(hAPP(hAPP(c_member(_1014293), hAPP(_1014295, _1014291)), _1014297)))], (10949 ^ _781013) ^ [_975116, _975118, _975120, _975122, _975124] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975116, _975118, _975120, _975122, c_Orderings_Obot__class_Obot(tc_fun(_975116, tc_HOL_Obool))), _975124)), -(_975124 = _975122)], (3476 ^ _781013) ^ [_833390, _833392, _833394, _833396, _833398, _833400, _833402, _833404] : [-(c_List_Omaps(_833404, _833400, _833396, _833392) = c_List_Omaps(_833402, _833398, _833394, _833390)), _833404 = _833402, _833400 = _833398, _833396 = _833394, _833392 = _833390], (39769 ^ _781013) ^ [_1551782, _1551784] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551782)), c_List_Obutlast(_1551782, _1551784)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551782)), _1551784)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (21029 ^ _781013) ^ [_1175060, _1175062, _1175064] : [class_Lattices_Odistrib__lattice(_1175060), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175060), _1175062)), -(_1175062 = c_Orderings_Obot__class_Obot(tc_fun(_1175060, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175060), _1175064)), -(_1175064 = c_Orderings_Obot__class_Obot(tc_fun(_1175060, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1175060), c_Big__Operators_Olattice__class_OSup__fin(_1175060, _1175062)), c_Big__Operators_Olattice__class_OSup__fin(_1175060, _1175064)) = c_Big__Operators_Olattice__class_OSup__fin(_1175060, hAPP(c_Set_OCollect(_1175060), hAPP(hAPP(c_COMBB(tc_fun(_1175060, tc_HOL_Obool), tc_HOL_Obool, _1175060), c_HOL_OEx(_1175060)), hAPP(hAPP(c_COMBB(tc_fun(_1175060, tc_fun(_1175060, tc_HOL_Obool)), tc_fun(_1175060, tc_HOL_Obool), _1175060), hAPP(c_COMBB(tc_fun(_1175060, tc_HOL_Obool), tc_HOL_Obool, _1175060), c_HOL_OEx(_1175060))), hAPP(hAPP(c_COMBC(_1175060, tc_fun(_1175060, tc_fun(_1175060, tc_HOL_Obool)), tc_fun(_1175060, tc_fun(_1175060, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1175060, tc_fun(tc_fun(_1175060, tc_HOL_Obool), tc_fun(_1175060, tc_HOL_Obool))), tc_fun(tc_fun(_1175060, tc_fun(_1175060, tc_HOL_Obool)), tc_fun(_1175060, tc_fun(_1175060, tc_HOL_Obool))), _1175060), c_COMBS(_1175060, tc_fun(_1175060, tc_HOL_Obool), tc_fun(_1175060, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1175060, tc_fun(_1175060, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1175060, tc_fun(tc_fun(_1175060, tc_HOL_Obool), tc_fun(_1175060, tc_HOL_Obool))), _1175060), hAPP(c_COMBB(tc_fun(_1175060, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1175060, tc_HOL_Obool), tc_fun(_1175060, tc_HOL_Obool)), _1175060), c_COMBS(_1175060, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1175060, tc_fun(_1175060, tc_HOL_Obool)), tc_fun(_1175060, tc_fun(_1175060, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1175060), hAPP(c_COMBB(tc_fun(_1175060, tc_HOL_Obool), tc_fun(_1175060, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1175060), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1175060), c_fconj))), hAPP(hAPP(c_COMBC(_1175060, tc_fun(_1175060, tc_fun(_1175060, _1175060)), tc_fun(_1175060, tc_fun(_1175060, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1175060, _1175060), tc_fun(_1175060, tc_HOL_Obool)), tc_fun(tc_fun(_1175060, tc_fun(_1175060, _1175060)), tc_fun(_1175060, tc_fun(_1175060, tc_HOL_Obool))), _1175060), c_COMBB(tc_fun(_1175060, _1175060), tc_fun(_1175060, tc_HOL_Obool), _1175060)), hAPP(hAPP(c_COMBB(tc_fun(_1175060, tc_HOL_Obool), tc_fun(tc_fun(_1175060, _1175060), tc_fun(_1175060, tc_HOL_Obool)), _1175060), c_COMBB(_1175060, tc_HOL_Obool, _1175060)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1175060)))))), hAPP(hAPP(c_COMBC(_1175060, tc_fun(_1175060, tc_HOL_Obool), tc_fun(_1175060, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1175060, tc_HOL_Obool), tc_fun(_1175060, tc_HOL_Obool)), _1175060), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1175060)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1175060), c_fconj), hAPP(hAPP(c_COMBC(_1175060, tc_fun(_1175060, tc_HOL_Obool), tc_HOL_Obool), c_member(_1175060)), _1175062)))), hAPP(hAPP(c_COMBC(_1175060, tc_fun(_1175060, tc_HOL_Obool), tc_HOL_Obool), c_member(_1175060)), _1175064))))))))], (45874 ^ _781013) ^ [_1698803, _1698805] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1698803, tc_HOL_Obool), _1698805) = hAPP(c_Set_OCollect(_1698803), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1698803, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1698803), c_HOL_OAll(tc_fun(_1698803, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1698803, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1698803, tc_HOL_Obool), tc_HOL_Obool), _1698803), hAPP(c_COMBS(tc_fun(_1698803, 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(_1698803, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1698803, tc_HOL_Obool), tc_fun(tc_fun(_1698803, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1698803, tc_HOL_Obool))), _1698805)))), c_member(_1698803)))))], (3550 ^ _781013) ^ [_834591, _834593, _834595, _834597] : [-(c_List_Olenlex(_834597, _834593) = c_List_Olenlex(_834595, _834591)), _834597 = _834595, _834593 = _834591], (10369 ^ _781013) ^ [_964772, _964774, _964776, _964778] : [hBOOL(hAPP(hAPP(c_member(_964772), _964774), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964772, tc_HOL_Obool)), _964776), _964778))), -(hBOOL(hAPP(hAPP(c_member(_964772), _964774), _964776)))], (38097 ^ _781013) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (17651 ^ _781013) ^ [_1110944, _1110946] : [17652 ^ _781013 : [(17655 ^ _781013) ^ [] : [_1110946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17653 ^ _781013) ^ [] : [_1110944 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110944), _1110946) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46776 ^ _781013) ^ [_1721756, _1721758, _1721760] : [c_Wellfounded_Owf(_1721756, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1721756, _1721756), tc_HOL_Obool)), _1721758), _1721760)), -(c_Wellfounded_Owf(_1721756, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1721756, _1721756), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1721756, _1721756), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1721756, _1721756, _1721756), _1721758), _1721758)), hAPP(hAPP(c_Relation_Orel__comp(_1721756, _1721756, _1721756), _1721760), _1721758))), _1721760)))], (21223 ^ _781013) ^ [_1179179, _1179181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179179)), -(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), _1179179), _1179181))))], (33352 ^ _781013) ^ [_1414087] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414087))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414087) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6648 ^ _781013) ^ [_890147, _890149, _890151, _890153] : [6649 ^ _781013 : [(6650 ^ _781013) ^ [_890236] : [_890151 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_890147, tc_Option_Ooption(_890149)), hAPP(c_COMBK(tc_Option_Ooption(_890149), _890147), c_Option_Ooption_ONone(_890149))), _890153), hAPP(c_Option_Ooption_OSome(_890149), _890236))]], -(c_Map_Odom(_890147, _890149, _890151) = hAPP(hAPP(c_Set_Oinsert(_890147), _890153), c_Orderings_Obot__class_Obot(tc_fun(_890147, tc_HOL_Obool))))], (49914 ^ _781013) ^ [_1795392] : [class_Orderings_Olinorder(_1795392), -(c_Finite__Set_Ofun__left__comm(_1795392, tc_List_Olist(_1795392), c_List_Olinorder__class_Oinsort__key(_1795392, _1795392, c_COMBI(_1795392))))], (22368 ^ _781013) ^ [_1200109, _1200111, _1200113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1200109), _1200111)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1200109), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1200111), _1200113)) = 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, _1200109), _1200111)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1200111), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1200111), _1200113))))], (21732 ^ _781013) ^ [_1189017, _1189019, _1189021] : [class_Rings_Olinordered__semidom(_1189017), 21735 ^ _781013 : [(21742 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1189019), _1189021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189017), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189017), _1189019)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189017), _1189021))))], (21736 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189017), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189017), _1189019)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189017), _1189021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1189019), _1189021)))]]], (36084 ^ _781013) ^ [_1468283, _1468285, _1468287, _1468289] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468283, _1468285), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1468287), _1468289))), -(_1468285 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1468283), _1468285) = _1468287)], (35957 ^ _781013) ^ [_1464147, _1464149, _1464151, _1464153, _1464155, _1464157] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464147, tc_fun(_1464149, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1464147, tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_fun(_1464149, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464149, tc_fun(tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_fun(_1464149, tc_HOL_Obool)), _1464147), c_COMBC(_1464149, tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464149, tc_prod(_1464147, _1464149)), tc_fun(_1464149, tc_fun(tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_HOL_Obool)), _1464147), hAPP(c_COMBB(tc_prod(_1464147, _1464149), tc_fun(tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_HOL_Obool), _1464149), c_member(tc_prod(_1464147, _1464149)))), c_Product__Type_OPair(_1464147, _1464149)))), _1464151)), hAPP(hAPP(c_COMBC(_1464147, tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_fun(_1464149, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464149, tc_fun(tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_fun(_1464149, tc_HOL_Obool)), _1464147), c_COMBC(_1464149, tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464149, tc_prod(_1464147, _1464149)), tc_fun(_1464149, tc_fun(tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_HOL_Obool)), _1464147), hAPP(c_COMBB(tc_prod(_1464147, _1464149), tc_fun(tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool), tc_HOL_Obool), _1464149), c_member(tc_prod(_1464147, _1464149)))), c_Product__Type_OPair(_1464147, _1464149)))), _1464153)), _1464155), _1464157)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1464147, _1464149)), hAPP(hAPP(c_Product__Type_OPair(_1464147, _1464149), _1464155), _1464157)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1464147, _1464149), tc_HOL_Obool)), _1464151), _1464153))))], (8493 ^ _781013) ^ [_927945, _927947, _927949, _927951, _927953] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_927945), _927947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927949, tc_HOL_Obool)), _927951), hAPP(c_Set_Oimage(_927945, _927949, _927953), _927947))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_927949), _927951)))], (2646 ^ _781013) ^ [_820283, _820285, _820287, _820289] : [-(c_Divides_OposDivAlg(_820289, _820285) = c_Divides_OposDivAlg(_820287, _820283)), _820289 = _820287, _820285 = _820283], (3342 ^ _781013) ^ [_831363, _831365, _831367, _831369] : [-(c_List_Olinorder__class_Osorted__list__of__set(_831369, _831365) = c_List_Olinorder__class_Osorted__list__of__set(_831367, _831363)), _831369 = _831367, _831365 = _831363], (8341 ^ _781013) ^ [_924143, _924145] : [hBOOL(hAPP(hAPP(c_member(_924143), _924145), c_Orderings_Obot__class_Obot(tc_fun(_924143, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_924143, tc_HOL_Obool)), _924145)))], (40892 ^ _781013) ^ [_1584724, _1584726, _1584728, _1584730] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1584724), tc_List_Olist(_1584724))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1584724), tc_List_Olist(_1584724)), _1584726), _1584728)), c_List_Olistrel1(_1584724, _1584730))), 40897 ^ _781013 : [(40902 ^ _781013) ^ [] : [-(_1584728 = hAPP(hAPP(c_List_Olist__update(_1584724, _1584726), 40896 ^ [_1584724, _1584726, _1584728, _1584730]), 40895 ^ [_1584724, _1584726, _1584728, _1584730]))], (40900 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40896 ^ [_1584724, _1584726, _1584728, _1584730]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584724)), _1584726))))], (40898 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584724, _1584724)), hAPP(hAPP(c_Product__Type_OPair(_1584724, _1584724), hAPP(hAPP(c_List_Onth(_1584724), _1584726), 40896 ^ [_1584724, _1584726, _1584728, _1584730])), 40895 ^ [_1584724, _1584726, _1584728, _1584730])), _1584730)))]]], (11498 ^ _781013) ^ [_987786, _987788, _987790] : [-(c_Fun_Oinj__on(_987786, _987788, _987790, c_Orderings_Obot__class_Obot(tc_fun(_987786, tc_HOL_Obool))))], (37544 ^ _781013) ^ [_1497866, _1497868, _1497870, _1497872, _1497874] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1497866, _1497868, _1497870), _1497872), _1497874) = hAPP(hAPP(_1497872, hAPP(c_Product__Type_Ofst(_1497866, _1497868), _1497874)), hAPP(c_Product__Type_Osnd(_1497866, _1497868), _1497874)))], (33572 ^ _781013) ^ [_1417897] : [-(c_Int_Osucc(c_Int_Opred(_1417897)) = _1417897)], (34291 ^ _781013) ^ [_1431354] : [-(c_Int_OBit1(_1431354) = 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)), _1431354)), _1431354))], (47938 ^ _781013) ^ [_1749292, _1749294, _1749296, _1749298, _1749300] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1749292, _1749294, _1749292, _1749296), hAPP(c_Product__Type_OPair(_1749294, _1749292), _1749298)), _1749300) = hAPP(_1749300, _1749298))], (30155 ^ _781013) ^ [_1344398, _1344400, _1344402, _1344404] : [class_Orderings_Olinorder(_1344398), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344398), _1344400), _1344402)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344398), _1344404), _1344402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344398), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344398), _1344400), _1344404)), _1344402)))], (36488 ^ _781013) ^ [_1476968, _1476970, _1476972, _1476974, _1476976] : [hBOOL(hAPP(hAPP(_1476968, _1476970), _1476972)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1476974, _1476976, tc_HOL_Obool), _1476968), hAPP(hAPP(c_Product__Type_OPair(_1476974, _1476976), _1476970), _1476972))))], (4060 ^ _781013) ^ [_842428, _842430, _842432, _842434] : [-(c_Relation_ODomain(_842434, _842430) = c_Relation_ODomain(_842432, _842428)), _842434 = _842432, _842430 = _842428], (25386 ^ _781013) ^ [_1254236, _1254238, _1254240, _1254242] : [class_Fields_Olinordered__field(_1254236), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254236), _1254238), c_Groups_Ozero__class_Ozero(_1254236))), 25393 ^ _781013 : [(25400 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254236), _1254242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1254236), _1254240), _1254238))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254236), _1254240), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1254236), _1254242), _1254238))))], (25394 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254236), _1254240), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1254236), _1254242), _1254238))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254236), _1254242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1254236), _1254240), _1254238))))]]], (34563 ^ _781013) ^ [_1435824, _1435826] : [class_Int_Onumber__ring(_1435824), 34566 ^ _781013 : [(34573 ^ _781013) ^ [] : [c_Int_Oiszero(_1435824, hAPP(c_Int_Onumber__class_Onumber__of(_1435824), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1435826), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1435824), _1435826) = c_Groups_Oone__class_Oone(_1435824))], (34567 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1435824), _1435826) = c_Groups_Oone__class_Oone(_1435824), -(c_Int_Oiszero(_1435824, hAPP(c_Int_Onumber__class_Onumber__of(_1435824), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1435826), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (34683 ^ _781013) ^ [_1438014, _1438016] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1438014)), c_Int_OBit0(_1438016)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1438014), _1438016)))], (7099 ^ _781013) ^ [_898846, _898848, _898850, _898852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898846, tc_HOL_Obool)), _898848), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898846, tc_HOL_Obool)), _898850), _898852))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898846, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898846, tc_HOL_Obool)), _898848), _898850)), _898852)))], (41320 ^ _781013) ^ [_1595384, _1595386, _1595388, _1595390] : [-(c_Map_Omap__upds(_1595384, _1595386, _1595388, _1595390, c_List_Olist_ONil(_1595386)) = _1595388)], (45317 ^ _781013) ^ [_1686477, _1686479] : [class_Enum_Oenum(_1686477), 45320 ^ _781013 : [(45328 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1686477), _1686479)), 45331 ^ _781013 : [(45332 ^ _781013) ^ [_1686695] : [-(hBOOL(hAPP(_1686479, _1686695)))]]], (45321 ^ _781013) ^ [] : [hBOOL(hAPP(_1686479, 45322 ^ [_1686477, _1686479])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1686477), _1686479)))]]], (46012 ^ _781013) ^ [_1701685, _1701687] : [class_Complete__Lattice_Ocomplete__lattice(_1701685), -(c_Complete__Lattice_OInf__class_OInf(_1701685, hAPP(c_List_Oset(_1701685), _1701687)) = hAPP(c_List_Ofoldl(_1701685, _1701685, c_Lattices_Osemilattice__inf__class_Oinf(_1701685), c_Orderings_Otop__class_Otop(_1701685)), _1701687))], (5290 ^ _781013) ^ [_861677, _861679, _861681, _861683, _861685, _861687, _861689, _861691] : [-(c_Lazy__Sequence_Oproduct(_861691, _861687, _861683, _861679) = c_Lazy__Sequence_Oproduct(_861689, _861685, _861681, _861677)), _861691 = _861689, _861687 = _861685, _861683 = _861681, _861679 = _861677], (51614 ^ _781013) ^ [_1824892, _1824894] : [hBOOL(hAPP(hAPP(c_fequal, _1824892), _1824894)), -(_1824892 = _1824894)], (34331 ^ _781013) ^ [_1432035, _1432037] : [class_Int_Onumber__ring(_1432035), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432035), _1432037), hAPP(c_Int_Onumber__class_Onumber__of(_1432035), c_Int_OBit1(c_Int_OPls))) = _1432037)], (41983 ^ _781013) ^ [_1610773, _1610775, _1610777, _1610779, _1610781, _1610783, _1610785, _1610787] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1610773, _1610773)), hAPP(hAPP(c_Product__Type_OPair(_1610773, _1610773), _1610775), _1610777)), _1610779)), _1610781 = hAPP(hAPP(c_List_Oappend(_1610773), _1610783), hAPP(hAPP(c_List_Olist_OCons(_1610773), _1610775), _1610785)), _1610787 = hAPP(hAPP(c_List_Oappend(_1610773), _1610783), hAPP(hAPP(c_List_Olist_OCons(_1610773), _1610777), _1610785)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610773), tc_List_Olist(_1610773))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610773), tc_List_Olist(_1610773)), _1610781), _1610787)), c_List_Olistrel1(_1610773, _1610779))))], (9761 ^ _781013) ^ [_953483, _953485] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953483, tc_HOL_Obool)), _953485), _953485) = _953485)], (38156 ^ _781013) ^ [_1512936, _1512938, _1512940] : [class_Rings_Oring__1(_1512936), -(hAPP(c_Int_Oring__1__class_Oof__int(_1512936), 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), _1512938), _1512940)), 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(_1512936), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1512936), _1512938)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1512936), _1512940)))], (42476 ^ _781013) ^ [_1622459, _1622461, _1622463] : [class_Groups_Omonoid__add(_1622459), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1622459), _1622461), hAPP(c_List_Ofoldl(_1622459, _1622459, c_Groups_Oplus__class_Oplus(_1622459), c_Groups_Ozero__class_Ozero(_1622459)), _1622463)) = hAPP(c_List_Ofoldl(_1622459, _1622459, c_Groups_Oplus__class_Oplus(_1622459), _1622461), _1622463))], (48459 ^ _781013) ^ [_1760862, _1760864] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1760862), tc_List_Olist(_1760862)), tc_HOL_Obool)), c_List_Olistrel1(_1760862, c_Transitive__Closure_Ortrancl(_1760862, _1760864))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1760862), c_List_Olistrel1(_1760862, _1760864)))))], (35569 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (34597 ^ _781013) ^ [_1436393, _1436395] : [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), _1436393))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1436395)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1436393))) = 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), _1436395), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436393)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31656 ^ _781013) ^ [_1378660, _1378662, _1378664, _1378666, _1378668, _1378670] : [class_Complete__Lattice_Ocomplete__lattice(_1378660), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378662, _1378660), _1378664), hAPP(hAPP(c_COMBB(tc_fun(_1378666, _1378660), _1378660, _1378662), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378666, _1378660), _1378668)), _1378670)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378666, _1378660), _1378668), hAPP(hAPP(c_COMBB(tc_fun(_1378662, _1378660), _1378660, _1378666), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378662, _1378660), _1378664)), hAPP(c_COMBC(_1378662, _1378666, _1378660), _1378670))))], (14825 ^ _781013) ^ [_1055858, _1055860] : [class_Rings_Ocomm__semiring__1(_1055858), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055858), _1055860), c_Groups_Ozero__class_Ozero(_1055858)) = _1055860)], (40147 ^ _781013) ^ [_1563910, _1563912, _1563914] : [_1563910 = hAPP(hAPP(c_List_Olist_OCons(_1563912), _1563914), _1563910)], (29058 ^ _781013) ^ [_1323141, _1323143, _1323145] : [class_Fields_Olinordered__field(_1323141), -(_1323143 = c_Groups_Ozero__class_Ozero(_1323141)), -(hAPP(c_Groups_Oabs__class_Oabs(_1323141), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323141), _1323145), _1323143)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323141), hAPP(c_Groups_Oabs__class_Oabs(_1323141), _1323145)), hAPP(c_Groups_Oabs__class_Oabs(_1323141), _1323143)))], (10151 ^ _781013) ^ [_960566, _960568, _960570, _960572] : [class_Lattices_Osemilattice__inf(_960566), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960566), _960568), _960570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960566), _960568), _960572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960566), _960568), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960566), _960570), _960572))))], (51120 ^ _781013) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (48365 ^ _781013) ^ [_1758584, _1758586, _1758588, _1758590, _1758592] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1758584, _1758584)), hAPP(hAPP(c_Product__Type_OPair(_1758584, _1758584), _1758586), _1758588)), _1758590)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1758584, _1758584)), hAPP(hAPP(c_Product__Type_OPair(_1758584, _1758584), _1758588), _1758592)), c_Transitive__Closure_Ortrancl(_1758584, _1758590))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1758584, _1758584)), hAPP(hAPP(c_Product__Type_OPair(_1758584, _1758584), _1758586), _1758592)), c_Transitive__Closure_Otrancl(_1758584, _1758590))))], (35799 ^ _781013) ^ [_1457766, _1457768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1457766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1457766), _1457768)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1457766), _1457768) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (50784 ^ _781013) ^ [_1813078, _1813080, _1813082, _1813084] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1813078, _1813080), c_Lazy__Sequence_Olazy__sequence_OInsert(_1813078, _1813082, _1813084)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1813080, _1813082)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1813078, _1813080), _1813084))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49029 ^ _781013) ^ [_1775067, _1775069] : [-(c_Relation_Oirrefl(_1775067, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1775067, _1775067), tc_HOL_Obool)), _1775069), c_Relation_OId(_1775067))))], (25276 ^ _781013) ^ [_1252104, _1252106, _1252108, _1252110] : [class_Fields_Ofield(_1252104), -(_1252106 = c_Groups_Ozero__class_Ozero(_1252104)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1252104), _1252108), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252104), _1252110), _1252106)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252104), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1252104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252104), _1252106), _1252108)), _1252110)), _1252106))], (32270 ^ _781013) ^ [_1393439, _1393441, _1393443, _1393445, _1393447, _1393449] : [c_Com_Ocom_OLocal(_1393439, _1393441, _1393443) = c_Com_Ocom_OCond(_1393445, _1393447, _1393449)], (24148 ^ _781013) ^ [_1231361, _1231363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231363)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1231361)), hAPP(c_Int_Onat, _1231363)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231361), _1231363)))], (34603 ^ _781013) ^ [_1436540, _1436542] : [-(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), _1436540)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1436542)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1436540))) = 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), _1436542)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436540)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (3850 ^ _781013) ^ [_839243, _839245, _839247, _839249] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_839249, _839245) = c_SetInterval_Oord__class_OatLeastLessThan(_839247, _839243)), _839249 = _839247, _839245 = _839243], (49860 ^ _781013) ^ [_1794212, _1794214, _1794216] : [class_Orderings_Olinorder(_1794212), hBOOL(hAPP(c_Finite__Set_Ofinite(_1794212), _1794214)), -(hBOOL(hAPP(hAPP(c_member(_1794212), _1794216), _1794214))), -(c_Big__Operators_Olattice_OInf__fin(_1794212, c_Orderings_Oord__class_Omin(_1794212), hAPP(hAPP(c_Set_Oinsert(_1794212), _1794216), _1794214)) = hAPP(hAPP(c_Finite__Set_Ofold(_1794212, _1794212, c_Orderings_Oord__class_Omin(_1794212)), _1794216), _1794214))], (4464 ^ _781013) ^ [_848634, _848636, _848638, _848640] : [-(c_HOL_OLet(_848640, _848636) = c_HOL_OLet(_848638, _848634)), _848640 = _848638, _848636 = _848634], (38664 ^ _781013) ^ [_1524667, _1524669, _1524671, _1524673, _1524675, _1524677, _1524679, _1524681] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1524667, _1524669), _1524671), _1524673), hAPP(hAPP(c_List_Ozip(_1524667, _1524669), hAPP(hAPP(c_List_Omap(_1524675, _1524667), _1524677), _1524679)), _1524681)) = hAPP(hAPP(c_List_Omap(tc_prod(_1524675, _1524669), _1524671), hAPP(c_Product__Type_Oprod_Oprod__case(_1524675, _1524669, _1524671), hAPP(hAPP(c_COMBB(tc_fun(_1524669, tc_prod(_1524667, _1524669)), tc_fun(_1524669, _1524671), _1524675), hAPP(c_COMBB(tc_prod(_1524667, _1524669), _1524671, _1524669), _1524673)), hAPP(hAPP(c_COMBB(_1524667, tc_fun(_1524669, tc_prod(_1524667, _1524669)), _1524675), c_Product__Type_OPair(_1524667, _1524669)), _1524677)))), hAPP(hAPP(c_List_Ozip(_1524675, _1524669), _1524679), _1524681)))], (44036 ^ _781013) ^ [_1657794, _1657796, _1657798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657794), _1657796)), _1657798)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1657794, _1657798)), _1657796) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657794), _1657796))], (51362 ^ _781013) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (48493 ^ _781013) ^ [_1761420, _1761422] : [-(hAPP(c_Relation_ODomain(_1761420, _1761420), c_Transitive__Closure_Ortrancl(_1761420, _1761422)) = c_Orderings_Otop__class_Otop(tc_fun(_1761420, tc_HOL_Obool)))], (5486 ^ _781013) ^ [_864657, _864659, _864661, _864663, _864665, _864667] : [-(c_COMBS(_864667, _864663, _864659) = c_COMBS(_864665, _864661, _864657)), _864667 = _864665, _864663 = _864661, _864659 = _864657], (38975 ^ _781013) ^ [_1532366, _1532368, _1532370] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1532366), _1532368)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1532366)), hAPP(c_Set_OCollect(tc_List_Olist(_1532366)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1532366), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1532366)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1532366), tc_fun(_1532366, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1532366, tc_HOL_Obool), tc_fun(tc_fun(_1532366, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1532366)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1532366, tc_HOL_Obool))), c_List_Oset(_1532366))), _1532368))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1532366), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1532366)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1532366)))), _1532370))))))], (4714 ^ _781013) ^ [_852325, _852327] : [_852327 = _852325, -(c_Int_Onumber__class_Onumber__of(_852327) = c_Int_Onumber__class_Onumber__of(_852325))], (34040 ^ _781013) ^ [_1426788, _1426790, _1426792] : [-(hAPP(c_Nat_Onat_Onat__rec(_1426788, _1426790, _1426792), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1426790)], (35627 ^ _781013) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (13305 ^ _781013) ^ [_1023506, _1023508] : [class_Groups_Oab__semigroup__mult(_1023506), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023506), _1023508)), -(_1023508 = c_Orderings_Obot__class_Obot(tc_fun(_1023506, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1023506), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023506), 13318 ^ [_1023506, _1023508]), 13319 ^ [_1023506, _1023508])), hAPP(hAPP(c_Set_Oinsert(_1023506), 13318 ^ [_1023506, _1023508]), hAPP(hAPP(c_Set_Oinsert(_1023506), 13319 ^ [_1023506, _1023508]), c_Orderings_Obot__class_Obot(tc_fun(_1023506, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1023506), hAPP(c_Finite__Set_Ofold1(_1023506, c_Groups_Otimes__class_Otimes(_1023506)), _1023508)), _1023508)))], (22194 ^ _781013) ^ [_1197239, _1197241] : [_1197239 = _1197241, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197239) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197241))], (6732 ^ _781013) ^ [_891818, _891820, _891822, _891824, _891826, _891828] : [c_Finite__Set_Ofolding__idem(_891818, _891820, _891822, _891824), hBOOL(hAPP(c_Finite__Set_Ofinite(_891818), _891826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891818, tc_HOL_Obool)), _891828), _891826)), -(hAPP(c_Fun_Ocomp(_891820, _891820, _891820, hAPP(_891824, _891826)), hAPP(_891824, _891828)) = hAPP(_891824, _891826))], (41799 ^ _781013) ^ [_1606129, _1606131, _1606133, _1606135] : [hAPP(hAPP(c_List_Oappend(_1606129), _1606131), _1606133) = hAPP(hAPP(c_List_Oappend(_1606129), _1606135), _1606133), -(_1606131 = _1606135)], (27952 ^ _781013) ^ [_1303018, _1303020, _1303022] : [class_Divides_Osemiring__div(_1303018), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1303018), c_Divides_Odiv__class_Omod(_1303018, _1303020, _1303022)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303018), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1303018), _1303020), _1303022)), _1303022)) = _1303020)], (48283 ^ _781013) ^ [_1756491, _1756493, _1756495, _1756497] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1756491, _1756491)), hAPP(hAPP(c_Product__Type_OPair(_1756491, _1756491), _1756493), _1756495)), c_Transitive__Closure_Otrancl(_1756491, _1756497))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1756491, _1756491)), hAPP(hAPP(c_Product__Type_OPair(_1756491, _1756491), _1756493), _1756495)), c_Transitive__Closure_Ortrancl(_1756491, _1756497))))], (13527 ^ _781013) ^ [_1028565, _1028567, _1028569, _1028571, _1028573, _1028575] : [class_Groups_Ocomm__monoid__add(_1028565), c_Fun_Oinj__on(_1028567, _1028569, _1028571, _1028573), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028569, _1028565), _1028575), hAPP(c_Set_Oimage(_1028567, _1028569, _1028571), _1028573)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028567, _1028565), hAPP(c_Fun_Ocomp(_1028569, _1028565, _1028567, _1028575), _1028571)), _1028573))], (31172 ^ _781013) ^ [_1364911, _1364913, _1364915, _1364917, _1364919, _1364921] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1364911), _1364913), _1364915), _1364917)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1364919), _1364917), _1364915), _1364921)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_1364911, _1364919)), _1364913), _1364915), _1364921)))], (19857 ^ _781013) ^ [_1152974, _1152976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1152974), _1152976)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152974), _1152976)))], (41330 ^ _781013) ^ [_1595567, _1595569] : [-(c_List_Olistrelp(_1595567, _1595569, c_List_Olist_ONil(_1595567), c_List_Olist_ONil(_1595567)))], (49740 ^ _781013) ^ [_1792022, _1792024, _1792026] : [class_Orderings_Olinorder(_1792022), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792022), _1792024)), -(c_Big__Operators_Olattice_OSup__fin(_1792022, c_Orderings_Oord__class_Omax(_1792022), hAPP(hAPP(c_Set_Oinsert(_1792022), _1792026), _1792024)) = hAPP(hAPP(c_Finite__Set_Ofold(_1792022, _1792022, c_Orderings_Oord__class_Omax(_1792022)), _1792026), _1792024))], (45699 ^ _781013) ^ [_1694470, _1694472, _1694474] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1694470, tc_HOL_Obool)), _1694472), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1694470, tc_HOL_Obool), _1694474)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1694470, tc_HOL_Obool), tc_fun(_1694470, tc_HOL_Obool)), _1694474), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1694470, tc_HOL_Obool)), _1694472)))], (37520 ^ _781013) ^ [_1497437, _1497439] : [hAPP(c_Int_ORep__Integ, _1497437) = hAPP(c_Int_ORep__Integ, _1497439), -(_1497437 = _1497439)], (13817 ^ _781013) ^ [_1034826, _1034828, _1034830, _1034832, _1034834] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1034826), 13820 ^ _781013 : [(13821 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034826), _1034828), _1034832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034826), _1034830), _1034834)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034826), _1034828), _1034834)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034826), _1034830), _1034832)), -(_1034828 = _1034830), -(_1034832 = _1034834)], (13831 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034826), _1034828), _1034832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034826), _1034830), _1034834)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034826), _1034828), _1034834)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034826), _1034830), _1034832))), 13834 ^ _781013 : [(13837 ^ _781013) ^ [] : [_1034832 = _1034834], (13835 ^ _781013) ^ [] : [_1034828 = _1034830]]]]], (29645 ^ _781013) ^ [_1333734, _1333736, _1333738] : [class_Orderings_Olinorder(_1333734), -(_1333736 = c_Orderings_Obot__class_Obot(tc_fun(_1333734, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1333734, tc_HOL_Obool)), _1333736), _1333738)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333734), _1333738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333734), hAPP(c_Finite__Set_Ofold1(_1333734, c_Orderings_Oord__class_Omin(_1333734)), _1333738)), hAPP(c_Finite__Set_Ofold1(_1333734, c_Orderings_Oord__class_Omin(_1333734)), _1333736))))], (35589 ^ _781013) ^ [_1454609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1454609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1454609))))], (21359 ^ _781013) ^ [] : [-(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))))], (1264 ^ _781013) ^ [_799555, _799557] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799555)), _799557 = _799555, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799557)], (19797 ^ _781013) ^ [_1152114, _1152116] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152114), _1152116))), -(_1152114 = _1152116), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152116), _1152114)))], (23513 ^ _781013) ^ [_1221111, _1221113, _1221115, _1221117] : [class_Rings_Odivision__ring(_1221111), -(_1221113 = c_Groups_Ozero__class_Ozero(_1221111)), _1221115 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221111), _1221117), _1221113), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221111), _1221115), _1221113) = _1221117)], (12582 ^ _781013) ^ [_1008409, _1008411, _1008413, _1008415] : [-(_1008409 = c_Orderings_Obot__class_Obot(tc_fun(_1008411, tc_HOL_Obool))), 12585 ^ _781013 : [(12586 ^ _781013) ^ [] : [-(hAPP(c_Set_Oimage(_1008413, _1008411, 12593 ^ [_1008409, _1008411, _1008413, _1008415]), _1008415) = _1008409), 12587 ^ _781013 : [(12588 ^ _781013) ^ [_1008550] : [c_Fun_Oinj__on(_1008411, _1008413, _1008550, _1008409), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008413, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1008411, _1008413, _1008550), _1008409)), _1008415))]]], (12597 ^ _781013) ^ [] : [12598 ^ _781013 : [(12599 ^ _781013) ^ [_1008742] : [hAPP(c_Set_Oimage(_1008413, _1008411, _1008742), _1008415) = _1008409]], 12601 ^ _781013 : [(12604 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008413, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1008411, _1008413, 12600 ^ [_1008409, _1008411, _1008413, _1008415]), _1008409)), _1008415)))], (12602 ^ _781013) ^ [] : [-(c_Fun_Oinj__on(_1008411, _1008413, 12600 ^ [_1008409, _1008411, _1008413, _1008415], _1008409))]]]]], (25776 ^ _781013) ^ [_1260657, _1260659] : [c_Nat__Transfer_Ois__nat(_1260657), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1260657), _1260659)))], (30021 ^ _781013) ^ [_1341904, _1341906, _1341908, _1341910] : [class_Orderings_Olinorder(_1341904), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341904), _1341906), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1341904), _1341908), _1341910)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1341904), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341904), _1341906), _1341908)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341904), _1341906), _1341910)))], (2854 ^ _781013) ^ [_823619, _823621, _823623, _823625] : [-(c_Option_Omap(_823625, _823621) = c_Option_Omap(_823623, _823619)), _823625 = _823623, _823621 = _823619], (3912 ^ _781013) ^ [_840212, _840214, _840216, _840218] : [-(c_Random_Oselect__weight(_840218, _840214) = c_Random_Oselect__weight(_840216, _840212)), _840218 = _840216, _840214 = _840212], (25754 ^ _781013) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37170 ^ _781013) ^ [_1490270, _1490272, _1490274] : [37172 ^ _781013 : [(37175 ^ _781013) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1490270, _1490272), 37171 ^ [_1490270, _1490272, _1490274]))], (37173 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1490272, 37171 ^ [_1490270, _1490272, _1490274]), _1490274)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1490270, _1490272), _1490274)))], (19897 ^ _781013) ^ [_1153708, _1153710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153708), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1153710)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1153708), _1153710)))], (6511 ^ _781013) ^ [_887544, _887546, _887548, _887550, _887552, _887554, _887556, _887558] : [hAPP(c_Fun_Ocomp(_887544, _887546, _887548, _887550), _887552) = hAPP(c_Fun_Ocomp(_887554, _887546, _887548, _887556), _887558), 6514 ^ _781013 : [(6515 ^ _781013) ^ [_887659] : [-(hAPP(_887550, hAPP(_887552, _887659)) = hAPP(_887556, hAPP(_887558, _887659)))]]], (9915 ^ _781013) ^ [_956117, _956119, _956121, _956123] : [class_Lattices_Olattice(_956117), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956117), _956119), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956117), _956121), _956123)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956117), _956121), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956117), _956119), _956123)))], (39681 ^ _781013) ^ [_1549356, _1549358, _1549360, _1549362, _1549364] : [-(c_Map_Odom(_1549356, _1549358, c_Map_Omap__upds(_1549356, _1549358, _1549360, _1549362, _1549364)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1549356, tc_HOL_Obool)), hAPP(c_List_Oset(_1549356), hAPP(hAPP(c_List_Otake(_1549356), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549358)), _1549364)), _1549362))), c_Map_Odom(_1549356, _1549358, _1549360)))], (41268 ^ _781013) ^ [_1594440, _1594442, _1594444] : [-(hAPP(hAPP(c_List_Olist__update(_1594440, c_List_Olist_ONil(_1594440)), _1594442), _1594444) = c_List_Olist_ONil(_1594440))], (25672 ^ _781013) ^ [_1258900, _1258902, _1258904, _1258906, _1258908, _1258910] : [class_Groups_Oordered__ab__group__add(_1258900), hBOOL(hAPP(c_Finite__Set_Ofinite(_1258902), _1258904)), 25682 ^ _781013 : [(25685 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258900), c_Groups_Ozero__class_Ozero(_1258900)), hAPP(_1258906, 25681 ^ [_1258900, _1258902, _1258904, _1258906, _1258908, _1258910])))], (25683 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1258902), 25681 ^ [_1258900, _1258902, _1258904, _1258906, _1258908, _1258910]), _1258904)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1258902, _1258900), _1258906), _1258904) = _1258908, hBOOL(hAPP(hAPP(c_member(_1258902), _1258910), _1258904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258900), hAPP(_1258906, _1258910)), _1258908)))], (24210 ^ _781013) ^ [_1232568, _1232570, _1232572] : [class_Groups_Oordered__ab__group__add(_1232568), -(hAPP(c_Set_Oimage(_1232568, _1232568, c_Groups_Ouminus__class_Ouminus(_1232568)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1232568, _1232570), _1232572)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1232568, hAPP(c_Groups_Ouminus__class_Ouminus(_1232568), _1232572), hAPP(c_Groups_Ouminus__class_Ouminus(_1232568), _1232570)))], (48281 ^ _781013) ^ [_1756442, _1756444, _1756446] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1756442, _1756442)), hAPP(hAPP(c_Product__Type_OPair(_1756442, _1756442), _1756444), _1756444)), c_Transitive__Closure_Ortrancl(_1756442, _1756446))))], (47299 ^ _781013) ^ [_1734563, _1734565, _1734567] : [c_Wellfounded_OwfP(_1734563, _1734565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1734563, tc_fun(_1734563, tc_HOL_Obool))), _1734567), _1734565)), -(c_Wellfounded_OwfP(_1734563, _1734567))], (13030 ^ _781013) ^ [_1017960, _1017962, _1017964, _1017966, _1017968, _1017970] : [c_Fun_Oinj__on(_1017960, _1017962, _1017964, _1017966), hAPP(_1017964, _1017968) = _1017970, hBOOL(hAPP(hAPP(c_member(_1017960), _1017968), _1017966)), -(hAPP(c_Fun_Othe__inv__into(_1017960, _1017962, _1017966, _1017964), _1017970) = _1017968)], (20506 ^ _781013) ^ [_1164080, _1164082, _1164084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1164082), _1164084)), -(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, _1164080)), _1164082)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1164080)), _1164084))))], (7775 ^ _781013) ^ [_911941, _911943] : [hBOOL(hAPP(hAPP(c_member(_911941), _911943), c_Orderings_Obot__class_Obot(tc_fun(_911941, tc_HOL_Obool))))], (21267 ^ _781013) ^ [_1180041, _1180043, _1180045] : [class_Orderings_Olinorder(_1180041), 21270 ^ _781013 : [(21277 ^ _781013) ^ [] : [_1180043 = _1180045, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1180041), _1180043) = hAPP(c_SetInterval_Oord__class_OlessThan(_1180041), _1180045))], (21271 ^ _781013) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1180041), _1180043) = hAPP(c_SetInterval_Oord__class_OlessThan(_1180041), _1180045), -(_1180043 = _1180045)]]], (47148 ^ _781013) ^ [_1730529, _1730531, _1730533] : [c_Wellfounded_Owf(_1730529, _1730531), c_Wellfounded_Owf(_1730529, _1730533), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1730529, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1730529, _1730529), _1730531)), hAPP(c_Relation_ORange(_1730529, _1730529), _1730533)) = c_Orderings_Obot__class_Obot(tc_fun(_1730529, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1730529, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1730529, _1730529), tc_HOL_Obool)), _1730531), _1730533)))], (1384 ^ _781013) ^ [_801055, _801057] : [-(class_Groups_Ouminus(_801055)), _801057 = _801055, class_Groups_Ouminus(_801057)], (21397 ^ _781013) ^ [_1182652, _1182654, _1182656] : [-(hAPP(c_Finite__Set_Ocard(_1182652), _1182654) = hAPP(c_Nat_OSuc, _1182656)), 21398 ^ _781013 : [(21399 ^ _781013) ^ [_1182752, _1182754] : [_1182654 = hAPP(hAPP(c_Set_Oinsert(_1182652), _1182754), _1182752), -(hBOOL(hAPP(hAPP(c_member(_1182652), _1182754), _1182752))), hAPP(c_Finite__Set_Ocard(_1182652), _1182752) = _1182656, 21410 ^ _781013 : [(21413 ^ _781013) ^ [] : [_1182752 = c_Orderings_Obot__class_Obot(tc_fun(_1182652, tc_HOL_Obool))], (21411 ^ _781013) ^ [] : [-(_1182656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (17757 ^ _781013) ^ [_1112387, _1112389, _1112391] : [17758 ^ _781013 : [(17761 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1112391, _1112389), _1112387))], (17759 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112387), _1112389)))]], 17764 ^ _781013 : [(17767 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1112391, _1112389), _1112387))], (17765 ^ _781013) ^ [] : [-(_1112387 = _1112389)]], 17770 ^ _781013 : [(17773 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1112391, _1112389), _1112387))], (17771 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112389), _1112387)))]], -(hBOOL(hAPP(hAPP(_1112391, _1112389), _1112387)))], (36464 ^ _781013) ^ [_1476421, _1476423, _1476425, _1476427, _1476429, _1476431] : [hBOOL(hAPP(hAPP(_1476421, _1476423), _1476425)), hBOOL(hAPP(hAPP(_1476427, _1476423), _1476425)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476429, tc_fun(_1476431, tc_HOL_Obool))), _1476421), _1476427), _1476423), _1476425)))], (7994 ^ _781013) ^ [_916405, _916407, _916409, _916411, _916413] : [_916405 = c_Option_Ooption_ONone(_916407), -(c_Map_Odom(_916409, _916407, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_916409, tc_Option_Ooption(_916407)), _916411), _916413), _916405)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916409, tc_HOL_Obool)), c_Map_Odom(_916409, _916407, _916411)), hAPP(hAPP(c_Set_Oinsert(_916409), _916413), c_Orderings_Obot__class_Obot(tc_fun(_916409, tc_HOL_Obool)))))], (12362 ^ _781013) ^ [_1004033, _1004035, _1004037, _1004039, _1004041] : [class_Groups_Oab__semigroup__mult(_1004033), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1004033, _1004033, c_Groups_Otimes__class_Otimes(_1004033), _1004035, _1004037), _1004039)), -(hBOOL(hAPP(hAPP(c_member(_1004033), _1004035), _1004037))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1004033, _1004033, c_Groups_Otimes__class_Otimes(_1004033), _1004041, hAPP(hAPP(c_Set_Oinsert(_1004033), _1004035), _1004037)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004033), _1004041), _1004039))))], (44286 ^ _781013) ^ [_1663429, _1663431] : [-(hAPP(c_List_Orev(_1663429), _1663431) = hAPP(c_List_Ofoldl(tc_List_Olist(_1663429), _1663429, hAPP(c_COMBC(_1663429, tc_List_Olist(_1663429), tc_List_Olist(_1663429)), c_List_Olist_OCons(_1663429)), c_List_Olist_ONil(_1663429)), _1663431))], (36446 ^ _781013) ^ [_1476080, _1476082, _1476084, _1476086, _1476088, _1476090] : [36447 ^ _781013 : [(36450 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1476086, _1476082), _1476084))], (36448 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1476080, _1476082), _1476084))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476088, tc_fun(_1476090, tc_HOL_Obool))), _1476086), _1476080), _1476082), _1476084)))], (19058 ^ _781013) ^ [_1137625, _1137627, _1137629, _1137631, _1137633] : [-(hBOOL(hAPP(hAPP(c_member(_1137625), _1137627), c_SetInterval_Oord_OatLeastAtMost(_1137625, _1137629, _1137631, _1137633)))), hBOOL(hAPP(hAPP(_1137629, _1137631), _1137627)), hBOOL(hAPP(hAPP(_1137629, _1137627), _1137633))], (35841 ^ _781013) ^ [_1458649, _1458651] : [-(_1458649 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1458649, _1458651) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1458649), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1458651)))], (17000 ^ _781013) ^ [_1096694, _1096696, _1096698, _1096700, _1096702] : [class_Groups_Ocomm__monoid__add(_1096694), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096696), _1096698)), 17007 ^ _781013 : [(17014 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1096696), _1096700), _1096698))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1096696, _1096694), hAPP(hAPP(c_COMBC(_1096696, _1096694, _1096694), hAPP(hAPP(c_COMBS(_1096696, _1096694, tc_fun(_1096694, _1096694)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1096694, tc_fun(_1096694, _1096694)), _1096696), c_If(_1096694)), hAPP(c_fequal, _1096700))), _1096702)), c_Groups_Ozero__class_Ozero(_1096694))), _1096698) = c_Groups_Ozero__class_Ozero(_1096694))], (17008 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1096696), _1096700), _1096698)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1096696, _1096694), hAPP(hAPP(c_COMBC(_1096696, _1096694, _1096694), hAPP(hAPP(c_COMBS(_1096696, _1096694, tc_fun(_1096694, _1096694)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1096694, tc_fun(_1096694, _1096694)), _1096696), c_If(_1096694)), hAPP(c_fequal, _1096700))), _1096702)), c_Groups_Ozero__class_Ozero(_1096694))), _1096698) = hAPP(_1096702, _1096700))]]], (2408 ^ _781013) ^ [_816656, _816658, _816660, _816662, _816664, _816666] : [-(c_Com_Ocom_OCond(_816666, _816662, _816658) = c_Com_Ocom_OCond(_816664, _816660, _816656)), _816666 = _816664, _816662 = _816660, _816658 = _816656], (30401 ^ _781013) ^ [_1349101, _1349103, _1349105] : [class_Orderings_Olinorder(_1349101), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349101), _1349103)), hBOOL(hAPP(hAPP(c_member(_1349101), _1349105), _1349103)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349101), _1349105), c_Big__Operators_Olinorder__class_OMax(_1349101, _1349103)) = c_Big__Operators_Olinorder__class_OMax(_1349101, _1349103))], (51238 ^ _781013) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (33310 ^ _781013) ^ [_1413310, _1413312] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413310)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413312)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413310), _1413312)))], (6898 ^ _781013) ^ [_894938, _894940, _894942, _894944, _894946] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_894938, _894940), _894942), _894944), _894946) = _894942, -(hAPP(_894942, _894944) = _894946)], (11570 ^ _781013) ^ [_989125, _989127, _989129, _989131] : [11572 ^ _781013 : [(11576 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_989125), 11574 ^ [_989125, _989127, _989129, _989131]), _989131)))], (11578 ^ _781013) ^ [] : [-(hAPP(_989129, 11571 ^ [_989125, _989127, _989129, _989131]) = hAPP(_989129, 11574 ^ [_989125, _989127, _989129, _989131]))], (11580 ^ _781013) ^ [] : [11571 ^ [_989125, _989127, _989129, _989131] = 11574 ^ [_989125, _989127, _989129, _989131]], (11573 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_989125), 11571 ^ [_989125, _989127, _989129, _989131]), _989131)))]], -(c_Fun_Oinj__on(_989125, _989127, _989129, _989131))], (41957 ^ _781013) ^ [_1610166, _1610168, _1610170, _1610172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610166), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610168)), _1610170))), -(hAPP(hAPP(c_List_Onth(_1610168), hAPP(hAPP(c_List_Oappend(_1610168), _1610170), _1610172)), _1610166) = hAPP(hAPP(c_List_Onth(_1610168), _1610170), _1610166))], (9239 ^ _781013) ^ [_944446, _944448, _944450, _944452] : [-(c_Map_Orestrict__map(_944446, _944448, _944450, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_944446, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_944446), _944452), c_Orderings_Obot__class_Obot(tc_fun(_944446, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_944446, tc_Option_Ooption(_944448)), _944450), _944452), c_Option_Ooption_ONone(_944448)))], (51234 ^ _781013) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (29068 ^ _781013) ^ [_1323299, _1323301, _1323303] : [class_Rings_Olinordered__idom(_1323299), -(hAPP(c_Groups_Oabs__class_Oabs(_1323299), hAPP(hAPP(c_Power_Opower__class_Opower(_1323299), hAPP(c_Groups_Ouminus__class_Ouminus(_1323299), _1323301)), _1323303)) = hAPP(c_Groups_Oabs__class_Oabs(_1323299), hAPP(hAPP(c_Power_Opower__class_Opower(_1323299), _1323301), _1323303)))], (18055 ^ _781013) ^ [_1117474, _1117476] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117474), _1117476) = _1117474, -(_1117476 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42653 ^ _781013) ^ [_1626345, _1626347, _1626349, _1626351] : [-(_1626345 = c_List_Olist_ONil(_1626347)), -(c_List_Olast(_1626349, hAPP(hAPP(c_List_Omap(_1626347, _1626349), _1626351), _1626345)) = hAPP(_1626351, c_List_Olast(_1626347, _1626345)))], (18023 ^ _781013) ^ [_1117039, _1117041] : [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), _1117039), _1117041))), 18026 ^ _781013 : [(18029 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1117041)))], (18027 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1117039)))]]], (40966 ^ _781013) ^ [_1587475] : [-(hAPP(c_List_Omap(_1587475, _1587475), c_COMBI(_1587475)) = c_Fun_Oid(tc_List_Olist(_1587475)))], (27902 ^ _781013) ^ [_1301955, _1301957] : [27903 ^ _781013 : [(27904 ^ _781013) ^ [_1302004] : [_1301955 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1301957), _1302004)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1301955, _1301957) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29303 ^ _781013) ^ [_1327563, _1327565, _1327567] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1327563), _1327565)), _1327567) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1327563), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1327565), _1327567))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1327563), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1327565, _1327567))), _1327567)))], (33336 ^ _781013) ^ [_1413787, _1413789, _1413791, _1413793, _1413795, _1413797, _1413799, _1413801] : [c_Equiv__Relations_Oequiv(_1413787, _1413789, _1413791), c_Equiv__Relations_Ocongruent2(_1413787, _1413793, _1413795, _1413791, _1413797, _1413799), hBOOL(hAPP(hAPP(c_member(_1413787), _1413801), _1413789)), -(c_Equiv__Relations_Ocongruent(_1413793, _1413795, _1413797, hAPP(_1413799, _1413801)))], (22224 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (11904 ^ _781013) ^ [_995733] : [class_Lattices_Oab__semigroup__idem__mult(_995733), -(c_Finite__Set_Ofun__left__comm__idem(_995733, _995733, c_Groups_Otimes__class_Otimes(_995733)))], (50944 ^ _781013) ^ [_1817493, _1817495, _1817497, _1817499] : [-(hAPP(hAPP(c_List_Oappend(_1817493), c_List_Oreplicate(_1817493, _1817495, _1817497)), hAPP(hAPP(c_List_Olist_OCons(_1817493), _1817497), _1817499)) = hAPP(hAPP(c_List_Olist_OCons(_1817493), _1817497), hAPP(hAPP(c_List_Oappend(_1817493), c_List_Oreplicate(_1817493, _1817495, _1817497)), _1817499)))], (13084 ^ _781013) ^ [_1018922, _1018924, _1018926, _1018928, _1018930] : [c_Fun_Oinj__on(_1018922, _1018924, _1018926, c_Orderings_Otop__class_Otop(tc_fun(_1018922, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1018924, tc_HOL_Obool)), _1018928), hAPP(c_Set_Oimage(_1018922, _1018924, _1018926), _1018930))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1018922, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1018922, _1018924, _1018926), _1018928)), _1018930)))], (8006 ^ _781013) ^ [_916654, _916656, _916658, _916660, _916662] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_916654), tc_Option_Ooption(_916656), _916658, hAPP(c_Option_Omap(_916654, _916656), _916660)), hAPP(c_COMBK(tc_Option_Ooption(_916654), _916658), c_Option_Ooption_ONone(_916654))), _916662) = c_Option_Ooption_ONone(_916656))], (17829 ^ _781013) ^ [_1113815, _1113817, _1113819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1113815), _1113817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113815), _1113819)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113817), _1113819))))], (51564 ^ _781013) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (51262 ^ _781013) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (43458 ^ _781013) ^ [_1646417, _1646419, _1646421, _1646423] : [hBOOL(hAPP(hAPP(c_member(_1646417), _1646419), hAPP(c_List_Oset(_1646417), _1646421))), -(hBOOL(hAPP(_1646423, _1646419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646417)), hAPP(c_List_Ofilter(_1646417, _1646423), _1646421))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646417)), _1646421))))], (37898 ^ _781013) ^ [_1506919, _1506921, _1506923, _1506925, _1506927] : [hBOOL(hAPP(hAPP(c_member(_1506919), _1506921), hAPP(c_Relation_OImage(_1506923, _1506919, _1506925), _1506927))), 37902 ^ _781013 : [(37905 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1506923), 37901 ^ [_1506919, _1506921, _1506923, _1506925, _1506927]), _1506927)))], (37903 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1506923, _1506919)), hAPP(hAPP(c_Product__Type_OPair(_1506923, _1506919), 37901 ^ [_1506919, _1506921, _1506923, _1506925, _1506927]), _1506921)), _1506925)))]]], (47508 ^ _781013) ^ [_1739095, _1739097, _1739099, _1739101, _1739103] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739095)), _1739097) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739099)), _1739101), 47514 ^ _781013 : [(47517 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1739103, hAPP(hAPP(c_List_Onth(_1739095), _1739097), 47513 ^ [_1739095, _1739097, _1739099, _1739101, _1739103])), hAPP(hAPP(c_List_Onth(_1739099), _1739101), 47513 ^ [_1739095, _1739097, _1739099, _1739101, _1739103])))], (47515 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47513 ^ [_1739095, _1739097, _1739099, _1739101, _1739103]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739095)), _1739097))))]], -(c_List_Olist__all2(_1739095, _1739099, _1739103, _1739097, _1739101))], (15221 ^ _781013) ^ [_1062667, _1062669, _1062671] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062667), _1062669)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1062667, tc_HOL_Obool)), _1062671), _1062669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1062667), _1062671)), hAPP(c_Finite__Set_Ocard(_1062667), _1062669))))], (19044 ^ _781013) ^ [_1137337, _1137339, _1137341, _1137343] : [hBOOL(hAPP(hAPP(_1137341, _1137343), _1137339)), -(hBOOL(hAPP(hAPP(c_member(_1137337), _1137339), c_SetInterval_Oord_OgreaterThan(_1137337, _1137341, _1137343))))], (14081 ^ _781013) ^ [_1040152, _1040154, _1040156] : [class_Groups_Ogroup__add(_1040152), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040152), _1040154), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040152), hAPP(c_Groups_Ouminus__class_Ouminus(_1040152), _1040154)), _1040156)) = _1040156)], (51584 ^ _781013) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (38308 ^ _781013) ^ [_1516971, _1516973, _1516975, _1516977, _1516979] : [38310 ^ _781013 : [(38313 ^ _781013) ^ [] : [hAPP(_1516975, 38309 ^ [_1516971, _1516973, _1516975, _1516977, _1516979]) = hAPP(_1516979, 38309 ^ [_1516971, _1516973, _1516975, _1516977, _1516979])], (38311 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1516971), 38309 ^ [_1516971, _1516973, _1516975, _1516977, _1516979]), hAPP(c_List_Oset(_1516971), _1516977))))]], -(hAPP(hAPP(c_List_Omap(_1516971, _1516973), _1516975), _1516977) = hAPP(hAPP(c_List_Omap(_1516971, _1516973), _1516979), _1516977))], (51316 ^ _781013) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (2112 ^ _781013) ^ [_811968, _811970, _811972, _811974, _811976, _811978, _811980, _811982, _811984, _811986] : [-(c_SetInterval_Oord_OatLeastLessThan(_811986, _811982, _811978, _811974, _811970) = c_SetInterval_Oord_OatLeastLessThan(_811984, _811980, _811976, _811972, _811968)), _811986 = _811984, _811982 = _811980, _811978 = _811976, _811974 = _811972, _811970 = _811968], (38379 ^ _781013) ^ [_1518710, _1518712, _1518714, _1518716] : [-(hBOOL(hAPP(hAPP(c_member(_1518710), _1518716), hAPP(c_Set_Oimage(tc_prod(_1518710, _1518712), _1518710, c_Product__Type_Ofst(_1518710, _1518712)), hAPP(c_List_Oset(tc_prod(_1518710, _1518712)), _1518714))))), -(hAPP(hAPP(c_Map_Omap__of(_1518710, _1518712), _1518714), _1518716) = c_Option_Ooption_ONone(_1518712))], (21642 ^ _781013) ^ [_1187487, _1187489] : [class_Rings_Olinordered__semidom(_1187487), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187487), c_Groups_Ozero__class_Ozero(_1187487)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187487), _1187489))))], (39505 ^ _781013) ^ [_1545066, _1545068] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1545066), _1545068)), -(c_Nitpick_Ocard_H(_1545066, _1545068) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1545066)), c_Hilbert__Choice_OEps(tc_List_Olist(_1545066), hAPP(hAPP(c_COMBS(tc_List_Olist(_1545066), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1545066)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1545066), tc_fun(_1545066, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1545066, tc_HOL_Obool), tc_fun(tc_fun(_1545066, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1545066)), c_fequal), c_List_Oset(_1545066))), _1545068))), c_List_Odistinct(_1545066)))))], (43998 ^ _781013) ^ [_1656989, _1656991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656989), _1656991)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1656989, _1656991)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1656991), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (31623 ^ _781013) ^ [_1377779, _1377781, _1377783, _1377785, _1377787] : [31625 ^ _781013 : [(31628 ^ _781013) ^ [] : [hBOOL(hAPP(_1377787, 31624 ^ [_1377779, _1377781, _1377783, _1377785, _1377787]))], (31626 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377779), 31624 ^ [_1377779, _1377781, _1377783, _1377785, _1377787]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377781, tc_fun(_1377779, tc_HOL_Obool)), _1377783), _1377785))))]], 31629 ^ _781013 : [(31630 ^ _781013) ^ [_1378001] : [hBOOL(hAPP(hAPP(c_member(_1377781), _1378001), _1377783)), 31633 ^ _781013 : [(31634 ^ _781013) ^ [_1378098] : [hBOOL(hAPP(hAPP(c_member(_1377779), _1378098), hAPP(_1377785, _1378001))), -(hBOOL(hAPP(_1377787, _1378098)))]]]]], (22518 ^ _781013) ^ [_1202495, _1202497, _1202499, _1202501] : [class_Groups_Ocomm__monoid__add(_1202495), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1202495), _1202497), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1202499)), hAPP(c_Nat_OSuc, _1202501))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1202495), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1202495, tc_Nat_Onat), _1202497), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1202499), _1202501)))], (13589 ^ _781013) ^ [_1030035, _1030037, _1030039, _1030041, _1030043, _1030045, _1030047] : [c_Big__Operators_Ocomm__monoid__big(_1030035, _1030037, _1030039, _1030041, _1030043), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1030037), _1030045))), -(hAPP(hAPP(_1030043, _1030047), _1030045) = _1030041)], (46895 ^ _781013) ^ [_1724111, _1724113] : [-(c_Wellfounded_Owf(_1724111, c_List_Omeasures(_1724111, _1724113)))], (8293 ^ _781013) ^ [_922833, _922835, _922837, _922839, _922841] : [class_Lattices_Olattice(_922833), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922835, _922833)), _922837), _922839), _922841) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922833), hAPP(_922837, _922841)), hAPP(_922839, _922841)))], (40952 ^ _781013) ^ [_1587247] : [-(hAPP(c_Option_Omap(_1587247, _1587247), c_COMBI(_1587247)) = c_Fun_Oid(tc_Option_Ooption(_1587247)))], (45852 ^ _781013) ^ [_1698367, _1698369, _1698371, _1698373] : [hBOOL(hAPP(hAPP(c_member(_1698367), _1698369), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1698367, tc_HOL_Obool), _1698371))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1698367, tc_HOL_Obool)), _1698373), _1698371)), -(hBOOL(hAPP(hAPP(c_member(_1698367), _1698369), _1698373)))], (23483 ^ _781013) ^ [_1220469, _1220471, _1220473, _1220475] : [class_Rings_Odivision__ring(_1220469), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220469), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220469), _1220471), _1220473)), _1220475) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220469), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220469), _1220471), _1220475)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220469), _1220473), _1220475)))], (50543 ^ _781013) ^ [_1808620, _1808622] : [-(c_FunDef_Ois__measure(_1808620, _1808622))], (13449 ^ _781013) ^ [_1026674, _1026676, _1026678, _1026680, _1026682, _1026684, _1026686] : [class_Rings_Osemiring__0(_1026674), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026674), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1026676, _1026674), _1026678), _1026680)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1026682, _1026674), _1026684), _1026686)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1026676, _1026674), hAPP(hAPP(c_COMBC(_1026676, tc_fun(_1026682, tc_HOL_Obool), _1026674), hAPP(hAPP(c_COMBB(tc_fun(_1026682, _1026674), tc_fun(tc_fun(_1026682, tc_HOL_Obool), _1026674), _1026676), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1026682, _1026674)), hAPP(hAPP(c_COMBC(_1026676, tc_fun(_1026682, _1026674), tc_fun(_1026682, _1026674)), hAPP(hAPP(c_COMBB(tc_fun(_1026674, _1026674), tc_fun(tc_fun(_1026682, _1026674), tc_fun(_1026682, _1026674)), _1026676), c_COMBB(_1026674, _1026674, _1026682)), hAPP(hAPP(c_COMBB(_1026674, tc_fun(_1026674, _1026674), _1026676), c_Groups_Otimes__class_Otimes(_1026674)), _1026678))), _1026684))), _1026686)), _1026680))], (30111 ^ _781013) ^ [_1343648, _1343650, _1343652, _1343654] : [class_Orderings_Olinorder(_1343648), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343648), _1343650), _1343652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343648), _1343650), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343648), _1343654), _1343652))))], (42140 ^ _781013) ^ [_1615065, _1615067, _1615069, _1615071] : [-(hAPP(hAPP(c_List_Odrop(_1615065), hAPP(c_Nat_OSuc, _1615067)), hAPP(hAPP(c_List_Olist_OCons(_1615065), _1615069), _1615071)) = hAPP(hAPP(c_List_Odrop(_1615065), _1615067), _1615071))], (22176 ^ _781013) ^ [_1196963, _1196965] : [_1196963 = _1196965, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1196963) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1196965))], (27855 ^ _781013) ^ [_1301187, _1301189] : [class_Divides_Osemiring__div(_1301187), -(c_Divides_Odiv__class_Omod(_1301187, _1301189, c_Groups_Oone__class_Oone(_1301187)) = c_Groups_Ozero__class_Ozero(_1301187))], (31244 ^ _781013) ^ [_1366400, _1366402, _1366404, _1366406, _1366408, _1366410] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1366400, _1366402, _1366404)), _1366406), _1366408), _1366410))), 31245 ^ _781013 : [(31252 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1366400, _1366406))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1366404), _1366406), _1366408), _1366410))], (31246 ^ _781013) ^ [] : [hBOOL(hAPP(_1366400, _1366406)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1366402), _1366406), _1366408), _1366410))]]], (26273 ^ _781013) ^ [_1269607, _1269609, _1269611] : [-(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)), _1269607)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1269609, _1269611)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1269609), _1269607), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1269611), _1269607)))], (530 ^ _781013) ^ [_789190, _789192, _789194, _789196] : [-(c_FunDef_Oreduction__pair(_789194, _789190)), c_FunDef_Oreduction__pair(_789196, _789192), _789196 = _789194, _789192 = _789190], (11650 ^ _781013) ^ [_990769] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_990769)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_990769), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_990769), c_Orderings_Otop__class_Otop(tc_fun(_990769, tc_HOL_Obool)))))], (50922 ^ _781013) ^ [_1817121, _1817123, _1817125] : [-(_1817121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1817123), c_List_Oreplicate(_1817123, _1817121, _1817125)) = c_List_Oreplicate(_1817123, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1817121), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1817125))], (45097 ^ _781013) ^ [_1681957, _1681959, _1681961, _1681963, _1681965] : [class_Orderings_Olinorder(_1681957), -(hAPP(c_List_Ofilter(_1681959, _1681961), c_List_Olinorder__class_Osort__key(_1681959, _1681957, _1681963, _1681965)) = c_List_Olinorder__class_Osort__key(_1681959, _1681957, _1681963, hAPP(c_List_Ofilter(_1681959, _1681961), _1681965)))], (46667 ^ _781013) ^ [_1718471, _1718473, _1718475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1718471, _1718471), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1718471, _1718471, _1718471), _1718473), _1718475)), _1718473)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1718471, tc_HOL_Obool), tc_fun(_1718471, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1718471, tc_HOL_Obool), tc_fun(_1718471, tc_HOL_Obool), tc_fun(_1718471, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1718471, _1718473)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1718471, tc_HOL_Obool), tc_fun(_1718471, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1718471, _1718475)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1718471, tc_HOL_Obool), tc_fun(_1718471, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1718471, tc_HOL_Obool), tc_fun(_1718471, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1718471, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1718471, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1718471, tc_HOL_Obool), tc_fun(_1718471, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1718471, _1718473))))], (12078 ^ _781013) ^ [_998991] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_998991, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_998991, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_998991, tc_HOL_Obool)))], (40705 ^ _781013) ^ [_1579181, _1579183, _1579185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1579181, _1579181), tc_HOL_Obool)), _1579183), _1579185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1579181), tc_List_Olist(_1579181)), tc_HOL_Obool)), c_List_Olistrel1(_1579181, _1579183)), c_List_Olistrel1(_1579181, _1579185))))], (15759 ^ _781013) ^ [_1072552, _1072554, _1072556, _1072558] : [class_Rings_Olinordered__comm__semiring__strict(_1072552), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072552), _1072554), _1072556)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072552), c_Groups_Ozero__class_Ozero(_1072552)), _1072558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072552), _1072558), _1072554)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072552), _1072558), _1072556))))], (19406 ^ _781013) ^ [_1144369, _1144371, _1144373, _1144375] : [class_Groups_Omonoid__mult(_1144369), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1144369), _1144371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144373), _1144375)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1144369), hAPP(hAPP(c_Power_Opower__class_Opower(_1144369), _1144371), _1144373)), _1144375))], (35583 ^ _781013) ^ [_1454526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1454526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1454526)))], (34801 ^ _781013) ^ [_1439965, _1439967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439965), _1439967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1439965)), c_Int_OBit0(_1439967))))], (16502 ^ _781013) ^ [_1086598, _1086600, _1086602, _1086604] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1086598), _1086600)), 16505 ^ _781013 : [(16512 ^ _781013) ^ [] : [hAPP(c_Finite__Set_Ocard(_1086602), hAPP(c_Set_Oimage(_1086598, _1086602, _1086604), _1086600)) = hAPP(c_Finite__Set_Ocard(_1086598), _1086600), -(c_Fun_Oinj__on(_1086598, _1086602, _1086604, _1086600))], (16506 ^ _781013) ^ [] : [c_Fun_Oinj__on(_1086598, _1086602, _1086604, _1086600), -(hAPP(c_Finite__Set_Ocard(_1086602), hAPP(c_Set_Oimage(_1086598, _1086602, _1086604), _1086600)) = hAPP(c_Finite__Set_Ocard(_1086598), _1086600))]]], (17947 ^ _781013) ^ [_1115663, _1115665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1115663), _1115665)), _1115665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20701 ^ _781013) ^ [_1167997, _1167999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1167997)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1167999)), -(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), _1167999), _1167997))))], (13646 ^ _781013) ^ [_1031341, _1031343] : [class_Rings_Ocomm__semiring__1(_1031341), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031341), c_Groups_Oone__class_Oone(_1031341)), _1031343) = _1031343)], (39842 ^ _781013) ^ [_1553890, _1553892] : [-(c_List_Olex(_1553890, _1553892) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1553890), tc_List_Olist(_1553890)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1553890, _1553892)))], (36530 ^ _781013) ^ [_1477877, _1477879, _1477881, _1477883, _1477885, _1477887] : [hBOOL(hAPP(hAPP(_1477877, _1477879), _1477881)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477883, tc_fun(_1477885, tc_HOL_Obool))), _1477887), _1477877), _1477879), _1477881)))], (8241 ^ _781013) ^ [_921773, _921775, _921777, _921779, _921781, _921783] : [c_Finite__Set_Ofolding(_921773, _921775, _921777, _921779), hBOOL(hAPP(c_Finite__Set_Ofinite(_921773), _921781)), hBOOL(hAPP(hAPP(c_member(_921773), _921783), _921781)), -(hAPP(_921779, _921781) = hAPP(c_Fun_Ocomp(_921775, _921775, _921775, hAPP(_921779, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921773, tc_HOL_Obool)), _921781), hAPP(hAPP(c_Set_Oinsert(_921773), _921783), c_Orderings_Obot__class_Obot(tc_fun(_921773, tc_HOL_Obool)))))), hAPP(_921777, _921783)))], (14517 ^ _781013) ^ [_1050293, _1050295, _1050297, _1050299, _1050301, _1050303] : [class_Groups_Ocomm__monoid__add(_1050293), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050295), _1050297)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1050295, _1050293), hAPP(hAPP(c_COMBS(_1050295, _1050293, _1050293), hAPP(hAPP(c_COMBS(_1050295, _1050293, tc_fun(_1050293, _1050293)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1050293, tc_fun(_1050293, _1050293)), _1050295), c_If(_1050293)), _1050299)), _1050301)), _1050303)), _1050297) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050293), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1050295, _1050293), _1050301), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1050295, tc_HOL_Obool)), _1050297), hAPP(c_Set_OCollect(_1050295), _1050299)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1050295, _1050293), _1050303), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1050295, tc_HOL_Obool)), _1050297), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1050295, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1050295), _1050299))))))], (41875 ^ _781013) ^ [_1607977, _1607979, _1607981, _1607983] : [-(hAPP(hAPP(c_List_Onth(_1607977), hAPP(hAPP(c_List_Oappend(_1607977), _1607979), hAPP(hAPP(c_List_Olist_OCons(_1607977), _1607981), _1607983))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607977)), _1607979)) = _1607981)], (5932 ^ _781013) ^ [_876632, _876634, _876636, _876638, _876640] : [c_Hoare__Mirabelle_Ohoare__valids(_876632, _876634, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_876632)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_876632), c_Hoare__Mirabelle_Opeek__and(_876632, _876636, _876638)), _876640), _876636)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_876632), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__valids(_876632, _876634, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_876632)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_876632), _876636), c_Com_Ocom_OWhile(_876638, _876640)), c_Hoare__Mirabelle_Opeek__and(_876632, _876636, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _876638)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_876632), tc_HOL_Obool)))))], (20853 ^ _781013) ^ [_1170834, _1170836, _1170838] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1170834), _1170836)), 20856 ^ _781013 : [(20863 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1170834), _1170838), _1170836))), -(hAPP(c_Finite__Set_Ocard(_1170834), hAPP(hAPP(c_Set_Oinsert(_1170834), _1170838), _1170836)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1170834), _1170836)))], (20857 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1170834), _1170838), _1170836)), -(hAPP(c_Finite__Set_Ocard(_1170834), hAPP(hAPP(c_Set_Oinsert(_1170834), _1170838), _1170836)) = hAPP(c_Finite__Set_Ocard(_1170834), _1170836))]]], (8667 ^ _781013) ^ [_931572, _931574, _931576, _931578] : [class_Lattices_Osemilattice__sup(_931572), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931572), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931572), _931574), _931576)), _931578) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931572), _931574), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931572), _931576), _931578)))], (27755 ^ _781013) ^ [_1299303, _1299305, _1299307] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1299303), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1299305, _1299307)), _1299307) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1299303), _1299305), _1299307))], (27958 ^ _781013) ^ [_1303151, _1303153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303151)), -(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, _1303153, _1303151))))], (35625 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (6096 ^ _781013) ^ [_879578, _879580, _879582] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _879578)), _879580), _879582)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _879578))), _879580), _879582)))], (14977 ^ _781013) ^ [_1058116, _1058118] : [class_Groups_Olinordered__ab__group__add(_1058116), 14980 ^ _781013 : [(14987 ^ _781013) ^ [] : [_1058118 = c_Groups_Ozero__class_Ozero(_1058116), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1058116), _1058118) = _1058118)], (14981 ^ _781013) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1058116), _1058118) = _1058118, -(_1058118 = c_Groups_Ozero__class_Ozero(_1058116))]]], (29036 ^ _781013) ^ [_1322763, _1322765, _1322767] : [class_Rings_Olinordered__idom(_1322763), 29039 ^ _781013 : [(29048 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322763), hAPP(c_Groups_Oabs__class_Oabs(_1322763), _1322765)), _1322767))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322763), _1322765), _1322767)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322763), hAPP(c_Groups_Ouminus__class_Ouminus(_1322763), _1322765)), _1322767))], (29040 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322763), hAPP(c_Groups_Oabs__class_Oabs(_1322763), _1322765)), _1322767)), 29043 ^ _781013 : [(29046 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322763), hAPP(c_Groups_Ouminus__class_Ouminus(_1322763), _1322765)), _1322767)))], (29044 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322763), _1322765), _1322767)))]]]]], (41254 ^ _781013) ^ [_1594167, _1594169, _1594171] : [-(hAPP(hAPP(c_List_Omap(_1594167, _1594169), _1594171), c_List_Olist_ONil(_1594167)) = c_List_Olist_ONil(_1594169))], (45725 ^ _781013) ^ [_1695202, _1695204, _1695206] : [class_Complete__Lattice_Ocomplete__lattice(_1695202), -(c_Complete__Lattice_OSup__class_OSup(_1695202, hAPP(hAPP(c_Set_Oinsert(_1695202), _1695204), _1695206)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1695202), _1695204), c_Complete__Lattice_OSup__class_OSup(_1695202, _1695206)))], (34000 ^ _781013) ^ [_1425319, _1425321] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425319)), hAPP(c_Nat_OSuc, _1425321)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1425319))), 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, _1425321))), 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)), _1425321)))))], (51302 ^ _781013) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (39283 ^ _781013) ^ [_1539985] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1539985) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 39286 ^ _781013 : [(39287 ^ _781013) ^ [_1540060] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1540060), hAPP(c_List_Oset(tc_Nat_Onat), _1539985))), -(_1540060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25874 ^ _781013) ^ [_1262234] : [class_Rings_Oring__1(_1262234), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262234), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1262234))], (27697 ^ _781013) ^ [_1298054, _1298056, _1298058, _1298060] : [class_Divides_Osemiring__div(_1298054), -(c_Divides_Odiv__class_Omod(_1298054, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298054), _1298056), _1298058), _1298060) = c_Divides_Odiv__class_Omod(_1298054, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298054), _1298056), c_Divides_Odiv__class_Omod(_1298054, _1298058, _1298060)), _1298060))], (35945 ^ _781013) ^ [_1462912, _1462914, _1462916, _1462918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462912, tc_fun(_1462914, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1462912, tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_fun(_1462914, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1462914, tc_fun(tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_fun(_1462914, tc_HOL_Obool)), _1462912), c_COMBC(_1462914, tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1462914, tc_prod(_1462912, _1462914)), tc_fun(_1462914, tc_fun(tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_HOL_Obool)), _1462912), hAPP(c_COMBB(tc_prod(_1462912, _1462914), tc_fun(tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_HOL_Obool), _1462914), c_member(tc_prod(_1462912, _1462914)))), c_Product__Type_OPair(_1462912, _1462914)))), _1462916)), hAPP(hAPP(c_COMBC(_1462912, tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_fun(_1462914, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1462914, tc_fun(tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_fun(_1462914, tc_HOL_Obool)), _1462912), c_COMBC(_1462914, tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1462914, tc_prod(_1462912, _1462914)), tc_fun(_1462914, tc_fun(tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_HOL_Obool)), _1462912), hAPP(c_COMBB(tc_prod(_1462912, _1462914), tc_fun(tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool), tc_HOL_Obool), _1462914), c_member(tc_prod(_1462912, _1462914)))), c_Product__Type_OPair(_1462912, _1462914)))), _1462918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1462912, _1462914), tc_HOL_Obool)), _1462916), _1462918)))], (39757 ^ _781013) ^ [_1551508, _1551510, _1551512] : [hBOOL(hAPP(hAPP(c_member(_1551508), _1551510), hAPP(c_List_Oset(_1551508), c_List_Obutlast(_1551508, _1551512)))), -(hBOOL(hAPP(hAPP(c_member(_1551508), _1551510), hAPP(c_List_Oset(_1551508), _1551512))))], (42396 ^ _781013) ^ [_1620697, _1620699, _1620701] : [hBOOL(hAPP(c_List_Odistinct(_1620697), _1620701)), -(hBOOL(hAPP(c_List_Odistinct(_1620697), hAPP(c_List_Orotate(_1620697, _1620699), _1620701))))], (48595 ^ _781013) ^ [_1763745, _1763747, _1763749, _1763751] : [-(c_Wellfounded_Owf(_1763745, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1763745, _1763745)), hAPP(hAPP(c_Product__Type_OPair(_1763745, _1763745), _1763747), _1763749)), _1763751))), c_Wellfounded_Owf(_1763745, _1763751), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763745, _1763745)), hAPP(hAPP(c_Product__Type_OPair(_1763745, _1763745), _1763749), _1763747)), c_Transitive__Closure_Ortrancl(_1763745, _1763751))))], (23453 ^ _781013) ^ [_1219844, _1219846] : [class_Rings_Odivision__ring(_1219844), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219844), c_Groups_Ozero__class_Ozero(_1219844)), _1219846) = c_Groups_Ozero__class_Ozero(_1219844))], (51554 ^ _781013) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (42206 ^ _781013) ^ [_1616583, _1616585, _1616587, _1616589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1616583), _1616585)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616587)), _1616589))), -(hAPP(hAPP(c_List_Onth(_1616587), hAPP(hAPP(c_List_Odrop(_1616587), _1616583), _1616589)), _1616585) = hAPP(hAPP(c_List_Onth(_1616587), _1616589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1616583), _1616585)))], (48695 ^ _781013) ^ [_1766128, _1766130] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1766128)), hAPP(c_Code__Numeral_Oof__nat, _1766130)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1766128), _1766130)))], (14602 ^ _781013) ^ [_1052148, _1052150] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052148), _1052150))), -(hAPP(c_Finite__Set_Ocard(_1052148), _1052150) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48275 ^ _781013) ^ [_1756317, _1756319, _1756321] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1756317, _1756317)), _1756319), _1756321)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1756317, _1756317)), _1756319), c_Transitive__Closure_Ortrancl(_1756317, _1756321))))], (40303 ^ _781013) ^ [_1567244, _1567246, _1567248, _1567250, _1567252] : [c_Relation_Orefl__on(_1567244, _1567246, _1567248), c_Relation_Orefl__on(_1567244, _1567250, _1567252), -(c_Relation_Orefl__on(_1567244, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567244, tc_HOL_Obool)), _1567246), _1567250), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1567244, _1567244), tc_HOL_Obool)), _1567248), _1567252)))], (472 ^ _781013) ^ [_788299, _788301, _788303, _788305, _788307, _788309] : [-(c_Enum_Oex__n__lists(_788307, _788303, _788299)), c_Enum_Oex__n__lists(_788309, _788305, _788301), _788309 = _788307, _788305 = _788303, _788301 = _788299], (27946 ^ _781013) ^ [_1302885, _1302887, _1302889] : [class_Divides_Osemiring__div(_1302885), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1302885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302885), _1302887), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1302885), _1302889), _1302887))), c_Divides_Odiv__class_Omod(_1302885, _1302889, _1302887)) = _1302889)], (31152 ^ _781013) ^ [_1364514, _1364516, _1364518, _1364520, _1364522, _1364524] : [hBOOL(hAPP(_1364514, _1364516)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1364518), _1364516), _1364520), _1364522)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1364514, _1364518, _1364524)), _1364516), _1364520), _1364522)))], (20371 ^ _781013) ^ [_1161589, _1161591] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161589), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1161589), _1161591)))))], (46250 ^ _781013) ^ [_1706945, _1706947, _1706949, _1706951, _1706953] : [-(c_List_Olist__all2(_1706945, _1706947, _1706949, _1706951, _1706953)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706945)), _1706951) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706947)), _1706953), 46256 ^ _781013 : [(46259 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1706949, hAPP(hAPP(c_List_Onth(_1706945), _1706951), 46255 ^ [_1706945, _1706947, _1706949, _1706951, _1706953])), hAPP(hAPP(c_List_Onth(_1706947), _1706953), 46255 ^ [_1706945, _1706947, _1706949, _1706951, _1706953])))], (46257 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46255 ^ [_1706945, _1706947, _1706949, _1706951, _1706953]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706945)), _1706951))))]]], (6719 ^ _781013) ^ [_891624, _891626, _891628] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_891624), _891626)), -(_891626 = c_Orderings_Obot__class_Obot(tc_fun(_891624, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_891624, _891628, _891626), 6726 ^ [_891624, _891626, _891628])))], (34659 ^ _781013) ^ [_1437619, _1437621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437619), _1437621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1437619)), c_Int_OBit0(_1437621))))], (41526 ^ _781013) ^ [_1600317, _1600319, _1600321] : [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), _1600317), _1600319))), -(hBOOL(hAPP(hAPP(_1600321, _1600317), _1600319))), 41533 ^ _781013 : [(41536 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 41531 ^ [_1600317, _1600319, _1600321]), 41532 ^ [_1600317, _1600319, _1600321])), -(hBOOL(hAPP(hAPP(_1600321, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 41531 ^ [_1600317, _1600319, _1600321]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 41532 ^ [_1600317, _1600319, _1600321])))], (41542 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1600321, 41531 ^ [_1600317, _1600319, _1600321]), 41532 ^ [_1600317, _1600319, _1600321]))], (41534 ^ _781013) ^ [] : [-(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), 41531 ^ [_1600317, _1600319, _1600321]), 41532 ^ [_1600317, _1600319, _1600321]))))]]], (34423 ^ _781013) ^ [] : [-(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)))))], (41754 ^ _781013) ^ [_1605059, _1605061, _1605063, _1605065] : [-(hAPP(hAPP(c_List_Oappend(_1605059), hAPP(hAPP(c_List_Oappend(_1605059), _1605061), _1605063)), _1605065) = hAPP(hAPP(c_List_Oappend(_1605059), _1605061), hAPP(hAPP(c_List_Oappend(_1605059), _1605063), _1605065)))], (11163 ^ _781013) ^ [_979948, _979950, _979952, _979954, _979956, _979958] : [-(hAPP(c_Map_Omap__add(_979948, _979950, _979952, _979954), _979956) = hAPP(c_Option_Ooption_OSome(_979950), _979958)), 11164 ^ _781013 : [(11167 ^ _781013) ^ [] : [hAPP(_979954, _979956) = c_Option_Ooption_ONone(_979950), hAPP(_979952, _979956) = hAPP(c_Option_Ooption_OSome(_979950), _979958)], (11165 ^ _781013) ^ [] : [hAPP(_979954, _979956) = hAPP(c_Option_Ooption_OSome(_979950), _979958)]]], (34971 ^ _781013) ^ [_1443229, _1443231] : [class_Int_Onumber__ring(_1443229), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1443229), _1443231), hAPP(c_Int_Onumber__class_Onumber__of(_1443229), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1443229), _1443231), _1443231))], (47106 ^ _781013) ^ [_1729112, _1729114, _1729116, _1729118] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1729112, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1729114, _1729112), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1729114, _1729112), tc_HOL_Obool)), _1729116), _1729118))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1729112, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1729114, _1729112), _1729116)), hAPP(c_Relation_ORange(_1729114, _1729112), _1729118)))))], (49804 ^ _781013) ^ [_1793356, _1793358, _1793360] : [class_Lattices_Olattice(_1793356), hBOOL(hAPP(c_Finite__Set_Ofinite(_1793356), _1793358)), -(hBOOL(hAPP(hAPP(c_member(_1793356), _1793360), _1793358))), -(c_Big__Operators_Olattice__class_OSup__fin(_1793356, hAPP(hAPP(c_Set_Oinsert(_1793356), _1793360), _1793358)) = hAPP(hAPP(c_Finite__Set_Ofold(_1793356, _1793356, c_Lattices_Osemilattice__sup__class_Osup(_1793356)), _1793360), _1793358))], (27206 ^ _781013) ^ [_1287601, _1287603] : [class_Groups_Oordered__ab__group__add(_1287601), -(hAPP(c_Set_Oimage(_1287601, _1287601, c_Groups_Ouminus__class_Ouminus(_1287601)), hAPP(c_SetInterval_Oord__class_OatLeast(_1287601), _1287603)) = hAPP(c_SetInterval_Oord__class_OatMost(_1287601), hAPP(c_Groups_Ouminus__class_Ouminus(_1287601), _1287603)))], (8455 ^ _781013) ^ [_926928, _926930, _926932, _926934, _926936] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926928, tc_HOL_Obool)), _926930), hAPP(c_Set_Oimage(_926932, _926928, _926934), _926936)))), 8456 ^ _781013 : [(8457 ^ _781013) ^ [_927008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926932, tc_HOL_Obool)), _927008), _926936)), _926930 = hAPP(c_Set_Oimage(_926932, _926928, _926934), _927008)]]], (24574 ^ _781013) ^ [_1239402, _1239404, _1239406, _1239408] : [class_Fields_Olinordered__field__inverse__zero(_1239402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239402), _1239404), _1239406)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239402), _1239408), c_Groups_Ozero__class_Ozero(_1239402))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239402), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239402), _1239406), _1239408)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239402), _1239404), _1239408))))], (48425 ^ _781013) ^ [_1760136, _1760138, _1760140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1760136, _1760136), tc_HOL_Obool)), _1760138), c_Transitive__Closure_Ortrancl(_1760136, _1760140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1760136, _1760136), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1760136, _1760138)), c_Transitive__Closure_Ortrancl(_1760136, _1760140))))], (44803 ^ _781013) ^ [_1675496, _1675498, _1675500] : [hBOOL(hAPP(hAPP(c_member(_1675496), _1675498), hAPP(c_List_Oset(_1675496), _1675500))), -(c_List_Oremdups(_1675496, hAPP(hAPP(c_List_Olist_OCons(_1675496), _1675498), _1675500)) = c_List_Oremdups(_1675496, _1675500))], (622 ^ _781013) ^ [_790532, _790534, _790536, _790538, _790540, _790542, _790544, _790546] : [-(c_Fun_Oinj__on(_790544, _790540, _790536, _790532)), c_Fun_Oinj__on(_790546, _790542, _790538, _790534), _790546 = _790544, _790542 = _790540, _790538 = _790536, _790534 = _790532], (24368 ^ _781013) ^ [_1235534, _1235536, _1235538, _1235540] : [class_Fields_Olinordered__field__inverse__zero(_1235534), 24371 ^ _781013 : [(24372 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235534), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1235534), _1235536), _1235538)), _1235540)), 24375 ^ _781013 : [(24382 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235534), c_Groups_Ozero__class_Ozero(_1235534)), _1235538))), 24385 ^ _781013 : [(24392 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235534), _1235538), c_Groups_Ozero__class_Ozero(_1235534)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235534), c_Groups_Ozero__class_Ozero(_1235534)), _1235540)))], (24386 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235534), _1235538), c_Groups_Ozero__class_Ozero(_1235534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235534), _1235540), _1235538)), _1235536)))]]], (24376 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235534), c_Groups_Ozero__class_Ozero(_1235534)), _1235538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235534), _1235536), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235534), _1235540), _1235538))))]]], (24398 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235534), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1235534), _1235536), _1235538)), _1235540))), 24401 ^ _781013 : [(24404 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235534), _1235536), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235534), _1235540), _1235538)))], (24402 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235534), c_Groups_Ozero__class_Ozero(_1235534)), _1235538)))]], 24405 ^ _781013 : [(24408 ^ _781013) ^ [] : [24409 ^ _781013 : [(24412 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235534), _1235540), _1235538)), _1235536))], (24410 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235534), _1235538), c_Groups_Ozero__class_Ozero(_1235534))))]], 24413 ^ _781013 : [(24416 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235534), c_Groups_Ozero__class_Ozero(_1235534)), _1235540))], (24414 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235534), _1235538), c_Groups_Ozero__class_Ozero(_1235534)))]]], (24406 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235534), c_Groups_Ozero__class_Ozero(_1235534)), _1235538))]]]]], (42270 ^ _781013) ^ [_1618303, _1618305, _1618307, _1618309] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618303) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1618305), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618303)), hAPP(hAPP(c_List_Olist_OCons(_1618305), _1618307), _1618309)) = hAPP(hAPP(c_List_Odrop(_1618305), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618303)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1618309))], (21818 ^ _781013) ^ [_1190493, _1190495] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1190493)), _1190495) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1190493), _1190495)))], (31668 ^ _781013) ^ [_1379226, _1379228, _1379230] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1379226), _1379228), _1379230) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379226, tc_fun(tc_fun(_1379226, tc_HOL_Obool), tc_HOL_Obool)), _1379228), hAPP(hAPP(c_COMBC(_1379226, tc_fun(tc_fun(_1379226, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1379226, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1379226, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1379226, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1379226, tc_HOL_Obool), tc_HOL_Obool)), _1379226), c_Set_Oinsert(tc_fun(_1379226, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1379226, tc_HOL_Obool), tc_fun(_1379226, tc_HOL_Obool), _1379226), c_Relation_OImage(_1379226, _1379226, _1379230)), hAPP(hAPP(c_COMBC(_1379226, tc_fun(_1379226, tc_HOL_Obool), tc_fun(_1379226, tc_HOL_Obool)), c_Set_Oinsert(_1379226)), c_Orderings_Obot__class_Obot(tc_fun(_1379226, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1379226, tc_HOL_Obool), tc_HOL_Obool)))))], (38037 ^ _781013) ^ [_1509710] : [-(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)), _1509710), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (27727 ^ _781013) ^ [_1298737, _1298739, _1298741, _1298743, _1298745, _1298747] : [class_Divides_Osemiring__div(_1298737), c_Divides_Odiv__class_Omod(_1298737, _1298739, _1298741) = c_Divides_Odiv__class_Omod(_1298737, _1298743, _1298741), c_Divides_Odiv__class_Omod(_1298737, _1298745, _1298741) = c_Divides_Odiv__class_Omod(_1298737, _1298747, _1298741), -(c_Divides_Odiv__class_Omod(_1298737, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298737), _1298739), _1298745), _1298741) = c_Divides_Odiv__class_Omod(_1298737, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298737), _1298743), _1298747), _1298741))], (5893 ^ _781013) ^ [_875842, _875844] : [-(c_HOL_OThe(_875842, hAPP(c_fequal, _875844)) = _875844)], (32340 ^ _781013) ^ [_1394655, _1394657, _1394659, _1394661, _1394663, _1394665] : [c_Com_Ocom_OLocal(_1394655, _1394657, _1394659) = c_Com_Ocom_OLocal(_1394661, _1394663, _1394665), 32343 ^ _781013 : [(32348 ^ _781013) ^ [] : [-(_1394659 = _1394665)], (32346 ^ _781013) ^ [] : [-(_1394657 = _1394663)], (32344 ^ _781013) ^ [] : [-(_1394655 = _1394661)]]], (43777 ^ _781013) ^ [_1653018, _1653020] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1653018, _1653020)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1653018), hAPP(c_Nat_OSuc, _1653020)))], (42865 ^ _781013) ^ [_1631460, _1631462, _1631464, _1631466, _1631468] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1631460, tc_HOL_Obool)), _1631462), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631464, tc_fun(_1631460, tc_HOL_Obool)), _1631466), _1631468)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1631464, tc_fun(_1631460, tc_HOL_Obool)), _1631466), hAPP(hAPP(c_COMBB(tc_fun(_1631460, tc_HOL_Obool), tc_fun(_1631460, tc_HOL_Obool), _1631464), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1631460, tc_HOL_Obool)), _1631462)), _1631468)))], (44857 ^ _781013) ^ [_1676664, _1676666, _1676668] : [class_Orderings_Olinorder(_1676664), c_List_Olinorder__class_Osorted(_1676664, _1676666), -(c_List_Olinorder__class_Osorted(_1676664, c_List_OdropWhile(_1676664, _1676668, _1676666)))], (41003 ^ _781013) ^ [_1588182, _1588184, _1588186, _1588188] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588184, _1588182), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1588182, tc_prod(_1588184, _1588182), 40999 ^ [_1588182, _1588184, _1588186, _1588188]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1588184, tc_fun(_1588182, tc_HOL_Obool)), _1588186), _1588188))), hAPP(hAPP(c_Product__Type_OSigma(_1588184, _1588182), _1588186), _1588188))))], (50180 ^ _781013) ^ [_1801110, _1801112, _1801114] : [hBOOL(hAPP(hAPP(c_member(_1801110), _1801112), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1801110, tc_HOL_Obool), _1801114))), 50184 ^ _781013 : [(50187 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1801110, tc_HOL_Obool)), 50183 ^ [_1801110, _1801112, _1801114]), _1801114)))], (50185 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801110), _1801112), 50183 ^ [_1801110, _1801112, _1801114])))]]], (51140 ^ _781013) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (51516 ^ _781013) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (45709 ^ _781013) ^ [_1694861, _1694863] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1694861, tc_HOL_Obool), _1694863) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1694861, tc_HOL_Obool), tc_fun(_1694861, tc_HOL_Obool)), _1694863), c_COMBI(tc_fun(_1694861, tc_HOL_Obool))))], (7473 ^ _781013) ^ [_905801, _905803, _905805, _905807, _905809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905801, tc_HOL_Obool)), _905803), _905805)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905801, tc_HOL_Obool)), _905807), _905809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905801, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905801, tc_HOL_Obool)), _905803), _905807)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905801, tc_HOL_Obool)), _905805), _905809))))], (32276 ^ _781013) ^ [_1393613, _1393615, _1393617] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_1393613, _1393615, _1393617)], (18738 ^ _781013) ^ [_1130237, _1130239, _1130241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130237), _1130239)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1130239), _1130241)), _1130237) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130239), _1130237)), _1130241))], (44675 ^ _781013) ^ [_1673027, _1673029, _1673031, _1673033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673027), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673029)), c_List_OtakeWhile(_1673029, _1673031, _1673033)))), -(hAPP(hAPP(c_List_Onth(_1673029), c_List_OtakeWhile(_1673029, _1673031, _1673033)), _1673027) = hAPP(hAPP(c_List_Onth(_1673029), _1673033), _1673027))], (40457 ^ _781013) ^ [_1571803, _1571805, _1571807, _1571809, _1571811, _1571813, _1571815, _1571817, _1571819, _1571821] : [-(c_Product__Type_Omap__pair(_1571803, _1571805, _1571807, _1571809, hAPP(c_Fun_Ocomp(_1571811, _1571805, _1571803, _1571813), _1571815), hAPP(c_Fun_Ocomp(_1571817, _1571809, _1571807, _1571819), _1571821)) = hAPP(c_Fun_Ocomp(tc_prod(_1571811, _1571817), tc_prod(_1571805, _1571809), tc_prod(_1571803, _1571807), c_Product__Type_Omap__pair(_1571811, _1571805, _1571817, _1571809, _1571813, _1571819)), c_Product__Type_Omap__pair(_1571803, _1571811, _1571807, _1571817, _1571815, _1571821)))], (51510 ^ _781013) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (33452 ^ _781013) ^ [_1415864] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415864)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415864)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415864))], (42781 ^ _781013) ^ [_1628582, _1628584, _1628586, _1628588, _1628590, _1628592] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628582, tc_fun(_1628584, tc_HOL_Obool)), _1628586), _1628588), _1628590)), hBOOL(hAPP(hAPP(c_member(_1628582), _1628592), _1628586)), -(hBOOL(hAPP(hAPP(_1628588, _1628592), _1628590)))], (46176 ^ _781013) ^ [_1705383, _1705385, _1705387, _1705389] : [_1705389 = c_List_Olist_ONil(_1705383), -(c_List_Olist__all2(_1705383, _1705385, _1705387, _1705389, c_List_Olist_ONil(_1705385)))], (20418 ^ _781013) ^ [_1162467, _1162469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162467), _1162469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1162467)), _1162469)))], (20476 ^ _781013) ^ [_1163391, _1163393] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1163391), _1163393)), hAPP(c_Nat_OSuc, _1163391))))], (44004 ^ _781013) ^ [_1657100, _1657102, _1657104, _1657106, _1657108, _1657110] : [class_Orderings_Olinorder(_1657100), c_List_Olinorder__class_Osorted(_1657100, hAPP(hAPP(c_List_Omap(_1657102, _1657100), _1657104), _1657106)), hBOOL(hAPP(_1657108, _1657110)), -(hAPP(c_List_Ofilter(_1657102, _1657108), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1657102, _1657100, _1657104), _1657110), _1657106)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1657102, _1657100, _1657104), _1657110), hAPP(c_List_Ofilter(_1657102, _1657108), _1657106)))], (21636 ^ _781013) ^ [_1187367, _1187369] : [21637 ^ _781013 : [(21638 ^ _781013) ^ [_1187420] : [_1187369 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1187367), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187420))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1187367), _1187369)))], (41005 ^ _781013) ^ [_1588268, _1588270, _1588272, _1588274, _1588276, _1588278] : [class_Groups_Ocomm__monoid__mult(_1588268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588270), _1588272)), 41015 ^ _781013 : [(41018 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1588274), hAPP(_1588276, 41014 ^ [_1588268, _1588270, _1588272, _1588274, _1588276, _1588278])))], (41016 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588270), 41014 ^ [_1588268, _1588270, _1588272, _1588274, _1588276, _1588278]), _1588272)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1588270, _1588268), hAPP(hAPP(c_COMBS(_1588270, tc_fun(_1588274, tc_HOL_Obool), _1588268), hAPP(hAPP(c_COMBB(tc_fun(_1588274, _1588268), tc_fun(tc_fun(_1588274, tc_HOL_Obool), _1588268), _1588270), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1588274, _1588268)), _1588278)), _1588276)), _1588272) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1588270, _1588274), _1588268), hAPP(c_Product__Type_Oprod_Oprod__case(_1588270, _1588274, _1588268), _1588278)), hAPP(hAPP(c_Product__Type_OSigma(_1588270, _1588274), _1588272), _1588276)))], (11482 ^ _781013) ^ [_987410, _987412, _987414, _987416, _987418] : [-(c_Fun_Oinj__on(_987410, _987412, _987414, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987410, tc_HOL_Obool)), _987416), _987418))), c_Fun_Oinj__on(_987410, _987412, _987414, _987416), c_Fun_Oinj__on(_987410, _987412, _987414, _987418), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_987412, tc_HOL_Obool)), hAPP(c_Set_Oimage(_987410, _987412, _987414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987410, tc_HOL_Obool)), _987416), _987418))), hAPP(c_Set_Oimage(_987410, _987412, _987414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987410, tc_HOL_Obool)), _987418), _987416))) = c_Orderings_Obot__class_Obot(tc_fun(_987412, tc_HOL_Obool))], (4670 ^ _781013) ^ [_851687, _851689, _851691, _851693] : [-(c_Product__Type_Ofst(_851693, _851689) = c_Product__Type_Ofst(_851691, _851687)), _851693 = _851691, _851689 = _851687], (43028 ^ _781013) ^ [_1636031, _1636033, _1636035, _1636037, _1636039, _1636041, _1636043] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636031, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636033, tc_fun(_1636031, tc_HOL_Obool)), _1636035), _1636037)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636039, tc_fun(_1636031, tc_HOL_Obool)), _1636041), _1636043)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636033, tc_fun(_1636031, tc_HOL_Obool)), _1636035), hAPP(hAPP(c_COMBB(tc_fun(_1636039, tc_fun(_1636031, tc_HOL_Obool)), tc_fun(_1636031, tc_HOL_Obool), _1636033), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636039, tc_fun(_1636031, tc_HOL_Obool)), _1636041)), hAPP(hAPP(c_COMBC(_1636033, tc_fun(_1636039, tc_fun(_1636031, tc_HOL_Obool)), tc_fun(_1636039, tc_fun(_1636031, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1636031, tc_HOL_Obool), tc_fun(_1636031, tc_HOL_Obool)), tc_fun(tc_fun(_1636039, tc_fun(_1636031, tc_HOL_Obool)), tc_fun(_1636039, tc_fun(_1636031, tc_HOL_Obool))), _1636033), c_COMBB(tc_fun(_1636031, tc_HOL_Obool), tc_fun(_1636031, tc_HOL_Obool), _1636039)), hAPP(hAPP(c_COMBB(tc_fun(_1636031, tc_HOL_Obool), tc_fun(tc_fun(_1636031, tc_HOL_Obool), tc_fun(_1636031, tc_HOL_Obool)), _1636033), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636031, tc_HOL_Obool))), _1636037))), _1636043))))], (30643 ^ _781013) ^ [_1353715, _1353717, _1353719] : [class_Orderings_Olinorder(_1353715), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353715), _1353717)), -(_1353717 = c_Orderings_Obot__class_Obot(tc_fun(_1353715, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1353715), _1353719), c_Big__Operators_Olattice_OSup__fin(_1353715, c_Orderings_Oord__class_Omax(_1353715), _1353717)) = c_Big__Operators_Olattice_OSup__fin(_1353715, c_Orderings_Oord__class_Omax(_1353715), hAPP(c_Set_OCollect(_1353715), hAPP(hAPP(c_COMBB(tc_fun(_1353715, tc_HOL_Obool), tc_HOL_Obool, _1353715), c_HOL_OEx(_1353715)), hAPP(hAPP(c_COMBC(_1353715, tc_fun(_1353715, tc_HOL_Obool), tc_fun(_1353715, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1353715, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1353715, tc_HOL_Obool), tc_fun(_1353715, tc_HOL_Obool)), _1353715), c_COMBS(_1353715, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1353715, tc_HOL_Obool), tc_fun(_1353715, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1353715), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1353715), c_fconj)), hAPP(hAPP(c_COMBC(_1353715, tc_fun(_1353715, _1353715), tc_fun(_1353715, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1353715, tc_HOL_Obool), tc_fun(tc_fun(_1353715, _1353715), tc_fun(_1353715, tc_HOL_Obool)), _1353715), c_COMBB(_1353715, tc_HOL_Obool, _1353715)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1353715), _1353719))))), hAPP(hAPP(c_COMBC(_1353715, tc_fun(_1353715, tc_HOL_Obool), tc_HOL_Obool), c_member(_1353715)), _1353717))))))], (51586 ^ _781013) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (48916 ^ _781013) ^ [_1772559, _1772561] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1772559, _1772559)), hAPP(hAPP(c_Product__Type_OPair(_1772559, _1772559), _1772561), _1772561)), c_Relation_OId(_1772559))))], (46921 ^ _781013) ^ [_1724635, _1724637, _1724639] : [c_Wellfounded_Owf(_1724635, _1724637), c_Wellfounded_Owf(_1724635, _1724639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1724635, _1724635), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1724635, _1724635, _1724635), _1724637), _1724639)), _1724637)), -(c_Wellfounded_Owf(_1724635, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1724635, _1724635), tc_HOL_Obool)), _1724637), _1724639)))], (39844 ^ _781013) ^ [_1553940, _1553942] : [-(hAPP(c_List_Olexn(_1553940, _1553942), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1553940), tc_List_Olist(_1553940)), tc_HOL_Obool)))], (50602 ^ _781013) ^ [_1809626, _1809628] : [class_HOL_Oequal(_1809626), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1809626), _1809628), _1809628)))], (36621 ^ _781013) ^ [_1479929, _1479931, _1479933, _1479935, _1479937, _1479939] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1479929, _1479931, _1479933), _1479935), hAPP(hAPP(c_Product__Type_OPair(_1479929, _1479931), _1479937), _1479939)) = hAPP(hAPP(_1479935, _1479937), _1479939))], (48223 ^ _781013) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (35261 ^ _781013) ^ [_1448124, _1448126, _1448128] : [class_Rings_Olinordered__idom(_1448124), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1448124), c_Groups_Ozero__class_Ozero(_1448124)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1448124), hAPP(hAPP(c_Power_Opower__class_Opower(_1448124), _1448126), 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(_1448124), _1448128), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (47429 ^ _781013) ^ [_1736961] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1736961), c_Int_OInteg)), -(_1736961 = hAPP(c_Int_ORep__Integ, 47432 ^ [_1736961]))], (29285 ^ _781013) ^ [_1327220, _1327222, _1327224] : [-(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), _1327220), _1327222)), _1327224)), _1327222) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1327224), _1327222))], (14123 ^ _781013) ^ [_1041131, _1041133, _1041135, _1041137, _1041139] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1041131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041131), _1041133), _1041135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041131), _1041137), _1041139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041131), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041131), _1041133), _1041137)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041131), _1041135), _1041139))))], (49187 ^ _781013) ^ [_1779033, _1779035, _1779037] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779033, _1779033)), _1779035), c_Transitive__Closure_Otrancl(_1779033, _1779037)))), 49188 ^ _781013 : [(49189 ^ _781013) ^ [_1779112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1779112)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1779033, _1779033)), _1779035), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1779033, _1779033), tc_HOL_Obool), _1779112), _1779037)))]]], (28774 ^ _781013) ^ [_1317914, _1317916, _1317918] : [class_Rings_Olinordered__idom(_1317914), -(hAPP(c_Groups_Oabs__class_Oabs(_1317914), hAPP(hAPP(c_Power_Opower__class_Opower(_1317914), _1317916), _1317918)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1317914), hAPP(c_Groups_Oabs__class_Oabs(_1317914), _1317916)), _1317918))], (41109 ^ _781013) ^ [_1591168, _1591170, _1591172] : [c_Equiv__Relations_Oequiv(_1591168, _1591170, _1591172), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1591168), c_List_Olists(_1591168, _1591170), c_List_Olistrel(_1591168, _1591172)))], (30553 ^ _781013) ^ [_1351871, _1351873, _1351875] : [class_Orderings_Olinorder(_1351871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351871), _1351873)), 30560 ^ _781013 : [(30567 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351871, tc_HOL_Obool)), _1351873), hAPP(hAPP(c_Set_Oinsert(_1351871), _1351875), c_Orderings_Obot__class_Obot(tc_fun(_1351871, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1351871, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1351871, hAPP(hAPP(c_Set_Oinsert(_1351871), _1351875), _1351873)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351871), _1351875), c_Big__Operators_Olinorder__class_OMax(_1351871, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351871, tc_HOL_Obool)), _1351873), hAPP(hAPP(c_Set_Oinsert(_1351871), _1351875), c_Orderings_Obot__class_Obot(tc_fun(_1351871, tc_HOL_Obool)))))))], (30561 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351871, tc_HOL_Obool)), _1351873), hAPP(hAPP(c_Set_Oinsert(_1351871), _1351875), c_Orderings_Obot__class_Obot(tc_fun(_1351871, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1351871, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1351871, hAPP(hAPP(c_Set_Oinsert(_1351871), _1351875), _1351873)) = _1351875)]]], (8625 ^ _781013) ^ [_930607, _930609, _930611] : [class_Lattices_Olattice(_930607), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930607), _930609), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930607), _930609), _930611)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930607), _930609), _930611))], (17879 ^ _781013) ^ [_1114646] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1114646) = _1114646)], (35809 ^ _781013) ^ [_1457933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1457933)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1457933) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1457933), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (13811 ^ _781013) ^ [_1034667, _1034669, _1034671, _1034673] : [class_Rings_Ocomm__semiring__1(_1034667), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034667), _1034669), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034667), _1034671), _1034673)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034667), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034667), _1034669), _1034671)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034667), _1034669), _1034673)))], (19981 ^ _781013) ^ [_1155193] : [hAPP(c_Nat_OSuc, _1155193) = _1155193], (39048 ^ _781013) ^ [_1534386, _1534388, _1534390] : [39050 ^ _781013 : [(39053 ^ _781013) ^ [] : [hBOOL(hAPP(_1534390, 39049 ^ [_1534386, _1534388, _1534390]))], (39051 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1534386), 39049 ^ [_1534386, _1534388, _1534390]), hAPP(c_List_Oset(_1534386), _1534388))))]], 39054 ^ _781013 : [(39055 ^ _781013) ^ [_1534570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1534570), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1534386)), _1534388))), -(hBOOL(hAPP(_1534390, hAPP(hAPP(c_List_Onth(_1534386), _1534388), _1534570))))]]], (38586 ^ _781013) ^ [_1523091, _1523093, _1523095, _1523097] : [-(hBOOL(hAPP(hAPP(c_member(_1523091), _1523093), hAPP(c_List_Oset(_1523091), _1523095)))), hBOOL(hAPP(hAPP(c_member(_1523091), _1523093), hAPP(c_List_Oset(_1523091), c_List_Oremove1(_1523091, _1523097, _1523095))))], (51130 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (1564 ^ _781013) ^ [_803305, _803307] : [-(class_Groups_Oab__semigroup__mult(_803305)), _803307 = _803305, class_Groups_Oab__semigroup__mult(_803307)], (41222 ^ _781013) ^ [_1593626, _1593628] : [-(hAPP(hAPP(c_List_Otake(_1593626), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1593628) = c_List_Olist_ONil(_1593626))], (22394 ^ _781013) ^ [_1200526, _1200528, _1200530, _1200532] : [class_Divides_Osemiring__div(_1200526), -(_1200528 = c_Groups_Ozero__class_Ozero(_1200526)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200526), _1200530), _1200528)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200526), _1200532), _1200528)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200526), _1200530), _1200532))], (51182 ^ _781013) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (51190 ^ _781013) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (26315 ^ _781013) ^ [_1270398, _1270400] : [hAPP(_1270398, 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), _1270398), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1270400)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1270398), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1270400)))], (29805 ^ _781013) ^ [_1336889, _1336891] : [class_Orderings_Olinorder(_1336889), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336889), _1336891)), -(c_Big__Operators_Olattice_OInf__fin(_1336889, c_Orderings_Oord__class_Omin(_1336889), _1336891) = hAPP(c_Finite__Set_Ofold1(_1336889, c_Orderings_Oord__class_Omin(_1336889)), _1336891))], (19314 ^ _781013) ^ [_1142776, _1142778, _1142780] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1142776), _1142778)), _1142780) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142776), _1142780)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142778), _1142780)))], (34837 ^ _781013) ^ [_1440660] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1440660))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1440660)))))], (16135 ^ _781013) ^ [_1079324, _1079326] : [class_Groups_Oordered__ab__group__add(_1079324), 16138 ^ _781013 : [(16145 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079324), _1079326), c_Groups_Ozero__class_Ozero(_1079324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079324), c_Groups_Ozero__class_Ozero(_1079324)), hAPP(c_Groups_Ouminus__class_Ouminus(_1079324), _1079326))))], (16139 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079324), c_Groups_Ozero__class_Ozero(_1079324)), hAPP(c_Groups_Ouminus__class_Ouminus(_1079324), _1079326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079324), _1079326), c_Groups_Ozero__class_Ozero(_1079324))))]]], (1324 ^ _781013) ^ [_800305, _800307] : [-(class_Lattices_Osemilattice__inf(_800305)), _800307 = _800305, class_Lattices_Osemilattice__inf(_800307)], (5538 ^ _781013) ^ [_865439, _865441, _865443, _865445] : [-(hAPP(_865445, _865441) = hAPP(_865443, _865439)), _865445 = _865443, _865441 = _865439], (43173 ^ _781013) ^ [_1640165, _1640167, _1640169, _1640171, _1640173] : [-(_1640165 = c_Orderings_Obot__class_Obot(tc_fun(_1640167, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640167, tc_fun(_1640169, tc_HOL_Obool)), _1640165), hAPP(hAPP(c_COMBC(_1640167, tc_fun(_1640169, tc_HOL_Obool), tc_fun(_1640169, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1640169, tc_HOL_Obool), tc_fun(tc_fun(_1640169, tc_HOL_Obool), tc_fun(_1640169, tc_HOL_Obool)), _1640167), c_Groups_Ominus__class_Ominus(tc_fun(_1640169, tc_HOL_Obool))), _1640171)), _1640173)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640169, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640167, tc_fun(_1640169, tc_HOL_Obool)), _1640165), _1640171)), _1640173))], (46949 ^ _781013) ^ [_1725307, _1725309] : [-(c_FunDef_Oreduction__pair(_1725307, _1725309)), c_Wellfounded_Owf(_1725307, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1725307, _1725307), tc_HOL_Obool), tc_fun(tc_prod(_1725307, _1725307), tc_HOL_Obool)), _1725309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1725307, _1725307), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1725307, _1725307, _1725307), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1725307, _1725307), tc_HOL_Obool), tc_fun(tc_prod(_1725307, _1725307), tc_HOL_Obool)), _1725309)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1725307, _1725307), tc_HOL_Obool), tc_fun(tc_prod(_1725307, _1725307), tc_HOL_Obool)), _1725309))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1725307, _1725307), tc_HOL_Obool), tc_fun(tc_prod(_1725307, _1725307), tc_HOL_Obool)), _1725309)))], (44743 ^ _781013) ^ [_1674473, _1674475] : [_1674475 = c_List_Olist_ONil(_1674473), -(c_List_Olist_ONil(_1674473) = c_List_Oremdups(_1674473, _1674475))], (45592 ^ _781013) ^ [_1692117, _1692119, _1692121, _1692123] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1692117, tc_HOL_Obool), tc_fun(_1692119, tc_HOL_Obool)), _1692121), hAPP(hAPP(c_COMBC(tc_fun(_1692117, tc_HOL_Obool), tc_fun(_1692117, tc_fun(_1692119, tc_HOL_Obool)), tc_fun(_1692119, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1692117, tc_fun(_1692119, tc_HOL_Obool))), _1692123)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1692117, tc_fun(_1692119, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692117, tc_HOL_Obool), _1692121)), _1692123))], (36790 ^ _781013) ^ [_1483174, _1483176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1483174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1483176)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1483174, _1483176), c_Divides_OposDivAlg(_1483174, _1483176))))], (43555 ^ _781013) ^ [_1649250, _1649252, _1649254, _1649256, _1649258] : [class_Orderings_Olinorder(_1649250), hBOOL(hAPP(hAPP(c_member(_1649252), _1649254), hAPP(c_List_Oset(_1649252), _1649256))), c_List_Olinorder__class_Osorted(_1649250, hAPP(hAPP(c_List_Omap(_1649252, _1649250), _1649258), _1649256)), hAPP(c_List_Ohd(_1649252), hAPP(c_List_Ofilter(_1649252, hAPP(hAPP(c_COMBB(_1649250, tc_HOL_Obool, _1649252), hAPP(c_fequal, hAPP(_1649258, _1649254))), _1649258)), _1649256)) = _1649254, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1649252, _1649250, _1649258), _1649254), c_List_Oremove1(_1649252, _1649254, _1649256)) = _1649256)], (39653 ^ _781013) ^ [_1548636, _1548638, _1548640, _1548642, _1548644] : [-(c_List_Olist_Olist__size(_1548636, _1548638, hAPP(hAPP(c_List_Omap(_1548640, _1548636), _1548642), _1548644)) = c_List_Olist_Olist__size(_1548640, hAPP(c_Fun_Ocomp(_1548636, tc_Nat_Onat, _1548640, _1548638), _1548642), _1548644))], (21351 ^ _781013) ^ [_1181499, _1181501] : [class_Orderings_Oorder(_1181499), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1181499, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1181499), _1181501), c_Orderings_Obot__class_Obot(tc_fun(_1181499, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1181499), _1181501)) = hAPP(hAPP(c_Set_Oinsert(_1181499), _1181501), c_Orderings_Obot__class_Obot(tc_fun(_1181499, tc_HOL_Obool))))], (18293 ^ _781013) ^ [_1121599, _1121601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121599), _1121601)), -(_1121601 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121599), 18296 ^ [_1121599, _1121601]))], (25132 ^ _781013) ^ [_1249396, _1249398, _1249400, _1249402] : [class_Fields_Olinordered__field(_1249396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249396), c_Groups_Ozero__class_Ozero(_1249396)), _1249398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249396), _1249400), _1249398)), _1249402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249396), _1249400), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249396), _1249402), _1249398))))], (50788 ^ _781013) ^ [_1813279, _1813281, _1813283, _1813285, _1813287] : [_1813279 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1813281, _1813283, _1813285, _1813287), _1813279) = c_Lazy__Sequence_Oempty(_1813283))], (17421 ^ _781013) ^ [_1106671, _1106673] : [-(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), _1106671)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1106673))))))], (49690 ^ _781013) ^ [_1791091, _1791093, _1791095] : [class_Lattices_Olattice(_1791091), hBOOL(hAPP(c_Finite__Set_Ofinite(_1791091), _1791093)), -(c_Big__Operators_Olattice__class_OSup__fin(_1791091, hAPP(hAPP(c_Set_Oinsert(_1791091), _1791095), _1791093)) = hAPP(hAPP(c_Finite__Set_Ofold(_1791091, _1791091, c_Lattices_Osemilattice__sup__class_Osup(_1791091)), _1791095), _1791093))], (9327 ^ _781013) ^ [_946346, _946348, _946350, _946352, _946354, _946356, _946358] : [hBOOL(hAPP(hAPP(c_member(_946346), _946348), _946350)), c_Nitpick_Ofold__graph_H(_946346, _946352, _946354, _946356, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946346, tc_HOL_Obool)), _946350), hAPP(hAPP(c_Set_Oinsert(_946346), _946348), c_Orderings_Obot__class_Obot(tc_fun(_946346, tc_HOL_Obool)))), _946358), -(c_Nitpick_Ofold__graph_H(_946346, _946352, _946354, _946356, _946350, hAPP(hAPP(_946354, _946348), _946358)))], (7923 ^ _781013) ^ [_914867, _914869, _914871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_914867), tc_HOL_Obool)), _914869), _914871)), -(c_Hoare__Mirabelle_Ohoare__derivs(_914867, _914871, _914869))], (20749 ^ _781013) ^ [_1168761, _1168763, _1168765, _1168767] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1168761, _1168763, _1168765), _1168767), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1168763)], (21295 ^ _781013) ^ [_1180456] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1180456)) = 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), _1180456))))], (49512 ^ _781013) ^ [_1787470, _1787472, _1787474, _1787476] : [-(hAPP(c_Finite__Set_Ofold__image(_1787470, _1787472, _1787474), _1787476) = c_Finite__Set_Ofold(_1787472, _1787470, hAPP(hAPP(c_COMBB(_1787470, tc_fun(_1787470, _1787470), _1787472), _1787474), _1787476)))], (40445 ^ _781013) ^ [_1571353, _1571355, _1571357, _1571359, _1571361, _1571363, _1571365, _1571367, _1571369] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571353, _1571355)), hAPP(hAPP(c_Product__Type_OPair(_1571353, _1571355), _1571357), _1571359)), _1571361)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571363, _1571365)), hAPP(hAPP(c_Product__Type_OPair(_1571363, _1571365), hAPP(_1571367, _1571357)), hAPP(_1571369, _1571359))), hAPP(c_Set_Oimage(tc_prod(_1571353, _1571355), tc_prod(_1571363, _1571365), c_Product__Type_Omap__pair(_1571353, _1571363, _1571355, _1571365, _1571367, _1571369)), _1571361))))], (50964 ^ _781013) ^ [_1817845, _1817847, _1817849] : [_1817847 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1817845, _1817847, _1817849) = c_List_Olist_ONil(_1817845))], (40856 ^ _781013) ^ [_1583665, _1583667, _1583669, _1583671, _1583673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583665, _1583665)), hAPP(hAPP(c_Product__Type_OPair(_1583665, _1583665), _1583667), _1583669)), _1583671)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1583665), tc_List_Olist(_1583665))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1583665), tc_List_Olist(_1583665)), hAPP(hAPP(c_List_Olist_OCons(_1583665), _1583667), _1583673)), hAPP(hAPP(c_List_Olist_OCons(_1583665), _1583669), _1583673))), c_List_Olistrel1(_1583665, _1583671))))], (7627 ^ _781013) ^ [_909174, _909176, _909178, _909180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909174, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909174, tc_HOL_Obool)), _909176), hAPP(hAPP(c_Set_Oinsert(_909174), _909178), c_Orderings_Obot__class_Obot(tc_fun(_909174, tc_HOL_Obool))))), _909180)), hBOOL(hAPP(hAPP(c_member(_909174), _909178), _909176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909174, tc_HOL_Obool)), _909176), hAPP(hAPP(c_Set_Oinsert(_909174), _909178), _909180))))], (35539 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (18041 ^ _781013) ^ [_1117323] : [-(_1117323 = 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)), _1117323)))], (48517 ^ _781013) ^ [_1761994, _1761996] : [-(c_Transitive__Closure_Otrancl(_1761994, _1761996) = hAPP(hAPP(c_Relation_Orel__comp(_1761994, _1761994, _1761994), c_Transitive__Closure_Ortrancl(_1761994, _1761996)), _1761996))], (2556 ^ _781013) ^ [_818934, _818936, _818938, _818940] : [-(c_Divides_Odivmod__int__rel(_818940, _818936) = c_Divides_Odivmod__int__rel(_818938, _818934)), _818940 = _818938, _818936 = _818934], (35695 ^ _781013) ^ [_1456224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1456224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1456224))))], (9999 ^ _781013) ^ [_957755, _957757, _957759] : [class_Lattices_Oboolean__algebra(_957755), -(hAPP(c_Groups_Ouminus__class_Ouminus(_957755), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_957755), _957757), _957759)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_957755), hAPP(c_Groups_Ouminus__class_Ouminus(_957755), _957757)), hAPP(c_Groups_Ouminus__class_Ouminus(_957755), _957759)))], (33644 ^ _781013) ^ [_1418924, _1418926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1418924), _1418926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1418924)), _1418926)))], (35853 ^ _781013) ^ [_1459015, _1459017] : [-(_1459015 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1459017, _1459015), c_Divides_Odivmod__int(_1459017, _1459015))))], (408 ^ _781013) ^ [_787359, _787361, _787363, _787365, _787367, _787369] : [-(c_Hoare__Mirabelle_Otriple__valid(_787367, _787363, _787359)), c_Hoare__Mirabelle_Otriple__valid(_787369, _787365, _787361), _787369 = _787367, _787365 = _787363, _787361 = _787359], (21459 ^ _781013) ^ [_1184239, _1184241] : [-(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, _1184239)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184241))))], (35065 ^ _781013) ^ [] : [-(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))))], (34343 ^ _781013) ^ [_1432223] : [class_Int_Onumber__ring(_1432223), -(c_Groups_Oone__class_Oone(_1432223) = hAPP(c_Int_Onumber__class_Onumber__of(_1432223), c_Int_OBit1(c_Int_OPls)))], (37870 ^ _781013) ^ [_1506227, _1506229, _1506231, _1506233, _1506235, _1506237] : [hAPP(c_Product__Type_Oapfst(_1506227, _1506229, _1506231, _1506233), _1506235) = hAPP(c_Product__Type_Oapfst(_1506227, _1506229, _1506231, _1506237), _1506235), -(hAPP(_1506233, hAPP(c_Product__Type_Ofst(_1506227, _1506231), _1506235)) = hAPP(_1506237, hAPP(c_Product__Type_Ofst(_1506227, _1506231), _1506235)))], (28044 ^ _781013) ^ [_1304581, _1304583] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304581, _1304583) = 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), _1304581), _1304583) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1304583), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304581, _1304583)))], (6605 ^ _781013) ^ [_889146, _889148] : [_889148 = c_Option_Ooption_ONone(_889146), -(c_Option_Oset(_889146, _889148) = c_Orderings_Obot__class_Obot(tc_fun(_889146, tc_HOL_Obool)))], (46498 ^ _781013) ^ [_1713238, _1713240, _1713242] : [46500 ^ _781013 : [(46503 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1713238), 46499 ^ [_1713238, _1713240, _1713242]), c_Wellfounded_Oacc(_1713238, _1713242)))], (46501 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1713238, _1713238)), hAPP(hAPP(c_Product__Type_OPair(_1713238, _1713238), 46499 ^ [_1713238, _1713240, _1713242]), _1713240)), _1713242)))]], -(hBOOL(hAPP(hAPP(c_member(_1713238), _1713240), c_Wellfounded_Oacc(_1713238, _1713242))))], (51572 ^ _781013) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (42765 ^ _781013) ^ [_1628210, _1628212, _1628214, _1628216] : [class_Complete__Lattice_Ocomplete__lattice(_1628210), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628212, _1628210), hAPP(c_List_Oset(_1628212), _1628214)), _1628216) = hAPP(c_List_Ofoldl(_1628210, _1628212, hAPP(c_COMBC(_1628212, _1628210, _1628210), hAPP(hAPP(c_COMBB(_1628210, tc_fun(_1628210, _1628210), _1628212), c_Lattices_Osemilattice__inf__class_Oinf(_1628210)), _1628216)), c_Orderings_Otop__class_Otop(_1628210)), _1628214))], (8861 ^ _781013) ^ [_935975, _935977, _935979] : [class_Lattices_Osemilattice__sup(_935975), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935975), _935977), _935979)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935975), _935979), _935977) = _935979)], (47049 ^ _781013) ^ [_1727753] : [-(c_Nitpick_Oone__frac(_1727753) = c_Nitpick_OAbs__Frac(_1727753, 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))))], (13074 ^ _781013) ^ [_1018765, _1018767] : [class_Lattices_Olattice(_1018765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018765), _1018767)), -(c_Big__Operators_Olattice__class_OInf__fin(_1018765, _1018767) = hAPP(c_Finite__Set_Ofold1(_1018765, c_Lattices_Osemilattice__inf__class_Oinf(_1018765)), _1018767))], (28650 ^ _781013) ^ [_1315508, _1315510, _1315512] : [class_Fields_Olinordered__field__inverse__zero(_1315508), -(hAPP(c_Groups_Oabs__class_Oabs(_1315508), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315508), _1315510), _1315512)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315508), hAPP(c_Groups_Oabs__class_Oabs(_1315508), _1315510)), hAPP(c_Groups_Oabs__class_Oabs(_1315508), _1315512)))], (5829 ^ _781013) ^ [_874679, _874681] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_874679, _874681)], (26128 ^ _781013) ^ [_1267036, _1267038] : [26130 ^ _781013 : [(26133 ^ _781013) ^ [] : [hBOOL(hAPP(_1267038, 26129 ^ [_1267036, _1267038]))], (26131 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26129 ^ [_1267036, _1267038]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1267036))))]], 26134 ^ _781013 : [(26135 ^ _781013) ^ [_1267191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1267191), _1267036)), -(hBOOL(hAPP(_1267038, _1267191)))]]], (2036 ^ _781013) ^ [_810668, _810670, _810672, _810674, _810676, _810678, _810680, _810682] : [-(c_Fun_Othe__inv__into(_810682, _810678, _810674, _810670) = c_Fun_Othe__inv__into(_810680, _810676, _810672, _810668)), _810682 = _810680, _810678 = _810676, _810674 = _810672, _810670 = _810668], (1354 ^ _781013) ^ [_800680, _800682] : [-(class_Lattices_Olattice(_800680)), _800682 = _800680, class_Lattices_Olattice(_800682)], (31401 ^ _781013) ^ [_1370977, _1370979, _1370981] : [hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(_1370977, tc_HOL_Obool, hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_HOL_Obool))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_HOL_Obool)), tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1370977, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_HOL_OAll(_1370977)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_HOL_Obool))), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_HOL_Obool)), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_HOL_Obool), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, _1370977), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBC(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(_1370977, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBS(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1370977, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1370977), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1370977), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1370977), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1370977, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_Com_Ocom), c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1370977)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))), hAPP(hAPP(c_COMBC(tc_Com_Ocom, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_Natural_Oevaln)), _1370979))))))))), _1370981)), -(c_Hoare__Mirabelle_Otriple__valid(_1370977, _1370979, _1370981))], (50848 ^ _781013) ^ [_1814830, _1814832, _1814834, _1814836, _1814838] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1814830, _1814832, _1814834), _1814836), _1814838)), -(hBOOL(hAPP(hAPP(_1814834, _1814838), _1814836)))], (49134 ^ _781013) ^ [_1777602, _1777604] : [-(c_Relation_Ototal__on(_1777602, c_Orderings_Obot__class_Obot(tc_fun(_1777602, tc_HOL_Obool)), _1777604))], (46206 ^ _781013) ^ [_1705984, _1705986, _1705988, _1705990, _1705992, _1705994, _1705996] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705984)), _1705986) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705988)), _1705990), 46209 ^ _781013 : [(46218 ^ _781013) ^ [] : [-(c_List_Olist__all2(_1705984, _1705988, _1705992, hAPP(hAPP(c_List_Oappend(_1705984), _1705986), _1705994), hAPP(hAPP(c_List_Oappend(_1705988), _1705990), _1705996))), c_List_Olist__all2(_1705984, _1705988, _1705992, _1705986, _1705990), c_List_Olist__all2(_1705984, _1705988, _1705992, _1705994, _1705996)], (46210 ^ _781013) ^ [] : [c_List_Olist__all2(_1705984, _1705988, _1705992, hAPP(hAPP(c_List_Oappend(_1705984), _1705986), _1705994), hAPP(hAPP(c_List_Oappend(_1705988), _1705990), _1705996)), 46213 ^ _781013 : [(46216 ^ _781013) ^ [] : [-(c_List_Olist__all2(_1705984, _1705988, _1705992, _1705994, _1705996))], (46214 ^ _781013) ^ [] : [-(c_List_Olist__all2(_1705984, _1705988, _1705992, _1705986, _1705990))]]]]], (38920 ^ _781013) ^ [_1531229, _1531231, _1531233, _1531235, _1531237] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1531229)), _1531231) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1531233)), _1531235), 38923 ^ _781013 : [(38930 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531229), _1531237), hAPP(c_List_Oset(_1531229), _1531231)))), -(hAPP(hAPP(c_Map_Omap__of(_1531229, _1531233), hAPP(hAPP(c_List_Ozip(_1531229, _1531233), _1531231), _1531235)), _1531237) = c_Option_Ooption_ONone(_1531233))], (38924 ^ _781013) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1531229, _1531233), hAPP(hAPP(c_List_Ozip(_1531229, _1531233), _1531231), _1531235)), _1531237) = c_Option_Ooption_ONone(_1531233), hBOOL(hAPP(hAPP(c_member(_1531229), _1531237), hAPP(c_List_Oset(_1531229), _1531231)))]]], (42458 ^ _781013) ^ [_1622040, _1622042] : [class_Lattices_Oab__semigroup__idem__mult(_1622040), -(_1622042 = c_List_Olist_ONil(_1622040)), -(hAPP(c_Finite__Set_Ofold1(_1622040, c_Groups_Otimes__class_Otimes(_1622040)), hAPP(c_List_Oset(_1622040), _1622042)) = hAPP(c_List_Ofoldl(_1622040, _1622040, c_Groups_Otimes__class_Otimes(_1622040), hAPP(c_List_Ohd(_1622040), _1622042)), hAPP(c_List_Otl(_1622040), _1622042)))], (5332 ^ _781013) ^ [_862348, _862350, _862352, _862354, _862356, _862358] : [-(c_Lazy__Sequence_Oappend(_862358, _862354, _862350) = c_Lazy__Sequence_Oappend(_862356, _862352, _862348)), _862358 = _862356, _862354 = _862352, _862350 = _862348], (14339 ^ _781013) ^ [_1046461, _1046463, _1046465, _1046467, _1046469] : [class_Groups_Ocomm__monoid__add(_1046461), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046463), _1046465)), -(hBOOL(hAPP(hAPP(c_member(_1046463), _1046467), _1046465))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046463, _1046461), _1046469), hAPP(hAPP(c_Set_Oinsert(_1046463), _1046467), _1046465)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046461), hAPP(_1046469, _1046467)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046463, _1046461), _1046469), _1046465)))], (6549 ^ _781013) ^ [_888117, _888119] : [_888117 = c_Option_Ooption_ONone(_888119), 6552 ^ _781013 : [(6553 ^ _781013) ^ [_888189] : [_888117 = hAPP(c_Option_Ooption_OSome(_888119), _888189)]]], (47181 ^ _781013) ^ [_1731209, _1731211, _1731213, _1731215] : [-(hAPP(c_Relation_ODomain(_1731209, _1731211), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1731209, _1731211), tc_HOL_Obool)), _1731213), _1731215)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1731209, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1731209, _1731211), _1731213)), hAPP(c_Relation_ODomain(_1731209, _1731211), _1731215)))], (50804 ^ _781013) ^ [_1813599, _1813601, _1813603, _1813605] : [-(c_New__Random__Sequence_Opos__empty(_1813599, _1813601, _1813603, _1813605) = c_New__DSequence_Opos__empty(_1813599))], (50608 ^ _781013) ^ [_1809715] : [class_HOL_Oequal(_1809715), -(c_HOL_Oequal__class_Oequal(_1809715) = c_fequal)], (29143 ^ _781013) ^ [_1324516, _1324518] : [class_Rings_Olinordered__idom(_1324516), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324516), c_Groups_Osgn__class_Osgn(_1324516, _1324518)), hAPP(c_Groups_Oabs__class_Oabs(_1324516), _1324518)) = _1324518)], (12888 ^ _781013) ^ [_1014811, _1014813, _1014815] : [-(hAPP(c_Set_Ovimage(_1014811, _1014813, _1014815), c_Orderings_Obot__class_Obot(tc_fun(_1014813, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1014811, tc_HOL_Obool)))], (29993 ^ _781013) ^ [_1341142, _1341144, _1341146] : [class_Orderings_Olinorder(_1341142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341142), _1341144)), -(_1341144 = c_Orderings_Obot__class_Obot(tc_fun(_1341142, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341142), _1341146), c_Big__Operators_Olattice_OInf__fin(_1341142, c_Orderings_Oord__class_Omin(_1341142), _1341144)) = c_Big__Operators_Olattice_OInf__fin(_1341142, c_Orderings_Oord__class_Omin(_1341142), hAPP(c_Set_OCollect(_1341142), hAPP(hAPP(c_COMBB(tc_fun(_1341142, tc_HOL_Obool), tc_HOL_Obool, _1341142), c_HOL_OEx(_1341142)), hAPP(hAPP(c_COMBC(_1341142, tc_fun(_1341142, tc_HOL_Obool), tc_fun(_1341142, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1341142, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1341142, tc_HOL_Obool), tc_fun(_1341142, tc_HOL_Obool)), _1341142), c_COMBS(_1341142, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1341142, tc_HOL_Obool), tc_fun(_1341142, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1341142), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1341142), c_fconj)), hAPP(hAPP(c_COMBC(_1341142, tc_fun(_1341142, _1341142), tc_fun(_1341142, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1341142, tc_HOL_Obool), tc_fun(tc_fun(_1341142, _1341142), tc_fun(_1341142, tc_HOL_Obool)), _1341142), c_COMBB(_1341142, tc_HOL_Obool, _1341142)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1341142), _1341146))))), hAPP(hAPP(c_COMBC(_1341142, tc_fun(_1341142, tc_HOL_Obool), tc_HOL_Obool), c_member(_1341142)), _1341144))))))], (43920 ^ _781013) ^ [_1655486, _1655488, _1655490] : [class_Orderings_Olinorder(_1655486), 43923 ^ _781013 : [(43942 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1655486, hAPP(hAPP(c_List_Oappend(_1655486), _1655488), _1655490))), c_List_Olinorder__class_Osorted(_1655486, _1655488), c_List_Olinorder__class_Osorted(_1655486, _1655490), 43952 ^ _781013 : [(43958 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1655486), 43951 ^ [_1655486, _1655488, _1655490]), 43954 ^ [_1655486, _1655488, _1655490]))], (43956 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655486), 43954 ^ [_1655486, _1655488, _1655490]), hAPP(c_List_Oset(_1655486), _1655490))))], (43953 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655486), 43951 ^ [_1655486, _1655488, _1655490]), hAPP(c_List_Oset(_1655486), _1655488))))]]], (43924 ^ _781013) ^ [] : [c_List_Olinorder__class_Osorted(_1655486, hAPP(hAPP(c_List_Oappend(_1655486), _1655488), _1655490)), 43927 ^ _781013 : [(43932 ^ _781013) ^ [_1655722] : [hBOOL(hAPP(hAPP(c_member(_1655486), _1655722), hAPP(c_List_Oset(_1655486), _1655488))), 43935 ^ _781013 : [(43936 ^ _781013) ^ [_1655832] : [hBOOL(hAPP(hAPP(c_member(_1655486), _1655832), hAPP(c_List_Oset(_1655486), _1655490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1655486), _1655722), _1655832)))]]], (43930 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1655486, _1655490))], (43928 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1655486, _1655488))]]]]], (42593 ^ _781013) ^ [_1625244, _1625246] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1625244), hAPP(c_List_Oset(tc_Nat_Onat), _1625246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1625244), 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)), _1625246))))], (31599 ^ _781013) ^ [] : [-(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)))], (35511 ^ _781013) ^ [_1453470] : [c_Int_OBit1(_1453470) = c_Int_OMin, -(_1453470 = c_Int_OMin)], (41740 ^ _781013) ^ [_1604690, _1604692, _1604694, _1604696, _1604698, _1604700] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604690)), _1604692) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604694)), _1604696), -(c_Map_Omap__upds(_1604690, _1604694, _1604698, _1604692, hAPP(hAPP(c_List_Oappend(_1604694), _1604696), _1604700)) = c_Map_Omap__upds(_1604690, _1604694, _1604698, _1604692, _1604696))], (42579 ^ _781013) ^ [_1624631, _1624633, _1624635] : [class_Orderings_Olinorder(_1624631), -(c_Big__Operators_Olattice_OSup__fin(_1624631, c_Orderings_Oord__class_Omax(_1624631), hAPP(c_List_Oset(_1624631), hAPP(hAPP(c_List_Olist_OCons(_1624631), _1624633), _1624635))) = hAPP(c_List_Ofoldl(_1624631, _1624631, c_Orderings_Oord__class_Omax(_1624631), _1624633), _1624635))], (48545 ^ _781013) ^ [_1762673] : [-(hAPP(c_Code__Numeral_Onat__of, _1762673) = c_Code__Numeral_Onat__of__aux(_1762673, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51018 ^ _781013) ^ [_1818618, _1818620] : [class_Lattices_Olattice(_1818618), -(class_Lattices_Osemilattice__inf(tc_fun(_1818620, _1818618)))], (6395 ^ _781013) ^ [_885382, _885384, _885386, _885388] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_885382, _885384)), _885386), _885388))), 6396 ^ _781013 : [(6397 ^ _781013) ^ [_885450] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885382), _885386), _885450)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885384), _885450), _885388))]]], (21987 ^ _781013) ^ [_1193441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193441)), -(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), _1193441))))], (25501 ^ _781013) ^ [_1256150, _1256152] : [c_Nat__Transfer_Onat__set(_1256150), c_Nat__Transfer_Onat__set(_1256152), 25508 ^ _781013 : [(25515 ^ _781013) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1256150) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1256152), -(_1256150 = _1256152)], (25509 ^ _781013) ^ [] : [_1256150 = _1256152, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1256150) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1256152))]]], (18147 ^ _781013) ^ [_1119057, _1119059, _1119061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119059), _1119061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119057), _1119059)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119057), _1119061))))], (10585 ^ _781013) ^ [_968398, _968400, _968402] : [class_Orderings_Oorder(_968398), -(_968400 = _968402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968398), _968400), _968402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968398), _968400), _968402)))], (39862 ^ _781013) ^ [_1555214, _1555216, _1555218, _1555220] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1555214), tc_List_Olist(_1555214))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1555214), tc_List_Olist(_1555214)), _1555218), _1555220)), c_List_Olistrel(_1555214, _1555216))), -(c_List_Olistrelp(_1555214, hAPP(hAPP(c_COMBC(_1555214, tc_fun(tc_prod(_1555214, _1555214), tc_HOL_Obool), tc_fun(_1555214, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555214, tc_fun(tc_fun(tc_prod(_1555214, _1555214), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1555214, _1555214), tc_HOL_Obool), tc_fun(_1555214, tc_HOL_Obool)), _1555214), c_COMBC(_1555214, tc_fun(tc_prod(_1555214, _1555214), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555214, tc_prod(_1555214, _1555214)), tc_fun(_1555214, tc_fun(tc_fun(tc_prod(_1555214, _1555214), tc_HOL_Obool), tc_HOL_Obool)), _1555214), hAPP(c_COMBB(tc_prod(_1555214, _1555214), tc_fun(tc_fun(tc_prod(_1555214, _1555214), tc_HOL_Obool), tc_HOL_Obool), _1555214), c_member(tc_prod(_1555214, _1555214)))), c_Product__Type_OPair(_1555214, _1555214)))), _1555216), _1555218, _1555220))], (39657 ^ _781013) ^ [_1548757, _1548759, _1548761, _1548763] : [hBOOL(hAPP(hAPP(c_member(_1548757), _1548759), hAPP(c_List_Oset(_1548757), hAPP(hAPP(c_List_Otake(_1548757), _1548761), _1548763)))), -(hBOOL(hAPP(hAPP(c_member(_1548757), _1548759), hAPP(c_List_Oset(_1548757), _1548763))))], (44715 ^ _781013) ^ [_1673937, _1673939] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673937)), c_List_Oremdups(_1673937, c_List_Oconcat(_1673937, _1673939))) = hAPP(c_Finite__Set_Ocard(_1673937), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1673937), tc_fun(_1673937, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1673937)), _1673939)), c_List_Oset(_1673937))))], (50900 ^ _781013) ^ [_1815830, _1815832, _1815834, _1815836] : [-(c_Predicate_Oconversep(_1815830, _1815832, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1815830, tc_fun(_1815832, tc_HOL_Obool))), _1815834), _1815836)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1815832, tc_fun(_1815830, tc_HOL_Obool))), c_Predicate_Oconversep(_1815830, _1815832, _1815834)), c_Predicate_Oconversep(_1815830, _1815832, _1815836)))], (20955 ^ _781013) ^ [_1172624, _1172626] : [-(c_Sum__Type_OPlus(_1172624, _1172626, c_Orderings_Otop__class_Otop(tc_fun(_1172624, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1172626, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1172624, _1172626), tc_HOL_Obool)))], (6278 ^ _781013) ^ [_883115, _883117, _883119, _883121, _883123] : [c_Com_Ocom_OCond(_883115, _883117, _883119) = c_Com_Ocom_OWhile(_883121, _883123)], (43153 ^ _781013) ^ [_1639541, _1639543, _1639545] : [-(hAPP(c_Set_OCollect(_1639541), hAPP(hAPP(c_COMBB(tc_fun(_1639543, tc_HOL_Obool), tc_HOL_Obool, _1639541), c_HOL_OAll(_1639543)), _1639545)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639543, tc_fun(_1639541, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1639543, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1639541, tc_HOL_Obool), tc_fun(_1639541, tc_HOL_Obool), _1639543), c_Set_OCollect(_1639541)), hAPP(c_COMBC(_1639541, _1639543, tc_HOL_Obool), _1639545))))], (6407 ^ _781013) ^ [_885628] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _885628))), -(hAPP(c_Com_Obody, _885628) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 6410 ^ [_885628]))], (48816 ^ _781013) ^ [_1769610, _1769612, _1769614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1769612, _1769610)), _1769614)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1769610, _1769612)), hAPP(c_Relation_Oconverse(_1769612, _1769610), _1769614))))], (39444 ^ _781013) ^ [_1543590, _1543592, _1543594, _1543596] : [class_Groups_Ocomm__monoid__add(_1543590), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1543590), _1543592), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1543594, _1543596))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1543590), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1543590), _1543592), c_List_Oupto(_1543594, _1543596))))], (31440 ^ _781013) ^ [_1372778, _1372780, _1372782] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1372778), _1372780)), 31446 ^ _781013 : [(31449 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1372782, 31445 ^ [_1372778, _1372780, _1372782])))], (31447 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372778), 31445 ^ [_1372778, _1372780, _1372782]), _1372780)))]], -(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(_1372778, tc_Nat_Onat), _1372782), _1372780))))], (44845 ^ _781013) ^ [_1676489, _1676491, _1676493, _1676495] : [hBOOL(hAPP(_1676489, _1676491)), -(c_List_OdropWhile(_1676493, _1676489, hAPP(hAPP(c_List_Olist_OCons(_1676493), _1676491), _1676495)) = c_List_OdropWhile(_1676493, _1676489, _1676495))], (8393 ^ _781013) ^ [_925541, _925543, _925545, _925547, _925549] : [hBOOL(hAPP(hAPP(c_member(_925541), _925543), hAPP(c_Set_Oimage(_925545, _925541, _925547), _925549))), 8397 ^ _781013 : [(8400 ^ _781013) ^ [] : [-(_925543 = hAPP(_925547, 8396 ^ [_925541, _925543, _925545, _925547, _925549]))], (8398 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_925545), 8396 ^ [_925541, _925543, _925545, _925547, _925549]), _925549)))]]], (34699 ^ _781013) ^ [_1438255] : [c_Int_OBit0(_1438255) = c_Int_OPls, -(_1438255 = c_Int_OPls)], (14544 ^ _781013) ^ [_1051081, _1051083, _1051085] : [hBOOL(hAPP(_1051081, _1051083)), -(hBOOL(hAPP(hAPP(c_member(_1051085), _1051083), hAPP(c_Set_OCollect(_1051085), _1051081))))], (11031 ^ _781013) ^ [_976994, _976996] : [_976996 = c_Orderings_Obot__class_Obot(tc_fun(_976994, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976994, tc_HOL_Obool)), _976996), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_976994, tc_HOL_Obool)), _976996))))], (50640 ^ _781013) ^ [_1810259, _1810261] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1810259), _1810261)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1810259)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1810261))))], (33618 ^ _781013) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (29311 ^ _781013) ^ [_1327782, _1327784] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1327782), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1327784), _1327782)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1327784), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1327784, _1327782)))], (37403 ^ _781013) ^ [_1494964, _1494966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494964), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1494966), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1494964, _1494966) = 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), _1494964), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1494966)))))], (20424 ^ _781013) ^ [_1162572, _1162574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162572), _1162574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162572), hAPP(c_Nat_OSuc, _1162574))))], (8613 ^ _781013) ^ [_930373, _930375, _930377] : [class_Lattices_Osemilattice__sup(_930373), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930373), _930375), _930377) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930373), _930377), _930375))], (18704 ^ _781013) ^ [_1129593, _1129595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129593), _1129595)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1129595), _1129593)), _1129593) = _1129595)], (5368 ^ _781013) ^ [_862888, _862890] : [_862890 = _862888, -(c_Groups_Ozero__class_Ozero(_862890) = c_Groups_Ozero__class_Ozero(_862888))], (39007 ^ _781013) ^ [_1533478, _1533480, _1533482] : [hBOOL(hAPP(c_List_Odistinct(_1533478), _1533480)), -(hBOOL(hAPP(c_List_Odistinct(_1533478), c_List_Osublist(_1533478, _1533480, _1533482))))], (14608 ^ _781013) ^ [_1052193, _1052195, _1052197, _1052199] : [class_Rings_Ocomm__semiring__1(_1052193), class_Rings_Ono__zero__divisors(_1052193), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052195), _1052197)), 14619 ^ _781013 : [(14629 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052195, _1052193), _1052199), _1052197) = c_Groups_Ozero__class_Ozero(_1052193)), 14630 ^ _781013 : [(14631 ^ _781013) ^ [_1052571] : [hBOOL(hAPP(hAPP(c_member(_1052195), _1052571), _1052197)), hAPP(_1052199, _1052571) = c_Groups_Ozero__class_Ozero(_1052193)]]], (14620 ^ _781013) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052195, _1052193), _1052199), _1052197) = c_Groups_Ozero__class_Ozero(_1052193), 14624 ^ _781013 : [(14627 ^ _781013) ^ [] : [-(hAPP(_1052199, 14623 ^ [_1052193, _1052195, _1052197, _1052199]) = c_Groups_Ozero__class_Ozero(_1052193))], (14625 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1052195), 14623 ^ [_1052193, _1052195, _1052197, _1052199]), _1052197)))]]]]], (35153 ^ _781013) ^ [_1446374, _1446376] : [class_Rings_Olinordered__idom(_1446374), 35156 ^ _781013 : [(35163 ^ _781013) ^ [] : [-(_1446376 = c_Groups_Ozero__class_Ozero(_1446374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446374), c_Groups_Ozero__class_Ozero(_1446374)), hAPP(hAPP(c_Power_Opower__class_Opower(_1446374), _1446376), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35157 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446374), c_Groups_Ozero__class_Ozero(_1446374)), hAPP(hAPP(c_Power_Opower__class_Opower(_1446374), _1446376), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1446376 = c_Groups_Ozero__class_Ozero(_1446374)]]], (40481 ^ _781013) ^ [_1572648, _1572650] : [c_Predicate_Oreflp(_1572648, _1572650), -(c_Relation_Orefl__on(_1572648, c_Orderings_Otop__class_Otop(tc_fun(_1572648, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1572648, _1572648)), hAPP(c_Product__Type_Oprod_Oprod__case(_1572648, _1572648, tc_HOL_Obool), _1572650))))], (45719 ^ _781013) ^ [_1695095, _1695097] : [class_Complete__Lattice_Ocomplete__lattice(_1695095), -(c_Complete__Lattice_OSup__class_OSup(_1695095, hAPP(hAPP(c_Set_Oinsert(_1695095), _1695097), c_Orderings_Obot__class_Obot(tc_fun(_1695095, tc_HOL_Obool)))) = _1695097)], (19739 ^ _781013) ^ [_1150805, _1150807, _1150809, _1150811] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1150805, _1150809)), c_Sum__Type_OPlus(_1150805, _1150809, _1150807, _1150811)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1150805), _1150807)), hAPP(c_Finite__Set_Ocard(_1150809), _1150811))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1150805), _1150807)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1150809), _1150811))], (41823 ^ _781013) ^ [_1606621, _1606623, _1606625, _1606627, _1606629, _1606631] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606621)), _1606623) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606625)), _1606627), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606621)), _1606629) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606625)), _1606631), -(hAPP(hAPP(c_List_Ozip(_1606621, _1606625), hAPP(hAPP(c_List_Oappend(_1606621), _1606623), _1606629)), hAPP(hAPP(c_List_Oappend(_1606625), _1606627), _1606631)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1606621, _1606625)), hAPP(hAPP(c_List_Ozip(_1606621, _1606625), _1606623), _1606627)), hAPP(hAPP(c_List_Ozip(_1606621, _1606625), _1606629), _1606631)))], (7911 ^ _781013) ^ [_914577, _914579, _914581, _914583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914577, tc_HOL_Obool)), _914579), _914581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914577, tc_HOL_Obool)), _914579), hAPP(hAPP(c_Set_Oinsert(_914577), _914583), _914581))))], (17823 ^ _781013) ^ [_1113692, _1113694, _1113696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1113692), _1113694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113696), _1113692)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113696), _1113694))))], (25026 ^ _781013) ^ [_1247412, _1247414, _1247416, _1247418] : [class_Fields_Olinordered__field__inverse__zero(_1247412), 25029 ^ _781013 : [(25030 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247412), _1247414), _1247416)), _1247418)), 25033 ^ _781013 : [(25040 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), c_Groups_Ozero__class_Ozero(_1247412)), _1247416))), 25043 ^ _781013 : [(25050 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), _1247416), c_Groups_Ozero__class_Ozero(_1247412)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), c_Groups_Ozero__class_Ozero(_1247412)), _1247418)))], (25044 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), _1247416), c_Groups_Ozero__class_Ozero(_1247412))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247412), _1247418), _1247416)), _1247414)))]]], (25034 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), c_Groups_Ozero__class_Ozero(_1247412)), _1247416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), _1247414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247412), _1247418), _1247416))))]]], (25056 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247412), _1247414), _1247416)), _1247418))), 25059 ^ _781013 : [(25062 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), _1247414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247412), _1247418), _1247416)))], (25060 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), c_Groups_Ozero__class_Ozero(_1247412)), _1247416)))]], 25063 ^ _781013 : [(25066 ^ _781013) ^ [] : [25067 ^ _781013 : [(25070 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247412), _1247418), _1247416)), _1247414))], (25068 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), _1247416), c_Groups_Ozero__class_Ozero(_1247412))))]], 25071 ^ _781013 : [(25074 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), c_Groups_Ozero__class_Ozero(_1247412)), _1247418))], (25072 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), _1247416), c_Groups_Ozero__class_Ozero(_1247412)))]]], (25064 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247412), c_Groups_Ozero__class_Ozero(_1247412)), _1247416))]]]]], (11720 ^ _781013) ^ [_992215, _992217] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_992215), c_Orderings_Otop__class_Otop(tc_fun(_992215, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_992215, _992215, _992217), c_Orderings_Otop__class_Otop(tc_fun(_992215, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_992215, tc_HOL_Obool)), -(c_Fun_Oinj__on(_992215, _992215, _992217, c_Orderings_Otop__class_Otop(tc_fun(_992215, tc_HOL_Obool))))], (33566 ^ _781013) ^ [_1417829] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1417829) = c_Int_OPls)], (10317 ^ _781013) ^ [_963552, _963554, _963556] : [class_Lattices_Olattice(_963552), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_963552), _963554), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963552), _963554), _963556)) = _963554)], (44129 ^ _781013) ^ [_1659517, _1659519] : [class_Orderings_Olinorder(_1659517), 44132 ^ _781013 : [(44133 ^ _781013) ^ [] : [c_List_Olinorder__class_Osorted(_1659517, _1659519), 44136 ^ _781013 : [(44137 ^ _781013) ^ [_1659688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659688), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659517)), _1659519))), 44140 ^ _781013 : [(44141 ^ _781013) ^ [_1659805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1659805), _1659688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659517), hAPP(hAPP(c_List_Onth(_1659517), _1659519), _1659805)), hAPP(hAPP(c_List_Onth(_1659517), _1659519), _1659688))))]]]]], (44147 ^ _781013) ^ [] : [44149 ^ _781013 : [(44155 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659517), hAPP(hAPP(c_List_Onth(_1659517), _1659519), 44151 ^ [_1659517, _1659519])), hAPP(hAPP(c_List_Onth(_1659517), _1659519), 44148 ^ [_1659517, _1659519])))], (44153 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 44151 ^ [_1659517, _1659519]), 44148 ^ [_1659517, _1659519])))], (44150 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44148 ^ [_1659517, _1659519]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659517)), _1659519))))]], -(c_List_Olinorder__class_Osorted(_1659517, _1659519))]]], (50988 ^ _781013) ^ [_1818223, _1818225] : [class_Lattices_Obounded__lattice(_1818223), -(class_Lattices_Obounded__lattice(tc_fun(_1818225, _1818223)))], (8469 ^ _781013) ^ [_927309, _927311, _927313, _927315, _927317, _927319, _927321, _927323, _927325, _927327, _927329] : [c_Finite__Set_Ofolding(_927309, _927311, _927313, _927315), -(hAPP(c_Fun_Ocomp(_927317, _927319, _927321, _927323), hAPP(c_Fun_Ocomp(_927325, _927317, _927321, _927327), _927329)) = hAPP(c_Fun_Ocomp(_927325, _927319, _927321, hAPP(c_Fun_Ocomp(_927317, _927319, _927325, _927323), _927327)), _927329))], (44918 ^ _781013) ^ [_1677888, _1677890, _1677892, _1677894, _1677896] : [-(c_List_OdropWhile(_1677888, _1677890, _1677892) = hAPP(hAPP(c_List_Olist_OCons(_1677888), _1677894), _1677896)), _1677892 = hAPP(hAPP(c_List_Oappend(_1677888), c_List_OtakeWhile(_1677888, _1677890, _1677892)), hAPP(hAPP(c_List_Olist_OCons(_1677888), _1677894), _1677896)), -(hBOOL(hAPP(_1677890, _1677894)))], (34611 ^ _781013) ^ [_1436721, _1436723] : [c_Int_OBit0(_1436721) = c_Int_OBit1(_1436723)], (10877 ^ _781013) ^ [_973571, _973573, _973575, _973577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973571, tc_HOL_Obool)), _973573), _973575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_973571, tc_HOL_Obool)), _973575), _973577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_973571, tc_HOL_Obool)), _973573), _973577)))], (42875 ^ _781013) ^ [_1631894, _1631896, _1631898, _1631900, _1631902] : [_1631894 = c_Orderings_Obot__class_Obot(tc_fun(_1631896, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1631898, tc_HOL_Obool)), _1631900), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631896, tc_fun(_1631898, tc_HOL_Obool)), _1631894), _1631902)) = _1631900)], (49832 ^ _781013) ^ [_1793784, _1793786, _1793788] : [class_Orderings_Olinorder(_1793784), hBOOL(hAPP(c_Finite__Set_Ofinite(_1793784), _1793786)), -(hBOOL(hAPP(hAPP(c_member(_1793784), _1793788), _1793786))), -(c_Big__Operators_Olinorder__class_OMin(_1793784, hAPP(hAPP(c_Set_Oinsert(_1793784), _1793788), _1793786)) = hAPP(hAPP(c_Finite__Set_Ofold(_1793784, _1793784, c_Orderings_Oord__class_Omin(_1793784)), _1793788), _1793786))], (33376 ^ _781013) ^ [_1414506, _1414508] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414506) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414508), 33379 ^ _781013 : [(33386 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414506)))), 33389 ^ _781013 : [(33396 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414508)))), -(_1414506 = _1414508)], (33390 ^ _781013) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414508))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414506) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (33380 ^ _781013) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414506))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414508)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (4028 ^ _781013) ^ [_841960, _841962] : [_841962 = _841960, -(c_Lazy__Sequence_Ohb__not__seq(_841962) = c_Lazy__Sequence_Ohb__not__seq(_841960))], (29094 ^ _781013) ^ [_1323746, _1323748] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1323746, _1323748) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1323746 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1323748), 29097 ^ [_1323746, _1323748]))], (20019 ^ _781013) ^ [_1155794, _1155796, _1155798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155794), _1155796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155796), _1155798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1155794)), _1155798)))], (51344 ^ _781013) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (37864 ^ _781013) ^ [_1506006, _1506008, _1506010, _1506012, _1506014, _1506016, _1506018] : [-(hAPP(c_Product__Type_Oapfst(_1506006, _1506008, _1506010, _1506012), hAPP(c_Product__Type_Oapsnd(_1506014, _1506010, _1506006, _1506016), _1506018)) = hAPP(hAPP(c_Product__Type_OPair(_1506008, _1506010), hAPP(_1506012, hAPP(c_Product__Type_Ofst(_1506006, _1506014), _1506018))), hAPP(_1506016, hAPP(c_Product__Type_Osnd(_1506006, _1506014), _1506018))))], (27124 ^ _781013) ^ [_1286058] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1286058) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1286058))], (9166 ^ _781013) ^ [_942944, _942946, _942948, _942950, _942952, _942954] : [-(hBOOL(hAPP(hAPP(c_member(_942944), _942946), _942948))), -(hAPP(c_Set_Oimage(_942944, tc_Option_Ooption(_942950), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942944, tc_Option_Ooption(_942950)), _942952), _942946), hAPP(c_Option_Ooption_OSome(_942950), _942954))), _942948) = hAPP(c_Set_Oimage(_942944, tc_Option_Ooption(_942950), _942952), _942948))], (49345 ^ _781013) ^ [_1783561, _1783563, _1783565, _1783567] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1783561, _1783561)), hAPP(hAPP(c_Product__Type_OPair(_1783561, _1783561), _1783563), _1783565)), c_Transitive__Closure_Otrancl(_1783561, _1783567))), 49349 ^ _781013 : [(49352 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783561, _1783561)), hAPP(hAPP(c_Product__Type_OPair(_1783561, _1783561), 49348 ^ [_1783561, _1783563, _1783565, _1783567]), _1783565)), _1783567)))], (49350 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783561, _1783561)), hAPP(hAPP(c_Product__Type_OPair(_1783561, _1783561), _1783563), 49348 ^ [_1783561, _1783563, _1783565, _1783567])), c_Transitive__Closure_Ortrancl(_1783561, _1783567))))]]], (37822 ^ _781013) ^ [_1505148, _1505150, _1505152] : [c_Equiv__Relations_Oequivp(_1505148, _1505150), -(hBOOL(hAPP(hAPP(_1505150, _1505152), _1505152)))], (25186 ^ _781013) ^ [_1250427, _1250429, _1250431, _1250433] : [class_Fields_Olinordered__field(_1250427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250427), _1250429), _1250431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250427), c_Groups_Ozero__class_Ozero(_1250427)), _1250433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250427), c_Groups_Ozero__class_Ozero(_1250427)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250427), _1250431), _1250429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250427), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250427), _1250433), _1250431)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250427), _1250433), _1250429))))], (12538 ^ _781013) ^ [_1007438, _1007440, _1007442] : [class_Lattices_Olattice(_1007438), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007438), _1007440)), -(_1007440 = c_Orderings_Obot__class_Obot(tc_fun(_1007438, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007438), _1007442)), -(_1007442 = c_Orderings_Obot__class_Obot(tc_fun(_1007438, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1007438, tc_HOL_Obool)), _1007440), _1007442) = c_Orderings_Obot__class_Obot(tc_fun(_1007438, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1007438, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1007438, tc_HOL_Obool)), _1007440), _1007442)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1007438), c_Big__Operators_Olattice__class_OInf__fin(_1007438, _1007440)), c_Big__Operators_Olattice__class_OInf__fin(_1007438, _1007442)))], (40125 ^ _781013) ^ [_1563450, _1563452, _1563454, _1563456, _1563458, _1563460] : [-(c_List_Ofoldr(_1563450, _1563452, _1563454, hAPP(hAPP(c_List_Olist_OCons(_1563450), _1563456), _1563458), _1563460) = hAPP(hAPP(_1563454, _1563456), c_List_Ofoldr(_1563450, _1563452, _1563454, _1563458, _1563460)))], (35049 ^ _781013) ^ [] : [-(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)))))], (4090 ^ _781013) ^ [_842875, _842877] : [_842877 = _842875, -(c_HOL_OEx(_842877) = c_HOL_OEx(_842875))], (44494 ^ _781013) ^ [_1668744, _1668746, _1668748, _1668750] : [-(c_List_Oconcat(_1668744, hAPP(hAPP(c_List_Omap(_1668746, tc_List_Olist(_1668744)), hAPP(hAPP(c_COMBC(_1668746, tc_List_Olist(_1668744), tc_List_Olist(_1668744)), hAPP(hAPP(c_COMBB(_1668744, tc_fun(tc_List_Olist(_1668744), tc_List_Olist(_1668744)), _1668746), c_List_Olist_OCons(_1668744)), _1668748)), c_List_Olist_ONil(_1668744))), _1668750)) = hAPP(hAPP(c_List_Omap(_1668746, _1668744), _1668748), _1668750))], (14195 ^ _781013) ^ [_1042695, _1042697, _1042699] : [class_Groups_Oab__group__add(_1042695), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042695), _1042697), _1042699) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042695), _1042697), hAPP(c_Groups_Ouminus__class_Ouminus(_1042695), _1042699)))], (50814 ^ _781013) ^ [_1813926, _1813928, _1813930, _1813932] : [-(c_New__Random__Sequence_Opos__map(_1813926, _1813928, _1813930, _1813932) = c_New__Random__Sequence_Opos__bind(_1813926, _1813928, _1813932, hAPP(c_Fun_Ocomp(_1813928, 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(_1813928))))), _1813926, c_New__Random__Sequence_Opos__single(_1813928)), _1813930)))], (46104 ^ _781013) ^ [_1703787, _1703789, _1703791, _1703793, _1703795, _1703797, _1703799] : [c_List_Olist__all2(_1703787, _1703789, _1703791, hAPP(hAPP(c_List_Omap(_1703793, _1703787), _1703795), _1703797), _1703799), -(c_List_Olist__all2(_1703793, _1703789, hAPP(hAPP(c_COMBB(_1703787, tc_fun(_1703789, tc_HOL_Obool), _1703793), _1703791), _1703795), _1703797, _1703799))], (29155 ^ _781013) ^ [_1324730, _1324732, _1324734] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1324730), _1324732)), _1324734) = 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), _1324730), _1324734)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1324732), _1324734))), 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, _1324730, _1324734)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1324732, _1324734))), _1324734)))], (12990 ^ _781013) ^ [_1017202, _1017204, _1017206, _1017208] : [-(hAPP(c_Set_Oimage(_1017202, _1017204, _1017206), hAPP(c_Set_Ovimage(_1017202, _1017204, _1017206), _1017208)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1017204, tc_HOL_Obool)), _1017208), hAPP(c_Set_Oimage(_1017202, _1017204, _1017206), c_Orderings_Otop__class_Otop(tc_fun(_1017202, tc_HOL_Obool)))))], (12456 ^ _781013) ^ [_1005795, _1005797, _1005799] : [class_Lattices_Olattice(_1005795), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005795), _1005797)), 12463 ^ _781013 : [(12470 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005795, tc_HOL_Obool)), _1005797), hAPP(hAPP(c_Set_Oinsert(_1005795), _1005799), c_Orderings_Obot__class_Obot(tc_fun(_1005795, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1005795, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1005795, hAPP(hAPP(c_Set_Oinsert(_1005795), _1005799), _1005797)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005795), _1005799), c_Big__Operators_Olattice__class_OInf__fin(_1005795, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005795, tc_HOL_Obool)), _1005797), hAPP(hAPP(c_Set_Oinsert(_1005795), _1005799), c_Orderings_Obot__class_Obot(tc_fun(_1005795, tc_HOL_Obool)))))))], (12464 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005795, tc_HOL_Obool)), _1005797), hAPP(hAPP(c_Set_Oinsert(_1005795), _1005799), c_Orderings_Obot__class_Obot(tc_fun(_1005795, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1005795, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1005795, hAPP(hAPP(c_Set_Oinsert(_1005795), _1005799), _1005797)) = _1005799)]]], (8106 ^ _781013) ^ [_918980, _918982, _918984, _918986, _918988] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_918980, tc_Option_Ooption(_918982)), _918984), _918986), hAPP(c_Option_Ooption_OSome(_918982), _918988)) = hAPP(c_COMBK(tc_Option_Ooption(_918982), _918980), c_Option_Ooption_ONone(_918982))], (46810 ^ _781013) ^ [_1722533] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1722533)))], (27889 ^ _781013) ^ [_1301730, _1301732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301730), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301730), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1301732, _1301730))))], (10299 ^ _781013) ^ [_963263, _963265, _963267] : [hBOOL(hAPP(hAPP(c_member(_963263), _963265), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_963263, tc_HOL_Obool)), _963267))), hBOOL(hAPP(hAPP(c_member(_963263), _963265), _963267))], (11207 ^ _781013) ^ [_980936, _980938, _980940, _980942, _980944, _980946] : [c_Finite__Set_Ofolding(_980936, _980938, _980940, _980942), hBOOL(hAPP(c_Finite__Set_Ofinite(_980936), _980944)), hBOOL(hAPP(c_Finite__Set_Ofinite(_980936), _980946)), -(hAPP(c_Fun_Ocomp(_980938, _980938, _980938, hAPP(_980942, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980936, tc_HOL_Obool)), _980944), _980946))), hAPP(_980942, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980936, tc_HOL_Obool)), _980944), _980946))) = hAPP(c_Fun_Ocomp(_980938, _980938, _980938, hAPP(_980942, _980944)), hAPP(_980942, _980946)))], (23973 ^ _781013) ^ [_1228529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1228529))))], (4652 ^ _781013) ^ [_851432, _851434] : [_851434 = _851432, -(c_Finite__Set_Ofinite(_851434) = c_Finite__Set_Ofinite(_851432))], (12660 ^ _781013) ^ [_1010044, _1010046, _1010048] : [class_Rings_Oidom(_1010044), 12663 ^ _781013 : [(12664 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010044), _1010046), _1010046) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010044), _1010048), _1010048), -(_1010046 = _1010048), -(_1010046 = hAPP(c_Groups_Ouminus__class_Ouminus(_1010044), _1010048))], (12674 ^ _781013) ^ [] : [12675 ^ _781013 : [(12678 ^ _781013) ^ [] : [_1010046 = hAPP(c_Groups_Ouminus__class_Ouminus(_1010044), _1010048)], (12676 ^ _781013) ^ [] : [_1010046 = _1010048]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010044), _1010046), _1010046) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010044), _1010048), _1010048))]]], (45069 ^ _781013) ^ [_1681481] : [class_Enum_Oenum(_1681481), -(hBOOL(hAPP(c_List_Odistinct(_1681481), c_Enum_Oenum__class_Oenum(_1681481))))], (4440 ^ _781013) ^ [_848264, _848266, _848268, _848270] : [-(c_Complete__Lattice_OSup__class_OSup(_848270, _848266) = c_Complete__Lattice_OSup__class_OSup(_848268, _848264)), _848270 = _848268, _848266 = _848264], (5769 ^ _781013) ^ [_872664, _872666, _872668, _872670, _872672, _872674] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_872664, _872666, _872668, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872664), _872670), _872672), _872674)) = hAPP(hAPP(hAPP(_872668, _872670), _872672), _872674))], (5715 ^ _781013) ^ [_871450, _871452, _871454, _871456, _871458, _871460, _871462] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871450), _871452), _871454), _871456) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871450), _871458), _871460), _871462)), _871452 = _871458, _871454 = _871460, _871456 = _871462], (2014 ^ _781013) ^ [_810279, _810281, _810283, _810285, _810287, _810289, _810291, _810293, _810295, _810297] : [-(c_Sum__Type_Osum_Osum__case(_810297, _810293, _810289, _810285, _810281) = c_Sum__Type_Osum_Osum__case(_810295, _810291, _810287, _810283, _810279)), _810297 = _810295, _810293 = _810291, _810289 = _810287, _810285 = _810283, _810281 = _810279], (41585 ^ _781013) ^ [_1601792, _1601794, _1601796, _1601798, _1601800] : [-(hAPP(hAPP(c_List_Olist_OCons(_1601792), _1601794), _1601796) = hAPP(hAPP(c_List_Oappend(_1601792), _1601798), _1601800)), 41586 ^ _781013 : [(41593 ^ _781013) ^ [_1601975] : [hAPP(hAPP(c_List_Olist_OCons(_1601792), _1601794), _1601975) = _1601798, _1601796 = hAPP(hAPP(c_List_Oappend(_1601792), _1601975), _1601800)], (41587 ^ _781013) ^ [] : [_1601798 = c_List_Olist_ONil(_1601792), hAPP(hAPP(c_List_Olist_OCons(_1601792), _1601794), _1601796) = _1601800]]], (43267 ^ _781013) ^ [_1642535, _1642537, _1642539] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642535)), hAPP(c_List_Ofilter(_1642535, _1642537), _1642539))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642535)), hAPP(c_List_Ofilter(_1642535, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1642535), c_fNot), _1642537)), _1642539))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642535)), _1642539))], (38535 ^ _781013) ^ [_1522015, _1522017, _1522019, _1522021, _1522023] : [hBOOL(hAPP(c_List_Odistinct(_1522015), hAPP(hAPP(c_List_Omap(tc_prod(_1522015, _1522017), _1522015), c_Product__Type_Ofst(_1522015, _1522017)), _1522019))), 38538 ^ _781013 : [(38545 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522015, _1522017)), hAPP(hAPP(c_Product__Type_OPair(_1522015, _1522017), _1522021), _1522023)), hAPP(c_List_Oset(tc_prod(_1522015, _1522017)), _1522019))), -(hAPP(hAPP(c_Map_Omap__of(_1522015, _1522017), _1522019), _1522021) = hAPP(c_Option_Ooption_OSome(_1522017), _1522023))], (38539 ^ _781013) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1522015, _1522017), _1522019), _1522021) = hAPP(c_Option_Ooption_OSome(_1522017), _1522023), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1522015, _1522017)), hAPP(hAPP(c_Product__Type_OPair(_1522015, _1522017), _1522021), _1522023)), hAPP(c_List_Oset(tc_prod(_1522015, _1522017)), _1522019))))]]], (11239 ^ _781013) ^ [_981650, _981652, _981654, _981656, _981658] : [c_Finite__Set_Ofolding__one(_981650, _981652, _981654), hBOOL(hAPP(c_Finite__Set_Ofinite(_981650), _981656)), -(_981656 = c_Orderings_Obot__class_Obot(tc_fun(_981650, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_981650), _981658)), -(_981658 = c_Orderings_Obot__class_Obot(tc_fun(_981650, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981650, tc_HOL_Obool)), _981656), _981658) = c_Orderings_Obot__class_Obot(tc_fun(_981650, tc_HOL_Obool)), -(hAPP(_981654, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_981650, tc_HOL_Obool)), _981656), _981658)) = hAPP(hAPP(_981652, hAPP(_981654, _981656)), hAPP(_981654, _981658)))], (1274 ^ _781013) ^ [_799680, _799682] : [-(class_Orderings_Owellorder(_799680)), _799682 = _799680, class_Orderings_Owellorder(_799682)], (4336 ^ _781013) ^ [_846592, _846594, _846596, _846598, _846600, _846602] : [-(c_List_Olinorder__class_Oinsort__key(_846602, _846598, _846594) = c_List_Olinorder__class_Oinsort__key(_846600, _846596, _846592)), _846602 = _846600, _846598 = _846596, _846594 = _846592], (29088 ^ _781013) ^ [_1323632, _1323634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1323632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1323634, _1323632)), _1323632)))], (4582 ^ _781013) ^ [_850403, _850405, _850407, _850409] : [-(c_Nitpick_Ouminus__frac(_850409, _850405) = c_Nitpick_Ouminus__frac(_850407, _850403)), _850409 = _850407, _850405 = _850403], (50812 ^ _781013) ^ [_1813878, _1813880, _1813882, _1813884, _1813886] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1813878), _1813880), _1813882), _1813884), _1813886) = c_New__DSequence_Oneg__single(_1813878, _1813880))], (11552 ^ _781013) ^ [_988740, _988742, _988744, _988746] : [c_Fun_Oinj__on(_988740, _988742, _988744, _988746), 11555 ^ _781013 : [(11556 ^ _781013) ^ [_988848] : [hBOOL(hAPP(hAPP(c_member(_988740), _988848), _988746)), 11559 ^ _781013 : [(11560 ^ _781013) ^ [_988950] : [hBOOL(hAPP(hAPP(c_member(_988740), _988950), _988746)), hAPP(_988744, _988848) = hAPP(_988744, _988950), -(_988848 = _988950)]]]]], (46607 ^ _781013) ^ [_1716325, _1716327, _1716329, _1716331, _1716333, _1716335, _1716337] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1716325, _1716327, _1716329), _1716331), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1716333, tc_fun(tc_prod(_1716327, _1716329), tc_HOL_Obool)), _1716335), _1716337)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1716333, tc_fun(tc_prod(_1716325, _1716329), tc_HOL_Obool)), _1716335), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1716327, _1716329), tc_HOL_Obool), tc_fun(tc_prod(_1716325, _1716329), tc_HOL_Obool), _1716333), hAPP(c_Relation_Orel__comp(_1716325, _1716327, _1716329), _1716331)), _1716337)))], (42074 ^ _781013) ^ [_1613597, _1613599, _1613601] : [-(hAPP(hAPP(c_List_Oappend(_1613597), hAPP(hAPP(c_List_Otake(_1613597), _1613599), _1613601)), hAPP(hAPP(c_List_Odrop(_1613597), _1613599), _1613601)) = _1613601)], (35933 ^ _781013) ^ [_1462571, _1462573, _1462575, _1462577] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1462571, tc_fun(_1462573, tc_HOL_Obool))), _1462575), _1462577)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1462571, _1462573)), hAPP(hAPP(c_Product__Type_OPair(_1462571, _1462573), _1462575), _1462577)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1462571, _1462573), tc_HOL_Obool)))))], (2366 ^ _781013) ^ [_816015, _816017] : [_816017 = _816015, -(c_Natural_Oevalc(_816017) = c_Natural_Oevalc(_816015))], (4762 ^ _781013) ^ [_853169, _853171, _853173, _853175, _853177, _853179, _853181, _853183] : [-(c_New__DSequence_Oneg__decr__bind(_853183, _853179, _853175, _853171) = c_New__DSequence_Oneg__decr__bind(_853181, _853177, _853173, _853169)), _853183 = _853181, _853179 = _853177, _853175 = _853173, _853171 = _853169], (44218 ^ _781013) ^ [_1661825, _1661827, _1661829] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1661825), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1661825))), _1661827))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661829), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1661825))), _1661827))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1661825), _1661825), hAPP(hAPP(c_COMBC(tc_List_Olist(_1661825), tc_Nat_Onat, _1661825), c_List_Onth(_1661825)), _1661829)), hAPP(c_List_Ofilter(tc_List_Olist(_1661825), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1661825)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661829)), c_Nat_Osize__class_Osize(tc_List_Olist(_1661825)))), c_List_Otranspose(_1661825, _1661827))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1661825)), _1661827), _1661829))], (2054 ^ _781013) ^ [_810969, _810971, _810973, _810975, _810977, _810979, _810981, _810983, _810985, _810987] : [-(c_Fun_Ooverride__on(_810987, _810983, _810979, _810975, _810971) = c_Fun_Ooverride__on(_810985, _810981, _810977, _810973, _810969)), _810987 = _810985, _810983 = _810981, _810979 = _810977, _810975 = _810973, _810971 = _810969], (39818 ^ _781013) ^ [_1553249, _1553251, _1553253, _1553255] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1553249), tc_List_Olist(_1553249))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1553249), tc_List_Olist(_1553249)), _1553251), _1553253)), c_List_Olex(_1553249, _1553255)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1553249), tc_List_Olist(_1553249))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1553249), tc_List_Olist(_1553249)), _1553251), _1553253)), c_List_Olexord(_1553249, _1553255))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553249)), _1553251) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553249)), _1553253)], (43504 ^ _781013) ^ [_1647745, _1647747, _1647749] : [-(c_List_Omap__filter(_1647745, _1647747, _1647749, c_List_Olist_ONil(_1647745)) = c_List_Olist_ONil(_1647747))], (37718 ^ _781013) ^ [_1501550] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1501550)], (43203 ^ _781013) ^ [_1640778, _1640780, _1640782, _1640784, _1640786] : [_1640778 = c_Orderings_Obot__class_Obot(tc_fun(_1640780, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640780, tc_fun(_1640782, tc_HOL_Obool)), _1640778), hAPP(hAPP(c_COMBB(tc_fun(_1640782, tc_HOL_Obool), tc_fun(_1640782, tc_HOL_Obool), _1640780), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640782, tc_HOL_Obool)), _1640784)), _1640786)) = c_Orderings_Otop__class_Otop(tc_fun(_1640782, tc_HOL_Obool)))], (8465 ^ _781013) ^ [_927173, _927175, _927177, _927179, _927181] : [-(hAPP(c_Set_Oimage(_927173, _927175, _927177), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927173, tc_HOL_Obool)), _927179), _927181)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927175, tc_HOL_Obool)), hAPP(c_Set_Oimage(_927173, _927175, _927177), _927179)), hAPP(c_Set_Oimage(_927173, _927175, _927177), _927181)))], (7527 ^ _781013) ^ [_906977, _906979, _906981, _906983] : [hBOOL(hAPP(hAPP(c_member(_906977), _906979), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906977, tc_HOL_Obool)), _906981), _906983))), hBOOL(hAPP(hAPP(c_member(_906977), _906979), _906983))], (7783 ^ _781013) ^ [_912097, _912099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912097, tc_HOL_Obool)), _912099), c_Orderings_Obot__class_Obot(tc_fun(_912097, tc_HOL_Obool)))), -(_912099 = c_Orderings_Obot__class_Obot(tc_fun(_912097, tc_HOL_Obool)))], (51588 ^ _781013) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (50746 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OPls))], (48970 ^ _781013) ^ [_1773547, _1773549] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1773547, _1773547), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1773547, _1773549)), c_Relation_OId(_1773547)) = c_Transitive__Closure_Ortrancl(_1773547, _1773549))], (19112 ^ _781013) ^ [_1138895, _1138897, _1138899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1138895), _1138897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1138895), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1138899), _1138897))))], (42506 ^ _781013) ^ [_1623181] : [class_Groups_Omonoid__add(_1623181), -(c_List_Omonoid__add__class_Olistsum(_1623181) = c_List_Ofoldl(_1623181, _1623181, c_Groups_Oplus__class_Oplus(_1623181), c_Groups_Ozero__class_Ozero(_1623181)))], (30009 ^ _781013) ^ [_1341686, _1341688, _1341690] : [class_Orderings_Olinorder(_1341686), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341686), _1341688), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1341686), _1341688), _1341690)) = _1341688)], (37618 ^ _781013) ^ [_1499472, _1499474, _1499476, _1499478, _1499480] : [hBOOL(hAPP(hAPP(_1499472, _1499474), _1499476)), -(hBOOL(hAPP(hAPP(_1499472, hAPP(c_Product__Type_Osnd(_1499478, _1499480), hAPP(hAPP(c_Product__Type_OPair(_1499478, _1499480), _1499476), _1499474))), hAPP(c_Product__Type_Ofst(_1499478, _1499480), hAPP(hAPP(c_Product__Type_OPair(_1499478, _1499480), _1499476), _1499474)))))], (51162 ^ _781013) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (46731 ^ _781013) ^ [_1720952, _1720954] : [c_Wellfounded_Owf(_1720952, _1720954), -(c_Wellfounded_Owf(tc_List_Olist(_1720952), c_List_Olenlex(_1720952, _1720954)))], (31846 ^ _781013) ^ [_1383674, _1383676, _1383678, _1383680, _1383682, _1383684, _1383686] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383674, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383676, tc_fun(_1383674, tc_HOL_Obool)), _1383678), _1383680)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383682, tc_fun(_1383674, tc_HOL_Obool)), _1383684), _1383686)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383676, tc_fun(_1383674, tc_HOL_Obool)), _1383678), hAPP(hAPP(c_COMBB(tc_fun(_1383682, tc_fun(_1383674, tc_HOL_Obool)), tc_fun(_1383674, tc_HOL_Obool), _1383676), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383682, tc_fun(_1383674, tc_HOL_Obool)), _1383684)), hAPP(hAPP(c_COMBC(_1383676, tc_fun(_1383682, tc_fun(_1383674, tc_HOL_Obool)), tc_fun(_1383682, tc_fun(_1383674, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1383674, tc_HOL_Obool), tc_fun(_1383674, tc_HOL_Obool)), tc_fun(tc_fun(_1383682, tc_fun(_1383674, tc_HOL_Obool)), tc_fun(_1383682, tc_fun(_1383674, tc_HOL_Obool))), _1383676), c_COMBB(tc_fun(_1383674, tc_HOL_Obool), tc_fun(_1383674, tc_HOL_Obool), _1383682)), hAPP(hAPP(c_COMBB(tc_fun(_1383674, tc_HOL_Obool), tc_fun(tc_fun(_1383674, tc_HOL_Obool), tc_fun(_1383674, tc_HOL_Obool)), _1383676), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383674, tc_HOL_Obool))), _1383680))), _1383686))))], (18281 ^ _781013) ^ [_1121340, _1121342, _1121344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121340), _1121342)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121340), _1121344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121342), _1121344)))], (39605 ^ _781013) ^ [_1547416, _1547418, _1547420] : [-(c_Hilbert__Choice_OEps(tc_prod(_1547416, _1547418), _1547420) = c_Hilbert__Choice_OEps(tc_prod(_1547416, _1547418), hAPP(c_Product__Type_Oprod_Oprod__case(_1547416, _1547418, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1547418, tc_prod(_1547416, _1547418)), tc_fun(_1547418, tc_HOL_Obool), _1547416), hAPP(c_COMBB(tc_prod(_1547416, _1547418), tc_HOL_Obool, _1547418), _1547420)), c_Product__Type_OPair(_1547416, _1547418)))))], (14949 ^ _781013) ^ [_1057711, _1057713, _1057715] : [class_Groups_Ogroup__add(_1057711), 14952 ^ _781013 : [(14959 ^ _781013) ^ [] : [_1057713 = _1057715, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057711), _1057713), _1057715) = c_Groups_Ozero__class_Ozero(_1057711))], (14953 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057711), _1057713), _1057715) = c_Groups_Ozero__class_Ozero(_1057711), -(_1057713 = _1057715)]]], (50271 ^ _781013) ^ [_1803300, _1803302, _1803304] : [c_List_Olist__all(_1803300, _1803302, _1803304), 50274 ^ _781013 : [(50275 ^ _781013) ^ [_1803389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1803389), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803300)), _1803304))), -(hBOOL(hAPP(_1803302, hAPP(hAPP(c_List_Onth(_1803300), _1803304), _1803389))))]]], (34517 ^ _781013) ^ [_1434894, _1434896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1434894)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1434896)), _1434894) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1434896), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1434894), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (19180 ^ _781013) ^ [_1140271, _1140273, _1140275, _1140277, _1140279, _1140281, _1140283, _1140285, _1140287, _1140289, _1140291] : [hAPP(_1140271, hAPP(_1140273, _1140275)) = hAPP(_1140277, hAPP(_1140279, _1140281)), -(hAPP(hAPP(c_Fun_Ocomp(_1140283, _1140285, _1140287, _1140271), _1140273), _1140275) = hAPP(hAPP(c_Fun_Ocomp(_1140289, _1140285, _1140291, _1140277), _1140279), _1140281))], (12054 ^ _781013) ^ [_998442, _998444, _998446, _998448] : [c_Fun_Oinj__on(_998442, tc_Option_Ooption(_998444), c_Map_Omap__add(_998442, _998444, _998446, _998448), c_Map_Odom(_998442, _998444, _998448)), -(c_Fun_Oinj__on(_998442, tc_Option_Ooption(_998444), _998448, c_Map_Odom(_998442, _998444, _998448)))], (20817 ^ _781013) ^ [_1170206, _1170208] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170206)), 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)), _1170206))), 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, _1170208))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8711 ^ _781013) ^ [_932420, _932422, _932424] : [_932422 = _932424, -(hAPP(hAPP(c_COMBC(_932420, tc_fun(_932420, tc_HOL_Obool), tc_HOL_Obool), c_member(_932420)), _932422) = hAPP(hAPP(c_COMBC(_932420, tc_fun(_932420, tc_HOL_Obool), tc_HOL_Obool), c_member(_932420)), _932424))], (41752 ^ _781013) ^ [_1604996, _1604998, _1605000, _1605002] : [-(hAPP(c_List_OremoveAll(_1604996, _1604998), hAPP(hAPP(c_List_Oappend(_1604996), _1605000), _1605002)) = hAPP(hAPP(c_List_Oappend(_1604996), hAPP(c_List_OremoveAll(_1604996, _1604998), _1605000)), hAPP(c_List_OremoveAll(_1604996, _1604998), _1605002)))], (19851 ^ _781013) ^ [_1152869, _1152871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152869), _1152871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1152869), _1152871)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12688 ^ _781013) ^ [_1010492, _1010494, _1010496] : [class_Rings_Oring(_1010492), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010492), hAPP(c_Groups_Ouminus__class_Ouminus(_1010492), _1010494)), _1010496) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010492), _1010494), hAPP(c_Groups_Ouminus__class_Ouminus(_1010492), _1010496)))], (38858 ^ _781013) ^ [_1529792, _1529794, _1529796, _1529798, _1529800] : [class_Orderings_Olinorder(_1529792), 38861 ^ _781013 : [(38870 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1529794), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1529794, _1529792, _1529796), _1529798), _1529800)))), -(hBOOL(hAPP(hAPP(c_member(_1529794), _1529798), hAPP(c_List_Oset(_1529794), _1529800)))), hBOOL(hAPP(c_List_Odistinct(_1529794), _1529800))], (38862 ^ _781013) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1529794), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1529794, _1529792, _1529796), _1529798), _1529800))), 38865 ^ _781013 : [(38868 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1529794), _1529800)))], (38866 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1529794), _1529798), hAPP(c_List_Oset(_1529794), _1529800)))]]]]], (3494 ^ _781013) ^ [_833691, _833693, _833695, _833697, _833699, _833701, _833703, _833705] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_833705, _833701, _833697, _833693) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_833703, _833699, _833695, _833691)), _833705 = _833703, _833701 = _833699, _833697 = _833695, _833693 = _833691], (10857 ^ _781013) ^ [_973213, _973215, _973217, _973219] : [class_Lattices_Osemilattice__sup(_973213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973213), _973215), _973217)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973213), _973215), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_973213), _973217), _973219))))], (1374 ^ _781013) ^ [_800930, _800932] : [-(class_Orderings_Obot(_800930)), _800932 = _800930, class_Orderings_Obot(_800932)], (48697 ^ _781013) ^ [_1766174, _1766176] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1766174), _1766176) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1766174, 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)))), _1766176))))], (21319 ^ _781013) ^ [_1180915, _1180917, _1180919] : [class_Orderings_Olinorder(_1180915), 21322 ^ _781013 : [(21329 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180915), _1180917), _1180919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180915, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1180915), _1180917)), hAPP(c_SetInterval_Oord__class_OlessThan(_1180915), _1180919))))], (21323 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180915, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1180915), _1180917)), hAPP(c_SetInterval_Oord__class_OlessThan(_1180915), _1180919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180915), _1180917), _1180919)))]]], (28284 ^ _781013) ^ [_1308965, _1308967, _1308969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1308965)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1308967, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1308969), _1308965)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1308969), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1308967), _1308969), _1308965))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1308967, _1308969)))], (42986 ^ _781013) ^ [_1634879, _1634881, _1634883, _1634885] : [42988 ^ _781013 : [(42991 ^ _781013) ^ [] : [hAPP(_1634885, 42987 ^ [_1634879, _1634881, _1634883, _1634885]) = c_Orderings_Otop__class_Otop(tc_fun(_1634879, tc_HOL_Obool))], (42989 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1634881), 42987 ^ [_1634879, _1634881, _1634883, _1634885]), _1634883)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1634879, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634881, tc_fun(_1634879, tc_HOL_Obool)), _1634883), _1634885))], (38264 ^ _781013) ^ [_1515683, _1515685, _1515687] : [c_Fun_Oinj__on(_1515683, _1515685, _1515687, c_Orderings_Otop__class_Otop(tc_fun(_1515683, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1515683), tc_List_Olist(_1515685), hAPP(c_List_Omap(_1515683, _1515685), _1515687), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1515683), tc_HOL_Obool))))], (49138 ^ _781013) ^ [_1777692, _1777694, _1777696] : [c_Wellfounded_Owf(_1777692, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777692, _1777692), tc_HOL_Obool), _1777694), _1777696)), -(c_Wellfounded_Owf(_1777692, _1777696))], (2982 ^ _781013) ^ [_825645, _825647] : [_825647 = _825645, -(c_SetInterval_Oord__class_OgreaterThan(_825647) = c_SetInterval_Oord__class_OgreaterThan(_825645))], (39488 ^ _781013) ^ [_1544633, _1544635, _1544637, _1544639, _1544641] : [class_Groups_Omonoid__add(_1544633), class_Groups_Oordered__ab__semigroup__add(_1544633), 39498 ^ _781013 : [(39501 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1544633), hAPP(_1544639, 39497 ^ [_1544633, _1544635, _1544637, _1544639, _1544641])), hAPP(_1544641, 39497 ^ [_1544633, _1544635, _1544637, _1544639, _1544641])))], (39499 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544635), 39497 ^ [_1544633, _1544635, _1544637, _1544639, _1544641]), hAPP(c_List_Oset(_1544635), _1544637))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1544633), hAPP(c_List_Omonoid__add__class_Olistsum(_1544633), hAPP(hAPP(c_List_Omap(_1544635, _1544633), _1544639), _1544637))), hAPP(c_List_Omonoid__add__class_Olistsum(_1544633), hAPP(hAPP(c_List_Omap(_1544635, _1544633), _1544641), _1544637)))))], (20651 ^ _781013) ^ [_1167092, _1167094, _1167096, _1167098] : [class_Rings_Olinordered__semidom(_1167092), hAPP(hAPP(c_Power_Opower__class_Opower(_1167092), _1167094), hAPP(c_Nat_OSuc, _1167096)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1167092), _1167098), hAPP(c_Nat_OSuc, _1167096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167092), c_Groups_Ozero__class_Ozero(_1167092)), _1167094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167092), c_Groups_Ozero__class_Ozero(_1167092)), _1167098)), -(_1167094 = _1167098)], (39438 ^ _781013) ^ [_1543447, _1543449, _1543451, _1543453] : [class_Groups_Ocomm__monoid__add(_1543447), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1543447), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1543447), _1543449), c_List_Oupto(_1543451, _1543453))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1543447), _1543449), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1543451, _1543453))))], (49152 ^ _781013) ^ [_1778029, _1778031, _1778033, _1778035, _1778037, _1778039] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1778029, _1778029)), hAPP(hAPP(c_Product__Type_OPair(_1778029, _1778029), _1778031), _1778033)), _1778035)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778029, _1778029)), hAPP(hAPP(c_Product__Type_OPair(_1778029, _1778029), _1778033), _1778037)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1778029, _1778029), tc_HOL_Obool), _1778039), _1778035))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778029, _1778029)), hAPP(hAPP(c_Product__Type_OPair(_1778029, _1778029), _1778031), _1778037)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1778029, _1778029), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1778039)), _1778035))))], (32070 ^ _781013) ^ [_1389938, _1389940, _1389942] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1389938, _1389940) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1389942, _1389940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1389942), _1389938)), -(_1389938 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1389942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1389940), 32077 ^ [_1389938, _1389940, _1389942])))], (3286 ^ _781013) ^ [_830509, _830511] : [_830511 = _830509, -(c_List_Oembed__list(_830511) = c_List_Oembed__list(_830509))], (40918 ^ _781013) ^ [_1585505, _1585507, _1585509, _1585511, _1585513, _1585515, _1585517] : [class_Rings_Osemiring__0(_1585505), c_Fun_Oinj__on(tc_prod(_1585507, _1585509), _1585505, hAPP(c_Product__Type_Oprod_Oprod__case(_1585507, _1585509, _1585505), hAPP(hAPP(c_COMBC(_1585507, tc_fun(_1585509, _1585505), tc_fun(_1585509, _1585505)), hAPP(hAPP(c_COMBB(tc_fun(_1585505, _1585505), tc_fun(tc_fun(_1585509, _1585505), tc_fun(_1585509, _1585505)), _1585507), c_COMBB(_1585505, _1585505, _1585509)), hAPP(hAPP(c_COMBB(_1585505, tc_fun(_1585505, _1585505), _1585507), c_Groups_Otimes__class_Otimes(_1585505)), _1585511))), _1585513)), hAPP(hAPP(c_Product__Type_OSigma(_1585507, _1585509), _1585515), hAPP(c_COMBK(tc_fun(_1585509, tc_HOL_Obool), _1585507), _1585517))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1585505), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1585507, _1585505), _1585511), _1585515)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1585509, _1585505), _1585513), _1585517)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1585505, _1585505), c_Fun_Oid(_1585505)), hAPP(c_Set_OCollect(_1585505), hAPP(hAPP(c_COMBB(tc_fun(_1585507, tc_HOL_Obool), tc_HOL_Obool, _1585505), c_HOL_OEx(_1585507)), hAPP(hAPP(c_COMBB(tc_fun(_1585507, tc_fun(_1585509, tc_HOL_Obool)), tc_fun(_1585507, tc_HOL_Obool), _1585505), hAPP(c_COMBB(tc_fun(_1585509, tc_HOL_Obool), tc_HOL_Obool, _1585507), c_HOL_OEx(_1585509))), hAPP(hAPP(c_COMBC(_1585505, tc_fun(_1585507, tc_fun(_1585509, tc_HOL_Obool)), tc_fun(_1585507, tc_fun(_1585509, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1585507, tc_fun(tc_fun(_1585509, tc_HOL_Obool), tc_fun(_1585509, tc_HOL_Obool))), tc_fun(tc_fun(_1585507, tc_fun(_1585509, tc_HOL_Obool)), tc_fun(_1585507, tc_fun(_1585509, tc_HOL_Obool))), _1585505), c_COMBS(_1585507, tc_fun(_1585509, tc_HOL_Obool), tc_fun(_1585509, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1585507, tc_fun(_1585509, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1585507, tc_fun(tc_fun(_1585509, tc_HOL_Obool), tc_fun(_1585509, tc_HOL_Obool))), _1585505), hAPP(c_COMBB(tc_fun(_1585509, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1585509, tc_HOL_Obool), tc_fun(_1585509, tc_HOL_Obool)), _1585507), c_COMBS(_1585509, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1585507, tc_fun(_1585509, tc_HOL_Obool)), tc_fun(_1585507, tc_fun(_1585509, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1585505), hAPP(c_COMBB(tc_fun(_1585509, tc_HOL_Obool), tc_fun(_1585509, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1585507), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1585509), c_fconj))), hAPP(hAPP(c_COMBC(_1585505, tc_fun(_1585507, tc_fun(_1585509, _1585505)), tc_fun(_1585507, tc_fun(_1585509, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1585509, _1585505), tc_fun(_1585509, tc_HOL_Obool)), tc_fun(tc_fun(_1585507, tc_fun(_1585509, _1585505)), tc_fun(_1585507, tc_fun(_1585509, tc_HOL_Obool))), _1585505), c_COMBB(tc_fun(_1585509, _1585505), tc_fun(_1585509, tc_HOL_Obool), _1585507)), hAPP(hAPP(c_COMBB(tc_fun(_1585505, tc_HOL_Obool), tc_fun(tc_fun(_1585509, _1585505), tc_fun(_1585509, tc_HOL_Obool)), _1585505), c_COMBB(_1585505, tc_HOL_Obool, _1585509)), c_fequal))), hAPP(hAPP(c_COMBC(_1585507, tc_fun(_1585509, _1585505), tc_fun(_1585509, _1585505)), hAPP(hAPP(c_COMBB(tc_fun(_1585505, _1585505), tc_fun(tc_fun(_1585509, _1585505), tc_fun(_1585509, _1585505)), _1585507), c_COMBB(_1585505, _1585505, _1585509)), hAPP(hAPP(c_COMBB(_1585505, tc_fun(_1585505, _1585505), _1585507), c_Groups_Otimes__class_Otimes(_1585505)), _1585511))), _1585513)))))), hAPP(hAPP(c_COMBC(_1585507, tc_fun(_1585509, tc_HOL_Obool), tc_fun(_1585509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1585509, tc_HOL_Obool), tc_fun(_1585509, tc_HOL_Obool)), _1585507), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1585509)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1585507), c_fconj), hAPP(hAPP(c_COMBC(_1585507, tc_fun(_1585507, tc_HOL_Obool), tc_HOL_Obool), c_member(_1585507)), _1585515)))), hAPP(hAPP(c_COMBC(_1585509, tc_fun(_1585509, tc_HOL_Obool), tc_HOL_Obool), c_member(_1585509)), _1585517))))))))], (40980 ^ _781013) ^ [_1587744, _1587746, _1587748, _1587750] : [class_Groups_Ocomm__monoid__add(_1587744), c_Fun_Oinj__on(_1587746, _1587744, _1587748, _1587750), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1587746, _1587744), _1587748), _1587750) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1587744, _1587744), c_Fun_Oid(_1587744)), hAPP(c_Set_Oimage(_1587746, _1587744, _1587748), _1587750)))], (46631 ^ _781013) ^ [_1717107, _1717109, _1717111, _1717113] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1717107, _1717109, _1717111), _1717113), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1717109, _1717111), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1717107, _1717111), tc_HOL_Obool)))], (42727 ^ _781013) ^ [_1627481, _1627483] : [-(_1627481 = c_List_Olist_ONil(_1627483)), -(c_List_Olast(_1627483, _1627481) = hAPP(hAPP(c_List_Onth(_1627483), _1627481), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627483)), _1627481)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (5745 ^ _781013) ^ [_871925, _871927, _871929, _871931] : [5746 ^ _781013 : [(5749 ^ _781013) ^ [] : [hBOOL(hAPP(_871929, _871931))], (5747 ^ _781013) ^ [] : [_871927 = _871931]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_871925), _871927), _871929), _871931)))], (51292 ^ _781013) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (44785 ^ _781013) ^ [_1675143, _1675145] : [c_List_Oremdups(_1675143, _1675145) = _1675145, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675143)), c_List_Oremdups(_1675143, _1675145)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675143)), _1675145))], (7597 ^ _781013) ^ [_908478, _908480, _908482, _908484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908478, tc_HOL_Obool)), _908480), hAPP(hAPP(c_Set_Oinsert(_908478), _908482), _908484))), 7600 ^ _781013 : [(7607 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_908478), _908482), _908480))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908478, tc_HOL_Obool)), _908480), _908484)))], (7601 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_908478), _908482), _908480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908478, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908478, tc_HOL_Obool)), _908480), hAPP(hAPP(c_Set_Oinsert(_908478), _908482), c_Orderings_Obot__class_Obot(tc_fun(_908478, tc_HOL_Obool))))), _908484)))]]], (18326 ^ _781013) ^ [_1122190, _1122192] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122190), _1122192)), _1122192) = _1122190)], (49302 ^ _781013) ^ [_1782070, _1782072, _1782074, _1782076, _1782078] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1782070, _1782070)), hAPP(hAPP(c_Product__Type_OPair(_1782070, _1782070), _1782072), _1782074)), c_Transitive__Closure_Ortrancl(_1782070, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1782070, _1782070), tc_HOL_Obool)), _1782076), _1782078)))), 49308 ^ _781013 : [(49314 ^ _781013) ^ [] : [49307 ^ [_1782070, _1782072, _1782074, _1782076, _1782078] = 49310 ^ [_1782070, _1782072, _1782074, _1782076, _1782078]], (49312 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782070, _1782070)), hAPP(hAPP(c_Product__Type_OPair(_1782070, _1782070), 49307 ^ [_1782070, _1782072, _1782074, _1782076, _1782078]), 49310 ^ [_1782070, _1782072, _1782074, _1782076, _1782078])), _1782078)))], (49309 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782070, _1782070)), hAPP(hAPP(c_Product__Type_OPair(_1782070, _1782070), _1782072), 49307 ^ [_1782070, _1782072, _1782074, _1782076, _1782078])), c_Transitive__Closure_Ortrancl(_1782070, _1782076))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782070, _1782070)), hAPP(hAPP(c_Product__Type_OPair(_1782070, _1782070), _1782072), _1782074)), c_Transitive__Closure_Ortrancl(_1782070, _1782076))))], (48273 ^ _781013) ^ [_1756070, _1756072, _1756074, _1756076] : [-(c_Transitive__Closure_Otrancl(_1756070, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1756070, _1756070)), hAPP(hAPP(c_Product__Type_OPair(_1756070, _1756070), _1756072), _1756074)), _1756076)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1756070, _1756070), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1756070, _1756076)), hAPP(c_Set_OCollect(tc_prod(_1756070, _1756070)), hAPP(c_Product__Type_Oprod_Oprod__case(_1756070, _1756070, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1756070, tc_fun(_1756070, tc_HOL_Obool), tc_fun(_1756070, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1756070, tc_HOL_Obool), tc_fun(_1756070, tc_HOL_Obool)), _1756070), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756070)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1756070), c_fconj), hAPP(hAPP(c_COMBC(_1756070, tc_fun(tc_prod(_1756070, _1756070), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1756070, _1756070), tc_fun(tc_fun(tc_prod(_1756070, _1756070), tc_HOL_Obool), tc_HOL_Obool), _1756070), c_member(tc_prod(_1756070, _1756070))), hAPP(hAPP(c_COMBC(_1756070, _1756070, tc_prod(_1756070, _1756070)), c_Product__Type_OPair(_1756070, _1756070)), _1756072))), c_Transitive__Closure_Ortrancl(_1756070, _1756076))))), hAPP(hAPP(c_COMBC(_1756070, tc_fun(tc_prod(_1756070, _1756070), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1756070, _1756070), tc_fun(tc_fun(tc_prod(_1756070, _1756070), tc_HOL_Obool), tc_HOL_Obool), _1756070), c_member(tc_prod(_1756070, _1756070))), hAPP(c_Product__Type_OPair(_1756070, _1756070), _1756074))), c_Transitive__Closure_Ortrancl(_1756070, _1756076)))))))], (43167 ^ _781013) ^ [_1639958, _1639960, _1639962, _1639964, _1639966] : [_1639958 = c_Orderings_Obot__class_Obot(tc_fun(_1639960, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639960, tc_fun(_1639962, tc_HOL_Obool)), _1639958), hAPP(hAPP(c_COMBC(_1639960, tc_fun(_1639962, tc_HOL_Obool), tc_fun(_1639962, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1639962, tc_HOL_Obool), tc_fun(tc_fun(_1639962, tc_HOL_Obool), tc_fun(_1639962, tc_HOL_Obool)), _1639960), c_Groups_Ominus__class_Ominus(tc_fun(_1639962, tc_HOL_Obool))), _1639964)), _1639966)) = c_Orderings_Otop__class_Otop(tc_fun(_1639962, tc_HOL_Obool)))], (40739 ^ _781013) ^ [_1579966, _1579968, _1579970, _1579972] : [-(hAPP(c_Set_OCollect(tc_prod(_1579966, _1579968)), hAPP(c_Product__Type_Oprod_Oprod__case(_1579966, _1579968, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1579966, tc_fun(_1579968, tc_HOL_Obool), tc_fun(_1579968, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1579968, tc_HOL_Obool), tc_fun(_1579968, tc_HOL_Obool)), _1579966), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1579968)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1579966), c_fconj), _1579970))), _1579972))) = hAPP(hAPP(c_Product__Type_OSigma(_1579966, _1579968), hAPP(c_Set_OCollect(_1579966), _1579970)), hAPP(c_COMBK(tc_fun(_1579968, tc_HOL_Obool), _1579966), hAPP(c_Set_OCollect(_1579968), _1579972))))], (7129 ^ _781013) ^ [_899590, _899592, _899594, _899596] : [7143 ^ _781013 : [(7146 ^ _781013) ^ [] : [-(hBOOL(hAPP(_899596, 7142 ^ [_899590, _899592, _899594, _899596])))], (7144 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899590), 7142 ^ [_899590, _899592, _899594, _899596]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899590, tc_HOL_Obool)), _899592), _899594))))]], 7130 ^ _781013 : [(7137 ^ _781013) ^ [_899799] : [hBOOL(hAPP(hAPP(c_member(_899590), _899799), _899594)), hBOOL(hAPP(_899596, _899799))], (7131 ^ _781013) ^ [_899703] : [hBOOL(hAPP(hAPP(c_member(_899590), _899703), _899592)), hBOOL(hAPP(_899596, _899703))]]], (45862 ^ _781013) ^ [_1698564, _1698566, _1698568, _1698570] : [hBOOL(hAPP(hAPP(c_member(_1698564), _1698566), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1698564, tc_HOL_Obool), _1698568))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1698564, tc_HOL_Obool)), _1698570), _1698568)), -(hBOOL(hAPP(hAPP(c_member(_1698564), _1698566), _1698570)))], (41476 ^ _781013) ^ [_1598796, _1598798] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598796)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598798)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598796), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598798)) = c_List_Olist_ONil(tc_Int_Oint))], (21562 ^ _781013) ^ [_1185932] : [hBOOL(hAPP(_1185932, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21563 ^ [_1185932]))), 21566 ^ _781013 : [(21567 ^ _781013) ^ [_1186032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186032)), -(hBOOL(hAPP(_1185932, _1186032)))]]], (28664 ^ _781013) ^ [_1315852, _1315854] : [class_Rings_Olinordered__idom(_1315852), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315852), hAPP(c_Groups_Oabs__class_Oabs(_1315852), _1315854)), hAPP(c_Groups_Oabs__class_Oabs(_1315852), _1315854)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315852), _1315854), _1315854))], (12476 ^ _781013) ^ [_1006265, _1006267, _1006269] : [class_Lattices_Olattice(_1006265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006265), _1006267)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006265), _1006269)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006265, tc_HOL_Obool)), _1006267), _1006269) = c_Orderings_Obot__class_Obot(tc_fun(_1006265, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006265), c_Big__Operators_Olattice__class_OSup__fin(_1006265, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006265, tc_HOL_Obool)), _1006267), _1006269))), c_Big__Operators_Olattice__class_OSup__fin(_1006265, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006265, tc_HOL_Obool)), _1006267), _1006269))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006265), c_Big__Operators_Olattice__class_OSup__fin(_1006265, _1006267)), c_Big__Operators_Olattice__class_OSup__fin(_1006265, _1006269)))], (25166 ^ _781013) ^ [_1250046, _1250048, _1250050, _1250052] : [class_Fields_Olinordered__field(_1250046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250046), _1250048), c_Groups_Ozero__class_Ozero(_1250046))), 25173 ^ _781013 : [(25180 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250046), _1250052), _1250048)), _1250050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250046), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250046), _1250050), _1250048)), _1250052)))], (25174 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250046), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250046), _1250050), _1250048)), _1250052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250046), _1250052), _1250048)), _1250050)))]]], (36500 ^ _781013) ^ [_1477244, _1477246, _1477248, _1477250] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1477244, tc_fun(_1477246, tc_HOL_Obool))), _1477248), _1477250))], (20325 ^ _781013) ^ [_1160938, _1160940] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160938), _1160940)), 20326 ^ _781013 : [(20333 ^ _781013) ^ [] : [_1160938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1160940 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20327 ^ _781013) ^ [] : [_1160938 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (21599 ^ _781013) ^ [_1186640, _1186642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186640)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186642))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186640), _1186642)))], (47436 ^ _781013) ^ [_1737065, _1737067, _1737069, _1737071, _1737073, _1737075] : [-(_1737065 = c_Orderings_Obot__class_Obot(tc_fun(_1737067, tc_HOL_Obool))), 47442 ^ _781013 : [(47445 ^ _781013) ^ [] : [c_Fun_Oinj__on(_1737069, _1737071, _1737073, hAPP(_1737075, 47441 ^ [_1737065, _1737067, _1737069, _1737071, _1737073, _1737075]))], (47443 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737067), 47441 ^ [_1737065, _1737067, _1737069, _1737071, _1737073, _1737075]), _1737065)))]], -(c_Fun_Oinj__on(_1737069, _1737071, _1737073, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1737067, tc_fun(_1737069, tc_HOL_Obool)), _1737065), _1737075)))], (42039 ^ _781013) ^ [_1612499, _1612501, _1612503, _1612505] : [-(c_List_Osublist(_1612499, hAPP(hAPP(c_List_Olist_OCons(_1612499), _1612501), _1612503), _1612505) = hAPP(hAPP(c_List_Oappend(_1612499), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1612499)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1612505)), hAPP(hAPP(c_List_Olist_OCons(_1612499), _1612501), c_List_Olist_ONil(_1612499))), c_List_Olist_ONil(_1612499))), c_List_Osublist(_1612499, _1612503, 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)), _1612505)))))], (7221 ^ _781013) ^ [_901505, _901507, _901509, _901511, _901513] : [class_Orderings_Oord(_901505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901507, _901505)), _901509), _901511)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901505), hAPP(_901509, _901513)), hAPP(_901511, _901513))))], (11976 ^ _781013) ^ [_996906] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_996906), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_996906)), c_Option_Ooption_ONone(_996906)), hAPP(c_Set_Oimage(_996906, tc_Option_Ooption(_996906), c_Option_Ooption_OSome(_996906)), c_Orderings_Otop__class_Otop(tc_fun(_996906, tc_HOL_Obool)))))], (3992 ^ _781013) ^ [_841428, _841430, _841432, _841434] : [-(c_Wellfounded_Oacc(_841434, _841430) = c_Wellfounded_Oacc(_841432, _841428)), _841434 = _841432, _841430 = _841428], (15115 ^ _781013) ^ [_1060648, _1060650, _1060652] : [-(hAPP(c_Set_OCollect(_1060648), hAPP(hAPP(c_COMBS(_1060648, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1060648), c_fdisj), _1060650)), _1060652)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1060648, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1060648), _1060650)), hAPP(c_Set_OCollect(_1060648), _1060652)))], (22560 ^ _781013) ^ [_1203476, _1203478, _1203480] : [-(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)), _1203476)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1203478), _1203480)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203478), _1203476)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203480), _1203476)))], (8066 ^ _781013) ^ [_918237, _918239, _918241] : [_918239 = _918241, -(hBOOL(hAPP(hAPP(c_member(_918237), _918239), hAPP(hAPP(c_Set_Oinsert(_918237), _918241), c_Orderings_Obot__class_Obot(tc_fun(_918237, tc_HOL_Obool))))))], (33986 ^ _781013) ^ [_1425104] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425104))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425104)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (38208 ^ _781013) ^ [] : [-(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))], (25904 ^ _781013) ^ [_1262771, _1262773, _1262775] : [class_Rings_Oring__1(_1262771), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262771), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1262773), _1262775)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1262771), hAPP(c_Int_Oring__1__class_Oof__int(_1262771), _1262773)), _1262775))], (26965 ^ _781013) ^ [_1282919, _1282921, _1282923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1282919)), 26968 ^ _781013 : [(26969 ^ _781013) ^ [_1283053] : [26971 ^ _781013 : [(26977 ^ _781013) ^ [] : [-(_1283053 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26973 ^ [_1282919, _1282921, _1282923, _1283053]), 26970 ^ [_1282919, _1282921, _1282923, _1283053]))], (26975 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26973 ^ [_1282919, _1282921, _1282923, _1283053]), _1282921)))], (26972 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26970 ^ [_1282919, _1282921, _1282923, _1283053]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1282919))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1283053), _1282923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1283053), _1282919)), _1282923)))]]], (15215 ^ _781013) ^ [_1062537, _1062539, _1062541, _1062543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1062537), hAPP(c_Set_Oimage(_1062539, _1062537, _1062541), _1062543))), hAPP(c_Finite__Set_Ocard(_1062539), _1062543))), c_Fun_Oinj__on(_1062539, _1062537, _1062541, _1062543)], (35503 ^ _781013) ^ [] : [c_Int_OMin = c_Int_OPls], (11848 ^ _781013) ^ [_994679, _994681, _994683, _994685, _994687, _994689] : [c_Fun_Oinj__on(_994679, _994681, hAPP(c_Fun_Ocomp(_994683, _994681, _994679, _994685), _994687), _994689), -(c_Fun_Oinj__on(_994679, _994683, _994687, _994689))], (36842 ^ _781013) ^ [_1484069, _1484071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484069)), 36845 ^ _781013 : [(36852 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484071))), 36855 ^ _781013 : [(36862 ^ _781013) ^ [] : [-(_1484069 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1484069, _1484071) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1484069), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1484071))))], (36856 ^ _781013) ^ [] : [_1484069 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1484069, _1484071) = 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)))]]], (36846 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484071)), -(c_Divides_Odivmod__int(_1484069, _1484071) = c_Divides_OposDivAlg(_1484069, _1484071))]]], (32444 ^ _781013) ^ [_1396642, _1396644, _1396646, _1396648] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396642), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1396642), _1396644), _1396646)), hAPP(c_Int_Onumber__class_Onumber__of(_1396642), _1396648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1396642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396642), _1396644), hAPP(c_Int_Onumber__class_Onumber__of(_1396642), _1396648))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396642), _1396646), hAPP(c_Int_Onumber__class_Onumber__of(_1396642), _1396648)))), class_Int_Onumber(_1396642), class_Rings_Oring(_1396642)], (32932 ^ _781013) ^ [_1405786, _1405788, _1405790, _1405792] : [class_Fields_Olinordered__field__inverse__zero(_1405786), class_Int_Onumber(_1405786), 32939 ^ _781013 : [(32940 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1405786), _1405788), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790))), _1405792)), 32943 ^ _781013 : [(32950 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), c_Groups_Ozero__class_Ozero(_1405786)), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790)))), 32953 ^ _781013 : [(32960 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790)), c_Groups_Ozero__class_Ozero(_1405786)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), c_Groups_Ozero__class_Ozero(_1405786)), _1405792)))], (32954 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790)), c_Groups_Ozero__class_Ozero(_1405786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1405786), _1405792), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790))), _1405788)))]]], (32944 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), c_Groups_Ozero__class_Ozero(_1405786)), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), _1405788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1405786), _1405792), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790)))))]]], (32966 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1405786), _1405788), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790))), _1405792))), 32969 ^ _781013 : [(32972 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), _1405788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1405786), _1405792), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790))))], (32970 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), c_Groups_Ozero__class_Ozero(_1405786)), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790))))]], 32973 ^ _781013 : [(32976 ^ _781013) ^ [] : [32977 ^ _781013 : [(32980 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1405786), _1405792), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790))), _1405788))], (32978 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790)), c_Groups_Ozero__class_Ozero(_1405786))))]], 32981 ^ _781013 : [(32984 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), c_Groups_Ozero__class_Ozero(_1405786)), _1405792))], (32982 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790)), c_Groups_Ozero__class_Ozero(_1405786)))]]], (32974 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405786), c_Groups_Ozero__class_Ozero(_1405786)), hAPP(c_Int_Onumber__class_Onumber__of(_1405786), _1405790)))]]]]], (15671 ^ _781013) ^ [_1070940, _1070942, _1070944] : [class_Groups_Oordered__comm__monoid__add(_1070940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070940), c_Groups_Ozero__class_Ozero(_1070940)), _1070942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070940), c_Groups_Ozero__class_Ozero(_1070940)), _1070944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070940), c_Groups_Ozero__class_Ozero(_1070940)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070940), _1070942), _1070944))))], (13619 ^ _781013) ^ [_1030703, _1030705, _1030707, _1030709, _1030711] : [class_Groups_Ocomm__monoid__mult(_1030703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030705), _1030707)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030705), _1030709)), 13633 ^ _781013 : [(13636 ^ _781013) ^ [] : [hAPP(_1030711, 13632 ^ [_1030703, _1030705, _1030707, _1030709, _1030711]) = c_Groups_Oone__class_Oone(_1030703)], (13634 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1030705), 13632 ^ [_1030703, _1030705, _1030707, _1030709, _1030711]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1030705, tc_HOL_Obool)), _1030707), _1030709))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1030703, _1030705, c_Groups_Otimes__class_Otimes(_1030703)), _1030711), c_Groups_Oone__class_Oone(_1030703)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1030705, tc_HOL_Obool)), _1030707), _1030709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030703), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1030703, _1030705, c_Groups_Otimes__class_Otimes(_1030703)), _1030711), c_Groups_Oone__class_Oone(_1030703)), _1030707)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1030703, _1030705, c_Groups_Otimes__class_Otimes(_1030703)), _1030711), c_Groups_Oone__class_Oone(_1030703)), _1030709)))], (7071 ^ _781013) ^ [_898205, _898207, _898209, _898211] : [hBOOL(hAPP(hAPP(c_member(_898205), _898207), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898205, tc_HOL_Obool)), _898209), _898211))), -(hBOOL(hAPP(hAPP(c_member(_898205), _898207), _898209))), -(hBOOL(hAPP(hAPP(c_member(_898205), _898207), _898211)))], (39144 ^ _781013) ^ [_1536788, _1536790, _1536792, _1536794] : [hBOOL(hAPP(hAPP(c_member(_1536788), _1536790), hAPP(c_List_Oset(_1536788), c_List_Osublist(_1536788, _1536792, _1536794)))), -(hBOOL(hAPP(hAPP(c_member(_1536788), _1536790), hAPP(c_List_Oset(_1536788), _1536792))))], (16442 ^ _781013) ^ [_1085287, _1085289, _1085291] : [-(c_Map_Odom(_1085287, _1085289, _1085291) = hAPP(c_Set_OCollect(_1085287), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1085287), c_fNot), hAPP(hAPP(c_COMBC(_1085287, tc_Option_Ooption(_1085289), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1085289), tc_fun(tc_Option_Ooption(_1085289), tc_HOL_Obool), _1085287), c_fequal), _1085291)), c_Option_Ooption_ONone(_1085289)))))], (42845 ^ _781013) ^ [_1630076, _1630078, _1630080, _1630082, _1630084, _1630086] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630076, tc_fun(_1630078, tc_fun(_1630080, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1630076, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1630078, _1630080), tc_HOL_Obool), tc_fun(_1630078, tc_fun(_1630080, tc_HOL_Obool)), _1630076), hAPP(c_COMBC(_1630078, tc_fun(tc_prod(_1630078, _1630080), tc_HOL_Obool), tc_fun(_1630080, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630080, tc_fun(tc_fun(tc_prod(_1630078, _1630080), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1630078, _1630080), tc_HOL_Obool), tc_fun(_1630080, tc_HOL_Obool)), _1630078), c_COMBC(_1630080, tc_fun(tc_prod(_1630078, _1630080), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630080, tc_prod(_1630078, _1630080)), tc_fun(_1630080, tc_fun(tc_fun(tc_prod(_1630078, _1630080), tc_HOL_Obool), tc_HOL_Obool)), _1630078), hAPP(c_COMBB(tc_prod(_1630078, _1630080), tc_fun(tc_fun(tc_prod(_1630078, _1630080), tc_HOL_Obool), tc_HOL_Obool), _1630080), c_member(tc_prod(_1630078, _1630080)))), c_Product__Type_OPair(_1630078, _1630080))))), _1630082)), _1630084), _1630086)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630078, _1630080)), hAPP(hAPP(c_Product__Type_OPair(_1630078, _1630080), _1630084), _1630086)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630076, tc_fun(tc_prod(_1630078, _1630080), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1630076, tc_HOL_Obool))), _1630082))))], (11371 ^ _781013) ^ [_984761, _984763, _984765, _984767, _984769] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_984761, _984763, hAPP(hAPP(c_Set_Oinsert(_984761), _984765), _984767)), _984769)), 11376 ^ _781013 : [(11381 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_984761), 11374 ^ [_984761, _984763, _984765, _984767, _984769]), 11375 ^ [_984761, _984763, _984765, _984767, _984769]))], (11379 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_984761, _984761, _984763, 11374 ^ [_984761, _984763, _984765, _984767, _984769], 11375 ^ [_984761, _984763, _984765, _984767, _984769]), _984769)))], (11377 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_984761), _984765), _984767) = hAPP(hAPP(c_Set_Oinsert(_984761), 11374 ^ [_984761, _984763, _984765, _984767, _984769]), 11375 ^ [_984761, _984763, _984765, _984767, _984769]))]]], (46409 ^ _781013) ^ [_1710536, _1710538] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1710536)), _1710538)), 46415 ^ _781013 : [(46418 ^ _781013) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1710536), 46414 ^ [_1710536, _1710538]))], (46416 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710536)), 46414 ^ [_1710536, _1710538]), hAPP(c_List_Oset(tc_List_Olist(_1710536)), _1710538))))]], 46422 ^ _781013 : [(46426 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710536)), 46424 ^ [_1710536, _1710538]), hAPP(c_List_Oset(tc_List_Olist(_1710536)), _1710538))))], (46428 ^ _781013) ^ [] : [46421 ^ [_1710536, _1710538] = 46424 ^ [_1710536, _1710538]], (46430 ^ _781013) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1710536, tc_HOL_Obool)), hAPP(c_List_Oset(_1710536), 46421 ^ [_1710536, _1710538])), hAPP(c_List_Oset(_1710536), 46424 ^ [_1710536, _1710538])) = c_Orderings_Obot__class_Obot(tc_fun(_1710536, tc_HOL_Obool))], (46423 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710536)), 46421 ^ [_1710536, _1710538]), hAPP(c_List_Oset(tc_List_Olist(_1710536)), _1710538))))]], -(hBOOL(hAPP(c_List_Odistinct(_1710536), c_List_Oconcat(_1710536, _1710538))))], (14570 ^ _781013) ^ [_1051698, _1051700] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051698), _1051700)), -(hAPP(c_Finite__Set_Ocard(_1051698), _1051700) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1051698, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1051698), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1051700))], (44232 ^ _781013) ^ [_1662343, _1662345] : [hAPP(c_List_Orev(_1662343), _1662345) = c_List_Olist_ONil(_1662343), -(_1662345 = c_List_Olist_ONil(_1662343))], (37189 ^ _781013) ^ [_1490660, _1490662, _1490664] : [37191 ^ _781013 : [(37194 ^ _781013) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1490660, _1490662), 37190 ^ [_1490660, _1490662, _1490664]))], (37192 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1490662, 37190 ^ [_1490660, _1490662, _1490664]), _1490664)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1490660, _1490662), _1490664)))], (38852 ^ _781013) ^ [_1529685, _1529687, _1529689] : [hBOOL(hAPP(c_List_Odistinct(_1529685), _1529687)), -(c_List_Oremove1(_1529685, _1529689, _1529687) = hAPP(c_List_OremoveAll(_1529685, _1529689), _1529687))], (23098 ^ _781013) ^ [_1213158] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1213158)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1213158)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17443 ^ _781013) ^ [_1107103] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1107103)), 17447 ^ _781013 : [(17448 ^ _781013) ^ [_1107183] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1107183), _1107103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107183), 17446 ^ [_1107103])))]]], (36653 ^ _781013) ^ [_1480850] : [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), _1480850))), 36656 ^ _781013 : [(36663 ^ _781013) ^ [] : [-(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), _1480850))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1480850)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1480850)), 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), _1480850)))))], (36657 ^ _781013) ^ [] : [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), _1480850)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1480850)) = 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), _1480850))))]]], (49150 ^ _781013) ^ [_1777967, _1777969, _1777971, _1777973] : [-(hAPP(hAPP(c_Nat_Ocompow(_1777967, _1777967), _1777969), hAPP(hAPP(c_Nat_Ocompow(_1777967, _1777967), _1777971), _1777973)) = hAPP(hAPP(c_Nat_Ocompow(_1777967, _1777967), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1777971), _1777969)), _1777973))], (7435 ^ _781013) ^ [_905136, _905138, _905140] : [class_Orderings_Oorder(_905136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905136), _905138), _905140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905136), _905140), _905138)), -(_905140 = _905138)], (44725 ^ _781013) ^ [_1674191, _1674193] : [c_List_Oremdups(_1674191, _1674193) = c_List_Olist_ONil(_1674191), -(_1674193 = c_List_Olist_ONil(_1674191))], (29559 ^ _781013) ^ [_1332363, _1332365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332363)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332365)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1332363), hAPP(c_Int_Onat, _1332365)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332363, _1332365)))], (49132 ^ _781013) ^ [_1777521, _1777523, _1777525, _1777527] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777521, _1777521), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1777523), _1777525)), _1777527) = hAPP(hAPP(c_Relation_Orel__comp(_1777521, _1777521, _1777521), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777521, _1777521), tc_HOL_Obool), _1777523), _1777527)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777521, _1777521), tc_HOL_Obool), _1777525), _1777527)))], (27477 ^ _781013) ^ [_1293513, _1293515] : [-(hAPP(c_Set_OPow(_1293513), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1293513, tc_HOL_Obool)), _1293515)) = hAPP(c_Set_OCollect(tc_fun(_1293513, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1293513, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1293513, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1293513, tc_HOL_Obool), tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1293513, tc_HOL_Obool)), c_COMBS(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1293513, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1293513, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1293513, tc_HOL_Obool), tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_fun(_1293513, tc_HOL_Obool)), tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_fun(_1293513, tc_HOL_Obool)), tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1293513, tc_HOL_Obool)), c_COMBB(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1293513, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1293513, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1293513, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1293513, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1293513, tc_HOL_Obool)), _1293515)), c_Set_OPow(_1293513))))))], (21513 ^ _781013) ^ [_1185180] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185180) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1185180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40946 ^ _781013) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (41456 ^ _781013) ^ [_1598372] : [-(c_List_Olists(_1598372, c_Orderings_Obot__class_Obot(tc_fun(_1598372, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1598372)), c_List_Olist_ONil(_1598372)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1598372), tc_HOL_Obool))))], (10827 ^ _781013) ^ [_972383, _972385, _972387, _972389, _972391] : [class_Groups_Oordered__ab__group__add(_972383), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_972383), _972385), _972387) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_972383), _972389), _972391), 10834 ^ _781013 : [(10841 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972383), _972389), _972391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972383), _972385), _972387)))], (10835 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972383), _972385), _972387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972383), _972389), _972391)))]]], (7855 ^ _781013) ^ [_913373, _913375, _913377, _913379] : [hBOOL(hAPP(hAPP(c_member(_913373), _913375), _913377)), -(hBOOL(hAPP(hAPP(c_member(_913373), _913375), hAPP(hAPP(c_Set_Oinsert(_913373), _913379), _913377))))], (10973 ^ _781013) ^ [_975587, _975589, _975591, _975593, _975595] : [-(hAPP(c_Map_Omap__add(_975587, _975589, _975591, _975593), _975595) = c_Option_Ooption_ONone(_975589)), hAPP(_975593, _975595) = c_Option_Ooption_ONone(_975589), hAPP(_975591, _975595) = c_Option_Ooption_ONone(_975589)], (3928 ^ _781013) ^ [_840446, _840448, _840450, _840452] : [-(c_Random_Opick(_840452, _840448) = c_Random_Opick(_840450, _840446)), _840452 = _840450, _840448 = _840446], (32268 ^ _781013) ^ [_1393374, _1393376, _1393378, _1393380, _1393382, _1393384] : [c_Com_Ocom_OCond(_1393374, _1393376, _1393378) = c_Com_Ocom_OLocal(_1393380, _1393382, _1393384)], (35847 ^ _781013) ^ [_1458702, _1458704] : [-(c_Divides_Odivmod__int__rel(_1458702, _1458704) = 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, _1458702))), 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), _1458704)))))), 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)), _1458704))), 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)), _1458704))))), 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)), _1458704)))), 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), _1458704))), 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))))))))], (27867 ^ _781013) ^ [_1301383, _1301385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301385)), -(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, _1301383, _1301385))))], (8953 ^ _781013) ^ [_937550, _937552] : [class_Lattices_Obounded__lattice__bot(_937550), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_937550), c_Orderings_Obot__class_Obot(_937550)), _937552) = _937552)], (51202 ^ _781013) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (32136 ^ _781013) ^ [_1391116] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1391116))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1391116)) = _1391116)], (7661 ^ _781013) ^ [_909817, _909819, _909821] : [hBOOL(hAPP(hAPP(c_member(_909817), _909819), _909821)), -(hAPP(hAPP(c_Set_Oinsert(_909817), _909819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909817, tc_HOL_Obool)), _909821), hAPP(hAPP(c_Set_Oinsert(_909817), _909819), c_Orderings_Obot__class_Obot(tc_fun(_909817, tc_HOL_Obool))))) = _909821)], (6944 ^ _781013) ^ [_895732, _895734] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895732, tc_HOL_Obool)), _895734), _895734)))], (28520 ^ _781013) ^ [_1313147, _1313149, _1313151, _1313153] : [class_Orderings_Olinorder(_1313147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313147), _1313149), _1313151)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313147), _1313149), _1313153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313147), _1313149), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313147), _1313151), _1313153))))], (34653 ^ _781013) ^ [_1437518, _1437520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1437518)), c_Int_OBit0(_1437520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437518), _1437520)))], (19845 ^ _781013) ^ [_1152731, _1152733, _1152735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152731), _1152733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1152731), _1152735)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1152733), _1152735))))], (32350 ^ _781013) ^ [_1394802, _1394804, _1394806, _1394808, _1394810, _1394812] : [-(c_Com_Ocom_OLocal(_1394802, _1394804, _1394806) = c_Com_Ocom_OLocal(_1394808, _1394810, _1394812)), _1394802 = _1394808, _1394804 = _1394810, _1394806 = _1394812], (4450 ^ _781013) ^ [_848413, _848415, _848417, _848419, _848421, _848423] : [-(c_Relation_Orel__comp(_848423, _848419, _848415) = c_Relation_Orel__comp(_848421, _848417, _848413)), _848423 = _848421, _848419 = _848417, _848415 = _848413], (24314 ^ _781013) ^ [_1234541, _1234543] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1234541, _1234543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1234543)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42549 ^ _781013) ^ [_1623980, _1623982, _1623984] : [class_Lattices_Olattice(_1623980), -(c_Big__Operators_Olattice__class_OSup__fin(_1623980, hAPP(c_List_Oset(_1623980), hAPP(hAPP(c_List_Olist_OCons(_1623980), _1623982), _1623984))) = hAPP(c_List_Ofoldl(_1623980, _1623980, c_Lattices_Osemilattice__sup__class_Osup(_1623980), _1623982), _1623984))], (20869 ^ _781013) ^ [_1171128, _1171130, _1171132] : [-(c_Map_Oran(_1171128, _1171130, _1171132) = hAPP(c_Set_OCollect(_1171130), hAPP(hAPP(c_COMBB(tc_fun(_1171128, tc_HOL_Obool), tc_HOL_Obool, _1171130), c_HOL_OEx(_1171128)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1171130), tc_fun(_1171128, tc_HOL_Obool), _1171130), hAPP(c_COMBC(_1171128, tc_Option_Ooption(_1171130), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1171130), tc_fun(tc_Option_Ooption(_1171130), tc_HOL_Obool), _1171128), c_fequal), _1171132))), c_Option_Ooption_OSome(_1171130)))))], (31078 ^ _781013) ^ [_1362979, _1362981, _1362983] : [31080 ^ _781013 : [(31083 ^ _781013) ^ [] : [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(_1362981, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 31079 ^ [_1362979, _1362981, _1362983]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1362981, 31079 ^ [_1362979, _1362981, _1362983])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31081 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31079 ^ [_1362979, _1362981, _1362983]), _1362979)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1362981, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1362983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1362983), hAPP(_1362981, _1362979))), 31093 ^ _781013 : [(31096 ^ _781013) ^ [] : [-(hAPP(_1362981, 31092 ^ [_1362979, _1362981, _1362983]) = _1362983)], (31094 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 31092 ^ [_1362979, _1362981, _1362983]), _1362979)))]]], (48075 ^ _781013) ^ [_1752389, _1752391] : [-(c_Transitive__Closure_Otrancl(_1752389, _1752391) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1752389, _1752389), tc_HOL_Obool)), _1752391), hAPP(hAPP(c_Relation_Orel__comp(_1752389, _1752389, _1752389), c_Transitive__Closure_Otrancl(_1752389, _1752391)), _1752391)))], (41194 ^ _781013) ^ [_1593124, _1593126, _1593128] : [c_List_Olist_ONil(_1593124) = hAPP(hAPP(c_List_Olist_OCons(_1593124), _1593126), _1593128)], (13409 ^ _781013) ^ [_1026077, _1026079] : [class_Groups_Oone(_1026077), 13412 ^ _781013 : [(13419 ^ _781013) ^ [] : [_1026079 = c_Groups_Oone__class_Oone(_1026077), -(c_Groups_Oone__class_Oone(_1026077) = _1026079)], (13413 ^ _781013) ^ [] : [c_Groups_Oone__class_Oone(_1026077) = _1026079, -(_1026079 = c_Groups_Oone__class_Oone(_1026077))]]], (42194 ^ _781013) ^ [_1616388, _1616390, _1616392, _1616394] : [_1616388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1616390), _1616388), hAPP(hAPP(c_List_Olist_OCons(_1616390), _1616392), _1616394)) = hAPP(hAPP(c_List_Olist_OCons(_1616390), _1616392), _1616394))], (9681 ^ _781013) ^ [_952268, _952270, _952272] : [class_Orderings_Oorder(_952268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952268), _952270), _952272)), _952270 = _952272], (39663 ^ _781013) ^ [_1548902, _1548904, _1548906] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1548902, tc_HOL_Obool)), hAPP(c_List_Oset(_1548902), hAPP(hAPP(c_List_Otake(_1548902), _1548904), _1548906))), hAPP(c_List_Oset(_1548902), _1548906))))], (21623 ^ _781013) ^ [_1187087, _1187089, _1187091] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187087)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187089)), _1187091)) = 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), _1187087), _1187089))), _1187091))], (8787 ^ _781013) ^ [_934713, _934715, _934717] : [class_Lattices_Osemilattice__sup(_934713), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934713), _934715), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934713), _934717), _934715))))], (26521 ^ _781013) ^ [_1274573, _1274575, _1274577, _1274579] : [class_Orderings_Olinorder(_1274573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274573), _1274575), _1274577)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274573), _1274577), _1274579)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274573, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1274573, _1274575, _1274577)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1274573, _1274577, _1274579)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1274573, _1274575), _1274579))], (44212 ^ _781013) ^ [_1661698] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1661698)), c_List_Otranspose__rel(_1661698)), c_List_Olist_ONil(tc_List_Olist(_1661698)))), -(c_List_Otranspose(_1661698, c_List_Olist_ONil(tc_List_Olist(_1661698))) = c_List_Olist_ONil(tc_List_Olist(_1661698)))], (42791 ^ _781013) ^ [_1628779, _1628781, _1628783, _1628785, _1628787, _1628789] : [hBOOL(hAPP(hAPP(c_member(_1628779), _1628781), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628783, tc_fun(_1628779, tc_HOL_Obool)), _1628785), _1628787))), -(hBOOL(hAPP(hAPP(c_member(_1628779), _1628781), hAPP(_1628787, _1628789)))), hBOOL(hAPP(hAPP(c_member(_1628783), _1628789), _1628785))], (34983 ^ _781013) ^ [_1443453, _1443455] : [class_Rings_Oring__1__no__zero__divisors(_1443453), 34986 ^ _781013 : [(34993 ^ _781013) ^ [] : [_1443455 = c_Groups_Ozero__class_Ozero(_1443453), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1443453), _1443455), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1443453))], (34987 ^ _781013) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1443453), _1443455), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1443453), -(_1443455 = c_Groups_Ozero__class_Ozero(_1443453))]]], (35595 ^ _781013) ^ [_1454710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1454710)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1454710), c_Int_OMin)))], (4490 ^ _781013) ^ [_849017, _849019, _849021, _849023, _849025, _849027] : [-(c_Nitpick_Otimes__frac(_849027, _849023, _849019) = c_Nitpick_Otimes__frac(_849025, _849021, _849017)), _849027 = _849025, _849023 = _849021, _849019 = _849017], (2576 ^ _781013) ^ [_819232, _819234, _819236, _819238] : [-(c_Divides_Opdivmod(_819238, _819234) = c_Divides_Opdivmod(_819236, _819232)), _819238 = _819236, _819234 = _819232], (42368 ^ _781013) ^ [_1620202, _1620204, _1620206] : [hAPP(c_List_Orotate(_1620202, _1620204), _1620206) = c_List_Olist_ONil(_1620202), -(_1620206 = c_List_Olist_ONil(_1620202))], (38914 ^ _781013) ^ [_1530926, _1530928, _1530930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530926), _1530928)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1530926)), hAPP(c_Set_OCollect(tc_List_Olist(_1530926)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1530926), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1530926)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1530926), tc_fun(_1530926, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1530926, tc_HOL_Obool), tc_fun(tc_fun(_1530926, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1530926)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1530926, tc_HOL_Obool))), c_List_Oset(_1530926))), _1530928))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1530926), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1530926)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1530926)))), _1530930))))))], (8426 ^ _781013) ^ [_926257, _926259, _926261, _926263] : [c_Orderings_Obot__class_Obot(tc_fun(_926257, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_926259, _926257, _926261), _926263), -(_926263 = c_Orderings_Obot__class_Obot(tc_fun(_926259, tc_HOL_Obool)))], (30973 ^ _781013) ^ [_1360843, _1360845, _1360847] : [class_Orderings_Olinorder(_1360843), hAPP(_1360845, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1360843), 30978 ^ [_1360843, _1360845, _1360847]), 30979 ^ [_1360843, _1360845, _1360847])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1360843), hAPP(_1360845, 30978 ^ [_1360843, _1360845, _1360847])), hAPP(_1360845, 30979 ^ [_1360843, _1360845, _1360847])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360843), _1360847)), -(_1360847 = c_Orderings_Obot__class_Obot(tc_fun(_1360843, tc_HOL_Obool))), -(hAPP(_1360845, c_Big__Operators_Olattice_OInf__fin(_1360843, c_Orderings_Oord__class_Omin(_1360843), _1360847)) = c_Big__Operators_Olattice_OInf__fin(_1360843, c_Orderings_Oord__class_Omin(_1360843), hAPP(c_Set_Oimage(_1360843, _1360843, _1360845), _1360847)))], (46324 ^ _781013) ^ [_1708676, _1708678, _1708680, _1708682, _1708684] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1708676, _1708678)), _1708680), hAPP(hAPP(c_Product__Type_OSigma(_1708676, _1708678), _1708682), _1708684))), 46328 ^ _781013 : [(46334 ^ _781013) ^ [] : [-(_1708680 = hAPP(hAPP(c_Product__Type_OPair(_1708676, _1708678), 46327 ^ [_1708676, _1708678, _1708680, _1708682, _1708684]), 46330 ^ [_1708676, _1708678, _1708680, _1708682, _1708684]))], (46332 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1708678), 46330 ^ [_1708676, _1708678, _1708680, _1708682, _1708684]), hAPP(_1708684, 46327 ^ [_1708676, _1708678, _1708680, _1708682, _1708684]))))], (46329 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1708676), 46327 ^ [_1708676, _1708678, _1708680, _1708682, _1708684]), _1708682)))]]], (41524 ^ _781013) ^ [_1600090, _1600092, _1600094, _1600096, _1600098] : [-(hAPP(hAPP(c_List_Ozip(_1600090, _1600092), _1600094), hAPP(hAPP(c_List_Olist_OCons(_1600092), _1600096), _1600098)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1600090, _1600092)), _1600090, c_List_Olist_ONil(tc_prod(_1600090, _1600092)), hAPP(hAPP(c_COMBC(_1600090, tc_fun(tc_List_Olist(_1600090), tc_List_Olist(tc_prod(_1600090, _1600092))), tc_fun(tc_List_Olist(_1600090), tc_List_Olist(tc_prod(_1600090, _1600092)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1600090, _1600092)), tc_List_Olist(tc_prod(_1600090, _1600092))), tc_fun(tc_fun(tc_List_Olist(_1600090), tc_List_Olist(tc_prod(_1600090, _1600092))), tc_fun(tc_List_Olist(_1600090), tc_List_Olist(tc_prod(_1600090, _1600092)))), _1600090), c_COMBB(tc_List_Olist(tc_prod(_1600090, _1600092)), tc_List_Olist(tc_prod(_1600090, _1600092)), tc_List_Olist(_1600090))), hAPP(hAPP(c_COMBB(tc_prod(_1600090, _1600092), tc_fun(tc_List_Olist(tc_prod(_1600090, _1600092)), tc_List_Olist(tc_prod(_1600090, _1600092))), _1600090), c_List_Olist_OCons(tc_prod(_1600090, _1600092))), hAPP(hAPP(c_COMBC(_1600090, _1600092, tc_prod(_1600090, _1600092)), c_Product__Type_OPair(_1600090, _1600092)), _1600096)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1600090), tc_List_Olist(_1600092), tc_List_Olist(tc_prod(_1600090, _1600092))), c_List_Ozip(_1600090, _1600092)), _1600098))), _1600094))], (44379 ^ _781013) ^ [_1665417, _1665419] : [c_List_Oconcat(_1665417, _1665419) = c_List_Olist_ONil(_1665417), 44382 ^ _781013 : [(44383 ^ _781013) ^ [_1665508] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665417)), _1665508), hAPP(c_List_Oset(tc_List_Olist(_1665417)), _1665419))), -(_1665508 = c_List_Olist_ONil(_1665417))]]], (38039 ^ _781013) ^ [_1509744] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1509744)), -(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))), _1509744)), c_FunDef_Omax__weak)))], (10489 ^ _781013) ^ [_967087, _967089, _967091] : [class_Orderings_Oorder(_967087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967087), _967089), _967091)), -(_967091 = _967089), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967087), _967089), _967091)))], (6312 ^ _781013) ^ [_883744, _883746, _883748] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_883744), hAPP(hAPP(c_Set_Oinsert(_883744), _883746), _883748))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_883744), _883748)))], (47285 ^ _781013) ^ [_1734313, _1734315] : [c_Wellfounded_OwfP(_1734313, _1734315), -(c_Wellfounded_Owf(_1734313, hAPP(c_Set_OCollect(tc_prod(_1734313, _1734313)), hAPP(c_Product__Type_Oprod_Oprod__case(_1734313, _1734313, tc_HOL_Obool), _1734315))))], (24290 ^ _781013) ^ [_1234074, _1234076, _1234078, _1234080] : [class_Orderings_Olinorder(_1234074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234074), _1234076), _1234078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234074), _1234078), _1234080)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234074, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1234074, _1234076, _1234078)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1234074, _1234078, _1234080)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1234074, _1234076, _1234080))], (51620 ^ _781013) ^ [_1824981, _1824983] : [_1824981 = _1824983, -(hBOOL(hAPP(hAPP(c_fequal, _1824981), _1824983)))], (25964 ^ _781013) ^ [_1263800, _1263802] : [class_Rings_Olinordered__idom(_1263800), 25967 ^ _781013 : [(25974 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1263802), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263800), hAPP(c_Int_Oring__1__class_Oof__int(_1263800), _1263802)), c_Groups_Ozero__class_Ozero(_1263800))))], (25968 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263800), hAPP(c_Int_Oring__1__class_Oof__int(_1263800), _1263802)), c_Groups_Ozero__class_Ozero(_1263800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1263802), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (28418 ^ _781013) ^ [_1311315, _1311317, _1311319, _1311321] : [class_Groups_Oordered__ab__group__add__abs(_1311315), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311315), hAPP(c_Groups_Oabs__class_Oabs(_1311315), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1311317, _1311315), _1311319), _1311321))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1311317, _1311315), hAPP(hAPP(c_COMBB(_1311315, _1311315, _1311317), c_Groups_Oabs__class_Oabs(_1311315)), _1311319)), _1311321))))], (35059 ^ _781013) ^ [_1444691, _1444693] : [class_Rings_Olinordered__idom(_1444691), -(hAPP(c_Groups_Oabs__class_Oabs(_1444691), hAPP(hAPP(c_Power_Opower__class_Opower(_1444691), _1444693), 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(_1444691), _1444693), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (6438 ^ _781013) ^ [_886162, _886164, _886166, _886168, _886170, _886172, _886174, _886176] : [c_Finite__Set_Ofolding__image__simple__idem(_886162, _886164, _886166, _886168, _886170, _886172), hBOOL(hAPP(c_Finite__Set_Ofinite(_886164), _886174)), -(hAPP(_886172, hAPP(hAPP(c_Set_Oinsert(_886164), _886176), _886174)) = hAPP(hAPP(_886166, hAPP(_886170, _886176)), hAPP(_886172, _886174)))], (1574 ^ _781013) ^ [_803430, _803432] : [-(class_Groups_Ocomm__monoid__mult(_803430)), _803432 = _803430, class_Groups_Ocomm__monoid__mult(_803432)], (26511 ^ _781013) ^ [_1274364, _1274366, _1274368] : [class_Orderings_Olinorder(_1274364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274364), _1274366), _1274368)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274364, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1274364), _1274366), c_Orderings_Obot__class_Obot(tc_fun(_1274364, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1274364, _1274366, _1274368)) = c_SetInterval_Oord__class_OatLeastAtMost(_1274364, _1274366, _1274368))], (28442 ^ _781013) ^ [_1311831, _1311833, _1311835] : [class_Orderings_Olinorder(_1311831), 28445 ^ _781013 : [(28452 ^ _781013) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311831), _1311833), _1311835) = _1311833, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311831), _1311833), _1311835)))], (28446 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311831), _1311833), _1311835)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311831), _1311833), _1311835) = _1311833)]]], (23405 ^ _781013) ^ [_1218828, _1218830, _1218832] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_1218828, _1218830, _1218832)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1218830)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1218832))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49756 ^ _781013) ^ [_1792480, _1792482, _1792484, _1792486, _1792488] : [c_Finite__Set_Ofolding__one(_1792480, _1792482, _1792484), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792480), _1792486)), -(hBOOL(hAPP(hAPP(c_member(_1792480), _1792488), _1792486))), -(hAPP(_1792484, hAPP(hAPP(c_Set_Oinsert(_1792480), _1792488), _1792486)) = hAPP(hAPP(c_Finite__Set_Ofold(_1792480, _1792480, _1792482), _1792488), _1792486))], (35497 ^ _781013) ^ [_1453291] : [c_Int_OBit0(_1453291) = c_Int_OMin], (42023 ^ _781013) ^ [_1612031, _1612033, _1612035, _1612037, _1612039, _1612041] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612031), tc_List_Olist(_1612031))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612031), tc_List_Olist(_1612031)), hAPP(hAPP(c_List_Oappend(_1612031), _1612033), hAPP(hAPP(c_List_Olist_OCons(_1612031), _1612035), c_List_Olist_ONil(_1612031)))), hAPP(hAPP(c_List_Oappend(_1612031), _1612037), hAPP(hAPP(c_List_Olist_OCons(_1612031), _1612039), c_List_Olist_ONil(_1612031))))), c_List_Olistrel1(_1612031, _1612041)))), 42024 ^ _781013 : [(42031 ^ _781013) ^ [] : [_1612033 = _1612037, hBOOL(hAPP(hAPP(c_member(tc_prod(_1612031, _1612031)), hAPP(hAPP(c_Product__Type_OPair(_1612031, _1612031), _1612035), _1612039)), _1612041))], (42025 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612031), tc_List_Olist(_1612031))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612031), tc_List_Olist(_1612031)), _1612033), _1612037)), c_List_Olistrel1(_1612031, _1612041))), _1612035 = _1612039]]], (32374 ^ _781013) ^ [_1395249, _1395251, _1395253, _1395255, _1395257] : [c_Com_Ocom_OWhile(_1395249, _1395251) = c_Com_Ocom_OLocal(_1395253, _1395255, _1395257)], (23823 ^ _781013) ^ [_1226123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226123), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1226123) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26341 ^ _781013) ^ [_1270921, _1270923, _1270925, _1270927, _1270929] : [class_Orderings_Oorder(_1270921), 26344 ^ _781013 : [(26365 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1270921, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1270921, _1270923, _1270925)), c_SetInterval_Oord__class_OatLeastAtMost(_1270921, _1270927, _1270929)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270921), _1270927), _1270929)), 26368 ^ _781013 : [(26371 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270921), _1270927), _1270923)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270921), _1270925), _1270929)), 26378 ^ _781013 : [(26381 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270921), _1270925), _1270929))], (26379 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270921), _1270927), _1270923))]]], (26369 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270921), _1270923), _1270925)))]]], (26345 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1270921, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1270921, _1270923, _1270925)), c_SetInterval_Oord__class_OatLeastAtMost(_1270921, _1270927, _1270929))), 26348 ^ _781013 : [(26349 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270921), _1270923), _1270925)), 26352 ^ _781013 : [(26357 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270921), _1270927), _1270923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270921), _1270925), _1270929)))], (26355 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270921), _1270925), _1270929)))], (26353 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270921), _1270927), _1270923)))]]], (26363 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270921), _1270927), _1270929)))]]]]], (50846 ^ _781013) ^ [_1814775, _1814777, _1814779, _1814781, _1814783] : [-(c_Predicate_Oconversep(_1814775, _1814777, c_Predicate_Opred__comp(_1814775, _1814779, _1814777, _1814781, _1814783)) = c_Predicate_Opred__comp(_1814777, _1814779, _1814775, c_Predicate_Oconversep(_1814779, _1814777, _1814783), c_Predicate_Oconversep(_1814775, _1814779, _1814781)))], (11049 ^ _781013) ^ [_977416, _977418, _977420, _977422] : [-(hBOOL(hAPP(hAPP(c_member(_977416), _977418), _977420))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977416, tc_HOL_Obool)), _977420), hAPP(hAPP(c_Set_Oinsert(_977416), _977418), _977422)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977416, tc_HOL_Obool)), _977420), _977422))], (22544 ^ _781013) ^ [_1203134, _1203136, _1203138, _1203140] : [class_Orderings_Olinorder(_1203134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203134), _1203136), _1203138)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1203134, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203134, _1203136), _1203140)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203134, _1203136), _1203138)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203134, _1203138), _1203140))], (43155 ^ _781013) ^ [_1639648, _1639650, _1639652, _1639654, _1639656] : [_1639648 = c_Orderings_Obot__class_Obot(tc_fun(_1639650, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1639652, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639650, tc_fun(_1639652, tc_HOL_Obool)), _1639648), _1639654)), _1639656) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1639652, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1639652, tc_HOL_Obool))), _1639656))], (30415 ^ _781013) ^ [_1349336, _1349338, _1349340, _1349342, _1349344] : [class_Orderings_Olinorder(_1349336), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349336, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1349336, _1349338, _1349340)), c_SetInterval_Oord__class_OatLeastAtMost(_1349336, _1349342, _1349344)) = c_SetInterval_Oord__class_OatLeastAtMost(_1349336, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349336), _1349338), _1349342), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349336), _1349340), _1349344)))], (32764 ^ _781013) ^ [_1402534, _1402536, _1402538, _1402540] : [class_Fields_Olinordered__field__inverse__zero(_1402534), class_Int_Onumber(_1402534), 32771 ^ _781013 : [(32772 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), _1402536), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1402534), _1402538), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540)))), 32775 ^ _781013 : [(32782 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), c_Groups_Ozero__class_Ozero(_1402534)), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540)))), 32785 ^ _781013 : [(32792 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540)), c_Groups_Ozero__class_Ozero(_1402534)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), _1402536), c_Groups_Ozero__class_Ozero(_1402534))))], (32786 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540)), c_Groups_Ozero__class_Ozero(_1402534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), _1402538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402534), _1402536), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540)))))]]], (32776 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), c_Groups_Ozero__class_Ozero(_1402534)), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402534), _1402536), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540))), _1402538)))]]], (32798 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), _1402536), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1402534), _1402538), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540))))), 32801 ^ _781013 : [(32804 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402534), _1402536), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540))), _1402538))], (32802 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), c_Groups_Ozero__class_Ozero(_1402534)), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540))))]], 32805 ^ _781013 : [(32808 ^ _781013) ^ [] : [32809 ^ _781013 : [(32812 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), _1402538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402534), _1402536), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540))))], (32810 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540)), c_Groups_Ozero__class_Ozero(_1402534))))]], 32813 ^ _781013 : [(32816 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), _1402536), c_Groups_Ozero__class_Ozero(_1402534)))], (32814 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540)), c_Groups_Ozero__class_Ozero(_1402534)))]]], (32806 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402534), c_Groups_Ozero__class_Ozero(_1402534)), hAPP(c_Int_Onumber__class_Onumber__of(_1402534), _1402540)))]]]]], (46847 ^ _781013) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (21718 ^ _781013) ^ [_1188806, _1188808, _1188810] : [class_Rings_Olinordered__semidom(_1188806), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188806), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188806), _1188808)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188806), _1188810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1188808), _1188810)))], (41704 ^ _781013) ^ [_1604068, _1604070] : [-(hAPP(hAPP(c_List_Oappend(_1604068), _1604070), c_List_Olist_ONil(_1604068)) = _1604070)], (51606 ^ _781013) ^ [_1824695, _1824697, _1824699, _1824701] : [-(hAPP(hAPP(c_COMBK(_1824695, _1824697), _1824699), _1824701) = _1824699)], (7743 ^ _781013) ^ [_911479, _911481] : [class_Orderings_Obot(_911479), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911479), c_Orderings_Obot__class_Obot(_911479)), _911481)))], (9373 ^ _781013) ^ [_947277, _947279, _947281] : [9374 ^ _781013 : [(9377 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_947277), _947281))], (9375 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_947277), _947279))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_947277), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947277, tc_HOL_Obool)), _947279), _947281))))], (14233 ^ _781013) ^ [_1043639, _1043641, _1043643, _1043645, _1043647, _1043649] : [class_Rings_Oordered__ring(_1043639), 14236 ^ _781013 : [(14243 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043639), _1043645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043639), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043639), _1043647), _1043641)), _1043643)), _1043649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043639), _1043641), _1043643)), _1043645)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043639), _1043647), _1043643)), _1043649))))], (14237 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043639), _1043641), _1043643)), _1043645)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043639), _1043647), _1043643)), _1043649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043639), _1043645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043639), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043639), _1043647), _1043641)), _1043643)), _1043649))))]]], (47175 ^ _781013) ^ [_1731062, _1731064, _1731066, _1731068, _1731070] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1731062, _1731064)), hAPP(hAPP(c_Product__Type_OPair(_1731062, _1731064), _1731066), _1731068)), _1731070)), -(hBOOL(hAPP(hAPP(c_member(_1731062), _1731066), hAPP(c_Relation_ODomain(_1731062, _1731064), _1731070))))], (37862 ^ _781013) ^ [_1505928, _1505930, _1505932, _1505934, _1505936, _1505938, _1505940] : [-(hAPP(c_Product__Type_Oapsnd(_1505928, _1505930, _1505932, _1505934), hAPP(c_Product__Type_Oapfst(_1505936, _1505932, _1505928, _1505938), _1505940)) = hAPP(hAPP(c_Product__Type_OPair(_1505932, _1505930), hAPP(_1505938, hAPP(c_Product__Type_Ofst(_1505936, _1505928), _1505940))), hAPP(_1505934, hAPP(c_Product__Type_Osnd(_1505936, _1505928), _1505940))))], (20231 ^ _781013) ^ [_1159299, _1159301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159299), hAPP(c_Nat_OSuc, _1159301))), -(_1159299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20239 ^ _781013 : [(20242 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20238 ^ [_1159299, _1159301]), _1159301)))], (20240 ^ _781013) ^ [] : [-(_1159299 = hAPP(c_Nat_OSuc, 20238 ^ [_1159299, _1159301]))]]], (35543 ^ _781013) ^ [_1453884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1453884)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1453884), c_Int_OMin)))], (36416 ^ _781013) ^ [_1475615, _1475617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1475615), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1475617, _1475615) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1475617), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1475615)))], (1784 ^ _781013) ^ [_806055, _806057] : [-(class_Groups_Ominus(_806055)), _806057 = _806055, class_Groups_Ominus(_806057)], (25814 ^ _781013) ^ [_1261184, _1261186] : [class_Int_Oring__char__0(_1261184), 25817 ^ _781013 : [(25824 ^ _781013) ^ [] : [_1261186 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1261184), _1261186) = c_Groups_Ozero__class_Ozero(_1261184))], (25818 ^ _781013) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1261184), _1261186) = c_Groups_Ozero__class_Ozero(_1261184), -(_1261186 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (662 ^ _781013) ^ [_791154, _791156, _791158, _791160, _791162, _791164, _791166, _791168, _791170, _791172] : [-(c_Typedef_Otype__definition(_791170, _791166, _791162, _791158, _791154)), c_Typedef_Otype__definition(_791172, _791168, _791164, _791160, _791156), _791172 = _791170, _791168 = _791166, _791164 = _791162, _791160 = _791158, _791156 = _791154], (48065 ^ _781013) ^ [_1752174, _1752176, _1752178, _1752180] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1752174, _1752174)), _1752176), c_Transitive__Closure_Otrancl(_1752174, _1752178))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1752174, _1752174), tc_HOL_Obool)), _1752178), _1752180)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1752174, _1752174)), _1752176), c_Transitive__Closure_Otrancl(_1752174, _1752180))))], (15163 ^ _781013) ^ [_1061529, _1061531, _1061533] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1061529), _1061531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1061529), _1061531)), hAPP(c_Finite__Set_Ocard(_1061529), hAPP(hAPP(c_Set_Oinsert(_1061529), _1061533), _1061531)))))], (23951 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35715 ^ _781013) ^ [_1456548] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1456548)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1456548)))], (11616 ^ _781013) ^ [_990038, _990040, _990042, _990044] : [c_Fun_Oinj__on(_990038, _990040, _990042, c_Orderings_Otop__class_Otop(tc_fun(_990038, tc_HOL_Obool))), -(c_Fun_Oinj__on(_990038, tc_fun(_990044, _990040), hAPP(hAPP(c_COMBB(_990040, tc_fun(_990044, _990040), _990038), c_COMBK(_990040, _990044)), _990042), c_Orderings_Otop__class_Otop(tc_fun(_990038, tc_HOL_Obool))))], (22188 ^ _781013) ^ [_1197154, _1197156] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197154) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197156), -(_1197154 = _1197156)], (47034 ^ _781013) ^ [_1727465] : [-(c_Nitpick_Ozero__frac(_1727465) = c_Nitpick_OAbs__Frac(_1727465, 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))))], (1972 ^ _781013) ^ [_809616, _809618, _809620, _809622, _809624, _809626] : [-(c_Partial__Function_Oflat__lub(_809626, _809622, _809618) = c_Partial__Function_Oflat__lub(_809624, _809620, _809616)), _809626 = _809624, _809622 = _809620, _809618 = _809616], (33284 ^ _781013) ^ [_1412890] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1412890))), -(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), _1412890)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34125 ^ _781013) ^ [_1428269] : [class_Int_Onumber__ring(_1428269), -(c_Int_Oiszero(_1428269, hAPP(c_Int_Onumber__class_Onumber__of(_1428269), c_Int_OPls)))], (51402 ^ _781013) ^ [_1822466] : [class_Lazy__Sequence_Osmall__lazy(_1822466), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1822466)))], (32394 ^ _781013) ^ [_1395586, _1395588, _1395590] : [class_Int_Onumber(_1395586), class_Orderings_Olinorder(_1395586), 32401 ^ _781013 : [(32408 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395586), hAPP(c_Int_Onumber__class_Onumber__of(_1395586), _1395590)), hAPP(c_Int_Onumber__class_Onumber__of(_1395586), _1395588)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395586), hAPP(c_Int_Onumber__class_Onumber__of(_1395586), _1395588)), hAPP(c_Int_Onumber__class_Onumber__of(_1395586), _1395590))))], (32402 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395586), hAPP(c_Int_Onumber__class_Onumber__of(_1395586), _1395588)), hAPP(c_Int_Onumber__class_Onumber__of(_1395586), _1395590))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395586), hAPP(c_Int_Onumber__class_Onumber__of(_1395586), _1395590)), hAPP(c_Int_Onumber__class_Onumber__of(_1395586), _1395588)))]]], (51222 ^ _781013) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (40377 ^ _781013) ^ [_1568805, _1568807, _1568809, _1568811] : [_1568805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1568807), hAPP(hAPP(c_List_Olist_OCons(_1568807), _1568809), _1568811)), _1568805) = _1568809)], (4378 ^ _781013) ^ [_847263, _847265, _847267, _847269, _847271, _847273, _847275, _847277, _847279, _847281] : [-(c_Finite__Set_Ofold__graph(_847281, _847277, _847273, _847269, _847265) = c_Finite__Set_Ofold__graph(_847279, _847275, _847271, _847267, _847263)), _847281 = _847279, _847277 = _847275, _847273 = _847271, _847269 = _847267, _847265 = _847263], (42585 ^ _781013) ^ [_1624766, _1624768, _1624770, _1624772] : [class_Complete__Lattice_Ocomplete__lattice(_1624766), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1624768, _1624766), hAPP(c_List_Oset(_1624768), _1624770)), _1624772) = hAPP(c_List_Ofoldl(_1624766, _1624768, hAPP(c_COMBC(_1624768, _1624766, _1624766), hAPP(hAPP(c_COMBB(_1624766, tc_fun(_1624766, _1624766), _1624768), c_Lattices_Osemilattice__sup__class_Osup(_1624766)), _1624772)), c_Orderings_Obot__class_Obot(_1624766)), _1624770))], (49235 ^ _781013) ^ [_1780372, _1780374] : [-(c_Transitive__Closure_Ortrancl(_1780372, _1780374) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1780372, _1780372), 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(_1780372, _1780372), tc_HOL_Obool), tc_fun(tc_prod(_1780372, _1780372), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1780372, _1780372), tc_HOL_Obool)), _1780374)))], (51286 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (22059 ^ _781013) ^ [_1194670, _1194672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1194670, _1194672))))], (24089 ^ _781013) ^ [_1230340, _1230342] : [24090 ^ _781013 : [(24093 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230342))], (24091 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230340))]], 24094 ^ _781013 : [(24101 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230340), _1230342)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1230340)), hAPP(c_Int_Onat, _1230342))))], (24095 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1230340)), hAPP(c_Int_Onat, _1230342))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230340), _1230342)))]]], (18496 ^ _781013) ^ [_1125226, _1125228] : [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), _1125226), _1125228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125228), _1125226)))], (33568 ^ _781013) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37341 ^ _781013) ^ [_1493715, _1493717, _1493719, _1493721, _1493723] : [-(hAPP(c_Product__Type_Osnd(_1493715, _1493717), hAPP(c_Product__Type_Oapsnd(_1493719, _1493717, _1493715, _1493721), _1493723)) = hAPP(_1493721, hAPP(c_Product__Type_Osnd(_1493715, _1493719), _1493723)))], (13064 ^ _781013) ^ [_1018608, _1018610] : [class_Lattices_Olattice(_1018608), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018608), _1018610)), -(c_Big__Operators_Olattice__class_OSup__fin(_1018608, _1018610) = hAPP(c_Finite__Set_Ofold1(_1018608, c_Lattices_Osemilattice__sup__class_Osup(_1018608)), _1018610))], (8991 ^ _781013) ^ [_938437, _938439, _938441, _938443, _938445, _938447, _938449, _938451, _938453] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_938437), _938439)), 8997 ^ _781013 : [(9000 ^ _781013) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_938441, _938443, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_938441)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_938441), hAPP(_938451, 8996 ^ [_938437, _938439, _938441, _938443, _938445, _938447, _938449, _938451, _938453])), hAPP(_938447, 8996 ^ [_938437, _938439, _938441, _938443, _938445, _938447, _938449, _938451, _938453])), hAPP(_938453, 8996 ^ [_938437, _938439, _938441, _938443, _938445, _938447, _938449, _938451, _938453]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_938441), tc_HOL_Obool))))], (8998 ^ _781013) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_938441, _938443, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_938441)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_938441), hAPP(_938445, 8996 ^ [_938437, _938439, _938441, _938443, _938445, _938447, _938449, _938451, _938453])), hAPP(_938447, 8996 ^ [_938437, _938439, _938441, _938443, _938445, _938447, _938449, _938451, _938453])), hAPP(_938449, 8996 ^ [_938437, _938439, _938441, _938443, _938445, _938447, _938449, _938451, _938453]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_938441), tc_HOL_Obool)))))]], c_Hoare__Mirabelle_Ohoare__derivs(_938441, _938443, hAPP(c_Set_Oimage(_938437, tc_Hoare__Mirabelle_Otriple(_938441), hAPP(hAPP(c_COMBS(_938437, tc_fun(_938441, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_938441)), hAPP(hAPP(c_COMBS(_938437, tc_Com_Ocom, tc_fun(tc_fun(_938441, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_938441))), hAPP(hAPP(c_COMBB(tc_fun(_938441, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_938441, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_938441))), _938437), c_Hoare__Mirabelle_Otriple_Otriple(_938441)), _938445)), _938447)), _938449)), _938439)), -(c_Hoare__Mirabelle_Ohoare__derivs(_938441, _938443, hAPP(c_Set_Oimage(_938437, tc_Hoare__Mirabelle_Otriple(_938441), hAPP(hAPP(c_COMBS(_938437, tc_fun(_938441, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_938441)), hAPP(hAPP(c_COMBS(_938437, tc_Com_Ocom, tc_fun(tc_fun(_938441, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_938441))), hAPP(hAPP(c_COMBB(tc_fun(_938441, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_938441, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_938441))), _938437), c_Hoare__Mirabelle_Otriple_Otriple(_938441)), _938451)), _938447)), _938453)), _938439)))], (39920 ^ _781013) ^ [_1557806, _1557808, _1557810] : [hBOOL(hAPP(hAPP(c_member(_1557808), _1557806), c_Orderings_Obot__class_Obot(tc_fun(_1557808, tc_HOL_Obool)))), -(hBOOL(hAPP(_1557810, _1557806)))], (35641 ^ _781013) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (4400 ^ _781013) ^ [_847652, _847654] : [_847654 = _847652, -(c_Orderings_Oord__class_Omax(_847654) = c_Orderings_Oord__class_Omax(_847652))], (12760 ^ _781013) ^ [_1011957, _1011959, _1011961, _1011963] : [c_Fun_Oinj__on(_1011957, _1011959, _1011961, c_Orderings_Otop__class_Otop(tc_fun(_1011957, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1011957, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1011957, _1011959, _1011961), hAPP(hAPP(c_Set_Oinsert(_1011959), _1011963), c_Orderings_Obot__class_Obot(tc_fun(_1011959, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1011957), c_HOL_OThe(_1011957, hAPP(hAPP(c_COMBC(_1011957, _1011959, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1011959, tc_fun(_1011959, tc_HOL_Obool), _1011957), c_fequal), _1011961)), _1011963))), c_Orderings_Obot__class_Obot(tc_fun(_1011957, tc_HOL_Obool))))))], (6310 ^ _781013) ^ [_883694] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_883694), c_Orderings_Obot__class_Obot(tc_fun(_883694, tc_HOL_Obool)))))], (50802 ^ _781013) ^ [_1813567, _1813569] : [-(hAPP(c_New__DSequence_Opos__empty(_1813567), _1813569) = c_Lazy__Sequence_Oempty(_1813567))], (17417 ^ _781013) ^ [_1106609] : [-(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)), _1106609)))))], (27417 ^ _781013) ^ [_1292000] : [-(hAPP(c_Set_OPow(_1292000), c_Orderings_Obot__class_Obot(tc_fun(_1292000, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1292000, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1292000, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1292000, tc_HOL_Obool), tc_HOL_Obool))))], (35377 ^ _781013) ^ [_1450469, _1450471, _1450473] : [class_Int_Onumber__ring(_1450469), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1450469), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1450469), _1450471), _1450473)), 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(_1450469), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450469), hAPP(hAPP(c_Power_Opower__class_Opower(_1450469), _1450471), 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(_1450469), _1450473), 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(_1450469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1450469), hAPP(c_Int_Onumber__class_Onumber__of(_1450469), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1450471)), _1450473)))], (32546 ^ _781013) ^ [_1398601, _1398603, _1398605, _1398607] : [class_Int_Onumber__ring(_1398601), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1398601), hAPP(c_Int_Onumber__class_Onumber__of(_1398601), _1398603)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1398601), hAPP(c_Int_Onumber__class_Onumber__of(_1398601), _1398605)), _1398607)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1398601), hAPP(c_Int_Onumber__class_Onumber__of(_1398601), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1398603), _1398605))), _1398607))], (7815 ^ _781013) ^ [_912667, _912669, _912671] : [-(hBOOL(hAPP(hAPP(c_member(_912667), _912669), hAPP(hAPP(c_Set_Oinsert(_912667), _912669), _912671))))], (50040 ^ _781013) ^ [_1797790, _1797792, _1797794, _1797796] : [class_Orderings_Olinorder(_1797790), hBOOL(hAPP(c_Finite__Set_Ofinite(_1797790), _1797792)), 50050 ^ _781013 : [(50053 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1797790), 50049 ^ [_1797790, _1797792, _1797794, _1797796]), _1797794))], (50051 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797790), 50049 ^ [_1797790, _1797792, _1797794, _1797796]), _1797792)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1797790), hAPP(hAPP(c_Finite__Set_Ofold(_1797790, _1797790, c_Orderings_Oord__class_Omax(_1797790)), _1797796), _1797792)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1797790), _1797794), _1797796))))], (48511 ^ _781013) ^ [_1761858, _1761860] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1761858, _1761858, _1761858), c_Transitive__Closure_Ortrancl(_1761858, _1761860)), c_Transitive__Closure_Ortrancl(_1761858, _1761860)) = c_Transitive__Closure_Ortrancl(_1761858, _1761860))], (48910 ^ _781013) ^ [_1772132, _1772134, _1772136, _1772138] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1772132, _1772132)), hAPP(hAPP(c_Product__Type_OPair(_1772132, _1772132), _1772136), _1772138)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1772132, _1772132), tc_HOL_Obool)), _1772134), c_Relation_OId(_1772132)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1772132, tc_fun(_1772132, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1772132, tc_fun(tc_prod(_1772132, _1772132), tc_HOL_Obool), tc_fun(_1772132, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1772132, tc_fun(tc_fun(tc_prod(_1772132, _1772132), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1772132, _1772132), tc_HOL_Obool), tc_fun(_1772132, tc_HOL_Obool)), _1772132), c_COMBC(_1772132, tc_fun(tc_prod(_1772132, _1772132), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1772132, tc_prod(_1772132, _1772132)), tc_fun(_1772132, tc_fun(tc_fun(tc_prod(_1772132, _1772132), tc_HOL_Obool), tc_HOL_Obool)), _1772132), hAPP(c_COMBB(tc_prod(_1772132, _1772132), tc_fun(tc_fun(tc_prod(_1772132, _1772132), tc_HOL_Obool), tc_HOL_Obool), _1772132), c_member(tc_prod(_1772132, _1772132)))), c_Product__Type_OPair(_1772132, _1772132)))), _1772134)), c_fequal), _1772136), _1772138)))], (23769 ^ _781013) ^ [_1225275, _1225277, _1225279] : [class_Orderings_Oorder(_1225275), 23772 ^ _781013 : [(23779 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225275), _1225277), _1225279))), -(c_Orderings_Obot__class_Obot(tc_fun(_1225275, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1225275, _1225277, _1225279))], (23773 ^ _781013) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1225275, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1225275, _1225277, _1225279), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225275), _1225277), _1225279))]]], (6635 ^ _781013) ^ [_889794, _889796, _889798, _889800, _889802, _889804, _889806, _889808, _889810] : [hAPP(c_Fun_Ocomp(_889794, _889796, _889798, _889800), _889802) = hAPP(c_Fun_Ocomp(_889804, _889796, _889798, _889806), _889808), -(hAPP(_889800, hAPP(_889802, _889810)) = hAPP(_889806, hAPP(_889808, _889810)))], (31950 ^ _781013) ^ [_1386823, _1386825, _1386827, _1386829, _1386831] : [_1386823 = c_Orderings_Obot__class_Obot(tc_fun(_1386825, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386827, tc_HOL_Obool)), _1386829), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386825, tc_fun(_1386827, tc_HOL_Obool)), _1386823), _1386831)) = _1386829)], (23567 ^ _781013) ^ [_1221997, _1221999, _1222001] : [class_Rings_Odivision__ring(_1221997), -(_1221999 = c_Groups_Ozero__class_Ozero(_1221997)), 23574 ^ _781013 : [(23581 ^ _781013) ^ [] : [_1222001 = _1221999, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221997), _1222001), _1221999) = c_Groups_Oone__class_Oone(_1221997))], (23575 ^ _781013) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221997), _1222001), _1221999) = c_Groups_Oone__class_Oone(_1221997), -(_1222001 = _1221999)]]], (39225 ^ _781013) ^ [_1538556, _1538558] : [class_Groups_Ocomm__monoid__add(_1538556), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1538556), _1538558) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1538556), hAPP(c_List_Onth(_1538556), _1538558)), 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(_1538556)), _1538558))))], (26481 ^ _781013) ^ [_1273641, _1273643, _1273645, _1273647] : [class_Groups_Ocomm__monoid__add(_1273641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1273643), _1273645)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1273641), _1273647), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1273643, _1273645)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273641), hAPP(_1273647, _1273643)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1273641), _1273647), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1273643, _1273645))))], (47710 ^ _781013) ^ [_1744366, _1744368, _1744370, _1744372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1744366, tc_HOL_Obool), tc_fun(_1744366, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1744366, tc_HOL_Obool), tc_fun(_1744366, tc_HOL_Obool)), _1744368), _1744370)), c_Wellfounded_Omax__ext(_1744366, _1744372))), 47713 ^ _781013 : [(47716 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1744366), _1744370)))], (47718 ^ _781013) ^ [] : [_1744370 = c_Orderings_Obot__class_Obot(tc_fun(_1744366, tc_HOL_Obool))], (47720 ^ _781013) ^ [_1744660] : [hBOOL(hAPP(hAPP(c_member(_1744366), _1744660), _1744368)), 47724 ^ _781013 : [(47727 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1744366, _1744366)), hAPP(hAPP(c_Product__Type_OPair(_1744366, _1744366), _1744660), 47723 ^ [_1744366, _1744368, _1744370, _1744372, _1744660])), _1744372)))], (47725 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744366), 47723 ^ [_1744366, _1744368, _1744370, _1744372, _1744660]), _1744370)))]]], (47714 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1744366), _1744368)))]]], (17783 ^ _781013) ^ [_1112850, _1112852, _1112854] : [_1112850 = _1112854, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112850), _1112852) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112854), _1112852))], (11095 ^ _781013) ^ [_978391, _978393, _978395] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978391, tc_HOL_Obool)), _978393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978391, tc_HOL_Obool)), _978395), _978393)) = c_Orderings_Obot__class_Obot(tc_fun(_978391, tc_HOL_Obool)))], (47901 ^ _781013) ^ [_1748445, _1748447, _1748449, _1748451] : [47902 ^ _781013 : [(47905 ^ _781013) ^ [] : [c_List_Olist__ex(_1748445, _1748447, _1748451)], (47903 ^ _781013) ^ [] : [hBOOL(hAPP(_1748447, _1748449))]], -(c_List_Olist__ex(_1748445, _1748447, hAPP(hAPP(c_List_Olist_OCons(_1748445), _1748449), _1748451)))], (28038 ^ _781013) ^ [_1304488, _1304490] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304488, _1304490) = 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), _1304488), _1304490) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51524 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (16347 ^ _781013) ^ [_1083245, _1083247] : [-(hAPP(c_Set_OCollect(_1083245), hAPP(hAPP(c_COMBC(_1083245, _1083245, tc_HOL_Obool), c_fequal), _1083247)) = hAPP(hAPP(c_Set_Oinsert(_1083245), _1083247), c_Orderings_Obot__class_Obot(tc_fun(_1083245, tc_HOL_Obool))))], (34927 ^ _781013) ^ [] : [-(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))))], (41069 ^ _781013) ^ [_1590126, _1590128, _1590130, _1590132] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1590126), _1590128)), 41075 ^ _781013 : [(41078 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1590130), hAPP(_1590132, 41074 ^ [_1590126, _1590128, _1590130, _1590132])))], (41076 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590126), 41074 ^ [_1590126, _1590128, _1590130, _1590132]), _1590128)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1590126, _1590130)), hAPP(hAPP(c_Product__Type_OSigma(_1590126, _1590130), _1590128), _1590132)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1590126, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1590130, tc_HOL_Obool), tc_Nat_Onat, _1590126), c_Finite__Set_Ocard(_1590130)), _1590132)), _1590128))], (45368 ^ _781013) ^ [_1687226, _1687228] : [class_Enum_Oenum(_1687226), 45371 ^ _781013 : [(45379 ^ _781013) ^ [] : [45380 ^ _781013 : [(45381 ^ _781013) ^ [_1687406] : [hBOOL(hAPP(_1687228, _1687406))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1687226), _1687228)))], (45372 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1687226), _1687228)), -(hBOOL(hAPP(_1687228, 45375 ^ [_1687226, _1687228])))]]], (29127 ^ _781013) ^ [_1324216, _1324218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1324216), _1324218)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1324218, _1324216) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1324218), _1324216), _1324216))], (10757 ^ _781013) ^ [_970887, _970889, _970891] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970887, tc_HOL_Obool)), _970889), _970891) = c_Orderings_Obot__class_Obot(tc_fun(_970887, tc_HOL_Obool)), 10760 ^ _781013 : [(10761 ^ _781013) ^ [_971011] : [hBOOL(hAPP(hAPP(c_member(_970887), _971011), _970889)), 10764 ^ _781013 : [(10765 ^ _781013) ^ [_971101] : [hBOOL(hAPP(hAPP(c_member(_970887), _971101), _970891)), _971011 = _971101]]]]], (38995 ^ _781013) ^ [_1532974, _1532976, _1532978, _1532980] : [-(hAPP(c_List_Oset(tc_prod(_1532974, _1532976)), hAPP(hAPP(c_List_Ozip(_1532974, _1532976), _1532978), _1532980)) = hAPP(c_Set_OCollect(tc_prod(_1532974, _1532976)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1532974, _1532976)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1532974, _1532976), 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(_1532974, _1532976)), 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(_1532974, _1532976)), 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(_1532974, _1532976), tc_fun(tc_Nat_Onat, tc_prod(_1532974, _1532976)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1532974, _1532976), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1532974, _1532976)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1532974, _1532976)), c_COMBB(tc_prod(_1532974, _1532976), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1532976, tc_prod(_1532974, _1532976)), hAPP(hAPP(c_COMBB(_1532974, tc_fun(_1532976, tc_prod(_1532974, _1532976)), tc_Nat_Onat), c_Product__Type_OPair(_1532974, _1532976)), hAPP(c_List_Onth(_1532974), _1532978))), hAPP(c_List_Onth(_1532976), _1532980)))))), 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(_1532974)), _1532978)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1532976)), _1532980)))))))], (24698 ^ _781013) ^ [_1241616, _1241618, _1241620] : [class_Fields_Olinordered__field(_1241616), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241616), _1241618), c_Groups_Ozero__class_Ozero(_1241616))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241616), _1241620), c_Groups_Ozero__class_Ozero(_1241616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241616), c_Groups_Ozero__class_Ozero(_1241616)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241616), _1241618), _1241620))))], (35873 ^ _781013) ^ [] : [-(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))], (41887 ^ _781013) ^ [_1608360, _1608362, _1608364, _1608366, _1608368] : [-(hAPP(hAPP(c_List_Olist__update(_1608360, hAPP(hAPP(c_List_Oappend(_1608360), _1608362), hAPP(hAPP(c_List_Olist_OCons(_1608360), _1608364), _1608366))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608360)), _1608362)), _1608368) = hAPP(hAPP(c_List_Oappend(_1608360), _1608362), hAPP(hAPP(c_List_Olist_OCons(_1608360), _1608368), _1608366)))], (34915 ^ _781013) ^ [_1442040, _1442042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1442040)), c_Int_OBit1(_1442042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1442040), _1442042)))], (48551 ^ _781013) ^ [_1762791, _1762793, _1762795, _1762797] : [-(hBOOL(hAPP(hAPP(c_member(_1762791), _1762793), hAPP(c_Relation_ODomain(_1762791, _1762791), _1762795)))), 48554 ^ _781013 : [(48561 ^ _781013) ^ [] : [_1762793 = _1762797, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1762791, _1762791)), hAPP(hAPP(c_Product__Type_OPair(_1762791, _1762791), _1762793), _1762797)), c_Transitive__Closure_Ortrancl(_1762791, _1762795))))], (48555 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1762791, _1762791)), hAPP(hAPP(c_Product__Type_OPair(_1762791, _1762791), _1762793), _1762797)), c_Transitive__Closure_Ortrancl(_1762791, _1762795))), -(_1762793 = _1762797)]]], (16103 ^ _781013) ^ [_1078782, _1078784] : [class_Groups_Oordered__ab__group__add(_1078782), 16106 ^ _781013 : [(16113 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078782), c_Groups_Ozero__class_Ozero(_1078782)), _1078784)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078782), hAPP(c_Groups_Ouminus__class_Ouminus(_1078782), _1078784)), c_Groups_Ozero__class_Ozero(_1078782))))], (16107 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078782), hAPP(c_Groups_Ouminus__class_Ouminus(_1078782), _1078784)), c_Groups_Ozero__class_Ozero(_1078782))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078782), c_Groups_Ozero__class_Ozero(_1078782)), _1078784)))]]], (17056 ^ _781013) ^ [_1098014, _1098016, _1098018, _1098020] : [class_Groups_Ocomm__monoid__mult(_1098014), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098016), _1098018)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1098016, _1098014), _1098020), _1098018) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1098014, _1098016, c_Groups_Otimes__class_Otimes(_1098014)), _1098020), c_Groups_Oone__class_Oone(_1098014)), _1098018))], (3206 ^ _781013) ^ [_829215, _829217, _829219, _829221, _829223, _829225, _829227, _829229, _829231, _829233] : [-(c_Map_Omap__upds(_829233, _829229, _829225, _829221, _829217) = c_Map_Omap__upds(_829231, _829227, _829223, _829219, _829215)), _829233 = _829231, _829229 = _829227, _829225 = _829223, _829221 = _829219, _829217 = _829215], (50952 ^ _781013) ^ [_1817684, _1817686, _1817688, _1817690] : [-(hBOOL(hAPP(_1817684, _1817686))), -(hAPP(c_List_Ofilter(_1817688, _1817684), c_List_Oreplicate(_1817688, _1817690, _1817686)) = c_List_Olist_ONil(_1817688))], (45942 ^ _781013) ^ [_1700208, _1700210, _1700212] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1700208, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1700208, tc_HOL_Obool), tc_HOL_Obool)), _1700210), _1700212)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1700208, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1700208, tc_HOL_Obool), _1700210)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1700208, tc_HOL_Obool), _1700212)))], (51370 ^ _781013) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (42677 ^ _781013) ^ [_1626683, _1626685, _1626687] : [-(_1626683 = c_List_Olist_ONil(_1626685)), -(c_List_Olast(_1626685, hAPP(hAPP(c_List_Oappend(_1626685), _1626687), _1626683)) = c_List_Olast(_1626685, _1626683))], (42402 ^ _781013) ^ [_1620806, _1620808, _1620810, _1620812] : [-(hAPP(c_List_Orotate(_1620806, _1620808), hAPP(c_List_Orotate(_1620806, _1620810), _1620812)) = hAPP(c_List_Orotate(_1620806, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1620808), _1620810)), _1620812))], (47073 ^ _781013) ^ [_1728328, _1728330, _1728332] : [_1728332 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1728328, _1728330), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1728328, _1728330), _1728332) = c_Orderings_Obot__class_Obot(tc_fun(_1728330, tc_HOL_Obool)))], (49898 ^ _781013) ^ [_1795032, _1795034, _1795036, _1795038, _1795040, _1795042] : [c_Finite__Set_Ofun__left__comm(_1795032, _1795034, _1795036), hBOOL(hAPP(c_Finite__Set_Ofinite(_1795032), _1795038)), -(hAPP(hAPP(_1795036, _1795040), hAPP(hAPP(c_Finite__Set_Ofold(_1795032, _1795034, _1795036), _1795042), _1795038)) = hAPP(hAPP(c_Finite__Set_Ofold(_1795032, _1795034, _1795036), hAPP(hAPP(_1795036, _1795040), _1795042)), _1795038))], (46745 ^ _781013) ^ [_1721186, _1721188] : [hBOOL(hAPP(hAPP(c_member(_1721186), 46746 ^ [_1721186, _1721188]), c_Wellfounded_Oacc(_1721186, _1721188))), -(c_Wellfounded_Owf(_1721186, _1721188))], (22230 ^ _781013) ^ [_1197845, _1197847] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1197845), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197847)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197845)), _1197847))], (39637 ^ _781013) ^ [_1548271, _1548273, _1548275] : [hBOOL(hAPP(c_List_Odistinct(_1548271), _1548273)), -(hBOOL(hAPP(c_List_Odistinct(_1548271), hAPP(hAPP(c_List_Otake(_1548271), _1548275), _1548273))))], (20436 ^ _781013) ^ [_1162778, _1162780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162778), _1162780)), 20439 ^ _781013 : [(20446 ^ _781013) ^ [] : [_1162780 = _1162778, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162780), hAPP(c_Nat_OSuc, _1162778))))], (20440 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162780), hAPP(c_Nat_OSuc, _1162778))), -(_1162780 = _1162778)]]], (11540 ^ _781013) ^ [_988491, _988493, _988495, _988497, _988499] : [c_Fun_Oinj__on(_988491, _988493, _988495, c_Orderings_Otop__class_Otop(tc_fun(_988491, tc_HOL_Obool))), c_Fun_Oinj__on(_988497, _988491, _988499, c_Orderings_Otop__class_Otop(tc_fun(_988497, tc_HOL_Obool))), -(c_Fun_Oinj__on(_988497, _988493, hAPP(c_Fun_Ocomp(_988491, _988493, _988497, _988495), _988499), c_Orderings_Otop__class_Otop(tc_fun(_988497, tc_HOL_Obool))))], (36699 ^ _781013) ^ [_1481683, _1481685] : [-(c_Divides_OnegDivAlg(_1481683, _1481685) = hAPP(c_Divides_Oadjust(_1481685), c_Divides_OnegDivAlg(_1481683, 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)))), _1481685)))), -(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), _1481683), _1481685)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1481685), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (38220 ^ _781013) ^ [_1514792, _1514794, _1514796] : [c_Fun_Oinj__on(_1514792, _1514794, _1514796, c_Orderings_Otop__class_Otop(tc_fun(_1514792, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1514792), tc_List_Olist(_1514794), hAPP(c_List_Omap(_1514792, _1514794), _1514796), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1514792), tc_HOL_Obool))))], (5436 ^ _781013) ^ [_863896, _863898] : [_863898 = _863896, -(tc_Lazy__Sequence_Olazy__sequence(_863898) = tc_Lazy__Sequence_Olazy__sequence(_863896))], (25928 ^ _781013) ^ [_1263209, _1263211] : [c_Nat__Transfer_Onat__set(_1263209), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1263211), _1263209)), -(c_Nat__Transfer_Ois__nat(_1263211))], (17635 ^ _781013) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7335 ^ _781013) ^ [_903466, _903468, _903470, _903472] : [class_Orderings_Oorder(_903466), _903468 = _903470, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903466), _903472), _903470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903466), _903472), _903468)))], (11506 ^ _781013) ^ [_987903, _987905, _987907, _987909, _987911] : [c_Fun_Oinj__on(_987903, _987905, _987907, c_Orderings_Otop__class_Otop(tc_fun(_987903, tc_HOL_Obool))), 11509 ^ _781013 : [(11516 ^ _781013) ^ [] : [_987909 = _987911, -(hAPP(c_Set_Oimage(_987903, _987905, _987907), _987909) = hAPP(c_Set_Oimage(_987903, _987905, _987907), _987911))], (11510 ^ _781013) ^ [] : [hAPP(c_Set_Oimage(_987903, _987905, _987907), _987909) = hAPP(c_Set_Oimage(_987903, _987905, _987907), _987911), -(_987909 = _987911)]]], (46987 ^ _781013) ^ [_1726220, _1726222, _1726224, _1726226] : [46989 ^ _781013 : [(46992 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1726222, hAPP(_1726224, 46988 ^ [_1726220, _1726222, _1726224, _1726226]))), hAPP(_1726222, 46988 ^ [_1726220, _1726222, _1726224, _1726226])))], (46990 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1726220, 46988 ^ [_1726220, _1726222, _1726224, _1726226])))]], -(c_Wellfounded_Owf(_1726226, hAPP(c_Set_OCollect(tc_prod(_1726226, _1726226)), hAPP(c_Product__Type_Oprod_Oprod__case(_1726226, _1726226, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1726226, tc_HOL_Obool), tc_fun(_1726226, tc_HOL_Obool), _1726226), hAPP(c_COMBS(_1726226, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1726226), c_fconj), _1726220))), hAPP(hAPP(c_COMBC(_1726226, tc_fun(_1726226, _1726226), tc_fun(_1726226, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1726226, tc_HOL_Obool), tc_fun(tc_fun(_1726226, _1726226), tc_fun(_1726226, tc_HOL_Obool)), _1726226), c_COMBB(_1726226, tc_HOL_Obool, _1726226)), c_fequal)), _1726224))))))], (35707 ^ _781013) ^ [_1456420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1456420), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1456420)), c_Int_OMin)))], (45588 ^ _781013) ^ [_1691984, _1691986] : [-(hAPP(c_Relation_OField(_1691984), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1691984, _1691984), tc_HOL_Obool), _1691986)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1691984, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1691984, _1691984), tc_HOL_Obool), tc_fun(_1691984, tc_HOL_Obool), c_Relation_OField(_1691984)), _1691986)))], (1424 ^ _781013) ^ [_801555, _801557] : [-(class_Enum_Oenum(_801555)), _801557 = _801555, class_Enum_Oenum(_801557)], (40437 ^ _781013) ^ [_1570321, _1570323, _1570325, _1570327] : [-(hAPP(c_Map_Omap__of(_1570321, _1570323), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1570321, _1570323)), _1570325), _1570327)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1570321, tc_Option_Ooption(_1570323)), hAPP(c_Map_Omap__of(_1570321, _1570323), _1570327)), hAPP(c_Product__Type_Ofst(_1570321, _1570323), _1570325)), hAPP(c_Option_Ooption_OSome(_1570323), hAPP(c_Product__Type_Osnd(_1570321, _1570323), _1570325))))], (23667 ^ _781013) ^ [_1223442] : [23668 ^ _781013 : [(23669 ^ _781013) ^ [_1223499] : [hBOOL(hAPP(_1223442, _1223499))]], 23671 ^ _781013 : [(23674 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1223442, hAPP(c_Int_Onat, 23670 ^ [_1223442]))))], (23672 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23670 ^ [_1223442])))]]], (37941 ^ _781013) ^ [_1507845, _1507847, _1507849, _1507851] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1507845), _1507847)), 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)), _1507845), _1507849)), 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)), _1507847), _1507851)), 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)), _1507847), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1507849), _1507851))), c_FunDef_Omin__strict)))], (14686 ^ _781013) ^ [] : [-(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))], (37776 ^ _781013) ^ [_1503835, _1503837] : [c_Equiv__Relations_Oequiv(_1503835, c_Orderings_Otop__class_Otop(tc_fun(_1503835, tc_HOL_Obool)), _1503837), -(c_Equiv__Relations_Oequivp(_1503835, hAPP(hAPP(c_COMBC(_1503835, tc_fun(tc_prod(_1503835, _1503835), tc_HOL_Obool), tc_fun(_1503835, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503835, tc_fun(tc_fun(tc_prod(_1503835, _1503835), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1503835, _1503835), tc_HOL_Obool), tc_fun(_1503835, tc_HOL_Obool)), _1503835), c_COMBC(_1503835, tc_fun(tc_prod(_1503835, _1503835), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503835, tc_prod(_1503835, _1503835)), tc_fun(_1503835, tc_fun(tc_fun(tc_prod(_1503835, _1503835), tc_HOL_Obool), tc_HOL_Obool)), _1503835), hAPP(c_COMBB(tc_prod(_1503835, _1503835), tc_fun(tc_fun(tc_prod(_1503835, _1503835), tc_HOL_Obool), tc_HOL_Obool), _1503835), c_member(tc_prod(_1503835, _1503835)))), c_Product__Type_OPair(_1503835, _1503835)))), _1503837)))], (48175 ^ _781013) ^ [_1754321, _1754323] : [-(c_Random_Opick(_1754321, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1754321), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1754321, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1754321, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1754321)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1754323)) = c_Random_Opick(_1754321, _1754323))], (20458 ^ _781013) ^ [_1163137, _1163139] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163137), _1163139) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20461 ^ _781013 : [(20464 ^ _781013) ^ [] : [-(_1163139 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20462 ^ _781013) ^ [] : [-(_1163137 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (50738 ^ _781013) ^ [_1811982] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1811982)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1811982))))], (30427 ^ _781013) ^ [_1349666, _1349668, _1349670, _1349672, _1349674] : [class_Orderings_Olinorder(_1349666), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349666, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1349666, _1349668, _1349670)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1349666, _1349672, _1349674)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1349666, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349666), _1349668), _1349672), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349666), _1349670), _1349674)))], (11876 ^ _781013) ^ [_995198, _995200] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_995198, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_995198, tc_HOL_Obool))), _995200) = c_Orderings_Otop__class_Otop(tc_fun(_995198, tc_HOL_Obool)))], (44073 ^ _781013) ^ [_1658492, _1658494] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1658492, _1658494) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1658492), _1658494)))], (34771 ^ _781013) ^ [_1439469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1439469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1439469)))], (27843 ^ _781013) ^ [_1300933, _1300935, _1300937, _1300939] : [class_Divides_Osemiring__div(_1300933), -(c_Divides_Odiv__class_Omod(_1300933, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300933), _1300935), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300933), _1300937), _1300939)), _1300939) = c_Divides_Odiv__class_Omod(_1300933, _1300935, _1300939))], (42976 ^ _781013) ^ [_1634650, _1634652, _1634654, _1634656] : [c_Orderings_Otop__class_Otop(tc_fun(_1634650, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634652, tc_fun(_1634650, tc_HOL_Obool)), _1634654), _1634656), 42979 ^ _781013 : [(42980 ^ _781013) ^ [_1634766] : [hBOOL(hAPP(hAPP(c_member(_1634652), _1634766), _1634654)), -(hAPP(_1634656, _1634766) = c_Orderings_Otop__class_Otop(tc_fun(_1634650, tc_HOL_Obool)))]]], (51210 ^ _781013) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (2148 ^ _781013) ^ [_812578, _812580, _812582, _812584, _812586, _812588] : [-(c_SetInterval_Oord_OatLeast(_812588, _812584, _812580) = c_SetInterval_Oord_OatLeast(_812586, _812582, _812578)), _812588 = _812586, _812584 = _812582, _812580 = _812578], (35849 ^ _781013) ^ [_1458817] : [-(c_Wellfounded_Ofinite__psubset(_1458817) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1458817, tc_HOL_Obool), tc_fun(_1458817, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1458817, tc_HOL_Obool), tc_fun(_1458817, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1458817, tc_HOL_Obool), tc_fun(tc_fun(_1458817, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1458817, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1458817, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1458817, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1458817, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1458817, tc_HOL_Obool)), c_COMBS(tc_fun(_1458817, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1458817, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1458817, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1458817, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1458817, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1458817, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1458817)))))], (16237 ^ _781013) ^ [_1081053, _1081055, _1081057] : [class_Groups_Ogroup__add(_1081053), 16240 ^ _781013 : [(16247 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081053), _1081055), _1081057) = c_Groups_Ozero__class_Ozero(_1081053), -(_1081055 = hAPP(c_Groups_Ouminus__class_Ouminus(_1081053), _1081057))], (16241 ^ _781013) ^ [] : [_1081055 = hAPP(c_Groups_Ouminus__class_Ouminus(_1081053), _1081057), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081053), _1081055), _1081057) = c_Groups_Ozero__class_Ozero(_1081053))]]], (2864 ^ _781013) ^ [_823768, _823770, _823772, _823774, _823776, _823778, _823780, _823782] : [-(c_Product__Type_Oapfst(_823782, _823778, _823774, _823770) = c_Product__Type_Oapfst(_823780, _823776, _823772, _823768)), _823782 = _823780, _823778 = _823776, _823774 = _823772, _823770 = _823768], (7379 ^ _781013) ^ [_904252, _904254, _904256, _904258] : [class_Orderings_Oord(_904252), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904252), _904254), _904256)), _904256 = _904258, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904252), _904254), _904258)))], (44612 ^ _781013) ^ [_1671949, _1671951, _1671953] : [44614 ^ _781013 : [(44617 ^ _781013) ^ [] : [hBOOL(hAPP(_1671951, 44613 ^ [_1671949, _1671951, _1671953]))], (44615 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1671949), 44613 ^ [_1671949, _1671951, _1671953]), hAPP(c_List_Oset(_1671949), _1671953))))]], -(c_List_OtakeWhile(_1671949, _1671951, _1671953) = _1671953)], (7689 ^ _781013) ^ [_910380, _910382] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910380, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_910380, tc_HOL_Obool))), _910382) = _910382)], (20490 ^ _781013) ^ [_1163716, _1163718] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1163716)), _1163718) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1163718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163716), _1163718)))], (13845 ^ _781013) ^ [_1035403, _1035405, _1035407, _1035409] : [class_Rings_Ocomm__semiring__1(_1035403), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035403), _1035405), _1035407)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035403), _1035409), _1035407)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035403), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035403), _1035405), _1035409)), _1035407))], (16029 ^ _781013) ^ [_1077511, _1077513, _1077515] : [class_Groups_Oordered__ab__group__add(_1077511), 16032 ^ _781013 : [(16039 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077511), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077511), _1077513), _1077515)), c_Groups_Ozero__class_Ozero(_1077511))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077511), _1077513), _1077515)))], (16033 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077511), _1077513), _1077515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077511), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077511), _1077513), _1077515)), c_Groups_Ozero__class_Ozero(_1077511))))]]], (4598 ^ _781013) ^ [_850637, _850639] : [_850639 = _850637, -(c_Nitpick_Odenom(_850639) = c_Nitpick_Odenom(_850637))], (32752 ^ _781013) ^ [_1402248, _1402250, _1402252] : [class_Int_Onumber__ring(_1402248), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402248), hAPP(c_Groups_Ouminus__class_Ouminus(_1402248), hAPP(c_Int_Onumber__class_Onumber__of(_1402248), _1402250))), _1402252) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402248), hAPP(c_Int_Onumber__class_Onumber__of(_1402248), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1402250))), _1402252))], (15123 ^ _781013) ^ [_1060903, _1060905] : [-(hAPP(c_Finite__Set_Ocard(_1060903), _1060905) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1060903, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1060903), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1060905))], (4272 ^ _781013) ^ [_845626, _845628, _845630, _845632] : [-(c_Finite__Set_Ofold1(_845632, _845628) = c_Finite__Set_Ofold1(_845630, _845626)), _845632 = _845630, _845628 = _845626], (31395 ^ _781013) ^ [_1369932, _1369934, _1369936] : [c_Hoare__Mirabelle_Otriple__valid(_1369932, _1369934, _1369936), -(hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(_1369932, tc_HOL_Obool, hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_HOL_Obool))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_HOL_Obool)), tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1369932, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_HOL_OAll(_1369932)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_HOL_Obool))), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_HOL_Obool)), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_HOL_Obool), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, _1369932), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBC(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(_1369932, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBS(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1369932, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1369932), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1369932), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1369932), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1369932, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_Com_Ocom), c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1369932)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))), hAPP(hAPP(c_COMBC(tc_Com_Ocom, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_Natural_Oevaln)), _1369934))))))))), _1369936)))], (13156 ^ _781013) ^ [_1020777, _1020779, _1020781] : [class_Lattices_Osemilattice__inf(_1020777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020777), _1020779)), -(_1020779 = c_Orderings_Obot__class_Obot(tc_fun(_1020777, tc_HOL_Obool))), 13167 ^ _781013 : [(13168 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020777), _1020781), hAPP(c_Finite__Set_Ofold1(_1020777, c_Lattices_Osemilattice__inf__class_Oinf(_1020777)), _1020779))), 13171 ^ _781013 : [(13172 ^ _781013) ^ [_1021070] : [hBOOL(hAPP(hAPP(c_member(_1020777), _1021070), _1020779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020777), _1020781), _1021070)))]]], (13178 ^ _781013) ^ [] : [13180 ^ _781013 : [(13183 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020777), _1020781), 13179 ^ [_1020777, _1020779, _1020781]))], (13181 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1020777), 13179 ^ [_1020777, _1020779, _1020781]), _1020779)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020777), _1020781), hAPP(c_Finite__Set_Ofold1(_1020777, c_Lattices_Osemilattice__inf__class_Oinf(_1020777)), _1020779))))]]], (37888 ^ _781013) ^ [_1506716, _1506718, _1506720, _1506722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1506716), _1506718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1506720), _1506722)), -(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), _1506716), _1506720)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1506718), _1506722))), c_FunDef_Opair__less)))], (23112 ^ _781013) ^ [_1213414, _1213416, _1213418] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1213416), _1213418)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213414), _1213416)), _1213418))], (51498 ^ _781013) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (38553 ^ _781013) ^ [_1522448, _1522450, _1522452, _1522454, _1522456] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522448, _1522450)), hAPP(hAPP(c_Product__Type_OPair(_1522448, _1522450), _1522452), _1522454)), hAPP(c_List_Oset(tc_prod(_1522448, _1522450)), _1522456))), -(hAPP(hAPP(c_Map_Omap__of(_1522448, _1522450), _1522456), _1522452) = hAPP(c_Option_Ooption_OSome(_1522450), 38556 ^ [_1522448, _1522450, _1522452, _1522454, _1522456]))], (21587 ^ _781013) ^ [_1186409, _1186411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186409)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186411))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186409), _1186411)))], (21672 ^ _781013) ^ [_1187974, _1187976] : [class_Rings_Olinordered__semidom(_1187974), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187974), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187974), _1187976)), c_Groups_Ozero__class_Ozero(_1187974)))], (40904 ^ _781013) ^ [_1585072, _1585074, _1585076, _1585078] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1585072), tc_List_Olist(_1585072))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1585072), tc_List_Olist(_1585072)), _1585074), _1585076)), c_List_Olistrel1(_1585072, _1585078)))), 40905 ^ _781013 : [(40906 ^ _781013) ^ [_1585205, _1585207] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585072, _1585072)), hAPP(hAPP(c_Product__Type_OPair(_1585072, _1585072), hAPP(hAPP(c_List_Onth(_1585072), _1585074), _1585205)), _1585207)), _1585078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1585205), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1585072)), _1585074))), _1585076 = hAPP(hAPP(c_List_Olist__update(_1585072, _1585074), _1585205), _1585207)]]], (12376 ^ _781013) ^ [_1004273, _1004275, _1004277, _1004279] : [hAPP(c_Set_Oimage(_1004273, _1004275, _1004277), c_Orderings_Otop__class_Otop(tc_fun(_1004273, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1004275, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1004275, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1004275, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1004273, _1004275, _1004277), _1004279))), hAPP(c_Set_Oimage(_1004273, _1004275, _1004277), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1004273, tc_HOL_Obool)), _1004279)))))], (36350 ^ _781013) ^ [_1474083, _1474085, _1474087, _1474089, _1474091] : [c_Equiv__Relations_Oequiv(_1474083, _1474085, _1474087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474083, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1474083, _1474083, _1474087), hAPP(hAPP(c_Set_Oinsert(_1474083), _1474089), c_Orderings_Obot__class_Obot(tc_fun(_1474083, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1474083, _1474083, _1474087), hAPP(hAPP(c_Set_Oinsert(_1474083), _1474091), c_Orderings_Obot__class_Obot(tc_fun(_1474083, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1474083), _1474089), _1474085)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1474083, _1474083)), hAPP(hAPP(c_Product__Type_OPair(_1474083, _1474083), _1474091), _1474089)), _1474087)))], (48233 ^ _781013) ^ [_1755367, _1755369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1755367), _1755369)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1755367)), hAPP(c_Code__Numeral_Oof__nat, _1755369))))], (3532 ^ _781013) ^ [_834290, _834292, _834294, _834296, _834298, _834300, _834302, _834304] : [-(c_Wellfounded_Olex__prod(_834304, _834300, _834296, _834292) = c_Wellfounded_Olex__prod(_834302, _834298, _834294, _834290)), _834304 = _834302, _834300 = _834298, _834296 = _834294, _834292 = _834290], (50626 ^ _781013) ^ [_1810041, _1810043, _1810045, _1810047, _1810049] : [-(_1810041 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1810043, _1810045, _1810047, _1810049), _1810041) = c_Lazy__Sequence_Ohb__bind(_1810043, _1810045, hAPP(_1810047, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1810041), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1810043, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1810045))), _1810049), _1810041)))], (42555 ^ _781013) ^ [_1624109, _1624111, _1624113] : [class_Lattices_Olattice(_1624109), -(c_Big__Operators_Olattice__class_OInf__fin(_1624109, hAPP(c_List_Oset(_1624109), hAPP(hAPP(c_List_Olist_OCons(_1624109), _1624111), _1624113))) = hAPP(c_List_Ofoldl(_1624109, _1624109, c_Lattices_Osemilattice__inf__class_Oinf(_1624109), _1624111), _1624113))], (8965 ^ _781013) ^ [_937782, _937784, _937786, _937788, _937790] : [class_Groups_Ominus(_937782), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937784, _937782)), _937786), _937788), _937790) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937782), hAPP(_937786, _937790)), hAPP(_937788, _937790)))], (21497 ^ _781013) ^ [_1184876] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1184876)), -(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)), _1184876))))], (9497 ^ _781013) ^ [_949423] : [class_Lattices_Osemilattice__inf(_949423), -(c_Finite__Set_Ofun__left__comm__idem(_949423, _949423, c_Lattices_Osemilattice__inf__class_Oinf(_949423)))], (28344 ^ _781013) ^ [_1309940, _1309942] : [class_Rings_Olinordered__idom(_1309940), 28347 ^ _781013 : [(28354 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309940), _1309942), c_Groups_Ozero__class_Ozero(_1309940))), -(c_Groups_Osgn__class_Osgn(_1309940, _1309942) = hAPP(c_Groups_Ouminus__class_Ouminus(_1309940), c_Groups_Oone__class_Oone(_1309940)))], (28348 ^ _781013) ^ [] : [c_Groups_Osgn__class_Osgn(_1309940, _1309942) = hAPP(c_Groups_Ouminus__class_Ouminus(_1309940), c_Groups_Oone__class_Oone(_1309940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309940), _1309942), c_Groups_Ozero__class_Ozero(_1309940))))]]], (46401 ^ _781013) ^ [_1710344, _1710346, _1710348, _1710350] : [-(c_List_Oconcat(_1710344, hAPP(hAPP(c_List_Omap(_1710346, tc_List_Olist(_1710344)), _1710348), _1710350)) = c_List_Omaps(_1710346, _1710344, _1710348, _1710350))], (1794 ^ _781013) ^ [_806180, _806182] : [-(class_Power_Opower(_806180)), _806182 = _806180, class_Power_Opower(_806182)], (42707 ^ _781013) ^ [_1627177, _1627179, _1627181, _1627183] : [-(hAPP(hAPP(c_List_Oappend(_1627177), _1627179), hAPP(hAPP(c_List_Olist_OCons(_1627177), _1627181), c_List_Olist_ONil(_1627177))) = _1627183), -(_1627183 = c_List_Olist_ONil(_1627177)), c_List_Obutlast(_1627177, _1627183) = _1627179, c_List_Olast(_1627177, _1627183) = _1627181], (37359 ^ _781013) ^ [_1494198, _1494200, _1494202, _1494204, _1494206] : [hAPP(c_Product__Type_Osnd(_1494198, _1494200), hAPP(hAPP(c_Product__Type_OPair(_1494198, _1494200), _1494202), _1494204)) = _1494206, -(_1494204 = _1494206)], (35577 ^ _781013) ^ [_1454413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1454413), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1454413)), c_Int_OMin)))], (40840 ^ _781013) ^ [_1582764, _1582766, _1582768, _1582770, _1582772, _1582774, _1582776, _1582778] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1582764, _1582766), tc_fun(tc_prod(_1582768, _1582770), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1582764, _1582766), _1582772), hAPP(c_COMBK(tc_fun(_1582766, tc_HOL_Obool), _1582764), _1582774))), hAPP(c_Product__Type_Oprod_Oprod__case(_1582764, _1582766, tc_fun(tc_prod(_1582768, _1582770), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1582764, tc_fun(_1582766, tc_fun(_1582768, tc_fun(_1582770, tc_HOL_Obool))), tc_fun(_1582766, tc_fun(tc_prod(_1582768, _1582770), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1582768, tc_fun(_1582770, tc_HOL_Obool)), tc_fun(tc_prod(_1582768, _1582770), tc_HOL_Obool)), tc_fun(tc_fun(_1582766, tc_fun(_1582768, tc_fun(_1582770, tc_HOL_Obool))), tc_fun(_1582766, tc_fun(tc_prod(_1582768, _1582770), tc_HOL_Obool))), _1582764), c_COMBB(tc_fun(_1582768, tc_fun(_1582770, tc_HOL_Obool)), tc_fun(tc_prod(_1582768, _1582770), tc_HOL_Obool), _1582766)), hAPP(hAPP(c_COMBB(tc_fun(_1582768, tc_HOL_Obool), tc_fun(tc_fun(_1582768, tc_fun(_1582770, tc_HOL_Obool)), tc_fun(tc_prod(_1582768, _1582770), tc_HOL_Obool)), _1582764), c_Product__Type_OSigma(_1582768, _1582770)), _1582776))), hAPP(hAPP(c_COMBB(tc_fun(_1582770, tc_HOL_Obool), tc_fun(_1582768, tc_fun(_1582770, tc_HOL_Obool)), _1582766), c_COMBK(tc_fun(_1582770, tc_HOL_Obool), _1582768)), _1582778)))) = hAPP(hAPP(c_Product__Type_OSigma(_1582768, _1582770), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1582764, tc_fun(_1582768, tc_HOL_Obool)), _1582772), _1582776)), hAPP(c_COMBK(tc_fun(_1582770, tc_HOL_Obool), _1582768), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1582766, tc_fun(_1582770, tc_HOL_Obool)), _1582774), _1582778))))], (50660 ^ _781013) ^ [_1810626, _1810628] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1810626)), c_Int_OBit0(_1810628))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1810626), _1810628)))], (49558 ^ _781013) ^ [_1788475, _1788477, _1788479, _1788481, _1788483, _1788485] : [c_Finite__Set_Ofun__left__comm__idem(_1788475, _1788477, _1788479), hBOOL(hAPP(c_Finite__Set_Ofinite(_1788475), _1788481)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1788475, _1788477, _1788479), _1788483), hAPP(hAPP(c_Set_Oinsert(_1788475), _1788485), _1788481)) = hAPP(hAPP(c_Finite__Set_Ofold(_1788475, _1788477, _1788479), hAPP(hAPP(_1788479, _1788485), _1788483)), _1788481))], (902 ^ _781013) ^ [_794740, _794742, _794744, _794746, _794748, _794750] : [-(c_Nitpick_Oless__frac(_794748, _794744, _794740)), c_Nitpick_Oless__frac(_794750, _794746, _794742), _794750 = _794748, _794746 = _794744, _794742 = _794740], (20400 ^ _781013) ^ [_1162149, _1162151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162149), hAPP(c_Nat_OSuc, _1162151))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162149), _1162151)))], (41863 ^ _781013) ^ [_1607707, _1607709, _1607711, _1607713, _1607715, _1607717] : [hAPP(hAPP(c_List_Olist_OCons(_1607707), _1607709), _1607711) = _1607713, _1607715 = hAPP(hAPP(c_List_Oappend(_1607707), _1607711), _1607717), -(hAPP(hAPP(c_List_Olist_OCons(_1607707), _1607709), _1607715) = hAPP(hAPP(c_List_Oappend(_1607707), _1607713), _1607717))], (44304 ^ _781013) ^ [_1663809, _1663811, _1663813] : [-(hAPP(c_List_Orev(_1663809), hAPP(hAPP(c_List_Oappend(_1663809), _1663811), _1663813)) = hAPP(hAPP(c_List_Oappend(_1663809), hAPP(c_List_Orev(_1663809), _1663813)), hAPP(c_List_Orev(_1663809), _1663811)))], (25782 ^ _781013) ^ [_1260742, _1260744] : [c_Nat__Transfer_Ois__nat(_1260742), c_Nat__Transfer_Ois__nat(_1260744), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1260742, _1260744)))], (8601 ^ _781013) ^ [_930155, _930157, _930159] : [class_Lattices_Osemilattice__sup(_930155), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930155), _930157), _930159) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930155), _930159), _930157))], (1664 ^ _781013) ^ [_804555, _804557] : [-(class_Nat_Osemiring__char__0(_804555)), _804557 = _804555, class_Nat_Osemiring__char__0(_804557)], (39828 ^ _781013) ^ [_1553536, _1553538, _1553540, _1553542, _1553544] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1553536), tc_List_Olist(_1553536))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1553536), tc_List_Olist(_1553536)), _1553538), _1553540)), hAPP(c_List_Olexn(_1553536, _1553542), _1553544))), 39831 ^ _781013 : [(39834 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553536)), _1553540) = _1553544)], (39832 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553536)), _1553538) = _1553544)]]], (21495 ^ _781013) ^ [_1184832] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1184832) = 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)), _1184832)))], (17811 ^ _781013) ^ [_1113430, _1113432, _1113434, _1113436] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113430), _1113432)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113434), _1113432)), _1113436)) = 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), _1113430), _1113434)), _1113432)), _1113436))], (5442 ^ _781013) ^ [_863981, _863983] : [_863983 = _863981, -(c_COMBI(_863983) = c_COMBI(_863981))], (50482 ^ _781013) ^ [_1807437, _1807439, _1807441] : [-(c_List_Olist__ex1(_1807437, _1807439, _1807441)), 50483 ^ _781013 : [(50484 ^ _781013) ^ [_1807531] : [hBOOL(hAPP(hAPP(c_member(_1807437), _1807531), hAPP(c_List_Oset(_1807437), _1807441))), hBOOL(hAPP(_1807439, _1807531)), 50492 ^ _781013 : [(50497 ^ _781013) ^ [] : [50491 ^ [_1807437, _1807439, _1807441, _1807531] = _1807531], (50495 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1807439, 50491 ^ [_1807437, _1807439, _1807441, _1807531])))], (50493 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1807437), 50491 ^ [_1807437, _1807439, _1807441, _1807531]), hAPP(c_List_Oset(_1807437), _1807441))))]]]]], (21682 ^ _781013) ^ [_1188175, _1188177] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188175), _1188177)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1188175)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1188177)))], (29327 ^ _781013) ^ [_1328162, _1328164] : [class_Orderings_Olinorder(_1328162), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328162), _1328164)), -(c_Big__Operators_Olinorder__class_OMin(_1328162, _1328164) = hAPP(c_Finite__Set_Ofold1(_1328162, c_Orderings_Oord__class_Omin(_1328162)), _1328164))], (23359 ^ _781013) ^ [_1217914, _1217916, _1217918] : [class_Groups_Oordered__ab__group__add(_1217914), -(hAPP(c_Set_Oimage(_1217914, _1217914, c_Groups_Ouminus__class_Ouminus(_1217914)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1217914, _1217916, _1217918)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1217914, hAPP(c_Groups_Ouminus__class_Ouminus(_1217914), _1217918), hAPP(c_Groups_Ouminus__class_Ouminus(_1217914), _1217916)))], (48513 ^ _781013) ^ [_1761902, _1761904] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1761902, _1761902, _1761902), _1761904), c_Transitive__Closure_Ortrancl(_1761902, _1761904)) = hAPP(hAPP(c_Relation_Orel__comp(_1761902, _1761902, _1761902), c_Transitive__Closure_Ortrancl(_1761902, _1761904)), _1761904))], (24480 ^ _781013) ^ [_1237695, _1237697, _1237699] : [class_Fields_Ofield__inverse__zero(_1237695), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1237695), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237695), _1237697), _1237699)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237695), _1237697), hAPP(c_Groups_Ouminus__class_Ouminus(_1237695), _1237699)))], (20593 ^ _781013) ^ [_1166033, _1166035, _1166037] : [class_Rings_Oring__1(_1166033), hBOOL(hAPP(hAPP(c_member(_1166033), _1166035), c_Int_Oring__1__class_OInts(_1166033))), hBOOL(hAPP(hAPP(c_member(_1166033), _1166037), c_Int_Oring__1__class_OInts(_1166033))), -(hBOOL(hAPP(hAPP(c_member(_1166033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166033), _1166035), _1166037)), c_Int_Oring__1__class_OInts(_1166033))))], (48417 ^ _781013) ^ [_1759926, _1759928, _1759930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1759926, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1759926, _1759926, _1759928), _1759930)), _1759930)), -(hAPP(c_Relation_OImage(_1759926, _1759926, c_Transitive__Closure_Ortrancl(_1759926, _1759928)), _1759930) = _1759930)], (1194 ^ _781013) ^ [_798680, _798682] : [-(class_Int_Oring__char__0(_798680)), _798682 = _798680, class_Int_Oring__char__0(_798682)], (46336 ^ _781013) ^ [_1708978, _1708980, _1708982] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1708978, tc_HOL_Obool)), _1708980)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1708978), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1708978, tc_HOL_Obool), _1708980))), 46346 ^ _781013 : [(46349 ^ _781013) ^ [] : [hAPP(c_Finite__Set_Ocard(_1708978), 46345 ^ [_1708978, _1708980, _1708982]) = _1708982], (46347 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1708978, tc_HOL_Obool)), 46345 ^ [_1708978, _1708980, _1708982]), _1708980)))]], 46353 ^ _781013 : [(46357 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1708978, tc_HOL_Obool)), 46355 ^ [_1708978, _1708980, _1708982]), _1708980)))], (46359 ^ _781013) ^ [] : [46352 ^ [_1708978, _1708980, _1708982] = 46355 ^ [_1708978, _1708980, _1708982]], (46361 ^ _781013) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1708978, tc_HOL_Obool)), 46352 ^ [_1708978, _1708980, _1708982]), 46355 ^ [_1708978, _1708980, _1708982]) = c_Orderings_Obot__class_Obot(tc_fun(_1708978, tc_HOL_Obool))], (46354 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1708978, tc_HOL_Obool)), 46352 ^ [_1708978, _1708980, _1708982]), _1708980)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1708982), hAPP(c_Finite__Set_Ocard(tc_fun(_1708978, tc_HOL_Obool)), _1708980)) = hAPP(c_Finite__Set_Ocard(_1708978), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1708978, tc_HOL_Obool), _1708980)))], (3878 ^ _781013) ^ [_839693, _839695, _839697, _839699] : [-(c_Random_Olog(_839699, _839695) = c_Random_Olog(_839697, _839693)), _839699 = _839697, _839695 = _839693], (28376 ^ _781013) ^ [_1310465, _1310467] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310465))), -(c_SMT_Oz3mod(_1310467, _1310465) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1310467, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1310465)))], (17596 ^ _781013) ^ [_1110031, _1110033, _1110035] : [hBOOL(hAPP(_1110031, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110033), _1110035))), 17599 ^ _781013 : [(17606 ^ _781013) ^ [_1110216] : [_1110033 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110035), _1110216), -(hBOOL(hAPP(_1110031, _1110216)))], (17600 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110033), _1110035)), -(hBOOL(hAPP(_1110031, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (4192 ^ _781013) ^ [_844418, _844420] : [_844420 = _844418, -(c_Relation_OId(_844420) = c_Relation_OId(_844418))], (40145 ^ _781013) ^ [_1563860, _1563862, _1563864] : [hAPP(hAPP(c_List_Olist_OCons(_1563860), _1563862), _1563864) = _1563864], (33316 ^ _781013) ^ [_1413443, _1413445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413443)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413443), _1413445)))], (20993 ^ _781013) ^ [_1173475, _1173477, _1173479] : [class_Lattices_Odistrib__lattice(_1173475), hBOOL(hAPP(c_Finite__Set_Ofinite(_1173475), _1173477)), -(_1173477 = c_Orderings_Obot__class_Obot(tc_fun(_1173475, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1173475), _1173479)), -(_1173479 = c_Orderings_Obot__class_Obot(tc_fun(_1173475, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1173475), c_Big__Operators_Olattice__class_OInf__fin(_1173475, _1173477)), c_Big__Operators_Olattice__class_OInf__fin(_1173475, _1173479)) = c_Big__Operators_Olattice__class_OInf__fin(_1173475, hAPP(c_Set_OCollect(_1173475), hAPP(hAPP(c_COMBB(tc_fun(_1173475, tc_HOL_Obool), tc_HOL_Obool, _1173475), c_HOL_OEx(_1173475)), hAPP(hAPP(c_COMBB(tc_fun(_1173475, tc_fun(_1173475, tc_HOL_Obool)), tc_fun(_1173475, tc_HOL_Obool), _1173475), hAPP(c_COMBB(tc_fun(_1173475, tc_HOL_Obool), tc_HOL_Obool, _1173475), c_HOL_OEx(_1173475))), hAPP(hAPP(c_COMBC(_1173475, tc_fun(_1173475, tc_fun(_1173475, tc_HOL_Obool)), tc_fun(_1173475, tc_fun(_1173475, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1173475, tc_fun(tc_fun(_1173475, tc_HOL_Obool), tc_fun(_1173475, tc_HOL_Obool))), tc_fun(tc_fun(_1173475, tc_fun(_1173475, tc_HOL_Obool)), tc_fun(_1173475, tc_fun(_1173475, tc_HOL_Obool))), _1173475), c_COMBS(_1173475, tc_fun(_1173475, tc_HOL_Obool), tc_fun(_1173475, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1173475, tc_fun(_1173475, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1173475, tc_fun(tc_fun(_1173475, tc_HOL_Obool), tc_fun(_1173475, tc_HOL_Obool))), _1173475), hAPP(c_COMBB(tc_fun(_1173475, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1173475, tc_HOL_Obool), tc_fun(_1173475, tc_HOL_Obool)), _1173475), c_COMBS(_1173475, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1173475, tc_fun(_1173475, tc_HOL_Obool)), tc_fun(_1173475, tc_fun(_1173475, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1173475), hAPP(c_COMBB(tc_fun(_1173475, tc_HOL_Obool), tc_fun(_1173475, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1173475), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1173475), c_fconj))), hAPP(hAPP(c_COMBC(_1173475, tc_fun(_1173475, tc_fun(_1173475, _1173475)), tc_fun(_1173475, tc_fun(_1173475, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1173475, _1173475), tc_fun(_1173475, tc_HOL_Obool)), tc_fun(tc_fun(_1173475, tc_fun(_1173475, _1173475)), tc_fun(_1173475, tc_fun(_1173475, tc_HOL_Obool))), _1173475), c_COMBB(tc_fun(_1173475, _1173475), tc_fun(_1173475, tc_HOL_Obool), _1173475)), hAPP(hAPP(c_COMBB(tc_fun(_1173475, tc_HOL_Obool), tc_fun(tc_fun(_1173475, _1173475), tc_fun(_1173475, tc_HOL_Obool)), _1173475), c_COMBB(_1173475, tc_HOL_Obool, _1173475)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1173475)))))), hAPP(hAPP(c_COMBC(_1173475, tc_fun(_1173475, tc_HOL_Obool), tc_fun(_1173475, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1173475, tc_HOL_Obool), tc_fun(_1173475, tc_HOL_Obool)), _1173475), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1173475)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1173475), c_fconj), hAPP(hAPP(c_COMBC(_1173475, tc_fun(_1173475, tc_HOL_Obool), tc_HOL_Obool), c_member(_1173475)), _1173477)))), hAPP(hAPP(c_COMBC(_1173475, tc_fun(_1173475, tc_HOL_Obool), tc_HOL_Obool), c_member(_1173475)), _1173479))))))))], (16734 ^ _781013) ^ [_1091250, _1091252, _1091254, _1091256, _1091258] : [class_Rings_Olinordered__semiring__strict(_1091250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091250), _1091252), _1091254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091250), _1091256), _1091258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091250), c_Groups_Ozero__class_Ozero(_1091250)), _1091252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091250), c_Groups_Ozero__class_Ozero(_1091250)), _1091256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091250), _1091252), _1091256)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091250), _1091254), _1091258))))], (41358 ^ _781013) ^ [_1596034, _1596036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1596034), _1596036)), -(c_List_Oupto(_1596036, _1596034) = c_List_Olist_ONil(tc_Int_Oint))], (10639 ^ _781013) ^ [_969157, _969159, _969161] : [class_Orderings_Oorder(_969157), 10642 ^ _781013 : [(10643 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969157), _969159), _969161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969157), _969159), _969161))), -(_969159 = _969161)], (10653 ^ _781013) ^ [] : [10654 ^ _781013 : [(10657 ^ _781013) ^ [] : [_969159 = _969161], (10655 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969157), _969159), _969161))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969157), _969159), _969161)))]]], (6792 ^ _781013) ^ [_892965, _892967] : [class_Orderings_Opreorder(_892965), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892965), _892967), _892967)))], (878 ^ _781013) ^ [_794422, _794424, _794426, _794428] : [-(c_Wellfounded_Owf(_794426, _794422)), c_Wellfounded_Owf(_794428, _794424), _794428 = _794426, _794424 = _794422], (51174 ^ _781013) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (46641 ^ _781013) ^ [_1717474, _1717476, _1717478, _1717480, _1717482, _1717484, _1717486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1717474, _1717476), tc_HOL_Obool)), _1717478), _1717480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1717476, _1717482), tc_HOL_Obool)), _1717484), _1717486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1717474, _1717482), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1717474, _1717476, _1717482), _1717478), _1717484)), hAPP(hAPP(c_Relation_Orel__comp(_1717474, _1717476, _1717482), _1717480), _1717486))))], (51602 ^ _781013) ^ [_1824641] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1824641)))], (51324 ^ _781013) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (46877 ^ _781013) ^ [_1723761, _1723763, _1723765, _1723767] : [c_Wellfounded_Owf(_1723761, _1723763), hBOOL(hAPP(hAPP(c_member(tc_prod(_1723761, _1723761)), hAPP(hAPP(c_Product__Type_OPair(_1723761, _1723761), _1723765), _1723767)), _1723763)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1723761, _1723761)), hAPP(hAPP(c_Product__Type_OPair(_1723761, _1723761), _1723767), _1723765)), _1723763))], (45013 ^ _781013) ^ [_1680303, _1680305, _1680307, _1680309, _1680311] : [-(c_Enum_Oproduct(_1680303, _1680305, hAPP(hAPP(c_List_Olist_OCons(_1680303), _1680307), _1680309), _1680311) = hAPP(hAPP(c_List_Oappend(tc_prod(_1680303, _1680305)), hAPP(hAPP(c_List_Omap(_1680305, tc_prod(_1680303, _1680305)), hAPP(c_Product__Type_OPair(_1680303, _1680305), _1680307)), _1680311)), c_Enum_Oproduct(_1680303, _1680305, _1680309, _1680311)))], (48730 ^ _781013) ^ [_1767151, _1767153, _1767155, _1767157] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1767151, _1767151)), hAPP(hAPP(c_Product__Type_OPair(_1767151, _1767151), _1767153), _1767155)), hAPP(c_Relation_Oconverse(_1767151, _1767151), c_Transitive__Closure_Otrancl(_1767151, _1767157)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1767151, _1767151)), hAPP(hAPP(c_Product__Type_OPair(_1767151, _1767151), _1767153), _1767155)), c_Transitive__Closure_Otrancl(_1767151, hAPP(c_Relation_Oconverse(_1767151, _1767151), _1767157)))))], (26251 ^ _781013) ^ [_1269052, _1269054, _1269056] : [class_Groups_Oordered__ab__group__add(_1269052), -(hAPP(c_Set_Oimage(_1269052, _1269052, c_Groups_Ouminus__class_Ouminus(_1269052)), c_SetInterval_Oord__class_OatLeastAtMost(_1269052, _1269054, _1269056)) = c_SetInterval_Oord__class_OatLeastAtMost(_1269052, hAPP(c_Groups_Ouminus__class_Ouminus(_1269052), _1269056), hAPP(c_Groups_Ouminus__class_Ouminus(_1269052), _1269054)))], (3022 ^ _781013) ^ [_826249, _826251, _826253, _826255, _826257, _826259, _826261, _826263] : [-(c_List_Omap__filter(_826263, _826259, _826255, _826251) = c_List_Omap__filter(_826261, _826257, _826253, _826249)), _826263 = _826261, _826259 = _826257, _826255 = _826253, _826251 = _826249], (51716 ^ _781013) ^ [] : [-(hAPP(c_Com_Obody, v_pname) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))], (50894 ^ _781013) ^ [_1815758, _1815760, _1815762] : [-(_1815760 = _1815762), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815758, _1815758, hAPP(hAPP(c_COMBB(tc_fun(_1815758, tc_HOL_Obool), tc_fun(_1815758, tc_HOL_Obool), _1815758), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1815758), c_fNot)), c_fequal)), _1815760), _1815762)))], (46553 ^ _781013) ^ [_1715125, _1715127, _1715129, _1715131] : [c_Wellfounded_Omax__extp(_1715125, _1715127, _1715129, _1715131), 46556 ^ _781013 : [(46559 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1715125), _1715131)))], (46561 ^ _781013) ^ [] : [_1715131 = c_Orderings_Obot__class_Obot(tc_fun(_1715125, tc_HOL_Obool))], (46563 ^ _781013) ^ [_1715341] : [hBOOL(hAPP(hAPP(c_member(_1715125), _1715341), _1715129)), 46567 ^ _781013 : [(46570 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1715127, _1715341), 46566 ^ [_1715125, _1715127, _1715129, _1715131, _1715341])))], (46568 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715125), 46566 ^ [_1715125, _1715127, _1715129, _1715131, _1715341]), _1715131)))]]], (46557 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1715125), _1715129)))]]], (23967 ^ _781013) ^ [_1228444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1228444))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228444)))], (44829 ^ _781013) ^ [_1676074, _1676076, _1676078] : [hBOOL(hAPP(c_List_Odistinct(_1676074), _1676076)), hBOOL(hAPP(hAPP(c_member(_1676074), _1676078), hAPP(c_List_Oset(_1676074), _1676076))), -(c_List_OdropWhile(_1676074, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1676074), c_fNot), hAPP(hAPP(c_COMBC(_1676074, _1676074, tc_HOL_Obool), c_fequal), _1676078)), hAPP(c_List_Orev(_1676074), _1676076)) = hAPP(hAPP(c_List_Olist_OCons(_1676074), _1676078), hAPP(c_List_Orev(_1676074), c_List_OtakeWhile(_1676074, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1676074), c_fNot), hAPP(hAPP(c_COMBC(_1676074, _1676074, tc_HOL_Obool), c_fequal), _1676078)), _1676076))))], (43111 ^ _781013) ^ [_1638373, _1638375, _1638377, _1638379, _1638381] : [hBOOL(hAPP(hAPP(c_member(_1638373), _1638375), _1638377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1638379, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638373, tc_fun(_1638379, tc_HOL_Obool)), _1638377), _1638381)), hAPP(_1638381, _1638375))))], (3246 ^ _781013) ^ [_829905, _829907, _829909, _829911] : [-(c_List_Olast(_829911, _829907) = c_List_Olast(_829909, _829905)), _829911 = _829909, _829907 = _829905], (34097 ^ _781013) ^ [_1427903] : [class_Rings_Osemiring__1(_1427903), -(c_Int_Oiszero(_1427903, c_Groups_Ozero__class_Ozero(_1427903)))], (45984 ^ _781013) ^ [_1701022, _1701024, _1701026] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1701022, tc_HOL_Obool)), _1701024), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1701022, tc_HOL_Obool), _1701026)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1701022, tc_HOL_Obool), tc_fun(_1701022, tc_HOL_Obool)), _1701026), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1701022, tc_HOL_Obool)), _1701024)))], (49105 ^ _781013) ^ [_1776823, _1776825, _1776827, _1776829] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776823, _1776823)), hAPP(hAPP(c_Product__Type_OPair(_1776823, _1776823), _1776825), _1776827)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1776823, _1776823), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1776829))), -(_1776825 = _1776827)], (7167 ^ _781013) ^ [_900436, _900438, _900440, _900442] : [7171 ^ _781013 : [(7174 ^ _781013) ^ [] : [hBOOL(hAPP(_900442, 7170 ^ [_900436, _900438, _900440, _900442]))], (7172 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900436), 7170 ^ [_900436, _900438, _900440, _900442]), _900438)))]], 7176 ^ _781013 : [(7179 ^ _781013) ^ [] : [hBOOL(hAPP(_900442, 7175 ^ [_900436, _900438, _900440, _900442]))], (7177 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900436), 7175 ^ [_900436, _900438, _900440, _900442]), _900440)))]], 7180 ^ _781013 : [(7181 ^ _781013) ^ [_900769] : [hBOOL(hAPP(hAPP(c_member(_900436), _900769), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900436, tc_HOL_Obool)), _900438), _900440))), -(hBOOL(hAPP(_900442, _900769)))]]], (31502 ^ _781013) ^ [_1374414, _1374416, _1374418, _1374420] : [c_Fun_Oinj__on(_1374414, tc_fun(tc_fun(_1374414, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1374414, tc_fun(tc_prod(_1374414, _1374414), tc_HOL_Obool), tc_fun(tc_fun(_1374414, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374414, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1374414, _1374414), tc_HOL_Obool), tc_fun(tc_fun(_1374414, tc_HOL_Obool), tc_HOL_Obool)), _1374414), c_Equiv__Relations_Oquotient(_1374414)), hAPP(hAPP(c_COMBC(_1374414, tc_fun(_1374414, tc_HOL_Obool), tc_fun(_1374414, tc_HOL_Obool)), c_Set_Oinsert(_1374414)), c_Orderings_Obot__class_Obot(tc_fun(_1374414, tc_HOL_Obool))))), _1374416), _1374418), hBOOL(hAPP(hAPP(c_member(_1374414), _1374420), _1374418)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1374414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374414, tc_HOL_Obool)), _1374418), hAPP(hAPP(c_Set_Oinsert(_1374414), _1374420), c_Orderings_Obot__class_Obot(tc_fun(_1374414, tc_HOL_Obool))))), _1374416) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1374414, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1374414), _1374418), _1374416)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1374414), hAPP(hAPP(c_Set_Oinsert(_1374414), _1374420), c_Orderings_Obot__class_Obot(tc_fun(_1374414, tc_HOL_Obool)))), _1374416)))], (426 ^ _781013) ^ [_787628, _787630, _787632, _787634] : [-(c_Predicate_Oreflp(_787632, _787628)), c_Predicate_Oreflp(_787634, _787630), _787634 = _787632, _787630 = _787628], (40091 ^ _781013) ^ [_1562480, _1562482, _1562484, _1562486, _1562488, _1562490] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1562480), tc_List_Olist(_1562480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1562480), tc_List_Olist(_1562480)), hAPP(hAPP(c_List_Olist_OCons(_1562480), _1562482), _1562484)), hAPP(hAPP(c_List_Olist_OCons(_1562480), _1562486), _1562488))), c_List_Olex(_1562480, _1562490)))), 40092 ^ _781013 : [(40099 ^ _781013) ^ [] : [_1562482 = _1562486, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1562480), tc_List_Olist(_1562480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1562480), tc_List_Olist(_1562480)), _1562484), _1562488)), c_List_Olex(_1562480, _1562490)))], (40093 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562480, _1562480)), hAPP(hAPP(c_Product__Type_OPair(_1562480, _1562480), _1562482), _1562486)), _1562490)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562480)), _1562484) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562480)), _1562488)]]], (23122 ^ _781013) ^ [_1213605, _1213607, _1213609] : [_1213605 = 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), _1213605), _1213607)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1213605), _1213609)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25442 ^ _781013) ^ [] : [-(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))))], (7951 ^ _781013) ^ [_915370, _915372, _915374, _915376, _915378, _915380] : [-(hAPP(hAPP(c_Option_Omap(_915370, _915372), _915374), hAPP(hAPP(c_Option_Omap(_915376, _915370), _915378), _915380)) = hAPP(hAPP(c_Option_Omap(_915376, _915372), hAPP(c_Fun_Ocomp(_915370, _915372, _915376, _915374), _915378)), _915380))], (19692 ^ _781013) ^ [_1149537, _1149539] : [class_Rings_Olinordered__idom(_1149537), hBOOL(hAPP(hAPP(c_member(_1149537), _1149539), c_Int_Oring__1__class_OInts(_1149537))), 19699 ^ _781013 : [(19706 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149537), _1149539), c_Groups_Ozero__class_Ozero(_1149537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149537), c_Groups_Oone__class_Oone(_1149537)), _1149539)), _1149539)), c_Groups_Ozero__class_Ozero(_1149537))))], (19700 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149537), c_Groups_Oone__class_Oone(_1149537)), _1149539)), _1149539)), c_Groups_Ozero__class_Ozero(_1149537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149537), _1149539), c_Groups_Ozero__class_Ozero(_1149537))))]]], (44936 ^ _781013) ^ [_1678339, _1678341, _1678343, _1678345, _1678347] : [class_Groups_Omonoid__add(_1678339), 44942 ^ _781013 : [(44947 ^ _781013) ^ [] : [hAPP(_1678347, 44941 ^ [_1678339, _1678341, _1678343, _1678345, _1678347]) = c_Groups_Ozero__class_Ozero(_1678339)], (44945 ^ _781013) ^ [] : [hBOOL(hAPP(_1678345, 44941 ^ [_1678339, _1678341, _1678343, _1678345, _1678347]))], (44943 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678341), 44941 ^ [_1678339, _1678341, _1678343, _1678345, _1678347]), hAPP(c_List_Oset(_1678341), _1678343))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1678339), hAPP(hAPP(c_List_Omap(_1678341, _1678339), _1678347), hAPP(c_List_Ofilter(_1678341, _1678345), _1678343))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1678339), hAPP(hAPP(c_List_Omap(_1678341, _1678339), _1678347), _1678343)))], (41889 ^ _781013) ^ [_1608454, _1608456, _1608458, _1608460] : [hBOOL(hAPP(hAPP(c_member(_1608454), _1608456), hAPP(c_List_Oset(_1608454), _1608458))), -(c_List_Oremove1(_1608454, _1608456, hAPP(hAPP(c_List_Oappend(_1608454), _1608458), _1608460)) = hAPP(hAPP(c_List_Oappend(_1608454), c_List_Oremove1(_1608454, _1608456, _1608458)), _1608460))], (9483 ^ _781013) ^ [_949068, _949070] : [class_Groups_Ogroup__add(_949068), -(hAPP(c_Groups_Ouminus__class_Ouminus(_949068), hAPP(c_Groups_Ouminus__class_Ouminus(_949068), _949070)) = _949070)], (32157 ^ _781013) ^ [_1391392, _1391394, _1391396] : [32159 ^ _781013 : [(32164 ^ _781013) ^ [] : [hBOOL(hAPP(_1391394, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 32158 ^ [_1391392, _1391394, _1391396]), _1391392)))], (32162 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1391394, 32158 ^ [_1391392, _1391394, _1391396])))], (32160 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32158 ^ [_1391392, _1391394, _1391396]), _1391392)))]], hBOOL(hAPP(_1391394, _1391396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1391396), _1391392)), -(hBOOL(hAPP(_1391394, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46673 ^ _781013) ^ [_1718872, _1718874, _1718876, _1718878, _1718880, _1718882, _1718884] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1718872, _1718874, _1718876, hAPP(hAPP(c_COMBC(_1718872, tc_fun(tc_prod(_1718872, _1718874), tc_HOL_Obool), tc_fun(_1718874, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1718874, tc_fun(tc_fun(tc_prod(_1718872, _1718874), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1718872, _1718874), tc_HOL_Obool), tc_fun(_1718874, tc_HOL_Obool)), _1718872), c_COMBC(_1718874, tc_fun(tc_prod(_1718872, _1718874), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1718874, tc_prod(_1718872, _1718874)), tc_fun(_1718874, tc_fun(tc_fun(tc_prod(_1718872, _1718874), tc_HOL_Obool), tc_HOL_Obool)), _1718872), hAPP(c_COMBB(tc_prod(_1718872, _1718874), tc_fun(tc_fun(tc_prod(_1718872, _1718874), tc_HOL_Obool), tc_HOL_Obool), _1718874), c_member(tc_prod(_1718872, _1718874)))), c_Product__Type_OPair(_1718872, _1718874)))), _1718878), hAPP(hAPP(c_COMBC(_1718874, tc_fun(tc_prod(_1718874, _1718876), tc_HOL_Obool), tc_fun(_1718876, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1718876, tc_fun(tc_fun(tc_prod(_1718874, _1718876), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1718874, _1718876), tc_HOL_Obool), tc_fun(_1718876, tc_HOL_Obool)), _1718874), c_COMBC(_1718876, tc_fun(tc_prod(_1718874, _1718876), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1718876, tc_prod(_1718874, _1718876)), tc_fun(_1718876, tc_fun(tc_fun(tc_prod(_1718874, _1718876), tc_HOL_Obool), tc_HOL_Obool)), _1718874), hAPP(c_COMBB(tc_prod(_1718874, _1718876), tc_fun(tc_fun(tc_prod(_1718874, _1718876), tc_HOL_Obool), tc_HOL_Obool), _1718876), c_member(tc_prod(_1718874, _1718876)))), c_Product__Type_OPair(_1718874, _1718876)))), _1718880)), _1718882), _1718884)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1718872, _1718876)), hAPP(hAPP(c_Product__Type_OPair(_1718872, _1718876), _1718882), _1718884)), hAPP(hAPP(c_Relation_Orel__comp(_1718872, _1718874, _1718876), _1718878), _1718880))))], (51536 ^ _781013) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (17184 ^ _781013) ^ [_1100840, _1100842, _1100844, _1100846, _1100848] : [class_Groups_Ocomm__monoid__mult(_1100840), hBOOL(hAPP(c_Finite__Set_Ofinite(_1100842), _1100844)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1100842), _1100846)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100842, tc_HOL_Obool)), _1100844), _1100846) = c_Orderings_Obot__class_Obot(tc_fun(_1100842, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1100842, _1100840), _1100848), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1100842, tc_HOL_Obool)), _1100844), _1100846)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100840), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1100842, _1100840), _1100848), _1100844)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1100842, _1100840), _1100848), _1100846)))], (48836 ^ _781013) ^ [_1769984, _1769986, _1769988, _1769990] : [-(hAPP(c_Relation_Oconverse(_1769984, _1769986), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1769984, _1769986), tc_HOL_Obool)), _1769988), _1769990)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1769986, _1769984), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1769984, _1769986), _1769988)), hAPP(c_Relation_Oconverse(_1769984, _1769986), _1769990)))], (15283 ^ _781013) ^ [_1063886, _1063888, _1063890] : [class_Groups_Oordered__comm__monoid__add(_1063886), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063886), c_Groups_Ozero__class_Ozero(_1063886)), _1063888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063886), c_Groups_Ozero__class_Ozero(_1063886)), _1063890)), 15294 ^ _781013 : [(15303 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063886), _1063888), _1063890) = c_Groups_Ozero__class_Ozero(_1063886)), _1063888 = c_Groups_Ozero__class_Ozero(_1063886), _1063890 = c_Groups_Ozero__class_Ozero(_1063886)], (15295 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063886), _1063888), _1063890) = c_Groups_Ozero__class_Ozero(_1063886), 15298 ^ _781013 : [(15301 ^ _781013) ^ [] : [-(_1063890 = c_Groups_Ozero__class_Ozero(_1063886))], (15299 ^ _781013) ^ [] : [-(_1063888 = c_Groups_Ozero__class_Ozero(_1063886))]]]]], (39673 ^ _781013) ^ [_1549151, _1549153, _1549155] : [-(c_List_Osublist(_1549151, _1549153, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1549155)) = hAPP(hAPP(c_List_Otake(_1549151), _1549155), _1549153))], (19360 ^ _781013) ^ [_1143546, _1143548] : [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), _1143546), _1143548))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1143546))), -(_1143548 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31041 ^ _781013) ^ [_1362226, _1362228] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1362226)), _1362228) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1362226), 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), _1362226)), _1362228))], (30217 ^ _781013) ^ [_1345490] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1345490) = c_Orderings_Oord__class_Omax(_1345490)), class_Lattices_Osemilattice__sup(_1345490), class_Orderings_Olinorder(_1345490)], (41248 ^ _781013) ^ [_1594058, _1594060, _1594062, _1594064] : [_1594064 = c_List_Olist_ONil(_1594060), -(c_List_Olist_ONil(_1594058) = hAPP(hAPP(c_List_Omap(_1594060, _1594058), _1594062), _1594064))], (13223 ^ _781013) ^ [_1022004, _1022006, _1022008, _1022010, _1022012, _1022014, _1022016] : [c_Sum__Type_Osum_Osum__case(_1022004, _1022006, _1022008, _1022010, _1022012) = c_Sum__Type_Osum_Osum__case(_1022004, _1022006, _1022008, _1022014, _1022016), 13226 ^ _781013 : [(13229 ^ _781013) ^ [] : [-(_1022012 = _1022016)], (13227 ^ _781013) ^ [] : [-(_1022010 = _1022014)]]], (17549 ^ _781013) ^ [_1109019, _1109021, _1109023, _1109025, _1109027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109019), _1109021)), 17552 ^ _781013 : [(17559 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109025), 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), _1109021), _1109019)), _1109023)), _1109027))), -(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), _1109019), _1109023)), _1109025)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109021), _1109023)), _1109027))))], (17553 ^ _781013) ^ [] : [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), _1109019), _1109023)), _1109025)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109021), _1109023)), _1109027))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109025), 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), _1109021), _1109019)), _1109023)), _1109027))))]]], (42322 ^ _781013) ^ [_1619620, _1619622, _1619624] : [_1619620 = c_List_Olist_ONil(_1619622), -(hAPP(c_List_Ohd(_1619622), hAPP(hAPP(c_List_Oappend(_1619622), _1619620), _1619624)) = hAPP(c_List_Ohd(_1619622), _1619624))], (4182 ^ _781013) ^ [_844269, _844271, _844273, _844275] : [-(c_Transitive__Closure_Ortrancl(_844275, _844271) = c_Transitive__Closure_Ortrancl(_844273, _844269)), _844275 = _844273, _844271 = _844269], (36100 ^ _781013) ^ [_1468508, _1468510] : [-(c_Divides_Odivmod__int(_1468508, _1468510) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1468508), _1468510)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1468508, _1468510)))], (40579 ^ _781013) ^ [_1575401, _1575403, _1575405, _1575407] : [hAPP(hAPP(c_Product__Type_OSigma(_1575401, _1575403), _1575405), hAPP(c_COMBK(tc_fun(_1575403, tc_HOL_Obool), _1575401), _1575407)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575401, _1575403), tc_HOL_Obool)), -(_1575405 = c_Orderings_Obot__class_Obot(tc_fun(_1575401, tc_HOL_Obool))), -(_1575407 = c_Orderings_Obot__class_Obot(tc_fun(_1575403, tc_HOL_Obool)))], (47340 ^ _781013) ^ [_1735445, _1735447] : [c_Wellfounded_Owf(_1735445, _1735447), -(c_Wellfounded_OwfP(_1735445, hAPP(hAPP(c_COMBC(_1735445, tc_fun(tc_prod(_1735445, _1735445), tc_HOL_Obool), tc_fun(_1735445, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1735445, tc_fun(tc_fun(tc_prod(_1735445, _1735445), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1735445, _1735445), tc_HOL_Obool), tc_fun(_1735445, tc_HOL_Obool)), _1735445), c_COMBC(_1735445, tc_fun(tc_prod(_1735445, _1735445), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1735445, tc_prod(_1735445, _1735445)), tc_fun(_1735445, tc_fun(tc_fun(tc_prod(_1735445, _1735445), tc_HOL_Obool), tc_HOL_Obool)), _1735445), hAPP(c_COMBB(tc_prod(_1735445, _1735445), tc_fun(tc_fun(tc_prod(_1735445, _1735445), tc_HOL_Obool), tc_HOL_Obool), _1735445), c_member(tc_prod(_1735445, _1735445)))), c_Product__Type_OPair(_1735445, _1735445)))), _1735447)))], (40601 ^ _781013) ^ [_1575906, _1575908, _1575910] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1575906, _1575908), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575906, _1575908), c_Orderings_Otop__class_Otop(tc_fun(_1575906, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1575908, tc_HOL_Obool), _1575906), _1575910))) = hAPP(hAPP(c_Product__Type_OSigma(_1575906, _1575908), c_Orderings_Otop__class_Otop(tc_fun(_1575906, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1575908, tc_HOL_Obool), _1575906), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1575908, tc_HOL_Obool)), _1575910))))], (17807 ^ _781013) ^ [_1113316, _1113318, _1113320] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113316), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113318), _1113320)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113316), _1113318)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113316), _1113320)))], (17953 ^ _781013) ^ [_1115751, _1115753, _1115755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1115751)), 17956 ^ _781013 : [(17963 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1115753), _1115755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1115751), _1115753)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1115751), _1115755))))], (17957 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1115751), _1115753)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1115751), _1115755))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1115753), _1115755)))]]], (14057 ^ _781013) ^ [_1039656, _1039658, _1039660] : [class_Groups_Ogroup__add(_1039656), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039656), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039656), _1039658), _1039660)), _1039660) = _1039658)], (42440 ^ _781013) ^ [_1621664, _1621666, _1621668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621664)), _1621666)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1621664, _1621668), _1621666) = _1621666)], (19124 ^ _781013) ^ [_1139103, _1139105, _1139107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1139103), _1139105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1139103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1139105), _1139107))))], (31924 ^ _781013) ^ [_1386194, _1386196] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386194, tc_fun(_1386194, tc_HOL_Obool)), _1386196), hAPP(hAPP(c_COMBC(_1386194, tc_fun(_1386194, tc_HOL_Obool), tc_fun(_1386194, tc_HOL_Obool)), c_Set_Oinsert(_1386194)), c_Orderings_Obot__class_Obot(tc_fun(_1386194, tc_HOL_Obool)))) = _1386196)], (21975 ^ _781013) ^ [_1193199, _1193201, _1193203, _1193205] : [class_Rings_Osemiring__1(_1193199), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193201, _1193199), hAPP(c_COMBK(_1193199, _1193201), _1193203)), _1193205) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193199), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1193199), hAPP(c_Finite__Set_Ocard(_1193201), _1193205))), _1193203))], (48013 ^ _781013) ^ [_1750886, _1750888] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1750886, _1750886)), c_Transitive__Closure_Otrancl(_1750886, _1750888))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1750886, _1750886)), _1750888)))], (21654 ^ _781013) ^ [_1187708, _1187710] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187708)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187710), 21657 ^ _781013 : [(21660 ^ _781013) ^ [] : [-(_1187710 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21658 ^ _781013) ^ [] : [-(_1187708 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42456 ^ _781013) ^ [_1621961, _1621963, _1621965] : [-(hAPP(c_List_Orotate(_1621961, _1621963), _1621965) = hAPP(hAPP(c_List_Oappend(_1621961), hAPP(hAPP(c_List_Odrop(_1621961), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1621963, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621961)), _1621965))), _1621965)), hAPP(hAPP(c_List_Otake(_1621961), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1621963, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621961)), _1621965))), _1621965)))], (42496 ^ _781013) ^ [_1622964, _1622966, _1622968, _1622970] : [-(hAPP(c_List_Ofoldl(_1622964, _1622966, _1622968, _1622970), c_List_Olist_ONil(_1622966)) = _1622970)], (34367 ^ _781013) ^ [_1432601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432601), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1432601)), c_Int_OPls)))], (16303 ^ _781013) ^ [_1082269, _1082271, _1082273, _1082275] : [hBOOL(hAPP(hAPP(c_member(_1082269), _1082271), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1082269, tc_HOL_Obool)), _1082273), hAPP(c_Set_OCollect(_1082269), _1082275)))), 16306 ^ _781013 : [(16309 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1082275, _1082271)))], (16307 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1082269), _1082271), _1082273)))]]], (11866 ^ _781013) ^ [_995034] : [c_Orderings_Otop__class_Otop(tc_fun(_995034, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_995034, tc_HOL_Obool))], (14353 ^ _781013) ^ [_1046711, _1046713, _1046715, _1046717, _1046719] : [class_Groups_Ocomm__monoid__add(_1046711), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046713), _1046715)), -(hBOOL(hAPP(hAPP(c_member(_1046713), _1046717), _1046715))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046713, _1046711), _1046719), hAPP(hAPP(c_Set_Oinsert(_1046713), _1046717), _1046715)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046711), hAPP(_1046719, _1046717)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046713, _1046711), _1046719), _1046715)))], (29727 ^ _781013) ^ [_1335355] : [class_Orderings_Olinorder(_1335355), -(c_Orderings_Oord_Omax(_1335355, hAPP(c_COMBC(_1335355, _1335355, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1335355))) = c_Orderings_Oord__class_Omin(_1335355))], (43185 ^ _781013) ^ [_1640443, _1640445, _1640447, _1640449, _1640451] : [-(_1640443 = c_Orderings_Obot__class_Obot(tc_fun(_1640445, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640447, tc_HOL_Obool)), _1640449), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1640445, tc_fun(_1640447, tc_HOL_Obool)), _1640443), _1640451)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640445, tc_fun(_1640447, tc_HOL_Obool)), _1640443), hAPP(hAPP(c_COMBB(tc_fun(_1640447, tc_HOL_Obool), tc_fun(_1640447, tc_HOL_Obool), _1640445), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640447, tc_HOL_Obool)), _1640449)), _1640451)))], (5554 ^ _781013) ^ [_865673, _865675, _865677, _865679] : [-(tc_fun(_865679, _865675) = tc_fun(_865677, _865673)), _865679 = _865677, _865675 = _865673], (51412 ^ _781013) ^ [_1822589, _1822591] : [-(class_Finite__Set_Ofinite(tc_sum(_1822589, _1822591))), class_Finite__Set_Ofinite(_1822589), class_Finite__Set_Ofinite(_1822591)], (30953 ^ _781013) ^ [_1360428, _1360430, _1360432] : [class_Orderings_Olinorder(_1360428), hAPP(_1360430, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360428), 30958 ^ [_1360428, _1360430, _1360432]), 30959 ^ [_1360428, _1360430, _1360432])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360428), hAPP(_1360430, 30958 ^ [_1360428, _1360430, _1360432])), hAPP(_1360430, 30959 ^ [_1360428, _1360430, _1360432])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360428), _1360432)), -(_1360432 = c_Orderings_Obot__class_Obot(tc_fun(_1360428, tc_HOL_Obool))), -(hAPP(_1360430, c_Big__Operators_Olattice_OSup__fin(_1360428, c_Orderings_Oord__class_Omax(_1360428), _1360432)) = c_Big__Operators_Olattice_OSup__fin(_1360428, c_Orderings_Oord__class_Omax(_1360428), hAPP(c_Set_Oimage(_1360428, _1360428, _1360430), _1360432)))], (43779 ^ _781013) ^ [_1653058, _1653060, _1653062] : [class_Orderings_Olinorder(_1653058), c_List_Olinorder__class_Osorted(_1653058, _1653060), hBOOL(hAPP(c_List_Odistinct(_1653058), _1653060)), c_List_Olinorder__class_Osorted(_1653058, _1653062), hBOOL(hAPP(c_List_Odistinct(_1653058), _1653062)), hAPP(c_List_Oset(_1653058), _1653060) = hAPP(c_List_Oset(_1653058), _1653062), -(_1653060 = _1653062)], (23917 ^ _781013) ^ [_1227580, _1227582] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1227580) = _1227582), _1227580 = hAPP(c_Int_Onat, _1227582), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227582))], (24123 ^ _781013) ^ [_1230919, _1230921] : [-(hBOOL(hAPP(_1230919, hAPP(c_Int_Onat, _1230921)))), 24127 ^ _781013 : [(24130 ^ _781013) ^ [] : [hBOOL(hAPP(_1230919, 24126 ^ [_1230919, _1230921]))], (24128 ^ _781013) ^ [] : [-(_1230921 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 24126 ^ [_1230919, _1230921]))]], 24131 ^ _781013 : [(24134 ^ _781013) ^ [] : [hBOOL(hAPP(_1230919, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24132 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230921), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (44879 ^ _781013) ^ [_1677054, _1677056, _1677058] : [44881 ^ _781013 : [(44884 ^ _781013) ^ [] : [hBOOL(hAPP(_1677056, 44880 ^ [_1677054, _1677056, _1677058]))], (44882 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1677054), 44880 ^ [_1677054, _1677056, _1677058]), hAPP(c_List_Oset(_1677054), _1677058))))]], -(c_List_OdropWhile(_1677054, _1677056, _1677058) = c_List_Olist_ONil(_1677054))], (5094 ^ _781013) ^ [_858703, _858705, _858707, _858709] : [-(c_Lazy__Sequence_Ohb__single(_858709, _858705) = c_Lazy__Sequence_Ohb__single(_858707, _858703)), _858709 = _858707, _858705 = _858703], (30777 ^ _781013) ^ [_1357102, _1357104, _1357106] : [class_Orderings_Olinorder(_1357102), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357102), _1357104)), -(_1357104 = c_Orderings_Obot__class_Obot(tc_fun(_1357102, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357102), _1357106)), -(_1357106 = c_Orderings_Obot__class_Obot(tc_fun(_1357102, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1357102, c_Orderings_Oord__class_Omax(_1357102), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1357102, tc_HOL_Obool)), _1357104), _1357106)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357102), c_Big__Operators_Olattice_OSup__fin(_1357102, c_Orderings_Oord__class_Omax(_1357102), _1357104)), c_Big__Operators_Olattice_OSup__fin(_1357102, c_Orderings_Oord__class_Omax(_1357102), _1357106)))], (27176 ^ _781013) ^ [_1286975, _1286977, _1286979] : [class_Groups_Ocomm__monoid__add(_1286975), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1286975), _1286977), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1286979))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1286975), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1286975), _1286977), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1286979))), hAPP(_1286977, hAPP(c_Nat_OSuc, _1286979))))], (50748 ^ _781013) ^ [_1812119, _1812121, _1812123] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1812119, _1812121), _1812123) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1812119, tc_Lazy__Sequence_Olazy__sequence(_1812119)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1812119, tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1812119, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_Nat_Onat)), _1812119), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1812119), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1812119)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1812119, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1812119), tc_Nat_Onat)), _1812119), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1812119))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1812119), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1812121))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1812119, _1812121))))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1812119), _1812123)))], (5867 ^ _781013) ^ [_875356, _875358, _875360, _875362] : [-(c_Com_Ocom_OWhile(_875356, _875358) = c_Com_Ocom_OWhile(_875360, _875362)), _875356 = _875360, _875358 = _875362], (41656 ^ _781013) ^ [_1603229, _1603231, _1603233] : [_1603233 = c_List_Olist_ONil(_1603229), -(hAPP(hAPP(c_List_Oappend(_1603229), _1603231), _1603233) = _1603231)], (49972 ^ _781013) ^ [_1796425, _1796427, _1796429, _1796431, _1796433, _1796435] : [c_Finite__Set_Ofun__left__comm(_1796425, _1796427, _1796429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1796425), _1796431)), -(hBOOL(hAPP(hAPP(c_member(_1796425), _1796433), _1796431))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1796425, _1796427, _1796429), _1796435), hAPP(hAPP(c_Set_Oinsert(_1796425), _1796433), _1796431)) = hAPP(hAPP(_1796429, _1796433), hAPP(hAPP(c_Finite__Set_Ofold(_1796425, _1796427, _1796429), _1796435), _1796431)))], (40028 ^ _781013) ^ [_1560378, _1560380, _1560382] : [c_Relation_Orefl__on(_1560378, _1560380, _1560382), 40031 ^ _781013 : [(40038 ^ _781013) ^ [_1560862] : [hBOOL(hAPP(hAPP(c_member(_1560378), _1560862), _1560380)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560378, _1560378)), hAPP(hAPP(c_Product__Type_OPair(_1560378, _1560378), _1560862), _1560862)), _1560382)))], (40032 ^ _781013) ^ [_1560589] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560378, _1560378)), _1560589), _1560382)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1560378, _1560378, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1560378, tc_fun(_1560378, tc_HOL_Obool), tc_fun(_1560378, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1560378, tc_HOL_Obool), tc_fun(_1560378, tc_HOL_Obool)), _1560378), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1560378)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560378), c_fconj), hAPP(hAPP(c_COMBC(_1560378, tc_fun(_1560378, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560378)), _1560380)))), hAPP(hAPP(c_COMBC(_1560378, tc_fun(_1560378, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560378)), _1560380))), _1560589)))]]], (31900 ^ _781013) ^ [_1385591, _1385593, _1385595, _1385597, _1385599] : [hBOOL(hAPP(hAPP(c_member(_1385591), _1385593), _1385595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1385597, tc_HOL_Obool)), hAPP(_1385599, _1385593)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385591, tc_fun(_1385597, tc_HOL_Obool)), _1385595), _1385599))))], (21945 ^ _781013) ^ [_1192798, _1192800] : [class_Orderings_Olinorder(_1192798), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192798), _1192800)), -(_1192800 = c_Orderings_Obot__class_Obot(tc_fun(_1192798, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1192798), c_Big__Operators_Olinorder__class_OMax(_1192798, _1192800)), _1192800)))], (44590 ^ _781013) ^ [_1671420, _1671422, _1671424, _1671426, _1671428] : [-(hAPP(hAPP(c_List_Ozip(_1671420, _1671422), _1671424), c_List_OtakeWhile(_1671422, _1671426, _1671428)) = c_List_OtakeWhile(tc_prod(_1671420, _1671422), hAPP(c_Fun_Ocomp(_1671422, tc_HOL_Obool, tc_prod(_1671420, _1671422), _1671426), c_Product__Type_Osnd(_1671420, _1671422)), hAPP(hAPP(c_List_Ozip(_1671420, _1671422), _1671424), _1671428)))], (8851 ^ _781013) ^ [_935814, _935816, _935818] : [class_Lattices_Osemilattice__sup(_935814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935814), _935816), _935818)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935814), _935816), _935818) = _935818)], (4504 ^ _781013) ^ [_849238, _849240] : [_849240 = _849238, -(c_Groups_Otimes__class_Otimes(_849240) = c_Groups_Otimes__class_Otimes(_849238))], (33770 ^ _781013) ^ [_1420949, _1420951] : [class_Int_Onumber__ring(_1420949), class_Rings_Olinordered__idom(_1420949), 33777 ^ _781013 : [(33784 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1420951)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420949), c_Groups_Ozero__class_Ozero(_1420949)), hAPP(c_Int_Onumber__class_Onumber__of(_1420949), _1420951))))], (33778 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420949), c_Groups_Ozero__class_Ozero(_1420949)), hAPP(c_Int_Onumber__class_Onumber__of(_1420949), _1420951))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1420951)))]]], (20627 ^ _781013) ^ [_1166638, _1166640] : [class_Rings_Oring__1(_1166638), hBOOL(hAPP(hAPP(c_member(_1166638), _1166640), c_Int_Oring__1__class_OInts(_1166638))), -(hBOOL(hAPP(hAPP(c_member(_1166638), hAPP(c_Groups_Ouminus__class_Ouminus(_1166638), _1166640)), c_Int_Oring__1__class_OInts(_1166638))))], (49632 ^ _781013) ^ [_1790024, _1790026, _1790028, _1790030] : [class_Orderings_Olinorder(_1790024), hBOOL(hAPP(c_Finite__Set_Ofinite(_1790024), _1790026)), hBOOL(hAPP(hAPP(c_member(_1790024), _1790028), _1790026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1790024), hAPP(hAPP(c_Finite__Set_Ofold(_1790024, _1790024, c_Orderings_Oord__class_Omin(_1790024)), _1790030), _1790026)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1790024), _1790028), _1790030))))], (50236 ^ _781013) ^ [_1802553, _1802555, _1802557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1802553), c_Nitpick_Oplus__frac(_1802553, _1802555, c_Nitpick_Ouminus__frac(_1802553, _1802557)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1802553, _1802555, _1802557))], (8424 ^ _781013) ^ [_926192, _926194, _926196] : [-(hAPP(c_Set_Oimage(_926192, _926194, _926196), c_Orderings_Obot__class_Obot(tc_fun(_926192, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_926194, tc_HOL_Obool)))], (19939 ^ _781013) ^ [_1154507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154507), 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)), _1154507)), _1154507)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (42641 ^ _781013) ^ [_1626190, _1626192, _1626194] : [-(_1626190 = c_List_Olist_ONil(_1626192)), -(c_List_Olast(_1626192, hAPP(hAPP(c_List_Olist_OCons(_1626192), _1626194), _1626190)) = c_List_Olast(_1626192, _1626190))], (14582 ^ _781013) ^ [_1051872, _1051874] : [class_Groups_Ozero(_1051872), 14585 ^ _781013 : [(14592 ^ _781013) ^ [] : [_1051874 = c_Groups_Ozero__class_Ozero(_1051872), -(c_Groups_Ozero__class_Ozero(_1051872) = _1051874)], (14586 ^ _781013) ^ [] : [c_Groups_Ozero__class_Ozero(_1051872) = _1051874, -(_1051874 = c_Groups_Ozero__class_Ozero(_1051872))]]], (31200 ^ _781013) ^ [_1365478, _1365480, _1365482, _1365484, _1365486, _1365488] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1365478, _1365480, _1365482)), _1365484), _1365486), _1365488)), 31205 ^ _781013 : [(31208 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1365480), _1365484), _1365486), _1365488)))], (31206 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1365478, _1365484)))]], 31209 ^ _781013 : [(31212 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1365482), _1365484), _1365486), _1365488)))], (31210 ^ _781013) ^ [] : [hBOOL(hAPP(_1365478, _1365484))]]], (45739 ^ _781013) ^ [_1695490, _1695492, _1695494, _1695496, _1695498] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1695490, tc_fun(_1695492, tc_HOL_Obool)), _1695494), hAPP(hAPP(c_COMBS(_1695490, tc_fun(_1695492, tc_HOL_Obool), tc_fun(_1695492, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1695492, tc_HOL_Obool), tc_fun(tc_fun(_1695492, tc_HOL_Obool), tc_fun(_1695492, tc_HOL_Obool)), _1695490), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1695492, tc_HOL_Obool))), _1695496)), _1695498)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1695492, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1695492, tc_HOL_Obool), hAPP(c_Set_Oimage(_1695490, tc_fun(_1695492, tc_HOL_Obool), _1695496), _1695494))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1695492, tc_HOL_Obool), hAPP(c_Set_Oimage(_1695490, tc_fun(_1695492, tc_HOL_Obool), _1695498), _1695494))))], (35679 ^ _781013) ^ [_1455968, _1455970] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1455968), _1455970), hAPP(c_Int_Onumber__class_Onumber__of(_1455968), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1455968), _1455970)), class_Fields_Ofield__inverse__zero(_1455968), class_Int_Onumber__ring(_1455968)], (50551 ^ _781013) ^ [_1808762, _1808764, _1808766, _1808768] : [class_HOL_Oequal(_1808762), class_Enum_Oenum(_1808764), 50558 ^ _781013 : [(50559 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1808764, _1808762)), _1808766), _1808768)), 50562 ^ _781013 : [(50563 ^ _781013) ^ [_1808984] : [hBOOL(hAPP(hAPP(c_member(_1808764), _1808984), hAPP(c_List_Oset(_1808764), c_Enum_Oenum__class_Oenum(_1808764)))), -(hAPP(_1808766, _1808984) = hAPP(_1808768, _1808984))]]], (50569 ^ _781013) ^ [] : [50571 ^ _781013 : [(50574 ^ _781013) ^ [] : [hAPP(_1808766, 50570 ^ [_1808762, _1808764, _1808766, _1808768]) = hAPP(_1808768, 50570 ^ [_1808762, _1808764, _1808766, _1808768])], (50572 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808764), 50570 ^ [_1808762, _1808764, _1808766, _1808768]), hAPP(c_List_Oset(_1808764), c_Enum_Oenum__class_Oenum(_1808764)))))]], -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1808764, _1808762)), _1808766), _1808768)))]]], (41121 ^ _781013) ^ [_1591387, _1591389, _1591391, _1591393] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1591387)), hAPP(hAPP(c_List_Olist_OCons(_1591387), _1591389), _1591391)), c_List_Olists(_1591387, _1591393))), 41124 ^ _781013 : [(41127 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1591387)), _1591391), c_List_Olists(_1591387, _1591393))))], (41125 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591387), _1591389), _1591393)))]]], (6142 ^ _781013) ^ [_880627, _880629, _880631, _880633, _880635] : [-(hBOOL(hAPP(_880627, _880629))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_880631), _880629), _880633)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_880627, _880635, _880631)), _880629), _880633)))], (31619 ^ _781013) ^ [_1377574, _1377576, _1377578, _1377580] : [-(hAPP(c_Relation_OImage(_1377574, _1377576, _1377578), _1377580) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377574, tc_fun(_1377576, tc_HOL_Obool)), _1377580), hAPP(hAPP(c_COMBB(tc_fun(_1377574, tc_HOL_Obool), tc_fun(_1377576, tc_HOL_Obool), _1377574), c_Relation_OImage(_1377574, _1377576, _1377578)), hAPP(hAPP(c_COMBC(_1377574, tc_fun(_1377574, tc_HOL_Obool), tc_fun(_1377574, tc_HOL_Obool)), c_Set_Oinsert(_1377574)), c_Orderings_Obot__class_Obot(tc_fun(_1377574, tc_HOL_Obool))))))], (5735 ^ _781013) ^ [_871811, _871813, _871815, _871817] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_871811), _871813), _871815), _871817)), -(_871813 = _871817), -(hBOOL(hAPP(_871815, _871817)))], (45680 ^ _781013) ^ [_1693939, _1693941, _1693943] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1693939, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1693939, tc_HOL_Obool), _1693941)), _1693943) = c_Orderings_Obot__class_Obot(tc_fun(_1693939, tc_HOL_Obool)), 45683 ^ _781013 : [(45684 ^ _781013) ^ [_1694074] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1693939, tc_HOL_Obool)), _1694074), _1693941)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1693939, tc_HOL_Obool)), _1694074), _1693943) = c_Orderings_Obot__class_Obot(tc_fun(_1693939, tc_HOL_Obool)))]]], (10957 ^ _781013) ^ [_975267, _975269, _975271, _975273] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975267, _975269, _975271, _975273, c_Orderings_Obot__class_Obot(tc_fun(_975267, tc_HOL_Obool))), _975273)))], (27389 ^ _781013) ^ [_1291411, _1291413] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1291411), _1291413)), -(_1291413 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1291411, 27393 ^ [_1291411, _1291413]), 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)), 27392 ^ [_1291411, _1291413]))))], (8511 ^ _781013) ^ [_928344, _928346, _928348, _928350] : [_928344 = c_Orderings_Obot__class_Obot(tc_fun(_928346, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_928346, _928348, hAPP(c_COMBK(_928348, _928346), _928350)), _928344) = c_Orderings_Obot__class_Obot(tc_fun(_928348, tc_HOL_Obool)))], (34393 ^ _781013) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (29307 ^ _781013) ^ [_1327699, _1327701] : [-(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), _1327699)), _1327701))))], (34531 ^ _781013) ^ [_1435207, _1435209] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1435207)))), _1435209) = 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)))), _1435207)), _1435209))], (4898 ^ _781013) ^ [_855387, _855389, _855391, _855393, _855395, _855397, _855399, _855401, _855403, _855405, _855407, _855409, _855411, _855413] : [-(c_New__Random__Sequence_Opos__decr__bind(_855413, _855409, _855405, _855401, _855397, _855393, _855389) = c_New__Random__Sequence_Opos__decr__bind(_855411, _855407, _855403, _855399, _855395, _855391, _855387)), _855413 = _855411, _855409 = _855407, _855405 = _855403, _855401 = _855399, _855397 = _855395, _855393 = _855391, _855389 = _855387], (19843 ^ _781013) ^ [_1152699] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1152699)), _1152699) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27063 ^ _781013) ^ [_1284837, _1284839, _1284841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284837)), 27066 ^ _781013 : [(27067 ^ _781013) ^ [_1284971] : [27069 ^ _781013 : [(27075 ^ _781013) ^ [] : [-(_1284971 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27071 ^ [_1284837, _1284839, _1284841, _1284971]), 27068 ^ [_1284837, _1284839, _1284841, _1284971]))], (27073 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27071 ^ [_1284837, _1284839, _1284841, _1284971]), _1284839)))], (27070 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27068 ^ [_1284837, _1284839, _1284841, _1284971]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1284837))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284971), _1284841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1284971), _1284837)), _1284841)))]]], (19452 ^ _781013) ^ [_1145234, _1145236, _1145238] : [class_Power_Opower(_1145234), class_Rings_Omult__zero(_1145234), class_Rings_Ono__zero__divisors(_1145234), class_Rings_Ozero__neq__one(_1145234), 19467 ^ _781013 : [(19476 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1145234), _1145236), _1145238) = c_Groups_Ozero__class_Ozero(_1145234)), _1145236 = c_Groups_Ozero__class_Ozero(_1145234), -(_1145238 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19468 ^ _781013) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1145234), _1145236), _1145238) = c_Groups_Ozero__class_Ozero(_1145234), 19471 ^ _781013 : [(19474 ^ _781013) ^ [] : [_1145238 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19472 ^ _781013) ^ [] : [-(_1145236 = c_Groups_Ozero__class_Ozero(_1145234))]]]]], (40077 ^ _781013) ^ [_1562082, _1562084, _1562086, _1562088, _1562090, _1562092] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1562082), tc_List_Olist(_1562082))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1562082), tc_List_Olist(_1562082)), hAPP(hAPP(c_List_Olist_OCons(_1562082), _1562084), _1562086)), hAPP(hAPP(c_List_Olist_OCons(_1562082), _1562088), _1562090))), c_List_Olex(_1562082, _1562092))), 40082 ^ _781013 : [(40085 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562082)), _1562086) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562082)), _1562090))], (40083 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562082, _1562082)), hAPP(hAPP(c_Product__Type_OPair(_1562082, _1562082), _1562084), _1562088)), _1562092)))]], 40086 ^ _781013 : [(40089 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1562082), tc_List_Olist(_1562082))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1562082), tc_List_Olist(_1562082)), _1562086), _1562090)), c_List_Olex(_1562082, _1562092))))], (40087 ^ _781013) ^ [] : [-(_1562084 = _1562088)]]], (51544 ^ _781013) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (24492 ^ _781013) ^ [_1237953, _1237955, _1237957] : [class_Fields_Olinordered__field__inverse__zero(_1237953), 24495 ^ _781013 : [(24510 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237953), c_Groups_Ozero__class_Ozero(_1237953)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237953), _1237955), _1237957)))), 24511 ^ _781013 : [(24518 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237953), _1237955), c_Groups_Ozero__class_Ozero(_1237953))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237953), _1237957), c_Groups_Ozero__class_Ozero(_1237953)))], (24512 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237953), c_Groups_Ozero__class_Ozero(_1237953)), _1237955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237953), c_Groups_Ozero__class_Ozero(_1237953)), _1237957))]]], (24496 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237953), c_Groups_Ozero__class_Ozero(_1237953)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237953), _1237955), _1237957))), 24501 ^ _781013 : [(24504 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237953), c_Groups_Ozero__class_Ozero(_1237953)), _1237957)))], (24502 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237953), c_Groups_Ozero__class_Ozero(_1237953)), _1237955)))]], 24505 ^ _781013 : [(24508 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237953), _1237957), c_Groups_Ozero__class_Ozero(_1237953))))], (24506 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237953), _1237955), c_Groups_Ozero__class_Ozero(_1237953))))]]]]], (22766 ^ _781013) ^ [_1206810, _1206812, _1206814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206810)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1206814), _1206810)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206812), _1206814)), _1206810))], (40545 ^ _781013) ^ [_1574498, _1574500, _1574502, _1574504, _1574506, _1574508] : [hBOOL(hAPP(hAPP(c_member(_1574498), _1574500), _1574502)), hBOOL(hAPP(hAPP(c_member(_1574504), _1574506), hAPP(_1574508, _1574500))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574498, _1574504)), hAPP(hAPP(c_Product__Type_OPair(_1574498, _1574504), _1574500), _1574506)), hAPP(hAPP(c_Product__Type_OSigma(_1574498, _1574504), _1574502), _1574508))))], (15041 ^ _781013) ^ [_1059032] : [class_Groups_Ogroup__add(_1059032), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1059032), c_Groups_Ozero__class_Ozero(_1059032)) = c_Groups_Ozero__class_Ozero(_1059032))], (38505 ^ _781013) ^ [_1521319, _1521321, _1521323, _1521325] : [hBOOL(hAPP(c_List_Odistinct(_1521319), hAPP(hAPP(c_List_Omap(tc_prod(_1521319, _1521321), _1521319), c_Product__Type_Ofst(_1521319, _1521321)), _1521323))), hBOOL(hAPP(c_List_Odistinct(_1521319), hAPP(hAPP(c_List_Omap(tc_prod(_1521319, _1521321), _1521319), c_Product__Type_Ofst(_1521319, _1521321)), _1521325))), 38512 ^ _781013 : [(38519 ^ _781013) ^ [] : [hAPP(c_List_Oset(tc_prod(_1521319, _1521321)), _1521323) = hAPP(c_List_Oset(tc_prod(_1521319, _1521321)), _1521325), -(hAPP(c_Map_Omap__of(_1521319, _1521321), _1521323) = hAPP(c_Map_Omap__of(_1521319, _1521321), _1521325))], (38513 ^ _781013) ^ [] : [hAPP(c_Map_Omap__of(_1521319, _1521321), _1521323) = hAPP(c_Map_Omap__of(_1521319, _1521321), _1521325), -(hAPP(c_List_Oset(tc_prod(_1521319, _1521321)), _1521323) = hAPP(c_List_Oset(tc_prod(_1521319, _1521321)), _1521325))]]], (33936 ^ _781013) ^ [_1423824, _1423826, _1423828, _1423830] : [-(c_Nat_Onat_Onat__case(_1423824, _1423826, _1423828, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423830)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1423824), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1423830))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1423824, _1423824), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1423824, tc_fun(_1423824, _1423824)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1423824, tc_fun(_1423824, _1423824)), tc_Int_Oint), c_If(_1423824)), c_Nat__Numeral_Oneg)), _1423826)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1423824, tc_Int_Oint), _1423828), c_Int_Onat))))], (41410 ^ _781013) ^ [_1597056, _1597058, _1597060] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597056), tc_List_Olist(_1597056))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597056), tc_List_Olist(_1597056)), _1597058), c_List_Olist_ONil(_1597056))), c_List_Olex(_1597056, _1597060)))], (43693 ^ _781013) ^ [_1651750, _1651752] : [c_List_Oupt(_1651750, _1651752) = c_List_Olist_ONil(tc_Nat_Onat), -(_1651752 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651752), _1651750)))], (33424 ^ _781013) ^ [_1415304, _1415306, _1415308] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415304))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415304)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415306)), _1415308)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415306)), _1415308))], (24254 ^ _781013) ^ [_1233439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1233439)), -(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, _1233439))))], (8631 ^ _781013) ^ [_930732, _930734, _930736] : [class_Lattices_Osemilattice__sup(_930732), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930732), _930734), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930732), _930734), _930736)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930732), _930734), _930736))], (37752 ^ _781013) ^ [_1503120, _1503122, _1503124, _1503126, _1503128, _1503130, _1503132, _1503134] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1503120, _1503122), tc_prod(_1503120, _1503122))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1503120, _1503122), tc_prod(_1503120, _1503122)), hAPP(hAPP(c_Product__Type_OPair(_1503120, _1503122), _1503124), _1503126)), hAPP(hAPP(c_Product__Type_OPair(_1503120, _1503122), _1503128), _1503130))), c_Wellfounded_Olex__prod(_1503120, _1503122, _1503132, _1503134))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1503120, _1503120)), hAPP(hAPP(c_Product__Type_OPair(_1503120, _1503120), _1503124), _1503128)), _1503132))), 37759 ^ _781013 : [(37762 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1503122, _1503122)), hAPP(hAPP(c_Product__Type_OPair(_1503122, _1503122), _1503126), _1503130)), _1503134)))], (37760 ^ _781013) ^ [] : [-(_1503124 = _1503128)]]], (49700 ^ _781013) ^ [_1791276, _1791278, _1791280] : [class_Lattices_Olattice(_1791276), hBOOL(hAPP(c_Finite__Set_Ofinite(_1791276), _1791278)), -(c_Big__Operators_Olattice__class_OInf__fin(_1791276, hAPP(hAPP(c_Set_Oinsert(_1791276), _1791280), _1791278)) = hAPP(hAPP(c_Finite__Set_Ofold(_1791276, _1791276, c_Lattices_Osemilattice__inf__class_Oinf(_1791276)), _1791280), _1791278))], (39422 ^ _781013) ^ [_1543101, _1543103, _1543105, _1543107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1543101), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1543103)), _1543105))), -(hBOOL(hAPP(hAPP(c_member(_1543103), _1543107), hAPP(c_List_Oset(_1543103), hAPP(hAPP(c_List_Olist__update(_1543103, _1543105), _1543101), _1543107)))))], (36691 ^ _781013) ^ [_1481524, _1481526] : [36692 ^ _781013 : [(36695 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1481526), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36693 ^ _781013) ^ [] : [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), _1481524), _1481526)))]], -(c_Divides_OnegDivAlg(_1481524, _1481526) = 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), _1481524), _1481526)))], (22041 ^ _781013) ^ [_1194364, _1194366, _1194368] : [class_Orderings_Olinorder(_1194364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1194364, tc_HOL_Obool)), _1194366), _1194368)), -(_1194366 = c_Orderings_Obot__class_Obot(tc_fun(_1194364, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1194364), _1194368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194364), c_Big__Operators_Olinorder__class_OMin(_1194364, _1194368)), c_Big__Operators_Olinorder__class_OMin(_1194364, _1194366))))], (31617 ^ _781013) ^ [_1377483, _1377485, _1377487, _1377489] : [-(hAPP(c_Set_Ovimage(_1377483, _1377485, _1377487), _1377489) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377485, tc_fun(_1377483, tc_HOL_Obool)), _1377489), hAPP(hAPP(c_COMBB(tc_fun(_1377485, tc_HOL_Obool), tc_fun(_1377483, tc_HOL_Obool), _1377485), c_Set_Ovimage(_1377483, _1377485, _1377487)), hAPP(hAPP(c_COMBC(_1377485, tc_fun(_1377485, tc_HOL_Obool), tc_fun(_1377485, tc_HOL_Obool)), c_Set_Oinsert(_1377485)), c_Orderings_Obot__class_Obot(tc_fun(_1377485, tc_HOL_Obool))))))], (4018 ^ _781013) ^ [_841811, _841813, _841815, _841817] : [-(c_Product__Type_OSigma(_841817, _841813) = c_Product__Type_OSigma(_841815, _841811)), _841817 = _841815, _841813 = _841811], (20029 ^ _781013) ^ [_1155963, _1155965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155963), _1155965)), -(hAPP(c_Nat_OSuc, _1155963) = _1155965), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1155963)), _1155965)))], (6625 ^ _781013) ^ [_889556, _889558, _889560, _889562, _889564, _889566, _889568] : [-(hAPP(c_Fun_Ocomp(_889556, _889558, _889560, _889562), hAPP(c_Fun_Ocomp(_889564, _889556, _889560, _889566), _889568)) = hAPP(c_Fun_Ocomp(_889564, _889558, _889560, hAPP(c_Fun_Ocomp(_889556, _889558, _889564, _889562), _889566)), _889568))], (14291 ^ _781013) ^ [_1045249, _1045251, _1045253, _1045255, _1045257] : [class_Rings_Ocomm__semiring__1(_1045249), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045249), _1045251), _1045253)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045249), _1045255), _1045257)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045249), _1045251), _1045255)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045249), _1045253), _1045257)))], (5990 ^ _781013) ^ [_877864, _877866] : [hBOOL(hAPP(c_Com_OWT, _877866)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_877864, _877866))))], (41927 ^ _781013) ^ [_1609400, _1609402, _1609404, _1609406, _1609408] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609400), tc_List_Olist(_1609400))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609400), tc_List_Olist(_1609400)), _1609402), _1609404)), c_List_Olexord(_1609400, _1609406))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609400), tc_List_Olist(_1609400))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609400), tc_List_Olist(_1609400)), hAPP(hAPP(c_List_Oappend(_1609400), _1609408), _1609402)), hAPP(hAPP(c_List_Oappend(_1609400), _1609408), _1609404))), c_List_Olexord(_1609400, _1609406))))], (18630 ^ _781013) ^ [_1127972, _1127974, _1127976, _1127978, _1127980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127972), _1127974)), -(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), _1127972), _1127976)), _1127978)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127974), _1127976)), _1127980)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1127978), 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), _1127974), _1127972)), _1127976)), _1127980)))], (27721 ^ _781013) ^ [_1298602, _1298604, _1298606, _1298608] : [class_Divides_Osemiring__div(_1298602), -(c_Divides_Odiv__class_Omod(_1298602, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298602), c_Divides_Odiv__class_Omod(_1298602, _1298604, _1298606)), _1298608), _1298606) = c_Divides_Odiv__class_Omod(_1298602, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298602), _1298604), _1298608), _1298606))], (21465 ^ _781013) ^ [_1184342, _1184344, _1184346] : [class_Nat_Osemiring__char__0(_1184342), 21468 ^ _781013 : [(21475 ^ _781013) ^ [] : [_1184344 = _1184346, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1184342), _1184344) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1184342), _1184346))], (21469 ^ _781013) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1184342), _1184344) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1184342), _1184346), -(_1184344 = _1184346)]]], (796 ^ _781013) ^ [_793221, _793223, _793225, _793227, _793229, _793231] : [-(c_Finite__Set_Ofolding__one__idem(_793229, _793225, _793221)), c_Finite__Set_Ofolding__one__idem(_793231, _793227, _793223), _793231 = _793229, _793227 = _793225, _793223 = _793221], (29587 ^ _781013) ^ [_1332848, _1332850, _1332852] : [class_Orderings_Olinorder(_1332848), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332848), _1332850)), -(_1332850 = c_Orderings_Obot__class_Obot(tc_fun(_1332848, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332848), _1332852)), -(_1332852 = c_Orderings_Obot__class_Obot(tc_fun(_1332848, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1332848, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332848, tc_HOL_Obool)), _1332850), _1332852)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332848), c_Big__Operators_Olinorder__class_OMin(_1332848, _1332850)), c_Big__Operators_Olinorder__class_OMin(_1332848, _1332852)))], (12036 ^ _781013) ^ [_998030, _998032, _998034, _998036, _998038] : [c_Fun_Oinj__on(_998030, _998032, _998034, _998036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998030, tc_HOL_Obool)), _998038), _998036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998032, tc_HOL_Obool)), hAPP(c_Set_Oimage(_998030, _998032, _998034), _998038)), hAPP(c_Set_Oimage(_998030, _998032, _998034), _998036))))], (32061 ^ _781013) ^ [_1389756, _1389758, _1389760, _1389762] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1389756, tc_Nat_Onat), _1389758), _1389760) = hAPP(c_Nat_OSuc, _1389762), 32065 ^ _781013 : [(32068 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1389758, 32064 ^ [_1389756, _1389758, _1389760, _1389762]))))], (32066 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389756), 32064 ^ [_1389756, _1389758, _1389760, _1389762]), _1389760)))]]], (26755 ^ _781013) ^ [_1278932, _1278934] : [c_Nat__Transfer_Ois__nat(_1278932), c_Nat__Transfer_Ois__nat(_1278934), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1278932, _1278934) = 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, _1278932), hAPP(c_Int_Onat, _1278934))))], (18165 ^ _781013) ^ [_1119420, _1119422] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119420), _1119422))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119420), _1119422)), -(_1119420 = _1119422)], (25470 ^ _781013) ^ [_1255673, _1255675] : [c_Nat__Transfer_Onat__set(_1255673), c_Nat__Transfer_Onat__set(_1255675), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1255673), _1255675)))], (37558 ^ _781013) ^ [_1498339, _1498341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1498339), 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)), _1498341)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1498339), _1498341) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1498339, _1498341)))], (31531 ^ _781013) ^ [_1375386, _1375388, _1375390, _1375392, _1375394, _1375396] : [hBOOL(hAPP(hAPP(c_member(_1375386), _1375388), _1375390)), hBOOL(hAPP(hAPP(_1375392, _1375388), _1375394)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1375386, tc_fun(_1375396, tc_HOL_Obool)), _1375390), _1375392), _1375394)))], (48307 ^ _781013) ^ [_1757174] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1757174)) = _1757174)], (23645 ^ _781013) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33312 ^ _781013) ^ [_1413356, _1413358] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413356)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413358)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1413356), _1413358)))], (5548 ^ _781013) ^ [_865588, _865590] : [_865590 = _865588, -(c_Orderings_Obot__class_Obot(_865590) = c_Orderings_Obot__class_Obot(_865588))], (46794 ^ _781013) ^ [_1722267, _1722269, _1722271] : [c_Wellfounded_Owf(_1722267, _1722269), -(c_Wellfounded_Owf(_1722267, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1722267, _1722267), tc_HOL_Obool)), _1722271), _1722269)))], (13693 ^ _781013) ^ [_1032310, _1032312, _1032314, _1032316, _1032318] : [class_Groups_Ocomm__monoid__add(_1032310), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032312), _1032314)), hBOOL(hAPP(hAPP(c_member(_1032312), _1032316), _1032314)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1032312, _1032310), _1032318), _1032314) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032310), hAPP(_1032318, _1032316)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1032312, _1032310), _1032318), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1032312, tc_HOL_Obool)), _1032314), hAPP(hAPP(c_Set_Oinsert(_1032312), _1032316), c_Orderings_Obot__class_Obot(tc_fun(_1032312, tc_HOL_Obool)))))))], (24974 ^ _781013) ^ [_1246459, _1246461, _1246463, _1246465] : [class_Fields_Olinordered__field__inverse__zero(_1246459), 24977 ^ _781013 : [(24978 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), _1246461), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1246459), _1246463), _1246465))), 24981 ^ _781013 : [(24988 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), c_Groups_Ozero__class_Ozero(_1246459)), _1246465))), 24991 ^ _781013 : [(24998 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), _1246465), c_Groups_Ozero__class_Ozero(_1246459)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), _1246461), c_Groups_Ozero__class_Ozero(_1246459))))], (24992 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), _1246465), c_Groups_Ozero__class_Ozero(_1246459))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), _1246463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246459), _1246461), _1246465))))]]], (24982 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), c_Groups_Ozero__class_Ozero(_1246459)), _1246465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246459), _1246461), _1246465)), _1246463)))]]], (25004 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), _1246461), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1246459), _1246463), _1246465)))), 25007 ^ _781013 : [(25010 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246459), _1246461), _1246465)), _1246463))], (25008 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), c_Groups_Ozero__class_Ozero(_1246459)), _1246465)))]], 25011 ^ _781013 : [(25014 ^ _781013) ^ [] : [25015 ^ _781013 : [(25018 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), _1246463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246459), _1246461), _1246465)))], (25016 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), _1246465), c_Groups_Ozero__class_Ozero(_1246459))))]], 25019 ^ _781013 : [(25022 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), _1246461), c_Groups_Ozero__class_Ozero(_1246459)))], (25020 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), _1246465), c_Groups_Ozero__class_Ozero(_1246459)))]]], (25012 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246459), c_Groups_Ozero__class_Ozero(_1246459)), _1246465))]]]]], (47234 ^ _781013) ^ [_1732545, _1732547, _1732549] : [-(hAPP(c_Relation_ODomain(_1732545, _1732547), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1732545, _1732547), tc_HOL_Obool), _1732549)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1732545, _1732547), tc_HOL_Obool), tc_fun(_1732545, tc_HOL_Obool)), _1732549), c_Relation_ODomain(_1732545, _1732547)))], (41943 ^ _781013) ^ [_1609870, _1609872, _1609874] : [-(hBOOL(hAPP(c_List_Odistinct(_1609870), hAPP(hAPP(c_List_Oappend(_1609870), _1609872), _1609874)))), hBOOL(hAPP(c_List_Odistinct(_1609870), _1609872)), hBOOL(hAPP(c_List_Odistinct(_1609870), _1609874)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1609870, tc_HOL_Obool)), hAPP(c_List_Oset(_1609870), _1609872)), hAPP(c_List_Oset(_1609870), _1609874)) = c_Orderings_Obot__class_Obot(tc_fun(_1609870, tc_HOL_Obool))], (12388 ^ _781013) ^ [_1004559, _1004561] : [class_Lattices_Olattice(_1004559), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1004559), _1004561), _1004561) = _1004561)], (39302 ^ _781013) ^ [_1540309, _1540311, _1540313, _1540315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1540309)), _1540311)), _1540313)), -(hAPP(hAPP(c_List_Olist__update(_1540309, _1540311), _1540313), _1540315) = _1540311)], (7407 ^ _781013) ^ [_904690, _904692, _904694] : [class_Orderings_Oorder(_904690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904690), _904692), _904694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904690), _904694), _904692)), -(_904692 = _904694)], (30027 ^ _781013) ^ [_1342063, _1342065, _1342067, _1342069] : [class_Orderings_Olinorder(_1342063), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342063), _1342065), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342063), _1342067), _1342069)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342063), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342063), _1342065), _1342067)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342063), _1342065), _1342069)))], (35859 ^ _781013) ^ [_1459059, _1459061, _1459063, _1459065, _1459067] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1459059, _1459061), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1459063), _1459065))), -(_1459061 = 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)), _1459067)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1459059, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1459061), _1459067)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1459063), _1459067)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1459061), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1459063, _1459067))), _1459065)))))], (40343 ^ _781013) ^ [_1568072, _1568074, _1568076, _1568078, _1568080, _1568082, _1568084] : [-(c_Map_Omap__upds(_1568072, _1568074, _1568076, hAPP(hAPP(c_List_Olist_OCons(_1568072), _1568078), _1568080), hAPP(hAPP(c_List_Olist_OCons(_1568074), _1568082), _1568084)) = c_Map_Omap__upds(_1568072, _1568074, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1568072, tc_Option_Ooption(_1568074)), _1568076), _1568078), hAPP(c_Option_Ooption_OSome(_1568074), _1568082)), _1568080, _1568084))], (32055 ^ _781013) ^ [_1389692, _1389694] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1389692))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1389694)), hAPP(c_Int_Onat, _1389692)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1389694), _1389692)), 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)))], (39587 ^ _781013) ^ [_1547044, _1547046, _1547048, _1547050] : [hBOOL(hAPP(_1547044, _1547046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1547048, c_Hilbert__Choice_OLeastM(_1547050, tc_Nat_Onat, _1547048, _1547044))), hAPP(_1547048, _1547046))))], (46238 ^ _781013) ^ [_1706629, _1706631, _1706633, _1706635, _1706637] : [c_List_Olist__all2(_1706629, _1706631, _1706633, _1706635, _1706637), 46241 ^ _781013 : [(46244 ^ _781013) ^ [_1706792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706792), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706629)), _1706635))), -(hBOOL(hAPP(hAPP(_1706633, hAPP(hAPP(c_List_Onth(_1706629), _1706635), _1706792)), hAPP(hAPP(c_List_Onth(_1706631), _1706637), _1706792))))], (46242 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706629)), _1706635) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706631)), _1706637))]]], (5048 ^ _781013) ^ [_857952, _857954, _857956, _857958, _857960, _857962, _857964, _857966] : [-(c_New__Random__Sequence_Opos__bind(_857966, _857962, _857958, _857954) = c_New__Random__Sequence_Opos__bind(_857964, _857960, _857956, _857952)), _857966 = _857964, _857962 = _857960, _857958 = _857956, _857954 = _857952], (18510 ^ _781013) ^ [_1125467, _1125469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1125467), _1125469)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1125467), _1125469) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19008 ^ _781013) ^ [_1136602, _1136604, _1136606, _1136608] : [hBOOL(hAPP(hAPP(_1136606, _1136604), _1136608)), -(hBOOL(hAPP(hAPP(c_member(_1136602), _1136604), c_SetInterval_Oord_OatMost(_1136602, _1136606, _1136608))))], (42881 ^ _781013) ^ [_1632027, _1632029, _1632031, _1632033, _1632035] : [-(_1632027 = c_Orderings_Obot__class_Obot(tc_fun(_1632029, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1632031, tc_HOL_Obool)), _1632033), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632029, tc_fun(_1632031, tc_HOL_Obool)), _1632027), _1632035)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632029, tc_fun(_1632031, tc_HOL_Obool)), _1632027), hAPP(hAPP(c_COMBB(tc_fun(_1632031, tc_HOL_Obool), tc_fun(_1632031, tc_HOL_Obool), _1632029), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1632031, tc_HOL_Obool)), _1632033)), _1632035)))], (9933 ^ _781013) ^ [_956528, _956530, _956532] : [class_Lattices_Olattice(_956528), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956528), _956530), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956528), _956530), _956532)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956528), _956530), _956532))], (35921 ^ _781013) ^ [_1461230, _1461232, _1461234, _1461236, _1461238, _1461240] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461230, tc_fun(_1461232, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1461230, tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_fun(_1461232, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461232, tc_fun(tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_fun(_1461232, tc_HOL_Obool)), _1461230), c_COMBC(_1461232, tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461232, tc_prod(_1461230, _1461232)), tc_fun(_1461232, tc_fun(tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_HOL_Obool)), _1461230), hAPP(c_COMBB(tc_prod(_1461230, _1461232), tc_fun(tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_HOL_Obool), _1461232), c_member(tc_prod(_1461230, _1461232)))), c_Product__Type_OPair(_1461230, _1461232)))), _1461234)), hAPP(hAPP(c_COMBC(_1461230, tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_fun(_1461232, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461232, tc_fun(tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_fun(_1461232, tc_HOL_Obool)), _1461230), c_COMBC(_1461232, tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461232, tc_prod(_1461230, _1461232)), tc_fun(_1461232, tc_fun(tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_HOL_Obool)), _1461230), hAPP(c_COMBB(tc_prod(_1461230, _1461232), tc_fun(tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool), tc_HOL_Obool), _1461232), c_member(tc_prod(_1461230, _1461232)))), c_Product__Type_OPair(_1461230, _1461232)))), _1461236)), _1461238), _1461240)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1461230, _1461232)), hAPP(hAPP(c_Product__Type_OPair(_1461230, _1461232), _1461238), _1461240)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1461230, _1461232), tc_HOL_Obool)), _1461234), _1461236))))], (28006 ^ _781013) ^ [_1303943, _1303945] : [class_Rings_Olinordered__idom(_1303943), 28009 ^ _781013 : [(28016 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303943), _1303945), c_Groups_Ozero__class_Ozero(_1303943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303943), c_Groups_Osgn__class_Osgn(_1303943, _1303945)), c_Groups_Ozero__class_Ozero(_1303943))))], (28010 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303943), c_Groups_Osgn__class_Osgn(_1303943, _1303945)), c_Groups_Ozero__class_Ozero(_1303943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303943), _1303945), c_Groups_Ozero__class_Ozero(_1303943))))]]], (34273 ^ _781013) ^ [_1431057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1431057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1431057))))], (25756 ^ _781013) ^ [_1260387, _1260389] : [c_Nat__Transfer_Ois__nat(_1260387), c_Nat__Transfer_Ois__nat(_1260389), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1260387), _1260389)))], (35833 ^ _781013) ^ [_1458435, _1458437, _1458439, _1458441] : [-(c_Nitpick_Oprod(_1458435, _1458437, _1458439, _1458441) = hAPP(c_Set_OCollect(tc_prod(_1458435, _1458437)), hAPP(c_Product__Type_Oprod_Oprod__case(_1458435, _1458437, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1458435, tc_fun(_1458437, tc_HOL_Obool), tc_fun(_1458437, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1458437, tc_HOL_Obool), tc_fun(_1458437, tc_HOL_Obool)), _1458435), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1458437)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1458435), c_fconj), hAPP(hAPP(c_COMBC(_1458435, tc_fun(_1458435, tc_HOL_Obool), tc_HOL_Obool), c_member(_1458435)), _1458439)))), hAPP(hAPP(c_COMBC(_1458437, tc_fun(_1458437, tc_HOL_Obool), tc_HOL_Obool), c_member(_1458437)), _1458441)))))], (48904 ^ _781013) ^ [_1771711, _1771713, _1771715, _1771717] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1771711, tc_fun(_1771711, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1771711, tc_fun(tc_prod(_1771711, _1771711), tc_HOL_Obool), tc_fun(_1771711, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1771711, tc_fun(tc_fun(tc_prod(_1771711, _1771711), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1771711, _1771711), tc_HOL_Obool), tc_fun(_1771711, tc_HOL_Obool)), _1771711), c_COMBC(_1771711, tc_fun(tc_prod(_1771711, _1771711), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1771711, tc_prod(_1771711, _1771711)), tc_fun(_1771711, tc_fun(tc_fun(tc_prod(_1771711, _1771711), tc_HOL_Obool), tc_HOL_Obool)), _1771711), hAPP(c_COMBB(tc_prod(_1771711, _1771711), tc_fun(tc_fun(tc_prod(_1771711, _1771711), tc_HOL_Obool), tc_HOL_Obool), _1771711), c_member(tc_prod(_1771711, _1771711)))), c_Product__Type_OPair(_1771711, _1771711)))), _1771713)), c_fequal), _1771715), _1771717)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1771711, _1771711)), hAPP(hAPP(c_Product__Type_OPair(_1771711, _1771711), _1771715), _1771717)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1771711, _1771711), tc_HOL_Obool)), _1771713), c_Relation_OId(_1771711)))))], (48924 ^ _781013) ^ [_1772710] : [-(c_Relation_Orefl__on(_1772710, c_Orderings_Otop__class_Otop(tc_fun(_1772710, tc_HOL_Obool)), c_Relation_OId(_1772710)))], (10011 ^ _781013) ^ [_958031, _958033, _958035] : [class_Lattices_Oboolean__algebra(_958031), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_958031), _958033), _958035) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_958031), _958033), hAPP(c_Groups_Ouminus__class_Ouminus(_958031), _958035)))], (44977 ^ _781013) ^ [_1679379, _1679381] : [hBOOL(hAPP(c_List_Odistinct(_1679379), _1679381)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1679379, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1679379), tc_fun(_1679379, tc_HOL_Obool)), c_List_Oset(_1679379)), c_Enum_Osublists(_1679379, _1679381)))))], (30241 ^ _781013) ^ [_1345915, _1345917, _1345919] : [class_Orderings_Olinorder(_1345915), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345915), _1345917), _1345919) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345915), _1345919), _1345917))], (31796 ^ _781013) ^ [_1382143, _1382145, _1382147] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382143, tc_fun(_1382145, tc_HOL_Obool)), _1382147), hAPP(c_COMBK(tc_fun(_1382145, tc_HOL_Obool), _1382143), c_Orderings_Obot__class_Obot(tc_fun(_1382145, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1382145, tc_HOL_Obool)))], (34081 ^ _781013) ^ [_1427644, _1427646] : [class_Int_Onumber__ring(_1427644), 34084 ^ _781013 : [(34091 ^ _781013) ^ [] : [c_Int_Oiszero(_1427644, hAPP(c_Int_Onumber__class_Onumber__of(_1427644), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1427646), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1427644), _1427646) = c_Groups_Ozero__class_Ozero(_1427644))], (34085 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1427644), _1427646) = c_Groups_Ozero__class_Ozero(_1427644), -(c_Int_Oiszero(_1427644, hAPP(c_Int_Onumber__class_Onumber__of(_1427644), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1427646), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (42733 ^ _781013) ^ [_1627561, _1627563, _1627565] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1627561)), _1627563), c_List_Olists(_1627561, _1627565))), -(_1627563 = c_List_Olist_ONil(_1627561)), 42742 ^ _781013 : [(42747 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1627561)), 42741 ^ [_1627561, _1627563, _1627565]), c_List_Olists(_1627561, _1627565))))], (42745 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1627561), 42740 ^ [_1627561, _1627563, _1627565]), _1627565)))], (42743 ^ _781013) ^ [] : [-(_1627563 = hAPP(hAPP(c_List_Olist_OCons(_1627561), 42740 ^ [_1627561, _1627563, _1627565]), 42741 ^ [_1627561, _1627563, _1627565]))]]], (44997 ^ _781013) ^ [_1679861, _1679863] : [_1679861 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1679863, _1679861, c_List_Olist_ONil(_1679863)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1679863)), c_List_Olist_ONil(_1679863)), c_List_Olist_ONil(tc_List_Olist(_1679863))))], (40009 ^ _781013) ^ [] : [c_Com_OWT__bodies, 40012 ^ _781013 : [(40013 ^ _781013) ^ [_1560169] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1560169), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), _1560169)))]]], (42801 ^ _781013) ^ [_1629000, _1629002, _1629004, _1629006, _1629008, _1629010] : [hBOOL(hAPP(hAPP(c_member(_1629000), _1629002), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629004, tc_fun(_1629000, tc_HOL_Obool)), _1629006), _1629008))), hBOOL(hAPP(hAPP(c_member(_1629004), _1629010), _1629006)), -(hBOOL(hAPP(hAPP(c_member(_1629000), _1629002), hAPP(_1629008, _1629010))))], (43227 ^ _781013) ^ [_1641501, _1641503] : [-(hBOOL(hAPP(c_List_Olistsp(_1641501, _1641503), c_List_Olist_ONil(_1641501))))], (51504 ^ _781013) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (13096 ^ _781013) ^ [_1019245, _1019247, _1019249, _1019251, _1019253, _1019255] : [class_Groups_Oab__semigroup__mult(_1019245), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019247), _1019249)), -(hBOOL(hAPP(hAPP(c_member(_1019247), _1019251), _1019249))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1019245, _1019247, c_Groups_Otimes__class_Otimes(_1019245)), _1019253), _1019255), hAPP(hAPP(c_Set_Oinsert(_1019247), _1019251), _1019249)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019245), hAPP(_1019253, _1019251)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1019245, _1019247, c_Groups_Otimes__class_Otimes(_1019245)), _1019253), _1019255), _1019249)))], (48123 ^ _781013) ^ [_1753329, _1753331] : [_1753329 = _1753331, -(c_Random_Oinc__shift(_1753329, _1753331) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (246 ^ _781013) ^ [_784988, _784990] : [-(class_Fields_Ofield(_784988)), _784990 = _784988, class_Fields_Ofield(_784990)], (6450 ^ _781013) ^ [_886427, _886429, _886431, _886433, _886435, _886437] : [-(hAPP(hAPP(c_Fun_Ocomp(_886427, _886429, _886431, _886433), _886435), _886437) = hAPP(_886433, hAPP(_886435, _886437)))], (8377 ^ _781013) ^ [_925193, _925195, _925197, _925199, _925201, _925203] : [hBOOL(hAPP(hAPP(c_member(_925193), _925195), _925197)), _925199 = hAPP(_925201, _925195), -(hBOOL(hAPP(hAPP(c_member(_925203), _925199), hAPP(c_Set_Oimage(_925193, _925203, _925201), _925197))))], (2190 ^ _781013) ^ [_813241, _813243, _813245, _813247, _813249, _813251, _813253, _813255] : [-(c_SetInterval_Oord_OatLeastAtMost(_813255, _813251, _813247, _813243) = c_SetInterval_Oord_OatLeastAtMost(_813253, _813249, _813245, _813241)), _813255 = _813253, _813251 = _813249, _813247 = _813245, _813243 = _813241], (43400 ^ _781013) ^ [_1645190, _1645192, _1645194, _1645196] : [-(hBOOL(hAPP(c_List_Olistsp(_1645190, hAPP(hAPP(c_COMBS(_1645190, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1645190), c_fconj), _1645192)), _1645194)), _1645196))), hBOOL(hAPP(c_List_Olistsp(_1645190, _1645192), _1645196)), hBOOL(hAPP(c_List_Olistsp(_1645190, _1645194), _1645196))], (25222 ^ _781013) ^ [_1251145, _1251147, _1251149, _1251151] : [class_Fields_Ofield__inverse__zero(_1251145), -(_1251147 = c_Groups_Ozero__class_Ozero(_1251145)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251145), _1251149), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251145), _1251151), _1251147)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251145), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251145), _1251151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251145), _1251149), _1251147))), _1251147))], (44095 ^ _781013) ^ [_1658914] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1658914) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1658914))))], (6132 ^ _781013) ^ [_880447, _880449, _880451, _880453, _880455] : [hBOOL(hAPP(_880447, _880449)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_880451), _880449), _880453)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_880447, _880451, _880455)), _880449), _880453)))], (4246 ^ _781013) ^ [_845243, _845245, _845247, _845249] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_845249, _845245) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_845247, _845243)), _845249 = _845247, _845245 = _845243], (28842 ^ _781013) ^ [_1319141, _1319143, _1319145, _1319147] : [class_Orderings_Olinorder(_1319141), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319141), _1319143), _1319145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319141), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319141), _1319147), _1319143)), _1319145)))], (17687 ^ _781013) ^ [_1111476, _1111478, _1111480] : [17688 ^ _781013 : [(17691 ^ _781013) ^ [] : [_1111476 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17689 ^ _781013) ^ [] : [_1111478 = _1111480]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111476), _1111478) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111476), _1111480))], (51462 ^ _781013) ^ [_1823228, _1823230] : [-(class_Finite__Set_Ofinite(tc_prod(_1823228, _1823230))), class_Finite__Set_Ofinite(_1823228), class_Finite__Set_Ofinite(_1823230)], (33516 ^ _781013) ^ [_1417035, _1417037] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417035)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417035)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417037)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417035)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417037))))], (35353 ^ _781013) ^ [_1450097, _1450099] : [-(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), _1450097)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1450099))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450097))) = 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), _1450099)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450097)))], (20244 ^ _781013) ^ [_1159479, _1159481] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159479), hAPP(c_Nat_OSuc, _1159481)))), 20245 ^ _781013 : [(20248 ^ _781013) ^ [_1159567] : [_1159479 = hAPP(c_Nat_OSuc, _1159567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159567), _1159481))], (20246 ^ _781013) ^ [] : [_1159479 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (21287 ^ _781013) ^ [_1180338] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1180338)) = _1180338)], (42871 ^ _781013) ^ [_1631714, _1631716, _1631718, _1631720] : [-(hAPP(c_Set_OCollect(_1631714), hAPP(hAPP(c_COMBB(tc_fun(_1631716, tc_HOL_Obool), tc_HOL_Obool, _1631714), c_HOL_OAll(_1631716)), hAPP(hAPP(c_COMBB(tc_fun(_1631716, tc_HOL_Obool), tc_fun(_1631716, tc_HOL_Obool), _1631714), hAPP(c_COMBS(_1631716, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1631716), c_fimplies), hAPP(hAPP(c_COMBC(_1631716, tc_fun(_1631716, tc_HOL_Obool), tc_HOL_Obool), c_member(_1631716)), _1631718)))), _1631720))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631716, tc_fun(_1631714, tc_HOL_Obool)), _1631718), hAPP(hAPP(c_COMBB(tc_fun(_1631714, tc_HOL_Obool), tc_fun(_1631714, tc_HOL_Obool), _1631716), c_Set_OCollect(_1631714)), hAPP(c_COMBC(_1631714, _1631716, tc_HOL_Obool), _1631720))))], (21361 ^ _781013) ^ [_1181720, _1181722, _1181724, _1181726] : [class_Rings_Ocomm__semiring__1(_1181720), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181720), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181720), c_Groups_Oone__class_Oone(_1181720)), c_Groups_Oone__class_Oone(_1181720))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1181720), hAPP(hAPP(c_COMBB(_1181720, _1181720, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1181720), _1181722)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1181720, _1181720), hAPP(hAPP(c_COMBB(_1181720, tc_fun(_1181720, _1181720), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1181720)), c_Nat_Osemiring__1__class_Oof__nat(_1181720))), _1181724))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1181726))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181720), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1181720), _1181726)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181720), _1181722), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181720), _1181722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181720), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1181720), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1181726), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1181724)))))], (34255 ^ _781013) ^ [_1430766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1430766)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430766), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (38790 ^ _781013) ^ [_1528407, _1528409, _1528411] : [class_Orderings_Olinorder(_1528407), -(c_List_Oremove1(_1528407, _1528409, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1528407, _1528407, c_COMBI(_1528407)), _1528409), _1528411)) = _1528411)], (40215 ^ _781013) ^ [_1565283, _1565285, _1565287, _1565289, _1565291, _1565293] : [-(c_List_Olistrelp(_1565283, _1565285, hAPP(hAPP(c_List_Olist_OCons(_1565283), _1565287), _1565289), hAPP(hAPP(c_List_Olist_OCons(_1565283), _1565291), _1565293))), hBOOL(hAPP(hAPP(_1565285, _1565287), _1565291)), c_List_Olistrelp(_1565283, _1565285, _1565289, _1565293)], (42923 ^ _781013) ^ [_1632816, _1632818, _1632820, _1632822, _1632824] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632816, tc_fun(_1632818, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1632816, tc_HOL_Obool)), _1632820), _1632822)), _1632824) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1632818, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632816, tc_fun(_1632818, tc_HOL_Obool)), _1632820), _1632824)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632816, tc_fun(_1632818, tc_HOL_Obool)), _1632822), _1632824)))], (36154 ^ _781013) ^ [_1469632, _1469634, _1469636, _1469638, _1469640] : [c_Equiv__Relations_Oequiv(_1469632, _1469634, _1469636), hBOOL(hAPP(hAPP(c_member(tc_prod(_1469632, _1469632)), hAPP(hAPP(c_Product__Type_OPair(_1469632, _1469632), _1469638), _1469640)), _1469636)), -(hAPP(c_Relation_OImage(_1469632, _1469632, _1469636), hAPP(hAPP(c_Set_Oinsert(_1469632), _1469638), c_Orderings_Obot__class_Obot(tc_fun(_1469632, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1469632, _1469632, _1469636), hAPP(hAPP(c_Set_Oinsert(_1469632), _1469640), c_Orderings_Obot__class_Obot(tc_fun(_1469632, tc_HOL_Obool)))))], (48784 ^ _781013) ^ [_1768828, _1768830] : [c_Wellfounded_Oacyclic(_1768828, _1768830), -(c_Wellfounded_Oacyclic(_1768828, hAPP(c_Relation_Oconverse(_1768828, _1768828), _1768830)))], (40948 ^ _781013) ^ [_1587173, _1587175] : [-(c_Product__Type_Oapfst(_1587173, _1587173, _1587175, c_Fun_Oid(_1587173)) = c_Fun_Oid(tc_prod(_1587173, _1587175)))], (33830 ^ _781013) ^ [_1421885] : [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), _1421885))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1421885)))], (13599 ^ _781013) ^ [_1030163, _1030165, _1030167, _1030169, _1030171] : [class_Groups_Ocomm__monoid__mult(_1030163), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030165), _1030167)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030165), _1030169)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030163), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1030163, _1030165, c_Groups_Otimes__class_Otimes(_1030163)), _1030171), c_Groups_Oone__class_Oone(_1030163)), _1030167)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1030163, _1030165, c_Groups_Otimes__class_Otimes(_1030163)), _1030171), c_Groups_Oone__class_Oone(_1030163)), _1030169)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030163), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1030163, _1030165, c_Groups_Otimes__class_Otimes(_1030163)), _1030171), c_Groups_Oone__class_Oone(_1030163)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1030165, tc_HOL_Obool)), _1030167), _1030169))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1030163, _1030165, c_Groups_Otimes__class_Otimes(_1030163)), _1030171), c_Groups_Oone__class_Oone(_1030163)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1030165, tc_HOL_Obool)), _1030167), _1030169))))], (19192 ^ _781013) ^ [_1140526, _1140528] : [-(_1140526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1140528), _1140526) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1140528), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1140528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1140526), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (27130 ^ _781013) ^ [_1286152] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1286152)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1286152)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1286152)))], (146 ^ _781013) ^ [_783454, _783456, _783458, _783460, _783462, _783464, _783466, _783468, _783470, _783472] : [-(c_Finite__Set_Ofolding__image(_783470, _783466, _783462, _783458, _783454)), c_Finite__Set_Ofolding__image(_783472, _783468, _783464, _783460, _783456), _783472 = _783470, _783468 = _783466, _783464 = _783462, _783460 = _783458, _783456 = _783454], (18546 ^ _781013) ^ [_1126088, _1126090, _1126092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126088), _1126090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126092), _1126088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1126088), _1126092)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1126090), _1126092))))], (35523 ^ _781013) ^ [_1453638] : [c_Int_OMin = c_Int_OBit1(_1453638), -(c_Int_OMin = _1453638)], (23084 ^ _781013) ^ [_1212965] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1212965)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1212965)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44081 ^ _781013) ^ [_1658693, _1658695] : [class_Orderings_Olinorder(_1658693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1658693), _1658695)), 44088 ^ _781013 : [(44093 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1658693), c_List_Olinorder__class_Osorted__list__of__set(_1658693, _1658695))))], (44091 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1658693, c_List_Olinorder__class_Osorted__list__of__set(_1658693, _1658695)))], (44089 ^ _781013) ^ [] : [-(hAPP(c_List_Oset(_1658693), c_List_Olinorder__class_Osorted__list__of__set(_1658693, _1658695)) = _1658695)]]], (35989 ^ _781013) ^ [_1466001, _1466003, _1466005, _1466007, _1466009] : [hBOOL(hAPP(hAPP(c_member(_1466001), _1466003), hAPP(c_Relation_OImage(_1466005, _1466001, _1466007), _1466009))), 35993 ^ _781013 : [(35996 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1466005, _1466001)), hAPP(hAPP(c_Product__Type_OPair(_1466005, _1466001), 35992 ^ [_1466001, _1466003, _1466005, _1466007, _1466009]), _1466003)), _1466007)))], (35994 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1466005), 35992 ^ [_1466001, _1466003, _1466005, _1466007, _1466009]), _1466009)))]]], (35555 ^ _781013) ^ [_1454092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1454092))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1454092)))], (39326 ^ _781013) ^ [_1540742, _1540744, _1540746, _1540748, _1540750] : [class_Groups_Ocomm__monoid__add(_1540742), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1540742), hAPP(hAPP(c_List_Omap(_1540744, _1540742), hAPP(hAPP(c_COMBS(_1540744, _1540742, _1540742), hAPP(hAPP(c_COMBB(_1540742, tc_fun(_1540742, _1540742), _1540744), c_Groups_Oplus__class_Oplus(_1540742)), _1540746)), _1540748)), _1540750)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1540742), hAPP(c_List_Omonoid__add__class_Olistsum(_1540742), hAPP(hAPP(c_List_Omap(_1540744, _1540742), _1540746), _1540750))), hAPP(c_List_Omonoid__add__class_Olistsum(_1540742), hAPP(hAPP(c_List_Omap(_1540744, _1540742), _1540748), _1540750))))], (5146 ^ _781013) ^ [_859477, _859479] : [_859479 = _859477, -(c_Set_OCollect(_859479) = c_Set_OCollect(_859477))], (50860 ^ _781013) ^ [_1815076, _1815078, _1815080, _1815082, _1815084] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815076, _1815078, _1815080), _1815082), _1815084)), -(hBOOL(hAPP(hAPP(_1815080, _1815084), _1815082)))], (1986 ^ _781013) ^ [_809837, _809839, _809841, _809843, _809845, _809847] : [-(c_Smallcheck_Oorelse(_809847, _809843, _809839) = c_Smallcheck_Oorelse(_809845, _809841, _809837)), _809847 = _809845, _809843 = _809841, _809839 = _809837], (37979 ^ _781013) ^ [_1508513] : [-(_1508513 = 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)), _1508513), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (39400 ^ _781013) ^ [_1542618, _1542620] : [class_Groups_Oordered__ab__group__add__abs(_1542618), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1542618), hAPP(c_Groups_Oabs__class_Oabs(_1542618), hAPP(c_List_Omonoid__add__class_Olistsum(_1542618), _1542620))), hAPP(c_List_Omonoid__add__class_Olistsum(_1542618), hAPP(hAPP(c_List_Omap(_1542618, _1542618), c_Groups_Oabs__class_Oabs(_1542618)), _1542620)))))], (37086 ^ _781013) ^ [_1488749, _1488751, _1488753, _1488755, _1488757, _1488759, _1488761] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1488749, _1488751), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1488753), _1488755))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1488757, _1488751), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1488759), _1488761))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1488751)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1488749), _1488757), _1488751), 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), _1488753), _1488759)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1488755), _1488761)), _1488751))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1488755), _1488761), _1488751)))))], (5404 ^ _781013) ^ [_863428, _863430] : [_863430 = _863428, -(tc_List_Olist(_863430) = tc_List_Olist(_863428))], (40611 ^ _781013) ^ [_1576358, _1576360, _1576362, _1576364, _1576366] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1576358, _1576360), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1576358, tc_HOL_Obool)), _1576362), _1576364)), hAPP(c_COMBK(tc_fun(_1576360, tc_HOL_Obool), _1576358), _1576366)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1576358, _1576360), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1576358, _1576360), _1576362), hAPP(c_COMBK(tc_fun(_1576360, tc_HOL_Obool), _1576358), _1576366))), hAPP(hAPP(c_Product__Type_OSigma(_1576358, _1576360), _1576364), hAPP(c_COMBK(tc_fun(_1576360, tc_HOL_Obool), _1576358), _1576366))))], (18175 ^ _781013) ^ [_1119589, _1119591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119589), _1119591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119589), _1119591))), -(_1119589 = _1119591)], (42076 ^ _781013) ^ [_1613663, _1613665] : [hAPP(c_List_Orotate1(_1613663), _1613665) = c_List_Olist_ONil(_1613663), -(_1613665 = c_List_Olist_ONil(_1613663))], (42292 ^ _781013) ^ [_1618918, _1618920, _1618922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618918), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618920)), _1618922))), -(_1618922 = hAPP(hAPP(c_List_Oappend(_1618920), hAPP(hAPP(c_List_Otake(_1618920), _1618918), _1618922)), hAPP(hAPP(c_List_Olist_OCons(_1618920), hAPP(hAPP(c_List_Onth(_1618920), _1618922), _1618918)), hAPP(hAPP(c_List_Odrop(_1618920), hAPP(c_Nat_OSuc, _1618918)), _1618922))))], (51590 ^ _781013) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (38403 ^ _781013) ^ [_1519128, _1519130, _1519132, _1519134, _1519136, _1519138] : [c_Typedef_Otype__definition(_1519128, _1519130, _1519132, _1519134, _1519136), -(hAPP(_1519134, hAPP(_1519132, _1519138)) = _1519138)], (43135 ^ _781013) ^ [_1639081, _1639083, _1639085, _1639087, _1639089] : [-(_1639081 = c_Orderings_Obot__class_Obot(tc_fun(_1639083, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639083, tc_fun(_1639085, tc_HOL_Obool)), _1639081), hAPP(hAPP(c_COMBB(tc_fun(_1639085, tc_HOL_Obool), tc_fun(_1639085, tc_HOL_Obool), _1639083), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639085, tc_HOL_Obool)), _1639087)), _1639089)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639085, tc_HOL_Obool)), _1639087), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639083, tc_fun(_1639085, tc_HOL_Obool)), _1639081), _1639089)))], (17713 ^ _781013) ^ [_1111901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111901), _1111901))], (34591 ^ _781013) ^ [_1436233, _1436235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436233), 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)))), _1436235)), 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)))), _1436233)) = 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), _1436235), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1436233))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (48754 ^ _781013) ^ [_1768046, _1768048, _1768050, _1768052, _1768054] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768046, _1768048)), hAPP(hAPP(c_Product__Type_OPair(_1768046, _1768048), _1768050), _1768052)), hAPP(c_Relation_Oconverse(_1768048, _1768046), _1768054))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1768048, _1768046)), hAPP(hAPP(c_Product__Type_OPair(_1768048, _1768046), _1768052), _1768050)), _1768054)))], (8357 ^ _781013) ^ [_924791, _924793, _924795, _924797, _924799, _924801] : [_924791 = hAPP(_924793, _924795), hBOOL(hAPP(hAPP(c_member(_924797), _924795), _924799)), -(hBOOL(hAPP(hAPP(c_member(_924801), _924791), hAPP(c_Set_Oimage(_924797, _924801, _924793), _924799))))], (40962 ^ _781013) ^ [_1587411, _1587413] : [-(c_Fun_Oinj__on(_1587411, _1587411, c_Fun_Oid(_1587411), _1587413))], (26985 ^ _781013) ^ [_1283327, _1283329, _1283331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1283327)), 26988 ^ _781013 : [(26989 ^ _781013) ^ [_1283461] : [26991 ^ _781013 : [(26997 ^ _781013) ^ [] : [-(_1283461 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26993 ^ [_1283327, _1283329, _1283331, _1283461]), 26990 ^ [_1283327, _1283329, _1283331, _1283461]))], (26995 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26993 ^ [_1283327, _1283329, _1283331, _1283461]), _1283329)))], (26992 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26990 ^ [_1283327, _1283329, _1283331, _1283461]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1283327))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1283331), _1283461)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1283331), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1283461), _1283327))))]]], (49120 ^ _781013) ^ [_1777206, _1777208, _1777210] : [49121 ^ _781013 : [(49122 ^ _781013) ^ [_1777282] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1777206, _1777206)), _1777208), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777206, _1777206), tc_HOL_Obool), _1777282), _1777210)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777206, _1777206)), _1777208), c_Transitive__Closure_Ortrancl(_1777206, _1777210))))], (11061 ^ _781013) ^ [_977675, _977677, _977679, _977681] : [-(hBOOL(hAPP(hAPP(c_member(_977675), _977677), _977679))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977675, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_977675), _977677), _977681)), _977679) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977675, tc_HOL_Obool)), _977681), _977679))], (23587 ^ _781013) ^ [_1222299, _1222301] : [class_Rings_Odivision__ring(_1222299), -(_1222301 = c_Groups_Ozero__class_Ozero(_1222299)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222299), _1222301), _1222301) = c_Groups_Oone__class_Oone(_1222299))], (266 ^ _781013) ^ [_785238, _785240] : [-(class_Fields_Olinordered__field__inverse__zero(_785238)), _785240 = _785238, class_Fields_Olinordered__field__inverse__zero(_785240)], (42232 ^ _781013) ^ [_1617297, _1617299, _1617301, _1617303, _1617305] : [-(hAPP(hAPP(c_List_Oappend(_1617297), _1617299), _1617301) = hAPP(hAPP(c_List_Oappend(_1617297), _1617303), _1617305)), 42235 ^ _781013 : [(42238 ^ _781013) ^ [] : [_1617299 = hAPP(hAPP(c_List_Otake(_1617297), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617297)), _1617299)), _1617303), _1617301 = hAPP(hAPP(c_List_Oappend(_1617297), hAPP(hAPP(c_List_Odrop(_1617297), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617297)), _1617299)), _1617303)), _1617305)], (42236 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617297)), _1617299)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617297)), _1617303))))]], 42243 ^ _781013 : [(42246 ^ _781013) ^ [] : [hAPP(hAPP(c_List_Otake(_1617297), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617297)), _1617303)), _1617299) = _1617303, hAPP(hAPP(c_List_Oappend(_1617297), hAPP(hAPP(c_List_Odrop(_1617297), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617297)), _1617303)), _1617299)), _1617301) = _1617305], (42244 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617297)), _1617299)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617297)), _1617303)))]]], (46436 ^ _781013) ^ [_1711292, _1711294, _1711296] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1711292, _1711294, _1711296, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1711294)], (24158 ^ _781013) ^ [_1231540, _1231542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231540)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231540), _1231542)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1231540)), hAPP(c_Int_Onat, _1231542)))], (6300 ^ _781013) ^ [_883529, _883531, _883533, _883535] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_883529), _883531), _883533)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_883529), _883531), _883535)), -(_883535 = _883533)], (21335 ^ _781013) ^ [_1181207, _1181209, _1181211] : [class_Orderings_Olinorder(_1181207), 21338 ^ _781013 : [(21345 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181207), _1181209), _1181211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1181207, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1181207), _1181209)), hAPP(c_SetInterval_Oord__class_OlessThan(_1181207), _1181211))))], (21339 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1181207, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1181207), _1181209)), hAPP(c_SetInterval_Oord__class_OlessThan(_1181207), _1181211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181207), _1181209), _1181211)))]]], (216 ^ _781013) ^ [_784613, _784615] : [-(class_Rings_Odivision__ring__inverse__zero(_784613)), _784615 = _784613, class_Rings_Odivision__ring__inverse__zero(_784615)], (51276 ^ _781013) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (36747 ^ _781013) ^ [_1482502, _1482504] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1482502, _1482502)), hAPP(hAPP(c_Product__Type_OPair(_1482502, _1482502), 36748 ^ [_1482502, _1482504]), 36748 ^ [_1482502, _1482504])), _1482504)), -(c_Nitpick_Orefl_H(_1482502, _1482504))], (5526 ^ _781013) ^ [_865269, _865271] : [_865271 = _865269, -(c_Set_Oinsert(_865271) = c_Set_Oinsert(_865269))], (3140 ^ _781013) ^ [_828142, _828144, _828146, _828148] : [-(c_List_Oupt(_828148, _828144) = c_List_Oupt(_828146, _828142)), _828148 = _828146, _828144 = _828142], (7577 ^ _781013) ^ [_907963, _907965, _907967, _907969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907963, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_907963), _907965), _907967)), _907969)), 7580 ^ _781013 : [(7583 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907963, tc_HOL_Obool)), _907967), _907969)))], (7581 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907963), _907965), _907969)))]]], (12682 ^ _781013) ^ [_1010363, _1010365, _1010367] : [class_Rings_Oring(_1010363), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010363), hAPP(c_Groups_Ouminus__class_Ouminus(_1010363), _1010365)), hAPP(c_Groups_Ouminus__class_Ouminus(_1010363), _1010367)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010363), _1010365), _1010367))], (12870 ^ _781013) ^ [_1014416, _1014418, _1014420, _1014422, _1014424] : [hBOOL(hAPP(hAPP(c_member(_1014420), hAPP(_1014422, _1014418)), _1014424)), -(hBOOL(hAPP(hAPP(c_member(_1014416), _1014418), hAPP(c_Set_Ovimage(_1014416, _1014420, _1014422), _1014424))))], (50732 ^ _781013) ^ [_1811899] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1811899))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1811899)))], (13839 ^ _781013) ^ [_1035244, _1035246, _1035248, _1035250] : [class_Rings_Ocomm__semiring__1(_1035244), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035244), _1035246), _1035248)), _1035250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035244), _1035246), _1035250)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035244), _1035248), _1035250)))], (35041 ^ _781013) ^ [_1444372] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1444372), 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), _1444372), _1444372))], (42749 ^ _781013) ^ [_1627844, _1627846, _1627848] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1627844)), _1627846), c_List_Olists(_1627844, _1627848)))), 42750 ^ _781013 : [(42753 ^ _781013) ^ [_1627972, _1627974] : [_1627846 = hAPP(hAPP(c_List_Olist_OCons(_1627844), _1627974), _1627972), hBOOL(hAPP(hAPP(c_member(_1627844), _1627974), _1627848)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1627844)), _1627972), c_List_Olists(_1627844, _1627848)))], (42751 ^ _781013) ^ [] : [_1627846 = c_List_Olist_ONil(_1627844)]]], (40169 ^ _781013) ^ [_1564284, _1564286, _1564288, _1564290] : [-(_1564284 = _1564286), -(hAPP(c_List_OremoveAll(_1564288, _1564284), hAPP(hAPP(c_List_Olist_OCons(_1564288), _1564286), _1564290)) = hAPP(hAPP(c_List_Olist_OCons(_1564288), _1564286), hAPP(c_List_OremoveAll(_1564288, _1564284), _1564290)))], (30235 ^ _781013) ^ [_1345824, _1345826] : [class_Orderings_Olinorder(_1345824), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345824), _1345826), _1345826) = _1345826)], (46637 ^ _781013) ^ [_1717292, _1717294, _1717296, _1717298, _1717300, _1717302] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1717292, _1717294, _1717296), _1717298), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1717294, _1717296), tc_HOL_Obool)), _1717300), _1717302)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1717292, _1717296), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1717292, _1717294, _1717296), _1717298), _1717300)), hAPP(hAPP(c_Relation_Orel__comp(_1717292, _1717294, _1717296), _1717298), _1717302)))], (13883 ^ _781013) ^ [_1036169, _1036171, _1036173, _1036175] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1036169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036169), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036169), _1036171), _1036173)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036169), _1036175), _1036173))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036169), _1036171), _1036175)))], (9008 ^ _781013) ^ [_939344, _939346, _939348, _939350, _939352] : [hBOOL(hAPP(hAPP(c_member(_939344), _939346), _939348)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_939344, tc_Option_Ooption(_939350)), c_Map_Orestrict__map(_939344, _939350, _939352, _939348)), _939346), c_Option_Ooption_ONone(_939350)) = c_Map_Orestrict__map(_939344, _939350, _939352, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939344, tc_HOL_Obool)), _939348), hAPP(hAPP(c_Set_Oinsert(_939344), _939346), c_Orderings_Obot__class_Obot(tc_fun(_939344, tc_HOL_Obool))))))], (5500 ^ _781013) ^ [_864878, _864880] : [_864880 = _864878, -(c_member(_864880) = c_member(_864878))], (31662 ^ _781013) ^ [_1378869, _1378871, _1378873, _1378875, _1378877, _1378879] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378869, tc_fun(_1378871, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378873, tc_fun(_1378869, tc_HOL_Obool)), _1378875), _1378877)), _1378879) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378873, tc_fun(_1378871, tc_HOL_Obool)), _1378875), hAPP(hAPP(c_COMBC(_1378873, tc_fun(_1378869, tc_fun(_1378871, tc_HOL_Obool)), tc_fun(_1378871, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1378869, tc_HOL_Obool), tc_fun(tc_fun(_1378869, tc_fun(_1378871, tc_HOL_Obool)), tc_fun(_1378871, tc_HOL_Obool)), _1378873), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378869, tc_fun(_1378871, tc_HOL_Obool))), _1378877)), _1378879)))], (1184 ^ _781013) ^ [_798555, _798557] : [-(class_Divides_Oring__div(_798555)), _798557 = _798555, class_Divides_Oring__div(_798557)], (15153 ^ _781013) ^ [_1061405, _1061407, _1061409, _1061411] : [class_Groups_Ocomm__monoid__mult(_1061405), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1061407), _1061409))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1061407, _1061405), _1061411), _1061409) = c_Groups_Oone__class_Oone(_1061405))], (46434 ^ _781013) ^ [_1711253, _1711255, _1711257, _1711259] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1711253, _1711255, _1711257, c_Code__Numeral_OSuc__code__numeral(_1711259)) = hAPP(_1711257, _1711259))], (36008 ^ _781013) ^ [_1466479] : [-(_1466479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1466479), 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)))))], (39671 ^ _781013) ^ [_1549096, _1549098, _1549100] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549096)), hAPP(hAPP(c_List_Otake(_1549096), _1549098), _1549100)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549096)), _1549100)), _1549098))], (18097 ^ _781013) ^ [_1118092, _1118094, _1118096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118092), _1118094)), _1118096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118092), _1118096)))], (25722 ^ _781013) ^ [_1259918, _1259920, _1259922] : [class_Int_Oring__char__0(_1259918), 25725 ^ _781013 : [(25732 ^ _781013) ^ [] : [_1259920 = _1259922, -(hAPP(c_Int_Oring__1__class_Oof__int(_1259918), _1259920) = hAPP(c_Int_Oring__1__class_Oof__int(_1259918), _1259922))], (25726 ^ _781013) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1259918), _1259920) = hAPP(c_Int_Oring__1__class_Oof__int(_1259918), _1259922), -(_1259920 = _1259922)]]], (43141 ^ _781013) ^ [_1639207, _1639209, _1639211, _1639213, _1639215] : [_1639207 = c_Orderings_Obot__class_Obot(tc_fun(_1639209, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639209, tc_fun(_1639211, tc_HOL_Obool)), _1639207), hAPP(hAPP(c_COMBC(_1639209, tc_fun(_1639211, tc_HOL_Obool), tc_fun(_1639211, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1639211, tc_HOL_Obool), tc_fun(tc_fun(_1639211, tc_HOL_Obool), tc_fun(_1639211, tc_HOL_Obool)), _1639209), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639211, tc_HOL_Obool))), _1639213)), _1639215)) = c_Orderings_Otop__class_Otop(tc_fun(_1639211, tc_HOL_Obool)))], (20187 ^ _781013) ^ [_1158460, _1158462] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158460)), hAPP(c_Nat_OSuc, _1158462)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158460), _1158462))], (44602 ^ _781013) ^ [_1671753, _1671755, _1671757] : [c_List_OtakeWhile(_1671753, _1671755, _1671757) = _1671757, 44605 ^ _781013 : [(44606 ^ _781013) ^ [_1671840] : [hBOOL(hAPP(hAPP(c_member(_1671753), _1671840), hAPP(c_List_Oset(_1671753), _1671757))), -(hBOOL(hAPP(_1671755, _1671840)))]]], (19927 ^ _781013) ^ [_1154275, _1154277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1154275), _1154277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154275), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1154277), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (24866 ^ _781013) ^ [_1244425, _1244427, _1244429] : [class_Fields_Olinordered__field(_1244425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244425), _1244427), c_Groups_Ozero__class_Ozero(_1244425))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244425), c_Groups_Ozero__class_Ozero(_1244425)), _1244429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244425), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1244425), _1244427), _1244429)), c_Groups_Ozero__class_Ozero(_1244425))))], (40109 ^ _781013) ^ [_1563004, _1563006, _1563008, _1563010, _1563012] : [-(hAPP(hAPP(c_List_Olist__update(_1563004, hAPP(hAPP(c_List_Olist_OCons(_1563004), _1563006), _1563008)), hAPP(c_Nat_OSuc, _1563010)), _1563012) = hAPP(hAPP(c_List_Olist_OCons(_1563004), _1563006), hAPP(hAPP(c_List_Olist__update(_1563004, _1563008), _1563010), _1563012)))], (29847 ^ _781013) ^ [_1337604, _1337606, _1337608] : [class_Orderings_Olinorder(_1337604), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337604), _1337606)), -(_1337606 = c_Orderings_Obot__class_Obot(tc_fun(_1337604, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337604), _1337608)), -(_1337608 = c_Orderings_Obot__class_Obot(tc_fun(_1337604, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1337604, c_Orderings_Oord__class_Omin(_1337604), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337604, tc_HOL_Obool)), _1337606), _1337608)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1337604), c_Big__Operators_Olattice_OInf__fin(_1337604, c_Orderings_Oord__class_Omin(_1337604), _1337606)), c_Big__Operators_Olattice_OInf__fin(_1337604, c_Orderings_Oord__class_Omin(_1337604), _1337608)))], (3150 ^ _781013) ^ [_828291, _828293, _828295, _828297, _828299, _828301, _828303, _828305, _828307, _828309] : [-(c_List_Ofoldr(_828309, _828305, _828301, _828297, _828293) = c_List_Ofoldr(_828307, _828303, _828299, _828295, _828291)), _828309 = _828307, _828305 = _828303, _828301 = _828299, _828297 = _828295, _828293 = _828291], (49174 ^ _781013) ^ [_1778711, _1778713, _1778715, _1778717] : [-(hAPP(hAPP(c_Nat_Ocompow(_1778711, _1778711), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1778713), _1778715)), _1778717) = hAPP(c_Fun_Ocomp(_1778711, _1778711, _1778711, hAPP(hAPP(c_Nat_Ocompow(_1778711, _1778711), _1778713), _1778717)), hAPP(hAPP(c_Nat_Ocompow(_1778711, _1778711), _1778715), _1778717)))], (48163 ^ _781013) ^ [_1754090, _1754092, _1754094, _1754096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1754090), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1754092), _1754094))), -(hAPP(c_Random_Opick(_1754092, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1754092)), _1754094), _1754096)), _1754090) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1754092), _1754094))], (42110 ^ _781013) ^ [_1614306, _1614308] : [hBOOL(hAPP(c_List_Odistinct(_1614306), _1614308)), -(hBOOL(hAPP(c_List_Odistinct(_1614306), hAPP(c_List_Orotate1(_1614306), _1614308))))], (10029 ^ _781013) ^ [_958460, _958462, _958464, _958466, _958468] : [c_Finite__Set_Ofun__left__comm__idem(_958460, _958462, _958464), -(c_Finite__Set_Ofun__left__comm__idem(_958466, _958462, hAPP(hAPP(c_COMBB(_958460, tc_fun(_958462, _958462), _958466), _958464), _958468)))], (28676 ^ _781013) ^ [_1316118] : [class_Rings_Olinordered__idom(_1316118), -(hAPP(c_Groups_Oabs__class_Oabs(_1316118), c_Groups_Oone__class_Oone(_1316118)) = c_Groups_Oone__class_Oone(_1316118))], (19777 ^ _781013) ^ [_1151705] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151705), hAPP(c_Nat_OSuc, _1151705))))], (17020 ^ _781013) ^ [_1097204, _1097206, _1097208, _1097210, _1097212] : [class_Groups_Ocomm__monoid__add(_1097204), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097206), _1097208)), 17027 ^ _781013 : [(17034 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1097206), _1097210), _1097208))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1097206, _1097204), hAPP(hAPP(c_COMBC(_1097206, _1097204, _1097204), hAPP(hAPP(c_COMBS(_1097206, _1097204, tc_fun(_1097204, _1097204)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1097204, tc_fun(_1097204, _1097204)), _1097206), c_If(_1097204)), hAPP(hAPP(c_COMBC(_1097206, _1097206, tc_HOL_Obool), c_fequal), _1097210))), _1097212)), c_Groups_Ozero__class_Ozero(_1097204))), _1097208) = c_Groups_Ozero__class_Ozero(_1097204))], (17028 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1097206), _1097210), _1097208)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1097206, _1097204), hAPP(hAPP(c_COMBC(_1097206, _1097204, _1097204), hAPP(hAPP(c_COMBS(_1097206, _1097204, tc_fun(_1097204, _1097204)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1097204, tc_fun(_1097204, _1097204)), _1097206), c_If(_1097204)), hAPP(hAPP(c_COMBC(_1097206, _1097206, tc_HOL_Obool), c_fequal), _1097210))), _1097212)), c_Groups_Ozero__class_Ozero(_1097204))), _1097208) = hAPP(_1097212, _1097210))]]], (46752 ^ _781013) ^ [_1721319, _1721321, _1721323] : [c_Wellfounded_Owf(_1721319, _1721321), -(hBOOL(hAPP(hAPP(c_member(_1721319), _1721323), c_Wellfounded_Oacc(_1721319, _1721321))))], (22920 ^ _781013) ^ [_1209804, _1209806, _1209808, _1209810] : [_1209804 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1209806), _1209808)), _1209810), -(_1209806 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1209804), _1209806) = _1209808), 22927 ^ _781013 : [(22930 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209810)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209810), _1209806))], (22928 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209806)))]], 22935 ^ _781013 : [(22938 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209806), _1209810)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1209810), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22936 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209806))]]], (49486 ^ _781013) ^ [_1786923, _1786925, _1786927, _1786929] : [class_Lattices_Osemilattice__sup(_1786923), hBOOL(hAPP(c_Finite__Set_Ofinite(_1786923), _1786925)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1786923, _1786923, c_Lattices_Osemilattice__sup__class_Osup(_1786923)), _1786927), hAPP(hAPP(c_Set_Oinsert(_1786923), _1786929), _1786925)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1786923), _1786929), hAPP(hAPP(c_Finite__Set_Ofold(_1786923, _1786923, c_Lattices_Osemilattice__sup__class_Osup(_1786923)), _1786927), _1786925)))], (6629 ^ _781013) ^ [_889673, _889675, _889677, _889679, _889681, _889683, _889685] : [hAPP(c_Fun_Ocomp(_889673, _889675, _889677, _889679), _889681) = _889683, -(hAPP(_889679, hAPP(_889681, _889685)) = hAPP(_889683, _889685))], (15085 ^ _781013) ^ [_1059928] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1059928, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1059928), hAPP(c_COMBK(tc_HOL_Obool, _1059928), c_fFalse)))], (20430 ^ _781013) ^ [_1162675, _1162677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162675), _1162677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1162675)), _1162677)))], (18576 ^ _781013) ^ [_1126628, _1126630, _1126632, _1126634, _1126636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126628), _1126630)), 18579 ^ _781013 : [(18586 ^ _781013) ^ [] : [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), _1126630), _1126628)), _1126632)), _1126634)), _1126636)), -(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), _1126630), _1126632)), _1126634)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126628), _1126632)), _1126636))))], (18580 ^ _781013) ^ [] : [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), _1126630), _1126632)), _1126634)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126628), _1126632)), _1126636))), -(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), _1126630), _1126628)), _1126632)), _1126634)), _1126636)))]]], (18053 ^ _781013) ^ [_1117446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1117446), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31279 ^ _781013) ^ [_1367113, _1367115, _1367117, _1367119] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1367113), _1367115), _1367117), _1367119)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1367113), _1367115), hAPP(c_Nat_OSuc, _1367117)), _1367119)))], (47238 ^ _781013) ^ [_1732697, _1732699, _1732701, _1732703] : [hBOOL(hAPP(c_Predicate_ODomainP(_1732697, _1732699, hAPP(hAPP(c_COMBC(_1732697, tc_fun(tc_prod(_1732697, _1732699), tc_HOL_Obool), tc_fun(_1732699, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1732699, tc_fun(tc_fun(tc_prod(_1732697, _1732699), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1732697, _1732699), tc_HOL_Obool), tc_fun(_1732699, tc_HOL_Obool)), _1732697), c_COMBC(_1732699, tc_fun(tc_prod(_1732697, _1732699), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1732699, tc_prod(_1732697, _1732699)), tc_fun(_1732699, tc_fun(tc_fun(tc_prod(_1732697, _1732699), tc_HOL_Obool), tc_HOL_Obool)), _1732697), hAPP(c_COMBB(tc_prod(_1732697, _1732699), tc_fun(tc_fun(tc_prod(_1732697, _1732699), tc_HOL_Obool), tc_HOL_Obool), _1732699), c_member(tc_prod(_1732697, _1732699)))), c_Product__Type_OPair(_1732697, _1732699)))), _1732701)), _1732703)), -(hBOOL(hAPP(hAPP(c_member(_1732697), _1732703), hAPP(c_Relation_ODomain(_1732697, _1732699), _1732701))))], (12904 ^ _781013) ^ [_1015260, _1015262, _1015264, _1015266, _1015268] : [-(hAPP(c_Set_Ovimage(_1015260, _1015262, _1015264), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1015262, tc_HOL_Obool)), _1015266), _1015268)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1015260, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1015260, _1015262, _1015264), _1015266)), hAPP(c_Set_Ovimage(_1015260, _1015262, _1015264), _1015268)))], (39456 ^ _781013) ^ [_1543888, _1543890, _1543892, _1543894, _1543896, _1543898, _1543900] : [-(hBOOL(hAPP(hAPP(c_member(_1543888), _1543890), hAPP(c_List_Oset(_1543888), _1543892)))), -(c_Map_Omap__upds(_1543888, _1543894, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1543888, tc_Option_Ooption(_1543894)), _1543896), _1543890), hAPP(c_Option_Ooption_OSome(_1543894), _1543898)), _1543892, _1543900) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1543888, tc_Option_Ooption(_1543894)), c_Map_Omap__upds(_1543888, _1543894, _1543896, _1543892, _1543900)), _1543890), hAPP(c_Option_Ooption_OSome(_1543894), _1543898)))], (34931 ^ _781013) ^ [_1442313, _1442315] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1442313)), c_Int_OBit1(_1442315)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1442313)), _1442315)))], (26175 ^ _781013) ^ [_1267768, _1267770, _1267772] : [class_Orderings_Oorder(_1267768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267768), _1267770), _1267772)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1267768, _1267772, _1267770) = c_Orderings_Obot__class_Obot(tc_fun(_1267768, tc_HOL_Obool)))], (38019 ^ _781013) ^ [_1509257, _1509259, _1509261, _1509263] : [-(hAPP(c_Relation_OField(_1509257), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1509257, _1509257)), hAPP(hAPP(c_Product__Type_OPair(_1509257, _1509257), _1509259), _1509261)), _1509263)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1509257, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1509257), _1509259), hAPP(hAPP(c_Set_Oinsert(_1509257), _1509261), c_Orderings_Obot__class_Obot(tc_fun(_1509257, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1509257), _1509263)))], (45139 ^ _781013) ^ [_1682686, _1682688] : [class_Enum_Oenum(_1682686), -(hBOOL(hAPP(hAPP(c_member(_1682686), _1682688), hAPP(c_List_Oset(_1682686), c_Enum_Oenum__class_Oenum(_1682686)))))], (19130 ^ _781013) ^ [_1139214, _1139216, _1139218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1139214), _1139216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1139214), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1139218), _1139216))))], (30499 ^ _781013) ^ [_1351050, _1351052, _1351054] : [class_Orderings_Olinorder(_1351050), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351050), _1351052)), hBOOL(hAPP(hAPP(c_member(_1351050), _1351054), _1351052)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351050), _1351054), c_Big__Operators_Olattice_OInf__fin(_1351050, c_Orderings_Oord__class_Omin(_1351050), _1351052)) = _1351054)], (50976 ^ _781013) ^ [_1818043, _1818045, _1818047] : [_1818045 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1818043) = c_List_Oreplicate(_1818043, _1818045, _1818047))], (43305 ^ _781013) ^ [_1643388, _1643390, _1643392] : [43307 ^ _781013 : [(43310 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1643390, 43306 ^ [_1643388, _1643390, _1643392])))], (43308 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1643388), 43306 ^ [_1643388, _1643390, _1643392]), hAPP(c_List_Oset(_1643388), _1643392))))]], -(hAPP(c_List_Ofilter(_1643388, _1643390), _1643392) = c_List_Olist_ONil(_1643388))], (45974 ^ _781013) ^ [_1700787, _1700789, _1700791] : [class_Complete__Lattice_Ocomplete__lattice(_1700787), -(c_Complete__Lattice_OInf__class_OInf(_1700787, hAPP(hAPP(c_Set_Oinsert(_1700787), _1700789), _1700791)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1700787), _1700789), c_Complete__Lattice_OInf__class_OInf(_1700787, _1700791)))], (45944 ^ _781013) ^ [_1700278, _1700280, _1700282] : [class_Complete__Lattice_Ocomplete__lattice(_1700278), hBOOL(hAPP(hAPP(c_member(_1700278), _1700280), _1700282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1700278), c_Complete__Lattice_OInf__class_OInf(_1700278, _1700282)), _1700280)))], (50461 ^ _781013) ^ [_1806928, _1806930, _1806932, _1806934, _1806936, _1806938] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1806928, _1806930, _1806932), _1806934), hAPP(hAPP(c_Product__Type_OPair(_1806928, _1806930), _1806936), _1806938)) = hAPP(hAPP(_1806934, _1806936), _1806938))], (16814 ^ _781013) ^ [_1092788, _1092790, _1092792, _1092794] : [class_Rings_Olinordered__semiring__strict(_1092788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092788), _1092790), _1092792)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092788), _1092794), _1092792))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092788), c_Groups_Ozero__class_Ozero(_1092788)), _1092792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092788), _1092790), _1092794)))], (10357 ^ _781013) ^ [_964492, _964494, _964496, _964498] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964492, tc_HOL_Obool)), c_Map_Odom(_964492, _964494, _964496)), c_Map_Odom(_964492, _964494, _964498)) = c_Orderings_Obot__class_Obot(tc_fun(_964492, tc_HOL_Obool)), -(c_Map_Omap__add(_964492, _964494, _964496, _964498) = c_Map_Omap__add(_964492, _964494, _964498, _964496))], (44721 ^ _781013) ^ [_1674082, _1674084, _1674086, _1674088] : [-(c_List_Oremdups(_1674082, hAPP(hAPP(c_List_Omap(_1674084, _1674082), _1674086), c_List_Oremdups(_1674084, _1674088))) = c_List_Oremdups(_1674082, hAPP(hAPP(c_List_Omap(_1674084, _1674082), _1674086), _1674088)))], (36645 ^ _781013) ^ [_1480665, _1480667, _1480669, _1480671, _1480673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1480665, _1480667)), hAPP(hAPP(c_Product__Type_OPair(_1480665, _1480667), _1480671), _1480673)), _1480669)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1480665, _1480667, _1480669), _1480671), _1480673)))], (5881 ^ _781013) ^ [_875618, _875620, _875622] : [hAPP(c_Com_Ocom_OBODY, _875618) = c_Com_Ocom_OSemi(_875620, _875622)], (50254 ^ _781013) ^ [_1802916] : [-(c_Nitpick_Onum(_1802916) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1802916, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1802916)))], (42118 ^ _781013) ^ [_1614470, _1614472] : [-(hAPP(hAPP(c_List_Odrop(_1614470), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1614472) = _1614472)], (51328 ^ _781013) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (24726 ^ _781013) ^ [_1242140, _1242142, _1242144, _1242146] : [class_Fields_Olinordered__field(_1242140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1242140), _1242142), _1242144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1242140), _1242146), c_Groups_Ozero__class_Ozero(_1242140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1242140), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242140), _1242144), _1242146)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242140), _1242142), _1242146))))], (32144 ^ _781013) ^ [_1391192, _1391194] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1391192), _1391194)), 32150 ^ _781013 : [(32153 ^ _781013) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (32151 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391192), 32149 ^ [_1391192, _1391194]), _1391194)))]], -(hAPP(c_Finite__Set_Ocard(_1391192), _1391194) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47213 ^ _781013) ^ [_1731940, _1731942, _1731944, _1731946] : [hBOOL(hAPP(hAPP(c_member(_1731940), _1731942), hAPP(c_Relation_ODomain(_1731940, _1731944), _1731946))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1731940, _1731944)), hAPP(hAPP(c_Product__Type_OPair(_1731940, _1731944), _1731942), 47216 ^ [_1731940, _1731942, _1731944, _1731946])), _1731946)))], (20711 ^ _781013) ^ [_1168150, _1168152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1168150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1168150), _1168152))))], (32246 ^ _781013) ^ [_1393015, _1393017, _1393019] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1393015, _1393017, _1393019))), -(hBOOL(hAPP(c_Com_OWT, _1393019)))], (44655 ^ _781013) ^ [_1672718, _1672720, _1672722, _1672724] : [-(hBOOL(hAPP(_1672718, _1672720))), -(c_List_OtakeWhile(_1672722, _1672718, hAPP(hAPP(c_List_Olist_OCons(_1672722), _1672720), _1672724)) = c_List_Olist_ONil(_1672722))], (28100 ^ _781013) ^ [_1305604, _1305606] : [class_Rings_Olinordered__idom(_1305604), 28103 ^ _781013 : [(28110 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305604), c_Groups_Ozero__class_Ozero(_1305604)), _1305606)), -(c_Groups_Osgn__class_Osgn(_1305604, _1305606) = c_Groups_Oone__class_Oone(_1305604))], (28104 ^ _781013) ^ [] : [c_Groups_Osgn__class_Osgn(_1305604, _1305606) = c_Groups_Oone__class_Oone(_1305604), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305604), c_Groups_Ozero__class_Ozero(_1305604)), _1305606)))]]], (38676 ^ _781013) ^ [_1525226, _1525228, _1525230, _1525232, _1525234, _1525236] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1525226, _1525228)), hAPP(hAPP(c_Product__Type_OPair(_1525226, _1525228), _1525230), _1525232)), hAPP(c_List_Oset(tc_prod(_1525226, _1525228)), hAPP(hAPP(c_List_Ozip(_1525226, _1525228), _1525234), _1525236)))), -(hBOOL(hAPP(hAPP(c_member(_1525228), _1525232), hAPP(c_List_Oset(_1525228), _1525236))))], (40119 ^ _781013) ^ [_1563321, _1563323, _1563325] : [class_Groups_Omonoid__add(_1563321), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1563321), hAPP(hAPP(c_List_Olist_OCons(_1563321), _1563323), _1563325)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1563321), _1563323), hAPP(c_List_Omonoid__add__class_Olistsum(_1563321), _1563325)))], (40413 ^ _781013) ^ [_1569621, _1569623, _1569625, _1569627, _1569629, _1569631] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1569621), tc_List_Olist(_1569621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1569621), tc_List_Olist(_1569621)), hAPP(hAPP(c_List_Olist_OCons(_1569621), _1569623), _1569625)), hAPP(hAPP(c_List_Olist_OCons(_1569621), _1569627), _1569629))), c_List_Olexord(_1569621, _1569631))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569621, _1569621)), hAPP(hAPP(c_Product__Type_OPair(_1569621, _1569621), _1569623), _1569627)), _1569631))), 40420 ^ _781013 : [(40423 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1569621), tc_List_Olist(_1569621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1569621), tc_List_Olist(_1569621)), _1569625), _1569629)), c_List_Olexord(_1569621, _1569631))))], (40421 ^ _781013) ^ [] : [-(_1569623 = _1569627)]]], (9975 ^ _781013) ^ [_957313, _957315] : [class_Lattices_Osemilattice__inf(_957313), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_957313), _957315), _957315) = _957315)], (38085 ^ _781013) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (42126 ^ _781013) ^ [_1614688, _1614690, _1614692, _1614694] : [-(hAPP(hAPP(c_List_Otake(_1614688), _1614690), hAPP(hAPP(c_List_Odrop(_1614688), _1614692), _1614694)) = hAPP(hAPP(c_List_Odrop(_1614688), _1614692), hAPP(hAPP(c_List_Otake(_1614688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1614690), _1614692)), _1614694)))], (36625 ^ _781013) ^ [_1480045, _1480047, _1480049, _1480051, _1480053] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1480045, _1480047, tc_HOL_Obool), _1480049), hAPP(hAPP(c_Product__Type_OPair(_1480045, _1480047), _1480051), _1480053))), -(hBOOL(hAPP(hAPP(_1480049, _1480051), _1480053)))], (13547 ^ _781013) ^ [_1029108, _1029110, _1029112, _1029114] : [hBOOL(hAPP(hAPP(c_member(_1029108), _1029110), _1029112)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029108, tc_Nat_Onat), _1029114), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1029108, tc_HOL_Obool)), _1029112), hAPP(hAPP(c_Set_Oinsert(_1029108), _1029110), c_Orderings_Obot__class_Obot(tc_fun(_1029108, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029108, tc_Nat_Onat), _1029114), _1029112)), hAPP(_1029114, _1029110)))], (47866 ^ _781013) ^ [_1747847, _1747849, _1747851] : [c_List_Olist__ex(_1747847, _1747849, _1747851), -(c_List_Olist__ex(_1747847, _1747849, hAPP(c_List_Orev(_1747847), _1747851)))], (21581 ^ _781013) ^ [_1186283, _1186285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186283), _1186285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186283)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186285))))], (39593 ^ _781013) ^ [_1547161, _1547163, _1547165, _1547167] : [hBOOL(hAPP(_1547161, _1547163)), 39596 ^ _781013 : [(39599 ^ _781013) ^ [_1547291] : [hBOOL(hAPP(_1547161, _1547291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1547167, c_Hilbert__Choice_OLeastM(_1547165, tc_Nat_Onat, _1547167, _1547161))), hAPP(_1547167, _1547291))))], (39597 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1547161, c_Hilbert__Choice_OLeastM(_1547165, tc_Nat_Onat, _1547167, _1547161))))]]], (46228 ^ _781013) ^ [_1706406, _1706408, _1706410, _1706412, _1706414, _1706416, _1706418] : [c_List_Olist__all2(_1706406, _1706408, _1706410, _1706412, _1706414), c_List_Olist__all2(_1706406, _1706408, _1706410, _1706416, _1706418), -(c_List_Olist__all2(_1706406, _1706408, _1706410, hAPP(hAPP(c_List_Oappend(_1706406), _1706412), _1706416), hAPP(hAPP(c_List_Oappend(_1706408), _1706414), _1706418)))], (19350 ^ _781013) ^ [_1143372, _1143374, _1143376] : [class_Rings_Oring__1__no__zero__divisors(_1143372), -(_1143374 = c_Groups_Ozero__class_Ozero(_1143372)), hAPP(hAPP(c_Power_Opower__class_Opower(_1143372), _1143374), _1143376) = c_Groups_Ozero__class_Ozero(_1143372)], (38660 ^ _781013) ^ [_1524537, _1524539] : [-(hAPP(hAPP(c_List_Ozip(_1524537, _1524537), _1524539), _1524539) = hAPP(hAPP(c_List_Omap(_1524537, tc_prod(_1524537, _1524537)), hAPP(hAPP(c_COMBS(_1524537, _1524537, tc_prod(_1524537, _1524537)), c_Product__Type_OPair(_1524537, _1524537)), c_COMBI(_1524537))), _1524539))], (6414 ^ _781013) ^ [_885739, _885741, _885743, _885745, _885747, _885749] : [c_Finite__Set_Ofolding__idem(_885739, _885741, _885743, _885745), hBOOL(hAPP(c_Finite__Set_Ofinite(_885739), _885747)), -(hAPP(_885745, hAPP(hAPP(c_Set_Oinsert(_885739), _885749), _885747)) = hAPP(c_Fun_Ocomp(_885741, _885741, _885741, hAPP(_885745, _885747)), hAPP(_885743, _885749)))], (45151 ^ _781013) ^ [_1682896, _1682898, _1682900, _1682902, _1682904] : [class_Orderings_Olinorder(_1682896), -(c_List_Olinorder__class_Osort__key(_1682898, _1682896, _1682900, hAPP(hAPP(c_List_Olist_OCons(_1682898), _1682902), _1682904)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1682898, _1682896, _1682900), _1682902), c_List_Olinorder__class_Osort__key(_1682898, _1682896, _1682900, _1682904)))], (50958 ^ _781013) ^ [_1817758, _1817760, _1817762] : [c_List_Oreplicate(_1817758, _1817760, _1817762) = c_List_Olist_ONil(_1817758), -(_1817760 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16063 ^ _781013) ^ [_1078132] : [class_Rings_Olinordered__semidom(_1078132), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078132), c_Groups_Ozero__class_Ozero(_1078132)), c_Groups_Oone__class_Oone(_1078132))))], (10117 ^ _781013) ^ [_959995, _959997, _959999] : [class_Lattices_Osemilattice__inf(_959995), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959995), _959997), _959999)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959995), _959997), _959999) = _959997)], (9859 ^ _781013) ^ [_954988, _954990, _954992, _954994] : [class_Lattices_Osemilattice__inf(_954988), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954988), _954990), _954992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954988), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954988), _954990), _954994)), _954992)))], (38648 ^ _781013) ^ [_1524295, _1524297, _1524299, _1524301] : [hBOOL(hAPP(c_List_Odistinct(_1524295), _1524297)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1524299, _1524295)), hAPP(hAPP(c_List_Ozip(_1524299, _1524295), _1524301), _1524297))))], (16554 ^ _781013) ^ [_1087736, _1087738, _1087740, _1087742, _1087744] : [class_Groups_Ocomm__monoid__mult(_1087736), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087738), _1087740)), 16561 ^ _781013 : [(16568 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1087738), _1087742), _1087740))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1087738, _1087736), hAPP(hAPP(c_COMBC(_1087738, _1087736, _1087736), hAPP(hAPP(c_COMBS(_1087738, _1087736, tc_fun(_1087736, _1087736)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1087736, tc_fun(_1087736, _1087736)), _1087738), c_If(_1087736)), hAPP(hAPP(c_COMBC(_1087738, _1087738, tc_HOL_Obool), c_fequal), _1087742))), _1087744)), c_Groups_Oone__class_Oone(_1087736))), _1087740) = c_Groups_Oone__class_Oone(_1087736))], (16562 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1087738), _1087742), _1087740)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1087738, _1087736), hAPP(hAPP(c_COMBC(_1087738, _1087736, _1087736), hAPP(hAPP(c_COMBS(_1087738, _1087736, tc_fun(_1087736, _1087736)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1087736, tc_fun(_1087736, _1087736)), _1087738), c_If(_1087736)), hAPP(hAPP(c_COMBC(_1087738, _1087738, tc_HOL_Obool), c_fequal), _1087742))), _1087744)), c_Groups_Oone__class_Oone(_1087736))), _1087740) = hAPP(_1087744, _1087742))]]], (50754 ^ _781013) ^ [_1812459, _1812461, _1812463, _1812465, _1812467] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1812459, _1812461, _1812463, _1812465, _1812467) = hAPP(c_Option_Ooption_Ooption__case(_1812459, tc_prod(_1812461, tc_Lazy__Sequence_Olazy__sequence(_1812461)), _1812463, hAPP(c_Product__Type_Oprod_Oprod__case(_1812461, tc_Lazy__Sequence_Olazy__sequence(_1812461), _1812459), _1812465)), hAPP(c_Lazy__Sequence_Oyield(_1812461), _1812467)))], (14527 ^ _781013) ^ [_1050676, _1050678, _1050680, _1050682, _1050684, _1050686] : [class_Groups_Oab__semigroup__mult(_1050676), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050678), _1050680)), 14537 ^ _781013 : [(14540 ^ _781013) ^ [] : [hAPP(_1050682, 14536 ^ [_1050676, _1050678, _1050680, _1050682, _1050684, _1050686]) = hAPP(_1050684, 14536 ^ [_1050676, _1050678, _1050680, _1050682, _1050684, _1050686])], (14538 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1050678), 14536 ^ [_1050676, _1050678, _1050680, _1050682, _1050684, _1050686]), _1050680)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1050676, _1050678, c_Groups_Otimes__class_Otimes(_1050676)), _1050682), _1050686), _1050680) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1050676, _1050678, c_Groups_Otimes__class_Otimes(_1050676)), _1050684), _1050686), _1050680))], (50378 ^ _781013) ^ [_1805368, _1805370, _1805372] : [c_List_Olist__all(_1805368, _1805370, _1805372), 50381 ^ _781013 : [(50382 ^ _781013) ^ [_1805449] : [hBOOL(hAPP(hAPP(c_member(_1805368), _1805449), hAPP(c_List_Oset(_1805368), _1805372))), -(hBOOL(hAPP(_1805370, _1805449)))]]], (31938 ^ _781013) ^ [_1386545, _1386547, _1386549, _1386551, _1386553] : [_1386545 = c_Orderings_Obot__class_Obot(tc_fun(_1386547, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386549, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386547, tc_fun(_1386549, tc_HOL_Obool)), _1386545), _1386551)), _1386553) = _1386553)], (36948 ^ _781013) ^ [_1485944, _1485946] : [-(c_Divides_Odivmod__nat(_1485946, _1485944) = 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), _1485946), _1485944), _1485944))), -(_1485944 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1485946), _1485944)))], (3256 ^ _781013) ^ [_830054, _830056, _830058, _830060] : [-(c_List_Obutlast(_830060, _830056) = c_List_Obutlast(_830058, _830054)), _830060 = _830058, _830056 = _830054], (7982 ^ _781013) ^ [_916097, _916099, _916101, _916103, _916105] : [-(hAPP(hAPP(c_Option_Omap(_916097, _916099), _916101), _916103) = hAPP(c_Option_Ooption_OSome(_916099), _916105)), 7983 ^ _781013 : [(7984 ^ _781013) ^ [_916165] : [_916103 = hAPP(c_Option_Ooption_OSome(_916097), _916165), hAPP(_916101, _916165) = _916105]]], (39293 ^ _781013) ^ [_1540153] : [39295 ^ _781013 : [(39298 ^ _781013) ^ [] : [39294 ^ [_1540153] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (39296 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 39294 ^ [_1540153]), hAPP(c_List_Oset(tc_Nat_Onat), _1540153))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1540153) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42498 ^ _781013) ^ [_1623003, _1623005, _1623007, _1623009, _1623011, _1623013] : [-(hAPP(c_List_Ofoldl(_1623003, _1623005, _1623007, _1623009), hAPP(hAPP(c_List_Oappend(_1623005), _1623011), _1623013)) = hAPP(c_List_Ofoldl(_1623003, _1623005, _1623007, hAPP(c_List_Ofoldl(_1623003, _1623005, _1623007, _1623009), _1623011)), _1623013))], (23393 ^ _781013) ^ [_1218570, _1218572, _1218574] : [class_Orderings_Olinorder(_1218570), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218570), _1218572), _1218574)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1218570, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1218570, _1218572, _1218574)), hAPP(hAPP(c_Set_Oinsert(_1218570), _1218574), c_Orderings_Obot__class_Obot(tc_fun(_1218570, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1218570, _1218572, _1218574))], (26463 ^ _781013) ^ [_1273258] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1273258)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1273258)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1273258)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (36330 ^ _781013) ^ [_1473546, _1473548, _1473550, _1473552, _1473554, _1473556, _1473558] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1473546, _1473548), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1473550), _1473552))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1473554, _1473548), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1473556), _1473558))), -(_1473548 = 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), _1473546), _1473554), _1473548), 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), _1473550), _1473556)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1473552), _1473558)), _1473548))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1473552), _1473558), _1473548)))))], (9869 ^ _781013) ^ [_955167, _955169, _955171, _955173, _955175] : [class_Lattices_Olattice(_955167), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955169, _955167)), _955171), _955173), _955175) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955167), hAPP(_955171, _955175)), hAPP(_955173, _955175)))], (41516 ^ _781013) ^ [_1599747, _1599749, _1599751, _1599753, _1599755] : [-(hAPP(hAPP(c_List_Ozip(_1599747, _1599749), hAPP(hAPP(c_List_Olist_OCons(_1599747), _1599751), _1599753)), _1599755) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1599747, _1599749)), _1599749, c_List_Olist_ONil(tc_prod(_1599747, _1599749)), hAPP(hAPP(c_COMBC(_1599749, tc_fun(tc_List_Olist(_1599749), tc_List_Olist(tc_prod(_1599747, _1599749))), tc_fun(tc_List_Olist(_1599749), tc_List_Olist(tc_prod(_1599747, _1599749)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1599747, _1599749)), tc_List_Olist(tc_prod(_1599747, _1599749))), tc_fun(tc_fun(tc_List_Olist(_1599749), tc_List_Olist(tc_prod(_1599747, _1599749))), tc_fun(tc_List_Olist(_1599749), tc_List_Olist(tc_prod(_1599747, _1599749)))), _1599749), c_COMBB(tc_List_Olist(tc_prod(_1599747, _1599749)), tc_List_Olist(tc_prod(_1599747, _1599749)), tc_List_Olist(_1599749))), hAPP(hAPP(c_COMBB(tc_prod(_1599747, _1599749), tc_fun(tc_List_Olist(tc_prod(_1599747, _1599749)), tc_List_Olist(tc_prod(_1599747, _1599749))), _1599749), c_List_Olist_OCons(tc_prod(_1599747, _1599749))), hAPP(c_Product__Type_OPair(_1599747, _1599749), _1599751)))), hAPP(c_List_Ozip(_1599747, _1599749), _1599753))), _1599755))], (26022 ^ _781013) ^ [_1264734, _1264736, _1264738] : [26024 ^ _781013 : [(26027 ^ _781013) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1264738, 26023 ^ [_1264734, _1264736, _1264738]))], (26025 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1264734), 26023 ^ [_1264734, _1264736, _1264738]), _1264736)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1264734, tc_Int_Oint), _1264738), _1264736) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1264734, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1264734), c_Int_Onat), _1264738)), _1264736)))], (29619 ^ _781013) ^ [_1333361, _1333363] : [29620 ^ _781013 : [(29623 ^ _781013) ^ [] : [_1333363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29621 ^ _781013) ^ [] : [-(_1333361 = 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), _1333361)), _1333363))))], (35963 ^ _781013) ^ [_1464804, _1464806, _1464808, _1464810, _1464812, _1464814] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1464804, _1464806)), hAPP(hAPP(c_Product__Type_OPair(_1464804, _1464806), _1464812), _1464814)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool)), _1464808), _1464810))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464804, tc_fun(_1464806, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1464804, tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_fun(_1464806, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464806, tc_fun(tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_fun(_1464806, tc_HOL_Obool)), _1464804), c_COMBC(_1464806, tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464806, tc_prod(_1464804, _1464806)), tc_fun(_1464806, tc_fun(tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_HOL_Obool)), _1464804), hAPP(c_COMBB(tc_prod(_1464804, _1464806), tc_fun(tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_HOL_Obool), _1464806), c_member(tc_prod(_1464804, _1464806)))), c_Product__Type_OPair(_1464804, _1464806)))), _1464808)), hAPP(hAPP(c_COMBC(_1464804, tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_fun(_1464806, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464806, tc_fun(tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_fun(_1464806, tc_HOL_Obool)), _1464804), c_COMBC(_1464806, tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464806, tc_prod(_1464804, _1464806)), tc_fun(_1464806, tc_fun(tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_HOL_Obool)), _1464804), hAPP(c_COMBB(tc_prod(_1464804, _1464806), tc_fun(tc_fun(tc_prod(_1464804, _1464806), tc_HOL_Obool), tc_HOL_Obool), _1464806), c_member(tc_prod(_1464804, _1464806)))), c_Product__Type_OPair(_1464804, _1464806)))), _1464810)), _1464812), _1464814)))], (49370 ^ _781013) ^ [_1784223, _1784225, _1784227, _1784229] : [49372 ^ _781013 : [(49377 ^ _781013) ^ [] : [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(_1784227, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 49371 ^ [_1784223, _1784225, _1784227, _1784229]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1784227, 49371 ^ [_1784223, _1784225, _1784227, _1784229])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (49375 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49371 ^ [_1784223, _1784225, _1784227, _1784229]), _1784225)))], (49373 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1784223), 49371 ^ [_1784223, _1784225, _1784227, _1784229])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1784223), _1784225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1784227, _1784223)), _1784229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1784229), hAPP(_1784227, _1784225))), 49391 ^ _781013 : [(49396 ^ _781013) ^ [] : [-(hAPP(_1784227, 49390 ^ [_1784223, _1784225, _1784227, _1784229]) = _1784229)], (49394 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 49390 ^ [_1784223, _1784225, _1784227, _1784229]), _1784225)))], (49392 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1784223), 49390 ^ [_1784223, _1784225, _1784227, _1784229])))]]], (48387 ^ _781013) ^ [_1759113, _1759115, _1759117, _1759119, _1759121] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1759113, _1759113)), hAPP(hAPP(c_Product__Type_OPair(_1759113, _1759113), _1759115), _1759117)), c_Transitive__Closure_Ortrancl(_1759113, _1759119))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1759113, _1759113)), hAPP(hAPP(c_Product__Type_OPair(_1759113, _1759113), _1759117), _1759121)), _1759119)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1759113, _1759113)), hAPP(hAPP(c_Product__Type_OPair(_1759113, _1759113), _1759115), _1759121)), c_Transitive__Closure_Otrancl(_1759113, _1759119))))], (25910 ^ _781013) ^ [_1262908] : [c_Nat__Transfer_Ois__nat(_1262908), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262908)))], (1882 ^ _781013) ^ [_808071, _808073, _808075, _808077, _808079, _808081, _808083, _808085] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_808085, _808081, _808077, _808073) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_808083, _808079, _808075, _808071)), _808085 = _808083, _808081 = _808079, _808077 = _808075, _808073 = _808071], (33510 ^ _781013) ^ [_1416918, _1416920] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416918))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416918)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416920)) = 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), _1416920)))], (11662 ^ _781013) ^ [_991005, _991007] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_991005, _991007)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_991005, _991007), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_991007), c_Orderings_Otop__class_Otop(tc_fun(_991007, tc_HOL_Obool)))))], (49336 ^ _781013) ^ [_1783249, _1783251, _1783253, _1783255, _1783257] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1783249, _1783249)), hAPP(hAPP(c_Product__Type_OPair(_1783249, _1783249), _1783251), _1783253)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783249, _1783249), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1783255)), _1783257))), 49340 ^ _781013 : [(49343 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783249, _1783249)), hAPP(hAPP(c_Product__Type_OPair(_1783249, _1783249), 49339 ^ [_1783249, _1783251, _1783253, _1783255, _1783257]), _1783253)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783249, _1783249), tc_HOL_Obool), _1783255), _1783257))))], (49341 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783249, _1783249)), hAPP(hAPP(c_Product__Type_OPair(_1783249, _1783249), _1783251), 49339 ^ [_1783249, _1783251, _1783253, _1783255, _1783257])), _1783257)))]]], (51596 ^ _781013) ^ [] : [-(class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))], (22486 ^ _781013) ^ [_1201989, _1201991, _1201993] : [class_Orderings_Oorder(_1201989), 22489 ^ _781013 : [(22496 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201989), _1201991), _1201993))), -(c_Orderings_Obot__class_Obot(tc_fun(_1201989, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1201989, _1201991), _1201993))], (22490 ^ _781013) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1201989, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1201989, _1201991), _1201993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201989), _1201991), _1201993))]]], (21483 ^ _781013) ^ [_1184616, _1184618] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1184616), _1184618)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184616)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184618))))], (47891 ^ _781013) ^ [_1748331, _1748333, _1748335, _1748337] : [c_List_Olist__ex(_1748331, _1748333, hAPP(hAPP(c_List_Olist_OCons(_1748331), _1748335), _1748337)), -(hBOOL(hAPP(_1748333, _1748335))), -(c_List_Olist__ex(_1748331, _1748333, _1748337))], (14460 ^ _781013) ^ [_1049098, _1049100, _1049102, _1049104, _1049106] : [class_Groups_Ocomm__monoid__mult(_1049098), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049100), _1049102)), hBOOL(hAPP(hAPP(c_member(_1049100), _1049104), _1049102)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1049100, _1049098), _1049106), _1049102) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049098), hAPP(_1049106, _1049104)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1049100, _1049098), _1049106), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049100, tc_HOL_Obool)), _1049102), hAPP(hAPP(c_Set_Oinsert(_1049100), _1049104), c_Orderings_Obot__class_Obot(tc_fun(_1049100, tc_HOL_Obool)))))))], (48605 ^ _781013) ^ [_1763971, _1763973, _1763975, _1763977, _1763979] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1763971), tc_List_Olist(_1763971))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1763971), tc_List_Olist(_1763971)), _1763973), _1763975)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1763971), c_List_Olistrel1(_1763971, _1763977)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1763971), tc_List_Olist(_1763971))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1763971), tc_List_Olist(_1763971)), hAPP(hAPP(c_List_Olist_OCons(_1763971), _1763979), _1763973)), hAPP(hAPP(c_List_Olist_OCons(_1763971), _1763979), _1763975))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1763971), c_List_Olistrel1(_1763971, _1763977)))))], (5024 ^ _781013) ^ [_857566, _857568] : [_857568 = _857566, -(c_New__Random__Sequence_Oneg__single(_857568) = c_New__Random__Sequence_Oneg__single(_857566))], (26335 ^ _781013) ^ [_1270790, _1270792, _1270794, _1270796] : [class_Orderings_Oorder(_1270790), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1270790, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1270790, _1270792), _1270794)), c_SetInterval_Oord__class_OatLeastAtMost(_1270790, _1270794, _1270796)) = c_Orderings_Obot__class_Obot(tc_fun(_1270790, tc_HOL_Obool)))], (644 ^ _781013) ^ [_790885, _790887, _790889, _790891, _790893, _790895] : [-(c_List_Olist__ex(_790893, _790889, _790885)), c_List_Olist__ex(_790895, _790891, _790887), _790895 = _790893, _790891 = _790889, _790887 = _790885], (44761 ^ _781013) ^ [_1674744, _1674746] : [c_List_Oremdups(_1674744, _1674746) = _1674746, -(hBOOL(hAPP(c_List_Odistinct(_1674744), _1674746)))], (17132 ^ _781013) ^ [_1099622, _1099624, _1099626] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1099622), _1099624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099622, tc_HOL_Obool)), _1099624), _1099626)), -(hAPP(c_Finite__Set_Ocard(_1099622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1099622, tc_HOL_Obool)), _1099626), _1099624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1099622), _1099626)), hAPP(c_Finite__Set_Ocard(_1099622), _1099624)))], (21931 ^ _781013) ^ [_1192571, _1192573, _1192575] : [class_Orderings_Olinorder(_1192571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192571), _1192573)), hBOOL(hAPP(hAPP(c_member(_1192571), _1192575), _1192573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192571), _1192575), c_Big__Operators_Olinorder__class_OMax(_1192571, _1192573))))], (18460 ^ _781013) ^ [_1124533, _1124535, _1124537] : [18461 ^ _781013 : [(18464 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124533), _1124537))], (18462 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1124535)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124533), _1124535)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124537), _1124535))))], (13975 ^ _781013) ^ [_1037946, _1037948, _1037950, _1037952] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1037946), 13978 ^ _781013 : [(13985 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037946), _1037950), _1037952)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037946), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037946), _1037948), _1037950)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037946), _1037948), _1037952))))], (13979 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037946), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037946), _1037948), _1037950)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037946), _1037948), _1037952))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037946), _1037950), _1037952)))]]], (35713 ^ _781013) ^ [_1456521] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1456521, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5318 ^ _781013) ^ [_862127, _862129, _862131, _862133, _862135, _862137] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_862137, _862133, _862129) = c_Lazy__Sequence_Olazy__sequence_OInsert(_862135, _862131, _862127)), _862137 = _862135, _862133 = _862131, _862129 = _862127], (7643 ^ _781013) ^ [_909571, _909573, _909575, _909577, _909579, _909581] : [_909571 = _909573, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909575, _909577), _909579), _909573), _909581), _909571) = _909581)], (8418 ^ _781013) ^ [_926075, _926077, _926079, _926081] : [_926081 = c_Orderings_Obot__class_Obot(tc_fun(_926075, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_926075, _926077, _926079), _926081) = c_Orderings_Obot__class_Obot(tc_fun(_926077, tc_HOL_Obool)))], (10995 ^ _781013) ^ [_976117, _976119, _976121, _976123] : [hBOOL(hAPP(hAPP(c_member(_976117), _976123), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976117, tc_HOL_Obool)), _976119), _976121))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976117, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_976117, tc_fun(_976117, tc_HOL_Obool), tc_HOL_Obool), c_member(_976117)), _976119)), hAPP(hAPP(c_COMBC(_976117, tc_fun(_976117, tc_HOL_Obool), tc_HOL_Obool), c_member(_976117)), _976121)), _976123)))], (40467 ^ _781013) ^ [_1572165, _1572167, _1572169, _1572171, _1572173, _1572175, _1572177] : [-(hAPP(c_Product__Type_Ofst(_1572165, _1572167), hAPP(c_Product__Type_Omap__pair(_1572169, _1572165, _1572171, _1572167, _1572173, _1572175), _1572177)) = hAPP(_1572173, hAPP(c_Product__Type_Ofst(_1572169, _1572171), _1572177)))], (12910 ^ _781013) ^ [_1015442, _1015444, _1015446, _1015448] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015442, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1015444, _1015442, _1015446), hAPP(c_Set_Ovimage(_1015444, _1015442, _1015446), _1015448))), _1015448)))], (4322 ^ _781013) ^ [_846371, _846373, _846375, _846377, _846379, _846381] : [-(c_Big__Operators_Olattice_OInf__fin(_846381, _846377, _846373) = c_Big__Operators_Olattice_OInf__fin(_846379, _846375, _846371)), _846381 = _846379, _846377 = _846375, _846373 = _846371], (41853 ^ _781013) ^ [_1607480, _1607482, _1607484, _1607486] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607480)), hAPP(hAPP(c_List_Oappend(_1607480), _1607482), _1607484)), c_List_Olists(_1607480, _1607486)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607480)), _1607482), c_List_Olists(_1607480, _1607486))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607480)), _1607484), c_List_Olists(_1607480, _1607486)))], (10945 ^ _781013) ^ [_974975, _974977, _974979, _974981] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974975, tc_HOL_Obool)), _974977), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974975, tc_HOL_Obool)), _974979), _974981)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974975, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974975, tc_HOL_Obool)), _974977), _974979)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974975, tc_HOL_Obool)), _974977), _974981)))], (3134 ^ _781013) ^ [_828057, _828059] : [_828059 = _828057, -(c_SetInterval_Oord__class_OatMost(_828059) = c_SetInterval_Oord__class_OatMost(_828057))], (24176 ^ _781013) ^ [_1231888, _1231890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231888), _1231890)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1231890), _1231888)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1231890)), hAPP(c_Int_Onat, _1231888)))], (41680 ^ _781013) ^ [_1603658, _1603660, _1603662] : [_1603658 = hAPP(hAPP(c_List_Oappend(_1603660), _1603662), _1603658), -(_1603662 = c_List_Olist_ONil(_1603660))], (6505 ^ _781013) ^ [_887502] : [-(hAPP(c_Com_Obody, _887502) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _887502))))], (40389 ^ _781013) ^ [_1568984, _1568986, _1568988, _1568990] : [-(c_List_Olist_Olist__size(_1568984, _1568986, hAPP(hAPP(c_List_Olist_OCons(_1568984), _1568988), _1568990)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1568986, _1568988)), c_List_Olist_Olist__size(_1568984, _1568986, _1568990))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29609 ^ _781013) ^ [_1333212, _1333214] : [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), _1333212)), _1333214))), _1333212 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1333214 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6006 ^ _781013) ^ [_878119, _878121] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_878119, _878121))), 6009 ^ _781013 : [(6012 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _878121)))], (6010 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _878119)))]]], (50652 ^ _781013) ^ [_1810486, _1810488] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1810486), _1810488)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1810486)), c_Int_OBit1(_1810488))))], (18664 ^ _781013) ^ [_1128808, _1128810, _1128812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128808), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128812), _1128810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128808), _1128810)), _1128812)))], (51630 ^ _781013) ^ [_1825112] : [hBOOL(hAPP(c_fNot, _1825112)), hBOOL(_1825112)], (18406 ^ _781013) ^ [_1123687, _1123689] : [_1123687 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1123687), _1123689), -(_1123689 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1123687 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31932 ^ _781013) ^ [_1386425, _1386427, _1386429, _1386431, _1386433] : [-(_1386425 = c_Orderings_Obot__class_Obot(tc_fun(_1386427, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1386429), _1386431), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386427, tc_fun(_1386429, tc_HOL_Obool)), _1386425), _1386433)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386427, tc_fun(_1386429, tc_HOL_Obool)), _1386425), hAPP(hAPP(c_COMBB(tc_fun(_1386429, tc_HOL_Obool), tc_fun(_1386429, tc_HOL_Obool), _1386427), hAPP(c_Set_Oinsert(_1386429), _1386431)), _1386433)))], (48766 ^ _781013) ^ [_1768386, _1768388, _1768390, _1768392, _1768394] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768386, _1768388)), hAPP(hAPP(c_Product__Type_OPair(_1768386, _1768388), _1768390), _1768392)), _1768394)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1768388, _1768386)), hAPP(hAPP(c_Product__Type_OPair(_1768388, _1768386), _1768392), _1768390)), hAPP(c_Relation_Oconverse(_1768386, _1768388), _1768394))))], (50762 ^ _781013) ^ [_1812668, _1812670, _1812672, _1812674, _1812676, _1812678] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1812668, _1812670, _1812672, _1812674, c_Lazy__Sequence_Olazy__sequence_OInsert(_1812670, _1812676, _1812678)) = hAPP(hAPP(_1812674, _1812676), _1812678))], (44191 ^ _781013) ^ [_1661029, _1661031, _1661033] : [44192 ^ _781013 : [(44195 ^ _781013) ^ [] : [_1661033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44193 ^ _781013) ^ [] : [-(_1661029 = c_List_Olist_ONil(tc_List_Olist(_1661031)))]], 44199 ^ _781013 : [(44202 ^ _781013) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661031)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1661031)), _1661029), 44198 ^ [_1661029, _1661031, _1661033])) = _1661033], (44200 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44198 ^ [_1661029, _1661031, _1661033]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1661031))), _1661029))))]], -(c_List_Otranspose(_1661031, _1661029) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1661031)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1661031)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1661031), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1661031)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1661031)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1661031), hAPP(hAPP(c_COMBB(tc_List_Olist(_1661031), tc_fun(tc_Nat_Onat, _1661031), tc_Nat_Onat), c_List_Onth(_1661031)), hAPP(c_List_Onth(tc_List_Olist(_1661031)), _1661029))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1661031))), _1661029)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1661033)))], (5926 ^ _781013) ^ [_876465, _876467] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _876465, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(_876467)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _876465, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_Com_Ostate), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies)), c_Natural_Oevalc(_876467))))), c_fequal))), _876467), c_fequal)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (22358 ^ _781013) ^ [_1199944, _1199946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199944), 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)), _1199946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1199944), _1199946)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27747 ^ _781013) ^ [_1299116, _1299118] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1299116), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1299118)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1299116, _1299118)))], (38270 ^ _781013) ^ [_1515816, _1515818] : [-(hAPP(hAPP(c_List_Omap(_1515816, _1515816), c_COMBI(_1515816)), _1515818) = _1515818)], (27715 ^ _781013) ^ [_1298467, _1298469, _1298471, _1298473] : [class_Divides_Osemiring__div(_1298467), -(c_Divides_Odiv__class_Omod(_1298467, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298467), _1298469), c_Divides_Odiv__class_Omod(_1298467, _1298471, _1298473)), _1298473) = c_Divides_Odiv__class_Omod(_1298467, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298467), _1298469), _1298471), _1298473))], (13020 ^ _781013) ^ [_1017779, _1017781, _1017783, _1017785, _1017787] : [c_Fun_Oinj__on(_1017779, _1017781, _1017783, _1017785), hBOOL(hAPP(hAPP(c_member(_1017779), _1017787), _1017785)), -(hAPP(c_Fun_Othe__inv__into(_1017779, _1017781, _1017785, _1017783), hAPP(_1017783, _1017787)) = _1017787)], (49172 ^ _781013) ^ [_1778655, _1778657, _1778659] : [-(hAPP(hAPP(c_Nat_Ocompow(_1778655, _1778655), hAPP(c_Nat_OSuc, _1778657)), _1778659) = hAPP(c_Fun_Ocomp(_1778655, _1778655, _1778655, _1778659), hAPP(hAPP(c_Nat_Ocompow(_1778655, _1778655), _1778657), _1778659)))], (29289 ^ _781013) ^ [_1327328, _1327330, _1327332] : [class_Orderings_Olinorder(_1327328), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327328), _1327330)), hBOOL(hAPP(hAPP(c_member(_1327328), _1327332), _1327330)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1327328), _1327332), c_Big__Operators_Olinorder__class_OMin(_1327328, _1327330)) = c_Big__Operators_Olinorder__class_OMin(_1327328, _1327330))], (21544 ^ _781013) ^ [_1185614] : [21545 ^ _781013 : [(21546 ^ _781013) ^ [_1185671] : [hBOOL(hAPP(_1185614, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185671)))]], 21548 ^ _781013 : [(21551 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1185614, 21547 ^ [_1185614])))], (21549 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21547 ^ [_1185614])))]]], (43733 ^ _781013) ^ [_1652362, _1652364] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1652362, _1652364))))], (14558 ^ _781013) ^ [_1051399, _1051401] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051399), _1051401)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1051399, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1051399, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1051399, tc_HOL_Obool), tc_fun(_1051399, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1051399, tc_HOL_Obool))), _1051401)))))], (27427 ^ _781013) ^ [_1292282, _1292284, _1292286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1292282, tc_HOL_Obool)), _1292284), _1292286)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1292282, tc_HOL_Obool)), _1292284), hAPP(c_Set_OPow(_1292282), _1292286))))], (45842 ^ _781013) ^ [_1698159, _1698161] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1698159), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1698159, tc_HOL_Obool), _1698161)))), 45843 ^ _781013 : [(45844 ^ _781013) ^ [_1698223] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1698159, tc_HOL_Obool)), _1698223), _1698161)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1698159), _1698223))]]], (5753 ^ _781013) ^ [_872070, _872072, _872074, _872076] : [-(hAPP(hAPP(c_Set_Oinsert(_872070), _872072), hAPP(hAPP(c_Set_Oinsert(_872070), _872074), _872076)) = hAPP(hAPP(c_Set_Oinsert(_872070), _872074), hAPP(hAPP(c_Set_Oinsert(_872070), _872072), _872076)))], (20412 ^ _781013) ^ [_1162368, _1162370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1162368)), _1162370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162368), _1162370)))], (13455 ^ _781013) ^ [_1027013, _1027015, _1027017, _1027019, _1027021] : [class_Rings_Osemiring__0(_1027013), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1027013), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027015, _1027013), _1027017), _1027019)), _1027021) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027015, _1027013), hAPP(hAPP(c_COMBC(_1027015, _1027013, _1027013), hAPP(hAPP(c_COMBB(_1027013, tc_fun(_1027013, _1027013), _1027015), c_Groups_Otimes__class_Otimes(_1027013)), _1027017)), _1027021)), _1027019))], (28772 ^ _781013) ^ [_1317885] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1317885), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34195 ^ _781013) ^ [_1429694, _1429696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1429694)), c_Int_OBit1(_1429696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429694), _1429696)))], (41746 ^ _781013) ^ [_1604843, _1604845, _1604847, _1604849, _1604851, _1604853] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604843)), _1604845) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604847)), _1604849), -(c_Map_Omap__upds(_1604843, _1604847, _1604851, hAPP(hAPP(c_List_Oappend(_1604843), _1604845), _1604853), _1604849) = c_Map_Omap__upds(_1604843, _1604847, _1604851, _1604845, _1604849))], (38762 ^ _781013) ^ [_1527816, _1527818, _1527820, _1527822, _1527824, _1527826] : [class_Orderings_Olinorder(_1527816), -(hAPP(_1527818, _1527820) = hAPP(_1527818, _1527822)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1527824, _1527816, _1527818), _1527822), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1527824, _1527816, _1527818), _1527820), _1527826)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1527824, _1527816, _1527818), _1527820), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1527824, _1527816, _1527818), _1527822), _1527826)))], (4510 ^ _781013) ^ [_849323, _849325, _849327, _849329, _849331, _849333] : [-(c_Nitpick_Oof__frac(_849333, _849329, _849325) = c_Nitpick_Oof__frac(_849331, _849327, _849323)), _849333 = _849331, _849329 = _849327, _849325 = _849323], (45763 ^ _781013) ^ [_1696012, _1696014] : [class_Complete__Lattice_Ocomplete__lattice(_1696012), -(c_Complete__Lattice_OSup__class_OSup(_1696012, hAPP(c_List_Oset(_1696012), _1696014)) = hAPP(c_List_Ofoldl(_1696012, _1696012, c_Lattices_Osemilattice__sup__class_Osup(_1696012), c_Orderings_Obot__class_Obot(_1696012)), _1696014))], (48872 ^ _781013) ^ [_1770954, _1770956, _1770958] : [hAPP(hAPP(c_Relation_Orel__comp(_1770954, _1770954, _1770954), hAPP(c_Relation_Oconverse(_1770954, _1770954), _1770956)), _1770956) = _1770956, hAPP(c_Relation_ODomain(_1770954, _1770954), _1770956) = _1770958, -(c_Equiv__Relations_Oequiv(_1770954, _1770958, _1770956))], (39683 ^ _781013) ^ [_1549432, _1549434, _1549436, _1549438, _1549440] : [hBOOL(hAPP(hAPP(c_member(_1549432), _1549434), hAPP(c_List_Oset(_1549432), _1549436))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1549438), hAPP(_1549440, _1549434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1549438), c_List_Olist_Olist__size(_1549432, _1549440, _1549436))))], (28718 ^ _781013) ^ [_1316911, _1316913, _1316915, _1316917] : [class_Orderings_Olinorder(_1316911), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316911), _1316913), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316911), _1316915), _1316917)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316911), _1316915), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316911), _1316913), _1316917)))], (23355 ^ _781013) ^ [_1217835, _1217837] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1217835), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1217837) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1217835, _1217837))], (30381 ^ _781013) ^ [_1348693, _1348695, _1348697] : [class_Groups_Olinordered__ab__group__add(_1348693), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1348693), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348693), _1348695), _1348697)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348693), hAPP(c_Groups_Ouminus__class_Ouminus(_1348693), _1348695)), hAPP(c_Groups_Ouminus__class_Ouminus(_1348693), _1348697)))], (50764 ^ _781013) ^ [_1812717, _1812719, _1812721] : [-(hAPP(c_Lazy__Sequence_Oyield(_1812717), c_Lazy__Sequence_Olazy__sequence_OInsert(_1812717, _1812719, _1812721)) = hAPP(c_Option_Ooption_OSome(tc_prod(_1812717, tc_Lazy__Sequence_Olazy__sequence(_1812717))), hAPP(hAPP(c_Product__Type_OPair(_1812717, tc_Lazy__Sequence_Olazy__sequence(_1812717)), _1812719), _1812721)))], (13749 ^ _781013) ^ [_1033636, _1033638, _1033640, _1033642] : [class_Groups_Ocancel__semigroup__add(_1033636), 13752 ^ _781013 : [(13759 ^ _781013) ^ [] : [_1033640 = _1033642, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033636), _1033638), _1033640) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033636), _1033638), _1033642))], (13753 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033636), _1033638), _1033640) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033636), _1033638), _1033642), -(_1033640 = _1033642)]]], (32006 ^ _781013) ^ [_1388441, _1388443, _1388445, _1388447] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1388441, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 32007 ^ [_1388441, _1388443, _1388445, _1388447])), _1388443) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1388441, 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), 32007 ^ [_1388441, _1388443, _1388445, _1388447]), _1388445))), _1388447), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1388441, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1388443) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1388441, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1388447))], (51042 ^ _781013) ^ [_1818934, _1818936] : [-(class_Finite__Set_Ofinite(tc_fun(_1818934, _1818936))), class_Finite__Set_Ofinite(_1818934), class_Finite__Set_Ofinite(_1818936)], (50984 ^ _781013) ^ [_1818167, _1818169] : [-(c_List_Oconcat(_1818167, c_List_Oreplicate(tc_List_Olist(_1818167), _1818169, c_List_Olist_ONil(_1818167))) = c_List_Olist_ONil(_1818167))], (35607 ^ _781013) ^ [_1454918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1454918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1454918)))], (34004 ^ _781013) ^ [_1425503, _1425505, _1425507, _1425509, _1425511] : [-(hAPP(c_Nat_Onat_Onat__rec(_1425503, _1425505, _1425507), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425509)), _1425511)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1425503), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1425509))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1425503, _1425503), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1425503, tc_fun(_1425503, _1425503)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1425503, tc_fun(_1425503, _1425503)), tc_Int_Oint), c_If(_1425503)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1425503, _1425505, _1425507), _1425511))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1425503, _1425503), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1425503, _1425503), tc_Int_Oint), _1425507), 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)), _1425511))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1425503, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1425503, _1425505, _1425507)), 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)), _1425511))))))], (41835 ^ _781013) ^ [_1606992, _1606994, _1606996] : [class_Groups_Omonoid__add(_1606992), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1606992), hAPP(hAPP(c_List_Oappend(_1606992), _1606994), _1606996)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1606992), hAPP(c_List_Omonoid__add__class_Olistsum(_1606992), _1606994)), hAPP(c_List_Omonoid__add__class_Olistsum(_1606992), _1606996)))], (46379 ^ _781013) ^ [_1709962, _1709964, _1709966] : [hBOOL(hAPP(hAPP(c_member(_1709962), _1709964), hAPP(c_List_Oset(_1709962), _1709966))), -(c_List_Oinsert(_1709962, _1709964, _1709966) = _1709966)], (38099 ^ _781013) ^ [_1511204, _1511206, _1511208, _1511210] : [c_Wellfounded_Omax__extp(_1511204, hAPP(hAPP(c_COMBC(_1511204, tc_fun(tc_prod(_1511204, _1511204), tc_HOL_Obool), tc_fun(_1511204, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511204, tc_fun(tc_fun(tc_prod(_1511204, _1511204), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511204, _1511204), tc_HOL_Obool), tc_fun(_1511204, tc_HOL_Obool)), _1511204), c_COMBC(_1511204, tc_fun(tc_prod(_1511204, _1511204), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511204, tc_prod(_1511204, _1511204)), tc_fun(_1511204, tc_fun(tc_fun(tc_prod(_1511204, _1511204), tc_HOL_Obool), tc_HOL_Obool)), _1511204), hAPP(c_COMBB(tc_prod(_1511204, _1511204), tc_fun(tc_fun(tc_prod(_1511204, _1511204), tc_HOL_Obool), tc_HOL_Obool), _1511204), c_member(tc_prod(_1511204, _1511204)))), c_Product__Type_OPair(_1511204, _1511204)))), _1511206), _1511208, _1511210), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1511204, tc_HOL_Obool), tc_fun(_1511204, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1511204, tc_HOL_Obool), tc_fun(_1511204, tc_HOL_Obool)), _1511208), _1511210)), c_Wellfounded_Omax__ext(_1511204, _1511206))))], (22702 ^ _781013) ^ [_1205712, _1205714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205712), 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)), _1205714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205712), _1205714)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33430 ^ _781013) ^ [_1415442, _1415444, _1415446] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415442)))), 33433 ^ _781013 : [(33440 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415444)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415442)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415444)), _1415446)) = 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), _1415442), _1415444))), _1415446))], (33434 ^ _781013) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415444))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415442)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415444)), _1415446)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415442)), _1415446))]]], (5899 ^ _781013) ^ [_875965, _875967] : [c_Hoare__Mirabelle_Ostate__not__singleton, c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _875965, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_Com_Ostate), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies)), c_Natural_Oevalc(_875967))))), c_fequal))), _875967), c_fequal)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _875965, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(_875967)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (8305 ^ _781013) ^ [_923190, _923192, _923194, _923196] : [hBOOL(hAPP(hAPP(c_member(_923190), _923196), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923190, tc_HOL_Obool)), _923192), _923194))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923190, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_923190, tc_fun(_923190, tc_HOL_Obool), tc_HOL_Obool), c_member(_923190)), _923192)), hAPP(hAPP(c_COMBC(_923190, tc_fun(_923190, tc_HOL_Obool), tc_HOL_Obool), c_member(_923190)), _923194)), _923196)))], (34417 ^ _781013) ^ [] : [-(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))))))], (22854 ^ _781013) ^ [_1208507, _1208509] : [-(c_Option_Ooption_Ooption__size(_1208507, _1208509, c_Option_Ooption_ONone(_1208507)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43751 ^ _781013) ^ [_1652639, _1652641, _1652643] : [class_Orderings_Olinorder(_1652639), c_List_Olinorder__class_Osorted(_1652639, _1652641), -(c_List_Olinorder__class_Osorted(_1652639, c_List_Oremove1(_1652639, _1652643, _1652641)))], (42142 ^ _781013) ^ [_1615121, _1615123, _1615125, _1615127, _1615129] : [hAPP(hAPP(c_List_Odrop(_1615121), _1615123), _1615125) = hAPP(hAPP(c_List_Olist_OCons(_1615121), _1615127), _1615129), -(hAPP(hAPP(c_List_Onth(_1615121), _1615125), _1615123) = _1615127)], (35247 ^ _781013) ^ [_1447861, _1447863, _1447865] : [class_Rings_Olinordered__semidom(_1447861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447861), hAPP(hAPP(c_Power_Opower__class_Opower(_1447861), _1447863), 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(_1447861), _1447865), 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(_1447861), c_Groups_Ozero__class_Ozero(_1447861)), _1447865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447861), _1447863), _1447865)))], (43161 ^ _781013) ^ [_1639813, _1639815, _1639817, _1639819, _1639821] : [-(_1639813 = c_Orderings_Obot__class_Obot(tc_fun(_1639815, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1639817, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639815, tc_fun(_1639817, tc_HOL_Obool)), _1639813), _1639819)), _1639821) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639815, tc_fun(_1639817, tc_HOL_Obool)), _1639813), hAPP(hAPP(c_COMBC(_1639815, tc_fun(_1639817, tc_HOL_Obool), tc_fun(_1639817, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1639817, tc_HOL_Obool), tc_fun(tc_fun(_1639817, tc_HOL_Obool), tc_fun(_1639817, tc_HOL_Obool)), _1639815), c_Groups_Ominus__class_Ominus(tc_fun(_1639817, tc_HOL_Obool))), _1639819)), _1639821)))], (17629 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (19945 ^ _781013) ^ [_1154637, _1154639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154637), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1154639), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154637), _1154639))), -(_1154637 = _1154639)], (31132 ^ _781013) ^ [_1364162, _1364164, _1364166, _1364168] : [-(hBOOL(hAPP(_1364162, _1364164))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1364162, _1364166)), _1364164), _1364168), _1364164)))], (1494 ^ _781013) ^ [_802430, _802432] : [-(class_Groups_Oordered__comm__monoid__add(_802430)), _802432 = _802430, class_Groups_Oordered__comm__monoid__add(_802432)], (17937 ^ _781013) ^ [_1115482, _1115484, _1115486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1115482), _1115484)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1115486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1115482), _1115486)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1115484), _1115486))))], (11123 ^ _781013) ^ [_979255, _979257, _979259, _979261, _979263, _979265, _979267] : [-(hBOOL(hAPP(hAPP(c_member(_979255), _979257), _979259))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_979255, _979261, _979263, _979265, _979259), _979267)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_979255, _979261, _979263, _979265, hAPP(hAPP(c_Set_Oinsert(_979255), _979257), _979259)), hAPP(hAPP(_979263, _979257), _979267))))], (8723 ^ _781013) ^ [_932791, _932793, _932795, _932797, _932799, _932801] : [-(hBOOL(hAPP(hAPP(c_member(_932791), _932793), _932795))), -(hAPP(c_Set_Oimage(_932791, _932797, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_932791, _932797), _932799), _932793), _932801)), _932795) = hAPP(c_Set_Oimage(_932791, _932797, _932799), _932795))], (40331 ^ _781013) ^ [_1567841, _1567843, _1567845, _1567847, _1567849, _1567851] : [_1567841 = _1567843, -(hAPP(hAPP(c_Map_Omap__of(_1567845, _1567847), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1567845, _1567847)), hAPP(hAPP(c_Product__Type_OPair(_1567845, _1567847), _1567841), _1567849)), _1567851)), _1567843) = hAPP(c_Option_Ooption_OSome(_1567847), _1567849))], (8925 ^ _781013) ^ [_937128, _937130, _937132] : [class_Lattices_Obounded__lattice__bot(_937128), 8928 ^ _781013 : [(8937 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_937128), _937130), _937132) = c_Orderings_Obot__class_Obot(_937128)), _937130 = c_Orderings_Obot__class_Obot(_937128), _937132 = c_Orderings_Obot__class_Obot(_937128)], (8929 ^ _781013) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_937128), _937130), _937132) = c_Orderings_Obot__class_Obot(_937128), 8932 ^ _781013 : [(8935 ^ _781013) ^ [] : [-(_937132 = c_Orderings_Obot__class_Obot(_937128))], (8933 ^ _781013) ^ [] : [-(_937130 = c_Orderings_Obot__class_Obot(_937128))]]]]], (13467 ^ _781013) ^ [_1027359, _1027361, _1027363, _1027365, _1027367] : [class_Groups_Oab__group__add(_1027359), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027361, _1027359), hAPP(hAPP(c_COMBS(_1027361, _1027359, _1027359), hAPP(hAPP(c_COMBB(_1027359, tc_fun(_1027359, _1027359), _1027361), c_Groups_Ominus__class_Ominus(_1027359)), _1027363)), _1027365)), _1027367) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1027359), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027361, _1027359), _1027363), _1027367)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027361, _1027359), _1027365), _1027367)))], (11121 ^ _781013) ^ [_979203, _979205, _979207, _979209] : [-(c_Map_Odom(_979203, _979205, c_Map_Orestrict__map(_979203, _979205, _979207, _979209)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979203, tc_HOL_Obool)), c_Map_Odom(_979203, _979205, _979207)), _979209))], (28290 ^ _781013) ^ [_1309119, _1309121] : [-(_1309119 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 28293 ^ _781013 : [(28300 ^ _781013) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1309121, _1309119) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1309121), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1309119)) = 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), _1309121), _1309119))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28294 ^ _781013) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1309121, _1309119) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1309121), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1309119)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1309121), _1309119)))]]], (51494 ^ _781013) ^ [_1823642, _1823644] : [-(class_Nat_Osize(tc_prod(_1823642, _1823644)))], (4804 ^ _781013) ^ [_853856, _853858] : [_853858 = _853856, -(c_Lazy__Sequence_Oyieldn(_853858) = c_Lazy__Sequence_Oyieldn(_853856))], (21241 ^ _781013) ^ [_1179447, _1179449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179449)), -(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), _1179447), _1179449))))], (29733 ^ _781013) ^ [_1335456] : [class_Orderings_Oord(_1335456), -(c_Orderings_Oord__class_Omin(_1335456) = c_Orderings_Oord_Omin(_1335456, c_Orderings_Oord__class_Oless__eq(_1335456)))], (36725 ^ _781013) ^ [_1482019, _1482021] : [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), _1482019))), 36728 ^ _781013 : [(36735 ^ _781013) ^ [] : [-(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), _1482021)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482019))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482021), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482019)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482019)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482021), 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), _1482019)))))], (36729 ^ _781013) ^ [] : [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), _1482021)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482019)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482021), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482019)) = 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), _1482021)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482019))))]]], (51144 ^ _781013) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (37548 ^ _781013) ^ [_1497962, _1497964, _1497966, _1497968, _1497970] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1497962, _1497964, _1497966), _1497968), _1497970) = hAPP(hAPP(_1497968, hAPP(c_Product__Type_Ofst(_1497962, _1497964), _1497970)), hAPP(c_Product__Type_Osnd(_1497962, _1497964), _1497970)))], (42931 ^ _781013) ^ [_1633145, _1633147, _1633149, _1633151] : [hBOOL(hAPP(hAPP(c_member(_1633147), _1633151), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633145, tc_fun(_1633147, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1633145, tc_HOL_Obool))), _1633149))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633145, tc_fun(_1633147, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1633145, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1633147, tc_HOL_Obool), tc_fun(_1633147, tc_HOL_Obool), _1633145), hAPP(c_COMBC(_1633147, tc_fun(_1633147, tc_HOL_Obool), tc_HOL_Obool), c_member(_1633147))), _1633149)), _1633151)))], (7721 ^ _781013) ^ [_911017, _911019, _911021] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_911017), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911017, tc_HOL_Obool)), _911019), _911021))), 7724 ^ _781013 : [(7727 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_911017), _911021)))], (7725 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_911017), _911019)))]]], (20943 ^ _781013) ^ [_1172398, _1172400, _1172402, _1172404] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1172398, _1172400)), c_Sum__Type_OPlus(_1172398, _1172400, _1172402, _1172404))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1172398), _1172402)))], (36900 ^ _781013) ^ [_1484965, _1484967] : [-(_1484965 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36903 ^ _781013 : [(36910 ^ _781013) ^ [] : [-(_1484967 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1484965, _1484967) = 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, _1484967))), 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)), _1484967)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484965))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1484967), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1484965), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1484965, _1484967)), 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), _1484967))))), c_Divides_Opdivmod(_1484965, _1484967)))))], (36904 ^ _781013) ^ [] : [_1484967 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1484965, _1484967) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484965))]]], (31214 ^ _781013) ^ [_1365764, _1365766, _1365768, _1365770, _1365772, _1365774] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1365764, _1365766, _1365768)), _1365770), _1365772), _1365774))), 31215 ^ _781013 : [(31222 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1365764, _1365770))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1365768), _1365770), _1365772), _1365774))], (31216 ^ _781013) ^ [] : [hBOOL(hAPP(_1365764, _1365770)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1365766), _1365770), _1365772), _1365774))]]], (47729 ^ _781013) ^ [_1744872, _1744874, _1744876, _1744878] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1744872, tc_HOL_Obool), tc_fun(_1744872, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1744872, tc_HOL_Obool), tc_fun(_1744872, tc_HOL_Obool)), _1744874), _1744876)), c_Wellfounded_Omax__ext(_1744872, _1744878)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1744872), _1744874)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1744872), _1744876)), -(_1744876 = c_Orderings_Obot__class_Obot(tc_fun(_1744872, tc_HOL_Obool))), 47743 ^ _781013 : [(47746 ^ _781013) ^ [_1745277] : [hBOOL(hAPP(hAPP(c_member(_1744872), _1745277), _1744876)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1744872, _1744872)), hAPP(hAPP(c_Product__Type_OPair(_1744872, _1744872), 47742 ^ [_1744872, _1744874, _1744876, _1744878]), _1745277)), _1744878))], (47744 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744872), 47742 ^ [_1744872, _1744874, _1744876, _1744878]), _1744874)))]]], (51434 ^ _781013) ^ [_1822874, _1822876] : [-(class_Nat_Osize(tc_sum(_1822874, _1822876)))], (290 ^ _781013) ^ [_785556, _785558] : [-(class_Fields_Ofield__inverse__zero(_785556)), _785558 = _785556, class_Fields_Ofield__inverse__zero(_785558)], (32364 ^ _781013) ^ [_1395025, _1395027] : [class_Int_Onumber__ring(_1395025), -(hAPP(c_Int_Onumber__class_Onumber__of(_1395025), _1395027) = hAPP(c_Int_Oring__1__class_Oof__int(_1395025), _1395027))], (5570 ^ _781013) ^ [_868669, _868671] : [hAPP(_868669, 5571 ^ [_868669, _868671]) = hAPP(_868671, 5571 ^ [_868669, _868671]), -(_868669 = _868671)], (48007 ^ _781013) ^ [_1750749] : [-(c_Transitive__Closure_Otrancl(_1750749, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1750749, _1750749), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1750749, _1750749), tc_HOL_Obool)))], (28022 ^ _781013) ^ [_1304211, _1304213] : [class_Rings_Olinordered__idom(_1304211), 28025 ^ _781013 : [(28032 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304211), c_Groups_Ozero__class_Ozero(_1304211)), _1304213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304211), c_Groups_Ozero__class_Ozero(_1304211)), c_Groups_Osgn__class_Osgn(_1304211, _1304213))))], (28026 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304211), c_Groups_Ozero__class_Ozero(_1304211)), c_Groups_Osgn__class_Osgn(_1304211, _1304213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304211), c_Groups_Ozero__class_Ozero(_1304211)), _1304213)))]]], (38166 ^ _781013) ^ [_1513238] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1513238)) = _1513238)], (5120 ^ _781013) ^ [_859086, _859088] : [_859088 = _859086, -(c_Groups_Oplus__class_Oplus(_859088) = c_Groups_Oplus__class_Oplus(_859086))], (6523 ^ _781013) ^ [_887793, _887795, _887797, _887799, _887801, _887803, _887805] : [c_Finite__Set_Ofolding__image__simple__idem(_887793, _887795, _887797, _887799, _887801, _887803), -(hAPP(hAPP(_887797, _887805), _887805) = _887805)], (41292 ^ _781013) ^ [_1594891, _1594893] : [_1594893 = c_List_Olist_ONil(_1594891), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594891)), _1594893) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21289 ^ _781013) ^ [_1180367, _1180369, _1180371] : [c_Hoare__Mirabelle_Otriple__valid(_1180367, hAPP(c_Nat_OSuc, _1180369), _1180371), -(c_Hoare__Mirabelle_Otriple__valid(_1180367, _1180369, _1180371))], (21993 ^ _781013) ^ [_1193532, _1193534, _1193536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193532), _1193534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193536)), -(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), _1193536)), _1193532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1193536)), _1193534))))], (50982 ^ _781013) ^ [_1818136, _1818138] : [-(c_List_Oreplicate(_1818136, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1818138) = c_List_Olist_ONil(_1818136))], (5703 ^ _781013) ^ [_871202, _871204] : [-(c_Set_Othe__elem(_871202, hAPP(hAPP(c_Set_Oinsert(_871202), _871204), c_Orderings_Obot__class_Obot(tc_fun(_871202, tc_HOL_Obool)))) = _871204)], (8959 ^ _781013) ^ [_937645, _937647, _937649, _937651, _937653] : [class_Lattices_Olattice(_937645), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937647, _937645)), _937649), _937651), _937653) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_937645), hAPP(_937649, _937653)), hAPP(_937651, _937653)))], (30617 ^ _781013) ^ [_1353166, _1353168, _1353170] : [class_Orderings_Olinorder(_1353166), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353166), _1353168)), hBOOL(hAPP(hAPP(c_member(_1353166), _1353170), _1353168)), 30628 ^ _781013 : [(30635 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353166, tc_HOL_Obool)), _1353168), hAPP(hAPP(c_Set_Oinsert(_1353166), _1353170), c_Orderings_Obot__class_Obot(tc_fun(_1353166, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353166, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1353166, _1353168) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353166), _1353170), c_Big__Operators_Olinorder__class_OMax(_1353166, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353166, tc_HOL_Obool)), _1353168), hAPP(hAPP(c_Set_Oinsert(_1353166), _1353170), c_Orderings_Obot__class_Obot(tc_fun(_1353166, tc_HOL_Obool)))))))], (30629 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353166, tc_HOL_Obool)), _1353168), hAPP(hAPP(c_Set_Oinsert(_1353166), _1353170), c_Orderings_Obot__class_Obot(tc_fun(_1353166, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353166, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1353166, _1353168) = _1353170)]]], (44416 ^ _781013) ^ [_1666320, _1666322] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666320)), c_List_Oconcat(_1666320, _1666322)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1666320), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1666320))), _1666322)))], (30051 ^ _781013) ^ [_1342619, _1342621, _1342623] : [class_Orderings_Olinorder(_1342619), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342619), _1342621), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342619), _1342621), _1342623))))], (48844 ^ _781013) ^ [_1770208, _1770210, _1770212] : [-(hAPP(c_Relation_ORange(_1770208, _1770210), hAPP(c_Relation_Oconverse(_1770210, _1770208), _1770212)) = hAPP(c_Relation_ODomain(_1770210, _1770208), _1770212))], (35701 ^ _781013) ^ [_1456325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1456325)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1456325), c_Int_OMin)))], (19807 ^ _781013) ^ [_1152182, _1152184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152182), _1152184)), 19810 ^ _781013 : [(19813 ^ _781013) ^ [] : [_1152182 = _1152184], (19811 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1152182), _1152184)))]]], (50820 ^ _781013) ^ [_1814073, _1814075, _1814077] : [-(hAPP(c_New__DSequence_Opos__single(_1814073, _1814075), _1814077) = hAPP(c_Lazy__Sequence_Osingle(_1814073), _1814075))], (26713 ^ _781013) ^ [_1278149] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1278149)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1278149))], (46311 ^ _781013) ^ [_1708337, _1708339, _1708341, _1708343, _1708345] : [46313 ^ _781013 : [(46316 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1708337, _1708339, tc_HOL_Obool), _1708345), 46312 ^ [_1708337, _1708339, _1708341, _1708343, _1708345]))], (46314 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1708337, _1708339)), 46312 ^ [_1708337, _1708339, _1708341, _1708343, _1708345]), hAPP(c_List_Oset(tc_prod(_1708337, _1708339)), hAPP(hAPP(c_List_Ozip(_1708337, _1708339), _1708341), _1708343)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708337)), _1708341) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708339)), _1708343), -(c_List_Olist__all2(_1708337, _1708339, _1708345, _1708341, _1708343))], (48309 ^ _781013) ^ [_1757203] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1757203)) = _1757203)], (40293 ^ _781013) ^ [_1567047, _1567049, _1567051, _1567053, _1567055] : [c_Relation_Orefl__on(_1567047, _1567049, _1567051), c_Relation_Orefl__on(_1567047, _1567053, _1567055), -(c_Relation_Orefl__on(_1567047, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567047, tc_HOL_Obool)), _1567049), _1567053), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567047, _1567047), tc_HOL_Obool)), _1567051), _1567055)))], (20757 ^ _781013) ^ [_1168949, _1168951, _1168953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1168949), _1168951)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1168953), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1168951), _1168949))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1168953), _1168949)), hAPP(c_Nat_OSuc, _1168951)))], (35783 ^ _781013) ^ [_1457516, _1457518] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1457516), hAPP(hAPP(c_Power_Opower__class_Opower(_1457516), hAPP(c_Int_Onumber__class_Onumber__of(_1457516), c_Int_OMin)), _1457518)) = c_Groups_Oone__class_Oone(_1457516)), class_Int_Onumber__ring(_1457516), class_Rings_Olinordered__idom(_1457516)], (21730 ^ _781013) ^ [] : [-(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)))], (5879 ^ _781013) ^ [_875570, _875572, _875574] : [c_Com_Ocom_OWhile(_875570, _875572) = hAPP(c_Com_Ocom_OBODY, _875574)], (24045 ^ _781013) ^ [_1229685, _1229687] : [-(hAPP(c_Int_Onat, _1229685) = _1229687), 24048 ^ _781013 : [(24051 ^ _781013) ^ [] : [_1229685 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229687)], (24049 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229685)))]], 24052 ^ _781013 : [(24055 ^ _781013) ^ [] : [_1229687 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24053 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229685))]]], (12140 ^ _781013) ^ [_1000050, _1000052, _1000054] : [class_Lattices_Olattice(_1000050), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000050), _1000052)), hBOOL(hAPP(hAPP(c_member(_1000050), _1000054), _1000052)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1000050), _1000054), c_Big__Operators_Olattice__class_OSup__fin(_1000050, _1000052)) = _1000054)], (22746 ^ _781013) ^ [_1206464, _1206466, _1206468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1206464), _1206466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206468), 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), _1206466), _1206468)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206464), _1206468))))], (3754 ^ _781013) ^ [_837755, _837757, _837759, _837761, _837763, _837765] : [-(c_Predicate_ODomainP(_837765, _837761, _837757) = c_Predicate_ODomainP(_837763, _837759, _837755)), _837765 = _837763, _837761 = _837759, _837757 = _837755], (27641 ^ _781013) ^ [_1296854, _1296856, _1296858, _1296860] : [class_Divides_Osemiring__div(_1296854), -(c_Divides_Odiv__class_Omod(_1296854, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296854), _1296856), _1296858), _1296860) = c_Divides_Odiv__class_Omod(_1296854, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296854), c_Divides_Odiv__class_Omod(_1296854, _1296856, _1296860)), _1296858), _1296860))], (13907 ^ _781013) ^ [_1036635, _1036637, _1036639, _1036641] : [class_Groups_Oordered__ab__semigroup__add(_1036635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036635), _1036637), _1036639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036635), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036635), _1036641), _1036637)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036635), _1036641), _1036639))))], (39279 ^ _781013) ^ [_1539860, _1539862, _1539864, _1539866, _1539868] : [-(hAPP(hAPP(c_List_Olist__update(_1539860, hAPP(hAPP(c_List_Olist__update(_1539860, _1539862), _1539864), _1539866)), _1539864), _1539868) = hAPP(hAPP(c_List_Olist__update(_1539860, _1539862), _1539864), _1539868))], (44867 ^ _781013) ^ [_1676803, _1676805] : [-(c_List_OdropWhile(_1676803, _1676805, c_List_Olist_ONil(_1676803)) = c_List_Olist_ONil(_1676803))], (22316 ^ _781013) ^ [_1199276, _1199278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199278)), -(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), _1199276), _1199278))))], (5426 ^ _781013) ^ [_863747, _863749, _863751, _863753] : [-(tc_prod(_863753, _863749) = tc_prod(_863751, _863747)), _863753 = _863751, _863749 = _863747], (14639 ^ _781013) ^ [_1052726, _1052728, _1052730, _1052732] : [class_Rings_Ocomm__semiring__1(_1052726), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052728), _1052730)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052728, _1052726), _1052732), _1052730) = c_Groups_Ozero__class_Ozero(_1052726)), 14648 ^ _781013 : [(14649 ^ _781013) ^ [_1052907] : [hBOOL(hAPP(hAPP(c_member(_1052728), _1052907), _1052730)), hAPP(_1052732, _1052907) = c_Groups_Ozero__class_Ozero(_1052726)]]], (51612 ^ _781013) ^ [_1824837, _1824839, _1824841, _1824843, _1824845, _1824847] : [-(hAPP(hAPP(hAPP(c_COMBS(_1824837, _1824839, _1824841), _1824843), _1824845), _1824847) = hAPP(hAPP(_1824843, _1824847), hAPP(_1824845, _1824847)))], (9705 ^ _781013) ^ [_952549, _952551, _952553] : [class_Orderings_Olinorder(_952549), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952549), _952551), _952553))), 9712 ^ _781013 : [(9719 ^ _781013) ^ [] : [_952553 = _952551, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952549), _952553), _952551))], (9713 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952549), _952553), _952551))), -(_952553 = _952551)]]], (18003 ^ _781013) ^ [_1116655, _1116657, _1116659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116655), _1116657)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116655), _1116659))), 18006 ^ _781013 : [(18009 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116657), _1116659)))], (18007 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1116655)))]]], (18069 ^ _781013) ^ [_1117689, _1117691] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117689), _1117691) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1117689 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1117691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29627 ^ _781013) ^ [_1333497, _1333499, _1333501] : [class_Orderings_Olinorder(_1333497), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333497), _1333499)), -(hBOOL(hAPP(hAPP(c_member(_1333497), _1333501), _1333499))), -(_1333499 = c_Orderings_Obot__class_Obot(tc_fun(_1333497, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1333497, hAPP(hAPP(c_Set_Oinsert(_1333497), _1333501), _1333499)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333497), _1333501), c_Big__Operators_Olinorder__class_OMin(_1333497, _1333499)))], (14897 ^ _781013) ^ [_1056884, _1056886] : [class_Rings_Omult__zero(_1056884), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056884), _1056886), c_Groups_Ozero__class_Ozero(_1056884)) = c_Groups_Ozero__class_Ozero(_1056884))], (41464 ^ _781013) ^ [_1598548, _1598550, _1598552, _1598554] : [-(_1598548 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1598550), _1598548), hAPP(hAPP(c_List_Olist_OCons(_1598550), _1598552), _1598554)) = hAPP(hAPP(c_List_Olist_OCons(_1598550), _1598552), hAPP(hAPP(c_List_Otake(_1598550), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1598548), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1598554)))], (37909 ^ _781013) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (37706 ^ _781013) ^ [_1501373, _1501375] : [c_Code__Numeral_OSuc__code__numeral(_1501373) = c_Code__Numeral_OSuc__code__numeral(_1501375), -(_1501373 = _1501375)], (34261 ^ _781013) ^ [_1430861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430861), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1430861)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20579 ^ _781013) ^ [_1165778, _1165780, _1165782] : [class_Rings_Oring__1(_1165778), hBOOL(hAPP(hAPP(c_member(_1165778), _1165780), c_Int_Oring__1__class_OInts(_1165778))), hBOOL(hAPP(hAPP(c_member(_1165778), _1165782), c_Int_Oring__1__class_OInts(_1165778))), -(hBOOL(hAPP(hAPP(c_member(_1165778), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165778), _1165780), _1165782)), c_Int_Oring__1__class_OInts(_1165778))))], (14327 ^ _781013) ^ [_1046209, _1046211, _1046213, _1046215] : [class_Rings_Ocomm__semiring__1(_1046209), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046209), _1046211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046209), _1046213), _1046215)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046209), _1046213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046209), _1046211), _1046215)))], (49148 ^ _781013) ^ [_1777896, _1777898, _1777900] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1777896, _1777896, _1777896), _1777898), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777896, _1777896), tc_HOL_Obool), _1777900), _1777898)) = hAPP(hAPP(c_Relation_Orel__comp(_1777896, _1777896, _1777896), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777896, _1777896), tc_HOL_Obool), _1777900), _1777898)), _1777898))], (26012 ^ _781013) ^ [_1264577, _1264579] : [class_Rings_Oring__1(_1264577), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264579)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1264577), hAPP(c_Int_Onat, _1264579)) = hAPP(c_Int_Oring__1__class_Oof__int(_1264577), _1264579))], (13479 ^ _781013) ^ [_1027709, _1027711, _1027713] : [class_Rings_Olinordered__semidom(_1027709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027709), c_Groups_Oone__class_Oone(_1027709)), _1027711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027709), c_Groups_Oone__class_Oone(_1027709)), _1027713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027709), c_Groups_Oone__class_Oone(_1027709)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1027709), _1027711), _1027713))))], (37078 ^ _781013) ^ [_1488588, _1488590, _1488592, _1488594] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1488588, _1488590), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1488592), _1488594))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1488588), _1488590) = _1488592)], (4562 ^ _781013) ^ [_850097, _850099] : [_850099 = _850097, -(c_Groups_Ouminus__class_Ouminus(_850099) = c_Groups_Ouminus__class_Ouminus(_850097))], (50800 ^ _781013) ^ [_1813456, _1813458, _1813460, _1813462, _1813464, _1813466, _1813468] : [-(c_New__Random__Sequence_Opos__decr__bind(_1813456, _1813458, _1813460, _1813462, _1813464, _1813466, _1813468) = c_New__DSequence_Opos__decr__bind(_1813456, _1813458, hAPP(hAPP(hAPP(_1813460, _1813464), _1813466), _1813468), hAPP(hAPP(c_COMBC(_1813456, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1813458))), hAPP(hAPP(c_COMBC(_1813456, 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(_1813458)))), hAPP(hAPP(c_COMBC(_1813456, 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(_1813458))))), _1813462), _1813464)), _1813466)), _1813468)))], (36709 ^ _781013) ^ [_1481755, _1481757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1481755)), 36712 ^ _781013 : [(36719 ^ _781013) ^ [] : [-(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), _1481757), _1481755)))), -(c_Divides_OnegDivAlg(_1481757, _1481755) = hAPP(c_Divides_Oadjust(_1481755), c_Divides_OnegDivAlg(_1481757, 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)))), _1481755))))], (36713 ^ _781013) ^ [] : [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), _1481757), _1481755))), -(c_Divides_OnegDivAlg(_1481757, _1481755) = 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), _1481757), _1481755)))]]], (12030 ^ _781013) ^ [_997907, _997909, _997911, _997913, _997915, _997917] : [c_Fun_Oinj__on(_997907, _997909, hAPP(c_Fun_Ocomp(_997911, _997909, _997907, _997913), _997915), _997917), -(c_Fun_Oinj__on(_997911, _997909, _997913, hAPP(c_Set_Oimage(_997907, _997911, _997915), _997917)))], (35969 ^ _781013) ^ [_1465467, _1465469, _1465471, _1465473] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1465469, _1465467)), _1465471), _1465473) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1465469), hAPP(hAPP(c_COMBC(_1465469, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1465467, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1465469), c_Smallcheck_Osmall__class_Osmall(_1465467)), hAPP(hAPP(c_COMBB(tc_fun(_1465467, tc_prod(_1465469, _1465467)), tc_fun(_1465467, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1465469), hAPP(c_COMBB(tc_prod(_1465469, _1465467), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1465467), _1465471)), c_Product__Type_OPair(_1465469, _1465467)))), _1465473)), _1465473)), class_Smallcheck_Osmall(_1465467), class_Smallcheck_Osmall(_1465469)], (40689 ^ _781013) ^ [_1578759, _1578761, _1578763, _1578765, _1578767, _1578769] : [hBOOL(hAPP(hAPP(c_member(_1578759), _1578761), _1578763)), 40692 ^ _781013 : [(40699 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578765, tc_HOL_Obool)), _1578767), _1578769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578765, _1578759), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1578765, _1578759), _1578767), hAPP(c_COMBK(tc_fun(_1578759, tc_HOL_Obool), _1578765), _1578763))), hAPP(hAPP(c_Product__Type_OSigma(_1578765, _1578759), _1578769), hAPP(c_COMBK(tc_fun(_1578759, tc_HOL_Obool), _1578765), _1578763)))))], (40693 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578765, _1578759), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1578765, _1578759), _1578767), hAPP(c_COMBK(tc_fun(_1578759, tc_HOL_Obool), _1578765), _1578763))), hAPP(hAPP(c_Product__Type_OSigma(_1578765, _1578759), _1578769), hAPP(c_COMBK(tc_fun(_1578759, tc_HOL_Obool), _1578765), _1578763)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578765, tc_HOL_Obool)), _1578767), _1578769)))]]], (32142 ^ _781013) ^ [_1391158] : [-(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, _1391158))))))], (23447 ^ _781013) ^ [_1219745, _1219747] : [class_Rings_Odivision__ring__inverse__zero(_1219745), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219745), _1219747), c_Groups_Ozero__class_Ozero(_1219745)) = c_Groups_Ozero__class_Ozero(_1219745))], (48617 ^ _781013) ^ [_1764426, _1764428, _1764430, _1764432] : [c_Wellfounded_Oacyclic(_1764426, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1764426, _1764426)), hAPP(hAPP(c_Product__Type_OPair(_1764426, _1764426), _1764428), _1764430)), _1764432)), 48620 ^ _781013 : [(48623 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764426, _1764426)), hAPP(hAPP(c_Product__Type_OPair(_1764426, _1764426), _1764430), _1764428)), c_Transitive__Closure_Ortrancl(_1764426, _1764432)))], (48621 ^ _781013) ^ [] : [-(c_Wellfounded_Oacyclic(_1764426, _1764432))]]], (18287 ^ _781013) ^ [_1121459, _1121461, _1121463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121461), _1121463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121459), _1121461)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121459), _1121463))))], (12766 ^ _781013) ^ [_1012190, _1012192, _1012194] : [class_Lattices_Olattice(_1012190), hAPP(_1012192, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1012190), 12771 ^ [_1012190, _1012192, _1012194]), 12772 ^ [_1012190, _1012192, _1012194])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1012190), hAPP(_1012192, 12771 ^ [_1012190, _1012192, _1012194])), hAPP(_1012192, 12772 ^ [_1012190, _1012192, _1012194])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012190), _1012194)), -(_1012194 = c_Orderings_Obot__class_Obot(tc_fun(_1012190, tc_HOL_Obool))), -(hAPP(_1012192, c_Big__Operators_Olattice__class_OInf__fin(_1012190, _1012194)) = c_Big__Operators_Olattice__class_OInf__fin(_1012190, hAPP(c_Set_Oimage(_1012190, _1012190, _1012192), _1012194)))], (7015 ^ _781013) ^ [_897087, _897089, _897091] : [-(_897087 = _897089), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897091, tc_HOL_Obool)), _897087), _897089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897091, tc_HOL_Obool)), _897089), _897087))], (47236 ^ _781013) ^ [_1732608, _1732610, _1732612] : [-(hAPP(c_Relation_ODomain(_1732608, _1732610), hAPP(c_Set_OCollect(tc_prod(_1732608, _1732610)), hAPP(c_Product__Type_Oprod_Oprod__case(_1732608, _1732610, tc_HOL_Obool), _1732612))) = hAPP(c_Set_OCollect(_1732608), hAPP(hAPP(c_COMBB(tc_fun(_1732610, tc_HOL_Obool), tc_HOL_Obool, _1732608), c_HOL_OEx(_1732610)), _1732612)))], (29119 ^ _781013) ^ [_1324114, _1324116] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1324114), _1324116))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1324114, _1324116) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1324114), _1324116), _1324116))], (50786 ^ _781013) ^ [_1813138, _1813140, _1813142, _1813144, _1813146, _1813148, _1813150] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1813138, _1813140, _1813142, _1813144), _1813146), _1813148), _1813150) = c_New__DSequence_Oneg__bind(_1813138, _1813140, hAPP(hAPP(hAPP(_1813142, _1813146), _1813148), _1813150), hAPP(hAPP(c_COMBC(_1813138, 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(_1813140)))), hAPP(hAPP(c_COMBC(_1813138, 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(_1813140))))), hAPP(hAPP(c_COMBC(_1813138, 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(_1813140)))))), _1813144), _1813146)), _1813148)), _1813150)))], (45817 ^ _781013) ^ [_1697383, _1697385, _1697387, _1697389] : [45819 ^ _781013 : [(45822 ^ _781013) ^ [] : [hBOOL(hAPP(_1697385, hAPP(hAPP(c_List_Onth(_1697387), _1697389), 45818 ^ [_1697383, _1697385, _1697387, _1697389])))], (45820 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45818 ^ [_1697383, _1697385, _1697387, _1697389]), _1697383)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1697383), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697387)), _1697389))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1697383), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697387)), c_List_OtakeWhile(_1697387, _1697385, _1697389)))))], (5831 ^ _781013) ^ [_874719, _874721] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_874719, _874721)], (7081 ^ _781013) ^ [_898359, _898361, _898363, _898365] : [7082 ^ _781013 : [(7085 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898359), _898361), _898365))], (7083 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898359), _898361), _898363))]], -(hBOOL(hAPP(hAPP(c_member(_898359), _898361), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898359, tc_HOL_Obool)), _898363), _898365))))], (6926 ^ _781013) ^ [_895467, _895469, _895471, _895473, _895475, _895477, _895479] : [-(_895467 = _895469), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895471, _895473), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895471, _895473), _895475), _895467), _895477)), _895469), _895479) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895471, _895473), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895471, _895473), _895475), _895469), _895479)), _895467), _895477))], (47346 ^ _781013) ^ [_1735760, _1735762] : [c_Wellfounded_OwfP(_1735760, _1735762), -(c_Wellfounded_Oacyclic(_1735760, hAPP(c_Set_OCollect(tc_prod(_1735760, _1735760)), hAPP(c_Product__Type_Oprod_Oprod__case(_1735760, _1735760, tc_HOL_Obool), _1735762))))], (15327 ^ _781013) ^ [_1064612, _1064614] : [class_Groups_Olinordered__ab__group__add(_1064612), 15330 ^ _781013 : [(15337 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064612), _1064614), c_Groups_Ozero__class_Ozero(_1064612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064612), _1064614), _1064614)), c_Groups_Ozero__class_Ozero(_1064612))))], (15331 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064612), _1064614), _1064614)), c_Groups_Ozero__class_Ozero(_1064612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064612), _1064614), c_Groups_Ozero__class_Ozero(_1064612))))]]], (38566 ^ _781013) ^ [_1522794, _1522796] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1522794, _1522796))))], (46849 ^ _781013) ^ [_1723245, _1723247] : [c_Wellfounded_Owf(_1723245, _1723247), -(c_Wellfounded_Owf(tc_fun(_1723245, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1723245, _1723247)))], (37925 ^ _781013) ^ [_1507505, _1507507, _1507509, _1507511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1507505), _1507507)), -(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), _1507505), _1507509)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1507507), _1507511))), c_FunDef_Opair__less)))], (50299 ^ _781013) ^ [_1803916, _1803918, _1803920] : [c_List_Olist__all(_1803916, _1803920, _1803918), 50302 ^ _781013 : [(50303 ^ _781013) ^ [_1803997] : [hBOOL(hAPP(hAPP(c_member(_1803916), _1803997), hAPP(c_List_Oset(_1803916), _1803918))), -(hBOOL(hAPP(_1803920, _1803997)))]]], (16167 ^ _781013) ^ [_1079866, _1079868] : [class_Groups_Olinordered__ab__group__add(_1079866), 16170 ^ _781013 : [(16177 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079866), c_Groups_Ozero__class_Ozero(_1079866)), _1079868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079866), hAPP(c_Groups_Ouminus__class_Ouminus(_1079866), _1079868)), _1079868)))], (16171 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079866), hAPP(c_Groups_Ouminus__class_Ouminus(_1079866), _1079868)), _1079868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079866), c_Groups_Ozero__class_Ozero(_1079866)), _1079868)))]]], (39189 ^ _781013) ^ [_1537858, _1537860, _1537862] : [class_Orderings_Olinorder(_1537858), -(hAPP(c_List_Oset(_1537858), c_List_Olinorder__class_Oinsort__insert__key(_1537858, _1537858, c_COMBI(_1537858), _1537860, _1537862)) = hAPP(hAPP(c_Set_Oinsert(_1537858), _1537860), hAPP(c_List_Oset(_1537858), _1537862)))], (35567 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (9206 ^ _781013) ^ [_943581, _943583, _943585, _943587, _943589, _943591] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_943581, tc_Option_Ooption(_943583)), c_Map_Orestrict__map(_943581, _943583, _943585, _943587)), _943589), _943591) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_943581, tc_Option_Ooption(_943583)), c_Map_Orestrict__map(_943581, _943583, _943585, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943581, tc_HOL_Obool)), _943587), hAPP(hAPP(c_Set_Oinsert(_943581), _943589), c_Orderings_Obot__class_Obot(tc_fun(_943581, tc_HOL_Obool)))))), _943589), _943591))], (42406 ^ _781013) ^ [_1620906, _1620908, _1620910, _1620912, _1620914] : [-(hAPP(c_List_Orotate(_1620906, _1620908), hAPP(hAPP(c_List_Omap(_1620910, _1620906), _1620912), _1620914)) = hAPP(hAPP(c_List_Omap(_1620910, _1620906), _1620912), hAPP(c_List_Orotate(_1620910, _1620908), _1620914)))], (20923 ^ _781013) ^ [_1172042, _1172044, _1172046, _1172048] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1172042, _1172044)), c_Sum__Type_OPlus(_1172042, _1172044, _1172046, _1172048)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172042), _1172046)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172044), _1172048))], (43613 ^ _781013) ^ [_1650353, _1650355, _1650357] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1650353), c_List_Oupt(_1650355, _1650357)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650355), _1650353), _1650357))], (2076 ^ _781013) ^ [_811358, _811360, _811362, _811364, _811366, _811368] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_811368, _811364, _811360) = c_Hoare__Mirabelle_Otriple_Otriple__size(_811366, _811362, _811358)), _811368 = _811366, _811364 = _811362, _811360 = _811358], (36196 ^ _781013) ^ [_1470537, _1470539, _1470541, _1470543, _1470545, _1470547, _1470549] : [c_Equiv__Relations_Oequiv(_1470537, _1470539, _1470541), hBOOL(hAPP(hAPP(c_member(tc_fun(_1470537, tc_HOL_Obool)), _1470543), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1470537), _1470539), _1470541))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1470537, tc_HOL_Obool)), _1470545), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1470537), _1470539), _1470541))), hBOOL(hAPP(hAPP(c_member(_1470537), _1470547), _1470543)), hBOOL(hAPP(hAPP(c_member(_1470537), _1470549), _1470545)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1470537, _1470537)), hAPP(hAPP(c_Product__Type_OPair(_1470537, _1470537), _1470547), _1470549)), _1470541)), -(_1470543 = _1470545)], (12840 ^ _781013) ^ [_1013794, _1013796, _1013798, _1013800, _1013802, _1013804] : [hAPP(_1013794, _1013796) = _1013798, hBOOL(hAPP(hAPP(c_member(_1013800), _1013798), _1013802)), -(hBOOL(hAPP(hAPP(c_member(_1013804), _1013796), hAPP(c_Set_Ovimage(_1013804, _1013800, _1013794), _1013802))))], (41316 ^ _781013) ^ [_1595318] : [-(hBOOL(hAPP(c_List_Odistinct(_1595318), c_List_Olist_ONil(_1595318))))], (19787 ^ _781013) ^ [_1151926, _1151928] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151926), _1151928) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151928), _1151926))], (15209 ^ _781013) ^ [_1062418, _1062420, _1062422, _1062424] : [c_Fun_Oinj__on(_1062418, _1062420, _1062422, _1062424), -(hAPP(c_Finite__Set_Ocard(_1062420), hAPP(c_Set_Oimage(_1062418, _1062420, _1062422), _1062424)) = hAPP(c_Finite__Set_Ocard(_1062418), _1062424))], (8619 ^ _781013) ^ [_930482, _930484, _930486] : [class_Lattices_Osemilattice__sup(_930482), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930482), _930484), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930482), _930484), _930486)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930482), _930484), _930486))], (9843 ^ _781013) ^ [_954698, _954700, _954702, _954704] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954698, tc_HOL_Obool)), _954700), _954702), _954704)), -(hBOOL(hAPP(_954700, _954704)))], (2882 ^ _781013) ^ [_824069, _824071, _824073, _824075, _824077, _824079, _824081, _824083] : [-(c_Product__Type_Oapsnd(_824083, _824079, _824075, _824071) = c_Product__Type_Oapsnd(_824081, _824077, _824073, _824069)), _824083 = _824081, _824079 = _824077, _824075 = _824073, _824071 = _824069], (1714 ^ _781013) ^ [_805180, _805182] : [-(class_Groups_Omonoid__add(_805180)), _805182 = _805180, class_Groups_Omonoid__add(_805182)], (20171 ^ _781013) ^ [_1158212, _1158214] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158212), _1158214))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158214)), _1158212)))], (38465 ^ _781013) ^ [_1520261, _1520263, _1520265] : [hBOOL(hAPP(c_List_Odistinct(_1520261), hAPP(hAPP(c_List_Omap(tc_prod(_1520261, _1520263), _1520261), c_Product__Type_Ofst(_1520261, _1520263)), _1520265))), -(hAPP(c_List_Oset(tc_prod(_1520261, _1520263)), _1520265) = hAPP(c_Set_OCollect(tc_prod(_1520261, _1520263)), hAPP(c_Product__Type_Oprod_Oprod__case(_1520261, _1520263, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1520261, tc_fun(_1520263, tc_Option_Ooption(_1520263)), tc_fun(_1520263, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1520263), tc_HOL_Obool), tc_fun(tc_fun(_1520263, tc_Option_Ooption(_1520263)), tc_fun(_1520263, tc_HOL_Obool)), _1520261), c_COMBB(tc_Option_Ooption(_1520263), tc_HOL_Obool, _1520263)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1520263), tc_fun(tc_Option_Ooption(_1520263), tc_HOL_Obool), _1520261), c_fequal), hAPP(c_Map_Omap__of(_1520261, _1520263), _1520265)))), c_Option_Ooption_OSome(_1520263)))))], (37584 ^ _781013) ^ [_1498782, _1498784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1498782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1498784), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1498782), _1498784) = 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), _1498782), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1498784)))))], (38286 ^ _781013) ^ [_1516371, _1516373, _1516375, _1516377] : [-(hAPP(c_Map_Omap__of(_1516371, _1516373), hAPP(hAPP(c_List_Omap(_1516371, tc_prod(_1516371, _1516373)), hAPP(hAPP(c_COMBS(_1516371, _1516373, tc_prod(_1516371, _1516373)), c_Product__Type_OPair(_1516371, _1516373)), _1516375)), _1516377)) = c_Map_Orestrict__map(_1516371, _1516373, hAPP(c_Fun_Ocomp(_1516373, tc_Option_Ooption(_1516373), _1516371, c_Option_Ooption_OSome(_1516373)), _1516375), hAPP(c_List_Oset(_1516371), _1516377)))], (27803 ^ _781013) ^ [_1300283] : [class_Groups_Osgn__if(_1300283), -(c_Groups_Osgn__class_Osgn(_1300283, c_Groups_Ozero__class_Ozero(_1300283)) = c_Groups_Ozero__class_Ozero(_1300283))], (24174 ^ _781013) ^ [_1231842, _1231844] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1231842), _1231844) = 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)), _1231842)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1231844))))], (44751 ^ _781013) ^ [_1674596, _1674598] : [class_Orderings_Olinorder(_1674596), c_List_Olinorder__class_Osorted(_1674596, _1674598), -(c_List_Olinorder__class_Osorted(_1674596, c_List_Oremdups(_1674596, _1674598)))], (39384 ^ _781013) ^ [_1542322, _1542324, _1542326, _1542328, _1542330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1542322), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1542324)), _1542326))), 39387 ^ _781013 : [(39394 ^ _781013) ^ [] : [-(_1542322 = _1542328), -(hAPP(hAPP(c_List_Onth(_1542324), hAPP(hAPP(c_List_Olist__update(_1542324, _1542326), _1542322), _1542330)), _1542328) = hAPP(hAPP(c_List_Onth(_1542324), _1542326), _1542328))], (39388 ^ _781013) ^ [] : [_1542322 = _1542328, -(hAPP(hAPP(c_List_Onth(_1542324), hAPP(hAPP(c_List_Olist__update(_1542324, _1542326), _1542322), _1542330)), _1542328) = _1542330)]]], (40711 ^ _781013) ^ [_1579332, _1579334, _1579336, _1579338, _1579340, _1579342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1579332, _1579334), tc_HOL_Obool)), _1579336), hAPP(hAPP(c_Product__Type_OSigma(_1579332, _1579334), _1579338), hAPP(c_COMBK(tc_fun(_1579334, tc_HOL_Obool), _1579332), _1579340)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579334, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579332, _1579334, _1579336), _1579342)), _1579340)))], (5909 ^ _781013) ^ [_876190] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _876190))), -(hAPP(c_Com_Obody, _876190) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 5912 ^ [_876190]))], (27005 ^ _781013) ^ [_1283735, _1283737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1283735)), 27014 ^ _781013 : [(27017 ^ _781013) ^ [] : [hBOOL(hAPP(_1283737, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27010 ^ [_1283735, _1283737]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 27011 ^ [_1283735, _1283737]), _1283735))))], (27015 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1283737, 27010 ^ [_1283735, _1283737])))]], 27018 ^ _781013 : [(27021 ^ _781013) ^ [] : [hBOOL(hAPP(_1283737, 27010 ^ [_1283735, _1283737]))], (27019 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1283737, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27010 ^ [_1283735, _1283737]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 27011 ^ [_1283735, _1283737]), _1283735)))))]], 27022 ^ _781013 : [(27032 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1283737, 27039 ^ [_1283735, _1283737]))), 27033 ^ _781013 : [(27034 ^ _781013) ^ [_1284282] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1284282), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1283735))), hBOOL(hAPP(_1283737, _1284282))]]], (27023 ^ _781013) ^ [] : [27024 ^ _781013 : [(27025 ^ _781013) ^ [_1284167] : [hBOOL(hAPP(_1283737, _1284167))]], 27027 ^ _781013 : [(27030 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1283737, 27026 ^ [_1283735, _1283737])))], (27028 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27026 ^ [_1283735, _1283737]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1283735))))]]]]], (35431 ^ _781013) ^ [_1451640, _1451642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451640)), -(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)))), _1451642))), 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)))), _1451640)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1451642), _1451640))], (46739 ^ _781013) ^ [_1721084, _1721086] : [c_Wellfounded_Owf(_1721084, _1721086), 46742 ^ _781013 : [(46743 ^ _781013) ^ [_1721153] : [-(hBOOL(hAPP(hAPP(c_member(_1721084), _1721153), c_Wellfounded_Oacc(_1721084, _1721086))))]]], (40461 ^ _781013) ^ [_1571993, _1571995, _1571997, _1571999, _1572001, _1572003] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1571993, _1571995), _1571993, tc_prod(_1571997, _1571999), c_Product__Type_Ofst(_1571993, _1571995)), c_Product__Type_Omap__pair(_1571997, _1571993, _1571999, _1571995, _1572001, _1572003)) = hAPP(c_Fun_Ocomp(_1571997, _1571993, tc_prod(_1571997, _1571999), _1572001), c_Product__Type_Ofst(_1571997, _1571999)))], (5827 ^ _781013) ^ [_874571, _874573, _874575, _874577, _874579] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_874571, _874573, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_874571)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874571), hAPP(hAPP(c_COMBC(_874571, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _874571), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _874571), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _874575))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _874577))), c_Com_Ocom_OWhile(_874577, _874579)), _874575)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_874571), tc_HOL_Obool)))))], (16926 ^ _781013) ^ [_1094894, _1094896, _1094898, _1094900, _1094902, _1094904] : [-(hAPP(c_Set_Oimage(_1094894, _1094896, hAPP(hAPP(c_COMBS(_1094894, _1094896, _1094896), hAPP(hAPP(c_COMBS(_1094894, _1094896, tc_fun(_1094896, _1094896)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1094896, tc_fun(_1094896, _1094896)), _1094894), c_If(_1094896)), _1094898)), _1094900)), _1094902)), _1094904) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1094896, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1094894, _1094896, _1094900), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1094894, tc_HOL_Obool)), _1094904), hAPP(c_Set_OCollect(_1094894), _1094898)))), hAPP(c_Set_Oimage(_1094894, _1094896, _1094902), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1094894, tc_HOL_Obool)), _1094904), hAPP(c_Set_OCollect(_1094894), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1094894), c_fNot), _1094898))))))], (17745 ^ _781013) ^ [_1112211, _1112213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112211), _1112213)), _1112213 = _1112211], (40019 ^ _781013) ^ [] : [40021 ^ _781013 : [(40024 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), 40020 ^ []))], (40022 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 40020 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))]], -(c_Com_OWT__bodies)], (23815 ^ _781013) ^ [] : [-(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))))], (36102 ^ _781013) ^ [_1468552, _1468554, _1468556] : [class_Rings_Osemiring__1(_1468552), hBOOL(hAPP(hAPP(c_member(_1468552), _1468554), c_Nat_Osemiring__1__class_ONats(_1468552))), hBOOL(hAPP(hAPP(c_member(_1468552), _1468556), c_Nat_Osemiring__1__class_ONats(_1468552))), -(hBOOL(hAPP(hAPP(c_member(_1468552), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1468552), _1468554), _1468556)), c_Nat_Osemiring__1__class_ONats(_1468552))))], (42374 ^ _781013) ^ [_1620297, _1620299, _1620301] : [_1620301 = c_List_Olist_ONil(_1620297), -(hAPP(c_List_Orotate(_1620297, _1620299), _1620301) = c_List_Olist_ONil(_1620297))], (10293 ^ _781013) ^ [_963121, _963123, _963125] : [hBOOL(hAPP(hAPP(c_member(_963121), _963123), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_963121, tc_HOL_Obool)), _963125))), hBOOL(hAPP(hAPP(c_member(_963121), _963123), _963125))], (41714 ^ _781013) ^ [_1604250, _1604252, _1604254] : [-(c_List_Olist_ONil(_1604250) = hAPP(hAPP(c_List_Oappend(_1604250), _1604252), _1604254)), _1604252 = c_List_Olist_ONil(_1604250), _1604254 = c_List_Olist_ONil(_1604250)], (40862 ^ _781013) ^ [_1583905, _1583907, _1583909, _1583911, _1583913, _1583915] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1583905), tc_List_Olist(_1583905))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1583905), tc_List_Olist(_1583905)), hAPP(hAPP(c_List_Olist_OCons(_1583905), _1583907), _1583909)), hAPP(hAPP(c_List_Olist_OCons(_1583905), _1583911), _1583913))), c_List_Olistrel1(_1583905, _1583915))), 40867 ^ _781013 : [(40870 ^ _781013) ^ [] : [-(_1583909 = _1583913)], (40868 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583905, _1583905)), hAPP(hAPP(c_Product__Type_OPair(_1583905, _1583905), _1583907), _1583911)), _1583915)))]], 40871 ^ _781013 : [(40874 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1583905), tc_List_Olist(_1583905))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1583905), tc_List_Olist(_1583905)), _1583909), _1583913)), c_List_Olistrel1(_1583905, _1583915))))], (40872 ^ _781013) ^ [] : [-(_1583907 = _1583911)]]], (11093 ^ _781013) ^ [_978307, _978309, _978311, _978313, _978315] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978307, tc_HOL_Obool)), hAPP(c_Set_Oimage(_978309, _978307, _978311), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978309, tc_HOL_Obool)), _978313), _978315))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978307, tc_HOL_Obool)), hAPP(c_Set_Oimage(_978309, _978307, _978311), _978313)), hAPP(c_Set_Oimage(_978309, _978307, _978311), _978315)))))], (42831 ^ _781013) ^ [_1629667, _1629669, _1629671, _1629673] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1629671), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629667, tc_fun(_1629671, tc_HOL_Obool)), _1629669), _1629673)))), 42832 ^ _781013 : [(42833 ^ _781013) ^ [_1629741] : [hBOOL(hAPP(hAPP(c_member(_1629667), _1629741), _1629669)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629671), hAPP(_1629673, _1629741)))]]], (19909 ^ _781013) ^ [_1153939, _1153941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1153939), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1153941), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1153939), _1153941)))], (41522 ^ _781013) ^ [_1600042, _1600044, _1600046] : [-(c_List_Olistset(_1600042, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1600042, tc_HOL_Obool)), _1600044), _1600046)) = c_List_Oset__Cons(_1600042, _1600044, c_List_Olistset(_1600042, _1600046)))], (17631 ^ _781013) ^ [_1110670, _1110672, _1110674] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110670), _1110672)), _1110674) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110672), _1110674)))], (34317 ^ _781013) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (5669 ^ _781013) ^ [_870582, _870584, _870586] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(_870582)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _870584), _870582), _870586)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _870584), _870582), _870586)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (11139 ^ _781013) ^ [_979525, _979527, _979529, _979531, _979533] : [-(hBOOL(hAPP(hAPP(c_member(_979525), _979527), c_Map_Odom(_979525, _979529, _979531)))), -(hAPP(c_Map_Omap__add(_979525, _979529, _979533, _979531), _979527) = hAPP(_979533, _979527))], (22630 ^ _781013) ^ [_1204569, _1204571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204569)), 22633 ^ _781013 : [(22642 ^ _781013) ^ [] : [-(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), _1204569), _1204571)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204571), _1204569)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204571))], (22634 ^ _781013) ^ [] : [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), _1204569), _1204571))), 22637 ^ _781013 : [(22640 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204571)))], (22638 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204571), _1204569)))]]]]], (49363 ^ _781013) ^ [_1784081, _1784083] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1784081, _1784081)), _1784083), c_Relation_OId(_1784081))), -(_1784083 = hAPP(hAPP(c_Product__Type_OPair(_1784081, _1784081), 49366 ^ [_1784081, _1784083]), 49366 ^ [_1784081, _1784083]))], (17803 ^ _781013) ^ [_1113228, _1113230, _1113232] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113230), _1113232)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113230), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113228), _1113232)))], (32224 ^ _781013) ^ [_1392613, _1392615, _1392617, _1392619, _1392621] : [c_Equiv__Relations_Oequiv(_1392613, _1392615, _1392617), hBOOL(hAPP(hAPP(c_member(tc_fun(_1392613, tc_HOL_Obool)), _1392619), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1392613), _1392615), _1392617))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1392613, tc_HOL_Obool)), _1392621), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1392613), _1392615), _1392617))), -(_1392619 = _1392621), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392613, tc_HOL_Obool)), _1392619), _1392621) = c_Orderings_Obot__class_Obot(tc_fun(_1392613, tc_HOL_Obool)))], (45782 ^ _781013) ^ [_1696385, _1696387, _1696389] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1696385, tc_HOL_Obool)), _1696387), _1696389))), 45788 ^ _781013 : [(45792 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1696385, tc_HOL_Obool)), 45790 ^ [_1696385, _1696387, _1696389]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1696385, tc_HOL_Obool)), _1696387), _1696389))))], (45794 ^ _781013) ^ [] : [45787 ^ [_1696385, _1696387, _1696389] = 45790 ^ [_1696385, _1696387, _1696389]], (45796 ^ _781013) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1696385, tc_HOL_Obool)), 45787 ^ [_1696385, _1696387, _1696389]), 45790 ^ [_1696385, _1696387, _1696389]) = c_Orderings_Obot__class_Obot(tc_fun(_1696385, tc_HOL_Obool))], (45789 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1696385, tc_HOL_Obool)), 45787 ^ [_1696385, _1696387, _1696389]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1696385, tc_HOL_Obool)), _1696387), _1696389))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1696385, tc_HOL_Obool)), _1696387), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1696385, tc_HOL_Obool), _1696389)) = c_Orderings_Obot__class_Obot(tc_fun(_1696385, tc_HOL_Obool)))], (43510 ^ _781013) ^ [_1647912, _1647914] : [c_List_Otranspose(_1647912, _1647914) = c_List_Olist_ONil(tc_List_Olist(_1647912)), 43513 ^ _781013 : [(43514 ^ _781013) ^ [_1648007] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1647912)), _1648007), hAPP(c_List_Oset(tc_List_Olist(_1647912)), _1647914))), -(_1648007 = c_List_Olist_ONil(_1647912))]]], (15365 ^ _781013) ^ [_1065287, _1065289, _1065291] : [class_Rings_Olinordered__ring__strict(_1065287), 15368 ^ _781013 : [(15383 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065287), c_Groups_Ozero__class_Ozero(_1065287)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065287), _1065289), _1065291)))), 15384 ^ _781013 : [(15391 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065287), _1065289), c_Groups_Ozero__class_Ozero(_1065287))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065287), _1065291), c_Groups_Ozero__class_Ozero(_1065287)))], (15385 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065287), c_Groups_Ozero__class_Ozero(_1065287)), _1065289)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065287), c_Groups_Ozero__class_Ozero(_1065287)), _1065291))]]], (15369 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065287), c_Groups_Ozero__class_Ozero(_1065287)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065287), _1065289), _1065291))), 15374 ^ _781013 : [(15377 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065287), c_Groups_Ozero__class_Ozero(_1065287)), _1065291)))], (15375 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065287), c_Groups_Ozero__class_Ozero(_1065287)), _1065289)))]], 15378 ^ _781013 : [(15381 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065287), _1065291), c_Groups_Ozero__class_Ozero(_1065287))))], (15379 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065287), _1065289), c_Groups_Ozero__class_Ozero(_1065287))))]]]]], (10517 ^ _781013) ^ [_967435, _967437, _967439] : [class_Orderings_Oorder(_967435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967435), _967437), _967439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967435), _967437), _967439))), -(_967437 = _967439)], (20117 ^ _781013) ^ [_1157317, _1157319] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1157317)), _1157319) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1157317), hAPP(c_Nat_OSuc, _1157319)))], (35211 ^ _781013) ^ [] : [-(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))))], (28458 ^ _781013) ^ [_1312087, _1312089, _1312091, _1312093] : [class_Orderings_Olinorder(_1312087), 28461 ^ _781013 : [(28470 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312087), _1312089), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312087), _1312091), _1312093)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312087), _1312089), _1312091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312087), _1312089), _1312093))], (28462 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312087), _1312089), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312087), _1312091), _1312093))), 28465 ^ _781013 : [(28468 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312087), _1312089), _1312093)))], (28466 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312087), _1312089), _1312091)))]]]]], (18779 ^ _781013) ^ [_1131048, _1131050, _1131052, _1131054, _1131056] : [class_Groups_Oordered__comm__monoid__add(_1131048), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131050), _1131052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1131050, tc_HOL_Obool)), _1131054), _1131052)), 18793 ^ _781013 : [(18796 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131048), c_Groups_Ozero__class_Ozero(_1131048)), hAPP(_1131056, 18792 ^ [_1131048, _1131050, _1131052, _1131054, _1131056])))], (18794 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1131050), 18792 ^ [_1131048, _1131050, _1131052, _1131054, _1131056]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1131050, tc_HOL_Obool)), _1131052), _1131054))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131048), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131050, _1131048), _1131056), _1131054)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131050, _1131048), _1131056), _1131052))))], (31566 ^ _781013) ^ [_1376157, _1376159, _1376161, _1376163, _1376165] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376157, tc_fun(_1376159, tc_HOL_Obool)), _1376161), _1376163), _1376165)), 31570 ^ _781013 : [(31573 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1376163, 31569 ^ [_1376157, _1376159, _1376161, _1376163, _1376165]), _1376165)))], (31571 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376157), 31569 ^ [_1376157, _1376159, _1376161, _1376163, _1376165]), _1376161)))]]], (44434 ^ _781013) ^ [_1666569, _1666571, _1666573] : [-(hAPP(c_List_Orev(_1666569), hAPP(hAPP(c_List_Otake(_1666569), _1666571), _1666573)) = hAPP(hAPP(c_List_Odrop(_1666569), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666569)), _1666573)), _1666571)), hAPP(c_List_Orev(_1666569), _1666573)))], (16269 ^ _781013) ^ [_1081689, _1081691, _1081693] : [class_Groups_Ocomm__monoid__add(_1081689), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081691, _1081689), _1081693), c_Orderings_Obot__class_Obot(tc_fun(_1081691, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1081689))], (39926 ^ _781013) ^ [_1557931, _1557933, _1557935] : [hBOOL(hAPP(c_Predicate_OPowp(_1557931, _1557933), _1557935)), 39929 ^ _781013 : [(39930 ^ _781013) ^ [_1558015] : [hBOOL(hAPP(hAPP(c_member(_1557931), _1558015), _1557935)), -(hBOOL(hAPP(_1557933, _1558015)))]]], (1900 ^ _781013) ^ [_808372, _808374, _808376, _808378, _808380, _808382] : [-(c_Hoare__Mirabelle_Opeek__and(_808382, _808378, _808374) = c_Hoare__Mirabelle_Opeek__and(_808380, _808376, _808372)), _808382 = _808380, _808378 = _808376, _808374 = _808372], (42771 ^ _781013) ^ [_1628381, _1628383, _1628385, _1628387, _1628389, _1628391] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628381, tc_fun(_1628383, tc_HOL_Obool)), _1628385), _1628387), _1628389)), -(hBOOL(hAPP(hAPP(_1628387, _1628391), _1628389))), hBOOL(hAPP(hAPP(c_member(_1628381), _1628391), _1628385))], (7393 ^ _781013) ^ [_904471, _904473, _904475, _904477] : [class_Orderings_Oorder(_904471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904471), _904473), _904475)), _904473 = _904477, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904471), _904477), _904475)))], (6517 ^ _781013) ^ [_887698, _887700, _887702, _887704] : [c_Finite__Set_Ofolding__one__idem(_887698, _887700, _887702), -(hAPP(hAPP(_887700, _887704), _887704) = _887704)], (24784 ^ _781013) ^ [_1243182, _1243184, _1243186, _1243188] : [class_Fields_Ofield__inverse__zero(_1243182), 24787 ^ _781013 : [(24788 ^ _781013) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243182), _1243184), _1243186) = _1243188, 24791 ^ _781013 : [(24798 ^ _781013) ^ [] : [_1243186 = c_Groups_Ozero__class_Ozero(_1243182), -(_1243188 = c_Groups_Ozero__class_Ozero(_1243182))], (24792 ^ _781013) ^ [] : [-(_1243186 = c_Groups_Ozero__class_Ozero(_1243182)), -(_1243184 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1243182), _1243188), _1243186))]]], (24804 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243182), _1243184), _1243186) = _1243188), 24807 ^ _781013 : [(24810 ^ _781013) ^ [] : [_1243184 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1243182), _1243188), _1243186)], (24808 ^ _781013) ^ [] : [_1243186 = c_Groups_Ozero__class_Ozero(_1243182)]], 24811 ^ _781013 : [(24814 ^ _781013) ^ [] : [_1243188 = c_Groups_Ozero__class_Ozero(_1243182)], (24812 ^ _781013) ^ [] : [-(_1243186 = c_Groups_Ozero__class_Ozero(_1243182))]]]]], (6575 ^ _781013) ^ [_888550, _888552, _888554, _888556] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_888550, _888552, _888554), _888556)), _888554 = c_Orderings_Obot__class_Obot(tc_fun(_888550, tc_HOL_Obool))], (37720 ^ _781013) ^ [_1501584] : [c_Code__Numeral_OSuc__code__numeral(_1501584) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (48946 ^ _781013) ^ [_1773075, _1773077, _1773079, _1773081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1773075, _1773077), tc_HOL_Obool)), _1773079), _1773081)), c_Relation_Osingle__valued(_1773075, _1773077, _1773081), -(c_Relation_Osingle__valued(_1773075, _1773077, _1773079))], (43392 ^ _781013) ^ [_1645017, _1645019, _1645021, _1645023] : [hBOOL(hAPP(c_List_Olistsp(_1645017, hAPP(hAPP(c_COMBS(_1645017, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1645017), c_fconj), _1645019)), _1645021)), _1645023)), 43395 ^ _781013 : [(43398 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1645017, _1645021), _1645023)))], (43396 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1645017, _1645019), _1645023)))]]], (20115 ^ _781013) ^ [_1157274, _1157276] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1157274)), _1157276) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1157274), _1157276)))], (14297 ^ _781013) ^ [_1045426, _1045428, _1045430, _1045432, _1045434] : [class_Rings_Ocomm__semiring__1(_1045426), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045426), _1045428), _1045430)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045426), _1045432), _1045434)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045426), _1045432), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045426), _1045428), _1045430)), _1045434)))], (37991 ^ _781013) ^ [_1508695, _1508697, _1508699, _1508701] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1508695), _1508697)), 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)), _1508699), _1508695)), 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)), _1508701), _1508697)), 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)), _1508699), _1508701)), _1508697)), c_FunDef_Omax__weak)))], (20388 ^ _781013) ^ [_1161930, _1161932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161930), _1161932)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1161930)), _1161932)))], (41821 ^ _781013) ^ [_1606562, _1606564, _1606566, _1606568, _1606570, _1606572] : [-(c_List_Ofoldr(_1606562, _1606564, _1606566, hAPP(hAPP(c_List_Oappend(_1606562), _1606568), _1606570), _1606572) = c_List_Ofoldr(_1606562, _1606564, _1606566, _1606568, c_List_Ofoldr(_1606562, _1606564, _1606566, _1606570, _1606572)))], (42192 ^ _781013) ^ [_1616297, _1616299, _1616301, _1616303] : [-(hAPP(hAPP(c_List_Odrop(_1616297), _1616299), hAPP(hAPP(c_List_Olist_OCons(_1616297), _1616301), _1616303)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1616297), hAPP(hAPP(c_List_Olist_OCons(_1616297), _1616301), _1616303), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1616297), tc_List_Olist(_1616297)), c_List_Odrop(_1616297)), _1616303), _1616299))], (41738 ^ _781013) ^ [_1604629, _1604631, _1604633] : [-(hAPP(c_List_Oset(_1604629), hAPP(hAPP(c_List_Oappend(_1604629), _1604631), _1604633)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1604629, tc_HOL_Obool)), hAPP(c_List_Oset(_1604629), _1604631)), hAPP(c_List_Oset(_1604629), _1604633)))], (41404 ^ _781013) ^ [_1596834, _1596836] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596834), tc_List_Olist(_1596834))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596834), tc_List_Olist(_1596834)), c_List_Olist_ONil(_1596834)), c_List_Olist_ONil(_1596834))), c_List_Olistrel(_1596834, _1596836))))], (21794 ^ _781013) ^ [_1190051, _1190053] : [class_Rings_Oring__1(_1190051), -(hBOOL(hAPP(hAPP(c_member(_1190051), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1190051), _1190053)), c_Int_Oring__1__class_OInts(_1190051))))], (37790 ^ _781013) ^ [_1504521, _1504523] : [c_Equiv__Relations_Oequivp(_1504521, _1504523), 37793 ^ _781013 : [(37800 ^ _781013) ^ [_1504714, _1504716] : [hAPP(_1504523, _1504716) = hAPP(_1504523, _1504714), -(hBOOL(hAPP(hAPP(_1504523, _1504716), _1504714)))], (37794 ^ _781013) ^ [_1504615, _1504617] : [hBOOL(hAPP(hAPP(_1504523, _1504617), _1504615)), -(hAPP(_1504523, _1504617) = hAPP(_1504523, _1504615))]]], (51708 ^ _781013) ^ [] : [-(c_Hoare__Mirabelle_Ostate__not__singleton)], (45633 ^ _781013) ^ [_1692991] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692991, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1692991, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1692991, tc_HOL_Obool)))], (51246 ^ _781013) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (6458 ^ _781013) ^ [_886613, _886615, _886617, _886619] : [_886617 = _886619, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_886613, _886615, hAPP(hAPP(c_Set_Oinsert(_886613), _886617), c_Orderings_Obot__class_Obot(tc_fun(_886613, tc_HOL_Obool)))), _886619)))], (41386 ^ _781013) ^ [_1596490, _1596492] : [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(_1596490)), _1596492))), _1596492 = c_List_Olist_ONil(_1596490)], (10503 ^ _781013) ^ [_967261, _967263, _967265] : [class_Orderings_Oorder(_967261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967261), _967263), _967265)), -(_967263 = _967265), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967261), _967263), _967265)))], (14657 ^ _781013) ^ [_1053056, _1053058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1053056), _1053058))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1053056), _1053058)))], (43553 ^ _781013) ^ [_1649124, _1649126, _1649128, _1649130, _1649132] : [-(hAPP(hAPP(c_List_Omap(_1649124, _1649126), _1649128), hAPP(c_List_Ofilter(_1649124, _1649130), _1649132)) = c_List_Omap__filter(_1649124, _1649126, hAPP(hAPP(c_COMBC(_1649124, tc_Option_Ooption(_1649126), tc_Option_Ooption(_1649126)), hAPP(hAPP(c_COMBS(_1649124, tc_Option_Ooption(_1649126), tc_fun(tc_Option_Ooption(_1649126), tc_Option_Ooption(_1649126))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1649126), tc_fun(tc_Option_Ooption(_1649126), tc_Option_Ooption(_1649126))), _1649124), c_If(tc_Option_Ooption(_1649126))), _1649130)), hAPP(hAPP(c_COMBB(_1649126, tc_Option_Ooption(_1649126), _1649124), c_Option_Ooption_OSome(_1649126)), _1649128))), c_Option_Ooption_ONone(_1649126)), _1649132))], (35383 ^ _781013) ^ [_1450684, _1450686, _1450688] : [class_Rings_Olinordered__idom(_1450684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1450684), c_Groups_Ozero__class_Ozero(_1450684)), hAPP(hAPP(c_Power_Opower__class_Opower(_1450684), _1450686), 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)))), _1450688))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1450684), c_Groups_Ozero__class_Ozero(_1450684)), _1450686)))], (18103 ^ _781013) ^ [_1118203, _1118205, _1118207, _1118209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118203), _1118205)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118207), _1118205) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118203), _1118209), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118207), _1118209)))], (37913 ^ _781013) ^ [_1507289, _1507291] : [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), _1507289), _1507291)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1507289), _1507291)))], (19020 ^ _781013) ^ [_1136847, _1136849, _1136851, _1136853] : [hBOOL(hAPP(hAPP(_1136851, _1136853), _1136849)), -(hBOOL(hAPP(hAPP(c_member(_1136847), _1136849), c_SetInterval_Oord_OatLeast(_1136847, _1136851, _1136853))))], (37568 ^ _781013) ^ [_1498506, _1498508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1498506)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1498508)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1498506), _1498508) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1498506, _1498508)))], (25830 ^ _781013) ^ [_1261410, _1261412, _1261414] : [class_Rings_Olinordered__idom(_1261410), 25833 ^ _781013 : [(25840 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1261412), _1261414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261410), hAPP(c_Int_Oring__1__class_Oof__int(_1261410), _1261412)), hAPP(c_Int_Oring__1__class_Oof__int(_1261410), _1261414))))], (25834 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261410), hAPP(c_Int_Oring__1__class_Oof__int(_1261410), _1261412)), hAPP(c_Int_Oring__1__class_Oof__int(_1261410), _1261414))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1261412), _1261414)))]]], (15973 ^ _781013) ^ [_1076512, _1076514, _1076516, _1076518] : [class_Rings_Olinordered__ring__strict(_1076512), 15976 ^ _781013 : [(15991 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076512), _1076514), _1076516)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076512), _1076518), _1076516)))), 15992 ^ _781013 : [(15999 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076512), _1076516), c_Groups_Ozero__class_Ozero(_1076512))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076512), _1076518), _1076514))], (15993 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076512), c_Groups_Ozero__class_Ozero(_1076512)), _1076516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076512), _1076514), _1076518))]]], (15977 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076512), _1076514), _1076516)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076512), _1076518), _1076516))), 15982 ^ _781013 : [(15985 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076512), _1076514), _1076518)))], (15983 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076512), c_Groups_Ozero__class_Ozero(_1076512)), _1076516)))]], 15986 ^ _781013 : [(15989 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076512), _1076518), _1076514)))], (15987 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076512), _1076516), c_Groups_Ozero__class_Ozero(_1076512))))]]]]], (36536 ^ _781013) ^ [_1478010, _1478012, _1478014, _1478016, _1478018, _1478020] : [hBOOL(hAPP(hAPP(_1478010, _1478012), _1478014)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478016, tc_fun(_1478018, tc_HOL_Obool))), _1478010), _1478020), _1478012), _1478014)))], (40687 ^ _781013) ^ [_1578686, _1578688, _1578690, _1578692] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1578686, _1578688)), hAPP(hAPP(c_Product__Type_OSigma(_1578686, _1578688), hAPP(hAPP(c_Set_Oinsert(_1578686), _1578690), c_Orderings_Obot__class_Obot(tc_fun(_1578686, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1578688, tc_HOL_Obool), _1578686), _1578692))) = hAPP(c_Finite__Set_Ocard(_1578688), _1578692))], (33564 ^ _781013) ^ [_1417800] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1417800), c_Int_OPls) = _1417800)], (40641 ^ _781013) ^ [_1577359, _1577361, _1577363, _1577365, _1577367] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1577359, _1577361), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577359, tc_HOL_Obool)), _1577363), _1577365)), hAPP(c_COMBK(tc_fun(_1577361, tc_HOL_Obool), _1577359), _1577367)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1577359, _1577361), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1577359, _1577361), _1577363), hAPP(c_COMBK(tc_fun(_1577361, tc_HOL_Obool), _1577359), _1577367))), hAPP(hAPP(c_Product__Type_OSigma(_1577359, _1577361), _1577365), hAPP(c_COMBK(tc_fun(_1577361, tc_HOL_Obool), _1577359), _1577367))))], (43318 ^ _781013) ^ [_1643604, _1643606, _1643608] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1643604, tc_HOL_Obool)), hAPP(c_List_Oset(_1643604), hAPP(c_List_Ofilter(_1643604, _1643606), _1643608))), hAPP(c_List_Oset(_1643604), _1643608))))], (48311 ^ _781013) ^ [_1757232, _1757234, _1757236, _1757238, _1757240] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1757232, _1757232)), hAPP(hAPP(c_Product__Type_OPair(_1757232, _1757232), _1757234), _1757236)), c_Transitive__Closure_Ortrancl(_1757232, _1757238))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1757232, _1757232)), hAPP(hAPP(c_Product__Type_OPair(_1757232, _1757232), _1757236), _1757240)), c_Transitive__Closure_Ortrancl(_1757232, _1757238))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757232, _1757232)), hAPP(hAPP(c_Product__Type_OPair(_1757232, _1757232), _1757234), _1757240)), c_Transitive__Closure_Ortrancl(_1757232, _1757238))))], (12970 ^ _781013) ^ [_1016758, _1016760, _1016762, _1016764] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1016758), hAPP(c_Set_Ovimage(_1016758, _1016760, _1016762), _1016764))), hAPP(c_Set_Oimage(_1016758, _1016760, _1016762), c_Orderings_Otop__class_Otop(tc_fun(_1016758, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1016760, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1016760), _1016764)))], (20293 ^ _781013) ^ [_1160346, _1160348, _1160350] : [class_Rings_Ocomm__semiring__1(_1160346), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1160346), _1160348), hAPP(c_Nat_OSuc, _1160350)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160346), _1160348), hAPP(hAPP(c_Power_Opower__class_Opower(_1160346), _1160348), _1160350)))], (40621 ^ _781013) ^ [_1576847, _1576849, _1576851, _1576853, _1576855] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1576847, _1576849), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1576847, tc_HOL_Obool)), _1576851), _1576853)), _1576855) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1576847, _1576849), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1576847, _1576849), _1576851), _1576855)), hAPP(hAPP(c_Product__Type_OSigma(_1576847, _1576849), _1576853), _1576855)))], (31827 ^ _781013) ^ [_1382963, _1382965, _1382967, _1382969, _1382971] : [31829 ^ _781013 : [(31832 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382963, tc_HOL_Obool)), hAPP(_1382969, 31828 ^ [_1382963, _1382965, _1382967, _1382969, _1382971])), _1382971))], (31830 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382965), 31828 ^ [_1382963, _1382965, _1382967, _1382969, _1382971]), _1382967)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382963, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382965, tc_fun(_1382963, tc_HOL_Obool)), _1382967), _1382969)), _1382971)))], (6585 ^ _781013) ^ [_888762, _888764, _888766] : [c_Map_Odom(_888762, _888764, _888766) = c_Orderings_Obot__class_Obot(tc_fun(_888762, tc_HOL_Obool)), -(_888766 = hAPP(c_COMBK(tc_Option_Ooption(_888764), _888762), c_Option_Ooption_ONone(_888764)))], (31980 ^ _781013) ^ [_1387603, _1387605, _1387607, _1387609, _1387611] : [-(_1387603 = c_Orderings_Obot__class_Obot(tc_fun(_1387605, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387605, tc_fun(_1387607, tc_HOL_Obool)), _1387603), hAPP(hAPP(c_COMBB(tc_fun(_1387607, tc_HOL_Obool), tc_fun(_1387607, tc_HOL_Obool), _1387605), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387607, tc_HOL_Obool)), _1387609)), _1387611)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387607, tc_HOL_Obool)), _1387609), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387605, tc_fun(_1387607, tc_HOL_Obool)), _1387603), _1387611)))], (25656 ^ _781013) ^ [_1258638, _1258640] : [class_Rings_Oring__1(_1258638), 25659 ^ _781013 : [(25666 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258640), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1258638), _1258640) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1258638), hAPP(c_Int_Onat, _1258640)))], (25660 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258640), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1258638), _1258640) = hAPP(c_Groups_Ouminus__class_Ouminus(_1258638), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1258638), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1258640)))))]]], (38133 ^ _781013) ^ [_1512419, _1512421, _1512423, _1512425] : [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), _1512419), _1512421)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1512423), _1512425))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1512419), _1512425) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1512423), _1512421))], (18217 ^ _781013) ^ [_1120176, _1120178] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120176), _1120178) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120178), _1120176) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1120176 = _1120178)], (5996 ^ _781013) ^ [_877957, _877959] : [hBOOL(hAPP(c_Com_OWT, _877957)), hBOOL(hAPP(c_Com_OWT, _877959)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_877957, _877959))))], (4880 ^ _781013) ^ [_855086, _855088, _855090, _855092, _855094, _855096, _855098, _855100] : [-(c_New__DSequence_Oneg__bind(_855100, _855096, _855092, _855088) = c_New__DSequence_Oneg__bind(_855098, _855094, _855090, _855086)), _855100 = _855098, _855096 = _855094, _855092 = _855090, _855088 = _855086], (17733 ^ _781013) ^ [_1112121, _1112123] : [-(_1112121 = _1112123), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112121), _1112123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112123), _1112121)))], (18123 ^ _781013) ^ [_1118575, _1118577, _1118579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118575), _1118577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118575), _1118579)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118577), _1118579))))], (44719 ^ _781013) ^ [_1674035, _1674037] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674035)), c_List_Oremdups(_1674035, _1674037))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674035)), _1674037))))], (12912 ^ _781013) ^ [_1015495, _1015497, _1015499, _1015501] : [hAPP(c_Set_Oimage(_1015495, _1015497, _1015499), c_Orderings_Otop__class_Otop(tc_fun(_1015495, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1015497, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1015495, _1015497, _1015499), hAPP(c_Set_Ovimage(_1015495, _1015497, _1015499), _1015501)) = _1015501)], (41546 ^ _781013) ^ [_1600808, _1600810, _1600812, _1600814, _1600816, _1600818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600808)), _1600810)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600812)), _1600814))), -(c_Map_Omap__upds(_1600808, _1600812, _1600816, hAPP(hAPP(c_List_Oappend(_1600808), _1600810), hAPP(hAPP(c_List_Olist_OCons(_1600808), _1600818), c_List_Olist_ONil(_1600808))), _1600814) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1600808, tc_Option_Ooption(_1600812)), c_Map_Omap__upds(_1600808, _1600812, _1600816, _1600810, _1600814)), _1600818), hAPP(c_Option_Ooption_OSome(_1600812), hAPP(hAPP(c_List_Onth(_1600812), _1600814), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600808)), _1600810)))))], (43575 ^ _781013) ^ [_1649732] : [class_Orderings_Olinorder(_1649732), -(c_List_Olinorder__class_Osorted(_1649732, c_List_Olist_ONil(_1649732)))], (42721 ^ _781013) ^ [_1627423, _1627425] : [-(_1627423 = c_List_Olist_ONil(_1627425)), -(hAPP(hAPP(c_List_Oappend(_1627425), c_List_Obutlast(_1627425, _1627423)), hAPP(hAPP(c_List_Olist_OCons(_1627425), c_List_Olast(_1627425, _1627423)), c_List_Olist_ONil(_1627425))) = _1627423)], (28562 ^ _781013) ^ [_1313916, _1313918, _1313920, _1313922] : [class_Orderings_Olinorder(_1313916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313916), _1313918), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313916), _1313920), _1313922))), 28569 ^ _781013 : [(28572 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313916), _1313918), _1313922)))], (28570 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313916), _1313918), _1313920)))]]], (49476 ^ _781013) ^ [_1786738, _1786740, _1786742] : [class_Complete__Lattice_Ocomplete__lattice(_1786738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1786738), _1786740)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1786738), _1786742), c_Complete__Lattice_OSup__class_OSup(_1786738, _1786740)) = hAPP(hAPP(c_Finite__Set_Ofold(_1786738, _1786738, c_Lattices_Osemilattice__sup__class_Osup(_1786738)), _1786742), _1786740))], (17809 ^ _781013) ^ [_1113373, _1113375, _1113377] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113373), _1113375)), _1113377) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113373), _1113377)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113375), _1113377)))], (46519 ^ _781013) ^ [_1713762, _1713764] : [-(c_List_Omeasures(_1713762, _1713764) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1713762), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1713762, tc_List_Olist(tc_fun(_1713762, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1713762, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1713762, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1713762), c_List_Omap(tc_fun(_1713762, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1713762, tc_Nat_Onat), _1713762, tc_Nat_Onat), c_COMBI(tc_fun(_1713762, tc_Nat_Onat))))), _1713764)))], (33912 ^ _781013) ^ [_1423305, _1423307] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423305) = hAPP(c_Nat_OSuc, _1423307), -(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(_1423305))), 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)), _1423307))))))], (17899 ^ _781013) ^ [_1114941] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1114941), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1114941)], (48635 ^ _781013) ^ [_1764847, _1764849, _1764851, _1764853] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1764847), tc_List_Olist(_1764847))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1764847), tc_List_Olist(_1764847)), _1764849), _1764851)), c_List_Olistrel1(_1764847, _1764853))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1764847), tc_List_Olist(_1764847))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1764847), tc_List_Olist(_1764847)), _1764849), _1764851)), c_List_Olistrel(_1764847, c_Transitive__Closure_Ortrancl(_1764847, _1764853)))))], (46086 ^ _781013) ^ [_1703389, _1703391, _1703393, _1703395, _1703397, _1703399, _1703401] : [c_List_Olist__all2(_1703389, _1703391, _1703393, hAPP(hAPP(c_List_Olist_OCons(_1703389), _1703395), _1703397), hAPP(hAPP(c_List_Olist_OCons(_1703391), _1703399), _1703401)), 46089 ^ _781013 : [(46092 ^ _781013) ^ [] : [-(c_List_Olist__all2(_1703389, _1703391, _1703393, _1703397, _1703401))], (46090 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1703393, _1703395), _1703399)))]]], (35465 ^ _781013) ^ [_1452246, _1452248] : [class_Rings_Oring__1(_1452246), 35468 ^ _781013 : [(35475 ^ _781013) ^ [] : [-(_1452248 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35478 ^ _781013 : [(35485 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1452248), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1452246), _1452248) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1452246), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1452246, _1452246)), tc_fun(tc_Int_Oint, _1452246)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1452246, _1452246), _1452246), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1452246, _1452246)), tc_fun(tc_Int_Oint, _1452246)), tc_Int_Oint), c_COMBB(tc_fun(_1452246, _1452246), _1452246, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1452246, tc_fun(tc_fun(_1452246, _1452246), _1452246), tc_Int_Oint), c_HOL_OLet(_1452246, _1452246)), c_Int_Oring__1__class_Oof__int(_1452246)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1452246, _1452246), tc_fun(_1452246, _1452246)), hAPP(hAPP(c_COMBB(tc_fun(_1452246, tc_fun(_1452246, _1452246)), tc_fun(tc_fun(_1452246, _1452246), tc_fun(_1452246, _1452246)), tc_Int_Oint), c_COMBS(_1452246, _1452246, _1452246)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1452246, _1452246), tc_fun(_1452246, tc_fun(_1452246, _1452246))), hAPP(hAPP(c_COMBB(tc_fun(_1452246, tc_fun(_1452246, _1452246)), tc_fun(tc_fun(_1452246, _1452246), tc_fun(_1452246, tc_fun(_1452246, _1452246))), tc_Int_Oint), c_COMBB(_1452246, tc_fun(_1452246, _1452246), _1452246)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1452246, tc_fun(_1452246, _1452246)), tc_Int_Oint), c_If(_1452246)), 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(_1452246, _1452246, _1452246), c_Groups_Oplus__class_Oplus(_1452246)), c_COMBI(_1452246))))), hAPP(hAPP(c_COMBC(_1452246, _1452246, _1452246), hAPP(hAPP(c_COMBB(_1452246, tc_fun(_1452246, _1452246), _1452246), c_Groups_Oplus__class_Oplus(_1452246)), hAPP(hAPP(c_COMBS(_1452246, _1452246, _1452246), c_Groups_Oplus__class_Oplus(_1452246)), c_COMBI(_1452246)))), c_Groups_Oone__class_Oone(_1452246))))), c_Divides_Odivmod__int(_1452248, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (35479 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1452248), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1452246), _1452248) = hAPP(c_Groups_Ouminus__class_Ouminus(_1452246), hAPP(c_Int_Oring__1__class_Oof__int(_1452246), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1452248))))]]], (35469 ^ _781013) ^ [] : [_1452248 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1452246), _1452248) = c_Groups_Ozero__class_Ozero(_1452246))]]], (32218 ^ _781013) ^ [_1392498] : [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), _1392498))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1392498) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1392498)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (29305 ^ _781013) ^ [_1327636, _1327638, _1327640] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1327636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1327638), _1327640)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1327638), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1327636), _1327638), _1327640))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1327636, _1327638)))], (13279 ^ _781013) ^ [_1023073, _1023075, _1023077, _1023079] : [c_Big__Operators_Osemilattice__big(_1023073, _1023075, _1023077), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023073), _1023079)), -(hAPP(_1023077, _1023079) = hAPP(c_Finite__Set_Ofold1(_1023073, _1023075), _1023079))], (30993 ^ _781013) ^ [_1361258, _1361260, _1361262] : [class_Orderings_Olinorder(_1361258), hAPP(_1361260, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361258), 30998 ^ [_1361258, _1361260, _1361262]), 30999 ^ [_1361258, _1361260, _1361262])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361258), hAPP(_1361260, 30998 ^ [_1361258, _1361260, _1361262])), hAPP(_1361260, 30999 ^ [_1361258, _1361260, _1361262])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361258), _1361262)), -(_1361262 = c_Orderings_Obot__class_Obot(tc_fun(_1361258, tc_HOL_Obool))), -(hAPP(_1361260, c_Big__Operators_Olinorder__class_OMax(_1361258, _1361262)) = c_Big__Operators_Olinorder__class_OMax(_1361258, hAPP(c_Set_Oimage(_1361258, _1361258, _1361260), _1361262)))], (6024 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (27463 ^ _781013) ^ [_1293223, _1293225] : [-(hAPP(c_Set_OPow(_1293223), _1293225) = hAPP(c_Set_OCollect(tc_fun(_1293223, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1293223, tc_HOL_Obool), tc_fun(_1293223, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1293223, tc_HOL_Obool))), _1293225)))], (43038 ^ _781013) ^ [_1636632, _1636634, _1636636, _1636638, _1636640] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636632, tc_fun(_1636634, tc_HOL_Obool)), _1636636), hAPP(hAPP(c_COMBB(tc_fun(_1636634, tc_HOL_Obool), tc_fun(_1636634, tc_HOL_Obool), _1636632), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636634, tc_HOL_Obool)), _1636638)), _1636640)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636634, tc_HOL_Obool)), _1636638), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636632, tc_fun(_1636634, tc_HOL_Obool)), _1636636), _1636640)))], (2506 ^ _781013) ^ [_818173, _818175, _818177, _818179, _818181, _818183] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_818183, _818179, _818175) = c_Smallcheck_Ofull__small__class_Ofull__small(_818181, _818177, _818173)), _818183 = _818181, _818179 = _818177, _818175 = _818173], (30679 ^ _781013) ^ [_1355330, _1355332] : [class_Orderings_Olinorder(_1355330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355330), _1355332)), -(_1355332 = c_Orderings_Obot__class_Obot(tc_fun(_1355330, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1355330), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355330), 30692 ^ [_1355330, _1355332]), 30693 ^ [_1355330, _1355332])), hAPP(hAPP(c_Set_Oinsert(_1355330), 30692 ^ [_1355330, _1355332]), hAPP(hAPP(c_Set_Oinsert(_1355330), 30693 ^ [_1355330, _1355332]), c_Orderings_Obot__class_Obot(tc_fun(_1355330, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1355330), c_Big__Operators_Olinorder__class_OMax(_1355330, _1355332)), _1355332)))], (42925 ^ _781013) ^ [_1632926, _1632928, _1632930, _1632932] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632926, tc_fun(_1632928, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1632926, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1632928, tc_HOL_Obool), tc_fun(_1632928, tc_HOL_Obool), _1632926), hAPP(c_COMBC(_1632928, tc_fun(_1632928, tc_HOL_Obool), tc_HOL_Obool), c_member(_1632928))), _1632930)), _1632932)), -(hBOOL(hAPP(hAPP(c_member(_1632928), _1632932), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632926, tc_fun(_1632928, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1632926, tc_HOL_Obool))), _1632930))))], (30271 ^ _781013) ^ [_1346526, _1346528, _1346530, _1346532] : [class_Orderings_Olinorder(_1346526), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346526), _1346528), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346526), _1346530), _1346532)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346526), _1346530), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346526), _1346528), _1346532)))], (15113 ^ _781013) ^ [_1060609] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1060609, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1060609), hAPP(c_COMBK(tc_HOL_Obool, _1060609), c_fTrue)))], (29391 ^ _781013) ^ [_1329384, _1329386, _1329388] : [class_Orderings_Olinorder(_1329384), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329384), _1329386)), hBOOL(hAPP(hAPP(c_member(_1329384), _1329388), _1329386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329384), hAPP(c_Finite__Set_Ofold1(_1329384, c_Orderings_Oord__class_Omin(_1329384)), _1329386)), _1329388)))], (24774 ^ _781013) ^ [_1243020, _1243022, _1243024, _1243026] : [class_Fields_Ofield__inverse__zero(_1243020), -(_1243022 = c_Groups_Ozero__class_Ozero(_1243020)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1243020), _1243024), _1243022)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1243020), _1243026), _1243022)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243020), _1243024), _1243026))], (34681 ^ _781013) ^ [_1437983] : [-(c_Int_OBit0(_1437983) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1437983), _1437983))], (47389 ^ _781013) ^ [_1736428, _1736430] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1736428, _1736428)), _1736430)), 47392 ^ _781013 : [(47399 ^ _781013) ^ [] : [c_Wellfounded_Oacyclic(_1736428, _1736430), -(c_Wellfounded_Owf(_1736428, _1736430))], (47393 ^ _781013) ^ [] : [c_Wellfounded_Owf(_1736428, _1736430), -(c_Wellfounded_Oacyclic(_1736428, _1736430))]]], (45425 ^ _781013) ^ [_1688347, _1688349, _1688351, _1688353] : [class_Orderings_Oorder(_1688347), class_Enum_Oenum(_1688349), 45432 ^ _781013 : [(45439 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1688349), hAPP(hAPP(c_COMBS(_1688349, _1688347, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1688347, tc_fun(_1688347, tc_HOL_Obool), _1688349), c_Orderings_Oord__class_Oless__eq(_1688347)), _1688351)), _1688353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1688349, _1688347)), _1688351), _1688353)))], (45433 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1688349, _1688347)), _1688351), _1688353)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1688349), hAPP(hAPP(c_COMBS(_1688349, _1688347, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1688347, tc_fun(_1688347, tc_HOL_Obool), _1688349), c_Orderings_Oord__class_Oless__eq(_1688347)), _1688351)), _1688353))))]]], (14564 ^ _781013) ^ [_1051556, _1051558] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051556), _1051558)), -(hAPP(c_Finite__Set_Ocard(_1051556), _1051558) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1051556, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1051556), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1051558))], (31912 ^ _781013) ^ [_1385929, _1385931, _1385933, _1385935, _1385937] : [_1385929 = c_Orderings_Obot__class_Obot(tc_fun(_1385931, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385931, tc_fun(_1385933, tc_HOL_Obool)), _1385929), hAPP(hAPP(c_COMBB(tc_fun(_1385933, tc_HOL_Obool), tc_fun(_1385933, tc_HOL_Obool), _1385931), hAPP(c_Set_Oinsert(_1385933), _1385935)), _1385937)) = c_Orderings_Obot__class_Obot(tc_fun(_1385933, tc_HOL_Obool)))], (31476 ^ _781013) ^ [_1373852, _1373854] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1373852), c_Orderings_Obot__class_Obot(tc_fun(_1373852, tc_HOL_Obool))), _1373854) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1373852, tc_HOL_Obool), tc_HOL_Obool)))], (13587 ^ _781013) ^ [_1029982, _1029984, _1029986] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1029982)), hAPP(c_Set_Oimage(_1029984, tc_Option_Ooption(_1029982), hAPP(c_Map_Omap__of(_1029984, _1029982), _1029986)), c_Orderings_Otop__class_Otop(tc_fun(_1029984, tc_HOL_Obool))))))], (37100 ^ _781013) ^ [_1489110, _1489112] : [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), _1489110), _1489112))), 37103 ^ _781013 : [(37112 ^ _781013) ^ [] : [-(c_Divides_OnegDivAlg(_1489110, _1489112) = hAPP(c_Divides_Oadjust(_1489112), c_Divides_OnegDivAlg(_1489110, 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)))), _1489112)))), -(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), _1489110), _1489112)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1489112), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37104 ^ _781013) ^ [] : [37105 ^ _781013 : [(37108 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1489112), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (37106 ^ _781013) ^ [] : [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), _1489110), _1489112)))]], -(c_Divides_OnegDivAlg(_1489110, _1489112) = 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), _1489110), _1489112)))]]], (42430 ^ _781013) ^ [_1621465] : [-(c_List_Orotate(_1621465, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1621465)))], (46737 ^ _781013) ^ [_1721039, _1721041] : [-(c_Wellfounded_Owf(_1721039, hAPP(c_Wellfounded_Omeasure(_1721039), _1721041)))], (32540 ^ _781013) ^ [_1398466, _1398468, _1398470] : [class_Int_Onumber__ring(_1398466), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1398466), hAPP(c_Int_Onumber__class_Onumber__of(_1398466), _1398468)), hAPP(c_Int_Onumber__class_Onumber__of(_1398466), _1398470)) = hAPP(c_Int_Onumber__class_Onumber__of(_1398466), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1398468), _1398470)))], (28882 ^ _781013) ^ [_1319932, _1319934] : [class_Groups_Oordered__ab__group__add__abs(_1319932), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319932), c_Groups_Ozero__class_Ozero(_1319932)), hAPP(c_Groups_Oabs__class_Oabs(_1319932), _1319934))))], (40277 ^ _781013) ^ [_1566646, _1566648, _1566650] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1566646, _1566648, _1566650)), 40279 ^ _781013 : [(40280 ^ _781013) ^ [_1566792] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1566646)), _1566792), _1566648)), -(c_Hoare__Mirabelle_Otriple__valid(_1566646, 40278 ^ [_1566646, _1566648, _1566650], _1566792))], (40289 ^ _781013) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1566646, 40278 ^ [_1566646, _1566648, _1566650], 40285 ^ [_1566646, _1566648, _1566650])], (40287 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1566646)), 40285 ^ [_1566646, _1566648, _1566650]), _1566650)))]]], (48804 ^ _781013) ^ [_1769360, _1769362] : [-(hAPP(c_Relation_OField(_1769360), hAPP(c_Relation_Oconverse(_1769360, _1769360), _1769362)) = hAPP(c_Relation_OField(_1769360), _1769362))], (24282 ^ _781013) ^ [_1233892, _1233894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233892), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1233892), _1233894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1233892))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1233894))))], (27691 ^ _781013) ^ [_1297945, _1297947, _1297949] : [class_Divides_Osemiring__div(_1297945), -(c_Divides_Odiv__class_Omod(_1297945, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1297945), _1297947), _1297949), _1297947) = c_Divides_Odiv__class_Omod(_1297945, _1297949, _1297947))], (44442 ^ _781013) ^ [_1667000, _1667002, _1667004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1667000), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667002)), _1667004))), -(hAPP(hAPP(c_List_Onth(_1667002), hAPP(c_List_Orev(_1667002), _1667004)), _1667000) = hAPP(hAPP(c_List_Onth(_1667002), _1667004), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667002)), _1667004)), hAPP(c_Nat_OSuc, _1667000))))], (31918 ^ _781013) ^ [_1386092, _1386094, _1386096, _1386098, _1386100] : [-(_1386092 = c_Orderings_Obot__class_Obot(tc_fun(_1386094, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386094, tc_fun(_1386096, tc_HOL_Obool)), _1386092), hAPP(hAPP(c_COMBB(tc_fun(_1386096, tc_HOL_Obool), tc_fun(_1386096, tc_HOL_Obool), _1386094), hAPP(c_Set_Oinsert(_1386096), _1386098)), _1386100)) = hAPP(hAPP(c_Set_Oinsert(_1386096), _1386098), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386094, tc_fun(_1386096, tc_HOL_Obool)), _1386092), _1386100)))], (51192 ^ _781013) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (49546 ^ _781013) ^ [_1788208, _1788210, _1788212, _1788214] : [class_Lattices_Osemilattice__inf(_1788208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1788208), _1788210)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1788208, _1788208, c_Lattices_Osemilattice__inf__class_Oinf(_1788208)), _1788212), hAPP(hAPP(c_Set_Oinsert(_1788208), _1788214), _1788210)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1788208), _1788214), hAPP(hAPP(c_Finite__Set_Ofold(_1788208, _1788208, c_Lattices_Osemilattice__inf__class_Oinf(_1788208)), _1788212), _1788210)))], (38816 ^ _781013) ^ [_1528871, _1528873] : [hAPP(c_Finite__Set_Ocard(_1528871), hAPP(c_List_Oset(_1528871), _1528873)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528871)), _1528873), -(hBOOL(hAPP(c_List_Odistinct(_1528871), _1528873)))], (13737 ^ _781013) ^ [_1033384, _1033386, _1033388] : [class_Rings_Ocomm__semiring__1(_1033384), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033384), _1033386), _1033388) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033384), _1033388), _1033386))], (1844 ^ _781013) ^ [_806805, _806807] : [-(class_Nat_Osize(_806805)), _806807 = _806805, class_Nat_Osize(_806807)], (49888 ^ _781013) ^ [_1794761, _1794763, _1794765, _1794767, _1794769, _1794771] : [c_Finite__Set_Ofun__left__comm(_1794761, _1794763, _1794765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1794761), _1794767)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1794761, _1794763, _1794765), _1794769), hAPP(hAPP(c_Set_Oinsert(_1794761), _1794771), _1794767)) = hAPP(hAPP(_1794765, _1794771), hAPP(hAPP(c_Finite__Set_Ofold(_1794761, _1794763, _1794765), _1794769), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1794761, tc_HOL_Obool)), _1794767), hAPP(hAPP(c_Set_Oinsert(_1794761), _1794771), c_Orderings_Obot__class_Obot(tc_fun(_1794761, tc_HOL_Obool)))))))], (51394 ^ _781013) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (19542 ^ _781013) ^ [_1146767, _1146769, _1146771] : [class_Rings_Olinordered__semidom(_1146767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146767), c_Groups_Oone__class_Oone(_1146767)), _1146769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146767), hAPP(hAPP(c_Power_Opower__class_Opower(_1146767), _1146769), _1146771)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146767), _1146769), hAPP(hAPP(c_Power_Opower__class_Opower(_1146767), _1146769), _1146771)))))], (16353 ^ _781013) ^ [_1083447, _1083449] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1083447), hAPP(c_Set_OCollect(_1083447), _1083449))), 16356 ^ _781013 : [(16363 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1083447), c_Orderings_Otop__class_Otop(tc_fun(_1083447, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1083447), hAPP(c_Set_OCollect(_1083447), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1083447), c_fNot), _1083449)))))], (16357 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1083447), hAPP(c_Set_OCollect(_1083447), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1083447), c_fNot), _1083449)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1083447), c_Orderings_Otop__class_Otop(tc_fun(_1083447, tc_HOL_Obool)))))]]], (8467 ^ _781013) ^ [_927247, _927249, _927251, _927253, _927255, _927257] : [-(hAPP(c_Set_Oimage(_927247, _927249, hAPP(c_Fun_Ocomp(_927251, _927249, _927247, _927253), _927255)), _927257) = hAPP(c_Set_Oimage(_927251, _927249, _927253), hAPP(c_Set_Oimage(_927247, _927251, _927255), _927257)))], (36136 ^ _781013) ^ [_1469157, _1469159] : [class_Rings_Osemiring__1(_1469157), -(hBOOL(hAPP(hAPP(c_member(_1469157), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1469157), _1469159)), c_Nat_Osemiring__1__class_ONats(_1469157))))], (300 ^ _781013) ^ [_785681, _785683, _785685, _785687, _785689, _785691, _785693, _785695, _785697, _785699, _785701, _785703] : [-(c_Equiv__Relations_Ocongruent2(_785701, _785697, _785693, _785689, _785685, _785681)), c_Equiv__Relations_Ocongruent2(_785703, _785699, _785695, _785691, _785687, _785683), _785703 = _785701, _785699 = _785697, _785695 = _785693, _785691 = _785689, _785687 = _785685, _785683 = _785681], (20287 ^ _781013) ^ [_1160215, _1160217, _1160219] : [class_Rings_Ocomm__semiring__1(_1160215), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160215), _1160217), hAPP(hAPP(c_Power_Opower__class_Opower(_1160215), _1160217), _1160219)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1160215), _1160217), hAPP(c_Nat_OSuc, _1160219)))], (51526 ^ _781013) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (4970 ^ _781013) ^ [_856663, _856665, _856667, _856669, _856671, _856673, _856675, _856677] : [-(c_New__DSequence_Opos__bind(_856677, _856673, _856669, _856665) = c_New__DSequence_Opos__bind(_856675, _856671, _856667, _856663)), _856677 = _856675, _856673 = _856671, _856669 = _856667, _856665 = _856663], (21151 ^ _781013) ^ [_1177937, _1177939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177937), _1177939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177939), _1177937)), -(_1177937 = _1177939)], (11345 ^ _781013) ^ [_984009, _984011, _984013, _984015, _984017] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_984009, _984011, hAPP(hAPP(c_Set_Oinsert(_984009), _984013), _984015)), _984017)), 11350 ^ _781013 : [(11355 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_984009), 11348 ^ [_984009, _984011, _984013, _984015, _984017]), 11349 ^ [_984009, _984011, _984013, _984015, _984017]))], (11353 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_984009, _984009, _984011, 11348 ^ [_984009, _984011, _984013, _984015, _984017], 11349 ^ [_984009, _984011, _984013, _984015, _984017]), _984017)))], (11351 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_984009), _984013), _984015) = hAPP(hAPP(c_Set_Oinsert(_984009), 11348 ^ [_984009, _984011, _984013, _984015, _984017]), 11349 ^ [_984009, _984011, _984013, _984015, _984017]))]]], (44018 ^ _781013) ^ [_1657389, _1657391] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1657389), hAPP(c_List_Onth(_1657389), _1657391)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657389)), _1657391))) = _1657391)], (42561 ^ _781013) ^ [_1624238, _1624240, _1624242] : [class_Orderings_Olinorder(_1624238), -(c_Big__Operators_Olinorder__class_OMin(_1624238, hAPP(c_List_Oset(_1624238), hAPP(hAPP(c_List_Olist_OCons(_1624238), _1624240), _1624242))) = hAPP(c_List_Ofoldl(_1624238, _1624238, c_Orderings_Oord__class_Omin(_1624238), _1624240), _1624242))], (48271 ^ _781013) ^ [_1755982, _1755984] : [-(c_Random_Oselect(_1755982, _1755984) = 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(_1755982, 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(_1755982)), _1755984)))), hAPP(hAPP(c_COMBB(_1755982, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1755982, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1755982, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1755982, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1755982), _1755984)), c_Code__Numeral_Onat__of))))], (9517 ^ _781013) ^ [_949637, _949639, _949641] : [class_Orderings_Opreorder(_949637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949637), _949639), _949641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949637), _949641), _949639))], (51170 ^ _781013) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (44111 ^ _781013) ^ [_1659190, _1659192, _1659194, _1659196] : [class_Orderings_Olinorder(_1659190), c_List_Olinorder__class_Osorted(_1659190, _1659192), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1659194), _1659196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659196), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659190)), _1659192))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659190), hAPP(hAPP(c_List_Onth(_1659190), _1659192), _1659194)), hAPP(hAPP(c_List_Onth(_1659190), _1659192), _1659196))))], (23140 ^ _781013) ^ [_1213898, _1213900, _1213902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1213898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1213898), _1213900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213902), _1213900)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213902), _1213898))))], (2812 ^ _781013) ^ [_822948, _822950, _822952, _822954, _822956, _822958] : [-(c_Hilbert__Choice_OGreatestM(_822958, _822954, _822950) = c_Hilbert__Choice_OGreatestM(_822956, _822952, _822948)), _822958 = _822956, _822954 = _822952, _822950 = _822948], (19388 ^ _781013) ^ [_1143970, _1143972, _1143974, _1143976] : [class_Groups_Ocomm__monoid__mult(_1143970), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1143970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143970), _1143972), _1143974)), _1143976) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143970), hAPP(hAPP(c_Power_Opower__class_Opower(_1143970), _1143972), _1143976)), hAPP(hAPP(c_Power_Opower__class_Opower(_1143970), _1143974), _1143976)))], (35069 ^ _781013) ^ [_1444863] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1444863))), 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), _1444863), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (2300 ^ _781013) ^ [_815036, _815038] : [_815038 = _815036, -(c_Nat_Onat_Onat__size(_815038) = c_Nat_Onat_Onat__size(_815036))], (2378 ^ _781013) ^ [_816185, _816187, _816189, _816191, _816193, _816195, _816197, _816199] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_816199, _816195, _816191, _816187) = c_Hoare__Mirabelle_Otriple_Otriple__case(_816197, _816193, _816189, _816185)), _816199 = _816197, _816195 = _816193, _816191 = _816189, _816187 = _816185], (50258 ^ _781013) ^ [_1802986, _1802988, _1802990, _1802992] : [class_Rings_Olinordered__semidom(_1802986), 50264 ^ _781013 : [(50267 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1802986), c_Groups_Ozero__class_Ozero(_1802986)), hAPP(_1802992, 50263 ^ [_1802986, _1802988, _1802990, _1802992])))], (50265 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802988), 50263 ^ [_1802986, _1802988, _1802990, _1802992]), _1802990)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1802986), c_Groups_Ozero__class_Ozero(_1802986)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1802988, _1802986), _1802992), _1802990))))], (8311 ^ _781013) ^ [_923413, _923415, _923417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_923413, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_923413, tc_fun(_923413, tc_HOL_Obool), tc_HOL_Obool), c_member(_923413)), _923415)), hAPP(hAPP(c_COMBC(_923413, tc_fun(_923413, tc_HOL_Obool), tc_HOL_Obool), c_member(_923413)), _923417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_923413, tc_HOL_Obool)), _923415), _923417)))], (46450 ^ _781013) ^ [_1712030, _1712032, _1712034, _1712036, _1712038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1712030, _1712032)), hAPP(_1712030, _1712034))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1712036, _1712036)), hAPP(hAPP(c_Product__Type_OPair(_1712036, _1712036), _1712032), _1712034)), c_List_Omeasures(_1712036, _1712038))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1712036, _1712036)), hAPP(hAPP(c_Product__Type_OPair(_1712036, _1712036), _1712032), _1712034)), c_List_Omeasures(_1712036, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1712036, tc_Nat_Onat)), _1712030), _1712038)))))], (48019 ^ _781013) ^ [_1750993, _1750995] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1750993, _1750993)), _1750995)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1750993, _1750993)), c_Transitive__Closure_Otrancl(_1750993, _1750995))))], (5200 ^ _781013) ^ [_860342, _860344, _860346, _860348] : [-(c_Product__Type_OPair(_860348, _860344) = c_Product__Type_OPair(_860346, _860342)), _860348 = _860346, _860344 = _860342], (31868 ^ _781013) ^ [_1384734, _1384736, _1384738, _1384740, _1384742, _1384744] : [-(hAPP(c_Relation_OImage(_1384734, _1384736, _1384738), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384740, tc_fun(_1384734, tc_HOL_Obool)), _1384742), _1384744)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384740, tc_fun(_1384736, tc_HOL_Obool)), _1384742), hAPP(hAPP(c_COMBB(tc_fun(_1384734, tc_HOL_Obool), tc_fun(_1384736, tc_HOL_Obool), _1384740), c_Relation_OImage(_1384734, _1384736, _1384738)), _1384744)))], (45590 ^ _781013) ^ [_1692047, _1692049, _1692051] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692047, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1692047, tc_HOL_Obool), tc_HOL_Obool)), _1692049), _1692051)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1692047, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692047, tc_HOL_Obool), _1692049)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692047, tc_HOL_Obool), _1692051)))], (20275 ^ _781013) ^ [_1159984] : [20276 ^ _781013 : [(20277 ^ _781013) ^ [_1160026] : [_1159984 = hAPP(c_Nat_OSuc, _1160026)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159984)))], (37419 ^ _781013) ^ [_1495319, _1495321, _1495323, _1495325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1495325, _1495321)), hAPP(_1495325, _1495323))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1495319, _1495319)), hAPP(hAPP(c_Product__Type_OPair(_1495319, _1495319), _1495321), _1495323)), hAPP(c_Wellfounded_Omeasure(_1495319), _1495325))))], (36587 ^ _781013) ^ [_1479105, _1479107, _1479109, _1479111, _1479113, _1479115] : [hAPP(hAPP(c_Product__Type_OPair(_1479105, _1479107), _1479109), _1479111) = hAPP(hAPP(c_Product__Type_OPair(_1479105, _1479107), _1479113), _1479115), 36590 ^ _781013 : [(36593 ^ _781013) ^ [] : [-(_1479111 = _1479115)], (36591 ^ _781013) ^ [] : [-(_1479109 = _1479113)]]], (11690 ^ _781013) ^ [_991584, _991586, _991588, _991590] : [c_Fun_Oinj__on(_991584, _991586, _991588, c_Orderings_Otop__class_Otop(tc_fun(_991584, tc_HOL_Obool))), 11693 ^ _781013 : [(11707 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_991586), _991590), hAPP(c_Set_Oimage(_991584, _991586, _991588), c_Orderings_Otop__class_Otop(tc_fun(_991584, tc_HOL_Obool)))))), 11708 ^ _781013 : [(11709 ^ _781013) ^ [_991987] : [_991590 = hAPP(_991588, _991987), 11713 ^ _781013 : [(11716 ^ _781013) ^ [] : [11712 ^ [_991584, _991586, _991588, _991590, _991987] = _991987], (11714 ^ _781013) ^ [] : [-(_991590 = hAPP(_991588, 11712 ^ [_991584, _991586, _991588, _991590, _991987]))]]]]], (11694 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_991586), _991590), hAPP(c_Set_Oimage(_991584, _991586, _991588), c_Orderings_Otop__class_Otop(tc_fun(_991584, tc_HOL_Obool))))), 11698 ^ _781013 : [(11701 ^ _781013) ^ [_991849] : [_991590 = hAPP(_991588, _991849), -(_991849 = 11697 ^ [_991584, _991586, _991588, _991590])], (11699 ^ _781013) ^ [] : [-(_991590 = hAPP(_991588, 11697 ^ [_991584, _991586, _991588, _991590]))]]]]], (49103 ^ _781013) ^ [_1776765, _1776767, _1776769] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776765, _1776765)), hAPP(hAPP(c_Product__Type_OPair(_1776765, _1776765), _1776767), _1776767)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1776765, _1776765), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1776769))))], (36631 ^ _781013) ^ [_1480174, _1480176, _1480178, _1480180] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1480174, _1480176, _1480178), hAPP(hAPP(c_COMBB(tc_fun(_1480176, tc_prod(_1480174, _1480176)), tc_fun(_1480176, _1480178), _1480174), hAPP(c_COMBB(tc_prod(_1480174, _1480176), _1480178, _1480176), _1480180)), c_Product__Type_OPair(_1480174, _1480176))) = _1480180)], (50518 ^ _781013) ^ [_1808198, _1808200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50519 ^ [_1808198, _1808200]), hAPP(_1808198, 50519 ^ [_1808198, _1808200]))), -(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)), _1808198)), _1808200)))))], (2520 ^ _781013) ^ [_818394, _818396, _818398, _818400, _818402, _818404] : [-(c_Smallcheck_Ofull__small_H(_818404, _818400, _818396) = c_Smallcheck_Ofull__small_H(_818402, _818398, _818394)), _818404 = _818402, _818400 = _818398, _818396 = _818394], (8529 ^ _781013) ^ [_928705, _928707, _928709] : [hBOOL(hAPP(hAPP(c_member(_928705), _928707), hAPP(c_fequal, _928709))), -(_928707 = _928709)], (30079 ^ _781013) ^ [_1343089, _1343091, _1343093, _1343095] : [class_Orderings_Olinorder(_1343089), 30082 ^ _781013 : [(30091 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343089), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343089), _1343091), _1343093)), _1343095))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343089), _1343091), _1343095)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343089), _1343093), _1343095))], (30083 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343089), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343089), _1343091), _1343093)), _1343095)), 30086 ^ _781013 : [(30089 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343089), _1343093), _1343095)))], (30087 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343089), _1343091), _1343095)))]]]]], (3086 ^ _781013) ^ [_827309, _827311, _827313, _827315, _827317, _827319] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_827319, _827315, _827311) = c_SetInterval_Oord__class_OatLeastAtMost(_827317, _827313, _827309)), _827319 = _827317, _827315 = _827313, _827311 = _827309], (29101 ^ _781013) ^ [_1323851, _1323853] : [29102 ^ _781013 : [(29103 ^ _781013) ^ [_1323900] : [_1323851 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1323853), _1323900)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1323851, _1323853) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36258 ^ _781013) ^ [_1471830, _1471832, _1471834, _1471836, _1471838] : [c_Equiv__Relations_Oequiv(_1471830, _1471832, _1471834), hBOOL(hAPP(hAPP(c_member(_1471830), _1471836), _1471832)), hBOOL(hAPP(hAPP(c_member(_1471830), _1471838), _1471832)), 36269 ^ _781013 : [(36276 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1471830, _1471830)), hAPP(hAPP(c_Product__Type_OPair(_1471830, _1471830), _1471836), _1471838)), _1471834)), -(hAPP(c_Relation_OImage(_1471830, _1471830, _1471834), hAPP(hAPP(c_Set_Oinsert(_1471830), _1471836), c_Orderings_Obot__class_Obot(tc_fun(_1471830, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1471830, _1471830, _1471834), hAPP(hAPP(c_Set_Oinsert(_1471830), _1471838), c_Orderings_Obot__class_Obot(tc_fun(_1471830, tc_HOL_Obool)))))], (36270 ^ _781013) ^ [] : [hAPP(c_Relation_OImage(_1471830, _1471830, _1471834), hAPP(hAPP(c_Set_Oinsert(_1471830), _1471836), c_Orderings_Obot__class_Obot(tc_fun(_1471830, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1471830, _1471830, _1471834), hAPP(hAPP(c_Set_Oinsert(_1471830), _1471838), c_Orderings_Obot__class_Obot(tc_fun(_1471830, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1471830, _1471830)), hAPP(hAPP(c_Product__Type_OPair(_1471830, _1471830), _1471836), _1471838)), _1471834)))]]], (3588 ^ _781013) ^ [_835144, _835146] : [_835146 = _835144, -(c_Wellfounded_Ofinite__psubset(_835146) = c_Wellfounded_Ofinite__psubset(_835144))], (6904 ^ _781013) ^ [_895047, _895049, _895051, _895053, _895055] : [hAPP(_895051, _895053) = _895055, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895047, _895049), _895051), _895053), _895055) = _895051)], (3938 ^ _781013) ^ [_840595, _840597, _840599, _840601] : [-(c_List_Omap(_840601, _840597) = c_List_Omap(_840599, _840595)), _840601 = _840599, _840597 = _840595], (7669 ^ _781013) ^ [_910020, _910022] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910020, tc_HOL_Obool)), _910022), c_Orderings_Obot__class_Obot(tc_fun(_910020, tc_HOL_Obool))) = _910022)], (27108 ^ _781013) ^ [_1285817, _1285819, _1285821] : [class_Orderings_Olinorder(_1285817), 27111 ^ _781013 : [(27118 ^ _781013) ^ [] : [_1285819 = _1285821, -(hAPP(c_SetInterval_Oord__class_OatMost(_1285817), _1285819) = hAPP(c_SetInterval_Oord__class_OatMost(_1285817), _1285821))], (27112 ^ _781013) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1285817), _1285819) = hAPP(c_SetInterval_Oord__class_OatMost(_1285817), _1285821), -(_1285819 = _1285821)]]], (43859 ^ _781013) ^ [_1654363, _1654365] : [class_Orderings_Olinorder(_1654363), c_List_Olinorder__class_Osorted(_1654363, _1654365), -(c_List_Olinorder__class_Osorted(_1654363, hAPP(c_List_Otl(_1654363), _1654365)))], (1144 ^ _781013) ^ [_798055, _798057] : [-(class_Groups_Oab__group__add(_798055)), _798057 = _798055, class_Groups_Oab__group__add(_798057)], (8153 ^ _781013) ^ [_919997, _919999, _920001, _920003, _920005, _920007, _920009, _920011] : [c_Finite__Set_Ofolding__image__simple__idem(_919997, _919999, _920001, _920003, _920005, _920007), hBOOL(hAPP(c_Finite__Set_Ofinite(_919999), _920009)), hBOOL(hAPP(c_Finite__Set_Ofinite(_919999), _920011)), -(hAPP(_920007, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_919999, tc_HOL_Obool)), _920009), _920011)) = hAPP(hAPP(_920001, hAPP(_920007, _920009)), hAPP(_920007, _920011)))], (34933 ^ _781013) ^ [_1442358, _1442360] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1442358)), c_Int_OBit1(_1442360)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1442358), c_Int_Osucc(_1442360))))], (4604 ^ _781013) ^ [_850722, _850724] : [_850724 = _850722, -(c_Nitpick_ORep__Frac(_850724) = c_Nitpick_ORep__Frac(_850722))], (26102 ^ _781013) ^ [_1266527, _1266529] : [26110 ^ _781013 : [(26113 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1266529, 26109 ^ [_1266527, _1266529])))], (26111 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26109 ^ [_1266527, _1266529]), _1266527)))]], 26103 ^ _781013 : [(26104 ^ _781013) ^ [_1266596] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1266596), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1266527))), hBOOL(hAPP(_1266529, _1266596))]]], (34395 ^ _781013) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (25980 ^ _781013) ^ [_1264062, _1264064] : [class_Rings_Olinordered__idom(_1264062), 25983 ^ _781013 : [(25990 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264062), c_Groups_Ozero__class_Ozero(_1264062)), hAPP(c_Int_Oring__1__class_Oof__int(_1264062), _1264064))))], (25984 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264062), c_Groups_Ozero__class_Ozero(_1264062)), hAPP(c_Int_Oring__1__class_Oof__int(_1264062), _1264064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264064)))]]], (20373 ^ _781013) ^ [_1161628, _1161630] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161628), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1161630), _1161628)))))], (11786 ^ _781013) ^ [_993625, _993627, _993629, _993631, _993633, _993635] : [c_Fun_Oinj__on(_993625, _993627, _993629, _993631), hBOOL(hAPP(hAPP(c_member(_993625), _993633), _993631)), hBOOL(hAPP(hAPP(c_member(_993625), _993635), _993631)), 11797 ^ _781013 : [(11804 ^ _781013) ^ [] : [_993633 = _993635, -(hAPP(_993629, _993633) = hAPP(_993629, _993635))], (11798 ^ _781013) ^ [] : [hAPP(_993629, _993633) = hAPP(_993629, _993635), -(_993633 = _993635)]]], (18310 ^ _781013) ^ [_1121892, _1121894, _1121896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121892), _1121894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121892), _1121896)), _1121894)))], (6699 ^ _781013) ^ [_891142, _891144, _891146, _891148, _891150] : [c_Finite__Set_Ofolding__one(_891142, _891144, _891146), hBOOL(hAPP(c_Finite__Set_Ofinite(_891142), _891148)), 6706 ^ _781013 : [(6713 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891142, tc_HOL_Obool)), _891148), hAPP(hAPP(c_Set_Oinsert(_891142), _891150), c_Orderings_Obot__class_Obot(tc_fun(_891142, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_891142, tc_HOL_Obool))), -(hAPP(_891146, hAPP(hAPP(c_Set_Oinsert(_891142), _891150), _891148)) = hAPP(hAPP(_891144, _891150), hAPP(_891146, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891142, tc_HOL_Obool)), _891148), hAPP(hAPP(c_Set_Oinsert(_891142), _891150), c_Orderings_Obot__class_Obot(tc_fun(_891142, tc_HOL_Obool)))))))], (6707 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891142, tc_HOL_Obool)), _891148), hAPP(hAPP(c_Set_Oinsert(_891142), _891150), c_Orderings_Obot__class_Obot(tc_fun(_891142, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_891142, tc_HOL_Obool)), -(hAPP(_891146, hAPP(hAPP(c_Set_Oinsert(_891142), _891150), _891148)) = _891150)]]], (29012 ^ _781013) ^ [_1322337, _1322339, _1322341] : [class_Groups_Oordered__ab__group__add__abs(_1322337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322337), _1322339), _1322341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322337), hAPP(c_Groups_Ouminus__class_Ouminus(_1322337), _1322339)), _1322341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322337), hAPP(c_Groups_Oabs__class_Oabs(_1322337), _1322339)), _1322341)))], (28736 ^ _781013) ^ [_1317340, _1317342] : [class_Groups_Oordered__ab__group__add__abs(_1317340), -(hAPP(c_Groups_Oabs__class_Oabs(_1317340), hAPP(c_Groups_Oabs__class_Oabs(_1317340), _1317342)) = hAPP(c_Groups_Oabs__class_Oabs(_1317340), _1317342))], (43667 ^ _781013) ^ [_1651311, _1651313] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651311), _1651313))), -(c_List_Oupt(_1651311, hAPP(c_Nat_OSuc, _1651313)) = c_List_Olist_ONil(tc_Nat_Onat))], (20382 ^ _781013) ^ [_1161795, _1161797] : [20383 ^ _781013 : [(20384 ^ _781013) ^ [_1161848] : [_1161797 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1161795), _1161848))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161795), _1161797)))], (50228 ^ _781013) ^ [_1802374, _1802376] : [-(c_Nitpick_Ouminus__frac(_1802374, _1802376) = c_Nitpick_OAbs__Frac(_1802374, 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(_1802374), _1802376))), hAPP(c_Nitpick_Odenom(_1802374), _1802376))))], (6892 ^ _781013) ^ [_894797, _894799, _894801] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_894797), _894799)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_894797), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894797, tc_HOL_Obool)), _894799), _894801))))], (17395 ^ _781013) ^ [_1106213, _1106215, _1106217] : [class_Rings_Olinordered__ring__strict(_1106213), 17398 ^ _781013 : [(17407 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106213), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106213), _1106215), _1106215)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106213), _1106217), _1106217))), c_Groups_Ozero__class_Ozero(_1106213)))), _1106215 = c_Groups_Ozero__class_Ozero(_1106213), _1106217 = c_Groups_Ozero__class_Ozero(_1106213)], (17399 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106213), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106213), _1106215), _1106215)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106213), _1106217), _1106217))), c_Groups_Ozero__class_Ozero(_1106213))), 17402 ^ _781013 : [(17405 ^ _781013) ^ [] : [-(_1106217 = c_Groups_Ozero__class_Ozero(_1106213))], (17403 ^ _781013) ^ [] : [-(_1106215 = c_Groups_Ozero__class_Ozero(_1106213))]]]]], (10353 ^ _781013) ^ [_964416, _964418, _964420, _964422] : [-(c_Nitpick_Ofold__graph_H(_964416, _964418, _964420, _964422, c_Orderings_Obot__class_Obot(tc_fun(_964416, tc_HOL_Obool)), _964422))], (21379 ^ _781013) ^ [_1182234, _1182236, _1182238] : [hAPP(c_Finite__Set_Ocard(_1182234), _1182236) = hAPP(c_Nat_OSuc, _1182238), 21384 ^ _781013 : [(21387 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1182234), 21382 ^ [_1182234, _1182236, _1182238]), 21383 ^ [_1182234, _1182236, _1182238]))], (21389 ^ _781013) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1182234), 21383 ^ [_1182234, _1182236, _1182238]) = _1182238)], (21391 ^ _781013) ^ [] : [_1182238 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(21383 ^ [_1182234, _1182236, _1182238] = c_Orderings_Obot__class_Obot(tc_fun(_1182234, tc_HOL_Obool)))], (21385 ^ _781013) ^ [] : [-(_1182236 = hAPP(hAPP(c_Set_Oinsert(_1182234), 21382 ^ [_1182234, _1182236, _1182238]), 21383 ^ [_1182234, _1182236, _1182238]))]]], (13553 ^ _781013) ^ [_1029299, _1029301, _1029303, _1029305] : [-(hBOOL(hAPP(hAPP(c_member(_1029299), _1029301), _1029303))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029299, tc_Nat_Onat), _1029305), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1029299, tc_HOL_Obool)), _1029303), hAPP(hAPP(c_Set_Oinsert(_1029299), _1029301), c_Orderings_Obot__class_Obot(tc_fun(_1029299, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029299, tc_Nat_Onat), _1029305), _1029303))], (15461 ^ _781013) ^ [_1066977, _1066979, _1066981] : [class_Rings_Oordered__cancel__semiring(_1066977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066977), c_Groups_Ozero__class_Ozero(_1066977)), _1066979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066977), _1066981), c_Groups_Ozero__class_Ozero(_1066977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066977), _1066981), _1066979)), c_Groups_Ozero__class_Ozero(_1066977))))], (37722 ^ _781013) ^ [_1501636, _1501638, _1501640, _1501642, _1501644, _1501646] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1501636, _1501636)), hAPP(hAPP(c_Product__Type_OPair(_1501636, _1501636), _1501638), _1501640)), hAPP(hAPP(c_Relation_Oinv__image(_1501642, _1501636), _1501644), _1501646))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1501642, _1501642)), hAPP(hAPP(c_Product__Type_OPair(_1501642, _1501642), hAPP(_1501646, _1501638)), hAPP(_1501646, _1501640))), _1501644)))], (48225 ^ _781013) ^ [] : [-(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))], (16087 ^ _781013) ^ [_1078514, _1078516] : [class_Groups_Olinordered__ab__group__add(_1078514), 16090 ^ _781013 : [(16097 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078514), c_Groups_Ozero__class_Ozero(_1078514)), _1078516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078514), hAPP(c_Groups_Ouminus__class_Ouminus(_1078514), _1078516)), _1078516)))], (16091 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078514), hAPP(c_Groups_Ouminus__class_Ouminus(_1078514), _1078516)), _1078516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078514), c_Groups_Ozero__class_Ozero(_1078514)), _1078516)))]]], (27757 ^ _781013) ^ [_1299354, _1299356, _1299358] : [-(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, _1299354, _1299356)), _1299358), _1299356) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1299354), _1299358), _1299356))], (28174 ^ _781013) ^ [_1306846, _1306848, _1306850, _1306852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1306846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1306848)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306848), _1306850)), -(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), _1306850), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1306852, _1306846))), _1306848)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1306850), _1306846))))], (26040 ^ _781013) ^ [] : [-(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))))], (21257 ^ _781013) ^ [_1179775, _1179777, _1179779, _1179781, _1179783] : [c_Hoare__Mirabelle_Otriple__valid(_1179775, hAPP(c_Nat_OSuc, _1179777), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1179775), _1179779), hAPP(c_Com_Ocom_OBODY, _1179781)), _1179783)), -(c_Hoare__Mirabelle_Otriple__valid(_1179775, _1179777, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1179775), _1179779), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1179781))), _1179783)))], (27421 ^ _781013) ^ [_1292157, _1292159, _1292161] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1292157, tc_HOL_Obool)), _1292159), hAPP(c_Set_OPow(_1292157), _1292161))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1292157, tc_HOL_Obool)), _1292159), _1292161)))], (920 ^ _781013) ^ [_795009, _795011, _795013, _795015, _795017, _795019] : [-(c_Nitpick_Oless__eq__frac(_795017, _795013, _795009)), c_Nitpick_Oless__eq__frac(_795019, _795015, _795011), _795019 = _795017, _795015 = _795013, _795011 = _795009], (9593 ^ _781013) ^ [_950898, _950900, _950902, _950904] : [class_Orderings_Oorder(_950898), _950900 = _950902, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950898), _950904), _950902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950898), _950904), _950900)))], (34765 ^ _781013) ^ [_1439350, _1439352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1439350), _1439352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1439350)), c_Int_OBit1(_1439352))))], (25480 ^ _781013) ^ [_1255820] : [c_Nat__Transfer_Onat__set(_1255820), 25483 ^ _781013 : [(25484 ^ _781013) ^ [_1255886] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1255886), _1255820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255886)))]]], (6424 ^ _781013) ^ [_885946, _885948, _885950, _885952, _885954] : [c_Finite__Set_Ofolding__one__idem(_885946, _885948, _885950), hBOOL(hAPP(c_Finite__Set_Ofinite(_885946), _885952)), -(_885952 = c_Orderings_Obot__class_Obot(tc_fun(_885946, tc_HOL_Obool))), -(hAPP(_885950, hAPP(hAPP(c_Set_Oinsert(_885946), _885954), _885952)) = hAPP(hAPP(_885948, _885954), hAPP(_885950, _885952)))], (20183 ^ _781013) ^ [_1158372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158372)), _1158372))], (16920 ^ _781013) ^ [_1094779] : [class_Rings_Olinordered__semidom(_1094779), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094779), c_Groups_Ozero__class_Ozero(_1094779)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094779), c_Groups_Oone__class_Oone(_1094779)), c_Groups_Oone__class_Oone(_1094779)))))], (31512 ^ _781013) ^ [_1374881, _1374883, _1374885] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1374881), hAPP(hAPP(c_Set_Oinsert(_1374881), _1374883), c_Orderings_Obot__class_Obot(tc_fun(_1374881, tc_HOL_Obool)))), _1374885) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1374881, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1374881, _1374881, _1374885), hAPP(hAPP(c_Set_Oinsert(_1374881), _1374883), c_Orderings_Obot__class_Obot(tc_fun(_1374881, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1374881, tc_HOL_Obool), tc_HOL_Obool))))], (10821 ^ _781013) ^ [_972235, _972237, _972239] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972235, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972235, tc_HOL_Obool)), _972237), _972239)), _972239)))], (988 ^ _781013) ^ [_796009, _796011, _796013, _796015, _796017, _796019, _796021, _796023] : [-(c_Nat__Transfer_Otransfer__morphism(_796021, _796017, _796013, _796009)), c_Nat__Transfer_Otransfer__morphism(_796023, _796019, _796015, _796011), _796023 = _796021, _796019 = _796017, _796015 = _796013, _796011 = _796009], (8323 ^ _781013) ^ [_923781, _923783, _923785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_923781, tc_HOL_Obool)), _923783), hAPP(hAPP(c_Set_Oinsert(_923781), _923785), c_Orderings_Obot__class_Obot(tc_fun(_923781, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_923781, _923785, _923783) = _923785)], (43968 ^ _781013) ^ [_1656496, _1656498] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656496)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656498)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656496), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656498)) = c_List_Olist_ONil(tc_Nat_Onat))], (44888 ^ _781013) ^ [_1677246, _1677248, _1677250] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677246)), c_List_OdropWhile(_1677246, _1677248, _1677250))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677246)), _1677250))))], (34044 ^ _781013) ^ [_1426874, _1426876, _1426878, _1426880, _1426882, _1426884, _1426886] : [c_Equiv__Relations_Oequiv(_1426874, _1426876, _1426878), c_Equiv__Relations_Ocongruent(_1426874, tc_fun(_1426880, tc_HOL_Obool), _1426878, _1426882), hBOOL(hAPP(hAPP(c_member(tc_fun(_1426874, tc_HOL_Obool)), _1426884), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1426874), _1426876), _1426878))), 34058 ^ _781013 : [(34061 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1426880, tc_HOL_Obool)), hAPP(_1426882, 34057 ^ [_1426874, _1426876, _1426878, _1426880, _1426882, _1426884, _1426886])), _1426886))], (34059 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1426874), 34057 ^ [_1426874, _1426876, _1426878, _1426880, _1426882, _1426884, _1426886]), _1426876)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1426880, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426874, tc_fun(_1426880, tc_HOL_Obool)), _1426884), _1426882)), _1426886)))], (20119 ^ _781013) ^ [_1157360, _1157362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1157360)), _1157362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157360), _1157362)))], (33632 ^ _781013) ^ [_1418766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1418766), 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), _1418766)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (37550 ^ _781013) ^ [_1498021, _1498023, _1498025, _1498027, _1498029, _1498031] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1498021, _1498023), _1498023, _1498025), hAPP(hAPP(c_COMBB(_1498027, tc_fun(_1498023, _1498025), tc_prod(_1498021, _1498023)), _1498029), hAPP(hAPP(c_COMBB(_1498021, _1498027, tc_prod(_1498021, _1498023)), _1498031), c_Product__Type_Ofst(_1498021, _1498023)))), c_Product__Type_Osnd(_1498021, _1498023)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1498021, _1498023, _1498025), hAPP(hAPP(c_COMBB(_1498027, tc_fun(_1498023, _1498025), _1498021), _1498029), _1498031)))], (48962 ^ _781013) ^ [_1773377, _1773379, _1773381] : [_1773379 = _1773381, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773377, _1773377)), hAPP(hAPP(c_Product__Type_OPair(_1773377, _1773377), _1773379), _1773381)), c_Relation_OId(_1773377))))], (51146 ^ _781013) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (22726 ^ _781013) ^ [_1206122, _1206124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1206122), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206124), _1206122)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206122), _1206124) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5410 ^ _781013) ^ [_863513, _863515, _863517, _863519] : [-(tc_sum(_863519, _863515) = tc_sum(_863517, _863513)), _863519 = _863517, _863515 = _863513], (50360 ^ _781013) ^ [_1805060, _1805062, _1805064, _1805066] : [c_List_Olist__all(_1805060, _1805062, hAPP(hAPP(c_List_Olist_OCons(_1805060), _1805064), _1805066)), 50363 ^ _781013 : [(50366 ^ _781013) ^ [] : [-(c_List_Olist__all(_1805060, _1805062, _1805066))], (50364 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1805062, _1805064)))]]], (40365 ^ _781013) ^ [_1568540, _1568542, _1568544, _1568546, _1568548] : [c_Relation_Orefl__on(_1568540, _1568542, _1568544), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568540, _1568540)), hAPP(hAPP(c_Product__Type_OPair(_1568540, _1568540), _1568546), _1568548)), _1568544)), -(hBOOL(hAPP(hAPP(c_member(_1568540), _1568548), _1568542)))], (31850 ^ _781013) ^ [_1383986, _1383988, _1383990, _1383992, _1383994] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383986, tc_HOL_Obool)), _1383988), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383990, tc_fun(_1383986, tc_HOL_Obool)), _1383992), _1383994)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383990, tc_fun(_1383986, tc_HOL_Obool)), _1383992), hAPP(hAPP(c_COMBB(tc_fun(_1383986, tc_HOL_Obool), tc_fun(_1383986, tc_HOL_Obool), _1383990), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383986, tc_HOL_Obool)), _1383988)), _1383994)))], (49730 ^ _781013) ^ [_1791831, _1791833, _1791835] : [class_Orderings_Olinorder(_1791831), hBOOL(hAPP(c_Finite__Set_Ofinite(_1791831), _1791833)), -(c_Big__Operators_Olattice_OInf__fin(_1791831, c_Orderings_Oord__class_Omin(_1791831), hAPP(hAPP(c_Set_Oinsert(_1791831), _1791835), _1791833)) = hAPP(hAPP(c_Finite__Set_Ofold(_1791831, _1791831, c_Orderings_Oord__class_Omin(_1791831)), _1791835), _1791833))], (43520 ^ _781013) ^ [_1648122, _1648124] : [43522 ^ _781013 : [(43525 ^ _781013) ^ [] : [43521 ^ [_1648122, _1648124] = c_List_Olist_ONil(_1648122)], (43523 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1648122)), 43521 ^ [_1648122, _1648124]), hAPP(c_List_Oset(tc_List_Olist(_1648122)), _1648124))))]], -(c_List_Otranspose(_1648122, _1648124) = c_List_Olist_ONil(tc_List_Olist(_1648122)))], (39406 ^ _781013) ^ [_1542759, _1542761, _1542763, _1542765] : [class_Groups_Oab__group__add(_1542759), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1542759), hAPP(c_List_Omonoid__add__class_Olistsum(_1542759), hAPP(hAPP(c_List_Omap(_1542761, _1542759), _1542763), _1542765))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1542759), hAPP(hAPP(c_List_Omap(_1542761, _1542759), hAPP(c_Fun_Ocomp(_1542759, _1542759, _1542761, c_Groups_Ouminus__class_Ouminus(_1542759)), _1542763)), _1542765)))], (7231 ^ _781013) ^ [_901690, _901692, _901694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901690, tc_HOL_Obool)), _901692), _901694)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901690, tc_HOL_Obool)), _901692), _901694) = _901694)], (16588 ^ _781013) ^ [_1088539, _1088541, _1088543] : [class_Groups_Oordered__comm__monoid__add(_1088539), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088539), _1088541), c_Groups_Ozero__class_Ozero(_1088539))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088539), _1088543), c_Groups_Ozero__class_Ozero(_1088539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088539), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088539), _1088541), _1088543)), c_Groups_Ozero__class_Ozero(_1088539))))], (36374 ^ _781013) ^ [_1474737, _1474739, _1474741, _1474743] : [_1474737 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1474739), _1474741)), _1474743), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1474737, _1474739), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1474741), _1474743)))), 36381 ^ _781013 : [(36384 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1474743), _1474739))], (36382 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474739)))]], 36389 ^ _781013 : [(36392 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1474739), _1474743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1474743), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36390 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474739))]]], (45872 ^ _781013) ^ [_1698761] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1698761, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1698761, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1698761, tc_HOL_Obool)))], (27924 ^ _781013) ^ [_1302300, _1302302] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1302300, _1302302)), _1302302) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34213 ^ _781013) ^ [_1430018, _1430020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430018), _1430020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1430018)), c_Int_OBit1(_1430020))))], (41454 ^ _781013) ^ [_1597953, _1597955, _1597957, _1597959] : [-(c_List_Opartition(_1597953, _1597955, hAPP(hAPP(c_List_Olist_OCons(_1597953), _1597957), _1597959)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1597953), tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1597953), tc_fun(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953))), tc_fun(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1597953), tc_fun(tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)))), tc_fun(tc_fun(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953))), tc_fun(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)))), tc_List_Olist(_1597953)), c_COMBS(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953))), tc_fun(tc_List_Olist(_1597953), tc_fun(tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)))), tc_List_Olist(_1597953)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)), tc_fun(tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953))), tc_List_Olist(_1597953)), hAPP(c_If(tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953))), hAPP(_1597955, _1597957)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1597953), tc_fun(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953))), tc_List_Olist(_1597953)), c_Product__Type_OPair(tc_List_Olist(_1597953), tc_List_Olist(_1597953))), hAPP(c_List_Olist_OCons(_1597953), _1597957))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1597953), tc_fun(tc_List_Olist(_1597953), tc_List_Olist(_1597953)), tc_fun(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953))), tc_fun(tc_fun(tc_List_Olist(_1597953), tc_List_Olist(_1597953)), tc_fun(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)))), tc_List_Olist(_1597953)), c_COMBB(tc_List_Olist(_1597953), tc_prod(tc_List_Olist(_1597953), tc_List_Olist(_1597953)), tc_List_Olist(_1597953))), c_Product__Type_OPair(tc_List_Olist(_1597953), tc_List_Olist(_1597953)))), hAPP(c_List_Olist_OCons(_1597953), _1597957)))), c_List_Opartition(_1597953, _1597955, _1597959)))], (9921 ^ _781013) ^ [_956260, _956262, _956264, _956266] : [class_Lattices_Osemilattice__inf(_956260), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956260), _956262), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956260), _956264), _956266)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956260), _956264), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956260), _956262), _956266)))], (19164 ^ _781013) ^ [_1139917, _1139919, _1139921, _1139923] : [class_Rings_Ocomm__semiring__1(_1139917), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139917), hAPP(hAPP(c_Power_Opower__class_Opower(_1139917), _1139919), _1139921)), hAPP(hAPP(c_Power_Opower__class_Opower(_1139917), _1139919), _1139923)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1139917), _1139919), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1139921), _1139923)))], (20492 ^ _781013) ^ [_1163762, _1163764] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163762), hAPP(c_Nat_OSuc, _1163764)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1163762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163762), _1163764)))], (43040 ^ _781013) ^ [_1636722, _1636724, _1636726, _1636728, _1636730] : [class_Complete__Lattice_Ocomplete__lattice(_1636722), class_Orderings_Olinorder(_1636722), 43047 ^ _781013 : [(43057 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1636722), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636724, _1636722), _1636726), _1636728)), _1636730))), 43058 ^ _781013 : [(43059 ^ _781013) ^ [_1637070] : [hBOOL(hAPP(hAPP(c_member(_1636724), _1637070), _1636726)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1636722), hAPP(_1636728, _1637070)), _1636730))]]], (43048 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1636722), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636724, _1636722), _1636726), _1636728)), _1636730)), 43052 ^ _781013 : [(43055 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1636722), hAPP(_1636728, 43051 ^ [_1636722, _1636724, _1636726, _1636728, _1636730])), _1636730)))], (43053 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1636724), 43051 ^ [_1636722, _1636724, _1636726, _1636728, _1636730]), _1636726)))]]]]], (21850 ^ _781013) ^ [_1191077, _1191079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191077), _1191079)), -(_1191079 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1191077), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 21853 ^ [_1191077, _1191079]))))], (51270 ^ _781013) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (814 ^ _781013) ^ [_793490, _793492, _793494, _793496, _793498, _793500] : [-(c_Finite__Set_Ofun__left__comm__idem(_793498, _793494, _793490)), c_Finite__Set_Ofun__left__comm__idem(_793500, _793496, _793492), _793500 = _793498, _793496 = _793494, _793492 = _793490], (40599 ^ _781013) ^ [_1575814, _1575816, _1575818] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1575814, _1575816), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575814, _1575816), _1575818), hAPP(c_COMBK(tc_fun(_1575816, tc_HOL_Obool), _1575814), c_Orderings_Otop__class_Otop(tc_fun(_1575816, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1575814, _1575816), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1575814, tc_HOL_Obool)), _1575818)), hAPP(c_COMBK(tc_fun(_1575816, tc_HOL_Obool), _1575814), c_Orderings_Otop__class_Otop(tc_fun(_1575816, tc_HOL_Obool)))))], (26083 ^ _781013) ^ [_1266155, _1266157, _1266159] : [class_Orderings_Oorder(_1266155), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1266155, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1266155, _1266157, _1266159)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1266155), _1266159)) = c_Orderings_Obot__class_Obot(tc_fun(_1266155, tc_HOL_Obool)))], (36639 ^ _781013) ^ [_1480530, _1480532, _1480534, _1480536, _1480538] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1480530, _1480532, _1480534), _1480536), _1480538)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1480530, _1480532)), hAPP(hAPP(c_Product__Type_OPair(_1480530, _1480532), _1480536), _1480538)), _1480534)))], (46782 ^ _781013) ^ [_1721955, _1721957, _1721959] : [c_Wellfounded_Owf(_1721955, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1721955, _1721955), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1721955, _1721955), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1721955, _1721955, _1721955), _1721957), _1721957)), hAPP(hAPP(c_Relation_Orel__comp(_1721955, _1721955, _1721955), _1721959), _1721957))), _1721959)), -(c_Wellfounded_Owf(_1721955, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1721955, _1721955), tc_HOL_Obool)), _1721957), _1721959)))], (19216 ^ _781013) ^ [_1140917, _1140919, _1140921] : [class_Rings_Olinordered__semidom(_1140917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140917), c_Groups_Oone__class_Oone(_1140917)), _1140919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1140921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140917), c_Groups_Oone__class_Oone(_1140917)), hAPP(hAPP(c_Power_Opower__class_Opower(_1140917), _1140919), _1140921))))], (43573 ^ _781013) ^ [_1649629, _1649631, _1649633] : [-(c_List_Osublist(_1649629, _1649631, _1649633) = hAPP(hAPP(c_List_Omap(tc_prod(_1649629, tc_Nat_Onat), _1649629), c_Product__Type_Ofst(_1649629, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1649629, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1649629, 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(_1649629, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1649629, tc_Nat_Onat))), _1649633)), hAPP(hAPP(c_List_Ozip(_1649629, tc_Nat_Onat), _1649631), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649629)), _1649631))))))], (17511 ^ _781013) ^ [_1108278, _1108280] : [_1108278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108278), _1108280) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41326 ^ _781013) ^ [_1595488, _1595490] : [-(c_List_Opartition(_1595488, _1595490, c_List_Olist_ONil(_1595488)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595488), tc_List_Olist(_1595488)), c_List_Olist_ONil(_1595488)), c_List_Olist_ONil(_1595488)))], (28534 ^ _781013) ^ [_1313396, _1313398, _1313400, _1313402] : [class_Orderings_Olinorder(_1313396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313396), _1313398), _1313400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313396), _1313398), _1313402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313396), _1313398), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313396), _1313400), _1313402))))], (39281 ^ _781013) ^ [_1539918, _1539920, _1539922, _1539924, _1539926, _1539928] : [-(c_Map_Omap__add(_1539918, _1539920, _1539922, c_Map_Omap__upds(_1539918, _1539920, _1539924, _1539926, _1539928)) = c_Map_Omap__upds(_1539918, _1539920, c_Map_Omap__add(_1539918, _1539920, _1539922, _1539924), _1539926, _1539928))], (17220 ^ _781013) ^ [_1101630, _1101632, _1101634, _1101636] : [class_Groups_Ocomm__monoid__add(_1101630), hBOOL(hAPP(c_Finite__Set_Ofinite(_1101632), _1101634)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1101632, _1101630), _1101636), _1101634) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1101630, _1101632, c_Groups_Oplus__class_Oplus(_1101630)), _1101636), c_Groups_Ozero__class_Ozero(_1101630)), _1101634))], (42090 ^ _781013) ^ [_1613888, _1613890, _1613892] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1613888, tc_HOL_Obool)), hAPP(c_List_Oset(_1613888), hAPP(hAPP(c_List_Odrop(_1613888), _1613890), _1613892))), hAPP(c_List_Oset(_1613888), _1613892))))], (20877 ^ _781013) ^ [_1171319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171319)), -(_1171319 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171319), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41242 ^ _781013) ^ [_1593955, _1593957, _1593959, _1593961] : [c_List_Olist_ONil(_1593955) = hAPP(hAPP(c_List_Omap(_1593957, _1593955), _1593959), _1593961), -(_1593961 = c_List_Olist_ONil(_1593957))], (10127 ^ _781013) ^ [_960156, _960158, _960160] : [class_Lattices_Osemilattice__inf(_960156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960156), _960158), _960160)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960156), _960160), _960158) = _960158)], (16800 ^ _781013) ^ [_1092519, _1092521, _1092523, _1092525] : [class_Rings_Olinordered__semiring(_1092519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092519), _1092521), _1092523)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092519), _1092525), _1092523))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092519), c_Groups_Ozero__class_Ozero(_1092519)), _1092523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092519), _1092521), _1092525)))], (41022 ^ _781013) ^ [_1588745, _1588747, _1588749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588745, _1588745), tc_HOL_Obool)), _1588747), hAPP(hAPP(c_Product__Type_OSigma(_1588745, _1588745), _1588749), hAPP(c_COMBK(tc_fun(_1588745, tc_HOL_Obool), _1588745), _1588749)))), 41028 ^ _781013 : [(41031 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588745, _1588745)), hAPP(hAPP(c_Product__Type_OPair(_1588745, _1588745), 41027 ^ [_1588745, _1588747, _1588749]), 41027 ^ [_1588745, _1588747, _1588749])), _1588747))], (41029 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588745), 41027 ^ [_1588745, _1588747, _1588749]), _1588749)))]], -(c_Relation_Orefl__on(_1588745, _1588749, _1588747))], (40107 ^ _781013) ^ [_1562936, _1562938, _1562940, _1562942, _1562944] : [-(hAPP(hAPP(c_List_Omap(_1562936, _1562938), _1562940), hAPP(hAPP(c_List_Olist_OCons(_1562936), _1562942), _1562944)) = hAPP(hAPP(c_List_Olist_OCons(_1562938), hAPP(_1562940, _1562942)), hAPP(hAPP(c_List_Omap(_1562936, _1562938), _1562940), _1562944)))], (26213 ^ _781013) ^ [_1268434, _1268436] : [class_Orderings_Oorder(_1268434), -(c_SetInterval_Oord__class_OatLeastAtMost(_1268434, _1268436, _1268436) = hAPP(hAPP(c_Set_Oinsert(_1268434), _1268436), c_Orderings_Obot__class_Obot(tc_fun(_1268434, tc_HOL_Obool))))], (34237 ^ _781013) ^ [_1430424, _1430426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430424), _1430426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1430424)), c_Int_OBit1(_1430426))))], (51228 ^ _781013) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (24204 ^ _781013) ^ [_1232433, _1232435, _1232437] : [class_Groups_Oordered__ab__group__add(_1232433), -(hAPP(c_Set_Oimage(_1232433, _1232433, c_Groups_Ouminus__class_Ouminus(_1232433)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1232433, _1232435, _1232437)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1232433, hAPP(c_Groups_Ouminus__class_Ouminus(_1232433), _1232437)), hAPP(c_Groups_Ouminus__class_Ouminus(_1232433), _1232435)))], (12746 ^ _781013) ^ [_1011670, _1011672, _1011674, _1011676, _1011678, _1011680] : [c_Fun_Oinj__on(_1011670, _1011672, _1011674, _1011676), hBOOL(hAPP(hAPP(c_member(_1011672), _1011678), hAPP(c_Set_Oimage(_1011670, _1011672, _1011674), _1011676))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1011670, tc_HOL_Obool)), _1011676), _1011680)), -(hBOOL(hAPP(hAPP(c_member(_1011670), hAPP(c_Fun_Othe__inv__into(_1011670, _1011672, _1011676, _1011674), _1011678)), _1011680)))], (41284 ^ _781013) ^ [_1594753] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594753)), c_List_Olist_ONil(_1594753)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28574 ^ _781013) ^ [_1314139, _1314141, _1314143, _1314145] : [class_Orderings_Olinorder(_1314139), 28577 ^ _781013 : [(28578 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314139), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314139), _1314141), _1314143)), _1314145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314139), _1314141), _1314145))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314139), _1314143), _1314145)))], (28588 ^ _781013) ^ [] : [28589 ^ _781013 : [(28592 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314139), _1314143), _1314145))], (28590 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314139), _1314141), _1314145))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314139), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314139), _1314141), _1314143)), _1314145)))]]], (22614 ^ _781013) ^ [_1204319, _1204321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204319)), 22617 ^ _781013 : [(22624 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204319), _1204321)), -(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), _1204321), _1204319))))], (22618 ^ _781013) ^ [] : [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), _1204321), _1204319))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204319), _1204321)))]]], (35763 ^ _781013) ^ [_1457192] : [class_Int_Onumber__ring(_1457192), -(hAPP(c_Int_Oring__1__class_Oof__int(_1457192), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1457192), c_Int_OMin))], (29157 ^ _781013) ^ [_1324813, _1324815, _1324817] : [class_Rings_Oordered__ring__abs(_1324813), -(hAPP(c_Groups_Oabs__class_Oabs(_1324813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324813), _1324815), _1324817)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324813), hAPP(c_Groups_Oabs__class_Oabs(_1324813), _1324815)), hAPP(c_Groups_Oabs__class_Oabs(_1324813), _1324817))), 29164 ^ _781013 : [(29167 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324813), _1324815), c_Groups_Ozero__class_Ozero(_1324813)))], (29165 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324813), c_Groups_Ozero__class_Ozero(_1324813)), _1324815))]], 29168 ^ _781013 : [(29171 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324813), _1324817), c_Groups_Ozero__class_Ozero(_1324813)))], (29169 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324813), c_Groups_Ozero__class_Ozero(_1324813)), _1324817))]]], (7311 ^ _781013) ^ [_903082, _903084, _903086, _903088] : [_903082 = _903084, hBOOL(hAPP(hAPP(c_member(_903086), _903084), _903088)), -(hBOOL(hAPP(hAPP(c_member(_903086), _903082), _903088)))], (20518 ^ _781013) ^ [_1164296] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1164296)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1164296)], (13559 ^ _781013) ^ [_1029390, _1029392, _1029394, _1029396, _1029398] : [class_Groups_Oab__group__add(_1029390), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029392), _1029394)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1029392, tc_HOL_Obool)), _1029396), _1029394)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029392, _1029390), _1029398), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1029392, tc_HOL_Obool)), _1029394), _1029396)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029390), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029392, _1029390), _1029398), _1029394)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029392, _1029390), _1029398), _1029396)))], (21303 ^ _781013) ^ [_1180647, _1180649, _1180651] : [class_Orderings_Oord(_1180647), 21306 ^ _781013 : [(21313 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180647), _1180649), _1180651)), -(hBOOL(hAPP(hAPP(c_member(_1180647), _1180649), hAPP(c_SetInterval_Oord__class_OlessThan(_1180647), _1180651))))], (21307 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1180647), _1180649), hAPP(c_SetInterval_Oord__class_OlessThan(_1180647), _1180651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180647), _1180649), _1180651)))]]], (32820 ^ _781013) ^ [_1403648, _1403650, _1403652, _1403654] : [class_Fields_Olinordered__field__inverse__zero(_1403648), class_Int_Onumber(_1403648), 32827 ^ _781013 : [(32828 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), hAPP(c_Int_Onumber__class_Onumber__of(_1403648), _1403650)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1403648), _1403652), _1403654))), 32831 ^ _781013 : [(32838 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), c_Groups_Ozero__class_Ozero(_1403648)), _1403654))), 32841 ^ _781013 : [(32848 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), _1403654), c_Groups_Ozero__class_Ozero(_1403648)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), hAPP(c_Int_Onumber__class_Onumber__of(_1403648), _1403650)), c_Groups_Ozero__class_Ozero(_1403648))))], (32842 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), _1403654), c_Groups_Ozero__class_Ozero(_1403648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), _1403652), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1403648), hAPP(c_Int_Onumber__class_Onumber__of(_1403648), _1403650)), _1403654))))]]], (32832 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), c_Groups_Ozero__class_Ozero(_1403648)), _1403654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1403648), hAPP(c_Int_Onumber__class_Onumber__of(_1403648), _1403650)), _1403654)), _1403652)))]]], (32854 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), hAPP(c_Int_Onumber__class_Onumber__of(_1403648), _1403650)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1403648), _1403652), _1403654)))), 32857 ^ _781013 : [(32860 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1403648), hAPP(c_Int_Onumber__class_Onumber__of(_1403648), _1403650)), _1403654)), _1403652))], (32858 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), c_Groups_Ozero__class_Ozero(_1403648)), _1403654)))]], 32861 ^ _781013 : [(32864 ^ _781013) ^ [] : [32865 ^ _781013 : [(32868 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), _1403652), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1403648), hAPP(c_Int_Onumber__class_Onumber__of(_1403648), _1403650)), _1403654)))], (32866 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), _1403654), c_Groups_Ozero__class_Ozero(_1403648))))]], 32869 ^ _781013 : [(32872 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), hAPP(c_Int_Onumber__class_Onumber__of(_1403648), _1403650)), c_Groups_Ozero__class_Ozero(_1403648)))], (32870 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), _1403654), c_Groups_Ozero__class_Ozero(_1403648)))]]], (32862 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403648), c_Groups_Ozero__class_Ozero(_1403648)), _1403654))]]]]], (27753 ^ _781013) ^ [_1299252, _1299254, _1299256] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1299252), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1299254, _1299256)), _1299256) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1299252), _1299254), _1299256))], (51540 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (46140 ^ _781013) ^ [_1704687, _1704689, _1704691, _1704693, _1704695] : [c_List_Olist__all2(_1704687, _1704689, _1704691, _1704693, _1704695), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704687)), _1704693) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704689)), _1704695))], (51284 ^ _781013) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (41196 ^ _781013) ^ [_1593176, _1593178] : [hAPP(c_List_Oset(_1593176), _1593178) = c_Orderings_Obot__class_Obot(tc_fun(_1593176, tc_HOL_Obool)), -(_1593178 = c_List_Olist_ONil(_1593176))], (4138 ^ _781013) ^ [_843585, _843587, _843589, _843591, _843593, _843595, _843597, _843599] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_843599, _843595, _843591, _843587) = c_New__Random__Sequence_Opos__not__random__dseq(_843597, _843593, _843589, _843585)), _843599 = _843597, _843595 = _843593, _843591 = _843589, _843587 = _843585], (31755 ^ _781013) ^ [_1381309, _1381311, _1381313, _1381315] : [class_Complete__Lattice_Ocomplete__lattice(_1381309), -(_1381311 = c_Orderings_Obot__class_Obot(tc_fun(_1381313, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381313, _1381309), _1381311), hAPP(c_COMBK(_1381309, _1381313), _1381315)) = _1381315)], (5837 ^ _781013) ^ [_874845, _874847, _874849, _874851] : [c_Com_Ocom_OSemi(_874845, _874847) = c_Com_Ocom_OWhile(_874849, _874851)], (50938 ^ _781013) ^ [_1817341, _1817343, _1817345, _1817347] : [-(c_Lazy__Sequence_Oappend(_1817341, c_Lazy__Sequence_Olazy__sequence_OInsert(_1817341, _1817343, _1817345), _1817347) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1817341, _1817343, c_Lazy__Sequence_Oappend(_1817341, _1817345, _1817347)))], (9893 ^ _781013) ^ [_955733, _955735, _955737] : [class_Lattices_Oboolean__algebra(_955733), 9896 ^ _781013 : [(9903 ^ _781013) ^ [] : [_955735 = _955737, -(hAPP(c_Groups_Ouminus__class_Ouminus(_955733), _955735) = hAPP(c_Groups_Ouminus__class_Ouminus(_955733), _955737))], (9897 ^ _781013) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_955733), _955735) = hAPP(c_Groups_Ouminus__class_Ouminus(_955733), _955737), -(_955735 = _955737)]]], (23377 ^ _781013) ^ [_1218263, _1218265, _1218267, _1218269] : [class_Orderings_Olinorder(_1218263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218263), _1218265), _1218267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218263), _1218267), _1218269)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1218263, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1218263, _1218265, _1218267)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218263, _1218267), _1218269)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1218263, _1218265, _1218269))], (42524 ^ _781013) ^ [_1623543, _1623545] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1623543), _1623545) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42527 ^ _781013 : [(42530 ^ _781013) ^ [_1623657] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1623657), hAPP(c_List_Oset(tc_Nat_Onat), _1623545))), -(_1623657 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42528 ^ _781013) ^ [] : [-(_1623543 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (47079 ^ _781013) ^ [_1728447, _1728449, _1728451] : [-(hAPP(c_Relation_ORange(_1728447, _1728449), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1728447, _1728449), tc_HOL_Obool), _1728451)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1728447, _1728449), tc_HOL_Obool), tc_fun(_1728449, tc_HOL_Obool)), _1728451), c_Relation_ORange(_1728447, _1728449)))], (22069 ^ _781013) ^ [_1194817, _1194819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194817), _1194819)), -(c_Nat__Transfer_Otsub(_1194819, _1194817) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1194819), _1194817))], (4282 ^ _781013) ^ [_845775, _845777, _845779, _845781] : [-(c_Big__Operators_Olattice__class_OSup__fin(_845781, _845777) = c_Big__Operators_Olattice__class_OSup__fin(_845779, _845775)), _845781 = _845779, _845777 = _845775], (29436 ^ _781013) ^ [_1330199, _1330201, _1330203] : [class_Orderings_Olinorder(_1330199), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330199), _1330201)), -(_1330201 = c_Orderings_Obot__class_Obot(tc_fun(_1330199, tc_HOL_Obool))), 29447 ^ _781013 : [(29457 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330199), hAPP(c_Finite__Set_Ofold1(_1330199, c_Orderings_Oord__class_Omin(_1330199)), _1330201)), _1330203))), 29458 ^ _781013 : [(29459 ^ _781013) ^ [_1330588] : [hBOOL(hAPP(hAPP(c_member(_1330199), _1330588), _1330201)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330199), _1330588), _1330203))]]], (29448 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330199), hAPP(c_Finite__Set_Ofold1(_1330199, c_Orderings_Oord__class_Omin(_1330199)), _1330201)), _1330203)), 29452 ^ _781013 : [(29455 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330199), 29451 ^ [_1330199, _1330201, _1330203]), _1330203)))], (29453 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330199), 29451 ^ [_1330199, _1330201, _1330203]), _1330201)))]]]]], (36130 ^ _781013) ^ [_1469062] : [class_Rings_Osemiring__1(_1469062), -(hBOOL(hAPP(hAPP(c_member(_1469062), c_Groups_Oone__class_Oone(_1469062)), c_Nat_Osemiring__1__class_ONats(_1469062))))], (13781 ^ _781013) ^ [_1034166, _1034168, _1034170, _1034172] : [class_Groups_Ocancel__semigroup__add(_1034166), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034166), _1034168), _1034170) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034166), _1034168), _1034172), -(_1034170 = _1034172)], (35023 ^ _781013) ^ [_1444059] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444059), 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, _1444059)))], (23835 ^ _781013) ^ [_1226313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226313), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1226313) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40111 ^ _781013) ^ [_1563072, _1563074, _1563076] : [-(hAPP(hAPP(c_List_Onth(_1563072), hAPP(hAPP(c_List_Olist_OCons(_1563072), _1563074), _1563076)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1563074)], (50706 ^ _781013) ^ [_1811440] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1811440)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1811440))))], (18344 ^ _781013) ^ [_1122576, _1122578, _1122580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122576), _1122578)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122576), _1122580)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122578), _1122580))))], (33882 ^ _781013) ^ [_1422817, _1422819] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422817), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422817)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422819)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1422817), _1422819)))], (3902 ^ _781013) ^ [_840063, _840065, _840067, _840069] : [-(c_Random_Oinc__shift(_840069, _840065) = c_Random_Oinc__shift(_840067, _840063)), _840069 = _840067, _840065 = _840063], (46977 ^ _781013) ^ [_1726029, _1726031, _1726033, _1726035] : [c_Wellfounded_Owf(_1726029, _1726031), c_Fun_Oinj__on(_1726029, _1726033, _1726035, c_Orderings_Otop__class_Otop(tc_fun(_1726029, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1726033, hAPP(c_Set_Oimage(tc_prod(_1726029, _1726029), tc_prod(_1726033, _1726033), c_Product__Type_Omap__pair(_1726029, _1726033, _1726029, _1726033, _1726035, _1726035)), _1726031)))], (13201 ^ _781013) ^ [_1021625, _1021627, _1021629] : [class_Lattices_Oab__semigroup__idem__mult(_1021625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021625), _1021627)), -(_1021627 = c_Orderings_Obot__class_Obot(tc_fun(_1021625, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021625), _1021629)), -(_1021629 = c_Orderings_Obot__class_Obot(tc_fun(_1021625, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1021625, c_Groups_Otimes__class_Otimes(_1021625)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1021625, tc_HOL_Obool)), _1021627), _1021629)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1021625), hAPP(c_Finite__Set_Ofold1(_1021625, c_Groups_Otimes__class_Otimes(_1021625)), _1021627)), hAPP(c_Finite__Set_Ofold1(_1021625, c_Groups_Otimes__class_Otimes(_1021625)), _1021629)))], (6118 ^ _781013) ^ [_880179, _880181, _880183, _880185, _880187] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_880179, _880181, _880183)), _880185), _880187)), 6123 ^ _781013 : [(6126 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_880181), _880185), _880187)))], (6124 ^ _781013) ^ [] : [-(hBOOL(hAPP(_880179, _880185)))]], 6127 ^ _781013 : [(6130 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_880183), _880185), _880187)))], (6128 ^ _781013) ^ [] : [hBOOL(hAPP(_880179, _880185))]]], (45015 ^ _781013) ^ [_1680381, _1680383] : [-(c_Enum_Oenum__the(_1680381, _1680383) = c_HOL_OThe(_1680381, _1680383))], (38487 ^ _781013) ^ [_1520981, _1520983, _1520985, _1520987] : [hBOOL(hAPP(c_List_Odistinct(_1520981), hAPP(hAPP(c_List_Omap(_1520983, _1520981), _1520985), _1520987))), 38490 ^ _781013 : [(38493 ^ _781013) ^ [] : [-(c_Fun_Oinj__on(_1520983, _1520981, _1520985, hAPP(c_List_Oset(_1520983), _1520987)))], (38491 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1520983), _1520987)))]]], (33458 ^ _781013) ^ [_1415923, _1415925] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415923))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415923), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415925)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51186 ^ _781013) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (9661 ^ _781013) ^ [_951948, _951950, _951952] : [class_Orderings_Opreorder(_951948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951948), _951950), _951952)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951948), _951952), _951950))], (51148 ^ _781013) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (3280 ^ _781013) ^ [_830424, _830426] : [_830426 = _830424, -(c_List_Oreturn__list(_830426) = c_List_Oreturn__list(_830424))], (49926 ^ _781013) ^ [_1795618, _1795620, _1795622, _1795624, _1795626] : [c_Finite__Set_Ofun__left__comm(_1795618, _1795620, _1795622), -(c_Finite__Set_Ofun__left__comm(_1795624, _1795620, hAPP(hAPP(c_COMBB(_1795618, tc_fun(_1795620, _1795620), _1795624), _1795622), _1795626)))], (31413 ^ _781013) ^ [_1372194, _1372196, _1372198, _1372200] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1372194))), _1372196), _1372198), _1372200)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _1372194)), _1372196), hAPP(c_Nat_OSuc, _1372198)), _1372200)))], (5186 ^ _781013) ^ [_860121, _860123, _860125, _860127, _860129, _860131] : [-(c_Predicate_Oconversep(_860131, _860127, _860123) = c_Predicate_Oconversep(_860129, _860125, _860121)), _860131 = _860129, _860127 = _860125, _860123 = _860121], (48265 ^ _781013) ^ [_1755875, _1755877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1755875)), -(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(_1755875), _1755877))), _1755875)))], (22374 ^ _781013) ^ [_1200266] : [-(_1200266 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1200266), _1200266) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8014 ^ _781013) ^ [_916881, _916883, _916885, _916887] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916881, tc_HOL_Obool)), _916883), hAPP(hAPP(c_Set_Oinsert(_916881), _916885), _916887)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916881, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916881, tc_HOL_Obool)), _916883), _916887)), hAPP(hAPP(c_Set_Oinsert(_916881), _916885), c_Orderings_Obot__class_Obot(tc_fun(_916881, tc_HOL_Obool)))))], (11916 ^ _781013) ^ [_995919, _995921] : [class_Lattices_Olattice(_995919), -(c_Big__Operators_Olattice__class_OSup__fin(_995919, hAPP(hAPP(c_Set_Oinsert(_995919), _995921), c_Orderings_Obot__class_Obot(tc_fun(_995919, tc_HOL_Obool)))) = _995921)], (29239 ^ _781013) ^ [_1326466, _1326468, _1326470] : [class_Rings_Olinordered__idom(_1326466), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326466), c_Groups_Ozero__class_Ozero(_1326466)), hAPP(hAPP(c_Power_Opower__class_Opower(_1326466), hAPP(c_Groups_Oabs__class_Oabs(_1326466), _1326468)), _1326470))))], (40443 ^ _781013) ^ [_1571062, _1571064, _1571066] : [-(hAPP(c_List_Olexn(_1571062, _1571064), hAPP(c_Nat_OSuc, _1571066)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1571062), tc_List_Olist(_1571062)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1571062, tc_List_Olist(_1571062)), tc_prod(_1571062, tc_List_Olist(_1571062))), tc_prod(tc_List_Olist(_1571062), tc_List_Olist(_1571062)), c_Product__Type_Omap__pair(tc_prod(_1571062, tc_List_Olist(_1571062)), tc_List_Olist(_1571062), tc_prod(_1571062, tc_List_Olist(_1571062)), tc_List_Olist(_1571062), hAPP(c_Product__Type_Oprod_Oprod__case(_1571062, tc_List_Olist(_1571062), tc_List_Olist(_1571062)), c_List_Olist_OCons(_1571062)), hAPP(c_Product__Type_Oprod_Oprod__case(_1571062, tc_List_Olist(_1571062), tc_List_Olist(_1571062)), c_List_Olist_OCons(_1571062)))), c_Wellfounded_Olex__prod(_1571062, tc_List_Olist(_1571062), _1571064, hAPP(c_List_Olexn(_1571062, _1571064), _1571066)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1571062), tc_List_Olist(_1571062))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1571062), tc_List_Olist(_1571062), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1571062), tc_fun(tc_List_Olist(_1571062), tc_HOL_Obool), tc_fun(tc_List_Olist(_1571062), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1571062), tc_HOL_Obool), tc_fun(tc_List_Olist(_1571062), tc_HOL_Obool)), tc_List_Olist(_1571062)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1571062))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1571062)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1571062), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1571062)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1571062)))), hAPP(c_Nat_OSuc, _1571066))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1571062), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1571062)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1571062)))), hAPP(c_Nat_OSuc, _1571066)))))))], (42104 ^ _781013) ^ [_1614207, _1614209] : [hBOOL(hAPP(c_List_Odistinct(_1614207), hAPP(c_List_Orotate1(_1614207), _1614209))), -(hBOOL(hAPP(c_List_Odistinct(_1614207), _1614209)))], (1864 ^ _781013) ^ [_807051, _807053, _807055, _807057, _807059, _807061] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_807059, _807055, _807051)), c_Hoare__Mirabelle_Ohoare__derivs(_807061, _807057, _807053), _807061 = _807059, _807057 = _807055, _807053 = _807051], (33358 ^ _781013) ^ [_1414193, _1414195] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1414193) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414195), 33361 ^ _781013 : [(33364 ^ _781013) ^ [] : [-(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), _1414195))))], (33362 ^ _781013) ^ [] : [-(_1414193 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414195)))]]], (17423 ^ _781013) ^ [_1106725] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1106725)), 17427 ^ _781013 : [(17428 ^ _781013) ^ [_1106805] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1106805), _1106725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1106805), 17426 ^ [_1106725])))]]], (40649 ^ _781013) ^ [_1577731, _1577733, _1577735, _1577737, _1577739, _1577741] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577731, _1577733)), hAPP(hAPP(c_Product__Type_OPair(_1577731, _1577733), _1577735), _1577737)), hAPP(hAPP(c_Product__Type_OSigma(_1577731, _1577733), _1577739), _1577741))), 40652 ^ _781013 : [(40655 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1577733), _1577737), hAPP(_1577741, _1577735))))], (40653 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1577731), _1577735), _1577739)))]]], (35743 ^ _781013) ^ [_1456900, _1456902] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1456900), _1456902) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 35744 ^ _781013 : [(35751 ^ _781013) ^ [] : [_1456900 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1456902 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (35745 ^ _781013) ^ [] : [_1456900 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1456902 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (8100 ^ _781013) ^ [_918838, _918840, _918842, _918844, _918846] : [hAPP(_918838, _918840) = hAPP(c_Option_Ooption_OSome(_918842), _918844), -(hBOOL(hAPP(hAPP(c_member(_918846), _918840), c_Map_Odom(_918846, _918842, _918838))))], (20201 ^ _781013) ^ [_1158770, _1158772, _1158774, _1158776] : [c_Sum__Type_OPlus(_1158770, _1158772, _1158774, _1158776) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1158770, _1158772), tc_HOL_Obool)), 20204 ^ _781013 : [(20207 ^ _781013) ^ [] : [-(_1158776 = c_Orderings_Obot__class_Obot(tc_fun(_1158772, tc_HOL_Obool)))], (20205 ^ _781013) ^ [] : [-(_1158774 = c_Orderings_Obot__class_Obot(tc_fun(_1158770, tc_HOL_Obool)))]]], (38662 ^ _781013) ^ [_1524601, _1524603, _1524605] : [-(hAPP(hAPP(c_List_Ozip(_1524601, _1524603), hAPP(hAPP(c_List_Omap(tc_prod(_1524601, _1524603), _1524601), c_Product__Type_Ofst(_1524601, _1524603)), _1524605)), hAPP(hAPP(c_List_Omap(tc_prod(_1524601, _1524603), _1524603), c_Product__Type_Osnd(_1524601, _1524603)), _1524605)) = _1524605)], (42635 ^ _781013) ^ [_1626138, _1626140, _1626142] : [-(_1626138 = c_List_Olist_ONil(_1626140)), -(c_List_Olast(_1626140, hAPP(hAPP(c_List_Olist_OCons(_1626140), _1626142), _1626138)) = c_List_Olast(_1626140, _1626138))], (42899 ^ _781013) ^ [_1632413, _1632415, _1632417, _1632419] : [class_Complete__Lattice_Ocomplete__lattice(_1632413), -(_1632415 = c_Orderings_Obot__class_Obot(tc_fun(_1632417, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632417, _1632413), _1632415), hAPP(c_COMBK(_1632413, _1632417), _1632419)) = _1632419)], (19875 ^ _781013) ^ [_1153302] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153302), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1153302)], (45253 ^ _781013) ^ [_1685235, _1685237, _1685239] : [class_Enum_Oenum(_1685235), class_Enum_Oenum(_1685237), 45260 ^ _781013 : [(45267 ^ _781013) ^ [] : [c_Enum_Oex__n__lists(_1685235, hAPP(hAPP(c_COMBB(tc_fun(_1685237, _1685235), tc_HOL_Obool, tc_List_Olist(_1685235)), _1685239), hAPP(hAPP(c_COMBB(tc_fun(_1685237, tc_Option_Ooption(_1685235)), tc_fun(_1685237, _1685235), tc_List_Olist(_1685235)), c_Fun_Ocomp(tc_Option_Ooption(_1685235), _1685235, _1685237, c_Option_Othe(_1685235))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1685237, _1685235)), tc_fun(_1685237, tc_Option_Ooption(_1685235)), tc_List_Olist(_1685235)), c_Map_Omap__of(_1685237, _1685235)), hAPP(c_List_Ozip(_1685237, _1685235), c_Enum_Oenum__class_Oenum(_1685237))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685237)), c_Enum_Oenum__class_Oenum(_1685237))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1685237, _1685235)), _1685239)))], (45261 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1685237, _1685235)), _1685239)), -(c_Enum_Oex__n__lists(_1685235, hAPP(hAPP(c_COMBB(tc_fun(_1685237, _1685235), tc_HOL_Obool, tc_List_Olist(_1685235)), _1685239), hAPP(hAPP(c_COMBB(tc_fun(_1685237, tc_Option_Ooption(_1685235)), tc_fun(_1685237, _1685235), tc_List_Olist(_1685235)), c_Fun_Ocomp(tc_Option_Ooption(_1685235), _1685235, _1685237, c_Option_Othe(_1685235))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1685237, _1685235)), tc_fun(_1685237, tc_Option_Ooption(_1685235)), tc_List_Olist(_1685235)), c_Map_Omap__of(_1685237, _1685235)), hAPP(c_List_Ozip(_1685237, _1685235), c_Enum_Oenum__class_Oenum(_1685237))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685237)), c_Enum_Oenum__class_Oenum(_1685237))))]]], (51410 ^ _781013) ^ [_1822565] : [-(class_Nat_Osize(tc_List_Olist(_1822565)))], (29267 ^ _781013) ^ [_1326986] : [_1326986 = 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), _1326986)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7817 ^ _781013) ^ [_912730, _912732, _912734, _912736] : [hBOOL(hAPP(hAPP(c_member(_912730), _912732), hAPP(hAPP(c_Set_Oinsert(_912730), _912734), _912736))), -(_912732 = _912734), -(hBOOL(hAPP(hAPP(c_member(_912730), _912732), _912736)))], (10965 ^ _781013) ^ [_975442, _975444, _975446, _975448, _975450] : [hAPP(c_Map_Omap__add(_975442, _975444, _975446, _975448), _975450) = c_Option_Ooption_ONone(_975444), 10968 ^ _781013 : [(10971 ^ _781013) ^ [] : [-(hAPP(_975446, _975450) = c_Option_Ooption_ONone(_975444))], (10969 ^ _781013) ^ [] : [-(hAPP(_975448, _975450) = c_Option_Ooption_ONone(_975444))]]], (1304 ^ _781013) ^ [_800055, _800057] : [-(class_Lattices_Obounded__lattice__bot(_800055)), _800057 = _800055, class_Lattices_Obounded__lattice__bot(_800057)], (1946 ^ _781013) ^ [_809131, _809133, _809135, _809137, _809139, _809141, _809143, _809145, _809147, _809149, _809151, _809153] : [-(c_Map_Omap__comp(_809153, _809149, _809145, _809141, _809137, _809133) = c_Map_Omap__comp(_809151, _809147, _809143, _809139, _809135, _809131)), _809153 = _809151, _809149 = _809147, _809145 = _809143, _809141 = _809139, _809137 = _809135, _809133 = _809131], (44663 ^ _781013) ^ [_1672841] : [-(c_List_Oreturn__list(_1672841) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1672841))], (23252 ^ _781013) ^ [_1215894, _1215896] : [-(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)), _1215894)), 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), _1215896), _1215894))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1215894), _1215896))], (36058 ^ _781013) ^ [_1467552, _1467554, _1467556, _1467558, _1467560, _1467562] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1467554, _1467556)), hAPP(hAPP(c_Product__Type_OPair(_1467554, _1467556), _1467560), _1467562)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1467552, tc_fun(tc_prod(_1467554, _1467556), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1467552, tc_HOL_Obool))), _1467558))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1467552, tc_fun(_1467554, tc_fun(_1467556, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1467552, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1467554, _1467556), tc_HOL_Obool), tc_fun(_1467554, tc_fun(_1467556, tc_HOL_Obool)), _1467552), hAPP(c_COMBC(_1467554, tc_fun(tc_prod(_1467554, _1467556), tc_HOL_Obool), tc_fun(_1467556, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467556, tc_fun(tc_fun(tc_prod(_1467554, _1467556), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1467554, _1467556), tc_HOL_Obool), tc_fun(_1467556, tc_HOL_Obool)), _1467554), c_COMBC(_1467556, tc_fun(tc_prod(_1467554, _1467556), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467556, tc_prod(_1467554, _1467556)), tc_fun(_1467556, tc_fun(tc_fun(tc_prod(_1467554, _1467556), tc_HOL_Obool), tc_HOL_Obool)), _1467554), hAPP(c_COMBB(tc_prod(_1467554, _1467556), tc_fun(tc_fun(tc_prod(_1467554, _1467556), tc_HOL_Obool), tc_HOL_Obool), _1467556), c_member(tc_prod(_1467554, _1467556)))), c_Product__Type_OPair(_1467554, _1467556))))), _1467558)), _1467560), _1467562)))], (32100 ^ _781013) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (48501 ^ _781013) ^ [_1761566, _1761568, _1761570, _1761572] : [48502 ^ _781013 : [(48505 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1761566, _1761566)), _1761568), c_Transitive__Closure_Ortrancl(_1761566, _1761572)))], (48503 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1761566, _1761566)), _1761568), c_Transitive__Closure_Ortrancl(_1761566, _1761570)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1761566, _1761566)), _1761568), c_Transitive__Closure_Ortrancl(_1761566, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1761566, _1761566), tc_HOL_Obool)), _1761570), _1761572)))))], (21265 ^ _781013) ^ [_1180013] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1180013))))], (51472 ^ _781013) ^ [_1823357, _1823359] : [-(class_Smallcheck_Osmall(tc_prod(_1823357, _1823359))), class_Smallcheck_Osmall(_1823357), class_Smallcheck_Osmall(_1823359)], (24216 ^ _781013) ^ [_1232703, _1232705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232703)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1232703)), _1232705) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1232703), _1232705)))], (48169 ^ _781013) ^ [_1754233, _1754235, _1754237, _1754239] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1754233), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1754235), _1754237)))), -(hAPP(c_Random_Opick(_1754235, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1754235)), _1754237), _1754239)), _1754233) = hAPP(c_Random_Opick(_1754235, _1754239), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1754233), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1754235), _1754237))))], (17529 ^ _781013) ^ [_1108566] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108566)))], (40876 ^ _781013) ^ [_1584275, _1584277, _1584279, _1584281, _1584283, _1584285] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1584275), tc_List_Olist(_1584275))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1584275), tc_List_Olist(_1584275)), hAPP(hAPP(c_List_Olist_OCons(_1584275), _1584277), _1584279)), hAPP(hAPP(c_List_Olist_OCons(_1584275), _1584281), _1584283))), c_List_Olistrel1(_1584275, _1584285)))), 40877 ^ _781013 : [(40884 ^ _781013) ^ [] : [_1584277 = _1584281, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1584275), tc_List_Olist(_1584275))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1584275), tc_List_Olist(_1584275)), _1584279), _1584283)), c_List_Olistrel1(_1584275, _1584285)))], (40878 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584275, _1584275)), hAPP(hAPP(c_Product__Type_OPair(_1584275, _1584275), _1584277), _1584281)), _1584285)), _1584279 = _1584283]]], (31419 ^ _781013) ^ [_1372360, _1372362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1372360)), _1372362)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1372360), _1372362)))], (23375 ^ _781013) ^ [_1218222, _1218224] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1218222, _1218224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1218224), hAPP(c_Nat_OSuc, _1218222)))], (49019 ^ _781013) ^ [_1774740, _1774742] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774740, _1774740), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1774740, _1774742)), c_Relation_OId(_1774740)) = c_Transitive__Closure_Ortrancl(_1774740, _1774742))], (938 ^ _781013) ^ [_795278, _795280, _795282, _795284, _795286, _795288] : [-(c_List_Olist__all(_795286, _795282, _795278)), c_List_Olist__all(_795288, _795284, _795280), _795288 = _795286, _795284 = _795282, _795280 = _795278], (32176 ^ _781013) ^ [_1391754, _1391756, _1391758] : [class_Orderings_Olinorder(_1391754), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391754), _1391756)), 32186 ^ _781013 : [(32189 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391754), _1391758), 32185 ^ [_1391754, _1391756, _1391758]))], (32187 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391754), 32185 ^ [_1391754, _1391756, _1391758]), _1391756)))]], hBOOL(hAPP(hAPP(c_member(_1391754), _1391758), _1391756)), -(c_Big__Operators_Olinorder__class_OMin(_1391754, _1391756) = _1391758)], (42671 ^ _781013) ^ [_1626578, _1626580, _1626582] : [_1626578 = c_List_Olist_ONil(_1626580), -(c_List_Olast(_1626580, hAPP(hAPP(c_List_Oappend(_1626580), _1626582), _1626578)) = c_List_Olast(_1626580, _1626582))], (39215 ^ _781013) ^ [_1538338, _1538340, _1538342, _1538344] : [hBOOL(hAPP(c_List_Odistinct(_1538338), _1538340)), -(hBOOL(hAPP(hAPP(c_member(_1538338), _1538342), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1538338, tc_HOL_Obool)), hAPP(c_List_Oset(_1538338), _1538340)), hAPP(hAPP(c_Set_Oinsert(_1538338), hAPP(hAPP(c_List_Onth(_1538338), _1538340), _1538344)), c_Orderings_Obot__class_Obot(tc_fun(_1538338, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1538338), hAPP(hAPP(c_List_Olist__update(_1538338, _1538340), _1538344), _1538342))))], (33848 ^ _781013) ^ [_1422182, _1422184] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422182), c_Int_OPls))), 33851 ^ _781013 : [(33858 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422184), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422182)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422184)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1422182), _1422184)))], (33852 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422184), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422182)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422184)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422182))]]], (40505 ^ _781013) ^ [_1573273, _1573275, _1573277] : [c_Predicate_Oreflp(_1573273, _1573275), -(hBOOL(hAPP(hAPP(_1573275, _1573277), _1573277)))], (8195 ^ _781013) ^ [_920868, _920870, _920872] : [hBOOL(hAPP(hAPP(c_member(_920868), _920870), c_Option_Oset(_920868, _920872))), -(_920872 = hAPP(c_Option_Ooption_OSome(_920868), _920870))], (41502 ^ _781013) ^ [_1599278, _1599280, _1599282, _1599284, _1599286] : [_1599278 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1599280, _1599282, _1599284), _1599278), _1599286) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599282), _1599280), c_List_Olist_ONil(_1599282)), _1599286))], (50994 ^ _781013) ^ [_1818302, _1818304] : [class_Complete__Lattice_Ocomplete__lattice(_1818302), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1818304, _1818302)))], (17863 ^ _781013) ^ [_1114332, _1114334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114332), _1114334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114334), _1114332)), -(_1114332 = _1114334)], (27751 ^ _781013) ^ [_1299201, _1299203, _1299205] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1299201), _1299203), _1299205) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1299201), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1299203, _1299205)), _1299205))], (23178 ^ _781013) ^ [] : [-(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))], (40765 ^ _781013) ^ [_1580587, _1580589, _1580591, _1580593, _1580595, _1580597, _1580599, _1580601, _1580603, _1580605] : [hAPP(c_Set_Oimage(_1580587, _1580589, _1580591), _1580593) = _1580595, hAPP(c_Set_Oimage(_1580597, _1580599, _1580601), _1580603) = _1580605, -(hAPP(c_Set_Oimage(tc_prod(_1580587, _1580597), tc_prod(_1580589, _1580599), c_Product__Type_Omap__pair(_1580587, _1580589, _1580597, _1580599, _1580591, _1580601)), hAPP(hAPP(c_Product__Type_OSigma(_1580587, _1580597), _1580593), hAPP(c_COMBK(tc_fun(_1580597, tc_HOL_Obool), _1580587), _1580603))) = hAPP(hAPP(c_Product__Type_OSigma(_1580589, _1580599), _1580595), hAPP(c_COMBK(tc_fun(_1580599, tc_HOL_Obool), _1580589), _1580605)))], (38654 ^ _781013) ^ [_1524416, _1524418, _1524420, _1524422] : [hBOOL(hAPP(c_List_Odistinct(_1524416), _1524418)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1524416, _1524420)), hAPP(hAPP(c_List_Ozip(_1524416, _1524420), _1524418), _1524422))))], (25146 ^ _781013) ^ [_1249665, _1249667, _1249669, _1249671] : [class_Fields_Olinordered__field(_1249665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249665), _1249667), c_Groups_Ozero__class_Ozero(_1249665))), 25153 ^ _781013 : [(25160 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249665), _1249671), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249665), _1249669), _1249667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249665), _1249669), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249665), _1249671), _1249667))))], (25154 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249665), _1249669), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249665), _1249671), _1249667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249665), _1249671), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249665), _1249669), _1249667))))]]], (11404 ^ _781013) ^ [_985655, _985657, _985659, _985661, _985663] : [class_Groups_Oab__semigroup__mult(_985655), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_985655, _985655, c_Groups_Otimes__class_Otimes(_985655), _985657, _985659), _985661)), hBOOL(hAPP(hAPP(c_member(_985655), _985663), _985659)), -(hBOOL(hAPP(hAPP(c_member(_985655), _985657), _985659))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_985655, _985655, c_Groups_Otimes__class_Otimes(_985655), _985663, hAPP(hAPP(c_Set_Oinsert(_985655), _985657), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985655, tc_HOL_Obool)), _985659), hAPP(hAPP(c_Set_Oinsert(_985655), _985663), c_Orderings_Obot__class_Obot(tc_fun(_985655, tc_HOL_Obool)))))), _985661)))], (15203 ^ _781013) ^ [_1062285, _1062287, _1062289, _1062291] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062285), _1062287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1062289), hAPP(c_Set_Oimage(_1062285, _1062289, _1062291), _1062287))), hAPP(c_Finite__Set_Ocard(_1062285), _1062287))))], (42448 ^ _781013) ^ [_1621829, _1621831, _1621833] : [-(hAPP(c_List_Otl(_1621829), hAPP(hAPP(c_List_Otake(_1621829), _1621831), _1621833)) = hAPP(hAPP(c_List_Otake(_1621829), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1621831), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1621829), _1621833)))], (43765 ^ _781013) ^ [_1652834, _1652836] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1652834), _1652836)) = c_List_Oupt(_1652834, _1652836))], (5984 ^ _781013) ^ [_877777, _877779] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_877777, _877779))), -(hBOOL(hAPP(c_Com_OWT, _877779)))], (45962 ^ _781013) ^ [_1700601] : [class_Complete__Lattice_Ocomplete__lattice(_1700601), -(c_Complete__Lattice_OInf__class_OInf(_1700601, c_Orderings_Obot__class_Obot(tc_fun(_1700601, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1700601))], (41318 ^ _781013) ^ [_1595347, _1595349, _1595351, _1595353] : [-(c_Map_Omap__upds(_1595347, _1595349, _1595351, c_List_Olist_ONil(_1595347), _1595353) = _1595351)], (39984 ^ _781013) ^ [_1559498, _1559500, _1559502] : [_1559498 = _1559500, 39987 ^ _781013 : [(39990 ^ _781013) ^ [_1559654] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559502, _1559502)), _1559654), hAPP(c_List_Oset(tc_prod(_1559502, _1559502)), hAPP(hAPP(c_List_Ozip(_1559502, _1559502), _1559498), _1559500)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1559502, _1559502, tc_HOL_Obool), c_fequal), _1559654)))], (39988 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1559502)), _1559498) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1559502)), _1559500))]]], (4080 ^ _781013) ^ [_842726, _842728, _842730, _842732] : [-(c_Relation_OId__on(_842732, _842728) = c_Relation_OId__on(_842730, _842726)), _842732 = _842730, _842728 = _842726], (33750 ^ _781013) ^ [_1420635, _1420637] : [class_Int_Onumber__ring(_1420635), class_Rings_Olinordered__idom(_1420635), 33757 ^ _781013 : [(33764 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420637), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420635), hAPP(c_Int_Onumber__class_Onumber__of(_1420635), _1420637)), c_Groups_Ozero__class_Ozero(_1420635))))], (33758 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420635), hAPP(c_Int_Onumber__class_Onumber__of(_1420635), _1420637)), c_Groups_Ozero__class_Ozero(_1420635))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420637), c_Int_OPls)))]]], (50816 ^ _781013) ^ [_1813989, _1813991, _1813993] : [-(hAPP(c_New__DSequence_Oneg__single(_1813989, _1813991), _1813993) = c_Lazy__Sequence_Ohb__single(_1813989, _1813991))], (8072 ^ _781013) ^ [_918358, _918360, _918362] : [hBOOL(hAPP(hAPP(c_member(_918358), _918360), hAPP(hAPP(c_Set_Oinsert(_918358), _918362), c_Orderings_Obot__class_Obot(tc_fun(_918358, tc_HOL_Obool))))), -(_918360 = _918362)], (19983 ^ _781013) ^ [_1155228] : [_1155228 = hAPP(c_Nat_OSuc, _1155228)], (50000 ^ _781013) ^ [_1796929, _1796931, _1796933, _1796935, _1796937] : [c_Finite__Set_Ofun__left__comm(_1796929, _1796931, _1796933), -(hAPP(hAPP(c_Finite__Set_Ofold(_1796929, _1796931, _1796933), _1796935), hAPP(c_List_Oset(_1796929), _1796937)) = hAPP(c_List_Ofoldl(_1796931, _1796929, hAPP(c_COMBC(_1796929, _1796931, _1796931), _1796933), _1796935), c_List_Oremdups(_1796929, _1796937)))], (4536 ^ _781013) ^ [_849714, _849716, _849718, _849720] : [-(c_Nitpick_Oinverse__frac(_849720, _849716) = c_Nitpick_Oinverse__frac(_849718, _849714)), _849720 = _849718, _849716 = _849714], (44991 ^ _781013) ^ [_1679704, _1679706] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1679704), tc_fun(_1679704, tc_HOL_Obool), c_List_Oset(_1679704)), hAPP(c_List_Oset(tc_List_Olist(_1679704)), c_Enum_Osublists(_1679704, _1679706))) = hAPP(c_Set_OPow(_1679704), hAPP(c_List_Oset(_1679704), _1679706)))], (44342 ^ _781013) ^ [_1664523, _1664525] : [-(hAPP(c_List_Oset(_1664523), hAPP(c_List_Orev(_1664523), _1664525)) = hAPP(c_List_Oset(_1664523), _1664525))], (18356 ^ _781013) ^ [_1122810, _1122812, _1122814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122810), _1122812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122810), _1122814)), 18363 ^ _781013 : [(18370 ^ _781013) ^ [] : [_1122812 = _1122814, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122812), _1122810) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122814), _1122810))], (18364 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122812), _1122810) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122814), _1122810), -(_1122812 = _1122814)]]], (6946 ^ _781013) ^ [_895767, _895769, _895771] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895767, tc_HOL_Obool)), _895769), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895767, tc_HOL_Obool)), _895769), _895771))))], (21822 ^ _781013) ^ [_1190579, _1190581] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1190579)), _1190581) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1190579), _1190581)))], (41805 ^ _781013) ^ [_1606238, _1606240, _1606242, _1606244] : [_1606240 = _1606244, -(hAPP(hAPP(c_List_Oappend(_1606238), _1606240), _1606242) = hAPP(hAPP(c_List_Oappend(_1606238), _1606244), _1606242))], (40243 ^ _781013) ^ [_1565866, _1565868, _1565870] : [40245 ^ _781013 : [(40248 ^ _781013) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1565866, hAPP(c_Nat_OSuc, _1565870), 40244 ^ [_1565866, _1565868, _1565870])], (40246 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1565866)), 40244 ^ [_1565866, _1565868, _1565870]), _1565868)))]], 40249 ^ _781013 : [(40250 ^ _781013) ^ [_1566039] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1565866)), _1566039), _1565868)), -(c_Hoare__Mirabelle_Otriple__valid(_1565866, _1565870, _1566039))]]], (40256 ^ _781013) ^ [_1566146, _1566148, _1566150, _1566152] : [-(hAPP(hAPP(c_List_Onth(_1566146), hAPP(hAPP(c_List_Olist_OCons(_1566146), _1566148), _1566150)), _1566152) = c_Nat_Onat_Onat__case(_1566146, _1566148, hAPP(c_List_Onth(_1566146), _1566150), _1566152))], (22676 ^ _781013) ^ [_1205301, _1205303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205301), _1205303)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205301), _1205303) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (38822 ^ _781013) ^ [_1528990, _1528992, _1528994, _1528996, _1528998] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528990)), _1528992) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528994)), _1528996), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528990)), _1528998) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528994)), _1528996), hBOOL(hAPP(c_List_Odistinct(_1528994), _1528996)), hAPP(c_Map_Omap__of(_1528994, _1528990), hAPP(hAPP(c_List_Ozip(_1528994, _1528990), _1528996), _1528992)) = hAPP(c_Map_Omap__of(_1528994, _1528990), hAPP(hAPP(c_List_Ozip(_1528994, _1528990), _1528996), _1528998)), -(_1528992 = _1528998)], (39412 ^ _781013) ^ [_1542924, _1542926] : [class_Groups_Ocomm__monoid__add(_1542924), hBOOL(hAPP(c_List_Odistinct(_1542924), _1542926)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1542924), _1542926) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1542924, _1542924), c_COMBI(_1542924)), hAPP(c_List_Oset(_1542924), _1542926)))], (36577 ^ _781013) ^ [_1478922, _1478924, _1478926, _1478928, _1478930, _1478932] : [-(hAPP(hAPP(c_Product__Type_OPair(_1478922, _1478924), _1478926), _1478928) = hAPP(hAPP(c_Product__Type_OPair(_1478922, _1478924), _1478930), _1478932)), _1478926 = _1478930, _1478928 = _1478932], (2346 ^ _781013) ^ [_815717, _815719, _815721, _815723] : [-(c_Orderings_Oord_Omin(_815723, _815719) = c_Orderings_Oord_Omin(_815721, _815717)), _815723 = _815721, _815719 = _815717], (6028 ^ _781013) ^ [_878421, _878423, _878425] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _878421))), _878423), _878425)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _878421)), _878423), _878425)))], (42298 ^ _781013) ^ [_1619107, _1619109, _1619111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619107), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619109)), _1619111))), -(hAPP(hAPP(c_List_Oappend(_1619109), hAPP(hAPP(c_List_Otake(_1619109), _1619107), _1619111)), hAPP(hAPP(c_List_Olist_OCons(_1619109), hAPP(c_List_Ohd(_1619109), hAPP(hAPP(c_List_Odrop(_1619109), _1619107), _1619111))), c_List_Olist_ONil(_1619109))) = hAPP(hAPP(c_List_Otake(_1619109), hAPP(c_Nat_OSuc, _1619107)), _1619111))], (36754 ^ _781013) ^ [_1482669] : [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), _1482669))), 36757 ^ _781013 : [(36764 ^ _781013) ^ [] : [-(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), _1482669)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482669)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482669)), 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), _1482669)))))], (36758 ^ _781013) ^ [] : [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), _1482669))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482669)) = 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)))]]], (41180 ^ _781013) ^ [_1592763, _1592765, _1592767] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1592763), tc_List_Olist(_1592763))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1592763), tc_List_Olist(_1592763)), c_List_Olist_ONil(_1592763)), _1592765)), c_List_Olistrel(_1592763, _1592767))), -(_1592765 = c_List_Olist_ONil(_1592763))], (5232 ^ _781013) ^ [_860810, _860812, _860814, _860816, _860818, _860820] : [-(c_Lazy__Sequence_Obind(_860820, _860816, _860812) = c_Lazy__Sequence_Obind(_860818, _860814, _860810)), _860820 = _860818, _860816 = _860814, _860812 = _860810], (38668 ^ _781013) ^ [_1524991, _1524993, _1524995, _1524997, _1524999, _1525001] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524991, _1524993)), hAPP(hAPP(c_Product__Type_OPair(_1524991, _1524993), _1524995), _1524997)), hAPP(c_List_Oset(tc_prod(_1524991, _1524993)), hAPP(hAPP(c_List_Ozip(_1524991, _1524993), _1524999), _1525001)))), 38671 ^ _781013 : [(38674 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524993), _1524997), hAPP(c_List_Oset(_1524993), _1525001))))], (38672 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524991), _1524995), hAPP(c_List_Oset(_1524991), _1524999))))]]], (39665 ^ _781013) ^ [_1548957, _1548959, _1548961, _1548963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1548957), _1548959)), -(hAPP(hAPP(c_List_Onth(_1548961), hAPP(hAPP(c_List_Otake(_1548961), _1548959), _1548963)), _1548957) = hAPP(hAPP(c_List_Onth(_1548961), _1548963), _1548957))], (25490 ^ _781013) ^ [_1255977] : [25492 ^ _781013 : [(25495 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25491 ^ [_1255977]))], (25493 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 25491 ^ [_1255977]), _1255977)))]], -(c_Nat__Transfer_Onat__set(_1255977))], (27170 ^ _781013) ^ [_1286864, _1286866] : [class_Orderings_Olinorder(_1286864), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1286864, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1286864), _1286866)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1286864), _1286866))], (51348 ^ _781013) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (43551 ^ _781013) ^ [_1649063, _1649065] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1649063))), c_List_Otranspose(_1649063, _1649065)) = c_List_Ofoldr(tc_List_Olist(_1649063), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1649063)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1649063))), _1649065, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31790 ^ _781013) ^ [_1382075, _1382077, _1382079, _1382081] : [-(_1382075 = c_Orderings_Obot__class_Obot(tc_fun(_1382077, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382077, tc_fun(_1382079, tc_HOL_Obool)), _1382075), hAPP(c_COMBK(tc_fun(_1382079, tc_HOL_Obool), _1382077), _1382081)) = _1382081)], (49442 ^ _781013) ^ [_1786004, _1786006, _1786008] : [-(hBOOL(hAPP(hAPP(c_member(_1786004), _1786006), hAPP(c_List_Oset(_1786004), _1786008)))), 49443 ^ _781013 : [(49444 ^ _781013) ^ [_1786093] : [49445 ^ _781013 : [(49446 ^ _781013) ^ [_1786166] : [_1786008 = hAPP(hAPP(c_List_Oappend(_1786004), _1786093), hAPP(hAPP(c_List_Olist_OCons(_1786004), _1786006), _1786166))]], -(hBOOL(hAPP(hAPP(c_member(_1786004), _1786006), hAPP(c_List_Oset(_1786004), _1786093))))]]], (8699 ^ _781013) ^ [_932156, _932158, _932160, _932162] : [hBOOL(hAPP(_932156, _932158)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932160, tc_HOL_Obool)), _932162), _932156), _932158)))], (32304 ^ _781013) ^ [_1394092, _1394094, _1394096] : [class_Int_Onumber__ring(_1394092), class_Int_Oring__char__0(_1394092), 32311 ^ _781013 : [(32318 ^ _781013) ^ [] : [_1394094 = _1394096, -(hAPP(c_Int_Onumber__class_Onumber__of(_1394092), _1394094) = hAPP(c_Int_Onumber__class_Onumber__of(_1394092), _1394096))], (32312 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1394092), _1394094) = hAPP(c_Int_Onumber__class_Onumber__of(_1394092), _1394096), -(_1394094 = _1394096)]]], (47679 ^ _781013) ^ [_1743490, _1743492, _1743494, _1743496, _1743498, _1743500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1743490, tc_HOL_Obool)), _1743492), _1743494)), 47685 ^ _781013 : [(47688 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1743496, tc_HOL_Obool)), hAPP(_1743498, 47684 ^ [_1743490, _1743492, _1743494, _1743496, _1743498, _1743500])), hAPP(_1743500, 47684 ^ [_1743490, _1743492, _1743494, _1743496, _1743498, _1743500])))], (47686 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743490), 47684 ^ [_1743490, _1743492, _1743494, _1743496, _1743498, _1743500]), _1743492)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1743490, _1743496), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1743490, _1743496), _1743492), _1743498)), hAPP(hAPP(c_Product__Type_OSigma(_1743490, _1743496), _1743494), _1743500))))], (51094 ^ _781013) ^ [_1819616, _1819618] : [-(class_HOL_Oequal(tc_fun(_1819616, _1819618))), class_Enum_Oenum(_1819616), class_HOL_Oequal(_1819618)], (46861 ^ _781013) ^ [_1723429, _1723431, _1723433] : [c_Wellfounded_Owf(_1723429, _1723431), hBOOL(hAPP(hAPP(c_member(tc_prod(_1723429, _1723429)), hAPP(hAPP(c_Product__Type_OPair(_1723429, _1723429), _1723433), _1723433)), _1723431))], (28070 ^ _781013) ^ [_1305043, _1305045] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1305043, _1305045) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1305043), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1305043), _1305045)), _1305045)))], (14105 ^ _781013) ^ [_1040666, _1040668, _1040670] : [class_Rings_Ocomm__semiring__1(_1040666), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040666), _1040668), _1040670)), _1040670) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040666), _1040668), c_Groups_Oone__class_Oone(_1040666))), _1040670))], (37496 ^ _781013) ^ [_1496953, _1496955, _1496957, _1496959] : [-(_1496953 = _1496955), hAPP(c_Product__Type_Ofst(_1496957, _1496959), _1496953) = hAPP(c_Product__Type_Ofst(_1496957, _1496959), _1496955), hAPP(c_Product__Type_Osnd(_1496957, _1496959), _1496953) = hAPP(c_Product__Type_Osnd(_1496957, _1496959), _1496955)], (51232 ^ _781013) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (10903 ^ _781013) ^ [_974102, _974104, _974106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974102, tc_HOL_Obool)), _974104), _974106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_974102, tc_HOL_Obool)), _974104), _974106))), -(_974104 = _974106)], (18330 ^ _781013) ^ [_1122264, _1122266, _1122268] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122264), _1122266)), _1122268) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122264), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122266), _1122268)))], (28062 ^ _781013) ^ [_1304801, _1304803, _1304805] : [-(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), _1304801), _1304803)), _1304803)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304801, _1304803))), _1304805) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1304801), _1304805))], (30439 ^ _781013) ^ [_1349984, _1349986, _1349988, _1349990] : [class_Orderings_Olinorder(_1349984), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349984, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1349984), _1349986)), c_SetInterval_Oord__class_OatLeastAtMost(_1349984, _1349988, _1349990)) = c_SetInterval_Oord__class_OatLeastAtMost(_1349984, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349984), _1349986), _1349988), _1349990))], (6452 ^ _781013) ^ [_886498, _886500, _886502, _886504] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_886498, _886500, hAPP(hAPP(c_Set_Oinsert(_886498), _886502), c_Orderings_Obot__class_Obot(tc_fun(_886498, tc_HOL_Obool)))), _886504)), -(_886502 = _886504)], (1214 ^ _781013) ^ [_798930, _798932] : [-(class_Groups_Osgn__if(_798930)), _798932 = _798930, class_Groups_Osgn__if(_798932)], (40814 ^ _781013) ^ [_1582077, _1582079, _1582081, _1582083, _1582085, _1582087] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1582077, _1582079), hAPP(hAPP(c_Set_Oinsert(_1582077), _1582081), _1582083)), hAPP(c_COMBK(tc_fun(_1582079, tc_HOL_Obool), _1582077), hAPP(hAPP(c_Set_Oinsert(_1582079), _1582085), _1582087))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1582077, _1582079)), hAPP(hAPP(c_Product__Type_OPair(_1582077, _1582079), _1582081), _1582085)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582077, _1582079), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1582077, _1582079), _1582083), hAPP(c_COMBK(tc_fun(_1582079, tc_HOL_Obool), _1582077), hAPP(hAPP(c_Set_Oinsert(_1582079), _1582085), _1582087)))), hAPP(hAPP(c_Product__Type_OSigma(_1582077, _1582079), hAPP(hAPP(c_Set_Oinsert(_1582077), _1582081), _1582083)), hAPP(c_COMBK(tc_fun(_1582079, tc_HOL_Obool), _1582077), _1582087)))))], (45495 ^ _781013) ^ [_1689858, _1689860, _1689862] : [class_Enum_Oenum(_1689858), class_Enum_Oenum(_1689860), class_HOL_Oequal(_1689860), 45506 ^ _781013 : [(45513 ^ _781013) ^ [] : [c_Enum_Oall__n__lists(_1689858, hAPP(hAPP(c_COMBB(tc_fun(_1689860, _1689858), tc_HOL_Obool, tc_List_Olist(_1689858)), _1689862), hAPP(hAPP(c_COMBB(tc_fun(_1689860, tc_Option_Ooption(_1689858)), tc_fun(_1689860, _1689858), tc_List_Olist(_1689858)), c_Fun_Ocomp(tc_Option_Ooption(_1689858), _1689858, _1689860, c_Option_Othe(_1689858))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1689860, _1689858)), tc_fun(_1689860, tc_Option_Ooption(_1689858)), tc_List_Olist(_1689858)), c_Map_Omap__of(_1689860, _1689858)), hAPP(c_List_Ozip(_1689860, _1689858), c_Enum_Oenum__class_Oenum(_1689860))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689860)), c_Enum_Oenum__class_Oenum(_1689860))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1689860, _1689858)), _1689862)))], (45507 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1689860, _1689858)), _1689862)), -(c_Enum_Oall__n__lists(_1689858, hAPP(hAPP(c_COMBB(tc_fun(_1689860, _1689858), tc_HOL_Obool, tc_List_Olist(_1689858)), _1689862), hAPP(hAPP(c_COMBB(tc_fun(_1689860, tc_Option_Ooption(_1689858)), tc_fun(_1689860, _1689858), tc_List_Olist(_1689858)), c_Fun_Ocomp(tc_Option_Ooption(_1689858), _1689858, _1689860, c_Option_Othe(_1689858))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1689860, _1689858)), tc_fun(_1689860, tc_Option_Ooption(_1689858)), tc_List_Olist(_1689858)), c_Map_Omap__of(_1689860, _1689858)), hAPP(c_List_Ozip(_1689860, _1689858), c_Enum_Oenum__class_Oenum(_1689860))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689860)), c_Enum_Oenum__class_Oenum(_1689860))))]]], (46715 ^ _781013) ^ [_1720712, _1720714] : [c_Wellfounded_Owf(_1720712, _1720714), -(c_Wellfounded_Owf(tc_List_Olist(_1720712), c_List_Olex(_1720712, _1720714)))], (19582 ^ _781013) ^ [_1147451, _1147453, _1147455, _1147457] : [class_Rings_Olinordered__semidom(_1147451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147453), _1147455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147451), c_Groups_Oone__class_Oone(_1147451)), _1147457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147451), hAPP(hAPP(c_Power_Opower__class_Opower(_1147451), _1147457), _1147453)), hAPP(hAPP(c_Power_Opower__class_Opower(_1147451), _1147457), _1147455))))], (34665 ^ _781013) ^ [_1437741, _1437743] : [c_Int_OBit0(_1437741) = c_Int_OBit0(_1437743), -(_1437741 = _1437743)], (43841 ^ _781013) ^ [_1654080, _1654082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1654080), _1654082)), -(c_List_Oupt(_1654080, _1654082) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1654080), c_List_Oupt(hAPP(c_Nat_OSuc, _1654080), _1654082)))], (3106 ^ _781013) ^ [_827615, _827617, _827619, _827621, _827623, _827625] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_827625, _827621, _827617) = c_SetInterval_Oord__class_OgreaterThanAtMost(_827623, _827619, _827615)), _827625 = _827623, _827621 = _827619, _827617 = _827615], (51652 ^ _781013) ^ [_1825362, _1825364] : [hBOOL(hAPP(hAPP(c_fconj, _1825362), _1825364)), -(hBOOL(_1825362))], (41186 ^ _781013) ^ [_1592910, _1592912, _1592914] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1592910), tc_List_Olist(_1592910))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1592910), tc_List_Olist(_1592910)), _1592912), c_List_Olist_ONil(_1592910))), c_List_Olistrel(_1592910, _1592914))), -(_1592912 = c_List_Olist_ONil(_1592910))], (14500 ^ _781013) ^ [_1049952, _1049954, _1049956, _1049958] : [class_Groups_Ocomm__monoid__mult(_1049952), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049954), _1049956)), 14510 ^ _781013 : [(14513 ^ _781013) ^ [] : [hAPP(_1049958, 14509 ^ [_1049952, _1049954, _1049956, _1049958]) = c_Groups_Oone__class_Oone(_1049952)], (14511 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1049954), 14509 ^ [_1049952, _1049954, _1049956, _1049958]), _1049956)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1049952, _1049954, c_Groups_Otimes__class_Otimes(_1049952)), _1049958), c_Groups_Oone__class_Oone(_1049952)), _1049956) = c_Groups_Oone__class_Oone(_1049952))], (22244 ^ _781013) ^ [_1198086, _1198088] : [class_Divides_Osemiring__div(_1198086), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1198086), _1198088), c_Groups_Oone__class_Oone(_1198086)) = _1198088)], (45471 ^ _781013) ^ [_1689257, _1689259, _1689261] : [class_Enum_Oenum(_1689257), class_Enum_Oenum(_1689259), class_HOL_Oequal(_1689259), 45482 ^ _781013 : [(45489 ^ _781013) ^ [] : [c_Enum_Oex__n__lists(_1689257, hAPP(hAPP(c_COMBB(tc_fun(_1689259, _1689257), tc_HOL_Obool, tc_List_Olist(_1689257)), _1689261), hAPP(hAPP(c_COMBB(tc_fun(_1689259, tc_Option_Ooption(_1689257)), tc_fun(_1689259, _1689257), tc_List_Olist(_1689257)), c_Fun_Ocomp(tc_Option_Ooption(_1689257), _1689257, _1689259, c_Option_Othe(_1689257))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1689259, _1689257)), tc_fun(_1689259, tc_Option_Ooption(_1689257)), tc_List_Olist(_1689257)), c_Map_Omap__of(_1689259, _1689257)), hAPP(c_List_Ozip(_1689259, _1689257), c_Enum_Oenum__class_Oenum(_1689259))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689259)), c_Enum_Oenum__class_Oenum(_1689259))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1689259, _1689257)), _1689261)))], (45483 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1689259, _1689257)), _1689261)), -(c_Enum_Oex__n__lists(_1689257, hAPP(hAPP(c_COMBB(tc_fun(_1689259, _1689257), tc_HOL_Obool, tc_List_Olist(_1689257)), _1689261), hAPP(hAPP(c_COMBB(tc_fun(_1689259, tc_Option_Ooption(_1689257)), tc_fun(_1689259, _1689257), tc_List_Olist(_1689257)), c_Fun_Ocomp(tc_Option_Ooption(_1689257), _1689257, _1689259, c_Option_Othe(_1689257))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1689259, _1689257)), tc_fun(_1689259, tc_Option_Ooption(_1689257)), tc_List_Olist(_1689257)), c_Map_Omap__of(_1689259, _1689257)), hAPP(c_List_Ozip(_1689259, _1689257), c_Enum_Oenum__class_Oenum(_1689259))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689259)), c_Enum_Oenum__class_Oenum(_1689259))))]]], (43651 ^ _781013) ^ [_1650996, _1650998, _1651000, _1651002, _1651004] : [class_Orderings_Olinorder(_1650996), c_List_Olinorder__class_Osorted(_1650996, hAPP(hAPP(c_List_Omap(_1650998, _1650996), _1651000), _1651002)), -(c_List_Olinorder__class_Osorted(_1650996, hAPP(hAPP(c_List_Omap(_1650998, _1650996), _1651000), c_List_Oremove1(_1650998, _1651004, _1651002))))], (20107 ^ _781013) ^ [_1157125, _1157127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157127), hAPP(c_Nat_OSuc, _1157125))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157125), _1157127))], (17659 ^ _781013) ^ [_1111091, _1111093, _1111095] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111091), _1111093) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111091), _1111095), -(_1111091 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1111093 = _1111095)], (46122 ^ _781013) ^ [_1704298, _1704300, _1704302, _1704304, _1704306, _1704308, _1704310] : [c_List_Olist__all2(_1704298, _1704306, hAPP(hAPP(c_COMBC(_1704298, tc_fun(_1704306, _1704300), tc_fun(_1704306, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1704300, tc_HOL_Obool), tc_fun(tc_fun(_1704306, _1704300), tc_fun(_1704306, tc_HOL_Obool)), _1704298), c_COMBB(_1704300, tc_HOL_Obool, _1704306)), _1704302)), _1704308), _1704304, _1704310), -(c_List_Olist__all2(_1704298, _1704300, _1704302, _1704304, hAPP(hAPP(c_List_Omap(_1704306, _1704300), _1704308), _1704310)))], (15717 ^ _781013) ^ [_1071761, _1071763, _1071765, _1071767] : [class_Rings_Olinordered__semidom(_1071761), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071761), c_Groups_Ozero__class_Ozero(_1071761)), _1071763)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071761), _1071765), _1071767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071761), _1071765), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071761), _1071763), _1071767))))], (6294 ^ _781013) ^ [_883446, _883448] : [class_Finite__Set_Ofinite(_883446), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_883446), _883448)))], (6822 ^ _781013) ^ [_893490, _893492, _893494, _893496] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_893490, _893492), _893494), _893496), hAPP(_893494, _893496)) = _893494)], (28984 ^ _781013) ^ [_1321850, _1321852] : [class_Groups_Oordered__ab__group__add__abs(_1321850), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321850), hAPP(c_Groups_Ouminus__class_Ouminus(_1321850), _1321852)), hAPP(c_Groups_Oabs__class_Oabs(_1321850), _1321852))))], (43484 ^ _781013) ^ [_1647050, _1647052, _1647054] : [hBOOL(hAPP(c_List_Olistsp(_1647050, hAPP(hAPP(c_COMBC(_1647050, tc_fun(_1647050, tc_HOL_Obool), tc_HOL_Obool), c_member(_1647050)), _1647052)), _1647054)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1647050)), _1647054), c_List_Olists(_1647050, _1647052))))], (45572 ^ _781013) ^ [_1691644, _1691646, _1691648] : [class_Complete__Lattice_Ocomplete__lattice(_1691644), hBOOL(hAPP(hAPP(c_member(_1691644), _1691646), _1691648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1691644), _1691646), c_Complete__Lattice_OSup__class_OSup(_1691644, _1691648))))], (25458 ^ _781013) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (28990 ^ _781013) ^ [_1321959, _1321961, _1321963] : [class_Groups_Oordered__ab__group__add__abs(_1321959), 28993 ^ _781013 : [(29002 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321959), hAPP(c_Groups_Oabs__class_Oabs(_1321959), _1321961)), _1321963))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321959), _1321961), _1321963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321959), hAPP(c_Groups_Ouminus__class_Ouminus(_1321959), _1321961)), _1321963))], (28994 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321959), hAPP(c_Groups_Oabs__class_Oabs(_1321959), _1321961)), _1321963)), 28997 ^ _781013 : [(29000 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321959), hAPP(c_Groups_Ouminus__class_Ouminus(_1321959), _1321961)), _1321963)))], (28998 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321959), _1321961), _1321963)))]]]]], (41963 ^ _781013) ^ [_1610313, _1610315, _1610317, _1610319] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610313), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610315)), _1610317)))), -(hAPP(hAPP(c_List_Onth(_1610315), hAPP(hAPP(c_List_Oappend(_1610315), _1610317), _1610319)), _1610313) = hAPP(hAPP(c_List_Onth(_1610315), _1610319), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1610313), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610315)), _1610317))))], (12394 ^ _781013) ^ [_1004650, _1004652, _1004654, _1004656, _1004658] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1004650)), hAPP(c_Set_Oimage(_1004652, tc_Option_Ooption(_1004650), _1004654), c_Orderings_Otop__class_Otop(tc_fun(_1004652, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1004650)), hAPP(c_Set_Oimage(_1004652, tc_Option_Ooption(_1004650), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1004652, tc_Option_Ooption(_1004650)), _1004654), _1004656), hAPP(c_Option_Ooption_OSome(_1004650), _1004658))), c_Orderings_Otop__class_Otop(tc_fun(_1004652, tc_HOL_Obool))))))], (1674 ^ _781013) ^ [_804680, _804682] : [-(class_Rings_Ozero__neq__one(_804680)), _804682 = _804680, class_Rings_Ozero__neq__one(_804682)], (13461 ^ _781013) ^ [_1027196, _1027198, _1027200, _1027202, _1027204] : [class_Rings_Osemiring__0(_1027196), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1027196), _1027198), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027200, _1027196), _1027202), _1027204)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027200, _1027196), hAPP(hAPP(c_COMBB(_1027196, _1027196, _1027200), hAPP(c_Groups_Otimes__class_Otimes(_1027196), _1027198)), _1027202)), _1027204))], (38626 ^ _781013) ^ [_1523814, _1523816, _1523818] : [class_Orderings_Olinorder(_1523814), hBOOL(hAPP(c_Finite__Set_Ofinite(_1523814), _1523816)), -(c_List_Olinorder__class_Osorted__list__of__set(_1523814, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1523814, tc_HOL_Obool)), _1523816), hAPP(hAPP(c_Set_Oinsert(_1523814), _1523818), c_Orderings_Obot__class_Obot(tc_fun(_1523814, tc_HOL_Obool))))) = c_List_Oremove1(_1523814, _1523818, c_List_Olinorder__class_Osorted__list__of__set(_1523814, _1523816)))], (43179 ^ _781013) ^ [_1640310, _1640312, _1640314, _1640316, _1640318] : [_1640310 = c_Orderings_Obot__class_Obot(tc_fun(_1640312, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640314, tc_HOL_Obool)), _1640316), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1640312, tc_fun(_1640314, tc_HOL_Obool)), _1640310), _1640318)) = _1640316)], (39308 ^ _781013) ^ [_1540432, _1540434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1540432), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1540434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1540434), _1540432)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1540434))))], (13094 ^ _781013) ^ [_1019145, _1019147, _1019149, _1019151, _1019153] : [-(hAPP(c_Fun_Othe__inv__into(_1019145, _1019147, _1019149, _1019151), _1019153) = c_HOL_OThe(_1019145, hAPP(hAPP(c_COMBS(_1019145, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1019145), c_fconj), hAPP(hAPP(c_COMBC(_1019145, tc_fun(_1019145, tc_HOL_Obool), tc_HOL_Obool), c_member(_1019145)), _1019149))), hAPP(hAPP(c_COMBC(_1019145, _1019147, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1019147, tc_fun(_1019147, tc_HOL_Obool), _1019145), c_fequal), _1019151)), _1019153))))], (33332 ^ _781013) ^ [_1413723] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413723)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413723))], (13002 ^ _781013) ^ [_1017449, _1017451, _1017453, _1017455] : [c_Fun_Oinj__on(_1017449, _1017451, _1017453, c_Orderings_Otop__class_Otop(tc_fun(_1017449, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1017449, _1017451, _1017453), hAPP(c_Set_Oimage(_1017449, _1017451, _1017453), _1017455)) = _1017455)], (18031 ^ _781013) ^ [_1117162, _1117164] : [-(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), _1117162), _1117164)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1117162)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1117164))], (40149 ^ _781013) ^ [_1563945, _1563947] : [-(c_Relation_Orefl__on(_1563945, _1563947, c_Relation_OId__on(_1563945, _1563947)))], (33464 ^ _781013) ^ [_1416025, _1416027] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416025)))), 33467 ^ _781013 : [(33474 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416027)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416025), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416027)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416025), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416027))))], (33468 ^ _781013) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416027))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416025), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416027)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416025))]]], (23138 ^ _781013) ^ [_1213870] : [-(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)), _1213870))))], (1364 ^ _781013) ^ [_800805, _800807] : [-(class_Orderings_Otop(_800805)), _800807 = _800805, class_Orderings_Otop(_800807)], (16301 ^ _781013) ^ [_1082155, _1082157, _1082159] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1082155, tc_HOL_Obool)), _1082157), _1082159) = hAPP(c_Set_OCollect(_1082155), hAPP(hAPP(c_COMBS(_1082155, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1082155), c_fdisj), hAPP(hAPP(c_COMBC(_1082155, tc_fun(_1082155, tc_HOL_Obool), tc_HOL_Obool), c_member(_1082155)), _1082157))), hAPP(hAPP(c_COMBC(_1082155, tc_fun(_1082155, tc_HOL_Obool), tc_HOL_Obool), c_member(_1082155)), _1082159))))], (39893 ^ _781013) ^ [_1557084, _1557086, _1557088] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1557084, _1557084)), hAPP(hAPP(c_Product__Type_OPair(_1557084, _1557084), 39894 ^ [_1557084, _1557086, _1557088]), 39894 ^ [_1557084, _1557086, _1557088])), _1557086))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1557084), tc_List_Olist(_1557084))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1557084), tc_List_Olist(_1557084)), _1557088), _1557088)), c_List_Olexord(_1557084, _1557086)))], (4312 ^ _781013) ^ [_846222, _846224, _846226, _846228] : [-(c_Big__Operators_Olinorder__class_OMax(_846228, _846224) = c_Big__Operators_Olinorder__class_OMax(_846226, _846222)), _846228 = _846226, _846224 = _846222], (47183 ^ _781013) ^ [_1731281, _1731283, _1731285, _1731287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1731281, _1731283), tc_HOL_Obool)), _1731285), _1731287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731281, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1731281, _1731283), _1731285)), hAPP(c_Relation_ODomain(_1731281, _1731283), _1731287))))], (40964 ^ _781013) ^ [_1587440] : [-(hAPP(c_List_Omap(_1587440, _1587440), c_Fun_Oid(_1587440)) = c_Fun_Oid(tc_List_Olist(_1587440)))], (23365 ^ _781013) ^ [_1218045] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _1218045)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28780 ^ _781013) ^ [_1318043, _1318045] : [class_Rings_Olinordered__idom(_1318043), -(hAPP(c_Groups_Oabs__class_Oabs(_1318043), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1318043), _1318045)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1318043), _1318045))], (49598 ^ _781013) ^ [_1789345, _1789347, _1789349, _1789351, _1789353] : [c_Finite__Set_Ofun__left__comm__idem(_1789345, _1789347, _1789349), -(hAPP(hAPP(c_Finite__Set_Ofold(_1789345, _1789347, _1789349), _1789351), hAPP(c_List_Oset(_1789345), _1789353)) = hAPP(c_List_Ofoldl(_1789347, _1789345, hAPP(c_COMBC(_1789345, _1789347, _1789347), _1789349), _1789351), _1789353))], (344 ^ _781013) ^ [_786419, _786421, _786423, _786425] : [-(c_Equiv__Relations_Oequivp(_786423, _786419)), c_Equiv__Relations_Oequivp(_786425, _786421), _786425 = _786423, _786421 = _786419], (26307 ^ _781013) ^ [_1270224, _1270226] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1270224, _1270226)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1270226)), _1270224))], (35689 ^ _781013) ^ [_1456141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1456141))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1456141)))], (34873 ^ _781013) ^ [_1441211, _1441213] : [class_Int_Onumber__ring(_1441211), -(hAPP(c_Int_Onumber__class_Onumber__of(_1441211), c_Int_OBit0(_1441213)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1441211), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1441211), c_Groups_Ozero__class_Ozero(_1441211)), hAPP(c_Int_Onumber__class_Onumber__of(_1441211), _1441213))), hAPP(c_Int_Onumber__class_Onumber__of(_1441211), _1441213)))], (11954 ^ _781013) ^ [_996579, _996581, _996583] : [class_Lattices_Obounded__lattice__top(_996579), 11957 ^ _781013 : [(11966 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_996579), _996581), _996583) = c_Orderings_Otop__class_Otop(_996579)), _996581 = c_Orderings_Otop__class_Otop(_996579), _996583 = c_Orderings_Otop__class_Otop(_996579)], (11958 ^ _781013) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_996579), _996581), _996583) = c_Orderings_Otop__class_Otop(_996579), 11961 ^ _781013 : [(11964 ^ _781013) ^ [] : [-(_996583 = c_Orderings_Otop__class_Otop(_996579))], (11962 ^ _781013) ^ [] : [-(_996581 = c_Orderings_Otop__class_Otop(_996579))]]]]], (27447 ^ _781013) ^ [_1292728, _1292730, _1292732, _1292734, _1292736] : [hAPP(c_Set_Oimage(_1292728, _1292730, _1292732), _1292734) = _1292736, -(hAPP(c_Set_Oimage(tc_fun(_1292728, tc_HOL_Obool), tc_fun(_1292730, tc_HOL_Obool), c_Set_Oimage(_1292728, _1292730, _1292732)), hAPP(c_Set_OPow(_1292728), _1292734)) = hAPP(c_Set_OPow(_1292730), _1292736))], (50872 ^ _781013) ^ [_1815320, _1815322, _1815324, _1815326, _1815328] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815320, _1815322, _1815324), _1815326), _1815328)), -(hBOOL(hAPP(hAPP(_1815324, _1815328), _1815326)))], (51424 ^ _781013) ^ [_1822745, _1822747] : [-(class_Enum_Oenum(tc_sum(_1822745, _1822747))), class_Enum_Oenum(_1822745), class_Enum_Oenum(_1822747)], (33790 ^ _781013) ^ [_1421254, _1421256] : [class_Int_Onumber__ring(_1421254), class_Rings_Olinordered__idom(_1421254), 33797 ^ _781013 : [(33804 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421256), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421254), hAPP(c_Int_Onumber__class_Onumber__of(_1421254), _1421256)), c_Groups_Ozero__class_Ozero(_1421254))))], (33798 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421254), hAPP(c_Int_Onumber__class_Onumber__of(_1421254), _1421256)), c_Groups_Ozero__class_Ozero(_1421254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421256), c_Int_OPls)))]]], (42974 ^ _781013) ^ [_1634508, _1634510, _1634512, _1634514, _1634516] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634508, tc_fun(_1634510, tc_HOL_Obool)), _1634512), hAPP(hAPP(c_COMBS(_1634508, tc_fun(_1634510, tc_HOL_Obool), tc_fun(_1634510, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1634510, tc_HOL_Obool), tc_fun(tc_fun(_1634510, tc_HOL_Obool), tc_fun(_1634510, tc_HOL_Obool)), _1634508), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1634510, tc_HOL_Obool))), _1634514)), _1634516)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1634510, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634508, tc_fun(_1634510, tc_HOL_Obool)), _1634512), _1634514)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634508, tc_fun(_1634510, tc_HOL_Obool)), _1634512), _1634516)))], (29549 ^ _781013) ^ [_1332192, _1332194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332194)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332192, _1332194)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1332192), hAPP(c_Int_Onat, _1332194)))], (236 ^ _781013) ^ [_784863, _784865] : [-(class_Fields_Olinordered__field(_784863)), _784865 = _784863, class_Fields_Olinordered__field(_784865)], (38385 ^ _781013) ^ [_1518791, _1518793, _1518795, _1518797, _1518799] : [c_Typedef_Otype__definition(_1518791, _1518793, _1518795, _1518797, _1518799), -(hAPP(c_Set_Oimage(_1518791, _1518793, _1518795), c_Orderings_Otop__class_Otop(tc_fun(_1518791, tc_HOL_Obool))) = _1518799)], (38365 ^ _781013) ^ [_1518312, _1518314, _1518316, _1518318, _1518320] : [hAPP(hAPP(c_Map_Omap__of(_1518312, _1518314), _1518316), _1518318) = hAPP(c_Option_Ooption_OSome(_1518314), _1518320), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1518312, _1518314)), hAPP(hAPP(c_Product__Type_OPair(_1518312, _1518314), _1518318), _1518320)), hAPP(c_List_Oset(tc_prod(_1518312, _1518314)), _1518316))))], (40954 ^ _781013) ^ [_1587282] : [-(hAPP(c_Option_Omap(_1587282, _1587282), c_Fun_Oid(_1587282)) = c_Fun_Oid(tc_Option_Ooption(_1587282)))], (50578 ^ _781013) ^ [] : [-(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)))], (51030 ^ _781013) ^ [_1818776, _1818778] : [class_Lattices_Oboolean__algebra(_1818776), -(class_Lattices_Oboolean__algebra(tc_fun(_1818778, _1818776)))], (40623 ^ _781013) ^ [_1576930, _1576932, _1576934, _1576936] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1576930), _1576932)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576934), _1576936)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576930, _1576934)), hAPP(hAPP(c_Product__Type_OSigma(_1576930, _1576934), _1576932), hAPP(c_COMBK(tc_fun(_1576934, tc_HOL_Obool), _1576930), _1576936)))))], (11025 ^ _781013) ^ [_976875, _976877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976875, tc_HOL_Obool)), _976877), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_976875, tc_HOL_Obool)), _976877))), -(_976877 = c_Orderings_Obot__class_Obot(tc_fun(_976875, tc_HOL_Obool)))], (34465 ^ _781013) ^ [_1434027, _1434029] : [class_Int_Onumber__ring(_1434027), class_Rings_Olinordered__idom(_1434027), 34472 ^ _781013 : [(34479 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1434029), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434027), hAPP(c_Int_Onumber__class_Onumber__of(_1434027), _1434029)), c_Groups_Oone__class_Oone(_1434027))))], (34473 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434027), hAPP(c_Int_Onumber__class_Onumber__of(_1434027), _1434029)), c_Groups_Oone__class_Oone(_1434027))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1434029), c_Int_OBit1(c_Int_OPls))))]]], (6730 ^ _781013) ^ [_891762, _891764, _891766] : [-(hAPP(c_Option_Omap(_891762, _891764), _891766) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_891764), _891762, c_Option_Ooption_ONone(_891764), hAPP(hAPP(c_COMBB(_891764, tc_Option_Ooption(_891764), _891762), c_Option_Ooption_OSome(_891764)), _891766)))], (11600 ^ _781013) ^ [_989774, _989776, _989778, _989780, _989782] : [c_Fun_Oinj__on(_989774, _989776, _989778, c_Orderings_Otop__class_Otop(tc_fun(_989774, tc_HOL_Obool))), hAPP(_989778, _989780) = hAPP(_989778, _989782), -(_989780 = _989782)], (30433 ^ _781013) ^ [_1349825, _1349827, _1349829, _1349831, _1349833] : [class_Orderings_Olinorder(_1349825), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349825, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1349825, _1349827, _1349829)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1349825, _1349831, _1349833)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1349825, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349825), _1349827), _1349831), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349825), _1349829), _1349833)))], (48083 ^ _781013) ^ [_1752653, _1752655, _1752657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1752653, _1752653), tc_HOL_Obool)), _1752655), _1752657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1752653, _1752653), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1752653, _1752653, _1752653), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1752653, _1752653), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1752653, _1752655)), _1752657)), _1752655)), _1752657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1752653, _1752653), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1752653, _1752655)), _1752657)))], (50501 ^ _781013) ^ [_1807866, _1807868, _1807870, _1807872] : [class_Rings_Olinordered__semidom(_1807866), 50507 ^ _781013 : [(50510 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1807866), c_Groups_Ozero__class_Ozero(_1807866)), hAPP(_1807872, 50506 ^ [_1807866, _1807868, _1807870, _1807872])))], (50508 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1807868), 50506 ^ [_1807866, _1807868, _1807870, _1807872]), _1807870)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1807866), c_Groups_Ozero__class_Ozero(_1807866)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1807868, _1807866), _1807872), _1807870))))], (36619 ^ _781013) ^ [_1479823, _1479825, _1479827, _1479829, _1479831, _1479833, _1479835, _1479837] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1479823, _1479825, _1479827), _1479829), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1479831, _1479833, tc_prod(_1479823, _1479825)), _1479835), _1479837)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1479831, _1479833, _1479827), hAPP(hAPP(c_COMBB(tc_fun(_1479833, tc_prod(_1479823, _1479825)), tc_fun(_1479833, _1479827), _1479831), hAPP(c_COMBB(tc_prod(_1479823, _1479825), _1479827, _1479833), hAPP(c_Product__Type_Oprod_Oprod__case(_1479823, _1479825, _1479827), _1479829))), _1479835)), _1479837))], (23134 ^ _781013) ^ [_1213778, _1213780] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1213778)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1213780)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213778), _1213780)))], (27085 ^ _781013) ^ [_1285281, _1285283, _1285285, _1285287, _1285289, _1285291, _1285293, _1285295] : [class_Groups_Ocomm__monoid__mult(_1285281), c_Fun_Oinj__on(_1285283, _1285285, _1285287, _1285289), _1285291 = hAPP(c_Set_Oimage(_1285283, _1285285, _1285287), _1285289), 27099 ^ _781013 : [(27102 ^ _781013) ^ [] : [hAPP(_1285293, 27098 ^ [_1285281, _1285283, _1285285, _1285287, _1285289, _1285291, _1285293, _1285295]) = hAPP(hAPP(c_Fun_Ocomp(_1285285, _1285281, _1285283, _1285295), _1285287), 27098 ^ [_1285281, _1285283, _1285285, _1285287, _1285289, _1285291, _1285293, _1285295])], (27100 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1285283), 27098 ^ [_1285281, _1285283, _1285285, _1285287, _1285289, _1285291, _1285293, _1285295]), _1285289)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1285285, _1285281), _1285295), _1285291) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1285283, _1285281), _1285293), _1285289))], (31817 ^ _781013) ^ [_1382705, _1382707, _1382709, _1382711, _1382713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382705, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382707, tc_fun(_1382705, tc_HOL_Obool)), _1382709), _1382711)), _1382713)), 31820 ^ _781013 : [(31821 ^ _781013) ^ [_1382838] : [hBOOL(hAPP(hAPP(c_member(_1382707), _1382838), _1382709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382705, tc_HOL_Obool)), hAPP(_1382711, _1382838)), _1382713)))]]], (43005 ^ _781013) ^ [_1635359, _1635361, _1635363, _1635365] : [43007 ^ _781013 : [(43010 ^ _781013) ^ [] : [hAPP(_1635365, 43006 ^ [_1635359, _1635361, _1635363, _1635365]) = c_Orderings_Otop__class_Otop(tc_fun(_1635361, tc_HOL_Obool))], (43008 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1635359), 43006 ^ [_1635359, _1635361, _1635363, _1635365]), _1635363)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635359, tc_fun(_1635361, tc_HOL_Obool)), _1635363), _1635365) = c_Orderings_Otop__class_Otop(tc_fun(_1635361, tc_HOL_Obool)))], (8981 ^ _781013) ^ [_938182, _938184, _938186, _938188, _938190, _938192] : [c_Finite__Set_Ofolding(_938182, _938184, _938186, _938188), hBOOL(hAPP(c_Finite__Set_Ofinite(_938182), _938190)), -(hAPP(_938188, hAPP(hAPP(c_Set_Oinsert(_938182), _938192), _938190)) = hAPP(c_Fun_Ocomp(_938184, _938184, _938184, hAPP(_938188, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938182, tc_HOL_Obool)), _938190), hAPP(hAPP(c_Set_Oinsert(_938182), _938192), c_Orderings_Obot__class_Obot(tc_fun(_938182, tc_HOL_Obool)))))), hAPP(_938186, _938192)))], (9503 ^ _781013) ^ [_949502, _949504, _949506] : [class_Orderings_Olinorder(_949502), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949502), _949504), _949506))), -(_949504 = _949506), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949502), _949506), _949504)))], (44024 ^ _781013) ^ [_1657508, _1657510, _1657512, _1657514] : [class_Groups_Ocomm__monoid__add(_1657508), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1657508), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1657508), _1657510), c_List_Oupt(_1657512, _1657514))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1657508), _1657510), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1657512, _1657514))))], (27988 ^ _781013) ^ [_1303637, _1303639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303637), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 27991 ^ _781013 : [(27994 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303637), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1303639, _1303637))))], (27992 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1303639, _1303637)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (40928 ^ _781013) ^ [_1586782] : [-(hAPP(c_Set_Oimage(_1586782, _1586782, c_Fun_Oid(_1586782)), c_Orderings_Otop__class_Otop(tc_fun(_1586782, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1586782, tc_HOL_Obool)))], (26089 ^ _781013) ^ [_1266297, _1266299] : [26097 ^ _781013 : [(26100 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1266299, 26096 ^ [_1266297, _1266299])))], (26098 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26096 ^ [_1266297, _1266299]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1266297))))]], 26090 ^ _781013 : [(26091 ^ _781013) ^ [_1266366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1266366), _1266297)), hBOOL(hAPP(_1266299, _1266366))]]], (42995 ^ _781013) ^ [_1635130, _1635132, _1635134, _1635136] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635130, tc_fun(_1635132, tc_HOL_Obool)), _1635134), _1635136) = c_Orderings_Otop__class_Otop(tc_fun(_1635132, tc_HOL_Obool)), 42998 ^ _781013 : [(42999 ^ _781013) ^ [_1635246] : [hBOOL(hAPP(hAPP(c_member(_1635130), _1635246), _1635134)), -(hAPP(_1635136, _1635246) = c_Orderings_Otop__class_Otop(tc_fun(_1635132, tc_HOL_Obool)))]]], (6760 ^ _781013) ^ [_892354, _892356, _892358, _892360, _892362] : [c_Finite__Set_Ofolding__one__idem(_892354, _892356, _892358), hBOOL(hAPP(c_Finite__Set_Ofinite(_892354), _892360)), -(_892362 = c_Orderings_Obot__class_Obot(tc_fun(_892354, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892354, tc_HOL_Obool)), _892362), _892360)), -(hAPP(hAPP(_892356, hAPP(_892358, _892362)), hAPP(_892358, _892360)) = hAPP(_892358, _892360))], (49071 ^ _781013) ^ [_1776085, _1776087, _1776089] : [c_Relation_Ototal__on(_1776085, _1776087, _1776089), -(c_Relation_Ototal__on(_1776085, _1776087, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1776085, _1776085), tc_HOL_Obool)), _1776089), c_Relation_OId(_1776085))))], (30481 ^ _781013) ^ [_1350736, _1350738, _1350740] : [class_Orderings_Olinorder(_1350736), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350736), _1350738)), -(_1350740 = c_Orderings_Obot__class_Obot(tc_fun(_1350736, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350736, tc_HOL_Obool)), _1350740), _1350738)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350736), c_Big__Operators_Olinorder__class_OMax(_1350736, _1350740)), c_Big__Operators_Olinorder__class_OMax(_1350736, _1350738)) = c_Big__Operators_Olinorder__class_OMax(_1350736, _1350738))], (39273 ^ _781013) ^ [_1539780, _1539782, _1539784, _1539786, _1539788, _1539790] : [-(_1539780 = _1539782), -(hAPP(hAPP(c_List_Olist__update(_1539784, hAPP(hAPP(c_List_Olist__update(_1539784, _1539786), _1539780), _1539788)), _1539782), _1539790) = hAPP(hAPP(c_List_Olist__update(_1539784, hAPP(hAPP(c_List_Olist__update(_1539784, _1539786), _1539782), _1539790)), _1539780), _1539788))], (13046 ^ _781013) ^ [_1018245, _1018247, _1018249, _1018251] : [c_Fun_Oinj__on(_1018245, _1018247, _1018249, c_Orderings_Otop__class_Otop(tc_fun(_1018245, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1018245, _1018247, c_Orderings_Otop__class_Otop(tc_fun(_1018245, tc_HOL_Obool)), _1018249), hAPP(_1018249, _1018251)) = _1018251)], (15087 ^ _781013) ^ [_1059985, _1059987, _1059989] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1059985), hAPP(c_Set_OCollect(_1059985), hAPP(hAPP(c_COMBS(_1059985, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1059985), c_fdisj), _1059987)), _1059989)))), 15090 ^ _781013 : [(15093 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1059985), hAPP(c_Set_OCollect(_1059985), _1059989))))], (15091 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1059985), hAPP(c_Set_OCollect(_1059985), _1059987))))]]], (12564 ^ _781013) ^ [_1007939, _1007941, _1007943, _1007945, _1007947] : [c_Fun_Oinj__on(_1007939, _1007941, _1007943, hAPP(hAPP(c_Set_Oinsert(_1007939), _1007945), _1007947)), 12567 ^ _781013 : [(12570 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1007941), hAPP(_1007943, _1007945)), hAPP(c_Set_Oimage(_1007939, _1007941, _1007943), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007939, tc_HOL_Obool)), _1007947), hAPP(hAPP(c_Set_Oinsert(_1007939), _1007945), c_Orderings_Obot__class_Obot(tc_fun(_1007939, tc_HOL_Obool)))))))], (12568 ^ _781013) ^ [] : [-(c_Fun_Oinj__on(_1007939, _1007941, _1007943, _1007947))]]], (28730 ^ _781013) ^ [_1317197, _1317199, _1317201, _1317203] : [class_Orderings_Olinorder(_1317197), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317197), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317197), _1317199), _1317201)), _1317203) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317197), _1317199), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317197), _1317201), _1317203)))], (7929 ^ _781013) ^ [_914972, _914974, _914976, _914978] : [c_Hoare__Mirabelle_Ohoare__derivs(_914972, _914974, _914976), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_914972), tc_HOL_Obool)), _914978), _914976)), -(c_Hoare__Mirabelle_Ohoare__derivs(_914972, _914974, _914978))], (41436 ^ _781013) ^ [_1597712, _1597714] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1597712), _1597714))), -(c_List_Oupto(_1597712, _1597714) = c_List_Olist_ONil(tc_Int_Oint))], (40944 ^ _781013) ^ [_1587118, _1587120, _1587122] : [-(hAPP(c_Fun_Ocomp(_1587118, _1587118, _1587120, c_Fun_Oid(_1587118)), _1587122) = _1587122)], (46387 ^ _781013) ^ [_1710122, _1710124] : [-(c_List_Oinsert(_1710122, _1710124, c_List_Olist_ONil(_1710122)) = hAPP(hAPP(c_List_Olist_OCons(_1710122), _1710124), c_List_Olist_ONil(_1710122)))], (32588 ^ _781013) ^ [_1399566, _1399568] : [class_Int_Onumber__ring(_1399566), -(hBOOL(hAPP(hAPP(c_member(_1399566), hAPP(c_Int_Onumber__class_Onumber__of(_1399566), _1399568)), c_Int_Oring__1__class_OInts(_1399566))))], (44360 ^ _781013) ^ [_1665005, _1665007] : [c_List_Olist_ONil(_1665005) = c_List_Oconcat(_1665005, _1665007), 44363 ^ _781013 : [(44364 ^ _781013) ^ [_1665096] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665005)), _1665096), hAPP(c_List_Oset(tc_List_Olist(_1665005)), _1665007))), -(_1665096 = c_List_Olist_ONil(_1665005))]]], (41484 ^ _781013) ^ [_1598931, _1598933] : [-(c_List_Oset__Cons(_1598931, _1598933, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1598931)), c_List_Olist_ONil(_1598931)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1598931), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1598931, tc_List_Olist(_1598931), hAPP(hAPP(c_COMBC(_1598931, tc_List_Olist(_1598931), tc_List_Olist(_1598931)), c_List_Olist_OCons(_1598931)), c_List_Olist_ONil(_1598931))), _1598933))], (19026 ^ _781013) ^ [_1136983, _1136985, _1136987, _1136989] : [hBOOL(hAPP(hAPP(c_member(_1136983), _1136985), c_SetInterval_Oord_OlessThan(_1136983, _1136987, _1136989))), -(hBOOL(hAPP(hAPP(_1136987, _1136985), _1136989)))], (43215 ^ _781013) ^ [_1641055, _1641057, _1641059, _1641061] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641055)), _1641057))), c_List_Ofoldr(tc_List_Olist(_1641059), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1641059)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1641059))), _1641061, 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(_1641055)), _1641057)), c_List_Ofoldr(tc_List_Olist(_1641059), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1641059)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1641059), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1641059)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1641059)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1641059), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1641059)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1641059), tc_List_Olist(_1641059), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1641059)))), _1641061), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (20516 ^ _781013) ^ [_1164264] : [-(hAPP(c_Nat_OSuc, _1164264) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1164264), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (15685 ^ _781013) ^ [_1071195, _1071197] : [class_Groups_Olinordered__ab__group__add(_1071195), 15688 ^ _781013 : [(15695 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071195), _1071197), c_Groups_Ozero__class_Ozero(_1071195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071195), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071195), _1071197), _1071197)), c_Groups_Ozero__class_Ozero(_1071195))))], (15689 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071195), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071195), _1071197), _1071197)), c_Groups_Ozero__class_Ozero(_1071195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071195), _1071197), c_Groups_Ozero__class_Ozero(_1071195))))]]], (44312 ^ _781013) ^ [_1664008, _1664010, _1664012] : [hAPP(c_List_Orev(_1664008), _1664010) = _1664012, -(_1664010 = hAPP(c_List_Orev(_1664008), _1664012))], (51256 ^ _781013) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (3178 ^ _781013) ^ [_828765, _828767, _828769, _828771, _828773, _828775, _828777, _828779] : [-(c_List_Olist_Olist__case(_828779, _828775, _828771, _828767) = c_List_Olist_Olist__case(_828777, _828773, _828769, _828765)), _828779 = _828777, _828775 = _828773, _828771 = _828769, _828767 = _828765], (39540 ^ _781013) ^ [_1545741, _1545743] : [39541 ^ _781013 : [(39542 ^ _781013) ^ [_1545787] : [hBOOL(hAPP(_1545741, _1545787))]], -(hBOOL(hAPP(_1545741, c_Hilbert__Choice_OEps(_1545743, _1545741))))], (19995 ^ _781013) ^ [_1155438] : [hAPP(c_Nat_OSuc, _1155438) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50774 ^ _781013) ^ [_1812919, _1812921, _1812923, _1812925, _1812927] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1812919, _1812921, _1812923) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1812919, _1812925, _1812927)), _1812921 = _1812925, _1812923 = _1812927], (2616 ^ _781013) ^ [_819836, _819838, _819840, _819842] : [-(c_Set_Othe__elem(_819842, _819838) = c_Set_Othe__elem(_819840, _819836)), _819842 = _819840, _819838 = _819836], (47601 ^ _781013) ^ [_1741378, _1741380, _1741382, _1741384, _1741386] : [hAPP(hAPP(c_List_Olist_OCons(_1741378), _1741380), _1741382) = hAPP(c_List_Ofilter(_1741378, _1741384), _1741386), 47606 ^ _781013 : [(47615 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1741384, _1741380)))], (47617 ^ _781013) ^ [] : [-(_1741382 = hAPP(c_List_Ofilter(_1741378, _1741384), 47605 ^ [_1741378, _1741380, _1741382, _1741384, _1741386]))], (47609 ^ _781013) ^ [_1741692] : [hBOOL(hAPP(hAPP(c_member(_1741378), _1741692), hAPP(c_List_Oset(_1741378), 47604 ^ [_1741378, _1741380, _1741382, _1741384, _1741386]))), hBOOL(hAPP(_1741384, _1741692))], (47607 ^ _781013) ^ [] : [-(_1741386 = hAPP(hAPP(c_List_Oappend(_1741378), 47604 ^ [_1741378, _1741380, _1741382, _1741384, _1741386]), hAPP(hAPP(c_List_Olist_OCons(_1741378), _1741380), 47605 ^ [_1741378, _1741380, _1741382, _1741384, _1741386])))]]], (39773 ^ _781013) ^ [_1551894, _1551896, _1551898, _1551900] : [_1551894 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551896)), _1551898)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1551896, hAPP(hAPP(c_List_Olist__update(_1551896, _1551898), _1551894), _1551900)) = c_List_Obutlast(_1551896, _1551898))], (40613 ^ _781013) ^ [_1576468, _1576470, _1576472, _1576474, _1576476] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1576468, _1576470), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1576468, tc_HOL_Obool)), _1576472), _1576474)), _1576476) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1576468, _1576470), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1576468, _1576470), _1576472), _1576476)), hAPP(hAPP(c_Product__Type_OSigma(_1576468, _1576470), _1576474), _1576476)))], (16616 ^ _781013) ^ [_1089049, _1089051, _1089053, _1089055] : [class_Groups_Oordered__comm__monoid__add(_1089049), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089049), c_Groups_Ozero__class_Ozero(_1089049)), _1089051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089049), _1089053), _1089055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089049), _1089053), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089049), _1089051), _1089055))))], (44967 ^ _781013) ^ [_1679105, _1679107, _1679109] : [-(c_Enum_On__lists(_1679105, hAPP(c_Nat_OSuc, _1679107), _1679109) = c_List_Oconcat(tc_List_Olist(_1679105), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1679105), tc_List_Olist(tc_List_Olist(_1679105))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1679105), tc_List_Olist(_1679105), tc_List_Olist(tc_List_Olist(_1679105))), hAPP(hAPP(c_COMBB(tc_fun(_1679105, tc_List_Olist(_1679105)), tc_fun(tc_List_Olist(_1679105), tc_List_Olist(tc_List_Olist(_1679105))), tc_List_Olist(_1679105)), c_List_Omap(_1679105, tc_List_Olist(_1679105))), hAPP(c_COMBC(_1679105, tc_List_Olist(_1679105), tc_List_Olist(_1679105)), c_List_Olist_OCons(_1679105)))), _1679109)), c_Enum_On__lists(_1679105, _1679107, _1679109))))], (21662 ^ _781013) ^ [_1187825, _1187827] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187825)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187827)), _1187825 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1187827 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45703 ^ _781013) ^ [_1694620, _1694622, _1694624, _1694626] : [-(hAPP(c_Set_Ovimage(_1694620, _1694622, _1694624), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1694622, tc_HOL_Obool), _1694626)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1694622, tc_HOL_Obool), tc_fun(_1694620, tc_HOL_Obool)), _1694626), c_Set_Ovimage(_1694620, _1694622, _1694624)))], (23647 ^ _781013) ^ [_1223145, _1223147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223147)), 23654 ^ _781013 : [(23661 ^ _781013) ^ [] : [_1223145 = _1223147, -(hAPP(c_Int_Onat, _1223145) = hAPP(c_Int_Onat, _1223147))], (23655 ^ _781013) ^ [] : [hAPP(c_Int_Onat, _1223145) = hAPP(c_Int_Onat, _1223147), -(_1223145 = _1223147)]]], (37694 ^ _781013) ^ [_1501076, _1501078, _1501080, _1501082, _1501084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1501076, _1501078)), hAPP(_1501076, _1501080))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1501082, _1501082)), hAPP(hAPP(c_Product__Type_OPair(_1501082, _1501082), _1501078), _1501080)), _1501084)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1501082, _1501082)), hAPP(hAPP(c_Product__Type_OPair(_1501082, _1501082), _1501078), _1501080)), c_Wellfounded_Omlex__prod(_1501082, _1501076, _1501084))))], (31118 ^ _781013) ^ [_1363879, _1363881, _1363883, _1363885, _1363887, _1363889] : [hBOOL(hAPP(_1363879, _1363881)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1363883), _1363881), _1363885), _1363887)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1363879, _1363883)), _1363887), _1363885), _1363889)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1363879, _1363883)), _1363881), _1363885), _1363889)))], (31838 ^ _781013) ^ [_1383303, _1383305, _1383307, _1383309, _1383311, _1383313] : [-(hAPP(c_Set_Oimage(_1383303, _1383305, _1383307), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383309, tc_fun(_1383303, tc_HOL_Obool)), _1383311), _1383313)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383309, tc_fun(_1383305, tc_HOL_Obool)), _1383311), hAPP(hAPP(c_COMBB(tc_fun(_1383303, tc_HOL_Obool), tc_fun(_1383305, tc_HOL_Obool), _1383309), c_Set_Oimage(_1383303, _1383305, _1383307)), _1383313)))], (46488 ^ _781013) ^ [_1712985, _1712987, _1712989] : [hBOOL(hAPP(hAPP(c_member(_1712985), _1712987), c_Wellfounded_Oacc(_1712985, _1712989))), 46491 ^ _781013 : [(46492 ^ _781013) ^ [_1713099] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1712985, _1712985)), hAPP(hAPP(c_Product__Type_OPair(_1712985, _1712985), _1713099), _1712987)), _1712989)), -(hBOOL(hAPP(hAPP(c_member(_1712985), _1713099), c_Wellfounded_Oacc(_1712985, _1712989))))]]], (50672 ^ _781013) ^ [_1810849, _1810851] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1810849), _1810851)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1810849), _1810851) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44681 ^ _781013) ^ [_1673180, _1673182, _1673184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673180)), c_List_OtakeWhile(_1673180, _1673182, _1673184))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673180)), _1673184))), hBOOL(hAPP(_1673182, hAPP(hAPP(c_List_Onth(_1673180), _1673184), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673180)), c_List_OtakeWhile(_1673180, _1673182, _1673184)))))], (8523 ^ _781013) ^ [_928538, _928540, _928542, _928544, _928546] : [hBOOL(hAPP(hAPP(c_member(_928538), _928540), _928542)), -(hAPP(c_Set_Oimage(_928538, _928544, hAPP(c_COMBK(_928544, _928538), _928546)), _928542) = hAPP(hAPP(c_Set_Oinsert(_928544), _928546), c_Orderings_Obot__class_Obot(tc_fun(_928544, tc_HOL_Obool))))], (568 ^ _781013) ^ [_789701, _789703, _789705, _789707] : [-(c_Wellfounded_OwfP(_789705, _789701)), c_Wellfounded_OwfP(_789707, _789703), _789707 = _789705, _789703 = _789701], (42909 ^ _781013) ^ [_1632562, _1632564, _1632566, _1632568] : [_1632562 = c_Orderings_Obot__class_Obot(tc_fun(_1632564, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632564, tc_fun(_1632566, tc_HOL_Obool)), _1632562), hAPP(c_COMBK(tc_fun(_1632566, tc_HOL_Obool), _1632564), _1632568)) = c_Orderings_Otop__class_Otop(tc_fun(_1632566, tc_HOL_Obool)))], (47309 ^ _781013) ^ [_1734722, _1734724, _1734726] : [c_Wellfounded_OwfP(_1734722, _1734724), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1734722, _1734724), _1734726)))], (2176 ^ _781013) ^ [_813020, _813022, _813024, _813026, _813028, _813030] : [-(c_SetInterval_Oord_OgreaterThan(_813030, _813026, _813022) = c_SetInterval_Oord_OgreaterThan(_813028, _813024, _813020)), _813030 = _813028, _813026 = _813024, _813022 = _813020], (18502 ^ _781013) ^ [_1125325, _1125327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125327), _1125325)), -(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), _1125325), _1125327))))], (5174 ^ _781013) ^ [_859951, _859953] : [_859953 = _859951, -(c_Lattices_Osemilattice__inf__class_Oinf(_859953) = c_Lattices_Osemilattice__inf__class_Oinf(_859951))], (10035 ^ _781013) ^ [_958573, _958575, _958577] : [class_Lattices_Olattice(_958573), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958573), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_958573), _958575), _958577)), _958575)))], (49920 ^ _781013) ^ [_1795483, _1795485, _1795487, _1795489, _1795491, _1795493] : [c_Finite__Set_Ofun__left__comm(_1795483, _1795485, _1795487), -(hAPP(hAPP(_1795487, _1795489), hAPP(hAPP(_1795487, _1795491), _1795493)) = hAPP(hAPP(_1795487, _1795491), hAPP(hAPP(_1795487, _1795489), _1795493)))], (48469 ^ _781013) ^ [_1761036, _1761038] : [_1761036 = _1761038, -(hAPP(c_Code__Numeral_Onat__of, _1761036) = hAPP(c_Code__Numeral_Onat__of, _1761038))], (27647 ^ _781013) ^ [_1296989, _1296991, _1296993, _1296995] : [class_Divides_Osemiring__div(_1296989), -(c_Divides_Odiv__class_Omod(_1296989, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296989), _1296991), _1296993), _1296995) = c_Divides_Odiv__class_Omod(_1296989, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296989), c_Divides_Odiv__class_Omod(_1296989, _1296991, _1296995)), c_Divides_Odiv__class_Omod(_1296989, _1296993, _1296995)), _1296995))], (33546 ^ _781013) ^ [_1417478, _1417480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417478), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417480)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417478)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417480))], (33592 ^ _781013) ^ [_1418171, _1418173] : [class_Int_Onumber__ring(_1418171), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1418171), _1418173), hAPP(c_Int_Onumber__class_Onumber__of(_1418171), c_Int_OPls)) = _1418173)], (39267 ^ _781013) ^ [_1539527, _1539529, _1539531, _1539533, _1539535, _1539537] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1539527, _1539529), hAPP(hAPP(c_List_Ozip(_1539527, _1539529), _1539531), _1539533)), _1539535), _1539537) = hAPP(hAPP(c_List_Ozip(_1539527, _1539529), hAPP(hAPP(c_List_Olist__update(_1539527, _1539531), _1539535), hAPP(c_Product__Type_Ofst(_1539527, _1539529), _1539537))), hAPP(hAPP(c_List_Olist__update(_1539529, _1539533), _1539535), hAPP(c_Product__Type_Osnd(_1539527, _1539529), _1539537))))], (18556 ^ _781013) ^ [_1126275, _1126277, _1126279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126275), _1126277)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126275), _1126279)), 18563 ^ _781013 : [(18570 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126277), _1126279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1126277), _1126275)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1126279), _1126275))))], (18564 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1126277), _1126275)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1126279), _1126275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126277), _1126279)))]]], (9493 ^ _781013) ^ [_949309, _949311, _949313] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949309, tc_HOL_Obool)), _949311), _949313) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949309, tc_HOL_Obool)), _949311), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_949309, tc_HOL_Obool)), _949313)))], (2446 ^ _781013) ^ [_817247, _817249, _817251, _817253] : [-(c_Com_Ocom_OWhile(_817253, _817249) = c_Com_Ocom_OWhile(_817251, _817247)), _817253 = _817251, _817249 = _817247], (28066 ^ _781013) ^ [_1304923, _1304925, _1304927] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1304923), _1304925)), _1304927) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1304923), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1304925), _1304927))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1304923), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304925, _1304927))), _1304927)))], (9825 ^ _781013) ^ [_954377, _954379] : [class_Lattices_Oboolean__algebra(_954377), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954377), _954379), hAPP(c_Groups_Ouminus__class_Ouminus(_954377), _954379)) = c_Orderings_Obot__class_Obot(_954377))], (2000 ^ _781013) ^ [_810058, _810060, _810062, _810064, _810066, _810068] : [-(c_Finite__Set_Ofold1Set(_810068, _810064, _810060) = c_Finite__Set_Ofold1Set(_810066, _810062, _810058)), _810068 = _810066, _810064 = _810062, _810060 = _810058], (32632 ^ _781013) ^ [_1400279, _1400281, _1400283, _1400285] : [class_Fields_Ofield__inverse__zero(_1400279), class_Int_Onumber(_1400279), 32639 ^ _781013 : [(32640 ^ _781013) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1400279), _1400281), _1400283) = hAPP(c_Int_Onumber__class_Onumber__of(_1400279), _1400285), 32643 ^ _781013 : [(32650 ^ _781013) ^ [] : [_1400283 = c_Groups_Ozero__class_Ozero(_1400279), -(hAPP(c_Int_Onumber__class_Onumber__of(_1400279), _1400285) = c_Groups_Ozero__class_Ozero(_1400279))], (32644 ^ _781013) ^ [] : [-(_1400283 = c_Groups_Ozero__class_Ozero(_1400279)), -(_1400281 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400279), hAPP(c_Int_Onumber__class_Onumber__of(_1400279), _1400285)), _1400283))]]], (32656 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1400279), _1400281), _1400283) = hAPP(c_Int_Onumber__class_Onumber__of(_1400279), _1400285)), 32659 ^ _781013 : [(32662 ^ _781013) ^ [] : [_1400281 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400279), hAPP(c_Int_Onumber__class_Onumber__of(_1400279), _1400285)), _1400283)], (32660 ^ _781013) ^ [] : [_1400283 = c_Groups_Ozero__class_Ozero(_1400279)]], 32663 ^ _781013 : [(32666 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1400279), _1400285) = c_Groups_Ozero__class_Ozero(_1400279)], (32664 ^ _781013) ^ [] : [-(_1400283 = c_Groups_Ozero__class_Ozero(_1400279))]]]]], (48423 ^ _781013) ^ [_1760059, _1760061, _1760063] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1760059, _1760059), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1760059, _1760059), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1760059, _1760061)), c_Transitive__Closure_Ortrancl(_1760059, _1760063))), c_Transitive__Closure_Ortrancl(_1760059, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1760059, _1760059), tc_HOL_Obool)), _1760061), _1760063)))))], (48866 ^ _781013) ^ [_1770815, _1770817, _1770819] : [c_Relation_Orefl__on(_1770815, _1770817, _1770819), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1770815, _1770815), tc_HOL_Obool)), _1770819), hAPP(hAPP(c_Relation_Orel__comp(_1770815, _1770815, _1770815), hAPP(c_Relation_Oconverse(_1770815, _1770815), _1770819)), _1770819))))], (38620 ^ _781013) ^ [_1523735] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1523735)), -(c_List_Onat__list(_1523735))], (6914 ^ _781013) ^ [_895298, _895300, _895302, _895304, _895306, _895308] : [_895298 = _895300, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895302, _895304), _895306), _895300), _895308), _895298) = _895308)], (43217 ^ _781013) ^ [_1641224, _1641226, _1641228, _1641230] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1641224)), _1641226), c_List_Olists(_1641224, _1641228))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1641224)), _1641226), c_List_Olists(_1641224, _1641230))), -(hBOOL(hAPP(c_List_Olistsp(_1641224, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1641224, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1641224, tc_fun(_1641224, tc_HOL_Obool), tc_HOL_Obool), c_member(_1641224)), _1641228)), hAPP(hAPP(c_COMBC(_1641224, tc_fun(_1641224, tc_HOL_Obool), tc_HOL_Obool), c_member(_1641224)), _1641230))), _1641226)))], (12946 ^ _781013) ^ [_1016201, _1016203, _1016205, _1016207] : [c_Finite__Set_Ofolding__one(_1016201, _1016203, _1016205), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016201), _1016207)), -(hAPP(_1016205, _1016207) = hAPP(c_Finite__Set_Ofold1(_1016201, _1016203), _1016207))], (1114 ^ _781013) ^ [_797680, _797682] : [-(class_Rings_Oordered__ring__abs(_797680)), _797682 = _797680, class_Rings_Oordered__ring__abs(_797682)], (13517 ^ _781013) ^ [_1028312, _1028314, _1028316, _1028318] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1028312), _1028314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028312, tc_HOL_Obool)), _1028314), _1028316)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028312, tc_Nat_Onat), _1028318), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1028312, tc_HOL_Obool)), _1028316), _1028314)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028312, tc_Nat_Onat), _1028318), _1028316)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028312, tc_Nat_Onat), _1028318), _1028314)))], (29141 ^ _781013) ^ [_1324474, _1324476] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1324474), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1324476)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1324474, _1324476)))], (5763 ^ _781013) ^ [_872447, _872449, _872451, _872453, _872455] : [c_Hoare__Mirabelle_Ohoare__derivs(_872447, _872449, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872447)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872447), _872451), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _872453))), _872455)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872447), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_872447, _872449, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872447)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872447), _872451), hAPP(c_Com_Ocom_OBODY, _872453)), _872455)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872447), tc_HOL_Obool)))))], (27809 ^ _781013) ^ [_1300370, _1300372] : [class_Rings_Olinordered__idom(_1300370), 27812 ^ _781013 : [(27819 ^ _781013) ^ [] : [_1300372 = c_Groups_Ozero__class_Ozero(_1300370), -(c_Groups_Osgn__class_Osgn(_1300370, _1300372) = c_Groups_Ozero__class_Ozero(_1300370))], (27813 ^ _781013) ^ [] : [c_Groups_Osgn__class_Osgn(_1300370, _1300372) = c_Groups_Ozero__class_Ozero(_1300370), -(_1300372 = c_Groups_Ozero__class_Ozero(_1300370))]]], (37214 ^ _781013) ^ [_1491150, _1491152] : [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), _1491150), _1491152))), 37217 ^ _781013 : [(37224 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1491152), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 37227 ^ _781013 : [(37236 ^ _781013) ^ [] : [-(c_Nitpick_Onorm__frac(_1491150, _1491152) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1491150), _1491152)), 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), _1491150))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1491152)))), -(_1491150 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1491152 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37228 ^ _781013) ^ [] : [37229 ^ _781013 : [(37232 ^ _781013) ^ [] : [_1491152 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (37230 ^ _781013) ^ [] : [_1491150 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1491150, _1491152) = 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)))]]], (37218 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1491152), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1491150, _1491152) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491150), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491152)))]]], (42390 ^ _781013) ^ [_1620594, _1620596, _1620598] : [hBOOL(hAPP(c_List_Odistinct(_1620594), hAPP(c_List_Orotate(_1620594, _1620596), _1620598))), -(hBOOL(hAPP(c_List_Odistinct(_1620594), _1620598)))], (9671 ^ _781013) ^ [_952108, _952110, _952112] : [class_Orderings_Opreorder(_952108), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952108), _952110), _952112)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952108), _952112), _952110))], (10887 ^ _781013) ^ [_973768, _973770, _973772, _973774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_973768, tc_HOL_Obool)), _973770), _973772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973768, tc_HOL_Obool)), _973772), _973774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_973768, tc_HOL_Obool)), _973770), _973774)))], (3292 ^ _781013) ^ [_830594, _830596] : [_830596 = _830594, -(c_List_Ohd(_830596) = c_List_Ohd(_830594))], (34977 ^ _781013) ^ [_1443346] : [class_Int_Onumber__ring(_1443346), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1443346), c_Groups_Oone__class_Oone(_1443346)), c_Groups_Oone__class_Oone(_1443346)) = hAPP(c_Int_Onumber__class_Onumber__of(_1443346), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (50541 ^ _781013) ^ [_1808595, _1808597] : [-(c_FunDef_Ois__measure(_1808595, _1808597))], (12918 ^ _781013) ^ [_1015638, _1015640, _1015642] : [-(hAPP(c_Finite__Set_Ofold1(_1015638, _1015640), hAPP(hAPP(c_Set_Oinsert(_1015638), _1015642), c_Orderings_Obot__class_Obot(tc_fun(_1015638, tc_HOL_Obool)))) = _1015642)], (16311 ^ _781013) ^ [_1082436, _1082438, _1082440, _1082442] : [-(hBOOL(hAPP(hAPP(c_member(_1082436), _1082438), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1082436, tc_HOL_Obool)), _1082440), hAPP(c_Set_OCollect(_1082436), _1082442))))), hBOOL(hAPP(hAPP(c_member(_1082436), _1082438), _1082440)), hBOOL(hAPP(_1082442, _1082438))], (36788 ^ _781013) ^ [_1483148] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1483148) = 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)))], (18992 ^ _781013) ^ [_1136279, _1136281, _1136283, _1136285, _1136287, _1136289] : [-(hBOOL(hAPP(hAPP(c_member(_1136279), _1136281), c_SetInterval_Oord_OatLeastLessThan(_1136279, _1136283, _1136285, _1136287, _1136289)))), hBOOL(hAPP(hAPP(_1136283, _1136287), _1136281)), hBOOL(hAPP(hAPP(_1136285, _1136281), _1136289))], (26753 ^ _781013) ^ [_1278885, _1278887] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1278885, _1278887)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1278887), _1278885)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (14249 ^ _781013) ^ [_1044078, _1044080, _1044082, _1044084, _1044086, _1044088] : [class_Rings_Oordered__ring(_1044078), 14252 ^ _781013 : [(14259 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044078), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044078), _1044080), _1044086)), _1044082)), _1044084)), _1044088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044078), _1044080), _1044082)), _1044084)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044078), _1044086), _1044082)), _1044088))))], (14253 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044078), _1044080), _1044082)), _1044084)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044078), _1044086), _1044082)), _1044088))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044078), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044078), _1044080), _1044086)), _1044082)), _1044084)), _1044088)))]]], (51358 ^ _781013) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (30799 ^ _781013) ^ [_1357478, _1357480] : [_1357478 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1357480, _1357478) = _1357480)], (31854 ^ _781013) ^ [_1384166, _1384168, _1384170, _1384172, _1384174] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384166, tc_fun(_1384168, tc_HOL_Obool)), _1384170), hAPP(hAPP(c_COMBC(_1384166, tc_fun(_1384168, tc_HOL_Obool), tc_fun(_1384168, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1384168, tc_HOL_Obool), tc_fun(tc_fun(_1384168, tc_HOL_Obool), tc_fun(_1384168, tc_HOL_Obool)), _1384166), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384168, tc_HOL_Obool))), _1384172)), _1384174)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384168, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384166, tc_fun(_1384168, tc_HOL_Obool)), _1384170), _1384172)), _1384174))], (6318 ^ _781013) ^ [_883851, _883853, _883855] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_883851), _883855)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_883851), hAPP(hAPP(c_Set_Oinsert(_883851), _883853), _883855))))], (23465 ^ _781013) ^ [_1220072, _1220074] : [class_Rings_Odivision__ring(_1220072), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220072), _1220074), c_Groups_Oone__class_Oone(_1220072)) = _1220074)], (38105 ^ _781013) ^ [_1511589, _1511591, _1511593, _1511595] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1511589, tc_HOL_Obool), tc_fun(_1511589, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1511589, tc_HOL_Obool), tc_fun(_1511589, tc_HOL_Obool)), _1511593), _1511595)), c_Wellfounded_Omax__ext(_1511589, _1511591))), -(c_Wellfounded_Omax__extp(_1511589, hAPP(hAPP(c_COMBC(_1511589, tc_fun(tc_prod(_1511589, _1511589), tc_HOL_Obool), tc_fun(_1511589, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511589, tc_fun(tc_fun(tc_prod(_1511589, _1511589), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511589, _1511589), tc_HOL_Obool), tc_fun(_1511589, tc_HOL_Obool)), _1511589), c_COMBC(_1511589, tc_fun(tc_prod(_1511589, _1511589), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511589, tc_prod(_1511589, _1511589)), tc_fun(_1511589, tc_fun(tc_fun(tc_prod(_1511589, _1511589), tc_HOL_Obool), tc_HOL_Obool)), _1511589), hAPP(c_COMBB(tc_prod(_1511589, _1511589), tc_fun(tc_fun(tc_prod(_1511589, _1511589), tc_HOL_Obool), tc_HOL_Obool), _1511589), c_member(tc_prod(_1511589, _1511589)))), c_Product__Type_OPair(_1511589, _1511589)))), _1511591), _1511593, _1511595))], (40936 ^ _781013) ^ [_1586940, _1586942, _1586944, _1586946, _1586948, _1586950, _1586952] : [hAPP(c_Fun_Ocomp(_1586940, _1586942, _1586944, _1586946), _1586948) = hAPP(c_Fun_Ocomp(_1586942, _1586942, _1586944, c_Fun_Oid(_1586942)), _1586950), -(hAPP(_1586946, hAPP(_1586948, _1586952)) = hAPP(_1586950, _1586952))], (25868 ^ _781013) ^ [_1262099, _1262101, _1262103] : [class_Rings_Oring__1(_1262099), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262099), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1262101), _1262103)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262099), hAPP(c_Int_Oring__1__class_Oof__int(_1262099), _1262101)), hAPP(c_Int_Oring__1__class_Oof__int(_1262099), _1262103)))], (10785 ^ _781013) ^ [_971408, _971410] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971408, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_971408, tc_HOL_Obool))), _971410) = c_Orderings_Obot__class_Obot(tc_fun(_971408, tc_HOL_Obool)))], (19781 ^ _781013) ^ [_1151764, _1151766, _1151768, _1151770, _1151772] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1151764, _1151766, _1151768), _1151770), hAPP(c_Nat_OSuc, _1151772)) = hAPP(hAPP(_1151768, _1151770), hAPP(hAPP(c_Power_Opower_Opower(_1151764, _1151766, _1151768), _1151770), _1151772)))], (51528 ^ _781013) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (29026 ^ _781013) ^ [_1322584, _1322586, _1322588] : [class_Groups_Oordered__ab__group__add__abs(_1322584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322584), hAPP(c_Groups_Oabs__class_Oabs(_1322584), _1322586)), _1322588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322584), hAPP(c_Groups_Ouminus__class_Ouminus(_1322584), _1322586)), _1322588)))], (4690 ^ _781013) ^ [_851985, _851987] : [_851987 = _851985, -(c_List_Oset(_851987) = c_List_Oset(_851985))], (28602 ^ _781013) ^ [_1314587, _1314589, _1314591] : [class_Groups_Oordered__ab__group__add__abs(_1314587), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314587), hAPP(c_Groups_Oabs__class_Oabs(_1314587), _1314589)), _1314591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314587), _1314589), _1314591)))], (29203 ^ _781013) ^ [_1325896, _1325898] : [class_Groups_Oordered__ab__group__add__abs(_1325896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325896), _1325898), c_Groups_Ozero__class_Ozero(_1325896))), -(hAPP(c_Groups_Oabs__class_Oabs(_1325896), _1325898) = hAPP(c_Groups_Ouminus__class_Ouminus(_1325896), _1325898))], (34879 ^ _781013) ^ [_1441371, _1441373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1441371)), c_Int_OBit0(_1441373))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441371), _1441373)))], (23739 ^ _781013) ^ [_1224654, _1224656, _1224658, _1224660, _1224662] : [class_Fields_Ofield__inverse__zero(_1224654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224656), _1224658)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1224656, _1224654), hAPP(hAPP(c_COMBS(_1224656, _1224654, _1224654), hAPP(hAPP(c_COMBB(_1224654, tc_fun(_1224654, _1224654), _1224656), c_Rings_Oinverse__class_Odivide(_1224654)), _1224660)), _1224662)), _1224658) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1224654), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1224656, _1224654), _1224660), _1224658)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1224656, _1224654), _1224662), _1224658)))], (33290 ^ _781013) ^ [_1412983] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1412983)))), -(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), _1412983)) = 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), _1412983))))], (24670 ^ _781013) ^ [_1241106, _1241108, _1241110] : [class_Fields_Olinordered__field(_1241106), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241106), c_Groups_Ozero__class_Ozero(_1241106)), _1241108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241106), _1241110), c_Groups_Ozero__class_Ozero(_1241106))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241106), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241106), _1241108), _1241110)), c_Groups_Ozero__class_Ozero(_1241106))))], (36601 ^ _781013) ^ [_1479399, _1479401, _1479403] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1479399, tc_HOL_Obool), tc_fun(_1479399, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1479399, tc_HOL_Obool), tc_fun(_1479399, tc_HOL_Obool)), _1479401), _1479403)), c_Wellfounded_Ofinite__psubset(_1479399))), 36604 ^ _781013 : [(36607 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1479399), _1479403)))], (36605 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1479399, tc_HOL_Obool)), _1479401), _1479403)))]]], (28658 ^ _781013) ^ [_1315693, _1315695, _1315697] : [class_Groups_Oordered__ab__group__add__abs(_1315693), -(hAPP(c_Groups_Oabs__class_Oabs(_1315693), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1315693), hAPP(c_Groups_Oabs__class_Oabs(_1315693), _1315695)), hAPP(c_Groups_Oabs__class_Oabs(_1315693), _1315697))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1315693), hAPP(c_Groups_Oabs__class_Oabs(_1315693), _1315695)), hAPP(c_Groups_Oabs__class_Oabs(_1315693), _1315697)))], (18079 ^ _781013) ^ [_1117832] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117832), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1117832)], (6280 ^ _781013) ^ [_883174, _883176, _883178, _883180, _883182] : [c_Com_Ocom_OSemi(_883174, _883176) = c_Com_Ocom_OCond(_883178, _883180, _883182)], (21431 ^ _781013) ^ [_1183560, _1183562, _1183564] : [class_Groups_Olinordered__ab__semigroup__add(_1183560), hBOOL(hAPP(c_Finite__Set_Ofinite(_1183560), _1183562)), -(_1183562 = c_Orderings_Obot__class_Obot(tc_fun(_1183560, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183560), _1183564), c_Big__Operators_Olinorder__class_OMax(_1183560, _1183562)) = c_Big__Operators_Olinorder__class_OMax(_1183560, hAPP(c_Set_OCollect(_1183560), hAPP(hAPP(c_COMBB(tc_fun(_1183560, tc_HOL_Obool), tc_HOL_Obool, _1183560), c_HOL_OEx(_1183560)), hAPP(hAPP(c_COMBC(_1183560, tc_fun(_1183560, tc_HOL_Obool), tc_fun(_1183560, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183560, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1183560, tc_HOL_Obool), tc_fun(_1183560, tc_HOL_Obool)), _1183560), c_COMBS(_1183560, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183560, tc_HOL_Obool), tc_fun(_1183560, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1183560), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1183560), c_fconj)), hAPP(hAPP(c_COMBC(_1183560, tc_fun(_1183560, _1183560), tc_fun(_1183560, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183560, tc_HOL_Obool), tc_fun(tc_fun(_1183560, _1183560), tc_fun(_1183560, tc_HOL_Obool)), _1183560), c_COMBB(_1183560, tc_HOL_Obool, _1183560)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1183560), _1183564))))), hAPP(hAPP(c_COMBC(_1183560, tc_fun(_1183560, tc_HOL_Obool), tc_HOL_Obool), c_member(_1183560)), _1183562))))))], (51452 ^ _781013) ^ [_1823099, _1823101] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1823099, _1823101))), class_Lazy__Sequence_Osmall__lazy(_1823099), class_Lazy__Sequence_Osmall__lazy(_1823101)], (46695 ^ _781013) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (19915 ^ _781013) ^ [_1154044, _1154046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154044), _1154046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1154044), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1154046), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (2900 ^ _781013) ^ [_824370, _824372, _824374, _824376, _824378, _824380] : [-(c_List_Olist_Olist__size(_824380, _824376, _824372) = c_List_Olist_Olist__size(_824378, _824374, _824370)), _824380 = _824378, _824376 = _824374, _824372 = _824370], (12236 ^ _781013) ^ [_1001990] : [class_Lattices_Oboolean__algebra(_1001990), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1001990), c_Orderings_Otop__class_Otop(_1001990)) = c_Orderings_Obot__class_Obot(_1001990))], (31601 ^ _781013) ^ [] : [-(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)))], (7449 ^ _781013) ^ [_905349, _905351, _905353, _905355] : [class_Orderings_Oorder(_905349), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905349), _905351), _905353)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905349), _905355), _905351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905349), _905355), _905353)))], (40313 ^ _781013) ^ [_1567459, _1567461, _1567463] : [hBOOL(hAPP(c_List_Odistinct(_1567459), hAPP(hAPP(c_List_Olist_OCons(_1567459), _1567461), _1567463))), 40316 ^ _781013 : [(40319 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1567459), _1567463)))], (40317 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1567459), _1567461), hAPP(c_List_Oset(_1567459), _1567463)))]]], (30369 ^ _781013) ^ [_1348347, _1348349, _1348351, _1348353] : [class_Orderings_Olinorder(_1348347), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348347), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348347), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348347), _1348349), _1348351)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348347), _1348349), _1348353))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348347), _1348349), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348347), _1348351), _1348353)))))], (19516 ^ _781013) ^ [_1146248, _1146250] : [class_Power_Opower(_1146248), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1146248), _1146250), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1146248))], (43603 ^ _781013) ^ [_1650206, _1650208, _1650210] : [class_Orderings_Olinorder(_1650206), c_List_Olinorder__class_Osorted(_1650206, _1650208), -(c_List_Olinorder__class_Osorted(_1650206, hAPP(hAPP(c_List_Odrop(_1650206), _1650210), _1650208)))], (10921 ^ _781013) ^ [_974407, _974409, _974411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_974407, tc_HOL_Obool)), _974409), _974411)), 10924 ^ _781013 : [(10927 ^ _781013) ^ [] : [_974409 = _974411], (10925 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974407, tc_HOL_Obool)), _974409), _974411)))]]], (37122 ^ _781013) ^ [_1489457, _1489459, _1489461] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1489457), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1489459), _1489461)))), 37125 ^ _781013 : [(37132 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489459), _1489461))), -(c_Smallcheck_Osmall_H(_1489457, _1489459, _1489461) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1489457, _1489459, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1489461), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1489457, _1489461)))], (37126 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489459), _1489461)), -(c_Smallcheck_Osmall_H(_1489457, _1489459, _1489461) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))]]], (50516 ^ _781013) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23459 ^ _781013) ^ [_1219943, _1219945, _1219947] : [class_Rings_Odivision__ring(_1219943), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1219943), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219943), _1219945), _1219947)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219943), hAPP(c_Groups_Ouminus__class_Ouminus(_1219943), _1219945)), _1219947))], (24764 ^ _781013) ^ [_1242858, _1242860, _1242862, _1242864] : [class_Fields_Ofield__inverse__zero(_1242858), -(_1242860 = c_Groups_Ozero__class_Ozero(_1242858)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242858), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242858), _1242860), _1242862)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242858), _1242860), _1242864)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242858), _1242862), _1242864))], (14207 ^ _781013) ^ [_1042933, _1042935, _1042937, _1042939, _1042941] : [class_Groups_Ocomm__monoid__add(_1042933), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042935), _1042937)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042935, _1042933), hAPP(hAPP(c_COMBS(_1042935, _1042933, _1042933), hAPP(hAPP(c_COMBB(_1042933, tc_fun(_1042933, _1042933), _1042935), c_Groups_Oplus__class_Oplus(_1042933)), _1042939)), _1042941)), _1042937) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042933), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042935, _1042933), _1042939), _1042937)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042935, _1042933), _1042941), _1042937)))], (51408 ^ _781013) ^ [_1822541] : [-(class_HOL_Oequal(tc_List_Olist(_1822541)))], (38290 ^ _781013) ^ [_1516474, _1516476, _1516478, _1516480] : [hAPP(c_List_Oset(_1516474), _1516476) = c_Map_Odom(_1516474, _1516478, _1516480), -(hAPP(c_Map_Omap__of(_1516474, _1516478), hAPP(hAPP(c_List_Omap(_1516474, tc_prod(_1516474, _1516478)), hAPP(hAPP(c_COMBS(_1516474, _1516478, tc_prod(_1516474, _1516478)), c_Product__Type_OPair(_1516474, _1516478)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1516478), _1516478, _1516474), c_Option_Othe(_1516478)), _1516480))), _1516476)) = _1516480)], (45167 ^ _781013) ^ [_1683350, _1683352] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1683350, _1683352)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1683352), tc_fun(_1683350, _1683352)), hAPP(hAPP(c_COMBB(tc_fun(_1683350, tc_Option_Ooption(_1683352)), tc_fun(_1683350, _1683352), tc_List_Olist(_1683352)), c_Fun_Ocomp(tc_Option_Ooption(_1683352), _1683352, _1683350, c_Option_Othe(_1683352))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1683350, _1683352)), tc_fun(_1683350, tc_Option_Ooption(_1683352)), tc_List_Olist(_1683352)), c_Map_Omap__of(_1683350, _1683352)), hAPP(c_List_Ozip(_1683350, _1683352), c_Enum_Oenum__class_Oenum(_1683350))))), c_Enum_On__lists(_1683352, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683350)), c_Enum_Oenum__class_Oenum(_1683350)), c_Enum_Oenum__class_Oenum(_1683352)))), class_Enum_Oenum(_1683350), class_HOL_Oequal(_1683350), class_Enum_Oenum(_1683352)], (8487 ^ _781013) ^ [_927798, _927800, _927802, _927804, _927806] : [hBOOL(hAPP(hAPP(c_member(_927798), _927800), _927802)), -(hAPP(hAPP(c_Set_Oinsert(_927804), hAPP(_927806, _927800)), hAPP(c_Set_Oimage(_927798, _927804, _927806), _927802)) = hAPP(c_Set_Oimage(_927798, _927804, _927806), _927802))], (8899 ^ _781013) ^ [_936634, _936636, _936638, _936640, _936642] : [class_Lattices_Osemilattice__sup(_936634), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936634), _936636), _936638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936634), _936640), _936642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936634), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_936634), _936636), _936640)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_936634), _936638), _936642))))], (18528 ^ _781013) ^ [_1125795, _1125797, _1125799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1125797), _1125799))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1125795), _1125799)), _1125797)))], (15125 ^ _781013) ^ [_1060948, _1060950, _1060952] : [class_Groups_Ocomm__monoid__add(_1060948), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1060950, _1060948), hAPP(c_COMBK(_1060948, _1060950), c_Groups_Ozero__class_Ozero(_1060948))), _1060952) = c_Groups_Ozero__class_Ozero(_1060948))], (19877 ^ _781013) ^ [_1153331, _1153333, _1153335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1153331), _1153333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153335), _1153331)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153335), _1153333))))], (10461 ^ _781013) ^ [_966621, _966623, _966625, _966627] : [class_Orderings_Oorder(_966621), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966621), _966623), _966625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966621), _966627), _966623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966621), _966627), _966625)))], (20689 ^ _781013) ^ [_1167791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1167791)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167791), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1167791)], (15701 ^ _781013) ^ [_1071478, _1071480] : [class_Groups_Olinordered__ab__group__add(_1071478), 15704 ^ _781013 : [(15711 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071478), c_Groups_Ozero__class_Ozero(_1071478)), _1071480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071478), c_Groups_Ozero__class_Ozero(_1071478)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071478), _1071480), _1071480))))], (15705 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071478), c_Groups_Ozero__class_Ozero(_1071478)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071478), _1071480), _1071480))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071478), c_Groups_Ozero__class_Ozero(_1071478)), _1071480)))]]], (51508 ^ _781013) ^ [] : [-(class_HOL_Oequal(tc_Code__Evaluation_Oterm))], (22206 ^ _781013) ^ [_1197450, _1197452] : [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)), _1197450)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1197452))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1197450), _1197452)))], (49986 ^ _781013) ^ [_1796677, _1796679, _1796681, _1796683, _1796685, _1796687] : [c_Finite__Set_Ofun__left__comm(_1796677, _1796679, _1796681), hBOOL(hAPP(c_Finite__Set_Ofinite(_1796677), _1796683)), -(hBOOL(hAPP(hAPP(c_member(_1796677), _1796685), _1796683))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1796677, _1796679, _1796681), _1796687), hAPP(hAPP(c_Set_Oinsert(_1796677), _1796685), _1796683)) = hAPP(hAPP(c_Finite__Set_Ofold(_1796677, _1796679, _1796681), hAPP(hAPP(_1796681, _1796685), _1796687)), _1796683))], (28792 ^ _781013) ^ [_1318307, _1318309] : [class_Groups_Oordered__ab__group__add__abs(_1318307), -(hAPP(c_Groups_Oabs__class_Oabs(_1318307), hAPP(c_Groups_Ouminus__class_Ouminus(_1318307), _1318309)) = hAPP(c_Groups_Oabs__class_Oabs(_1318307), _1318309))], (38164 ^ _781013) ^ [_1513113, _1513115, _1513117, _1513119] : [-(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), _1513113), _1513115)), 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), _1513117), _1513119)), 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), _1513113), _1513117)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1513115), _1513119))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1513113), _1513119)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1513115), _1513117)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (14903 ^ _781013) ^ [_1056983, _1056985] : [class_Rings_Omult__zero(_1056983), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056983), c_Groups_Ozero__class_Ozero(_1056983)), _1056985) = c_Groups_Ozero__class_Ozero(_1056983))], (49946 ^ _781013) ^ [_1795976] : [class_Groups_Oab__semigroup__mult(_1795976), -(c_Finite__Set_Ofun__left__comm(_1795976, _1795976, c_Groups_Otimes__class_Otimes(_1795976)))], (43388 ^ _781013) ^ [_1644880, _1644882, _1644884, _1644886] : [-(hAPP(c_List_Ofilter(_1644880, _1644882), c_List_Oremove1(_1644880, _1644884, _1644886)) = c_List_Oremove1(_1644880, _1644884, hAPP(c_List_Ofilter(_1644880, _1644882), _1644886)))], (44985 ^ _781013) ^ [_1679569, _1679571, _1679573, _1679575] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1679569)), _1679571), hAPP(c_List_Oset(tc_List_Olist(_1679569)), c_Enum_On__lists(_1679569, _1679573, _1679575)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679569)), _1679571) = _1679573)], (43014 ^ _781013) ^ [_1635589, _1635591, _1635593, _1635595, _1635597, _1635599] : [class_Complete__Lattice_Ocomplete__lattice(_1635589), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635591, _1635589), _1635593), hAPP(hAPP(c_COMBB(tc_fun(_1635595, _1635589), _1635589, _1635591), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635595, _1635589), _1635597)), _1635599)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635595, _1635589), _1635597), hAPP(hAPP(c_COMBB(tc_fun(_1635591, _1635589), _1635589, _1635595), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635591, _1635589), _1635593)), hAPP(c_COMBC(_1635591, _1635595, _1635589), _1635599))))], (25892 ^ _781013) ^ [_1262557, _1262559] : [class_Rings_Oring__1(_1262557), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262557), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1262559)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1262557), hAPP(c_Int_Oring__1__class_Oof__int(_1262557), _1262559)))], (45157 ^ _781013) ^ [_1683033, _1683035] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1683033, _1683035)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1683035), tc_fun(_1683033, _1683035)), hAPP(hAPP(c_COMBB(tc_fun(_1683033, tc_Option_Ooption(_1683035)), tc_fun(_1683033, _1683035), tc_List_Olist(_1683035)), c_Fun_Ocomp(tc_Option_Ooption(_1683035), _1683035, _1683033, c_Option_Othe(_1683035))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1683033, _1683035)), tc_fun(_1683033, tc_Option_Ooption(_1683035)), tc_List_Olist(_1683035)), c_Map_Omap__of(_1683033, _1683035)), hAPP(c_List_Ozip(_1683033, _1683035), c_Enum_Oenum__class_Oenum(_1683033))))), c_Enum_On__lists(_1683035, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683033)), c_Enum_Oenum__class_Oenum(_1683033)), c_Enum_Oenum__class_Oenum(_1683035)))), class_Enum_Oenum(_1683033), class_Enum_Oenum(_1683035)], (33604 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (31047 ^ _781013) ^ [_1362367, _1362369, _1362371, _1362373, _1362375] : [class_Groups_Ocomm__monoid__add(_1362367), class_Groups_Ocomm__monoid__mult(_1362367), _1362369 = _1362371, c_Nat__Transfer_Onat__set(_1362371), 31065 ^ _781013 : [(31068 ^ _781013) ^ [] : [hAPP(_1362373, 31064 ^ [_1362367, _1362369, _1362371, _1362373, _1362375]) = hAPP(_1362375, 31064 ^ [_1362367, _1362369, _1362371, _1362373, _1362375])], (31066 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31064 ^ [_1362367, _1362369, _1362371, _1362373, _1362375])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1362367), _1362373), _1362369) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1362367), _1362375), _1362371))], (45596 ^ _781013) ^ [_1692297, _1692299] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1692297, tc_HOL_Obool), tc_HOL_Obool)), _1692299), hAPP(c_Set_OPow(_1692297), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692297, tc_HOL_Obool), _1692299)))))], (21806 ^ _781013) ^ [_1190261, _1190263] : [class_Orderings_Olinorder(_1190261), -(c_Big__Operators_Olinorder__class_OMin(_1190261, hAPP(hAPP(c_Set_Oinsert(_1190261), _1190263), c_Orderings_Obot__class_Obot(tc_fun(_1190261, tc_HOL_Obool)))) = _1190263)], (6854 ^ _781013) ^ [_894073, _894075, _894077, _894079] : [hBOOL(hAPP(hAPP(c_member(_894073), _894075), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894073, tc_HOL_Obool)), _894077), _894079))), -(hBOOL(hAPP(hAPP(c_member(_894073), _894075), _894077))), -(hBOOL(hAPP(hAPP(c_member(_894073), _894075), _894079)))], (51396 ^ _781013) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (16321 ^ _781013) ^ [_1082639, _1082641, _1082643] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1082639, tc_HOL_Obool)), _1082641), _1082643) = hAPP(c_Set_OCollect(_1082639), hAPP(hAPP(c_COMBS(_1082639, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1082639), c_fconj), hAPP(hAPP(c_COMBC(_1082639, tc_fun(_1082639, tc_HOL_Obool), tc_HOL_Obool), c_member(_1082639)), _1082641))), hAPP(hAPP(c_COMBC(_1082639, tc_fun(_1082639, tc_HOL_Obool), tc_HOL_Obool), c_member(_1082639)), _1082643))))], (33900 ^ _781013) ^ [_1423102] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1423102)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423102) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43289 ^ _781013) ^ [_1643029, _1643031, _1643033, _1643035, _1643037] : [-(hAPP(c_List_Ofilter(_1643029, _1643031), hAPP(hAPP(c_List_Omap(_1643033, _1643029), _1643035), _1643037)) = hAPP(hAPP(c_List_Omap(_1643033, _1643029), _1643035), hAPP(c_List_Ofilter(_1643033, hAPP(c_Fun_Ocomp(_1643029, tc_HOL_Obool, _1643033, _1643031), _1643035)), _1643037)))], (8535 ^ _781013) ^ [_928800, _928802, _928804] : [_928802 = _928804, -(hBOOL(hAPP(hAPP(c_member(_928800), _928802), hAPP(c_fequal, _928804))))], (15131 ^ _781013) ^ [_1061063, _1061065, _1061067] : [class_Groups_Ocomm__monoid__mult(_1061063), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1061065, _1061063), _1061067), c_Orderings_Obot__class_Obot(tc_fun(_1061065, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1061063))], (25422 ^ _781013) ^ [_1254923, _1254925] : [c_Nat__Transfer_Onat__set(_1254923), c_Nat__Transfer_Onat__set(_1254925), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1254923), _1254925) = 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), _1254923)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1254925))))], (6836 ^ _781013) ^ [_893723, _893725, _893727, _893729] : [6837 ^ _781013 : [(6840 ^ _781013) ^ [] : [_893725 = _893729], (6838 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_893723), _893725), _893727))]], -(hBOOL(hAPP(hAPP(c_member(_893723), _893725), hAPP(hAPP(c_Set_Oinsert(_893723), _893729), _893727))))], (4824 ^ _781013) ^ [_854162, _854164, _854166, _854168, _854170, _854172, _854174, _854176] : [-(c_Lazy__Sequence_Ohb__bind(_854176, _854172, _854168, _854164) = c_Lazy__Sequence_Ohb__bind(_854174, _854170, _854166, _854162)), _854176 = _854174, _854172 = _854170, _854168 = _854166, _854164 = _854162], (13403 ^ _781013) ^ [_1025804, _1025806, _1025808, _1025810, _1025812, _1025814] : [class_Groups_Ocomm__monoid__add(_1025804), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1025806, _1025804), hAPP(hAPP(c_COMBC(_1025806, tc_fun(_1025808, tc_HOL_Obool), _1025804), hAPP(hAPP(c_COMBB(tc_fun(_1025808, _1025804), tc_fun(tc_fun(_1025808, tc_HOL_Obool), _1025804), _1025806), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1025808, _1025804)), _1025810)), _1025812)), _1025814) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1025808, _1025804), hAPP(hAPP(c_COMBC(_1025808, tc_fun(_1025806, tc_HOL_Obool), _1025804), hAPP(hAPP(c_COMBB(tc_fun(_1025806, _1025804), tc_fun(tc_fun(_1025806, tc_HOL_Obool), _1025804), _1025808), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1025806, _1025804)), hAPP(c_COMBC(_1025806, _1025808, _1025804), _1025810))), _1025814)), _1025812))], (20739 ^ _781013) ^ [_1168606, _1168608] : [-(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), _1168606), _1168608)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168606)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168608))], (37969 ^ _781013) ^ [_1508407] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1508407)), -(_1508407 = 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))), _1508407)), c_FunDef_Omax__strict)))], (50290 ^ _781013) ^ [_1803740, _1803742, _1803744] : [50292 ^ _781013 : [(50295 ^ _781013) ^ [] : [hBOOL(hAPP(_1803744, 50291 ^ [_1803740, _1803742, _1803744]))], (50293 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803740), 50291 ^ [_1803740, _1803742, _1803744]), hAPP(c_List_Oset(_1803740), _1803742))))]], -(c_List_Olist__all(_1803740, _1803744, _1803742))], (48651 ^ _781013) ^ [_1765345] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1765345), 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, _1765345)) = _1765345)], (49874 ^ _781013) ^ [_1794432, _1794434, _1794436, _1794438, _1794440, _1794442] : [c_Finite__Set_Ofun__left__comm(_1794432, _1794434, _1794436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1794432), _1794438)), hBOOL(hAPP(hAPP(c_member(_1794432), _1794440), _1794438)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1794432, _1794434, _1794436), _1794442), _1794438) = hAPP(hAPP(_1794436, _1794440), hAPP(hAPP(c_Finite__Set_Ofold(_1794432, _1794434, _1794436), _1794442), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1794432, tc_HOL_Obool)), _1794438), hAPP(hAPP(c_Set_Oinsert(_1794432), _1794440), c_Orderings_Obot__class_Obot(tc_fun(_1794432, tc_HOL_Obool)))))))], (51594 ^ _781013) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (6170 ^ _781013) ^ [_881107, _881109, _881111, _881113, _881115, _881117] : [-(c_Com_Ocom_OCond(_881107, _881109, _881111) = c_Com_Ocom_OCond(_881113, _881115, _881117)), _881107 = _881113, _881109 = _881115, _881111 = _881117], (11073 ^ _781013) ^ [_977823, _977825, _977827, _977829] : [-(hBOOL(hAPP(hAPP(c_member(_977823), _977825), _977827))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977823, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_977823), _977825), _977829)), _977827) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977823, tc_HOL_Obool)), _977829), _977827))], (23499 ^ _781013) ^ [_1220881, _1220883, _1220885, _1220887] : [class_Rings_Odivision__ring(_1220881), -(_1220883 = c_Groups_Ozero__class_Ozero(_1220881)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220881), _1220885), _1220883) = _1220887, -(_1220885 