TSTP Solution File: SWW382+1 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW382+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n009.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 12:26:04 EDT 2023
% Result : Theorem 226.14s 217.81s
% Output : Proof 226.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWW382+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.14 % Command : nanocop.sh %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 22:14:48 EDT 2023
% 0.15/0.36 % CPUTime :
% 226.14/217.81
% 226.14/217.81 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 226.14/217.81 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 226.14/217.81 %-----------------------------------------------------
% 226.14/217.81 ncf(matrix, plain, [(51671 ^ _2062105) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, v_y)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))], !, (4548 ^ _780119) ^ [_849104, _849106] : [_849106 = _849104, -(c_New__DSequence_Opos__empty(_849106) = c_New__DSequence_Opos__empty(_849104))], (27216 ^ _780119) ^ [_1282671, _1282673, _1282675] : [class_Groups_Olinordered__ab__semigroup__add(_1282671), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282671), _1282673)), -(_1282673 = c_Orderings_Obot__class_Obot(tc_fun(_1282671, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1282671), _1282675), c_Big__Operators_Olinorder__class_OMax(_1282671, _1282673)) = c_Big__Operators_Olinorder__class_OMax(_1282671, hAPP(c_Set_OCollect(_1282671), hAPP(hAPP(c_COMBB(tc_fun(_1282671, tc_HOL_Obool), tc_HOL_Obool, _1282671), c_HOL_OEx(_1282671)), hAPP(hAPP(c_COMBC(_1282671, tc_fun(_1282671, tc_HOL_Obool), tc_fun(_1282671, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1282671, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1282671, tc_HOL_Obool), tc_fun(_1282671, tc_HOL_Obool)), _1282671), c_COMBS(_1282671, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1282671, tc_HOL_Obool), tc_fun(_1282671, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1282671), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1282671), c_fconj)), hAPP(hAPP(c_COMBC(_1282671, tc_fun(_1282671, _1282671), tc_fun(_1282671, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1282671, tc_HOL_Obool), tc_fun(tc_fun(_1282671, _1282671), tc_fun(_1282671, tc_HOL_Obool)), _1282671), c_COMBB(_1282671, tc_HOL_Obool, _1282671)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1282671), _1282675))))), hAPP(hAPP(c_COMBC(_1282671, tc_fun(_1282671, tc_HOL_Obool), tc_HOL_Obool), c_member(_1282671)), _1282673))))))], (34873 ^ _780119) ^ [_1434887, _1434889, _1434891, _1434893, _1434895] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1434887, _1434889, _1434891), _1434893), _1434895) = hAPP(hAPP(_1434893, hAPP(c_Product__Type_Ofst(_1434887, _1434889), _1434895)), hAPP(c_Product__Type_Osnd(_1434887, _1434889), _1434895)))], (38552 ^ _780119) ^ [_1526045, _1526047, _1526049, _1526051] : [38554 ^ _780119 : [(38557 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1526045, _1526045, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1526045, tc_fun(_1526045, _1526047), tc_fun(_1526045, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526047, tc_HOL_Obool), tc_fun(tc_fun(_1526045, _1526047), tc_fun(_1526045, tc_HOL_Obool)), _1526045), c_COMBB(_1526047, tc_HOL_Obool, _1526045)), hAPP(hAPP(c_COMBB(_1526047, tc_fun(_1526047, tc_HOL_Obool), _1526045), c_fequal), _1526051))), _1526051)), 38553 ^ [_1526045, _1526047, _1526049, _1526051]))], (38555 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526045, _1526045)), 38553 ^ [_1526045, _1526047, _1526049, _1526051]), _1526049)))]], -(c_Equiv__Relations_Ocongruent(_1526045, _1526047, _1526049, _1526051))], (28214 ^ _780119) ^ [_1301699] : [class_Orderings_Olinorder(_1301699), -(c_Finite__Set_Ofun__left__comm__idem(_1301699, _1301699, c_Orderings_Oord__class_Omax(_1301699)))], (21214 ^ _780119) ^ [_1166084, _1166086, _1166088, _1166090] : [class_Fields_Olinordered__field(_1166084), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166084), c_Groups_Ozero__class_Ozero(_1166084)), _1166086)), 21221 ^ _780119 : [(21228 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166084), _1166088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166084), _1166090), _1166086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166084), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166084), _1166088), _1166086)), _1166090)))], (21222 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166084), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166084), _1166088), _1166086)), _1166090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166084), _1166088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166084), _1166090), _1166086))))]]], (51563 ^ _780119) ^ [_1820350, _1820352] : [hBOOL(hAPP(hAPP(c_fequal, _1820350), _1820352)), -(_1820350 = _1820352)], (11690 ^ _780119) ^ [_990663, _990665, _990667] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990663), _990665)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990667), _990665)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990663), _990667))], (50294 ^ _780119) ^ [_1799489, _1799491, _1799493, _1799495, _1799497] : [-(_1799489 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1799491, _1799493, _1799495, _1799497), _1799489) = c_Lazy__Sequence_Ohb__bind(_1799491, _1799493, hAPP(_1799495, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1799489), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1799491, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1799493))), _1799497), _1799489)))], (15158 ^ _780119) ^ [_1057473, _1057475] : [class_Groups_Ogroup__add(_1057473), 15161 ^ _780119 : [(15168 ^ _780119) ^ [] : [_1057475 = c_Groups_Ozero__class_Ozero(_1057473), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1057473), _1057475) = c_Groups_Ozero__class_Ozero(_1057473))], (15162 ^ _780119) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1057473), _1057475) = c_Groups_Ozero__class_Ozero(_1057473), -(_1057475 = c_Groups_Ozero__class_Ozero(_1057473))]]], (22093 ^ _780119) ^ [_1183636, _1183638] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183636))), -(c_SMT_Oz3mod(_1183638, _1183636) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183638, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183636)))], (13734 ^ _780119) ^ [_1029789, _1029791, _1029793] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029789)), _1029791) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029789)), _1029793), -(_1029791 = _1029793)], (46406 ^ _780119) ^ [_1715461, _1715463, _1715465] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1715461)), _1715463), c_List_Olists(_1715461, _1715465))), -(_1715463 = c_List_Olist_ONil(_1715461)), 