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220881), _1220887), _1220883))], (29535 ^ _781013) ^ [_1331984, _1331986, _1331988] : [class_Orderings_Olinorder(_1331984), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331984), _1331986)), -(_1331986 = c_Orderings_Obot__class_Obot(tc_fun(_1331984, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1331984, hAPP(hAPP(c_Set_Oinsert(_1331984), _1331988), _1331986)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331984), _1331988), c_Big__Operators_Olinorder__class_OMin(_1331984, _1331986)))], (29683 ^ _781013) ^ [_1334530, _1334532, _1334534] : [class_Orderings_Olinorder(_1334530), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334530), _1334532)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334530), _1334534)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334530, tc_HOL_Obool)), _1334532), _1334534) = c_Orderings_Obot__class_Obot(tc_fun(_1334530, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334530), c_Big__Operators_Olinorder__class_OMin(_1334530, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334530, tc_HOL_Obool)), _1334532), _1334534))), c_Big__Operators_Olinorder__class_OMin(_1334530, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334530, tc_HOL_Obool)), _1334532), _1334534))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334530), c_Big__Operators_Olinorder__class_OMin(_1334530, _1334532)), c_Big__Operators_Olinorder__class_OMin(_1334530, _1334534)))], (33930 ^ _781013) ^ [_1423695, _1423697] : [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(_1423697))), 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)), _1423695))))), -(hAPP(c_Nat_OSuc, _1423695) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423697))], (25846 ^ _781013) ^ [_1261687, _1261689, _1261691] : [class_Rings_Olinordered__idom(_1261687), 25849 ^ _781013 : [(25856 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261689), _1261691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261687), hAPP(c_Int_Oring__1__class_Oof__int(_1261687), _1261689)), hAPP(c_Int_Oring__1__class_Oof__int(_1261687), _1261691))))], (25850 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261687), hAPP(c_Int_Oring__1__class_Oof__int(_1261687), _1261689)), hAPP(c_Int_Oring__1__class_Oof__int(_1261687), _1261691))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261689), _1261691)))]]], (20544 ^ _781013) ^ [_1164674, _1164676, _1164678, _1164680] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1164674), hAPP(c_Set_OCollect(_1164674), _1164676))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1164678), hAPP(c_Set_OCollect(_1164678), hAPP(hAPP(c_COMBB(tc_fun(_1164674, tc_HOL_Obool), tc_HOL_Obool, _1164678), c_HOL_OEx(_1164674)), hAPP(hAPP(c_COMBC(_1164678, tc_fun(_1164674, tc_HOL_Obool), tc_fun(_1164674, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1164674, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1164674, tc_HOL_Obool), tc_fun(_1164674, tc_HOL_Obool)), _1164678), c_COMBS(_1164674, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1164674, tc_HOL_Obool), tc_fun(_1164674, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1164678), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1164674), c_fconj)), hAPP(hAPP(c_COMBC(_1164678, tc_fun(_1164674, _1164678), tc_fun(_1164674, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1164678, tc_HOL_Obool), tc_fun(tc_fun(_1164674, _1164678), tc_fun(_1164674, tc_HOL_Obool)), _1164678), c_COMBB(_1164678, tc_HOL_Obool, _1164674)), c_fequal)), _1164680)))), _1164676))))))], (14035 ^ _781013) ^ [_1039109, _1039111, _1039113, _1039115] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1039109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039109), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039109), _1039111), _1039113)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039109), _1039111), _1039115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039109), _1039113), _1039115)))], (25615 ^ _781013) ^ [_1257839, _1257841, _1257843, _1257845, _1257847] : [class_Fields_Ofield(_1257839), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257841), _1257843)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257841), _1257845)), 25629 ^ _781013 : [(25632 ^ _781013) ^ [] : [-(hAPP(_1257847, 25628 ^ [_1257839, _1257841, _1257843, _1257845, _1257847]) = c_Groups_Ozero__class_Ozero(_1257839))], (25630 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1257841), 25628 ^ [_1257839, _1257841, _1257843, _1257845, _1257847]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1257841, tc_HOL_Obool)), _1257843), _1257845))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1257841, _1257839), _1257847), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257841, tc_HOL_Obool)), _1257843), _1257845)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1257839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257839), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1257841, _1257839), _1257847), _1257843)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1257841, _1257839), _1257847), _1257845))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1257841, _1257839), _1257847), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1257841, tc_HOL_Obool)), _1257843), _1257845))))], (14303 ^ _781013) ^ [_1045603, _1045605, _1045607, _1045609, _1045611] : [class_Rings_Ocomm__semiring__1(_1045603), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045603), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045603), _1045605), _1045607)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045603), _1045609), _1045611)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045603), _1045605), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045603), _1045607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045603), _1045609), _1045611))))], (42683 ^ _781013) ^ [_1626735, _1626737] : [-(_1626735 = c_List_Olist_ONil(_1626737)), -(hBOOL(hAPP(hAPP(c_member(_1626737), c_List_Olast(_1626737, _1626735)), hAPP(c_List_Oset(_1626737), _1626735))))], (48353 ^ _781013) ^ [_1758318, _1758320, _1758322, _1758324] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1758318, _1758318)), hAPP(hAPP(c_Product__Type_OPair(_1758318, _1758318), _1758320), _1758322)), c_Transitive__Closure_Ortrancl(_1758318, _1758324)))), 48354 ^ _781013 : [(48357 ^ _781013) ^ [] : [-(_1758320 = _1758322), hBOOL(hAPP(hAPP(c_member(tc_prod(_1758318, _1758318)), hAPP(hAPP(c_Product__Type_OPair(_1758318, _1758318), _1758320), _1758322)), c_Transitive__Closure_Otrancl(_1758318, _1758324)))], (48355 ^ _781013) ^ [] : [_1758320 = _1758322]]], (43679 ^ _781013) ^ [_1651489, _1651491, _1651493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651489), _1651491)), -(c_List_Oupt(_1651489, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1651491), _1651493)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1651489, _1651491)), c_List_Oupt(_1651491, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1651491), _1651493))))], (32370 ^ _781013) ^ [_1395138, _1395140, _1395142, _1395144] : [hAPP(c_Com_Ocom_OBODY, _1395138) = c_Com_Ocom_OLocal(_1395140, _1395142, _1395144)], (27148 ^ _781013) ^ [_1286461, _1286463, _1286465] : [class_Orderings_Oorder(_1286461), 27151 ^ _781013 : [(27158 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286461), _1286463), _1286465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286461, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1286461), _1286463)), hAPP(c_SetInterval_Oord__class_OatMost(_1286461), _1286465))))], (27152 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286461, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1286461), _1286463)), hAPP(c_SetInterval_Oord__class_OatMost(_1286461), _1286465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286461), _1286463), _1286465)))]]], (14011 ^ _781013) ^ [_1038643, _1038645, _1038647, _1038649, _1038651] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1038643), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038643), _1038645), _1038647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038643), _1038649), _1038651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038643), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038643), _1038645), _1038649)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038643), _1038647), _1038651))))], (40453 ^ _781013) ^ [_1571643, _1571645, _1571647, _1571649, _1571651, _1571653] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1571643, _1571645), _1571645, tc_prod(_1571647, _1571649), c_Product__Type_Osnd(_1571643, _1571645)), c_Product__Type_Omap__pair(_1571647, _1571643, _1571649, _1571645, _1571651, _1571653)) = hAPP(c_Fun_Ocomp(_1571649, _1571645, tc_prod(_1571647, _1571649), _1571653), c_Product__Type_Osnd(_1571647, _1571649)))], (4592 ^ _781013) ^ [_850552, _850554] : [_850554 = _850552, -(c_Nitpick_Onum(_850554) = c_Nitpick_Onum(_850552))], (10683 ^ _781013) ^ [_969812, _969814, _969816] : [class_Orderings_Oorder(_969812), 10686 ^ _781013 : [(10695 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969812), _969814), _969816))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969812), _969814), _969816)), -(_969814 = _969816)], (10687 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969812), _969814), _969816)), 10690 ^ _781013 : [(10693 ^ _781013) ^ [] : [_969814 = _969816], (10691 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969812), _969814), _969816)))]]]]], (33576 ^ _781013) ^ [_1417950] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1417950), c_Int_OPls) = _1417950)], (20963 ^ _781013) ^ [_1172849, _1172851, _1172853, _1172855] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1172849), _1172851)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172853), _1172855)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1172849, _1172853)), c_Sum__Type_OPlus(_1172849, _1172853, _1172851, _1172855)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1172849), _1172851)), hAPP(c_Finite__Set_Ocard(_1172853), _1172855)))], (18081 ^ _781013) ^ [_1117861] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1117861) = _1117861)], (45631 ^ _781013) ^ [_1692955, _1692957] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692955, tc_HOL_Obool), hAPP(c_Set_OPow(_1692955), _1692957)) = _1692957)], (49514 ^ _781013) ^ [_1787523, _1787525, _1787527, _1787529, _1787531, _1787533] : [c_Finite__Set_Ofolding(_1787523, _1787525, _1787527, _1787529), hBOOL(hAPP(c_Finite__Set_Ofinite(_1787523), _1787531)), -(hAPP(hAPP(_1787529, _1787531), _1787533) = hAPP(hAPP(c_Finite__Set_Ofold(_1787523, _1787525, _1787527), _1787533), _1787531))], (13765 ^ _781013) ^ [_1033901, _1033903, _1033905, _1033907] : [class_Groups_Ocancel__semigroup__add(_1033901), 13768 ^ _781013 : [(13775 ^ _781013) ^ [] : [_1033903 = _1033907, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033901), _1033903), _1033905) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033901), _1033907), _1033905))], (13769 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033901), _1033903), _1033905) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033901), _1033907), _1033905), -(_1033903 = _1033907)]]], (20512 ^ _781013) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37208 ^ _781013) ^ [_1491013, _1491015, _1491017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491013, tc_fun(_1491013, tc_HOL_Obool))), _1491015), _1491017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491013, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1491013, _1491017)), c_Wellfounded_Oaccp(_1491013, _1491015))))], (48972 ^ _781013) ^ [_1773594] : [-(c_Transitive__Closure_Ortrancl(_1773594, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1773594, _1773594), tc_HOL_Obool))) = c_Relation_OId(_1773594))], (5895 ^ _781013) ^ [_875873, _875875, _875877, _875879, _875881] : [-(c_Option_Ooption_Ooption__rec(_875873, _875875, _875877, _875879, hAPP(c_Option_Ooption_OSome(_875875), _875881)) = hAPP(_875879, _875881))], (38880 ^ _781013) ^ [_1530194, _1530196, _1530198] : [hBOOL(hAPP(hAPP(c_member(_1530194), _1530196), hAPP(c_List_Oset(_1530194), _1530198))), -(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(_1530194)), _1530198))))], (43581 ^ _781013) ^ [_1649809, _1649811] : [class_Orderings_Olinorder(_1649809), -(c_List_Olinorder__class_Osorted(_1649809, hAPP(hAPP(c_List_Olist_OCons(_1649809), _1649811), c_List_Olist_ONil(_1649809))))], (35501 ^ _781013) ^ [] : [c_Int_OPls = c_Int_OMin], (47055 ^ _781013) ^ [_1727859, _1727861, _1727863] : [-(hAPP(c_Relation_ORange(_1727859, _1727861), hAPP(c_Set_OCollect(tc_prod(_1727859, _1727861)), hAPP(c_Product__Type_Oprod_Oprod__case(_1727859, _1727861, tc_HOL_Obool), _1727863))) = hAPP(c_Set_OCollect(_1727861), hAPP(hAPP(c_COMBB(tc_fun(_1727859, tc_HOL_Obool), tc_HOL_Obool, _1727861), c_HOL_OEx(_1727859)), hAPP(c_COMBC(_1727859, _1727861, tc_HOL_Obool), _1727863))))], (26727 ^ _781013) ^ [_1278431, _1278433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1278431), _1278433)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1278433, _1278431) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (4474 ^ _781013) ^ [_848783, _848785, _848787, _848789] : [-(c_Nitpick_Oint__lcm(_848789, _848785) = c_Nitpick_Oint__lcm(_848787, _848783)), _848789 = _848787, _848785 = _848783], (46764 ^ _781013) ^ [_1721546, _1721548] : [c_Wellfounded_Owf(_1721546, _1721548), -(c_Wellfounded_Owf(_1721546, hAPP(hAPP(c_Relation_Orel__comp(_1721546, _1721546, _1721546), _1721548), _1721548)))], (14001 ^ _781013) ^ [_1038448, _1038450, _1038452, _1038454] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1038448), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038448), _1038450), _1038452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038448), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038448), _1038454), _1038450)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038448), _1038454), _1038452))))], (18468 ^ _781013) ^ [_1124713, _1124715, _1124717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124713), _1124715)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124713), _1124717))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1124713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124715), _1124717)))], (40523 ^ _781013) ^ [_1573751, _1573753, _1573755, _1573757, _1573759, _1573761, _1573763, _1573765] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573751, _1573753)), _1573755), hAPP(c_Set_Oimage(tc_prod(_1573757, _1573759), tc_prod(_1573751, _1573753), c_Product__Type_Omap__pair(_1573757, _1573751, _1573759, _1573753, _1573761, _1573763)), _1573765))), 40528 ^ _781013 : [(40531 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573757, _1573759)), hAPP(hAPP(c_Product__Type_OPair(_1573757, _1573759), 40526 ^ [_1573751, _1573753, _1573755, _1573757, _1573759, _1573761, _1573763, _1573765]), 40527 ^ [_1573751, _1573753, _1573755, _1573757, _1573759, _1573761, _1573763, _1573765])), _1573765)))], (40529 ^ _781013) ^ [] : [-(_1573755 = hAPP(hAPP(c_Product__Type_OPair(_1573751, _1573753), hAPP(_1573761, 40526 ^ [_1573751, _1573753, _1573755, _1573757, _1573759, _1573761, _1573763, _1573765])), hAPP(_1573763, 40527 ^ [_1573751, _1573753, _1573755, _1573757, _1573759, _1573761, _1573763, _1573765])))]]], (43962 ^ _781013) ^ [_1656343, _1656345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656343)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656345))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656343), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656345)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656343)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656343)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656345))))], (29080 ^ _781013) ^ [_1323546, _1323548] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1323546, _1323548)) = _1323548), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1323546), _1323548) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1323546, _1323548)))], (34941 ^ _781013) ^ [_1442574, _1442576] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1442574), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1442576))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1442574), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442576))), 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))))], (51436 ^ _781013) ^ [_1822901] : [class_Finite__Set_Ofinite(_1822901), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1822901)))], (9251 ^ _781013) ^ [_944694, _944696, _944698, _944700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944694, tc_HOL_Obool)), _944696), hAPP(hAPP(c_Set_Oinsert(_944694), _944698), _944700))), 9254 ^ _781013 : [(9261 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_944694), _944698), _944700))), 9264 ^ _781013 : [(9271 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_944694), _944698), _944696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944694, tc_HOL_Obool)), _944696), _944700)))], (9265 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_944694), _944698), _944696)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944694, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_944694, tc_HOL_Obool)), _944696), hAPP(hAPP(c_Set_Oinsert(_944694), _944698), c_Orderings_Obot__class_Obot(tc_fun(_944694, tc_HOL_Obool))))), _944700)))]]], (9255 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_944694), _944698), _944700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944694, tc_HOL_Obool)), _944696), _944700)))]]], (48221 ^ _781013) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (35449 ^ _781013) ^ [_1451986] : [-(_1451986 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 35452 ^ _781013 : [(35459 ^ _781013) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1451986, 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, _1451986) = 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), _1451986), 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)))], (35453 ^ _781013) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1451986, 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, _1451986) = 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), _1451986), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (45385 ^ _781013) ^ [_1687469, _1687471, _1687473] : [class_Enum_Oenum(_1687469), class_Enum_Oenum(_1687471), 45392 ^ _781013 : [(45399 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1687471), hAPP(hAPP(c_COMBB(tc_fun(_1687469, tc_HOL_Obool), tc_HOL_Obool, _1687471), c_Enum_Oenum__class_Oenum__all(_1687469)), hAPP(hAPP(c_COMBB(tc_fun(_1687469, tc_prod(_1687471, _1687469)), tc_fun(_1687469, tc_HOL_Obool), _1687471), hAPP(c_COMBB(tc_prod(_1687471, _1687469), tc_HOL_Obool, _1687469), _1687473)), c_Product__Type_OPair(_1687471, _1687469))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1687471, _1687469)), _1687473)))], (45393 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1687471, _1687469)), _1687473)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1687471), hAPP(hAPP(c_COMBB(tc_fun(_1687469, tc_HOL_Obool), tc_HOL_Obool, _1687471), c_Enum_Oenum__class_Oenum__all(_1687469)), hAPP(hAPP(c_COMBB(tc_fun(_1687469, tc_prod(_1687471, _1687469)), tc_fun(_1687469, tc_HOL_Obool), _1687471), hAPP(c_COMBB(tc_prod(_1687471, _1687469), tc_HOL_Obool, _1687469), _1687473)), c_Product__Type_OPair(_1687471, _1687469))))))]]], (39856 ^ _781013) ^ [_1554837, _1554839, _1554841, _1554843] : [c_List_Olistrelp(_1554837, hAPP(hAPP(c_COMBC(_1554837, tc_fun(tc_prod(_1554837, _1554837), tc_HOL_Obool), tc_fun(_1554837, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554837, tc_fun(tc_fun(tc_prod(_1554837, _1554837), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1554837, _1554837), tc_HOL_Obool), tc_fun(_1554837, tc_HOL_Obool)), _1554837), c_COMBC(_1554837, tc_fun(tc_prod(_1554837, _1554837), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554837, tc_prod(_1554837, _1554837)), tc_fun(_1554837, tc_fun(tc_fun(tc_prod(_1554837, _1554837), tc_HOL_Obool), tc_HOL_Obool)), _1554837), hAPP(c_COMBB(tc_prod(_1554837, _1554837), tc_fun(tc_fun(tc_prod(_1554837, _1554837), tc_HOL_Obool), tc_HOL_Obool), _1554837), c_member(tc_prod(_1554837, _1554837)))), c_Product__Type_OPair(_1554837, _1554837)))), _1554839), _1554841, _1554843), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1554837), tc_List_Olist(_1554837))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1554837), tc_List_Olist(_1554837)), _1554841), _1554843)), c_List_Olistrel(_1554837, _1554839))))], (48205 ^ _781013) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12786 ^ _781013) ^ [_1012593, _1012595, _1012597] : [class_Lattices_Olattice(_1012593), hAPP(_1012595, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1012593), 12791 ^ [_1012593, _1012595, _1012597]), 12792 ^ [_1012593, _1012595, _1012597])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1012593), hAPP(_1012595, 12791 ^ [_1012593, _1012595, _1012597])), hAPP(_1012595, 12792 ^ [_1012593, _1012595, _1012597])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012593), _1012597)), -(_1012597 = c_Orderings_Obot__class_Obot(tc_fun(_1012593, tc_HOL_Obool))), -(hAPP(_1012595, c_Big__Operators_Olattice__class_OSup__fin(_1012593, _1012597)) = c_Big__Operators_Olattice__class_OSup__fin(_1012593, hAPP(c_Set_Oimage(_1012593, _1012593, _1012595), _1012597)))], (38371 ^ _781013) ^ [_1518477, _1518479, _1518481] : [-(c_Map_Odom(_1518477, _1518479, hAPP(c_Map_Omap__of(_1518477, _1518479), _1518481)) = hAPP(c_Set_Oimage(tc_prod(_1518477, _1518479), _1518477, c_Product__Type_Ofst(_1518477, _1518479)), hAPP(c_List_Oset(tc_prod(_1518477, _1518479)), _1518481)))], (1394 ^ _781013) ^ [_801180, _801182] : [-(class_Lazy__Sequence_Osmall__lazy(_801180)), _801182 = _801180, class_Lazy__Sequence_Osmall__lazy(_801182)], (29933 ^ _781013) ^ [_1339203, _1339205, _1339207] : [class_Orderings_Olinorder(_1339203), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339203), _1339205)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339203), _1339207)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339203, tc_HOL_Obool)), _1339205), _1339207) = c_Orderings_Obot__class_Obot(tc_fun(_1339203, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1339203), c_Big__Operators_Olattice_OInf__fin(_1339203, c_Orderings_Oord__class_Omin(_1339203), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339203, tc_HOL_Obool)), _1339205), _1339207))), c_Big__Operators_Olattice_OInf__fin(_1339203, c_Orderings_Oord__class_Omin(_1339203), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339203, tc_HOL_Obool)), _1339205), _1339207))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1339203), c_Big__Operators_Olattice_OInf__fin(_1339203, c_Orderings_Oord__class_Omin(_1339203), _1339205)), c_Big__Operators_Olattice_OInf__fin(_1339203, c_Orderings_Oord__class_Omin(_1339203), _1339207)))], (21509 ^ _781013) ^ [_1185052, _1185054, _1185056] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1185052, tc_Nat_Onat), _1185054), _1185056)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1185052, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1185052), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1185054)), _1185056))], (45405 ^ _781013) ^ [_1687908, _1687910, _1687912] : [class_Enum_Oenum(_1687908), class_Enum_Oenum(_1687910), 45412 ^ _781013 : [(45419 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1687910), hAPP(hAPP(c_COMBB(tc_fun(_1687908, tc_HOL_Obool), tc_HOL_Obool, _1687910), c_Enum_Oenum__class_Oenum__ex(_1687908)), hAPP(hAPP(c_COMBB(tc_fun(_1687908, tc_prod(_1687910, _1687908)), tc_fun(_1687908, tc_HOL_Obool), _1687910), hAPP(c_COMBB(tc_prod(_1687910, _1687908), tc_HOL_Obool, _1687908), _1687912)), c_Product__Type_OPair(_1687910, _1687908))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1687910, _1687908)), _1687912)))], (45413 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1687910, _1687908)), _1687912)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1687910), hAPP(hAPP(c_COMBB(tc_fun(_1687908, tc_HOL_Obool), tc_HOL_Obool, _1687910), c_Enum_Oenum__class_Oenum__ex(_1687908)), hAPP(hAPP(c_COMBB(tc_fun(_1687908, tc_prod(_1687910, _1687908)), tc_fun(_1687908, tc_HOL_Obool), _1687910), hAPP(c_COMBB(tc_prod(_1687910, _1687908), tc_HOL_Obool, _1687908), _1687912)), c_Product__Type_OPair(_1687910, _1687908))))))]]], (35541 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (49660 ^ _781013) ^ [_1790558, _1790560] : [class_Complete__Lattice_Ocomplete__lattice(_1790558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1790558), _1790560)), -(c_Complete__Lattice_OSup__class_OSup(_1790558, _1790560) = hAPP(hAPP(c_Finite__Set_Ofold(_1790558, _1790558, c_Lattices_Osemilattice__sup__class_Osup(_1790558)), c_Orderings_Obot__class_Obot(_1790558)), _1790560))], (17324 ^ _781013) ^ [_1104335, _1104337, _1104339, _1104341] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1104335), _1104337)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104339), _1104341)), 17331 ^ _781013 : [(17332 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1104335), _1104337)), hAPP(c_Finite__Set_Ocard(_1104339), _1104341)))), 17333 ^ _781013 : [(17334 ^ _781013) ^ [_1104546] : [c_Fun_Oinj__on(_1104335, _1104339, _1104546, _1104337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1104339, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1104335, _1104339, _1104546), _1104337)), _1104341))]]], (17342 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1104335), _1104337)), hAPP(c_Finite__Set_Ocard(_1104339), _1104341))), 17346 ^ _781013 : [(17349 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1104339, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1104335, _1104339, 17345 ^ [_1104335, _1104337, _1104339, _1104341]), _1104337)), _1104341)))], (17347 ^ _781013) ^ [] : [-(c_Fun_Oinj__on(_1104335, _1104339, 17345 ^ [_1104335, _1104337, _1104339, _1104341], _1104337))]]]]], (1764 ^ _781013) ^ [_805805, _805807] : [-(class_Rings_Osemiring(_805805)), _805807 = _805805, class_Rings_Osemiring(_805807)], (20805 ^ _781013) ^ [_1169932, _1169934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1169932)), -(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), _1169932), _1169934))))], (2844 ^ _781013) ^ [_823470, _823472, _823474, _823476] : [-(c_Predicate_OPowp(_823476, _823472) = c_Predicate_OPowp(_823474, _823470)), _823476 = _823474, _823472 = _823470], (43687 ^ _781013) ^ [_1651658] : [class_Orderings_Olinorder(_1651658), -(c_List_Olinorder__class_Osorted(_1651658, c_List_Olist_ONil(_1651658)))], (38953 ^ _781013) ^ [_1531930, _1531932, _1531934] : [hBOOL(hAPP(hAPP(c_member(_1531930), _1531932), hAPP(c_List_Oset(_1531930), _1531934))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1531930)), c_List_Oremove1(_1531930, _1531932, _1531934)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1531930)), _1531934)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43349 ^ _781013) ^ [_1644283, _1644285, _1644287] : [43351 ^ _781013 : [(43354 ^ _781013) ^ [] : [hBOOL(hAPP(_1644285, 43350 ^ [_1644283, _1644285, _1644287]))], (43352 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1644283), 43350 ^ [_1644283, _1644285, _1644287]), hAPP(c_List_Oset(_1644283), _1644287))))]], -(hBOOL(hAPP(c_List_Olistsp(_1644283, _1644285), _1644287)))], (10851 ^ _781013) ^ [_972961, _972963, _972965, _972967] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972961, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972961, tc_HOL_Obool)), _972963), _972965)), _972967) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972961, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972961, tc_HOL_Obool)), _972963), _972967)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972961, tc_HOL_Obool)), _972965), _972967)))], (5661 ^ _781013) ^ [_870439, _870441, _870443] : [class_Orderings_Obot(_870439), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_870441, _870439)), _870443) = c_Orderings_Obot__class_Obot(_870439))], (42972 ^ _781013) ^ [_1634424, _1634426, _1634428, _1634430, _1634432] : [-(hAPP(hAPP(c_Set_Oinsert(_1634424), _1634426), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634428, tc_fun(_1634424, tc_HOL_Obool)), _1634430), _1634432)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634428, tc_fun(_1634424, tc_HOL_Obool)), _1634430), hAPP(hAPP(c_COMBB(tc_fun(_1634424, tc_HOL_Obool), tc_fun(_1634424, tc_HOL_Obool), _1634428), hAPP(c_Set_Oinsert(_1634424), _1634426)), _1634432)))], (44625 ^ _781013) ^ [_1672237, _1672239, _1672241] : [hBOOL(hAPP(c_List_Odistinct(_1672237), _1672239)), -(hBOOL(hAPP(c_List_Odistinct(_1672237), c_List_OtakeWhile(_1672237, _1672241, _1672239))))], (44436 ^ _781013) ^ [_1666635, _1666637, _1666639] : [-(hAPP(c_List_Orev(_1666635), hAPP(hAPP(c_List_Odrop(_1666635), _1666637), _1666639)) = hAPP(hAPP(c_List_Otake(_1666635), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666635)), _1666639)), _1666637)), hAPP(c_List_Orev(_1666635), _1666639)))], (18726 ^ _781013) ^ [_1129963, _1129965, _1129967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129963), _1129965)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1129967), _1129965)), _1129963) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1129967), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1129965), _1129963)))], (25798 ^ _781013) ^ [_1260958, _1260960] : [class_Int_Oring__char__0(_1260958), 25801 ^ _781013 : [(25808 ^ _781013) ^ [] : [_1260960 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1260958) = hAPP(c_Int_Oring__1__class_Oof__int(_1260958), _1260960))], (25802 ^ _781013) ^ [] : [c_Groups_Ozero__class_Ozero(_1260958) = hAPP(c_Int_Oring__1__class_Oof__int(_1260958), _1260960), -(_1260960 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (38049 ^ _781013) ^ [_1509875, _1509877] : [-(c_Relation_OId__on(_1509875, _1509877) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1509875, tc_fun(tc_prod(_1509875, _1509875), tc_HOL_Obool)), _1509877), hAPP(hAPP(c_COMBC(_1509875, tc_fun(tc_prod(_1509875, _1509875), tc_HOL_Obool), tc_fun(tc_prod(_1509875, _1509875), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1509875, _1509875), tc_fun(tc_fun(tc_prod(_1509875, _1509875), tc_HOL_Obool), tc_fun(tc_prod(_1509875, _1509875), tc_HOL_Obool)), _1509875), c_Set_Oinsert(tc_prod(_1509875, _1509875))), hAPP(hAPP(c_COMBS(_1509875, _1509875, tc_prod(_1509875, _1509875)), c_Product__Type_OPair(_1509875, _1509875)), c_COMBI(_1509875)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509875, _1509875), tc_HOL_Obool)))))], (28370 ^ _781013) ^ [_1310376, _1310378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310376)), -(c_SMT_Oz3mod(_1310378, _1310376) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1310378, _1310376))], (7992 ^ _781013) ^ [_916309, _916311, _916313, _916315, _916317, _916319, _916321] : [-(hAPP(c_Fun_Ocomp(_916309, _916311, _916313, _916315), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_916313, _916309), _916317), _916319), _916321)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_916313, _916311), hAPP(c_Fun_Ocomp(_916309, _916311, _916313, _916315), _916317)), _916319), hAPP(_916315, _916321)))], (12340 ^ _781013) ^ [_1003684, _1003686, _1003688] : [class_Lattices_Olattice(_1003684), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003684), _1003686)), -(_1003686 = c_Orderings_Obot__class_Obot(tc_fun(_1003684, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003684), _1003688)), -(_1003688 = c_Orderings_Obot__class_Obot(tc_fun(_1003684, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1003684, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003684, tc_HOL_Obool)), _1003686), _1003688)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1003684), c_Big__Operators_Olattice__class_OInf__fin(_1003684, _1003686)), c_Big__Operators_Olattice__class_OInf__fin(_1003684, _1003688)))], (29229 ^ _781013) ^ [_1326301, _1326303] : [class_Groups_Oordered__ab__group__add__abs(_1326301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326301), _1326303), c_Groups_Ozero__class_Ozero(_1326301))), -(hAPP(c_Groups_Oabs__class_Oabs(_1326301), _1326303) = hAPP(c_Groups_Ouminus__class_Ouminus(_1326301), _1326303))], (9419 ^ _781013) ^ [_948020, _948022, _948024] : [class_Groups_Oordered__ab__group__add(_948020), 9422 ^ _781013 : [(9429 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948020), hAPP(c_Groups_Ouminus__class_Ouminus(_948020), _948024)), _948022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948020), hAPP(c_Groups_Ouminus__class_Ouminus(_948020), _948022)), _948024)))], (9423 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948020), hAPP(c_Groups_Ouminus__class_Ouminus(_948020), _948022)), _948024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948020), hAPP(c_Groups_Ouminus__class_Ouminus(_948020), _948024)), _948022)))]]], (15117 ^ _781013) ^ [_1060721, _1060723, _1060725] : [-(hAPP(c_Set_OCollect(_1060721), hAPP(hAPP(c_COMBS(_1060721, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1060721), c_fconj), _1060723)), _1060725)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1060721, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1060721), _1060723)), hAPP(c_Set_OCollect(_1060721), _1060725)))], (51548 ^ _781013) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (28480 ^ _781013) ^ [_1312467, _1312469, _1312471, _1312473] : [class_Orderings_Olinorder(_1312467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312467), _1312469), _1312471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312467), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312467), _1312469), _1312473)), _1312471)))], (7193 ^ _781013) ^ [_900999, _901001, _901003] : [_900999 = _901001, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901003, tc_HOL_Obool)), _901001), _900999)))], (6272 ^ _781013) ^ [_882945, _882947, _882949, _882951] : [hAPP(c_Com_Ocom_OBODY, _882945) = c_Com_Ocom_OCond(_882947, _882949, _882951)], (34355 ^ _781013) ^ [_1432405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1432405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1432405))))], (40639 ^ _781013) ^ [_1577276, _1577278, _1577280, _1577282, _1577284] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1577276, _1577278), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577276, tc_HOL_Obool)), _1577280), _1577282)), _1577284) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1577276, _1577278), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1577276, _1577278), _1577280), _1577284)), hAPP(hAPP(c_Product__Type_OSigma(_1577276, _1577278), _1577282), _1577284)))], (18838 ^ _781013) ^ [_1132719, _1132721, _1132723, _1132725, _1132727] : [class_Groups_Ocomm__monoid__mult(_1132719), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132721), _1132723)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132721), _1132725)), 18852 ^ _781013 : [(18855 ^ _781013) ^ [] : [hAPP(_1132727, 18851 ^ [_1132719, _1132721, _1132723, _1132725, _1132727]) = c_Groups_Oone__class_Oone(_1132719)], (18853 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1132721), 18851 ^ [_1132719, _1132721, _1132723, _1132725, _1132727]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1132721, tc_HOL_Obool)), _1132723), _1132725))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1132721, _1132719), _1132727), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1132721, tc_HOL_Obool)), _1132723), _1132725)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132719), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1132721, _1132719), _1132727), _1132723)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1132721, _1132719), _1132727), _1132725)))], (31607 ^ _781013) ^ [_1377266, _1377268, _1377270, _1377272, _1377274, _1377276] : [hBOOL(hAPP(hAPP(c_member(_1377266), _1377268), _1377270)), hBOOL(hAPP(hAPP(c_member(_1377272), _1377274), hAPP(_1377276, _1377268))), -(hBOOL(hAPP(hAPP(c_member(_1377272), _1377274), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377266, tc_fun(_1377272, tc_HOL_Obool)), _1377270), _1377276))))], (29197 ^ _781013) ^ [_1325783, _1325785] : [class_Groups_Oordered__ab__group__add__abs(_1325783), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325783), hAPP(c_Groups_Ouminus__class_Ouminus(_1325783), hAPP(c_Groups_Oabs__class_Oabs(_1325783), _1325785))), c_Groups_Ozero__class_Ozero(_1325783))))], (31672 ^ _781013) ^ [_1379426, _1379428, _1379430, _1379432, _1379434, _1379436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1379426, _1379428), tc_HOL_Obool)), _1379430), _1379432)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379426, tc_HOL_Obool)), _1379434), _1379436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379428, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379426, _1379428, _1379430), _1379434)), hAPP(c_Relation_OImage(_1379426, _1379428, _1379432), _1379436))))], (7109 ^ _781013) ^ [_899191, _899193, _899195, _899197] : [7110 ^ _781013 : [(7111 ^ _781013) ^ [_899301] : [hBOOL(hAPP(hAPP(c_member(_899191), _899301), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899191, tc_HOL_Obool)), _899193), _899195))), hBOOL(hAPP(_899197, _899301))]], 7119 ^ _781013 : [(7122 ^ _781013) ^ [] : [-(hBOOL(hAPP(_899197, 7118 ^ [_899191, _899193, _899195, _899197])))], (7120 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899191), 7118 ^ [_899191, _899193, _899195, _899197]), _899193)))]], 7124 ^ _781013 : [(7127 ^ _781013) ^ [] : [-(hBOOL(hAPP(_899197, 7123 ^ [_899191, _899193, _899195, _899197])))], (7125 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899191), 7123 ^ [_899191, _899193, _899195, _899197]), _899195)))]]], (41662 ^ _781013) ^ [_1603348, _1603350, _1603352] : [hAPP(hAPP(c_List_Oappend(_1603348), _1603350), _1603352) = c_List_Olist_ONil(_1603348), 41665 ^ _781013 : [(41668 ^ _781013) ^ [] : [-(_1603352 = c_List_Olist_ONil(_1603348))], (41666 ^ _781013) ^ [] : [-(_1603350 = c_List_Olist_ONil(_1603348))]]], (33552 ^ _781013) ^ [_1417589, _1417591] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417589), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417591)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417589)) = 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), _1417591), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1417589)))), 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)))], (17801 ^ _781013) ^ [_1113177, _1113179, _1113181] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113177), _1113179)), _1113181) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113177), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113179), _1113181)))], (37882 ^ _781013) ^ [_1506531, _1506533, _1506535, _1506537, _1506539] : [-(hAPP(c_Product__Type_Osnd(_1506531, _1506533), hAPP(c_Product__Type_Oapfst(_1506535, _1506531, _1506533, _1506537), _1506539)) = hAPP(c_Product__Type_Osnd(_1506535, _1506533), _1506539))], (48135 ^ _781013) ^ [_1753449, _1753451, _1753453] : [-(_1753449 = c_List_Olist_ONil(_1753451)), -(hBOOL(hAPP(hAPP(c_member(_1753451), hAPP(c_Product__Type_Ofst(_1753451, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1753451, _1753449), _1753453))), hAPP(c_List_Oset(_1753451), _1753449))))], (25948 ^ _781013) ^ [_1263547, _1263549] : [class_Rings_Olinordered__idom(_1263547), 25951 ^ _781013 : [(25958 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263547), c_Groups_Ozero__class_Ozero(_1263547)), hAPP(c_Int_Oring__1__class_Oof__int(_1263547), _1263549))))], (25952 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263547), c_Groups_Ozero__class_Ozero(_1263547)), hAPP(c_Int_Oring__1__class_Oof__int(_1263547), _1263549))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263549)))]]], (43209 ^ _781013) ^ [_1640947, _1640949, _1640951, _1640953, _1640955] : [-(_1640947 = c_Orderings_Obot__class_Obot(tc_fun(_1640949, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640949, tc_fun(_1640951, tc_HOL_Obool)), _1640947), hAPP(hAPP(c_COMBB(tc_fun(_1640951, tc_HOL_Obool), tc_fun(_1640951, tc_HOL_Obool), _1640949), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640951, tc_HOL_Obool)), _1640953)), _1640955)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640951, tc_HOL_Obool)), _1640953), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1640949, tc_fun(_1640951, tc_HOL_Obool)), _1640947), _1640955)))], (1124 ^ _781013) ^ [_797805, _797807] : [-(class_Rings_Olinordered__ring(_797805)), _797807 = _797805, class_Rings_Olinordered__ring(_797807)], (49219 ^ _781013) ^ [_1779790, _1779792, _1779794] : [49221 ^ _781013 : [(49222 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779790), 49220 ^ [_1779790, _1779792, _1779794]), _1779792)))], (49227 ^ _781013) ^ [] : [49220 ^ [_1779790, _1779792, _1779794] = 49223 ^ [_1779790, _1779792, _1779794]], (49231 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779790, _1779790)), hAPP(hAPP(c_Product__Type_OPair(_1779790, _1779790), 49223 ^ [_1779790, _1779792, _1779794]), 49220 ^ [_1779790, _1779792, _1779794])), _1779794))], (49229 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779790, _1779790)), hAPP(hAPP(c_Product__Type_OPair(_1779790, _1779790), 49220 ^ [_1779790, _1779792, _1779794]), 49223 ^ [_1779790, _1779792, _1779794])), _1779794))], (49225 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779790), 49223 ^ [_1779790, _1779792, _1779794]), _1779792)))]], -(c_Relation_Ototal__on(_1779790, _1779792, _1779794))], (3064 ^ _781013) ^ [_826920, _826922, _826924, _826926, _826928, _826930, _826932, _826934, _826936, _826938] : [-(c_List_Olinorder__class_Oinsort__insert__key(_826938, _826934, _826930, _826926, _826922) = c_List_Olinorder__class_Oinsort__insert__key(_826936, _826932, _826928, _826924, _826920)), _826938 = _826936, _826934 = _826932, _826930 = _826928, _826926 = _826924, _826922 = _826920], (10433 ^ _781013) ^ [_966155, _966157, _966159, _966161] : [class_Orderings_Oorder(_966155), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966155), _966157), _966159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966155), _966161), _966157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966155), _966161), _966159)))], (26555 ^ _781013) ^ [_1275308, _1275310, _1275312] : [class_Orderings_Olinorder(_1275308), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275308), _1275310), _1275312)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275308, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1275308, _1275310, _1275312)), hAPP(c_SetInterval_Oord__class_OatLeast(_1275308), _1275312)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1275308), _1275310))], (18859 ^ _781013) ^ [_1133214, _1133216] : [class_Groups_Olinordered__ab__group__add(_1133214), 18862 ^ _781013 : [(18869 ^ _781013) ^ [] : [_1133216 = c_Groups_Ozero__class_Ozero(_1133214), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133214), _1133216), _1133216) = c_Groups_Ozero__class_Ozero(_1133214))], (18863 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133214), _1133216), _1133216) = c_Groups_Ozero__class_Ozero(_1133214), -(_1133216 = c_Groups_Ozero__class_Ozero(_1133214))]]], (30141 ^ _781013) ^ [_1344149, _1344151, _1344153, _1344155] : [class_Orderings_Olinorder(_1344149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344149), _1344151), _1344153)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344149), _1344155), _1344153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344149), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344149), _1344151), _1344155)), _1344153)))], (4680 ^ _781013) ^ [_851836, _851838, _851840, _851842] : [-(c_Product__Type_Osnd(_851842, _851838) = c_Product__Type_Osnd(_851840, _851836)), _851842 = _851840, _851838 = _851836], (45992 ^ _781013) ^ [_1701372, _1701374, _1701376] : [class_Complete__Lattice_Ocomplete__lattice(_1701372), -(c_Complete__Lattice_OInf__class_OInf(_1701372, hAPP(hAPP(c_Set_Oinsert(_1701372), _1701374), hAPP(hAPP(c_Set_Oinsert(_1701372), _1701376), c_Orderings_Obot__class_Obot(tc_fun(_1701372, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1701372), _1701374), _1701376))], (16199 ^ _781013) ^ [_1080408, _1080410] : [class_Groups_Oordered__ab__group__add(_1080408), 16202 ^ _781013 : [(16209 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080408), _1080410), c_Groups_Ozero__class_Ozero(_1080408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080408), c_Groups_Ozero__class_Ozero(_1080408)), hAPP(c_Groups_Ouminus__class_Ouminus(_1080408), _1080410))))], (16203 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080408), c_Groups_Ozero__class_Ozero(_1080408)), hAPP(c_Groups_Ouminus__class_Ouminus(_1080408), _1080410))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080408), _1080410), c_Groups_Ozero__class_Ozero(_1080408))))]]], (27659 ^ _781013) ^ [_1297275, _1297277, _1297279, _1297281] : [class_Divides_Osemiring__div(_1297275), -(c_Divides_Odiv__class_Omod(_1297275, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297275), _1297277), _1297279), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297275), _1297281), _1297279)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297275), c_Divides_Odiv__class_Omod(_1297275, _1297277, _1297281)), _1297279))], (5697 ^ _781013) ^ [_871101, _871103, _871105] : [_871103 = _871105, -(hAPP(c_Option_Ooption_OSome(_871101), _871103) = hAPP(c_Option_Ooption_OSome(_871101), _871105))], (39771 ^ _781013) ^ [_1551830, _1551832] : [-(c_List_Obutlast(_1551830, _1551832) = hAPP(hAPP(c_List_Otake(_1551830), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551830)), _1551832)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1551832))], (9062 ^ _781013) ^ [_940496, _940498, _940500, _940502, _940504, _940506] : [hBOOL(hAPP(hAPP(c_member(_940496), _940498), _940500)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_940496, tc_Option_Ooption(_940502)), c_Map_Orestrict__map(_940496, _940502, _940504, _940500)), _940498), _940506) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_940496, tc_Option_Ooption(_940502)), c_Map_Orestrict__map(_940496, _940502, _940504, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940496, tc_HOL_Obool)), _940500), hAPP(hAPP(c_Set_Oinsert(_940496), _940498), c_Orderings_Obot__class_Obot(tc_fun(_940496, tc_HOL_Obool)))))), _940498), _940506))], (34421 ^ _781013) ^ [] : [-(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)))))], (4034 ^ _781013) ^ [_842045, _842047] : [_842047 = _842045, -(c_Relation_OField(_842047) = c_Relation_OField(_842045))], (32708 ^ _781013) ^ [_1401469, _1401471, _1401473, _1401475] : [class_Fields_Ofield__inverse__zero(_1401469), class_Int_Onumber(_1401469), 32715 ^ _781013 : [(32716 ^ _781013) ^ [] : [_1401471 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1401469), _1401473), hAPP(c_Int_Onumber__class_Onumber__of(_1401469), _1401475)), 32719 ^ _781013 : [(32726 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1401469), _1401475) = c_Groups_Ozero__class_Ozero(_1401469), -(_1401471 = c_Groups_Ozero__class_Ozero(_1401469))], (32720 ^ _781013) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1401469), _1401475) = c_Groups_Ozero__class_Ozero(_1401469)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401469), _1401471), hAPP(c_Int_Onumber__class_Onumber__of(_1401469), _1401475)) = _1401473)]]], (32732 ^ _781013) ^ [] : [-(_1401471 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1401469), _1401473), hAPP(c_Int_Onumber__class_Onumber__of(_1401469), _1401475))), 32735 ^ _781013 : [(32738 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401469), _1401471), hAPP(c_Int_Onumber__class_Onumber__of(_1401469), _1401475)) = _1401473], (32736 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1401469), _1401475) = c_Groups_Ozero__class_Ozero(_1401469)]], 32739 ^ _781013 : [(32742 ^ _781013) ^ [] : [_1401471 = c_Groups_Ozero__class_Ozero(_1401469)], (32740 ^ _781013) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1401469), _1401475) = c_Groups_Ozero__class_Ozero(_1401469))]]]]], (10427 ^ _781013) ^ [_966002, _966004, _966006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966002, tc_HOL_Obool)), _966006), _966004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966002, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966002, tc_HOL_Obool)), _966004)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966002, tc_HOL_Obool)), _966006))))], (47089 ^ _781013) ^ [_1728657, _1728659, _1728661] : [-(hAPP(c_Set_Oimage(tc_prod(_1728657, _1728659), _1728659, c_Product__Type_Osnd(_1728657, _1728659)), _1728661) = hAPP(c_Relation_ORange(_1728657, _1728659), _1728661))], (17260 ^ _781013) ^ [_1102452, _1102454, _1102456] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1102452), _1102454)), hBOOL(hAPP(hAPP(c_member(_1102452), _1102456), _1102454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1102452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1102452, tc_HOL_Obool)), _1102454), hAPP(hAPP(c_Set_Oinsert(_1102452), _1102456), c_Orderings_Obot__class_Obot(tc_fun(_1102452, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1102452), _1102454))))], (37931 ^ _781013) ^ [_1507642, _1507644, _1507646, _1507648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1507642), _1507644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1507646), _1507648)), -(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), _1507642), _1507646)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1507644), _1507648))), c_FunDef_Opair__leq)))], (21373 ^ _781013) ^ [_1182146, _1182148, _1182150] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182146), _1182148))), -(c_Smallcheck_Osmall_H(_1182150, _1182146, _1182148) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1182150, _1182146, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1182148), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1182150, _1182148)))], (5579 ^ _781013) ^ [_868828, _868830] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_868828, _868830, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_868828), tc_HOL_Obool))))], (28248 ^ _781013) ^ [_1308253, _1308255, _1308257] : [-(hBOOL(hAPP(_1308253, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1308255, _1308257)))), 28251 ^ _781013 : [(28254 ^ _781013) ^ [] : [hBOOL(hAPP(_1308253, _1308255))], (28252 ^ _781013) ^ [] : [-(_1308257 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 28257 ^ _781013 : [(28258 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1308257)))], (28264 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 28260 ^ [_1308253, _1308255, _1308257]), _1308257)))], (28268 ^ _781013) ^ [] : [hBOOL(hAPP(_1308253, 28260 ^ [_1308253, _1308255, _1308257]))], (28266 ^ _781013) ^ [] : [-(_1308255 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1308257), 28259 ^ [_1308253, _1308255, _1308257])), 28260 ^ [_1308253, _1308255, _1308257]))], (28262 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 28260 ^ [_1308253, _1308255, _1308257])))]], 28269 ^ _781013 : [(28270 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1308257), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28276 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 28272 ^ [_1308253, _1308255, _1308257]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28280 ^ _781013) ^ [] : [hBOOL(hAPP(_1308253, 28272 ^ [_1308253, _1308255, _1308257]))], (28278 ^ _781013) ^ [] : [-(_1308255 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1308257), 28271 ^ [_1308253, _1308255, _1308257])), 28272 ^ [_1308253, _1308255, _1308257]))], (28274 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1308257), 28272 ^ [_1308253, _1308255, _1308257])))]]], (5358 ^ _781013) ^ [_862739, _862741, _862743, _862745] : [-(c_List_Ofilter(_862745, _862741) = c_List_Ofilter(_862743, _862739)), _862745 = _862743, _862741 = _862739], (30731 ^ _781013) ^ [_1356315, _1356317, _1356319] : [class_Orderings_Olinorder(_1356315), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356315), _1356317)), -(_1356317 = c_Orderings_Obot__class_Obot(tc_fun(_1356315, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1356315, c_Orderings_Oord__class_Omax(_1356315), hAPP(hAPP(c_Set_Oinsert(_1356315), _1356319), _1356317)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356315), _1356319), c_Big__Operators_Olattice_OSup__fin(_1356315, c_Orderings_Oord__class_Omax(_1356315), _1356317)))], (42968 ^ _781013) ^ [_1634263, _1634265, _1634267, _1634269, _1634271] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634263, tc_fun(_1634265, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1634263), _1634267), _1634269)), _1634271) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1634265, tc_HOL_Obool)), hAPP(_1634271, _1634267)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634263, tc_fun(_1634265, tc_HOL_Obool)), _1634269), _1634271)))], (20 ^ _781013) ^ [_781273, _781275, _781277, _781279] : [-(c_Option_Ois__none(_781277, _781273)), c_Option_Ois__none(_781279, _781275), _781279 = _781277, _781275 = _781273], (41129 ^ _781013) ^ [_1591568, _1591570, _1591572, _1591574] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1591568)), hAPP(hAPP(c_List_Olist_OCons(_1591568), _1591570), _1591572)), c_List_Olists(_1591568, _1591574)))), hBOOL(hAPP(hAPP(c_member(_1591568), _1591570), _1591574)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1591568)), _1591572), c_List_Olists(_1591568, _1591574)))], (19975 ^ _781013) ^ [_1155093, _1155095] : [_1155093 = _1155095, -(hAPP(c_Nat_OSuc, _1155093) = hAPP(c_Nat_OSuc, _1155095))], (32564 ^ _781013) ^ [_1399040, _1399042, _1399044, _1399046] : [class_Int_Onumber__ring(_1399040), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399040), hAPP(c_Int_Onumber__class_Onumber__of(_1399040), _1399042)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399040), hAPP(c_Int_Onumber__class_Onumber__of(_1399040), _1399044)), _1399046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399040), hAPP(c_Int_Onumber__class_Onumber__of(_1399040), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1399042), _1399044))), _1399046))], (41811 ^ _781013) ^ [_1606353, _1606355, _1606357, _1606359, _1606361, _1606363] : [hAPP(hAPP(c_List_Oappend(_1606353), _1606355), _1606357) = _1606359, _1606361 = hAPP(hAPP(c_List_Oappend(_1606353), _1606357), _1606363), -(hAPP(hAPP(c_List_Oappend(_1606353), _1606355), _1606361) = hAPP(hAPP(c_List_Oappend(_1606353), _1606359), _1606363))], (12898 ^ _781013) ^ [_1015050, _1015052, _1015054, _1015056, _1015058] : [-(hAPP(c_Set_Ovimage(_1015050, _1015052, _1015054), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1015052, tc_HOL_Obool)), _1015056), _1015058)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1015050, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1015050, _1015052, _1015054), _1015056)), hAPP(c_Set_Ovimage(_1015050, _1015052, _1015054), _1015058)))], (36930 ^ _781013) ^ [_1485600, _1485602] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1485600), _1485602)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1485600), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1485602)))], (5883 ^ _781013) ^ [_875666, _875668, _875670] : [c_Com_Ocom_OSemi(_875666, _875668) = hAPP(c_Com_Ocom_OBODY, _875670)], (45519 ^ _781013) ^ [_1690459, _1690461, _1690463, _1690465, _1690467, _1690469, _1690471, _1690473] : [c_Fun_Oinj__on(_1690459, _1690461, _1690463, _1690465), 45525 ^ _781013 : [(45528 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1690459, tc_HOL_Obool)), hAPP(_1690471, 45524 ^ [_1690459, _1690461, _1690463, _1690465, _1690467, _1690469, _1690471, _1690473])), _1690465))], (45526 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1690467), 45524 ^ [_1690459, _1690461, _1690463, _1690465, _1690467, _1690469, _1690471, _1690473]), _1690469)))]], hBOOL(hAPP(hAPP(c_member(_1690467), _1690473), _1690469)), -(hAPP(c_Set_Oimage(_1690459, _1690461, _1690463), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1690467, tc_fun(_1690459, tc_HOL_Obool)), _1690469), _1690471)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1690467, tc_fun(_1690461, tc_HOL_Obool)), _1690469), hAPP(hAPP(c_COMBB(tc_fun(_1690459, tc_HOL_Obool), tc_fun(_1690461, tc_HOL_Obool), _1690467), c_Set_Oimage(_1690459, _1690461, _1690463)), _1690471)))], (51542 ^ _781013) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (15083 ^ _781013) ^ [_1059883, _1059885] : [-(hAPP(c_Set_OCollect(_1059883), hAPP(hAPP(c_COMBC(_1059883, tc_fun(_1059883, tc_HOL_Obool), tc_HOL_Obool), c_member(_1059883)), _1059885)) = _1059885)], (7861 ^ _781013) ^ [_913498, _913500, _913502] : [hBOOL(hAPP(hAPP(c_member(_913498), _913500), _913502)), -(hAPP(hAPP(c_Set_Oinsert(_913498), _913500), _913502) = _913502)], (43454 ^ _781013) ^ [_1646260, _1646262, _1646264] : [-(hAPP(c_List_Oset(_1646260), hAPP(c_List_Ofilter(_1646260, _1646262), _1646264)) = hAPP(c_Set_OCollect(_1646260), hAPP(hAPP(c_COMBS(_1646260, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1646260), c_fconj), hAPP(hAPP(c_COMBC(_1646260, tc_fun(_1646260, tc_HOL_Obool), tc_HOL_Obool), c_member(_1646260)), hAPP(c_List_Oset(_1646260), _1646264)))), _1646262)))], (20695 ^ _781013) ^ [_1167888, _1167890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1167888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167888), hAPP(c_Nat_OSuc, _1167890))), _1167888)))], (40113 ^ _781013) ^ [_1563115, _1563117, _1563119, _1563121, _1563123] : [-(hAPP(hAPP(c_List_Olist__update(_1563115, hAPP(hAPP(c_List_Olist_OCons(_1563115), _1563117), _1563119)), _1563121), _1563123) = c_Nat_Onat_Onat__case(tc_List_Olist(_1563115), hAPP(hAPP(c_List_Olist_OCons(_1563115), _1563123), _1563119), hAPP(hAPP(c_COMBB(tc_List_Olist(_1563115), tc_List_Olist(_1563115), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1563115), _1563117)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1563115, tc_List_Olist(_1563115)), c_List_Olist__update(_1563115, _1563119)), _1563123)), _1563121))], (47067 ^ _781013) ^ [_1728215, _1728217, _1728219] : [hAPP(c_Relation_ORange(_1728215, _1728217), _1728219) = c_Orderings_Obot__class_Obot(tc_fun(_1728217, tc_HOL_Obool)), -(_1728219 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1728215, _1728217), tc_HOL_Obool)))], (40609 ^ _781013) ^ [_1576243, _1576245, _1576247, _1576249, _1576251] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1576243, _1576245), _1576247), hAPP(hAPP(c_COMBS(_1576243, tc_fun(_1576245, tc_HOL_Obool), tc_fun(_1576245, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576245, tc_HOL_Obool), tc_fun(tc_fun(_1576245, tc_HOL_Obool), tc_fun(_1576245, tc_HOL_Obool)), _1576243), c_Groups_Ominus__class_Ominus(tc_fun(_1576245, tc_HOL_Obool))), _1576249)), _1576251)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1576243, _1576245), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1576243, _1576245), _1576247), _1576249)), hAPP(hAPP(c_Product__Type_OSigma(_1576243, _1576245), _1576247), _1576251)))], (20478 ^ _781013) ^ [_1163448, _1163450, _1163452] : [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, _1163448)), _1163450)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1163448)), _1163452))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1163450), _1163452)))], (6599 ^ _781013) ^ [_889053, _889055] : [c_Option_Oset(_889053, _889055) = c_Orderings_Obot__class_Obot(tc_fun(_889053, tc_HOL_Obool)), -(_889055 = c_Option_Ooption_ONone(_889053))], (11632 ^ _781013) ^ [_990395, _990397] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_990395, _990397)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_990395, _990397), tc_HOL_Obool)))), 11635 ^ _781013 : [(11638 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_990397), c_Orderings_Otop__class_Otop(tc_fun(_990397, tc_HOL_Obool)))))], (11636 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_990395), c_Orderings_Otop__class_Otop(tc_fun(_990395, tc_HOL_Obool)))))]]], (19528 ^ _781013) ^ [_1146498, _1146500, _1146502, _1146504] : [class_Rings_Olinordered__semidom(_1146498), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146498), hAPP(hAPP(c_Power_Opower__class_Opower(_1146498), _1146500), _1146502)), hAPP(hAPP(c_Power_Opower__class_Opower(_1146498), _1146504), _1146502))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146498), c_Groups_Ozero__class_Ozero(_1146498)), _1146504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146498), _1146500), _1146504)))], (46814 ^ _781013) ^ [_1722583, _1722585] : [c_Wellfounded_Owf(_1722583, _1722585), -(c_Wellfounded_Owf(tc_fun(_1722583, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1722583, _1722585)))], (16375 ^ _781013) ^ [_1083952, _1083954, _1083956] : [-(hAPP(c_Set_OCollect(_1083952), hAPP(hAPP(c_COMBS(_1083952, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1083952), c_fimplies), _1083954)), _1083956)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1083952, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1083952, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1083952), _1083954))), hAPP(c_Set_OCollect(_1083952), _1083956)))], (14714 ^ _781013) ^ [_1054079, _1054081] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1054079), _1054081)))), -(_1054081 = c_Orderings_Obot__class_Obot(tc_fun(_1054079, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054079), _1054081))], (5615 ^ _781013) ^ [_869499, _869501, _869503] : [class_Orderings_Obot(_869499), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_869501, _869499)), _869503) = c_Orderings_Obot__class_Obot(_869499))], (48854 ^ _781013) ^ [_1770427, _1770429, _1770431, _1770433, _1770435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1770427, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1770429, _1770427, _1770431), _1770433)), _1770435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1770429, tc_HOL_Obool)), _1770433), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1770429, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1770427, _1770429, hAPP(c_Relation_Oconverse(_1770429, _1770427), _1770431)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1770427, tc_HOL_Obool)), _1770435))))))], (48093 ^ _781013) ^ [_1752933, _1752935] : [48094 ^ _781013 : [(48097 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1752935), _1752933))], (48095 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1752933), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1752933, _1752935) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (10599 ^ _781013) ^ [_968614, _968616, _968618] : [class_Orderings_Olinorder(_968614), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968614), _968616), _968618))), 10606 ^ _781013 : [(10613 ^ _781013) ^ [] : [_968616 = _968618, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968614), _968616), _968618)))], (10607 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968614), _968616), _968618)), -(_968616 = _968618)]]], (9819 ^ _781013) ^ [_954256, _954258, _954260, _954262, _954264] : [c_Finite__Set_Ofun__left__comm__idem(_954256, _954258, _954260), -(hAPP(hAPP(_954260, _954262), hAPP(hAPP(_954260, _954262), _954264)) = hAPP(hAPP(_954260, _954262), _954264))], (8139 ^ _781013) ^ [_919750, _919752, _919754, _919756, _919758] : [c_Finite__Set_Ofolding__one__idem(_919750, _919752, _919754), hBOOL(hAPP(c_Finite__Set_Ofinite(_919750), _919756)), hBOOL(hAPP(hAPP(c_member(_919750), _919758), _919756)), -(hAPP(hAPP(_919752, _919758), hAPP(_919754, _919756)) = hAPP(_919754, _919756))], (25636 ^ _781013) ^ [_1258335, _1258337] : [c_Nat__Transfer_Ois__nat(_1258335), c_Nat__Transfer_Onat__set(_1258337), 25643 ^ _781013 : [(25650 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1258335)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258337))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1258335), _1258337)))], (25644 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1258335), _1258337)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1258335)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258337))))]]], (51658 ^ _781013) ^ [_1825449, _1825451] : [hBOOL(hAPP(hAPP(c_fconj, _1825449), _1825451)), -(hBOOL(_1825451))], (6034 ^ _781013) ^ [_878546, _878548, _878550] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _878546)), _878548), _878550)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _878546))), _878548), _878550)))], (31349 ^ _781013) ^ [_1368666, _1368668, _1368670, _1368672, _1368674] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_1368666, _1368668)), _1368670), _1368672), _1368674)), 31353 ^ _781013 : [(31356 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1368668), 31352 ^ [_1368666, _1368668, _1368670, _1368672, _1368674]), _1368672), _1368674)))], (31354 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1368666), _1368670), _1368672), 31352 ^ [_1368666, _1368668, _1368670, _1368672, _1368674])))]]], (42003 ^ _781013) ^ [_1611401, _1611403, _1611405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1611401), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611403)), _1611405))), -(hAPP(hAPP(c_List_Otake(_1611403), hAPP(c_Nat_OSuc, _1611401)), _1611405) = hAPP(hAPP(c_List_Oappend(_1611403), hAPP(hAPP(c_List_Otake(_1611403), _1611401), _1611405)), hAPP(hAPP(c_List_Olist_OCons(_1611403), hAPP(hAPP(c_List_Onth(_1611403), _1611405), _1611401)), c_List_Olist_ONil(_1611403))))], (38802 ^ _781013) ^ [_1528653, _1528655] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1528653), hAPP(c_List_Oset(_1528653), _1528655))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528653)), _1528655))))], (34511 ^ _781013) ^ [_1434767, _1434769] : [class_Int_Onumber__ring(_1434767), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434767), hAPP(c_Int_Onumber__class_Onumber__of(_1434767), _1434769)), c_Groups_Oone__class_Oone(_1434767)) = hAPP(c_Int_Onumber__class_Onumber__of(_1434767), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1434769), c_Int_OBit1(c_Int_OPls))))], (42009 ^ _781013) ^ [_1611621, _1611623, _1611625, _1611627, _1611629, _1611631] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611621), tc_List_Olist(_1611621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611621), tc_List_Olist(_1611621)), hAPP(hAPP(c_List_Oappend(_1611621), _1611623), hAPP(hAPP(c_List_Olist_OCons(_1611621), _1611625), c_List_Olist_ONil(_1611621)))), hAPP(hAPP(c_List_Oappend(_1611621), _1611627), hAPP(hAPP(c_List_Olist_OCons(_1611621), _1611629), c_List_Olist_ONil(_1611621))))), c_List_Olistrel1(_1611621, _1611631))), 42014 ^ _781013 : [(42017 ^ _781013) ^ [] : [-(_1611625 = _1611629)], (42015 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611621), tc_List_Olist(_1611621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611621), tc_List_Olist(_1611621)), _1611623), _1611627)), c_List_Olistrel1(_1611621, _1611631))))]], 42018 ^ _781013 : [(42021 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611621, _1611621)), hAPP(hAPP(c_Product__Type_OPair(_1611621, _1611621), _1611625), _1611629)), _1611631)))], (42019 ^ _781013) ^ [] : [-(_1611623 = _1611627)]]], (23759 ^ _781013) ^ [_1225112, _1225114, _1225116] : [class_Orderings_Oorder(_1225112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225112), _1225114), _1225116)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1225112, _1225116, _1225114) = c_Orderings_Obot__class_Obot(tc_fun(_1225112, tc_HOL_Obool)))], (15787 ^ _781013) ^ [_1073090, _1073092, _1073094, _1073096] : [class_Rings_Olinordered__semiring__strict(_1073090), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073090), _1073092), _1073094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073090), c_Groups_Ozero__class_Ozero(_1073090)), _1073096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073090), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073090), _1073092), _1073096)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073090), _1073094), _1073096))))], (34891 ^ _781013) ^ [_1441594, _1441596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1441594)), c_Int_OBit0(_1441596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441594), _1441596)))], (7259 ^ _781013) ^ [_902193, _902195, _902197, _902199] : [_902193 = _902195, 7262 ^ _781013 : [(7269 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_902197), _902195), _902199)), -(hBOOL(hAPP(hAPP(c_member(_902197), _902193), _902199)))], (7263 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_902197), _902193), _902199)), -(hBOOL(hAPP(hAPP(c_member(_902197), _902195), _902199)))]]], (32454 ^ _781013) ^ [_1396885, _1396887, _1396889] : [class_Int_Onumber__ring(_1396885), class_Rings_Olinordered__idom(_1396885), 32461 ^ _781013 : [(32468 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1396887), _1396889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396885), hAPP(c_Int_Onumber__class_Onumber__of(_1396885), _1396887)), hAPP(c_Int_Onumber__class_Onumber__of(_1396885), _1396889))))], (32462 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396885), hAPP(c_Int_Onumber__class_Onumber__of(_1396885), _1396887)), hAPP(c_Int_Onumber__class_Onumber__of(_1396885), _1396889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1396887), _1396889)))]]], (17813 ^ _781013) ^ [_1113501, _1113503, _1113505, _1113507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1113501), _1113503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1113505), _1113507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113501), _1113505)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113503), _1113507))))], (2928 ^ _781013) ^ [_824812, _824814, _824816, _824818] : [-(c_List_Olistset(_824818, _824814) = c_List_Olistset(_824816, _824812)), _824818 = _824816, _824814 = _824812], (29086 ^ _781013) ^ [_1323605] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1323605, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36918 ^ _781013) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (40157 ^ _781013) ^ [_1564088, _1564090, _1564092, _1564094] : [-(_1564088 = _1564090), -(c_List_Oremove1(_1564092, _1564088, hAPP(hAPP(c_List_Olist_OCons(_1564092), _1564090), _1564094)) = hAPP(hAPP(c_List_Olist_OCons(_1564092), _1564090), c_List_Oremove1(_1564092, _1564088, _1564094)))], (35645 ^ _781013) ^ [_1455407, _1455409] : [class_Int_Onumber__ring(_1455407), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1455407), hAPP(c_Int_Onumber__class_Onumber__of(_1455407), c_Int_OMin)), _1455409) = hAPP(c_Groups_Ouminus__class_Ouminus(_1455407), _1455409))], (39568 ^ _781013) ^ [_1546443, _1546445, _1546447, _1546449] : [class_Orderings_Oord(_1546443), -(hAPP(c_Hilbert__Choice_OGreatestM(_1546445, _1546443, _1546447), _1546449) = c_Hilbert__Choice_OEps(_1546445, hAPP(hAPP(c_COMBS(_1546445, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546445), c_fconj), _1546449)), hAPP(hAPP(c_COMBB(tc_fun(_1546445, tc_HOL_Obool), tc_HOL_Obool, _1546445), c_HOL_OAll(_1546445)), hAPP(hAPP(c_COMBB(tc_fun(_1546445, tc_HOL_Obool), tc_fun(_1546445, tc_HOL_Obool), _1546445), hAPP(c_COMBS(_1546445, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546445), c_fimplies), _1546449))), hAPP(hAPP(c_COMBB(_1546443, tc_fun(_1546445, tc_HOL_Obool), _1546445), hAPP(c_COMBC(_1546445, _1546443, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1546443, tc_fun(_1546443, tc_HOL_Obool), _1546445), c_Orderings_Oord__class_Oless__eq(_1546443)), _1546447))), _1546447))))))], (7107 ^ _781013) ^ [_899086, _899088, _899090, _899092] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899086, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899086, tc_HOL_Obool)), _899088), _899090)), _899092) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899086, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899086, tc_HOL_Obool)), _899088), _899092)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899086, tc_HOL_Obool)), _899090), _899092)))], (7965 ^ _781013) ^ [_915733, _915735, _915737, _915739] : [_915739 = c_Option_Ooption_ONone(_915733), -(hAPP(hAPP(c_Option_Omap(_915733, _915735), _915737), _915739) = c_Option_Ooption_ONone(_915735))], (44665 ^ _781013) ^ [_1672869, _1672871, _1672873, _1672875, _1672877] : [hBOOL(hAPP(hAPP(c_member(_1672869), _1672871), hAPP(c_List_Oset(_1672869), _1672873))), -(hBOOL(hAPP(_1672875, _1672871))), -(c_List_OtakeWhile(_1672869, _1672875, hAPP(hAPP(c_List_Oappend(_1672869), _1672873), _1672877)) = c_List_OtakeWhile(_1672869, _1672875, _1672873))], (1474 ^ _781013) ^ [_802180, _802182] : [-(class_Rings_Olinordered__semiring__strict(_802180)), _802182 = _802180, class_Rings_Olinordered__semiring__strict(_802182)], (12850 ^ _781013) ^ [_1014011, _1014013, _1014015, _1014017, _1014019] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1014011, _1014013, _1014015), _1014017), _1014019)), -(hBOOL(hAPP(_1014017, hAPP(_1014015, _1014019))))], (17919 ^ _781013) ^ [_1115239, _1115241] : [-(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)), _1115239), _1115241))], (51288 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (47270 ^ _781013) ^ [_1733811, _1733813, _1733815, _1733817] : [47271 ^ _781013 : [(47272 ^ _781013) ^ [_1733865] : [hBOOL(hAPP(hAPP(_1733815, _1733817), _1733865))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1733811, _1733813, _1733815), _1733817)))], (28748 ^ _781013) ^ [_1317536, _1317538] : [class_Groups_Oordered__ab__group__add__abs(_1317536), 28751 ^ _781013 : [(28758 ^ _781013) ^ [] : [_1317538 = c_Groups_Ozero__class_Ozero(_1317536), -(hAPP(c_Groups_Oabs__class_Oabs(_1317536), _1317538) = c_Groups_Ozero__class_Ozero(_1317536))], (28752 ^ _781013) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1317536), _1317538) = c_Groups_Ozero__class_Ozero(_1317536), -(_1317538 = c_Groups_Ozero__class_Ozero(_1317536))]]], (8705 ^ _781013) ^ [_932285, _932287, _932289] : [hAPP(hAPP(c_COMBC(_932285, tc_fun(_932285, tc_HOL_Obool), tc_HOL_Obool), c_member(_932285)), _932287) = hAPP(hAPP(c_COMBC(_932285, tc_fun(_932285, tc_HOL_Obool), tc_HOL_Obool), c_member(_932285)), _932289), -(_932287 = _932289)], (37365 ^ _781013) ^ [_1494311, _1494313] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1494311, _1494313) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1494311, _1494313)))], (49466 ^ _781013) ^ [_1786507, _1786509, _1786511, _1786513, _1786515] : [class_Complete__Lattice_Ocomplete__lattice(_1786507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1786509), _1786511)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1786507), _1786513), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1786509, _1786507), _1786511), _1786515)) = hAPP(hAPP(c_Finite__Set_Ofold(_1786509, _1786507, hAPP(hAPP(c_COMBB(_1786507, tc_fun(_1786507, _1786507), _1786509), c_Lattices_Osemilattice__inf__class_Oinf(_1786507)), _1786515)), _1786513), _1786511))], (38568 ^ _781013) ^ [_1522824, _1522826, _1522828] : [hBOOL(hAPP(c_List_Odistinct(_1522824), _1522826)), -(hBOOL(hAPP(c_List_Odistinct(_1522824), c_List_Oremove1(_1522824, _1522828, _1522826))))], (15119 ^ _781013) ^ [_1060794, _1060796] : [-(hAPP(c_Set_OCollect(_1060794), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1060794), c_fNot), _1060796)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1060794, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1060794), _1060796)))], (51628 ^ _781013) ^ [] : [-(hBOOL(c_fTrue))], (26673 ^ _781013) ^ [_1277450, _1277452, _1277454] : [class_Orderings_Oorder(_1277450), 26676 ^ _781013 : [(26683 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277450), _1277454), _1277452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277450, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1277450), _1277452)), hAPP(c_SetInterval_Oord__class_OatLeast(_1277450), _1277454))))], (26677 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277450, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1277450), _1277452)), hAPP(c_SetInterval_Oord__class_OatLeast(_1277450), _1277454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277450), _1277454), _1277452)))]]], (39177 ^ _781013) ^ [_1537561, _1537563] : [-(hAPP(c_List_Oset(_1537561), _1537563) = hAPP(c_Set_OCollect(_1537561), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1537561), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1537561, 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)), _1537561), 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)), _1537561), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1537561, tc_fun(tc_Nat_Onat, _1537561), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1537561, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1537561), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1537561), c_COMBB(_1537561, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1537561), _1537563))))), 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(_1537561)), _1537563))))))], (36296 ^ _781013) ^ [_1472711, _1472713, _1472715, _1472717, _1472719] : [c_Equiv__Relations_Oequiv(_1472711, _1472713, _1472715), hBOOL(hAPP(hAPP(c_member(tc_prod(_1472711, _1472711)), hAPP(hAPP(c_Product__Type_OPair(_1472711, _1472711), _1472717), _1472719)), _1472715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472711, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1472711, _1472711, _1472715), hAPP(hAPP(c_Set_Oinsert(_1472711), _1472717), c_Orderings_Obot__class_Obot(tc_fun(_1472711, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1472711, _1472711, _1472715), hAPP(hAPP(c_Set_Oinsert(_1472711), _1472719), c_Orderings_Obot__class_Obot(tc_fun(_1472711, tc_HOL_Obool)))))))], (18336 ^ _781013) ^ [_1122417, _1122419] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122417), _1122419)), _1122417)))], (50970 ^ _781013) ^ [_1817956, _1817958, _1817960] : [c_List_Olist_ONil(_1817956) = c_List_Oreplicate(_1817956, _1817958, _1817960), -(_1817958 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25601 ^ _781013) ^ [_1257594, _1257596, _1257598] : [class_Groups_Ocomm__monoid__add(_1257594), class_Groups_Ocomm__monoid__mult(_1257594), c_Nat__Transfer_Onat__set(_1257596), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1257594), _1257598), _1257596) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1257594), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1257594, tc_Nat_Onat), _1257598), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1257596)))], (36637 ^ _781013) ^ [_1480426, _1480428, _1480430] : [-(hAPP(c_Divides_Oadjust(_1480426), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480428), _1480430)) = 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), _1480430), _1480426)), 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)))), _1480428)), 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)))), _1480428)), _1480430))))], (19050 ^ _781013) ^ [_1137476, _1137478, _1137480, _1137482, _1137484] : [hBOOL(hAPP(hAPP(c_member(_1137476), _1137478), c_SetInterval_Oord_OatLeastAtMost(_1137476, _1137480, _1137482, _1137484))), 19053 ^ _781013 : [(19056 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1137480, _1137478), _1137484)))], (19054 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1137480, _1137482), _1137478)))]]], (23230 ^ _781013) ^ [_1215454, _1215456, _1215458] : [-(hBOOL(hAPP(_1215454, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1215456), _1215458)))), 23233 ^ _781013 : [(23236 ^ _781013) ^ [] : [hBOOL(hAPP(_1215454, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23234 ^ _781013) ^ [] : [-(_1215458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 23237 ^ _781013 : [(23242 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 23240 ^ [_1215454, _1215456, _1215458]), _1215458)))], (23244 ^ _781013) ^ [] : [-(_1215456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215458), 23239 ^ [_1215454, _1215456, _1215458])), 23240 ^ [_1215454, _1215456, _1215458]))], (23246 ^ _781013) ^ [] : [hBOOL(hAPP(_1215454, 23239 ^ [_1215454, _1215456, _1215458]))], (23238 ^ _781013) ^ [] : [_1215458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (33350 ^ _781013) ^ [_1414038, _1414040] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414038)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1414040)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1414038), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1414040))))], (26141 ^ _781013) ^ [_1267292, _1267294] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1267292), hAPP(c_Nat_OSuc, _1267294)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1267292, _1267294))], (51514 ^ _781013) ^ [_1823837] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1823837)))], (34741 ^ _781013) ^ [_1438910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1438910), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1438910)), c_Int_OPls)))], (18338 ^ _781013) ^ [_1122453, _1122455, _1122457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122453), _1122455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122457), _1122455)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122457), _1122453))))], (21079 ^ _781013) ^ [_1176617, _1176619, _1176621] : [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), _1176617), _1176619)), _1176621))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176621), _1176617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176619)))], (36024 ^ _781013) ^ [_1466634, _1466636, _1466638, _1466640, _1466642, _1466644] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1466634, _1466636), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1466638), _1466640))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1466634, _1466636), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1466642), _1466644))), -(_1466636 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1466638 = _1466642)], (51200 ^ _781013) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (39755 ^ _781013) ^ [_1551455, _1551457, _1551459, _1551461] : [-(hAPP(hAPP(c_List_Omap(_1551455, _1551457), _1551459), c_List_Obutlast(_1551455, _1551461)) = c_List_Obutlast(_1551457, hAPP(hAPP(c_List_Omap(_1551455, _1551457), _1551459), _1551461)))], (20731 ^ _781013) ^ [_1168483, _1168485] : [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), _1168483), _1168485))), 20734 ^ _781013 : [(20737 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168485)))], (20735 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168483)))]]], (7051 ^ _781013) ^ [_897709, _897711, _897713, _897715] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897709, tc_HOL_Obool)), _897711), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897709, tc_HOL_Obool)), _897713), _897715)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897709, tc_HOL_Obool)), _897713), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897709, tc_HOL_Obool)), _897711), _897715)))], (23439 ^ _781013) ^ [_1219555, _1219557] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1219555, _1219557))))], (35529 ^ _781013) ^ [_1453713] : [c_Int_OMin = _1453713, -(c_Int_OMin = c_Int_OBit1(_1453713))], (47978 ^ _781013) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (51134 ^ _781013) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (40990 ^ _781013) ^ [_1587937, _1587939, _1587941, _1587943] : [class_Groups_Ocomm__monoid__mult(_1587937), c_Fun_Oinj__on(_1587939, _1587937, _1587941, _1587943), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1587939, _1587937), _1587941), _1587943) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1587937, _1587937), c_Fun_Oid(_1587937)), hAPP(c_Set_Oimage(_1587939, _1587937, _1587941), _1587943)))], (2586 ^ _781013) ^ [_819381, _819383, _819385, _819387, _819389, _819391] : [-(c_Smallcheck_Osmall_H(_819391, _819387, _819383) = c_Smallcheck_Osmall_H(_819389, _819385, _819381)), _819391 = _819389, _819387 = _819385, _819383 = _819381], (18942 ^ _781013) ^ [_1134989, _1134991, _1134993, _1134995, _1134997, _1134999] : [class_Groups_Ocomm__monoid__add(_1134989), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134991), _1134993)), 18952 ^ _781013 : [(18953 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1134991), 18951 ^ [_1134989, _1134991, _1134993, _1134995, _1134997, _1134999]), _1134993)))], (18958 ^ _781013) ^ [] : [18951 ^ [_1134989, _1134991, _1134993, _1134995, _1134997, _1134999] = 18954 ^ [_1134989, _1134991, _1134993, _1134995, _1134997, _1134999]], (18962 ^ _781013) ^ [] : [hAPP(_1134997, hAPP(_1134995, 18951 ^ [_1134989, _1134991, _1134993, _1134995, _1134997, _1134999])) = c_Groups_Ozero__class_Ozero(_1134989)], (18960 ^ _781013) ^ [] : [-(hAPP(_1134995, 18951 ^ [_1134989, _1134991, _1134993, _1134995, _1134997, _1134999]) = hAPP(_1134995, 18954 ^ [_1134989, _1134991, _1134993, _1134995, _1134997, _1134999]))], (18956 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1134991), 18954 ^ [_1134989, _1134991, _1134993, _1134995, _1134997, _1134999]), _1134993)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1134999, _1134989), _1134997), hAPP(c_Set_Oimage(_1134991, _1134999, _1134995), _1134993)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1134991, _1134989), hAPP(c_Fun_Ocomp(_1134999, _1134989, _1134991, _1134997), _1134995)), _1134993))], (33612 ^ _781013) ^ [_1418451, _1418453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1418451)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1418453)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1418451)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1418453), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1418451))))], (28870 ^ _781013) ^ [_1319610, _1319612, _1319614, _1319616] : [class_Groups_Oordered__ab__group__add__abs(_1319610), -(hAPP(c_Groups_Oabs__class_Oabs(_1319610), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319612, _1319610), hAPP(hAPP(c_COMBB(_1319610, _1319610, _1319612), c_Groups_Oabs__class_Oabs(_1319610)), _1319614)), _1319616)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319612, _1319610), hAPP(hAPP(c_COMBB(_1319610, _1319610, _1319612), c_Groups_Oabs__class_Oabs(_1319610)), _1319614)), _1319616))], (17705 ^ _781013) ^ [_1111749, _1111751, _1111753] : [17706 ^ _781013 : [(17709 ^ _781013) ^ [] : [_1111751 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17707 ^ _781013) ^ [] : [_1111749 = _1111753]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111749), _1111751) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111753), _1111751))], (5938 ^ _781013) ^ [_876859] : [-(c_Hoare__Mirabelle_OMGT(_876859) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _876859), c_Natural_Oevalc(_876859)))], (27491 ^ _781013) ^ [_1294107, _1294109, _1294111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1294107)), 27494 ^ _781013 : [(27495 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1294109, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1294111), _1294107)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1294111, _1294107))), 27498 ^ _781013 : [(27499 ^ _781013) ^ [_1294308, _1294310] : [-(hBOOL(hAPP(hAPP(_1294109, _1294310), _1294308))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1294308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294308), _1294107)), _1294111 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1294107), _1294310)), _1294308)]]], (27513 ^ _781013) ^ [] : [27516 ^ _781013 : [(27519 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 27515 ^ [_1294107, _1294109, _1294111]), _1294107)))], (27521 ^ _781013) ^ [] : [-(_1294111 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1294107), 27514 ^ [_1294107, _1294109, _1294111])), 27515 ^ [_1294107, _1294109, _1294111]))], (27523 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1294109, 27514 ^ [_1294107, _1294109, _1294111]), 27515 ^ [_1294107, _1294109, _1294111]))], (27517 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27515 ^ [_1294107, _1294109, _1294111])))]], -(hBOOL(hAPP(hAPP(_1294109, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1294111), _1294107)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1294111, _1294107))))]]], (40727 ^ _781013) ^ [_1579677, _1579679, _1579681, _1579683] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579677, _1579679)), hAPP(hAPP(c_Product__Type_OSigma(_1579677, _1579679), _1579681), hAPP(c_COMBK(tc_fun(_1579679, tc_HOL_Obool), _1579677), _1579683)))), -(_1579681 = c_Orderings_Obot__class_Obot(tc_fun(_1579677, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1579679), _1579683)))], (7543 ^ _781013) ^ [_907229, _907231, _907233, _907235] : [hBOOL(hAPP(hAPP(c_member(_907229), _907231), _907233)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907229, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_907229), _907231), _907235)), _907233) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907229, tc_HOL_Obool)), _907235), _907233))], (7561 ^ _781013) ^ [_907634, _907636, _907638, _907640] : [-(hBOOL(hAPP(hAPP(c_member(_907634), _907636), _907638))), 7564 ^ _781013 : [(7571 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907634, tc_HOL_Obool)), _907638), _907640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907634, tc_HOL_Obool)), _907638), hAPP(hAPP(c_Set_Oinsert(_907634), _907636), _907640))))], (7565 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907634, tc_HOL_Obool)), _907638), hAPP(hAPP(c_Set_Oinsert(_907634), _907636), _907640))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907634, tc_HOL_Obool)), _907638), _907640)))]]], (35403 ^ _781013) ^ [_1451074, _1451076] : [class_Rings_Oring__1(_1451074), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1451074), hAPP(c_Groups_Ouminus__class_Ouminus(_1451074), c_Groups_Oone__class_Oone(_1451074))), 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)))), _1451076))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1451074), c_Groups_Oone__class_Oone(_1451074)))], (24246 ^ _781013) ^ [_1233295, _1233297] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1233295, _1233297)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1233297), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1233295), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (2688 ^ _781013) ^ [_820970, _820972, _820974, _820976] : [-(c_Divides_Odivmod__nat__rel(_820976, _820972) = c_Divides_Odivmod__nat__rel(_820974, _820970)), _820976 = _820974, _820972 = _820970], (37534 ^ _781013) ^ [_1497657, _1497659, _1497661, _1497663, _1497665] : [hAPP(c_Product__Type_Ofst(_1497657, _1497659), hAPP(hAPP(c_Product__Type_OPair(_1497657, _1497659), _1497661), _1497663)) = _1497665, -(_1497661 = _1497665)], (44432 ^ _781013) ^ [_1666523, _1666525] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1666523), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1666523))), c_List_Otranspose(_1666523, _1666525)))))], (49908 ^ _781013) ^ [_1795251, _1795253, _1795255, _1795257, _1795259] : [c_Finite__Set_Ofun__left__comm(_1795251, _1795253, _1795255), -(hAPP(c_Fun_Ocomp(_1795253, _1795253, _1795253, hAPP(_1795255, _1795257)), hAPP(_1795255, _1795259)) = hAPP(c_Fun_Ocomp(_1795253, _1795253, _1795253, hAPP(_1795255, _1795259)), hAPP(_1795255, _1795257)))], (48577 ^ _781013) ^ [_1763308, _1763310, _1763312, _1763314] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763308, _1763308)), hAPP(hAPP(c_Product__Type_OPair(_1763308, _1763308), _1763310), _1763312)), c_Transitive__Closure_Ortrancl(_1763308, _1763314))), hBOOL(hAPP(hAPP(c_member(_1763308), _1763312), c_Wellfounded_Oacc(_1763308, _1763314))), -(hBOOL(hAPP(hAPP(c_member(_1763308), _1763310), c_Wellfounded_Oacc(_1763308, _1763314))))], (14391 ^ _781013) ^ [_1047591, _1047593, _1047595, _1047597, _1047599] : [class_Groups_Ocomm__monoid__add(_1047591), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047593), _1047595)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047593), _1047597)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1047593, tc_HOL_Obool)), _1047595), _1047597) = c_Orderings_Obot__class_Obot(tc_fun(_1047593, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047593, _1047591), _1047599), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1047593, tc_HOL_Obool)), _1047595), _1047597)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047591), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047593, _1047591), _1047599), _1047595)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047593, _1047591), _1047599), _1047597)))], (17367 ^ _781013) ^ [_1105694, _1105696, _1105698] : [class_Rings_Olinordered__ring(_1105694), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105694), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105694), _1105696), _1105696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105694), _1105698), _1105698))), c_Groups_Ozero__class_Ozero(_1105694)))], (29869 ^ _781013) ^ [_1337971, _1337973, _1337975] : [class_Orderings_Olinorder(_1337971), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337971), _1337973)), -(hBOOL(hAPP(hAPP(c_member(_1337971), _1337975), _1337973))), -(_1337973 = c_Orderings_Obot__class_Obot(tc_fun(_1337971, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1337971, c_Orderings_Oord__class_Omin(_1337971), hAPP(hAPP(c_Set_Oinsert(_1337971), _1337975), _1337973)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1337971), _1337975), c_Big__Operators_Olattice_OInf__fin(_1337971, c_Orderings_Oord__class_Omin(_1337971), _1337973)))], (13851 ^ _781013) ^ [_1035562, _1035564, _1035566, _1035568, _1035570] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1035562), 13854 ^ _781013 : [(13855 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035562), _1035564), _1035566)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035562), _1035568), _1035570)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035562), _1035564), _1035570)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035562), _1035568), _1035566)), -(_1035564 = _1035568), -(_1035566 = _1035570)], (13865 ^ _781013) ^ [] : [13866 ^ _781013 : [(13869 ^ _781013) ^ [] : [_1035566 = _1035570], (13867 ^ _781013) ^ [] : [_1035564 = _1035568]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035562), _1035564), _1035566)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035562), _1035568), _1035570)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035562), _1035564), _1035570)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035562), _1035568), _1035566)))]]], (50189 ^ _781013) ^ [_1801302, _1801304, _1801306, _1801308, _1801310, _1801312] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1801302, _1801304)), _1801306), hAPP(hAPP(c_Relation_Orel__comp(_1801302, _1801308, _1801304), _1801310), _1801312))), 50195 ^ _781013 : [(50200 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801308, _1801304)), hAPP(hAPP(c_Product__Type_OPair(_1801308, _1801304), 50193 ^ [_1801302, _1801304, _1801306, _1801308, _1801310, _1801312]), 50194 ^ [_1801302, _1801304, _1801306, _1801308, _1801310, _1801312])), _1801312)))], (50198 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801302, _1801308)), hAPP(hAPP(c_Product__Type_OPair(_1801302, _1801308), 50192 ^ [_1801302, _1801304, _1801306, _1801308, _1801310, _1801312]), 50193 ^ [_1801302, _1801304, _1801306, _1801308, _1801310, _1801312])), _1801310)))], (50196 ^ _781013) ^ [] : [-(_1801306 = hAPP(hAPP(c_Product__Type_OPair(_1801302, _1801304), 50192 ^ [_1801302, _1801304, _1801306, _1801308, _1801310, _1801312]), 50194 ^ [_1801302, _1801304, _1801306, _1801308, _1801310, _1801312]))]]], (38298 ^ _781013) ^ [_1516727, _1516729, _1516731, _1516733, _1516735] : [hAPP(hAPP(c_List_Omap(_1516727, _1516729), _1516731), _1516733) = hAPP(hAPP(c_List_Omap(_1516727, _1516729), _1516735), _1516733), 38301 ^ _781013 : [(38302 ^ _781013) ^ [_1516850] : [hBOOL(hAPP(hAPP(c_member(_1516727), _1516850), hAPP(c_List_Oset(_1516727), _1516733))), -(hAPP(_1516731, _1516850) = hAPP(_1516735, _1516850))]]], (17373 ^ _781013) ^ [_1105838, _1105840, _1105842] : [class_Rings_Olinordered__ring__strict(_1105838), 17376 ^ _781013 : [(17377 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105838), c_Groups_Ozero__class_Ozero(_1105838)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105838), _1105840), _1105840)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105838), _1105842), _1105842)))), _1105840 = c_Groups_Ozero__class_Ozero(_1105838), _1105842 = c_Groups_Ozero__class_Ozero(_1105838)], (17387 ^ _781013) ^ [] : [17388 ^ _781013 : [(17391 ^ _781013) ^ [] : [-(_1105842 = c_Groups_Ozero__class_Ozero(_1105838))], (17389 ^ _781013) ^ [] : [-(_1105840 = c_Groups_Ozero__class_Ozero(_1105838))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105838), c_Groups_Ozero__class_Ozero(_1105838)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105838), _1105840), _1105840)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105838), _1105842), _1105842)))))]]], (31745 ^ _781013) ^ [_1381060, _1381062, _1381064, _1381066, _1381068] : [-(hBOOL(hAPP(hAPP(c_member(_1381060), _1381062), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381064, tc_fun(_1381060, tc_HOL_Obool)), _1381066), _1381068)))), 31746 ^ _781013 : [(31747 ^ _781013) ^ [_1381142] : [hBOOL(hAPP(hAPP(c_member(_1381064), _1381142), _1381066)), hBOOL(hAPP(hAPP(c_member(_1381060), _1381062), hAPP(_1381068, _1381142)))]]], (50888 ^ _781013) ^ [_1815620, _1815622, _1815624] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815620, _1815620, hAPP(hAPP(c_COMBB(tc_fun(_1815620, tc_HOL_Obool), tc_fun(_1815620, tc_HOL_Obool), _1815620), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1815620), c_fNot)), c_fequal)), _1815622), _1815624)), _1815622 = _1815624], (5773 ^ _781013) ^ [_872780, _872782, _872784, _872786, _872788] : [5776 ^ _781013 : [(5779 ^ _781013) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_872782, _872784, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872782)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872782), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _872782), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 5775 ^ [_872780, _872782, _872784, _872786, _872788]))), _872786), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _872782), hAPP(_872788, 5774 ^ [_872780, _872782, _872784, _872786, _872788])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872782), tc_HOL_Obool))))], (5777 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_872780, 5774 ^ [_872780, _872782, _872784, _872786, _872788]), 5775 ^ [_872780, _872782, _872784, _872786, _872788])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_872782, _872784, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872782)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872782), _872780), _872786), _872788)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872782), tc_HOL_Obool)))))], (46904 ^ _781013) ^ [_1724357, _1724359] : [46906 ^ _781013 : [(46907 ^ _781013) ^ [_1724382] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1724357, _1724357)), hAPP(hAPP(c_Product__Type_OPair(_1724357, _1724357), hAPP(46905 ^ [_1724357, _1724359], hAPP(c_Nat_OSuc, _1724382))), hAPP(46905 ^ [_1724357, _1724359], _1724382))), _1724359)))]], -(c_Wellfounded_Owf(_1724357, _1724359))], (21748 ^ _781013) ^ [_1189294, _1189296, _1189298] : [class_Rings_Osemiring__1(_1189294), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1189296), _1189298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1189294), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189294), _1189296)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189294), _1189298)))], (7637 ^ _781013) ^ [_909429, _909431, _909433, _909435, _909437] : [hAPP(_909429, _909431) = hAPP(c_Option_Ooption_OSome(_909433), _909435), -(hBOOL(hAPP(hAPP(c_member(_909433), _909435), c_Map_Oran(_909437, _909433, _909429))))], (22562 ^ _781013) ^ [_1203552, _1203554] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203552), _1203554) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1203554 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22571 ^ _781013 : [(22574 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203552), _1203554)))], (22572 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203552)))]], 22575 ^ _781013 : [(22578 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203554), _1203552)))], (22576 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203552), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (31798 ^ _781013) ^ [_1382222, _1382224, _1382226, _1382228] : [c_Orderings_Obot__class_Obot(tc_fun(_1382222, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382224, tc_fun(_1382222, tc_HOL_Obool)), _1382226), _1382228), 31801 ^ _781013 : [(31802 ^ _781013) ^ [_1382338] : [hBOOL(hAPP(hAPP(c_member(_1382224), _1382338), _1382226)), -(hAPP(_1382228, _1382338) = c_Orderings_Obot__class_Obot(tc_fun(_1382222, tc_HOL_Obool)))]]], (38560 ^ _781013) ^ [_1522631, _1522633, _1522635] : [hBOOL(hAPP(c_List_Odistinct(_1522631), _1522633)), -(hAPP(c_List_Oset(_1522631), c_List_Oremove1(_1522631, _1522635, _1522633)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1522631, tc_HOL_Obool)), hAPP(c_List_Oset(_1522631), _1522633)), hAPP(hAPP(c_Set_Oinsert(_1522631), _1522635), c_Orderings_Obot__class_Obot(tc_fun(_1522631, tc_HOL_Obool)))))], (33918 ^ _781013) ^ [_1423428, _1423430] : [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(_1423428))), 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)), _1423430))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423428) = hAPP(c_Nat_OSuc, _1423430))], (28510 ^ _781013) ^ [_1312986, _1312988, _1312990] : [class_Orderings_Olinorder(_1312986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312986), _1312988), _1312990)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312986), _1312990), _1312988) = _1312988)], (37431 ^ _781013) ^ [_1495609, _1495611] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1495609, _1495609)), hAPP(hAPP(c_Product__Type_OPair(_1495609, _1495609), 37432 ^ [_1495609, _1495611]), 37432 ^ [_1495609, _1495611])), _1495611))), -(c_Relation_Oirrefl(_1495609, _1495611))], (38180 ^ _781013) ^ [_1513605, _1513607, _1513609, _1513611] : [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), _1513605), _1513607)), 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), _1513609), _1513611)), 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), _1513605), _1513611)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1513609), _1513607))))], (8446 ^ _781013) ^ [_926724, _926726, _926728, _926730, _926732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926724, tc_HOL_Obool)), _926726), hAPP(c_Set_Oimage(_926728, _926724, _926730), _926732))), 8450 ^ _781013 : [(8453 ^ _781013) ^ [] : [-(_926726 = hAPP(c_Set_Oimage(_926728, _926724, _926730), 8449 ^ [_926724, _926726, _926728, _926730, _926732]))], (8451 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926728, tc_HOL_Obool)), 8449 ^ [_926724, _926726, _926728, _926730, _926732]), _926732)))]]], (47470 ^ _781013) ^ [_1738207, _1738209] : [47472 ^ _781013 : [(47475 ^ _781013) ^ [] : [hBOOL(hAPP(_1738207, hAPP(c_Int_OAbs__Integ, 47471 ^ [_1738207, _1738209])))], (47473 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 47471 ^ [_1738207, _1738209]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1738207, _1738209)))], (19921 ^ _781013) ^ [_1154170, _1154172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154170), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1154172), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1154170), _1154172)))], (23128 ^ _781013) ^ [_1213714, _1213716, _1213718] : [-(_1213714 = 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), _1213714), _1213716)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1213714), _1213718)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213716), _1213718))], (6948 ^ _781013) ^ [_895815, _895817, _895819] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895815, tc_HOL_Obool)), _895817), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895815, tc_HOL_Obool)), _895819), _895817))))], (3446 ^ _781013) ^ [_832935, _832937, _832939, _832941] : [-(c_List_Olist__update(_832941, _832937) = c_List_Olist__update(_832939, _832935)), _832941 = _832939, _832937 = _832935], (44330 ^ _781013) ^ [_1664317, _1664319, _1664321] : [_1664319 = _1664321, -(hAPP(c_List_Orev(_1664317), _1664319) = hAPP(c_List_Orev(_1664317), _1664321))], (440 ^ _781013) ^ [_787821, _787823, _787825, _787827, _787829, _787831, _787833, _787835] : [-(c_List_Olistrelp(_787833, _787829, _787825, _787821)), c_List_Olistrelp(_787835, _787831, _787827, _787823), _787835 = _787833, _787831 = _787829, _787827 = _787825, _787823 = _787821], (33334 ^ _781013) ^ [_1413755] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413755) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413755)))], (33126 ^ _781013) ^ [_1409610, _1409612, _1409614, _1409616] : [class_Fields_Olinordered__field__inverse__zero(_1409610), class_Int_Onumber(_1409610), 33133 ^ _781013 : [(33134 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409610), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1409610), _1409612), _1409614)), hAPP(c_Int_Onumber__class_Onumber__of(_1409610), _1409616))), 33137 ^ _781013 : [(33144 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1409610), c_Groups_Ozero__class_Ozero(_1409610)), _1409614))), 33147 ^ _781013 : [(33154 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1409610), _1409614), c_Groups_Ozero__class_Ozero(_1409610)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409610), c_Groups_Ozero__class_Ozero(_1409610)), hAPP(c_Int_Onumber__class_Onumber__of(_1409610), _1409616))))], (33148 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1409610), _1409614), c_Groups_Ozero__class_Ozero(_1409610))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409610), hAPP(c_Int_Onumber__class_Onumber__of(_1409610), _1409616)), _1409614)), _1409612)))]]], (33138 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1409610), c_Groups_Ozero__class_Ozero(_1409610)), _1409614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409610), _1409612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409610), hAPP(c_Int_Onumber__class_Onumber__of(_1409610), _1409616)), _1409614))))]]], (33160 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409610), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1409610), _1409612), _1409614)), hAPP(c_Int_Onumber__class_Onumber__of(_1409610), _1409616)))), 33163 ^ _781013 : [(33166 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409610), _1409612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409610), hAPP(c_Int_Onumber__class_Onumber__of(_1409610), _1409616)), _1409614)))], (33164 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1409610), c_Groups_Ozero__class_Ozero(_1409610)), _1409614)))]], 33167 ^ _781013 : [(33170 ^ _781013) ^ [] : [33171 ^ _781013 : [(33174 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409610), hAPP(c_Int_Onumber__class_Onumber__of(_1409610), _1409616)), _1409614)), _1409612))], (33172 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1409610), _1409614), c_Groups_Ozero__class_Ozero(_1409610))))]], 33175 ^ _781013 : [(33178 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409610), c_Groups_Ozero__class_Ozero(_1409610)), hAPP(c_Int_Onumber__class_Onumber__of(_1409610), _1409616)))], (33176 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1409610), _1409614), c_Groups_Ozero__class_Ozero(_1409610)))]]], (33168 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1409610), c_Groups_Ozero__class_Ozero(_1409610)), _1409614))]]]]], (35007 ^ _781013) ^ [] : [-(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))))], (40493 ^ _781013) ^ [_1572884, _1572886, _1572888, _1572890, _1572892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1572884), tc_List_Olist(_1572884))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1572884), tc_List_Olist(_1572884)), hAPP(hAPP(c_List_Olist_OCons(_1572884), _1572886), _1572888)), _1572890)), c_List_Olistrel(_1572884, _1572892))), 40498 ^ _781013 : [(40503 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1572884), tc_List_Olist(_1572884))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1572884), tc_List_Olist(_1572884)), _1572888), 40497 ^ [_1572884, _1572886, _1572888, _1572890, _1572892])), c_List_Olistrel(_1572884, _1572892))))], (40501 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572884, _1572884)), hAPP(hAPP(c_Product__Type_OPair(_1572884, _1572884), _1572886), 40496 ^ [_1572884, _1572886, _1572888, _1572890, _1572892])), _1572892)))], (40499 ^ _781013) ^ [] : [-(_1572890 = hAPP(hAPP(c_List_Olist_OCons(_1572884), 40496 ^ [_1572884, _1572886, _1572888, _1572890, _1572892]), 40497 ^ [_1572884, _1572886, _1572888, _1572890, _1572892]))]]], (12694 ^ _781013) ^ [_1010621, _1010623, _1010625] : [class_Rings_Oring(_1010621), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1010621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010621), _1010623), _1010625)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010621), hAPP(c_Groups_Ouminus__class_Ouminus(_1010621), _1010623)), _1010625))], (19987 ^ _781013) ^ [_1155298] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1155298)], (43508 ^ _781013) ^ [_1647824, _1647826, _1647828, _1647830] : [-(c_List_Otranspose(_1647824, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1647826), tc_List_Olist(_1647824)), hAPP(c_List_Omap(_1647826, _1647824), _1647828)), _1647830)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1647826), tc_List_Olist(_1647824)), hAPP(c_List_Omap(_1647826, _1647824), _1647828)), c_List_Otranspose(_1647826, _1647830)))], (50091 ^ _781013) ^ [_1798882, _1798884, _1798886, _1798888] : [class_Lattices_Osemilattice__sup(_1798882), hBOOL(hAPP(c_Finite__Set_Ofinite(_1798882), _1798884)), 50101 ^ _781013 : [(50104 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1798882), 50100 ^ [_1798882, _1798884, _1798886, _1798888]), _1798886))], (50102 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798882), 50100 ^ [_1798882, _1798884, _1798886, _1798888]), _1798884)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1798882), hAPP(hAPP(c_Finite__Set_Ofold(_1798882, _1798882, c_Lattices_Osemilattice__sup__class_Osup(_1798882)), _1798888), _1798884)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1798882), _1798886), _1798888))))], (10075 ^ _781013) ^ [_959257, _959259, _959261, _959263] : [class_Lattices_Osemilattice__inf(_959257), 10078 ^ _781013 : [(10087 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959257), _959259), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959257), _959261), _959263)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959257), _959259), _959261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959257), _959259), _959263))], (10079 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959257), _959259), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959257), _959261), _959263))), 10082 ^ _781013 : [(10085 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959257), _959259), _959263)))], (10083 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959257), _959259), _959261)))]]]]], (47860 ^ _781013) ^ [_1747758, _1747760, _1747762] : [c_List_Olist__ex(_1747758, _1747760, hAPP(c_List_Orev(_1747758), _1747762)), -(c_List_Olist__ex(_1747758, _1747760, _1747762))], (46841 ^ _781013) ^ [_1723140, _1723142, _1723144] : [c_Wellfounded_Owf(_1723140, _1723142), -(c_Wellfounded_Owf(_1723140, c_Wellfounded_Omlex__prod(_1723140, _1723144, _1723142)))], (11003 ^ _781013) ^ [_976364, _976366, _976368] : [-(c_Map_Omap__add(_976364, _976366, _976368, hAPP(c_COMBK(tc_Option_Ooption(_976366), _976364), c_Option_Ooption_ONone(_976366))) = _976368)], (29815 ^ _781013) ^ [_1337052, _1337054, _1337056] : [class_Orderings_Olinorder(_1337052), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337052), _1337054)), -(_1337054 = c_Orderings_Obot__class_Obot(tc_fun(_1337052, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1337052, c_Orderings_Oord__class_Omin(_1337052), hAPP(hAPP(c_Set_Oinsert(_1337052), _1337056), _1337054)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1337052), _1337056), c_Big__Operators_Olattice_OInf__fin(_1337052, c_Orderings_Oord__class_Omin(_1337052), _1337054)))], (23325 ^ _781013) ^ [_1217270] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1217270)), c_Option_Ooption_ONone(_1217270)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48778 ^ _781013) ^ [_1768743, _1768745] : [c_Wellfounded_Oacyclic(_1768743, hAPP(c_Relation_Oconverse(_1768743, _1768743), _1768745)), -(c_Wellfounded_Oacyclic(_1768743, _1768745))], (50884 ^ _781013) ^ [_1815540, _1815542, _1815544] : [-(c_Predicate_Oconversep(_1815540, _1815542, c_Predicate_Oconversep(_1815542, _1815540, _1815544)) = _1815544)], (29405 ^ _781013) ^ [_1329621, _1329623, _1329625] : [class_Orderings_Olinorder(_1329621), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329621), _1329623)), -(_1329623 = c_Orderings_Obot__class_Obot(tc_fun(_1329621, tc_HOL_Obool))), 29416 ^ _781013 : [(29417 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329621), _1329625), hAPP(c_Finite__Set_Ofold1(_1329621, c_Orderings_Oord__class_Omin(_1329621)), _1329623))), 29420 ^ _781013 : [(29421 ^ _781013) ^ [_1329914] : [hBOOL(hAPP(hAPP(c_member(_1329621), _1329914), _1329623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329621), _1329625), _1329914)))]]], (29427 ^ _781013) ^ [] : [29429 ^ _781013 : [(29432 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329621), _1329625), 29428 ^ [_1329621, _1329623, _1329625]))], (29430 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329621), 29428 ^ [_1329621, _1329623, _1329625]), _1329623)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329621), _1329625), hAPP(c_Finite__Set_Ofold1(_1329621, c_Orderings_Oord__class_Omin(_1329621)), _1329623))))]]], (5532 ^ _781013) ^ [_865354, _865356] : [_865356 = _865354, -(c_Hoare__Mirabelle_OMGT(_865356) = c_Hoare__Mirabelle_OMGT(_865354))], (8273 ^ _781013) ^ [_922371, _922373, _922375, _922377, _922379, _922381, _922383, _922385] : [c_Finite__Set_Ofolding__image__simple(_922371, _922373, _922375, _922377, _922379, _922381), hBOOL(hAPP(c_Finite__Set_Ofinite(_922373), _922383)), hBOOL(hAPP(hAPP(c_member(_922373), _922385), _922383)), -(hAPP(_922381, _922383) = hAPP(hAPP(_922375, hAPP(_922379, _922385)), hAPP(_922381, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922373, tc_HOL_Obool)), _922383), hAPP(hAPP(c_Set_Oinsert(_922373), _922385), c_Orderings_Obot__class_Obot(tc_fun(_922373, tc_HOL_Obool)))))))], (51336 ^ _781013) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (47909 ^ _781013) ^ [_1748590, _1748592, _1748594, _1748596, _1748598, _1748600, _1748602] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1748590, _1748592, _1748594, _1748596), _1748598), _1748600), _1748602) = hAPP(hAPP(_1748600, hAPP(c_Product__Type_Ofst(_1748592, _1748594), hAPP(_1748598, _1748602))), hAPP(c_Product__Type_Osnd(_1748592, _1748594), hAPP(_1748598, _1748602))))], (28406 ^ _781013) ^ [_1311021, _1311023, _1311025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1311021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1311023), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1311025), 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), _1311025), _1311023))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1311021)))))], (10853 ^ _781013) ^ [_973045, _973047, _973049, _973051] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_973045, tc_HOL_Obool)), _973047), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_973045, tc_HOL_Obool)), _973049), _973051)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_973045, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_973045, tc_HOL_Obool)), _973047), _973049)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_973045, tc_HOL_Obool)), _973047), _973051)))], (15241 ^ _781013) ^ [_1063125, _1063127, _1063129] : [class_Groups_Oordered__comm__monoid__add(_1063125), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063125), _1063127), c_Groups_Ozero__class_Ozero(_1063125))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063125), _1063129), c_Groups_Ozero__class_Ozero(_1063125))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063125), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063125), _1063127), _1063129)), c_Groups_Ozero__class_Ozero(_1063125))))], (38005 ^ _781013) ^ [_1508976, _1508978, _1508980, _1508982] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1508976), _1508978)), 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)), _1508976), _1508980)), 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)), _1508978), _1508982)), 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)), _1508978), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1508980), _1508982))), c_FunDef_Omin__weak)))], (29887 ^ _781013) ^ [_1338220, _1338222, _1338224] : [class_Orderings_Olinorder(_1338220), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338220), _1338222)), 29894 ^ _781013 : [(29901 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1338220, tc_HOL_Obool)), _1338222), hAPP(hAPP(c_Set_Oinsert(_1338220), _1338224), c_Orderings_Obot__class_Obot(tc_fun(_1338220, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1338220, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1338220, c_Orderings_Oord__class_Omin(_1338220), hAPP(hAPP(c_Set_Oinsert(_1338220), _1338224), _1338222)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338220), _1338224), c_Big__Operators_Olattice_OInf__fin(_1338220, c_Orderings_Oord__class_Omin(_1338220), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1338220, tc_HOL_Obool)), _1338222), hAPP(hAPP(c_Set_Oinsert(_1338220), _1338224), c_Orderings_Obot__class_Obot(tc_fun(_1338220, tc_HOL_Obool)))))))], (29895 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1338220, tc_HOL_Obool)), _1338222), hAPP(hAPP(c_Set_Oinsert(_1338220), _1338224), c_Orderings_Obot__class_Obot(tc_fun(_1338220, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1338220, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1338220, c_Orderings_Oord__class_Omin(_1338220), hAPP(hAPP(c_Set_Oinsert(_1338220), _1338224), _1338222)) = _1338224)]]], (36116 ^ _781013) ^ [_1468807, _1468809, _1468811] : [class_Rings_Osemiring__1(_1468807), hBOOL(hAPP(hAPP(c_member(_1468807), _1468809), c_Nat_Osemiring__1__class_ONats(_1468807))), hBOOL(hAPP(hAPP(c_member(_1468807), _1468811), c_Nat_Osemiring__1__class_ONats(_1468807))), -(hBOOL(hAPP(hAPP(c_member(_1468807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1468807), _1468809), _1468811)), c_Nat_Osemiring__1__class_ONats(_1468807))))], (9621 ^ _781013) ^ [_951336, _951338, _951340] : [class_Orderings_Oorder(_951336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951336), _951338), _951340)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951336), _951340), _951338))], (37357 ^ _781013) ^ [_1494154, _1494156, _1494158, _1494160] : [-(hAPP(c_Product__Type_Osnd(_1494154, _1494156), hAPP(hAPP(c_Product__Type_OPair(_1494154, _1494156), _1494158), _1494160)) = _1494160)], (10855 ^ _781013) ^ [_973129, _973131, _973133, _973135] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_973129, tc_HOL_Obool)), _973131), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_973129, tc_HOL_Obool)), _973133), _973135)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_973129, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_973129, tc_HOL_Obool)), _973131), _973133)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_973129, tc_HOL_Obool)), _973131), _973135)))], (190 ^ _781013) ^ [_784168, _784170, _784172, _784174, _784176, _784178, _784180, _784182, _784184, _784186] : [-(c_Big__Operators_Ocomm__monoid__big(_784184, _784180, _784176, _784172, _784168)), c_Big__Operators_Ocomm__monoid__big(_784186, _784182, _784178, _784174, _784170), _784186 = _784184, _784182 = _784180, _784178 = _784176, _784174 = _784172, _784170 = _784168], (49952 ^ _781013) ^ [_1796055, _1796057, _1796059, _1796061, _1796063, _1796065] : [c_Finite__Set_Ofun__left__comm(_1796055, _1796057, _1796059), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1796055, _1796057, _1796059, _1796061, _1796063), _1796065)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1796055, _1796057, _1796059), _1796061), _1796063) = _1796065)], (34529 ^ _781013) ^ [_1435158, _1435160] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1435158), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1435160)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1435158), 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)))), _1435160)))], (35039 ^ _781013) ^ [_1444340] : [-(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)))), _1444340) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444340), _1444340))], (36282 ^ _781013) ^ [_1472378, _1472380, _1472382, _1472384, _1472386] : [hAPP(c_Relation_OImage(_1472378, _1472378, _1472380), hAPP(hAPP(c_Set_Oinsert(_1472378), _1472382), c_Orderings_Obot__class_Obot(tc_fun(_1472378, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1472378, _1472378, _1472380), hAPP(hAPP(c_Set_Oinsert(_1472378), _1472384), c_Orderings_Obot__class_Obot(tc_fun(_1472378, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1472378, _1472386, _1472380), hBOOL(hAPP(hAPP(c_member(_1472378), _1472384), _1472386)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472378, _1472378)), hAPP(hAPP(c_Product__Type_OPair(_1472378, _1472378), _1472382), _1472384)), _1472380)))], (46146 ^ _781013) ^ [_1704804, _1704806, _1704808, _1704810, _1704812, _1704814] : [c_List_Olist__all2(_1704804, _1704806, _1704808, _1704810, _1704812), -(c_List_Olist__all2(_1704804, _1704806, _1704808, hAPP(hAPP(c_List_Odrop(_1704804), _1704814), _1704810), hAPP(hAPP(c_List_Odrop(_1704806), _1704814), _1704812)))], (8317 ^ _781013) ^ [_923588, _923590, _923592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_923588, tc_HOL_Obool)), _923590), _923592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_923588, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_923588, tc_fun(_923588, tc_HOL_Obool), tc_HOL_Obool), c_member(_923588)), _923590)), hAPP(hAPP(c_COMBC(_923588, tc_fun(_923588, tc_HOL_Obool), tc_HOL_Obool), c_member(_923588)), _923592))))], (50808 ^ _781013) ^ [_1813696, _1813698, _1813700, _1813702, _1813704, _1813706, _1813708] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1813696, _1813698, _1813700, _1813702), _1813704), _1813706), _1813708) = c_New__DSequence_Opos__bind(_1813696, _1813698, hAPP(hAPP(hAPP(_1813700, _1813704), _1813706), _1813708), hAPP(hAPP(c_COMBC(_1813696, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1813698))), hAPP(hAPP(c_COMBC(_1813696, 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(_1813698)))), hAPP(hAPP(c_COMBC(_1813696, 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(_1813698))))), _1813702), _1813704)), _1813706)), _1813708)))], (3684 ^ _781013) ^ [_836704, _836706, _836708, _836710] : [-(c_Nitpick_Onumber__of__frac(_836710, _836706) = c_Nitpick_Onumber__of__frac(_836708, _836704)), _836710 = _836708, _836706 = _836704], (35629 ^ _781013) ^ [_1455197] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1455197), c_Int_OMin) = c_Int_Opred(_1455197))], (17985 ^ _781013) ^ [_1116305, _1116307, _1116309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116305), _1116307)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116309), _1116307))), 17988 ^ _781013 : [(17991 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116305), _1116309)))], (17989 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1116307)))]]], (34885 ^ _781013) ^ [_1441472, _1441474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441472), _1441474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1441472)), c_Int_OBit0(_1441474))))], (20811 ^ _781013) ^ [_1170029, _1170031] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170029)), -(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)), _1170029))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1170031))))) = 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)), _1170029))), 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, _1170031))))))], (14309 ^ _781013) ^ [_1045780, _1045782, _1045784, _1045786] : [class_Rings_Ocomm__semiring__1(_1045780), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045780), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045780), _1045782), _1045784)), _1045786) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045780), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045780), _1045782), _1045786)), _1045784))], (40441 ^ _781013) ^ [_1570527, _1570529, _1570531] : [-(c_List_Oset__Cons(_1570527, _1570529, _1570531) = hAPP(c_Set_OCollect(tc_List_Olist(_1570527)), hAPP(hAPP(c_COMBB(tc_fun(_1570527, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1570527)), c_HOL_OEx(_1570527)), hAPP(hAPP(c_COMBB(tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool)), tc_fun(_1570527, tc_HOL_Obool), tc_List_Olist(_1570527)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), tc_HOL_Obool, _1570527), c_HOL_OEx(tc_List_Olist(_1570527)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1570527), tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool)), tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1570527, tc_fun(tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool))), tc_fun(tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool)), tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool))), tc_List_Olist(_1570527)), c_COMBS(_1570527, tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1570527, tc_fun(tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool))), tc_List_Olist(_1570527)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1570527), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool)), _1570527), c_COMBS(tc_List_Olist(_1570527), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool)), tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1570527)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), tc_fun(tc_List_Olist(_1570527), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1570527), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1570527)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1570527), tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_List_Olist(_1570527))), tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1570527), tc_List_Olist(_1570527)), tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool)), tc_fun(tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_List_Olist(_1570527))), tc_fun(_1570527, tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool))), tc_List_Olist(_1570527)), c_COMBB(tc_fun(tc_List_Olist(_1570527), tc_List_Olist(_1570527)), tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), _1570527)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1570527), tc_List_Olist(_1570527)), tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool)), tc_List_Olist(_1570527)), c_COMBB(tc_List_Olist(_1570527), tc_HOL_Obool, tc_List_Olist(_1570527))), c_fequal))), c_List_Olist_OCons(_1570527)))))), hAPP(hAPP(c_COMBC(_1570527, tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool)), _1570527), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1570527))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570527), c_fconj), hAPP(hAPP(c_COMBC(_1570527, tc_fun(_1570527, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570527)), _1570529)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1570527), tc_fun(tc_List_Olist(_1570527), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1570527))), _1570531)))))))], (24230 ^ _781013) ^ [_1232995, _1232997, _1232999, _1233001] : [class_Orderings_Oorder(_1232995), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1232995, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1232995, _1232997, _1232999)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1232995, _1232999, _1233001)) = c_Orderings_Obot__class_Obot(tc_fun(_1232995, tc_HOL_Obool)))], (47800 ^ _781013) ^ [_1746542, _1746544, _1746546] : [c_List_Olist__ex(_1746542, _1746544, _1746546), 47804 ^ _781013 : [(47807 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1746544, hAPP(hAPP(c_List_Onth(_1746542), _1746546), 47803 ^ [_1746542, _1746544, _1746546]))))], (47805 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47803 ^ [_1746542, _1746544, _1746546]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746542)), _1746546))))]]], (49089 ^ _781013) ^ [_1776522, _1776524, _1776526] : [c_Relation_Ototal__on(_1776522, _1776524, _1776526), -(c_Relation_Ototal__on(_1776522, _1776524, hAPP(c_Relation_Oconverse(_1776522, _1776522), _1776526)))], (51322 ^ _781013) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (49432 ^ _781013) ^ [_1785749, _1785751, _1785753] : [hBOOL(hAPP(hAPP(c_member(_1785749), _1785751), hAPP(c_List_Oset(_1785749), _1785753))), 49437 ^ _781013 : [(49440 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1785749), _1785751), hAPP(c_List_Oset(_1785749), 49435 ^ [_1785749, _1785751, _1785753])))], (49438 ^ _781013) ^ [] : [-(_1785753 = hAPP(hAPP(c_List_Oappend(_1785749), 49435 ^ [_1785749, _1785751, _1785753]), hAPP(hAPP(c_List_Olist_OCons(_1785749), _1785751), 49436 ^ [_1785749, _1785751, _1785753])))]]], (46470 ^ _781013) ^ [_1712544, _1712546, _1712548] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712544)), _1712546), c_Wellfounded_Oacc(tc_List_Olist(_1712544), c_List_Olistrel1(_1712544, _1712548)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712544)), _1712546), c_List_Olists(_1712544, c_Wellfounded_Oacc(_1712544, _1712548)))))], (34103 ^ _781013) ^ [_1427980, _1427982] : [class_Rings_Osemiring__1(_1427980), 34106 ^ _781013 : [(34113 ^ _781013) ^ [] : [_1427982 = c_Groups_Ozero__class_Ozero(_1427980), -(c_Int_Oiszero(_1427980, _1427982))], (34107 ^ _781013) ^ [] : [c_Int_Oiszero(_1427980, _1427982), -(_1427982 = c_Groups_Ozero__class_Ozero(_1427980))]]], (6971 ^ _781013) ^ [_896311, _896313, _896315] : [hBOOL(hAPP(hAPP(c_member(_896311), _896313), _896315)), -(hBOOL(hAPP(_896315, _896313)))], (14265 ^ _781013) ^ [_1044517, _1044519, _1044521, _1044523, _1044525, _1044527] : [class_Rings_Oordered__ring(_1044517), 14268 ^ _781013 : [(14275 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044517), _1044523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044517), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044517), _1044525), _1044519)), _1044521)), _1044527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044517), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044517), _1044519), _1044521)), _1044523)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044517), _1044525), _1044521)), _1044527))))], (14269 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044517), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044517), _1044519), _1044521)), _1044523)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044517), _1044525), _1044521)), _1044527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044517), _1044523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044517), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044517), _1044525), _1044519)), _1044521)), _1044527))))]]], (34399 ^ _781013) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (46721 ^ _781013) ^ [_1720799, _1720801, _1720803, _1720805] : [c_Wellfounded_Owf(_1720799, _1720801), c_Wellfounded_Owf(_1720803, _1720805), -(c_Wellfounded_Owf(tc_prod(_1720799, _1720803), c_Wellfounded_Olex__prod(_1720799, _1720803, _1720801, _1720805)))], (45547 ^ _781013) ^ [_1691177, _1691179, _1691181] : [45549 ^ _781013 : [(45552 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1691179, 45548 ^ [_1691177, _1691179, _1691181])))], (45550 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1691177), 45548 ^ [_1691177, _1691179, _1691181]), hAPP(c_List_Oset(_1691177), c_List_OdropWhile(_1691177, _1691179, _1691181)))))]], -(c_List_OtakeWhile(_1691177, _1691179, _1691181) = hAPP(c_List_Ofilter(_1691177, _1691179), _1691181))], (18095 ^ _781013) ^ [_1118067] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1118067)))], (37246 ^ _781013) ^ [_1491642, _1491644, _1491646] : [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), _1491642), _1491644))), -(hBOOL(hAPP(hAPP(_1491646, _1491642), _1491644))), 37253 ^ _781013 : [(37256 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1491646, 37251 ^ [_1491642, _1491644, _1491646]), 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)))), 37252 ^ [_1491642, _1491644, _1491646])))), -(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), 37251 ^ [_1491642, _1491644, _1491646]), 37252 ^ [_1491642, _1491644, _1491646])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 37252 ^ [_1491642, _1491644, _1491646]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37266 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1491646, 37251 ^ [_1491642, _1491644, _1491646]), 37252 ^ [_1491642, _1491644, _1491646]))], (37254 ^ _781013) ^ [] : [-(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), 37251 ^ [_1491642, _1491644, _1491646]), 37252 ^ [_1491642, _1491644, _1491646]))))]]], (34541 ^ _781013) ^ [_1435438, _1435440] : [class_Int_Onumber__ring(_1435438), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1435438), c_Groups_Oone__class_Oone(_1435438)), hAPP(c_Int_Onumber__class_Onumber__of(_1435438), _1435440)) = hAPP(c_Int_Onumber__class_Onumber__of(_1435438), 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), _1435440))))], (37506 ^ _781013) ^ [_1497140, _1497142, _1497144, _1497146] : [hAPP(c_Product__Type_Ofst(_1497140, _1497142), _1497144) = hAPP(c_Product__Type_Ofst(_1497140, _1497142), _1497146), hAPP(c_Product__Type_Osnd(_1497140, _1497142), _1497144) = hAPP(c_Product__Type_Osnd(_1497140, _1497142), _1497146), -(_1497144 = _1497146)], (3594 ^ _781013) ^ [_835229, _835231, _835233, _835235, _835237, _835239] : [-(c_Wellfounded_Omlex__prod(_835239, _835235, _835231) = c_Wellfounded_Omlex__prod(_835237, _835233, _835229)), _835239 = _835237, _835235 = _835233, _835231 = _835229], (20973 ^ _781013) ^ [_1173060, _1173062] : [class_Int_Oring__char__0(_1173060), hBOOL(hAPP(hAPP(c_member(_1173060), _1173062), c_Int_Oring__1__class_OInts(_1173060))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173060), c_Groups_Oone__class_Oone(_1173060)), _1173062)), _1173062) = c_Groups_Ozero__class_Ozero(_1173060)], (8885 ^ _781013) ^ [_936385, _936387, _936389, _936391] : [class_Lattices_Osemilattice__sup(_936385), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936385), _936387), _936389)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936385), _936391), _936389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936385), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_936385), _936387), _936391)), _936389)))], (44496 ^ _781013) ^ [_1668831, _1668833, _1668835, _1668837] : [class_Orderings_Olinorder(_1668831), c_List_Olinorder__class_Osorted(_1668831, hAPP(c_List_Orev(_1668831), _1668833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1668835), _1668837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668837), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668831)), _1668833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1668831), hAPP(hAPP(c_List_Onth(_1668831), _1668833), _1668837)), hAPP(hAPP(c_List_Onth(_1668831), _1668833), _1668835))))], (51330 ^ _781013) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (11898 ^ _781013) ^ [_995558, _995560, _995562, _995564] : [c_Fun_Oinj__on(_995558, _995560, _995562, c_Orderings_Otop__class_Otop(tc_fun(_995558, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_995560, tc_HOL_Obool)), hAPP(c_Set_Oimage(_995558, _995560, _995562), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_995558, tc_HOL_Obool)), _995564))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_995560, tc_HOL_Obool)), hAPP(c_Set_Oimage(_995558, _995560, _995562), _995564)))))], (9164 ^ _781013) ^ [_942882, _942884, _942886, _942888, _942890] : [-(c_Map_Orestrict__map(_942882, _942884, _942886, hAPP(hAPP(c_Set_Oinsert(_942882), _942888), _942890)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942882, tc_Option_Ooption(_942884)), c_Map_Orestrict__map(_942882, _942884, _942886, _942890)), _942888), hAPP(_942886, _942888)))], (27479 ^ _781013) ^ [_1293811, _1293813, _1293815] : [hBOOL(hAPP(c_Predicate_OPowp(_1293811, hAPP(hAPP(c_COMBC(_1293811, tc_fun(_1293811, tc_HOL_Obool), tc_HOL_Obool), c_member(_1293811)), _1293813)), _1293815)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1293811, tc_HOL_Obool)), _1293815), hAPP(c_Set_OPow(_1293811), _1293813))))], (44773 ^ _781013) ^ [_1674924, _1674926] : [hBOOL(hAPP(c_List_Odistinct(_1674924), _1674926)), -(c_List_Oremdups(_1674924, _1674926) = _1674926)], (26115 ^ _781013) ^ [_1266782, _1266784] : [26117 ^ _781013 : [(26120 ^ _781013) ^ [] : [hBOOL(hAPP(_1266784, 26116 ^ [_1266782, _1266784]))], (26118 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26116 ^ [_1266782, _1266784]), _1266782)))]], 26121 ^ _781013 : [(26122 ^ _781013) ^ [_1266933] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1266933), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1266782))), -(hBOOL(hAPP(_1266784, _1266933)))]]], (5581 ^ _781013) ^ [_868861, _868863, _868865, _868867] : [c_Hoare__Mirabelle_Ohoare__derivs(_868861, _868863, _868865), c_Hoare__Mirabelle_Ohoare__derivs(_868861, _868867, _868863), -(c_Hoare__Mirabelle_Ohoare__derivs(_868861, _868867, _868865))], (7148 ^ _781013) ^ [_900014, _900016, _900018, _900020] : [7150 ^ _781013 : [(7153 ^ _781013) ^ [] : [hBOOL(hAPP(_900020, 7149 ^ [_900014, _900016, _900018, _900020]))], (7151 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900014), 7149 ^ [_900014, _900016, _900018, _900020]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900014, tc_HOL_Obool)), _900016), _900018))))]], 7154 ^ _781013 : [(7161 ^ _781013) ^ [_900331] : [hBOOL(hAPP(hAPP(c_member(_900014), _900331), _900018)), -(hBOOL(hAPP(_900020, _900331)))], (7155 ^ _781013) ^ [_900234] : [hBOOL(hAPP(hAPP(c_member(_900014), _900234), _900016)), -(hBOOL(hAPP(_900020, _900234)))]]], (45731 ^ _781013) ^ [_1695323] : [class_Complete__Lattice_Ocomplete__lattice(_1695323), -(c_Complete__Lattice_OSup__class_OSup(_1695323, c_Orderings_Otop__class_Otop(tc_fun(_1695323, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1695323))], (15573 ^ _781013) ^ [_1069087, _1069089, _1069091, _1069093, _1069095] : [class_Rings_Oordered__semiring(_1069087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069087), _1069089), _1069091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069087), _1069093), _1069095)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069087), c_Groups_Ozero__class_Ozero(_1069087)), _1069089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069087), c_Groups_Ozero__class_Ozero(_1069087)), _1069093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069087), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069087), _1069089), _1069093)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069087), _1069091), _1069095))))], (47960 ^ _781013) ^ [_1749858, _1749860] : [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), _1749858), _1749860)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749858), _1749860)))], (9875 ^ _781013) ^ [_955304, _955306, _955308, _955310] : [class_Lattices_Osemilattice__inf(_955304), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955304), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955304), _955306), _955308)), _955310) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955304), _955306), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955304), _955308), _955310)))], (49750 ^ _781013) ^ [_1792213, _1792215, _1792217] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792213), _1792215)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1792213, tc_HOL_Obool)), _1792217), _1792215) = hAPP(hAPP(c_Finite__Set_Ofold(_1792213, tc_fun(_1792213, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1792213, tc_HOL_Obool), tc_fun(tc_fun(_1792213, tc_HOL_Obool), tc_fun(_1792213, tc_HOL_Obool)), _1792213), hAPP(c_COMBC(tc_fun(_1792213, tc_HOL_Obool), tc_fun(_1792213, tc_HOL_Obool), tc_fun(_1792213, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1792213, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1792213, tc_fun(_1792213, tc_HOL_Obool), tc_fun(_1792213, tc_HOL_Obool)), c_Set_Oinsert(_1792213)), c_Orderings_Obot__class_Obot(tc_fun(_1792213, tc_HOL_Obool))))), _1792217), _1792215))], (43239 ^ _781013) ^ [_1641810, _1641812, _1641814, _1641816, _1641818, _1641820, _1641822] : [43241 ^ _781013 : [(43244 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1641818, 43240 ^ [_1641810, _1641812, _1641814, _1641816, _1641818, _1641820, _1641822]), _1641820), _1641822))], (43242 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1641810), 43240 ^ [_1641810, _1641812, _1641814, _1641816, _1641818, _1641820, _1641822]), _1641816)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641810, tc_fun(_1641812, tc_fun(_1641814, tc_HOL_Obool))), _1641816), _1641818), _1641820), _1641822)))], (50545 ^ _781013) ^ [_1808645, _1808647, _1808649] : [c_FunDef_Ois__measure(_1808645, _1808647), -(c_FunDef_Ois__measure(tc_prod(_1808649, _1808645), hAPP(hAPP(c_COMBB(_1808645, tc_Nat_Onat, tc_prod(_1808649, _1808645)), _1808647), c_Product__Type_Osnd(_1808649, _1808645))))], (31138 ^ _781013) ^ [_1364218, _1364220, _1364222, _1364224, _1364226, _1364228] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1364218, _1364220, _1364222)), _1364224), _1364226), _1364228)), 31143 ^ _781013 : [(31146 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1364220), _1364224), _1364226), _1364228)))], (31144 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1364218, _1364224)))]], 31147 ^ _781013 : [(31150 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1364222), _1364224), _1364226), _1364228)))], (31148 ^ _781013) ^ [] : [hBOOL(hAPP(_1364218, _1364224))]]], (47972 ^ _781013) ^ [_1750074, _1750076] : [c_Wellfounded_Owf(_1750074, _1750076), -(c_Wellfounded_Owf(_1750074, c_Transitive__Closure_Otrancl(_1750074, _1750076)))], (34163 ^ _781013) ^ [_1429042, _1429044] : [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), _1429042))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1429044), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1429042))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1429044), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429042))), 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), _1429044))), c_COMBI(tc_Int_Oint))))], (40956 ^ _781013) ^ [_1587317, _1587319] : [-(hAPP(c_Fun_Oid(_1587317), _1587319) = _1587319)], (40345 ^ _781013) ^ [_1568154, _1568156, _1568158, _1568160] : [c_Relation_Orefl__on(_1568154, _1568156, _1568158), hBOOL(hAPP(hAPP(c_member(_1568154), _1568160), _1568156)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568154, _1568154)), hAPP(hAPP(c_Product__Type_OPair(_1568154, _1568154), _1568160), _1568160)), _1568158)))], (17743 ^ _781013) ^ [_1112183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112183), _1112183))], (42857 ^ _781013) ^ [_1631048, _1631050, _1631052, _1631054, _1631056, _1631058] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631048, tc_fun(_1631050, tc_HOL_Obool)), _1631052), hAPP(hAPP(c_COMBC(_1631048, tc_fun(_1631054, tc_fun(_1631050, tc_HOL_Obool)), tc_fun(_1631050, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1631054, tc_HOL_Obool), tc_fun(tc_fun(_1631054, tc_fun(_1631050, tc_HOL_Obool)), tc_fun(_1631050, tc_HOL_Obool)), _1631048), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631054, tc_fun(_1631050, tc_HOL_Obool))), _1631056)), _1631058)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631054, tc_fun(_1631050, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1631048, tc_fun(_1631054, tc_HOL_Obool)), _1631052), _1631056)), _1631058))], (51520 ^ _781013) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (51710 ^ _781013) ^ [_1826088] : [hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _1826088), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY, _1826088))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (42382 ^ _781013) ^ [_1620430, _1620432, _1620434] : [-(hAPP(c_List_Oset(_1620430), hAPP(c_List_Orotate(_1620430, _1620432), _1620434)) = hAPP(c_List_Oset(_1620430), _1620434))], (12708 ^ _781013) ^ [_1010911, _1010913, _1010915, _1010917, _1010919, _1010921, _1010923, _1010925] : [c_Finite__Set_Ofolding__image(_1010911, _1010913, _1010915, _1010917, _1010919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010913), _1010921)), -(hAPP(hAPP(_1010919, hAPP(hAPP(c_COMBS(_1010913, _1010911, _1010911), hAPP(hAPP(c_COMBB(_1010911, tc_fun(_1010911, _1010911), _1010913), _1010915), _1010923)), _1010925)), _1010921) = hAPP(hAPP(_1010915, hAPP(hAPP(_1010919, _1010923), _1010921)), hAPP(hAPP(_1010919, _1010925), _1010921)))], (46385 ^ _781013) ^ [_1710073, _1710075, _1710077] : [-(hAPP(c_List_Oset(_1710073), c_List_Oinsert(_1710073, _1710075, _1710077)) = hAPP(hAPP(c_Set_Oinsert(_1710073), _1710075), hAPP(c_List_Oset(_1710073), _1710077)))], (5104 ^ _781013) ^ [_858852, _858854] : [_858854 = _858852, -(c_New__Random__Sequence_Opos__single(_858854) = c_New__Random__Sequence_Opos__single(_858852))], (47457 ^ _781013) ^ [_1737769, _1737771, _1737773, _1737775] : [hAPP(c_List_Oset(_1737769), hAPP(hAPP(c_List_Omap(tc_prod(_1737769, _1737771), _1737769), c_Product__Type_Ofst(_1737769, _1737771)), _1737773)) = hAPP(c_List_Oset(_1737769), hAPP(hAPP(c_List_Omap(tc_prod(_1737769, _1737771), _1737769), c_Product__Type_Ofst(_1737769, _1737771)), _1737775)), 47463 ^ _781013 : [(47466 ^ _781013) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1737769, _1737771), _1737773), 47462 ^ [_1737769, _1737771, _1737773, _1737775]) = hAPP(hAPP(c_Map_Omap__of(_1737769, _1737771), _1737775), 47462 ^ [_1737769, _1737771, _1737773, _1737775])], (47464 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737769), 47462 ^ [_1737769, _1737771, _1737773, _1737775]), hAPP(c_List_Oset(_1737769), hAPP(hAPP(c_List_Omap(tc_prod(_1737769, _1737771), _1737769), c_Product__Type_Ofst(_1737769, _1737771)), _1737773)))))]], -(hAPP(c_Map_Omap__of(_1737769, _1737771), _1737773) = hAPP(c_Map_Omap__of(_1737769, _1737771), _1737775))], (22075 ^ _781013) ^ [_1194940, _1194942, _1194944] : [hBOOL(hAPP(_1194940, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1194942), _1194944)))), 22078 ^ _781013 : [(22085 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1194942), _1194944)), -(hBOOL(hAPP(_1194940, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22079 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1194944), _1194942)), -(hBOOL(hAPP(_1194940, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1194942)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1194944)))))]]], (39617 ^ _781013) ^ [_1547770, _1547772, _1547774] : [-(c_List_Olist_Olist__size(_1547770, _1547772, _1547774) = 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(_1547770, tc_Nat_Onat), _1547772), _1547774))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1547770)), _1547774)))], (41107 ^ _781013) ^ [_1591130] : [-(c_List_Olists(_1591130, c_Orderings_Otop__class_Otop(tc_fun(_1591130, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1591130), tc_HOL_Obool)))], (5755 ^ _781013) ^ [_872131, _872133, _872135] : [-(hAPP(hAPP(c_Set_Oinsert(_872131), _872133), hAPP(hAPP(c_Set_Oinsert(_872131), _872133), _872135)) = hAPP(hAPP(c_Set_Oinsert(_872131), _872133), _872135))], (44097 ^ _781013) ^ [_1658949, _1658951, _1658953] : [class_Orderings_Olinorder(_1658949), hBOOL(hAPP(hAPP(c_member(_1658949), _1658951), hAPP(c_List_Oset(_1658949), _1658953))), c_List_Olinorder__class_Osorted(_1658949, _1658953), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658949, _1658949, c_COMBI(_1658949)), _1658951), c_List_Oremove1(_1658949, _1658951, _1658953)) = _1658953)], (9785 ^ _781013) ^ [_953773, _953775, _953777] : [class_Orderings_Olinorder(_953773), 9788 ^ _781013 : [(9789 ^ _781013) ^ [] : [-(_953775 = _953777), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953773), _953775), _953777))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953773), _953777), _953775)))], (9799 ^ _781013) ^ [] : [9800 ^ _781013 : [(9803 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953773), _953777), _953775))], (9801 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953773), _953775), _953777))]], _953775 = _953777]]], (34425 ^ _781013) ^ [_1433408, _1433410] : [class_Int_Onumber__ring(_1433408), class_Rings_Olinordered__idom(_1433408), 34432 ^ _781013 : [(34439 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1433410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433408), c_Groups_Oone__class_Oone(_1433408)), hAPP(c_Int_Onumber__class_Onumber__of(_1433408), _1433410))))], (34433 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433408), c_Groups_Oone__class_Oone(_1433408)), hAPP(c_Int_Onumber__class_Onumber__of(_1433408), _1433410))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1433410)))]]], (43364 ^ _781013) ^ [_1644580, _1644582, _1644584, _1644586, _1644588, _1644590] : [class_Orderings_Olinorder(_1644580), -(hBOOL(hAPP(_1644582, _1644584))), -(hAPP(c_List_Ofilter(_1644586, _1644582), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1644586, _1644580, _1644588), _1644584), _1644590)) = hAPP(c_List_Ofilter(_1644586, _1644582), _1644590))], (51212 ^ _781013) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (44731 ^ _781013) ^ [_1674278, _1674280] : [_1674280 = c_List_Olist_ONil(_1674278), -(c_List_Oremdups(_1674278, _1674280) = c_List_Olist_ONil(_1674278))], (34639 ^ _781013) ^ [_1437237, _1437239] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1437237)), c_Int_OBit0(_1437239)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1437237), _1437239)))], (23801 ^ _781013) ^ [_1225713, _1225715, _1225717, _1225719] : [class_Orderings_Olinorder(_1225713), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225713), _1225715), _1225717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225713), _1225717), _1225719)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1225713, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1225713, _1225715, _1225717)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1225713, _1225717, _1225719)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1225713, _1225715, _1225719))], (51574 ^ _781013) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (48661 ^ _781013) ^ [_1765549, _1765551] : [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), _1765549), _1765551)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1765549), _1765551)))], (19264 ^ _781013) ^ [_1141798, _1141800, _1141802, _1141804] : [class_Rings_Olinordered__semidom(_1141798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1141800), _1141802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141798), c_Groups_Ozero__class_Ozero(_1141798)), _1141804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141798), _1141804), c_Groups_Oone__class_Oone(_1141798))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141798), hAPP(hAPP(c_Power_Opower__class_Opower(_1141798), _1141804), _1141802)), hAPP(hAPP(c_Power_Opower__class_Opower(_1141798), _1141804), _1141800))))], (29279 ^ _781013) ^ [_1327176] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327176), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1327176) = _1327176)], (19873 ^ _781013) ^ [_1153276] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153276) = _1153276)], (18760 ^ _781013) ^ [_1130657, _1130659, _1130661, _1130663] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_1130657)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1130657), _1130659), _1130661), _1130663)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40816 ^ _781013) ^ [_1582230, _1582232, _1582234, _1582236] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1582230), _1582232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582230, _1582230), tc_HOL_Obool)), _1582234), hAPP(hAPP(c_Product__Type_OSigma(_1582230, _1582230), _1582232), hAPP(c_COMBK(tc_fun(_1582230, tc_HOL_Obool), _1582230), _1582232)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1582230, tc_HOL_Obool)), _1582236), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1582230), _1582232), _1582234))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1582230), _1582236)))], (46200 ^ _781013) ^ [_1705867, _1705869, _1705871, _1705873, _1705875] : [c_List_Olist__all2(_1705867, _1705869, _1705871, _1705873, hAPP(c_List_Orev(_1705869), _1705875)), -(c_List_Olist__all2(_1705867, _1705869, _1705871, hAPP(c_List_Orev(_1705867), _1705873), _1705875))], (6995 ^ _781013) ^ [_896688, _896690, _896692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896688, tc_HOL_Obool)), _896690), _896692)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896688, tc_HOL_Obool)), _896690), _896692) = _896692)], (32272 ^ _781013) ^ [_1393501, _1393503, _1393505, _1393507, _1393509] : [c_Com_Ocom_OSemi(_1393501, _1393503) = c_Com_Ocom_OLocal(_1393505, _1393507, _1393509)], (1584 ^ _781013) ^ [_803555, _803557] : [-(class_Groups_Oab__semigroup__add(_803555)), _803557 = _803555, class_Groups_Oab__semigroup__add(_803557)], (46697 ^ _781013) ^ [_1720387, _1720389, _1720391, _1720393, _1720395, _1720397, _1720399, _1720401] : [hBOOL(hAPP(hAPP(_1720387, _1720389), _1720391)), hBOOL(hAPP(hAPP(_1720393, _1720391), _1720395)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1720397, _1720399, _1720401, _1720387, _1720393), _1720389), _1720395)))], (43456 ^ _781013) ^ [_1646343, _1646345, _1646347, _1646349, _1646351] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646343)), hAPP(c_List_Ofilter(_1646343, _1646345), hAPP(hAPP(c_List_Omap(_1646347, _1646343), _1646349), _1646351))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646347)), hAPP(c_List_Ofilter(_1646347, hAPP(c_Fun_Ocomp(_1646343, tc_HOL_Obool, _1646347, _1646345), _1646349)), _1646351)))], (37604 ^ _781013) ^ [_1499158, _1499160, _1499162, _1499164, _1499166] : [-(c_Product__Type_Oprod_Oprod__size(_1499158, _1499160, _1499162, _1499164, _1499166) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1499162, hAPP(c_Product__Type_Ofst(_1499158, _1499160), _1499166))), hAPP(_1499164, hAPP(c_Product__Type_Osnd(_1499158, _1499160), _1499166)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51058 ^ _781013) ^ [_1819142, _1819144] : [class_Orderings_Oorder(_1819142), -(class_Orderings_Oorder(tc_fun(_1819144, _1819142)))], (36994 ^ _781013) ^ [_1486612, _1486614, _1486616, _1486618, _1486620, _1486622, _1486624] : [c_Equiv__Relations_Oequiv(_1486612, _1486614, _1486616), c_Equiv__Relations_Ocongruent(_1486612, tc_fun(_1486618, tc_HOL_Obool), _1486616, _1486620), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486612, tc_fun(_1486618, tc_HOL_Obool)), _1486622), _1486620) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486612, tc_fun(_1486618, tc_HOL_Obool)), _1486624), _1486620), hBOOL(hAPP(hAPP(c_member(tc_fun(_1486612, tc_HOL_Obool)), _1486622), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1486612), _1486614), _1486616))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1486612, tc_HOL_Obool)), _1486624), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1486612), _1486614), _1486616))), 37016 ^ _781013 : [(37020 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486612), 37018 ^ [_1486612, _1486614, _1486616, _1486618, _1486620, _1486622, _1486624]), _1486614)))], (37022 ^ _781013) ^ [] : [-(hAPP(_1486620, 37015 ^ [_1486612, _1486614, _1486616, _1486618, _1486620, _1486622, _1486624]) = hAPP(_1486620, 37018 ^ [_1486612, _1486614, _1486616, _1486618, _1486620, _1486622, _1486624]))], (37024 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486612, _1486612)), hAPP(hAPP(c_Product__Type_OPair(_1486612, _1486612), 37015 ^ [_1486612, _1486614, _1486616, _1486618, _1486620, _1486622, _1486624]), 37018 ^ [_1486612, _1486614, _1486616, _1486618, _1486620, _1486622, _1486624])), _1486616))], (37017 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486612), 37015 ^ [_1486612, _1486614, _1486616, _1486618, _1486620, _1486622, _1486624]), _1486614)))]], -(_1486622 = _1486624)], (15169 ^ _781013) ^ [_1061662, _1061664, _1061666] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1061662), _1061664)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1061662, tc_HOL_Obool)), _1061666), _1061664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1061662), _1061666)), hAPP(c_Finite__Set_Ocard(_1061662), _1061664))))], (15359 ^ _781013) ^ [_1065178, _1065180] : [class_Rings_Olinordered__ring(_1065178), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065178), c_Groups_Ozero__class_Ozero(_1065178)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065178), _1065180), _1065180))))], (46365 ^ _781013) ^ [_1709756, _1709758, _1709760] : [-(hBOOL(hAPP(hAPP(c_member(_1709756), _1709758), hAPP(c_List_Oset(_1709756), _1709760)))), -(c_List_Oinsert(_1709756, _1709758, _1709760) = hAPP(hAPP(c_List_Olist_OCons(_1709756), _1709758), _1709760))], (1414 ^ _781013) ^ [_801430, _801432] : [-(class_Smallcheck_Osmall(_801430)), _801432 = _801430, class_Smallcheck_Osmall(_801432)], (8781 ^ _781013) ^ [_934606, _934608, _934610] : [class_Lattices_Olattice(_934606), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934606), _934608), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934606), _934610), _934608))))], (10943 ^ _781013) ^ [_974902, _974904, _974906, _974908] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974902, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974902, tc_HOL_Obool)), _974904), _974906)), _974908) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974902, tc_HOL_Obool)), _974904), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974902, tc_HOL_Obool)), _974906), _974908)))], (43271 ^ _781013) ^ [_1642695, _1642697, _1642699, _1642701] : [hBOOL(hAPP(c_List_Olistsp(_1642695, _1642697), hAPP(hAPP(c_List_Oappend(_1642695), _1642699), _1642701))), 43274 ^ _781013 : [(43277 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1642695, _1642697), _1642701)))], (43275 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1642695, _1642697), _1642699)))]]], (19418 ^ _781013) ^ [_1144599, _1144601, _1144603, _1144605] : [class_Rings_Olinordered__semidom(_1144599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144599), _1144601), _1144603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144599), c_Groups_Ozero__class_Ozero(_1144599)), _1144601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144599), hAPP(hAPP(c_Power_Opower__class_Opower(_1144599), _1144601), _1144605)), hAPP(hAPP(c_Power_Opower__class_Opower(_1144599), _1144603), _1144605))))], (42841 ^ _781013) ^ [_1629895, _1629897, _1629899, _1629901, _1629903, _1629905] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629895, tc_fun(_1629897, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1629899, _1629895, _1629901), _1629903)), _1629905) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629899, tc_fun(_1629897, tc_HOL_Obool)), _1629903), hAPP(hAPP(c_COMBB(_1629895, tc_fun(_1629897, tc_HOL_Obool), _1629899), _1629905), _1629901)))], (22111 ^ _781013) ^ [_1195631, _1195633, _1195635, _1195637, _1195639] : [class_Groups_Oordered__ab__semigroup__add(_1195631), class_Rings_Osemiring__1(_1195631), 22121 ^ _781013 : [(22124 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195631), hAPP(_1195637, 22120 ^ [_1195631, _1195633, _1195635, _1195637, _1195639])), _1195639))], (22122 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1195633), 22120 ^ [_1195631, _1195633, _1195635, _1195637, _1195639]), _1195635)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195631), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1195633, _1195631), _1195637), _1195635)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195631), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1195631), hAPP(c_Finite__Set_Ocard(_1195633), _1195635))), _1195639))))], (34225 ^ _781013) ^ [_1430221, _1430223] : [_1430221 = _1430223, -(c_Int_OBit1(_1430221) = c_Int_OBit1(_1430223))], (19370 ^ _781013) ^ [_1143652, _1143654] : [19371 ^ _781013 : [(19374 ^ _781013) ^ [] : [_1143654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19372 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1143652))]], -(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), _1143652), _1143654))))], (40783 ^ _781013) ^ [_1581224, _1581226, _1581228, _1581230] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1581224), tc_List_Olist(_1581224))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1581224), tc_List_Olist(_1581224)), _1581226), _1581228)), c_List_Olistrel1(_1581224, _1581230))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1581224)), _1581226) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1581224)), _1581228))], (17477 ^ _781013) ^ [_1107712, _1107714, _1107716, _1107718, _1107720, _1107722] : [hBOOL(hAPP(hAPP(c_member(_1107712), _1107714), _1107716)), -(hAPP(c_Fun_Ooverride__on(_1107712, _1107718, _1107720, _1107722, _1107716), _1107714) = hAPP(_1107722, _1107714))], (16183 ^ _781013) ^ [_1080134, _1080136] : [class_Groups_Oordered__ab__group__add(_1080134), 16186 ^ _781013 : [(16193 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080134), c_Groups_Ozero__class_Ozero(_1080134)), _1080136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080134), hAPP(c_Groups_Ouminus__class_Ouminus(_1080134), _1080136)), c_Groups_Ozero__class_Ozero(_1080134))))], (16187 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080134), hAPP(c_Groups_Ouminus__class_Ouminus(_1080134), _1080136)), c_Groups_Ozero__class_Ozero(_1080134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080134), c_Groups_Ozero__class_Ozero(_1080134)), _1080136)))]]], (48882 ^ _781013) ^ [_1771133, _1771135] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1771133, _1771133)), _1771135)), c_Wellfounded_Oacyclic(_1771133, _1771135), -(c_Wellfounded_Owf(_1771133, hAPP(c_Relation_Oconverse(_1771133, _1771133), _1771135)))], (49237 ^ _781013) ^ [_1780443] : [-(c_Nat_Ofunpow(_1780443) = c_Nat_Ocompow(_1780443, _1780443))], (12856 ^ _781013) ^ [_1014118, _1014120, _1014122, _1014124, _1014126] : [hBOOL(hAPP(_1014124, hAPP(_1014122, _1014126))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1014118, _1014120, _1014122), _1014124), _1014126)))], (13126 ^ _781013) ^ [_1020035, _1020037, _1020039, _1020041, _1020043, _1020045] : [-(hBOOL(hAPP(hAPP(c_member(_1020035), _1020037), _1020039))), 13129 ^ _781013 : [(13136 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1020035), _1020041), _1020039))), -(hAPP(c_Set_Ovimage(_1020043, _1020035, hAPP(hAPP(c_COMBC(_1020043, _1020035, _1020035), hAPP(hAPP(c_COMBC(_1020043, _1020035, tc_fun(_1020035, _1020035)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1020035, tc_fun(_1020035, _1020035)), _1020043), c_If(_1020035)), hAPP(hAPP(c_COMBC(_1020043, tc_fun(_1020043, tc_HOL_Obool), tc_HOL_Obool), c_member(_1020043)), _1020045))), _1020037)), _1020041)), _1020039) = c_Orderings_Obot__class_Obot(tc_fun(_1020043, tc_HOL_Obool)))], (13130 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1020035), _1020041), _1020039)), -(hAPP(c_Set_Ovimage(_1020043, _1020035, hAPP(hAPP(c_COMBC(_1020043, _1020035, _1020035), hAPP(hAPP(c_COMBC(_1020043, _1020035, tc_fun(_1020035, _1020035)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1020035, tc_fun(_1020035, _1020035)), _1020043), c_If(_1020035)), hAPP(hAPP(c_COMBC(_1020043, tc_fun(_1020043, tc_HOL_Obool), tc_HOL_Obool), c_member(_1020043)), _1020045))), _1020037)), _1020041)), _1020039) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1020043, tc_HOL_Obool)), _1020045))]]], (49178 ^ _781013) ^ [_1778835, _1778837, _1778839] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1778835, _1778835)), _1778837), c_Transitive__Closure_Otrancl(_1778835, _1778839))), 49182 ^ _781013 : [(49185 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778835, _1778835)), _1778837), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1778835, _1778835), tc_HOL_Obool), 49181 ^ [_1778835, _1778837, _1778839]), _1778839))))], (49183 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 49181 ^ [_1778835, _1778837, _1778839])))]]], (23136 ^ _781013) ^ [_1213824, _1213826] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213824), _1213826)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1213824)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1213826)))], (20895 ^ _781013) ^ [_1171567, _1171569] : [class_Int_Oring__char__0(_1171567), hBOOL(hAPP(hAPP(c_member(_1171567), _1171569), c_Int_Oring__1__class_OInts(_1171567))), 20902 ^ _781013 : [(20909 ^ _781013) ^ [] : [_1171569 = c_Groups_Ozero__class_Ozero(_1171567), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171567), _1171569), _1171569) = c_Groups_Ozero__class_Ozero(_1171567))], (20903 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171567), _1171569), _1171569) = c_Groups_Ozero__class_Ozero(_1171567), -(_1171569 = c_Groups_Ozero__class_Ozero(_1171567))]]], (16902 ^ _781013) ^ [_1094456, _1094458, _1094460] : [class_Rings_Olinordered__idom(_1094456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094456), c_Groups_Ozero__class_Ozero(_1094456)), _1094458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094456), c_Groups_Ozero__class_Ozero(_1094456)), _1094460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094456), _1094460), c_Groups_Oone__class_Oone(_1094456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094456), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094456), _1094460), _1094458)), _1094458)))], (13640 ^ _781013) ^ [_1031246, _1031248] : [class_Rings_Ocomm__semiring__1(_1031246), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031246), _1031248), c_Groups_Oone__class_Oone(_1031246)) = _1031248)], (11191 ^ _781013) ^ [_980546, _980548, _980550, _980552, _980554, _980556, _980558, _980560] : [c_Finite__Set_Ofolding__image__simple(_980546, _980548, _980550, _980552, _980554, _980556), hBOOL(hAPP(c_Finite__Set_Ofinite(_980548), _980558)), hBOOL(hAPP(c_Finite__Set_Ofinite(_980548), _980560)), -(hAPP(hAPP(_980550, hAPP(_980556, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980548, tc_HOL_Obool)), _980558), _980560))), hAPP(_980556, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980548, tc_HOL_Obool)), _980558), _980560))) = hAPP(hAPP(_980550, hAPP(_980556, _980558)), hAPP(_980556, _980560)))], (24486 ^ _781013) ^ [_1237824, _1237826, _1237828] : [class_Fields_Ofield__inverse__zero(_1237824), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237824), hAPP(c_Groups_Ouminus__class_Ouminus(_1237824), _1237826)), hAPP(c_Groups_Ouminus__class_Ouminus(_1237824), _1237828)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237824), _1237826), _1237828))], (56 ^ _781013) ^ [_781819, _781821, _781823, _781825, _781827, _781829, _781831, _781833, _781835, _781837, _781839, _781841] : [-(c_Finite__Set_Ofolding__image__simple__idem(_781839, _781835, _781831, _781827, _781823, _781819)), c_Finite__Set_Ofolding__image__simple__idem(_781841, _781837, _781833, _781829, _781825, _781821), _781841 = _781839, _781837 = _781835, _781833 = _781831, _781829 = _781827, _781825 = _781823, _781821 = _781819], (48625 ^ _781013) ^ [_1764621, _1764623, _1764625, _1764627] : [-(c_Wellfounded_Oacyclic(_1764621, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1764621, _1764621)), hAPP(hAPP(c_Product__Type_OPair(_1764621, _1764621), _1764623), _1764625)), _1764627))), c_Wellfounded_Oacyclic(_1764621, _1764627), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764621, _1764621)), hAPP(hAPP(c_Product__Type_OPair(_1764621, _1764621), _1764625), _1764623)), c_Transitive__Closure_Ortrancl(_1764621, _1764627))))], (6361 ^ _781013) ^ [_884691, _884693, _884695] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884691, _884693)), _884695), _884695)), hBOOL(hAPP(_884691, _884695)), 6369 ^ _781013 : [(6372 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884691, _884693)), 6368 ^ [_884691, _884693, _884695]), _884695)))], (6370 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_884693), _884695), 6368 ^ [_884691, _884693, _884695])))]]], (33730 ^ _781013) ^ [_1420313, _1420315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420313)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420313), _1420315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420313), c_Int_OPls)))], (11109 ^ _781013) ^ [_978784, _978786, _978788, _978790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978784, tc_HOL_Obool)), _978790), _978786)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978784, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978784, tc_HOL_Obool)), _978786), _978788)), _978790) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978784, tc_HOL_Obool)), _978786), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978784, tc_HOL_Obool)), _978788), _978790)))], (7521 ^ _781013) ^ [_906846, _906848, _906850, _906852] : [hBOOL(hAPP(hAPP(c_member(_906846), _906848), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906846, tc_HOL_Obool)), _906850), _906852))), -(hBOOL(hAPP(hAPP(c_member(_906846), _906848), _906850)))], (44898 ^ _781013) ^ [_1677444, _1677446, _1677448, _1677450, _1677452] : [-(c_List_OdropWhile(_1677444, _1677446, hAPP(hAPP(c_List_Omap(_1677448, _1677444), _1677450), _1677452)) = hAPP(hAPP(c_List_Omap(_1677448, _1677444), _1677450), c_List_OdropWhile(_1677448, hAPP(c_Fun_Ocomp(_1677444, tc_HOL_Obool, _1677448, _1677446), _1677450), _1677452)))], (40235 ^ _781013) ^ [_1565675, _1565677, _1565679, _1565681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565675)), _1565677)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565675)), _1565679))), _1565677 = hAPP(hAPP(c_List_Olist_OCons(_1565675), _1565681), _1565679)], (38317 ^ _781013) ^ [_1517237] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1517237)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1517237), tc_HOL_Obool))))], (13927 ^ _781013) ^ [_1037025, _1037027, _1037029, _1037031] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1037025), 13930 ^ _781013 : [(13937 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037025), _1037029), _1037031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037025), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037025), _1037027), _1037029)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037025), _1037027), _1037031))))], (13931 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037025), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037025), _1037027), _1037029)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037025), _1037027), _1037031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037025), _1037029), _1037031)))]]], (46609 ^ _781013) ^ [_1716429, _1716431, _1716433, _1716435, _1716437, _1716439, _1716441] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1716429, _1716431, _1716433), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1716435, tc_fun(tc_prod(_1716429, _1716431), tc_HOL_Obool)), _1716437), _1716439)), _1716441) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1716435, tc_fun(tc_prod(_1716429, _1716433), tc_HOL_Obool)), _1716437), hAPP(hAPP(c_COMBC(_1716435, tc_fun(tc_prod(_1716431, _1716433), tc_HOL_Obool), tc_fun(tc_prod(_1716429, _1716433), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1716429, _1716431), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1716431, _1716433), tc_HOL_Obool), tc_fun(tc_prod(_1716429, _1716433), tc_HOL_Obool)), _1716435), c_Relation_Orel__comp(_1716429, _1716431, _1716433)), _1716439)), _1716441)))], (39152 ^ _781013) ^ [_1536976, _1536978, _1536980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1536976), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1536978)), _1536980))), -(hBOOL(hAPP(hAPP(c_member(_1536978), hAPP(hAPP(c_List_Onth(_1536978), _1536980), _1536976)), hAPP(c_List_Oset(_1536978), _1536980))))], (15231 ^ _781013) ^ [_1062858, _1062860, _1062862, _1062864, _1062866] : [class_Groups_Ocomm__monoid__mult(_1062858), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062860), _1062862)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1062860, _1062858), hAPP(hAPP(c_COMBS(_1062860, _1062858, _1062858), hAPP(hAPP(c_COMBB(_1062858, tc_fun(_1062858, _1062858), _1062860), c_Groups_Otimes__class_Otimes(_1062858)), _1062864)), _1062866)), _1062862) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062858), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1062860, _1062858), _1062864), _1062862)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1062860, _1062858), _1062866), _1062862)))], (40459 ^ _781013) ^ [_1571898, _1571900, _1571902, _1571904, _1571906, _1571908, _1571910, _1571912, _1571914, _1571916] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1571898, _1571900), tc_prod(_1571902, _1571904), tc_prod(_1571906, _1571908), c_Product__Type_Omap__pair(_1571898, _1571902, _1571900, _1571904, _1571910, _1571912)), c_Product__Type_Omap__pair(_1571906, _1571898, _1571908, _1571900, _1571914, _1571916)) = c_Product__Type_Omap__pair(_1571906, _1571902, _1571908, _1571904, hAPP(c_Fun_Ocomp(_1571898, _1571902, _1571906, _1571910), _1571914), hAPP(c_Fun_Ocomp(_1571900, _1571904, _1571908, _1571912), _1571916)))], (16377 ^ _781013) ^ [_1084033, _1084035, _1084037] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1084033), _1084035)), 16380 ^ _781013 : [(16381 ^ _781013) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084033, tc_Nat_Onat), _1084037), _1084035) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 16384 ^ _781013 : [(16385 ^ _781013) ^ [_1084195] : [hBOOL(hAPP(hAPP(c_member(_1084033), _1084195), _1084035)), -(hAPP(_1084037, _1084195) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (16391 ^ _781013) ^ [] : [16393 ^ _781013 : [(16396 ^ _781013) ^ [] : [hAPP(_1084037, 16392 ^ [_1084033, _1084035, _1084037]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16394 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1084033), 16392 ^ [_1084033, _1084035, _1084037]), _1084035)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084033, tc_Nat_Onat), _1084037), _1084035) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (40615 ^ _781013) ^ [_1576551, _1576553, _1576555, _1576557] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1576551, _1576553)), hAPP(hAPP(c_Product__Type_OSigma(_1576551, _1576553), _1576555), hAPP(c_COMBK(tc_fun(_1576553, tc_HOL_Obool), _1576551), _1576557))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1576551), _1576555)), hAPP(c_Finite__Set_Ocard(_1576553), _1576557)))], (10809 ^ _781013) ^ [_971993, _971995, _971997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971993, tc_HOL_Obool)), _971995), _971997)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971993, tc_HOL_Obool)), _971997), _971995) = _971995)], (39655 ^ _781013) ^ [_1548692, _1548694, _1548696, _1548698, _1548700] : [-(hAPP(hAPP(c_List_Otake(_1548692), _1548694), hAPP(hAPP(c_List_Omap(_1548696, _1548692), _1548698), _1548700)) = hAPP(hAPP(c_List_Omap(_1548696, _1548692), _1548698), hAPP(hAPP(c_List_Otake(_1548696), _1548694), _1548700)))], (51220 ^ _781013) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (11878 ^ _781013) ^ [_995244, _995246] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_995244, tc_HOL_Obool)), _995246), c_Orderings_Otop__class_Otop(tc_fun(_995244, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_995244, tc_HOL_Obool)))], (44400 ^ _781013) ^ [_1665877, _1665879, _1665881] : [-(hAPP(c_List_Ofilter(_1665877, _1665879), c_List_Oconcat(_1665877, _1665881)) = c_List_Oconcat(_1665877, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1665877), tc_List_Olist(_1665877)), c_List_Ofilter(_1665877, _1665879)), _1665881)))], (22502 ^ _781013) ^ [_1202214, _1202216, _1202218, _1202220, _1202222] : [class_Orderings_Olinorder(_1202214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1202214, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1202214, _1202216), _1202218)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1202214, _1202220), _1202222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202214), _1202218), _1202216))), 22513 ^ _781013 : [(22516 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202214), _1202218), _1202222)))], (22514 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202214), _1202220), _1202216)))]]], (34325 ^ _781013) ^ [_1431934, _1431936] : [class_Int_Onumber__ring(_1431934), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1431934), hAPP(c_Int_Onumber__class_Onumber__of(_1431934), c_Int_OBit1(c_Int_OPls))), _1431936) = _1431936)], (39607 ^ _781013) ^ [_1547494, _1547496, _1547498, _1547500] : [-(c_Hilbert__Choice_OEps(tc_prod(_1547494, _1547496), hAPP(c_Product__Type_Oprod_Oprod__case(_1547494, _1547496, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1547494, tc_fun(_1547496, tc_HOL_Obool), tc_fun(_1547496, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1547496, tc_HOL_Obool), tc_fun(_1547496, tc_HOL_Obool)), _1547494), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1547496)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547494), c_fconj), hAPP(c_fequal, _1547498)))), hAPP(c_fequal, _1547500)))) = hAPP(hAPP(c_Product__Type_OPair(_1547494, _1547496), _1547498), _1547500))], (40355 ^ _781013) ^ [_1568345, _1568347, _1568349, _1568351, _1568353] : [c_Relation_Orefl__on(_1568345, _1568347, _1568349), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568345, _1568345)), hAPP(hAPP(c_Product__Type_OPair(_1568345, _1568345), _1568351), _1568353)), _1568349)), -(hBOOL(hAPP(hAPP(c_member(_1568345), _1568351), _1568347)))], (28074 ^ _781013) ^ [_1305137, _1305139, _1305141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305137, tc_HOL_Obool)), _1305139), _1305141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1305137, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1305137, _1305139)), c_Predicate_OPowp(_1305137, _1305141))))], (26257 ^ _781013) ^ [_1269183, _1269185] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1269183, _1269185)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1269183), hAPP(c_Nat_OSuc, _1269185)))], (2566 ^ _781013) ^ [_819083, _819085, _819087, _819089] : [-(c_Groups_Osgn__class_Osgn(_819089, _819085) = c_Groups_Osgn__class_Osgn(_819087, _819083)), _819089 = _819087, _819085 = _819083], (8207 ^ _781013) ^ [_921084, _921086, _921088, _921090, _921092] : [hAPP(_921084, _921086) = c_Option_Ooption_ONone(_921088), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921090, tc_HOL_Obool)), c_Map_Odom(_921090, _921088, _921084)), hAPP(hAPP(c_Set_Oinsert(_921090), _921086), _921092)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921090, tc_HOL_Obool)), c_Map_Odom(_921090, _921088, _921084)), _921092))], (18300 ^ _781013) ^ [_1121706, _1121708] : [18301 ^ _781013 : [(18302 ^ _781013) ^ [_1121756] : [_1121708 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121706), _1121756)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121706), _1121708)))], (45705 ^ _781013) ^ [_1694681, _1694683, _1694685, _1694687] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1694681, tc_fun(_1694683, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1694681, tc_HOL_Obool), _1694685)), _1694687) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1694681, tc_HOL_Obool), tc_fun(_1694683, tc_HOL_Obool)), _1694685), hAPP(hAPP(c_COMBC(tc_fun(_1694681, tc_HOL_Obool), tc_fun(_1694681, tc_fun(_1694683, tc_HOL_Obool)), tc_fun(_1694683, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1694681, tc_fun(_1694683, tc_HOL_Obool))), _1694687)))], (41895 ^ _781013) ^ [_1608601, _1608603, _1608605, _1608607] : [-(hBOOL(hAPP(hAPP(c_member(_1608601), _1608603), hAPP(c_List_Oset(_1608601), _1608605)))), -(c_List_Oremove1(_1608601, _1608603, hAPP(hAPP(c_List_Oappend(_1608601), _1608605), _1608607)) = hAPP(hAPP(c_List_Oappend(_1608601), _1608605), c_List_Oremove1(_1608601, _1608603, _1608607)))], (34999 ^ _781013) ^ [_1443694] : [class_Rings_Osemiring__1(_1443694), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1443694), c_Groups_Ozero__class_Ozero(_1443694)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1443694))], (34959 ^ _781013) ^ [_1442921, _1442923, _1442925] : [class_Int_Onumber__ring(_1442921), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1442921), hAPP(c_Int_Onumber__class_Onumber__of(_1442921), _1442923)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1442925))) = hAPP(hAPP(c_HOL_OLet(_1442921, _1442921), hAPP(hAPP(c_Power_Opower__class_Opower(_1442921), hAPP(c_Int_Onumber__class_Onumber__of(_1442921), _1442923)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442925))), hAPP(hAPP(c_COMBS(_1442921, _1442921, _1442921), c_Groups_Otimes__class_Otimes(_1442921)), c_COMBI(_1442921))))], (842 ^ _781013) ^ [_793884, _793886, _793888, _793890, _793892, _793894] : [-(c_Finite__Set_Ofolding__one(_793892, _793888, _793884)), c_Finite__Set_Ofolding__one(_793894, _793890, _793886), _793894 = _793892, _793890 = _793888, _793886 = _793884], (24622 ^ _781013) ^ [_1240261, _1240263, _1240265] : [class_Fields_Olinordered__field__inverse__zero(_1240261), 24625 ^ _781013 : [(24640 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240261), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240261), _1240263), _1240265)), c_Groups_Ozero__class_Ozero(_1240261)))), 24641 ^ _781013 : [(24648 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240261), _1240263), c_Groups_Ozero__class_Ozero(_1240261))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240261), c_Groups_Ozero__class_Ozero(_1240261)), _1240265))], (24642 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240261), c_Groups_Ozero__class_Ozero(_1240261)), _1240263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240261), _1240265), c_Groups_Ozero__class_Ozero(_1240261)))]]], (24626 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240261), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240261), _1240263), _1240265)), c_Groups_Ozero__class_Ozero(_1240261))), 24631 ^ _781013 : [(24634 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240261), _1240265), c_Groups_Ozero__class_Ozero(_1240261))))], (24632 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240261), c_Groups_Ozero__class_Ozero(_1240261)), _1240263)))]], 24635 ^ _781013 : [(24638 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240261), c_Groups_Ozero__class_Ozero(_1240261)), _1240265)))], (24636 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240261), _1240263), c_Groups_Ozero__class_Ozero(_1240261))))]]]]], (43374 ^ _781013) ^ [_1644722, _1644724, _1644726, _1644728] : [-(hBOOL(hAPP(_1644722, _1644724))), -(hAPP(c_List_OremoveAll(_1644726, _1644724), hAPP(c_List_Ofilter(_1644726, _1644722), _1644728)) = hAPP(c_List_Ofilter(_1644726, _1644722), _1644728))], (35507 ^ _781013) ^ [] : [-(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))], (40753 ^ _781013) ^ [_1580352, _1580354, _1580356, _1580358] : [_1580352 = c_Orderings_Obot__class_Obot(tc_fun(_1580354, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1580354, _1580356), _1580356, c_Product__Type_Osnd(_1580354, _1580356)), hAPP(hAPP(c_Product__Type_OSigma(_1580354, _1580356), _1580352), hAPP(c_COMBK(tc_fun(_1580356, tc_HOL_Obool), _1580354), _1580358))) = c_Orderings_Obot__class_Obot(tc_fun(_1580356, tc_HOL_Obool)))], (10191 ^ _781013) ^ [_961309, _961311, _961313] : [class_Lattices_Oboolean__algebra(_961309), 10194 ^ _781013 : [(10201 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961309), _961313), _961311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961309), hAPP(c_Groups_Ouminus__class_Ouminus(_961309), _961311)), hAPP(c_Groups_Ouminus__class_Ouminus(_961309), _961313))))], (10195 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961309), hAPP(c_Groups_Ouminus__class_Ouminus(_961309), _961311)), hAPP(c_Groups_Ouminus__class_Ouminus(_961309), _961313))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961309), _961313), _961311)))]]], (31686 ^ _781013) ^ [_1379816, _1379818, _1379820, _1379822, _1379824] : [class_Complete__Lattice_Ocomplete__lattice(_1379816), 31689 ^ _781013 : [(31690 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1379816), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379818, _1379816), _1379820), _1379822)), _1379824)), 31693 ^ _781013 : [(31694 ^ _781013) ^ [_1379997] : [hBOOL(hAPP(hAPP(c_member(_1379818), _1379997), _1379820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1379816), hAPP(_1379822, _1379997)), _1379824)))]]], (31700 ^ _781013) ^ [] : [31702 ^ _781013 : [(31705 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1379816), hAPP(_1379822, 31701 ^ [_1379816, _1379818, _1379820, _1379822, _1379824])), _1379824))], (31703 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1379818), 31701 ^ [_1379816, _1379818, _1379820, _1379822, _1379824]), _1379820)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1379816), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379818, _1379816), _1379820), _1379822)), _1379824)))]]], (48920 ^ _781013) ^ [_1772638] : [-(hAPP(c_Relation_ODomain(_1772638, _1772638), c_Relation_OId(_1772638)) = c_Orderings_Otop__class_Otop(tc_fun(_1772638, tc_HOL_Obool)))], (43269 ^ _781013) ^ [_1642611, _1642613, _1642615, _1642617] : [-(hAPP(c_List_Ofilter(_1642611, _1642613), hAPP(hAPP(c_List_Oappend(_1642611), _1642615), _1642617)) = hAPP(hAPP(c_List_Oappend(_1642611), hAPP(c_List_Ofilter(_1642611, _1642613), _1642615)), hAPP(c_List_Ofilter(_1642611, _1642613), _1642617)))], (30039 ^ _781013) ^ [_1342381, _1342383, _1342385, _1342387] : [class_Orderings_Olinorder(_1342381), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342381), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342381), _1342383), _1342385)), _1342387) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342381), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342381), _1342383), _1342387)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342381), _1342385), _1342387)))], (14724 ^ _781013) ^ [_1054245] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054245), c_Orderings_Otop__class_Otop(tc_fun(_1054245, 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(_1054245), c_Orderings_Otop__class_Otop(tc_fun(_1054245, tc_HOL_Obool))))))], (31684 ^ _781013) ^ [_1379742, _1379744, _1379746, _1379748, _1379750] : [-(hAPP(c_Relation_OImage(_1379742, _1379744, _1379746), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379742, tc_HOL_Obool)), _1379748), _1379750)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379744, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379742, _1379744, _1379746), _1379748)), hAPP(c_Relation_OImage(_1379742, _1379744, _1379746), _1379750)))], (31968 ^ _781013) ^ [_1387289, _1387291, _1387293, _1387295, _1387297] : [-(_1387289 = c_Orderings_Obot__class_Obot(tc_fun(_1387291, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387291, tc_fun(_1387293, tc_HOL_Obool)), _1387289), hAPP(hAPP(c_COMBC(_1387291, tc_fun(_1387293, tc_HOL_Obool), tc_fun(_1387293, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1387293, tc_HOL_Obool), tc_fun(tc_fun(_1387293, tc_HOL_Obool), tc_fun(_1387293, tc_HOL_Obool)), _1387291), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387293, tc_HOL_Obool))), _1387295)), _1387297)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387293, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387291, tc_fun(_1387293, tc_HOL_Obool)), _1387289), _1387295)), _1387297))], (36306 ^ _781013) ^ [_1472992, _1472994, _1472996, _1472998, _1473000] : [c_Equiv__Relations_Oequiv(_1472992, _1472994, _1472996), hBOOL(hAPP(hAPP(c_member(_1472992), _1472998), _1472994)), hBOOL(hAPP(hAPP(c_member(_1472992), _1473000), _1472994)), 36317 ^ _781013 : [(36324 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1472992, _1472992)), hAPP(hAPP(c_Product__Type_OPair(_1472992, _1472992), _1472998), _1473000)), _1472996)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472992), hAPP(hAPP(c_Set_Oinsert(_1472992), _1472998), c_Orderings_Obot__class_Obot(tc_fun(_1472992, tc_HOL_Obool)))), _1472996) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472992), hAPP(hAPP(c_Set_Oinsert(_1472992), _1473000), c_Orderings_Obot__class_Obot(tc_fun(_1472992, tc_HOL_Obool)))), _1472996))], (36318 ^ _781013) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472992), hAPP(hAPP(c_Set_Oinsert(_1472992), _1472998), c_Orderings_Obot__class_Obot(tc_fun(_1472992, tc_HOL_Obool)))), _1472996) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472992), hAPP(hAPP(c_Set_Oinsert(_1472992), _1473000), c_Orderings_Obot__class_Obot(tc_fun(_1472992, tc_HOL_Obool)))), _1472996), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472992, _1472992)), hAPP(hAPP(c_Product__Type_OPair(_1472992, _1472992), _1472998), _1473000)), _1472996)))]]], (48802 ^ _781013) ^ [_1769268, _1769270, _1769272, _1769274, _1769276] : [-(hAPP(c_Relation_Oconverse(_1769268, _1769270), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1769272, tc_fun(tc_prod(_1769268, _1769270), tc_HOL_Obool)), _1769274), _1769276)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1769272, tc_fun(tc_prod(_1769270, _1769268), tc_HOL_Obool)), _1769274), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1769268, _1769270), tc_HOL_Obool), tc_fun(tc_prod(_1769270, _1769268), tc_HOL_Obool), _1769272), c_Relation_Oconverse(_1769268, _1769270)), _1769276)))], (30015 ^ _781013) ^ [_1341795, _1341797, _1341799] : [class_Orderings_Olinorder(_1341795), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1341795), _1341797), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341795), _1341797), _1341799)) = _1341797)], (27234 ^ _781013) ^ [_1288185, _1288187] : [class_Orderings_Oorder(_1288185), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288185, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1288185), _1288187)), hAPP(c_SetInterval_Oord__class_OatLeast(_1288185), _1288187)) = hAPP(hAPP(c_Set_Oinsert(_1288185), _1288187), c_Orderings_Obot__class_Obot(tc_fun(_1288185, tc_HOL_Obool))))], (7881 ^ _781013) ^ [_913915, _913917, _913919, _913921, _913923, _913925, _913927] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_913915, tc_Option_Ooption(_913917)), _913919), _913921), hAPP(c_Option_Ooption_OSome(_913917), _913923)), _913925) = hAPP(c_Option_Ooption_OSome(_913917), _913927)), 7882 ^ _781013 : [(7889 ^ _781013) ^ [] : [-(_913925 = _913921), hAPP(_913919, _913925) = hAPP(c_Option_Ooption_OSome(_913917), _913927)], (7883 ^ _781013) ^ [] : [_913925 = _913921, _913923 = _913927]]], (19749 ^ _781013) ^ [_1151010, _1151012, _1151014, _1151016] : [19750 ^ _781013 : [(19753 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1151014), _1151016)))], (19751 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1151010), _1151012)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1151010, _1151014)), c_Sum__Type_OPlus(_1151010, _1151014, _1151012, _1151016)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33962 ^ _781013) ^ [_1424527, _1424529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1424527)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424529))), -(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(_1424529))), 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), _1424527)), c_Int_Onat))))))], (16534 ^ _781013) ^ [_1087226, _1087228, _1087230, _1087232, _1087234] : [class_Groups_Ocomm__monoid__mult(_1087226), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087228), _1087230)), 16541 ^ _781013 : [(16548 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1087228), _1087232), _1087230))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1087228, _1087226), hAPP(hAPP(c_COMBC(_1087228, _1087226, _1087226), hAPP(hAPP(c_COMBS(_1087228, _1087226, tc_fun(_1087226, _1087226)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1087226, tc_fun(_1087226, _1087226)), _1087228), c_If(_1087226)), hAPP(c_fequal, _1087232))), _1087234)), c_Groups_Oone__class_Oone(_1087226))), _1087230) = c_Groups_Oone__class_Oone(_1087226))], (16542 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1087228), _1087232), _1087230)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1087228, _1087226), hAPP(hAPP(c_COMBC(_1087228, _1087226, _1087226), hAPP(hAPP(c_COMBS(_1087228, _1087226, tc_fun(_1087226, _1087226)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1087226, tc_fun(_1087226, _1087226)), _1087228), c_If(_1087226)), hAPP(c_fequal, _1087232))), _1087234)), c_Groups_Oone__class_Oone(_1087226))), _1087230) = hAPP(_1087234, _1087232))]]], (5817 ^ _781013) ^ [_874242, _874244, _874246, _874248, _874250, _874252, _874254] : [c_Hoare__Mirabelle_Ohoare__derivs(_874242, _874244, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_874242)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874242), _874246), _874248), _874250)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_874242), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_874242, _874244, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_874242)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874242), _874250), _874252), _874254)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_874242), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_874242, _874244, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_874242)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874242), _874246), c_Com_Ocom_OSemi(_874248, _874252)), _874254)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_874242), tc_HOL_Obool)))))], (31188 ^ _781013) ^ [_1365223, _1365225] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _1365223), _1365225), _1365223)))], (6874 ^ _781013) ^ [_894458, _894460, _894462, _894464] : [hBOOL(hAPP(hAPP(c_member(_894458), _894460), _894462)), -(hBOOL(hAPP(hAPP(c_member(_894458), _894460), _894464))), -(hBOOL(hAPP(hAPP(c_member(_894458), _894460), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894458, tc_HOL_Obool)), _894462), _894464))))], (7091 ^ _781013) ^ [_898604, _898606, _898608] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898604, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898604, tc_HOL_Obool)), _898606), _898608)), _898608) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898604, tc_HOL_Obool)), _898606), _898608))], (48922 ^ _781013) ^ [_1772674] : [-(hAPP(c_Relation_ORange(_1772674, _1772674), c_Relation_OId(_1772674)) = c_Orderings_Otop__class_Otop(tc_fun(_1772674, tc_HOL_Obool)))], (16081 ^ _781013) ^ [_1078418] : [class_Rings_Olinordered__semidom(_1078418), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078418), c_Groups_Oone__class_Oone(_1078418)), c_Groups_Ozero__class_Ozero(_1078418)))], (18129 ^ _781013) ^ [_1118698, _1118700, _1118702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118698), _1118700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118698), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118702), _1118700))))], (29498 ^ _781013) ^ [_1331299, _1331301, _1331303] : [class_Orderings_Olinorder(_1331299), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331299), _1331301)), -(_1331301 = c_Orderings_Obot__class_Obot(tc_fun(_1331299, tc_HOL_Obool))), 29509 ^ _781013 : [(29510 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331299), _1331303), hAPP(c_Finite__Set_Ofold1(_1331299, c_Orderings_Oord__class_Omin(_1331299)), _1331301))), 29513 ^ _781013 : [(29514 ^ _781013) ^ [_1331592] : [hBOOL(hAPP(hAPP(c_member(_1331299), _1331592), _1331301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331299), _1331303), _1331592)))]]], (29520 ^ _781013) ^ [] : [29522 ^ _781013 : [(29525 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331299), _1331303), 29521 ^ [_1331299, _1331301, _1331303]))], (29523 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331299), 29521 ^ [_1331299, _1331301, _1331303]), _1331301)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331299), _1331303), hAPP(c_Finite__Set_Ofold1(_1331299, c_Orderings_Oord__class_Omin(_1331299)), _1331301))))]]], (18316 ^ _781013) ^ [_1122003, _1122005, _1122007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122003), _1122005)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122003), _1122007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122007), _1122005)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122007), _1122003))))], (49496 ^ _781013) ^ [_1787146, _1787148, _1787150] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1787146), _1787148)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1787146, tc_HOL_Obool)), _1787148), _1787150) = hAPP(hAPP(c_Finite__Set_Ofold(_1787146, tc_fun(_1787146, tc_HOL_Obool), c_Set_Oinsert(_1787146)), _1787150), _1787148))], (25533 ^ _781013) ^ [_1256592] : [c_Nat__Transfer_Onat__set(_1256592), -(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), _1256592)) = _1256592)], (47162 ^ _781013) ^ [_1730800, _1730802, _1730804] : [47164 ^ _781013 : [(47167 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730800, tc_HOL_Obool)), 47163 ^ [_1730800, _1730802, _1730804]), _1730804))], (47165 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1730800, tc_HOL_Obool)), 47163 ^ [_1730800, _1730802, _1730804]), _1730802)))]], -(_1730802 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1730800, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730800, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1730800, tc_HOL_Obool), _1730802)), _1730804)))], (31709 ^ _781013) ^ [_1380310, _1380312, _1380314, _1380316, _1380318] : [class_Complete__Lattice_Ocomplete__lattice(_1380310), class_Orderings_Olinorder(_1380310), 31716 ^ _781013 : [(31726 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380310), _1380312), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380314, _1380310), _1380316), _1380318)))), 31727 ^ _781013 : [(31728 ^ _781013) ^ [_1380658] : [hBOOL(hAPP(hAPP(c_member(_1380314), _1380658), _1380316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380310), _1380312), hAPP(_1380318, _1380658)))]]], (31717 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380310), _1380312), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380314, _1380310), _1380316), _1380318))), 31721 ^ _781013 : [(31724 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380310), _1380312), hAPP(_1380318, 31720 ^ [_1380310, _1380312, _1380314, _1380316, _1380318]))))], (31722 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1380314), 31720 ^ [_1380310, _1380312, _1380314, _1380316, _1380318]), _1380316)))]]]]], (29783 ^ _781013) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (48930 ^ _781013) ^ [_1772801, _1772803] : [-(c_Relation_Osingle__valued(_1772801, _1772801, c_Relation_OId__on(_1772801, _1772803)))], (12254 ^ _781013) ^ [_1002291, _1002293, _1002295] : [class_Lattices_Olattice(_1002291), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002291), _1002293)), -(_1002293 = c_Orderings_Obot__class_Obot(tc_fun(_1002291, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1002291, hAPP(hAPP(c_Set_Oinsert(_1002291), _1002295), _1002293)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1002291), _1002295), c_Big__Operators_Olattice__class_OSup__fin(_1002291, _1002293)))], (36510 ^ _781013) ^ [_1477495, _1477497, _1477499, _1477501, _1477503, _1477505] : [hBOOL(hAPP(hAPP(_1477495, _1477497), _1477499)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477501, tc_fun(_1477503, tc_HOL_Obool))), _1477495), _1477505)), -(hBOOL(hAPP(hAPP(_1477505, _1477497), _1477499)))], (12700 ^ _781013) ^ [_1010750, _1010752, _1010754] : [class_Rings_Oring(_1010750), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1010750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010750), _1010752), _1010754)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010750), _1010752), hAPP(c_Groups_Ouminus__class_Ouminus(_1010750), _1010754)))], (31516 ^ _781013) ^ [_1375040, _1375042] : [31518 ^ _781013 : [(31521 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1375042), 31517 ^ [_1375040, _1375042]))], (31519 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 31517 ^ [_1375040, _1375042]), _1375040)))]], -(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)), _1375042), _1375040))], (51398 ^ _781013) ^ [] : [-(class_HOL_Oequal(tc_Com_Ostate))], (13801 ^ _781013) ^ [_1034500, _1034502, _1034504, _1034506] : [class_Groups_Ocancel__semigroup__add(_1034500), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034500), _1034502), _1034504) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034500), _1034506), _1034504), -(_1034502 = _1034506)], (7777 ^ _781013) ^ [_911978, _911980, _911982] : [_911978 = c_Orderings_Obot__class_Obot(tc_fun(_911980, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_911980), _911982), _911978))], (35169 ^ _781013) ^ [_1446598, _1446600, _1446602] : [class_Rings_Olinordered__idom(_1446598), 35172 ^ _781013 : [(35181 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1446598), hAPP(hAPP(c_Power_Opower__class_Opower(_1446598), _1446600), 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(_1446598), _1446602), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1446598)), _1446600 = c_Groups_Ozero__class_Ozero(_1446598), _1446602 = c_Groups_Ozero__class_Ozero(_1446598)], (35173 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1446598), hAPP(hAPP(c_Power_Opower__class_Opower(_1446598), _1446600), 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(_1446598), _1446602), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1446598), 35176 ^ _781013 : [(35179 ^ _781013) ^ [] : [-(_1446602 = c_Groups_Ozero__class_Ozero(_1446598))], (35177 ^ _781013) ^ [] : [-(_1446600 = c_Groups_Ozero__class_Ozero(_1446598))]]]]], (23737 ^ _781013) ^ [_1224625] : [-(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)), _1224625)) = _1224625)], (16259 ^ _781013) ^ [_1081414, _1081416] : [class_Groups_Ogroup__add(_1081414), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1081414), c_Groups_Ozero__class_Ozero(_1081414)), _1081416) = hAPP(c_Groups_Ouminus__class_Ouminus(_1081414), _1081416))], (6536 ^ _781013) ^ [_887955, _887957] : [6537 ^ _781013 : [(6538 ^ _781013) ^ [_888003] : [_887955 = hAPP(c_Option_Ooption_OSome(_887957), _888003)]], _887955 = c_Option_Ooption_ONone(_887957)], (1084 ^ _781013) ^ [_797305, _797307] : [-(class_Rings_Oring__no__zero__divisors(_797305)), _797307 = _797305, class_Rings_Oring__no__zero__divisors(_797307)], (35719 ^ _781013) ^ [_1456599, _1456601] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1456599), _1456601) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1456599 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1456599 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (10137 ^ _781013) ^ [_960317, _960319, _960321, _960323] : [class_Lattices_Osemilattice__inf(_960317), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960317), _960319), _960321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960317), _960319), _960323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960317), _960319), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960317), _960321), _960323))))], (28382 ^ _781013) ^ [_1310515, _1310517, _1310519] : [class_Orderings_Olinorder(_1310515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310515), _1310517)), hBOOL(hAPP(hAPP(c_member(_1310515), _1310519), _1310517)), 28393 ^ _781013 : [(28400 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310515, tc_HOL_Obool)), _1310517), hAPP(hAPP(c_Set_Oinsert(_1310515), _1310519), c_Orderings_Obot__class_Obot(tc_fun(_1310515, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1310515, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1310515, _1310517) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310515), _1310519), c_Big__Operators_Olinorder__class_OMin(_1310515, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310515, tc_HOL_Obool)), _1310517), hAPP(hAPP(c_Set_Oinsert(_1310515), _1310519), c_Orderings_Obot__class_Obot(tc_fun(_1310515, tc_HOL_Obool)))))))], (28394 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310515, tc_HOL_Obool)), _1310517), hAPP(hAPP(c_Set_Oinsert(_1310515), _1310519), c_Orderings_Obot__class_Obot(tc_fun(_1310515, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1310515, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1310515, _1310517) = _1310519)]]], (46959 ^ _781013) ^ [_1725628, _1725630, _1725632, _1725634] : [c_FunDef_Oreduction__pair(_1725628, _1725630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1725628, _1725628), tc_HOL_Obool)), _1725632), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1725628, _1725628), tc_HOL_Obool), tc_fun(tc_prod(_1725628, _1725628), tc_HOL_Obool)), _1725630))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1725628, _1725628), tc_HOL_Obool)), _1725634), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1725628, _1725628), tc_HOL_Obool), tc_fun(tc_prod(_1725628, _1725628), tc_HOL_Obool)), _1725630))), c_Wellfounded_Owf(_1725628, _1725634), -(c_Wellfounded_Owf(_1725628, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1725628, _1725628), tc_HOL_Obool)), _1725632), _1725634)))], (33504 ^ _781013) ^ [_1416839, _1416841] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416839)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416839)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416841)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416839)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416841))))], (5346 ^ _781013) ^ [_862569, _862571] : [_862571 = _862569, -(c_List_Olist_OCons(_862571) = c_List_Olist_OCons(_862569))], (21107 ^ _781013) ^ [_1177089, _1177091, _1177093, _1177095, _1177097] : [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), _1177089), _1177091)), _1177093)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1177089), _1177095)), _1177097))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177093), _1177089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177097), _1177089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177091), _1177095)))], (32197 ^ _781013) ^ [_1392126, _1392128, _1392130] : [class_Orderings_Olinorder(_1392126), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392126), _1392128)), 32207 ^ _781013 : [(32210 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1392126), 32206 ^ [_1392126, _1392128, _1392130]), _1392130))], (32208 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1392126), 32206 ^ [_1392126, _1392128, _1392130]), _1392128)))]], hBOOL(hAPP(hAPP(c_member(_1392126), _1392130), _1392128)), -(c_Big__Operators_Olinorder__class_OMax(_1392126, _1392128) = _1392130)], (9495 ^ _781013) ^ [_949366, _949368, _949370] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949366, tc_HOL_Obool)), _949368), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_949366, tc_HOL_Obool)), _949370)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949366, tc_HOL_Obool)), _949368), _949370))], (40533 ^ _781013) ^ [_1574084, _1574086, _1574088, _1574090, _1574092, _1574094] : [-(hAPP(c_Set_Oimage(_1574084, tc_prod(_1574086, _1574088), hAPP(hAPP(c_COMBS(_1574084, _1574088, tc_prod(_1574086, _1574088)), hAPP(hAPP(c_COMBB(_1574086, tc_fun(_1574088, tc_prod(_1574086, _1574088)), _1574084), c_Product__Type_OPair(_1574086, _1574088)), _1574090)), _1574092)), _1574094) = hAPP(hAPP(c_Product__Type_OSigma(_1574086, _1574088), hAPP(c_Set_Oimage(_1574084, _1574086, _1574090), _1574094)), hAPP(hAPP(c_COMBB(tc_fun(_1574084, tc_HOL_Obool), tc_fun(_1574088, tc_HOL_Obool), _1574086), c_Set_Oimage(_1574084, _1574088, _1574092)), hAPP(hAPP(c_COMBC(_1574086, tc_fun(_1574084, tc_HOL_Obool), tc_fun(_1574084, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574084, tc_HOL_Obool), tc_fun(tc_fun(_1574084, tc_HOL_Obool), tc_fun(_1574084, tc_HOL_Obool)), _1574086), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1574084, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1574086, tc_HOL_Obool), tc_fun(_1574084, tc_HOL_Obool), _1574086), c_Set_Ovimage(_1574084, _1574086, _1574090)), hAPP(hAPP(c_COMBC(_1574086, tc_fun(_1574086, tc_HOL_Obool), tc_fun(_1574086, tc_HOL_Obool)), c_Set_Oinsert(_1574086)), c_Orderings_Obot__class_Obot(tc_fun(_1574086, tc_HOL_Obool)))))), _1574094))))], (40163 ^ _781013) ^ [_1564169, _1564171, _1564173, _1564175] : [_1564169 = _1564171, -(hAPP(c_List_OremoveAll(_1564173, _1564169), hAPP(hAPP(c_List_Olist_OCons(_1564173), _1564171), _1564175)) = hAPP(c_List_OremoveAll(_1564173, _1564169), _1564175))], (34897 ^ _781013) ^ [_1441695, _1441697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441695), _1441697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1441695)), c_Int_OBit0(_1441697))))], (48842 ^ _781013) ^ [_1770163, _1770165, _1770167] : [-(hAPP(c_Relation_ODomain(_1770163, _1770165), hAPP(c_Relation_Oconverse(_1770165, _1770163), _1770167)) = hAPP(c_Relation_ORange(_1770165, _1770163), _1770167))], (43545 ^ _781013) ^ [_1648820, _1648822, _1648824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1648820), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1648822))), c_List_Otranspose(_1648822, _1648824)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1648822)), c_List_Otranspose(_1648822, _1648824)), _1648820) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1648822), _1648822), hAPP(hAPP(c_COMBC(tc_List_Olist(_1648822), tc_Nat_Onat, _1648822), c_List_Onth(_1648822)), _1648820)), hAPP(c_List_Ofilter(tc_List_Olist(_1648822), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1648822)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1648820)), c_Nat_Osize__class_Osize(tc_List_Olist(_1648822)))), _1648824)))], (5374 ^ _781013) ^ [_862973, _862975, _862977, _862979] : [-(c_List_Oconcat(_862979, _862975) = c_List_Oconcat(_862977, _862973)), _862979 = _862977, _862975 = _862973], (28914 ^ _781013) ^ [_1320443, _1320445] : [class_Groups_Oordered__ab__group__add__abs(_1320443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320443), hAPP(c_Groups_Oabs__class_Oabs(_1320443), _1320445)), c_Groups_Ozero__class_Ozero(_1320443)))], (51196 ^ _781013) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (13443 ^ _781013) ^ [_1026579, _1026581] : [class_Groups_Omonoid__mult(_1026579), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026579), c_Groups_Oone__class_Oone(_1026579)), _1026581) = _1026581)], (23403 ^ _781013) ^ [_1218779, _1218781] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_1218779, _1218781)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1218779)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1218781))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6559 ^ _781013) ^ [_888311, _888313, _888315, _888317] : [-(hAPP(c_Option_Ooption_Ooption__case(_888311, _888313, _888315, _888317), c_Option_Ooption_ONone(_888313)) = _888315)], (20083 ^ _781013) ^ [_1156816, _1156818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156816), hAPP(c_Nat_OSuc, _1156818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156816), _1156818))), -(_1156816 = _1156818)], (558 ^ _781013) ^ [_789576, _789578] : [-(c_Nitpick_Ounknown(_789576)), _789578 = _789576, c_Nitpick_Ounknown(_789578)], (29347 ^ _781013) ^ [_1328542, _1328544, _1328546] : [hBOOL(hAPP(_1328542, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1328544, _1328546))), 29350 ^ _781013 : [(29357 ^ _781013) ^ [] : [-(_1328546 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29360 ^ _781013 : [(29361 ^ _781013) ^ [_1328790, _1328792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1328790), _1328546)), _1328544 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1328546), _1328792)), _1328790), -(hBOOL(hAPP(_1328542, _1328790)))]]], (29351 ^ _781013) ^ [] : [_1328546 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1328542, _1328544)))]]], (11674 ^ _781013) ^ [_991273, _991275, _991277, _991279, _991281] : [c_Fun_Oinj__on(_991273, _991275, _991277, c_Orderings_Otop__class_Otop(tc_fun(_991273, tc_HOL_Obool))), 11677 ^ _781013 : [(11684 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_991273), _991279), _991281)), -(hBOOL(hAPP(hAPP(c_member(_991275), hAPP(_991277, _991279)), hAPP(c_Set_Oimage(_991273, _991275, _991277), _991281))))], (11678 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_991275), hAPP(_991277, _991279)), hAPP(c_Set_Oimage(_991273, _991275, _991277), _991281))), -(hBOOL(hAPP(hAPP(c_member(_991273), _991279), _991281)))]]], (42154 ^ _781013) ^ [_1615415, _1615417, _1615419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615415)), _1615417)), _1615419)), -(hAPP(hAPP(c_List_Odrop(_1615415), _1615419), _1615417) = c_List_Olist_ONil(_1615415))], (30227 ^ _781013) ^ [_1345619, _1345621, _1345623, _1345625] : [class_Groups_Oordered__ab__group__add(_1345619), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1345619), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345619), _1345621), _1345623)), _1345625) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345619), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1345619), _1345621), _1345625)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1345619), _1345623), _1345625)))], (48227 ^ _781013) ^ [_1755262, _1755264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1755262)), hAPP(c_Code__Numeral_Oof__nat, _1755264))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1755262), _1755264)))], (39530 ^ _781013) ^ [_1545566, _1545568] : [39531 ^ _781013 : [(39532 ^ _781013) ^ [_1545612] : [hBOOL(hAPP(_1545566, _1545612))]], -(hBOOL(hAPP(_1545566, c_Hilbert__Choice_OEps(_1545568, _1545566))))], (14157 ^ _781013) ^ [_1041782, _1041784, _1041786, _1041788, _1041790, _1041792] : [class_Rings_Oring(_1041782), 14160 ^ _781013 : [(14167 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041782), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041782), _1041784), _1041790)), _1041786)), _1041788) = _1041792, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041782), _1041784), _1041786)), _1041788) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041782), _1041790), _1041786)), _1041792))], (14161 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041782), _1041784), _1041786)), _1041788) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041782), _1041790), _1041786)), _1041792), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041782), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041782), _1041784), _1041790)), _1041786)), _1041788) = _1041792)]]], (51076 ^ _781013) ^ [_1819379, _1819381] : [class_Orderings_Obot(_1819379), -(class_Orderings_Obot(tc_fun(_1819381, _1819379)))], (45905 ^ _781013) ^ [_1699496, _1699498, _1699500] : [class_Complete__Lattice_Ocomplete__lattice(_1699496), class_Orderings_Olinorder(_1699496), 45912 ^ _781013 : [(45922 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1699496), c_Complete__Lattice_OInf__class_OInf(_1699496, _1699498)), _1699500))), 45923 ^ _781013 : [(45924 ^ _781013) ^ [_1699802] : [hBOOL(hAPP(hAPP(c_member(_1699496), _1699802), _1699498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1699496), _1699802), _1699500))]]], (45913 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1699496), c_Complete__Lattice_OInf__class_OInf(_1699496, _1699498)), _1699500)), 45917 ^ _781013 : [(45920 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1699496), 45916 ^ [_1699496, _1699498, _1699500]), _1699500)))], (45918 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699496), 45916 ^ [_1699496, _1699498, _1699500]), _1699498)))]]]]], (23162 ^ _781013) ^ [_1214289, _1214291, _1214293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214289)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214289), _1214291)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214289), _1214293)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1214291), _1214293))], (3172 ^ _781013) ^ [_828680, _828682] : [_828682 = _828680, -(c_List_Otranspose__rel(_828682) = c_List_Otranspose__rel(_828680))], (10179 ^ _781013) ^ [_961086, _961088, _961090, _961092] : [class_Lattices_Osemilattice__inf(_961086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961086), _961088), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_961086), _961090), _961092))), 10186 ^ _781013 : [(10189 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961086), _961088), _961092)))], (10187 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961086), _961088), _961090)))]]], (25740 ^ _781013) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (44370 ^ _781013) ^ [_1665211, _1665213] : [44372 ^ _781013 : [(44375 ^ _781013) ^ [] : [44371 ^ [_1665211, _1665213] = c_List_Olist_ONil(_1665211)], (44373 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665211)), 44371 ^ [_1665211, _1665213]), hAPP(c_List_Oset(tc_List_Olist(_1665211)), _1665213))))]], -(c_List_Olist_ONil(_1665211) = c_List_Oconcat(_1665211, _1665213))], (3704 ^ _781013) ^ [_837002, _837004, _837006, _837008] : [-(c_Wellfounded_Oaccp(_837008, _837004) = c_Wellfounded_Oaccp(_837006, _837002)), _837008 = _837006, _837004 = _837002], (32670 ^ _781013) ^ [_1400874, _1400876, _1400878, _1400880] : [class_Fields_Ofield__inverse__zero(_1400874), class_Int_Onumber(_1400874), 32677 ^ _781013 : [(32678 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1400874), _1400876) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1400874), _1400878), _1400880), 32681 ^ _781013 : [(32688 ^ _781013) ^ [] : [_1400880 = c_Groups_Ozero__class_Ozero(_1400874), -(hAPP(c_Int_Onumber__class_Onumber__of(_1400874), _1400876) = c_Groups_Ozero__class_Ozero(_1400874))], (32682 ^ _781013) ^ [] : [-(_1400880 = c_Groups_Ozero__class_Ozero(_1400874)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400874), hAPP(c_Int_Onumber__class_Onumber__of(_1400874), _1400876)), _1400880) = _1400878)]]], (32694 ^ _781013) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1400874), _1400876) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1400874), _1400878), _1400880)), 32697 ^ _781013 : [(32700 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400874), hAPP(c_Int_Onumber__class_Onumber__of(_1400874), _1400876)), _1400880) = _1400878], (32698 ^ _781013) ^ [] : [_1400880 = c_Groups_Ozero__class_Ozero(_1400874)]], 32701 ^ _781013 : [(32704 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1400874), _1400876) = c_Groups_Ozero__class_Ozero(_1400874)], (32702 ^ _781013) ^ [] : [-(_1400880 = c_Groups_Ozero__class_Ozero(_1400874))]]]]], (27934 ^ _781013) ^ [_1302585, _1302587, _1302589, _1302591] : [class_Divides_Osemiring__div(_1302585), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1302585), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1302585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302585), _1302587), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1302585), _1302589), _1302587))), c_Divides_Odiv__class_Omod(_1302585, _1302589, _1302587))), _1302591) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1302585), _1302589), _1302591))], (3462 ^ _781013) ^ [_833169, _833171, _833173, _833175, _833177, _833179] : [-(c_List_Oinsert(_833179, _833175, _833171) = c_List_Oinsert(_833177, _833173, _833169)), _833179 = _833177, _833175 = _833173, _833171 = _833169], (34613 ^ _781013) ^ [_1436762, _1436764] : [c_Int_OBit1(_1436762) = c_Int_OBit0(_1436764)], (41376 ^ _781013) ^ [_1596308] : [class_Orderings_Olinorder(_1596308), -(c_List_Olinorder__class_Osorted__list__of__set(_1596308, c_Orderings_Obot__class_Obot(tc_fun(_1596308, tc_HOL_Obool))) = c_List_Olist_ONil(_1596308))], (5885 ^ _781013) ^ [_875708] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _875708)], (48716 ^ _781013) ^ [_1766746, _1766748, _1766750, _1766752] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766746, _1766746)), hAPP(hAPP(c_Product__Type_OPair(_1766746, _1766746), _1766748), _1766750)), c_Transitive__Closure_Ortrancl(_1766746, hAPP(c_Relation_Oconverse(_1766746, _1766746), _1766752)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1766746, _1766746)), hAPP(hAPP(c_Product__Type_OPair(_1766746, _1766746), _1766750), _1766748)), c_Transitive__Closure_Ortrancl(_1766746, _1766752))))], (48838 ^ _781013) ^ [_1770059, _1770061, _1770063, _1770065] : [-(hAPP(c_Relation_Oconverse(_1770059, _1770059), hAPP(hAPP(c_Relation_Oinv__image(_1770061, _1770059), _1770063), _1770065)) = hAPP(hAPP(c_Relation_Oinv__image(_1770061, _1770059), hAPP(c_Relation_Oconverse(_1770061, _1770061), _1770063)), _1770065))], (3922 ^ _781013) ^ [_840361, _840363] : [_840363 = _840361, -(c_List_Omonoid__add__class_Olistsum(_840363) = c_List_Omonoid__add__class_Olistsum(_840361))], (38174 ^ _781013) ^ [_1513393, _1513395, _1513397, _1513399] : [-(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), _1513393), _1513395)), 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), _1513397), _1513399)), 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), _1513393), _1513397)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1513395), _1513399))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (40151 ^ _781013) ^ [_1563989, _1563991, _1563993, _1563995] : [_1563989 = _1563991, -(c_List_Oremove1(_1563993, _1563989, hAPP(hAPP(c_List_Olist_OCons(_1563993), _1563991), _1563995)) = _1563995)], (44260 ^ _781013) ^ [_1662823, _1662825] : [-(hAPP(c_List_Orev(_1662823), c_List_Oconcat(_1662823, _1662825)) = c_List_Oconcat(_1662823, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1662823), tc_List_Olist(_1662823)), c_List_Orev(_1662823)), hAPP(c_List_Orev(tc_List_Olist(_1662823)), _1662825))))], (4786 ^ _781013) ^ [_853555, _853557, _853559, _853561, _853563, _853565, _853567, _853569] : [-(c_Option_Ooption_Ooption__case(_853569, _853565, _853561, _853557) = c_Option_Ooption_Ooption__case(_853567, _853563, _853559, _853555)), _853569 = _853567, _853565 = _853563, _853561 = _853559, _853557 = _853555], (31525 ^ _781013) ^ [_1375215, _1375217, _1375219, _1375221] : [hBOOL(hAPP(hAPP(c_member(_1375215), _1375217), _1375219)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1375215, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1375215, _1375215, _1375221), hAPP(hAPP(c_Set_Oinsert(_1375215), _1375217), c_Orderings_Obot__class_Obot(tc_fun(_1375215, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1375215), _1375219), _1375221))))], (46941 ^ _781013) ^ [_1725018, _1725020] : [c_FunDef_Oreduction__pair(_1725018, _1725020), 46944 ^ _781013 : [(46947 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1725018, _1725018), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1725018, _1725018, _1725018), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1725018, _1725018), tc_HOL_Obool), tc_fun(tc_prod(_1725018, _1725018), tc_HOL_Obool)), _1725020)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1725018, _1725018), tc_HOL_Obool), tc_fun(tc_prod(_1725018, _1725018), tc_HOL_Obool)), _1725020))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1725018, _1725018), tc_HOL_Obool), tc_fun(tc_prod(_1725018, _1725018), tc_HOL_Obool)), _1725020))))], (46945 ^ _781013) ^ [] : [-(c_Wellfounded_Owf(_1725018, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1725018, _1725018), tc_HOL_Obool), tc_fun(tc_prod(_1725018, _1725018), tc_HOL_Obool)), _1725020)))]]], (48207 ^ _781013) ^ [_1754956, _1754958] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1754956)), hAPP(c_Code__Numeral_Oof__nat, _1754958)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1754956), _1754958)))], (35561 ^ _781013) ^ [_1454175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1454175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1454175))))], (44910 ^ _781013) ^ [_1677707, _1677709, _1677711, _1677713, _1677715] : [c_List_OdropWhile(_1677707, _1677709, _1677711) = hAPP(hAPP(c_List_Olist_OCons(_1677707), _1677713), _1677715), 44913 ^ _781013 : [(44916 ^ _781013) ^ [] : [hBOOL(hAPP(_1677709, _1677713))], (44914 ^ _781013) ^ [] : [-(_1677711 = hAPP(hAPP(c_List_Oappend(_1677707), c_List_OtakeWhile(_1677707, _1677709, _1677711)), hAPP(hAPP(c_List_Olist_OCons(_1677707), _1677713), _1677715)))]]], (11854 ^ _781013) ^ [_994788, _994790, _994792, _994794, _994796] : [c_Fun_Oinj__on(_994788, _994790, _994792, _994794), -(c_Fun_Oinj__on(_994788, _994790, _994792, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_994788, tc_HOL_Obool)), _994794), _994796)))], (41384 ^ _781013) ^ [_1596432, _1596434, _1596436] : [-(hAPP(hAPP(c_Map_Omap__of(_1596432, _1596434), c_List_Olist_ONil(tc_prod(_1596432, _1596434))), _1596436) = c_Option_Ooption_ONone(_1596434))], (28770 ^ _781013) ^ [_1317859] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1317859) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4156 ^ _781013) ^ [_843886, _843888] : [_843888 = _843886, -(c_New__DSequence_Opos__not__seq(_843888) = c_New__DSequence_Opos__not__seq(_843886))], (4646 ^ _781013) ^ [_851347, _851349] : [_851349 = _851347, -(c_HOL_Obool_Obool__size(_851349) = c_HOL_Obool_Obool__size(_851347))], (19076 ^ _781013) ^ [_1137985, _1137987, _1137989, _1137991, _1137993] : [-(hBOOL(hAPP(hAPP(c_member(_1137985), _1137987), c_SetInterval_Oord_OgreaterThanLessThan(_1137985, _1137989, _1137991, _1137993)))), hBOOL(hAPP(hAPP(_1137989, _1137991), _1137987)), hBOOL(hAPP(hAPP(_1137989, _1137987), _1137993))], (5787 ^ _781013) ^ [_873314, _873316] : [-(c_Set_Othe__elem(_873314, _873316) = c_HOL_OThe(_873314, hAPP(hAPP(c_COMBB(tc_fun(_873314, tc_HOL_Obool), tc_HOL_Obool, _873314), hAPP(c_fequal, _873316)), hAPP(hAPP(c_COMBC(_873314, tc_fun(_873314, tc_HOL_Obool), tc_fun(_873314, tc_HOL_Obool)), c_Set_Oinsert(_873314)), c_Orderings_Obot__class_Obot(tc_fun(_873314, tc_HOL_Obool))))))], (42138 ^ _781013) ^ [_1615022, _1615024, _1615026] : [-(hAPP(hAPP(c_List_Odrop(_1615022), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1615022), _1615024), _1615026)) = _1615026)], (21125 ^ _781013) ^ [_1177438, _1177440, _1177442, _1177444, _1177446, _1177448] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1177438), _1177440)), _1177442) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1177444), _1177446)), _1177448), 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), _1177444), _1177446)), _1177448))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177448), _1177444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177444), _1177438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177440), _1177446)))], (42200 ^ _781013) ^ [_1616511, _1616513, _1616515, _1616517] : [-(_1616511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1616513), _1616511), hAPP(hAPP(c_List_Olist_OCons(_1616513), _1616515), _1616517)) = hAPP(hAPP(c_List_Odrop(_1616513), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1616511), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1616517))], (44928 ^ _781013) ^ [_1678102, _1678104, _1678106] : [-(c_List_OdropWhile(_1678102, _1678104, _1678106) = hAPP(hAPP(c_List_Odrop(_1678102), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678102)), c_List_OtakeWhile(_1678102, _1678104, _1678106))), _1678106))], (42098 ^ _781013) ^ [_1614081, _1614083, _1614085] : [hBOOL(hAPP(c_List_Odistinct(_1614081), _1614083)), -(hBOOL(hAPP(c_List_Odistinct(_1614081), hAPP(hAPP(c_List_Odrop(_1614081), _1614085), _1614083))))], (19318 ^ _781013) ^ [_1142890, _1142892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1142890)), 19321 ^ _781013 : [(19330 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142890), _1142892) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1142890 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1142892 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (19322 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142890), _1142892) = c_Groups_Oone__class_Oone(tc_Int_Oint), 19325 ^ _781013 : [(19328 ^ _781013) ^ [] : [-(_1142892 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (19326 ^ _781013) ^ [] : [-(_1142890 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (35359 ^ _781013) ^ [_1450186] : [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, _1450186, 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, _1450186, 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))], (47793 ^ _781013) ^ [_1746323, _1746325, _1746327] : [c_Wellfounded_Owf(_1746323, _1746325), hBOOL(hAPP(hAPP(c_member(tc_prod(_1746323, _1746323)), hAPP(hAPP(c_Product__Type_OPair(_1746323, _1746323), hAPP(_1746327, hAPP(c_Nat_OSuc, 47796 ^ [_1746323, _1746325, _1746327]))), hAPP(_1746327, 47796 ^ [_1746323, _1746325, _1746327]))), _1746325))], (34685 ^ _781013) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (27132 ^ _781013) ^ [_1286193, _1286195, _1286197] : [class_Orderings_Oord(_1286193), 27135 ^ _781013 : [(27142 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286193), _1286195), _1286197)), -(hBOOL(hAPP(hAPP(c_member(_1286193), _1286195), hAPP(c_SetInterval_Oord__class_OatMost(_1286193), _1286197))))], (27136 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1286193), _1286195), hAPP(c_SetInterval_Oord__class_OatMost(_1286193), _1286197))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286193), _1286195), _1286197)))]]], (45769 ^ _781013) ^ [_1696127, _1696129] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1696127, tc_HOL_Obool)), _1696129)), 45775 ^ _781013 : [(45778 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1696127), 45774 ^ [_1696127, _1696129]))], (45776 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1696127, tc_HOL_Obool)), 45774 ^ [_1696127, _1696129]), _1696129)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1696127), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1696127, tc_HOL_Obool), _1696129))))], (45934 ^ _781013) ^ [_1699998, _1700000, _1700002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1699998, tc_HOL_Obool), tc_HOL_Obool)), _1700000), _1700002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1699998, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1699998, tc_HOL_Obool), _1700002)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1699998, tc_HOL_Obool), _1700000))))], (26689 ^ _781013) ^ [] : [-(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)))], (26715 ^ _781013) ^ [_1278181, _1278183] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1278181, _1278183) = 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), _1278181), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1278183))))], (40597 ^ _781013) ^ [_1575756, _1575758, _1575760] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1575756, _1575758), _1575760), hAPP(c_COMBK(tc_fun(_1575758, tc_HOL_Obool), _1575756), c_Orderings_Obot__class_Obot(tc_fun(_1575758, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575756, _1575758), tc_HOL_Obool)))], (5623 ^ _781013) ^ [_869666, _869668, _869670] : [hAPP(hAPP(c_Set_Oinsert(_869666), _869668), _869670) = c_Orderings_Obot__class_Obot(tc_fun(_869666, tc_HOL_Obool))], (41448 ^ _781013) ^ [_1597895, _1597897, _1597899] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1597895))), -(c_List_Osublist(_1597897, hAPP(hAPP(c_List_Olist_OCons(_1597897), _1597899), c_List_Olist_ONil(_1597897)), _1597895) = c_List_Olist_ONil(_1597897))], (13325 ^ _781013) ^ [_1023960, _1023962, _1023964] : [class_Lattices_Oab__semigroup__idem__mult(_1023960), hAPP(_1023962, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023960), 13330 ^ [_1023960, _1023962, _1023964]), 13331 ^ [_1023960, _1023962, _1023964])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023960), hAPP(_1023962, 13330 ^ [_1023960, _1023962, _1023964])), hAPP(_1023962, 13331 ^ [_1023960, _1023962, _1023964])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023960), _1023964)), -(_1023964 = c_Orderings_Obot__class_Obot(tc_fun(_1023960, tc_HOL_Obool))), -(hAPP(_1023962, hAPP(c_Finite__Set_Ofold1(_1023960, c_Groups_Otimes__class_Otimes(_1023960)), _1023964)) = hAPP(c_Finite__Set_Ofold1(_1023960, c_Groups_Otimes__class_Otimes(_1023960)), hAPP(c_Set_Oimage(_1023960, _1023960, _1023962), _1023964)))], (4256 ^ _781013) ^ [_845392, _845394, _845396, _845398] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_845398, _845394) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_845396, _845392)), _845398 = _845396, _845394 = _845392], (48153 ^ _781013) ^ [_1753768, _1753770, _1753772] : [-(c_Random_Oselect__weight(_1753768, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1753768)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1753768), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1753770)), _1753772)) = c_Random_Oselect__weight(_1753768, _1753772))], (41286 ^ _781013) ^ [_1594800, _1594802] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594800)), _1594802) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1594802 = c_List_Olist_ONil(_1594800))], (2606 ^ _781013) ^ [_819687, _819689, _819691, _819693] : [-(c_Nitpick_Onat__gcd(_819693, _819689) = c_Nitpick_Onat__gcd(_819691, _819687)), _819693 = _819691, _819689 = _819687], (12968 ^ _781013) ^ [_1016674, _1016676, _1016678, _1016680, _1016682] : [-(hAPP(c_Set_Ovimage(_1016674, _1016676, _1016678), hAPP(hAPP(c_Set_Oinsert(_1016676), _1016680), _1016682)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016674, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1016674, _1016676, _1016678), hAPP(hAPP(c_Set_Oinsert(_1016676), _1016680), c_Orderings_Obot__class_Obot(tc_fun(_1016676, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1016674, _1016676, _1016678), _1016682)))], (14409 ^ _781013) ^ [_1047986, _1047988, _1047990, _1047992, _1047994] : [class_Groups_Oab__group__add(_1047986), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047988), _1047990)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047988), _1047992)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047988, _1047986), _1047994), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1047988, tc_HOL_Obool)), _1047990), _1047992)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1047986), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047986), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047988, _1047986), _1047994), _1047990)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047988, _1047986), _1047994), _1047992))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047988, _1047986), _1047994), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1047988, tc_HOL_Obool)), _1047990), _1047992))))], (33670 ^ _781013) ^ [_1419313, _1419315] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1419313), _1419315), hAPP(c_Int_Onumber__class_Onumber__of(_1419313), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1419313)), class_Fields_Ofield__inverse__zero(_1419313), class_Int_Onumber__ring(_1419313)], (6102 ^ _781013) ^ [_879699, _879701, _879703] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _879699))), _879701), _879703)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _879699)), _879701), _879703)))], (27589 ^ _781013) ^ [_1295952, _1295954] : [class_Divides_Osemiring__div(_1295952), -(c_Divides_Odiv__class_Omod(_1295952, c_Groups_Ozero__class_Ozero(_1295952), _1295954) = c_Groups_Ozero__class_Ozero(_1295952))], (29107 ^ _781013) ^ [_1323972, _1323974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1323972), _1323974)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1323972, _1323974) = _1323972)], (48129 ^ _781013) ^ [_1753406, _1753408] : [-(_1753406 = _1753408), -(c_Random_Oinc__shift(_1753406, _1753408) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1753408), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (28712 ^ _781013) ^ [_1316768, _1316770, _1316772, _1316774] : [class_Orderings_Olinorder(_1316768), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316768), _1316770), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316768), _1316772), _1316774)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316768), _1316772), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316768), _1316770), _1316774)))], (51532 ^ _781013) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (6026 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (31974 ^ _781013) ^ [_1387434, _1387436, _1387438, _1387440, _1387442] : [_1387434 = c_Orderings_Obot__class_Obot(tc_fun(_1387436, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387436, tc_fun(_1387438, tc_HOL_Obool)), _1387434), hAPP(hAPP(c_COMBB(tc_fun(_1387438, tc_HOL_Obool), tc_fun(_1387438, tc_HOL_Obool), _1387436), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387438, tc_HOL_Obool)), _1387440)), _1387442)) = c_Orderings_Obot__class_Obot(tc_fun(_1387438, tc_HOL_Obool)))], (3370 ^ _781013) ^ [_831813, _831815, _831817, _831819, _831821, _831823] : [-(c_Enum_On__lists(_831823, _831819, _831815) = c_Enum_On__lists(_831821, _831817, _831813)), _831823 = _831821, _831819 = _831817, _831815 = _831813], (38226 ^ _781013) ^ [_1514923, _1514925, _1514927, _1514929, _1514931] : [hAPP(hAPP(c_List_Omap(_1514923, _1514925), _1514927), _1514929) = hAPP(hAPP(c_List_Omap(_1514923, _1514925), _1514927), _1514931), c_Fun_Oinj__on(_1514923, _1514925, _1514927, c_Orderings_Otop__class_Otop(tc_fun(_1514923, tc_HOL_Obool))), -(_1514929 = _1514931)], (8551 ^ _781013) ^ [_929114, _929116, _929118, _929120, _929122, _929124, _929126, _929128] : [c_Finite__Set_Ofolding(_929114, _929116, _929118, _929120), hBOOL(hAPP(c_Finite__Set_Ofinite(_929114), _929122)), -(hAPP(c_Fun_Ocomp(_929116, _929116, _929124, hAPP(_929118, _929126)), hAPP(c_Fun_Ocomp(_929116, _929116, _929124, hAPP(_929120, _929122)), _929128)) = hAPP(c_Fun_Ocomp(_929116, _929116, _929124, hAPP(_929120, _929122)), hAPP(c_Fun_Ocomp(_929116, _929116, _929124, hAPP(_929118, _929126)), _929128)))], (30297 ^ _781013) ^ [_1347072] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1347072), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1347072)], (2998 ^ _781013) ^ [_825879, _825881, _825883, _825885, _825887, _825889] : [-(c_List_Opartition(_825889, _825885, _825881) = c_List_Opartition(_825887, _825883, _825879)), _825889 = _825887, _825885 = _825883, _825881 = _825879], (17777 ^ _781013) ^ [_1112751, _1112753, _1112755] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112751), _1112753) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112755), _1112753), -(_1112751 = _1112755)], (33626 ^ _781013) ^ [_1418705] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1418705), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1418705)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1418705)))], (33270 ^ _781013) ^ [_1412583, _1412585, _1412587, _1412589, _1412591, _1412593] : [c_Equiv__Relations_Oequiv(_1412583, _1412585, _1412587), c_Equiv__Relations_Ocongruent(_1412583, tc_fun(_1412589, tc_HOL_Obool), _1412587, _1412591), hBOOL(hAPP(hAPP(c_member(_1412583), _1412593), _1412585)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412583, tc_fun(_1412589, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1412583, _1412583, _1412587), hAPP(hAPP(c_Set_Oinsert(_1412583), _1412593), c_Orderings_Obot__class_Obot(tc_fun(_1412583, tc_HOL_Obool))))), _1412591) = hAPP(_1412591, _1412593))], (40260 ^ _781013) ^ [_1566256, _1566258, _1566260] : [c_Hoare__Mirabelle_Ohoare__valids(_1566256, _1566258, _1566260), 40263 ^ _781013 : [(40264 ^ _781013) ^ [_1566365] : [40266 ^ _781013 : [(40269 ^ _781013) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1566256, _1566365, 40265 ^ [_1566256, _1566258, _1566260, _1566365])], (40267 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1566256)), 40265 ^ [_1566256, _1566258, _1566260, _1566365]), _1566258)))]], 40270 ^ _781013 : [(40271 ^ _781013) ^ [_1566537] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1566256)), _1566537), _1566260)), -(c_Hoare__Mirabelle_Otriple__valid(_1566256, _1566365, _1566537))]]]]], (35761 ^ _781013) ^ [_1457159] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1457159)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1457159)))], (44402 ^ _781013) ^ [_1665953, _1665955, _1665957, _1665959] : [hAPP(c_List_Orev(_1665953), _1665955) = hAPP(hAPP(c_List_Olist_OCons(_1665953), _1665957), _1665959), -(_1665955 = hAPP(hAPP(c_List_Oappend(_1665953), hAPP(c_List_Orev(_1665953), _1665959)), hAPP(hAPP(c_List_Olist_OCons(_1665953), _1665957), c_List_Olist_ONil(_1665953))))], (6470 ^ _781013) ^ [_886849, _886851, _886853, _886855] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_886849, _886851)), _886853), _886855)), 6474 ^ _781013 : [(6477 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886851), 6473 ^ [_886849, _886851, _886853, _886855]), _886855)))], (6475 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886849), _886853), 6473 ^ [_886849, _886851, _886853, _886855])))]]], (19378 ^ _781013) ^ [_1143789, _1143791, _1143793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1143789)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1143789), _1143791)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1143789), _1143793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143791), _1143793)))], (42041 ^ _781013) ^ [_1612586, _1612588, _1612590, _1612592] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612586), tc_List_Olist(_1612586))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612586), tc_List_Olist(_1612586)), _1612588), _1612590)), c_List_Olistrel1(_1612586, _1612592))), 42046 ^ _781013 : [(42053 ^ _781013) ^ [] : [-(_1612590 = hAPP(hAPP(c_List_Oappend(_1612586), 42048 ^ [_1612586, _1612588, _1612590, _1612592]), hAPP(hAPP(c_List_Olist_OCons(_1612586), 42045 ^ [_1612586, _1612588, _1612590, _1612592]), 42049 ^ [_1612586, _1612588, _1612590, _1612592])))], (42051 ^ _781013) ^ [] : [-(_1612588 = hAPP(hAPP(c_List_Oappend(_1612586), 42048 ^ [_1612586, _1612588, _1612590, _1612592]), hAPP(hAPP(c_List_Olist_OCons(_1612586), 42044 ^ [_1612586, _1612588, _1612590, _1612592]), 42049 ^ [_1612586, _1612588, _1612590, _1612592])))], (42047 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612586, _1612586)), hAPP(hAPP(c_Product__Type_OPair(_1612586, _1612586), 42044 ^ [_1612586, _1612588, _1612590, _1612592]), 42045 ^ [_1612586, _1612588, _1612590, _1612592])), _1612592)))]]], (11730 ^ _781013) ^ [_992410, _992412] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_992410), c_Orderings_Otop__class_Otop(tc_fun(_992410, tc_HOL_Obool)))), c_Fun_Oinj__on(_992410, _992410, _992412, c_Orderings_Otop__class_Otop(tc_fun(_992410, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_992410, _992410, _992412), c_Orderings_Otop__class_Otop(tc_fun(_992410, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_992410, tc_HOL_Obool)))], (38592 ^ _781013) ^ [_1523214, _1523216, _1523218, _1523220] : [-(_1523214 = _1523216), 38595 ^ _781013 : [(38602 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1523218), _1523214), hAPP(c_List_Oset(_1523218), _1523220))), -(hBOOL(hAPP(hAPP(c_member(_1523218), _1523214), hAPP(c_List_Oset(_1523218), c_List_Oremove1(_1523218, _1523216, _1523220)))))], (38596 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1523218), _1523214), hAPP(c_List_Oset(_1523218), c_List_Oremove1(_1523218, _1523216, _1523220)))), -(hBOOL(hAPP(hAPP(c_member(_1523218), _1523214), hAPP(c_List_Oset(_1523218), _1523220))))]]], (3266 ^ _781013) ^ [_830203, _830205, _830207, _830209, _830211, _830213] : [-(c_List_Oremove1(_830213, _830209, _830205) = c_List_Oremove1(_830211, _830207, _830203)), _830213 = _830211, _830209 = _830207, _830205 = _830203], (30467 ^ _781013) ^ [_1350528, _1350530, _1350532] : [class_Orderings_Olinorder(_1350528), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350528), _1350530)), -(_1350530 = c_Orderings_Obot__class_Obot(tc_fun(_1350528, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1350528, hAPP(hAPP(c_Set_Oinsert(_1350528), _1350532), _1350530)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350528), _1350532), c_Big__Operators_Olinorder__class_OMax(_1350528, _1350530)))], (43621 ^ _781013) ^ [_1650497, _1650499] : [class_Orderings_Olinorder(_1650497), -(_1650499 = c_List_Olist_ONil(_1650497)), c_List_Olinorder__class_Osorted(_1650497, _1650499), -(c_List_Olinorder__class_Osorted(_1650497, c_List_Obutlast(_1650497, _1650499)))], (18682 ^ _781013) ^ [_1129167, _1129169, _1129171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129167), _1129169)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1129171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1129169), _1129167)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1129171), _1129169)), _1129167))], (20045 ^ _781013) ^ [_1156189, _1156191] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156189), _1156191))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156189), hAPP(c_Nat_OSuc, _1156191))), -(_1156191 = _1156189)], (9305 ^ _781013) ^ [_945859, _945861, _945863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_945859), _945861)), hBOOL(hAPP(_945863, c_Orderings_Obot__class_Obot(tc_fun(_945859, tc_HOL_Obool)))), 9316 ^ _781013 : [(9319 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_945859), 9314 ^ [_945859, _945861, _945863]), 9315 ^ [_945859, _945861, _945863]))], (9321 ^ _781013) ^ [] : [-(hBOOL(hAPP(_945863, 9315 ^ [_945859, _945861, _945863])))], (9323 ^ _781013) ^ [] : [hBOOL(hAPP(_945863, hAPP(hAPP(c_Set_Oinsert(_945859), 9314 ^ [_945859, _945861, _945863]), 9315 ^ [_945859, _945861, _945863])))], (9317 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_945859), 9315 ^ [_945859, _945861, _945863])))]], -(hBOOL(hAPP(_945863, _945861)))], (6214 ^ _781013) ^ [_881929, _881931, _881933, _881935, _881937] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_881929, _881931, _881933)), _881935), _881937)), 6219 ^ _781013 : [(6222 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_881931), _881935), _881937)))], (6220 ^ _781013) ^ [] : [-(hBOOL(hAPP(_881929, _881935)))]], 6223 ^ _781013 : [(6226 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_881933), _881935), _881937)))], (6224 ^ _781013) ^ [] : [hBOOL(hAPP(_881929, _881935))]]], (46611 ^ _781013) ^ [_1716561, _1716563, _1716565, _1716567] : [hAPP(hAPP(c_Relation_Orel__comp(_1716561, _1716561, _1716561), _1716563), _1716565) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1716561, _1716561), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1716561, _1716561, _1716561), _1716563), _1716567) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1716561, _1716561), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1716561, _1716561, _1716561), _1716563), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1716561, _1716561), tc_HOL_Obool)), _1716565), _1716567)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1716561, _1716561), tc_HOL_Obool)))], (35235 ^ _781013) ^ [_1447583, _1447585, _1447587] : [class_Rings_Ocomm__semiring__1(_1447583), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1447583), _1447585), 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)))), _1447587)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1447583), hAPP(hAPP(c_Power_Opower__class_Opower(_1447583), _1447585), _1447587)), hAPP(hAPP(c_Power_Opower__class_Opower(_1447583), _1447585), _1447587)))], (25118 ^ _781013) ^ [_1249127, _1249129, _1249131, _1249133] : [class_Fields_Olinordered__field(_1249127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249127), c_Groups_Ozero__class_Ozero(_1249127)), _1249129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249127), _1249131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249127), _1249133), _1249129))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249127), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249127), _1249131), _1249129)), _1249133)))], (27194 ^ _781013) ^ [_1287347, _1287349, _1287351] : [class_Orderings_Oorder(_1287347), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287347, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1287347), _1287349)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1287347, _1287349, _1287351)) = c_Orderings_Obot__class_Obot(tc_fun(_1287347, tc_HOL_Obool)))], (32049 ^ _781013) ^ [_1389587, _1389589] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1389587)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1389589)), hAPP(c_Int_Onat, _1389587)) = hAPP(c_Int_Onat, _1389589))], (42424 ^ _781013) ^ [_1621281, _1621283, _1621285] : [-(hAPP(hAPP(c_List_Odrop(_1621281), hAPP(c_Nat_OSuc, _1621283)), _1621285) = hAPP(hAPP(c_List_Odrop(_1621281), _1621283), hAPP(c_List_Otl(_1621281), _1621285)))], (27972 ^ _781013) ^ [_1303381, _1303383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303381)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303381), _1303383)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1303381, _1303383) = _1303381)], (41901 ^ _781013) ^ [_1608679, _1608681, _1608683, _1608685] : [41902 ^ _781013 : [(41905 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1608679), _1608681), hAPP(c_List_Oset(_1608679), c_List_Obutlast(_1608679, _1608685))))], (41903 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1608679), _1608681), hAPP(c_List_Oset(_1608679), c_List_Obutlast(_1608679, _1608683))))]], -(hBOOL(hAPP(hAPP(c_member(_1608679), _1608681), hAPP(c_List_Oset(_1608679), c_List_Obutlast(_1608679, hAPP(hAPP(c_List_Oappend(_1608679), _1608683), _1608685))))))], (33740 ^ _781013) ^ [_1420443, _1420445] : [33741 ^ _781013 : [(33744 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420443), c_Int_OPls))], (33742 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420443), _1420445))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420443)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420445))))], (2966 ^ _781013) ^ [_825411, _825413, _825415, _825417] : [-(c_List_Olexord(_825417, _825413) = c_List_Olexord(_825415, _825411)), _825417 = _825415, _825413 = _825411], (31621 ^ _781013) ^ [_1377665, _1377667, _1377669, _1377671] : [-(hAPP(c_Set_Oimage(_1377665, _1377667, _1377669), _1377671) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377665, tc_fun(_1377667, tc_HOL_Obool)), _1377671), hAPP(hAPP(c_COMBC(_1377665, tc_fun(_1377667, tc_HOL_Obool), tc_fun(_1377667, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1377667, tc_fun(tc_fun(_1377667, tc_HOL_Obool), tc_fun(_1377667, tc_HOL_Obool)), _1377665), c_Set_Oinsert(_1377667)), _1377669)), c_Orderings_Obot__class_Obot(tc_fun(_1377667, tc_HOL_Obool)))))], (44687 ^ _781013) ^ [_1673348, _1673350, _1673352, _1673354, _1673356] : [-(c_Map_Omap__upds(_1673348, _1673350, _1673352, _1673354, _1673356) = c_Map_Omap__add(_1673348, _1673350, _1673352, hAPP(c_Map_Omap__of(_1673348, _1673350), hAPP(c_List_Orev(tc_prod(_1673348, _1673350)), hAPP(hAPP(c_List_Ozip(_1673348, _1673350), _1673354), _1673356)))))], (37712 ^ _781013) ^ [_1501454, _1501456] : [_1501454 = _1501456, -(c_Code__Numeral_OSuc__code__numeral(_1501454) = c_Code__Numeral_OSuc__code__numeral(_1501456))], (31285 ^ _781013) ^ [_1367265, _1367267, _1367269, _1367271] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1367265, _1367267)), _1367269), _1367271), _1367269)), hBOOL(hAPP(_1367265, _1367269)), 31293 ^ _781013 : [(31296 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1367265, _1367267)), 31292 ^ [_1367265, _1367267, _1367269, _1367271]), _1367271), _1367269)))], (31294 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1367267), _1367269), _1367271), 31292 ^ [_1367265, _1367267, _1367269, _1367271])))]]], (32106 ^ _781013) ^ [_1390727] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1390727))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390727)))], (38023 ^ _781013) ^ [_1509389, _1509391, _1509393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509389, _1509389), tc_HOL_Obool)), _1509391), _1509393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509389, tc_HOL_Obool)), hAPP(c_Relation_OField(_1509389), _1509391)), hAPP(c_Relation_OField(_1509389), _1509393))))], (47211 ^ _781013) ^ [_1731873, _1731875, _1731877] : [-(hAPP(c_Set_Oimage(tc_prod(_1731873, _1731875), _1731873, c_Product__Type_Ofst(_1731873, _1731875)), _1731877) = hAPP(c_Relation_ODomain(_1731873, _1731875), _1731877))], (1334 ^ _781013) ^ [_800430, _800432] : [-(class_Lattices_Odistrib__lattice(_800430)), _800432 = _800430, class_Lattices_Odistrib__lattice(_800432)], (34547 ^ _781013) ^ [_1435565, _1435567] : [class_Int_Onumber__ring(_1435565), 34550 ^ _781013 : [(34557 ^ _781013) ^ [] : [c_Int_Oiszero(_1435565, hAPP(c_Int_Onumber__class_Onumber__of(_1435565), 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), _1435567)))), -(c_Groups_Oone__class_Oone(_1435565) = hAPP(c_Int_Onumber__class_Onumber__of(_1435565), _1435567))], (34551 ^ _781013) ^ [] : [c_Groups_Oone__class_Oone(_1435565) = hAPP(c_Int_Onumber__class_Onumber__of(_1435565), _1435567), -(c_Int_Oiszero(_1435565, hAPP(c_Int_Onumber__class_Onumber__of(_1435565), 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), _1435567)))))]]], (33656 ^ _781013) ^ [_1419124] : [-(c_Int_Opred(_1419124) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1419124), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (4546 ^ _781013) ^ [_849863, _849865] : [_849865 = _849863, -(c_Nitpick_Ofrac(_849865) = c_Nitpick_Ofrac(_849863))], (31267 ^ _781013) ^ [_1366866, _1366868, _1366870] : [31268 ^ _781013 : [(31269 ^ _781013) ^ [_1366925] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1366866), _1366868), _1366925), _1366870))]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1366866), _1366868), _1366870)))], (41486 ^ _781013) ^ [_1599006, _1599008] : [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), _1599006), _1599008))), 41489 ^ _781013 : [(41496 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1599006), _1599008))), -(c_List_Oupto(_1599006, _1599008) = c_List_Olist_ONil(tc_Int_Oint))], (41490 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1599006), _1599008)), -(c_List_Oupto(_1599006, _1599008) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1599006), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1599006), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1599008)))]]], (48968 ^ _781013) ^ [_1773500, _1773502] : [-(c_Transitive__Closure_Ortrancl(_1773500, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1773500, _1773500), tc_HOL_Obool)), _1773502), c_Relation_OId(_1773500))) = c_Transitive__Closure_Ortrancl(_1773500, _1773502))], (5226 ^ _781013) ^ [_860725, _860727] : [_860727 = _860725, -(c_Orderings_Oord__class_Oless(_860727) = c_Orderings_Oord__class_Oless(_860725))], (43067 ^ _781013) ^ [_1637240, _1637242, _1637244, _1637246, _1637248, _1637250] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1637240, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1637242, _1637240, _1637244), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637246, tc_fun(_1637242, tc_HOL_Obool)), _1637248), _1637250))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637246, tc_fun(_1637240, tc_HOL_Obool)), _1637248), hAPP(hAPP(c_COMBB(tc_fun(_1637242, tc_HOL_Obool), tc_fun(_1637240, tc_HOL_Obool), _1637246), c_Relation_OImage(_1637242, _1637240, _1637244)), _1637250)))))], (17789 ^ _781013) ^ [_1112973, _1112975, _1112977] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112973), _1112975) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112973), _1112977), -(_1112975 = _1112977)], (28642 ^ _781013) ^ [_1315322, _1315324, _1315326] : [class_Groups_Oordered__ab__group__add__abs(_1315322), -(hAPP(c_Groups_Oabs__class_Oabs(_1315322), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1315322), _1315324), _1315326)) = hAPP(c_Groups_Oabs__class_Oabs(_1315322), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1315322), _1315326), _1315324)))], (16944 ^ _781013) ^ [_1095447, _1095449, _1095451, _1095453, _1095455] : [class_Groups_Ocomm__monoid__mult(_1095447), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095449), _1095451)), -(hBOOL(hAPP(hAPP(c_member(_1095449), _1095453), _1095451))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1095449, _1095447), _1095455), hAPP(hAPP(c_Set_Oinsert(_1095449), _1095453), _1095451)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095447), hAPP(_1095455, _1095453)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1095449, _1095447), _1095455), _1095451)))], (42334 ^ _781013) ^ [_1619789, _1619791, _1619793] : [-(_1619789 = c_List_Olist_ONil(_1619791)), -(hAPP(c_List_Ohd(_1619791), hAPP(hAPP(c_List_Oappend(_1619791), _1619789), _1619793)) = hAPP(c_List_Ohd(_1619791), _1619789))], (38495 ^ _781013) ^ [_1521132, _1521134, _1521136, _1521138] : [-(hBOOL(hAPP(c_List_Odistinct(_1521132), hAPP(hAPP(c_List_Omap(_1521134, _1521132), _1521136), _1521138)))), hBOOL(hAPP(c_List_Odistinct(_1521134), _1521138)), c_Fun_Oinj__on(_1521134, _1521132, _1521136, hAPP(c_List_Oset(_1521134), _1521138))], (27106 ^ _781013) ^ [_1285789] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1285789))))], (48009 ^ _781013) ^ [_1750791, _1750793] : [-(hAPP(c_Relation_ODomain(_1750791, _1750791), c_Transitive__Closure_Otrancl(_1750791, _1750793)) = hAPP(c_Relation_ODomain(_1750791, _1750791), _1750793))], (35491 ^ _781013) ^ [_1453159, _1453161] : [class_Int_Onumber__ring(_1453159), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453159), hAPP(c_Int_Onumber__class_Onumber__of(_1453159), 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)))), _1453161))) = hAPP(c_Int_Onumber__class_Onumber__of(_1453159), c_Int_OMin))], (23643 ^ _781013) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27749 ^ _781013) ^ [_1299158, _1299160] : [-(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, _1299158, _1299160)), _1299160) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1299158), _1299160))], (15637 ^ _781013) ^ [_1070309, _1070311, _1070313] : [class_Rings_Oordered__cancel__semiring(_1070309), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070309), _1070311), _1070313)), c_Groups_Ozero__class_Ozero(_1070309)))), 15642 ^ _781013 : [(15649 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070309), _1070311), c_Groups_Ozero__class_Ozero(_1070309))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070309), c_Groups_Ozero__class_Ozero(_1070309)), _1070313))], (15643 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070309), c_Groups_Ozero__class_Ozero(_1070309)), _1070311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070309), _1070313), c_Groups_Ozero__class_Ozero(_1070309)))]]], (24460 ^ _781013) ^ [_1237249, _1237251, _1237253, _1237255] : [class_Fields_Olinordered__field(_1237249), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237249), c_Groups_Ozero__class_Ozero(_1237249)), _1237251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237249), _1237253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237249), _1237255), _1237251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237249), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237249), _1237253), _1237251)), _1237255)))], (26451 ^ _781013) ^ [_1273008, _1273010] : [class_Groups_Oordered__ab__group__add(_1273008), -(hAPP(c_Set_Oimage(_1273008, _1273008, c_Groups_Ouminus__class_Ouminus(_1273008)), hAPP(c_SetInterval_Oord__class_OlessThan(_1273008), _1273010)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1273008), hAPP(c_Groups_Ouminus__class_Ouminus(_1273008), _1273010)))], (6555 ^ _781013) ^ [_888235, _888237] : [hAPP(c_Option_Ooption_OSome(_888235), _888237) = c_Option_Ooption_ONone(_888235)], (7953 ^ _781013) ^ [_915438, _915440, _915442, _915444, _915446] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_915438), tc_Option_Ooption(_915440), tc_Option_Ooption(_915442), hAPP(c_Option_Omap(_915438, _915440), _915444)), hAPP(c_Option_Omap(_915442, _915438), _915446)) = hAPP(c_Option_Omap(_915442, _915440), hAPP(c_Fun_Ocomp(_915438, _915440, _915442, _915444), _915446)))], (22800 ^ _781013) ^ [_1207587, _1207589, _1207591] : [class_Rings_Osemiring__1(_1207587), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1207587, _1207589, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1207591) = _1207591)], (23735 ^ _781013) ^ [_1224579, _1224581] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1224579), _1224581) = 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)), _1224579)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1224581))))], (37624 ^ _781013) ^ [_1499635, _1499637] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1499635), _1499637) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1499635, _1499637)))], (22424 ^ _781013) ^ [_1200944, _1200946, _1200948, _1200950] : [class_Divides_Osemiring__div(_1200944), 22427 ^ _781013 : [(22434 ^ _781013) ^ [] : [-(_1200946 = c_Groups_Ozero__class_Ozero(_1200944)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200944), _1200946), _1200948)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200944), _1200946), _1200950)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200944), _1200948), _1200950))], (22428 ^ _781013) ^ [] : [_1200946 = c_Groups_Ozero__class_Ozero(_1200944), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200944), _1200946), _1200948)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200944), _1200946), _1200950)) = c_Groups_Ozero__class_Ozero(_1200944))]]], (26614 ^ _781013) ^ [_1276439, _1276441] : [-(hBOOL(hAPP(_1276439, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1276439, _1276441)), 26622 ^ _781013 : [(26625 ^ _781013) ^ [_1276677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1276677), 26621 ^ [_1276439, _1276441])), hBOOL(hAPP(_1276439, _1276677))], (26631 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1276439, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 26621 ^ [_1276439, _1276441]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (26623 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26621 ^ [_1276439, _1276441]), _1276441)))]]], (24316 ^ _781013) ^ [_1234581, _1234583, _1234585, _1234587] : [class_Fields_Olinordered__field__inverse__zero(_1234581), 24319 ^ _781013 : [(24320 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234581), _1234583), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234581), _1234585), _1234587))), 24323 ^ _781013 : [(24330 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234581), c_Groups_Ozero__class_Ozero(_1234581)), _1234587))), 24333 ^ _781013 : [(24340 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234581), _1234587), c_Groups_Ozero__class_Ozero(_1234581)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234581), _1234583), c_Groups_Ozero__class_Ozero(_1234581))))], (24334 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234581), _1234587), c_Groups_Ozero__class_Ozero(_1234581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234581), _1234585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234581), _1234583), _1234587))))]]], (24324 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234581), c_Groups_Ozero__class_Ozero(_1234581)), _1234587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234581), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234581), _1234583), _1234587)), _1234585)))]]], (24346 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234581), _1234583), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234581), _1234585), _1234587)))), 24349 ^ _781013 : [(24352 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234581), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234581), _1234583), _1234587)), _1234585))], (24350 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234581), c_Groups_Ozero__class_Ozero(_1234581)), _1234587)))]], 24353 ^ _781013 : [(24356 ^ _781013) ^ [] : [24357 ^ _781013 : [(24360 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234581), _1234585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234581), _1234583), _1234587)))], (24358 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234581), _1234587), c_Groups_Ozero__class_Ozero(_1234581))))]], 24361 ^ _781013 : [(24364 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234581), _1234583), c_Groups_Ozero__class_Ozero(_1234581)))], (24362 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234581), _1234587), c_Groups_Ozero__class_Ozero(_1234581)))]]], (24354 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234581), c_Groups_Ozero__class_Ozero(_1234581)), _1234587))]]]]], (4292 ^ _781013) ^ [_845924, _845926, _845928, _845930] : [-(c_Big__Operators_Olattice__class_OInf__fin(_845930, _845926) = c_Big__Operators_Olattice__class_OInf__fin(_845928, _845924)), _845930 = _845928, _845926 = _845924], (17517 ^ _781013) ^ [_1108361, _1108363] : [-(_1108361 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108361), _1108363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1108361), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1108363)))], (23254 ^ _781013) ^ [_1215944, _1215946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1215944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1215944), _1215946)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1215946), _1215944) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1215946), _1215944)), _1215944)))], (22456 ^ _781013) ^ [_1201511, _1201513] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1201511), _1201513)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1201513), _1201511))], (17677 ^ _781013) ^ [_1111364, _1111366, _1111368] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111364), _1111366) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111364), _1111368), -(_1111366 = _1111368), -(_1111364 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1104 ^ _781013) ^ [_797555, _797557] : [-(class_Groups_Oordered__ab__group__add(_797555)), _797557 = _797555, class_Groups_Oordered__ab__group__add(_797557)], (40844 ^ _781013) ^ [_1583318, _1583320, _1583322] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1583318), _1583320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583318, _1583318), tc_HOL_Obool)), _1583322), hAPP(hAPP(c_Product__Type_OSigma(_1583318, _1583318), _1583320), hAPP(c_COMBK(tc_fun(_1583318, tc_HOL_Obool), _1583318), _1583320)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1583318, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1583318), _1583320), _1583322))))], (18522 ^ _781013) ^ [_1125676, _1125678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1125676), _1125678)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1125676), _1125678) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4610 ^ _781013) ^ [_850807, _850809] : [_850809 = _850807, -(c_List_Onth(_850809) = c_List_Onth(_850807))], (21553 ^ _781013) ^ [_1185775] : [21555 ^ _781013 : [(21558 ^ _781013) ^ [] : [hBOOL(hAPP(_1185775, 21554 ^ [_1185775]))], (21556 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21554 ^ [_1185775])))]], 21559 ^ _781013 : [(21560 ^ _781013) ^ [_1185902] : [-(hBOOL(hAPP(_1185775, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185902))))]]], (51272 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (46639 ^ _781013) ^ [_1717383, _1717385, _1717387, _1717389, _1717391, _1717393] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1717383, _1717385, _1717387), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1717383, _1717385), tc_HOL_Obool)), _1717389), _1717391)), _1717393) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1717383, _1717387), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1717383, _1717385, _1717387), _1717389), _1717393)), hAPP(hAPP(c_Relation_Orel__comp(_1717383, _1717385, _1717387), _1717391), _1717393)))], (31327 ^ _781013) ^ [_1368188, _1368190, _1368192, _1368194, _1368196] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1368188, _1368190)), _1368192), _1368194), _1368196))), 31328 ^ _781013 : [(31335 ^ _781013) ^ [] : [hBOOL(hAPP(_1368188, _1368192)), 31338 ^ _781013 : [(31339 ^ _781013) ^ [_1368425] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1368190), _1368192), _1368194), _1368425)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1368188, _1368190)), _1368425), _1368194), _1368196))]]], (31329 ^ _781013) ^ [] : [_1368196 = _1368192, -(hBOOL(hAPP(_1368188, _1368192)))]]], (14807 ^ _781013) ^ [_1055573, _1055575] : [class_Groups_Ocomm__monoid__add(_1055573), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055573), c_Groups_Ozero__class_Ozero(_1055573)), _1055575) = _1055575)], (43430 ^ _781013) ^ [_1645812, _1645814, _1645816, _1645818] : [-(hBOOL(hAPP(c_List_Olistsp(_1645812, _1645814), hAPP(hAPP(c_List_Olist_OCons(_1645812), _1645816), _1645818)))), hBOOL(hAPP(_1645814, _1645816)), hBOOL(hAPP(c_List_Olistsp(_1645812, _1645814), _1645818))], (33704 ^ _781013) ^ [] : [-(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))))], (26535 ^ _781013) ^ [_1274842, _1274844, _1274846, _1274848] : [class_Orderings_Olinorder(_1274842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274842), _1274844), _1274846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274842), _1274846), _1274848)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274842, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1274842, _1274844, _1274846)), c_SetInterval_Oord__class_OatLeastAtMost(_1274842, _1274846, _1274848)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1274842, _1274844, _1274848))], (44983 ^ _781013) ^ [_1679516, _1679518, _1679520] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1679516))), c_Enum_On__lists(_1679516, _1679518, _1679520)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679516)), _1679520)), _1679518))], (42536 ^ _781013) ^ [_1623754, _1623756] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1623754), _1623756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1623754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42542 ^ _781013 : [(42545 ^ _781013) ^ [] : [42541 ^ [_1623754, _1623756] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42543 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42541 ^ [_1623754, _1623756]), hAPP(c_List_Oset(tc_Nat_Onat), _1623756))))]]], (3768 ^ _781013) ^ [_837976, _837978, _837980, _837982, _837984, _837986] : [-(c_Predicate_ORangeP(_837986, _837982, _837978) = c_Predicate_ORangeP(_837984, _837980, _837976)), _837986 = _837984, _837982 = _837980, _837978 = _837976], (33562 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (46134 ^ _781013) ^ [_1704600, _1704602, _1704604] : [c_List_Olist__all2(_1704604, _1704604, c_fequal, _1704600, _1704602), -(_1704600 = _1704602)], (44344 ^ _781013) ^ [_1664563, _1664565, _1664567, _1664569] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664563)), _1664565) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664567)), _1664569), -(hAPP(hAPP(c_List_Ozip(_1664563, _1664567), hAPP(c_List_Orev(_1664563), _1664565)), hAPP(c_List_Orev(_1664567), _1664569)) = hAPP(c_List_Orev(tc_prod(_1664563, _1664567)), hAPP(hAPP(c_List_Ozip(_1664563, _1664567), _1664565), _1664569)))], (46194 ^ _781013) ^ [_1705756, _1705758, _1705760, _1705762, _1705764] : [c_List_Olist__all2(_1705756, _1705758, _1705760, hAPP(c_List_Orev(_1705756), _1705762), _1705764), -(c_List_Olist__all2(_1705756, _1705758, _1705760, _1705762, hAPP(c_List_Orev(_1705758), _1705764)))], (50586 ^ _781013) ^ [_1809394, _1809396, _1809398] : [class_HOL_Oequal(_1809394), 50589 ^ _781013 : [(50596 ^ _781013) ^ [] : [_1809396 = _1809398, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1809394), _1809396), _1809398)))], (50590 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1809394), _1809396), _1809398)), -(_1809396 = _1809398)]]], (47692 ^ _781013) ^ [_1743881, _1743883, _1743885] : [47694 ^ _781013 : [(47697 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1743881), 47693 ^ [_1743881, _1743883, _1743885]), c_Wellfounded_Oacc(_1743881, _1743885)))], (47695 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1743881, _1743881)), hAPP(hAPP(c_Product__Type_OPair(_1743881, _1743881), 47693 ^ [_1743881, _1743883, _1743885]), _1743883)), _1743885)))]], -(hBOOL(hAPP(hAPP(c_member(_1743881), _1743883), c_Wellfounded_Oacc(_1743881, _1743885))))], (50429 ^ _781013) ^ [_1806392, _1806394] : [c_List_Olist__ex1(_1806392, _1806394, c_List_Olist_ONil(_1806392))], (27411 ^ _781013) ^ [_1291877, _1291879] : [hAPP(c_Set_OPow(_1291877), _1291879) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1291877, tc_HOL_Obool), tc_HOL_Obool))], (11019 ^ _781013) ^ [_976781] : [class_Lattices_Osemilattice__sup(_976781), -(c_Finite__Set_Ofun__left__comm__idem(_976781, _976781, c_Lattices_Osemilattice__sup__class_Osup(_976781)))], (23733 ^ _781013) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23727 ^ _781013) ^ [_1224412, _1224414, _1224416] : [class_Fields_Ofield__inverse__zero(_1224412), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1224412), c_Groups_Oone__class_Oone(_1224412)), hAPP(hAPP(c_Power_Opower__class_Opower(_1224412), _1224414), _1224416)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1224412), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1224412), c_Groups_Oone__class_Oone(_1224412)), _1224414)), _1224416))], (22007 ^ _781013) ^ [_1193805, _1193807] : [class_Rings_Olinordered__semidom(_1193805), 22010 ^ _781013 : [(22017 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193805), c_Groups_Ozero__class_Ozero(_1193805)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1193805), _1193807))))], (22011 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193805), c_Groups_Ozero__class_Ozero(_1193805)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1193805), _1193807))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193807)))]]], (14433 ^ _781013) ^ [_1048582, _1048584, _1048586] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048582), _1048584)), 14436 ^ _781013 : [(14443 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1048582), _1048586), _1048584))), -(hAPP(c_Finite__Set_Ocard(_1048582), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048582, tc_HOL_Obool)), _1048584), hAPP(hAPP(c_Set_Oinsert(_1048582), _1048586), c_Orderings_Obot__class_Obot(tc_fun(_1048582, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1048582), _1048584))], (14437 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1048582), _1048586), _1048584)), -(hAPP(c_Finite__Set_Ocard(_1048582), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048582, tc_HOL_Obool)), _1048584), hAPP(hAPP(c_Set_Oinsert(_1048582), _1048586), c_Orderings_Obot__class_Obot(tc_fun(_1048582, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1048582), _1048584)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (20299 ^ _781013) ^ [_1160477, _1160479, _1160481] : [class_Power_Opower(_1160477), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1160477), _1160479), hAPP(c_Nat_OSuc, _1160481)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160477), _1160479), hAPP(hAPP(c_Power_Opower__class_Opower(_1160477), _1160479), _1160481)))], (10771 ^ _781013) ^ [_971201, _971203, _971205] : [10773 ^ _781013 : [(10779 ^ _781013) ^ [] : [-(10772 ^ [_971201, _971203, _971205] = 10775 ^ [_971201, _971203, _971205])], (10777 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_971201), 10775 ^ [_971201, _971203, _971205]), _971205)))], (10774 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_971201), 10772 ^ [_971201, _971203, _971205]), _971203)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971201, tc_HOL_Obool)), _971203), _971205) = c_Orderings_Obot__class_Obot(tc_fun(_971201, tc_HOL_Obool)))], (37728 ^ _781013) ^ [_1501823, _1501825, _1501827, _1501829, _1501831, _1501833] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1501829, _1501829)), hAPP(hAPP(c_Product__Type_OPair(_1501829, _1501829), hAPP(_1501833, _1501825)), hAPP(_1501833, _1501827))), _1501831)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1501823, _1501823)), hAPP(hAPP(c_Product__Type_OPair(_1501823, _1501823), _1501825), _1501827)), hAPP(hAPP(c_Relation_Oinv__image(_1501829, _1501823), _1501831), _1501833))))], (47754 ^ _781013) ^ [_1745505, _1745507, _1745509, _1745511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1745505), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745507)), _1745509))), 47760 ^ _781013 : [(47763 ^ _781013) ^ [] : [hBOOL(hAPP(_1745511, 47759 ^ [_1745505, _1745507, _1745509, _1745511]))], (47761 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745507), 47759 ^ [_1745505, _1745507, _1745509, _1745511]), hAPP(c_List_Oset(_1745507), _1745509))))]], -(hBOOL(hAPP(_1745511, hAPP(hAPP(c_List_Onth(_1745507), _1745509), _1745505))))], (9881 ^ _781013) ^ [_955447, _955449, _955451, _955453] : [class_Lattices_Olattice(_955447), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955447), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955447), _955449), _955451)), _955453) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955447), _955449), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955447), _955451), _955453)))], (18083 ^ _781013) ^ [_1117899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117899), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1117899 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44318 ^ _781013) ^ [_1664103, _1664105, _1664107] : [_1664105 = hAPP(c_List_Orev(_1664103), _1664107), -(hAPP(c_List_Orev(_1664103), _1664105) = _1664107)], (45713 ^ _781013) ^ [_1695002] : [class_Complete__Lattice_Ocomplete__lattice(_1695002), -(c_Complete__Lattice_OSup__class_OSup(_1695002, c_Orderings_Obot__class_Obot(tc_fun(_1695002, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1695002))], (756 ^ _781013) ^ [_792599, _792601, _792603, _792605, _792607, _792609] : [-(c_Relation_Ototal__on(_792607, _792603, _792599)), c_Relation_Ototal__on(_792609, _792605, _792601), _792609 = _792607, _792605 = _792603, _792601 = _792599], (21708 ^ _781013) ^ [_1188631, _1188633, _1188635] : [class_Rings_Olinordered__semidom(_1188631), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1188633), _1188635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188631), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188631), _1188633)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188631), _1188635))))], (6374 ^ _781013) ^ [_884927, _884929, _884931] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884927, _884929)), _884931), _884931))), 6375 ^ _781013 : [(6378 ^ _781013) ^ [_885027] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_884929), _884931), _885027)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884927, _884929)), _885027), _884931))], (6376 ^ _781013) ^ [] : [-(hBOOL(hAPP(_884927, _884931)))]]], (39462 ^ _781013) ^ [_1543996, _1543998, _1544000, _1544002, _1544004] : [class_Groups_Ocomm__monoid__add(_1543996), hBOOL(hAPP(hAPP(c_member(_1543998), _1544000), hAPP(c_List_Oset(_1543998), _1544002))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1543996), hAPP(hAPP(c_List_Omap(_1543998, _1543996), _1544004), _1544002)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1543996), hAPP(_1544004, _1544000)), hAPP(c_List_Omonoid__add__class_Olistsum(_1543996), hAPP(hAPP(c_List_Omap(_1543998, _1543996), _1544004), c_List_Oremove1(_1543998, _1544000, _1544002)))))], (47116 ^ _781013) ^ [_1729648, _1729650, _1729652, _1729654] : [hBOOL(hAPP(hAPP(c_member(_1729650), _1729654), hAPP(c_Relation_ORange(_1729648, _1729650), _1729652))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1729648, _1729650, hAPP(hAPP(c_COMBC(_1729648, tc_fun(tc_prod(_1729648, _1729650), tc_HOL_Obool), tc_fun(_1729650, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1729650, tc_fun(tc_fun(tc_prod(_1729648, _1729650), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1729648, _1729650), tc_HOL_Obool), tc_fun(_1729650, tc_HOL_Obool)), _1729648), c_COMBC(_1729650, tc_fun(tc_prod(_1729648, _1729650), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1729650, tc_prod(_1729648, _1729650)), tc_fun(_1729650, tc_fun(tc_fun(tc_prod(_1729648, _1729650), tc_HOL_Obool), tc_HOL_Obool)), _1729648), hAPP(c_COMBB(tc_prod(_1729648, _1729650), tc_fun(tc_fun(tc_prod(_1729648, _1729650), tc_HOL_Obool), tc_HOL_Obool), _1729650), c_member(tc_prod(_1729648, _1729650)))), c_Product__Type_OPair(_1729648, _1729650)))), _1729652)), _1729654)))], (6681 ^ _781013) ^ [_890897, _890899, _890901, _890903, _890905] : [c_Finite__Set_Ofolding__one(_890897, _890899, _890901), hBOOL(hAPP(c_Finite__Set_Ofinite(_890897), _890903)), -(hBOOL(hAPP(hAPP(c_member(_890897), _890905), _890903))), -(_890903 = c_Orderings_Obot__class_Obot(tc_fun(_890897, tc_HOL_Obool))), -(hAPP(_890901, hAPP(hAPP(c_Set_Oinsert(_890897), _890905), _890903)) = hAPP(hAPP(_890899, _890905), hAPP(_890901, _890903)))], (32558 ^ _781013) ^ [_1398905, _1398907, _1398909] : [class_Int_Onumber__ring(_1398905), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398905), hAPP(c_Int_Onumber__class_Onumber__of(_1398905), _1398907)), hAPP(c_Int_Onumber__class_Onumber__of(_1398905), _1398909)) = hAPP(c_Int_Onumber__class_Onumber__of(_1398905), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1398907), _1398909)))], (23897 ^ _781013) ^ [_1227321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227321)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1227321)) = _1227321)], (47257 ^ _781013) ^ [_1733570, _1733572, _1733574, _1733576, _1733578] : [hBOOL(hAPP(hAPP(_1733570, _1733572), _1733574)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1733576, _1733578, _1733570), _1733572)))], (5757 ^ _781013) ^ [_872182, _872184, _872186, _872188, _872190] : [c_Hoare__Mirabelle_Ohoare__derivs(_872182, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872182)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872182), _872184), hAPP(c_Com_Ocom_OBODY, _872186)), _872188)), _872190), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872182)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872182), _872184), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _872186))), _872188)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872182), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_872182, _872190, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872182)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872182), _872184), hAPP(c_Com_Ocom_OBODY, _872186)), _872188)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872182), tc_HOL_Obool)))))], (13493 ^ _781013) ^ [_1027964, _1027966] : [class_Rings_Oring__1__no__zero__divisors(_1027964), 13496 ^ _781013 : [(13497 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1027964), _1027966), _1027966) = c_Groups_Oone__class_Oone(_1027964), -(_1027966 = c_Groups_Oone__class_Oone(_1027964)), -(_1027966 = hAPP(c_Groups_Ouminus__class_Ouminus(_1027964), c_Groups_Oone__class_Oone(_1027964)))], (13507 ^ _781013) ^ [] : [13508 ^ _781013 : [(13511 ^ _781013) ^ [] : [_1027966 = hAPP(c_Groups_Ouminus__class_Ouminus(_1027964), c_Groups_Oone__class_Oone(_1027964))], (13509 ^ _781013) ^ [] : [_1027966 = c_Groups_Oone__class_Oone(_1027964)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1027964), _1027966), _1027966) = c_Groups_Oone__class_Oone(_1027964))]]], (51356 ^ _781013) ^ [] : [-(class_HOL_Oequal(tc_Nat_Onat))], (50427 ^ _781013) ^ [_1806345, _1806347, _1806349] : [-(c_Product__Type_Ointernal__split(_1806345, _1806347, _1806349) = c_Product__Type_Oprod_Oprod__case(_1806345, _1806347, _1806349))], (17106 ^ _781013) ^ [_1099125, _1099127, _1099129, _1099131, _1099133, _1099135] : [c_Fun_Oinj__on(_1099125, _1099127, _1099129, _1099131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099127, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1099125, _1099127, _1099129), _1099131)), _1099133)), c_Fun_Oinj__on(_1099127, _1099125, _1099135, _1099133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099125, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1099127, _1099125, _1099135), _1099133)), _1099131)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099125), _1099131)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099127), _1099133)), -(hAPP(c_Finite__Set_Ocard(_1099125), _1099131) = hAPP(c_Finite__Set_Ocard(_1099127), _1099133))], (33586 ^ _781013) ^ [_1418084] : [class_Int_Onumber__ring(_1418084), -(hAPP(c_Int_Onumber__class_Onumber__of(_1418084), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1418084))], (4368 ^ _781013) ^ [_847114, _847116, _847118, _847120] : [-(c_List_Oremdups(_847120, _847116) = c_List_Oremdups(_847118, _847114)), _847120 = _847118, _847116 = _847114], (50904 ^ _781013) ^ [_1815992, _1815994, _1815996, _1815998, _1816000] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815992, _1815994, hAPP(hAPP(c_COMBC(_1815992, tc_fun(tc_prod(_1815992, _1815994), tc_HOL_Obool), tc_fun(_1815994, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1815994, tc_fun(tc_fun(tc_prod(_1815992, _1815994), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1815992, _1815994), tc_HOL_Obool), tc_fun(_1815994, tc_HOL_Obool)), _1815992), c_COMBC(_1815994, tc_fun(tc_prod(_1815992, _1815994), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1815994, tc_prod(_1815992, _1815994)), tc_fun(_1815994, tc_fun(tc_fun(tc_prod(_1815992, _1815994), tc_HOL_Obool), tc_HOL_Obool)), _1815992), hAPP(c_COMBB(tc_prod(_1815992, _1815994), tc_fun(tc_fun(tc_prod(_1815992, _1815994), tc_HOL_Obool), tc_HOL_Obool), _1815994), c_member(tc_prod(_1815992, _1815994)))), c_Product__Type_OPair(_1815992, _1815994)))), _1815996)), _1815998), _1816000)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1815994, _1815992)), hAPP(hAPP(c_Product__Type_OPair(_1815994, _1815992), _1815998), _1816000)), hAPP(c_Relation_Oconverse(_1815992, _1815994), _1815996))))], (33638 ^ _781013) ^ [_1418857] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1418857), 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), _1418857)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1418857)))], (974 ^ _781013) ^ [_795816, _795818, _795820, _795822] : [-(c_FunDef_Ois__measure(_795820, _795816)), c_FunDef_Ois__measure(_795822, _795818), _795822 = _795820, _795818 = _795816], (48045 ^ _781013) ^ [_1751634, _1751636, _1751638, _1751640, _1751642] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1751634, _1751634)), hAPP(hAPP(c_Product__Type_OPair(_1751634, _1751634), _1751636), _1751638)), c_Transitive__Closure_Otrancl(_1751634, _1751640))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1751634, _1751634)), hAPP(hAPP(c_Product__Type_OPair(_1751634, _1751634), _1751638), _1751642)), _1751640)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1751634, _1751634)), hAPP(hAPP(c_Product__Type_OPair(_1751634, _1751634), _1751636), _1751642)), c_Transitive__Closure_Otrancl(_1751634, _1751640))))], (18434 ^ _781013) ^ [_1124055, _1124057, _1124059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1124055)), 18437 ^ _781013 : [(18444 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124057), _1124059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124055), _1124057)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124055), _1124059))))], (18438 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124055), _1124057)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124055), _1124059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124057), _1124059)))]]], (47352 ^ _781013) ^ [_1735867, _1735869] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1735867), c_Int_OInteg)), hBOOL(hAPP(_1735869, hAPP(c_Int_ORep__Integ, 47357 ^ [_1735867, _1735869]))), -(hBOOL(hAPP(_1735869, _1735867)))], (16928 ^ _781013) ^ [_1095042, _1095044, _1095046, _1095048, _1095050] : [-(c_Map_Odom(_1095042, _1095044, hAPP(hAPP(c_COMBS(_1095042, tc_Option_Ooption(_1095044), tc_Option_Ooption(_1095044)), hAPP(hAPP(c_COMBS(_1095042, tc_Option_Ooption(_1095044), tc_fun(tc_Option_Ooption(_1095044), tc_Option_Ooption(_1095044))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1095044), tc_fun(tc_Option_Ooption(_1095044), tc_Option_Ooption(_1095044))), _1095042), c_If(tc_Option_Ooption(_1095044))), _1095046)), _1095048)), _1095050)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1095042, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095042, tc_HOL_Obool)), c_Map_Odom(_1095042, _1095044, _1095048)), hAPP(c_Set_OCollect(_1095042), _1095046))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095042, tc_HOL_Obool)), c_Map_Odom(_1095042, _1095044, _1095050)), hAPP(c_Set_OCollect(_1095042), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1095042), c_fNot), _1095046)))))], (19596 ^ _781013) ^ [_1147716, _1147718, _1147720, _1147722] : [class_Rings_Olinordered__semidom(_1147716), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147716), c_Groups_Oone__class_Oone(_1147716)), _1147718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147716), hAPP(hAPP(c_Power_Opower__class_Opower(_1147716), _1147718), _1147720)), hAPP(hAPP(c_Power_Opower__class_Opower(_1147716), _1147718), _1147722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147720), _1147722)))], (16045 ^ _781013) ^ [_1077794, _1077796, _1077798, _1077800, _1077802, _1077804] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1077794), -(_1077796 = c_Groups_Ozero__class_Ozero(_1077794)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077794), _1077798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077794), _1077796), _1077802)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077794), _1077800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077794), _1077796), _1077804)), _1077798 = _1077800, -(_1077802 = _1077804)], (27271 ^ _781013) ^ [_1288974, _1288976, _1288978, _1288980, _1288982] : [class_Groups_Ocomm__monoid__mult(_1288974), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288976), _1288978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288976, tc_HOL_Obool)), _1288980), _1288978)), 27285 ^ _781013 : [(27288 ^ _781013) ^ [] : [hAPP(_1288982, 27284 ^ [_1288974, _1288976, _1288978, _1288980, _1288982]) = c_Groups_Oone__class_Oone(_1288974)], (27286 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1288976), 27284 ^ [_1288974, _1288976, _1288978, _1288980, _1288982]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288976, tc_HOL_Obool)), _1288978), _1288980))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1288976, _1288974), _1288982), _1288980) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1288976, _1288974), _1288982), _1288978))], (51384 ^ _781013) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (51012 ^ _781013) ^ [_1818539, _1818541] : [class_Lattices_Olattice(_1818539), -(class_Lattices_Osemilattice__sup(tc_fun(_1818541, _1818539)))], (2600 ^ _781013) ^ [_819602, _819604] : [_819604 = _819602, -(c_Divides_Oadjust(_819604) = c_Divides_Oadjust(_819602))], (8693 ^ _781013) ^ [_932045, _932047, _932049, _932051] : [hBOOL(hAPP(_932045, _932047)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932049, tc_HOL_Obool)), _932045), _932051), _932047)))], (35829 ^ _781013) ^ [_1458269, _1458271] : [-(c_Fun_Oinj__on(tc_fun(_1458269, _1458271), tc_fun(tc_prod(_1458269, _1458271), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1458269, _1458271), tc_HOL_Obool), tc_fun(tc_prod(_1458269, _1458271), tc_HOL_Obool), tc_fun(_1458269, _1458271)), c_Set_OCollect(tc_prod(_1458269, _1458271))), hAPP(hAPP(c_COMBB(tc_fun(_1458269, tc_fun(_1458271, tc_HOL_Obool)), tc_fun(tc_prod(_1458269, _1458271), tc_HOL_Obool), tc_fun(_1458269, _1458271)), c_Product__Type_Oprod_Oprod__case(_1458269, _1458271, tc_HOL_Obool)), hAPP(c_COMBB(_1458271, tc_fun(_1458271, tc_HOL_Obool), _1458269), hAPP(c_COMBC(_1458271, _1458271, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1458269, _1458271), tc_HOL_Obool))))], (38206 ^ _781013) ^ [_1514410] : [-(_1514410 = 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), 38203 ^ [_1514410]), 38204 ^ [_1514410])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (26699 ^ _781013) ^ [_1277888, _1277890] : [class_Orderings_Olinorder(_1277888), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277888, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1277888), _1277890)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1277888), _1277890))], (9491 ^ _781013) ^ [_949236, _949238, _949240] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_949236, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_949236, tc_HOL_Obool)), _949238), _949240)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949236, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_949236, tc_HOL_Obool)), _949238)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_949236, tc_HOL_Obool)), _949240)))], (36778 ^ _781013) ^ [_1483079, _1483081] : [-(c_Divides_OposDivAlg(_1483079, _1483081) = hAPP(c_Divides_Oadjust(_1483081), c_Divides_OposDivAlg(_1483079, 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)))), _1483081)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1483079), _1483081))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1483081), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9815 ^ _781013) ^ [_954158, _954160] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954158, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_954158, tc_HOL_Obool)), _954160)), _954160) = c_Orderings_Obot__class_Obot(tc_fun(_954158, tc_HOL_Obool)))], (42328 ^ _781013) ^ [_1619733, _1619735, _1619737] : [-(_1619733 = c_List_Olist_ONil(_1619735)), -(hAPP(c_List_Ohd(_1619735), hAPP(hAPP(c_List_Oappend(_1619735), _1619733), _1619737)) = hAPP(c_List_Ohd(_1619735), _1619733))], (47809 ^ _781013) ^ [_1746712, _1746714, _1746716] : [-(c_List_Olist__ex(_1746712, _1746714, _1746716)), 47810 ^ _781013 : [(47811 ^ _781013) ^ [_1746777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746777), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746712)), _1746716))), hBOOL(hAPP(_1746714, hAPP(hAPP(c_List_Onth(_1746712), _1746716), _1746777)))]]], (35051 ^ _781013) ^ [] : [-(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)))))], (25555 ^ _781013) ^ [_1256897] : [c_Nat__Transfer_Onat__set(_1256897), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1256897) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1256897)))], (15489 ^ _781013) ^ [_1067487, _1067489, _1067491] : [class_Rings_Oordered__ring(_1067487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067487), _1067489), c_Groups_Ozero__class_Ozero(_1067487))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067487), _1067491), c_Groups_Ozero__class_Ozero(_1067487))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067487), c_Groups_Ozero__class_Ozero(_1067487)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067487), _1067489), _1067491))))], (51642 ^ _781013) ^ [_1825223, _1825225] : [hBOOL(_1825223), hBOOL(_1825225), -(hBOOL(hAPP(hAPP(c_fconj, _1825223), _1825225)))], (5126 ^ _781013) ^ [_859171, _859173] : [_859173 = _859171, -(c_Nat_Osize__class_Osize(_859173) = c_Nat_Osize__class_Osize(_859171))], (44709 ^ _781013) ^ [_1673856] : [c_List_Onat__list(_1673856), -(c_List_Oembed__list(c_List_Oreturn__list(_1673856)) = _1673856)], (28700 ^ _781013) ^ [_1316518, _1316520, _1316522] : [class_Orderings_Olinorder(_1316518), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316518), _1316520), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316518), _1316520), _1316522)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316518), _1316520), _1316522))], (45009 ^ _781013) ^ [_1680024, _1680026, _1680028] : [-(c_Enum_Osublists(_1680024, hAPP(hAPP(c_List_Olist_OCons(_1680024), _1680026), _1680028)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1680024)), tc_List_Olist(tc_List_Olist(_1680024))), c_Enum_Osublists(_1680024, _1680028)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1680024)), tc_List_Olist(tc_List_Olist(_1680024)), tc_List_Olist(tc_List_Olist(_1680024))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1680024)), tc_fun(tc_List_Olist(tc_List_Olist(_1680024)), tc_List_Olist(tc_List_Olist(_1680024))), tc_List_Olist(tc_List_Olist(_1680024))), c_List_Oappend(tc_List_Olist(_1680024))), hAPP(c_List_Omap(tc_List_Olist(_1680024), tc_List_Olist(_1680024)), hAPP(c_List_Olist_OCons(_1680024), _1680026)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1680024))))))], (47083 ^ _781013) ^ [_1728544, _1728546, _1728548] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1728544, _1728546)), _1728548)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1728546), hAPP(c_Relation_ORange(_1728544, _1728546), _1728548))))], (33182 ^ _781013) ^ [_1410679, _1410681, _1410683, _1410685] : [class_Fields_Olinordered__field__inverse__zero(_1410679), class_Int_Onumber(_1410679), 33189 ^ _781013 : [(33190 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410679), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1410679), _1410681), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683))), _1410685)), 33193 ^ _781013 : [(33200 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410679), c_Groups_Ozero__class_Ozero(_1410679)), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683)))), 33203 ^ _781013 : [(33210 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410679), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683)), c_Groups_Ozero__class_Ozero(_1410679)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410679), c_Groups_Ozero__class_Ozero(_1410679)), _1410685)))], (33204 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410679), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683)), c_Groups_Ozero__class_Ozero(_1410679))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410679), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1410679), _1410685), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683))), _1410681)))]]], (33194 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410679), c_Groups_Ozero__class_Ozero(_1410679)), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410679), _1410681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1410679), _1410685), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683)))))]]], (33216 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410679), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1410679), _1410681), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683))), _1410685))), 33219 ^ _781013 : [(33222 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410679), _1410681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1410679), _1410685), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683))))], (33220 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410679), c_Groups_Ozero__class_Ozero(_1410679)), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683))))]], 33223 ^ _781013 : [(33226 ^ _781013) ^ [] : [33227 ^ _781013 : [(33230 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410679), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1410679), _1410685), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683))), _1410681))], (33228 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410679), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683)), c_Groups_Ozero__class_Ozero(_1410679))))]], 33231 ^ _781013 : [(33234 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410679), c_Groups_Ozero__class_Ozero(_1410679)), _1410685))], (33232 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410679), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683)), c_Groups_Ozero__class_Ozero(_1410679)))]]], (33224 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410679), c_Groups_Ozero__class_Ozero(_1410679)), hAPP(c_Int_Onumber__class_Onumber__of(_1410679), _1410683)))]]]]], (25432 ^ _781013) ^ [_1255090, _1255092] : [c_Nat__Transfer_Onat__set(_1255090), c_Nat__Transfer_Onat__set(_1255092), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1255090), _1255092) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1255090)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1255092))))], (20071 ^ _781013) ^ [_1156585, _1156587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1156585)), hAPP(c_Nat_OSuc, _1156587))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156585), _1156587)))], (15447 ^ _781013) ^ [_1066722, _1066724, _1066726] : [class_Rings_Oordered__cancel__semiring(_1066722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066722), c_Groups_Ozero__class_Ozero(_1066722)), _1066724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066722), _1066726), c_Groups_Ozero__class_Ozero(_1066722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066722), _1066724), _1066726)), c_Groups_Ozero__class_Ozero(_1066722))))], (51230 ^ _781013) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (8217 ^ _781013) ^ [_921358, _921360, _921362, _921364, _921366] : [-(c_Map_Omap__comp(_921358, _921360, _921362, hAPP(c_COMBK(tc_Option_Ooption(_921360), _921358), c_Option_Ooption_ONone(_921360)), _921364, _921366) = c_Option_Ooption_ONone(_921360))], (6654 ^ _781013) ^ [_890335, _890337] : [-(c_Map_Oran(_890335, _890337, hAPP(c_COMBK(tc_Option_Ooption(_890337), _890335), c_Option_Ooption_ONone(_890337))) = c_Orderings_Obot__class_Obot(tc_fun(_890337, tc_HOL_Obool)))], (33248 ^ _781013) ^ [_1412000, _1412002, _1412004, _1412006, _1412008, _1412010, _1412012, _1412014, _1412016, _1412018] : [c_Equiv__Relations_Oequiv(_1412000, _1412002, _1412004), c_Equiv__Relations_Oequiv(_1412006, _1412008, _1412010), c_Equiv__Relations_Ocongruent2(_1412000, _1412006, tc_fun(_1412012, tc_HOL_Obool), _1412004, _1412010, _1412014), hBOOL(hAPP(hAPP(c_member(_1412000), _1412016), _1412002)), hBOOL(hAPP(hAPP(c_member(_1412006), _1412018), _1412008)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412000, tc_fun(_1412012, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1412000, _1412000, _1412004), hAPP(hAPP(c_Set_Oinsert(_1412000), _1412016), c_Orderings_Obot__class_Obot(tc_fun(_1412000, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1412006, tc_fun(_1412012, tc_HOL_Obool)), tc_fun(_1412012, tc_HOL_Obool), _1412000), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412006, tc_fun(_1412012, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1412006, _1412006, _1412010), hAPP(hAPP(c_Set_Oinsert(_1412006), _1412018), c_Orderings_Obot__class_Obot(tc_fun(_1412006, tc_HOL_Obool)))))), _1412014)) = hAPP(hAPP(_1412014, _1412016), _1412018))], (50525 ^ _781013) ^ [] : [-(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))))], (21573 ^ _781013) ^ [_1186132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186132)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29313 ^ _781013) ^ [_1327829, _1327831] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1327829), _1327831)), _1327831) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1327829), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1327829, _1327831)))], (3402 ^ _781013) ^ [_832289, _832291] : [_832291 = _832289, -(c_Option_Othe(_832291) = c_Option_Othe(_832289))], (38576 ^ _781013) ^ [_1522972, _1522974] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1522972, _1522974)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1522972, _1522974))], (51522 ^ _781013) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (33070 ^ _781013) ^ [_1408541, _1408543, _1408545, _1408547] : [class_Fields_Olinordered__field__inverse__zero(_1408541), class_Int_Onumber(_1408541), 33077 ^ _781013 : [(33078 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408541), hAPP(c_Int_Onumber__class_Onumber__of(_1408541), _1408543)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1408541), _1408545), _1408547))), 33081 ^ _781013 : [(33088 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408541), c_Groups_Ozero__class_Ozero(_1408541)), _1408547))), 33091 ^ _781013 : [(33098 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408541), _1408547), c_Groups_Ozero__class_Ozero(_1408541)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408541), hAPP(c_Int_Onumber__class_Onumber__of(_1408541), _1408543)), c_Groups_Ozero__class_Ozero(_1408541))))], (33092 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408541), _1408547), c_Groups_Ozero__class_Ozero(_1408541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408541), _1408545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408541), hAPP(c_Int_Onumber__class_Onumber__of(_1408541), _1408543)), _1408547))))]]], (33082 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408541), c_Groups_Ozero__class_Ozero(_1408541)), _1408547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408541), hAPP(c_Int_Onumber__class_Onumber__of(_1408541), _1408543)), _1408547)), _1408545)))]]], (33104 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408541), hAPP(c_Int_Onumber__class_Onumber__of(_1408541), _1408543)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1408541), _1408545), _1408547)))), 33107 ^ _781013 : [(33110 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408541), hAPP(c_Int_Onumber__class_Onumber__of(_1408541), _1408543)), _1408547)), _1408545))], (33108 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408541), c_Groups_Ozero__class_Ozero(_1408541)), _1408547)))]], 33111 ^ _781013 : [(33114 ^ _781013) ^ [] : [33115 ^ _781013 : [(33118 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408541), _1408545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408541), hAPP(c_Int_Onumber__class_Onumber__of(_1408541), _1408543)), _1408547)))], (33116 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408541), _1408547), c_Groups_Ozero__class_Ozero(_1408541))))]], 33119 ^ _781013 : [(33122 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408541), hAPP(c_Int_Onumber__class_Onumber__of(_1408541), _1408543)), c_Groups_Ozero__class_Ozero(_1408541)))], (33120 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408541), _1408547), c_Groups_Ozero__class_Ozero(_1408541)))]]], (33112 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408541), c_Groups_Ozero__class_Ozero(_1408541)), _1408547))]]]]], (36228 ^ _781013) ^ [_1471127, _1471129, _1471131, _1471133] : [-(hAPP(c_Relation_OImage(_1471127, _1471129, _1471131), hAPP(hAPP(c_Set_Oinsert(_1471127), _1471133), c_Orderings_Obot__class_Obot(tc_fun(_1471127, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1471129), hAPP(hAPP(c_COMBC(_1471129, tc_fun(tc_prod(_1471127, _1471129), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1471127, _1471129), tc_fun(tc_fun(tc_prod(_1471127, _1471129), tc_HOL_Obool), tc_HOL_Obool), _1471129), c_member(tc_prod(_1471127, _1471129))), hAPP(c_Product__Type_OPair(_1471127, _1471129), _1471133))), _1471131)))], (46855 ^ _781013) ^ [_1723334, _1723336, _1723338] : [c_Wellfounded_Owf(_1723334, _1723336), -(c_Wellfounded_Owf(tc_List_Olist(_1723334), hAPP(c_List_Olexn(_1723334, _1723336), _1723338)))], (40321 ^ _781013) ^ [_1567626, _1567628, _1567630] : [-(hBOOL(hAPP(c_List_Odistinct(_1567626), hAPP(hAPP(c_List_Olist_OCons(_1567626), _1567628), _1567630)))), -(hBOOL(hAPP(hAPP(c_member(_1567626), _1567628), hAPP(c_List_Oset(_1567626), _1567630)))), hBOOL(hAPP(c_List_Odistinct(_1567626), _1567630))], (42358 ^ _781013) ^ [_1620008, _1620010, _1620012] : [-(_1620008 = c_List_Olist_ONil(_1620010)), -(hAPP(c_List_Ohd(_1620010), hAPP(c_List_Orotate(_1620010, _1620012), _1620008)) = hAPP(hAPP(c_List_Onth(_1620010), _1620008), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1620012, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620010)), _1620008))))], (46996 ^ _781013) ^ [_1726613, _1726615, _1726617, _1726619] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1726613), _1726615)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1726613), _1726617)), -(_1726617 = c_Orderings_Obot__class_Obot(tc_fun(_1726613, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1726613, tc_HOL_Obool), tc_fun(_1726613, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1726613, tc_HOL_Obool), tc_fun(_1726613, tc_HOL_Obool)), _1726615), _1726617)), c_Wellfounded_Omax__ext(_1726613, _1726619)))), 47010 ^ _781013 : [(47013 ^ _781013) ^ [_1727018] : [hBOOL(hAPP(hAPP(c_member(_1726613), _1727018), _1726617)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1726613, _1726613)), hAPP(hAPP(c_Product__Type_OPair(_1726613, _1726613), 47009 ^ [_1726613, _1726615, _1726617, _1726619]), _1727018)), _1726619))], (47011 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726613), 47009 ^ [_1726613, _1726615, _1726617, _1726619]), _1726615)))]]], (15095 ^ _781013) ^ [_1060180, _1060182, _1060184] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1060180), hAPP(c_Set_OCollect(_1060180), hAPP(hAPP(c_COMBS(_1060180, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1060180), c_fdisj), _1060182)), _1060184))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060180), hAPP(c_Set_OCollect(_1060180), _1060182))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060180), hAPP(c_Set_OCollect(_1060180), _1060184)))], (11133 ^ _781013) ^ [_979465, _979467, _979469, _979471, _979473] : [-(hBOOL(hAPP(hAPP(c_member(_979465), _979467), c_Map_Odom(_979465, _979469, _979471)))), -(hAPP(c_Map_Omap__add(_979465, _979469, _979471, _979473), _979467) = hAPP(_979473, _979467))], (6252 ^ _781013) ^ [_882619, _882621, _882623] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_882619, _882621, _882623)))), hBOOL(hAPP(c_Com_OWT, _882621)), hBOOL(hAPP(c_Com_OWT, _882623))], (37062 ^ _781013) ^ [_1488315, _1488317, _1488319] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1488315, _1488317), _1488319)), -(c_Divides_Odivmod__nat(_1488315, _1488317) = _1488319)], (30917 ^ _781013) ^ [_1359731, _1359733] : [class_Orderings_Olinorder(_1359731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359731), _1359733)), -(_1359733 = c_Orderings_Obot__class_Obot(tc_fun(_1359731, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359731), c_Big__Operators_Olattice_OInf__fin(_1359731, c_Orderings_Oord__class_Omin(_1359731), _1359733)), c_Big__Operators_Olattice_OSup__fin(_1359731, c_Orderings_Oord__class_Omax(_1359731), _1359733))))], (8060 ^ _781013) ^ [_918122, _918124, _918126] : [hBOOL(hAPP(hAPP(c_member(_918122), _918124), hAPP(hAPP(c_Set_Oinsert(_918122), _918126), c_Orderings_Obot__class_Obot(tc_fun(_918122, tc_HOL_Obool))))), -(_918124 = _918126)], (43390 ^ _781013) ^ [_1644929, _1644931, _1644933, _1644935] : [-(hAPP(c_List_Ofilter(_1644929, _1644931), hAPP(c_List_Ofilter(_1644929, _1644933), _1644935)) = hAPP(c_List_Ofilter(_1644929, hAPP(hAPP(c_COMBS(_1644929, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1644929), c_fconj), _1644933)), _1644931)), _1644935))], (50057 ^ _781013) ^ [_1798154, _1798156, _1798158, _1798160] : [class_Orderings_Olinorder(_1798154), hBOOL(hAPP(c_Finite__Set_Ofinite(_1798154), _1798156)), 50067 ^ _781013 : [(50070 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1798154), _1798158), 50066 ^ [_1798154, _1798156, _1798158, _1798160]))], (50068 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798154), 50066 ^ [_1798154, _1798156, _1798158, _1798160]), _1798156)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1798154), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1798154), _1798158), _1798160)), hAPP(hAPP(c_Finite__Set_Ofold(_1798154, _1798154, c_Orderings_Oord__class_Omin(_1798154)), _1798160), _1798156))))], (6276 ^ _781013) ^ [_883056, _883058, _883060, _883062, _883064] : [c_Com_Ocom_OWhile(_883056, _883058) = c_Com_Ocom_OCond(_883060, _883062, _883064)], (22380 ^ _781013) ^ [_1200306] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1200306), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51194 ^ _781013) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (11756 ^ _781013) ^ [_992946, _992948, _992950, _992952, _992954] : [c_Fun_Oinj__on(_992946, _992948, _992950, c_Orderings_Otop__class_Otop(tc_fun(_992946, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_992946, _992948, _992950), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_992946, tc_HOL_Obool)), _992952), _992954)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_992948, tc_HOL_Obool)), hAPP(c_Set_Oimage(_992946, _992948, _992950), _992952)), hAPP(c_Set_Oimage(_992946, _992948, _992950), _992954)))], (47570 ^ _781013) ^ [_1740604, _1740606, _1740608, _1740610] : [47572 ^ _781013 : [(47575 ^ _781013) ^ [] : [hBOOL(hAPP(_1740608, 47571 ^ [_1740604, _1740606, _1740608, _1740610]))], (47573 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740604), 47571 ^ [_1740604, _1740606, _1740608, _1740610]), hAPP(c_List_Oset(_1740604), _1740606))))]], -(c_List_OtakeWhile(_1740604, _1740608, hAPP(hAPP(c_List_Oappend(_1740604), _1740606), _1740610)) = hAPP(hAPP(c_List_Oappend(_1740604), _1740606), c_List_OtakeWhile(_1740604, _1740608, _1740610)))], (5679 ^ _781013) ^ [_870812, _870814] : [hAPP(c_Com_Ocom_OBODY, _870812) = hAPP(c_Com_Ocom_OBODY, _870814), -(_870812 = _870814)], (38756 ^ _781013) ^ [_1527665, _1527667, _1527669, _1527671, _1527673, _1527675, _1527677] : [hAPP(hAPP(c_List_Omap(_1527665, _1527667), _1527669), _1527671) = hAPP(hAPP(c_List_Omap(_1527673, _1527667), _1527675), _1527677), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1527665)), _1527671) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1527673)), _1527677))], (34579 ^ _781013) ^ [_1436089] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436089))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1436089)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41833 ^ _781013) ^ [_1606930, _1606932, _1606934] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606930)), hAPP(hAPP(c_List_Oappend(_1606930), _1606932), _1606934)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606930)), _1606932)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606930)), _1606934)))], (48918 ^ _781013) ^ [_1772605] : [-(hAPP(c_Relation_Oconverse(_1772605, _1772605), c_Relation_OId(_1772605)) = c_Relation_OId(_1772605))], (50866 ^ _781013) ^ [_1815183, _1815185, _1815187, _1815189, _1815191] : [hBOOL(hAPP(hAPP(_1815187, _1815191), _1815189)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815183, _1815185, _1815187), _1815189), _1815191)))], (45233 ^ _781013) ^ [_1684688, _1684690, _1684692] : [class_Enum_Oenum(_1684688), class_Enum_Oenum(_1684690), 45240 ^ _781013 : [(45247 ^ _781013) ^ [] : [c_Enum_Oall__n__lists(_1684688, hAPP(hAPP(c_COMBB(tc_fun(_1684690, _1684688), tc_HOL_Obool, tc_List_Olist(_1684688)), _1684692), hAPP(hAPP(c_COMBB(tc_fun(_1684690, tc_Option_Ooption(_1684688)), tc_fun(_1684690, _1684688), tc_List_Olist(_1684688)), c_Fun_Ocomp(tc_Option_Ooption(_1684688), _1684688, _1684690, c_Option_Othe(_1684688))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1684690, _1684688)), tc_fun(_1684690, tc_Option_Ooption(_1684688)), tc_List_Olist(_1684688)), c_Map_Omap__of(_1684690, _1684688)), hAPP(c_List_Ozip(_1684690, _1684688), c_Enum_Oenum__class_Oenum(_1684690))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684690)), c_Enum_Oenum__class_Oenum(_1684690))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1684690, _1684688)), _1684692)))], (45241 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1684690, _1684688)), _1684692)), -(c_Enum_Oall__n__lists(_1684688, hAPP(hAPP(c_COMBB(tc_fun(_1684690, _1684688), tc_HOL_Obool, tc_List_Olist(_1684688)), _1684692), hAPP(hAPP(c_COMBB(tc_fun(_1684690, tc_Option_Ooption(_1684688)), tc_fun(_1684690, _1684688), tc_List_Olist(_1684688)), c_Fun_Ocomp(tc_Option_Ooption(_1684688), _1684688, _1684690, c_Option_Othe(_1684688))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1684690, _1684688)), tc_fun(_1684690, tc_Option_Ooption(_1684688)), tc_List_Olist(_1684688)), c_Map_Omap__of(_1684690, _1684688)), hAPP(c_List_Ozip(_1684690, _1684688), c_Enum_Oenum__class_Oenum(_1684690))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684690)), c_Enum_Oenum__class_Oenum(_1684690))))]]], (3628 ^ _781013) ^ [_835748, _835750, _835752, _835754, _835756, _835758, _835760, _835762, _835764, _835766, _835768, _835770] : [-(c_Product__Type_Omap__pair(_835770, _835766, _835762, _835758, _835754, _835750) = c_Product__Type_Omap__pair(_835768, _835764, _835760, _835756, _835752, _835748)), _835770 = _835768, _835766 = _835764, _835762 = _835760, _835758 = _835756, _835754 = _835752, _835750 = _835748], (22554 ^ _781013) ^ [_1203341, _1203343, _1203345, _1203347] : [class_Orderings_Oorder(_1203341), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1203341, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203341, _1203343), _1203345)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203341, _1203345), _1203347)) = c_Orderings_Obot__class_Obot(tc_fun(_1203341, tc_HOL_Obool)))], (47063 ^ _781013) ^ [_1728081, _1728083, _1728085, _1728087] : [-(hAPP(c_Relation_ORange(_1728081, _1728083), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1728081, _1728083), tc_HOL_Obool)), _1728085), _1728087)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1728083, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1728081, _1728083), _1728085)), hAPP(c_Relation_ORange(_1728081, _1728083), _1728087)))], (7729 ^ _781013) ^ [_911164, _911166, _911168] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_911164), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911164, tc_HOL_Obool)), _911166), _911168)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_911164), _911166)), hBOOL(hAPP(c_Finite__Set_Ofinite(_911164), _911168))], (47482 ^ _781013) ^ [_1738402] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 47478 ^ [_1738402]), c_Int_OInteg)))], (16231 ^ _781013) ^ [_1080948, _1080950] : [class_Groups_Ogroup__add(_1080948), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080948), hAPP(c_Groups_Ouminus__class_Ouminus(_1080948), _1080950)), _1080950) = c_Groups_Ozero__class_Ozero(_1080948))], (27861 ^ _781013) ^ [_1301278, _1301280, _1301282] : [class_Divides_Osemiring__div(_1301278), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1301278), c_Divides_Odiv__class_Omod(_1301278, _1301280, _1301282)), _1301282) = c_Groups_Ozero__class_Ozero(_1301278))], (46110 ^ _781013) ^ [_1703926, _1703928, _1703930, _1703932, _1703934, _1703936, _1703938] : [c_List_Olist__all2(_1703932, _1703928, hAPP(hAPP(c_COMBB(_1703926, tc_fun(_1703928, tc_HOL_Obool), _1703932), _1703930), _1703934), _1703936, _1703938), -(c_List_Olist__all2(_1703926, _1703928, _1703930, hAPP(hAPP(c_List_Omap(_1703932, _1703926), _1703934), _1703936), _1703938))], (6581 ^ _781013) ^ [_888669, _888671, _888673] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_888669, _888671, c_Orderings_Obot__class_Obot(tc_fun(_888669, tc_HOL_Obool))), _888673))], (26691 ^ _781013) ^ [_1277760, _1277762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277760)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1277760, _1277762)))], (51136 ^ _781013) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (43446 ^ _781013) ^ [_1646141, _1646143, _1646145, _1646147] : [-(hBOOL(hAPP(_1646141, _1646143))), -(hAPP(c_List_Ofilter(_1646145, _1646141), hAPP(hAPP(c_List_Olist_OCons(_1646145), _1646143), _1646147)) = hAPP(c_List_Ofilter(_1646145, _1646141), _1646147))], (35621 ^ _781013) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5472 ^ _781013) ^ [_864436, _864438, _864440, _864442, _864444, _864446] : [-(c_COMBC(_864446, _864442, _864438) = c_COMBC(_864444, _864440, _864436)), _864446 = _864444, _864442 = _864440, _864438 = _864436], (50806 ^ _781013) ^ [_1813635, _1813637, _1813639, _1813641, _1813643] : [-(hAPP(c_New__DSequence_Opos__bind(_1813635, _1813637, _1813639, _1813641), _1813643) = hAPP(c_Lazy__Sequence_Obind(_1813635, _1813637, hAPP(_1813639, _1813643)), hAPP(hAPP(c_COMBC(_1813635, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1813637)), _1813641), _1813643)))], (49526 ^ _781013) ^ [_1787762, _1787764, _1787766, _1787768] : [class_Orderings_Olinorder(_1787762), hBOOL(hAPP(c_Finite__Set_Ofinite(_1787762), _1787764)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1787762, _1787762, c_Orderings_Oord__class_Omax(_1787762)), _1787766), hAPP(hAPP(c_Set_Oinsert(_1787762), _1787768), _1787764)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1787762), _1787768), hAPP(hAPP(c_Finite__Set_Ofold(_1787762, _1787762, c_Orderings_Oord__class_Omax(_1787762)), _1787766), _1787764)))], (44302 ^ _781013) ^ [_1663755, _1663757, _1663759] : [-(c_List_Oconcat(_1663755, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1663755)), _1663757), _1663759)) = hAPP(hAPP(c_List_Oappend(_1663755), c_List_Oconcat(_1663755, _1663757)), c_List_Oconcat(_1663755, _1663759)))], (31682 ^ _781013) ^ [_1379665, _1379667, _1379669, _1379671, _1379673] : [-(hAPP(c_Relation_OImage(_1379665, _1379667, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1379665, _1379667), tc_HOL_Obool)), _1379669), _1379671)), _1379673) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379667, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379665, _1379667, _1379669), _1379673)), hAPP(c_Relation_OImage(_1379665, _1379667, _1379671), _1379673)))], (23441 ^ _781013) ^ [_1219586, _1219588, _1219590, _1219592] : [class_Fields_Ofield__inverse__zero(_1219586), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1219586), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219586), _1219588), _1219590)), _1219592) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219586), hAPP(hAPP(c_Power_Opower__class_Opower(_1219586), _1219588), _1219592)), hAPP(hAPP(c_Power_Opower__class_Opower(_1219586), _1219590), _1219592)))], (35823 ^ _781013) ^ [] : [-(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)))))], (43117 ^ _781013) ^ [_1638520, _1638522, _1638524, _1638526, _1638528] : [class_Complete__Lattice_Ocomplete__lattice(_1638520), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1638522, tc_HOL_Obool)), _1638524), _1638526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1638520), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638522, _1638520), _1638526), _1638528)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638522, _1638520), _1638524), _1638528))))], (43498 ^ _781013) ^ [_1647414, _1647416, _1647418] : [-(c_List_Olistsp(_1647414, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1647414, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1647414, tc_fun(_1647414, tc_HOL_Obool), tc_HOL_Obool), c_member(_1647414)), _1647416)), hAPP(hAPP(c_COMBC(_1647414, tc_fun(_1647414, tc_HOL_Obool), tc_HOL_Obool), c_member(_1647414)), _1647418))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1647414), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1647414), tc_fun(tc_List_Olist(_1647414), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1647414))), c_List_Olists(_1647414, _1647416))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1647414), tc_fun(tc_List_Olist(_1647414), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1647414))), c_List_Olists(_1647414, _1647418))))], (35317 ^ _781013) ^ [_1449182, _1449184, _1449186] : [class_Int_Onumber__ring(_1449182), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1449182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1449182), _1449184), _1449186)), 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(_1449182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1449182), hAPP(hAPP(c_Power_Opower__class_Opower(_1449182), _1449184), 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(_1449182), _1449186), 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(_1449182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1449182), hAPP(c_Int_Onumber__class_Onumber__of(_1449182), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1449184)), _1449186)))], (39080 ^ _781013) ^ [_1535194, _1535196] : [hBOOL(hAPP(c_List_Odistinct(_1535194), _1535196)), 39083 ^ _781013 : [(39084 ^ _781013) ^ [_1535326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1535326), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1535194)), _1535196))), 39087 ^ _781013 : [(39088 ^ _781013) ^ [_1535453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1535453), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1535194)), _1535196))), -(_1535326 = _1535453), hAPP(hAPP(c_List_Onth(_1535194), _1535196), _1535326) = hAPP(hAPP(c_List_Onth(_1535194), _1535196), _1535453)]]]]], (29829 ^ _781013) ^ [_1337272, _1337274, _1337276] : [class_Orderings_Olinorder(_1337272), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337272), _1337274)), -(_1337276 = c_Orderings_Obot__class_Obot(tc_fun(_1337272, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1337272, tc_HOL_Obool)), _1337276), _1337274)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1337272), c_Big__Operators_Olattice_OInf__fin(_1337272, c_Orderings_Oord__class_Omin(_1337272), _1337276)), c_Big__Operators_Olattice_OInf__fin(_1337272, c_Orderings_Oord__class_Omin(_1337272), _1337274)) = c_Big__Operators_Olattice_OInf__fin(_1337272, c_Orderings_Oord__class_Omin(_1337272), _1337274))], (40241 ^ _781013) ^ [_1565811, _1565813, _1565815] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1565811, tc_HOL_Obool)), hAPP(c_List_Oset(_1565811), _1565813)), hAPP(c_List_Oset(_1565811), hAPP(hAPP(c_List_Olist_OCons(_1565811), _1565815), _1565813)))))], (17078 ^ _781013) ^ [_1098551, _1098553, _1098555] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1098551), _1098553)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098551), _1098555)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1098551, tc_HOL_Obool)), _1098553), _1098555) = c_Orderings_Obot__class_Obot(tc_fun(_1098551, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1098551), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1098551, tc_HOL_Obool)), _1098553), _1098555)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1098551), _1098553)), hAPP(c_Finite__Set_Ocard(_1098551), _1098555)))], (8032 ^ _781013) ^ [_917447, _917449, _917451] : [-(hAPP(hAPP(c_Set_Oinsert(_917447), _917449), _917451) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917447, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_917447), _917449), c_Orderings_Obot__class_Obot(tc_fun(_917447, tc_HOL_Obool)))), _917451))], (15009 ^ _781013) ^ [_1058574, _1058576] : [class_Groups_Olinordered__ab__group__add(_1058574), 15012 ^ _781013 : [(15019 ^ _781013) ^ [] : [_1058576 = c_Groups_Ozero__class_Ozero(_1058574), -(_1058576 = hAPP(c_Groups_Ouminus__class_Ouminus(_1058574), _1058576))], (15013 ^ _781013) ^ [] : [_1058576 = hAPP(c_Groups_Ouminus__class_Ouminus(_1058574), _1058576), -(_1058576 = c_Groups_Ozero__class_Ozero(_1058574))]]], (29785 ^ _781013) ^ [_1336529, _1336531, _1336533] : [class_Orderings_Olinorder(_1336529), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336529), _1336531)), hBOOL(hAPP(hAPP(c_member(_1336529), _1336533), _1336531)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1336529), _1336533), c_Big__Operators_Olattice_OInf__fin(_1336529, c_Orderings_Oord__class_Omin(_1336529), _1336531)) = c_Big__Operators_Olattice_OInf__fin(_1336529, c_Orderings_Oord__class_Omin(_1336529), _1336531))], (33014 ^ _781013) ^ [_1407427, _1407429, _1407431, _1407433] : [class_Fields_Olinordered__field__inverse__zero(_1407427), class_Int_Onumber(_1407427), 33021 ^ _781013 : [(33022 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407427), _1407429), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1407427), _1407431), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433)))), 33025 ^ _781013 : [(33032 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407427), c_Groups_Ozero__class_Ozero(_1407427)), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433)))), 33035 ^ _781013 : [(33042 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407427), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433)), c_Groups_Ozero__class_Ozero(_1407427)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407427), _1407429), c_Groups_Ozero__class_Ozero(_1407427))))], (33036 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407427), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433)), c_Groups_Ozero__class_Ozero(_1407427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407427), _1407431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1407427), _1407429), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433)))))]]], (33026 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407427), c_Groups_Ozero__class_Ozero(_1407427)), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1407427), _1407429), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433))), _1407431)))]]], (33048 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407427), _1407429), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1407427), _1407431), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433))))), 33051 ^ _781013 : [(33054 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1407427), _1407429), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433))), _1407431))], (33052 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407427), c_Groups_Ozero__class_Ozero(_1407427)), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433))))]], 33055 ^ _781013 : [(33058 ^ _781013) ^ [] : [33059 ^ _781013 : [(33062 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407427), _1407431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1407427), _1407429), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433))))], (33060 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407427), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433)), c_Groups_Ozero__class_Ozero(_1407427))))]], 33063 ^ _781013 : [(33066 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407427), _1407429), c_Groups_Ozero__class_Ozero(_1407427)))], (33064 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407427), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433)), c_Groups_Ozero__class_Ozero(_1407427)))]]], (33056 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407427), c_Groups_Ozero__class_Ozero(_1407427)), hAPP(c_Int_Onumber__class_Onumber__of(_1407427), _1407433)))]]]]], (28904 ^ _781013) ^ [_1320288, _1320290] : [class_Groups_Oordered__ab__group__add__abs(_1320288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320288), c_Groups_Ozero__class_Ozero(_1320288)), _1320290)), -(hAPP(c_Groups_Oabs__class_Oabs(_1320288), _1320290) = _1320290)], (36222 ^ _781013) ^ [_1471070, _1471072] : [-(_1471070 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1471072, _1471070), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1471072), _1471070)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1471072, _1471070)))))], (20177 ^ _781013) ^ [_1158257, _1158259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158259)), _1158257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158257), _1158259))], (9739 ^ _781013) ^ [_953119, _953121, _953123, _953125, _953127] : [-(c_Map_Omap__add(_953119, _953121, _953123, c_Map_Omap__add(_953119, _953121, _953125, _953127)) = c_Map_Omap__add(_953119, _953121, c_Map_Omap__add(_953119, _953121, _953123, _953125), _953127))], (12908 ^ _781013) ^ [_1015393, _1015395, _1015397, _1015399, _1015401] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1015393, _1015395, _1015397), _1015399), _1015401), c_Orderings_Obot__class_Obot(tc_fun(_1015395, tc_HOL_Obool))) = _1015401)], (47021 ^ _781013) ^ [] : [-(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))))], (11293 ^ _781013) ^ [_982792, _982794, _982796, _982798, _982800, _982802, _982804] : [c_Nitpick_Ofold__graph_H(_982792, _982794, _982796, _982798, _982800, hAPP(hAPP(_982796, _982802), _982804)), 11298 ^ _781013 : [(11301 ^ _781013) ^ [] : [-(hAPP(hAPP(_982796, _982802), _982804) = _982798)], (11299 ^ _781013) ^ [] : [-(_982800 = c_Orderings_Obot__class_Obot(tc_fun(_982792, tc_HOL_Obool)))]], 11304 ^ _781013 : [(11309 ^ _781013) ^ [] : [-(c_Nitpick_Ofold__graph_H(_982792, _982794, _982796, _982798, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982792, tc_HOL_Obool)), _982800), hAPP(hAPP(c_Set_Oinsert(_982792), 11302 ^ [_982792, _982794, _982796, _982798, _982800, _982802, _982804]), c_Orderings_Obot__class_Obot(tc_fun(_982792, tc_HOL_Obool)))), 11303 ^ [_982792, _982794, _982796, _982798, _982800, _982802, _982804]))], (11307 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_982792), 11302 ^ [_982792, _982794, _982796, _982798, _982800, _982802, _982804]), _982800)))], (11305 ^ _781013) ^ [] : [-(hAPP(hAPP(_982796, _982802), _982804) = hAPP(hAPP(_982796, 11302 ^ [_982792, _982794, _982796, _982798, _982800, _982802, _982804]), 11303 ^ [_982792, _982794, _982796, _982798, _982800, _982802, _982804]))]]], (7595 ^ _781013) ^ [_908345, _908347, _908349, _908351, _908353, _908355, _908357] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_908345), tc_Option_Ooption(_908347), _908349, hAPP(c_Option_Omap(_908345, _908347), _908351)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_908349, tc_Option_Ooption(_908345)), _908353), _908355), hAPP(c_Option_Ooption_OSome(_908345), _908357))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_908349, tc_Option_Ooption(_908347)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_908345), tc_Option_Ooption(_908347), _908349, hAPP(c_Option_Omap(_908345, _908347), _908351)), _908353)), _908355), hAPP(c_Option_Ooption_OSome(_908347), hAPP(_908351, _908357))))], (41518 ^ _781013) ^ [_1599948, _1599950, _1599952, _1599954, _1599956, _1599958] : [-(hAPP(c_List_Olist_Olist__case(_1599948, _1599950, _1599952, _1599954), hAPP(hAPP(c_List_Olist_OCons(_1599950), _1599956), _1599958)) = hAPP(hAPP(_1599954, _1599956), _1599958))], (6872 ^ _781013) ^ [_894418, _894420] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894418, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_894418, tc_HOL_Obool))), _894420)))], (19815 ^ _781013) ^ [_1152309, _1152311] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152309), _1152311))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1152309), _1152311)), -(_1152309 = _1152311)], (26219 ^ _781013) ^ [_1268543, _1268545, _1268547, _1268549] : [class_Orderings_Oorder(_1268543), 26222 ^ _781013 : [(26231 ^ _781013) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1268543, _1268545, _1268547) = hAPP(hAPP(c_Set_Oinsert(_1268543), _1268549), c_Orderings_Obot__class_Obot(tc_fun(_1268543, tc_HOL_Obool)))), _1268545 = _1268547, _1268547 = _1268549], (26223 ^ _781013) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1268543, _1268545, _1268547) = hAPP(hAPP(c_Set_Oinsert(_1268543), _1268549), c_Orderings_Obot__class_Obot(tc_fun(_1268543, tc_HOL_Obool))), 26226 ^ _781013 : [(26229 ^ _781013) ^ [] : [-(_1268547 = _1268549)], (26227 ^ _781013) ^ [] : [-(_1268545 = _1268547)]]]]], (23206 ^ _781013) ^ [_1215017, _1215019, _1215021] : [hBOOL(hAPP(_1215017, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1215019), _1215021))), 23209 ^ _781013 : [(23216 ^ _781013) ^ [] : [-(_1215021 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 23219 ^ _781013 : [(23220 ^ _781013) ^ [_1215269, _1215271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1215269), _1215021)), _1215019 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215021), _1215271)), _1215269), -(hBOOL(hAPP(_1215017, _1215271)))]]], (23210 ^ _781013) ^ [] : [_1215021 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1215017, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (40976 ^ _781013) ^ [_1587658, _1587660, _1587662, _1587664] : [-(c_Product__Type_Oapsnd(_1587658, _1587660, _1587662, _1587664) = c_Product__Type_Omap__pair(_1587662, _1587662, _1587658, _1587660, c_Fun_Oid(_1587662), _1587664))], (27083 ^ _781013) ^ [_1285245] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1285245) = 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), _1285245))))], (10799 ^ _781013) ^ [_971774, _971776, _971778, _971780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971774, tc_HOL_Obool)), _971776), _971778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971774, tc_HOL_Obool)), _971776), _971780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971774, tc_HOL_Obool)), _971776), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971774, tc_HOL_Obool)), _971778), _971780))))], (23114 ^ _781013) ^ [_1213465] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213465), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1213465)], (35729 ^ _781013) ^ [_1456716, _1456718] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1456716), _1456718) = c_Groups_Oone__class_Oone(tc_Int_Oint), 35734 ^ _781013 : [(35737 ^ _781013) ^ [] : [-(_1456718 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35735 ^ _781013) ^ [] : [-(_1456716 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 35738 ^ _781013 : [(35741 ^ _781013) ^ [] : [-(_1456718 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35739 ^ _781013) ^ [] : [-(_1456716 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (19791 ^ _781013) ^ [_1152003, _1152005] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1152003), _1152005) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1152003), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1152005)))], (28972 ^ _781013) ^ [_1321534, _1321536, _1321538] : [class_Groups_Oordered__ab__group__add__abs(_1321534), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1321534), hAPP(c_Groups_Oabs__class_Oabs(_1321534), _1321536)), hAPP(c_Groups_Oabs__class_Oabs(_1321534), _1321538))), hAPP(c_Groups_Oabs__class_Oabs(_1321534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1321534), _1321536), _1321538)))))], (37518 ^ _781013) ^ [_1497376, _1497378, _1497380] : [-(hAPP(c_Product__Type_Ofst(_1497376, _1497378), _1497380) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1497376, _1497378, _1497376), c_COMBK(_1497376, _1497378)), _1497380))], (34267 ^ _781013) ^ [_1430974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1430974))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1430974)))], (43819 ^ _781013) ^ [_1653694, _1653696, _1653698, _1653700] : [class_Orderings_Olinorder(_1653694), 43822 ^ _781013 : [(43831 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1653694, hAPP(hAPP(c_List_Olist_OCons(_1653694), _1653696), hAPP(hAPP(c_List_Olist_OCons(_1653694), _1653698), _1653700)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1653694), _1653696), _1653698)), c_List_Olinorder__class_Osorted(_1653694, hAPP(hAPP(c_List_Olist_OCons(_1653694), _1653698), _1653700))], (43823 ^ _781013) ^ [] : [c_List_Olinorder__class_Osorted(_1653694, hAPP(hAPP(c_List_Olist_OCons(_1653694), _1653696), hAPP(hAPP(c_List_Olist_OCons(_1653694), _1653698), _1653700))), 43826 ^ _781013 : [(43829 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1653694, hAPP(hAPP(c_List_Olist_OCons(_1653694), _1653698), _1653700)))], (43827 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1653694), _1653696), _1653698)))]]]]], (2240 ^ _781013) ^ [_814064, _814066, _814068, _814070, _814072, _814074, _814076, _814078] : [-(c_Sum__Type_OPlus(_814078, _814074, _814070, _814066) = c_Sum__Type_OPlus(_814076, _814072, _814068, _814064)), _814078 = _814076, _814074 = _814072, _814070 = _814068, _814066 = _814064], (47842 ^ _781013) ^ [_1747485, _1747487, _1747489, _1747491] : [c_List_Olist__ex(_1747485, _1747487, hAPP(hAPP(c_List_Oappend(_1747485), _1747489), _1747491)), -(c_List_Olist__ex(_1747485, _1747487, _1747489)), -(c_List_Olist__ex(_1747485, _1747487, _1747491))], (3888 ^ _781013) ^ [_839842, _839844, _839846, _839848, _839850, _839852] : [-(c_Random_Ominus__shift(_839852, _839848, _839844) = c_Random_Ominus__shift(_839850, _839846, _839842)), _839852 = _839850, _839848 = _839846, _839844 = _839842], (10787 ^ _781013) ^ [_971454, _971456, _971458, _971460] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971454, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_971454), _971456), _971458)), hAPP(hAPP(c_Set_Oinsert(_971454), _971456), _971460)) = hAPP(hAPP(c_Set_Oinsert(_971454), _971456), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971454, tc_HOL_Obool)), _971458), _971460)))], (35267 ^ _781013) ^ [_1448267, _1448269, _1448271] : [class_Rings_Olinordered__idom(_1448267), 35270 ^ _781013 : [(35279 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1448267), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1448267), hAPP(hAPP(c_Power_Opower__class_Opower(_1448267), _1448269), 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(_1448267), _1448271), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1448267)))), _1448269 = c_Groups_Ozero__class_Ozero(_1448267), _1448271 = c_Groups_Ozero__class_Ozero(_1448267)], (35271 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1448267), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1448267), hAPP(hAPP(c_Power_Opower__class_Opower(_1448267), _1448269), 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(_1448267), _1448271), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1448267))), 35274 ^ _781013 : [(35277 ^ _781013) ^ [] : [-(_1448271 = c_Groups_Ozero__class_Ozero(_1448267))], (35275 ^ _781013) ^ [] : [-(_1448269 = c_Groups_Ozero__class_Ozero(_1448267))]]]]], (22470 ^ _781013) ^ [_1201764, _1201766, _1201768] : [class_Orderings_Oorder(_1201764), 22473 ^ _781013 : [(22480 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201764), _1201766), _1201768))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1201764, _1201766), _1201768) = c_Orderings_Obot__class_Obot(tc_fun(_1201764, tc_HOL_Obool)))], (22474 ^ _781013) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1201764, _1201766), _1201768) = c_Orderings_Obot__class_Obot(tc_fun(_1201764, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201764), _1201766), _1201768))]]], (37744 ^ _781013) ^ [_1502235, _1502237] : [-(c_FunDef_Orp__inv__image(_1502235, _1502237) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool), tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool), tc_fun(tc_fun(_1502237, _1502235), tc_prod(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool), tc_fun(tc_fun(_1502237, _1502235), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool), tc_fun(tc_fun(_1502237, _1502235), tc_prod(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1502237, _1502235), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)), tc_fun(tc_fun(_1502237, _1502235), tc_prod(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool), tc_fun(tc_fun(_1502237, _1502235), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool), tc_fun(tc_fun(_1502237, _1502235), tc_prod(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool))))), tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1502237, _1502235), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)), tc_fun(tc_fun(_1502237, _1502235), tc_prod(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool))), tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1502237, _1502235), tc_fun(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1502237, _1502235), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)), tc_fun(tc_fun(_1502237, _1502235), tc_prod(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)))), tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool)), c_COMBS(tc_fun(_1502237, _1502235), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1502237, _1502235), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)), tc_fun(tc_fun(_1502237, _1502235), tc_fun(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)))), tc_fun(tc_prod(_1502235, _1502235), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool))), tc_fun(_1502237, _1502235)), c_Product__Type_OPair(tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool), tc_fun(tc_prod(_1502237, _1502237), tc_HOL_Obool)))), c_Relation_Oinv__image(_1502235, _1502237))))), c_Relation_Oinv__image(_1502235, _1502237))))], (35241 ^ _781013) ^ [_1447730, _1447732, _1447734] : [class_Rings_Oring__1(_1447730), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1447730), hAPP(c_Groups_Ouminus__class_Ouminus(_1447730), _1447732)), 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)))), _1447734)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1447730), _1447732), 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)))), _1447734)))], (29139 ^ _781013) ^ [_1324432, _1324434] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1324432, _1324434)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1324432), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1324434)))], (38057 ^ _781013) ^ [_1510201, _1510203, _1510205, _1510207] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1510201, _1510201)), hAPP(hAPP(c_Product__Type_OPair(_1510201, _1510201), _1510203), _1510205)), c_Relation_OId__on(_1510201, _1510207))), 38060 ^ _781013 : [(38063 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1510201), _1510203), _1510207)))], (38061 ^ _781013) ^ [] : [-(_1510203 = _1510205)]]], (50388 ^ _781013) ^ [_1805558, _1805560, _1805562] : [50390 ^ _781013 : [(50393 ^ _781013) ^ [] : [hBOOL(hAPP(_1805560, 50389 ^ [_1805558, _1805560, _1805562]))], (50391 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805558), 50389 ^ [_1805558, _1805560, _1805562]), hAPP(c_List_Oset(_1805558), _1805562))))]], -(c_List_Olist__all(_1805558, _1805560, _1805562))], (2540 ^ _781013) ^ [_818700, _818702] : [_818702 = _818700, -(c_Nat_Osemiring__1__class_ONats(_818702) = c_Nat_Osemiring__1__class_ONats(_818700))], (20003 ^ _781013) ^ [_1155573, _1155575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1155573)), _1155575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155573), _1155575)))], (5803 ^ _781013) ^ [_873813, _873815, _873817, _873819, _873821, _873823] : [c_Hoare__Mirabelle_Ohoare__derivs(_873813, _873815, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873813)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873813), _873817), _873819), _873821)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873813), tc_HOL_Obool)))), 5810 ^ _781013 : [(5813 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_873823, 5808 ^ [_873813, _873815, _873817, _873819, _873821, _873823]), 5809 ^ [_873813, _873815, _873817, _873819, _873821, _873823]))], (5811 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_873821, 5808 ^ [_873813, _873815, _873817, _873819, _873821, _873823]), 5809 ^ [_873813, _873815, _873817, _873819, _873821, _873823])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_873813, _873815, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873813)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873813), _873817), _873819), _873823)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873813), tc_HOL_Obool)))))], (39647 ^ _781013) ^ [_1548517, _1548519, _1548521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1548517)), _1548519)), _1548521)), -(hAPP(hAPP(c_List_Otake(_1548517), _1548521), _1548519) = _1548519)], (6464 ^ _781013) ^ [_886734, _886736, _886738, _886740] : [c_Finite__Set_Ofolding__one(_886734, _886736, _886738), -(hAPP(_886738, hAPP(hAPP(c_Set_Oinsert(_886734), _886740), c_Orderings_Obot__class_Obot(tc_fun(_886734, tc_HOL_Obool)))) = _886740)], (11103 ^ _781013) ^ [_978599, _978601, _978603, _978605] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978599, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978599, tc_HOL_Obool)), _978601), _978603)), _978605) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978599, tc_HOL_Obool)), _978601), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978599, tc_HOL_Obool)), _978603), _978605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978599, tc_HOL_Obool)), _978605), _978601)))], (43020 ^ _781013) ^ [_1635798, _1635800, _1635802, _1635804, _1635806, _1635808] : [class_Complete__Lattice_Ocomplete__lattice(_1635798), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635800, tc_fun(_1635802, _1635798)), _1635804), _1635806), _1635808) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635800, _1635798), _1635804), hAPP(hAPP(c_COMBC(_1635800, _1635802, _1635798), _1635806), _1635808)))], (26407 ^ _781013) ^ [_1272084, _1272086, _1272088, _1272090] : [class_Orderings_Oorder(_1272084), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1272084, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1272084, _1272086, _1272088)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1272084, _1272088, _1272090)) = c_Orderings_Obot__class_Obot(tc_fun(_1272084, tc_HOL_Obool)))], (19989 ^ _781013) ^ [_1155333] : [hAPP(c_Nat_OSuc, _1155333) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17877 ^ _781013) ^ [_1114595, _1114597, _1114599] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1114595), _1114597)), _1114599) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1114595), _1114599)), _1114597))], (10311 ^ _781013) ^ [_963443, _963445, _963447] : [class_Lattices_Olattice(_963443), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963443), _963445), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_963443), _963445), _963447)) = _963445)], (4708 ^ _781013) ^ [_852240, _852242] : [_852242 = _852240, -(c_Lazy__Sequence_Ohit__bound(_852242) = c_Lazy__Sequence_Ohit__bound(_852240))], (4002 ^ _781013) ^ [_841577, _841579, _841581, _841583] : [-(c_List_Olistrel(_841583, _841579) = c_List_Olistrel(_841581, _841577)), _841583 = _841581, _841579 = _841577], (50766 ^ _781013) ^ [_1812798, _1812800, _1812802, _1812804, _1812806] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1812798, _1812800, _1812802) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1812798, _1812804, _1812806), 50769 ^ _781013 : [(50772 ^ _781013) ^ [] : [-(_1812802 = _1812806)], (50770 ^ _781013) ^ [] : [-(_1812800 = _1812804)]]], (40717 ^ _781013) ^ [_1579513, _1579515, _1579517, _1579519] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579513, _1579515)), hAPP(hAPP(c_Product__Type_OSigma(_1579513, _1579515), _1579517), hAPP(c_COMBK(tc_fun(_1579515, tc_HOL_Obool), _1579513), _1579519)))), -(_1579519 = c_Orderings_Obot__class_Obot(tc_fun(_1579515, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1579513), _1579517)))], (19522 ^ _781013) ^ [_1146343, _1146345, _1146347, _1146349] : [class_Groups_Omonoid__mult(_1146343), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1146343), _1146345), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1146347), _1146349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146343), hAPP(hAPP(c_Power_Opower__class_Opower(_1146343), _1146345), _1146347)), hAPP(hAPP(c_Power_Opower__class_Opower(_1146343), _1146345), _1146349)))], (43490 ^ _781013) ^ [_1647189, _1647191, _1647193] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1647189)), _1647193), c_List_Olists(_1647189, _1647191))), -(hBOOL(hAPP(c_List_Olistsp(_1647189, hAPP(hAPP(c_COMBC(_1647189, tc_fun(_1647189, tc_HOL_Obool), tc_HOL_Obool), c_member(_1647189)), _1647191)), _1647193)))], (38288 ^ _781013) ^ [] : [-(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))], (51180 ^ _781013) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (39880 ^ _781013) ^ [_1556347, _1556349, _1556351, _1556353] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1556347), tc_List_Olist(_1556347))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1556347), tc_List_Olist(_1556347)), _1556349), _1556351)), c_List_Olistrel(_1556347, _1556353)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1556347)), _1556349) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1556347)), _1556351), 39886 ^ _781013 : [(39889 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1556347, _1556347, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1556347, tc_fun(tc_prod(_1556347, _1556347), tc_HOL_Obool), tc_fun(_1556347, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1556347, tc_fun(tc_fun(tc_prod(_1556347, _1556347), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1556347, _1556347), tc_HOL_Obool), tc_fun(_1556347, tc_HOL_Obool)), _1556347), c_COMBC(_1556347, tc_fun(tc_prod(_1556347, _1556347), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1556347, tc_prod(_1556347, _1556347)), tc_fun(_1556347, tc_fun(tc_fun(tc_prod(_1556347, _1556347), tc_HOL_Obool), tc_HOL_Obool)), _1556347), hAPP(c_COMBB(tc_prod(_1556347, _1556347), tc_fun(tc_fun(tc_prod(_1556347, _1556347), tc_HOL_Obool), tc_HOL_Obool), _1556347), c_member(tc_prod(_1556347, _1556347)))), c_Product__Type_OPair(_1556347, _1556347)))), _1556353)), 39885 ^ [_1556347, _1556349, _1556351, _1556353]))], (39887 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556347, _1556347)), 39885 ^ [_1556347, _1556349, _1556351, _1556353]), hAPP(c_List_Oset(tc_prod(_1556347, _1556347)), hAPP(hAPP(c_List_Ozip(_1556347, _1556347), _1556349), _1556351)))))]]], (14550 ^ _781013) ^ [_1051188, _1051190, _1051192] : [14551 ^ _781013 : [(14554 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051188), hAPP(c_Set_OCollect(_1051188), _1051192)))], (14552 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051188), hAPP(c_Set_OCollect(_1051188), _1051190)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1051188), hAPP(c_Set_OCollect(_1051188), hAPP(hAPP(c_COMBS(_1051188, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1051188), c_fconj), _1051190)), _1051192)))))], (35043 ^ _781013) ^ [_1444407, _1444409, _1444411] : [class_Groups_Omonoid__mult(_1444407), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1444407), _1444409), 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)))), _1444411)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1444407), hAPP(hAPP(c_Power_Opower__class_Opower(_1444407), _1444409), _1444411)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (1654 ^ _781013) ^ [_804430, _804432] : [-(class_Rings_Ocomm__semiring(_804430)), _804432 = _804430, class_Rings_Ocomm__semiring(_804432)], (44637 ^ _781013) ^ [_1672404, _1672406, _1672408] : [class_Orderings_Olinorder(_1672404), c_List_Olinorder__class_Osorted(_1672404, _1672406), -(c_List_Olinorder__class_Osorted(_1672404, c_List_OtakeWhile(_1672404, _1672408, _1672406)))], (41879 ^ _781013) ^ [_1608103, _1608105, _1608107, _1608109] : [-(hAPP(hAPP(c_List_Otake(_1608103), _1608105), hAPP(hAPP(c_List_Oappend(_1608103), _1608107), _1608109)) = hAPP(hAPP(c_List_Oappend(_1608103), hAPP(hAPP(c_List_Otake(_1608103), _1608105), _1608107)), hAPP(hAPP(c_List_Otake(_1608103), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1608105), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608103)), _1608107))), _1608109)))], (3608 ^ _781013) ^ [_835450, _835452, _835454, _835456] : [-(c_List_Olexn(_835456, _835452) = c_List_Olexn(_835454, _835450)), _835456 = _835454, _835452 = _835450], (21593 ^ _781013) ^ [_1186514, _1186516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186514), _1186516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186514)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186516))))], (23407 ^ _781013) ^ [_1218880, _1218882, _1218884, _1218886, _1218888] : [class_Fields_Ofield(_1218880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1218882), _1218884)), -(hAPP(_1218886, _1218888) = c_Groups_Ozero__class_Ozero(_1218880)), 23418 ^ _781013 : [(23425 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1218882), _1218888), _1218884))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1218882, _1218880), _1218886), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1218882, tc_HOL_Obool)), _1218884), hAPP(hAPP(c_Set_Oinsert(_1218882), _1218888), c_Orderings_Obot__class_Obot(tc_fun(_1218882, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1218882, _1218880), _1218886), _1218884))], (23419 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1218882), _1218888), _1218884)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1218882, _1218880), _1218886), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1218882, tc_HOL_Obool)), _1218884), hAPP(hAPP(c_Set_Oinsert(_1218882), _1218888), c_Orderings_Obot__class_Obot(tc_fun(_1218882, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218880), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1218882, _1218880), _1218886), _1218884)), hAPP(_1218886, _1218888)))]]], (27595 ^ _781013) ^ [_1296043, _1296045] : [class_Divides_Osemiring__div(_1296043), -(c_Divides_Odiv__class_Omod(_1296043, _1296045, c_Groups_Ozero__class_Ozero(_1296043)) = _1296045)], (1244 ^ _781013) ^ [_799305, _799307] : [-(class_Rings_Oring(_799305)), _799307 = _799305, class_Rings_Oring(_799307)], (48928 ^ _781013) ^ [_1772767, _1772769] : [-(hAPP(c_Relation_OImage(_1772767, _1772767, c_Relation_OId(_1772767)), _1772769) = _1772769)], (44631 ^ _781013) ^ [_1672336, _1672338, _1672340, _1672342, _1672344] : [-(hBOOL(hAPP(_1672336, _1672338))), -(c_List_OtakeWhile(_1672340, _1672336, hAPP(hAPP(c_List_Oappend(_1672340), _1672342), hAPP(hAPP(c_List_Olist_OCons(_1672340), _1672338), _1672344))) = c_List_OtakeWhile(_1672340, _1672336, _1672342))], (13289 ^ _781013) ^ [_1023238, _1023240, _1023242, _1023244, _1023246, _1023248, _1023250] : [c_Big__Operators_Ocomm__monoid__big(_1023238, _1023240, _1023242, _1023244, _1023246), 13292 ^ _781013 : [(13299 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1023240), _1023248))), -(hAPP(hAPP(_1023246, _1023250), _1023248) = _1023244)], (13293 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1023240), _1023248)), -(hAPP(hAPP(_1023246, _1023250), _1023248) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1023238, _1023240, _1023242), _1023250), _1023244), _1023248))]]], (30715 ^ _781013) ^ [_1356039, _1356041] : [class_Orderings_Olinorder(_1356039), -(c_Big__Operators_Olattice_OSup__fin(_1356039, c_Orderings_Oord__class_Omax(_1356039), hAPP(hAPP(c_Set_Oinsert(_1356039), _1356041), c_Orderings_Obot__class_Obot(tc_fun(_1356039, tc_HOL_Obool)))) = _1356041)], (17304 ^ _781013) ^ [_1103515, _1103517, _1103519, _1103521, _1103523, _1103525] : [class_Groups_Ocomm__monoid__add(_1103515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1103517), _1103519)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1103517, _1103515), _1103521), _1103519) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1103523, _1103515), hAPP(hAPP(c_COMBB(tc_fun(_1103517, tc_HOL_Obool), _1103515, _1103523), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1103517, _1103515), _1103521)), hAPP(hAPP(c_COMBB(tc_fun(_1103517, tc_HOL_Obool), tc_fun(_1103517, tc_HOL_Obool), _1103523), c_Set_OCollect(_1103517)), hAPP(hAPP(c_COMBB(tc_fun(_1103517, tc_HOL_Obool), tc_fun(_1103517, tc_HOL_Obool), _1103523), hAPP(c_COMBS(_1103517, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1103517), c_fconj), hAPP(hAPP(c_COMBC(_1103517, tc_fun(_1103517, tc_HOL_Obool), tc_HOL_Obool), c_member(_1103517)), _1103519)))), hAPP(c_COMBC(_1103517, _1103523, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1103523, tc_fun(_1103523, tc_HOL_Obool), _1103517), c_fequal), _1103525)))))), hAPP(c_Set_Oimage(_1103517, _1103523, _1103525), _1103519)))], (44930 ^ _781013) ^ [_1678152, _1678154, _1678156, _1678158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678152), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678154)), c_List_OdropWhile(_1678154, _1678156, _1678158)))), -(hAPP(hAPP(c_List_Onth(_1678154), c_List_OdropWhile(_1678154, _1678156, _1678158)), _1678152) = hAPP(hAPP(c_List_Onth(_1678154), _1678158), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1678152), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678154)), c_List_OtakeWhile(_1678154, _1678156, _1678158)))))], (50131 ^ _781013) ^ [_1799913, _1799915] : [-(c_Wellfounded_Owf(_1799913, _1799915)), 50134 ^ _781013 : [(50137 ^ _781013) ^ [_1800133] : [hBOOL(hAPP(hAPP(c_member(_1799913), _1800133), 50132 ^ [_1799913, _1799915])), 50141 ^ _781013 : [(50144 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1799913), 50140 ^ [_1799913, _1799915, _1800133]), 50132 ^ [_1799913, _1799915])))], (50142 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1799913, _1799913)), hAPP(hAPP(c_Product__Type_OPair(_1799913, _1799913), 50140 ^ [_1799913, _1799915, _1800133]), _1800133)), _1799915)))]]], (50135 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1799913), 50133 ^ [_1799913, _1799915]), 50132 ^ [_1799913, _1799915])))]]], (14921 ^ _781013) ^ [_1057280, _1057282] : [class_Groups_Ogroup__add(_1057280), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057280), _1057282), c_Groups_Ozero__class_Ozero(_1057280)) = _1057282)], (22286 ^ _781013) ^ [_1198795, _1198797, _1198799, _1198801, _1198803] : [class_Orderings_Olinorder(_1198795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198795), _1198797), _1198799)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198795), _1198801), _1198803)), 22297 ^ _781013 : [(22306 ^ _781013) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1198795, _1198797), _1198799) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1198795, _1198801), _1198803)), _1198797 = _1198801, _1198799 = _1198803], (22298 ^ _781013) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1198795, _1198797), _1198799) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1198795, _1198801), _1198803), 22301 ^ _781013 : [(22304 ^ _781013) ^ [] : [-(_1198799 = _1198803)], (22302 ^ _781013) ^ [] : [-(_1198797 = _1198801)]]]]], (4116 ^ _781013) ^ [_843266, _843268] : [_843268 = _843266, -(c_Nat_Ofunpow(_843268) = c_Nat_Ofunpow(_843266))], (11357 ^ _781013) ^ [_984400, _984402, _984404, _984406, _984408] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_984400, _984402, hAPP(hAPP(c_Set_Oinsert(_984400), _984404), _984406)), _984408))), 11358 ^ _781013 : [(11359 ^ _781013) ^ [_984504, _984506] : [hAPP(hAPP(c_Set_Oinsert(_984400), _984404), _984406) = hAPP(hAPP(c_Set_Oinsert(_984400), _984506), _984504), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_984400, _984400, _984402, _984506, _984504), _984408)), -(hBOOL(hAPP(hAPP(c_member(_984400), _984506), _984504)))]]], (35771 ^ _781013) ^ [] : [-(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))], (12400 ^ _781013) ^ [_1004851, _1004853, _1004855] : [class_Lattices_Olattice(_1004851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004851), _1004853)), -(hBOOL(hAPP(hAPP(c_member(_1004851), _1004855), _1004853))), -(_1004853 = c_Orderings_Obot__class_Obot(tc_fun(_1004851, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1004851, hAPP(hAPP(c_Set_Oinsert(_1004851), _1004855), _1004853)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004851), _1004855), c_Big__Operators_Olattice__class_OSup__fin(_1004851, _1004853)))], (39749 ^ _781013) ^ [_1551302, _1551304, _1551306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1551302), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551304)), _1551306))), -(c_List_Obutlast(_1551304, hAPP(hAPP(c_List_Otake(_1551304), _1551302), _1551306)) = hAPP(hAPP(c_List_Otake(_1551304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1551302), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1551306))], (44020 ^ _781013) ^ [_1657438, _1657440] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1657438, _1657440) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1657438, hAPP(c_Nat_OSuc, _1657440))))], (50946 ^ _781013) ^ [_1817577, _1817579, _1817581, _1817583] : [hBOOL(hAPP(_1817577, _1817579)), -(hAPP(c_List_Ofilter(_1817581, _1817577), c_List_Oreplicate(_1817581, _1817583, _1817579)) = c_List_Oreplicate(_1817581, _1817583, _1817579))], (10705 ^ _781013) ^ [_970148, _970150, _970152] : [class_Orderings_Olinorder(_970148), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970148), _970150), _970152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970148), _970152), _970150)))], (40463 ^ _781013) ^ [_1572064, _1572066, _1572068] : [-(hAPP(c_Product__Type_Omap__pair(_1572064, _1572064, _1572066, _1572066, c_COMBI(_1572064), c_COMBI(_1572066)), _1572068) = _1572068)], (32378 ^ _781013) ^ [_1395346, _1395348] : [class_Int_Onumber__ring(_1395346), 32381 ^ _781013 : [(32388 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1395348)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1395346), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1395348)) = hAPP(c_Int_Onumber__class_Onumber__of(_1395346), _1395348))], (32382 ^ _781013) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1395348))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1395346), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1395348)) = c_Groups_Ozero__class_Ozero(_1395346))]]], (21917 ^ _781013) ^ [_1192344, _1192346, _1192348] : [class_Orderings_Olinorder(_1192344), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192344), _1192346)), hBOOL(hAPP(hAPP(c_member(_1192344), _1192348), _1192346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192344), c_Big__Operators_Olinorder__class_OMin(_1192344, _1192346)), _1192348)))], (36623 ^ _781013) ^ [_1479987, _1479989, _1479991, _1479993, _1479995, _1479997] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1479987, _1479989, _1479991), _1479993), hAPP(hAPP(c_Product__Type_OPair(_1479987, _1479989), _1479995), _1479997)) = hAPP(hAPP(_1479993, _1479995), _1479997))], (19903 ^ _781013) ^ [_1153813, _1153815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1153813), _1153815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153813), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1153815)))], (35213 ^ _781013) ^ [_1447276, _1447278] : [class_Rings_Oring__1__no__zero__divisors(_1447276), 35216 ^ _781013 : [(35217 ^ _781013) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1447276), _1447278), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1447276), -(_1447278 = c_Groups_Oone__class_Oone(_1447276)), -(_1447278 = hAPP(c_Groups_Ouminus__class_Ouminus(_1447276), c_Groups_Oone__class_Oone(_1447276)))], (35227 ^ _781013) ^ [] : [35228 ^ _781013 : [(35231 ^ _781013) ^ [] : [_1447278 = hAPP(c_Groups_Ouminus__class_Ouminus(_1447276), c_Groups_Oone__class_Oone(_1447276))], (35229 ^ _781013) ^ [] : [_1447278 = c_Groups_Oone__class_Oone(_1447276)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1447276), _1447278), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1447276))]]], (7673 ^ _781013) ^ [_910102, _910104, _910106] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_910102), _910104)), 7676 ^ _781013 : [(7683 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_910102), _910106)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_910102), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910102, tc_HOL_Obool)), _910106), _910104))))], (7677 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_910102), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910102, tc_HOL_Obool)), _910106), _910104))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_910102), _910106)))]]], (42414 ^ _781013) ^ [_1621109, _1621111, _1621113] : [-(_1621109 = c_List_Olist_ONil(_1621111)), -(hAPP(c_List_Otl(_1621111), hAPP(hAPP(c_List_Oappend(_1621111), _1621109), _1621113)) = hAPP(hAPP(c_List_Oappend(_1621111), hAPP(c_List_Otl(_1621111), _1621109)), _1621113))], (43382 ^ _781013) ^ [_1644822, _1644824, _1644826, _1644828] : [-(hBOOL(hAPP(_1644822, _1644824))), -(c_List_Oremove1(_1644826, _1644824, hAPP(c_List_Ofilter(_1644826, _1644822), _1644828)) = hAPP(c_List_Ofilter(_1644826, _1644822), _1644828))], (25320 ^ _781013) ^ [_1252922, _1252924, _1252926] : [class_Fields_Olinordered__field(_1252922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252922), _1252924), _1252926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252922), _1252924), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252922), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1252922), _1252924), _1252926)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1252922), c_Groups_Oone__class_Oone(_1252922)), c_Groups_Oone__class_Oone(_1252922))))))], (35067 ^ _781013) ^ [_1444826] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1444826)), 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, _1444826, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (13713 ^ _781013) ^ [_1032812, _1032814, _1032816, _1032818] : [class_Rings_Ocomm__semiring__1(_1032812), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032812), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032812), _1032814), _1032816)), _1032818) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032812), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032812), _1032814), _1032818)), _1032816))], (47220 ^ _781013) ^ [_1732097, _1732099, _1732101, _1732103] : [47221 ^ _781013 : [(47222 ^ _781013) ^ [_1732172] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1732097, _1732101)), hAPP(hAPP(c_Product__Type_OPair(_1732097, _1732101), _1732099), _1732172)), _1732103))]], -(hBOOL(hAPP(hAPP(c_member(_1732097), _1732099), hAPP(c_Relation_ODomain(_1732097, _1732101), _1732103))))], (24288 ^ _781013) ^ [_1234033] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1234033) = 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), _1234033), c_Int_Onat)))))], (7701 ^ _781013) ^ [_910633, _910635, _910637] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910633, tc_HOL_Obool)), _910635), _910637) = c_Orderings_Obot__class_Obot(tc_fun(_910633, tc_HOL_Obool))), _910635 = c_Orderings_Obot__class_Obot(tc_fun(_910633, tc_HOL_Obool)), _910637 = c_Orderings_Obot__class_Obot(tc_fun(_910633, tc_HOL_Obool))], (45672 ^ _781013) ^ [_1693768, _1693770] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1693768), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1693768, tc_HOL_Obool), _1693770))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1693768, tc_HOL_Obool)), _1693770)))], (32118 ^ _781013) ^ [_1390859] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1390859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390859), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (544 ^ _781013) ^ [_789383, _789385, _789387, _789389] : [-(c_Nitpick_Owf_H(_789387, _789383)), c_Nitpick_Owf_H(_789389, _789385), _789389 = _789387, _789385 = _789383], (17475 ^ _781013) ^ [_1107651, _1107653, _1107655, _1107657] : [-(c_Fun_Ooverride__on(_1107651, _1107653, _1107655, _1107657, c_Orderings_Obot__class_Obot(tc_fun(_1107651, tc_HOL_Obool))) = _1107655)], (42116 ^ _781013) ^ [_1614411, _1614413, _1614415, _1614417] : [-(hAPP(hAPP(c_List_Odrop(_1614411), _1614413), hAPP(hAPP(c_List_Odrop(_1614411), _1614415), _1614417)) = hAPP(hAPP(c_List_Odrop(_1614411), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1614413), _1614415)), _1614417))], (41514 ^ _781013) ^ [_1599697] : [-(c_List_Olistset(_1599697, c_List_Olist_ONil(tc_fun(_1599697, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1599697)), c_List_Olist_ONil(_1599697)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1599697), tc_HOL_Obool))))], (13363 ^ _781013) ^ [_1024826, _1024828, _1024830, _1024832] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1024826)), hAPP(c_Set_Oimage(_1024828, tc_Option_Ooption(_1024826), _1024830), c_Orderings_Otop__class_Otop(tc_fun(_1024828, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1024826)), hAPP(c_Set_Oimage(_1024828, tc_Option_Ooption(_1024826), c_Map_Omap__add(_1024828, _1024826, _1024830, hAPP(c_Map_Omap__of(_1024828, _1024826), _1024832))), c_Orderings_Otop__class_Otop(tc_fun(_1024828, tc_HOL_Obool))))))], (21051 ^ _781013) ^ [_1176159, _1176161, _1176163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176159)), _1176159 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1176159), _1176163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176161), _1176159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1176163)))], (38551 ^ _781013) ^ [_1522401, _1522403] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1522401, _1522403) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1522401), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1522403), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (38170 ^ _781013) ^ [] : [-(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))))))], (38115 ^ _781013) ^ [_1512016, _1512018, _1512020, _1512022] : [c_FunDef_Oreduction__pair(_1512016, _1512018), -(c_FunDef_Oreduction__pair(_1512020, hAPP(hAPP(c_FunDef_Orp__inv__image(_1512016, _1512020), _1512018), _1512022)))], (9837 ^ _781013) ^ [_954587, _954589, _954591, _954593] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954587, tc_HOL_Obool)), _954589), _954591), _954593)), -(hBOOL(hAPP(_954591, _954593)))], (42352 ^ _781013) ^ [_1619941, _1619943] : [-(_1619941 = c_List_Olist_ONil(_1619943)), -(hAPP(c_List_Orotate1(_1619943), _1619941) = hAPP(hAPP(c_List_Oappend(_1619943), hAPP(c_List_Otl(_1619943), _1619941)), hAPP(hAPP(c_List_Olist_OCons(_1619943), hAPP(c_List_Ohd(_1619943), _1619941)), c_List_Olist_ONil(_1619943))))], (26711 ^ _781013) ^ [_1278110, _1278112] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1278110), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1278112) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1278110, _1278112))], (45711 ^ _781013) ^ [_1694912, _1694914, _1694916, _1694918] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1694912, _1694914), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1694912, tc_HOL_Obool), _1694916)), _1694918) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1694912, tc_HOL_Obool), tc_fun(tc_prod(_1694912, _1694914), tc_HOL_Obool)), _1694916), hAPP(hAPP(c_COMBC(tc_fun(_1694912, tc_HOL_Obool), tc_fun(_1694912, tc_fun(_1694914, tc_HOL_Obool)), tc_fun(tc_prod(_1694912, _1694914), tc_HOL_Obool)), c_Product__Type_OSigma(_1694912, _1694914)), _1694918)))], (42340 ^ _781013) ^ [_1619843, _1619845] : [-(_1619843 = c_List_Olist_ONil(_1619845)), -(hBOOL(hAPP(hAPP(c_member(_1619845), hAPP(c_List_Ohd(_1619845), _1619843)), hAPP(c_List_Oset(_1619845), _1619843))))], (47142 ^ _781013) ^ [_1730411, _1730413, _1730415, _1730417] : [47143 ^ _781013 : [(47144 ^ _781013) ^ [_1730465] : [hBOOL(hAPP(hAPP(_1730415, _1730465), _1730417))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1730411, _1730413, _1730415), _1730417)))], (36494 ^ _781013) ^ [_1477097, _1477099, _1477101, _1477103, _1477105] : [hBOOL(hAPP(hAPP(_1477097, _1477099), _1477101)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1477103, _1477105, tc_HOL_Obool), _1477097), hAPP(hAPP(c_Product__Type_OPair(_1477103, _1477105), _1477099), _1477101))))], (14730 ^ _781013) ^ [_1054362, _1054364, _1054366] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054362), _1054364)), 14733 ^ _781013 : [(14734 ^ _781013) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054362, tc_Nat_Onat), _1054366), _1054364) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 14737 ^ _781013 : [(14738 ^ _781013) ^ [_1054524] : [hBOOL(hAPP(hAPP(c_member(_1054362), _1054524), _1054364)), -(hAPP(_1054366, _1054524) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (14744 ^ _781013) ^ [] : [14746 ^ _781013 : [(14749 ^ _781013) ^ [] : [hAPP(_1054366, 14745 ^ [_1054362, _1054364, _1054366]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (14747 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1054362), 14745 ^ [_1054362, _1054364, _1054366]), _1054364)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1054362, tc_Nat_Onat), _1054366), _1054364) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (50248 ^ _781013) ^ [_1802799, _1802801, _1802803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1802799), c_Nitpick_Oplus__frac(_1802799, _1802801, c_Nitpick_Ouminus__frac(_1802799, _1802803)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1802799, _1802801, _1802803))], (40747 ^ _781013) ^ [_1580259, _1580261, _1580263, _1580265] : [-(_1580259 = c_Orderings_Obot__class_Obot(tc_fun(_1580261, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1580263, _1580261), _1580263, c_Product__Type_Ofst(_1580263, _1580261)), hAPP(hAPP(c_Product__Type_OSigma(_1580263, _1580261), _1580265), hAPP(c_COMBK(tc_fun(_1580261, tc_HOL_Obool), _1580263), _1580259))) = _1580265)], (12706 ^ _781013) ^ [_1010879, _1010881] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1010879, tc_HOL_Obool)), _1010881)))], (47980 ^ _781013) ^ [_1750190, _1750192] : [c_Wellfounded_Oacyclic(_1750190, _1750192), 47983 ^ _781013 : [(47984 ^ _781013) ^ [_1750275] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1750190, _1750190)), hAPP(hAPP(c_Product__Type_OPair(_1750190, _1750190), _1750275), _1750275)), c_Transitive__Closure_Otrancl(_1750190, _1750192)))]]], (16856 ^ _781013) ^ [_1093595, _1093597, _1093599, _1093601] : [class_Rings_Olinordered__semiring__strict(_1093595), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093595), _1093597), _1093599)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093595), _1093601), _1093599))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093595), c_Groups_Ozero__class_Ozero(_1093595)), _1093599)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093595), _1093597), _1093601)))], (50165 ^ _781013) ^ [_1800710, _1800712, _1800714, _1800716, _1800718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800710, tc_HOL_Obool)), _1800712), _1800714)), 50171 ^ _781013 : [(50176 ^ _781013) ^ [] : [hBOOL(hAPP(_1800718, 50170 ^ [_1800710, _1800712, _1800714, _1800716, _1800718]))], (50174 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1800716, 50170 ^ [_1800710, _1800712, _1800714, _1800716, _1800718])))], (50172 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1800710), 50170 ^ [_1800710, _1800712, _1800714, _1800716, _1800718]), _1800712)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800710, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1800710, tc_HOL_Obool)), _1800712), hAPP(c_Set_OCollect(_1800710), _1800716))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1800710, tc_HOL_Obool)), _1800714), hAPP(c_Set_OCollect(_1800710), _1800718)))))], (25252 ^ _781013) ^ [_1251679, _1251681, _1251683, _1251685] : [class_Fields_Ofield(_1251679), -(_1251681 = c_Groups_Ozero__class_Ozero(_1251679)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251679), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251679), _1251683), _1251681)), _1251685) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251679), _1251683), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251679), _1251681), _1251685))), _1251681))], (23953 ^ _781013) ^ [_1228166, _1228168, _1228170] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228166), _1228168), _1228170) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1228166), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1228166, tc_Int_Oint), _1228168), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1228170))), class_Groups_Ocomm__monoid__add(_1228166), class_Groups_Ocomm__monoid__mult(_1228166)], (17565 ^ _781013) ^ [_1109428, _1109430, _1109432] : [hBOOL(hAPP(_1109428, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109430), _1109432))), 17568 ^ _781013 : [(17575 ^ _781013) ^ [_1109619] : [_1109430 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109432), _1109619), -(hBOOL(hAPP(_1109428, _1109619)))], (17569 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109430), _1109432)), -(hBOOL(hAPP(_1109428, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (43761 ^ _781013) ^ [_1652778, _1652780] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1652778, _1652780)))], (3396 ^ _781013) ^ [_832204, _832206] : [_832206 = _832204, -(c_Enum_Oenum__class_Oenum__all(_832206) = c_Enum_Oenum__class_Oenum__all(_832204))], (29759 ^ _781013) ^ [_1335987, _1335989, _1335991] : [class_Orderings_Olinorder(_1335987), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335987), _1335989)), hBOOL(hAPP(hAPP(c_member(_1335987), _1335991), _1335989)), 29770 ^ _781013 : [(29777 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335987, tc_HOL_Obool)), _1335989), hAPP(hAPP(c_Set_Oinsert(_1335987), _1335991), c_Orderings_Obot__class_Obot(tc_fun(_1335987, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1335987, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1335987, c_Orderings_Oord__class_Omin(_1335987), _1335989) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1335987), _1335991), c_Big__Operators_Olattice_OInf__fin(_1335987, c_Orderings_Oord__class_Omin(_1335987), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335987, tc_HOL_Obool)), _1335989), hAPP(hAPP(c_Set_Oinsert(_1335987), _1335991), c_Orderings_Obot__class_Obot(tc_fun(_1335987, tc_HOL_Obool)))))))], (29771 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335987, tc_HOL_Obool)), _1335989), hAPP(hAPP(c_Set_Oinsert(_1335987), _1335991), c_Orderings_Obot__class_Obot(tc_fun(_1335987, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1335987, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1335987, c_Orderings_Oord__class_Omin(_1335987), _1335989) = _1335991)]]], (10281 ^ _781013) ^ [_962898, _962900] : [class_Lattices_Obounded__lattice__bot(_962898), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_962898), c_Orderings_Obot__class_Obot(_962898)), _962900) = c_Orderings_Obot__class_Obot(_962898))], (51116 ^ _781013) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (15849 ^ _781013) ^ [_1074250, _1074252, _1074254] : [class_Rings_Olinordered__semiring__strict(_1074250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074250), c_Groups_Ozero__class_Ozero(_1074250)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074250), _1074252), _1074254))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074250), c_Groups_Ozero__class_Ozero(_1074250)), _1074254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074250), c_Groups_Ozero__class_Ozero(_1074250)), _1074252)))], (47081 ^ _781013) ^ [_1728510, _1728512] : [-(hAPP(c_Relation_ORange(_1728510, _1728510), c_Relation_OId__on(_1728510, _1728512)) = _1728512)], (16373 ^ _781013) ^ [_1083880, _1083882, _1083884, _1083886] : [-(hAPP(c_Set_Ovimage(_1083880, _1083882, _1083884), _1083886) = hAPP(c_Set_OCollect(_1083880), hAPP(hAPP(c_COMBC(_1083880, tc_fun(_1083882, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1083882, tc_fun(tc_fun(_1083882, tc_HOL_Obool), tc_HOL_Obool), _1083880), c_member(_1083882)), _1083884)), _1083886)))], (40207 ^ _781013) ^ [_1565126, _1565128, _1565130, _1565132, _1565134, _1565136] : [c_List_Olistrelp(_1565126, _1565128, hAPP(hAPP(c_List_Olist_OCons(_1565126), _1565130), _1565132), hAPP(hAPP(c_List_Olist_OCons(_1565126), _1565134), _1565136)), 40210 ^ _781013 : [(40213 ^ _781013) ^ [] : [-(c_List_Olistrelp(_1565126, _1565128, _1565132, _1565136))], (40211 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1565128, _1565130), _1565134)))]]], (34361 ^ _781013) ^ [_1432506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1432506)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432506), c_Int_OPls)))], (38636 ^ _781013) ^ [_1524039, _1524041, _1524043, _1524045, _1524047] : [hBOOL(hAPP(hAPP(c_member(_1524039), _1524041), hAPP(c_List_Oset(_1524039), _1524043))), -(hAPP(hAPP(c_Map_Omap__of(_1524039, _1524045), hAPP(hAPP(c_List_Ozip(_1524039, _1524045), _1524043), hAPP(hAPP(c_List_Omap(_1524039, _1524045), _1524047), _1524043))), _1524041) = hAPP(c_Option_Ooption_OSome(_1524045), hAPP(_1524047, _1524041)))], (18253 ^ _781013) ^ [_1120786, _1120788, _1120790, _1120792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120786), _1120788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120790), _1120792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120786), _1120790)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120788), _1120792))))], (7359 ^ _781013) ^ [_903870, _903872, _903874, _903876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903870, tc_HOL_Obool)), _903872), _903874)), hBOOL(hAPP(hAPP(c_member(_903870), _903876), _903872)), -(hBOOL(hAPP(hAPP(c_member(_903870), _903876), _903874)))], (28548 ^ _781013) ^ [_1313645, _1313647, _1313649, _1313651, _1313653] : [class_Orderings_Olinorder(_1313645), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313645), _1313647), _1313649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313645), _1313651), _1313653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313645), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313645), _1313647), _1313651)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313645), _1313649), _1313653))))], (7105 ^ _781013) ^ [_899013, _899015, _899017, _899019] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899013, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899013, tc_HOL_Obool)), _899015), _899017)), _899019) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899013, tc_HOL_Obool)), _899015), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899013, tc_HOL_Obool)), _899017), _899019)))], (41470 ^ _781013) ^ [_1598637, _1598639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598637)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598639))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598637), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598639)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598637)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598637)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1598639))))], (6952 ^ _781013) ^ [_895899, _895901, _895903] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895899, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895899, tc_HOL_Obool)), _895901), _895903)), _895901)))], (22005 ^ _781013) ^ [_1193768] : [-(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, _1193768)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14201 ^ _781013) ^ [_1042814, _1042816, _1042818] : [class_Groups_Ogroup__add(_1042814), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042814), _1042816), hAPP(c_Groups_Ouminus__class_Ouminus(_1042814), _1042818)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042814), _1042816), _1042818))], (27895 ^ _781013) ^ [_1301850, _1301852] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1301850, _1301852) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1301850 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1301852), 27898 ^ [_1301850, _1301852]))], (50716 ^ _781013) ^ [_1811613] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1811613)), c_Int_OMin))], (37488 ^ _781013) ^ [_1496802, _1496804, _1496806, _1496808] : [_1496802 = _1496804, 37491 ^ _781013 : [(37494 ^ _781013) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1496806, _1496808), _1496802) = hAPP(c_Product__Type_Osnd(_1496806, _1496808), _1496804))], (37492 ^ _781013) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1496806, _1496808), _1496802) = hAPP(c_Product__Type_Ofst(_1496806, _1496808), _1496804))]]], (29273 ^ _781013) ^ [_1327085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327085), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1327085) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1327085))], (19186 ^ _781013) ^ [_1140443, _1140445] : [_1140443 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1140445), _1140443) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28888 ^ _781013) ^ [_1320035, _1320037] : [class_Groups_Oordered__ab__group__add__abs(_1320035), 28891 ^ _781013 : [(28898 ^ _781013) ^ [] : [_1320037 = c_Groups_Ozero__class_Ozero(_1320035), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320035), hAPP(c_Groups_Oabs__class_Oabs(_1320035), _1320037)), c_Groups_Ozero__class_Ozero(_1320035))))], (28892 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320035), hAPP(c_Groups_Oabs__class_Oabs(_1320035), _1320037)), c_Groups_Ozero__class_Ozero(_1320035))), -(_1320037 = c_Groups_Ozero__class_Ozero(_1320035))]]], (37349 ^ _781013) ^ [_1493945, _1493947, _1493949, _1493951, _1493953, _1493955] : [hAPP(_1493951, hAPP(c_Product__Type_Osnd(_1493949, _1493945), _1493953)) = hAPP(_1493955, hAPP(c_Product__Type_Osnd(_1493949, _1493945), _1493953)), -(hAPP(c_Product__Type_Oapsnd(_1493945, _1493947, _1493949, _1493951), _1493953) = hAPP(c_Product__Type_Oapsnd(_1493945, _1493947, _1493949, _1493955), _1493953))], (19198 ^ _781013) ^ [_1140588, _1140590, _1140592, _1140594] : [class_Rings_Olinordered__semidom(_1140588), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140588), _1140590), _1140592)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140588), c_Groups_Ozero__class_Ozero(_1140588)), _1140590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1140594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140588), hAPP(hAPP(c_Power_Opower__class_Opower(_1140588), _1140590), _1140594)), hAPP(hAPP(c_Power_Opower__class_Opower(_1140588), _1140592), _1140594))))], (40789 ^ _781013) ^ [_1581411, _1581413, _1581415] : [c_Relation_Orefl__on(_1581411, _1581413, _1581415), 40792 ^ _781013 : [(40795 ^ _781013) ^ [_1581593] : [hBOOL(hAPP(hAPP(c_member(_1581411), _1581593), _1581413)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581411, _1581411)), hAPP(hAPP(c_Product__Type_OPair(_1581411, _1581411), _1581593), _1581593)), _1581415)))], (40793 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581411, _1581411), tc_HOL_Obool)), _1581415), hAPP(hAPP(c_Product__Type_OSigma(_1581411, _1581411), _1581413), hAPP(c_COMBK(tc_fun(_1581411, tc_HOL_Obool), _1581411), _1581413)))))]]], (47129 ^ _781013) ^ [_1730170, _1730172, _1730174, _1730176, _1730178] : [hBOOL(hAPP(hAPP(_1730170, _1730172), _1730174)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1730176, _1730178, _1730170), _1730174)))], (15617 ^ _781013) ^ [_1069933, _1069935, _1069937] : [class_Rings_Oordered__ring(_1069933), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069933), c_Groups_Ozero__class_Ozero(_1069933)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069933), _1069935), _1069937)))), 15622 ^ _781013 : [(15629 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069933), _1069935), c_Groups_Ozero__class_Ozero(_1069933))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069933), _1069937), c_Groups_Ozero__class_Ozero(_1069933)))], (15623 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069933), c_Groups_Ozero__class_Ozero(_1069933)), _1069935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069933), c_Groups_Ozero__class_Ozero(_1069933)), _1069937))]]], (41552 ^ _781013) ^ [_1601083, _1601085, _1601087, _1601089, _1601091] : [hAPP(hAPP(c_List_Oappend(_1601083), _1601085), hAPP(hAPP(c_List_Olist_OCons(_1601083), _1601087), c_List_Olist_ONil(_1601083))) = hAPP(hAPP(c_List_Oappend(_1601083), _1601089), hAPP(hAPP(c_List_Olist_OCons(_1601083), _1601091), c_List_Olist_ONil(_1601083))), 41555 ^ _781013 : [(41558 ^ _781013) ^ [] : [-(_1601087 = _1601091)], (41556 ^ _781013) ^ [] : [-(_1601085 = _1601089)]]], (31852 ^ _781013) ^ [_1384076, _1384078, _1384080, _1384082, _1384084] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384076, tc_HOL_Obool)), _1384078), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384080, tc_fun(_1384076, tc_HOL_Obool)), _1384082), _1384084)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384080, tc_fun(_1384076, tc_HOL_Obool)), _1384082), hAPP(hAPP(c_COMBB(tc_fun(_1384076, tc_HOL_Obool), tc_fun(_1384076, tc_HOL_Obool), _1384080), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384076, tc_HOL_Obool)), _1384078)), _1384084)))], (51052 ^ _781013) ^ [_1819063, _1819065] : [class_Lattices_Olattice(_1819063), -(class_Lattices_Olattice(tc_fun(_1819065, _1819063)))], (13537 ^ _781013) ^ [_1028778, _1028780, _1028782, _1028784, _1028786] : [class_Groups_Ocomm__monoid__mult(_1028778), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028780), _1028782)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1028778, _1028780, c_Groups_Otimes__class_Otimes(_1028778)), hAPP(hAPP(c_COMBS(_1028780, _1028778, _1028778), hAPP(hAPP(c_COMBB(_1028778, tc_fun(_1028778, _1028778), _1028780), c_Groups_Otimes__class_Otimes(_1028778)), _1028784)), _1028786)), c_Groups_Oone__class_Oone(_1028778)), _1028782) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028778), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1028778, _1028780, c_Groups_Otimes__class_Otimes(_1028778)), _1028784), c_Groups_Oone__class_Oone(_1028778)), _1028782)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1028778, _1028780, c_Groups_Otimes__class_Otimes(_1028778)), _1028786), c_Groups_Oone__class_Oone(_1028778)), _1028782)))], (13237 ^ _781013) ^ [_1022268, _1022270, _1022272, _1022274, _1022276] : [c_Fun_Oinj__on(_1022268, _1022270, _1022272, _1022274), hBOOL(hAPP(hAPP(c_member(_1022270), _1022276), hAPP(c_Set_Oimage(_1022268, _1022270, _1022272), _1022274))), -(hAPP(_1022272, hAPP(c_Fun_Othe__inv__into(_1022268, _1022270, _1022274, _1022272), _1022276)) = _1022276)], (32876 ^ _781013) ^ [_1404717, _1404719, _1404721, _1404723] : [class_Fields_Olinordered__field__inverse__zero(_1404717), class_Int_Onumber(_1404717), 32883 ^ _781013 : [(32884 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1404717), _1404719), _1404721)), hAPP(c_Int_Onumber__class_Onumber__of(_1404717), _1404723))), 32887 ^ _781013 : [(32894 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), c_Groups_Ozero__class_Ozero(_1404717)), _1404721))), 32897 ^ _781013 : [(32904 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), _1404721), c_Groups_Ozero__class_Ozero(_1404717)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), c_Groups_Ozero__class_Ozero(_1404717)), hAPP(c_Int_Onumber__class_Onumber__of(_1404717), _1404723))))], (32898 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), _1404721), c_Groups_Ozero__class_Ozero(_1404717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1404717), hAPP(c_Int_Onumber__class_Onumber__of(_1404717), _1404723)), _1404721)), _1404719)))]]], (32888 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), c_Groups_Ozero__class_Ozero(_1404717)), _1404721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), _1404719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1404717), hAPP(c_Int_Onumber__class_Onumber__of(_1404717), _1404723)), _1404721))))]]], (32910 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1404717), _1404719), _1404721)), hAPP(c_Int_Onumber__class_Onumber__of(_1404717), _1404723)))), 32913 ^ _781013 : [(32916 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), _1404719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1404717), hAPP(c_Int_Onumber__class_Onumber__of(_1404717), _1404723)), _1404721)))], (32914 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), c_Groups_Ozero__class_Ozero(_1404717)), _1404721)))]], 32917 ^ _781013 : [(32920 ^ _781013) ^ [] : [32921 ^ _781013 : [(32924 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1404717), hAPP(c_Int_Onumber__class_Onumber__of(_1404717), _1404723)), _1404721)), _1404719))], (32922 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), _1404721), c_Groups_Ozero__class_Ozero(_1404717))))]], 32925 ^ _781013 : [(32928 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), c_Groups_Ozero__class_Ozero(_1404717)), hAPP(c_Int_Onumber__class_Onumber__of(_1404717), _1404723)))], (32926 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), _1404721), c_Groups_Ozero__class_Ozero(_1404717)))]]], (32918 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404717), c_Groups_Ozero__class_Ozero(_1404717)), _1404721))]]]]], (31844 ^ _781013) ^ [_1383553, _1383555, _1383557, _1383559, _1383561] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383553, tc_fun(_1383555, tc_HOL_Obool)), _1383557), hAPP(hAPP(c_COMBS(_1383553, tc_fun(_1383555, tc_HOL_Obool), tc_fun(_1383555, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383555, tc_HOL_Obool), tc_fun(tc_fun(_1383555, tc_HOL_Obool), tc_fun(_1383555, tc_HOL_Obool)), _1383553), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1383555, tc_HOL_Obool))), _1383559)), _1383561)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1383555, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383553, tc_fun(_1383555, tc_HOL_Obool)), _1383557), _1383559)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383553, tc_fun(_1383555, tc_HOL_Obool)), _1383557), _1383561)))], (37746 ^ _781013) ^ [_1502748, _1502750, _1502752, _1502754, _1502756, _1502758] : [-(c_Product__Type_Oprod_Oprod__rec(_1502748, _1502750, _1502752, _1502754, hAPP(hAPP(c_Product__Type_OPair(_1502748, _1502750), _1502756), _1502758)) = hAPP(hAPP(_1502754, _1502756), _1502758))], (3578 ^ _781013) ^ [_834995, _834997, _834999, _835001] : [-(c_Wellfounded_Omin__ext(_835001, _834997) = c_Wellfounded_Omin__ext(_834999, _834995)), _835001 = _834999, _834997 = _834995], (2356 ^ _781013) ^ [_815866, _815868, _815870, _815872] : [-(c_Nitpick_Onat__lcm(_815872, _815868) = c_Nitpick_Onat__lcm(_815870, _815866)), _815872 = _815870, _815868 = _815866], (4222 ^ _781013) ^ [_844873, _844875, _844877, _844879] : [-(c_Complete__Lattice_OInf__class_OInf(_844879, _844875) = c_Complete__Lattice_OInf__class_OInf(_844877, _844873)), _844879 = _844877, _844875 = _844873], (44809 ^ _781013) ^ [_1675621, _1675623, _1675625] : [-(hBOOL(hAPP(hAPP(c_member(_1675621), _1675623), hAPP(c_List_Oset(_1675621), _1675625)))), -(c_List_Oremdups(_1675621, hAPP(hAPP(c_List_Olist_OCons(_1675621), _1675623), _1675625)) = hAPP(hAPP(c_List_Olist_OCons(_1675621), _1675623), c_List_Oremdups(_1675621, _1675625)))], (23301 ^ _781013) ^ [_1216849, _1216851, _1216853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1216849)), 23304 ^ _781013 : [(23305 ^ _781013) ^ [] : [-(_1216851 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1216853), _1216849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216849), _1216851)), _1216853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1216853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216849), hAPP(c_Nat_OSuc, _1216851))))], (23315 ^ _781013) ^ [] : [_1216851 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1216853), _1216849), 23318 ^ _781013 : [(23321 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1216853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216849), hAPP(c_Nat_OSuc, _1216851)))))], (23319 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216849), _1216851)), _1216853)))]]]]], (33718 ^ _781013) ^ [_1420088, _1420090] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420088)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420090)))), 33721 ^ _781013 : [(33724 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1420090))], (33722 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420088), _1420090)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420088), _1420090))], (40978 ^ _781013) ^ [_1587701, _1587703] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1587701, _1587703, tc_prod(_1587701, _1587703)), c_Product__Type_OPair(_1587701, _1587703)) = c_Fun_Oid(tc_prod(_1587701, _1587703)))], (43440 ^ _781013) ^ [_1646006, _1646008, _1646010, _1646012] : [hBOOL(hAPP(_1646006, _1646008)), -(hAPP(c_List_Ofilter(_1646010, _1646006), hAPP(hAPP(c_List_Olist_OCons(_1646010), _1646008), _1646012)) = hAPP(hAPP(c_List_Olist_OCons(_1646010), _1646008), hAPP(c_List_Ofilter(_1646010, _1646006), _1646012)))], (5978 ^ _781013) ^ [_877671, _877673] : [hBOOL(hAPP(c_Com_OWT, _877671)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_877673, _877671))))], (46679 ^ _781013) ^ [_1719507, _1719509, _1719511, _1719513, _1719515, _1719517, _1719519] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1719507, _1719511)), hAPP(hAPP(c_Product__Type_OPair(_1719507, _1719511), _1719517), _1719519)), hAPP(hAPP(c_Relation_Orel__comp(_1719507, _1719509, _1719511), _1719513), _1719515))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1719507, _1719509, _1719511, hAPP(hAPP(c_COMBC(_1719507, tc_fun(tc_prod(_1719507, _1719509), tc_HOL_Obool), tc_fun(_1719509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719509, tc_fun(tc_fun(tc_prod(_1719507, _1719509), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1719507, _1719509), tc_HOL_Obool), tc_fun(_1719509, tc_HOL_Obool)), _1719507), c_COMBC(_1719509, tc_fun(tc_prod(_1719507, _1719509), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719509, tc_prod(_1719507, _1719509)), tc_fun(_1719509, tc_fun(tc_fun(tc_prod(_1719507, _1719509), tc_HOL_Obool), tc_HOL_Obool)), _1719507), hAPP(c_COMBB(tc_prod(_1719507, _1719509), tc_fun(tc_fun(tc_prod(_1719507, _1719509), tc_HOL_Obool), tc_HOL_Obool), _1719509), c_member(tc_prod(_1719507, _1719509)))), c_Product__Type_OPair(_1719507, _1719509)))), _1719513), hAPP(hAPP(c_COMBC(_1719509, tc_fun(tc_prod(_1719509, _1719511), tc_HOL_Obool), tc_fun(_1719511, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719511, tc_fun(tc_fun(tc_prod(_1719509, _1719511), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1719509, _1719511), tc_HOL_Obool), tc_fun(_1719511, tc_HOL_Obool)), _1719509), c_COMBC(_1719511, tc_fun(tc_prod(_1719509, _1719511), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719511, tc_prod(_1719509, _1719511)), tc_fun(_1719511, tc_fun(tc_fun(tc_prod(_1719509, _1719511), tc_HOL_Obool), tc_HOL_Obool)), _1719509), hAPP(c_COMBB(tc_prod(_1719509, _1719511), tc_fun(tc_fun(tc_prod(_1719509, _1719511), tc_HOL_Obool), tc_HOL_Obool), _1719511), c_member(tc_prod(_1719509, _1719511)))), c_Product__Type_OPair(_1719509, _1719511)))), _1719515)), _1719517), _1719519)))], (5705 ^ _781013) ^ [_871273, _871275, _871277, _871279, _871281, _871283, _871285] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871273), _871275), _871277), _871279) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871273), _871281), _871283), _871285), 5708 ^ _781013 : [(5713 ^ _781013) ^ [] : [-(_871279 = _871285)], (5711 ^ _781013) ^ [] : [-(_871277 = _871283)], (5709 ^ _781013) ^ [] : [-(_871275 = _871281)]]], (39269 ^ _781013) ^ [_1539620, _1539622, _1539624, _1539626, _1539628, _1539630, _1539632] : [-(hAPP(hAPP(c_List_Ozip(_1539620, _1539622), hAPP(hAPP(c_List_Olist__update(_1539620, _1539624), _1539626), _1539628)), hAPP(hAPP(c_List_Olist__update(_1539622, _1539630), _1539626), _1539632)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1539620, _1539622), hAPP(hAPP(c_List_Ozip(_1539620, _1539622), _1539624), _1539630)), _1539626), hAPP(hAPP(c_Product__Type_OPair(_1539620, _1539622), _1539628), _1539632)))], (7835 ^ _781013) ^ [_913028, _913030, _913032, _913034] : [-(hBOOL(hAPP(hAPP(c_member(_913028), _913030), _913032))), -(hBOOL(hAPP(hAPP(c_member(_913028), _913030), _913034))), 7842 ^ _781013 : [(7849 ^ _781013) ^ [] : [_913032 = _913034, -(hAPP(hAPP(c_Set_Oinsert(_913028), _913030), _913032) = hAPP(hAPP(c_Set_Oinsert(_913028), _913030), _913034))], (7843 ^ _781013) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_913028), _913030), _913032) = hAPP(hAPP(c_Set_Oinsert(_913028), _913030), _913034), -(_913032 = _913034)]]], (34647 ^ _781013) ^ [_1437396, _1437398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437396), _1437398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1437396)), c_Int_OBit0(_1437398))))], (43358 ^ _781013) ^ [_1644473, _1644475, _1644477] : [hBOOL(hAPP(c_List_Odistinct(_1644473), _1644475)), -(hBOOL(hAPP(c_List_Odistinct(_1644473), hAPP(c_List_Ofilter(_1644473, _1644477), _1644475))))], (26901 ^ _781013) ^ [_1281769, _1281771, _1281773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281769)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1281771), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1281773)), 26911 ^ _781013 : [(26917 ^ _781013) ^ [] : [-(_1281771 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26913 ^ [_1281769, _1281771, _1281773]), 26910 ^ [_1281769, _1281771, _1281773]))], (26915 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26913 ^ [_1281769, _1281771, _1281773]), _1281773)))], (26912 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26910 ^ [_1281769, _1281771, _1281773]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1281769))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1281771), _1281769) = _1281771)], (51118 ^ _781013) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (23327 ^ _781013) ^ [_1217302, _1217304, _1217306] : [class_Orderings_Olinorder(_1217302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217302), _1217304), _1217306)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1217302, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1217302), _1217304), c_Orderings_Obot__class_Obot(tc_fun(_1217302, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1217302, _1217304, _1217306)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217302, _1217304), _1217306))], (17419 ^ _781013) ^ [_1106640] : [-(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)), _1106640)))))], (30805 ^ _781013) ^ [_1357555, _1357557] : [-(_1357555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1357557, _1357555) = c_Nitpick_Onat__gcd(_1357555, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357557, _1357555)))], (13613 ^ _781013) ^ [_1030588, _1030590] : [class_Rings_Ocomm__ring__1(_1030588), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1030588), _1030590) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030588), hAPP(c_Groups_Ouminus__class_Ouminus(_1030588), c_Groups_Oone__class_Oone(_1030588))), _1030590))], (30535 ^ _781013) ^ [_1351634, _1351636, _1351638] : [class_Orderings_Olinorder(_1351634), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351634), _1351636)), -(hBOOL(hAPP(hAPP(c_member(_1351634), _1351638), _1351636))), -(_1351636 = c_Orderings_Obot__class_Obot(tc_fun(_1351634, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1351634, hAPP(hAPP(c_Set_Oinsert(_1351634), _1351638), _1351636)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351634), _1351638), c_Big__Operators_Olinorder__class_OMax(_1351634, _1351636)))], (35147 ^ _781013) ^ [_1446264, _1446266] : [class_Rings_Olinordered__idom(_1446264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446264), hAPP(hAPP(c_Power_Opower__class_Opower(_1446264), _1446266), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1446264)))], (46407 ^ _781013) ^ [_1710476, _1710478, _1710480, _1710482, _1710484] : [-(c_List_Omaps(_1710476, _1710478, _1710480, hAPP(hAPP(c_List_Olist_OCons(_1710476), _1710482), _1710484)) = hAPP(hAPP(c_List_Oappend(_1710478), hAPP(_1710480, _1710482)), c_List_Omaps(_1710476, _1710478, _1710480, _1710484)))], (6884 ^ _781013) ^ [_894618, _894620, _894622, _894624] : [hBOOL(hAPP(hAPP(c_member(_894618), _894620), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894618, tc_HOL_Obool)), _894622), _894624))), 6887 ^ _781013 : [(6890 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894618), _894620), _894624))], (6888 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894618), _894620), _894622)))]]], (39954 ^ _781013) ^ [_1558488, _1558490] : [hBOOL(hAPP(_1558490, 39955 ^ [_1558488, _1558490])), 39958 ^ _781013 : [(39959 ^ _781013) ^ [_1558595] : [hBOOL(hAPP(hAPP(c_member(_1558488), _1558595), c_Orderings_Otop__class_Otop(tc_fun(_1558488, tc_HOL_Obool)))), -(hBOOL(hAPP(_1558490, _1558595)))]]], (48846 ^ _781013) ^ [_1770253, _1770255] : [-(c_Transitive__Closure_Otrancl(_1770253, hAPP(c_Relation_Oconverse(_1770253, _1770253), _1770255)) = hAPP(c_Relation_Oconverse(_1770253, _1770253), c_Transitive__Closure_Otrancl(_1770253, _1770255)))], (6228 ^ _781013) ^ [_882187, _882189, _882191, _882193, _882195] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_882187, _882189, _882191)), _882193), _882195))), 6229 ^ _781013 : [(6236 ^ _781013) ^ [] : [-(hBOOL(hAPP(_882187, _882193))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_882191), _882193), _882195))], (6230 ^ _781013) ^ [] : [hBOOL(hAPP(_882187, _882193)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_882189), _882193), _882195))]]], (49017 ^ _781013) ^ [] : [-(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))))], (51592 ^ _781013) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (13473 ^ _781013) ^ [_1027560, _1027562, _1027564, _1027566] : [class_Groups_Oab__group__add(_1027560), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027562, _1027560), hAPP(hAPP(c_COMBB(_1027560, _1027560, _1027562), c_Groups_Ouminus__class_Ouminus(_1027560)), _1027564)), _1027566) = hAPP(c_Groups_Ouminus__class_Ouminus(_1027560), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027562, _1027560), _1027564), _1027566)))], (14093 ^ _781013) ^ [_1040390, _1040392] : [class_Rings_Ocomm__semiring__1(_1040390), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040390), _1040392), _1040392) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040390), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040390), c_Groups_Oone__class_Oone(_1040390)), c_Groups_Oone__class_Oone(_1040390))), _1040392))], (27926 ^ _781013) ^ [_1302335, _1302337, _1302339] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1302335), _1302337)), _1302339) = 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), _1302335), _1302339)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1302337), _1302339))), 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, _1302335, _1302339)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1302337, _1302339))), _1302339)))], (20500 ^ _781013) ^ [_1163949, _1163951, _1163953] : [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, _1163949)), _1163951)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1163949)), _1163953))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1163951), _1163953)))], (27403 ^ _781013) ^ [_1291678, _1291680, _1291682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291678, tc_HOL_Obool)), _1291680), _1291682)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1291678, tc_HOL_Obool)), _1291680), hAPP(c_Set_OPow(_1291678), _1291682))))], (36894 ^ _781013) ^ [_1484887, _1484889] : [_1484887 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1484887, _1484889) = 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)))], (40777 ^ _781013) ^ [_1580989, _1580991, _1580993, _1580995, _1580997] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1580989), tc_List_Olist(_1580989))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1580989), tc_List_Olist(_1580989)), _1580991), _1580993)), c_List_Olistrel1(_1580989, _1580995))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1580989), tc_List_Olist(_1580989))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1580989), tc_List_Olist(_1580989)), hAPP(hAPP(c_List_Olist_OCons(_1580989), _1580997), _1580991)), hAPP(hAPP(c_List_Olist_OCons(_1580989), _1580997), _1580993))), c_List_Olistrel1(_1580989, _1580995))))], (18263 ^ _781013) ^ [_1120977, _1120979, _1120981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120977), _1120979)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120977), _1120981)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120979), _1120981))))], (28742 ^ _781013) ^ [_1317445, _1317447] : [class_Orderings_Olinorder(_1317445), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317445), _1317447), _1317447) = _1317447)], (31597 ^ _781013) ^ [] : [-(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)))], (45678 ^ _781013) ^ [_1693879] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1693879, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1693879, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1693879, tc_HOL_Obool)))], (31640 ^ _781013) ^ [_1378215, _1378217, _1378219, _1378221, _1378223] : [31642 ^ _781013 : [(31648 ^ _781013) ^ [] : [hBOOL(hAPP(_1378223, 31644 ^ [_1378215, _1378217, _1378219, _1378221, _1378223]))], (31646 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1378215), 31644 ^ [_1378215, _1378217, _1378219, _1378221, _1378223]), hAPP(_1378221, 31641 ^ [_1378215, _1378217, _1378219, _1378221, _1378223]))))], (31643 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1378217), 31641 ^ [_1378215, _1378217, _1378219, _1378221, _1378223]), _1378219)))]], 31649 ^ _781013 : [(31650 ^ _781013) ^ [_1378525] : [hBOOL(hAPP(hAPP(c_member(_1378215), _1378525), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378217, tc_fun(_1378215, tc_HOL_Obool)), _1378219), _1378221))), -(hBOOL(hAPP(_1378223, _1378525)))]]], (18614 ^ _781013) ^ [_1127581, _1127583, _1127585, _1127587, _1127589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127581), _1127583)), 18617 ^ _781013 : [(18624 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127587), 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), _1127583), _1127581)), _1127585)), _1127589))), -(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), _1127581), _1127585)), _1127587)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127583), _1127585)), _1127589))))], (18618 ^ _781013) ^ [] : [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), _1127581), _1127585)), _1127587)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127583), _1127585)), _1127589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127587), 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), _1127583), _1127581)), _1127585)), _1127589))))]]], (29149 ^ _781013) ^ [_1324623, _1324625] : [class_Rings_Olinordered__idom(_1324623), -(hAPP(c_Groups_Oabs__class_Oabs(_1324623), _1324625) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324623), _1324625), c_Groups_Osgn__class_Osgn(_1324623, _1324625)))], (48860 ^ _781013) ^ [_1770618, _1770620, _1770622, _1770624, _1770626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1770620, tc_HOL_Obool)), _1770624), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1770620, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1770618, _1770620, hAPP(c_Relation_Oconverse(_1770620, _1770618), _1770622)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1770618, tc_HOL_Obool)), _1770626))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1770618, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1770620, _1770618, _1770622), _1770624)), _1770626)))], (18984 ^ _781013) ^ [_1136126, _1136128, _1136130, _1136132, _1136134, _1136136] : [hBOOL(hAPP(hAPP(c_member(_1136126), _1136128), c_SetInterval_Oord_OatLeastLessThan(_1136126, _1136130, _1136132, _1136134, _1136136))), 18987 ^ _781013 : [(18990 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1136132, _1136128), _1136136)))], (18988 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1136130, _1136134), _1136128)))]]], (22218 ^ _781013) ^ [_1197661, _1197663] : [_1197661 = _1197663, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197661) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197663))], (29191 ^ _781013) ^ [_1325630, _1325632, _1325634] : [class_Groups_Oordered__ab__group__add__abs(_1325630), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325630), hAPP(c_Groups_Oabs__class_Oabs(_1325630), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1325630), _1325632), _1325634))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325630), hAPP(c_Groups_Oabs__class_Oabs(_1325630), _1325632)), hAPP(c_Groups_Oabs__class_Oabs(_1325630), _1325634)))))], (10335 ^ _781013) ^ [_963979, _963981, _963983, _963985] : [class_Lattices_Odistrib__lattice(_963979), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_963979), _963981), _963983)), _963985) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_963979), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963979), _963981), _963985)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963979), _963983), _963985)))], (26745 ^ _781013) ^ [_1278714, _1278716, _1278718] : [class_Orderings_Oorder(_1278714), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278714, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1278714, _1278716, _1278718)), hAPP(c_SetInterval_Oord__class_OatLeast(_1278714), _1278718)) = c_Orderings_Obot__class_Obot(tc_fun(_1278714, tc_HOL_Obool)))], (36142 ^ _781013) ^ [_1469284, _1469286, _1469288, _1469290, _1469292] : [hBOOL(hAPP(hAPP(c_member(_1469284), _1469286), hAPP(c_Relation_OImage(_1469288, _1469284, _1469290), hAPP(hAPP(c_Set_Oinsert(_1469288), _1469292), c_Orderings_Obot__class_Obot(tc_fun(_1469288, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1469288, _1469284)), hAPP(hAPP(c_Product__Type_OPair(_1469288, _1469284), _1469292), _1469286)), _1469290)))], (24029 ^ _781013) ^ [_1229493, _1229495] : [hAPP(c_Int_Onat, _1229493) = _1229495, 24032 ^ _781013 : [(24039 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229493))), -(_1229495 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24033 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229493)), -(_1229493 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229495))]]], (17174 ^ _781013) ^ [_1100571, _1100573, _1100575, _1100577, _1100579] : [class_Groups_Ocomm__monoid__mult(_1100571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1100573), _1100575)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1100573, _1100571), _1100577), hAPP(hAPP(c_Set_Oinsert(_1100573), _1100579), _1100575)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100571), hAPP(_1100577, _1100579)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1100573, _1100571), _1100577), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100573, tc_HOL_Obool)), _1100575), hAPP(hAPP(c_Set_Oinsert(_1100573), _1100579), c_Orderings_Obot__class_Obot(tc_fun(_1100573, tc_HOL_Obool)))))))], (44389 ^ _781013) ^ [_1665623, _1665625] : [44391 ^ _781013 : [(44394 ^ _781013) ^ [] : [44390 ^ [_1665623, _1665625] = c_List_Olist_ONil(_1665623)], (44392 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665623)), 44390 ^ [_1665623, _1665625]), hAPP(c_List_Oset(tc_List_Olist(_1665623)), _1665625))))]], -(c_List_Oconcat(_1665623, _1665625) = c_List_Olist_ONil(_1665623))], (7421 ^ _781013) ^ [_904903, _904905, _904907, _904909] : [class_Orderings_Opreorder(_904903), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904903), _904905), _904907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904903), _904907), _904909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904903), _904905), _904909)))], (8575 ^ _781013) ^ [_929648, _929650, _929652, _929654, _929656, _929658, _929660, _929662] : [c_Finite__Set_Ofolding(_929648, _929650, _929652, _929654), hBOOL(hAPP(c_Finite__Set_Ofinite(_929648), _929656)), hBOOL(hAPP(c_Finite__Set_Ofinite(_929648), _929658)), -(hAPP(c_Fun_Ocomp(_929650, _929650, _929660, hAPP(_929654, _929658)), hAPP(c_Fun_Ocomp(_929650, _929650, _929660, hAPP(_929654, _929656)), _929662)) = hAPP(c_Fun_Ocomp(_929650, _929650, _929660, hAPP(_929654, _929656)), hAPP(c_Fun_Ocomp(_929650, _929650, _929660, hAPP(_929654, _929658)), _929662)))], (33328 ^ _781013) ^ [_1413659] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413659)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1413659)))], (20983 ^ _781013) ^ [_1173246, _1173248, _1173250] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1173246), _1173248)), hBOOL(hAPP(hAPP(c_member(_1173246), _1173250), _1173248)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1173246), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1173246, tc_HOL_Obool)), _1173248), hAPP(hAPP(c_Set_Oinsert(_1173246), _1173250), c_Orderings_Obot__class_Obot(tc_fun(_1173246, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1173246), _1173248))], (3744 ^ _781013) ^ [_837606, _837608, _837610, _837612] : [-(c_Map_Omap__of(_837612, _837608) = c_Map_Omap__of(_837610, _837606)), _837612 = _837610, _837608 = _837606], (26413 ^ _781013) ^ [_1272211, _1272213, _1272215, _1272217] : [class_Orderings_Oorder(_1272211), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1272211, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1272211, _1272213, _1272215)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1272211, _1272215, _1272217)) = c_Orderings_Obot__class_Obot(tc_fun(_1272211, tc_HOL_Obool)))], (42851 ^ _781013) ^ [_1630559, _1630561, _1630563, _1630565, _1630567, _1630569] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630561, _1630563)), hAPP(hAPP(c_Product__Type_OPair(_1630561, _1630563), _1630567), _1630569)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630559, tc_fun(tc_prod(_1630561, _1630563), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1630559, tc_HOL_Obool))), _1630565))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630559, tc_fun(_1630561, tc_fun(_1630563, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1630559, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1630561, _1630563), tc_HOL_Obool), tc_fun(_1630561, tc_fun(_1630563, tc_HOL_Obool)), _1630559), hAPP(c_COMBC(_1630561, tc_fun(tc_prod(_1630561, _1630563), tc_HOL_Obool), tc_fun(_1630563, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630563, tc_fun(tc_fun(tc_prod(_1630561, _1630563), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1630561, _1630563), tc_HOL_Obool), tc_fun(_1630563, tc_HOL_Obool)), _1630561), c_COMBC(_1630563, tc_fun(tc_prod(_1630561, _1630563), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630563, tc_prod(_1630561, _1630563)), tc_fun(_1630563, tc_fun(tc_fun(tc_prod(_1630561, _1630563), tc_HOL_Obool), tc_HOL_Obool)), _1630561), hAPP(c_COMBB(tc_prod(_1630561, _1630563), tc_fun(tc_fun(tc_prod(_1630561, _1630563), tc_HOL_Obool), tc_HOL_Obool), _1630563), c_member(tc_prod(_1630561, _1630563)))), c_Product__Type_OPair(_1630561, _1630563))))), _1630565)), _1630567), _1630569)))], (1724 ^ _781013) ^ [_805305, _805307] : [-(class_Rings_Osemiring__1(_805305)), _805307 = _805305, class_Rings_Osemiring__1(_805307)], (8016 ^ _781013) ^ [_916964, _916966, _916968, _916970] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916964, tc_HOL_Obool)), _916966), hAPP(hAPP(c_Set_Oinsert(_916964), _916968), _916970)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916964, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916964, tc_HOL_Obool)), _916966), hAPP(hAPP(c_Set_Oinsert(_916964), _916968), c_Orderings_Obot__class_Obot(tc_fun(_916964, tc_HOL_Obool))))), _916970))], (16712 ^ _781013) ^ [_1090827, _1090829, _1090831, _1090833, _1090835] : [class_Rings_Olinordered__semiring__strict(_1090827), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090827), _1090829), _1090831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090827), _1090833), _1090835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090827), c_Groups_Ozero__class_Ozero(_1090827)), _1090831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090827), c_Groups_Ozero__class_Ozero(_1090827)), _1090833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090827), _1090829), _1090833)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090827), _1090831), _1090835))))], (14847 ^ _781013) ^ [_1056194, _1056196, _1056198] : [class_Rings_Ono__zero__divisors(_1056194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056194), _1056196), _1056198) = c_Groups_Ozero__class_Ozero(_1056194), -(_1056196 = c_Groups_Ozero__class_Ozero(_1056194)), -(_1056198 = c_Groups_Ozero__class_Ozero(_1056194))], (11007 ^ _781013) ^ [_976435, _976437, _976439, _976441] : [class_Lattices_Olattice(_976435), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976435), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976435), _976437), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976435), _976439), _976441))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976435), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976435), _976437), _976439)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976435), _976437), _976441)))))], (19839 ^ _781013) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (46476 ^ _781013) ^ [_1712687, _1712689, _1712691] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712687)), _1712689), c_List_Olists(_1712687, c_Wellfounded_Oacc(_1712687, _1712691)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712687)), _1712689), c_Wellfounded_Oacc(tc_List_Olist(_1712687), c_List_Olistrel1(_1712687, _1712691)))))], (37658 ^ _781013) ^ [_1500226, _1500228, _1500230] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1500226, _1500228), _1500230))), _1500226 = 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), _1500230)), _1500228)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1500230)), 37665 ^ _781013 : [(37668 ^ _781013) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1500230) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37666 ^ _781013) ^ [] : [-(_1500228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 37669 ^ _781013 : [(37672 ^ _781013) ^ [] : [37673 ^ _781013 : [(37676 ^ _781013) ^ [] : [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), _1500230))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1500230)), _1500228))], (37674 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1500228)))]], 37681 ^ _781013 : [(37684 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1500228), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1500230))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1500230)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37682 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1500228))]]], (37670 ^ _781013) ^ [] : [_1500228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (39368 ^ _781013) ^ [_1542028, _1542030, _1542032, _1542034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1542028), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1542030)), _1542032))), 39371 ^ _781013 : [(39378 ^ _781013) ^ [] : [hAPP(hAPP(c_List_Onth(_1542030), _1542032), _1542028) = _1542034, -(hAPP(hAPP(c_List_Olist__update(_1542030, _1542032), _1542028), _1542034) = _1542032)], (39372 ^ _781013) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1542030, _1542032), _1542028), _1542034) = _1542032, -(hAPP(hAPP(c_List_Onth(_1542030), _1542032), _1542028) = _1542034)]]], (32020 ^ _781013) ^ [_1388947, _1388949, _1388951, _1388953, _1388955, _1388957, _1388959, _1388961] : [hBOOL(hAPP(hAPP(c_member(_1388947), _1388949), _1388951)), hBOOL(hAPP(hAPP(hAPP(_1388953, _1388949), _1388955), _1388957)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388947, tc_fun(_1388959, tc_fun(_1388961, tc_HOL_Obool))), _1388951), _1388953), _1388955), _1388957)))], (7503 ^ _781013) ^ [_906512, _906514, _906516] : [_906512 = _906514, 7506 ^ _781013 : [(7509 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906516, tc_HOL_Obool)), _906514), _906512)))], (7507 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906516, tc_HOL_Obool)), _906512), _906514)))]]], (21881 ^ _781013) ^ [_1191623] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1191623)) = 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), _1191623)))], (26321 ^ _781013) ^ [_1270521, _1270523, _1270525, _1270527] : [class_Orderings_Olinorder(_1270521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270521), _1270523), _1270525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270521), _1270525), _1270527)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270521, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1270521, _1270523), _1270525)), c_SetInterval_Oord__class_OatLeastAtMost(_1270521, _1270525, _1270527)) = c_SetInterval_Oord__class_OatLeastAtMost(_1270521, _1270523, _1270527))], (28764 ^ _781013) ^ [_1317768] : [class_Groups_Oordered__ab__group__add__abs(_1317768), -(hAPP(c_Groups_Oabs__class_Oabs(_1317768), c_Groups_Ozero__class_Ozero(_1317768)) = c_Groups_Ozero__class_Ozero(_1317768))], (6282 ^ _781013) ^ [_883233, _883235, _883237, _883239, _883241] : [c_Com_Ocom_OCond(_883233, _883235, _883237) = c_Com_Ocom_OSemi(_883239, _883241)], (19644 ^ _781013) ^ [_1148621, _1148623, _1148625] : [class_Rings_Oring__1(_1148621), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1148621), hAPP(c_Groups_Ouminus__class_Ouminus(_1148621), _1148623)), _1148625) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148621), hAPP(hAPP(c_Power_Opower__class_Opower(_1148621), hAPP(c_Groups_Ouminus__class_Ouminus(_1148621), c_Groups_Oone__class_Oone(_1148621))), _1148625)), hAPP(hAPP(c_Power_Opower__class_Opower(_1148621), _1148623), _1148625)))], (35623 ^ _781013) ^ [_1455132] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1455132) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1455132))], (45031 ^ _781013) ^ [_1680698, _1680700, _1680702, _1680704] : [class_Enum_Oenum(_1680698), class_Enum_Oenum(_1680700), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680700)), _1680702) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680698)), c_Enum_Oenum__class_Oenum(_1680698)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680700)), _1680704) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680698)), c_Enum_Oenum__class_Oenum(_1680698)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1680700), _1680700, _1680698, c_Option_Othe(_1680700)), hAPP(c_Map_Omap__of(_1680698, _1680700), hAPP(hAPP(c_List_Ozip(_1680698, _1680700), c_Enum_Oenum__class_Oenum(_1680698)), _1680702))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1680700), _1680700, _1680698, c_Option_Othe(_1680700)), hAPP(c_Map_Omap__of(_1680698, _1680700), hAPP(hAPP(c_List_Ozip(_1680698, _1680700), c_Enum_Oenum__class_Oenum(_1680698)), _1680704))), -(_1680702 = _1680704)], (22666 ^ _781013) ^ [_1205136, _1205138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205138), 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), _1205136), _1205138)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41873 ^ _781013) ^ [_1607916, _1607918, _1607920, _1607922] : [-(hAPP(hAPP(c_List_Oappend(_1607916), hAPP(hAPP(c_List_Olist_OCons(_1607916), _1607918), _1607920)), _1607922) = hAPP(hAPP(c_List_Olist_OCons(_1607916), _1607918), hAPP(hAPP(c_List_Oappend(_1607916), _1607920), _1607922)))], (43258 ^ _781013) ^ [_1642312, _1642314, _1642316, _1642318, _1642320] : [43260 ^ _781013 : [(43263 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1642318, 43259 ^ [_1642312, _1642314, _1642316, _1642318, _1642320]), _1642320))], (43261 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1642312), 43259 ^ [_1642312, _1642314, _1642316, _1642318, _1642320]), _1642316)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642312, tc_fun(_1642314, tc_HOL_Obool)), _1642316), _1642318), _1642320)))], (35323 ^ _781013) ^ [_1449397, _1449399, _1449401] : [class_Rings_Olinordered__idom(_1449397), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1449397), c_Groups_Ozero__class_Ozero(_1449397)), hAPP(hAPP(c_Power_Opower__class_Opower(_1449397), _1449399), 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)))), _1449401)))))], (4426 ^ _781013) ^ [_848043, _848045, _848047, _848049, _848051, _848053] : [-(c_Divides_Odiv__class_Omod(_848053, _848049, _848045) = c_Divides_Odiv__class_Omod(_848051, _848047, _848043)), _848053 = _848051, _848049 = _848047, _848045 = _848043], (48736 ^ _781013) ^ [_1767344, _1767346, _1767348, _1767350] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1767344, _1767344)), hAPP(hAPP(c_Product__Type_OPair(_1767344, _1767344), _1767346), _1767348)), c_Transitive__Closure_Otrancl(_1767344, hAPP(c_Relation_Oconverse(_1767344, _1767344), _1767350)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1767344, _1767344)), hAPP(hAPP(c_Product__Type_OPair(_1767344, _1767344), _1767346), _1767348)), hAPP(c_Relation_Oconverse(_1767344, _1767344), c_Transitive__Closure_Otrancl(_1767344, _1767350)))))], (7285 ^ _781013) ^ [_902639, _902641, _902643] : [class_Orderings_Oorder(_902639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902639), _902641), _902643)), 7292 ^ _781013 : [(7299 ^ _781013) ^ [] : [_902643 = _902641, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902639), _902643), _902641)))], (7293 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902639), _902643), _902641)), -(_902643 = _902641)]]], (9631 ^ _781013) ^ [_951496, _951498, _951500] : [class_Orderings_Opreorder(_951496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951496), _951498), _951500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951496), _951500), _951498))], (508 ^ _781013) ^ [_788837, _788839, _788841, _788843, _788845, _788847, _788849, _788851] : [-(c_Wellfounded_Omax__extp(_788849, _788845, _788841, _788837)), c_Wellfounded_Omax__extp(_788851, _788847, _788843, _788839), _788851 = _788849, _788847 = _788845, _788843 = _788841, _788839 = _788837], (14576 ^ _781013) ^ [_1051825, _1051827] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1051825), _1051827))), -(hAPP(c_Finite__Set_Ocard(_1051825), _1051827) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10341 ^ _781013) ^ [_964138, _964140, _964142, _964144] : [class_Lattices_Odistrib__lattice(_964138), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_964138), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_964138), _964140), _964142)), _964144) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_964138), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_964138), _964140), _964144)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_964138), _964142), _964144)))], (12248 ^ _781013) ^ [_1002186, _1002188] : [class_Lattices_Oboolean__algebra(_1002186), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1002186), hAPP(c_Groups_Ouminus__class_Ouminus(_1002186), _1002188)), _1002188) = c_Orderings_Otop__class_Otop(_1002186))], (11205 ^ _781013) ^ [_980879, _980881, _980883, _980885, _980887] : [-(hAPP(c_Map_Omap__add(_980879, _980881, _980883, _980885), _980887) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_980881), _980881, hAPP(_980883, _980887), c_Option_Ooption_OSome(_980881)), hAPP(_980885, _980887)))], (1064 ^ _781013) ^ [_797055, _797057] : [-(class_Rings_Oring__1__no__zero__divisors(_797055)), _797057 = _797055, class_Rings_Oring__1__no__zero__divisors(_797057)], (27184 ^ _781013) ^ [_1287152, _1287154, _1287156] : [class_Orderings_Olinorder(_1287152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287152), _1287154), _1287156)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287152, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1287152), _1287154)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1287152, _1287154, _1287156)) = hAPP(c_SetInterval_Oord__class_OatMost(_1287152), _1287156))], (39836 ^ _781013) ^ [_1553739, _1553741, _1553743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1553739, _1553739), tc_HOL_Obool)), _1553741), _1553743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1553739), tc_List_Olist(_1553739)), tc_HOL_Obool)), c_List_Olistrel(_1553739, _1553741)), c_List_Olistrel(_1553739, _1553743))))], (44075 ^ _781013) ^ [_1658530, _1658532, _1658534, _1658536, _1658538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658530), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1658532), _1658534))), -(hAPP(hAPP(c_List_Onth(_1658536), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1658536), _1658538), c_List_Oupt(_1658534, _1658532))), _1658530) = hAPP(_1658538, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1658534), _1658530)))], (12220 ^ _781013) ^ [_1001739, _1001741, _1001743, _1001745, _1001747, _1001749] : [c_Fun_Oinj__on(_1001739, _1001741, _1001743, _1001745), -(hBOOL(hAPP(hAPP(c_member(_1001741), _1001747), hAPP(c_Set_Oimage(_1001739, _1001741, _1001743), _1001745)))), -(c_Fun_Oinj__on(_1001739, _1001741, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1001739, _1001741), _1001743), _1001749), _1001747), _1001745))], (21285 ^ _781013) ^ [_1180300] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1180300)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1180300), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1180300)))], (21171 ^ _781013) ^ [_1178245, _1178247] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178245), _1178247))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178247), _1178245)))], (41601 ^ _781013) ^ [_1602163, _1602165, _1602167, _1602169, _1602171] : [hAPP(hAPP(c_List_Oappend(_1602163), _1602165), _1602167) = hAPP(hAPP(c_List_Olist_OCons(_1602163), _1602169), _1602171), 41606 ^ _781013 : [(41609 ^ _781013) ^ [] : [-(_1602167 = hAPP(hAPP(c_List_Olist_OCons(_1602163), _1602169), _1602171))], (41607 ^ _781013) ^ [] : [-(_1602165 = c_List_Olist_ONil(_1602163))]], 41611 ^ _781013 : [(41614 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1602163), 41610 ^ [_1602163, _1602165, _1602167, _1602169, _1602171]), _1602167) = _1602171)], (41612 ^ _781013) ^ [] : [-(_1602165 = hAPP(hAPP(c_List_Olist_OCons(_1602163), _1602169), 41610 ^ [_1602163, _1602165, _1602167, _1602169, _1602171]))]]], (35939 ^ _781013) ^ [_1462728, _1462730, _1462732, _1462734] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1462728, _1462730)), hAPP(hAPP(c_Product__Type_OPair(_1462728, _1462730), _1462732), _1462734)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1462728, _1462730), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1462728, tc_fun(_1462730, tc_HOL_Obool))), _1462732), _1462734)))], (23965 ^ _781013) ^ [_1228389, _1228391] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1228389), _1228391)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1228391), _1228389)))], (14663 ^ _781013) ^ [_1053155, _1053157, _1053159] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1053155), _1053157)), 14666 ^ _781013 : [(14667 ^ _781013) ^ [] : [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(_1053155, tc_Nat_Onat), _1053159), _1053157))), 14670 ^ _781013 : [(14671 ^ _781013) ^ [_1053323] : [hBOOL(hAPP(hAPP(c_member(_1053155), _1053323), _1053157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1053159, _1053323))))]]], (14677 ^ _781013) ^ [] : [14679 ^ _781013 : [(14682 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1053159, 14678 ^ [_1053155, _1053157, _1053159])))], (14680 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1053155), 14678 ^ [_1053155, _1053157, _1053159]), _1053157)))]], -(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(_1053155, tc_Nat_Onat), _1053159), _1053157))))]]], (40337 ^ _781013) ^ [_1567988, _1567990, _1567992, _1567994, _1567996, _1567998] : [-(_1567988 = _1567990), -(hAPP(hAPP(c_Map_Omap__of(_1567992, _1567994), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1567992, _1567994)), hAPP(hAPP(c_Product__Type_OPair(_1567992, _1567994), _1567988), _1567996)), _1567998)), _1567990) = hAPP(hAPP(c_Map_Omap__of(_1567992, _1567994), _1567998), _1567990))], (20195 ^ _781013) ^ [_1158632, _1158634, _1158636] : [_1158634 = _1158636, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158632)), _1158634) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158632)), _1158636))], (46403 ^ _781013) ^ [_1710392, _1710394, _1710396, _1710398] : [-(c_List_Omaps(_1710392, _1710394, _1710396, _1710398) = c_List_Oconcat(_1710394, hAPP(hAPP(c_List_Omap(_1710392, tc_List_Olist(_1710394)), _1710396), _1710398)))], (22756 ^ _781013) ^ [_1206651, _1206653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1206653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206651), _1206653)), _1206651)))], (19340 ^ _781013) ^ [_1143191, _1143193, _1143195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1143191), _1143193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1143195), _1143191)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1143195), _1143193))))], (11470 ^ _781013) ^ [_987011, _987013, _987015, _987017, _987019, _987021, _987023] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_987011), tc_Option_Ooption(_987013), tc_sum(_987015, _987017), hAPP(c_Option_Omap(_987011, _987013), _987019)), c_Sum__Type_Osum_Osum__case(_987015, tc_Option_Ooption(_987011), _987017, _987021, _987023)) = c_Sum__Type_Osum_Osum__case(_987015, tc_Option_Ooption(_987013), _987017, hAPP(c_Fun_Ocomp(tc_Option_Ooption(_987011), tc_Option_Ooption(_987013), _987015, hAPP(c_Option_Omap(_987011, _987013), _987019)), _987021), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_987011), tc_Option_Ooption(_987013), _987017, hAPP(c_Option_Omap(_987011, _987013), _987019)), _987023)))], (3352 ^ _781013) ^ [_831512, _831514, _831516, _831518, _831520, _831522, _831524, _831526] : [-(c_List_Olinorder__class_Osort__key(_831526, _831522, _831518, _831514) = c_List_Olinorder__class_Osort__key(_831524, _831520, _831516, _831512)), _831526 = _831524, _831522 = _831520, _831518 = _831516, _831514 = _831512], (1614 ^ _781013) ^ [_803930, _803932] : [-(class_Groups_Ocomm__monoid__add(_803930)), _803932 = _803930, class_Groups_Ocomm__monoid__add(_803932)], (3196 ^ _781013) ^ [_829066, _829068, _829070, _829072] : [-(c_List_Otranspose(_829072, _829068) = c_List_Otranspose(_829070, _829066)), _829072 = _829070, _829068 = _829066], (30893 ^ _781013) ^ [_1359207, _1359209, _1359211] : [class_Orderings_Olinorder(_1359207), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359207), _1359209)), hBOOL(hAPP(hAPP(c_member(_1359207), _1359211), _1359209)), 30904 ^ _781013 : [(30911 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359207, tc_HOL_Obool)), _1359209), hAPP(hAPP(c_Set_Oinsert(_1359207), _1359211), c_Orderings_Obot__class_Obot(tc_fun(_1359207, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1359207, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1359207, c_Orderings_Oord__class_Omax(_1359207), _1359209) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359207), _1359211), c_Big__Operators_Olattice_OSup__fin(_1359207, c_Orderings_Oord__class_Omax(_1359207), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359207, tc_HOL_Obool)), _1359209), hAPP(hAPP(c_Set_Oinsert(_1359207), _1359211), c_Orderings_Obot__class_Obot(tc_fun(_1359207, tc_HOL_Obool)))))))], (30905 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359207, tc_HOL_Obool)), _1359209), hAPP(hAPP(c_Set_Oinsert(_1359207), _1359211), c_Orderings_Obot__class_Obot(tc_fun(_1359207, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1359207, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1359207, c_Orderings_Oord__class_Omax(_1359207), _1359209) = _1359211)]]], (34419 ^ _781013) ^ [_1433337] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1433337))) = 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)))), _1433337))], (25521 ^ _781013) ^ [_1256423, _1256425] : [c_Nat__Transfer_Onat__set(_1256423), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1256425), _1256423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256425)))], (20679 ^ _781013) ^ [_1167602, _1167604, _1167606] : [class_Rings_Olinordered__semidom(_1167602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167602), c_Groups_Oone__class_Oone(_1167602)), _1167604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167602), c_Groups_Oone__class_Oone(_1167602)), hAPP(hAPP(c_Power_Opower__class_Opower(_1167602), _1167604), hAPP(c_Nat_OSuc, _1167606)))))], (18636 ^ _781013) ^ [_1128173, _1128175, _1128177, _1128179, _1128181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128173), _1128175)), 18639 ^ _781013 : [(18646 ^ _781013) ^ [] : [_1128179 = 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), _1128175), _1128173)), _1128177)), _1128181), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128173), _1128177)), _1128179) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128175), _1128177)), _1128181))], (18640 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128173), _1128177)), _1128179) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128175), _1128177)), _1128181), -(_1128179 = 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), _1128175), _1128173)), _1128177)), _1128181))]]], (37179 ^ _781013) ^ [_1490474, _1490476, _1490478] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1490474, _1490476), _1490478)), 37182 ^ _781013 : [(37183 ^ _781013) ^ [_1490559] : [hBOOL(hAPP(hAPP(_1490476, _1490559), _1490478)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1490474, _1490476), _1490559)))]]], (5384 ^ _781013) ^ [_863122, _863124, _863126, _863128, _863130, _863132] : [-(c_List_Oreplicate(_863132, _863128, _863124) = c_List_Oreplicate(_863130, _863126, _863122)), _863132 = _863130, _863128 = _863126, _863124 = _863122], (5260 ^ _781013) ^ [_861252, _861254] : [_861254 = _861252, -(c_Lazy__Sequence_Osingle(_861254) = c_Lazy__Sequence_Osingle(_861252))], (15071 ^ _781013) ^ [_1059671, _1059673, _1059675] : [hBOOL(hAPP(hAPP(c_member(_1059671), _1059673), hAPP(c_Set_OCollect(_1059671), _1059675))), -(hBOOL(hAPP(_1059675, _1059673)))], (19789 ^ _781013) ^ [_1151963, _1151965] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151963), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1151965)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1151963), _1151965))], (49790 ^ _781013) ^ [_1793132, _1793134, _1793136] : [class_Groups_Oab__semigroup__mult(_1793132), hBOOL(hAPP(c_Finite__Set_Ofinite(_1793132), _1793134)), -(hBOOL(hAPP(hAPP(c_member(_1793132), _1793136), _1793134))), -(hAPP(c_Finite__Set_Ofold1(_1793132, c_Groups_Otimes__class_Otimes(_1793132)), hAPP(hAPP(c_Set_Oinsert(_1793132), _1793136), _1793134)) = hAPP(hAPP(c_Finite__Set_Ofold(_1793132, _1793132, c_Groups_Otimes__class_Otimes(_1793132)), _1793136), _1793134))], (44256 ^ _781013) ^ [_1662734] : [-(hAPP(c_List_Orev(_1662734), c_List_Olist_ONil(_1662734)) = c_List_Olist_ONil(_1662734))], (17351 ^ _781013) ^ [_1104862, _1104864, _1104866, _1104868, _1104870, _1104872, _1104874] : [class_Groups_Ocomm__monoid__add(_1104862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104864), _1104866)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104868), _1104870)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104864, _1104862), hAPP(hAPP(c_COMBS(_1104864, tc_fun(_1104868, tc_HOL_Obool), _1104862), hAPP(hAPP(c_COMBB(tc_fun(_1104868, _1104862), tc_fun(tc_fun(_1104868, tc_HOL_Obool), _1104862), _1104864), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104868, _1104862)), _1104872)), hAPP(hAPP(c_COMBB(tc_fun(_1104868, tc_HOL_Obool), tc_fun(_1104868, tc_HOL_Obool), _1104864), c_Set_OCollect(_1104868)), hAPP(hAPP(c_COMBB(tc_fun(_1104868, tc_HOL_Obool), tc_fun(_1104868, tc_HOL_Obool), _1104864), hAPP(c_COMBS(_1104868, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1104868), c_fconj), hAPP(hAPP(c_COMBC(_1104868, tc_fun(_1104868, tc_HOL_Obool), tc_HOL_Obool), c_member(_1104868)), _1104870)))), _1104874)))), _1104866) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104868, _1104862), hAPP(hAPP(c_COMBS(_1104868, tc_fun(_1104864, tc_HOL_Obool), _1104862), hAPP(hAPP(c_COMBB(tc_fun(_1104864, _1104862), tc_fun(tc_fun(_1104864, tc_HOL_Obool), _1104862), _1104868), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104864, _1104862)), hAPP(c_COMBC(_1104864, _1104868, _1104862), _1104872))), hAPP(hAPP(c_COMBB(tc_fun(_1104864, tc_HOL_Obool), tc_fun(_1104864, tc_HOL_Obool), _1104868), c_Set_OCollect(_1104864)), hAPP(hAPP(c_COMBB(tc_fun(_1104864, tc_HOL_Obool), tc_fun(_1104864, tc_HOL_Obool), _1104868), hAPP(c_COMBS(_1104864, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1104864), c_fconj), hAPP(hAPP(c_COMBC(_1104864, tc_fun(_1104864, tc_HOL_Obool), tc_HOL_Obool), c_member(_1104864)), _1104866)))), hAPP(c_COMBC(_1104864, _1104868, tc_HOL_Obool), _1104874))))), _1104870))], (34505 ^ _781013) ^ [_1434646, _1434648] : [class_Int_Onumber__ring(_1434646), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434646), c_Groups_Oone__class_Oone(_1434646)), hAPP(c_Int_Onumber__class_Onumber__of(_1434646), _1434648)) = hAPP(c_Int_Onumber__class_Onumber__of(_1434646), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1434648)))], (40403 ^ _781013) ^ [_1569259, _1569261, _1569263, _1569265, _1569267, _1569269] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569259, _1569259)), hAPP(hAPP(c_Product__Type_OPair(_1569259, _1569259), _1569261), _1569263)), _1569265)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1569259), tc_List_Olist(_1569259))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1569259), tc_List_Olist(_1569259)), _1569267), _1569269)), c_List_Olistrel(_1569259, _1569265))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1569259), tc_List_Olist(_1569259))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1569259), tc_List_Olist(_1569259)), hAPP(hAPP(c_List_Olist_OCons(_1569259), _1569261), _1569267)), hAPP(hAPP(c_List_Olist_OCons(_1569259), _1569263), _1569269))), c_List_Olistrel(_1569259, _1569265))))], (48701 ^ _781013) ^ [_1766230, _1766232] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1766230), _1766232) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1766230), _1766232))], (37876 ^ _781013) ^ [_1506376, _1506378, _1506380, _1506382, _1506384, _1506386] : [hAPP(_1506382, hAPP(c_Product__Type_Ofst(_1506376, _1506380), _1506384)) = hAPP(_1506386, hAPP(c_Product__Type_Ofst(_1506376, _1506380), _1506384)), -(hAPP(c_Product__Type_Oapfst(_1506376, _1506378, _1506380, _1506382), _1506384) = hAPP(c_Product__Type_Oapfst(_1506376, _1506378, _1506380, _1506386), _1506384))], (22898 ^ _781013) ^ [_1209422, _1209424] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209422), _1209424))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209422), hAPP(c_Nat_OSuc, _1209424)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (30325 ^ _781013) ^ [_1347618, _1347620, _1347622, _1347624] : [class_Orderings_Olinorder(_1347618), 30328 ^ _781013 : [(30329 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347618), _1347620), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347618), _1347622), _1347624))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347618), _1347620), _1347622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347618), _1347620), _1347624)))], (30339 ^ _781013) ^ [] : [30340 ^ _781013 : [(30343 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347618), _1347620), _1347624))], (30341 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347618), _1347620), _1347622))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347618), _1347620), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347618), _1347622), _1347624))))]]], (51064 ^ _781013) ^ [_1819221, _1819223] : [class_Orderings_Otop(_1819221), -(class_Orderings_Otop(tc_fun(_1819223, _1819221)))], (31784 ^ _781013) ^ [_1381938, _1381940, _1381942, _1381944] : [_1381938 = c_Orderings_Obot__class_Obot(tc_fun(_1381940, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381940, tc_fun(_1381942, tc_HOL_Obool)), _1381938), hAPP(c_COMBK(tc_fun(_1381942, tc_HOL_Obool), _1381940), _1381944)) = c_Orderings_Obot__class_Obot(tc_fun(_1381942, tc_HOL_Obool)))], (30641 ^ _781013) ^ [_1353672, _1353674] : [-(c_Nitpick_Onat__lcm(_1353672, _1353674) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1353672), _1353674)), c_Nitpick_Onat__gcd(_1353672, _1353674)))], (44592 ^ _781013) ^ [_1671494, _1671496, _1671498, _1671500, _1671502] : [-(hAPP(hAPP(c_List_Ozip(_1671494, _1671496), c_List_OtakeWhile(_1671494, _1671498, _1671500)), _1671502) = c_List_OtakeWhile(tc_prod(_1671494, _1671496), hAPP(c_Fun_Ocomp(_1671494, tc_HOL_Obool, tc_prod(_1671494, _1671496), _1671498), c_Product__Type_Ofst(_1671494, _1671496)), hAPP(hAPP(c_List_Ozip(_1671494, _1671496), _1671500), _1671502)))], (45121 ^ _781013) ^ [_1682383, _1682385, _1682387, _1682389] : [class_Orderings_Olinorder(_1682383), -(hAPP(c_List_Oset(_1682385), c_List_Olinorder__class_Osort__key(_1682385, _1682383, _1682387, _1682389)) = hAPP(c_List_Oset(_1682385), _1682389))], (34827 ^ _781013) ^ [_1440457, _1440459] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1440457)), c_Int_OBit0(_1440459)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1440457), _1440459)))], (8683 ^ _781013) ^ [_931880, _931882, _931884, _931886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931880, tc_HOL_Obool)), _931882), _931884)), hBOOL(hAPP(_931882, _931886)), -(hBOOL(hAPP(_931884, _931886)))], (26491 ^ _781013) ^ [_1273860, _1273862, _1273864, _1273866, _1273868] : [class_Groups_Ocomm__monoid__add(_1273860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1273862), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273864), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1273860), _1273866), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1273862, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273864), _1273868))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273860), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1273860), _1273866), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1273862, _1273864))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1273860), _1273866), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273864), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273864), _1273868)))))], (16444 ^ _781013) ^ [_1085364, _1085366, _1085368, _1085370, _1085372, _1085374] : [class_Groups_Ocomm__monoid__mult(_1085364), c_Fun_Oinj__on(_1085366, _1085368, _1085370, _1085372), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1085368, _1085364), _1085374), hAPP(c_Set_Oimage(_1085366, _1085368, _1085370), _1085372)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1085366, _1085364), hAPP(c_Fun_Ocomp(_1085368, _1085364, _1085366, _1085374), _1085370)), _1085372))], (18241 ^ _781013) ^ [_1120564, _1120566, _1120568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120564), _1120566)), _1120568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120564), _1120568)))], (50634 ^ _781013) ^ [_1810154, _1810156] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1810154)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1810156))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1810154), _1810156)))], (48932 ^ _781013) ^ [_1772830, _1772832, _1772834] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1772830, _1772830, _1772832), c_Relation_OId(_1772830)), _1772834) = _1772834)], (42607 ^ _781013) ^ [_1625554, _1625556, _1625558] : [42608 ^ _781013 : [(42609 ^ _781013) ^ [_1625643, _1625645] : [_1625556 = hAPP(hAPP(c_List_Olist_OCons(_1625554), _1625645), _1625643)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625554), tc_List_Olist(_1625554))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625554), tc_List_Olist(_1625554)), c_List_Olist_ONil(_1625554)), _1625556)), c_List_Olexord(_1625554, _1625558))))], (11085 ^ _781013) ^ [_978071, _978073, _978075, _978077] : [hBOOL(hAPP(hAPP(c_member(_978071), _978073), _978075)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978071, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_978071), _978073), _978077)), _978075) = hAPP(hAPP(c_Set_Oinsert(_978071), _978073), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978071, tc_HOL_Obool)), _978077), _978075)))], (14474 ^ _781013) ^ [_1049423, _1049425, _1049427, _1049429, _1049431, _1049433] : [class_Rings_Olinordered__semiring__1__strict(_1049423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049423), _1049425), _1049427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049423), _1049429), _1049427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049423), c_Groups_Ozero__class_Ozero(_1049423)), _1049431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049423), c_Groups_Ozero__class_Ozero(_1049423)), _1049433)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049423), _1049431), _1049433) = c_Groups_Oone__class_Oone(_1049423), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049423), _1049431), _1049425)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049423), _1049433), _1049429))), _1049427)))], (51088 ^ _781013) ^ [_1819537, _1819539] : [class_Groups_Ominus(_1819537), -(class_Groups_Ominus(tc_fun(_1819539, _1819537)))], (22450 ^ _781013) ^ [_1201364, _1201366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1201364), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1201366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1201366), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1201364))))), -(_1201364 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1201366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1201366), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1201364))))], (47379 ^ _781013) ^ [_1736285, _1736287] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1736285, _1736285)), _1736287)), c_Wellfounded_Oacyclic(_1736285, _1736287), -(c_Wellfounded_Owf(_1736285, _1736287))], (10551 ^ _781013) ^ [_967863, _967865, _967867] : [class_Orderings_Opreorder(_967863), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967863), _967865), _967867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967863), _967865), _967867)))], (18386 ^ _781013) ^ [_1123334, _1123336, _1123338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123334), _1123336)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123334), _1123338)), 18393 ^ _781013 : [(18400 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123336), _1123338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1123336), _1123334)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1123338), _1123334))))], (18394 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1123336), _1123334)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1123338), _1123334))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123336), _1123338)))]]], (16986 ^ _781013) ^ [_1096419, _1096421, _1096423, _1096425, _1096427] : [class_Groups_Ocomm__monoid__mult(_1096419), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096421), _1096423)), c_Fun_Oinj__on(_1096421, _1096421, _1096425, _1096423), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1096421, _1096419), _1096427), hAPP(c_Set_Oimage(_1096421, _1096421, _1096425), _1096423)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1096421, _1096419), hAPP(c_Fun_Ocomp(_1096421, _1096419, _1096421, _1096427), _1096425)), _1096423))], (33998 ^ _781013) ^ [_1425247, _1425249] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1425247)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425249)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1425249))), 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, _1425247))), 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), _1425247)), c_Int_Onat)))))], (51556 ^ _781013) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (50632 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (51166 ^ _781013) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (20113 ^ _781013) ^ [_1157231, _1157233] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1157231), hAPP(c_Nat_OSuc, _1157233)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1157231), _1157233)))], (43541 ^ _781013) ^ [_1648594, _1648596, _1648598, _1648600, _1648602] : [-(c_List_Omap__filter(_1648594, _1648596, _1648598, hAPP(hAPP(c_List_Olist_OCons(_1648594), _1648600), _1648602)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1648596), _1648596, c_List_Omap__filter(_1648594, _1648596, _1648598, _1648602), hAPP(hAPP(c_COMBC(_1648596, tc_List_Olist(_1648596), tc_List_Olist(_1648596)), c_List_Olist_OCons(_1648596)), c_List_Omap__filter(_1648594, _1648596, _1648598, _1648602))), hAPP(_1648598, _1648600)))], (51692 ^ _781013) ^ [_1825844, _1825846] : [hBOOL(_1825844), -(hBOOL(hAPP(hAPP(c_fimplies, _1825846), _1825844)))], (47999 ^ _781013) ^ [_1750555, _1750557] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1750555, _1750555), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1750555, _1750557)), hAPP(hAPP(c_Product__Type_OSigma(_1750555, _1750555), hAPP(c_Relation_OField(_1750555), _1750557)), hAPP(c_COMBK(tc_fun(_1750555, tc_HOL_Obool), _1750555), hAPP(c_Relation_OField(_1750555), _1750557))))))], (7533 ^ _781013) ^ [_907109, _907111, _907113] : [class_Orderings_Olinorder(_907109), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907109), _907111), _907113))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907109), _907113), _907111)))], (16518 ^ _781013) ^ [_1086882, _1086884, _1086886, _1086888] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1086882), _1086884)), hAPP(c_Finite__Set_Ocard(_1086886), hAPP(c_Set_Oimage(_1086882, _1086886, _1086888), _1086884)) = hAPP(c_Finite__Set_Ocard(_1086882), _1086884), -(c_Fun_Oinj__on(_1086882, _1086886, _1086888, _1086884))], (51236 ^ _781013) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (1824 ^ _781013) ^ [_806555, _806557] : [-(class_Groups_Oone(_806555)), _806557 = _806555, class_Groups_Oone(_806557)], (25262 ^ _781013) ^ [_1251857, _1251859, _1251861, _1251863, _1251865] : [class_Fields_Ofield(_1251857), -(_1251859 = c_Groups_Ozero__class_Ozero(_1251857)), -(_1251861 = c_Groups_Ozero__class_Ozero(_1251857)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251857), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251857), _1251863), _1251859)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251857), _1251865), _1251861)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251857), _1251863), _1251861)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251857), _1251865), _1251859))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251857), _1251859), _1251861)))], (48748 ^ _781013) ^ [_1767787, _1767789, _1767791, _1767793] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1767787), tc_List_Olist(_1767787))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1767787), tc_List_Olist(_1767787)), _1767789), _1767791)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1767787), tc_List_Olist(_1767787)), c_List_Olistrel1(_1767787, _1767793)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1767787), tc_List_Olist(_1767787))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1767787), tc_List_Olist(_1767787)), _1767789), _1767791)), c_List_Olistrel1(_1767787, hAPP(c_Relation_Oconverse(_1767787, _1767787), _1767793)))))], (28360 ^ _781013) ^ [_1310202, _1310204] : [class_Rings_Olinordered__idom(_1310202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310202), _1310204), c_Groups_Ozero__class_Ozero(_1310202))), -(c_Groups_Osgn__class_Osgn(_1310202, _1310204) = hAPP(c_Groups_Ouminus__class_Ouminus(_1310202), c_Groups_Oone__class_Oone(_1310202)))], (51530 ^ _781013) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (26705 ^ _781013) ^ [_1277999, _1278001] : [class_Orderings_Olinorder(_1277999), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277999, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1277999), _1278001)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1277999), _1278001))], (50646 ^ _781013) ^ [_1810385, _1810387] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1810385)), c_Int_OBit1(_1810387))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1810385), _1810387)))], (11117 ^ _781013) ^ [_979035, _979037, _979039, _979041] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979035, tc_HOL_Obool)), _979037), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979035, tc_HOL_Obool)), _979039), _979041)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979035, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979035, tc_HOL_Obool)), _979037), _979039)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979035, tc_HOL_Obool)), _979037), _979041)))], (19142 ^ _781013) ^ [_1139484, _1139486, _1139488] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1139484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1139486), _1139488)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1139484), _1139486)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1139484), _1139488)))], (7275 ^ _781013) ^ [_902454, _902456, _902458, _902460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902454, tc_HOL_Obool)), _902456), _902458)), hBOOL(hAPP(hAPP(c_member(_902454), _902460), _902456)), -(hBOOL(hAPP(hAPP(c_member(_902454), _902460), _902458)))], (2914 ^ _781013) ^ [_824591, _824593, _824595, _824597, _824599, _824601] : [-(c_List_Oset__Cons(_824601, _824597, _824593) = c_List_Oset__Cons(_824599, _824595, _824591)), _824601 = _824599, _824597 = _824595, _824593 = _824591], (27415 ^ _781013) ^ [_1291955, _1291957] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1291955, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1291955, tc_HOL_Obool))), hAPP(c_Set_OPow(_1291955), _1291957))))], (19891 ^ _781013) ^ [_1153604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153604)), -(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)), _1153604))))], (23102 ^ _781013) ^ [_1213229] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1213229) = _1213229)], (19779 ^ _781013) ^ [_1151736] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1151736))))], (1554 ^ _781013) ^ [_803180, _803182] : [-(class_Rings_Olinordered__semidom(_803180)), _803182 = _803180, class_Rings_Olinordered__semidom(_803182)], (18328 ^ _781013) ^ [_1122227, _1122229] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122227), _1122229)), _1122227) = _1122229)], (9817 ^ _781013) ^ [_954207, _954209] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954207, tc_HOL_Obool)), _954209), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_954207, tc_HOL_Obool)), _954209)) = c_Orderings_Obot__class_Obot(tc_fun(_954207, tc_HOL_Obool)))], (20141 ^ _781013) ^ [_1157705, _1157707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1157705)), hAPP(c_Nat_OSuc, _1157707))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157705), _1157707)))], (17881 ^ _781013) ^ [_1114687, _1114689] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1114687), _1114689), 17884 ^ _781013 : [(17887 ^ _781013) ^ [] : [-(_1114689 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17885 ^ _781013) ^ [] : [-(_1114687 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (46897 ^ _781013) ^ [_1724154, _1724156] : [c_Wellfounded_Owf(_1724154, _1724156), 46901 ^ _781013 : [(46902 ^ _781013) ^ [_1724290] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1724154, _1724154)), hAPP(hAPP(c_Product__Type_OPair(_1724154, _1724154), hAPP(_1724290, hAPP(c_Nat_OSuc, 46900 ^ [_1724154, _1724156, _1724290]))), hAPP(_1724290, 46900 ^ [_1724154, _1724156, _1724290]))), _1724156))]]], (2698 ^ _781013) ^ [_821119, _821121] : [_821121 = _821119, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_821121) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_821119))], (7827 ^ _781013) ^ [_912864, _912866, _912868, _912870] : [7828 ^ _781013 : [(7831 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_912864), _912866), _912870))], (7829 ^ _781013) ^ [] : [_912866 = _912868]], -(hBOOL(hAPP(hAPP(c_member(_912864), _912866), hAPP(hAPP(c_Set_Oinsert(_912864), _912868), _912870))))], (29133 ^ _781013) ^ [_1324331, _1324333] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1324331), _1324333)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1324331) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (51366 ^ _781013) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (9963 ^ _781013) ^ [_957105, _957107, _957109, _957111] : [class_Groups_Ouminus(_957105), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957107, _957105)), _957109), _957111) = hAPP(c_Groups_Ouminus__class_Ouminus(_957105), hAPP(_957109, _957111)))], (12156 ^ _781013) ^ [_1000328, _1000330] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000328, tc_HOL_Obool)), _1000330), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000328, tc_HOL_Obool)), _1000330)) = c_Orderings_Otop__class_Otop(tc_fun(_1000328, tc_HOL_Obool)))], (43711 ^ _781013) ^ [_1651985, _1651987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651985), _1651987)), -(c_List_Oupt(_1651987, _1651985) = c_List_Olist_ONil(tc_Nat_Onat))], (34789 ^ _781013) ^ [_1439748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439748), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1439748)), c_Int_OPls)))], (31664 ^ _781013) ^ [_1378988, _1378990, _1378992, _1378994, _1378996, _1378998] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378988, tc_fun(_1378990, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378992, tc_fun(_1378988, tc_HOL_Obool)), _1378994), _1378996)), _1378998) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378992, tc_fun(_1378990, tc_HOL_Obool)), _1378994), hAPP(hAPP(c_COMBC(_1378992, tc_fun(_1378988, tc_fun(_1378990, tc_HOL_Obool)), tc_fun(_1378990, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1378988, tc_HOL_Obool), tc_fun(tc_fun(_1378988, tc_fun(_1378990, tc_HOL_Obool)), tc_fun(_1378990, tc_HOL_Obool)), _1378992), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378988, tc_fun(_1378990, tc_HOL_Obool))), _1378996)), _1378998)))], (41670 ^ _781013) ^ [_1603477, _1603479, _1603481] : [-(hAPP(hAPP(c_List_Oappend(_1603477), _1603479), _1603481) = c_List_Olist_ONil(_1603477)), _1603479 = c_List_Olist_ONil(_1603477), _1603481 = c_List_Olist_ONil(_1603477)], (27613 ^ _781013) ^ [_1296318, _1296320] : [class_Rings_Olinordered__idom(_1296318), -(c_Groups_Osgn__class_Osgn(_1296318, c_Groups_Osgn__class_Osgn(_1296318, _1296320)) = c_Groups_Osgn__class_Osgn(_1296318, _1296320))], (26565 ^ _781013) ^ [_1275503, _1275505, _1275507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275503)), 26571 ^ _781013 : [(26574 ^ _781013) ^ [] : [hBOOL(hAPP(_1275505, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26570 ^ [_1275503, _1275505, _1275507]), _1275503)))], (26572 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1275505, 26570 ^ [_1275503, _1275505, _1275507])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275507)), 26579 ^ _781013 : [(26580 ^ _781013) ^ [_1275792] : [hBOOL(hAPP(_1275505, _1275792)), -(hBOOL(hAPP(_1275505, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1275792), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1275507), _1275503)))))]]], (5506 ^ _781013) ^ [_864963, _864965, _864967, _864969, _864971, _864973] : [-(c_Map_Odom(_864973, _864969, _864965) = c_Map_Odom(_864971, _864967, _864963)), _864973 = _864971, _864969 = _864967, _864965 = _864963], (9849 ^ _781013) ^ [_954809, _954811, _954813, _954815] : [class_Lattices_Osemilattice__inf(_954809), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954809), _954811), _954813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954809), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954809), _954815), _954811)), _954813)))], (6386 ^ _781013) ^ [_885204, _885206, _885208, _885210] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_885204, _885206)), _885208), _885210)), 6390 ^ _781013 : [(6393 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885206), 6389 ^ [_885204, _885206, _885208, _885210]), _885210)))], (6391 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885204), _885208), 6389 ^ [_885204, _885206, _885208, _885210])))]]], (21481 ^ _781013) ^ [] : [-(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))))], (51160 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11948 ^ _781013) ^ [_996484, _996486] : [class_Lattices_Obounded__lattice__top(_996484), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_996484), _996486), c_Orderings_Otop__class_Otop(_996484)) = _996486)], (36454 ^ _781013) ^ [_1476263, _1476265, _1476267, _1476269, _1476271, _1476273] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476263, tc_fun(_1476265, tc_HOL_Obool))), _1476267), _1476269), _1476271), _1476273)), -(hBOOL(hAPP(hAPP(_1476267, _1476271), _1476273))), -(hBOOL(hAPP(hAPP(_1476269, _1476271), _1476273)))], (8729 ^ _781013) ^ [_932870, _932872, _932874, _932876, _932878, _932880, _932882, _932884] : [c_Finite__Set_Ofolding__image__simple(_932870, _932872, _932874, _932876, _932878, _932880), hBOOL(hAPP(c_Finite__Set_Ofinite(_932872), _932882)), -(hBOOL(hAPP(hAPP(c_member(_932872), _932884), _932882))), -(hAPP(_932880, hAPP(hAPP(c_Set_Oinsert(_932872), _932884), _932882)) = hAPP(hAPP(_932874, hAPP(_932878, _932884)), hAPP(_932880, _932882)))], (21842 ^ _781013) ^ [_1190951] : [_1190951 = 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), _1190951)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37387 ^ _781013) ^ [_1494666] : [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), _1494666))), -(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), _1494666)) = 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), _1494666))))], (17847 ^ _781013) ^ [_1114082, _1114084] : [_1114082 = _1114084, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114082), _1114084)))], (1914 ^ _781013) ^ [_808593, _808595, _808597, _808599, _808601, _808603, _808605, _808607, _808609, _808611] : [-(c_Option_Ooption_Ooption__rec(_808611, _808607, _808603, _808599, _808595) = c_Option_Ooption_Ooption__rec(_808609, _808605, _808601, _808597, _808593)), _808611 = _808609, _808607 = _808605, _808603 = _808601, _808599 = _808597, _808595 = _808593], (20163 ^ _781013) ^ [_1158054, _1158056] : [20164 ^ _781013 : [(20167 ^ _781013) ^ [] : [_1158054 = hAPP(c_Nat_OSuc, _1158056)], (20165 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158054), _1158056))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158054), hAPP(c_Nat_OSuc, _1158056))))], (50348 ^ _781013) ^ [_1804850, _1804852, _1804854, _1804856] : [-(c_List_Olist__all(_1804850, _1804852, hAPP(hAPP(c_List_Oappend(_1804850), _1804854), _1804856))), c_List_Olist__all(_1804850, _1804852, _1804854), c_List_Olist__all(_1804850, _1804852, _1804856)], (31496 ^ _781013) ^ [_1374291, _1374293, _1374295] : [_1374293 = c_Orderings_Obot__class_Obot(tc_fun(_1374291, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1374291), _1374293), _1374295) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1374291, tc_HOL_Obool), tc_HOL_Obool)))], (5266 ^ _781013) ^ [_861337, _861339] : [_861339 = _861337, -(c_Lazy__Sequence_Oempty(_861339) = c_Lazy__Sequence_Oempty(_861337))], (50720 ^ _781013) ^ [_1811691] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1811691)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1811691), c_Int_OMin)))], (46635 ^ _781013) ^ [_1717217, _1717219, _1717221, _1717223, _1717225, _1717227, _1717229] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1717217, _1717219, _1717221), hAPP(hAPP(c_Relation_Orel__comp(_1717217, _1717223, _1717219), _1717225), _1717227)), _1717229) = hAPP(hAPP(c_Relation_Orel__comp(_1717217, _1717223, _1717221), _1717225), hAPP(hAPP(c_Relation_Orel__comp(_1717223, _1717219, _1717221), _1717227), _1717229)))], (12098 ^ _781013) ^ [_999351, _999353, _999355] : [class_Lattices_Olattice(_999351), hBOOL(hAPP(c_Finite__Set_Ofinite(_999351), _999353)), hBOOL(hAPP(hAPP(c_member(_999351), _999355), _999353)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_999351), _999355), c_Big__Operators_Olattice__class_OSup__fin(_999351, _999353)) = c_Big__Operators_Olattice__class_OSup__fin(_999351, _999353))], (9217 ^ _781013) ^ [_943878] : [-(c_Finite__Set_Ofun__left__comm__idem(_943878, tc_fun(_943878, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_943878, tc_HOL_Obool), tc_fun(tc_fun(_943878, tc_HOL_Obool), tc_fun(_943878, tc_HOL_Obool)), _943878), hAPP(c_COMBC(tc_fun(_943878, tc_HOL_Obool), tc_fun(_943878, tc_HOL_Obool), tc_fun(_943878, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_943878, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_943878, tc_fun(_943878, tc_HOL_Obool), tc_fun(_943878, tc_HOL_Obool)), c_Set_Oinsert(_943878)), c_Orderings_Obot__class_Obot(tc_fun(_943878, tc_HOL_Obool))))))], (29799 ^ _781013) ^ [_1336776, _1336778] : [class_Orderings_Olinorder(_1336776), -(c_Big__Operators_Olattice_OInf__fin(_1336776, c_Orderings_Oord__class_Omin(_1336776), hAPP(hAPP(c_Set_Oinsert(_1336776), _1336778), c_Orderings_Obot__class_Obot(tc_fun(_1336776, tc_HOL_Obool)))) = _1336778)], (12862 ^ _781013) ^ [_1014231, _1014233] : [-(hAPP(c_Set_Ovimage(_1014231, _1014231, c_COMBI(_1014231)), _1014233) = _1014233)], (17280 ^ _781013) ^ [_1102914, _1102916, _1102918, _1102920, _1102922] : [class_Groups_Ocomm__monoid__add(_1102914), hBOOL(hAPP(c_Finite__Set_Ofinite(_1102916), _1102918)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102916, _1102914), _1102920), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102916, tc_HOL_Obool)), _1102918), _1102922)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102916, _1102914), hAPP(hAPP(c_COMBC(_1102916, _1102914, _1102914), hAPP(hAPP(c_COMBS(_1102916, _1102914, tc_fun(_1102914, _1102914)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1102914, tc_fun(_1102914, _1102914)), _1102916), c_If(_1102914)), hAPP(hAPP(c_COMBC(_1102916, tc_fun(_1102916, tc_HOL_Obool), tc_HOL_Obool), c_member(_1102916)), _1102922))), _1102920)), c_Groups_Ozero__class_Ozero(_1102914))), _1102918))], (51566 ^ _781013) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (40647 ^ _781013) ^ [_1577643, _1577645] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1577643, _1577645), c_Orderings_Otop__class_Otop(tc_fun(_1577643, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1577645, tc_HOL_Obool), _1577643), c_Orderings_Otop__class_Otop(tc_fun(_1577645, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1577643, _1577645), tc_HOL_Obool)))], (48495 ^ _781013) ^ [_1761459, _1761461] : [-(hAPP(c_Relation_ORange(_1761459, _1761459), c_Transitive__Closure_Ortrancl(_1761459, _1761461)) = c_Orderings_Otop__class_Otop(tc_fun(_1761459, tc_HOL_Obool)))], (41324 ^ _781013) ^ [_1595451, _1595453] : [-(hAPP(hAPP(c_List_Otake(_1595451), _1595453), c_List_Olist_ONil(_1595451)) = c_List_Olist_ONil(_1595451))], (26143 ^ _781013) ^ [_1267330, _1267332, _1267334] : [class_Orderings_Oorder(_1267330), 26146 ^ _781013 : [(26153 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267330), _1267332), _1267334))), -(c_Orderings_Obot__class_Obot(tc_fun(_1267330, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1267330, _1267332, _1267334))], (26147 ^ _781013) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1267330, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1267330, _1267332, _1267334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267330), _1267332), _1267334))]]], (16007 ^ _781013) ^ [_1077118, _1077120] : [class_Rings_Olinordered__ring(_1077118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077118), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077118), _1077120), _1077120)), c_Groups_Ozero__class_Ozero(_1077118)))], (31990 ^ _781013) ^ [_1387883, _1387885, _1387887, _1387889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387883, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1387883, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31991 ^ [_1387883, _1387885, _1387887, _1387889])), _1387885)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1387883, 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), 31991 ^ [_1387883, _1387885, _1387887, _1387889]), _1387887))), _1387889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387883, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1387883, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1387885)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1387883, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1387889))))], (44815 ^ _781013) ^ [_1675695, _1675697] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675695)), c_List_Oremdups(_1675695, _1675697)) = hAPP(c_Finite__Set_Ocard(_1675695), hAPP(c_List_Oset(_1675695), _1675697)))], (10747 ^ _781013) ^ [_970684, _970686, _970688, _970690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_970684, tc_HOL_Obool)), _970686), _970688)), hBOOL(hAPP(hAPP(c_member(_970684), _970690), _970686)), -(hBOOL(hAPP(hAPP(c_member(_970684), _970690), _970688)))], (24059 ^ _781013) ^ [_1229924, _1229926] : [_1229924 = hAPP(c_Int_Onat, _1229926), 24062 ^ _781013 : [(24069 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229926))), -(_1229924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24063 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229926)), -(_1229926 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229924))]]], (16672 ^ _781013) ^ [_1090065, _1090067, _1090069, _1090071] : [class_Rings_Olinordered__ring__strict(_1090065), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090065), c_Groups_Ozero__class_Ozero(_1090065)), _1090067)), 16679 ^ _781013 : [(16686 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090065), _1090069), _1090071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090065), _1090067), _1090069)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090065), _1090067), _1090071))))], (16680 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090065), _1090067), _1090069)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090065), _1090067), _1090071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090065), _1090069), _1090071)))]]], (27224 ^ _781013) ^ [_1287990, _1287992, _1287994] : [class_Orderings_Olinorder(_1287990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287990), _1287992), _1287994)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287990, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1287990), _1287992)), c_SetInterval_Oord__class_OatLeastAtMost(_1287990, _1287992, _1287994)) = hAPP(c_SetInterval_Oord__class_OatMost(_1287990), _1287994))], (39740 ^ _781013) ^ [_1551052, _1551054, _1551056, _1551058] : [39742 ^ _781013 : [(39745 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1551056, 39741 ^ [_1551052, _1551054, _1551056, _1551058])), hAPP(_1551058, 39741 ^ [_1551052, _1551054, _1551056, _1551058])))], (39743 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1551052), 39741 ^ [_1551052, _1551054, _1551056, _1551058]), hAPP(c_List_Oset(_1551052), _1551054))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1551052, _1551056, _1551054)), c_List_Olist_Olist__size(_1551052, _1551058, _1551054))))], (39517 ^ _781013) ^ [_1545348, _1545350] : [39518 ^ _781013 : [(39519 ^ _781013) ^ [_1545394] : [hBOOL(hAPP(_1545348, _1545394))]], -(hBOOL(hAPP(_1545348, c_Hilbert__Choice_OEps(_1545350, _1545348))))], (14217 ^ _781013) ^ [_1043200, _1043202, _1043204, _1043206, _1043208, _1043210] : [class_Rings_Oordered__ring(_1043200), 14220 ^ _781013 : [(14227 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043200), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043200), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043200), _1043202), _1043208)), _1043204)), _1043206)), _1043210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043200), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043200), _1043202), _1043204)), _1043206)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043200), _1043208), _1043204)), _1043210))))], (14221 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043200), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043200), _1043202), _1043204)), _1043206)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043200), _1043208), _1043204)), _1043210))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043200), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043200), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043200), _1043202), _1043208)), _1043204)), _1043206)), _1043210)))]]], (5783 ^ _781013) ^ [_873202, _873204, _873206] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_873202, _873204, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873202)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873202), _873206), c_Com_Ocom_OSKIP), _873206)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873202), tc_HOL_Obool)))))], (45351 ^ _781013) ^ [_1686973, _1686975] : [class_Enum_Oenum(_1686973), 45354 ^ _781013 : [(45361 ^ _781013) ^ [] : [hBOOL(hAPP(_1686975, 45362 ^ [_1686973, _1686975])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1686973), _1686975)))], (45355 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1686973), _1686975)), 45358 ^ _781013 : [(45359 ^ _781013) ^ [_1687099] : [-(hBOOL(hAPP(_1686975, _1687099)))]]]]], (47944 ^ _781013) ^ [_1749516, _1749518, _1749520, _1749522, _1749524, _1749526, _1749528] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1749516, _1749518, _1749520, _1749522), _1749524), _1749526), _1749528) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1749518, _1749520, _1749522), _1749526), hAPP(_1749524, _1749528)))], (17040 ^ _781013) ^ [_1097742, _1097744, _1097746, _1097748] : [class_Groups_Ocomm__monoid__mult(_1097742), 17043 ^ _781013 : [(17050 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1097744), _1097746))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1097744, _1097742), _1097748), _1097746) = c_Groups_Oone__class_Oone(_1097742))], (17044 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1097744), _1097746)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1097744, _1097742), _1097748), _1097746) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1097742, _1097744, c_Groups_Otimes__class_Otimes(_1097742)), _1097748), c_Groups_Oone__class_Oone(_1097742)), _1097746))]]], (14321 ^ _781013) ^ [_1046066, _1046068, _1046070, _1046072] : [class_Rings_Ocomm__semiring__1(_1046066), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046066), _1046068), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046066), _1046070), _1046072)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046066), _1046068), _1046070)), _1046072))], (49146 ^ _781013) ^ [_1777832, _1777834, _1777836] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777832, _1777832), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1777834)), _1777836) = hAPP(hAPP(c_Relation_Orel__comp(_1777832, _1777832, _1777832), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777832, _1777832), tc_HOL_Obool), _1777834), _1777836)), _1777836))], (11882 ^ _781013) ^ [_995331, _995333] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_995331, tc_HOL_Obool)), _995333), c_Orderings_Otop__class_Otop(tc_fun(_995331, tc_HOL_Obool))) = _995333)], (8008 ^ _781013) ^ [_916718, _916720, _916722, _916724, _916726] : [hAPP(_916718, _916720) = c_Option_Ooption_ONone(_916722), -(c_Map_Oran(_916724, _916722, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_916724, tc_Option_Ooption(_916722)), _916718), _916720), hAPP(c_Option_Ooption_OSome(_916722), _916726))) = hAPP(hAPP(c_Set_Oinsert(_916722), _916726), c_Map_Oran(_916724, _916722, _916718)))], (12060 ^ _781013) ^ [_998561, _998563, _998565, _998567] : [c_Fun_Oinj__on(_998561, tc_Option_Ooption(_998563), _998567, c_Map_Odom(_998561, _998563, _998567)), -(c_Fun_Oinj__on(_998561, tc_Option_Ooption(_998563), c_Map_Omap__add(_998561, _998563, _998565, _998567), c_Map_Odom(_998561, _998563, _998567)))], (44649 ^ _781013) ^ [_1672591, _1672593, _1672595, _1672597] : [hBOOL(hAPP(_1672591, _1672593)), -(c_List_OtakeWhile(_1672595, _1672591, hAPP(hAPP(c_List_Olist_OCons(_1672595), _1672593), _1672597)) = hAPP(hAPP(c_List_Olist_OCons(_1672595), _1672593), c_List_OtakeWhile(_1672595, _1672591, _1672597)))], (46545 ^ _781013) ^ [_1714485, _1714487, _1714489, _1714491, _1714493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1714485, _1714487)), hAPP(_1714485, _1714489))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1714491, _1714491)), hAPP(hAPP(c_Product__Type_OPair(_1714491, _1714491), _1714487), _1714489)), c_List_Omeasures(_1714491, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1714491, tc_Nat_Onat)), _1714485), _1714493)))))], (50309 ^ _781013) ^ [_1804130, _1804132, _1804134] : [c_List_Olist__all(_1804130, _1804132, _1804134), 50312 ^ _781013 : [(50313 ^ _781013) ^ [_1804211] : [hBOOL(hAPP(hAPP(c_member(_1804130), _1804211), hAPP(c_List_Oset(_1804130), _1804134))), -(hBOOL(hAPP(_1804132, _1804211)))]]], (40930 ^ _781013) ^ [_1586824, _1586826] : [-(hAPP(c_Set_Oimage(_1586824, _1586824, c_Fun_Oid(_1586824)), _1586826) = _1586826)], (41322 ^ _781013) ^ [_1595421] : [-(c_List_Obutlast(_1595421, c_List_Olist_ONil(_1595421)) = c_List_Olist_ONil(_1595421))], (50886 ^ _781013) ^ [_1815575] : [-(c_Predicate_Oconversep(_1815575, _1815575, c_fequal) = c_fequal)], (20829 ^ _781013) ^ [_1170415, _1170417, _1170419] : [class_Rings_Olinordered__semidom(_1170415), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170415), c_Groups_Ozero__class_Ozero(_1170415)), _1170417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170415), _1170417), c_Groups_Oone__class_Oone(_1170415))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170415), hAPP(hAPP(c_Power_Opower__class_Opower(_1170415), _1170417), hAPP(c_Nat_OSuc, _1170419))), c_Groups_Oone__class_Oone(_1170415))))], (25310 ^ _781013) ^ [_1252707, _1252709, _1252711] : [class_Fields_Olinordered__field(_1252707), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252707), _1252709), _1252711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252707), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252707), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1252707), _1252709), _1252711)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1252707), c_Groups_Oone__class_Oone(_1252707)), c_Groups_Oone__class_Oone(_1252707)))), _1252711)))], (6064 ^ _781013) ^ [_879021, _879023, _879025, _879027, _879029] : [hBOOL(hAPP(_879021, _879023)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_879025), _879023), _879027)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_879021, _879025)), _879027), _879029)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_879021, _879025)), _879023), _879029)))], (31037 ^ _781013) ^ [_1362154, _1362156, _1362158] : [-(c_Nat_Onat_Onat__case(_1362154, _1362156, _1362158, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1362156)], (47228 ^ _781013) ^ [_1732328, _1732330, _1732332, _1732334] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1732328, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1732328, _1732330), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1732328, _1732330), tc_HOL_Obool)), _1732332), _1732334))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1732328, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1732328, _1732330), _1732332)), hAPP(c_Relation_ODomain(_1732328, _1732330), _1732334)))))], (43034 ^ _781013) ^ [_1636433, _1636435, _1636437, _1636439, _1636441] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636433, tc_HOL_Obool)), _1636435), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636437, tc_fun(_1636433, tc_HOL_Obool)), _1636439), _1636441)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636437, tc_fun(_1636433, tc_HOL_Obool)), _1636439), hAPP(hAPP(c_COMBB(tc_fun(_1636433, tc_HOL_Obool), tc_fun(_1636433, tc_HOL_Obool), _1636437), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636433, tc_HOL_Obool)), _1636435)), _1636441)))], (46893 ^ _781013) ^ [] : [-(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)))))], (38710 ^ _781013) ^ [_1526318, _1526320, _1526322, _1526324, _1526326, _1526328] : [-(hAPP(hAPP(c_List_Ozip(_1526318, _1526320), _1526322), hAPP(hAPP(c_List_Omap(_1526324, _1526320), _1526326), _1526328)) = hAPP(hAPP(c_List_Omap(tc_prod(_1526318, _1526324), tc_prod(_1526318, _1526320)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526318, _1526324, tc_prod(_1526318, _1526320)), hAPP(hAPP(c_COMBC(_1526318, tc_fun(_1526324, _1526320), tc_fun(_1526324, tc_prod(_1526318, _1526320))), hAPP(hAPP(c_COMBB(tc_fun(_1526320, tc_prod(_1526318, _1526320)), tc_fun(tc_fun(_1526324, _1526320), tc_fun(_1526324, tc_prod(_1526318, _1526320))), _1526318), c_COMBB(_1526320, tc_prod(_1526318, _1526320), _1526324)), c_Product__Type_OPair(_1526318, _1526320))), _1526326))), hAPP(hAPP(c_List_Ozip(_1526318, _1526324), _1526322), _1526328)))], (2938 ^ _781013) ^ [_824961, _824963, _824965, _824967, _824969, _824971, _824973, _824975] : [-(c_Nat_Onat_Onat__case(_824975, _824971, _824967, _824963) = c_Nat_Onat_Onat__case(_824973, _824969, _824965, _824961)), _824975 = _824973, _824971 = _824969, _824967 = _824965, _824963 = _824961], (17434 ^ _781013) ^ [_1106912] : [17436 ^ _781013 : [(17439 ^ _781013) ^ [_1107022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17435 ^ [_1106912, _1107022]), _1107022))], (17437 ^ _781013) ^ [_1106988] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 17435 ^ [_1106912, _1106988]), _1106912)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1106912)))], (5110 ^ _781013) ^ [_858937, _858939, _858941, _858943] : [-(c_New__DSequence_Opos__single(_858943, _858939) = c_New__DSequence_Opos__single(_858941, _858937)), _858943 = _858941, _858939 = _858937], (20823 ^ _781013) ^ [_1170332, _1170334] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170332))), -(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)), _1170332))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1170334)))) = 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)), _1170332))), 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, _1170334))))))], (12572 ^ _781013) ^ [_1008158, _1008160, _1008162, _1008164, _1008166] : [-(c_Fun_Oinj__on(_1008158, _1008160, _1008162, hAPP(hAPP(c_Set_Oinsert(_1008158), _1008164), _1008166))), c_Fun_Oinj__on(_1008158, _1008160, _1008162, _1008166), -(hBOOL(hAPP(hAPP(c_member(_1008160), hAPP(_1008162, _1008164)), hAPP(c_Set_Oimage(_1008158, _1008160, _1008162), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008158, tc_HOL_Obool)), _1008166), hAPP(hAPP(c_Set_Oinsert(_1008158), _1008164), c_Orderings_Obot__class_Obot(tc_fun(_1008158, tc_HOL_Obool))))))))], (42304 ^ _781013) ^ [_1619309, _1619311, _1619313] : [-(_1619309 = c_List_Olist_ONil(_1619311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619313), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619311)), _1619309))), -(hAPP(c_List_Ohd(_1619311), hAPP(hAPP(c_List_Odrop(_1619311), _1619313), _1619309)) = hAPP(hAPP(c_List_Onth(_1619311), _1619309), _1619313))], (31230 ^ _781013) ^ [_1366114, _1366116, _1366118, _1366120, _1366122, _1366124] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1366114, _1366116, _1366118)), _1366120), _1366122), _1366124)), 31235 ^ _781013 : [(31238 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1366116), _1366120), _1366122), _1366124)))], (31236 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1366114, _1366120)))]], 31239 ^ _781013 : [(31242 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1366118), _1366120), _1366122), _1366124)))], (31240 ^ _781013) ^ [] : [hBOOL(hAPP(_1366114, _1366120))]]], (18762 ^ _781013) ^ [_1130704, _1130706, _1130708] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1130704), _1130706)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1130704), _1130708)), 18772 ^ _781013 : [(18775 ^ _781013) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18773 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1130704), 18771 ^ [_1130704, _1130706, _1130708]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1130704, tc_HOL_Obool)), _1130706), _1130708))))]], -(hAPP(c_Finite__Set_Ocard(_1130704), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1130704, tc_HOL_Obool)), _1130706), _1130708)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1130704), _1130706)), hAPP(c_Finite__Set_Ocard(_1130704), _1130708)))], (45127 ^ _781013) ^ [_1682492] : [class_Enum_Oenum(_1682492), -(c_Orderings_Otop__class_Otop(tc_fun(_1682492, tc_HOL_Obool)) = hAPP(c_List_Oset(_1682492), c_Enum_Oenum__class_Oenum(_1682492)))], (6529 ^ _781013) ^ [_887909, _887911] : [-(_887909 = c_Option_Ooption_ONone(_887911)), -(_887909 = hAPP(c_Option_Ooption_OSome(_887911), 6532 ^ [_887909, _887911]))], (28694 ^ _781013) ^ [_1316409, _1316411, _1316413] : [class_Orderings_Olinorder(_1316409), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316409), _1316411), _1316413) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316409), _1316413), _1316411))], (8661 ^ _781013) ^ [_931429, _931431, _931433, _931435] : [class_Lattices_Olattice(_931429), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931429), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931429), _931431), _931433)), _931435) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931429), _931431), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931429), _931433), _931435)))], (1534 ^ _781013) ^ [_802930, _802932] : [-(class_Groups_Ocancel__semigroup__add(_802930)), _802932 = _802930, class_Groups_Ocancel__semigroup__add(_802932)], (17725 ^ _781013) ^ [_1111987, _1111989] : [17726 ^ _781013 : [(17729 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111989), _1111987))], (17727 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111987), _1111989))]], _1111987 = _1111989], (12190 ^ _781013) ^ [_1001019, _1001021, _1001023, _1001025, _1001027, _1001029] : [c_Fun_Oinj__on(_1001019, _1001021, _1001023, _1001025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001019, tc_HOL_Obool)), _1001027), _1001025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001019, tc_HOL_Obool)), _1001029), _1001025)), -(hAPP(c_Set_Oimage(_1001019, _1001021, _1001023), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1001019, tc_HOL_Obool)), _1001027), _1001029)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1001021, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1001019, _1001021, _1001023), _1001027)), hAPP(c_Set_Oimage(_1001019, _1001021, _1001023), _1001029)))], (44414 ^ _781013) ^ [_1666257, _1666259, _1666261] : [-(hAPP(c_List_Orev(_1666257), hAPP(hAPP(c_List_Olist_OCons(_1666257), _1666259), _1666261)) = hAPP(hAPP(c_List_Oappend(_1666257), hAPP(c_List_Orev(_1666257), _1666261)), hAPP(hAPP(c_List_Olist_OCons(_1666257), _1666259), c_List_Olist_ONil(_1666257))))], (3566 ^ _781013) ^ [_834825, _834827] : [_834827 = _834825, -(c_Int_Oint__ge__less__than(_834827) = c_Int_Oint__ge__less__than(_834825))], (10421 ^ _781013) ^ [_965855, _965857, _965859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965855, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_965855, tc_HOL_Obool)), _965857)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_965855, tc_HOL_Obool)), _965859))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965855, tc_HOL_Obool)), _965859), _965857)))], (38778 ^ _781013) ^ [_1528180, _1528182, _1528184] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528180)), _1528182) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1528180)), _1528184)), _1528182 = _1528184], (48549 ^ _781013) ^ [_1762739, _1762741] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1762739), tc_List_Olist(_1762739)), tc_HOL_Obool)), c_List_Olistrel(_1762739, _1762741)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1762739), c_List_Olistrel1(_1762739, _1762741)))))], (48025 ^ _781013) ^ [_1751106, _1751108, _1751110, _1751112, _1751114] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1751106, _1751106)), hAPP(hAPP(c_Product__Type_OPair(_1751106, _1751106), _1751108), _1751110)), _1751112)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1751106, _1751106)), hAPP(hAPP(c_Product__Type_OPair(_1751106, _1751106), _1751110), _1751114)), _1751112)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1751106, _1751106)), hAPP(hAPP(c_Product__Type_OPair(_1751106, _1751106), _1751108), _1751114)), c_Transitive__Closure_Otrancl(_1751106, _1751112))))], (48011 ^ _781013) ^ [_1750831, _1750833] : [-(hAPP(c_Relation_ORange(_1750831, _1750831), c_Transitive__Closure_Otrancl(_1750831, _1750833)) = hAPP(c_Relation_ORange(_1750831, _1750831), _1750833))], (25742 ^ _781013) ^ [_1260209, _1260211] : [c_Nat__Transfer_Ois__nat(_1260209), c_Nat__Transfer_Ois__nat(_1260211), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1260209), _1260211)))], (892 ^ _781013) ^ [_794615, _794617] : [-(class_Rings_Oinverse(_794615)), _794617 = _794615, class_Rings_Oinverse(_794617)], (34627 ^ _781013) ^ [_1437029, _1437031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1437029)), c_Int_OBit0(_1437031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1437029), _1437031)))], (38172 ^ _781013) ^ [_1513349] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1513349) = 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), _1513349), 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))))))], (22842 ^ _781013) ^ [_1208305, _1208307, _1208309] : [class_Divides_Osemiring__div(_1208305), -(_1208307 = c_Groups_Ozero__class_Ozero(_1208305)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208305), _1208309), _1208307)), _1208307) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208305), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208305), _1208309), _1208307)), c_Groups_Oone__class_Oone(_1208305)))], (18247 ^ _781013) ^ [_1120675, _1120677, _1120679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120675), _1120677)), _1120679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120677), _1120679)))], (51698 ^ _781013) ^ [_1825931, _1825933] : [hBOOL(hAPP(hAPP(c_fimplies, _1825931), _1825933)), hBOOL(_1825931), -(hBOOL(_1825933))], (37526 ^ _781013) ^ [_1497522, _1497524] : [_1497522 = _1497524, -(hAPP(c_Int_ORep__Integ, _1497522) = hAPP(c_Int_ORep__Integ, _1497524))], (28160 ^ _781013) ^ [_1306575, _1306577, _1306579, _1306581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1306575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306577), _1306579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1306579), 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), _1306577), _1306575)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1306577), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1306581, _1306575))), _1306579))))], (34807 ^ _781013) ^ [_1440087, _1440089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1440087)), c_Int_OBit0(_1440089))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440087), _1440089)))], (45584 ^ _781013) ^ [_1691870, _1691872, _1691874, _1691876] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1691870, tc_HOL_Obool), hAPP(c_Set_Oimage(_1691872, tc_fun(_1691870, tc_HOL_Obool), _1691874), _1691876)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1691872, tc_fun(_1691870, tc_HOL_Obool)), _1691876), _1691874))], (5897 ^ _781013) ^ [_875918, _875920, _875922, _875924, _875926] : [-(hAPP(c_Option_Ooption_Ooption__case(_875918, _875920, _875922, _875924), hAPP(c_Option_Ooption_OSome(_875920), _875926)) = hAPP(_875924, _875926))], (46911 ^ _781013) ^ [_1724458, _1724460, _1724462] : [c_Wellfounded_Owf(_1724458, _1724460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1724458, tc_HOL_Obool)), _1724462), hAPP(c_Relation_OImage(_1724458, _1724458, _1724460), _1724462))), -(_1724462 = c_Orderings_Obot__class_Obot(tc_fun(_1724458, tc_HOL_Obool)))], (36934 ^ _781013) ^ [_1485687, _1485689, _1485691] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1485687), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1485689)), _1485691)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1485687, _1485689), hAPP(c_Divides_OnegateSnd, _1485691))))], (7483 ^ _781013) ^ [_906046, _906048, _906050, _906052, _906054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906046, tc_HOL_Obool)), _906048), _906050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906046, tc_HOL_Obool)), _906052), _906054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906046, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906046, tc_HOL_Obool)), _906048), _906054)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906046, tc_HOL_Obool)), _906050), _906052))))], (34949 ^ _781013) ^ [_1442764] : [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), _1442764))), 34952 ^ _781013 : [(34955 ^ _781013) ^ [] : [-(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(_1442764)))))], (34953 ^ _781013) ^ [] : [-(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(_1442764)))))]]], (18231 ^ _781013) ^ [_1120387] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1120387) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44588 ^ _781013) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (23613 ^ _781013) ^ [_1222635, _1222637, _1222639] : [class_Rings_Odivision__ring(_1222635), -(_1222637 = c_Groups_Ozero__class_Ozero(_1222635)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1222635), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222635), _1222639), _1222637)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222635), _1222639), hAPP(c_Groups_Ouminus__class_Ouminus(_1222635), _1222637)))], (45658 ^ _781013) ^ [_1693467, _1693469, _1693471] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1693467, tc_HOL_Obool)), _1693469), _1693471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1693467, tc_HOL_Obool)), _1693469), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1693467, tc_HOL_Obool), _1693471))))], (20039 ^ _781013) ^ [_1156087, _1156089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156087), _1156089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156087), hAPP(c_Nat_OSuc, _1156089))))], (724 ^ _781013) ^ [_792137, _792139, _792141, _792143] : [-(c_Relation_Oirrefl(_792141, _792137)), c_Relation_Oirrefl(_792143, _792139), _792143 = _792141, _792139 = _792137], (19729 ^ _781013) ^ [_1150630, _1150632] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1150630, _1150632)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1150630, _1150632), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1150632), c_Orderings_Otop__class_Otop(tc_fun(_1150632, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1150630), c_Orderings_Otop__class_Otop(tc_fun(_1150630, tc_HOL_Obool)))))], (41406 ^ _781013) ^ [_1596908, _1596910, _1596912] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596908), tc_List_Olist(_1596908))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596908), tc_List_Olist(_1596908)), _1596910), c_List_Olist_ONil(_1596908))), c_List_Olexord(_1596908, _1596912)))], (19158 ^ _781013) ^ [_1139822, _1139824] : [class_Rings_Ocomm__semiring__1(_1139822), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1139822), _1139824), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1139822))], (16884 ^ _781013) ^ [_1094133, _1094135, _1094137] : [class_Rings_Olinordered__idom(_1094133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094133), c_Groups_Ozero__class_Ozero(_1094133)), _1094135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094133), c_Groups_Ozero__class_Ozero(_1094133)), _1094137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094133), _1094137), c_Groups_Oone__class_Oone(_1094133))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094133), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094133), _1094135), _1094137)), _1094135)))], (37070 ^ _781013) ^ [_1488443, _1488445] : [-(c_Divides_Odivmod__nat(_1488443, _1488445) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1488443, _1488445)))], (5152 ^ _781013) ^ [_859562, _859564, _859566, _859568, _859570, _859572, _859574, _859576, _859578, _859580] : [-(c_Predicate_Opred__comp(_859580, _859576, _859572, _859568, _859564) = c_Predicate_Opred__comp(_859578, _859574, _859570, _859566, _859562)), _859580 = _859578, _859576 = _859574, _859572 = _859570, _859568 = _859566, _859564 = _859562], (1234 ^ _781013) ^ [_799180, _799182] : [-(class_Rings_Oring__1(_799180)), _799182 = _799180, class_Rings_Oring__1(_799182)], (47135 ^ _781013) ^ [_1730296, _1730298, _1730300, _1730302] : [hBOOL(hAPP(c_Predicate_ORangeP(_1730296, _1730298, _1730300), _1730302)), -(hBOOL(hAPP(hAPP(_1730300, 47138 ^ [_1730296, _1730298, _1730300, _1730302]), _1730302)))], (36920 ^ _781013) ^ [_1485410, _1485412, _1485414, _1485416, _1485418, _1485420] : [-(hAPP(c_Product__Type_Oapsnd(_1485410, _1485412, _1485414, _1485416), hAPP(hAPP(c_Product__Type_OPair(_1485414, _1485410), _1485418), _1485420)) = hAPP(hAPP(c_Product__Type_OPair(_1485414, _1485412), _1485418), hAPP(_1485416, _1485420)))], (7209 ^ _781013) ^ [_901243, _901245, _901247, _901249] : [hBOOL(hAPP(hAPP(c_member(_901243), _901245), _901247)), -(hBOOL(hAPP(hAPP(c_member(_901243), _901245), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901243, tc_HOL_Obool)), _901247), _901249))))], (21533 ^ _781013) ^ [_1185444] : [-(hBOOL(hAPP(_1185444, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21540 ^ [_1185444])))), 21534 ^ _781013 : [(21535 ^ _781013) ^ [_1185496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185496)), hBOOL(hAPP(_1185444, _1185496))]]], (30875 ^ _781013) ^ [_1358835, _1358837, _1358839] : [class_Orderings_Olinorder(_1358835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358835), _1358837)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358835), _1358839)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1358835, tc_HOL_Obool)), _1358837), _1358839) = c_Orderings_Obot__class_Obot(tc_fun(_1358835, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358835), c_Big__Operators_Olattice_OSup__fin(_1358835, c_Orderings_Oord__class_Omax(_1358835), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1358835, tc_HOL_Obool)), _1358837), _1358839))), c_Big__Operators_Olattice_OSup__fin(_1358835, c_Orderings_Oord__class_Omax(_1358835), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1358835, tc_HOL_Obool)), _1358837), _1358839))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358835), c_Big__Operators_Olattice_OSup__fin(_1358835, c_Orderings_Oord__class_Omax(_1358835), _1358837)), c_Big__Operators_Olattice_OSup__fin(_1358835, c_Orderings_Oord__class_Omax(_1358835), _1358839)))], (31882 ^ _781013) ^ [_1385111, _1385113, _1385115, _1385117, _1385119] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1385111, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1385113, _1385111, _1385115), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385113, tc_HOL_Obool)), _1385117), _1385119))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385111, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1385113, _1385111, _1385115), _1385117)), hAPP(c_Relation_OImage(_1385113, _1385111, _1385115), _1385119)))))], (39868 ^ _781013) ^ [_1555618, _1555620, _1555622, _1555624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1555618), tc_List_Olist(_1555618))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1555618), tc_List_Olist(_1555618)), _1555620), _1555622)), c_List_Olistrel(_1555618, _1555624))), 39871 ^ _781013 : [(39874 ^ _781013) ^ [_1555954] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1555618, _1555618)), _1555954), hAPP(c_List_Oset(tc_prod(_1555618, _1555618)), hAPP(hAPP(c_List_Ozip(_1555618, _1555618), _1555620), _1555622)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1555618, _1555618, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1555618, tc_fun(tc_prod(_1555618, _1555618), tc_HOL_Obool), tc_fun(_1555618, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555618, tc_fun(tc_fun(tc_prod(_1555618, _1555618), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1555618, _1555618), tc_HOL_Obool), tc_fun(_1555618, tc_HOL_Obool)), _1555618), c_COMBC(_1555618, tc_fun(tc_prod(_1555618, _1555618), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555618, tc_prod(_1555618, _1555618)), tc_fun(_1555618, tc_fun(tc_fun(tc_prod(_1555618, _1555618), tc_HOL_Obool), tc_HOL_Obool)), _1555618), hAPP(c_COMBB(tc_prod(_1555618, _1555618), tc_fun(tc_fun(tc_prod(_1555618, _1555618), tc_HOL_Obool), tc_HOL_Obool), _1555618), c_member(tc_prod(_1555618, _1555618)))), c_Product__Type_OPair(_1555618, _1555618)))), _1555624)), _1555954)))], (39872 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555618)), _1555620) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555618)), _1555622))]]], (8475 ^ _781013) ^ [_927472, _927474, _927476, _927478, _927480, _927482] : [c_Finite__Set_Ofolding(_927472, _927474, _927476, _927478), -(hAPP(c_Fun_Ocomp(_927474, _927474, _927474, hAPP(_927476, _927480)), hAPP(_927476, _927482)) = hAPP(c_Fun_Ocomp(_927474, _927474, _927474, hAPP(_927476, _927482)), hAPP(_927476, _927480)))], (2226 ^ _781013) ^ [_813843, _813845, _813847, _813849, _813851, _813853] : [-(c_Power_Opower_Opower(_813853, _813849, _813845) = c_Power_Opower_Opower(_813851, _813847, _813843)), _813853 = _813851, _813849 = _813847, _813845 = _813843], (3618 ^ _781013) ^ [_835599, _835601, _835603, _835605] : [-(c_List_Omeasures(_835605, _835601) = c_List_Omeasures(_835603, _835599)), _835605 = _835603, _835601 = _835599], (43673 ^ _781013) ^ [_1651360, _1651362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651360), _1651362)), -(c_List_Oupt(_1651360, hAPP(c_Nat_OSuc, _1651362)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1651360, _1651362)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1651362), c_List_Olist_ONil(tc_Nat_Onat))))], (23058 ^ _781013) ^ [_1212500, _1212502] : [23066 ^ _781013 : [(23069 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1212502, 23065 ^ [_1212500, _1212502])))], (23067 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 23065 ^ [_1212500, _1212502]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212500))))]], 23059 ^ _781013 : [(23060 ^ _781013) ^ [_1212568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1212568), _1212500)), hBOOL(hAPP(_1212502, _1212568))]]], (48461 ^ _781013) ^ [] : [-(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))], (36482 ^ _781013) ^ [_1476797, _1476799, _1476801, _1476803, _1476805, _1476807, _1476809] : [hBOOL(hAPP(hAPP(c_member(_1476797), _1476799), hAPP(hAPP(_1476801, _1476803), _1476805))), -(hBOOL(hAPP(hAPP(c_member(_1476797), _1476799), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1476807, _1476809, tc_fun(_1476797, tc_HOL_Obool)), _1476801), hAPP(hAPP(c_Product__Type_OPair(_1476807, _1476809), _1476803), _1476805)))))], (2656 ^ _781013) ^ [_820432, _820434, _820436, _820438, _820440, _820442, _820444, _820446, _820448, _820450] : [-(c_Product__Type_Oprod_Oprod__size(_820450, _820446, _820442, _820438, _820434) = c_Product__Type_Oprod_Oprod__size(_820448, _820444, _820440, _820436, _820432)), _820450 = _820448, _820446 = _820444, _820442 = _820440, _820438 = _820436, _820434 = _820432], (44228 ^ _781013) ^ [_1662152, _1662154] : [-(c_List_Oconcat(_1662152, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1662152), tc_List_Olist(_1662152)), c_List_Olist_Olist__case(tc_List_Olist(_1662152), _1662152, c_List_Olist_ONil(_1662152), hAPP(hAPP(c_COMBB(tc_List_Olist(_1662152), tc_fun(tc_List_Olist(_1662152), tc_List_Olist(_1662152)), _1662152), c_COMBK(tc_List_Olist(_1662152), tc_List_Olist(_1662152))), hAPP(hAPP(c_COMBC(_1662152, tc_List_Olist(_1662152), tc_List_Olist(_1662152)), c_List_Olist_OCons(_1662152)), c_List_Olist_ONil(_1662152))))), _1662154)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1662152), _1662152), c_List_Ohd(_1662152)), hAPP(c_List_Ofilter(tc_List_Olist(_1662152), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1662152)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1662152), tc_List_Olist(_1662152), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1662152)))), _1662154)))], (6567 ^ _781013) ^ [_888442, _888444] : [_888444 = c_Option_Ooption_ONone(_888442), -(c_Option_Ois__none(_888442, _888444))], (26853 ^ _781013) ^ [_1280847, _1280849, _1280851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1280847)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1280849), _1280851)), 26860 ^ _781013 : [(26861 ^ _781013) ^ [_1281037] : [26863 ^ _781013 : [(26869 ^ _781013) ^ [] : [-(_1281037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26865 ^ [_1280847, _1280849, _1280851, _1281037]), 26862 ^ [_1280847, _1280849, _1280851, _1281037]))], (26867 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26865 ^ [_1280847, _1280849, _1280851, _1281037]), _1280851)))], (26864 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26862 ^ [_1280847, _1280849, _1280851, _1281037]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1280847))))]], -(_1281037 = _1280849), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1281037), _1280847) = _1280849]]], (34609 ^ _781013) ^ [_1436622, _1436624, _1436626] : [-(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), _1436622)), 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))), _1436624))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1436626))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1436626)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436622), 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), _1436626), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1436624)))))], (15105 ^ _781013) ^ [_1060409, _1060411, _1060413] : [-(hAPP(hAPP(c_Set_Oinsert(_1060409), _1060411), hAPP(c_Set_OCollect(_1060409), _1060413)) = hAPP(c_Set_OCollect(_1060409), hAPP(hAPP(c_COMBS(_1060409, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1060409), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1060409), c_fNot), hAPP(hAPP(c_COMBC(_1060409, _1060409, tc_HOL_Obool), c_fequal), _1060411)))), _1060413)))], (8114 ^ _781013) ^ [_919183, _919185, _919187, _919189, _919191, _919193, _919195] : [c_Map_Omap__comp(_919183, _919185, _919187, _919189, _919191, _919193) = hAPP(c_Option_Ooption_OSome(_919185), _919195), 8118 ^ _781013 : [(8121 ^ _781013) ^ [] : [-(hAPP(_919189, 8117 ^ [_919183, _919185, _919187, _919189, _919191, _919193, _919195]) = hAPP(c_Option_Ooption_OSome(_919185), _919195))], (8119 ^ _781013) ^ [] : [-(hAPP(_919191, _919193) = hAPP(c_Option_Ooption_OSome(_919183), 8117 ^ [_919183, _919185, _919187, _919189, _919191, _919193, _919195]))]]], (35669 ^ _781013) ^ [_1455823] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1455823), hAPP(c_Int_Onumber__class_Onumber__of(_1455823), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1455823)), class_Int_Onumber__ring(_1455823), class_Rings_Olinordered__idom(_1455823)], (34711 ^ _781013) ^ [_1438423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1438423)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1438423), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22023 ^ _781013) ^ [_1194058, _1194060, _1194062] : [class_Orderings_Olinorder(_1194058), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1194058, tc_HOL_Obool)), _1194060), _1194062)), -(_1194060 = c_Orderings_Obot__class_Obot(tc_fun(_1194058, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1194058), _1194062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194058), c_Big__Operators_Olinorder__class_OMax(_1194058, _1194060)), c_Big__Operators_Olinorder__class_OMax(_1194058, _1194062))))], (34943 ^ _781013) ^ [_1442625, _1442627] : [class_Int_Onumber__ring(_1442625), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1442625), c_Groups_Oone__class_Oone(_1442625)), c_Groups_Oone__class_Oone(_1442625))), hAPP(c_Int_Onumber__class_Onumber__of(_1442625), _1442627)) = hAPP(c_Int_Onumber__class_Onumber__of(_1442625), c_Int_OBit0(_1442627)))], (32298 ^ _781013) ^ [_1393991, _1393993] : [class_Int_Onumber__ring(_1393991), -(hAPP(c_Int_Oring__1__class_Oof__int(_1393991), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393993)) = hAPP(c_Int_Onumber__class_Onumber__of(_1393991), _1393993))], (17489 ^ _781013) ^ [_1107894, _1107896, _1107898] : [class_Rings_Olinordered__ring__strict(_1107894), 17492 ^ _781013 : [(17501 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107894), _1107896), _1107896)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107894), _1107898), _1107898)) = c_Groups_Ozero__class_Ozero(_1107894)), _1107896 = c_Groups_Ozero__class_Ozero(_1107894), _1107898 = c_Groups_Ozero__class_Ozero(_1107894)], (17493 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107894), _1107896), _1107896)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107894), _1107898), _1107898)) = c_Groups_Ozero__class_Ozero(_1107894), 17496 ^ _781013 : [(17499 ^ _781013) ^ [] : [-(_1107898 = c_Groups_Ozero__class_Ozero(_1107894))], (17497 ^ _781013) ^ [] : [-(_1107896 = c_Groups_Ozero__class_Ozero(_1107894))]]]]], (51320 ^ _781013) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (20607 ^ _781013) ^ [_1166288, _1166290, _1166292] : [class_Rings_Oring__1(_1166288), hBOOL(hAPP(hAPP(c_member(_1166288), _1166290), c_Int_Oring__1__class_OInts(_1166288))), hBOOL(hAPP(hAPP(c_member(_1166288), _1166292), c_Int_Oring__1__class_OInts(_1166288))), -(hBOOL(hAPP(hAPP(c_member(_1166288), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1166288), _1166290), _1166292)), c_Int_Oring__1__class_OInts(_1166288))))], (49004 ^ _781013) ^ [_1774352, _1774354, _1774356] : [49007 ^ _781013 : [(49013 ^ _781013) ^ [] : [49006 ^ [_1774352, _1774354, _1774356] = 49009 ^ [_1774352, _1774354, _1774356]], (49011 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774352, _1774354)), hAPP(hAPP(c_Product__Type_OPair(_1774352, _1774354), 49005 ^ [_1774352, _1774354, _1774356]), 49009 ^ [_1774352, _1774354, _1774356])), _1774356)))], (49008 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774352, _1774354)), hAPP(hAPP(c_Product__Type_OPair(_1774352, _1774354), 49005 ^ [_1774352, _1774354, _1774356]), 49006 ^ [_1774352, _1774354, _1774356])), _1774356)))]], -(c_Relation_Osingle__valued(_1774352, _1774354, _1774356))], (5833 ^ _781013) ^ [_874759, _874761] : [c_Com_Ocom_OSemi(_874759, _874761) = c_Com_Ocom_OSKIP], (8871 ^ _781013) ^ [_936136, _936138, _936140, _936142] : [class_Lattices_Osemilattice__sup(_936136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936136), _936138), _936140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936136), _936142), _936140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936136), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_936136), _936138), _936142)), _936140)))], (4658 ^ _781013) ^ [_851517, _851519] : [_851519 = _851517, -(c_Orderings_Oord__class_Oless__eq(_851519) = c_Orderings_Oord__class_Oless__eq(_851517))], (51400 ^ _781013) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (28876 ^ _781013) ^ [_1319783, _1319785, _1319787, _1319789] : [class_Fields_Olinordered__field(_1319783), -(hAPP(c_Groups_Oabs__class_Oabs(_1319783), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319785, _1319783), _1319787), _1319789)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319785, _1319783), hAPP(hAPP(c_COMBB(_1319783, _1319783, _1319785), c_Groups_Oabs__class_Oabs(_1319783)), _1319787)), _1319789))], (21680 ^ _781013) ^ [_1188129, _1188131] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1188129)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1188131)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188129), _1188131)))], (37335 ^ _781013) ^ [_1493580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1493580)), 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), _1493580)) = 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), _1493580))))))], (9467 ^ _781013) ^ [_948827, _948829, _948831] : [class_Groups_Ogroup__add(_948827), 9470 ^ _781013 : [(9477 ^ _781013) ^ [] : [_948831 = hAPP(c_Groups_Ouminus__class_Ouminus(_948827), _948829), -(_948829 = hAPP(c_Groups_Ouminus__class_Ouminus(_948827), _948831))], (9471 ^ _781013) ^ [] : [_948829 = hAPP(c_Groups_Ouminus__class_Ouminus(_948827), _948831), -(_948831 = hAPP(c_Groups_Ouminus__class_Ouminus(_948827), _948829))]]], (51282 ^ _781013) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (40391 ^ _781013) ^ [_1569059, _1569061, _1569063, _1569065] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1569059) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1569061), hAPP(hAPP(c_List_Olist_OCons(_1569061), _1569063), _1569065)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1569059)) = _1569063)], (27439 ^ _781013) ^ [_1292558, _1292560, _1292562] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1292558, tc_HOL_Obool)), _1292560), hAPP(c_Set_OPow(_1292558), _1292562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1292558, tc_HOL_Obool)), _1292560), _1292562)))], (21648 ^ _781013) ^ [_1187590, _1187592] : [class_Rings_Olinordered__semidom(_1187590), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187590), c_Groups_Ozero__class_Ozero(_1187590)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187590), _1187592))))], (49398 ^ _781013) ^ [_1784867, _1784869, _1784871] : [hBOOL(hAPP(hAPP(c_member(_1784867), _1784869), hAPP(c_List_Oset(_1784867), _1784871))), -(_1784871 = hAPP(hAPP(c_List_Oappend(_1784867), 49401 ^ [_1784867, _1784869, _1784871]), hAPP(hAPP(c_List_Olist_OCons(_1784867), _1784869), 49402 ^ [_1784867, _1784869, _1784871])))], (31603 ^ _781013) ^ [_1377088, _1377090] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1377088, 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(_1377088, tc_HOL_Obool)), tc_fun(_1377088, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1377088, tc_HOL_Obool)), tc_fun(_1377088, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1377088, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1377090)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1377088, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1377090))], (34293 ^ _781013) ^ [_1431400] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1431400)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431400))))], (38981 ^ _781013) ^ [_1532669, _1532671, _1532673] : [-(hAPP(c_List_Oset(_1532669), hAPP(c_List_OremoveAll(_1532669, _1532671), _1532673)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1532669, tc_HOL_Obool)), hAPP(c_List_Oset(_1532669), _1532673)), hAPP(hAPP(c_Set_Oinsert(_1532669), _1532671), c_Orderings_Obot__class_Obot(tc_fun(_1532669, tc_HOL_Obool)))))], (27471 ^ _781013) ^ [_1293402, _1293404] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1293402), _1293404)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1293402, tc_HOL_Obool)), hAPP(c_Set_OPow(_1293402), _1293404))))], (4696 ^ _781013) ^ [_852070, _852072] : [_852072 = _852070, -(c_Enum_Oenum__class_Oenum(_852072) = c_Enum_Oenum__class_Oenum(_852070))], (21617 ^ _781013) ^ [_1186976, _1186978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186976), _1186978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186976)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186978))))], (5180 ^ _781013) ^ [_860036, _860038] : [_860038 = _860036, -(c_Lattices_Osemilattice__sup__class_Osup(_860038) = c_Lattices_Osemilattice__sup__class_Osup(_860036))], (24818 ^ _781013) ^ [_1243676, _1243678, _1243680, _1243682] : [class_Fields_Ofield__inverse__zero(_1243676), 24821 ^ _781013 : [(24822 ^ _781013) ^ [] : [_1243678 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243676), _1243680), _1243682), 24825 ^ _781013 : [(24832 ^ _781013) ^ [] : [_1243682 = c_Groups_Ozero__class_Ozero(_1243676), -(_1243678 = c_Groups_Ozero__class_Ozero(_1243676))], (24826 ^ _781013) ^ [] : [-(_1243682 = c_Groups_Ozero__class_Ozero(_1243676)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1243676), _1243678), _1243682) = _1243680)]]], (24838 ^ _781013) ^ [] : [-(_1243678 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243676), _1243680), _1243682)), 24841 ^ _781013 : [(24844 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1243676), _1243678), _1243682) = _1243680], (24842 ^ _781013) ^ [] : [_1243682 = c_Groups_Ozero__class_Ozero(_1243676)]], 24845 ^ _781013 : [(24848 ^ _781013) ^ [] : [_1243678 = c_Groups_Ozero__class_Ozero(_1243676)], (24846 ^ _781013) ^ [] : [-(_1243682 = c_Groups_Ozero__class_Ozero(_1243676))]]]]], (43500 ^ _781013) ^ [_1647546, _1647548, _1647550, _1647552] : [-(c_List_Omap__filter(_1647546, _1647548, _1647550, _1647552) = hAPP(hAPP(c_List_Omap(_1647546, _1647548), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1647548), _1647548, _1647546, c_Option_Othe(_1647548)), _1647550)), hAPP(c_List_Ofilter(_1647546, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1647546), c_fNot), hAPP(hAPP(c_COMBC(_1647546, tc_Option_Ooption(_1647548), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1647548), tc_fun(tc_Option_Ooption(_1647548), tc_HOL_Obool), _1647546), c_fequal), _1647550)), c_Option_Ooption_ONone(_1647548)))), _1647552)))], (40175 ^ _781013) ^ [_1564354, _1564356, _1564358, _1564360] : [-(hAPP(hAPP(c_List_Olist__update(_1564354, hAPP(hAPP(c_List_Olist_OCons(_1564354), _1564356), _1564358)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1564360) = hAPP(hAPP(c_List_Olist_OCons(_1564354), _1564360), _1564358))], (18350 ^ _781013) ^ [_1122699, _1122701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122699), _1122701)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122701), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122701), _1122699)) = _1122699)], (7768 ^ _781013) ^ [_911872, _911874] : [-(_911874 = c_Orderings_Obot__class_Obot(tc_fun(_911872, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_911872), 7771 ^ [_911872, _911874]), _911874)))], (43032 ^ _781013) ^ [_1636343, _1636345, _1636347, _1636349, _1636351] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636343, tc_HOL_Obool)), _1636345), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636347, tc_fun(_1636343, tc_HOL_Obool)), _1636349), _1636351)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636347, tc_fun(_1636343, tc_HOL_Obool)), _1636349), hAPP(hAPP(c_COMBB(tc_fun(_1636343, tc_HOL_Obool), tc_fun(_1636343, tc_HOL_Obool), _1636347), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636343, tc_HOL_Obool)), _1636345)), _1636351)))], (2678 ^ _781013) ^ [_820821, _820823, _820825, _820827] : [-(c_Divides_Odivmod__nat(_820827, _820823) = c_Divides_Odivmod__nat(_820825, _820821)), _820827 = _820825, _820823 = _820821], (31962 ^ _781013) ^ [_1387082, _1387084, _1387086, _1387088, _1387090] : [_1387082 = c_Orderings_Obot__class_Obot(tc_fun(_1387084, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387084, tc_fun(_1387086, tc_HOL_Obool)), _1387082), hAPP(hAPP(c_COMBC(_1387084, tc_fun(_1387086, tc_HOL_Obool), tc_fun(_1387086, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1387086, tc_HOL_Obool), tc_fun(tc_fun(_1387086, tc_HOL_Obool), tc_fun(_1387086, tc_HOL_Obool)), _1387084), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387086, tc_HOL_Obool))), _1387088)), _1387090)) = c_Orderings_Obot__class_Obot(tc_fun(_1387086, tc_HOL_Obool)))], (6573 ^ _781013) ^ [_888525] : [-(c_Option_Ois__none(_888525, c_Option_Ooption_ONone(_888525)))], (35549 ^ _781013) ^ [_1453979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1453979), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1453979)), c_Int_OMin)))], (22458 ^ _781013) ^ [_1201551, _1201553] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1201551), _1201553)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1201551)), hAPP(c_Nat_OSuc, _1201553)))], (19068 ^ _781013) ^ [_1137836, _1137838, _1137840, _1137842, _1137844] : [hBOOL(hAPP(hAPP(c_member(_1137836), _1137838), c_SetInterval_Oord_OgreaterThanLessThan(_1137836, _1137840, _1137842, _1137844))), 19071 ^ _781013 : [(19074 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1137840, _1137838), _1137844)))], (19072 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1137840, _1137842), _1137838)))]]], (23829 ^ _781013) ^ [_1226226] : [hAPP(c_Int_Onat, _1226226) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226226), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24107 ^ _781013) ^ [_1230656, _1230658] : [hBOOL(hAPP(_1230656, hAPP(c_Int_Onat, _1230658))), 24110 ^ _781013 : [(24117 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230658), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1230656, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24111 ^ _781013) ^ [_1230756] : [_1230658 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230756), -(hBOOL(hAPP(_1230656, _1230756)))]]], (7215 ^ _781013) ^ [_901374, _901376, _901378, _901380] : [hBOOL(hAPP(hAPP(c_member(_901374), _901376), _901378)), -(hBOOL(hAPP(hAPP(c_member(_901374), _901376), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901374, tc_HOL_Obool)), _901380), _901378))))], (39320 ^ _781013) ^ [_1540617, _1540619, _1540621] : [class_Groups_Omonoid__add(_1540617), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1540617), hAPP(hAPP(c_List_Omap(_1540619, _1540617), hAPP(c_COMBK(_1540617, _1540619), c_Groups_Ozero__class_Ozero(_1540617))), _1540621)) = c_Groups_Ozero__class_Ozero(_1540617))], (51290 ^ _781013) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (21357 ^ _781013) ^ [_1181658, _1181660, _1181662, _1181664] : [-(c_Hoare__Mirabelle_Otriple__valid(_1181658, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1181658), _1181660), hAPP(c_Com_Ocom_OBODY, _1181662)), _1181664)))], (8809 ^ _781013) ^ [_935076, _935078, _935080, _935082] : [class_Lattices_Osemilattice__sup(_935076), 8812 ^ _781013 : [(8821 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935076), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935076), _935078), _935080)), _935082))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935076), _935078), _935082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935076), _935080), _935082))], (8813 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935076), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935076), _935078), _935080)), _935082)), 8816 ^ _781013 : [(8819 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935076), _935080), _935082)))], (8817 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935076), _935078), _935082)))]]]]], (40573 ^ _781013) ^ [_1575135, _1575137, _1575139, _1575141, _1575143, _1575145] : [class_Groups_Ocomm__monoid__add(_1575135), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1575137, _1575135), hAPP(hAPP(c_COMBC(_1575137, tc_fun(_1575139, tc_HOL_Obool), _1575135), hAPP(hAPP(c_COMBB(tc_fun(_1575139, _1575135), tc_fun(tc_fun(_1575139, tc_HOL_Obool), _1575135), _1575137), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1575139, _1575135)), _1575141)), _1575143)), _1575145) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1575137, _1575139), _1575135), hAPP(c_Product__Type_Oprod_Oprod__case(_1575137, _1575139, _1575135), _1575141)), hAPP(hAPP(c_Product__Type_OSigma(_1575137, _1575139), _1575145), hAPP(c_COMBK(tc_fun(_1575139, tc_HOL_Obool), _1575137), _1575143))))], (45741 ^ _781013) ^ [_1695619, _1695621, _1695623] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1695619, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1695619, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1695619, tc_HOL_Obool), tc_HOL_Obool)), _1695621), _1695623))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1695619, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1695619, tc_HOL_Obool), _1695621)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1695619, tc_HOL_Obool), _1695623)))))], (51550 ^ _781013) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (25898 ^ _781013) ^ [_1262668, _1262670] : [class_Rings_Oring__1(_1262668), -(hBOOL(hAPP(hAPP(c_member(_1262668), hAPP(c_Int_Oring__1__class_Oof__int(_1262668), _1262670)), c_Int_Oring__1__class_OInts(_1262668))))], (51342 ^ _781013) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (6561 ^ _781013) ^ [_888365, _888367] : [c_Option_Ois__none(_888365, _888367), -(_888367 = c_Option_Ooption_ONone(_888365))], (36502 ^ _781013) ^ [_1477286, _1477288, _1477290] : [-(c_Fun_Oinj__on(tc_prod(_1477286, _1477288), tc_prod(_1477288, _1477286), hAPP(c_Product__Type_Oprod_Oprod__case(_1477286, _1477288, tc_prod(_1477288, _1477286)), hAPP(c_COMBC(_1477288, _1477286, tc_prod(_1477288, _1477286)), c_Product__Type_OPair(_1477288, _1477286))), _1477290))], (42512 ^ _781013) ^ [_1623276, _1623278, _1623280] : [class_Groups_Omonoid__add(_1623276), -(hAPP(c_List_Ofoldl(_1623276, _1623276, c_Groups_Oplus__class_Oplus(_1623276), _1623278), _1623280) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1623276), _1623278), c_List_Ofoldr(_1623276, _1623276, c_Groups_Oplus__class_Oplus(_1623276), _1623280, c_Groups_Ozero__class_Ozero(_1623276))))], (51006 ^ _781013) ^ [_1818460, _1818462] : [class_Lattices_Obounded__lattice(_1818460), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1818462, _1818460)))], (27791 ^ _781013) ^ [_1300101, _1300103] : [c_Nat__Transfer_Ois__nat(_1300101), c_Nat__Transfer_Ois__nat(_1300103), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1300101, _1300103)))], (28072 ^ _781013) ^ [_1305090, _1305092] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1305090), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1305092), _1305090)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1305092), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1305092, _1305090)))], (30033 ^ _781013) ^ [_1342222, _1342224, _1342226, _1342228] : [class_Orderings_Olinorder(_1342222), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342222), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342222), _1342224), _1342226)), _1342228) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342222), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342222), _1342224), _1342228)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342222), _1342226), _1342228)))], (39996 ^ _781013) ^ [_1559809, _1559811, _1559813] : [-(_1559809 = _1559811), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1559813)), _1559809) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1559813)), _1559811), 40002 ^ _781013 : [(40005 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1559813, _1559813, tc_HOL_Obool), c_fequal), 40001 ^ [_1559809, _1559811, _1559813]))], (40003 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559813, _1559813)), 40001 ^ [_1559809, _1559811, _1559813]), hAPP(c_List_Oset(tc_prod(_1559813, _1559813)), hAPP(hAPP(c_List_Ozip(_1559813, _1559813), _1559809), _1559811)))))]]], (24228 ^ _781013) ^ [_1232937, _1232939, _1232941] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1232937, tc_Nat_Onat), _1232939), _1232941) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1232937, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1232937), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1232939)), _1232941)))], (17835 ^ _781013) ^ [_1113938] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1113938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113938), _1113938)))))], (39645 ^ _781013) ^ [_1548441, _1548443, _1548445, _1548447, _1548449] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1548441, _1548443)), _1548445), hAPP(hAPP(c_List_Ozip(_1548441, _1548443), _1548447), _1548449)) = hAPP(hAPP(c_List_Ozip(_1548441, _1548443), hAPP(hAPP(c_List_Otake(_1548441), _1548445), _1548447)), hAPP(hAPP(c_List_Otake(_1548443), _1548445), _1548449)))], (27200 ^ _781013) ^ [_1287474, _1287476, _1287478] : [class_Orderings_Oorder(_1287474), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287474, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1287474), _1287476)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1287474, _1287476, _1287478)) = c_Orderings_Obot__class_Obot(tc_fun(_1287474, tc_HOL_Obool)))], (13515 ^ _781013) ^ [_1028271, _1028273, _1028275] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1028271), c_Map_Odom(_1028271, _1028273, hAPP(c_Map_Omap__of(_1028271, _1028273), _1028275)))))], (39332 ^ _781013) ^ [_1540973, _1540975, _1540977, _1540979, _1540981] : [class_Rings_Osemiring__0(_1540973), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1540973), hAPP(hAPP(c_List_Omap(_1540975, _1540973), hAPP(hAPP(c_COMBC(_1540975, _1540973, _1540973), hAPP(hAPP(c_COMBB(_1540973, tc_fun(_1540973, _1540973), _1540975), c_Groups_Otimes__class_Otimes(_1540973)), _1540977)), _1540979)), _1540981)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1540973), hAPP(c_List_Omonoid__add__class_Olistsum(_1540973), hAPP(hAPP(c_List_Omap(_1540975, _1540973), _1540977), _1540981))), _1540979))], (47911 ^ _781013) ^ [_1748663, _1748665, _1748667, _1748669, _1748671, _1748673, _1748675, _1748677] : [class_Groups_Ocomm__monoid__add(_1748663), class_Orderings_Oord(_1748665), _1748667 = _1748669, _1748671 = _1748673, 47929 ^ _781013 : [(47934 ^ _781013) ^ [] : [hAPP(_1748675, 47928 ^ [_1748663, _1748665, _1748667, _1748669, _1748671, _1748673, _1748675, _1748677]) = hAPP(_1748677, 47928 ^ [_1748663, _1748665, _1748667, _1748669, _1748671, _1748673, _1748675, _1748677])], (47932 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1748665), 47928 ^ [_1748663, _1748665, _1748667, _1748669, _1748671, _1748673, _1748675, _1748677]), _1748673)))], (47930 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1748665), _1748669), 47928 ^ [_1748663, _1748665, _1748667, _1748669, _1748671, _1748673, _1748675, _1748677])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1748665, _1748663), _1748675), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1748665, _1748667), _1748671)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1748665, _1748663), _1748677), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1748665, _1748669), _1748673)))], (34169 ^ _781013) ^ [_1429199, _1429201] : [-(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), _1429199)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1429201), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1429199))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22856 ^ _781013) ^ [_1208538, _1208540, _1208542] : [class_Orderings_Olinorder(_1208538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208538), _1208540), _1208542)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1208538, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1208538), _1208540)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1208538, _1208540), _1208542)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1208538), _1208542))], (38525 ^ _781013) ^ [_1521754, _1521756, _1521758, _1521760, _1521762] : [hBOOL(hAPP(c_List_Odistinct(_1521754), hAPP(hAPP(c_List_Omap(tc_prod(_1521754, _1521756), _1521754), c_Product__Type_Ofst(_1521754, _1521756)), _1521758))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1521754, _1521756)), hAPP(hAPP(c_Product__Type_OPair(_1521754, _1521756), _1521760), _1521762)), hAPP(c_List_Oset(tc_prod(_1521754, _1521756)), _1521758))), -(hAPP(hAPP(c_Map_Omap__of(_1521754, _1521756), _1521758), _1521760) = hAPP(c_Option_Ooption_OSome(_1521756), _1521762))], (42921 ^ _781013) ^ [_1632767, _1632769, _1632771] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632767, tc_fun(_1632769, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1632767, tc_HOL_Obool))), _1632771) = c_Orderings_Otop__class_Otop(tc_fun(_1632769, tc_HOL_Obool)))], (22852 ^ _781013) ^ [_1208469] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1208469), hAPP(c_Nat_OSuc, _1208469)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1208469), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (45749 ^ _781013) ^ [_1695840, _1695842] : [class_Complete__Lattice_Ocomplete__lattice(_1695840), hBOOL(hAPP(c_Finite__Set_Ofinite(_1695840), _1695842)), -(_1695842 = c_Orderings_Obot__class_Obot(tc_fun(_1695840, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1695840, _1695842) = c_Complete__Lattice_OSup__class_OSup(_1695840, _1695842))], (23281 ^ _781013) ^ [_1216451, _1216453, _1216455] : [-(hBOOL(hAPP(_1216451, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1216453), _1216455)))), 23282 ^ _781013 : [(23289 ^ _781013) ^ [_1216619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216455), _1216619)), _1216453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1216453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216455), hAPP(c_Nat_OSuc, _1216619)))), hBOOL(hAPP(_1216451, _1216619))], (23283 ^ _781013) ^ [] : [_1216455 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1216451, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (8402 ^ _781013) ^ [_925725, _925727, _925729, _925731, _925733] : [-(hBOOL(hAPP(hAPP(c_member(_925725), _925727), hAPP(c_Set_Oimage(_925729, _925725, _925731), _925733)))), 8403 ^ _781013 : [(8404 ^ _781013) ^ [_925795] : [hBOOL(hAPP(hAPP(c_member(_925729), _925795), _925733)), _925727 = hAPP(_925731, _925795)]]], (43879 ^ _781013) ^ [_1654687, _1654689] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1654687), _1654689) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1654687, _1654689)))], (23875 ^ _781013) ^ [_1226982, _1226984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226982)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226984)), 23882 ^ _781013 : [(23889 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226982), _1226984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1226982)), hAPP(c_Int_Onat, _1226984))))], (23883 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1226982)), hAPP(c_Int_Onat, _1226984))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226982), _1226984)))]]], (46438 ^ _781013) ^ [_1711342, _1711344, _1711346] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1711342, hAPP(hAPP(c_COMBC(_1711342, tc_fun(tc_prod(_1711342, _1711342), tc_HOL_Obool), tc_fun(_1711342, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711342, tc_fun(tc_fun(tc_prod(_1711342, _1711342), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1711342, _1711342), tc_HOL_Obool), tc_fun(_1711342, tc_HOL_Obool)), _1711342), c_COMBC(_1711342, tc_fun(tc_prod(_1711342, _1711342), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711342, tc_prod(_1711342, _1711342)), tc_fun(_1711342, tc_fun(tc_fun(tc_prod(_1711342, _1711342), tc_HOL_Obool), tc_HOL_Obool)), _1711342), hAPP(c_COMBB(tc_prod(_1711342, _1711342), tc_fun(tc_fun(tc_prod(_1711342, _1711342), tc_HOL_Obool), tc_HOL_Obool), _1711342), c_member(tc_prod(_1711342, _1711342)))), c_Product__Type_OPair(_1711342, _1711342)))), _1711344)), _1711346)), -(hBOOL(hAPP(hAPP(c_member(_1711342), _1711346), c_Wellfounded_Oacc(_1711342, _1711344))))], (34845 ^ _781013) ^ [_1440790] : [-(c_Int_Opred(c_Int_OBit0(_1440790)) = c_Int_OBit1(c_Int_Opred(_1440790)))], (34621 ^ _781013) ^ [_1436907, _1436909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436907), _1436909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1436907)), c_Int_OBit0(_1436909))))], (8649 ^ _781013) ^ [_931143, _931145, _931147, _931149] : [class_Lattices_Osemilattice__sup(_931143), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931143), _931145), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931143), _931147), _931149)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931143), _931147), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931143), _931145), _931149)))], (48301 ^ _781013) ^ [] : [-(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))))], (48155 ^ _781013) ^ [_1753821, _1753823] : [-(c_Random_Oselect__weight(_1753821, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1753821), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1753821, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1753821, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1753821)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1753823)) = c_Random_Oselect__weight(_1753821, _1753823))], (40960 ^ _781013) ^ [_1587377, _1587379] : [-(hAPP(c_Set_Ovimage(_1587377, _1587377, c_Fun_Oid(_1587377)), _1587379) = _1587379)], (43127 ^ _781013) ^ [_1638729, _1638731, _1638733, _1638735] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638729, tc_fun(_1638731, tc_HOL_Obool)), _1638733), _1638735) = hAPP(c_Set_OCollect(_1638731), hAPP(hAPP(c_COMBB(tc_fun(_1638729, tc_HOL_Obool), tc_HOL_Obool, _1638731), c_HOL_OAll(_1638729)), hAPP(hAPP(c_COMBB(tc_fun(_1638729, tc_HOL_Obool), tc_fun(_1638729, tc_HOL_Obool), _1638731), hAPP(c_COMBS(_1638729, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1638729), c_fimplies), hAPP(hAPP(c_COMBC(_1638729, tc_fun(_1638729, tc_HOL_Obool), tc_HOL_Obool), c_member(_1638729)), _1638733)))), hAPP(hAPP(c_COMBC(_1638731, tc_fun(_1638729, tc_fun(_1638731, tc_HOL_Obool)), tc_fun(_1638729, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1638731, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1638729, tc_fun(_1638731, tc_HOL_Obool)), tc_fun(_1638729, tc_HOL_Obool)), _1638731), c_COMBB(tc_fun(_1638731, tc_HOL_Obool), tc_HOL_Obool, _1638729)), c_member(_1638731))), _1638735)))))], (29321 ^ _781013) ^ [_1328019, _1328021, _1328023, _1328025] : [class_Orderings_Olinorder(_1328019), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328019, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1328019, _1328021, _1328023)), hAPP(c_SetInterval_Oord__class_OatMost(_1328019), _1328025)) = c_SetInterval_Oord__class_OatLeastAtMost(_1328019, _1328021, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1328019), _1328023), _1328025)))], (39362 ^ _781013) ^ [_1541889, _1541891, _1541893, _1541895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1541889), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1541891)), _1541893))), -(hAPP(hAPP(c_List_Onth(_1541891), hAPP(hAPP(c_List_Olist__update(_1541891, _1541893), _1541889), _1541895)), _1541889) = _1541895)], (11936 ^ _781013) ^ [_996290, _996292] : [class_Lattices_Obounded__lattice__top(_996290), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_996290), c_Orderings_Otop__class_Otop(_996290)), _996292) = c_Orderings_Otop__class_Otop(_996290))], (48147 ^ _781013) ^ [_1753706, _1753708] : [-(_1753706 = c_List_Olist_ONil(_1753708)), -(c_Random_Oselect__weight(_1753708, hAPP(hAPP(c_List_Omap(_1753708, tc_prod(tc_Code__Numeral_Ocode__numeral, _1753708)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1753708), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1753706)) = c_Random_Oselect(_1753708, _1753706))], (33522 ^ _781013) ^ [_1417114, _1417116] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417114))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417114)), _1417116) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1417116))], (35033 ^ _781013) ^ [_1444223, _1444225] : [class_Rings_Oring__1(_1444223), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1444223), hAPP(c_Groups_Ouminus__class_Ouminus(_1444223), _1444225)), 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(_1444223), _1444225), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (31605 ^ _781013) ^ [_1377184, _1377186, _1377188, _1377190] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1377184, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1377186)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1377184, tc_HOL_Obool), tc_Nat_Onat), _1377188), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1377190))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1377184, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1377190, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1377186), _1377190))), _1377188))], (11930 ^ _781013) ^ [_996191, _996193] : [class_Lattices_Obounded__lattice__top(_996191), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_996191), _996193), c_Orderings_Otop__class_Otop(_996191)) = c_Orderings_Otop__class_Otop(_996191))], (37552 ^ _781013) ^ [_1498122, _1498124, _1498126, _1498128, _1498130] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1498122, _1498124, _1498126), _1498128), _1498130) = hAPP(hAPP(_1498128, hAPP(c_Product__Type_Ofst(_1498122, _1498124), _1498130)), hAPP(c_Product__Type_Osnd(_1498122, _1498124), _1498130)))], (9831 ^ _781013) ^ [_954482, _954484] : [class_Lattices_Oboolean__algebra(_954482), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954482), hAPP(c_Groups_Ouminus__class_Ouminus(_954482), _954484)), _954484) = c_Orderings_Obot__class_Obot(_954482))], (5887 ^ _781013) ^ [_875743] : [hAPP(c_Com_Ocom_OBODY, _875743) = c_Com_Ocom_OSKIP], (40842 ^ _781013) ^ [_1583038, _1583040, _1583042, _1583044] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1583038, _1583040), _1583042), _1583044) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1583038, tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool)), _1583042), hAPP(hAPP(c_COMBS(_1583038, tc_fun(_1583040, tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool)), tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1583040, tc_HOL_Obool), tc_fun(tc_fun(_1583040, tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool)), tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool)), _1583038), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1583040, tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool))), _1583044)), hAPP(hAPP(c_COMBC(_1583038, tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool), tc_fun(_1583040, tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1583040, tc_fun(tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool), tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool), tc_fun(_1583040, tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool))), _1583038), c_COMBC(_1583040, tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool), tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1583040, tc_prod(_1583038, _1583040)), tc_fun(_1583040, tc_fun(tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool), tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool))), _1583038), hAPP(c_COMBB(tc_prod(_1583038, _1583040), tc_fun(tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool), tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool)), _1583040), c_Set_Oinsert(tc_prod(_1583038, _1583040)))), c_Product__Type_OPair(_1583038, _1583040)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583038, _1583040), tc_HOL_Obool))))))], (48375 ^ _781013) ^ [_1758851, _1758853, _1758855, _1758857] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1758851, _1758851)), hAPP(hAPP(c_Product__Type_OPair(_1758851, _1758851), _1758853), _1758855)), c_Transitive__Closure_Ortrancl(_1758851, _1758857))), -(_1758853 = _1758855), 48382 ^ _781013 : [(48385 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1758851, _1758851)), hAPP(hAPP(c_Product__Type_OPair(_1758851, _1758851), _1758853), _1758855)), c_Transitive__Closure_Otrancl(_1758851, _1758857))))], (48383 ^ _781013) ^ [] : [_1758853 = _1758855]]], (13389 ^ _781013) ^ [_1025479, _1025481, _1025483, _1025485, _1025487] : [class_Rings_Oring(_1025479), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025481), _1025483)), hBOOL(hAPP(hAPP(c_member(_1025481), _1025485), _1025483)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1025481, _1025479), _1025487), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025481, tc_HOL_Obool)), _1025483), hAPP(hAPP(c_Set_Oinsert(_1025481), _1025485), c_Orderings_Obot__class_Obot(tc_fun(_1025481, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025479), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1025481, _1025479), _1025487), _1025483)), hAPP(_1025487, _1025485)))], (41428 ^ _781013) ^ [_1597497, _1597499, _1597501, _1597503] : [-(hAPP(hAPP(c_List_Otake(_1597497), _1597499), hAPP(hAPP(c_List_Olist_OCons(_1597497), _1597501), _1597503)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1597497), c_List_Olist_ONil(_1597497), hAPP(hAPP(c_COMBB(tc_List_Olist(_1597497), tc_List_Olist(_1597497), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1597497), _1597501)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1597497), tc_List_Olist(_1597497)), c_List_Otake(_1597497)), _1597503)), _1597499))], (20185 ^ _781013) ^ [_1158403, _1158405, _1158407] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158403)), _1158405)), hAPP(c_Nat_OSuc, _1158407)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158403), _1158405)), _1158407))], (8913 ^ _781013) ^ [_936905, _936907, _936909, _936911] : [class_Lattices_Osemilattice__sup(_936905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936905), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_936905), _936907), _936909)), _936911)), 8920 ^ _781013 : [(8923 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936905), _936909), _936911)))], (8921 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936905), _936907), _936911)))]]], (27996 ^ _781013) ^ [_1303786, _1303788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1303786), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303788), _1303786)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1303786, _1303788) = _1303786)], (37355 ^ _781013) ^ [_1494100, _1494102, _1494104] : [-(hAPP(c_Product__Type_Osnd(_1494100, _1494102), _1494104) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1494100, _1494102, _1494102), hAPP(c_COMBK(tc_fun(_1494102, _1494102), _1494100), c_COMBI(_1494102))), _1494104))], (2462 ^ _781013) ^ [_817481, _817483, _817485, _817487, _817489, _817491] : [-(c_Nat_Onat_Onat__rec(_817491, _817487, _817483) = c_Nat_Onat_Onat__rec(_817489, _817485, _817481)), _817491 = _817489, _817487 = _817485, _817483 = _817481], (8589 ^ _781013) ^ [_929973, _929975] : [class_Lattices_Osemilattice__sup(_929973), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_929973), _929975), _929975) = _929975)], (6058 ^ _781013) ^ [_878971, _878973, _878975] : [-(hBOOL(hAPP(_878971, _878973))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_878971, _878975)), _878973), _878973)))], (43587 ^ _781013) ^ [_1649904, _1649906, _1649908] : [class_Orderings_Olinorder(_1649904), -(c_List_Olinorder__class_Osorted(_1649904, hAPP(c_List_Ofilter(_1649904, hAPP(hAPP(c_COMBC(_1649904, _1649904, tc_HOL_Obool), c_fequal), hAPP(_1649906, _1649908))), _1649908)))], (7756 ^ _781013) ^ [_911632, _911634] : [_911634 = c_Orderings_Obot__class_Obot(tc_fun(_911632, tc_HOL_Obool)), 7759 ^ _781013 : [(7760 ^ _781013) ^ [_911712] : [hBOOL(hAPP(hAPP(c_member(_911632), _911712), _911634))]]], (21263 ^ _781013) ^ [_1179932, _1179934, _1179936] : [-(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), _1179932)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1179934))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1179936))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1179936), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1179932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1179932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1179936), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1179934)))))], (49083 ^ _781013) ^ [_1776431, _1776433, _1776435] : [c_Relation_Ototal__on(_1776431, _1776433, hAPP(c_Relation_Oconverse(_1776431, _1776431), _1776435)), -(c_Relation_Ototal__on(_1776431, _1776433, _1776435))], (19552 ^ _781013) ^ [_1146978, _1146980, _1146982] : [class_Rings_Olinordered__semidom(_1146978), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146978), c_Groups_Oone__class_Oone(_1146978)), _1146980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146978), c_Groups_Oone__class_Oone(_1146978)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146978), _1146980), hAPP(hAPP(c_Power_Opower__class_Opower(_1146978), _1146980), _1146982)))))], (1294 ^ _781013) ^ [_799930, _799932] : [-(class_Lattices_Obounded__lattice__top(_799930)), _799932 = _799930, class_Lattices_Obounded__lattice__top(_799932)], (33238 ^ _781013) ^ [_1411793, _1411795, _1411797, _1411799] : [c_Equiv__Relations_Oequiv(_1411793, _1411795, _1411797), hBOOL(hAPP(hAPP(c_member(_1411793), _1411799), _1411795)), -(hBOOL(hAPP(hAPP(c_member(_1411793), _1411799), hAPP(c_Relation_OImage(_1411793, _1411793, _1411797), hAPP(hAPP(c_Set_Oinsert(_1411793), _1411799), c_Orderings_Obot__class_Obot(tc_fun(_1411793, tc_HOL_Obool)))))))], (4530 ^ _781013) ^ [_849629, _849631] : [_849631 = _849629, -(c_Int_Oring__1__class_Oof__int(_849631) = c_Int_Oring__1__class_Oof__int(_849629))], (9435 ^ _781013) ^ [_948303, _948305, _948307] : [class_Groups_Ogroup__add(_948303), 9438 ^ _781013 : [(9445 ^ _781013) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_948303), _948307) = _948305, -(hAPP(c_Groups_Ouminus__class_Ouminus(_948303), _948305) = _948307)], (9439 ^ _781013) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_948303), _948305) = _948307, -(hAPP(c_Groups_Ouminus__class_Ouminus(_948303), _948307) = _948305)]]], (39720 ^ _781013) ^ [_1550391, _1550393, _1550395, _1550397] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1550391), tc_List_Olist(_1550391))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1550391), tc_List_Olist(_1550391)), _1550393), _1550395)), c_List_Olexord(_1550391, _1550397)))), 39721 ^ _781013 : [(39728 ^ _781013) ^ [_1550698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1550698), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550391)), _1550393)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550391)), _1550395)))), hAPP(hAPP(c_List_Otake(_1550391), _1550698), _1550393) = hAPP(hAPP(c_List_Otake(_1550391), _1550698), _1550395), hBOOL(hAPP(hAPP(c_member(tc_prod(_1550391, _1550391)), hAPP(hAPP(c_Product__Type_OPair(_1550391, _1550391), hAPP(hAPP(c_List_Onth(_1550391), _1550393), _1550698)), hAPP(hAPP(c_List_Onth(_1550391), _1550395), _1550698))), _1550397))], (39722 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550391)), _1550393)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550391)), _1550395))), hAPP(hAPP(c_List_Otake(_1550391), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550391)), _1550393)), _1550395) = _1550393]]], (40189 ^ _781013) ^ [_1564630, _1564632, _1564634, _1564636, _1564638, _1564640] : [-(hAPP(hAPP(c_List_Ozip(_1564630, _1564632), hAPP(hAPP(c_List_Olist_OCons(_1564630), _1564634), _1564636)), hAPP(hAPP(c_List_Olist_OCons(_1564632), _1564638), _1564640)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1564630, _1564632)), hAPP(hAPP(c_Product__Type_OPair(_1564630, _1564632), _1564634), _1564638)), hAPP(hAPP(c_List_Ozip(_1564630, _1564632), _1564636), _1564640)))], (23698 ^ _781013) ^ [_1223961] : [23700 ^ _781013 : [(23703 ^ _781013) ^ [] : [hBOOL(hAPP(_1223961, hAPP(c_Int_Onat, 23699 ^ [_1223961])))], (23701 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23699 ^ [_1223961])))]], 23704 ^ _781013 : [(23705 ^ _781013) ^ [_1224094] : [-(hBOOL(hAPP(_1223961, _1224094)))]]], (32104 ^ _781013) ^ [_1390693] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1390693)))], (50527 ^ _781013) ^ [_1808376, _1808378, _1808380] : [c_FunDef_Ois__measure(_1808376, _1808378), -(c_FunDef_Ois__measure(tc_prod(_1808376, _1808380), hAPP(hAPP(c_COMBB(_1808376, tc_Nat_Onat, tc_prod(_1808376, _1808380)), _1808378), c_Product__Type_Ofst(_1808376, _1808380))))], (46707 ^ _781013) ^ [_1720582] : [-(c_Wellfounded_Owf(_1720582, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1720582, _1720582), tc_HOL_Obool))))], (44737 ^ _781013) ^ [_1674386, _1674388] : [c_List_Olist_ONil(_1674386) = c_List_Oremdups(_1674386, _1674388), -(_1674388 = c_List_Olist_ONil(_1674386))], (24740 ^ _781013) ^ [_1242409, _1242411, _1242413, _1242415, _1242417] : [class_Fields_Ofield(_1242409), -(_1242411 = c_Groups_Ozero__class_Ozero(_1242409)), -(_1242413 = c_Groups_Ozero__class_Ozero(_1242409)), 24751 ^ _781013 : [(24758 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242409), _1242415), _1242413) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242409), _1242417), _1242411), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242409), _1242415), _1242411) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242409), _1242417), _1242413))], (24752 ^ _781013) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242409), _1242415), _1242411) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242409), _1242417), _1242413), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242409), _1242415), _1242413) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242409), _1242417), _1242411))]]], (3304 ^ _781013) ^ [_830764, _830766, _830768, _830770] : [-(c_Enum_Osublists(_830770, _830766) = c_Enum_Osublists(_830768, _830764)), _830770 = _830768, _830766 = _830764], (26259 ^ _781013) ^ [_1269225, _1269227, _1269229, _1269231] : [class_Groups_Ocomm__monoid__add(_1269225), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1269225), _1269227), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1269229), hAPP(c_Nat_OSuc, _1269231))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1269225), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1269225, tc_Nat_Onat), _1269227), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1269229, _1269231)))], (15053 ^ _781013) ^ [_1059324, _1059326, _1059328] : [class_Groups_Ocomm__monoid__mult(_1059324), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1059326, _1059324), hAPP(c_COMBK(_1059324, _1059326), c_Groups_Oone__class_Oone(_1059324))), _1059328) = c_Groups_Oone__class_Oone(_1059324))], (1224 ^ _781013) ^ [_799055, _799057] : [-(class_Groups_Oabs__if(_799055)), _799057 = _799055, class_Groups_Oabs__if(_799057)], (19486 ^ _781013) ^ [_1145726, _1145728, _1145730] : [class_Rings_Olinordered__semidom(_1145726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145726), c_Groups_Oone__class_Oone(_1145726)), _1145728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145726), c_Groups_Oone__class_Oone(_1145726)), hAPP(hAPP(c_Power_Opower__class_Opower(_1145726), _1145728), _1145730))))], (51000 ^ _781013) ^ [_1818381, _1818383] : [class_Lattices_Obounded__lattice(_1818381), -(class_Lattices_Obounded__lattice__top(tc_fun(_1818383, _1818381)))], (1024 ^ _781013) ^ [_796555, _796557] : [-(class_Lattices_Obounded__lattice(_796555)), _796557 = _796555, class_Lattices_Obounded__lattice(_796557)], (34921 ^ _781013) ^ [_1442141, _1442143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1442141), _1442143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1442141)), c_Int_OBit1(_1442143))))], (42573 ^ _781013) ^ [_1624496, _1624498, _1624500] : [class_Orderings_Olinorder(_1624496), -(c_Big__Operators_Olattice_OInf__fin(_1624496, c_Orderings_Oord__class_Omin(_1624496), hAPP(c_List_Oset(_1624496), hAPP(hAPP(c_List_Olist_OCons(_1624496), _1624498), _1624500))) = hAPP(c_List_Ofoldl(_1624496, _1624496, c_Orderings_Oord__class_Omin(_1624496), _1624498), _1624500))], (35851 ^ _781013) ^ [_1458977, _1458979] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1458977, _1458979) = c_Smallcheck_Ofull__small_H(_1458977, hAPP(c_Code__Numeral_Oint__of, _1458979), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1458979))))], (35717 ^ _781013) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (19785 ^ _781013) ^ [_1151875, _1151877, _1151879] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151875), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151877), _1151879)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151877), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151875), _1151879)))], (8769 ^ _781013) ^ [_934392, _934394, _934396] : [class_Lattices_Olattice(_934392), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934392), _934394), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934392), _934394), _934396))))], (2396 ^ _781013) ^ [_816486, _816488] : [_816488 = _816486, -(c_SetInterval_Oord__class_OatLeast(_816488) = c_SetInterval_Oord__class_OatLeast(_816486))], (12418 ^ _781013) ^ [_1005088, _1005090, _1005092] : [class_Lattices_Olattice(_1005088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005088), _1005090)), -(hBOOL(hAPP(hAPP(c_member(_1005088), _1005092), _1005090))), -(_1005090 = c_Orderings_Obot__class_Obot(tc_fun(_1005088, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1005088, hAPP(hAPP(c_Set_Oinsert(_1005088), _1005092), _1005090)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005088), _1005092), c_Big__Operators_Olattice__class_OInf__fin(_1005088, _1005090)))], (16400 ^ _781013) ^ [_1084453, _1084455, _1084457] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1084453), _1084455)), 16403 ^ _781013 : [(16423 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084453, tc_Nat_Onat), _1084457), _1084455) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 16424 ^ _781013 : [(16425 ^ _781013) ^ [_1084934] : [hBOOL(hAPP(hAPP(c_member(_1084453), _1084934), _1084455)), hAPP(_1084457, _1084934) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 16433 ^ _781013 : [(16438 ^ _781013) ^ [] : [hAPP(_1084457, 16432 ^ [_1084453, _1084455, _1084457, _1084934]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16436 ^ _781013) ^ [] : [_1084934 = 16432 ^ [_1084453, _1084455, _1084457, _1084934]], (16434 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1084453), 16432 ^ [_1084453, _1084455, _1084457, _1084934]), _1084455)))]]]]], (16404 ^ _781013) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084453, tc_Nat_Onat), _1084457), _1084455) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 16408 ^ _781013 : [(16413 ^ _781013) ^ [_1084773] : [hBOOL(hAPP(hAPP(c_member(_1084453), _1084773), _1084455)), -(16407 ^ [_1084453, _1084455, _1084457] = _1084773), -(hAPP(_1084457, _1084773) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16411 ^ _781013) ^ [] : [-(hAPP(_1084457, 16407 ^ [_1084453, _1084455, _1084457]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (16409 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1084453), 16407 ^ [_1084453, _1084455, _1084457]), _1084455)))]]]]], (6910 ^ _781013) ^ [_895162, _895164, _895166, _895168, _895170, _895172] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895162, _895164), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895162, _895164), _895166), _895168), _895170)), _895168), _895172) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895162, _895164), _895166), _895168), _895172))], (18135 ^ _781013) ^ [_1118809, _1118811, _1118813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118809), _1118811)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118811), _1118813))))], (37367 ^ _781013) ^ [_1494346, _1494348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494346), 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)), _1494348)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1494346, _1494348) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1494346, _1494348)))], (23947 ^ _781013) ^ [_1228081, _1228083] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1228081, _1228083)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1228083), _1228081))], (8026 ^ _781013) ^ [_917288, _917290, _917292, _917294] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_917288), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917288, tc_HOL_Obool)), _917290), _917294))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_917288), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917288, tc_HOL_Obool)), _917290), hAPP(hAPP(c_Set_Oinsert(_917288), _917292), _917294)))))], (51294 ^ _781013) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (4928 ^ _781013) ^ [_855976, _855978, _855980, _855982, _855984, _855986, _855988, _855990] : [-(c_New__DSequence_Opos__decr__bind(_855990, _855986, _855982, _855978) = c_New__DSequence_Opos__decr__bind(_855988, _855984, _855980, _855976)), _855990 = _855988, _855986 = _855984, _855982 = _855980, _855978 = _855976], (42290 ^ _781013) ^ [_1618811, _1618813, _1618815, _1618817, _1618819] : [-(hAPP(hAPP(c_List_Ozip(_1618811, _1618813), hAPP(hAPP(c_List_Oappend(_1618811), _1618815), _1618817)), _1618819) = hAPP(hAPP(c_List_Oappend(tc_prod(_1618811, _1618813)), hAPP(hAPP(c_List_Ozip(_1618811, _1618813), _1618815), hAPP(hAPP(c_List_Otake(_1618813), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618811)), _1618815)), _1618819))), hAPP(hAPP(c_List_Ozip(_1618811, _1618813), _1618817), hAPP(hAPP(c_List_Odrop(_1618813), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618811)), _1618815)), _1618819))))], (47701 ^ _781013) ^ [_1744118, _1744120, _1744122] : [-(hBOOL(hAPP(hAPP(c_member(_1744118), _1744120), c_Wellfounded_Oacc(_1744118, _1744122)))), 47705 ^ _781013 : [(47708 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1744118), 47704 ^ [_1744118, _1744120, _1744122]), c_Wellfounded_Oacc(_1744118, _1744122)))], (47706 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1744118, _1744118)), hAPP(hAPP(c_Product__Type_OPair(_1744118, _1744118), 47704 ^ [_1744118, _1744120, _1744122]), _1744120)), _1744122)))]]], (7693 ^ _781013) ^ [_910480, _910482, _910484] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910480, tc_HOL_Obool)), _910482), _910484) = c_Orderings_Obot__class_Obot(tc_fun(_910480, tc_HOL_Obool)), 7696 ^ _781013 : [(7699 ^ _781013) ^ [] : [-(_910484 = c_Orderings_Obot__class_Obot(tc_fun(_910480, tc_HOL_Obool)))], (7697 ^ _781013) ^ [] : [-(_910482 = c_Orderings_Obot__class_Obot(tc_fun(_910480, tc_HOL_Obool)))]]], (29701 ^ _781013) ^ [_1334878, _1334880, _1334882] : [class_Orderings_Olinorder(_1334878), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334878), _1334880)), -(_1334880 = c_Orderings_Obot__class_Obot(tc_fun(_1334878, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334878), _1334882)), -(_1334882 = c_Orderings_Obot__class_Obot(tc_fun(_1334878, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334878, tc_HOL_Obool)), _1334880), _1334882) = c_Orderings_Obot__class_Obot(tc_fun(_1334878, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1334878, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334878, tc_HOL_Obool)), _1334880), _1334882)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334878), c_Big__Operators_Olinorder__class_OMin(_1334878, _1334880)), c_Big__Operators_Olinorder__class_OMin(_1334878, _1334882)))], (5210 ^ _781013) ^ [_860491, _860493, _860495, _860497] : [-(c_Relation_Oconverse(_860497, _860493) = c_Relation_Oconverse(_860495, _860491)), _860497 = _860495, _860493 = _860491], (42276 ^ _781013) ^ [_1618384, _1618386, _1618388, _1618390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1618384), _1618386)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618388)), _1618390))), -(hAPP(hAPP(c_List_Otake(_1618388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1618384), _1618386)), _1618390) = hAPP(hAPP(c_List_Oappend(_1618388), hAPP(hAPP(c_List_Otake(_1618388), _1618384), _1618390)), hAPP(hAPP(c_List_Otake(_1618388), _1618386), hAPP(hAPP(c_List_Odrop(_1618388), _1618384), _1618390))))], (32278 ^ _781013) ^ [_1393659, _1393661, _1393663] : [c_Com_Ocom_OLocal(_1393659, _1393661, _1393663) = c_Com_Ocom_OSKIP], (27928 ^ _781013) ^ [_1302418, _1302420, _1302422, _1302424] : [class_Divides_Osemiring__div(_1302418), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1302418), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1302418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302418), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1302418), _1302420), _1302422)), _1302422)), c_Divides_Odiv__class_Omod(_1302418, _1302420, _1302422))), _1302424) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1302418), _1302420), _1302424))], (38113 ^ _781013) ^ [] : [-(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)))], (32494 ^ _781013) ^ [_1397547, _1397549, _1397551] : [class_Int_Onumber(_1397547), class_Orderings_Oord(_1397547), 32501 ^ _781013 : [(32508 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397547), hAPP(c_Int_Onumber__class_Onumber__of(_1397547), _1397549)), hAPP(c_Int_Onumber__class_Onumber__of(_1397547), _1397551)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1397547), hAPP(c_Int_Onumber__class_Onumber__of(_1397547), _1397549)), hAPP(c_Int_Onumber__class_Onumber__of(_1397547), _1397551)) = hAPP(c_Int_Onumber__class_Onumber__of(_1397547), _1397551))], (32502 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397547), hAPP(c_Int_Onumber__class_Onumber__of(_1397547), _1397549)), hAPP(c_Int_Onumber__class_Onumber__of(_1397547), _1397551))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1397547), hAPP(c_Int_Onumber__class_Onumber__of(_1397547), _1397549)), hAPP(c_Int_Onumber__class_Onumber__of(_1397547), _1397551)) = hAPP(c_Int_Onumber__class_Onumber__of(_1397547), _1397549))]]], (41308 ^ _781013) ^ [_1595177, _1595179, _1595181, _1595183, _1595185] : [class_Orderings_Olinorder(_1595177), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1595179, _1595177, _1595181), _1595183), _1595185) = c_List_Olist_ONil(_1595179)], (48497 ^ _781013) ^ [_1761498, _1761500] : [-(c_Relation_Orefl__on(_1761498, c_Orderings_Otop__class_Otop(tc_fun(_1761498, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1761498, _1761500)))], (5458 ^ _781013) ^ [_864215, _864217, _864219, _864221, _864223, _864225] : [-(c_COMBB(_864225, _864221, _864217) = c_COMBB(_864223, _864219, _864215)), _864225 = _864223, _864221 = _864219, _864217 = _864215], (10363 ^ _781013) ^ [_964641, _964643, _964645, _964647] : [hBOOL(hAPP(hAPP(c_member(_964641), _964643), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964641, tc_HOL_Obool)), _964645), _964647))), -(hBOOL(hAPP(hAPP(c_member(_964641), _964643), _964647)))], (47592 ^ _781013) ^ [_1741157, _1741159] : [47594 ^ _781013 : [(47597 ^ _781013) ^ [] : [47593 ^ [_1741157, _1741159] = c_Orderings_Obot__class_Obot(tc_fun(_1741157, tc_HOL_Obool))], (47595 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1741157, tc_HOL_Obool)), 47593 ^ [_1741157, _1741159]), hAPP(c_Relation_OImage(_1741157, _1741157, _1741159), 47593 ^ [_1741157, _1741159]))))]], -(c_Wellfounded_Owf(_1741157, _1741159))], (20153 ^ _781013) ^ [_1157936, _1157938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157936), hAPP(c_Nat_OSuc, _1157938))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157936), _1157938))), -(_1157936 = hAPP(c_Nat_OSuc, _1157938))], (35443 ^ _781013) ^ [_1451910] : [_1451910 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1451910) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31484 ^ _781013) ^ [_1374033, _1374035, _1374037] : [_1374035 = c_Orderings_Obot__class_Obot(tc_fun(_1374033, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1374033, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1374033), _1374035), _1374037))], (21179 ^ _781013) ^ [_1178319, _1178321, _1178323, _1178325, _1178327, _1178329] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178319), _1178321)), _1178323) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178325), _1178327)), _1178329), 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), _1178325), _1178327)), _1178329)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178323), _1178319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178329)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178325), _1178319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178327), _1178321)))], (12206 ^ _781013) ^ [_1001404, _1001406, _1001408, _1001410, _1001412, _1001414] : [c_Fun_Oinj__on(_1001404, _1001406, _1001408, _1001410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001404, tc_HOL_Obool)), _1001412), _1001410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001404, tc_HOL_Obool)), _1001414), _1001410)), -(hAPP(c_Set_Oimage(_1001404, _1001406, _1001408), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1001404, tc_HOL_Obool)), _1001412), _1001414)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1001406, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1001404, _1001406, _1001408), _1001412)), hAPP(c_Set_Oimage(_1001404, _1001406, _1001408), _1001414)))], (40934 ^ _781013) ^ [_1586899, _1586901] : [-(c_Product__Type_Omap__pair(_1586899, _1586899, _1586901, _1586901, c_Fun_Oid(_1586899), c_Fun_Oid(_1586901)) = c_Fun_Oid(tc_prod(_1586899, _1586901)))], (44354 ^ _781013) ^ [_1664850, _1664852, _1664854, _1664856, _1664858] : [-(c_List_Ofoldr(_1664850, _1664852, _1664854, _1664856, _1664858) = hAPP(c_List_Ofoldl(_1664852, _1664850, hAPP(c_COMBC(_1664850, _1664852, _1664852), _1664854), _1664858), hAPP(c_List_Orev(_1664850), _1664856)))], (49055 ^ _781013) ^ [_1775681, _1775683, _1775685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1775681, _1775681), tc_HOL_Obool)), c_Relation_OId(_1775681)), _1775683)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1775681, _1775681), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1775681, _1775681, _1775681), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1775681, _1775681), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1775681, _1775685)), _1775683)), _1775685)), _1775683)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1775681, _1775681), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1775681, _1775685)), _1775683)))], (8287 ^ _781013) ^ [_922696, _922698, _922700, _922702, _922704] : [class_Groups_Ominus(_922696), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922698, _922696)), _922700), _922702), _922704) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_922696), hAPP(_922700, _922704)), hAPP(_922702, _922704)))], (38983 ^ _781013) ^ [_1532736, _1532738, _1532740] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1532736)), c_List_Osublist(_1532736, _1532738, _1532740)) = 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(_1532736)), _1532738)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1532740)))))], (21830 ^ _781013) ^ [_1190771] : [class_Nat_Osemiring__char__0(_1190771), -(c_Fun_Oinj__on(tc_Nat_Onat, _1190771, c_Nat_Osemiring__1__class_Oof__nat(_1190771), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (44661 ^ _781013) ^ [_1672776, _1672778, _1672780, _1672782, _1672784] : [-(c_List_OtakeWhile(_1672776, _1672778, hAPP(hAPP(c_List_Omap(_1672780, _1672776), _1672782), _1672784)) = hAPP(hAPP(c_List_Omap(_1672780, _1672776), _1672782), c_List_OtakeWhile(_1672780, hAPP(c_Fun_Ocomp(_1672776, tc_HOL_Obool, _1672780, _1672778), _1672782), _1672784)))], (35899 ^ _781013) ^ [_1459879, _1459881, _1459883, _1459885, _1459887, _1459889] : [c_Equiv__Relations_Ocongruent(_1459879, _1459881, _1459883, _1459885), hBOOL(hAPP(hAPP(c_member(tc_prod(_1459879, _1459879)), hAPP(hAPP(c_Product__Type_OPair(_1459879, _1459879), _1459887), _1459889)), _1459883)), -(hAPP(_1459885, _1459887) = hAPP(_1459885, _1459889))], (4636 ^ _781013) ^ [_851198, _851200, _851202, _851204] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_851204, _851200) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_851202, _851198)), _851204 = _851202, _851200 = _851198], (17148 ^ _781013) ^ [_1100042, _1100044, _1100046, _1100048, _1100050, _1100052] : [class_Rings_Olinordered__semiring__1(_1100042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100042), _1100044), _1100046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100042), _1100048), _1100046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100042), c_Groups_Ozero__class_Ozero(_1100042)), _1100050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100042), c_Groups_Ozero__class_Ozero(_1100042)), _1100052)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100042), _1100050), _1100052) = c_Groups_Oone__class_Oone(_1100042), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100042), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100042), _1100050), _1100044)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100042), _1100052), _1100048))), _1100046)))], (17523 ^ _781013) ^ [_1108423, _1108425, _1108427] : [class_Rings_Olinordered__ring(_1108423), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108423), c_Groups_Ozero__class_Ozero(_1108423)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108423), _1108425), _1108425)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108423), _1108427), _1108427)))))], (13573 ^ _781013) ^ [_1029707, _1029709, _1029711, _1029713, _1029715] : [class_Groups_Ocomm__monoid__add(_1029707), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029709), _1029711)), c_Fun_Oinj__on(_1029709, _1029709, _1029713, _1029711), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029709, _1029707), _1029715), hAPP(c_Set_Oimage(_1029709, _1029709, _1029713), _1029711)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029709, _1029707), hAPP(c_Fun_Ocomp(_1029709, _1029707, _1029709, _1029715), _1029713)), _1029711))], (29467 ^ _781013) ^ [_1330749, _1330751, _1330753] : [class_Orderings_Olinorder(_1330749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330749), _1330751)), -(_1330751 = c_Orderings_Obot__class_Obot(tc_fun(_1330749, tc_HOL_Obool))), 29478 ^ _781013 : [(29488 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330749), hAPP(c_Finite__Set_Ofold1(_1330749, c_Orderings_Oord__class_Omin(_1330749)), _1330751)), _1330753))), 29489 ^ _781013 : [(29490 ^ _781013) ^ [_1331138] : [hBOOL(hAPP(hAPP(c_member(_1330749), _1331138), _1330751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330749), _1331138), _1330753))]]], (29479 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330749), hAPP(c_Finite__Set_Ofold1(_1330749, c_Orderings_Oord__class_Omin(_1330749)), _1330751)), _1330753)), 29483 ^ _781013 : [(29486 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330749), 29482 ^ [_1330749, _1330751, _1330753]), _1330753)))], (29484 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330749), 29482 ^ [_1330749, _1330751, _1330753]), _1330751)))]]]]], (21239 ^ _781013) ^ [] : [-(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))))], (9363 ^ _781013) ^ [_947076, _947078, _947080, _947082] : [hBOOL(hAPP(hAPP(c_member(_947076), _947078), _947080)), hBOOL(hAPP(hAPP(c_member(_947076), _947078), _947082)), -(hBOOL(hAPP(hAPP(c_member(_947076), _947078), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947076, tc_HOL_Obool)), _947080), _947082))))], (51334 ^ _781013) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (17695 ^ _781013) ^ [_1111637, _1111639, _1111641] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111637), _1111639) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111641), _1111639), -(_1111637 = _1111641), -(_1111639 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43496 ^ _781013) ^ [_1647334, _1647336, _1647338] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647334)), hAPP(c_List_Ofilter(_1647334, _1647336), _1647338)) = 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(_1647334)), _1647338)))), hAPP(hAPP(c_COMBB(_1647334, tc_HOL_Obool, tc_Nat_Onat), _1647336), hAPP(c_List_Onth(_1647334), _1647338))))))], (16351 ^ _781013) ^ [_1083344, _1083346, _1083348] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1083344, tc_HOL_Obool)), _1083346), _1083348) = hAPP(c_Set_OCollect(_1083344), hAPP(hAPP(c_COMBS(_1083344, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1083344), c_fconj), hAPP(hAPP(c_COMBC(_1083344, tc_fun(_1083344, tc_HOL_Obool), tc_HOL_Obool), c_member(_1083344)), _1083346))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1083344), c_fNot), hAPP(hAPP(c_COMBC(_1083344, tc_fun(_1083344, tc_HOL_Obool), tc_HOL_Obool), c_member(_1083344)), _1083348)))))], (50114 ^ _781013) ^ [_1799394, _1799396] : [c_Wellfounded_Owf(_1799394, _1799396), 50117 ^ _781013 : [(50118 ^ _781013) ^ [_1799526] : [50119 ^ _781013 : [(50120 ^ _781013) ^ [_1799631] : [hBOOL(hAPP(hAPP(c_member(_1799394), _1799631), _1799526))]], 50122 ^ _781013 : [(50125 ^ _781013) ^ [_1799753] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1799394, _1799394)), hAPP(hAPP(c_Product__Type_OPair(_1799394, _1799394), _1799753), 50121 ^ [_1799394, _1799396, _1799526])), _1799396)), hBOOL(hAPP(hAPP(c_member(_1799394), _1799753), _1799526))], (50123 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1799394), 50121 ^ [_1799394, _1799396, _1799526]), _1799526)))]]]]], (34006 ^ _781013) ^ [_1425655, _1425657, _1425659, _1425661] : [-(hAPP(c_Nat_Onat_Onat__rec(_1425655, _1425657, _1425659), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425661)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1425655), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1425661))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1425655, _1425655), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1425655, tc_fun(_1425655, _1425655)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1425655, tc_fun(_1425655, _1425655)), tc_Int_Oint), c_If(_1425655)), c_Nat__Numeral_Oneg)), _1425657)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1425655, _1425655), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1425655, _1425655), tc_Int_Oint), _1425659), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1425655, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1425655, _1425657, _1425659)), c_Int_Onat)))))], (7511 ^ _781013) ^ [_906661, _906663, _906665, _906667, _906669] : [class_Orderings_Oord(_906661), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906663, _906661)), _906665), _906667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906661), hAPP(_906665, _906669)), hAPP(_906667, _906669))))], (34535 ^ _781013) ^ [_1435311, _1435313] : [class_Int_Onumber__ring(_1435311), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1435311), hAPP(c_Int_Onumber__class_Onumber__of(_1435311), _1435313)), c_Groups_Oone__class_Oone(_1435311)) = hAPP(c_Int_Onumber__class_Onumber__of(_1435311), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1435313), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (26651 ^ _781013) ^ [_1277101, _1277103] : [c_Nat__Transfer_Ois__nat(_1277101), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1277101, _1277103)))], (9451 ^ _781013) ^ [_948544, _948546, _948548] : [class_Groups_Oordered__ab__group__add(_948544), 9454 ^ _781013 : [(9461 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948544), _948548), hAPP(c_Groups_Ouminus__class_Ouminus(_948544), _948546))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948544), _948546), hAPP(c_Groups_Ouminus__class_Ouminus(_948544), _948548))))], (9455 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948544), _948546), hAPP(c_Groups_Ouminus__class_Ouminus(_948544), _948548))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948544), _948548), hAPP(c_Groups_Ouminus__class_Ouminus(_948544), _948546))))]]], (43102 ^ _781013) ^ [_1638110, _1638112, _1638114, _1638116, _1638118] : [43104 ^ _781013 : [(43107 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1638110, tc_HOL_Obool)), _1638112), hAPP(_1638118, 43103 ^ [_1638110, _1638112, _1638114, _1638116, _1638118])))], (43105 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1638114), 43103 ^ [_1638110, _1638112, _1638114, _1638116, _1638118]), _1638116)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1638110, tc_HOL_Obool)), _1638112), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638114, tc_fun(_1638110, tc_HOL_Obool)), _1638116), _1638118))))], (18598 ^ _781013) ^ [_1127220, _1127222, _1127224, _1127226, _1127228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127220), _1127222)), 18601 ^ _781013 : [(18608 ^ _781013) ^ [] : [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), _1127222), _1127220)), _1127224)), _1127226) = _1127228, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127222), _1127224)), _1127226) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127220), _1127224)), _1127228))], (18602 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127222), _1127224)), _1127226) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127220), _1127224)), _1127228), -(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), _1127222), _1127220)), _1127224)), _1127226) = _1127228)]]], (48722 ^ _781013) ^ [_1766927, _1766929, _1766931, _1766933] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766927, _1766927)), hAPP(hAPP(c_Product__Type_OPair(_1766927, _1766927), _1766929), _1766931)), c_Transitive__Closure_Ortrancl(_1766927, _1766933))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1766927, _1766927)), hAPP(hAPP(c_Product__Type_OPair(_1766927, _1766927), _1766931), _1766929)), c_Transitive__Closure_Ortrancl(_1766927, hAPP(c_Relation_Oconverse(_1766927, _1766927), _1766933)))))], (47840 ^ _781013) ^ [_1747436, _1747438] : [c_List_Olist__ex(_1747436, _1747438, c_List_Olist_ONil(_1747436))], (34585 ^ _781013) ^ [_1436178] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436178)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1436178)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1436178)), 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)))))], (5278 ^ _781013) ^ [_861507, _861509] : [_861509 = _861507, -(c_Groups_Ominus__class_Ominus(_861509) = c_Groups_Ominus__class_Ominus(_861507))], (51568 ^ _781013) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (51306 ^ _781013) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (51608 ^ _781013) ^ [_1824733, _1824735, _1824737, _1824739, _1824741, _1824743] : [-(hAPP(hAPP(hAPP(c_COMBB(_1824733, _1824735, _1824737), _1824739), _1824741), _1824743) = hAPP(_1824739, hAPP(_1824741, _1824743)))], (39314 ^ _781013) ^ [_1540549, _1540551, _1540553, _1540555, _1540557, _1540559] : [-(hBOOL(hAPP(hAPP(c_member(_1540549), _1540551), hAPP(c_List_Oset(_1540549), _1540553)))), -(hAPP(c_Map_Omap__upds(_1540549, _1540555, _1540557, _1540553, _1540559), _1540551) = hAPP(_1540557, _1540551))], (8481 ^ _781013) ^ [_927617, _927619, _927621, _927623, _927625, _927627, _927629, _927631] : [c_Finite__Set_Ofolding(_927617, _927619, _927621, _927623), -(hAPP(c_Fun_Ocomp(_927619, _927619, _927625, hAPP(_927621, _927627)), hAPP(c_Fun_Ocomp(_927619, _927619, _927625, hAPP(_927621, _927629)), _927631)) = hAPP(c_Fun_Ocomp(_927619, _927619, _927625, hAPP(_927621, _927629)), hAPP(c_Fun_Ocomp(_927619, _927619, _927625, hAPP(_927621, _927627)), _927631)))], (19150 ^ _781013) ^ [_1139680, _1139682, _1139684] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1139680), _1139682)), _1139684) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1139680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1139682), _1139684)))], (42174 ^ _781013) ^ [_1615903, _1615905, _1615907, _1615909] : [hAPP(hAPP(c_List_Oappend(_1615903), _1615905), _1615907) = _1615909, 42177 ^ _781013 : [(42180 ^ _781013) ^ [] : [-(_1615907 = hAPP(hAPP(c_List_Odrop(_1615903), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615903)), _1615905)), _1615909))], (42178 ^ _781013) ^ [] : [-(_1615905 = hAPP(hAPP(c_List_Otake(_1615903), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615903)), _1615905)), _1615909))]]], (41202 ^ _781013) ^ [_1593273, _1593275] : [_1593275 = c_List_Olist_ONil(_1593273), -(hAPP(c_List_Oset(_1593273), _1593275) = c_Orderings_Obot__class_Obot(tc_fun(_1593273, tc_HOL_Obool)))], (37764 ^ _781013) ^ [_1503445, _1503447, _1503449, _1503451, _1503453, _1503455, _1503457, _1503459] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1503445, _1503447), tc_prod(_1503445, _1503447))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1503445, _1503447), tc_prod(_1503445, _1503447)), hAPP(hAPP(c_Product__Type_OPair(_1503445, _1503447), _1503449), _1503451)), hAPP(hAPP(c_Product__Type_OPair(_1503445, _1503447), _1503453), _1503455))), c_Wellfounded_Olex__prod(_1503445, _1503447, _1503457, _1503459)))), 37765 ^ _781013 : [(37768 ^ _781013) ^ [] : [_1503449 = _1503453, hBOOL(hAPP(hAPP(c_member(tc_prod(_1503447, _1503447)), hAPP(hAPP(c_Product__Type_OPair(_1503447, _1503447), _1503451), _1503455)), _1503459))], (37766 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1503445, _1503445)), hAPP(hAPP(c_Product__Type_OPair(_1503445, _1503445), _1503449), _1503453)), _1503457))]]], (17969 ^ _781013) ^ [_1116034, _1116036, _1116038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1116034)), 17972 ^ _781013 : [(17979 ^ _781013) ^ [] : [_1116036 = _1116038, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116034), _1116036) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116034), _1116038))], (17973 ^ _781013) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116034), _1116036) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116034), _1116038), -(_1116036 = _1116038)]]], (12268 ^ _781013) ^ [_1002499, _1002501, _1002503] : [class_Lattices_Olattice(_1002499), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002499), _1002501)), -(_1002501 = c_Orderings_Obot__class_Obot(tc_fun(_1002499, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1002499, hAPP(hAPP(c_Set_Oinsert(_1002499), _1002503), _1002501)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1002499), _1002503), c_Big__Operators_Olattice__class_OInf__fin(_1002499, _1002501)))], (34819 ^ _781013) ^ [_1440295, _1440297] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1440295)), c_Int_OBit1(_1440297)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1440295), _1440297)))], (45115 ^ _781013) ^ [_1682288, _1682290, _1682292] : [class_Orderings_Olinorder(_1682288), -(c_List_Olinorder__class_Osort__key(_1682290, _1682288, _1682292, c_List_Olist_ONil(_1682290)) = c_List_Olist_ONil(_1682290))], (26065 ^ _781013) ^ [_1265883, _1265885] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1265883, _1265885))))], (27218 ^ _781013) ^ [_1287847, _1287849] : [class_Orderings_Olinorder(_1287847), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287847, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1287847), _1287849)), hAPP(hAPP(c_Set_Oinsert(_1287847), _1287849), c_Orderings_Obot__class_Obot(tc_fun(_1287847, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1287847), _1287849))], (42893 ^ _781013) ^ [_1632286, _1632288, _1632290, _1632292, _1632294] : [-(_1632286 = c_Orderings_Obot__class_Obot(tc_fun(_1632288, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1632290, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632288, tc_fun(_1632290, tc_HOL_Obool)), _1632286), _1632292)), _1632294) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632288, tc_fun(_1632290, tc_HOL_Obool)), _1632286), hAPP(hAPP(c_COMBC(_1632288, tc_fun(_1632290, tc_HOL_Obool), tc_fun(_1632290, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1632290, tc_HOL_Obool), tc_fun(tc_fun(_1632290, tc_HOL_Obool), tc_fun(_1632290, tc_HOL_Obool)), _1632288), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1632290, tc_HOL_Obool))), _1632292)), _1632294)))], (38065 ^ _781013) ^ [_1510362, _1510364, _1510366, _1510368] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1510362, _1510362)), hAPP(hAPP(c_Product__Type_OPair(_1510362, _1510362), _1510364), _1510366)), c_Relation_OId__on(_1510362, _1510368)))), _1510364 = _1510366, hBOOL(hAPP(hAPP(c_member(_1510362), _1510364), _1510368))], (22440 ^ _781013) ^ [_1201250, _1201252] : [class_Divides_Osemiring__div(_1201250), -(_1201252 = c_Groups_Ozero__class_Ozero(_1201250)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1201250), _1201252), _1201252) = c_Groups_Oone__class_Oone(_1201250))], (1044 ^ _781013) ^ [_796805, _796807] : [-(class_Groups_Oordered__ab__group__add__abs(_796805)), _796807 = _796805, class_Groups_Oordered__ab__group__add__abs(_796807)], (51538 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (9150 ^ _781013) ^ [_942659, _942661, _942663, _942665, _942667] : [hBOOL(hAPP(hAPP(c_member(_942659), _942661), _942663)), -(hAPP(c_Map_Orestrict__map(_942659, _942665, _942667, _942663), _942661) = hAPP(_942667, _942661))], (1524 ^ _781013) ^ [_802805, _802807] : [-(class_Rings_Oordered__comm__semiring(_802805)), _802807 = _802805, class_Rings_Oordered__comm__semiring(_802807)], (14423 ^ _781013) ^ [_1048347, _1048349, _1048351] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048347), _1048349)), hBOOL(hAPP(hAPP(c_member(_1048347), _1048351), _1048349)), -(hAPP(c_Finite__Set_Ocard(_1048347), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048347, tc_HOL_Obool)), _1048349), hAPP(hAPP(c_Set_Oinsert(_1048347), _1048351), c_Orderings_Obot__class_Obot(tc_fun(_1048347, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1048347), _1048349)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (51214 ^ _781013) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (5272 ^ _781013) ^ [_861422, _861424] : [_861424 = _861422, -(c_List_Otl(_861424) = c_List_Otl(_861422))], (2432 ^ _781013) ^ [_817026, _817028, _817030, _817032, _817034, _817036] : [-(c_Com_Ocom_OLocal(_817036, _817032, _817028) = c_Com_Ocom_OLocal(_817034, _817030, _817026)), _817036 = _817034, _817032 = _817030, _817028 = _817026], (34821 ^ _781013) ^ [_1440338, _1440340] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1440338)), c_Int_OBit0(_1440340)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1440338), _1440340)))], (43543 ^ _781013) ^ [_1648677, _1648679, _1648681, _1648683] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1648677, tc_Nat_Onat), _1648677), c_Product__Type_Ofst(_1648677, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1648677, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1648677, tc_Nat_Onat)), _1648679), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1648677, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1648677, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1648677, tc_Nat_Onat), _1648681), _1648683))) = hAPP(hAPP(c_List_Omap(tc_prod(_1648677, tc_Nat_Onat), _1648677), c_Product__Type_Ofst(_1648677, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1648677, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1648677, tc_Nat_Onat)), _1648679), c_Product__Type_Osnd(_1648677, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1648677, tc_Nat_Onat), _1648681), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1648683)))))], (51128 ^ _781013) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (48926 ^ _781013) ^ [_1772741] : [-(c_Relation_Osingle__valued(_1772741, _1772741, c_Relation_OId(_1772741)))], (44795 ^ _781013) ^ [_1675341, _1675343, _1675345] : [hBOOL(hAPP(c_List_Odistinct(_1675341), _1675343)), -(c_List_Oremove1(_1675341, _1675345, c_List_Oremdups(_1675341, _1675343)) = c_List_Oremdups(_1675341, c_List_Oremove1(_1675341, _1675345, _1675343)))], (50108 ^ _781013) ^ [_1799246, _1799248, _1799250] : [class_Divides_Osemiring__div(_1799246), -(_1799248 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1799246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1799246), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1799246), _1799248), _1799250)), _1799250)), c_Divides_Odiv__class_Omod(_1799246, _1799248, _1799250)))], (22772 ^ _781013) ^ [_1206941, _1206943, _1206945, _1206947, _1206949] : [class_Groups_Ocomm__monoid__add(_1206941), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206943), _1206945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206945), _1206947)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206941), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1206941), _1206949), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206943), _1206945))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1206941), _1206949), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206945), _1206947))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1206941), _1206949), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206943), _1206947)))], (33664 ^ _781013) ^ [_1419258] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1419258), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419258)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1419258)))], (47276 ^ _781013) ^ [_1733929, _1733931, _1733933, _1733935, _1733937, _1733939, _1733941, _1733943] : [47278 ^ _781013 : [(47281 ^ _781013) ^ [] : [hAPP(c_Fun_Ocomp(_1733933, _1733933, _1733935, hAPP(_1733937, 47277 ^ [_1733929, _1733931, _1733933, _1733935, _1733937, _1733939, _1733941, _1733943])), _1733939) = hAPP(c_Fun_Ocomp(_1733935, _1733933, _1733935, _1733939), hAPP(_1733941, 47277 ^ [_1733929, _1733931, _1733933, _1733935, _1733937, _1733939, _1733941, _1733943]))], (47279 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733929), 47277 ^ [_1733929, _1733931, _1733933, _1733935, _1733937, _1733939, _1733941, _1733943]), hAPP(c_List_Oset(_1733929), _1733931))))]], -(hAPP(c_List_Ofoldl(_1733933, _1733929, hAPP(c_COMBC(_1733929, _1733933, _1733933), _1733937), hAPP(_1733939, _1733943)), _1733931) = hAPP(_1733939, hAPP(c_List_Ofoldl(_1733935, _1733929, hAPP(c_COMBC(_1733929, _1733935, _1733935), _1733941), _1733943), _1733931)))], (13437 ^ _781013) ^ [_1026484, _1026486] : [class_Groups_Ocomm__monoid__mult(_1026484), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026484), c_Groups_Oone__class_Oone(_1026484)), _1026486) = _1026486)], (4040 ^ _781013) ^ [_842130, _842132, _842134, _842136] : [-(c_List_Olistrel1(_842136, _842132) = c_List_Olistrel1(_842134, _842130)), _842136 = _842134, _842132 = _842130], (3714 ^ _781013) ^ [_837151, _837153, _837155, _837157, _837159, _837161] : [-(c_FunDef_Oin__rel(_837161, _837157, _837153) = c_FunDef_Oin__rel(_837159, _837155, _837151)), _837161 = _837159, _837157 = _837155, _837153 = _837151], (5667 ^ _781013) ^ [_870536, _870538] : [-(c_Option_Oset(_870536, hAPP(c_Option_Ooption_OSome(_870536), _870538)) = hAPP(hAPP(c_Set_Oinsert(_870536), _870538), c_Orderings_Obot__class_Obot(tc_fun(_870536, tc_HOL_Obool))))], (45990 ^ _781013) ^ [_1701292, _1701294, _1701296] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1701292, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1701292, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1701292, tc_HOL_Obool), _1701294)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1701292, tc_HOL_Obool), _1701296))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1701292, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1701292, tc_HOL_Obool), tc_HOL_Obool)), _1701294), _1701296)))))], (38708 ^ _781013) ^ [_1526214, _1526216, _1526218, _1526220, _1526222, _1526224] : [-(hAPP(hAPP(c_List_Ozip(_1526214, _1526216), hAPP(hAPP(c_List_Omap(_1526218, _1526214), _1526220), _1526222)), _1526224) = hAPP(hAPP(c_List_Omap(tc_prod(_1526218, _1526216), tc_prod(_1526214, _1526216)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526218, _1526216, tc_prod(_1526214, _1526216)), hAPP(hAPP(c_COMBB(_1526214, tc_fun(_1526216, tc_prod(_1526214, _1526216)), _1526218), c_Product__Type_OPair(_1526214, _1526216)), _1526220))), hAPP(hAPP(c_List_Ozip(_1526218, _1526216), _1526222), _1526224)))], (12718 ^ _781013) ^ [_1011172, _1011174, _1011176] : [class_Rings_Olinordered__idom(_1011172), -(_1011174 = _1011176), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011172), _1011174), _1011176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011172), _1011176), _1011174)))], (40127 ^ _781013) ^ [_1563533, _1563535, _1563537, _1563539, _1563541] : [hAPP(hAPP(c_List_Olist_OCons(_1563533), _1563535), _1563537) = hAPP(hAPP(c_List_Olist_OCons(_1563533), _1563539), _1563541), 40130 ^ _781013 : [(40133 ^ _781013) ^ [] : [-(_1563537 = _1563541)], (40131 ^ _781013) ^ [] : [-(_1563535 = _1563539)]]], (22950 ^ _781013) ^ [_1210291, _1210293, _1210295] : [hBOOL(hAPP(_1210291, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1210293), _1210295))), 22953 ^ _781013 : [(22978 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210295), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22981 ^ _781013 : [(22982 ^ _781013) ^ [_1210955] : [-(hBOOL(hAPP(_1210291, _1210955))), 22983 ^ _781013 : [(22984 ^ _781013) ^ [_1211029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210295), _1211029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211029), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1210293 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1210295), _1210955)), _1211029)]]]]], (22960 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210295)), 22963 ^ _781013 : [(22964 ^ _781013) ^ [_1210625] : [-(hBOOL(hAPP(_1210291, _1210625))), 22965 ^ _781013 : [(22966 ^ _781013) ^ [_1210696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210696), _1210295)), _1210293 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1210295), _1210625)), _1210696)]]]]], (22954 ^ _781013) ^ [] : [_1210295 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1210291, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (19993 ^ _781013) ^ [_1155403] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1155403)], (31765 ^ _781013) ^ [_1381464, _1381466, _1381468, _1381470] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381464, tc_fun(_1381466, tc_HOL_Obool)), _1381468), _1381470) = c_Orderings_Obot__class_Obot(tc_fun(_1381466, tc_HOL_Obool)), 31768 ^ _781013 : [(31769 ^ _781013) ^ [_1381580] : [hBOOL(hAPP(hAPP(c_member(_1381464), _1381580), _1381468)), -(hAPP(_1381470, _1381580) = c_Orderings_Obot__class_Obot(tc_fun(_1381466, tc_HOL_Obool)))]]], (36689 ^ _781013) ^ [_1481480] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1481480) = 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), _1481480), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (19933 ^ _781013) ^ [_1154398] : [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)), _1154398)), _1154398)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154398), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (4110 ^ _781013) ^ [_843181, _843183] : [_843183 = _843181, -(c_Fun_Oid(_843183) = c_Fun_Oid(_843181))], (34349 ^ _781013) ^ [_1432322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1432322))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1432322)))], (29569 ^ _781013) ^ [_1332534, _1332536, _1332538] : [class_Orderings_Olinorder(_1332534), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332534), _1332536)), -(_1332538 = c_Orderings_Obot__class_Obot(tc_fun(_1332534, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332534, tc_HOL_Obool)), _1332538), _1332536)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332534), c_Big__Operators_Olinorder__class_OMin(_1332534, _1332538)), c_Big__Operators_Olinorder__class_OMin(_1332534, _1332536)) = c_Big__Operators_Olinorder__class_OMin(_1332534, _1332536))], (17909 ^ _781013) ^ [_1115096, _1115098] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1115096), _1115098) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1115096 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1115098 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12158 ^ _781013) ^ [_1000377, _1000379] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000377, tc_HOL_Obool)), _1000379) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1000377, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1000377, tc_HOL_Obool))), _1000379))], (7795 ^ _781013) ^ [_912329, _912331, _912333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912329, tc_HOL_Obool)), _912331), _912333)), hBOOL(hAPP(c_Finite__Set_Ofinite(_912329), _912333)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_912329), _912331)))], (19312 ^ _781013) ^ [_1142733, _1142735] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1142733)), _1142735) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142733), _1142735)))], (43422 ^ _781013) ^ [_1645669, _1645671, _1645673, _1645675] : [hBOOL(hAPP(c_List_Olistsp(_1645669, _1645671), hAPP(hAPP(c_List_Olist_OCons(_1645669), _1645673), _1645675))), 43425 ^ _781013 : [(43428 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1645669, _1645671), _1645675)))], (43426 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1645671, _1645673)))]]], (18308 ^ _781013) ^ [_1121856, _1121858] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121856), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121858), _1121856))))], (9527 ^ _781013) ^ [_949797, _949799, _949801, _949803] : [class_Orderings_Oorder(_949797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949797), _949799), _949801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949797), _949803), _949799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949797), _949803), _949801)))], (33578 ^ _781013) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (45445 ^ _781013) ^ [_1688737, _1688739, _1688741, _1688743] : [class_Orderings_Oorder(_1688737), class_Enum_Oenum(_1688739), 45452 ^ _781013 : [(45461 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1688739, _1688737)), _1688741), _1688743))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1688739, _1688737)), _1688741), _1688743)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1688739), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1688739), c_fNot), hAPP(hAPP(c_COMBS(_1688739, _1688737, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1688737, tc_fun(_1688737, tc_HOL_Obool), _1688739), c_fequal), _1688741)), _1688743))))], (45453 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1688739, _1688737)), _1688741), _1688743)), 45456 ^ _781013 : [(45459 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1688739), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1688739), c_fNot), hAPP(hAPP(c_COMBS(_1688739, _1688737, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1688737, tc_fun(_1688737, tc_HOL_Obool), _1688739), c_fequal), _1688741)), _1688743)))))], (45457 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1688739, _1688737)), _1688741), _1688743)))]]]]], (2750 ^ _781013) ^ [_821963, _821965, _821967, _821969, _821971, _821973, _821975, _821977] : [-(c_Map_Orestrict__map(_821977, _821973, _821969, _821965) = c_Map_Orestrict__map(_821975, _821971, _821967, _821963)), _821977 = _821975, _821973 = _821971, _821969 = _821967, _821965 = _821963], (28920 ^ _781013) ^ [_1320547, _1320549] : [class_Groups_Oordered__ab__group__add__abs(_1320547), 28923 ^ _781013 : [(28930 ^ _781013) ^ [] : [-(_1320549 = c_Groups_Ozero__class_Ozero(_1320547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320547), c_Groups_Ozero__class_Ozero(_1320547)), hAPP(c_Groups_Oabs__class_Oabs(_1320547), _1320549))))], (28924 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320547), c_Groups_Ozero__class_Ozero(_1320547)), hAPP(c_Groups_Oabs__class_Oabs(_1320547), _1320549))), _1320549 = c_Groups_Ozero__class_Ozero(_1320547)]]], (39205 ^ _781013) ^ [_1538182, _1538184, _1538186] : [class_Orderings_Olinorder(_1538182), -(hBOOL(hAPP(hAPP(c_member(_1538182), _1538184), hAPP(c_List_Oset(_1538182), _1538186)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1538182, _1538182, c_COMBI(_1538182), _1538184, _1538186) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1538182, _1538182, c_COMBI(_1538182)), _1538184), _1538186))], (34843 ^ _781013) ^ [_1440761] : [-(c_Int_Opred(c_Int_OBit1(_1440761)) = c_Int_OBit0(_1440761))], (15065 ^ _781013) ^ [_1059546, _1059548, _1059550] : [hBOOL(hAPP(hAPP(c_member(_1059546), _1059548), hAPP(c_Set_OCollect(_1059546), _1059550))), -(hBOOL(hAPP(_1059550, _1059548)))], (50281 ^ _781013) ^ [_1803514, _1803516, _1803518] : [50283 ^ _781013 : [(50286 ^ _781013) ^ [] : [hBOOL(hAPP(_1803516, hAPP(hAPP(c_List_Onth(_1803514), _1803518), 50282 ^ [_1803514, _1803516, _1803518])))], (50284 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50282 ^ [_1803514, _1803516, _1803518]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803514)), _1803518))))]], -(c_List_Olist__all(_1803514, _1803516, _1803518))], (44839 ^ _781013) ^ [_1676371, _1676373, _1676375] : [hBOOL(hAPP(c_List_Odistinct(_1676371), _1676373)), -(hBOOL(hAPP(c_List_Odistinct(_1676371), c_List_OdropWhile(_1676371, _1676375, _1676373))))], (8123 ^ _781013) ^ [_919387, _919389, _919391, _919393, _919395, _919397, _919399] : [-(c_Map_Omap__comp(_919387, _919389, _919391, _919393, _919395, _919397) = hAPP(c_Option_Ooption_OSome(_919389), _919399)), 8124 ^ _781013 : [(8125 ^ _781013) ^ [_919465] : [hAPP(_919395, _919397) = hAPP(c_Option_Ooption_OSome(_919387), _919465), hAPP(_919393, _919465) = hAPP(c_Option_Ooption_OSome(_919389), _919399)]]], (21489 ^ _781013) ^ [_1184721, _1184723] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184721)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184723))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1184721), _1184723)))], (14819 ^ _781013) ^ [_1055763, _1055765] : [class_Rings_Ocomm__semiring__1(_1055763), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055763), c_Groups_Ozero__class_Ozero(_1055763)), _1055765) = _1055765)], (2 ^ _781013) ^ [_781040] : [-(_781040 = _781040)], (26435 ^ _781013) ^ [_1272690, _1272692, _1272694] : [class_Orderings_Olinorder(_1272690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272690), _1272692), _1272694)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272690, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1272690, _1272692, _1272694)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1272690), _1272694)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1272690), _1272692))], (42450 ^ _781013) ^ [_1621884, _1621886, _1621888] : [-(_1621884 = c_List_Olist_ONil(_1621886)), -(hAPP(hAPP(c_List_Otake(_1621886), hAPP(c_Nat_OSuc, _1621888)), _1621884) = hAPP(hAPP(c_List_Olist_OCons(_1621886), hAPP(c_List_Ohd(_1621886), _1621884)), hAPP(hAPP(c_List_Otake(_1621886), _1621888), hAPP(c_List_Otl(_1621886), _1621884))))], (50928 ^ _781013) ^ [_1817178, _1817180, _1817182] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1817178, _1817180), _1817182) = c_Lazy__Sequence_Oproduct(_1817178, _1817180, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1817178, _1817182), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1817180, _1817182))), class_Lazy__Sequence_Osmall__lazy(_1817178), class_Lazy__Sequence_Osmall__lazy(_1817180)], (47819 ^ _781013) ^ [_1746932, _1746934, _1746936, _1746938, _1746940, _1746942, _1746944, _1746946] : [class_Groups_Ocomm__monoid__add(_1746932), c_Fun_Oinj__on(_1746934, _1746936, _1746938, _1746940), _1746942 = hAPP(c_Set_Oimage(_1746934, _1746936, _1746938), _1746940), 47833 ^ _781013 : [(47836 ^ _781013) ^ [] : [hAPP(_1746944, 47832 ^ [_1746932, _1746934, _1746936, _1746938, _1746940, _1746942, _1746944, _1746946]) = hAPP(_1746946, hAPP(_1746938, 47832 ^ [_1746932, _1746934, _1746936, _1746938, _1746940, _1746942, _1746944, _1746946]))], (47834 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1746934), 47832 ^ [_1746932, _1746934, _1746936, _1746938, _1746940, _1746942, _1746944, _1746946]), _1746940)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1746936, _1746932), _1746946), _1746942) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1746934, _1746932), _1746944), _1746940))], (36230 ^ _781013) ^ [_1471230, _1471232, _1471234, _1471236, _1471238] : [c_Equiv__Relations_Oequiv(_1471230, _1471232, _1471234), 36233 ^ _781013 : [(36244 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1471230, _1471230)), hAPP(hAPP(c_Product__Type_OPair(_1471230, _1471230), _1471236), _1471238)), _1471234))), hAPP(c_Relation_OImage(_1471230, _1471230, _1471234), hAPP(hAPP(c_Set_Oinsert(_1471230), _1471236), c_Orderings_Obot__class_Obot(tc_fun(_1471230, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1471230, _1471230, _1471234), hAPP(hAPP(c_Set_Oinsert(_1471230), _1471238), c_Orderings_Obot__class_Obot(tc_fun(_1471230, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1471230), _1471236), _1471232)), hBOOL(hAPP(hAPP(c_member(_1471230), _1471238), _1471232))], (36234 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1471230, _1471230)), hAPP(hAPP(c_Product__Type_OPair(_1471230, _1471230), _1471236), _1471238)), _1471234)), 36237 ^ _781013 : [(36242 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471230), _1471238), _1471232)))], (36240 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471230), _1471236), _1471232)))], (36238 ^ _781013) ^ [] : [-(hAPP(c_Relation_OImage(_1471230, _1471230, _1471234), hAPP(hAPP(c_Set_Oinsert(_1471230), _1471236), c_Orderings_Obot__class_Obot(tc_fun(_1471230, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1471230, _1471230, _1471234), hAPP(hAPP(c_Set_Oinsert(_1471230), _1471238), c_Orderings_Obot__class_Obot(tc_fun(_1471230, tc_HOL_Obool)))))]]]]], (14151 ^ _781013) ^ [_1041673, _1041675] : [class_Rings_Olinordered__semidom(_1041673), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041673), _1041675), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041673), _1041675), c_Groups_Oone__class_Oone(_1041673)))))], (27703 ^ _781013) ^ [_1298189, _1298191, _1298193, _1298195] : [class_Divides_Osemiring__div(_1298189), -(c_Divides_Odiv__class_Omod(_1298189, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298189), _1298191), _1298193), _1298195) = c_Divides_Odiv__class_Omod(_1298189, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298189), c_Divides_Odiv__class_Omod(_1298189, _1298191, _1298195)), _1298193), _1298195))], (50666 ^ _781013) ^ [_1810727, _1810729] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1810727), _1810729)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1810727)), c_Int_OBit0(_1810729))))], (20221 ^ _781013) ^ [_1159129, _1159131] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1159129), c_Groups_Ozero__class_Ozero(_1159129)), hAPP(c_Nat_OSuc, _1159131)) = c_Groups_Ozero__class_Ozero(_1159129)), class_Power_Opower(_1159129), class_Rings_Osemiring__0(_1159129)], (42490 ^ _781013) ^ [_1622849, _1622851, _1622853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1622849), _1622851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1622849), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1622851), _1622853))))], (41304 ^ _781013) ^ [_1595107, _1595109, _1595111, _1595113] : [-(c_List_Ofoldr(_1595107, _1595109, _1595111, c_List_Olist_ONil(_1595107), _1595113) = _1595113)], (14381 ^ _781013) ^ [_1047322, _1047324, _1047326, _1047328, _1047330] : [class_Groups_Ocomm__monoid__add(_1047322), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047324), _1047326)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047324, _1047322), _1047328), hAPP(hAPP(c_Set_Oinsert(_1047324), _1047330), _1047326)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047322), hAPP(_1047328, _1047330)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047324, _1047322), _1047328), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1047324, tc_HOL_Obool)), _1047326), hAPP(hAPP(c_Set_Oinsert(_1047324), _1047330), c_Orderings_Obot__class_Obot(tc_fun(_1047324, tc_HOL_Obool)))))))], (18047 ^ _781013) ^ [_1117355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1117355)), _1117355 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29074 ^ _781013) ^ [_1323447, _1323449] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1323447, _1323449)) = _1323449, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1323447), _1323449) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23817 ^ _781013) ^ [_1225996, _1225998, _1226000, _1226002] : [class_Orderings_Oorder(_1225996), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1225996, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1225996, _1225998, _1226000)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1225996, _1226000, _1226002)) = c_Orderings_Obot__class_Obot(tc_fun(_1225996, tc_HOL_Obool)))], (47619 ^ _781013) ^ [_1741896, _1741898, _1741900, _1741902, _1741904] : [-(hAPP(hAPP(c_List_Olist_OCons(_1741896), _1741898), _1741900) = hAPP(c_List_Ofilter(_1741896, _1741902), _1741904)), 47620 ^ _781013 : [(47621 ^ _781013) ^ [_1742024, _1742026] : [_1741904 = hAPP(hAPP(c_List_Oappend(_1741896), _1742026), hAPP(hAPP(c_List_Olist_OCons(_1741896), _1741898), _1742024)), 47627 ^ _781013 : [(47630 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1741902, 47626 ^ [_1741896, _1741898, _1741900, _1741902, _1741904, _1742024, _1742026])))], (47628 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1741896), 47626 ^ [_1741896, _1741898, _1741900, _1741902, _1741904, _1742024, _1742026]), hAPP(c_List_Oset(_1741896), _1742026))))]], hBOOL(hAPP(_1741902, _1741898)), _1741900 = hAPP(c_List_Ofilter(_1741896, _1741902), _1742024)]]], (27619 ^ _781013) ^ [_1296411, _1296413, _1296415, _1296417] : [class_Divides_Oring__div(_1296411), c_Divides_Odiv__class_Omod(_1296411, _1296413, _1296415) = c_Divides_Odiv__class_Omod(_1296411, _1296417, _1296415), -(c_Divides_Odiv__class_Omod(_1296411, hAPP(c_Groups_Ouminus__class_Ouminus(_1296411), _1296413), _1296415) = c_Divides_Odiv__class_Omod(_1296411, hAPP(c_Groups_Ouminus__class_Ouminus(_1296411), _1296417), _1296415))], (7349 ^ _781013) ^ [_903685, _903687, _903689, _903691] : [hBOOL(hAPP(hAPP(c_member(_903685), _903687), _903689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903685, tc_HOL_Obool)), _903689), _903691)), -(hBOOL(hAPP(hAPP(c_member(_903685), _903687), _903691)))], (35998 ^ _781013) ^ [_1466217, _1466219, _1466221, _1466223, _1466225] : [-(hBOOL(hAPP(hAPP(c_member(_1466217), _1466219), hAPP(c_Relation_OImage(_1466221, _1466217, _1466223), _1466225)))), 35999 ^ _781013 : [(36000 ^ _781013) ^ [_1466303] : [hBOOL(hAPP(hAPP(c_member(_1466221), _1466303), _1466225)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1466221, _1466217)), hAPP(hAPP(c_Product__Type_OPair(_1466221, _1466217), _1466303), _1466219)), _1466223))]]], (25922 ^ _781013) ^ [_1263060, _1263062, _1263064, _1263066] : [class_Rings_Oring__1(_1263060), -(hAPP(c_Int_Oring__1__class_Oof__int(_1263060), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263062, tc_Int_Oint), _1263064), _1263066)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263062, _1263060), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1263060, _1263062), c_Int_Oring__1__class_Oof__int(_1263060)), _1263064)), _1263066))], (44689 ^ _781013) ^ [_1673412, _1673414] : [-(_1673412 = c_List_Olist_ONil(_1673414)), hBOOL(hAPP(c_List_Odistinct(_1673414), _1673412)), -(c_List_OtakeWhile(_1673414, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1673414), c_fNot), hAPP(hAPP(c_COMBC(_1673414, _1673414, tc_HOL_Obool), c_fequal), c_List_Olast(_1673414, _1673412))), _1673412) = c_List_Obutlast(_1673414, _1673412))], (10989 ^ _781013) ^ [_975918, _975920, _975922, _975924] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975918, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_975918, tc_fun(_975918, tc_HOL_Obool), tc_HOL_Obool), c_member(_975918)), _975920)), hAPP(hAPP(c_COMBC(_975918, tc_fun(_975918, tc_HOL_Obool), tc_HOL_Obool), c_member(_975918)), _975922)), _975924)), -(hBOOL(hAPP(hAPP(c_member(_975918), _975924), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975918, tc_HOL_Obool)), _975920), _975922))))], (34777 ^ _781013) ^ [_1439552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1439552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1439552))))], (40657 ^ _781013) ^ [_1577928, _1577930, _1577932, _1577934, _1577936, _1577938] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577928, _1577930)), hAPP(hAPP(c_Product__Type_OPair(_1577928, _1577930), _1577932), _1577934)), hAPP(hAPP(c_Product__Type_OSigma(_1577928, _1577930), _1577936), _1577938)))), hBOOL(hAPP(hAPP(c_member(_1577928), _1577932), _1577936)), hBOOL(hAPP(hAPP(c_member(_1577930), _1577934), hAPP(_1577938, _1577932)))], (51484 ^ _781013) ^ [_1823513, _1823515] : [-(class_Enum_Oenum(tc_prod(_1823513, _1823515))), class_Enum_Oenum(_1823513), class_Enum_Oenum(_1823515)], (21177 ^ _781013) ^ [_1178291] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178291), _1178291)))], (2482 ^ _781013) ^ [_817787, _817789] : [_817789 = _817787, -(c_Int_Osucc(_817789) = c_Int_Osucc(_817787))], (20843 ^ _781013) ^ [_1170676, _1170678, _1170680] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1170676), _1170678)), -(hBOOL(hAPP(hAPP(c_member(_1170676), _1170680), _1170678))), -(hAPP(c_Finite__Set_Ocard(_1170676), hAPP(hAPP(c_Set_Oinsert(_1170676), _1170680), _1170678)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1170676), _1170678)))], (23250 ^ _781013) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2956 ^ _781013) ^ [_825262, _825264, _825266, _825268] : [-(c_Fun_Ofun__upd(_825268, _825264) = c_Fun_Ofun__upd(_825266, _825262)), _825268 = _825266, _825264 = _825262], (5877 ^ _781013) ^ [_875522, _875524, _875526] : [hAPP(c_Com_Ocom_OBODY, _875522) = c_Com_Ocom_OWhile(_875524, _875526)], (29125 ^ _781013) ^ [_1324169, _1324171, _1324173] : [-(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), _1324169), _1324171)), _1324173), _1324171) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1324173, _1324171))], (23623 ^ _781013) ^ [_1222783, _1222785, _1222787] : [class_Rings_Odivision__ring(_1222783), -(_1222785 = c_Groups_Ozero__class_Ozero(_1222783)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222783), hAPP(c_Groups_Ouminus__class_Ouminus(_1222783), _1222787)), hAPP(c_Groups_Ouminus__class_Ouminus(_1222783), _1222785)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222783), _1222787), _1222785))], (2636 ^ _781013) ^ [_820134, _820136, _820138, _820140] : [-(c_Divides_OnegDivAlg(_820140, _820136) = c_Divides_OnegDivAlg(_820138, _820134)), _820140 = _820138, _820136 = _820134], (24684 ^ _781013) ^ [_1241361, _1241363, _1241365] : [class_Fields_Olinordered__field(_1241361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241361), _1241363), c_Groups_Ozero__class_Ozero(_1241361))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241361), c_Groups_Ozero__class_Ozero(_1241361)), _1241365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241361), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241361), _1241363), _1241365)), c_Groups_Ozero__class_Ozero(_1241361))))], (21297 ^ _781013) ^ [_1180494, _1180496, _1180498] : [class_Groups_Ocomm__monoid__add(_1180494), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1180494), _1180496), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1180498))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180494), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1180494), _1180496), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1180498))), hAPP(_1180496, _1180498)))], (7243 ^ _781013) ^ [_901932, _901934, _901936, _901938] : [_901932 = _901934, 7246 ^ _781013 : [(7253 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_901936), _901938), _901934)), -(hBOOL(hAPP(hAPP(c_member(_901936), _901938), _901932)))], (7247 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_901936), _901938), _901932)), -(hBOOL(hAPP(hAPP(c_member(_901936), _901938), _901934)))]]], (1164 ^ _781013) ^ [_798305, _798307] : [-(class_Rings_Ocomm__ring__1(_798305)), _798307 = _798305, class_Rings_Ocomm__ring__1(_798307)], (30233 ^ _781013) ^ [_1345778, _1345780] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1345778)), hAPP(c_Nat_OSuc, _1345780)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1345778), _1345780)))], (48840 ^ _781013) ^ [_1770118, _1770120, _1770122] : [-(hAPP(c_Relation_ORange(_1770118, _1770120), _1770122) = hAPP(c_Relation_ODomain(_1770120, _1770118), hAPP(c_Relation_Oconverse(_1770118, _1770120), _1770122)))], (35793 ^ _781013) ^ [_1457681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1457681)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1457681) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (34783 ^ _781013) ^ [_1439653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1439653)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439653), c_Int_OPls)))], (31666 ^ _781013) ^ [_1379107, _1379109, _1379111, _1379113, _1379115, _1379117] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379107, tc_fun(_1379109, tc_HOL_Obool)), _1379111), hAPP(hAPP(c_COMBC(_1379107, tc_fun(_1379113, tc_fun(_1379109, tc_HOL_Obool)), tc_fun(_1379109, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1379113, tc_HOL_Obool), tc_fun(tc_fun(_1379113, tc_fun(_1379109, tc_HOL_Obool)), tc_fun(_1379109, tc_HOL_Obool)), _1379107), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379113, tc_fun(_1379109, tc_HOL_Obool))), _1379115)), _1379117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379113, tc_fun(_1379109, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379107, tc_fun(_1379113, tc_HOL_Obool)), _1379111), _1379115)), _1379117))], (48321 ^ _781013) ^ [_1757505, _1757507, _1757509, _1757511, _1757513] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1757505, _1757505)), hAPP(hAPP(c_Product__Type_OPair(_1757505, _1757505), _1757507), _1757509)), c_Transitive__Closure_Ortrancl(_1757505, _1757511))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1757505, _1757505)), hAPP(hAPP(c_Product__Type_OPair(_1757505, _1757505), _1757509), _1757513)), _1757511)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757505, _1757505)), hAPP(hAPP(c_Product__Type_OPair(_1757505, _1757505), _1757507), _1757513)), c_Transitive__Closure_Ortrancl(_1757505, _1757511))))], (17454 ^ _781013) ^ [_1107290] : [17456 ^ _781013 : [(17459 ^ _781013) ^ [_1107400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17455 ^ [_1107290, _1107400]), _1107400))], (17457 ^ _781013) ^ [_1107366] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 17455 ^ [_1107290, _1107366]), _1107290)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1107290)))], (41787 ^ _781013) ^ [_1605884, _1605886, _1605888, _1605890] : [hAPP(hAPP(c_List_Oappend(_1605884), _1605886), _1605888) = hAPP(hAPP(c_List_Oappend(_1605884), _1605886), _1605890), -(_1605888 = _1605890)], (47579 ^ _781013) ^ [_1740838, _1740840, _1740842, _1740844, _1740846] : [class_Orderings_Olinorder(_1740838), 47585 ^ _781013 : [(47588 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1740838), hAPP(_1740844, _1740846)), hAPP(_1740844, 47584 ^ [_1740838, _1740840, _1740842, _1740844, _1740846])))], (47586 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740840), 47584 ^ [_1740838, _1740840, _1740842, _1740844, _1740846]), hAPP(c_List_Oset(_1740840), _1740842))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1740840, _1740838, _1740844), _1740846), _1740842) = hAPP(hAPP(c_List_Olist_OCons(_1740840), _1740846), _1740842))], (27964 ^ _781013) ^ [_1303244, _1303246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303244)), 27967 ^ _781013 : [(27970 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1303246, _1303244)), _1303244)))], (27968 ^ _781013) ^ [] : [-(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, _1303246, _1303244))))]]], (10947 ^ _781013) ^ [_975059, _975061, _975063, _975065, _975067] : [-(c_Map_Orestrict__map(_975059, _975061, c_Map_Orestrict__map(_975059, _975061, _975063, _975065), _975067) = c_Map_Orestrict__map(_975059, _975061, _975063, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975059, tc_HOL_Obool)), _975065), _975067)))], (5577 ^ _781013) ^ [_868795, _868797] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_868795, _868797, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_868795), tc_HOL_Obool))))], (41149 ^ _781013) ^ [_1592030, _1592032, _1592034] : [41151 ^ _781013 : [(41154 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1592030), 41150 ^ [_1592030, _1592032, _1592034]), _1592034))], (41152 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592030), 41150 ^ [_1592030, _1592032, _1592034]), hAPP(c_List_Oset(_1592030), _1592032))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1592030)), _1592032), c_List_Olists(_1592030, _1592034))))], (31033 ^ _781013) ^ [_1362064, _1362066] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1362064)), _1362066) = 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), _1362064)), _1362066))], (47417 ^ _781013) ^ [_1736784, _1736786] : [-(c_Nitpick_Owf_H(_1736784, _1736786)), c_Wellfounded_Oacyclic(_1736784, _1736786), 47422 ^ _781013 : [(47425 ^ _781013) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (47423 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1736784, _1736784)), _1736786))]]], (27322 ^ _781013) ^ [_1290006, _1290008, _1290010, _1290012, _1290014] : [class_Groups_Ocomm__monoid__add(_1290006), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290008), _1290010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290008, tc_HOL_Obool)), _1290012), _1290010)), 27336 ^ _781013 : [(27339 ^ _781013) ^ [] : [hAPP(_1290014, 27335 ^ [_1290006, _1290008, _1290010, _1290012, _1290014]) = c_Groups_Ozero__class_Ozero(_1290006)], (27337 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290008), 27335 ^ [_1290006, _1290008, _1290010, _1290012, _1290014]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290008, tc_HOL_Obool)), _1290010), _1290012))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1290008, _1290006), _1290014), _1290012) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1290008, _1290006), _1290014), _1290010))], (17230 ^ _781013) ^ [_1101825, _1101827, _1101829, _1101831] : [class_Groups_Ocomm__monoid__add(_1101825), 17233 ^ _781013 : [(17240 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1101827), _1101829))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1101827, _1101825), _1101831), _1101829) = c_Groups_Ozero__class_Ozero(_1101825))], (17234 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1101827), _1101829)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1101827, _1101825), _1101831), _1101829) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1101825, _1101827, c_Groups_Oplus__class_Oplus(_1101825)), _1101831), c_Groups_Ozero__class_Ozero(_1101825)), _1101829))]]], (37886 ^ _781013) ^ [_1506649, _1506651, _1506653, _1506655, _1506657, _1506659, _1506661] : [-(hAPP(c_Product__Type_Oapsnd(_1506649, _1506651, _1506653, _1506655), hAPP(c_Product__Type_Oapfst(_1506657, _1506653, _1506649, _1506659), _1506661)) = hAPP(c_Product__Type_Oapfst(_1506657, _1506653, _1506651, _1506659), hAPP(c_Product__Type_Oapsnd(_1506649, _1506651, _1506657, _1506655), _1506661)))], (26445 ^ _781013) ^ [_1272885, _1272887] : [class_Groups_Oordered__ab__group__add(_1272885), -(hAPP(c_Set_Oimage(_1272885, _1272885, c_Groups_Ouminus__class_Ouminus(_1272885)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1272885), _1272887)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1272885), hAPP(c_Groups_Ouminus__class_Ouminus(_1272885), _1272887)))], (15531 ^ _781013) ^ [_1068280, _1068282, _1068284, _1068286] : [class_Rings_Oordered__comm__semiring(_1068280), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068280), _1068282), _1068284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068280), c_Groups_Ozero__class_Ozero(_1068280)), _1068286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068280), _1068286), _1068282)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068280), _1068286), _1068284))))], (33650 ^ _781013) ^ [_1419021, _1419023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1419021)), _1419023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1419021), _1419023)))], (18233 ^ _781013) ^ [_1120413, _1120415, _1120417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120413), _1120415)), _1120417)), 18236 ^ _781013 : [(18239 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120415), _1120417)))], (18237 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120413), _1120417)))]]], (47098 ^ _781013) ^ [_1728881, _1728883, _1728885, _1728887] : [47099 ^ _781013 : [(47100 ^ _781013) ^ [_1728956] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1728885, _1728881)), hAPP(hAPP(c_Product__Type_OPair(_1728885, _1728881), _1728956), _1728883)), _1728887))]], -(hBOOL(hAPP(hAPP(c_member(_1728881), _1728883), hAPP(c_Relation_ORange(_1728885, _1728881), _1728887))))], (21907 ^ _781013) ^ [_1192145, _1192147, _1192149] : [class_Rings_Oring__1(_1192145), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1192147), _1192149)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1192145), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1192149), _1192147)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1192145), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1192145), _1192149)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1192145), _1192147)))], (12920 ^ _781013) ^ [_1015684, _1015686, _1015688, _1015690] : [_1015684 = c_Finite__Set_Ofold1(_1015686, _1015688), -(hAPP(_1015684, hAPP(hAPP(c_Set_Oinsert(_1015686), _1015690), c_Orderings_Obot__class_Obot(tc_fun(_1015686, tc_HOL_Obool)))) = _1015690)], (26829 ^ _781013) ^ [_1280397, _1280399, _1280401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1280397)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1280399), _1280401)), 26836 ^ _781013 : [(26837 ^ _781013) ^ [_1280587] : [26839 ^ _781013 : [(26845 ^ _781013) ^ [] : [-(_1280587 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26841 ^ [_1280397, _1280399, _1280401, _1280587]), 26838 ^ [_1280397, _1280399, _1280401, _1280587]))], (26843 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26841 ^ [_1280397, _1280399, _1280401, _1280587]), _1280401)))], (26840 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26838 ^ [_1280397, _1280399, _1280401, _1280587]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1280397))))]], -(_1280587 = _1280399), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1280587), _1280397) = _1280399]]], (39631 ^ _781013) ^ [_1548172, _1548174, _1548176, _1548178] : [hBOOL(hAPP(_1548172, _1548174)), -(hBOOL(hAPP(_1548172, c_Hilbert__Choice_OLeastM(_1548176, tc_Nat_Onat, _1548178, _1548172))))], (50334 ^ _781013) ^ [_1804609, _1804611, _1804613] : [c_List_Olist__all(_1804609, _1804611, _1804613), -(c_List_Olist__all(_1804609, _1804611, hAPP(c_List_Orev(_1804609), _1804613)))], (17837 ^ _781013) ^ [_1113978] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1113978), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113978), _1113978))))], (6912 ^ _781013) ^ [_895231, _895233, _895235, _895237, _895239] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895231, _895233), _895235), _895237), _895239), _895237) = _895239)], (35109 ^ _781013) ^ [_1445585, _1445587, _1445589] : [class_Rings_Olinordered__semidom(_1445585), hAPP(hAPP(c_Power_Opower__class_Opower(_1445585), _1445587), 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(_1445585), _1445589), 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(_1445585), c_Groups_Ozero__class_Ozero(_1445585)), _1445587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445585), c_Groups_Ozero__class_Ozero(_1445585)), _1445589)), -(_1445587 = _1445589)], (2976 ^ _781013) ^ [_825560, _825562] : [_825562 = _825560, -(c_Set_OBall(_825562) = c_Set_OBall(_825560))], (8263 ^ _781013) ^ [_922241, _922243, _922245, _922247] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922241, tc_HOL_Obool)), _922243), _922245), _922247)), -(hBOOL(hAPP(_922243, _922247))), -(hBOOL(hAPP(_922245, _922247)))], (51442 ^ _781013) ^ [_1822976] : [-(class_HOL_Oequal(tc_Option_Ooption(_1822976)))], (31856 ^ _781013) ^ [_1384275, _1384277, _1384279, _1384281, _1384283] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384275, tc_fun(_1384277, tc_HOL_Obool)), _1384279), hAPP(hAPP(c_COMBB(tc_fun(_1384277, tc_HOL_Obool), tc_fun(_1384277, tc_HOL_Obool), _1384275), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384277, tc_HOL_Obool)), _1384281)), _1384283)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384277, tc_HOL_Obool)), _1384281), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384275, tc_fun(_1384277, tc_HOL_Obool)), _1384279), _1384283)))], (42665 ^ _781013) ^ [_1626512, _1626514, _1626516] : [-(_1626512 = c_List_Olist_ONil(_1626514)), -(c_List_Olast(_1626514, hAPP(hAPP(c_List_Oappend(_1626514), _1626516), _1626512)) = c_List_Olast(_1626514, _1626512))], (7909 ^ _781013) ^ [_914532, _914534, _914536] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914532, tc_HOL_Obool)), _914534), hAPP(hAPP(c_Set_Oinsert(_914532), _914536), _914534))))], (30763 ^ _781013) ^ [_1356867, _1356869, _1356871] : [class_Orderings_Olinorder(_1356867), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356867), _1356869)), hBOOL(hAPP(hAPP(c_member(_1356867), _1356871), _1356869)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1356867), _1356871), c_Big__Operators_Olattice_OSup__fin(_1356867, c_Orderings_Oord__class_Omax(_1356867), _1356869)) = _1356871)], (31514 ^ _781013) ^ [_1374968, _1374970, _1374972] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1374968, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1374970)), _1374972) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1374968, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1374968, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1374970)), _1374972)), hAPP(_1374972, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36633 ^ _781013) ^ [_1480242, _1480244, _1480246] : [-(c_HOL_OThe(tc_prod(_1480242, _1480244), _1480246) = c_HOL_OThe(tc_prod(_1480242, _1480244), hAPP(c_Product__Type_Oprod_Oprod__case(_1480242, _1480244, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1480244, tc_prod(_1480242, _1480244)), tc_fun(_1480244, tc_HOL_Obool), _1480242), hAPP(c_COMBB(tc_prod(_1480242, _1480244), tc_HOL_Obool, _1480244), _1480246)), c_Product__Type_OPair(_1480242, _1480244)))))], (20573 ^ _781013) ^ [_1165683] : [class_Rings_Oring__1(_1165683), -(hBOOL(hAPP(hAPP(c_member(_1165683), c_Groups_Ozero__class_Ozero(_1165683)), c_Int_Oring__1__class_OInts(_1165683))))], (48647 ^ _781013) ^ [_1765265] : [-(c_Code__Numeral_OSuc__code__numeral(_1765265) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1765265))))], (14333 ^ _781013) ^ [_1046352, _1046354, _1046356] : [class_Rings_Ocomm__semiring__1(_1046352), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046352), _1046354), _1046356) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046352), _1046356), _1046354))], (42082 ^ _781013) ^ [_1613754, _1613756] : [_1613756 = c_List_Olist_ONil(_1613754), -(hAPP(c_List_Orotate1(_1613754), _1613756) = c_List_Olist_ONil(_1613754))], (41192 ^ _781013) ^ [_1593072, _1593074, _1593076] : [hAPP(hAPP(c_List_Olist_OCons(_1593072), _1593074), _1593076) = c_List_Olist_ONil(_1593072)], (43147 ^ _781013) ^ [_1639414, _1639416, _1639418, _1639420, _1639422] : [-(_1639414 = c_Orderings_Obot__class_Obot(tc_fun(_1639416, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639416, tc_fun(_1639418, tc_HOL_Obool)), _1639414), hAPP(hAPP(c_COMBC(_1639416, tc_fun(_1639418, tc_HOL_Obool), tc_fun(_1639418, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1639418, tc_HOL_Obool), tc_fun(tc_fun(_1639418, tc_HOL_Obool), tc_fun(_1639418, tc_HOL_Obool)), _1639416), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639418, tc_HOL_Obool))), _1639420)), _1639422)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639418, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639416, tc_fun(_1639418, tc_HOL_Obool)), _1639414), _1639420)), _1639422))], (4702 ^ _781013) ^ [_852155, _852157] : [_852157 = _852155, -(c_Nat_Osemiring__1__class_Oof__nat(_852157) = c_Nat_Osemiring__1__class_Oof__nat(_852155))], (46800 ^ _781013) ^ [_1722374, _1722376, _1722378] : [c_Wellfounded_Owf(_1722374, _1722376), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1722374, _1722374), tc_HOL_Obool)), _1722378), _1722376)), -(c_Wellfounded_Owf(_1722374, _1722378))], (49197 ^ _781013) ^ [_1779301, _1779303, _1779305] : [c_Relation_Ototal__on(_1779301, _1779303, _1779305), 49200 ^ _781013 : [(49201 ^ _781013) ^ [_1779445] : [hBOOL(hAPP(hAPP(c_member(_1779301), _1779445), _1779303)), 49204 ^ _781013 : [(49205 ^ _781013) ^ [_1779585] : [hBOOL(hAPP(hAPP(c_member(_1779301), _1779585), _1779303)), -(_1779445 = _1779585), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779301, _1779301)), hAPP(hAPP(c_Product__Type_OPair(_1779301, _1779301), _1779445), _1779585)), _1779305))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779301, _1779301)), hAPP(hAPP(c_Product__Type_OPair(_1779301, _1779301), _1779585), _1779445)), _1779305)))]]]]], (9569 ^ _781013) ^ [_950482, _950484, _950486, _950488] : [class_Orderings_Oord(_950482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950482), _950484), _950486)), _950486 = _950488, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950482), _950484), _950488)))], (40645 ^ _781013) ^ [_1577584, _1577586] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1577584, _1577584), tc_HOL_Obool)), c_Relation_OId__on(_1577584, _1577586)), hAPP(hAPP(c_Product__Type_OSigma(_1577584, _1577584), _1577586), hAPP(c_COMBK(tc_fun(_1577584, tc_HOL_Obool), _1577584), _1577586)))))], (46395 ^ _781013) ^ [_1710280, _1710282, _1710284] : [-(hBOOL(hAPP(hAPP(c_member(_1710280), _1710282), hAPP(c_List_Oset(_1710280), _1710284)))), -(c_List_Oinsert(_1710280, _1710282, _1710284) = hAPP(hAPP(c_List_Olist_OCons(_1710280), _1710282), _1710284))], (11668 ^ _781013) ^ [_991130, _991132, _991134, _991136] : [class_Groups_Oab__semigroup__mult(_991130), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991130), _991132), _991134)), _991136) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991130), _991132), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991130), _991134), _991136)))], (40375 ^ _781013) ^ [_1568735, _1568737, _1568739] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1568735)), hAPP(hAPP(c_List_Olist_OCons(_1568735), _1568737), _1568739)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1568735)), _1568739)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16349 ^ _781013) ^ [_1083298, _1083300] : [-(hAPP(c_Set_OCollect(_1083298), hAPP(c_fequal, _1083300)) = hAPP(hAPP(c_Set_Oinsert(_1083298), _1083300), c_Orderings_Obot__class_Obot(tc_fun(_1083298, tc_HOL_Obool))))], (7691 ^ _781013) ^ [_910421, _910423] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910421, tc_HOL_Obool)), _910423), c_Orderings_Obot__class_Obot(tc_fun(_910421, tc_HOL_Obool))) = _910423)], (956 ^ _781013) ^ [_795547, _795549, _795551, _795553, _795555, _795557] : [-(c_List_Olist__ex1(_795555, _795551, _795547)), c_List_Olist__ex1(_795557, _795553, _795549), _795557 = _795555, _795553 = _795551, _795549 = _795547], (7061 ^ _781013) ^ [_897978, _897980, _897982, _897984] : [-(hBOOL(hAPP(hAPP(c_member(_897978), _897980), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897978, tc_HOL_Obool)), _897982), _897984)))), hBOOL(hAPP(hAPP(c_member(_897978), _897980), _897982)), -(hBOOL(hAPP(hAPP(c_member(_897978), _897980), _897984)))], (8607 ^ _781013) ^ [_930264, _930266, _930268] : [class_Lattices_Olattice(_930264), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930264), _930266), _930268) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930264), _930268), _930266))], (46935 ^ _781013) ^ [_1724896] : [class_Orderings_Owellorder(_1724896), -(c_Wellfounded_Owf(_1724896, hAPP(c_Set_OCollect(tc_prod(_1724896, _1724896)), hAPP(c_Product__Type_Oprod_Oprod__case(_1724896, _1724896, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1724896)))))], (10329 ^ _781013) ^ [_963820, _963822, _963824, _963826] : [class_Lattices_Odistrib__lattice(_963820), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_963820), _963822), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963820), _963824), _963826)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963820), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_963820), _963822), _963824)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_963820), _963822), _963826)))], (42314 ^ _781013) ^ [_1619508, _1619510, _1619512] : [-(hAPP(c_List_Ohd(_1619508), hAPP(hAPP(c_List_Olist_OCons(_1619508), _1619510), _1619512)) = _1619510)], (46788 ^ _781013) ^ [_1722160, _1722162, _1722164] : [c_Wellfounded_Owf(_1722160, _1722162), -(c_Wellfounded_Owf(_1722160, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1722160, _1722160), tc_HOL_Obool)), _1722162), _1722164)))], (42659 ^ _781013) ^ [_1626405, _1626407, _1626409] : [_1626405 = c_List_Olist_ONil(_1626407), -(c_List_Olast(_1626407, hAPP(hAPP(c_List_Oappend(_1626407), _1626409), _1626405)) = c_List_Olast(_1626407, _1626409))], (51600 ^ _781013) ^ [_1824617] : [-(class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(_1824617)))], (47250 ^ _781013) ^ [_1733405, _1733407, _1733409, _1733411] : [hBOOL(hAPP(hAPP(c_member(_1733405), _1733407), hAPP(c_Relation_ODomain(_1733405, _1733409), _1733411))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1733405, _1733409)), hAPP(hAPP(c_Product__Type_OPair(_1733405, _1733409), _1733407), 47253 ^ [_1733405, _1733407, _1733409, _1733411])), _1733411)))], (18141 ^ _781013) ^ [_1118938, _1118940, _1118942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118938), _1118940)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118938), _1118942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118940), _1118942)))], (39098 ^ _781013) ^ [_1535654, _1535656] : [39100 ^ _781013 : [(39104 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39102 ^ [_1535654, _1535656]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1535654)), _1535656))))], (39106 ^ _781013) ^ [] : [39099 ^ [_1535654, _1535656] = 39102 ^ [_1535654, _1535656]], (39108 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1535654), _1535656), 39099 ^ [_1535654, _1535656]) = hAPP(hAPP(c_List_Onth(_1535654), _1535656), 39102 ^ [_1535654, _1535656]))], (39101 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39099 ^ [_1535654, _1535656]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1535654)), _1535656))))]], -(hBOOL(hAPP(c_List_Odistinct(_1535654), _1535656)))], (20542 ^ _781013) ^ [_1164642] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1164642) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1164642)))], (23086 ^ _781013) ^ [_1213010, _1213012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213010)), -(c_SMT_Oz3div(_1213012, _1213010) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213012), _1213010))], (39450 ^ _781013) ^ [_1543733, _1543735, _1543737, _1543739] : [class_Rings_Osemiring__1(_1543733), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1543733), hAPP(hAPP(c_List_Omap(_1543735, _1543733), hAPP(c_COMBK(_1543733, _1543735), _1543737)), _1543739)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1543733), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1543733), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1543735)), _1543739))), _1543737))], (5030 ^ _781013) ^ [_857651, _857653, _857655, _857657, _857659, _857661, _857663, _857665] : [-(c_New__Random__Sequence_Opos__map(_857665, _857661, _857657, _857653) = c_New__Random__Sequence_Opos__map(_857663, _857659, _857655, _857651)), _857665 = _857663, _857661 = _857659, _857657 = _857655, _857653 = _857651], (34373 ^ _781013) ^ [_1432702, _1432704] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1432702), _1432704), hAPP(c_Int_Onumber__class_Onumber__of(_1432702), c_Int_OBit1(c_Int_OPls))) = _1432704), class_Fields_Ofield(_1432702), class_Int_Onumber__ring(_1432702)], (48567 ^ _781013) ^ [_1763087, _1763089, _1763091, _1763093] : [hBOOL(hAPP(hAPP(c_member(_1763087), _1763089), c_Wellfounded_Oacc(_1763087, _1763091))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1763087, _1763087)), hAPP(hAPP(c_Product__Type_OPair(_1763087, _1763087), _1763093), _1763089)), c_Transitive__Closure_Ortrancl(_1763087, _1763091))), -(hBOOL(hAPP(hAPP(c_member(_1763087), _1763093), c_Wellfounded_Oacc(_1763087, _1763091))))], (14111 ^ _781013) ^ [_1040811, _1040813, _1040815] : [class_Rings_Ocomm__ring__1(_1040811), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040811), _1040813), _1040815) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040811), _1040813), hAPP(c_Groups_Ouminus__class_Ouminus(_1040811), _1040815)))], (38391 ^ _781013) ^ [_1518904, _1518906, _1518908, _1518910, _1518912] : [c_Typedef_Otype__definition(_1518904, _1518906, _1518908, _1518910, _1518912), -(hAPP(c_Set_Oimage(_1518906, _1518904, _1518910), _1518912) = c_Orderings_Otop__class_Otop(tc_fun(_1518904, tc_HOL_Obool)))], (21511 ^ _781013) ^ [_1185110, _1185112, _1185114] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1185110, tc_Nat_Onat), _1185112), _1185114)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1185110, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1185110), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1185112)), _1185114))], (34401 ^ _781013) ^ [_1433076] : [class_Int_Onumber__ring(_1433076), c_Int_Oiszero(_1433076, hAPP(c_Int_Onumber__class_Onumber__of(_1433076), c_Int_OBit1(c_Int_OPls)))], (23431 ^ _781013) ^ [_1219421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219421)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219421) = 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, _1219421))))], (34957 ^ _781013) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (2736 ^ _781013) ^ [_821742, _821744, _821746, _821748, _821750, _821752] : [-(c_Map_Oran(_821752, _821748, _821744) = c_Map_Oran(_821750, _821746, _821742)), _821752 = _821750, _821748 = _821746, _821744 = _821742], (38111 ^ _781013) ^ [] : [-(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)))], (6983 ^ _781013) ^ [_896503, _896505, _896507] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896503, tc_HOL_Obool)), _896505), _896507) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896503, tc_HOL_Obool)), _896507), _896505))], (48447 ^ _781013) ^ [_1760646, _1760648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1760646), _1760648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1760646)), hAPP(c_Code__Numeral_Onat__of, _1760648))))], (18450 ^ _781013) ^ [_1124356, _1124358, _1124360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124356), _1124358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1124360), _1124358))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1124358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124356), _1124360)))], (48453 ^ _781013) ^ [_1760751, _1760753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1760751)), hAPP(c_Code__Numeral_Onat__of, _1760753))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1760751), _1760753)))], (12808 ^ _781013) ^ [_1013048, _1013050, _1013052, _1013054] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1013048), _1013050)), -(hAPP(c_Set_Oimage(_1013048, _1013052, _1013054), _1013050) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1013052, tc_HOL_Obool), _1013048, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013052, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1013048, tc_fun(_1013052, tc_HOL_Obool), tc_fun(_1013052, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1013052, tc_fun(tc_fun(_1013052, tc_HOL_Obool), tc_fun(_1013052, tc_HOL_Obool)), _1013048), c_Set_Oinsert(_1013052)), _1013054)), c_Orderings_Obot__class_Obot(tc_fun(_1013052, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1013052, tc_HOL_Obool))), _1013050))], (22268 ^ _781013) ^ [_1198488, _1198490, _1198492, _1198494, _1198496] : [class_Orderings_Olinorder(_1198488), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1198488, _1198490), _1198492) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1198488, _1198494), _1198496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198488), _1198490), _1198492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198488), _1198494), _1198496)), -(_1198490 = _1198494)], (11013 ^ _781013) ^ [_976608, _976610, _976612, _976614] : [class_Lattices_Olattice(_976608), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976608), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976608), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976608), _976610), _976612)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976608), _976610), _976614))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976608), _976610), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976608), _976612), _976614)))))], (48157 ^ _781013) ^ [_1753884, _1753886, _1753888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1753884), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1753886), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1753886)), _1753888)))), -(hBOOL(hAPP(hAPP(c_member(_1753886), hAPP(c_Random_Opick(_1753886, _1753888), _1753884)), hAPP(c_List_Oset(_1753886), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1753886), _1753886), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1753886)), _1753888)))))], (23676 ^ _781013) ^ [_1223585] : [-(hBOOL(hAPP(_1223585, 23683 ^ [_1223585]))), 23677 ^ _781013 : [(23678 ^ _781013) ^ [_1223637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223637)), hBOOL(hAPP(_1223585, hAPP(c_Int_Onat, _1223637)))]]], (5789 ^ _781013) ^ [_873384, _873386, _873388, _873390, _873392, _873394] : [c_Hoare__Mirabelle_Ohoare__derivs(_873384, _873386, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873384)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873384), _873388), _873390), _873392)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873384), tc_HOL_Obool)))), 5796 ^ _781013 : [(5799 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_873388, 5794 ^ [_873384, _873386, _873388, _873390, _873392, _873394]), 5795 ^ [_873384, _873386, _873388, _873390, _873392, _873394]))], (5797 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_873394, 5794 ^ [_873384, _873386, _873388, _873390, _873392, _873394]), 5795 ^ [_873384, _873386, _873388, _873390, _873392, _873394])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_873384, _873386, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873384)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873384), _873394), _873390), _873392)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873384), tc_HOL_Obool)))))], (45998 ^ _781013) ^ [_1701513, _1701515] : [class_Complete__Lattice_Ocomplete__lattice(_1701513), hBOOL(hAPP(c_Finite__Set_Ofinite(_1701513), _1701515)), -(_1701515 = c_Orderings_Obot__class_Obot(tc_fun(_1701513, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1701513, _1701515) = c_Complete__Lattice_OInf__class_OInf(_1701513, _1701515))], (45664 ^ _781013) ^ [_1693598, _1693600, _1693602] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1693598, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1693598, tc_HOL_Obool)), _1693600), _1693602)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1693598, tc_HOL_Obool)), _1693600), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1693598, tc_HOL_Obool), _1693602)))], (40974 ^ _781013) ^ [_1587615, _1587617, _1587619, _1587621] : [-(c_Product__Type_Oapfst(_1587615, _1587617, _1587619, _1587621) = c_Product__Type_Omap__pair(_1587615, _1587617, _1587619, _1587619, _1587621, c_Fun_Oid(_1587619)))], (2768 ^ _781013) ^ [_822264, _822266, _822268, _822270, _822272, _822274, _822276, _822278] : [-(c_Nitpick_Osetsum_H(_822278, _822274, _822270, _822266) = c_Nitpick_Osetsum_H(_822276, _822272, _822268, _822264)), _822278 = _822276, _822274 = _822272, _822270 = _822268, _822266 = _822264], (50712 ^ _781013) ^ [_1811538] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1811538)), c_Int_OPls))], (21605 ^ _781013) ^ [_1186745, _1186747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186745), _1186747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186745)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186747))))], (51610 ^ _781013) ^ [_1824785, _1824787, _1824789, _1824791, _1824793, _1824795] : [-(hAPP(hAPP(hAPP(c_COMBC(_1824785, _1824787, _1824789), _1824791), _1824793), _1824795) = hAPP(hAPP(_1824791, _1824795), _1824793))], (15815 ^ _781013) ^ [_1073614, _1073616, _1073618] : [class_Rings_Olinordered__semiring__strict(_1073614), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073614), _1073616), c_Groups_Ozero__class_Ozero(_1073614))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073614), c_Groups_Ozero__class_Ozero(_1073614)), _1073618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073614), _1073616), _1073618)), c_Groups_Ozero__class_Ozero(_1073614))))], (9186 ^ _781013) ^ [_943268, _943270, _943272, _943274, _943276] : [class_Groups_Oab__group__add(_943268), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_943268), _943270), _943272) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_943268), _943274), _943276), 9193 ^ _781013 : [(9200 ^ _781013) ^ [] : [_943274 = _943276, -(_943270 = _943272)], (9194 ^ _781013) ^ [] : [_943270 = _943272, -(_943274 = _943276)]]], (21760 ^ _781013) ^ [_1189564, _1189566] : [class_Groups_Olinordered__ab__group__add(_1189564), hBOOL(hAPP(c_Finite__Set_Ofinite(_1189564), _1189566)), -(_1189566 = c_Orderings_Obot__class_Obot(tc_fun(_1189564, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1189564), c_Big__Operators_Olinorder__class_OMax(_1189564, _1189566)) = c_Big__Operators_Olinorder__class_OMin(_1189564, hAPP(c_Set_Oimage(_1189564, _1189564, c_Groups_Ouminus__class_Ouminus(_1189564)), _1189566)))], (7089 ^ _781013) ^ [_898544, _898546, _898548] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898544, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898544, tc_HOL_Obool)), _898546), _898548)), _898548) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898544, tc_HOL_Obool)), _898546), _898548))], (6864 ^ _781013) ^ [_894233, _894235, _894237, _894239] : [6865 ^ _781013 : [(6868 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894233), _894235), _894239))], (6866 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894233), _894235), _894237))]], -(hBOOL(hAPP(hAPP(c_member(_894233), _894235), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894233, tc_HOL_Obool)), _894239), _894237))))], (14753 ^ _781013) ^ [_1054797, _1054799] : [hAPP(c_Set_OCollect(_1054797), _1054799) = c_Orderings_Obot__class_Obot(tc_fun(_1054797, tc_HOL_Obool)), 14756 ^ _781013 : [(14757 ^ _781013) ^ [_1054882] : [hBOOL(hAPP(_1054799, _1054882))]]], (22238 ^ _781013) ^ [_1197987, _1197989] : [class_Divides_Osemiring__div(_1197987), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1197987), c_Groups_Ozero__class_Ozero(_1197987)), _1197989) = c_Groups_Ozero__class_Ozero(_1197987))], (8438 ^ _781013) ^ [_926485, _926487, _926489, _926491, _926493] : [-(hAPP(c_Set_Oimage(_926485, _926487, _926489), hAPP(hAPP(c_Set_Oinsert(_926485), _926491), _926493)) = hAPP(hAPP(c_Set_Oinsert(_926487), hAPP(_926489, _926491)), hAPP(c_Set_Oimage(_926485, _926487, _926489), _926493)))], (9607 ^ _781013) ^ [_951117, _951119, _951121, _951123] : [class_Orderings_Oord(_951117), _951119 = _951121, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951117), _951121), _951123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951117), _951119), _951123)))], (47203 ^ _781013) ^ [_1731726, _1731728] : [-(hAPP(c_Relation_ODomain(_1731726, _1731726), c_Relation_OId__on(_1731726, _1731728)) = _1731728)], (1054 ^ _781013) ^ [_796930, _796932] : [-(class_Groups_Olinordered__ab__group__add(_796930)), _796932 = _796930, class_Groups_Olinordered__ab__group__add(_796932)], (21367 ^ _781013) ^ [_1182055, _1182057, _1182059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182055), _1182057)), -(c_Smallcheck_Osmall_H(_1182059, _1182055, _1182057) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (28656 ^ _781013) ^ [_1315647, _1315649] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1315647)), hAPP(c_Nat_OSuc, _1315649)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1315647), _1315649)))], (27413 ^ _781013) ^ [_1291915, _1291917] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1291915, tc_HOL_Obool)), _1291917), hAPP(c_Set_OPow(_1291915), _1291917))))], (31453 ^ _781013) ^ [_1373038, _1373040, _1373042, _1373044] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1373038), _1373040))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373042), hAPP(c_Set_Oimage(_1373038, _1373042, _1373044), _1373040))), 31461 ^ _781013 : [(31464 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1373038), hAPP(c_Set_OCollect(_1373038), hAPP(hAPP(c_COMBS(_1373038, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1373038), c_fconj), hAPP(hAPP(c_COMBC(_1373038, tc_fun(_1373038, tc_HOL_Obool), tc_HOL_Obool), c_member(_1373038)), _1373040))), hAPP(hAPP(c_COMBC(_1373038, _1373042, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1373042, tc_fun(_1373042, tc_HOL_Obool), _1373038), c_fequal), _1373044)), hAPP(_1373044, 31460 ^ [_1373038, _1373040, _1373042, _1373044]))))))], (31462 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373038), 31460 ^ [_1373038, _1373040, _1373042, _1373044]), _1373040)))]]], (47051 ^ _781013) ^ [_1727781, _1727783] : [-(c_Nitpick_Onumber__of__frac(_1727781, _1727783) = c_Nitpick_OAbs__Frac(_1727781, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1727783), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (39259 ^ _781013) ^ [_1539420, _1539422, _1539424] : [-(hAPP(hAPP(c_List_Olist__update(_1539420, _1539422), _1539424), hAPP(hAPP(c_List_Onth(_1539420), _1539422), _1539424)) = _1539422)], (44310 ^ _781013) ^ [_1663955, _1663957] : [-(hAPP(c_List_Orev(_1663955), hAPP(c_List_Orev(_1663955), _1663957)) = _1663957)], (50910 ^ _781013) ^ [_1816375, _1816377, _1816379, _1816381, _1816383] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1816377, _1816375)), hAPP(hAPP(c_Product__Type_OPair(_1816377, _1816375), _1816381), _1816383)), hAPP(c_Relation_Oconverse(_1816375, _1816377), _1816379))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1816375, _1816377, hAPP(hAPP(c_COMBC(_1816375, tc_fun(tc_prod(_1816375, _1816377), tc_HOL_Obool), tc_fun(_1816377, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1816377, tc_fun(tc_fun(tc_prod(_1816375, _1816377), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1816375, _1816377), tc_HOL_Obool), tc_fun(_1816377, tc_HOL_Obool)), _1816375), c_COMBC(_1816377, tc_fun(tc_prod(_1816375, _1816377), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1816377, tc_prod(_1816375, _1816377)), tc_fun(_1816377, tc_fun(tc_fun(tc_prod(_1816375, _1816377), tc_HOL_Obool), tc_HOL_Obool)), _1816375), hAPP(c_COMBB(tc_prod(_1816375, _1816377), tc_fun(tc_fun(tc_prod(_1816375, _1816377), tc_HOL_Obool), tc_HOL_Obool), _1816377), c_member(tc_prod(_1816375, _1816377)))), c_Product__Type_OPair(_1816375, _1816377)))), _1816379)), _1816381), _1816383)))], (3522 ^ _781013) ^ [_834141, _834143, _834145, _834147] : [-(c_List_Olex(_834147, _834143) = c_List_Olex(_834145, _834141)), _834147 = _834145, _834143 = _834141], (19316 ^ _781013) ^ [_1142833, _1142835, _1142837] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142833), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1142835), _1142837)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142833), _1142835)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142833), _1142837)))], (40958 ^ _781013) ^ [_1587347, _1587349] : [-(hAPP(c_Fun_Oid(_1587347), _1587349) = _1587349)], (4162 ^ _781013) ^ [_843971, _843973, _843975, _843977] : [-(c_Nat_Ocompow(_843977, _843973) = c_Nat_Ocompow(_843975, _843971)), _843977 = _843975, _843973 = _843971], (23949 ^ _781013) ^ [_1228119] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _1228119)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42970 ^ _781013) ^ [_1634340, _1634342, _1634344, _1634346, _1634348] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634340, tc_fun(_1634342, tc_HOL_Obool)), _1634344), hAPP(hAPP(c_COMBB(tc_fun(_1634342, tc_HOL_Obool), tc_fun(_1634342, tc_HOL_Obool), _1634340), hAPP(c_Set_Oinsert(_1634342), _1634346)), _1634348)) = hAPP(hAPP(c_Set_Oinsert(_1634342), _1634346), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634340, tc_fun(_1634342, tc_HOL_Obool)), _1634344), _1634348)))], (44244 ^ _781013) ^ [_1662546, _1662548] : [c_List_Olist_ONil(_1662546) = hAPP(c_List_Orev(_1662546), _1662548), -(_1662548 = c_List_Olist_ONil(_1662546))], (16013 ^ _781013) ^ [_1077228, _1077230, _1077232] : [class_Groups_Oordered__ab__group__add(_1077228), 16016 ^ _781013 : [(16023 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077228), _1077230), _1077232)), c_Groups_Ozero__class_Ozero(_1077228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077228), _1077230), _1077232)))], (16017 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077228), _1077230), _1077232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077228), _1077230), _1077232)), c_Groups_Ozero__class_Ozero(_1077228))))]]], (33498 ^ _781013) ^ [_1416734, _1416736] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416734))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416734)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416736)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3976 ^ _781013) ^ [_841194, _841196] : [_841196 = _841194, -(c_Random_Orange(_841196) = c_Random_Orange(_841194))], (16756 ^ _781013) ^ [_1091673, _1091675, _1091677, _1091679, _1091681] : [class_Rings_Olinordered__semiring__strict(_1091673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091673), _1091675), _1091677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091673), _1091679), _1091681)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091673), c_Groups_Ozero__class_Ozero(_1091673)), _1091675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091673), c_Groups_Ozero__class_Ozero(_1091673)), _1091679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091673), _1091675), _1091679)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091673), _1091677), _1091681))))], (26067 ^ _781013) ^ [_1265914, _1265916, _1265918] : [class_Orderings_Olinorder(_1265914), 26070 ^ _781013 : [(26077 ^ _781013) ^ [] : [_1265916 = _1265918, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1265914), _1265916) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1265914), _1265918))], (26071 ^ _781013) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1265914), _1265916) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1265914), _1265918), -(_1265916 = _1265918)]]], (5952 ^ _781013) ^ [_877210, _877212] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_877210, _877212))), 5955 ^ _781013 : [(5958 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _877212)))], (5956 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _877210)))]]], (49257 ^ _781013) ^ [_1780913, _1780915] : [-(c_List_Orotate(_1780913, _1780915) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1780913), tc_List_Olist(_1780913)), _1780915), c_List_Orotate1(_1780913)))], (46770 ^ _781013) ^ [_1721639, _1721641] : [c_Wellfounded_Owf(_1721639, hAPP(hAPP(c_Relation_Orel__comp(_1721639, _1721639, _1721639), _1721641), _1721641)), -(c_Wellfounded_Owf(_1721639, _1721641))], (31775 ^ _781013) ^ [_1381693, _1381695, _1381697, _1381699] : [31777 ^ _781013 : [(31780 ^ _781013) ^ [] : [hAPP(_1381699, 31776 ^ [_1381693, _1381695, _1381697, _1381699]) = c_Orderings_Obot__class_Obot(tc_fun(_1381695, tc_HOL_Obool))], (31778 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381693), 31776 ^ [_1381693, _1381695, _1381697, _1381699]), _1381697)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381693, tc_fun(_1381695, tc_HOL_Obool)), _1381697), _1381699) = c_Orderings_Obot__class_Obot(tc_fun(_1381695, tc_HOL_Obool)))], (40589 ^ _781013) ^ [_1575563, _1575565, _1575567, _1575569] : [40590 ^ _781013 : [(40593 ^ _781013) ^ [] : [_1575569 = c_Orderings_Obot__class_Obot(tc_fun(_1575565, tc_HOL_Obool))], (40591 ^ _781013) ^ [] : [_1575567 = c_Orderings_Obot__class_Obot(tc_fun(_1575563, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1575563, _1575565), _1575567), hAPP(c_COMBK(tc_fun(_1575565, tc_HOL_Obool), _1575563), _1575569)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575563, _1575565), tc_HOL_Obool)))], (33658 ^ _781013) ^ [_1419161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1419161), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419161)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51518 ^ _781013) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (1624 ^ _781013) ^ [_804055, _804057] : [-(class_Rings_Ocomm__semiring__1(_804055)), _804057 = _804055, class_Rings_Ocomm__semiring__1(_804057)], (37160 ^ _781013) ^ [_1490084, _1490086, _1490088] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1490084, _1490086), _1490088)), 37163 ^ _781013 : [(37164 ^ _781013) ^ [_1490169] : [hBOOL(hAPP(hAPP(_1490086, _1490169), _1490088)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1490084, _1490086), _1490169)))]]], (1484 ^ _781013) ^ [_802305, _802307] : [-(class_Groups_Oordered__ab__semigroup__add(_802305)), _802307 = _802305, class_Groups_Oordered__ab__semigroup__add(_802307)], (41298 ^ _781013) ^ [_1594988, _1594990] : [-(c_List_Osublist(_1594988, c_List_Olist_ONil(_1594988), _1594990) = c_List_Olist_ONil(_1594988))], (8717 ^ _781013) ^ [_932582, _932584, _932586, _932588, _932590, _932592] : [hBOOL(hAPP(hAPP(c_member(_932582), _932584), _932586)), -(hAPP(c_Set_Oimage(_932582, _932588, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_932582, _932588), _932590), _932584), _932592)), _932586) = hAPP(hAPP(c_Set_Oinsert(_932588), _932592), hAPP(c_Set_Oimage(_932582, _932588, _932590), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_932582, tc_HOL_Obool)), _932586), hAPP(hAPP(c_Set_Oinsert(_932582), _932584), c_Orderings_Obot__class_Obot(tc_fun(_932582, tc_HOL_Obool)))))))], (21519 ^ _781013) ^ [_1185257] : [_1185257 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185257) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43891 ^ _781013) ^ [_1654961, _1654963, _1654965] : [class_Orderings_Olinorder(_1654961), 43894 ^ _781013 : [(43907 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1654961, hAPP(hAPP(c_List_Olist_OCons(_1654961), _1654963), _1654965))), c_List_Olinorder__class_Osorted(_1654961, _1654965), 43913 ^ _781013 : [(43916 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1654961), _1654963), 43912 ^ [_1654961, _1654963, _1654965]))], (43914 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1654961), 43912 ^ [_1654961, _1654963, _1654965]), hAPP(c_List_Oset(_1654961), _1654965))))]]], (43895 ^ _781013) ^ [] : [c_List_Olinorder__class_Osorted(_1654961, hAPP(hAPP(c_List_Olist_OCons(_1654961), _1654963), _1654965)), 43898 ^ _781013 : [(43901 ^ _781013) ^ [_1655147] : [hBOOL(hAPP(hAPP(c_member(_1654961), _1655147), hAPP(c_List_Oset(_1654961), _1654965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1654961), _1654963), _1655147)))], (43899 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1654961, _1654965))]]]]], (30183 ^ _781013) ^ [_1344918, _1344920, _1344922, _1344924] : [class_Orderings_Olinorder(_1344918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344918), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344918), _1344920), _1344922)), _1344924)), 30190 ^ _781013 : [(30193 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344918), _1344922), _1344924)))], (30191 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344918), _1344920), _1344924)))]]], (50916 ^ _781013) ^ [_1816764, _1816766] : [class_Lazy__Sequence_Osmall__lazy(_1816764), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1816764), _1816766) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1816764), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1816764)), c_List_Olist_ONil(_1816764)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1816764))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1816766)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1816764, tc_List_Olist(_1816764)), tc_List_Olist(_1816764), c_Lazy__Sequence_Oproduct(_1816764, tc_List_Olist(_1816764), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1816764, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1816766), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1816764), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1816766), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1816764, tc_List_Olist(_1816764), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1816764))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1816764), tc_List_Olist(_1816764)), tc_fun(tc_List_Olist(_1816764), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1816764))), _1816764), hAPP(c_COMBB(tc_List_Olist(_1816764), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1816764)), tc_List_Olist(_1816764)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1816764)))), c_List_Olist_OCons(_1816764))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1816764)))))], (11175 ^ _781013) ^ [_980199, _980201, _980203, _980205, _980207, _980209] : [hAPP(c_Map_Omap__add(_980199, _980201, _980203, _980205), _980207) = hAPP(c_Option_Ooption_OSome(_980201), _980209), -(hAPP(_980205, _980207) = hAPP(c_Option_Ooption_OSome(_980201), _980209)), 11182 ^ _781013 : [(11185 ^ _781013) ^ [] : [-(hAPP(_980203, _980207) = hAPP(c_Option_Ooption_OSome(_980201), _980209))], (11183 ^ _781013) ^ [] : [-(hAPP(_980205, _980207) = c_Option_Ooption_ONone(_980201))]]], (15343 ^ _781013) ^ [_1064895, _1064897] : [class_Groups_Olinordered__ab__group__add(_1064895), 15346 ^ _781013 : [(15353 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064895), c_Groups_Ozero__class_Ozero(_1064895)), _1064897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064895), c_Groups_Ozero__class_Ozero(_1064895)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064895), _1064897), _1064897))))], (15347 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064895), c_Groups_Ozero__class_Ozero(_1064895)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064895), _1064897), _1064897))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064895), c_Groups_Ozero__class_Ozero(_1064895)), _1064897)))]]], (31013 ^ _781013) ^ [_1361661, _1361663, _1361665] : [class_Orderings_Olinorder(_1361661), hAPP(_1361663, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1361661), 31018 ^ [_1361661, _1361663, _1361665]), 31019 ^ [_1361661, _1361663, _1361665])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1361661), hAPP(_1361663, 31018 ^ [_1361661, _1361663, _1361665])), hAPP(_1361663, 31019 ^ [_1361661, _1361663, _1361665])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361661), _1361665)), -(_1361665 = c_Orderings_Obot__class_Obot(tc_fun(_1361661, tc_HOL_Obool))), -(hAPP(_1361663, c_Big__Operators_Olinorder__class_OMin(_1361661, _1361665)) = c_Big__Operators_Olinorder__class_OMin(_1361661, hAPP(c_Set_Oimage(_1361661, _1361661, _1361663), _1361665)))], (7867 ^ _781013) ^ [_913637, _913639, _913641, _913643, _913645, _913647, _913649] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_913637, tc_Option_Ooption(_913639)), _913641), _913643), hAPP(c_Option_Ooption_OSome(_913639), _913645)), _913647) = hAPP(c_Option_Ooption_OSome(_913639), _913649), 7872 ^ _781013 : [(7875 ^ _781013) ^ [] : [-(_913645 = _913649)], (7873 ^ _781013) ^ [] : [-(_913647 = _913643)]], 7876 ^ _781013 : [(7879 ^ _781013) ^ [] : [-(hAPP(_913641, _913647) = hAPP(c_Option_Ooption_OSome(_913639), _913649))], (7877 ^ _781013) ^ [] : [_913647 = _913643]]], (40383 ^ _781013) ^ [_1568912, _1568914, _1568916, _1568918] : [-(_1568912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1568914), hAPP(hAPP(c_List_Olist_OCons(_1568914), _1568916), _1568918)), _1568912) = hAPP(hAPP(c_List_Onth(_1568914), _1568918), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1568912), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (33560 ^ _781013) ^ [_1417725, _1417727] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417725)), hAPP(c_Nat_OSuc, _1417727)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417725))), 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)), _1417727)))))], (45011 ^ _781013) ^ [_1680158, _1680160, _1680162] : [-(hAPP(c_List_Oset(tc_List_Olist(_1680158)), c_Enum_On__lists(_1680158, _1680160, _1680162)) = hAPP(c_Set_OCollect(tc_List_Olist(_1680158)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1680158), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1680158)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1680158), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1680158)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1680158)))), _1680160))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1680158), tc_fun(_1680158, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1680158, tc_HOL_Obool), tc_fun(tc_fun(_1680158, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1680158)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1680158, tc_HOL_Obool))), c_List_Oset(_1680158))), hAPP(c_List_Oset(_1680158), _1680162)))))], (5940 ^ _781013) ^ [_876892, _876894, _876896, _876898, _876900] : [c_Hoare__Mirabelle_Ohoare__derivs(_876892, _876894, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_876892)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_876892), c_Hoare__Mirabelle_Opeek__and(_876892, _876896, _876898)), _876900), _876896)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_876892), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_876892, _876894, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_876892)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_876892), _876896), c_Com_Ocom_OWhile(_876898, _876900)), c_Hoare__Mirabelle_Opeek__and(_876892, _876896, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _876898)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_876892), tc_HOL_Obool)))))], (14315 ^ _781013) ^ [_1045923, _1045925, _1045927, _1045929] : [class_Rings_Ocomm__semiring__1(_1045923), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045923), _1045925), _1045927)), _1045929) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045923), _1045925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045923), _1045927), _1045929)))], (11910 ^ _781013) ^ [_995812, _995814] : [class_Lattices_Olattice(_995812), -(c_Big__Operators_Olattice__class_OInf__fin(_995812, hAPP(hAPP(c_Set_Oinsert(_995812), _995814), c_Orderings_Obot__class_Obot(tc_fun(_995812, tc_HOL_Obool)))) = _995814)], (40135 ^ _781013) ^ [_1563670, _1563672, _1563674, _1563676, _1563678] : [-(hAPP(hAPP(c_List_Olist_OCons(_1563670), _1563672), _1563674) = hAPP(hAPP(c_List_Olist_OCons(_1563670), _1563676), _1563678)), _1563672 = _1563676, _1563674 = _1563678], (11151 ^ _781013) ^ [_979743, _979745, _979747, _979749, _979751, _979753] : [hAPP(c_Map_Omap__add(_979743, _979745, _979747, _979749), _979751) = hAPP(c_Option_Ooption_OSome(_979745), _979753), -(hAPP(_979749, _979751) = hAPP(c_Option_Ooption_OSome(_979745), _979753)), 11158 ^ _781013 : [(11161 ^ _781013) ^ [] : [-(hAPP(_979747, _979751) = hAPP(c_Option_Ooption_OSome(_979745), _979753))], (11159 ^ _781013) ^ [] : [-(hAPP(_979749, _979751) = c_Option_Ooption_ONone(_979745))]]], (36561 ^ _781013) ^ [_1478574, _1478576, _1478578] : [hBOOL(hAPP(_1478574, hAPP(hAPP(c_Product__Type_OPair(_1478576, _1478578), 36562 ^ [_1478574, _1478576, _1478578]), 36563 ^ [_1478574, _1478576, _1478578]))), 36566 ^ _781013 : [(36567 ^ _781013) ^ [_1478721] : [-(hBOOL(hAPP(_1478574, _1478721)))]]], (43069 ^ _781013) ^ [_1637334, _1637336, _1637338, _1637340, _1637342] : [class_Complete__Lattice_Ocomplete__lattice(_1637334), 43072 ^ _781013 : [(43073 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1637334), _1637336), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637338, _1637334), _1637340), _1637342))), 43076 ^ _781013 : [(43077 ^ _781013) ^ [_1637515] : [hBOOL(hAPP(hAPP(c_member(_1637338), _1637515), _1637340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1637334), _1637336), hAPP(_1637342, _1637515))))]]], (43083 ^ _781013) ^ [] : [43085 ^ _781013 : [(43088 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1637334), _1637336), hAPP(_1637342, 43084 ^ [_1637334, _1637336, _1637338, _1637340, _1637342])))], (43086 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1637338), 43084 ^ [_1637334, _1637336, _1637338, _1637340, _1637342]), _1637340)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1637334), _1637336), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637338, _1637334), _1637340), _1637342))))]]], (42689 ^ _781013) ^ [_1626788, _1626790, _1626792] : [-(c_List_Olast(_1626788, hAPP(hAPP(c_List_Oappend(_1626788), _1626790), hAPP(hAPP(c_List_Olist_OCons(_1626788), _1626792), c_List_Olist_ONil(_1626788)))) = _1626792)], (28436 ^ _781013) ^ [_1311724, _1311726, _1311728] : [class_Orderings_Olinorder(_1311724), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311724), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311724), _1311726), _1311728)), _1311728)))], (28188 ^ _781013) ^ [_1307111, _1307113, _1307115, _1307117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307111)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1307113), _1307115)), -(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), _1307115), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1307117, _1307111))), _1307113))))], (1694 ^ _781013) ^ [_804930, _804932] : [-(class_Orderings_Olinorder(_804930)), _804932 = _804930, class_Orderings_Olinorder(_804932)], (16472 ^ _781013) ^ [_1085926, _1085928, _1085930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1085926), _1085928)), -(hBOOL(hAPP(hAPP(c_member(_1085926), _1085930), _1085928))), -(hAPP(c_Finite__Set_Ocard(_1085926), hAPP(hAPP(c_Set_Oinsert(_1085926), _1085930), _1085928)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1085926), _1085928)))], (13052 ^ _781013) ^ [_1018372, _1018374, _1018376, _1018378] : [c_Fun_Oinj__on(_1018372, _1018374, _1018376, _1018378), -(c_Fun_Oinj__on(_1018374, _1018372, c_Fun_Othe__inv__into(_1018372, _1018374, _1018378, _1018376), hAPP(c_Set_Oimage(_1018372, _1018374, _1018376), _1018378)))], (36741 ^ _781013) ^ [_1482382, _1482384] : [c_Nitpick_Orefl_H(_1482382, _1482384), 36744 ^ _781013 : [(36745 ^ _781013) ^ [_1482460] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1482382, _1482382)), hAPP(hAPP(c_Product__Type_OPair(_1482382, _1482382), _1482460), _1482460)), _1482384)))]]], (38886 ^ _781013) ^ [_1530315, _1530317, _1530319, _1530321, _1530323] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1530315)), _1530317) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1530319)), _1530321), 38889 ^ _781013 : [(38898 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1530315, _1530319), _1530317), _1530321) = _1530323), hAPP(hAPP(c_List_Omap(tc_prod(_1530315, _1530319), _1530315), c_Product__Type_Ofst(_1530315, _1530319)), _1530323) = _1530317, hAPP(hAPP(c_List_Omap(tc_prod(_1530315, _1530319), _1530319), c_Product__Type_Osnd(_1530315, _1530319)), _1530323) = _1530321], (38890 ^ _781013) ^ [] : [hAPP(hAPP(c_List_Ozip(_1530315, _1530319), _1530317), _1530321) = _1530323, 38893 ^ _781013 : [(38896 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1530315, _1530319), _1530319), c_Product__Type_Osnd(_1530315, _1530319)), _1530323) = _1530321)], (38894 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1530315, _1530319), _1530315), c_Product__Type_Ofst(_1530315, _1530319)), _1530323) = _1530317)]]]]], (24304 ^ _781013) ^ [_1234339, _1234341, _1234343] : [class_Fields_Ofield(_1234339), -(_1234341 = c_Groups_Oone__class_Oone(_1234339)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1234339), hAPP(c_Power_Opower__class_Opower(_1234339), _1234341)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1234343)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234339), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1234339), hAPP(hAPP(c_Power_Opower__class_Opower(_1234339), _1234341), _1234343)), c_Groups_Oone__class_Oone(_1234339))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1234339), _1234341), c_Groups_Oone__class_Oone(_1234339))))], (31956 ^ _781013) ^ [_1386956, _1386958, _1386960, _1386962, _1386964] : [-(_1386956 = c_Orderings_Obot__class_Obot(tc_fun(_1386958, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386960, tc_HOL_Obool)), _1386962), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386958, tc_fun(_1386960, tc_HOL_Obool)), _1386956), _1386964)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386958, tc_fun(_1386960, tc_HOL_Obool)), _1386956), hAPP(hAPP(c_COMBB(tc_fun(_1386960, tc_HOL_Obool), tc_fun(_1386960, tc_HOL_Obool), _1386958), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386960, tc_HOL_Obool)), _1386962)), _1386964)))], (38178 ^ _781013) ^ [_1513546] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1513546) = 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, _1513546)), 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))))))))], (15137 ^ _781013) ^ [_1061172, _1061174, _1061176] : [class_Groups_Ocomm__monoid__mult(_1061172), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1061174, _1061172), _1061176), c_Orderings_Obot__class_Obot(tc_fun(_1061174, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1061172))], (5352 ^ _781013) ^ [_862654, _862656] : [_862656 = _862654, -(c_List_Oappend(_862656) = c_List_Oappend(_862654))], (47205 ^ _781013) ^ [_1731760, _1731762, _1731764] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1731760, _1731762)), _1731764)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1731760), hAPP(c_Relation_ODomain(_1731760, _1731762), _1731764))))], (29739 ^ _781013) ^ [_1335543, _1335545] : [class_Orderings_Olinorder(_1335543), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335543), _1335545)), -(_1335545 = c_Orderings_Obot__class_Obot(tc_fun(_1335543, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1335543), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1335543), 29752 ^ [_1335543, _1335545]), 29753 ^ [_1335543, _1335545])), hAPP(hAPP(c_Set_Oinsert(_1335543), 29752 ^ [_1335543, _1335545]), hAPP(hAPP(c_Set_Oinsert(_1335543), 29753 ^ [_1335543, _1335545]), c_Orderings_Obot__class_Obot(tc_fun(_1335543, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1335543), c_Big__Operators_Olinorder__class_OMin(_1335543, _1335545)), _1335545)))], (44238 ^ _781013) ^ [_1662434, _1662436] : [_1662436 = c_List_Olist_ONil(_1662434), -(hAPP(c_List_Orev(_1662434), _1662436) = c_List_Olist_ONil(_1662434))], (42434 ^ _781013) ^ [_1621551, _1621553, _1621555] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1621551, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621553)), _1621555)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1621553, _1621551), _1621555) = _1621555)], (50760 ^ _781013) ^ [_1812617, _1812619, _1812621] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1812617)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1812617, _1812619, _1812621)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1812617)), _1812621)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48822 ^ _781013) ^ [_1769731, _1769733] : [-(c_List_Olistrel1(_1769731, hAPP(c_Relation_Oconverse(_1769731, _1769731), _1769733)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1769731), tc_List_Olist(_1769731)), c_List_Olistrel1(_1769731, _1769733)))], (11860 ^ _781013) ^ [_994901, _994903] : [-(c_Fun_Oinj__on(_994901, tc_Option_Ooption(_994901), c_Option_Ooption_OSome(_994901), _994903))], (38682 ^ _781013) ^ [_1525407, _1525409, _1525411, _1525413, _1525415, _1525417] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1525407, _1525409)), hAPP(hAPP(c_Product__Type_OPair(_1525407, _1525409), _1525411), _1525413)), hAPP(c_List_Oset(tc_prod(_1525407, _1525409)), hAPP(hAPP(c_List_Ozip(_1525407, _1525409), _1525415), _1525417)))), -(hBOOL(hAPP(hAPP(c_member(_1525407), _1525411), hAPP(c_List_Oset(_1525407), _1525415))))], (36826 ^ _781013) ^ [_1483820, _1483822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1483820)), 36829 ^ _781013 : [(36836 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1483822), _1483820))), -(c_Divides_OposDivAlg(_1483822, _1483820) = hAPP(c_Divides_Oadjust(_1483820), c_Divides_OposDivAlg(_1483822, 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)))), _1483820))))], (36830 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1483822), _1483820)), -(c_Divides_OposDivAlg(_1483822, _1483820) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1483822))]]], (44448 ^ _781013) ^ [_1667177, _1667179, _1667181] : [44450 ^ _781013 : [(44453 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1667177), tc_List_Olist(_1667177), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1667177), tc_fun(tc_List_Olist(_1667177), tc_Nat_Onat), tc_fun(tc_List_Olist(_1667177), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1667177), tc_Nat_Onat), tc_fun(tc_List_Olist(_1667177), tc_HOL_Obool)), tc_List_Olist(_1667177)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1667177))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1667177)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1667177))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1667177)))), 44449 ^ [_1667177, _1667179, _1667181]))], (44451 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667177), tc_List_Olist(_1667177))), 44449 ^ [_1667177, _1667179, _1667181]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1667177), tc_List_Olist(_1667177))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1667177), tc_List_Olist(_1667177)), _1667179), _1667181)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1667177))), _1667179) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1667177))), _1667181), 44458 ^ _781013 : [(44465 ^ _781013) ^ [] : [_1667179 = _1667181, -(c_List_Oconcat(_1667177, _1667179) = c_List_Oconcat(_1667177, _1667181))], (44459 ^ _781013) ^ [] : [c_List_Oconcat(_1667177, _1667179) = c_List_Oconcat(_1667177, _1667181), -(_1667179 = _1667181)]]], (41881 ^ _781013) ^ [_1608185, _1608187, _1608189, _1608191, _1608193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1608185), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608187)), _1608189))), -(hAPP(hAPP(c_List_Olist__update(_1608187, hAPP(hAPP(c_List_Oappend(_1608187), _1608189), _1608191)), _1608185), _1608193) = hAPP(hAPP(c_List_Oappend(_1608187), hAPP(hAPP(c_List_Olist__update(_1608187, _1608189), _1608185), _1608193)), _1608191))], (13008 ^ _781013) ^ [_1017587, _1017589, _1017591, _1017593] : [hBOOL(hAPP(hAPP(c_member(_1017587), _1017589), _1017591)), -(hAPP(c_Set_Ovimage(_1017593, _1017587, hAPP(c_COMBK(_1017587, _1017593), _1017589)), _1017591) = c_Orderings_Otop__class_Otop(tc_fun(_1017593, tc_HOL_Obool)))], (50658 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (3456 ^ _781013) ^ [_833084, _833086] : [_833086 = _833084, -(c_Finite__Set_Ocard(_833086) = c_Finite__Set_Ocard(_833084))], (18676 ^ _781013) ^ [_1129056, _1129058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129056), _1129058)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1129056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1129058), _1129056)) = _1129058)], (6669 ^ _781013) ^ [_890632, _890634, _890636, _890638, _890640, _890642] : [-(c_Map_Omap__comp(_890632, _890634, _890636, _890638, _890640, _890642) = c_Option_Ooption_ONone(_890634)), 6670 ^ _781013 : [(6673 ^ _781013) ^ [_890744] : [hAPP(_890640, _890642) = hAPP(c_Option_Ooption_OSome(_890632), _890744), hAPP(_890638, _890744) = c_Option_Ooption_ONone(_890634)], (6671 ^ _781013) ^ [] : [hAPP(_890640, _890642) = c_Option_Ooption_ONone(_890632)]]], (49646 ^ _781013) ^ [_1790291, _1790293, _1790295, _1790297] : [class_Orderings_Olinorder(_1790291), hBOOL(hAPP(c_Finite__Set_Ofinite(_1790291), _1790293)), hBOOL(hAPP(hAPP(c_member(_1790291), _1790295), _1790293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1790291), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1790291), _1790295), _1790297)), hAPP(hAPP(c_Finite__Set_Ofold(_1790291, _1790291, c_Orderings_Oord__class_Omax(_1790291)), _1790297), _1790293))))], (21205 ^ _781013) ^ [_1178824, _1178826, _1178828, _1178830, _1178832] : [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), _1178824), _1178826)), _1178828)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178824), _1178830)), _1178832))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178832), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178824), _1178832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178824), _1178828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178830), _1178826)))], (37750 ^ _781013) ^ [_1502820, _1502822, _1502824, _1502826] : [-(c_Map_Omap__add(_1502820, _1502822, _1502824, hAPP(c_Map_Omap__of(_1502820, _1502822), _1502826)) = c_List_Ofoldr(tc_prod(_1502820, _1502822), tc_fun(_1502820, tc_Option_Ooption(_1502822)), hAPP(c_Product__Type_Oprod_Oprod__case(_1502820, _1502822, tc_fun(tc_fun(_1502820, tc_Option_Ooption(_1502822)), tc_fun(_1502820, tc_Option_Ooption(_1502822)))), hAPP(hAPP(c_COMBC(_1502820, tc_fun(_1502822, tc_Option_Ooption(_1502822)), tc_fun(_1502822, tc_fun(tc_fun(_1502820, tc_Option_Ooption(_1502822)), tc_fun(_1502820, tc_Option_Ooption(_1502822))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1502822), tc_fun(tc_fun(_1502820, tc_Option_Ooption(_1502822)), tc_fun(_1502820, tc_Option_Ooption(_1502822)))), tc_fun(tc_fun(_1502822, tc_Option_Ooption(_1502822)), tc_fun(_1502822, tc_fun(tc_fun(_1502820, tc_Option_Ooption(_1502822)), tc_fun(_1502820, tc_Option_Ooption(_1502822))))), _1502820), c_COMBB(tc_Option_Ooption(_1502822), tc_fun(tc_fun(_1502820, tc_Option_Ooption(_1502822)), tc_fun(_1502820, tc_Option_Ooption(_1502822))), _1502822)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1502820, tc_Option_Ooption(_1502822)), tc_fun(tc_Option_Ooption(_1502822), tc_fun(_1502820, tc_Option_Ooption(_1502822)))), tc_fun(tc_Option_Ooption(_1502822), tc_fun(tc_fun(_1502820, tc_Option_Ooption(_1502822)), tc_fun(_1502820, tc_Option_Ooption(_1502822)))), _1502820), c_COMBC(tc_fun(_1502820, tc_Option_Ooption(_1502822)), tc_Option_Ooption(_1502822), tc_fun(_1502820, tc_Option_Ooption(_1502822)))), hAPP(c_COMBC(tc_fun(_1502820, tc_Option_Ooption(_1502822)), _1502820, tc_fun(tc_Option_Ooption(_1502822), tc_fun(_1502820, tc_Option_Ooption(_1502822)))), c_Fun_Ofun__upd(_1502820, tc_Option_Ooption(_1502822)))))), c_Option_Ooption_OSome(_1502822))), _1502826, _1502824))], (6341 ^ _781013) ^ [_884292, _884294, _884296, _884298] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884292, _884294)), _884296), _884298))), 6342 ^ _781013 : [(6349 ^ _781013) ^ [] : [hBOOL(hAPP(_884292, _884296)), 6352 ^ _781013 : [(6353 ^ _781013) ^ [_884511] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_884294), _884296), _884511)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884292, _884294)), _884511), _884298))]]], (6343 ^ _781013) ^ [] : [_884298 = _884296, -(hBOOL(hAPP(_884292, _884296)))]]], (17875 ^ _781013) ^ [_1114538, _1114540, _1114542] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1114538), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1114540), _1114542)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1114538), _1114540)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1114538), _1114542)))], (44288 ^ _781013) ^ [_1663484, _1663486, _1663488] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1663484), tc_List_Olist(_1663484), c_List_Oappend(_1663484), _1663486), _1663488) = hAPP(hAPP(c_List_Oappend(_1663484), _1663486), c_List_Oconcat(_1663484, _1663488)))], (41158 ^ _781013) ^ [_1592250, _1592252] : [-(c_List_Olists(_1592250, _1592252) = hAPP(c_Set_OCollect(tc_List_Olist(_1592250)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592250), tc_fun(_1592250, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1592250, tc_HOL_Obool), tc_fun(tc_fun(_1592250, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1592250)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1592250, tc_HOL_Obool))), c_List_Oset(_1592250))), _1592252)))], (6977 ^ _781013) ^ [_896404, _896406, _896408] : [hBOOL(hAPP(_896408, _896406)), -(hBOOL(hAPP(hAPP(c_member(_896404), _896406), _896408)))], (6746 ^ _781013) ^ [_892089, _892091, _892093, _892095, _892097, _892099] : [c_Finite__Set_Ofolding__idem(_892089, _892091, _892093, _892095), hBOOL(hAPP(c_Finite__Set_Ofinite(_892089), _892097)), hBOOL(hAPP(hAPP(c_member(_892089), _892099), _892097)), -(hAPP(c_Fun_Ocomp(_892091, _892091, _892091, hAPP(_892095, _892097)), hAPP(_892093, _892099)) = hAPP(_892095, _892097))], (9981 ^ _781013) ^ [_957404, _957406] : [class_Lattices_Oboolean__algebra(_957404), -(hAPP(c_Groups_Ouminus__class_Ouminus(_957404), hAPP(c_Groups_Ouminus__class_Ouminus(_957404), _957406)) = _957406)], (22866 ^ _781013) ^ [_1208737, _1208739, _1208741] : [class_Orderings_Oorder(_1208737), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1208737, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1208737), _1208739)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1208737, _1208739), _1208741)) = c_Orderings_Obot__class_Obot(tc_fun(_1208737, tc_HOL_Obool)))], (34279 ^ _781013) ^ [_1431158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1431158)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431158), c_Int_OPls)))], (20763 ^ _781013) ^ [_1169098, _1169100, _1169102] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1169098), _1169100)), 20766 ^ _781013 : [(20786 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1169098, tc_Nat_Onat), _1169102), _1169100) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 20787 ^ _781013 : [(20788 ^ _781013) ^ [_1169579] : [hBOOL(hAPP(hAPP(c_member(_1169098), _1169579), _1169100)), hAPP(_1169102, _1169579) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20796 ^ _781013 : [(20801 ^ _781013) ^ [] : [hAPP(_1169102, 20795 ^ [_1169098, _1169100, _1169102, _1169579]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20799 ^ _781013) ^ [] : [_1169579 = 20795 ^ [_1169098, _1169100, _1169102, _1169579]], (20797 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1169098), 20795 ^ [_1169098, _1169100, _1169102, _1169579]), _1169100)))]]]]], (20767 ^ _781013) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1169098, tc_Nat_Onat), _1169102), _1169100) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20771 ^ _781013 : [(20776 ^ _781013) ^ [_1169418] : [hBOOL(hAPP(hAPP(c_member(_1169098), _1169418), _1169100)), -(20770 ^ [_1169098, _1169100, _1169102] = _1169418), -(hAPP(_1169102, _1169418) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20774 ^ _781013) ^ [] : [-(hAPP(_1169102, 20770 ^ [_1169098, _1169100, _1169102]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20772 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1169098), 20770 ^ [_1169098, _1169100, _1169102]), _1169100)))]]]]], (48241 ^ _781013) ^ [_1755539, _1755541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1755539)), hAPP(c_Code__Numeral_Oof__nat, _1755541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755539), _1755541)))], (47108 ^ _781013) ^ [_1729194, _1729196, _1729198, _1729200] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1729194, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1729194, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1729196, _1729194), _1729198)), hAPP(c_Relation_ORange(_1729196, _1729194), _1729200))), hAPP(c_Relation_ORange(_1729196, _1729194), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1729196, _1729194), tc_HOL_Obool)), _1729198), _1729200)))))], (39846 ^ _781013) ^ [_1553983, _1553985, _1553987, _1553989] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1553983), tc_List_Olist(_1553983))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1553983), tc_List_Olist(_1553983)), _1553985), _1553987)), c_List_Olistrel(_1553983, _1553989))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553983)), _1553985) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553983)), _1553987))], (35075 ^ _781013) ^ [_1444994, _1444996] : [class_Fields_Olinordered__field__inverse__zero(_1444994), class_Int_Onumber__ring(_1444994), 35082 ^ _781013 : [(35089 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444994), c_Groups_Ozero__class_Ozero(_1444994)), _1444996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444994), c_Groups_Ozero__class_Ozero(_1444994)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1444994), _1444996), hAPP(c_Int_Onumber__class_Onumber__of(_1444994), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35083 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444994), c_Groups_Ozero__class_Ozero(_1444994)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1444994), _1444996), hAPP(c_Int_Onumber__class_Onumber__of(_1444994), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444994), c_Groups_Ozero__class_Ozero(_1444994)), _1444996)))]]], (36960 ^ _781013) ^ [_1486074, _1486076] : [_1486074 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1486076, _1486074) = 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), _1486076)))], (12902 ^ _781013) ^ [_1015198, _1015200, _1015202, _1015204, _1015206, _1015208] : [-(hAPP(c_Set_Ovimage(_1015198, _1015200, hAPP(c_Fun_Ocomp(_1015202, _1015200, _1015198, _1015204), _1015206)), _1015208) = hAPP(c_Set_Ovimage(_1015198, _1015202, _1015206), hAPP(c_Set_Ovimage(_1015202, _1015200, _1015204), _1015208)))], (9184 ^ _781013) ^ [_943224, _943226, _943228, _943230] : [-(hAPP(c_Map_Orestrict__map(_943224, _943226, _943228, c_Orderings_Obot__class_Obot(tc_fun(_943224, tc_HOL_Obool))), _943230) = c_Option_Ooption_ONone(_943226))], (10847 ^ _781013) ^ [_972738, _972740, _972742, _972744] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972738, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972738, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972738, tc_HOL_Obool)), _972740), _972742)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972738, tc_HOL_Obool)), _972742), _972744))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972738, tc_HOL_Obool)), _972744), _972740)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972738, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972738, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972738, tc_HOL_Obool)), _972740), _972742)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972738, tc_HOL_Obool)), _972742), _972744))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972738, tc_HOL_Obool)), _972744), _972740)))], (25539 ^ _781013) ^ [_1256677] : [c_Nat__Transfer_Onat__set(_1256677), 25542 ^ _781013 : [(25549 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1256677))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1256677)))], (25543 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1256677)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1256677))))]]], (17715 ^ _781013) ^ [_1111938, _1111940] : [-(_1111938 = _1111940), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111938), _1111940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111940), _1111938)))], (8673 ^ _781013) ^ [_931715, _931717, _931719, _931721] : [hBOOL(hAPP(_931715, _931717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931719, tc_HOL_Obool)), _931715), _931721)), -(hBOOL(hAPP(_931721, _931717)))], (26401 ^ _781013) ^ [_1271957, _1271959, _1271961] : [class_Orderings_Oorder(_1271957), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1271957, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1271957), _1271959)), c_SetInterval_Oord__class_OatLeastAtMost(_1271957, _1271959, _1271961)) = c_Orderings_Obot__class_Obot(tc_fun(_1271957, tc_HOL_Obool)))], (1684 ^ _781013) ^ [_804805, _804807] : [-(class_Orderings_Opreorder(_804805)), _804807 = _804805, class_Orderings_Opreorder(_804807)], (8643 ^ _781013) ^ [_931000, _931002, _931004, _931006] : [class_Lattices_Olattice(_931000), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931000), _931002), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931000), _931004), _931006)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931000), _931004), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931000), _931002), _931006)))], (24924 ^ _781013) ^ [_1245526, _1245528, _1245530, _1245532, _1245534] : [class_Fields_Olinordered__field(_1245526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245526), c_Groups_Ozero__class_Ozero(_1245526)), _1245528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245526), _1245528), _1245530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245526), c_Groups_Ozero__class_Ozero(_1245526)), _1245532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245526), _1245532), _1245534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245526), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245526), _1245528), _1245534)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245526), _1245530), _1245532))))], (12154 ^ _781013) ^ [_1000279, _1000281] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000279, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000279, tc_HOL_Obool)), _1000281)), _1000281) = c_Orderings_Otop__class_Otop(tc_fun(_1000279, tc_HOL_Obool)))], (43420 ^ _781013) ^ [_1645588, _1645590, _1645592] : [-(c_List_Olistsp(_1645588, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1645588, tc_HOL_Obool)), _1645590), _1645592)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1645588), tc_HOL_Obool)), c_List_Olistsp(_1645588, _1645590)), c_List_Olistsp(_1645588, _1645592)))], (15829 ^ _781013) ^ [_1073869, _1073871, _1073873, _1073875] : [class_Rings_Olinordered__ring__strict(_1073869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073869), _1073871), c_Groups_Ozero__class_Ozero(_1073869))), 15836 ^ _781013 : [(15843 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073869), _1073875), _1073873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073869), _1073871), _1073873)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073869), _1073871), _1073875))))], (15837 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073869), _1073871), _1073873)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073869), _1073871), _1073875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073869), _1073875), _1073873)))]]], (38337 ^ _781013) ^ [_1517653, _1517655, _1517657, _1517659, _1517661] : [hAPP(hAPP(c_List_Omap(_1517653, _1517655), _1517657), _1517659) = hAPP(hAPP(c_List_Omap(_1517653, _1517655), _1517657), _1517661), c_Fun_Oinj__on(_1517653, _1517655, _1517657, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517653, tc_HOL_Obool)), hAPP(c_List_Oset(_1517653), _1517659)), hAPP(c_List_Oset(_1517653), _1517661))), -(_1517659 = _1517661)], (28090 ^ _781013) ^ [_1305449, _1305451] : [class_Rings_Olinordered__idom(_1305449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305449), c_Groups_Ozero__class_Ozero(_1305449)), _1305451)), -(c_Groups_Osgn__class_Osgn(_1305449, _1305451) = c_Groups_Oone__class_Oone(_1305449))], (42821 ^ _781013) ^ [_1629444, _1629446, _1629448, _1629450, _1629452, _1629454, _1629456, _1629458] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629444, tc_fun(_1629446, tc_fun(_1629448, tc_HOL_Obool))), _1629450), _1629452), _1629454), _1629456)), hBOOL(hAPP(hAPP(c_member(_1629444), _1629458), _1629450)), -(hBOOL(hAPP(hAPP(hAPP(_1629452, _1629458), _1629454), _1629456)))], (39810 ^ _781013) ^ [_1552998, _1553000, _1553002, _1553004] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1552998), tc_List_Olist(_1552998))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1552998), tc_List_Olist(_1552998)), _1553000), _1553002)), c_List_Olex(_1552998, _1553004))), 39813 ^ _781013 : [(39816 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552998)), _1553000) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552998)), _1553002))], (39814 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1552998), tc_List_Olist(_1552998))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1552998), tc_List_Olist(_1552998)), _1553000), _1553002)), c_List_Olexord(_1552998, _1553004))))]]], (51172 ^ _781013) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (46405 ^ _781013) ^ [_1710440, _1710442, _1710444] : [-(c_List_Omaps(_1710440, _1710442, _1710444, c_List_Olist_ONil(_1710440)) = c_List_Olist_ONil(_1710442))], (6288 ^ _781013) ^ [_883363, _883365] : [class_Finite__Set_Ofinite(_883363), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_883363), _883365)))], (50431 ^ _781013) ^ [_1806420, _1806422] : [class_Enum_Oenum(_1806420), 50434 ^ _781013 : [(50448 ^ _781013) ^ [] : [c_List_Olist__ex1(_1806420, _1806422, c_Enum_Oenum__class_Oenum(_1806420)), 50452 ^ _781013 : [(50455 ^ _781013) ^ [_1806819] : [hBOOL(hAPP(_1806422, _1806819)), -(_1806819 = 50451 ^ [_1806420, _1806422])], (50453 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1806422, 50451 ^ [_1806420, _1806422])))]]], (50435 ^ _781013) ^ [] : [-(c_List_Olist__ex1(_1806420, _1806422, c_Enum_Oenum__class_Oenum(_1806420))), 50436 ^ _781013 : [(50437 ^ _781013) ^ [_1806535] : [hBOOL(hAPP(_1806422, _1806535)), 50441 ^ _781013 : [(50444 ^ _781013) ^ [] : [50440 ^ [_1806420, _1806422, _1806535] = _1806535], (50442 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1806422, 50440 ^ [_1806420, _1806422, _1806535])))]]]]]]], (46283 ^ _781013) ^ [_1707739, _1707741, _1707743, _1707745, _1707747, _1707749, _1707751, _1707753] : [c_List_Olist__all2(_1707739, _1707741, _1707743, _1707745, _1707747), hBOOL(hAPP(hAPP(_1707743, _1707749), _1707751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707753), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707741)), _1707747))), -(c_List_Olist__all2(_1707739, _1707741, _1707743, hAPP(hAPP(c_List_Olist__update(_1707739, _1707745), _1707753), _1707749), hAPP(hAPP(c_List_Olist__update(_1707741, _1707747), _1707753), _1707751)))], (5639 ^ _781013) ^ [_869992, _869994, _869996, _869998, _870000] : [-(hAPP(hAPP(c_Set_Oinsert(_869992), _869994), hAPP(hAPP(c_Set_Oinsert(_869992), _869996), c_Orderings_Obot__class_Obot(tc_fun(_869992, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_869992), _869998), hAPP(hAPP(c_Set_Oinsert(_869992), _870000), c_Orderings_Obot__class_Obot(tc_fun(_869992, tc_HOL_Obool))))), 5640 ^ _781013 : [(5647 ^ _781013) ^ [] : [_869994 = _870000, _869996 = _869998], (5641 ^ _781013) ^ [] : [_869994 = _869998, _869996 = _870000]]], (5448 ^ _781013) ^ [_864066, _864068, _864070, _864072] : [-(c_COMBK(_864072, _864068) = c_COMBK(_864070, _864066)), _864072 = _864070, _864068 = _864066], (10913 ^ _781013) ^ [_974230, _974232, _974234] : [10914 ^ _781013 : [(10917 ^ _781013) ^ [] : [_974232 = _974234], (10915 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_974230, tc_HOL_Obool)), _974232), _974234))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974230, tc_HOL_Obool)), _974232), _974234)))], (22105 ^ _781013) ^ [_1195504, _1195506] : [class_Rings_Osemiring__1(_1195504), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1195504), _1195506) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1195504, hAPP(hAPP(c_COMBC(_1195504, _1195504, _1195504), c_Groups_Oplus__class_Oplus(_1195504)), c_Groups_Oone__class_Oone(_1195504)), _1195506, c_Groups_Ozero__class_Ozero(_1195504)))], (33298 ^ _781013) ^ [_1413094, _1413096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413094)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413096))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1413094), _1413096)))], (10097 ^ _781013) ^ [_959637, _959639, _959641, _959643] : [class_Lattices_Osemilattice__inf(_959637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959637), _959639), _959641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959637), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959637), _959639), _959643)), _959641)))], (50744 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (28978 ^ _781013) ^ [_1321687, _1321689, _1321691] : [class_Groups_Oordered__ab__group__add__abs(_1321687), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321687), hAPP(c_Groups_Oabs__class_Oabs(_1321687), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1321687), hAPP(c_Groups_Oabs__class_Oabs(_1321687), _1321689)), hAPP(c_Groups_Oabs__class_Oabs(_1321687), _1321691)))), hAPP(c_Groups_Oabs__class_Oabs(_1321687), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1321687), _1321689), _1321691)))))], (47966 ^ _781013) ^ [_1749963, _1749965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749963), _1749965)), -(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), _1749963), _1749965)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (45690 ^ _781013) ^ [_1694207, _1694209, _1694211] : [45692 ^ _781013 : [(45695 ^ _781013) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1694207, tc_HOL_Obool)), 45691 ^ [_1694207, _1694209, _1694211]), _1694211) = c_Orderings_Obot__class_Obot(tc_fun(_1694207, tc_HOL_Obool))], (45693 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1694207, tc_HOL_Obool)), 45691 ^ [_1694207, _1694209, _1694211]), _1694209)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1694207, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1694207, tc_HOL_Obool), _1694209)), _1694211) = c_Orderings_Obot__class_Obot(tc_fun(_1694207, tc_HOL_Obool)))], (6078 ^ _781013) ^ [_879278, _879280] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _879278) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _879280), -(hBOOL(hAPP(c_Com_OWT, _879280)))], (28622 ^ _781013) ^ [_1314928, _1314930, _1314932] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314928), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314930, _1314932)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314928), _1314930), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314928), _1314932)))], (18113 ^ _781013) ^ [_1118384, _1118386, _1118388, _1118390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118384), _1118386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1118388), _1118390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118384), _1118388)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118386), _1118390))))], (48463 ^ _781013) ^ [_1760951, _1760953] : [hAPP(c_Code__Numeral_Onat__of, _1760951) = hAPP(c_Code__Numeral_Onat__of, _1760953), -(_1760951 = _1760953)], (12180 ^ _781013) ^ [_1000840, _1000842, _1000844] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1000840), _1000842)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000840, tc_HOL_Obool)), _1000842), hAPP(c_Set_Oimage(_1000840, _1000840, _1000844), _1000842))), -(c_Fun_Oinj__on(_1000840, _1000840, _1000844, _1000842))], (32102 ^ _781013) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (41001 ^ _781013) ^ [_1588128, _1588130, _1588132, _1588134] : [-(c_Fun_Oinj__on(_1588128, tc_prod(_1588130, _1588128), 40999 ^ [_1588128, _1588130, _1588132, _1588134], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1588130, tc_fun(_1588128, tc_HOL_Obool)), _1588132), _1588134)))], (19630 ^ _781013) ^ [_1148356, _1148358, _1148360, _1148362] : [class_Rings_Olinordered__semidom(_1148356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1148358), _1148360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148356), c_Groups_Oone__class_Oone(_1148356)), _1148362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148356), hAPP(hAPP(c_Power_Opower__class_Opower(_1148356), _1148362), _1148358)), hAPP(hAPP(c_Power_Opower__class_Opower(_1148356), _1148362), _1148360))))], (44556 ^ _781013) ^ [_1670325, _1670327, _1670329] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1670325), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1670325))), _1670327))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670329), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1670325))), _1670327))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1670325))), hAPP(c_List_Ofilter(tc_List_Olist(_1670325), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1670325)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670329)), c_Nat_Osize__class_Osize(tc_List_Olist(_1670325)))), c_List_Otranspose(_1670325, _1670327))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670325)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1670325)), _1670327), _1670329)))], (25916 ^ _781013) ^ [_1262981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262981)), -(c_Nat__Transfer_Ois__nat(_1262981))], (25697 ^ _781013) ^ [_1259420, _1259422, _1259424, _1259426, _1259428] : [class_Groups_Oordered__ab__group__add(_1259420), hBOOL(hAPP(c_Finite__Set_Ofinite(_1259422), _1259424)), 25707 ^ _781013 : [(25710 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259420), c_Groups_Ozero__class_Ozero(_1259420)), hAPP(_1259426, 25706 ^ [_1259420, _1259422, _1259424, _1259426, _1259428])))], (25708 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1259422), 25706 ^ [_1259420, _1259422, _1259424, _1259426, _1259428]), _1259424)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1259422, _1259420), _1259426), _1259424) = c_Groups_Ozero__class_Ozero(_1259420), hBOOL(hAPP(hAPP(c_member(_1259422), _1259428), _1259424)), -(hAPP(_1259426, _1259428) = c_Groups_Ozero__class_Ozero(_1259420))], (49962 ^ _781013) ^ [_1796238, _1796240, _1796242, _1796244, _1796246] : [c_Finite__Set_Ofun__left__comm(_1796238, _1796240, _1796242), hBOOL(hAPP(c_Finite__Set_Ofinite(_1796238), _1796244)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1796238, _1796240, _1796242, _1796246, _1796244), hAPP(hAPP(c_Finite__Set_Ofold(_1796238, _1796240, _1796242), _1796246), _1796244))))], (51138 ^ _781013) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (36094 ^ _781013) ^ [_1468413] : [class_Rings_Osemiring__1(_1468413), -(hBOOL(hAPP(hAPP(c_member(_1468413), c_Groups_Ozero__class_Ozero(_1468413)), c_Nat_Osemiring__1__class_ONats(_1468413))))], (3728 ^ _781013) ^ [_837372, _837374] : [_837374 = _837372, -(c_List_Otake(_837374) = c_List_Otake(_837372))], (47767 ^ _781013) ^ [_1745791, _1745793, _1745795] : [class_Orderings_Olinorder(_1745791), 47773 ^ _781013 : [(47776 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1745791), _1745795), 47772 ^ [_1745791, _1745793, _1745795]))], (47774 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745791), 47772 ^ [_1745791, _1745793, _1745795]), hAPP(c_List_Oset(_1745791), _1745793))))]], c_List_Olinorder__class_Osorted(_1745791, _1745793), -(c_List_Olinorder__class_Osorted(_1745791, hAPP(hAPP(c_List_Olist_OCons(_1745791), _1745795), _1745793)))], (44042 ^ _781013) ^ [_1657925, _1657927] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1657925, _1657927) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1657925), hAPP(c_Nat_OSuc, _1657927))))], (46030 ^ _781013) ^ [_1702149, _1702151, _1702153, _1702155, _1702157] : [-(c_List_Olist__all2(_1702149, _1702151, _1702153, _1702155, _1702157)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702149)), _1702155) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702151)), _1702157), 46036 ^ _781013 : [(46039 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1702149, _1702151, tc_HOL_Obool), _1702153), 46035 ^ [_1702149, _1702151, _1702153, _1702155, _1702157]))], (46037 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1702149, _1702151)), 46035 ^ [_1702149, _1702151, _1702153, _1702155, _1702157]), hAPP(c_List_Oset(tc_prod(_1702149, _1702151)), hAPP(hAPP(c_List_Ozip(_1702149, _1702151), _1702155), _1702157)))))]]], (42697 ^ _781013) ^ [_1626988, _1626990, _1626992, _1626994] : [hAPP(hAPP(c_List_Oappend(_1626988), _1626990), hAPP(hAPP(c_List_Olist_OCons(_1626988), _1626992), c_List_Olist_ONil(_1626988))) = _1626994, 42700 ^ _781013 : [(42705 ^ _781013) ^ [] : [-(c_List_Olast(_1626988, _1626994) = _1626992)], (42703 ^ _781013) ^ [] : [-(c_List_Obutlast(_1626988, _1626994) = _1626990)], (42701 ^ _781013) ^ [] : [_1626994 = c_List_Olist_ONil(_1626988)]]], (34383 ^ _781013) ^ [_1432853, _1432855] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1432853), _1432855), hAPP(c_Int_Onumber__class_Onumber__of(_1432853), c_Int_OBit1(c_Int_OPls))) = _1432855), class_Fields_Ofield(_1432853), class_Int_Onumber__ring(_1432853)], (22130 ^ _781013) ^ [_1196078, _1196080, _1196082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1196078), _1196080)), -(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)), _1196078)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1196082), _1196080)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1196082), _1196078)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1196080), _1196078)))], (33574 ^ _781013) ^ [_1417924] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1417924) = _1417924)], (4726 ^ _781013) ^ [_852495, _852497] : [_852497 = _852495, -(c_Int_OBit1(_852497) = c_Int_OBit1(_852495))], (19963 ^ _781013) ^ [_1154904, _1154906] : [hAPP(c_Nat_OSuc, _1154904) = hAPP(c_Nat_OSuc, _1154906), -(_1154904 = _1154906)], (21901 ^ _781013) ^ [_1192024, _1192026] : [class_Rings_Osemiring__1(_1192024), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1192024), hAPP(c_Nat_OSuc, _1192026)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192024), c_Groups_Oone__class_Oone(_1192024)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1192024), _1192026)))], (35571 ^ _781013) ^ [_1454318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1454318)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1454318), c_Int_OMin)))], (49780 ^ _781013) ^ [_1792917, _1792919, _1792921, _1792923] : [class_Complete__Lattice_Ocomplete__lattice(_1792917), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792919), _1792921)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1792919, _1792917), _1792921), _1792923) = hAPP(hAPP(c_Finite__Set_Ofold(_1792919, _1792917, hAPP(hAPP(c_COMBB(_1792917, tc_fun(_1792917, _1792917), _1792919), c_Lattices_Osemilattice__inf__class_Oinf(_1792917)), _1792923)), c_Orderings_Otop__class_Otop(_1792917)), _1792921))], (14045 ^ _781013) ^ [_1039304, _1039306, _1039308, _1039310] : [class_Rings_Ocomm__semiring(_1039304), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039304), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039304), _1039306), _1039308)), _1039310) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039304), _1039306), _1039310)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039304), _1039308), _1039310)))], (23895 ^ _781013) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33992 ^ _781013) ^ [_1425195] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425195)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425195)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1425195)))], (2786 ^ _781013) ^ [_822565, _822567, _822569, _822571] : [-(c_Nitpick_Ocard_H(_822571, _822567) = c_Nitpick_Ocard_H(_822569, _822565)), _822571 = _822569, _822567 = _822565], (20135 ^ _781013) ^ [_1157587, _1157589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157587), _1157589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157587), hAPP(c_Nat_OSuc, _1157589))))], (27773 ^ _781013) ^ [_1299688, _1299690, _1299692, _1299694] : [class_Divides_Oring__div(_1299688), -(c_Divides_Odiv__class_Omod(_1299688, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1299688), _1299690), _1299692), _1299694) = c_Divides_Odiv__class_Omod(_1299688, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1299688), c_Divides_Odiv__class_Omod(_1299688, _1299690, _1299694)), c_Divides_Odiv__class_Omod(_1299688, _1299692, _1299694)), _1299694))], (37052 ^ _781013) ^ [_1488158, _1488160, _1488162, _1488164] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1488158, _1488160), _1488162)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1488158, _1488160), _1488164)), -(_1488162 = _1488164)], (36770 ^ _781013) ^ [_1482938, _1482940] : [36771 ^ _781013 : [(36774 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1482940), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36772 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1482938), _1482940))]], -(c_Divides_OposDivAlg(_1482938, _1482940) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482938))], (4212 ^ _781013) ^ [_844724, _844726, _844728, _844730] : [-(c_HOL_OThe(_844730, _844726) = c_HOL_OThe(_844728, _844724)), _844730 = _844728, _844726 = _844724], (28966 ^ _781013) ^ [_1321381, _1321383, _1321385] : [class_Groups_Oordered__ab__group__add__abs(_1321381), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1321381), hAPP(c_Groups_Oabs__class_Oabs(_1321381), _1321383)), hAPP(c_Groups_Oabs__class_Oabs(_1321381), _1321385))), hAPP(c_Groups_Oabs__class_Oabs(_1321381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1321381), _1321385), _1321383)))))], (44274 ^ _781013) ^ [_1663173, _1663175, _1663177] : [hAPP(hAPP(c_List_Olist_OCons(_1663173), _1663175), c_List_Olist_ONil(_1663173)) = hAPP(c_List_Orev(_1663173), _1663177), -(_1663177 = hAPP(hAPP(c_List_Olist_OCons(_1663173), _1663175), c_List_Olist_ONil(_1663173)))], (48481 ^ _781013) ^ [_1761227, _1761229] : [_1761227 = _1761229, -(hAPP(c_Code__Numeral_Onat__of, _1761227) = hAPP(c_Code__Numeral_Onat__of, _1761229))], (50202 ^ _781013) ^ [_1801680, _1801682, _1801684, _1801686] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1801680, _1801682)), _1801684), hAPP(c_Relation_Oconverse(_1801682, _1801680), _1801686))), 50207 ^ _781013 : [(50210 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801682, _1801680)), hAPP(hAPP(c_Product__Type_OPair(_1801682, _1801680), 50205 ^ [_1801680, _1801682, _1801684, _1801686]), 50206 ^ [_1801680, _1801682, _1801684, _1801686])), _1801686)))], (50208 ^ _781013) ^ [] : [-(_1801684 = hAPP(hAPP(c_Product__Type_OPair(_1801680, _1801682), 50206 ^ [_1801680, _1801682, _1801684, _1801686]), 50205 ^ [_1801680, _1801682, _1801684, _1801686]))]]], (42364 ^ _781013) ^ [_1620078, _1620080, _1620082] : [-(hAPP(c_List_Otl(_1620078), hAPP(hAPP(c_List_Odrop(_1620078), _1620080), _1620082)) = hAPP(hAPP(c_List_Odrop(_1620078), _1620080), hAPP(c_List_Otl(_1620078), _1620082)))], (51562 ^ _781013) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (5839 ^ _781013) ^ [_874898, _874900, _874902, _874904] : [c_Com_Ocom_OWhile(_874898, _874900) = c_Com_Ocom_OSemi(_874902, _874904)], (21883 ^ _781013) ^ [_1191658] : [-(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), _1191658))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10447 ^ _781013) ^ [_966388, _966390, _966392, _966394] : [class_Orderings_Opreorder(_966388), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966388), _966390), _966392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966388), _966392), _966394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966388), _966390), _966394)))], (23045 ^ _781013) ^ [_1212231, _1212233] : [23047 ^ _781013 : [(23050 ^ _781013) ^ [] : [hBOOL(hAPP(_1212233, 23046 ^ [_1212231, _1212233]))], (23048 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 23046 ^ [_1212231, _1212233]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212231))))]], 23051 ^ _781013 : [(23052 ^ _781013) ^ [_1212384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1212384), _1212231)), -(hBOOL(hAPP(_1212233, _1212384)))]]], (2826 ^ _781013) ^ [_823169, _823171, _823173, _823175, _823177, _823179, _823181, _823183] : [-(c_Hilbert__Choice_OLeastM(_823183, _823179, _823175, _823171) = c_Hilbert__Choice_OLeastM(_823181, _823177, _823173, _823169)), _823183 = _823181, _823179 = _823177, _823175 = _823173, _823171 = _823169], (40557 ^ _781013) ^ [_1574782, _1574784, _1574786, _1574788, _1574790, _1574792] : [hBOOL(hAPP(hAPP(c_member(_1574782), _1574784), _1574786)), 40560 ^ _781013 : [(40567 ^ _781013) ^ [] : [_1574790 = _1574792, -(hAPP(hAPP(c_Product__Type_OSigma(_1574788, _1574782), _1574790), hAPP(c_COMBK(tc_fun(_1574782, tc_HOL_Obool), _1574788), _1574786)) = hAPP(hAPP(c_Product__Type_OSigma(_1574788, _1574782), _1574792), hAPP(c_COMBK(tc_fun(_1574782, tc_HOL_Obool), _1574788), _1574786)))], (40561 ^ _781013) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1574788, _1574782), _1574790), hAPP(c_COMBK(tc_fun(_1574782, tc_HOL_Obool), _1574788), _1574786)) = hAPP(hAPP(c_Product__Type_OSigma(_1574788, _1574782), _1574792), hAPP(c_COMBK(tc_fun(_1574782, tc_HOL_Obool), _1574788), _1574786)), -(_1574790 = _1574792)]]], (41262 ^ _781013) ^ [_1594331, _1594333, _1594335, _1594337] : [_1594337 = c_List_Olist_ONil(_1594331), -(hAPP(hAPP(c_List_Omap(_1594331, _1594333), _1594335), _1594337) = c_List_Olist_ONil(_1594333))], (8749 ^ _781013) ^ [_933635, _933637, _933639, _933641, _933643, _933645] : [c_Finite__Set_Ofolding(_933635, _933637, _933639, _933641), hBOOL(hAPP(c_Finite__Set_Ofinite(_933635), _933643)), -(hBOOL(hAPP(hAPP(c_member(_933635), _933645), _933643))), -(hAPP(_933641, hAPP(hAPP(c_Set_Oinsert(_933635), _933645), _933643)) = hAPP(c_Fun_Ocomp(_933637, _933637, _933637, hAPP(_933641, _933643)), hAPP(_933639, _933645)))], (45181 ^ _781013) ^ [_1683717, _1683719] : [class_Orderings_Olinorder(_1683717), -(c_List_Olinorder__class_Osorted__list__of__set(_1683717, hAPP(c_List_Oset(_1683717), _1683719)) = c_List_Olinorder__class_Osort__key(_1683717, _1683717, c_COMBI(_1683717), c_List_Oremdups(_1683717, _1683719)))], (40469 ^ _781013) ^ [_1572225, _1572227, _1572229, _1572231, _1572233, _1572235] : [-(c_Product__Type_Omap__pair(_1572225, _1572227, _1572229, _1572231, _1572233, _1572235) = hAPP(c_Product__Type_Oprod_Oprod__case(_1572225, _1572229, tc_prod(_1572227, _1572231)), hAPP(hAPP(c_COMBC(_1572225, tc_fun(_1572229, _1572231), tc_fun(_1572229, tc_prod(_1572227, _1572231))), hAPP(hAPP(c_COMBB(tc_fun(_1572231, tc_prod(_1572227, _1572231)), tc_fun(tc_fun(_1572229, _1572231), tc_fun(_1572229, tc_prod(_1572227, _1572231))), _1572225), c_COMBB(_1572231, tc_prod(_1572227, _1572231), _1572229)), hAPP(hAPP(c_COMBB(_1572227, tc_fun(_1572231, tc_prod(_1572227, _1572231)), _1572225), c_Product__Type_OPair(_1572227, _1572231)), _1572233))), _1572235)))], (9381 ^ _781013) ^ [_947436, _947438, _947440] : [-(hBOOL(hAPP(hAPP(c_member(_947436), _947438), _947440))), -(hBOOL(hAPP(hAPP(c_member(_947436), _947438), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_947436, tc_HOL_Obool)), _947440))))], (9759 ^ _781013) ^ [_953434, _953436, _953438] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953434, tc_HOL_Obool)), _953436), _953438) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953434, tc_HOL_Obool)), _953438), _953436))], (25531 ^ _781013) ^ [_1256564] : [-(c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), _1256564))))], (44819 ^ _781013) ^ [_1675783, _1675785, _1675787] : [hBOOL(hAPP(c_List_Odistinct(_1675783), _1675785)), hBOOL(hAPP(hAPP(c_member(_1675783), _1675787), hAPP(c_List_Oset(_1675783), _1675785))), -(c_List_OtakeWhile(_1675783, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1675783), c_fNot), hAPP(hAPP(c_COMBC(_1675783, _1675783, tc_HOL_Obool), c_fequal), _1675787)), hAPP(c_List_Orev(_1675783), _1675785)) = hAPP(c_List_Orev(_1675783), hAPP(c_List_Otl(_1675783), c_List_OdropWhile(_1675783, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1675783), c_fNot), hAPP(hAPP(c_COMBC(_1675783, _1675783, tc_HOL_Obool), c_fequal), _1675787)), _1675785))))], (26159 ^ _781013) ^ [_1267549, _1267551, _1267553] : [class_Orderings_Oorder(_1267549), 26162 ^ _781013 : [(26169 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267549), _1267551), _1267553))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1267549, _1267551, _1267553) = c_Orderings_Obot__class_Obot(tc_fun(_1267549, tc_HOL_Obool)))], (26163 ^ _781013) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1267549, _1267551, _1267553) = c_Orderings_Obot__class_Obot(tc_fun(_1267549, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267549), _1267551), _1267553))]]], (38047 ^ _781013) ^ [] : [-(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)))))], (29971 ^ _781013) ^ [_1340025, _1340027, _1340029] : [class_Orderings_Olinorder(_1340025), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340025), _1340027)), -(_1340027 = c_Orderings_Obot__class_Obot(tc_fun(_1340025, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340025), _1340029)), -(_1340029 = c_Orderings_Obot__class_Obot(tc_fun(_1340025, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340025), c_Big__Operators_Olattice_OInf__fin(_1340025, c_Orderings_Oord__class_Omin(_1340025), _1340027)), c_Big__Operators_Olattice_OInf__fin(_1340025, c_Orderings_Oord__class_Omin(_1340025), _1340029)) = c_Big__Operators_Olattice_OInf__fin(_1340025, c_Orderings_Oord__class_Omin(_1340025), hAPP(c_Set_OCollect(_1340025), hAPP(hAPP(c_COMBB(tc_fun(_1340025, tc_HOL_Obool), tc_HOL_Obool, _1340025), c_HOL_OEx(_1340025)), hAPP(hAPP(c_COMBB(tc_fun(_1340025, tc_fun(_1340025, tc_HOL_Obool)), tc_fun(_1340025, tc_HOL_Obool), _1340025), hAPP(c_COMBB(tc_fun(_1340025, tc_HOL_Obool), tc_HOL_Obool, _1340025), c_HOL_OEx(_1340025))), hAPP(hAPP(c_COMBC(_1340025, tc_fun(_1340025, tc_fun(_1340025, tc_HOL_Obool)), tc_fun(_1340025, tc_fun(_1340025, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1340025, tc_fun(tc_fun(_1340025, tc_HOL_Obool), tc_fun(_1340025, tc_HOL_Obool))), tc_fun(tc_fun(_1340025, tc_fun(_1340025, tc_HOL_Obool)), tc_fun(_1340025, tc_fun(_1340025, tc_HOL_Obool))), _1340025), c_COMBS(_1340025, tc_fun(_1340025, tc_HOL_Obool), tc_fun(_1340025, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1340025, tc_fun(_1340025, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1340025, tc_fun(tc_fun(_1340025, tc_HOL_Obool), tc_fun(_1340025, tc_HOL_Obool))), _1340025), hAPP(c_COMBB(tc_fun(_1340025, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1340025, tc_HOL_Obool), tc_fun(_1340025, tc_HOL_Obool)), _1340025), c_COMBS(_1340025, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1340025, tc_fun(_1340025, tc_HOL_Obool)), tc_fun(_1340025, tc_fun(_1340025, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1340025), hAPP(c_COMBB(tc_fun(_1340025, tc_HOL_Obool), tc_fun(_1340025, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1340025), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1340025), c_fconj))), hAPP(hAPP(c_COMBC(_1340025, tc_fun(_1340025, tc_fun(_1340025, _1340025)), tc_fun(_1340025, tc_fun(_1340025, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1340025, _1340025), tc_fun(_1340025, tc_HOL_Obool)), tc_fun(tc_fun(_1340025, tc_fun(_1340025, _1340025)), tc_fun(_1340025, tc_fun(_1340025, tc_HOL_Obool))), _1340025), c_COMBB(tc_fun(_1340025, _1340025), tc_fun(_1340025, tc_HOL_Obool), _1340025)), hAPP(hAPP(c_COMBB(tc_fun(_1340025, tc_HOL_Obool), tc_fun(tc_fun(_1340025, _1340025), tc_fun(_1340025, tc_HOL_Obool)), _1340025), c_COMBB(_1340025, tc_HOL_Obool, _1340025)), c_fequal))), c_Orderings_Oord__class_Omax(_1340025)))))), hAPP(hAPP(c_COMBC(_1340025, tc_fun(_1340025, tc_HOL_Obool), tc_fun(_1340025, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1340025, tc_HOL_Obool), tc_fun(_1340025, tc_HOL_Obool)), _1340025), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1340025)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1340025), c_fconj), hAPP(hAPP(c_COMBC(_1340025, tc_fun(_1340025, tc_HOL_Obool), tc_HOL_Obool), c_member(_1340025)), _1340027)))), hAPP(hAPP(c_COMBC(_1340025, tc_fun(_1340025, tc_HOL_Obool), tc_HOL_Obool), c_member(_1340025)), _1340029))))))))], (45932 ^ _781013) ^ [_1699956] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1699956, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1699956, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1699956, tc_HOL_Obool)))], (39854 ^ _781013) ^ [_1554708, _1554710] : [-(c_List_Olenlex(_1554708, _1554710) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1554708)), tc_List_Olist(_1554708)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1554708), c_Wellfounded_Oless__than, c_List_Olex(_1554708, _1554710))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1554708), tc_List_Olist(_1554708), tc_prod(tc_Nat_Onat, tc_List_Olist(_1554708))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1554708), tc_prod(tc_Nat_Onat, tc_List_Olist(_1554708))), tc_List_Olist(_1554708)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1554708))), c_Nat_Osize__class_Osize(tc_List_Olist(_1554708)))), c_COMBI(tc_List_Olist(_1554708)))))], (31840 ^ _781013) ^ [_1383387, _1383389, _1383391, _1383393, _1383395, _1383397] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383387, tc_fun(_1383389, tc_HOL_Obool)), _1383391), hAPP(hAPP(c_COMBB(_1383393, tc_fun(_1383389, tc_HOL_Obool), _1383387), _1383395), _1383397)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383393, tc_fun(_1383389, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1383387, _1383393, _1383397), _1383391)), _1383395))], (49710 ^ _781013) ^ [_1791461, _1791463, _1791465] : [class_Orderings_Olinorder(_1791461), hBOOL(hAPP(c_Finite__Set_Ofinite(_1791461), _1791463)), -(c_Big__Operators_Olinorder__class_OMin(_1791461, hAPP(hAPP(c_Set_Oinsert(_1791461), _1791465), _1791463)) = hAPP(hAPP(c_Finite__Set_Ofold(_1791461, _1791461, c_Orderings_Oord__class_Omin(_1791461)), _1791465), _1791463))], (18658 ^ _781013) ^ [_1128689, _1128691, _1128693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128689), _1128691)), _1128693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128689), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128693), _1128691))))], (23104 ^ _781013) ^ [_1213255, _1213257] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213255), _1213257)), _1213255)))], (35009 ^ _781013) ^ [_1443827, _1443829] : [class_Rings_Ocomm__semiring__1(_1443827), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1443827), _1443829), _1443829) = hAPP(hAPP(c_Power_Opower__class_Opower(_1443827), _1443829), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (37782 ^ _781013) ^ [_1504156, _1504158] : [c_Equiv__Relations_Oequivp(_1504156, hAPP(hAPP(c_COMBC(_1504156, tc_fun(tc_prod(_1504156, _1504156), tc_HOL_Obool), tc_fun(_1504156, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504156, tc_fun(tc_fun(tc_prod(_1504156, _1504156), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1504156, _1504156), tc_HOL_Obool), tc_fun(_1504156, tc_HOL_Obool)), _1504156), c_COMBC(_1504156, tc_fun(tc_prod(_1504156, _1504156), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504156, tc_prod(_1504156, _1504156)), tc_fun(_1504156, tc_fun(tc_fun(tc_prod(_1504156, _1504156), tc_HOL_Obool), tc_HOL_Obool)), _1504156), hAPP(c_COMBB(tc_prod(_1504156, _1504156), tc_fun(tc_fun(tc_prod(_1504156, _1504156), tc_HOL_Obool), tc_HOL_Obool), _1504156), c_member(tc_prod(_1504156, _1504156)))), c_Product__Type_OPair(_1504156, _1504156)))), _1504158)), -(c_Equiv__Relations_Oequiv(_1504156, c_Orderings_Otop__class_Otop(tc_fun(_1504156, tc_HOL_Obool)), _1504158))], (43717 ^ _781013) ^ [_1652078, _1652080, _1652082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1652078), _1652080)), _1652082)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1652080), c_List_Oupt(_1652078, _1652082)) = c_List_Oupt(_1652078, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1652078), _1652080)))], (11067 ^ _781013) ^ [_977750, _977752, _977754, _977756] : [-(hBOOL(hAPP(hAPP(c_member(_977750), _977752), _977754))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977750, tc_HOL_Obool)), _977754), hAPP(hAPP(c_Set_Oinsert(_977750), _977752), _977756)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977750, tc_HOL_Obool)), _977754), _977756))], (6938 ^ _781013) ^ [_895619, _895621, _895623, _895625, _895627] : [hAPP(_895619, _895621) = _895623, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895625, _895627), _895619), _895621), _895623) = _895619)], (14025 ^ _781013) ^ [_1038914, _1038916, _1038918, _1038920] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1038914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038914), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038914), _1038916), _1038918)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038914), _1038920), _1038918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038914), _1038916), _1038920)))], (17889 ^ _781013) ^ [_1114798, _1114800] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1114798), _1114800)), _1114798 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1114800 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (44308 ^ _781013) ^ [_1663911, _1663913] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663911)), hAPP(c_List_Orev(_1663911), _1663913)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663911)), _1663913))], (17092 ^ _781013) ^ [_1098850, _1098852, _1098854, _1098856, _1098858] : [c_Fun_Oinj__on(_1098850, _1098852, _1098854, _1098856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1098852, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1098850, _1098852, _1098854), _1098856)), _1098858)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098852), _1098858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1098850), _1098856)), hAPP(c_Finite__Set_Ocard(_1098852), _1098858))))], (3654 ^ _781013) ^ [_836233, _836235, _836237, _836239, _836241, _836243, _836245, _836247] : [-(c_Recdef_Osame__fst(_836247, _836243, _836239, _836235) = c_Recdef_Osame__fst(_836245, _836241, _836237, _836233)), _836247 = _836245, _836243 = _836241, _836239 = _836237, _836235 = _836233], (46460 ^ _781013) ^ [_1712303, _1712305, _1712307, _1712309] : [hBOOL(hAPP(hAPP(c_member(_1712303), _1712305), c_Wellfounded_Oacc(_1712303, _1712307))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712303)), _1712309), c_Wellfounded_Oacc(tc_List_Olist(_1712303), c_List_Olistrel1(_1712303, _1712307)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712303)), hAPP(hAPP(c_List_Olist_OCons(_1712303), _1712305), _1712309)), c_Wellfounded_Oacc(tc_List_Olist(_1712303), c_List_Olistrel1(_1712303, _1712307)))))], (13261 ^ _781013) ^ [_1022774, _1022776, _1022778] : [class_Groups_Oab__semigroup__mult(_1022774), -(_1022776 = c_Orderings_Obot__class_Obot(tc_fun(_1022774, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022774), _1022776)), -(hBOOL(hAPP(hAPP(c_member(_1022774), _1022778), _1022776))), -(hAPP(c_Finite__Set_Ofold1(_1022774, c_Groups_Otimes__class_Otimes(_1022774)), hAPP(hAPP(c_Set_Oinsert(_1022774), _1022778), _1022776)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022774), _1022778), hAPP(c_Finite__Set_Ofold1(_1022774, c_Groups_Otimes__class_Otimes(_1022774)), _1022776)))], (12230 ^ _781013) ^ [_1001899] : [class_Lattices_Oboolean__algebra(_1001899), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1001899), c_Orderings_Obot__class_Obot(_1001899)) = c_Orderings_Otop__class_Otop(_1001899))], (16602 ^ _781013) ^ [_1088794, _1088796, _1088798] : [class_Groups_Oordered__comm__monoid__add(_1088794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088794), _1088796), c_Groups_Ozero__class_Ozero(_1088794))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088794), _1088798), c_Groups_Ozero__class_Ozero(_1088794))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088794), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088794), _1088796), _1088798)), c_Groups_Ozero__class_Ozero(_1088794))))], (41392 ^ _781013) ^ [_1596584, _1596586] : [-(_1596586 = c_List_Olist_ONil(_1596584)), -(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(_1596584)), _1596586))))], (12166 ^ _781013) ^ [_1000593, _1000595, _1000597] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1000593), _1000595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000593, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1000593, _1000593, _1000597), _1000595)), _1000595)), c_Fun_Oinj__on(_1000593, _1000593, _1000597, _1000595), -(hAPP(c_Set_Oimage(_1000593, _1000593, _1000597), _1000595) = _1000595)], (9745 ^ _781013) ^ [_953303, _953305, _953307] : [class_Orderings_Olinorder(_953303), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953303), _953305), _953307))), -(_953305 = _953307), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953303), _953307), _953305)))], (38840 ^ _781013) ^ [_1529371, _1529373, _1529375, _1529377] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1529371)), _1529373) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1529375)), _1529377), -(hAPP(hAPP(c_List_Omap(tc_prod(_1529371, _1529375), _1529371), c_Product__Type_Ofst(_1529371, _1529375)), hAPP(hAPP(c_List_Ozip(_1529371, _1529375), _1529373), _1529377)) = _1529373)], (3678 ^ _781013) ^ [_836619, _836621] : [_836621 = _836619, -(c_Nitpick_Oone__frac(_836621) = c_Nitpick_Oone__frac(_836619))], (51244 ^ _781013) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (51242 ^ _781013) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (13873 ^ _781013) ^ [_1035974, _1035976, _1035978, _1035980] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1035974), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035974), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035974), _1035976), _1035978)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035974), _1035976), _1035980))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035974), _1035978), _1035980)))], (25078 ^ _781013) ^ [_1248365, _1248367, _1248369, _1248371] : [class_Fields_Olinordered__field(_1248365), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248365), c_Groups_Ozero__class_Ozero(_1248365)), _1248367)), 25085 ^ _781013 : [(25092 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248365), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248365), _1248369), _1248367)), _1248371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248365), _1248369), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248365), _1248371), _1248367))))], (25086 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248365), _1248369), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248365), _1248371), _1248367))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248365), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248365), _1248369), _1248367)), _1248371)))]]], (25499 ^ _781013) ^ [_1256125] : [-(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)), _1256125)))], (32594 ^ _781013) ^ [_1399669, _1399671, _1399673, _1399675] : [class_Fields_Ofield__inverse__zero(_1399669), class_Int_Onumber(_1399669), 32601 ^ _781013 : [(32602 ^ _781013) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1399669), _1399671), hAPP(c_Int_Onumber__class_Onumber__of(_1399669), _1399673)) = _1399675, 32605 ^ _781013 : [(32612 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1399669), _1399673) = c_Groups_Ozero__class_Ozero(_1399669), -(_1399675 = c_Groups_Ozero__class_Ozero(_1399669))], (32606 ^ _781013) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1399669), _1399673) = c_Groups_Ozero__class_Ozero(_1399669)), -(_1399671 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399669), _1399675), hAPP(c_Int_Onumber__class_Onumber__of(_1399669), _1399673)))]]], (32618 ^ _781013) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1399669), _1399671), hAPP(c_Int_Onumber__class_Onumber__of(_1399669), _1399673)) = _1399675), 32621 ^ _781013 : [(32624 ^ _781013) ^ [] : [_1399671 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399669), _1399675), hAPP(c_Int_Onumber__class_Onumber__of(_1399669), _1399673))], (32622 ^ _781013) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1399669), _1399673) = c_Groups_Ozero__class_Ozero(_1399669)]], 32625 ^ _781013 : [(32628 ^ _781013) ^ [] : [_1399675 = c_Groups_Ozero__class_Ozero(_1399669)], (32626 ^ _781013) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1399669), _1399673) = c_Groups_Ozero__class_Ozero(_1399669))]]]]], (20101 ^ _781013) ^ [_1157080, _1157082] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157080), _1157082))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157082), hAPP(c_Nat_OSuc, _1157080))))], (50686 ^ _781013) ^ [_1811103, _1811105] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1811103)), c_Int_OBit1(_1811105)))], (21463 ^ _781013) ^ [_1184299, _1184301] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184299), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184301)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1184299), _1184301)))], (51582 ^ _781013) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (6656 ^ _781013) ^ [_890406, _890408, _890410, _890412, _890414, _890416] : [c_Map_Omap__comp(_890406, _890408, _890410, _890412, _890414, _890416) = c_Option_Ooption_ONone(_890408), -(hAPP(_890414, _890416) = c_Option_Ooption_ONone(_890406)), 6664 ^ _781013 : [(6667 ^ _781013) ^ [] : [-(hAPP(_890412, 6663 ^ [_890406, _890408, _890410, _890412, _890414, _890416]) = c_Option_Ooption_ONone(_890408))], (6665 ^ _781013) ^ [] : [-(hAPP(_890414, _890416) = hAPP(c_Option_Ooption_OSome(_890406), 6663 ^ [_890406, _890408, _890410, _890412, _890414, _890416]))]]], (46018 ^ _781013) ^ [_1701824, _1701826, _1701828, _1701830, _1701832] : [c_List_Olist__all2(_1701824, _1701826, _1701828, _1701830, _1701832), 46021 ^ _781013 : [(46024 ^ _781013) ^ [_1701990] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1701824, _1701826)), _1701990), hAPP(c_List_Oset(tc_prod(_1701824, _1701826)), hAPP(hAPP(c_List_Ozip(_1701824, _1701826), _1701830), _1701832)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1701824, _1701826, tc_HOL_Obool), _1701828), _1701990)))], (46022 ^ _781013) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701824)), _1701830) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701826)), _1701832))]]], (1464 ^ _781013) ^ [_802055, _802057] : [-(class_Groups_Olinordered__ab__semigroup__add(_802055)), _802057 = _802055, class_Groups_Olinordered__ab__semigroup__add(_802057)], (37198 ^ _781013) ^ [_1490846, _1490848, _1490850, _1490852] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1490846, _1490848), _1490850)), hBOOL(hAPP(hAPP(_1490848, _1490852), _1490850)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1490846, _1490848), _1490852)))], (42500 ^ _781013) ^ [_1623068, _1623070, _1623072] : [class_Groups_Oab__semigroup__add(_1623068), -(c_List_Ofoldr(_1623068, _1623068, c_Groups_Oplus__class_Oplus(_1623068), _1623070, _1623072) = hAPP(c_List_Ofoldl(_1623068, _1623068, c_Groups_Oplus__class_Oplus(_1623068), _1623072), _1623070))], (8503 ^ _781013) ^ [_928136, _928138, _928140, _928142, _928144] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928136, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928136, tc_HOL_Obool)), hAPP(c_Set_Oimage(_928138, _928136, _928140), _928142)), hAPP(c_Set_Oimage(_928138, _928136, _928140), _928144))), hAPP(c_Set_Oimage(_928138, _928136, _928140), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928138, tc_HOL_Obool)), _928142), _928144)))))], (6042 ^ _781013) ^ [_878699, _878701] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _878699), _878701)), -(_878701 = _878699)], (38087 ^ _781013) ^ [_1510772, _1510774, _1510776, _1510778, _1510780, _1510782] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1510772, tc_HOL_Obool), tc_fun(_1510772, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1510772, tc_HOL_Obool), tc_fun(_1510772, tc_HOL_Obool)), _1510774), _1510776)), c_Wellfounded_Omax__ext(_1510772, _1510778))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1510772, tc_HOL_Obool), tc_fun(_1510772, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1510772, tc_HOL_Obool), tc_fun(_1510772, tc_HOL_Obool)), _1510780), _1510782)), c_Wellfounded_Omax__ext(_1510772, _1510778))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1510772, tc_HOL_Obool), tc_fun(_1510772, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1510772, tc_HOL_Obool), tc_fun(_1510772, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1510772, tc_HOL_Obool)), _1510774), _1510780)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1510772, tc_HOL_Obool)), _1510776), _1510782))), c_Wellfounded_Omax__ext(_1510772, _1510778))))], (9909 ^ _781013) ^ [_955974, _955976, _955978, _955980] : [class_Lattices_Osemilattice__inf(_955974), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955974), _955976), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955974), _955978), _955980)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955974), _955978), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955974), _955976), _955980)))], (48141 ^ _781013) ^ [_1753513, _1753515, _1753517] : [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, _1753513), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1753513)), _1753515)))), -(hBOOL(hAPP(hAPP(c_member(_1753513), hAPP(c_Product__Type_Ofst(_1753513, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1753513, _1753515), _1753517))), hAPP(c_List_Oset(_1753513), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1753513), _1753513), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1753513)), _1753515)))))], (22872 ^ _781013) ^ [_1208868, _1208870, _1208872] : [class_Groups_Ocomm__monoid__add(_1208868), hAPP(_1208870, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1208868), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1208868), _1208870), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1208872)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1208868), _1208870), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1208872)))], (8505 ^ _781013) ^ [_928220, _928222, _928224, _928226, _928228, _928230] : [c_Finite__Set_Ofolding__image__simple(_928220, _928222, _928224, _928226, _928228, _928230), -(hAPP(_928230, c_Orderings_Obot__class_Obot(tc_fun(_928222, tc_HOL_Obool))) = _928226)], (38162 ^ _781013) ^ [] : [-(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))))))], (49680 ^ _781013) ^ [_1790896, _1790898, _1790900] : [class_Lattices_Oab__semigroup__idem__mult(_1790896), hBOOL(hAPP(c_Finite__Set_Ofinite(_1790896), _1790898)), -(hAPP(c_Finite__Set_Ofold1(_1790896, c_Groups_Otimes__class_Otimes(_1790896)), hAPP(hAPP(c_Set_Oinsert(_1790896), _1790900), _1790898)) = hAPP(hAPP(c_Finite__Set_Ofold(_1790896, _1790896, c_Groups_Otimes__class_Otimes(_1790896)), _1790900), _1790898))], (11283 ^ _781013) ^ [_982507, _982509, _982511, _982513, _982515, _982517, _982519] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_982507, _982509, _982511, _982513, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982507, tc_HOL_Obool)), _982515), hAPP(hAPP(c_Set_Oinsert(_982507), _982517), c_Orderings_Obot__class_Obot(tc_fun(_982507, tc_HOL_Obool))))), _982519)), hBOOL(hAPP(hAPP(c_member(_982507), _982517), _982515)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_982507, _982509, _982511, _982513, _982515), hAPP(hAPP(_982511, _982517), _982519))))], (5420 ^ _781013) ^ [_863662, _863664] : [_863664 = _863662, -(tc_Option_Ooption(_863664) = tc_Option_Ooption(_863662))], (39138 ^ _781013) ^ [_1536664, _1536666, _1536668, _1536670] : [-(hBOOL(hAPP(hAPP(c_member(_1536664), _1536666), hAPP(c_List_Oset(_1536664), _1536668)))), hBOOL(hAPP(hAPP(c_member(_1536664), _1536666), hAPP(c_List_Oset(_1536664), c_List_Osublist(_1536664, _1536668, _1536670))))], (28946 ^ _781013) ^ [_1320917, _1320919, _1320921] : [class_Groups_Oordered__ab__group__add__abs(_1320917), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320917), hAPP(c_Groups_Oabs__class_Oabs(_1320917), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320917), _1320919), _1320921))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320917), hAPP(c_Groups_Oabs__class_Oabs(_1320917), _1320919)), hAPP(c_Groups_Oabs__class_Oabs(_1320917), _1320921)))))], (18089 ^ _781013) ^ [_1117980] : [_1117980 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117980), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (33540 ^ _781013) ^ [_1417403, _1417405] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417403)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417403)), _1417405)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1417403))), _1417405))], (27128 ^ _781013) ^ [_1286120] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1286120)) = hAPP(c_Nat_OSuc, _1286120))], (44352 ^ _781013) ^ [_1664793, _1664795, _1664797, _1664799, _1664801] : [-(hAPP(c_List_Ofoldl(_1664793, _1664795, _1664797, _1664799), _1664801) = c_List_Ofoldr(_1664795, _1664793, hAPP(c_COMBC(_1664793, _1664795, _1664793), _1664797), hAPP(c_List_Orev(_1664795), _1664801), _1664799))], (48792 ^ _781013) ^ [_1769011, _1769013, _1769015, _1769017, _1769019] : [-(hAPP(c_Relation_Oconverse(_1769011, _1769013), hAPP(hAPP(c_Relation_Orel__comp(_1769011, _1769015, _1769013), _1769017), _1769019)) = hAPP(hAPP(c_Relation_Orel__comp(_1769013, _1769015, _1769011), hAPP(c_Relation_Oconverse(_1769015, _1769013), _1769019)), hAPP(c_Relation_Oconverse(_1769011, _1769015), _1769017)))], (21857 ^ _781013) ^ [_1191196, _1191198] : [21858 ^ _781013 : [(21859 ^ _781013) ^ [_1191252] : [_1191198 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1191196), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1191252)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191196), _1191198)))], (38347 ^ _781013) ^ [_1517872, _1517874, _1517876, _1517878, _1517880, _1517882] : [-(hBOOL(hAPP(hAPP(c_member(_1517872), _1517874), hAPP(c_List_Oset(_1517872), _1517876)))), -(hAPP(hAPP(c_List_Omap(_1517872, _1517878), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1517872, _1517878), _1517880), _1517874), _1517882)), _1517876) = hAPP(hAPP(c_List_Omap(_1517872, _1517878), _1517880), _1517876))], (39167 ^ _781013) ^ [_1537325, _1537327, _1537329] : [-(hBOOL(hAPP(hAPP(c_member(_1537325), _1537327), hAPP(c_List_Oset(_1537325), _1537329)))), 39168 ^ _781013 : [(39169 ^ _781013) ^ [_1537399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1537399), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1537325)), _1537329))), hAPP(hAPP(c_List_Onth(_1537325), _1537329), _1537399) = _1537327]]], (34175 ^ _781013) ^ [_1429253, _1429255, _1429257] : [class_Int_Onumber__ring(_1429253), 34178 ^ _781013 : [(34185 ^ _781013) ^ [] : [-(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), _1429255)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1429253), _1429257), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1429255))) = c_Groups_Oone__class_Oone(_1429253))], (34179 ^ _781013) ^ [] : [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), _1429255))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1429253), _1429257), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1429255))) = hAPP(hAPP(c_HOL_OLet(_1429253, _1429253), hAPP(hAPP(c_Power_Opower__class_Opower(_1429253), _1429257), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429255))), hAPP(hAPP(c_COMBS(_1429253, _1429253, _1429253), hAPP(hAPP(c_COMBB(_1429253, tc_fun(_1429253, _1429253), _1429253), c_Groups_Otimes__class_Otimes(_1429253)), hAPP(c_Groups_Otimes__class_Otimes(_1429253), _1429257))), c_COMBI(_1429253))))]]], (49065 ^ _781013) ^ [_1775974, _1775976, _1775978] : [c_Relation_Ototal__on(_1775974, _1775976, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1775974, _1775974), tc_HOL_Obool)), _1775978), c_Relation_OId(_1775974))), -(c_Relation_Ototal__on(_1775974, _1775976, _1775978))], (42166 ^ _781013) ^ [_1615675, _1615677, _1615679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615675)), _1615679)), _1615677)), -(hAPP(hAPP(c_List_Odrop(_1615675), _1615677), _1615679) = c_List_Olist_ONil(_1615675))], (8108 ^ _781013) ^ [_919040, _919042, _919044, _919046, _919048, _919050] : [hAPP(_919040, _919042) = c_Option_Ooption_ONone(_919044), -(c_Map_Omap__comp(_919044, _919046, _919048, _919050, _919040, _919042) = c_Option_Ooption_ONone(_919046))], (50752 ^ _781013) ^ [_1812431] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1812431), _1812431)))], (22003 ^ _781013) ^ [_1193734] : [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, _1193734)))))], (25581 ^ _781013) ^ [_1257291, _1257293] : [c_Nat__Transfer_Onat__set(_1257291), c_Nat__Transfer_Onat__set(_1257293), 25588 ^ _781013 : [(25595 ^ _781013) ^ [] : [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), _1257291)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1257293))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1257291), _1257293)))], (25589 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1257291), _1257293)), -(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), _1257291)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1257293))))]]], (35437 ^ _781013) ^ [_1451763, _1451765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451763), 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)))), _1451765))), 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)))), _1451763)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1451765), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1451763))], (8078 ^ _781013) ^ [_918477, _918479, _918481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918477, tc_HOL_Obool)), _918479), hAPP(hAPP(c_Set_Oinsert(_918477), _918481), c_Orderings_Obot__class_Obot(tc_fun(_918477, tc_HOL_Obool))))), -(_918479 = c_Orderings_Obot__class_Obot(tc_fun(_918477, tc_HOL_Obool))), -(_918479 = hAPP(hAPP(c_Set_Oinsert(_918477), _918481), c_Orderings_Obot__class_Obot(tc_fun(_918477, tc_HOL_Obool))))], (30253 ^ _781013) ^ [_1346133, _1346135, _1346137] : [class_Orderings_Olinorder(_1346133), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346133), _1346135), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346133), _1346135), _1346137)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346133), _1346135), _1346137))], (38051 ^ _781013) ^ [_1509999, _1510001] : [-(c_Relation_OId__on(_1509999, _1510001) = hAPP(c_Product__Type_Oprod_Oprod__case(_1509999, _1509999, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1509999, tc_HOL_Obool, tc_fun(_1509999, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509999, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1509999, tc_HOL_Obool)), _1509999), c_COMBC(_1509999, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509999, tc_HOL_Obool), tc_fun(_1509999, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1509999), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509999), c_fconj)), c_fequal))), _1510001)))], (7369 ^ _781013) ^ [_904055, _904057, _904059, _904061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904055, tc_HOL_Obool)), _904057), _904059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904055, tc_HOL_Obool)), _904059), _904061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904055, tc_HOL_Obool)), _904057), _904061)))], (47881 ^ _781013) ^ [_1748114, _1748116, _1748118] : [-(c_List_Olist__ex(_1748114, _1748116, _1748118)), 47882 ^ _781013 : [(47883 ^ _781013) ^ [_1748171] : [hBOOL(hAPP(hAPP(c_member(_1748114), _1748171), hAPP(c_List_Oset(_1748114), _1748118))), hBOOL(hAPP(_1748116, _1748171))]]], (32244 ^ _781013) ^ [_1392974, _1392976, _1392978] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_1392974, _1392976, _1392978)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1392978)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38459 ^ _781013) ^ [_1520082, _1520084, _1520086] : [hBOOL(hAPP(c_List_Odistinct(_1520082), hAPP(hAPP(c_List_Omap(tc_prod(_1520082, _1520084), _1520082), c_Product__Type_Ofst(_1520082, _1520084)), _1520086))), -(c_Map_Oran(_1520082, _1520084, hAPP(c_Map_Omap__of(_1520082, _1520084), _1520086)) = hAPP(c_Set_Oimage(tc_prod(_1520082, _1520084), _1520084, c_Product__Type_Osnd(_1520082, _1520084)), hAPP(c_List_Oset(tc_prod(_1520082, _1520084)), _1520086)))], (172 ^ _781013) ^ [_783899, _783901, _783903, _783905, _783907, _783909] : [-(c_Big__Operators_Osemilattice__big(_783907, _783903, _783899)), c_Big__Operators_Osemilattice__big(_783909, _783905, _783901), _783909 = _783907, _783905 = _783903, _783901 = _783899], (5655 ^ _781013) ^ [_870308, _870310, _870312] : [hAPP(hAPP(c_Set_Oinsert(_870308), _870310), c_Orderings_Obot__class_Obot(tc_fun(_870308, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_870308), _870312), c_Orderings_Obot__class_Obot(tc_fun(_870308, tc_HOL_Obool))), -(_870310 = _870312)], (43881 ^ _781013) ^ [_1654724, _1654726] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1654724, _1654726)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1654724), _1654726))], (1034 ^ _781013) ^ [_796680, _796682] : [-(class_Rings_Olinordered__semiring__1__strict(_796680)), _796682 = _796680, class_Rings_Olinordered__semiring__1__strict(_796682)], (30811 ^ _781013) ^ [_1357603, _1357605, _1357607] : [class_Orderings_Olinorder(_1357603), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357603), _1357605)), -(hBOOL(hAPP(hAPP(c_member(_1357603), _1357607), _1357605))), -(_1357605 = c_Orderings_Obot__class_Obot(tc_fun(_1357603, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1357603, c_Orderings_Oord__class_Omax(_1357603), hAPP(hAPP(c_Set_Oinsert(_1357603), _1357607), _1357605)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357603), _1357607), c_Big__Operators_Olattice_OSup__fin(_1357603, c_Orderings_Oord__class_Omax(_1357603), _1357605)))], (2704 ^ _781013) ^ [_821204, _821206, _821208, _821210, _821212, _821214, _821216, _821218, _821220, _821222] : [-(c_Product__Type_Oprod_Oprod__rec(_821222, _821218, _821214, _821210, _821206) = c_Product__Type_Oprod_Oprod__rec(_821220, _821216, _821212, _821208, _821204)), _821222 = _821220, _821218 = _821216, _821214 = _821212, _821210 = _821208, _821206 = _821204], (33480 ^ _781013) ^ [_1416298, _1416300, _1416302, _1416304, _1416306, _1416308, _1416310, _1416312, _1416314] : [c_Equiv__Relations_Oequiv(_1416298, _1416300, _1416302), c_Equiv__Relations_Oequiv(_1416304, _1416306, _1416308), c_Equiv__Relations_Ocongruent2(_1416298, _1416304, tc_fun(_1416310, tc_HOL_Obool), _1416302, _1416308, _1416312), hBOOL(hAPP(hAPP(c_member(_1416304), _1416314), _1416306)), -(c_Equiv__Relations_Ocongruent(_1416298, tc_fun(_1416310, tc_HOL_Obool), _1416302, hAPP(hAPP(c_COMBB(tc_fun(_1416304, tc_fun(_1416310, tc_HOL_Obool)), tc_fun(_1416310, tc_HOL_Obool), _1416298), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416304, tc_fun(_1416310, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1416304, _1416304, _1416308), hAPP(hAPP(c_Set_Oinsert(_1416304), _1416314), c_Orderings_Obot__class_Obot(tc_fun(_1416304, tc_HOL_Obool)))))), _1416312)))], (6405 ^ _781013) ^ [_885600] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _885600), _885600)))], (47036 ^ _781013) ^ [_1727492, _1727494, _1727496, _1727498] : [-(_1727492 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1727494, tc_HOL_Obool), tc_HOL_Obool))), 47042 ^ _781013 : [(47045 ^ _781013) ^ [] : [c_Fun_Oinj__on(_1727494, _1727496, _1727498, 47041 ^ [_1727492, _1727494, _1727496, _1727498])], (47043 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1727494, tc_HOL_Obool)), 47041 ^ [_1727492, _1727494, _1727496, _1727498]), _1727492)))]], -(c_Fun_Oinj__on(_1727494, _1727496, _1727498, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1727494, tc_HOL_Obool), _1727492)))], (22162 ^ _781013) ^ [_1196684, _1196686] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1196684), _1196686))))], (40968 ^ _781013) ^ [_1587510, _1587512, _1587514, _1587516] : [c_Finite__Set_Ofolding(_1587510, _1587512, _1587514, _1587516), -(hAPP(_1587516, c_Orderings_Obot__class_Obot(tc_fun(_1587510, tc_HOL_Obool))) = c_Fun_Oid(_1587512))], (14069 ^ _781013) ^ [_1039874, _1039876, _1039878] : [class_Groups_Oab__group__add(_1039874), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1039874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039874), _1039876), _1039878)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039874), hAPP(c_Groups_Ouminus__class_Ouminus(_1039874), _1039876)), hAPP(c_Groups_Ouminus__class_Ouminus(_1039874), _1039878)))], (48209 ^ _781013) ^ [_1755017, _1755019] : [hAPP(c_Code__Numeral_Oof__nat, _1755017) = hAPP(c_Code__Numeral_Oof__nat, _1755019), -(_1755017 = _1755019)], (48185 ^ _781013) ^ [_1754641, _1754643] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1754641), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1754643), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 48192 ^ _781013 : [(48199 ^ _781013) ^ [] : [_1754641 = _1754643, -(hAPP(c_Code__Numeral_Oof__nat, _1754641) = hAPP(c_Code__Numeral_Oof__nat, _1754643))], (48193 ^ _781013) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1754641) = hAPP(c_Code__Numeral_Oof__nat, _1754643), -(_1754641 = _1754643)]]], (30299 ^ _781013) ^ [_1347101, _1347103, _1347105, _1347107] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1347101), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347101), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347101), _1347103), _1347105)), _1347107) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347101), _1347103), _1347107)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347101), _1347105), _1347107)))], (35601 ^ _781013) ^ [_1454805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1454805), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1454805)), c_Int_OMin)))], (37084 ^ _781013) ^ [_1488703, _1488705] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1488703, _1488705), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1488703), _1488705)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1488703, _1488705)))))], (31043 ^ _781013) ^ [_1362274, _1362276] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1362274), hAPP(c_Nat_OSuc, _1362276)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1362276), 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)), _1362276)), _1362274))], (11189 ^ _781013) ^ [_980465, _980467, _980469, _980471, _980473, _980475] : [-(c_Map_Omap__add(_980465, _980467, _980469, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_980465, tc_Option_Ooption(_980467)), _980471), _980473), hAPP(c_Option_Ooption_OSome(_980467), _980475))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_980465, tc_Option_Ooption(_980467)), c_Map_Omap__add(_980465, _980467, _980469, _980471)), _980473), hAPP(c_Option_Ooption_OSome(_980467), _980475)))], (48177 ^ _781013) ^ [_1754384, _1754386] : [-(c_Random_Oselect__weight(_1754384, _1754386) = 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(_1754384, 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, _1754384), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1754384)), _1754386)))), hAPP(hAPP(c_COMBB(_1754384, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1754384, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1754384, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1754384, _1754386))))], (51670 ^ _781013) ^ [_1825623, _1825625] : [hBOOL(_1825623), -(hBOOL(hAPP(hAPP(c_fdisj, _1825625), _1825623)))], (37919 ^ _781013) ^ [_1507394, _1507396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1507394), _1507396)), -(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), _1507394), _1507396)), c_Wellfounded_Oless__than)))], (22250 ^ _781013) ^ [_1198181, _1198183, _1198185, _1198187, _1198189] : [class_Orderings_Olinorder(_1198181), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1198181, _1198183), _1198185) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1198181, _1198187), _1198189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198181), _1198183), _1198185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198181), _1198187), _1198189)), -(_1198185 = _1198189)], (26042 ^ _781013) ^ [_1265212, _1265214, _1265216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1265212, 26043 ^ [_1265212, _1265214, _1265216])), hAPP(_1265214, 26043 ^ [_1265212, _1265214, _1265216]))), -(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), _1265214), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1265216))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1265212), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1265216))) = 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)), _1265214)), _1265212)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1265216)))], (10207 ^ _781013) ^ [_961592, _961594, _961596] : [class_Lattices_Oboolean__algebra(_961592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961592), _961594), _961596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961592), hAPP(c_Groups_Ouminus__class_Ouminus(_961592), _961596)), hAPP(c_Groups_Ouminus__class_Ouminus(_961592), _961594))))], (1404 ^ _781013) ^ [_801305, _801307] : [-(class_Finite__Set_Ofinite(_801305)), _801307 = _801305, class_Finite__Set_Ofinite(_801307)], (28612 ^ _781013) ^ [_1314756, _1314758] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1314756), _1314758) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314756, _1314758)), _1314758))], (16225 ^ _781013) ^ [_1080843, _1080845] : [class_Groups_Oab__group__add(_1080843), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080843), hAPP(c_Groups_Ouminus__class_Ouminus(_1080843), _1080845)), _1080845) = c_Groups_Ozero__class_Ozero(_1080843))], (23841 ^ _781013) ^ [_1226406, _1226408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226406)), 23844 ^ _781013 : [(23851 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226408), _1226406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1226408)), hAPP(c_Int_Onat, _1226406))))], (23845 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1226408)), hAPP(c_Int_Onat, _1226406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226408), _1226406)))]]], (33938 ^ _781013) ^ [_1423941, _1423943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1423941)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423943))), -(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(_1423943))), 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), _1423941)), c_Int_Onat))))))], (21973 ^ _781013) ^ [_1193158] : [-(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)))), _1193158)) = 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), _1193158), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (6920 ^ _781013) ^ [_895407, _895409, _895411, _895413, _895415, _895417] : [-(_895407 = _895409), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_895411, _895413), _895415), _895409), _895417), _895407) = hAPP(_895415, _895407))], (41756 ^ _781013) ^ [_1605144, _1605146, _1605148, _1605150, _1605152] : [hAPP(hAPP(c_List_Oappend(_1605144), _1605146), _1605148) = hAPP(hAPP(c_List_Oappend(_1605144), _1605150), _1605152), 41762 ^ _781013 : [(41765 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1605144), 41759 ^ [_1605144, _1605146, _1605148, _1605150, _1605152]), _1605148) = _1605152)], (41763 ^ _781013) ^ [] : [-(_1605146 = hAPP(hAPP(c_List_Oappend(_1605144), _1605150), 41759 ^ [_1605144, _1605146, _1605148, _1605150, _1605152]))]], 41766 ^ _781013 : [(41769 ^ _781013) ^ [] : [-(_1605148 = hAPP(hAPP(c_List_Oappend(_1605144), 41759 ^ [_1605144, _1605146, _1605148, _1605150, _1605152]), _1605152))], (41767 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1605144), _1605146), 41759 ^ [_1605144, _1605146, _1605148, _1605150, _1605152]) = _1605150)]]], (15193 ^ _781013) ^ [_1062098, _1062100] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062098), c_Orderings_Otop__class_Otop(tc_fun(_1062098, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1062098), _1062100) = hAPP(c_Finite__Set_Ocard(_1062098), c_Orderings_Otop__class_Otop(tc_fun(_1062098, tc_HOL_Obool))), -(_1062100 = c_Orderings_Otop__class_Otop(tc_fun(_1062098, tc_HOL_Obool)))], (17853 ^ _781013) ^ [_1114169, _1114171, _1114173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114169), _1114171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114171), _1114173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114169), _1114173)))], (21800 ^ _781013) ^ [_1190154, _1190156] : [class_Orderings_Olinorder(_1190154), -(c_Big__Operators_Olinorder__class_OMax(_1190154, hAPP(hAPP(c_Set_Oinsert(_1190154), _1190156), c_Orderings_Obot__class_Obot(tc_fun(_1190154, tc_HOL_Obool)))) = _1190156)], (39619 ^ _781013) ^ [_1547850, _1547852, _1547854, _1547856, _1547858, _1547860, _1547862] : [hBOOL(hAPP(hAPP(c_member(_1547850), _1547852), hAPP(c_List_Oset(_1547850), hAPP(hAPP(c_List_Otake(_1547850), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1547854)), _1547856)), _1547858)))), -(c_Map_Omap__upds(_1547850, _1547854, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1547850, tc_Option_Ooption(_1547854)), _1547860), _1547852), hAPP(c_Option_Ooption_OSome(_1547854), _1547862)), _1547858, _1547856) = c_Map_Omap__upds(_1547850, _1547854, _1547860, _1547858, _1547856))], (31848 ^ _781013) ^ [_1383877, _1383879, _1383881, _1383883, _1383885] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383877, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383879, tc_fun(_1383877, tc_HOL_Obool)), _1383881), _1383883)), _1383885) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383879, tc_fun(_1383877, tc_HOL_Obool)), _1383881), hAPP(hAPP(c_COMBC(_1383879, tc_fun(_1383877, tc_HOL_Obool), tc_fun(_1383877, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383877, tc_HOL_Obool), tc_fun(tc_fun(_1383877, tc_HOL_Obool), tc_fun(_1383877, tc_HOL_Obool)), _1383879), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383877, tc_HOL_Obool))), _1383883)), _1383885)))], (31072 ^ _781013) ^ [_1362830, _1362832, _1362834, _1362836] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1362830))), _1362832), _1362834), _1362836)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _1362830)), _1362832), hAPP(c_Nat_OSuc, _1362834)), _1362836)))], (40633 ^ _781013) ^ [_1577133, _1577135, _1577137] : [c_Equiv__Relations_Oequiv(_1577133, _1577135, _1577137), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1577133, _1577133), tc_HOL_Obool)), _1577137), hAPP(hAPP(c_Product__Type_OSigma(_1577133, _1577133), _1577135), hAPP(c_COMBK(tc_fun(_1577133, tc_HOL_Obool), _1577133), _1577135)))))], (37068 ^ _781013) ^ [_1488410, _1488412] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1488410, _1488412), c_Divides_Odivmod__nat(_1488410, _1488412))))], (33974 ^ _781013) ^ [_1424838, _1424840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424838)), hAPP(c_Nat_OSuc, _1424840))), -(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(_1424838))), 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)), _1424840)))))], (48976 ^ _781013) ^ [_1773677, _1773679, _1773681, _1773683, _1773685, _1773687] : [c_Relation_Osingle__valued(_1773677, _1773679, _1773681), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773677, _1773679)), hAPP(hAPP(c_Product__Type_OPair(_1773677, _1773679), _1773683), _1773685)), _1773681)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773677, _1773679)), hAPP(hAPP(c_Product__Type_OPair(_1773677, _1773679), _1773683), _1773687)), _1773681)), -(_1773685 = _1773687)], (27409 ^ _781013) ^ [_1291823, _1291825, _1291827] : [hAPP(c_Set_Oimage(_1291825, tc_fun(_1291825, tc_HOL_Obool), _1291823), _1291827) = hAPP(c_Set_OPow(_1291825), _1291827)], (44594 ^ _781013) ^ [_1671568, _1671570, _1671572, _1671574] : [hBOOL(hAPP(hAPP(c_member(_1671568), _1671570), hAPP(c_List_Oset(_1671568), c_List_OtakeWhile(_1671568, _1671572, _1671574)))), 44597 ^ _781013 : [(44600 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1671572, _1671570)))], (44598 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1671568), _1671570), hAPP(c_List_Oset(_1671568), _1671574))))]]], (3324 ^ _781013) ^ [_831062, _831064, _831066, _831068, _831070, _831072, _831074, _831076] : [-(c_Enum_Oproduct(_831076, _831072, _831068, _831064) = c_Enum_Oproduct(_831074, _831070, _831066, _831062)), _831076 = _831074, _831072 = _831070, _831068 = _831066, _831064 = _831062], (26501 ^ _781013) ^ [_1274151, _1274153, _1274155] : [class_Orderings_Olinorder(_1274151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274151), _1274153), _1274155)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274151, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1274151, _1274153), _1274155)), hAPP(hAPP(c_Set_Oinsert(_1274151), _1274155), c_Orderings_Obot__class_Obot(tc_fun(_1274151, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1274151, _1274153, _1274155))], (26697 ^ _781013) ^ [_1277847, _1277849] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1277847), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1277849), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1277847, _1277849))], (47954 ^ _781013) ^ [_1749763, _1749765, _1749767, _1749769, _1749771] : [-(_1749763 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1749765, _1749767, _1749763, _1749769), _1749771) = hAPP(hAPP(c_Product__Type_Oscomp(_1749767, _1749765, _1749767, tc_prod(_1749765, _1749767)), hAPP(_1749769, _1749771)), c_Random_Oiterate(_1749765, _1749767, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1749763), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1749769)))], (50328 ^ _781013) ^ [_1804520, _1804522, _1804524] : [c_List_Olist__all(_1804520, _1804522, hAPP(c_List_Orev(_1804520), _1804524)), -(c_List_Olist__all(_1804520, _1804522, _1804524))], (51450 ^ _781013) ^ [_1823075] : [-(class_Nat_Osize(tc_Option_Ooption(_1823075)))], (9337 ^ _781013) ^ [_946585, _946587, _946589, _946591] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946585, tc_HOL_Obool)), _946587), _946589), _946591)), 9340 ^ _781013 : [(9343 ^ _781013) ^ [] : [-(hBOOL(hAPP(_946589, _946591)))], (9341 ^ _781013) ^ [] : [-(hBOOL(hAPP(_946587, _946591)))]]], (19863 ^ _781013) ^ [_1153085, _1153087, _1153089, _1153091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1153085), _1153087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1153089), _1153091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153085), _1153089)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153087), _1153091))))], (38154 ^ _781013) ^ [] : [-(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))], (46482 ^ _781013) ^ [_1712830, _1712832, _1712834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1712830, _1712830), tc_HOL_Obool)), _1712832), _1712834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1712830, tc_HOL_Obool)), c_Wellfounded_Oacc(_1712830, _1712834)), c_Wellfounded_Oacc(_1712830, _1712832))))], (42384 ^ _781013) ^ [_1620473, _1620475] : [hBOOL(hAPP(c_List_Odistinct(_1620473), _1620475)), -(hBOOL(hAPP(c_List_Odistinct(_1620473), hAPP(c_List_Otl(_1620473), _1620475))))], (34485 ^ _781013) ^ [_1434341, _1434343] : [class_Int_Onumber__ring(_1434341), class_Rings_Olinordered__idom(_1434341), 34492 ^ _781013 : [(34499 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1434343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434341), c_Groups_Oone__class_Oone(_1434341)), hAPP(c_Int_Onumber__class_Onumber__of(_1434341), _1434343))))], (34493 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434341), c_Groups_Oone__class_Oone(_1434341)), hAPP(c_Int_Onumber__class_Onumber__of(_1434341), _1434343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1434343)))]]], (34813 ^ _781013) ^ [_1440188, _1440190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440188), _1440190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1440188)), c_Int_OBit0(_1440190))))], (29175 ^ _781013) ^ [_1325208, _1325210, _1325212] : [class_Rings_Olinordered__idom(_1325208), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325208), c_Groups_Ozero__class_Ozero(_1325208)), _1325210)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325208), hAPP(c_Groups_Oabs__class_Oabs(_1325208), _1325212)), _1325210) = hAPP(c_Groups_Oabs__class_Oabs(_1325208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325208), _1325212), _1325210)))], (32570 ^ _781013) ^ [_1399209, _1399211, _1399213] : [class_Int_Onumber__ring(_1399209), -(hAPP(c_Int_Onumber__class_Onumber__of(_1399209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1399211), _1399213)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1399209), hAPP(c_Int_Onumber__class_Onumber__of(_1399209), _1399211)), hAPP(c_Int_Onumber__class_Onumber__of(_1399209), _1399213)))], (39074 ^ _781013) ^ [_1535016, _1535018, _1535020, _1535022, _1535024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1535016), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1535018)), _1535020))), -(hAPP(hAPP(c_List_Onth(_1535022), hAPP(hAPP(c_List_Omap(_1535018, _1535022), _1535024), _1535020)), _1535016) = hAPP(_1535024, hAPP(hAPP(c_List_Onth(_1535018), _1535020), _1535016)))], (35071 ^ _781013) ^ [_1444907, _1444909] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1444907)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1444909))) = 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), _1444907), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1444909))))], (14779 ^ _781013) ^ [_1055142, _1055144] : [class_Groups_Ocomm__monoid__add(_1055142), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055142), _1055144), c_Groups_Ozero__class_Ozero(_1055142)) = _1055144)], (1594 ^ _781013) ^ [_803680, _803682] : [-(class_Rings_Oordered__semiring(_803680)), _803682 = _803680, class_Rings_Oordered__semiring(_803682)], (8367 ^ _781013) ^ [_924984, _924986, _924988, _924990] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_924984), _924986)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_924988), hAPP(c_Set_Oimage(_924984, _924988, _924990), _924986))))], (36364 ^ _781013) ^ [_1474436, _1474438, _1474440, _1474442, _1474444, _1474446] : [c_Equiv__Relations_Oequiv(_1474436, _1474438, _1474440), hBOOL(hAPP(hAPP(c_member(_1474436), _1474442), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474436, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1474436, _1474436, _1474440), hAPP(hAPP(c_Set_Oinsert(_1474436), _1474444), c_Orderings_Obot__class_Obot(tc_fun(_1474436, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1474436, _1474436, _1474440), hAPP(hAPP(c_Set_Oinsert(_1474436), _1474446), c_Orderings_Obot__class_Obot(tc_fun(_1474436, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1474436, _1474436)), hAPP(hAPP(c_Product__Type_OPair(_1474436, _1474436), _1474444), _1474446)), _1474440)))], (23323 ^ _781013) ^ [_1217233, _1217235] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1217233)), hAPP(c_Option_Ooption_OSome(_1217233), _1217235)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48699 ^ _781013) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (32474 ^ _781013) ^ [_1397216, _1397218, _1397220] : [class_Int_Onumber__ring(_1397216), class_Rings_Olinordered__idom(_1397216), 32481 ^ _781013 : [(32488 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397218), _1397220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397216), hAPP(c_Int_Onumber__class_Onumber__of(_1397216), _1397218)), hAPP(c_Int_Onumber__class_Onumber__of(_1397216), _1397220))))], (32482 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397216), hAPP(c_Int_Onumber__class_Onumber__of(_1397216), _1397218)), hAPP(c_Int_Onumber__class_Onumber__of(_1397216), _1397220))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397218), _1397220)))]]], (36635 ^ _781013) ^ [_1480320, _1480322, _1480324, _1480326] : [-(c_HOL_OThe(tc_prod(_1480320, _1480322), hAPP(c_Product__Type_Oprod_Oprod__case(_1480320, _1480322, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1480320, tc_fun(_1480322, tc_HOL_Obool), tc_fun(_1480322, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1480322, tc_HOL_Obool), tc_fun(_1480322, tc_HOL_Obool)), _1480320), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1480322)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1480320), c_fconj), hAPP(c_fequal, _1480324)))), hAPP(c_fequal, _1480326)))) = hAPP(hAPP(c_Product__Type_OPair(_1480320, _1480322), _1480324), _1480326))], (48848 ^ _781013) ^ [_1770296, _1770298] : [c_Wellfounded_Owf(_1770296, hAPP(c_Relation_Oconverse(_1770296, _1770296), _1770298)), -(c_Wellfounded_Owf(_1770296, hAPP(c_Relation_Oconverse(_1770296, _1770296), c_Transitive__Closure_Otrancl(_1770296, _1770298))))], (3314 ^ _781013) ^ [_830913, _830915, _830917, _830919] : [-(c_Enum_Oenum__the(_830919, _830915) = c_Enum_Oenum__the(_830917, _830913)), _830919 = _830917, _830915 = _830913], (51126 ^ _781013) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (26751 ^ _781013) ^ [_1278841] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1278841)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1278841)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1278841), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (49259 ^ _781013) ^ [_1780956, _1780958, _1780960, _1780962, _1780964] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780956, _1780956)), hAPP(hAPP(c_Product__Type_OPair(_1780956, _1780956), _1780958), _1780960)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1780956, _1780956), tc_HOL_Obool), _1780962), _1780964))), 49264 ^ _781013 : [(49267 ^ _781013) ^ [] : [-(_1780958 = _1780960)], (49265 ^ _781013) ^ [] : [-(_1780962 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 49270 ^ _781013 : [(49275 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780956, _1780956)), hAPP(hAPP(c_Product__Type_OPair(_1780956, _1780956), 49268 ^ [_1780956, _1780958, _1780960, _1780962, _1780964]), _1780960)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1780956, _1780956), tc_HOL_Obool), 49269 ^ [_1780956, _1780958, _1780960, _1780962, _1780964]), _1780964))))], (49273 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780956, _1780956)), hAPP(hAPP(c_Product__Type_OPair(_1780956, _1780956), _1780958), 49268 ^ [_1780956, _1780958, _1780960, _1780962, _1780964])), _1780964)))], (49271 ^ _781013) ^ [] : [-(_1780962 = hAPP(c_Nat_OSuc, 49269 ^ [_1780956, _1780958, _1780960, _1780962, _1780964]))]]], (26241 ^ _781013) ^ [_1268887, _1268889, _1268891] : [class_Orderings_Oorder(_1268887), _1268889 = _1268891, -(c_SetInterval_Oord__class_OatLeastAtMost(_1268887, _1268889, _1268891) = hAPP(hAPP(c_Set_Oinsert(_1268887), _1268889), c_Orderings_Obot__class_Obot(tc_fun(_1268887, tc_HOL_Obool))))], (8299 ^ _781013) ^ [_922991, _922993, _922995, _922997] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922991, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_922991, tc_fun(_922991, tc_HOL_Obool), tc_HOL_Obool), c_member(_922991)), _922993)), hAPP(hAPP(c_COMBC(_922991, tc_fun(_922991, tc_HOL_Obool), tc_HOL_Obool), c_member(_922991)), _922995)), _922997)), -(hBOOL(hAPP(hAPP(c_member(_922991), _922997), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922991, tc_HOL_Obool)), _922993), _922995))))], (10323 ^ _781013) ^ [_963661, _963663, _963665, _963667] : [class_Lattices_Odistrib__lattice(_963661), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963661), _963663), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_963661), _963665), _963667)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_963661), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963661), _963663), _963665)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963661), _963663), _963667)))], (31098 ^ _781013) ^ [_1363429, _1363431, _1363433] : [31100 ^ _781013 : [(31103 ^ _781013) ^ [] : [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(_1363431, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 31099 ^ [_1363429, _1363431, _1363433]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1363431, 31099 ^ [_1363429, _1363431, _1363433])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31101 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31099 ^ [_1363429, _1363431, _1363433]), _1363429)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1363431, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1363433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1363433), hAPP(_1363431, _1363429))), 31113 ^ _781013 : [(31116 ^ _781013) ^ [] : [-(hAPP(_1363431, 31112 ^ [_1363429, _1363431, _1363433]) = _1363433)], (31114 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 31112 ^ [_1363429, _1363431, _1363433]), _1363429)))]]], (51354 ^ _781013) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (39945 ^ _781013) ^ [_1558309, _1558311] : [39947 ^ _781013 : [(39950 ^ _781013) ^ [] : [hBOOL(hAPP(_1558311, 39946 ^ [_1558309, _1558311]))], (39948 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558309), 39946 ^ [_1558309, _1558311]), c_Orderings_Otop__class_Otop(tc_fun(_1558309, tc_HOL_Obool)))))]], 39951 ^ _781013 : [(39952 ^ _781013) ^ [_1558461] : [-(hBOOL(hAPP(_1558311, _1558461)))]]], (39338 ^ _781013) ^ [_1541176, _1541178, _1541180, _1541182, _1541184] : [class_Rings_Osemiring__0(_1541176), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1541176), hAPP(hAPP(c_List_Omap(_1541178, _1541176), hAPP(hAPP(c_COMBB(_1541176, _1541176, _1541178), hAPP(c_Groups_Otimes__class_Otimes(_1541176), _1541180)), _1541182)), _1541184)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1541176), _1541180), hAPP(c_List_Omonoid__add__class_Olistsum(_1541176), hAPP(hAPP(c_List_Omap(_1541178, _1541176), _1541182), _1541184))))], (39112 ^ _781013) ^ [_1536086, _1536088, _1536090, _1536092] : [hBOOL(hAPP(c_List_Odistinct(_1536086), _1536088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1536090), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1536086)), _1536088))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1536092), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1536086)), _1536088))), 39123 ^ _781013 : [(39130 ^ _781013) ^ [] : [_1536090 = _1536092, -(hAPP(hAPP(c_List_Onth(_1536086), _1536088), _1536090) = hAPP(hAPP(c_List_Onth(_1536086), _1536088), _1536092))], (39124 ^ _781013) ^ [] : [hAPP(hAPP(c_List_Onth(_1536086), _1536088), _1536090) = hAPP(hAPP(c_List_Onth(_1536086), _1536088), _1536092), -(_1536090 = _1536092)]]], (8094 ^ _781013) ^ [_918780, _918782, _918784, _918786] : [-(hAPP(_918786, _918782) = c_Option_Ooption_ONone(_918784)), -(hBOOL(hAPP(hAPP(c_member(_918780), _918782), c_Map_Odom(_918780, _918784, _918786))))], (41570 ^ _781013) ^ [_1601499, _1601501, _1601503, _1601505, _1601507] : [hAPP(hAPP(c_List_Olist_OCons(_1601499), _1601501), _1601503) = hAPP(hAPP(c_List_Oappend(_1601499), _1601505), _1601507), 41575 ^ _781013 : [(41578 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1601499), _1601501), _1601503) = _1601507)], (41576 ^ _781013) ^ [] : [-(_1601505 = c_List_Olist_ONil(_1601499))]], 41580 ^ _781013 : [(41583 ^ _781013) ^ [] : [-(_1601503 = hAPP(hAPP(c_List_Oappend(_1601499), 41579 ^ [_1601499, _1601501, _1601503, _1601505, _1601507]), _1601507))], (41581 ^ _781013) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1601499), _1601501), 41579 ^ [_1601499, _1601501, _1601503, _1601505, _1601507]) = _1601505)]]], (38397 ^ _781013) ^ [_1519017, _1519019, _1519021, _1519023, _1519025, _1519027] : [c_Typedef_Otype__definition(_1519017, _1519019, _1519021, _1519023, _1519025), -(hBOOL(hAPP(hAPP(c_member(_1519019), hAPP(_1519021, _1519027)), _1519025)))], (21457 ^ _781013) ^ [_1184200, _1184202] : [-(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), _1184200))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184202))))], (6613 ^ _781013) ^ [_889278, _889280, _889282, _889284, _889286] : [c_Finite__Set_Ofolding__idem(_889278, _889280, _889282, _889284), -(hAPP(c_Fun_Ocomp(_889280, _889280, _889280, hAPP(_889282, _889286)), hAPP(_889282, _889286)) = hAPP(_889282, _889286))], (37138 ^ _781013) ^ [_1489743, _1489745] : [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), _1489743), _1489745))), 37141 ^ _781013 : [(37150 ^ _781013) ^ [] : [-(c_Divides_OposDivAlg(_1489743, _1489745) = hAPP(c_Divides_Oadjust(_1489745), c_Divides_OposDivAlg(_1489743, 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)))), _1489745)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489743), _1489745))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1489745), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37142 ^ _781013) ^ [] : [37143 ^ _781013 : [(37146 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1489745), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (37144 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489743), _1489745))]], -(c_Divides_OposDivAlg(_1489743, _1489745) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489743))]]], (42160 ^ _781013) ^ [_1615556, _1615558, _1615560] : [hAPP(hAPP(c_List_Odrop(_1615556), _1615558), _1615560) = c_List_Olist_ONil(_1615556), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615556)), _1615560)), _1615558)))], (25406 ^ _781013) ^ [_1254617, _1254619, _1254621, _1254623] : [class_Fields_Olinordered__field(_1254617), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254617), c_Groups_Ozero__class_Ozero(_1254617)), _1254619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1254617), _1254621), _1254619)), _1254623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254617), _1254621), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1254617), _1254623), _1254619))))], (48894 ^ _781013) ^ [_1771464, _1771466, _1771468, _1771470, _1771472, _1771474] : [c_Relation_Osingle__valued(_1771464, _1771466, hAPP(c_Relation_Oconverse(_1771466, _1771464), _1771468)), -(_1771470 = c_Orderings_Obot__class_Obot(tc_fun(_1771472, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1771466, _1771464, _1771468), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1771472, tc_fun(_1771466, tc_HOL_Obool)), _1771470), _1771474)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1771472, tc_fun(_1771464, tc_HOL_Obool)), _1771470), hAPP(hAPP(c_COMBB(tc_fun(_1771466, tc_HOL_Obool), tc_fun(_1771464, tc_HOL_Obool), _1771472), c_Relation_OImage(_1771466, _1771464, _1771468)), _1771474)))], (39643 ^ _781013) ^ [_1548382, _1548384, _1548386, _1548388] : [-(hAPP(hAPP(c_List_Otake(_1548382), _1548384), hAPP(hAPP(c_List_Otake(_1548382), _1548386), _1548388)) = hAPP(hAPP(c_List_Otake(_1548382), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1548384), _1548386)), _1548388))], (41220 ^ _781013) ^ [_1593591] : [-(hAPP(c_List_Oset(_1593591), c_List_Olist_ONil(_1593591)) = c_Orderings_Obot__class_Obot(tc_fun(_1593591, tc_HOL_Obool)))], (22598 ^ _781013) ^ [_1204078, _1204080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204078)), 22601 ^ _781013 : [(22608 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204080)), -(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), _1204080), _1204078))))], (22602 ^ _781013) ^ [] : [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), _1204080), _1204078))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204080)))]]], (44022 ^ _781013) ^ [_1657476] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1657476) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1657476)))], (46297 ^ _781013) ^ [_1708038, _1708040, _1708042, _1708044, _1708046, _1708048, _1708050, _1708052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708038), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708040)), _1708042))), c_List_Olist__all2(_1708040, _1708044, _1708046, _1708042, _1708048), hBOOL(hAPP(hAPP(_1708046, _1708050), _1708052)), -(c_List_Olist__all2(_1708040, _1708044, _1708046, hAPP(hAPP(c_List_Olist__update(_1708040, _1708042), _1708038), _1708050), hAPP(hAPP(c_List_Olist__update(_1708044, _1708048), _1708038), _1708052)))], (8541 ^ _781013) ^ [_928901, _928903, _928905, _928907, _928909, _928911] : [c_Finite__Set_Ofolding(_928901, _928903, _928905, _928907), hBOOL(hAPP(c_Finite__Set_Ofinite(_928901), _928909)), -(hAPP(c_Fun_Ocomp(_928903, _928903, _928903, hAPP(_928905, _928911)), hAPP(_928907, _928909)) = hAPP(c_Fun_Ocomp(_928903, _928903, _928903, hAPP(_928907, _928909)), hAPP(_928905, _928911)))], (41234 ^ _781013) ^ [_1593791, _1593793, _1593795] : [41235 ^ _781013 : [(41238 ^ _781013) ^ [] : [_1593795 = c_List_Olist_ONil(_1593791)], (41236 ^ _781013) ^ [] : [_1593793 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1593791), _1593793), _1593795) = c_List_Olist_ONil(_1593791))], (5841 ^ _781013) ^ [_874954, _874956, _874958, _874960] : [c_Com_Ocom_OSemi(_874954, _874956) = c_Com_Ocom_OSemi(_874958, _874960), 5844 ^ _781013 : [(5847 ^ _781013) ^ [] : [-(_874956 = _874960)], (5845 ^ _781013) ^ [] : [-(_874954 = _874958)]]], (18155 ^ _781013) ^ [_1119242, _1119244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119242), _1119244)), _1119242))], (51184 ^ _781013) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (38846 ^ _781013) ^ [_1529528, _1529530, _1529532, _1529534] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1529528)), _1529530) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1529532)), _1529534), -(hAPP(hAPP(c_List_Omap(tc_prod(_1529528, _1529532), _1529532), c_Product__Type_Osnd(_1529528, _1529532)), hAPP(hAPP(c_List_Ozip(_1529528, _1529532), _1529530), _1529534)) = _1529534)], (10661 ^ _781013) ^ [_969455, _969457, _969459] : [class_Orderings_Opreorder(_969455), 10664 ^ _781013 : [(10673 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969455), _969457), _969459))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969455), _969457), _969459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969455), _969459), _969457)))], (10665 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969455), _969457), _969459)), 10668 ^ _781013 : [(10671 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969455), _969459), _969457))], (10669 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969455), _969457), _969459)))]]]]], (11640 ^ _781013) ^ [_990560, _990562] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_990560, _990562)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_990560, _990562), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_990560), c_Orderings_Otop__class_Otop(tc_fun(_990560, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_990562), c_Orderings_Otop__class_Otop(tc_fun(_990562, tc_HOL_Obool))))], (44358 ^ _781013) ^ [_1664939, _1664941, _1664943] : [-(c_List_Oconcat(_1664939, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1664939)), _1664941), _1664943)) = hAPP(hAPP(c_List_Oappend(_1664939), _1664941), c_List_Oconcat(_1664939, _1664943)))], (7305 ^ _781013) ^ [_902939, _902941, _902943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902939, tc_HOL_Obool)), _902941), _902943)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902939, tc_HOL_Obool)), _902941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902939, tc_HOL_Obool)), _902943), _902941)) = _902943)], (26633 ^ _781013) ^ [_1276829, _1276831] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1276829, _1276831))))], (7093 ^ _781013) ^ [_898685, _898687, _898689, _898691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898685, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898685, tc_HOL_Obool)), _898687), _898689)), _898691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898685, tc_HOL_Obool)), _898687), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898685, tc_HOL_Obool)), _898689), _898691))))], (51304 ^ _781013) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (36444 ^ _781013) ^ [_1476019] : [-(c_Divides_Oadjust(_1476019) = 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)), _1476019))))), 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)), _1476019))))), 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))))))))], (9725 ^ _781013) ^ [_952808, _952810, _952812, _952814] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952808, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952808, tc_HOL_Obool)), _952810), _952812)), _952814) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952808, tc_HOL_Obool)), _952810), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952808, tc_HOL_Obool)), _952812), _952814)))], (10393 ^ _781013) ^ [_965294, _965296, _965298, _965300] : [class_Orderings_Oord(_965294), 10396 ^ _781013 : [(10405 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_965296, _965294)), _965298), _965300))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965296, _965294)), _965298), _965300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965296, _965294)), _965300), _965298)))], (10397 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_965296, _965294)), _965298), _965300)), 10400 ^ _781013 : [(10403 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965296, _965294)), _965300), _965298))], (10401 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965296, _965294)), _965298), _965300)))]]]]], (23909 ^ _781013) ^ [_1227465, _1227467] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1227465) = _1227467, 23912 ^ _781013 : [(23915 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227467)))], (23913 ^ _781013) ^ [] : [-(_1227465 = hAPP(c_Int_Onat, _1227467))]]], (37748 ^ _781013) ^ [] : [-(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))], (33888 ^ _781013) ^ [_1422893, _1422895, _1422897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422893), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422893)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1422895)), _1422897)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43763 ^ _781013) ^ [_1652806, _1652808] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1652806, _1652808)))], (1544 ^ _781013) ^ [_803055, _803057] : [-(class_Rings_Olinordered__semiring(_803055)), _803057 = _803055, class_Rings_Olinordered__semiring(_803057)], (17841 ^ _781013) ^ [_1114036, _1114038] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114036), _1114038))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114038), _1114036)))], (5691 ^ _781013) ^ [_871006, _871008, _871010] : [hAPP(c_Option_Ooption_OSome(_871006), _871008) = hAPP(c_Option_Ooption_OSome(_871006), _871010), -(_871008 = _871010)], (10983 ^ _781013) ^ [_975770, _975772, _975774, _975776, _975778, _975780] : [hAPP(_975770, _975772) = hAPP(c_Option_Ooption_OSome(_975774), _975776), -(hAPP(c_Map_Omap__add(_975778, _975774, _975780, _975770), _975772) = hAPP(c_Option_Ooption_OSome(_975774), _975776))], (5946 ^ _781013) ^ [_877119, _877121] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_877119, _877121))), -(hBOOL(hAPP(c_Com_OWT, _877121)))], (36344 ^ _781013) ^ [_1473856, _1473858, _1473860, _1473862] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1473856, _1473858), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1473860), _1473862))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1473856), _1473858), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1473862), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1473860)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1473860)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1473862), 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), _1473858), _1473862))))))], (49604 ^ _781013) ^ [_1789490, _1789492, _1789494, _1789496] : [class_Lattices_Osemilattice__sup(_1789490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1789490), _1789492)), hBOOL(hAPP(hAPP(c_member(_1789490), _1789494), _1789492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1789490), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1789490), _1789494), _1789496)), hAPP(hAPP(c_Finite__Set_Ofold(_1789490, _1789490, c_Lattices_Osemilattice__sup__class_Osup(_1789490)), _1789496), _1789492))))], (51598 ^ _781013) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (35025 ^ _781013) ^ [_1444094] : [-(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)))), _1444094) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1444094)))], (22414 ^ _781013) ^ [_1200816, _1200818, _1200820] : [class_Divides_Osemiring__div(_1200816), -(_1200818 = c_Groups_Ozero__class_Ozero(_1200816)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200816), _1200820), _1200818)), _1200818) = _1200820)], (11838 ^ _781013) ^ [_994504, _994506, _994508, _994510, _994512] : [c_Fun_Oinj__on(_994504, _994506, _994508, _994510), c_Fun_Oinj__on(_994504, _994506, _994508, _994512), -(c_Fun_Oinj__on(_994504, _994506, _994508, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994504, tc_HOL_Obool)), _994510), _994512)))], (17751 ^ _781013) ^ [_1112299, _1112301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112299), _1112301)), _1112299 = _1112301], (14600 ^ _781013) ^ [_1052122, _1052124] : [-(hAPP(c_Set_OCollect(_1052122), _1052124) = _1052124)], (36064 ^ _781013) ^ [_1468041, _1468043, _1468045] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468041, _1468041), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1468043), _1468045))), -(_1468041 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1468043 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (31894 ^ _781013) ^ [_1385386, _1385388, _1385390, _1385392, _1385394, _1385396] : [hBOOL(hAPP(hAPP(c_member(_1385386), _1385388), _1385390)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385386, tc_fun(_1385392, tc_HOL_Obool)), _1385390), hAPP(hAPP(c_COMBB(tc_fun(_1385392, tc_HOL_Obool), tc_fun(_1385392, tc_HOL_Obool), _1385386), hAPP(c_Set_Oinsert(_1385392), _1385394)), _1385396)) = hAPP(hAPP(c_Set_Oinsert(_1385392), _1385394), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385386, tc_fun(_1385392, tc_HOL_Obool)), _1385390), _1385396)))], (48521 ^ _781013) ^ [_1762069, _1762071] : [-(c_Transitive__Closure_Ortrancl(_1762069, c_Transitive__Closure_Otrancl(_1762069, _1762071)) = c_Transitive__Closure_Ortrancl(_1762069, _1762071))], (7762 ^ _781013) ^ [_911763, _911765] : [7763 ^ _781013 : [(7764 ^ _781013) ^ [_911816] : [hBOOL(hAPP(hAPP(c_member(_911763), _911816), _911765))]], _911765 = c_Orderings_Obot__class_Obot(tc_fun(_911763, tc_HOL_Obool))], (41082 ^ _781013) ^ [_1590463, _1590465, _1590467, _1590469] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1590463), _1590465)), 41088 ^ _781013 : [(41091 ^ _781013) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1590467), hAPP(_1590469, 41087 ^ [_1590463, _1590465, _1590467, _1590469])))], (41089 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590463), 41087 ^ [_1590463, _1590465, _1590467, _1590469]), _1590465)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1590463, _1590467)), hAPP(hAPP(c_Product__Type_OSigma(_1590463, _1590467), _1590465), _1590469))))], (18592 ^ _781013) ^ [_1127019, _1127021, _1127023, _1127025, _1127027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127019), _1127021)), -(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), _1127021), _1127023)), _1127025)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127019), _1127023)), _1127027)) = 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), _1127021), _1127019)), _1127023)), _1127025)), _1127027))], (22404 ^ _781013) ^ [_1200688, _1200690, _1200692] : [class_Divides_Osemiring__div(_1200688), -(_1200690 = c_Groups_Ozero__class_Ozero(_1200688)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200688), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200688), _1200690), _1200692)), _1200690) = _1200692)], (30305 ^ _781013) ^ [_1347260, _1347262, _1347264, _1347266] : [class_Orderings_Olinorder(_1347260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347260), _1347262), _1347264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347260), _1347262), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347260), _1347264), _1347266))))], (9951 ^ _781013) ^ [_956887, _956889, _956891] : [class_Lattices_Olattice(_956887), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956887), _956889), _956891) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956887), _956891), _956889))], (35663 ^ _781013) ^ [_1455726] : [class_Int_Onumber__ring(_1455726), -(hAPP(c_Int_Onumber__class_Onumber__of(_1455726), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1455726), c_Groups_Oone__class_Oone(_1455726)))], (38425 ^ _781013) ^ [_1519492, _1519494, _1519496, _1519498, _1519500, _1519502, _1519504] : [c_Typedef_Otype__definition(_1519492, _1519494, _1519496, _1519498, _1519500), hBOOL(hAPP(hAPP(c_member(_1519494), _1519502), _1519500)), hBOOL(hAPP(hAPP(c_member(_1519494), _1519504), _1519500)), 38436 ^ _781013 : [(38443 ^ _781013) ^ [] : [_1519502 = _1519504, -(hAPP(_1519498, _1519502) = hAPP(_1519498, _1519504))], (38437 ^ _781013) ^ [] : [hAPP(_1519498, _1519502) = hAPP(_1519498, _1519504), -(_1519502 = _1519504)]]], (12300 ^ _781013) ^ [_1003021, _1003023, _1003025] : [class_Lattices_Olattice(_1003021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003021), _1003023)), -(_1003025 = c_Orderings_Obot__class_Obot(tc_fun(_1003021, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1003021, tc_HOL_Obool)), _1003025), _1003023)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1003021), c_Big__Operators_Olattice__class_OInf__fin(_1003021, _1003025)), c_Big__Operators_Olattice__class_OInf__fin(_1003021, _1003023)) = c_Big__Operators_Olattice__class_OInf__fin(_1003021, _1003023))], (6542 ^ _781013) ^ [_888071, _888073] : [-(_888071 = hAPP(c_Option_Ooption_OSome(_888073), 6543 ^ [_888071, _888073])), -(_888071 = c_Option_Ooption_ONone(_888073))], (8335 ^ _781013) ^ [_924032, _924034] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_924032, tc_HOL_Obool)), _924034)), -(hBOOL(hAPP(hAPP(c_member(_924032), _924034), c_Orderings_Obot__class_Obot(tc_fun(_924032, tc_HOL_Obool)))))], (49049 ^ _781013) ^ [_1775498, _1775500, _1775502, _1775504, _1775506] : [c_Relation_Osingle__valued(_1775498, _1775500, hAPP(c_Relation_Oconverse(_1775500, _1775498), _1775502)), -(hAPP(c_Relation_OImage(_1775500, _1775498, _1775502), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1775500, tc_HOL_Obool)), _1775504), _1775506)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1775498, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1775500, _1775498, _1775502), _1775504)), hAPP(c_Relation_OImage(_1775500, _1775498, _1775502), _1775506)))], (37852 ^ _781013) ^ [_1505623, _1505625, _1505627, _1505629, _1505631, _1505633, _1505635] : [hBOOL(hAPP(_1505623, _1505625)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1505627, _1505627)), hAPP(hAPP(c_Product__Type_OPair(_1505627, _1505627), _1505629), _1505631)), hAPP(_1505633, _1505625))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1505635, _1505627), tc_prod(_1505635, _1505627))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1505635, _1505627), tc_prod(_1505635, _1505627)), hAPP(hAPP(c_Product__Type_OPair(_1505635, _1505627), _1505625), _1505629)), hAPP(hAPP(c_Product__Type_OPair(_1505635, _1505627), _1505625), _1505631))), c_Recdef_Osame__fst(_1505635, _1505627, _1505623, _1505633))))], (19795 ^ _781013) ^ [_1152089] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1152089)) = _1152089)], (27465 ^ _781013) ^ [_1293297, _1293299] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1293297, tc_HOL_Obool)), hAPP(c_Set_OPow(_1293297), _1293299))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1293297), _1293299)))], (42124 ^ _781013) ^ [_1614623, _1614625, _1614627, _1614629, _1614631] : [-(hAPP(hAPP(c_List_Odrop(_1614623), _1614625), hAPP(hAPP(c_List_Omap(_1614627, _1614623), _1614629), _1614631)) = hAPP(hAPP(c_List_Omap(_1614627, _1614623), _1614629), hAPP(hAPP(c_List_Odrop(_1614627), _1614625), _1614631)))], (41332 ^ _781013) ^ [_1595598] : [class_Groups_Omonoid__add(_1595598), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1595598), c_List_Olist_ONil(_1595598)) = c_Groups_Ozero__class_Ozero(_1595598))], (41344 ^ _781013) ^ [_1595812, _1595814, _1595816] : [-(hAPP(hAPP(c_Map_Omap__of(_1595812, _1595814), c_List_Olist_ONil(tc_prod(_1595812, _1595814))), _1595816) = c_Option_Ooption_ONone(_1595814))], (2306 ^ _781013) ^ [_815121, _815123, _815125, _815127] : [-(c_Int_Onat__aux(_815127, _815123) = c_Int_Onat__aux(_815125, _815121)), _815127 = _815125, _815123 = _815121], (49021 ^ _781013) ^ [_1774787, _1774789] : [-(c_Transitive__Closure_Otrancl(_1774787, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774787, _1774787), tc_HOL_Obool)), _1774789), c_Relation_OId(_1774787))) = c_Transitive__Closure_Ortrancl(_1774787, _1774789))], (42346 ^ _781013) ^ [_1619894, _1619896] : [-(_1619894 = c_List_Olist_ONil(_1619896)), -(hAPP(c_List_Ohd(_1619896), _1619894) = hAPP(hAPP(c_List_Onth(_1619896), _1619894), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27240 ^ _781013) ^ [_1288328, _1288330, _1288332] : [class_Orderings_Olinorder(_1288328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288328), _1288330), _1288332)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288328, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1288328), _1288330)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1288328, _1288330, _1288332)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1288328), _1288332))], (23489 ^ _781013) ^ [_1220628] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220628)) = _1220628)], (27607 ^ _781013) ^ [_1296217, _1296219, _1296221] : [class_Divides_Osemiring__div(_1296217), -(c_Divides_Odiv__class_Omod(_1296217, c_Divides_Odiv__class_Omod(_1296217, _1296219, _1296221), _1296221) = c_Divides_Odiv__class_Omod(_1296217, _1296219, _1296221))], (11079 ^ _781013) ^ [_977900, _977902, _977904, _977906] : [hBOOL(hAPP(hAPP(c_member(_977900), _977902), _977904)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977900, tc_HOL_Obool)), _977904), hAPP(hAPP(c_Set_Oinsert(_977900), _977902), _977906)) = hAPP(hAPP(c_Set_Oinsert(_977900), _977902), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977900, tc_HOL_Obool)), _977904), _977906)))], (35365 ^ _781013) ^ [_1450277] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1450277, 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, _1450277, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (48956 ^ _781013) ^ [_1773260, _1773262, _1773264] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773260, _1773260)), hAPP(hAPP(c_Product__Type_OPair(_1773260, _1773260), _1773262), _1773264)), c_Relation_OId(_1773260))), -(_1773262 = _1773264)], (28620 ^ _781013) ^ [_1314894, _1314896] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314894, _1314896)), _1314894)))], (16972 ^ _781013) ^ [_1096058, _1096060, _1096062, _1096064, _1096066] : [class_Groups_Ocomm__monoid__mult(_1096058), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096060), _1096062)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096060), _1096064)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096058), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1096060, _1096058), _1096066), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1096060, tc_HOL_Obool)), _1096062), _1096064))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1096060, _1096058), _1096066), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1096060, tc_HOL_Obool)), _1096062), _1096064))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096058), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1096060, _1096058), _1096066), _1096062)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1096060, _1096058), _1096066), _1096064)))], (24075 ^ _781013) ^ [_1230116, _1230118] : [-(_1230116 = hAPP(c_Int_Onat, _1230118)), 24078 ^ _781013 : [(24081 ^ _781013) ^ [] : [_1230118 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230116)], (24079 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230118)))]], 24082 ^ _781013 : [(24085 ^ _781013) ^ [] : [_1230116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24083 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230118))]]], (34615 ^ _781013) ^ [_1436806, _1436808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1436806)), c_Int_OBit0(_1436808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436806), _1436808)))], (13959 ^ _781013) ^ [_1037639, _1037641, _1037643, _1037645] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1037639), 13962 ^ _781013 : [(13969 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037639), _1037641), _1037645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037639), _1037641), _1037643)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037639), _1037645), _1037643))))], (13963 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037639), _1037641), _1037643)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037639), _1037645), _1037643))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037639), _1037641), _1037645)))]]], (41997 ^ _781013) ^ [_1611152, _1611154, _1611156, _1611158, _1611160, _1611162, _1611164] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611152, _1611152)), hAPP(hAPP(c_Product__Type_OPair(_1611152, _1611152), _1611154), _1611156)), _1611158)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611152), tc_List_Olist(_1611152))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611152), tc_List_Olist(_1611152)), hAPP(hAPP(c_List_Oappend(_1611152), _1611160), hAPP(hAPP(c_List_Olist_OCons(_1611152), _1611154), _1611162))), hAPP(hAPP(c_List_Oappend(_1611152), _1611160), hAPP(hAPP(c_List_Olist_OCons(_1611152), _1611156), _1611164)))), c_List_Olexord(_1611152, _1611158))))], (490 ^ _781013) ^ [_788568, _788570, _788572, _788574, _788576, _788578] : [-(c_Enum_Oall__n__lists(_788576, _788572, _788568)), c_Enum_Oall__n__lists(_788578, _788574, _788570), _788578 = _788576, _788574 = _788572, _788570 = _788568], (35657 ^ _781013) ^ [_1455629] : [class_Int_Onumber__ring(_1455629), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1455629), c_Groups_Oone__class_Oone(_1455629)) = hAPP(c_Int_Onumber__class_Onumber__of(_1455629), c_Int_OMin))], (49111 ^ _781013) ^ [_1776966, _1776968, _1776970, _1776972] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1776966, _1776968), tc_fun(_1776966, _1776968)), _1776970), c_Fun_Ocomp(_1776968, _1776968, _1776966, _1776972)) = c_Fun_Ocomp(_1776968, _1776968, _1776966, hAPP(hAPP(c_Nat_Ocompow(_1776968, _1776968), _1776970), _1776972)))], (30721 ^ _781013) ^ [_1356152, _1356154] : [class_Orderings_Olinorder(_1356152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356152), _1356154)), -(c_Big__Operators_Olattice_OSup__fin(_1356152, c_Orderings_Oord__class_Omax(_1356152), _1356154) = hAPP(c_Finite__Set_Ofold1(_1356152, c_Orderings_Oord__class_Omax(_1356152)), _1356154))], (8387 ^ _781013) ^ [_925386, _925388, _925390, _925392, _925394] : [hBOOL(hAPP(hAPP(c_member(_925386), _925388), _925390)), -(hBOOL(hAPP(hAPP(c_member(_925392), hAPP(_925394, _925388)), hAPP(c_Set_Oimage(_925386, _925392, _925394), _925390))))], (30393 ^ _781013) ^ [_1348971, _1348973] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1348971), _1348973)), _1348973) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1348971), _1348973))], (34679 ^ _781013) ^ [_1437942, _1437944] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1437942)), _1437944) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1437942), _1437944)))], (32414 ^ _781013) ^ [_1395913, _1395915, _1395917, _1395919] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395913), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1395913), _1395915), _1395917)), hAPP(c_Int_Onumber__class_Onumber__of(_1395913), _1395919)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1395913), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395913), _1395915), hAPP(c_Int_Onumber__class_Onumber__of(_1395913), _1395919))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395913), _1395917), hAPP(c_Int_Onumber__class_Onumber__of(_1395913), _1395919)))), class_Int_Onumber(_1395913), class_Rings_Osemiring(_1395913)], (47541 ^ _781013) ^ [_1740047, _1740049] : [class_Orderings_Olinorder(_1740047), hBOOL(hAPP(c_Finite__Set_Ofinite(_1740047), _1740049)), 47549 ^ _781013 : [(47552 ^ _781013) ^ [] : [-(c_List_Olinorder__class_Osorted(_1740047, 47548 ^ [_1740047, _1740049]))], (47554 ^ _781013) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1740047), 47548 ^ [_1740047, _1740049])))], (47556 ^ _781013) ^ [_1740373] : [-(_1740373 = 47548 ^ [_1740047, _1740049]), hAPP(c_List_Oset(_1740047), _1740373) = _1740049, c_List_Olinorder__class_Osorted(_1740047, _1740373), hBOOL(hAPP(c_List_Odistinct(_1740047), _1740373))], (47550 ^ _781013) ^ [] : [-(hAPP(c_List_Oset(_1740047), 47548 ^ [_1740047, _1740049]) = _1740049)]]], (2258 ^ _781013) ^ [_814365, _814367, _814369, _814371, _814373, _814375, _814377, _814379] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_814379, _814375, _814371, _814367) = c_Nat_Osemiring__1__class_Oof__nat__aux(_814377, _814373, _814369, _814365)), _814379 = _814377, _814375 = _814373, _814371 = _814369, _814367 = _814365], (50714 ^ _781013) ^ [_1811577] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1811577)))], (47948 ^ _781013) ^ [_1749658, _1749660, _1749662, _1749664, _1749666] : [_1749658 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1749660, _1749662, _1749658, _1749664), _1749666) = hAPP(c_Product__Type_OPair(_1749660, _1749662), _1749666))], (45882 ^ _781013) ^ [_1699062, _1699064, _1699066] : [class_Complete__Lattice_Ocomplete__lattice(_1699062), 45885 ^ _781013 : [(45886 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699062), _1699064), c_Complete__Lattice_OInf__class_OInf(_1699062, _1699066))), 45889 ^ _781013 : [(45890 ^ _781013) ^ [_1699220] : [hBOOL(hAPP(hAPP(c_member(_1699062), _1699220), _1699066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699062), _1699064), _1699220)))]]], (45896 ^ _781013) ^ [] : [45898 ^ _781013 : [(45901 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699062), _1699064), 45897 ^ [_1699062, _1699064, _1699066]))], (45899 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699062), 45897 ^ [_1699062, _1699064, _1699066]), _1699066)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699062), _1699064), c_Complete__Lattice_OInf__class_OInf(_1699062, _1699066))))]]], (42068 ^ _781013) ^ [_1613404, _1613406, _1613408, _1613410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613404), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613406)), _1613408))), -(hAPP(hAPP(c_List_Olist__update(_1613406, _1613408), _1613404), _1613410) = hAPP(hAPP(c_List_Oappend(_1613406), hAPP(hAPP(c_List_Otake(_1613406), _1613404), _1613408)), hAPP(hAPP(c_List_Olist_OCons(_1613406), _1613410), hAPP(hAPP(c_List_Odrop(_1613406), hAPP(c_Nat_OSuc, _1613404)), _1613408))))], (31478 ^ _781013) ^ [_1373916, _1373918, _1373920] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1373916, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1373916), _1373918), _1373920), -(_1373918 = c_Orderings_Obot__class_Obot(tc_fun(_1373916, tc_HOL_Obool)))], (23933 ^ _781013) ^ [_1227833, _1227835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227833), hAPP(c_Int_Onat, _1227835))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1227833)), _1227835)))], (21812 ^ _781013) ^ [_1190368, _1190370, _1190372] : [class_Rings_Osemiring__1(_1190368), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1190368), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1190370), _1190372)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1190368), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1190368), _1190370)), _1190372))], (45562 ^ _781013) ^ [_1691447, _1691449, _1691451, _1691453] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1691447, tc_HOL_Obool)), _1691449), _1691451)), hBOOL(hAPP(hAPP(c_member(_1691447), _1691453), _1691449)), -(hBOOL(hAPP(hAPP(c_member(_1691447), _1691453), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1691447, tc_HOL_Obool), _1691451))))], (24526 ^ _781013) ^ [_1238543, _1238545, _1238547] : [class_Fields_Olinordered__field__inverse__zero(_1238543), 24529 ^ _781013 : [(24544 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238543), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1238543), _1238545), _1238547)), c_Groups_Ozero__class_Ozero(_1238543)))), 24545 ^ _781013 : [(24552 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238543), _1238545), c_Groups_Ozero__class_Ozero(_1238543))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238543), c_Groups_Ozero__class_Ozero(_1238543)), _1238547))], (24546 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238543), c_Groups_Ozero__class_Ozero(_1238543)), _1238545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238543), _1238547), c_Groups_Ozero__class_Ozero(_1238543)))]]], (24530 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238543), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1238543), _1238545), _1238547)), c_Groups_Ozero__class_Ozero(_1238543))), 24535 ^ _781013 : [(24538 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238543), _1238547), c_Groups_Ozero__class_Ozero(_1238543))))], (24536 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238543), c_Groups_Ozero__class_Ozero(_1238543)), _1238545)))]], 24539 ^ _781013 : [(24542 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238543), c_Groups_Ozero__class_Ozero(_1238543)), _1238547)))], (24540 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238543), _1238545), c_Groups_Ozero__class_Ozero(_1238543))))]]]]], (39231 ^ _781013) ^ [_1538689, _1538691, _1538693, _1538695, _1538697, _1538699] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1538689)), _1538691) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1538693)), _1538695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538689, tc_HOL_Obool)), hAPP(c_List_Oset(_1538689), _1538691)), _1538697)), -(c_Map_Orestrict__map(_1538689, _1538693, c_Map_Omap__upds(_1538689, _1538693, _1538699, _1538691, _1538695), _1538697) = c_Map_Omap__upds(_1538689, _1538693, c_Map_Orestrict__map(_1538689, _1538693, _1538699, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1538689, tc_HOL_Obool)), _1538697), hAPP(c_List_Oset(_1538689), _1538691))), _1538691, _1538695))], (19306 ^ _781013) ^ [_1142616] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142616), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1142616)], (45295 ^ _781013) ^ [_1686143, _1686145] : [class_Enum_Oenum(_1686143), 45298 ^ _781013 : [(45299 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1686143)), _1686145)), -(hBOOL(hAPP(_1686145, c_Option_Ooption_ONone(_1686143)))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1686143), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1686143), tc_HOL_Obool, _1686143), _1686145), c_Option_Ooption_OSome(_1686143)))))], (45309 ^ _781013) ^ [] : [45310 ^ _781013 : [(45313 ^ _781013) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1686143), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1686143), tc_HOL_Obool, _1686143), _1686145), c_Option_Ooption_OSome(_1686143))))], (45311 ^ _781013) ^ [] : [hBOOL(hAPP(_1686145, c_Option_Ooption_ONone(_1686143)))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1686143)), _1686145)))]]], (45053 ^ _781013) ^ [_1681181, _1681183] : [class_Orderings_Olinorder(_1681181), -(c_List_Olinorder__class_Osort__key(_1681181, _1681181, c_COMBI(_1681181), _1681183) = hAPP(c_List_Ofoldl(tc_List_Olist(_1681181), _1681181, hAPP(c_COMBC(_1681181, tc_List_Olist(_1681181), tc_List_Olist(_1681181)), c_List_Olinorder__class_Oinsort__key(_1681181, _1681181, c_COMBI(_1681181))), c_List_Olist_ONil(_1681181)), _1681183))], (23367 ^ _781013) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16644 ^ _781013) ^ [_1089555, _1089557, _1089559] : [class_Groups_Oordered__comm__monoid__add(_1089555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089555), c_Groups_Ozero__class_Ozero(_1089555)), _1089557)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089555), c_Groups_Ozero__class_Ozero(_1089555)), _1089559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089555), c_Groups_Ozero__class_Ozero(_1089555)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089555), _1089557), _1089559))))], (1704 ^ _781013) ^ [_805055, _805057] : [-(class_Groups_Omonoid__mult(_805055)), _805057 = _805055, class_Groups_Omonoid__mult(_805057)], (832 ^ _781013) ^ [_793759, _793761] : [-(class_Lattices_Oab__semigroup__idem__mult(_793759)), _793761 = _793759, class_Lattices_Oab__semigroup__idem__mult(_793761)], (45029 ^ _781013) ^ [_1680628, _1680630, _1680632, _1680634] : [-(hAPP(c_List_Oset(tc_prod(_1680628, _1680630)), c_Enum_Oproduct(_1680628, _1680630, _1680632, _1680634)) = hAPP(hAPP(c_Product__Type_OSigma(_1680628, _1680630), hAPP(c_List_Oset(_1680628), _1680632)), hAPP(c_COMBK(tc_fun(_1680630, tc_HOL_Obool), _1680628), hAPP(c_List_Oset(_1680630), _1680634))))], (41224 ^ _781013) ^ [_1593679, _1593681, _1593683] : [hAPP(hAPP(c_List_Otake(_1593679), _1593681), _1593683) = c_List_Olist_ONil(_1593679), -(_1593681 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1593683 = c_List_Olist_ONil(_1593679))], (51206 ^ _781013) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (37828 ^ _781013) ^ [_1505237, _1505239, _1505241, _1505243] : [c_Equiv__Relations_Oequivp(_1505237, _1505239), hBOOL(hAPP(hAPP(_1505239, _1505241), _1505243)), -(hBOOL(hAPP(hAPP(_1505239, _1505243), _1505241)))], (27457 ^ _781013) ^ [_1293026, _1293028, _1293030, _1293032, _1293034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1293026, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1293028, _1293026, _1293030), _1293032)), _1293034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1293026, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1293028, tc_HOL_Obool), tc_fun(_1293026, tc_HOL_Obool), c_Set_Oimage(_1293028, _1293026, _1293030)), hAPP(c_Set_OPow(_1293028), _1293032))), hAPP(c_Set_OPow(_1293026), _1293034))))], (35769 ^ _781013) ^ [_1457285] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1457285), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1457285))], (36966 ^ _781013) ^ [_1486163, _1486165] : [-(_1486163 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1486165, _1486163) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1486165), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1486163)))], (24880 ^ _781013) ^ [_1244680, _1244682, _1244684, _1244686, _1244688] : [class_Fields_Olinordered__field(_1244680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244680), c_Groups_Ozero__class_Ozero(_1244680)), _1244682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244680), _1244682), _1244684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244680), c_Groups_Ozero__class_Ozero(_1244680)), _1244686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244680), _1244686), _1244688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244680), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1244680), _1244682), _1244688)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1244680), _1244684), _1244686))))], (45586 ^ _781013) ^ [_1691927, _1691929, _1691931, _1691933] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1691927, tc_fun(_1691929, tc_HOL_Obool)), _1691931), _1691933) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1691929, tc_HOL_Obool), hAPP(c_Set_Oimage(_1691927, tc_fun(_1691929, tc_HOL_Obool), _1691933), _1691931)))], (37466 ^ _781013) ^ [_1496321] : [-(hAPP(c_Int_Onat, _1496321) = 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, _1496321)), 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)))))))], (11584 ^ _781013) ^ [_989517, _989519, _989521, _989523, _989525] : [c_Fun_Oinj__on(_989517, _989519, _989521, c_Orderings_Otop__class_Otop(tc_fun(_989517, tc_HOL_Obool))), 11587 ^ _781013 : [(11594 ^ _781013) ^ [] : [_989523 = _989525, -(hAPP(_989521, _989523) = hAPP(_989521, _989525))], (11588 ^ _781013) ^ [] : [hAPP(_989521, _989523) = hAPP(_989521, _989525), -(_989523 = _989525)]]], (35831 ^ _781013) ^ [_1458389] : [-(c_Int_Oint__ge__less__than2(_1458389) = 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), _1458389)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (17531 ^ _781013) ^ [_1108600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108600), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5220 ^ _781013) ^ [_860640, _860642] : [_860642 = _860640, -(c_If(_860642) = c_If(_860640))], (39061 ^ _781013) ^ [_1534697, _1534699, _1534701] : [39063 ^ _781013 : [(39066 ^ _781013) ^ [] : [hBOOL(hAPP(_1534701, hAPP(hAPP(c_List_Onth(_1534697), _1534699), 39062 ^ [_1534697, _1534699, _1534701])))], (39064 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39062 ^ [_1534697, _1534699, _1534701]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1534697)), _1534699))))]], 39067 ^ _781013 : [(39068 ^ _781013) ^ [_1534899] : [hBOOL(hAPP(hAPP(c_member(_1534697), _1534899), hAPP(c_List_Oset(_1534697), _1534699))), -(hBOOL(hAPP(_1534701, _1534899)))]]], (37606 ^ _781013) ^ [_1499225, _1499227, _1499229, _1499231, _1499233, _1499235] : [hBOOL(hAPP(_1499225, _1499227)), hBOOL(hAPP(_1499229, _1499231)), 37613 ^ _781013 : [(37616 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1499229, hAPP(c_Product__Type_Osnd(_1499233, _1499235), hAPP(hAPP(c_Product__Type_OPair(_1499233, _1499235), _1499227), _1499231)))))], (37614 ^ _781013) ^ [] : [-(hBOOL(hAPP(_1499225, hAPP(c_Product__Type_Ofst(_1499233, _1499235), hAPP(hAPP(c_Product__Type_OPair(_1499233, _1499235), _1499227), _1499231)))))]]], (33950 ^ _781013) ^ [_1424252, _1424254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424252)), hAPP(c_Nat_OSuc, _1424254))), -(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(_1424252))), 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)), _1424254)))))], (276 ^ _781013) ^ [_785363, _785365, _785367, _785369] : [-(c_Int_Oiszero(_785367, _785363)), c_Int_Oiszero(_785369, _785365), _785369 = _785367, _785365 = _785363], (20889 ^ _781013) ^ [_1171508, _1171510] : [-(_1171508 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1171508), _1171510) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171508), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1171510)))], (50750 ^ _781013) ^ [_1812314, _1812316, _1812318, _1812320, _1812322, _1812324, _1812326] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1812314, _1812316, _1812318, _1812320, _1812322, _1812324, _1812326) = c_New__DSequence_Oneg__decr__bind(_1812314, _1812316, hAPP(hAPP(hAPP(_1812318, _1812322), _1812324), _1812326), hAPP(hAPP(c_COMBC(_1812314, 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(_1812316)))), hAPP(hAPP(c_COMBC(_1812314, 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(_1812316))))), hAPP(hAPP(c_COMBC(_1812314, 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(_1812316)))))), _1812320), _1812322)), _1812324)), _1812326)))], (19432 ^ _781013) ^ [_1144868, _1144870, _1144872] : [class_Rings_Olinordered__semidom(_1144868), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144868), c_Groups_Ozero__class_Ozero(_1144868)), _1144870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144868), c_Groups_Ozero__class_Ozero(_1144868)), hAPP(hAPP(c_Power_Opower__class_Opower(_1144868), _1144870), _1144872))))], (37806 ^ _781013) ^ [_1504819, _1504821] : [-(c_Equiv__Relations_Oequivp(_1504819, _1504821)), 37811 ^ _781013 : [(37814 ^ _781013) ^ [] : [hAPP(_1504821, 37807 ^ [_1504819, _1504821]) = hAPP(_1504821, 37808 ^ [_1504819, _1504821])], (37812 ^ _781013) ^ [] : [-(hBOOL(hAPP(hAPP(_1504821, 37807 ^ [_1504819, _1504821]), 37808 ^ [_1504819, _1504821])))]], 37815 ^ _781013 : [(37818 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(_1504821, 37807 ^ [_1504819, _1504821]), 37808 ^ [_1504819, _1504821]))], (37816 ^ _781013) ^ [] : [-(hAPP(_1504821, 37807 ^ [_1504819, _1504821]) = hAPP(_1504821, 37808 ^ [_1504819, _1504821]))]]], (44514 ^ _781013) ^ [_1669168, _1669170, _1669172] : [class_Orderings_Olinorder(_1669168), c_List_Olinorder__class_Osorted(_1669168, hAPP(c_List_Orev(_1669168), _1669170)), 44521 ^ _781013 : [(44528 ^ _781013) ^ [] : [-(_1669170 = c_List_Olist_ONil(_1669168)), -(c_List_Ofoldr(_1669168, _1669168, c_Orderings_Oord__class_Omax(_1669168), _1669170, _1669172) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1669168), hAPP(hAPP(c_List_Onth(_1669168), _1669170), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1669172))], (44522 ^ _781013) ^ [] : [_1669170 = c_List_Olist_ONil(_1669168), -(c_List_Ofoldr(_1669168, _1669168, c_Orderings_Oord__class_Omax(_1669168), _1669170, _1669172) = _1669172)]]], (12980 ^ _781013) ^ [_1016959, _1016961, _1016963, _1016965, _1016967] : [hAPP(c_Set_Oimage(_1016959, _1016961, _1016963), c_Orderings_Otop__class_Otop(tc_fun(_1016959, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1016961, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016959, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1016959, _1016961, _1016963), _1016965)), _1016967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016961, tc_HOL_Obool)), _1016965), hAPP(c_Set_Oimage(_1016959, _1016961, _1016963), _1016967))))], (3816 ^ _781013) ^ [_838724, _838726, _838728, _838730] : [-(c_Wellfounded_Omax__ext(_838730, _838726) = c_Wellfounded_Omax__ext(_838728, _838724)), _838730 = _838728, _838726 = _838724], (19394 ^ _781013) ^ [_1144129, _1144131, _1144133] : [class_Groups_Omonoid__mult(_1144129), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144129), hAPP(hAPP(c_Power_Opower__class_Opower(_1144129), _1144131), _1144133)), _1144131) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144129), _1144131), hAPP(hAPP(c_Power_Opower__class_Opower(_1144129), _1144131), _1144133)))], (12956 ^ _781013) ^ [_1016390, _1016392, _1016394, _1016396, _1016398] : [hBOOL(hAPP(hAPP(c_member(_1016390), _1016392), hAPP(c_Set_Ovimage(_1016390, _1016394, _1016396), hAPP(hAPP(c_Set_Oinsert(_1016394), _1016398), c_Orderings_Obot__class_Obot(tc_fun(_1016394, tc_HOL_Obool)))))), -(hAPP(_1016396, _1016392) = _1016398)], (10233 ^ _781013) ^ [_962054, _962056, _962058] : [class_Groups_Oordered__ab__group__add(_962054), 10236 ^ _781013 : [(10243 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962054), hAPP(c_Groups_Ouminus__class_Ouminus(_962054), _962058)), _962056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962054), hAPP(c_Groups_Ouminus__class_Ouminus(_962054), _962056)), _962058)))], (10237 ^ _781013) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962054), hAPP(c_Groups_Ouminus__class_Ouminus(_962054), _962056)), _962058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962054), hAPP(c_Groups_Ouminus__class_Ouminus(_962054), _962058)), _962056)))]]], (33836 ^ _781013) ^ [_1421970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1421970)), -(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), _1421970))))], (7649 ^ _781013) ^ [_909680, _909682, _909684, _909686, _909688, _909690] : [-(_909680 = _909682), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909684, _909686), _909688), _909682), _909690), _909680) = hAPP(_909688, _909680))], (7711 ^ _781013) ^ [_910820, _910822, _910824] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_910820), _910822)), hBOOL(hAPP(c_Finite__Set_Ofinite(_910820), _910824)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_910820), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910820, tc_HOL_Obool)), _910822), _910824))))], (9241 ^ _781013) ^ [_944517, _944519, _944521, _944523, _944525] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_944517, _944517, _944519, _944521, _944523), _944525)), -(hBOOL(hAPP(hAPP(c_member(_944517), _944521), _944523))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_944517, _944519, hAPP(hAPP(c_Set_Oinsert(_944517), _944521), _944523)), _944525)))], (42647 ^ _781013) ^ [_1626244, _1626246, _1626248] : [_1626244 = c_List_Olist_ONil(_1626246), -(c_List_Olast(_1626246, hAPP(hAPP(c_List_Olist_OCons(_1626246), _1626248), _1626244)) = _1626248)]], input).
% 48.35/47.06 ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY, v_pname))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))],start(51718 ^ 0)).
% 48.35/47.06 ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY, v_pname))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))],extension(51710 ^ 1,bind([[_1826088], [v_pname]]))).
% 48.35/47.06 ncf('1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))), hAPP(c_Com_Obody, v_pname) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y)],extension(8100 ^ 2,bind([[_918838, _918840, _918842, _918844, _918846], [c_Com_Obody, v_pname, tc_Com_Ocom, v_y, tc_Com_Opname]]))).
% 48.35/47.06 ncf('1.1.1.1',plain,[-(hAPP(c_Com_Obody, v_pname) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))],extension(51716 ^ 3)).
% 48.35/47.06 %-----------------------------------------------------
% 48.35/47.06 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------