46415 ^ _780119 : [(46418 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715461), 46413 ^ [_1715461, _1715463, _1715465]), _1715465)))], (46420 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1715461)), 46414 ^ [_1715461, _1715463, _1715465]), c_List_Olists(_1715461, _1715465))))], (46416 ^ _780119) ^ [] : [-(_1715463 = hAPP(hAPP(c_List_Olist_OCons(_1715461), 46413 ^ [_1715461, _1715463, _1715465]), 46414 ^ [_1715461, _1715463, _1715465]))]]], (24146 ^ _780119) ^ [_1222170, _1222172] : [24154 ^ _780119 : [(24157 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1222172, 24153 ^ [_1222170, _1222172])))], (24155 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24153 ^ [_1222170, _1222172]), _1222170)))]], 24147 ^ _780119 : [(24148 ^ _780119) ^ [_1222238] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1222238), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1222170))), hBOOL(hAPP(_1222172, _1222238))]]], (44086 ^ _780119) ^ [_1661978, _1661980, _1661982] : [-(hBOOL(hAPP(hAPP(c_member(_1661978), _1661980), hAPP(c_List_Oset(_1661978), _1661982)))), 44087 ^ _780119 : [(44088 ^ _780119) ^ [_1662052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662052), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661978)), _1661982))), hAPP(hAPP(c_List_Onth(_1661978), _1661982), _1662052) = _1661980]]], (33805 ^ _780119) ^ [_1414175, _1414177, _1414179, _1414181, _1414183] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1414175, _1414177), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1414179), _1414181))), -(_1414177 = 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), _1414183), _1414175), _1414177), 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), _1414183), _1414179)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1414183), _1414181)), _1414177))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1414183), _1414181), _1414177)))))], (24172 ^ _780119) ^ [_1222673, _1222675] : [24174 ^ _780119 : [(24177 ^ _780119) ^ [] : [hBOOL(hAPP(_1222675, 24173 ^ [_1222673, _1222675]))], (24175 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24173 ^ [_1222673, _1222675]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1222673))))]], 24178 ^ _780119 : [(24179 ^ _780119) ^ [_1222826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1222826), _1222673)), -(hBOOL(hAPP(_1222675, _1222826)))]]], (36848 ^ _780119) ^ [_1480709, _1480711, _1480713, _1480715, _1480717] : [c_Fun_Oinj__on(_1480709, _1480711, _1480713, _1480715), hBOOL(hAPP(hAPP(c_member(_1480709), _1480717), _1480715)), -(hAPP(c_Fun_Othe__inv__into(_1480709, _1480711, _1480715, _1480713), hAPP(_1480713, _1480717)) = _1480717)], (28754 ^ _780119) ^ [_1311356] : [class_Orderings_Oord(_1311356), -(c_Orderings_Oord__class_Omin(_1311356) = c_Orderings_Oord_Omin(_1311356, c_Orderings_Oord__class_Oless__eq(_1311356)))], (9654 ^ _780119) ^ [_947072, _947074, _947076] : [class_Lattices_Olattice(_947072), hBOOL(hAPP(c_Finite__Set_Ofinite(_947072), _947074)), hBOOL(hAPP(c_Finite__Set_Ofinite(_947072), _947076)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947072, tc_HOL_Obool)), _947074), _947076) = c_Orderings_Obot__class_Obot(tc_fun(_947072, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_947072), c_Big__Operators_Olattice__class_OSup__fin(_947072, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_947072, tc_HOL_Obool)), _947074), _947076))), c_Big__Operators_Olattice__class_OSup__fin(_947072, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947072, tc_HOL_Obool)), _947074), _947076))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_947072), c_Big__Operators_Olattice__class_OSup__fin(_947072, _947074)), c_Big__Operators_Olattice__class_OSup__fin(_947072, _947076)))], (33505 ^ _780119) ^ [_1403893, _1403895] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1403893), hAPP(hAPP(c_Power_Opower__class_Opower(_1403893), hAPP(c_Int_Onumber__class_Onumber__of(_1403893), c_Int_OMin)), _1403895)) = c_Groups_Oone__class_Oone(_1403893)), class_Int_Onumber__ring(_1403893), class_Rings_Olinordered__idom(_1403893)], (8130 ^ _780119) ^ [_919511, _919513, _919515, _919517, _919519] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919511, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919511, tc_HOL_Obool)), hAPP(c_Set_Oimage(_919513, _919511, _919515), _919517)), hAPP(c_Set_Oimage(_919513, _919511, _919515), _919519))), hAPP(c_Set_Oimage(_919513, _919511, _919515), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919513, tc_HOL_Obool)), _919517), _919519)))))], (27868 ^ _780119) ^ [_1294708, _1294710, _1294712, _1294714] : [class_Orderings_Olinorder(_1294708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294708), _1294710), _1294712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294708), _1294710), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1294708), _1294712), _1294714))))], (39455 ^ _780119) ^ [_1547537, _1547539] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547537, _1547537), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1547537, _1547539)), hAPP(hAPP(c_Product__Type_OSigma(_1547537, _1547537), hAPP(c_Relation_OField(_1547537), _1547539)), hAPP(c_COMBK(tc_fun(_1547537, tc_HOL_Obool), _1547537), hAPP(c_Relation_OField(_1547537), _1547539))))))], (49506 ^ _780119) ^ [_1783300, _1783302, _1783304, _1783306, _1783308] : [class_Orderings_Olinorder(_1783300), 49512 ^ _780119 : [(49515 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1783300), hAPP(_1783306, _1783308)), hAPP(_1783306, 49511 ^ [_1783300, _1783302, _1783304, _1783306, _1783308])))], (49513 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1783302), 49511 ^ [_1783300, _1783302, _1783304, _1783306, _1783308]), hAPP(c_List_Oset(_1783302), _1783304))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1783302, _1783300, _1783306), _1783308), _1783304) = hAPP(hAPP(c_List_Olist_OCons(_1783302), _1783308), _1783304))], (40804 ^ _780119) ^ [_1580179, _1580181, _1580183] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1580179), _1580181)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1580179, tc_HOL_Obool)), _1580183), _1580181) = hAPP(hAPP(c_Finite__Set_Ofold(_1580179, tc_fun(_1580179, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1580179, tc_HOL_Obool), tc_fun(tc_fun(_1580179, tc_HOL_Obool), tc_fun(_1580179, tc_HOL_Obool)), _1580179), hAPP(c_COMBC(tc_fun(_1580179, tc_HOL_Obool), tc_fun(_1580179, tc_HOL_Obool), tc_fun(_1580179, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1580179, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1580179, tc_fun(_1580179, tc_HOL_Obool), tc_fun(_1580179, tc_HOL_Obool)), c_Set_Oinsert(_1580179)), c_Orderings_Obot__class_Obot(tc_fun(_1580179, tc_HOL_Obool))))), _1580183), _1580181))], (51227 ^ _780119) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (24725 ^ _780119) ^ [] : [-(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)))], (47528 ^ _780119) ^ [_1738544, _1738546] : [-(hAPP(c_List_Orev(_1738544), _1738546) = hAPP(c_List_Ofoldl(tc_List_Olist(_1738544), _1738544, hAPP(c_COMBC(_1738544, tc_List_Olist(_1738544), tc_List_Olist(_1738544)), c_List_Olist_OCons(_1738544)), c_List_Olist_ONil(_1738544)), _1738546))], (45710 ^ _780119) ^ [_1700236, _1700238, _1700240, _1700242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1700236), _1700238)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700240)), _1700242))), -(hAPP(hAPP(c_List_Onth(_1700240), hAPP(hAPP(c_List_Odrop(_1700240), _1700236), _1700242)), _1700238) = hAPP(hAPP(c_List_Onth(_1700240), _1700242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1700236), _1700238)))], (18306 ^ _780119) ^ [_1113980, _1113982] : [class_Groups_Olinordered__ab__group__add(_1113980), 18309 ^ _780119 : [(18316 ^ _780119) ^ [] : [_1113982 = c_Groups_Ozero__class_Ozero(_1113980), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113980), _1113982), _1113982) = c_Groups_Ozero__class_Ozero(_1113980))], (18310 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113980), _1113982), _1113982) = c_Groups_Ozero__class_Ozero(_1113980), -(_1113982 = c_Groups_Ozero__class_Ozero(_1113980))]]], (46143 ^ _780119) ^ [_1709835, _1709837] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1709835), hAPP(c_List_Oset(tc_Nat_Onat), _1709837))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1709835), 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)), _1709837))))], (44538 ^ _780119) ^ [_1672352] : [-(hAPP(c_Code__Numeral_Onat__of, _1672352) = c_Code__Numeral_Onat__of__aux(_1672352, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51275 ^ _780119) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (37577 ^ _780119) ^ [_1499545] : [-(c_Nitpick_Oone__frac(_1499545) = c_Nitpick_OAbs__Frac(_1499545, 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))))], (46975 ^ _780119) ^ [_1727261, _1727263, _1727265] : [class_Orderings_Olinorder(_1727261), 46978 ^ _780119 : [(46985 ^ _780119) ^ [] : [c_List_Olinorder__class_Osorted(_1727261, _1727265), -(c_List_Olinorder__class_Osorted(_1727261, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1727261, _1727261, c_COMBI(_1727261)), _1727263), _1727265)))], (46979 ^ _780119) ^ [] : [c_List_Olinorder__class_Osorted(_1727261, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1727261, _1727261, c_COMBI(_1727261)), _1727263), _1727265)), -(c_List_Olinorder__class_Osorted(_1727261, _1727265))]]], (914 ^ _780119) ^ [_794066, _794068, _794070, _794072] : [-(c_FunDef_Ois__measure(_794070, _794066)), c_FunDef_Ois__measure(_794072, _794068), _794072 = _794070, _794068 = _794066], (23008 ^ _780119) ^ [] : [-(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))], (51069 ^ _780119) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (50546 ^ _780119) ^ [_1805535, _1805537, _1805539, _1805541] : [hBOOL(hAPP(hAPP(c_member(_1805535), _1805537), hAPP(c_List_Oset(_1805535), c_List_Oreplicate(_1805535, _1805539, _1805541)))), 50549 ^ _780119 : [(50552 ^ _780119) ^ [] : [_1805539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50550 ^ _780119) ^ [] : [-(_1805537 = _1805541)]]], (25185 ^ _780119) ^ [_1241097, _1241099, _1241101] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1241097), _1241099), _1241101) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1241097), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1241097, tc_Int_Oint), _1241099), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1241101))), class_Groups_Ocomm__monoid__add(_1241097), class_Groups_Ocomm__monoid__mult(_1241097)], (18818 ^ _780119) ^ [_1123218, _1123220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123218), _1123220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1123218), _1123220)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35029 ^ _780119) ^ [_1437980, _1437982, _1437984, _1437986, _1437988, _1437990] : [-(c_Product__Type_Oprod_Oprod__rec(_1437980, _1437982, _1437984, _1437986, hAPP(hAPP(c_Product__Type_OPair(_1437980, _1437982), _1437988), _1437990)) = hAPP(hAPP(_1437986, _1437988), _1437990))], (45239 ^ _780119) ^ [_1687233, _1687235, _1687237, _1687239] : [-(hAPP(hAPP(c_List_Otake(_1687233), _1687235), hAPP(hAPP(c_List_Oappend(_1687233), _1687237), _1687239)) = hAPP(hAPP(c_List_Oappend(_1687233), hAPP(hAPP(c_List_Otake(_1687233), _1687235), _1687237)), hAPP(hAPP(c_List_Otake(_1687233), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1687235), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687233)), _1687237))), _1687239)))], (45886 ^ _780119) ^ [_1704196, _1704198] : [hBOOL(hAPP(c_List_Odistinct(_1704196), _1704198)), -(hBOOL(hAPP(c_List_Odistinct(_1704196), hAPP(c_List_Otl(_1704196), _1704198))))], (47389 ^ _780119) ^ [_1735174, _1735176, _1735178] : [47390 ^ _780119 : [(47393 ^ _780119) ^ [] : [_1735178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47391 ^ _780119) ^ [] : [-(_1735174 = c_List_Olist_ONil(tc_List_Olist(_1735176)))]], 47397 ^ _780119 : [(47400 ^ _780119) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735176)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1735176)), _1735174), 47396 ^ [_1735174, _1735176, _1735178])) = _1735178], (47398 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47396 ^ [_1735174, _1735176, _1735178]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1735176))), _1735174))))]], -(c_List_Otranspose(_1735176, _1735174) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1735176)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1735176)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1735176), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1735176)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1735176)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1735176), hAPP(hAPP(c_COMBB(tc_List_Olist(_1735176), tc_fun(tc_Nat_Onat, _1735176), tc_Nat_Onat), c_List_Onth(_1735176)), hAPP(c_List_Onth(tc_List_Olist(_1735176)), _1735174))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1735176))), _1735174)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1735178)))], (47825 ^ _780119) ^ [_1746447, _1746449, _1746451] : [hBOOL(hAPP(c_List_Odistinct(_1746447), _1746449)), -(hBOOL(hAPP(c_List_Odistinct(_1746447), c_List_OtakeWhile(_1746447, _1746451, _1746449))))], (6143 ^ _780119) ^ [_878056, _878058, _878060] : [-(hBOOL(hAPP(hAPP(c_member(_878056), _878058), hAPP(hAPP(c_Set_Oinsert(_878056), _878058), _878060))))], (3394 ^ _780119) ^ [_831091, _831093] : [_831093 = _831091, -(c_Code__Numeral_OSuc__code__numeral(_831093) = c_Code__Numeral_OSuc__code__numeral(_831091))], (480 ^ _780119) ^ [_787541, _787543, _787545, _787547] : [-(c_Relation_Oirrefl(_787545, _787541)), c_Relation_Oirrefl(_787547, _787543), _787547 = _787545, _787543 = _787541], (24233 ^ _780119) ^ [_1223814, _1223816, _1223818, _1223820] : [class_Orderings_Oorder(_1223814), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1223814, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1223814, _1223816, _1223818)), c_SetInterval_Oord__class_OatLeastAtMost(_1223814, _1223818, _1223820)) = c_Orderings_Obot__class_Obot(tc_fun(_1223814, tc_HOL_Obool)))], (28748 ^ _780119) ^ [_1311269] : [class_Orderings_Oord(_1311269), -(c_Orderings_Oord__class_Omax(_1311269) = c_Orderings_Oord_Omax(_1311269, c_Orderings_Oord__class_Oless__eq(_1311269)))], (37702 ^ _780119) ^ [_1503098, _1503100, _1503102, _1503104] : [hBOOL(hAPP(hAPP(c_member(_1503098), _1503104), hAPP(c_Relation_ODomain(_1503098, _1503100), _1503102))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1503098, _1503100, hAPP(hAPP(c_COMBC(_1503098, tc_fun(tc_prod(_1503098, _1503100), tc_HOL_Obool), tc_fun(_1503100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503100, tc_fun(tc_fun(tc_prod(_1503098, _1503100), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1503098, _1503100), tc_HOL_Obool), tc_fun(_1503100, tc_HOL_Obool)), _1503098), c_COMBC(_1503100, tc_fun(tc_prod(_1503098, _1503100), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503100, tc_prod(_1503098, _1503100)), tc_fun(_1503100, tc_fun(tc_fun(tc_prod(_1503098, _1503100), tc_HOL_Obool), tc_HOL_Obool)), _1503098), hAPP(c_COMBB(tc_prod(_1503098, _1503100), tc_fun(tc_fun(tc_prod(_1503098, _1503100), tc_HOL_Obool), tc_HOL_Obool), _1503100), c_member(tc_prod(_1503098, _1503100)))), c_Product__Type_OPair(_1503098, _1503100)))), _1503102)), _1503104)))], (45464 ^ _780119) ^ [_1693886, _1693888, _1693890, _1693892, _1693894, _1693896] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693886), tc_List_Olist(_1693886))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693886), tc_List_Olist(_1693886)), hAPP(hAPP(c_List_Olist_OCons(_1693886), _1693888), _1693890)), hAPP(hAPP(c_List_Olist_OCons(_1693886), _1693892), _1693894))), c_List_Olistrel1(_1693886, _1693896))), 45469 ^ _780119 : [(45472 ^ _780119) ^ [] : [-(_1693890 = _1693894)], (45470 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1693886, _1693886)), hAPP(hAPP(c_Product__Type_OPair(_1693886, _1693886), _1693888), _1693892)), _1693896)))]], 45473 ^ _780119 : [(45476 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693886), tc_List_Olist(_1693886))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693886), tc_List_Olist(_1693886)), _1693890), _1693894)), c_List_Olistrel1(_1693886, _1693896))))], (45474 ^ _780119) ^ [] : [-(_1693888 = _1693892)]]], (15612 ^ _780119) ^ [_1064594, _1064596, _1064598] : [class_Groups_Oordered__comm__monoid__add(_1064594), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064594), c_Groups_Ozero__class_Ozero(_1064594)), _1064596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064594), c_Groups_Ozero__class_Ozero(_1064594)), _1064598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064594), c_Groups_Ozero__class_Ozero(_1064594)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064594), _1064596), _1064598))))], (11798 ^ _780119) ^ [_992467, _992469] : [_992467 = _992469, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992467), _992469)))], (39837 ^ _780119) ^ [_1557138] : [-(hAPP(c_Relation_ORange(_1557138, _1557138), c_Relation_OId(_1557138)) = c_Orderings_Otop__class_Otop(tc_fun(_1557138, tc_HOL_Obool)))], (50033 ^ _780119) ^ [_1794522, _1794524, _1794526] : [c_FunDef_Ois__measure(_1794522, _1794524), -(c_FunDef_Ois__measure(tc_prod(_1794522, _1794526), hAPP(hAPP(c_COMBB(_1794522, tc_Nat_Onat, tc_prod(_1794522, _1794526)), _1794524), c_Product__Type_Ofst(_1794522, _1794526))))], (20662 ^ _780119) ^ [_1155763, _1155765, _1155767, _1155769, _1155771] : [class_Fields_Olinordered__field(_1155763), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155763), c_Groups_Ozero__class_Ozero(_1155763)), _1155765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155763), _1155765), _1155767)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155763), c_Groups_Ozero__class_Ozero(_1155763)), _1155769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155763), _1155769), _1155771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155763), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155763), _1155765), _1155771)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155763), _1155767), _1155769))))], (21446 ^ _780119) ^ [_1170881, _1170883, _1170885, _1170887] : [class_Divides_Osemiring__div(_1170881), -(c_Divides_Odiv__class_Omod(_1170881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170881), _1170883), _1170885), _1170887) = c_Divides_Odiv__class_Omod(_1170881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170881), _1170883), c_Divides_Odiv__class_Omod(_1170881, _1170885, _1170887)), _1170887))], (50927 ^ _780119) ^ [_1813545, _1813547, _1813549] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1813545, _1813547, _1813549) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1813545)], (2674 ^ _780119) ^ [_819741, _819743, _819745, _819747] : [-(c_Predicate_OPowp(_819747, _819743) = c_Predicate_OPowp(_819745, _819741)), _819747 = _819745, _819743 = _819741], (51165 ^ _780119) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (10578 ^ _780119) ^ [_967267, _967269, _967271, _967273, _967275, _967277] : [hBOOL(hAPP(hAPP(c_member(_967267), _967269), _967271)), -(c_Map_Orestrict__map(_967267, _967273, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_967267, tc_Option_Ooption(_967273)), _967275), _967269), _967277), _967271) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_967267, tc_Option_Ooption(_967273)), c_Map_Orestrict__map(_967267, _967273, _967275, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967267, tc_HOL_Obool)), _967271), hAPP(hAPP(c_Set_Oinsert(_967267), _967269), c_Orderings_Obot__class_Obot(tc_fun(_967267, tc_HOL_Obool)))))), _967269), _967277))], (35495 ^ _780119) ^ [_1450272, _1450274, _1450276] : [-(hAPP(c_Relation_OField(_1450272), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1450272, _1450272), tc_HOL_Obool)), _1450274), _1450276)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450272, tc_HOL_Obool)), hAPP(c_Relation_OField(_1450272), _1450274)), hAPP(c_Relation_OField(_1450272), _1450276)))], (40285 ^ _780119) ^ [_1568299, _1568301, _1568303] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568299, _1568299)), _1568301), c_Transitive__Closure_Otrancl(_1568299, _1568303)))), 40286 ^ _780119 : [(40287 ^ _780119) ^ [_1568378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1568378)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568299, _1568299)), _1568301), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1568299, _1568299), tc_HOL_Obool), _1568378), _1568303)))]]], (43410 ^ _780119) ^ [_1643181, _1643183, _1643185, _1643187] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643181), tc_List_Olist(_1643181))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643181), tc_List_Olist(_1643181)), _1643183), _1643185)), c_List_Olistrel(_1643181, _1643187))), 43413 ^ _780119 : [(43416 ^ _780119) ^ [_1643517] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643181, _1643181)), _1643517), hAPP(c_List_Oset(tc_prod(_1643181, _1643181)), hAPP(hAPP(c_List_Ozip(_1643181, _1643181), _1643183), _1643185)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1643181, _1643181, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1643181, tc_fun(tc_prod(_1643181, _1643181), tc_HOL_Obool), tc_fun(_1643181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1643181, tc_fun(tc_fun(tc_prod(_1643181, _1643181), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1643181, _1643181), tc_HOL_Obool), tc_fun(_1643181, tc_HOL_Obool)), _1643181), c_COMBC(_1643181, tc_fun(tc_prod(_1643181, _1643181), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1643181, tc_prod(_1643181, _1643181)), tc_fun(_1643181, tc_fun(tc_fun(tc_prod(_1643181, _1643181), tc_HOL_Obool), tc_HOL_Obool)), _1643181), hAPP(c_COMBB(tc_prod(_1643181, _1643181), tc_fun(tc_fun(tc_prod(_1643181, _1643181), tc_HOL_Obool), tc_HOL_Obool), _1643181), c_member(tc_prod(_1643181, _1643181)))), c_Product__Type_OPair(_1643181, _1643181)))), _1643187)), _1643517)))], (43414 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643181)), _1643183) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643181)), _1643185))]]], (29950 ^ _780119) ^ [_1339642, _1339644, _1339646, _1339648] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1339642), _1339644)), 29956 ^ _780119 : [(29959 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1339646), hAPP(_1339648, 29955 ^ [_1339642, _1339644, _1339646, _1339648])))], (29957 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339642), 29955 ^ [_1339642, _1339644, _1339646, _1339648]), _1339644)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1339646), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339642, tc_fun(_1339646, tc_HOL_Obool)), _1339644), _1339648))))], (17244 ^ _780119) ^ [_1093308, _1093310, _1093312, _1093314] : [class_Rings_Olinordered__ring__strict(_1093308), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093308), _1093310), c_Groups_Ozero__class_Ozero(_1093308))), 17251 ^ _780119 : [(17258 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093308), _1093314), _1093312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093308), _1093310), _1093312)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093308), _1093310), _1093314))))], (17252 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093308), _1093310), _1093312)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093308), _1093310), _1093314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093308), _1093314), _1093312)))]]], (41545 ^ _780119) ^ [_1598648, _1598650, _1598652, _1598654] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1598648, tc_HOL_Obool)), _1598650), _1598652)), hBOOL(hAPP(hAPP(c_member(_1598648), _1598654), _1598650)), -(hBOOL(hAPP(hAPP(c_member(_1598648), _1598654), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1598648, tc_HOL_Obool), _1598652))))], (19923 ^ _780119) ^ [_1142375, _1142377, _1142379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1142375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1142375), _1142377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142379), _1142377)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142379), _1142375))))], (20786 ^ _780119) ^ [_1158072, _1158074, _1158076, _1158078] : [class_Fields_Olinordered__field__inverse__zero(_1158072), 20789 ^ _780119 : [(20790 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158072), _1158074), _1158076)), _1158078)), 20793 ^ _780119 : [(20800 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), c_Groups_Ozero__class_Ozero(_1158072)), _1158076))), 20803 ^ _780119 : [(20810 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), _1158076), c_Groups_Ozero__class_Ozero(_1158072)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), c_Groups_Ozero__class_Ozero(_1158072)), _1158078)))], (20804 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), _1158076), c_Groups_Ozero__class_Ozero(_1158072))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158072), _1158078), _1158076)), _1158074)))]]], (20794 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), c_Groups_Ozero__class_Ozero(_1158072)), _1158076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), _1158074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158072), _1158078), _1158076))))]]], (20816 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158072), _1158074), _1158076)), _1158078))), 20819 ^ _780119 : [(20822 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), _1158074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158072), _1158078), _1158076)))], (20820 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), c_Groups_Ozero__class_Ozero(_1158072)), _1158076)))]], 20823 ^ _780119 : [(20826 ^ _780119) ^ [] : [20827 ^ _780119 : [(20830 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158072), _1158078), _1158076)), _1158074))], (20828 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), _1158076), c_Groups_Ozero__class_Ozero(_1158072))))]], 20831 ^ _780119 : [(20834 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), c_Groups_Ozero__class_Ozero(_1158072)), _1158078))], (20832 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), _1158076), c_Groups_Ozero__class_Ozero(_1158072)))]]], (20824 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158072), c_Groups_Ozero__class_Ozero(_1158072)), _1158076))]]]]], (12645 ^ _780119) ^ [_1009303, _1009305, _1009307, _1009309] : [-(hAPP(c_Map_Orestrict__map(_1009303, _1009305, hAPP(c_COMBK(tc_Option_Ooption(_1009305), _1009303), c_Option_Ooption_ONone(_1009305)), _1009307), _1009309) = c_Option_Ooption_ONone(_1009305))], (4274 ^ _780119) ^ [_844747, _844749, _844751, _844753] : [-(c_List_Omeasures(_844753, _844749) = c_List_Omeasures(_844751, _844747)), _844753 = _844751, _844749 = _844747], (13506 ^ _780119) ^ [_1025964, _1025966, _1025968] : [hBOOL(hAPP(hAPP(c_member(_1025964), _1025966), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025964, tc_HOL_Obool)), _1025968))), hBOOL(hAPP(hAPP(c_member(_1025964), _1025966), _1025968))], (4120 ^ _780119) ^ [_842400, _842402, _842404, _842406, _842408, _842410] : [-(c_Enum_On__lists(_842410, _842406, _842402) = c_Enum_On__lists(_842408, _842404, _842400)), _842410 = _842408, _842406 = _842404, _842402 = _842400], (6344 ^ _780119) ^ [_882217, _882219, _882221, _882223, _882225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882217, tc_HOL_Obool)), _882219), hAPP(c_Set_Oimage(_882221, _882217, _882223), _882225))), 6348 ^ _780119 : [(6351 ^ _780119) ^ [] : [-(_882219 = hAPP(c_Set_Oimage(_882221, _882217, _882223), 6347 ^ [_882217, _882219, _882221, _882223, _882225]))], (6349 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882221, tc_HOL_Obool)), 6347 ^ [_882217, _882219, _882221, _882223, _882225]), _882225)))]]], (18510 ^ _780119) ^ [_1117808, _1117810] : [class_Rings_Oring__1(_1117808), hBOOL(hAPP(hAPP(c_member(_1117808), _1117810), c_Int_Oring__1__class_OInts(_1117808))), -(hBOOL(hAPP(hAPP(c_member(_1117808), hAPP(c_Groups_Ouminus__class_Ouminus(_1117808), _1117810)), c_Int_Oring__1__class_OInts(_1117808))))], (10112 ^ _780119) ^ [_956449, _956451, _956453, _956455] : [hBOOL(hAPP(hAPP(c_member(_956449), _956451), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956449, tc_HOL_Obool)), _956453), _956455))), -(hBOOL(hAPP(hAPP(c_member(_956449), _956451), _956455)))], (26339 ^ _780119) ^ [_1260874, _1260876, _1260878] : [class_Fields_Olinordered__field__inverse__zero(_1260874), -(hAPP(c_Groups_Oabs__class_Oabs(_1260874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1260874), _1260876), _1260878)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1260874), hAPP(c_Groups_Oabs__class_Oabs(_1260874), _1260876)), hAPP(c_Groups_Oabs__class_Oabs(_1260874), _1260878)))], (33289 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (40638 ^ _780119) ^ [_1576924, _1576926, _1576928, _1576930, _1576932, _1576934] : [c_Finite__Set_Ofun__left__comm__idem(_1576924, _1576926, _1576928), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576924), _1576930)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1576924, _1576926, _1576928), _1576932), hAPP(hAPP(c_Set_Oinsert(_1576924), _1576934), _1576930)) = hAPP(hAPP(_1576928, _1576934), hAPP(hAPP(c_Finite__Set_Ofold(_1576924, _1576926, _1576928), _1576932), _1576930)))], (51003 ^ _780119) ^ [_1814546, _1814548] : [class_Orderings_Oorder(_1814546), -(class_Orderings_Oorder(tc_fun(_1814548, _1814546)))], (40446 ^ _780119) ^ [_1572205, _1572207, _1572209, _1572211, _1572213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572205, _1572205)), hAPP(hAPP(c_Product__Type_OPair(_1572205, _1572205), _1572207), _1572209)), c_Transitive__Closure_Ortrancl(_1572205, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572205, _1572205), tc_HOL_Obool)), _1572211), _1572213)))), 40452 ^ _780119 : [(40456 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572205, _1572205)), hAPP(hAPP(c_Product__Type_OPair(_1572205, _1572205), 40451 ^ [_1572205, _1572207, _1572209, _1572211, _1572213]), 40454 ^ [_1572205, _1572207, _1572209, _1572211, _1572213])), _1572213)))], (40458 ^ _780119) ^ [] : [40451 ^ [_1572205, _1572207, _1572209, _1572211, _1572213] = 40454 ^ [_1572205, _1572207, _1572209, _1572211, _1572213]], (40453 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572205, _1572205)), hAPP(hAPP(c_Product__Type_OPair(_1572205, _1572205), _1572207), 40451 ^ [_1572205, _1572207, _1572209, _1572211, _1572213])), c_Transitive__Closure_Ortrancl(_1572205, _1572211))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572205, _1572205)), hAPP(hAPP(c_Product__Type_OPair(_1572205, _1572205), _1572207), _1572209)), c_Transitive__Closure_Ortrancl(_1572205, _1572211))))], (37203 ^ _780119) ^ [_1491406] : [-(c_Wellfounded_Owf(_1491406, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1491406, _1491406), tc_HOL_Obool))))], (34134 ^ _780119) ^ [_1421058, _1421060] : [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), _1421058))), 34137 ^ _780119 : [(34144 ^ _780119) ^ [] : [-(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), _1421060)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421058))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421060), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421058)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421058)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421060), 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), _1421058)))))], (34138 ^ _780119) ^ [] : [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), _1421060)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421058)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421060), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421058)) = 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), _1421060)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421058))))]]], (41347 ^ _780119) ^ [_1592850, _1592852, _1592854, _1592856, _1592858, _1592860] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592850, tc_fun(_1592852, tc_fun(_1592854, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1592850, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1592852, _1592854), tc_HOL_Obool), tc_fun(_1592852, tc_fun(_1592854, tc_HOL_Obool)), _1592850), hAPP(c_COMBC(_1592852, tc_fun(tc_prod(_1592852, _1592854), tc_HOL_Obool), tc_fun(_1592854, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1592854, tc_fun(tc_fun(tc_prod(_1592852, _1592854), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1592852, _1592854), tc_HOL_Obool), tc_fun(_1592854, tc_HOL_Obool)), _1592852), c_COMBC(_1592854, tc_fun(tc_prod(_1592852, _1592854), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1592854, tc_prod(_1592852, _1592854)), tc_fun(_1592854, tc_fun(tc_fun(tc_prod(_1592852, _1592854), tc_HOL_Obool), tc_HOL_Obool)), _1592852), hAPP(c_COMBB(tc_prod(_1592852, _1592854), tc_fun(tc_fun(tc_prod(_1592852, _1592854), tc_HOL_Obool), tc_HOL_Obool), _1592854), c_member(tc_prod(_1592852, _1592854)))), c_Product__Type_OPair(_1592852, _1592854))))), _1592856)), _1592858), _1592860)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592852, _1592854)), hAPP(hAPP(c_Product__Type_OPair(_1592852, _1592854), _1592858), _1592860)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592850, tc_fun(tc_prod(_1592852, _1592854), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1592850, tc_HOL_Obool))), _1592856))))], (50072 ^ _780119) ^ [] : [-(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)))], (31565 ^ _780119) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (5452 ^ _780119) ^ [_863652, _863654, _863656, _863658] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_863658, _863654) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_863656, _863652)), _863658 = _863656, _863654 = _863652], (45610 ^ _780119) ^ [_1698036, _1698038] : [hBOOL(hAPP(c_List_Odistinct(_1698036), hAPP(c_List_Orotate1(_1698036), _1698038))), -(hBOOL(hAPP(c_List_Odistinct(_1698036), _1698038)))], (32053 ^ _780119) ^ [_1377377, _1377379] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1377377, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377379)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1377377, 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)))), _1377379)))], (36870 ^ _780119) ^ [_1481126, _1481128, _1481130, _1481132] : [c_Fun_Oinj__on(_1481126, _1481128, _1481130, c_Orderings_Otop__class_Otop(tc_fun(_1481126, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1481126, _1481128, c_Orderings_Otop__class_Otop(tc_fun(_1481126, tc_HOL_Obool)), _1481130), hAPP(_1481130, _1481132)) = _1481132)], (32567 ^ _780119) ^ [_1387197] : [-(c_Int_Opred(c_Int_OBit0(_1387197)) = c_Int_OBit1(c_Int_Opred(_1387197)))], (37614 ^ _780119) ^ [_1500739, _1500741, _1500743, _1500745] : [hBOOL(hAPP(hAPP(c_member(_1500739), _1500741), hAPP(c_Relation_ORange(_1500743, _1500739), _1500745))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1500743, _1500739)), hAPP(hAPP(c_Product__Type_OPair(_1500743, _1500739), 37617 ^ [_1500739, _1500741, _1500743, _1500745]), _1500741)), _1500745)))], (35321 ^ _780119) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (40048 ^ _780119) ^ [_1561945, _1561947, _1561949, _1561951, _1561953] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561947, _1561945)), hAPP(hAPP(c_Product__Type_OPair(_1561947, _1561945), _1561951), _1561949)), _1561953)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561945, _1561947)), hAPP(hAPP(c_Product__Type_OPair(_1561945, _1561947), _1561949), _1561951)), hAPP(c_Relation_Oconverse(_1561947, _1561945), _1561953))))], (41453 ^ _780119) ^ [_1596755, _1596757, _1596759, _1596761, _1596763] : [-(_1596755 = c_Orderings_Obot__class_Obot(tc_fun(_1596757, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596757, tc_fun(_1596759, tc_HOL_Obool)), _1596755), hAPP(hAPP(c_COMBC(_1596757, tc_fun(_1596759, tc_HOL_Obool), tc_fun(_1596759, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1596759, tc_HOL_Obool), tc_fun(tc_fun(_1596759, tc_HOL_Obool), tc_fun(_1596759, tc_HOL_Obool)), _1596757), c_Groups_Ominus__class_Ominus(tc_fun(_1596759, tc_HOL_Obool))), _1596761)), _1596763)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1596759, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596757, tc_fun(_1596759, tc_HOL_Obool)), _1596755), _1596761)), _1596763))], (45940 ^ _780119) ^ [_1705247, _1705249, _1705251] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1705247, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705249)), _1705251)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1705249, _1705247), _1705251) = _1705251)], (41633 ^ _780119) ^ [_1600975, _1600977, _1600979] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1600975, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1600975, tc_HOL_Obool), _1600977)), _1600979) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1600975, tc_HOL_Obool), tc_fun(_1600975, tc_HOL_Obool)), _1600977), hAPP(hAPP(c_COMBC(tc_fun(_1600975, tc_HOL_Obool), tc_fun(_1600975, tc_HOL_Obool), tc_fun(_1600975, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1600975, tc_HOL_Obool))), _1600979)))], (39805 ^ _780119) ^ [_1556289, _1556291, _1556293, _1556295, _1556297] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1556289, _1556289)), hAPP(hAPP(c_Product__Type_OPair(_1556289, _1556289), _1556291), _1556293)), c_Transitive__Closure_Ortrancl(_1556289, _1556295))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1556289, _1556289)), hAPP(hAPP(c_Product__Type_OPair(_1556289, _1556289), _1556293), _1556297)), _1556295)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556289, _1556289)), hAPP(hAPP(c_Product__Type_OPair(_1556289, _1556289), _1556291), _1556297)), c_Transitive__Closure_Otrancl(_1556289, _1556295))))], (32103 ^ _780119) ^ [_1378576, _1378578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1378576)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1378578))), -(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(_1378578))), 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), _1378576)), c_Int_Onat))))))], (51355 ^ _780119) ^ [_1817969] : [-(class_Nat_Osize(tc_List_Olist(_1817969)))], (28988 ^ _780119) ^ [_1317292, _1317294, _1317296] : [class_Orderings_Olinorder(_1317292), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317292), _1317294)), hBOOL(hAPP(hAPP(c_member(_1317292), _1317296), _1317294)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317292), _1317296), c_Big__Operators_Olattice_OSup__fin(_1317292, c_Orderings_Oord__class_Omax(_1317292), _1317294)) = _1317296)], (45604 ^ _780119) ^ [_1697910, _1697912, _1697914] : [hBOOL(hAPP(c_List_Odistinct(_1697910), _1697912)), -(hBOOL(hAPP(c_List_Odistinct(_1697910), hAPP(hAPP(c_List_Odrop(_1697910), _1697914), _1697912))))], (10380 ^ _780119) ^ [_963077, _963079, _963081, _963083] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_963077), _963079)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963077, tc_HOL_Obool)), _963079), _963081)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_963077, tc_Nat_Onat), _963083), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963077, tc_HOL_Obool)), _963081), _963079)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_963077, tc_Nat_Onat), _963083), _963081)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_963077, tc_Nat_Onat), _963083), _963079)))], (33373 ^ _780119) ^ [_1401895, _1401897] : [class_Int_Onumber__ring(_1401895), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401895), hAPP(c_Int_Onumber__class_Onumber__of(_1401895), c_Int_OMin)), _1401897) = hAPP(c_Groups_Ouminus__class_Ouminus(_1401895), _1401897))], (26129 ^ _780119) ^ [_1256601] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1256601)) = hAPP(c_Nat_OSuc, _1256601))], (20031 ^ _780119) ^ [_1144335, _1144337, _1144339, _1144341] : [class_Fields_Ofield(_1144335), -(_1144337 = c_Groups_Ozero__class_Ozero(_1144335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1144339), _1144341)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1144335), _1144337), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144341), _1144339)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144335), hAPP(hAPP(c_Power_Opower__class_Opower(_1144335), _1144337), _1144341)), hAPP(hAPP(c_Power_Opower__class_Opower(_1144335), _1144337), _1144339)))], (36766 ^ _780119) ^ [_1478902, _1478904, _1478906] : [-(c_Fun_Oinj__on(tc_prod(_1478902, _1478904), tc_prod(_1478904, _1478902), hAPP(c_Product__Type_Oprod_Oprod__case(_1478902, _1478904, tc_prod(_1478904, _1478902)), hAPP(c_COMBC(_1478904, _1478902, tc_prod(_1478904, _1478902)), c_Product__Type_OPair(_1478904, _1478902))), _1478906))], (46061 ^ _780119) ^ [_1707772, _1707774] : [class_Complete__Lattice_Ocomplete__lattice(_1707772), -(c_Complete__Lattice_OSup__class_OSup(_1707772, hAPP(c_List_Oset(_1707772), _1707774)) = hAPP(c_List_Ofoldl(_1707772, _1707772, c_Lattices_Osemilattice__sup__class_Osup(_1707772), c_Orderings_Obot__class_Obot(_1707772)), _1707774))], (38257 ^ _780119) ^ [_1519557, _1519559] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1519557, _1519559), 38258 ^ [_1519557, _1519559])), -(c_Wellfounded_OwfP(_1519557, _1519559))], (4510 ^ _780119) ^ [_848497, _848499] : [_848499 = _848497, -(c_Lazy__Sequence_Oyieldn(_848499) = c_Lazy__Sequence_Oyieldn(_848497))], (51223 ^ _780119) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (36225 ^ _780119) ^ [_1467231, _1467233, _1467235, _1467237, _1467239] : [c_Fun_Oinj__on(_1467231, _1467233, _1467235, c_Orderings_Otop__class_Otop(tc_fun(_1467231, tc_HOL_Obool))), hAPP(_1467235, _1467237) = hAPP(_1467235, _1467239), -(_1467237 = _1467239)], (12397 ^ _780119) ^ [_1004121, _1004123] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004121), _1004123) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 12400 ^ _780119 : [(12403 ^ _780119) ^ [] : [-(_1004123 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12401 ^ _780119) ^ [] : [-(_1004121 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (33899 ^ _780119) ^ [_1416092, _1416094, _1416096, _1416098, _1416100] : [hBOOL(hAPP(hAPP(_1416092, _1416094), _1416096)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1416098, _1416100, tc_HOL_Obool), _1416092), hAPP(hAPP(c_Product__Type_OPair(_1416098, _1416100), _1416094), _1416096))))], (14558 ^ _780119) ^ [_1047173, _1047175] : [class_Groups_Omonoid__mult(_1047173), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1047173), c_Groups_Oone__class_Oone(_1047173)), _1047175) = c_Groups_Oone__class_Oone(_1047173))], (31225 ^ _780119) ^ [_1363941, _1363943] : [_1363941 = _1363943, -(c_Int_OBit1(_1363941) = c_Int_OBit1(_1363943))], (51421 ^ _780119) ^ [_1818815, _1818817] : [-(class_Smallcheck_Osmall(tc_prod(_1818815, _1818817))), class_Smallcheck_Osmall(_1818815), class_Smallcheck_Osmall(_1818817)], (47087 ^ _780119) ^ [_1729069, _1729071] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1729069, _1729071)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1729071), _1729069))], (38032 ^ _780119) ^ [_1513923, _1513925] : [-(hAPP(c_Fun_Oid(_1513923), _1513925) = _1513925)], (26107 ^ _780119) ^ [_1256270] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1256270))))], (25454 ^ _780119) ^ [_1245656, _1245658, _1245660] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1245656, tc_Nat_Onat), _1245658), _1245660) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1245656, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1245656), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1245658)), _1245660)))], (8426 ^ _780119) ^ [_926237, _926239, _926241, _926243, _926245, _926247, _926249] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_926237, _926239, _926241, _926243, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926237, tc_HOL_Obool)), _926245), hAPP(hAPP(c_Set_Oinsert(_926237), _926247), c_Orderings_Obot__class_Obot(tc_fun(_926237, tc_HOL_Obool))))), _926249)), hBOOL(hAPP(hAPP(c_member(_926237), _926247), _926245)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_926237, _926239, _926241, _926243, _926245), hAPP(hAPP(_926241, _926247), _926249))))], (32333 ^ _780119) ^ [_1383128, _1383130] : [c_Int_OBit0(_1383128) = c_Int_OBit1(_1383130)], (9320 ^ _780119) ^ [_940497, _940499] : [class_Lattices_Olattice(_940497), -(c_Big__Operators_Olattice__class_OSup__fin(_940497, hAPP(hAPP(c_Set_Oinsert(_940497), _940499), c_Orderings_Obot__class_Obot(tc_fun(_940497, tc_HOL_Obool)))) = _940499)], (2398 ^ _780119) ^ [_815451, _815453, _815455, _815457] : [-(c_Divides_Opdivmod(_815457, _815453) = c_Divides_Opdivmod(_815455, _815451)), _815457 = _815455, _815453 = _815451], (3472 ^ _780119) ^ [_832302, _832304, _832306, _832308] : [-(c_Transitive__Closure_Ortrancl(_832308, _832304) = c_Transitive__Closure_Ortrancl(_832306, _832302)), _832308 = _832306, _832304 = _832302], (49940 ^ _780119) ^ [_1792768, _1792770] : [class_Enum_Oenum(_1792768), 49943 ^ _780119 : [(49957 ^ _780119) ^ [] : [c_List_Olist__ex1(_1792768, _1792770, c_Enum_Oenum__class_Oenum(_1792768)), 49961 ^ _780119 : [(49964 ^ _780119) ^ [_1793167] : [hBOOL(hAPP(_1792770, _1793167)), -(_1793167 = 49960 ^ [_1792768, _1792770])], (49962 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1792770, 49960 ^ [_1792768, _1792770])))]]], (49944 ^ _780119) ^ [] : [-(c_List_Olist__ex1(_1792768, _1792770, c_Enum_Oenum__class_Oenum(_1792768))), 49945 ^ _780119 : [(49946 ^ _780119) ^ [_1792883] : [hBOOL(hAPP(_1792770, _1792883)), 49950 ^ _780119 : [(49953 ^ _780119) ^ [] : [49949 ^ [_1792768, _1792770, _1792883] = _1792883], (49951 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1792770, 49949 ^ [_1792768, _1792770, _1792883])))]]]]]]], (51619 ^ _780119) ^ [_1821081, _1821083] : [hBOOL(_1821081), -(hBOOL(hAPP(hAPP(c_fdisj, _1821083), _1821081)))], (38788 ^ _780119) ^ [_1531689, _1531691, _1531693, _1531695, _1531697, _1531699] : [c_Fun_Oinj__on(_1531689, _1531691, _1531693, _1531695), 38791 ^ _780119 : [(38798 ^ _780119) ^ [] : [c_Fun_Oinj__on(_1531689, _1531697, hAPP(c_Fun_Ocomp(_1531691, _1531697, _1531689, _1531699), _1531693), _1531695), -(c_Fun_Oinj__on(_1531691, _1531697, _1531699, hAPP(c_Set_Oimage(_1531689, _1531691, _1531693), _1531695)))], (38792 ^ _780119) ^ [] : [c_Fun_Oinj__on(_1531691, _1531697, _1531699, hAPP(c_Set_Oimage(_1531689, _1531691, _1531693), _1531695)), -(c_Fun_Oinj__on(_1531689, _1531697, hAPP(c_Fun_Ocomp(_1531691, _1531697, _1531689, _1531699), _1531693), _1531695))]]], (36758 ^ _780119) ^ [_1478687, _1478689, _1478691, _1478693] : [hAPP(c_Set_Oimage(_1478687, _1478689, _1478691), c_Orderings_Otop__class_Otop(tc_fun(_1478687, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1478689, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1478687, _1478689, _1478691), hAPP(c_Set_Ovimage(_1478687, _1478689, _1478691), _1478693)) = _1478693)], (31685 ^ _780119) ^ [_1371441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371441), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1371441)), c_Int_OPls)))], (32549 ^ _780119) ^ [_1386864, _1386866] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1386864)), c_Int_OBit1(_1386866)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1386864), _1386866)))], (32065 ^ _780119) ^ [_1377671, _1377673] : [class_Int_Onumber__ring(_1377671), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1377671), hAPP(c_Int_Onumber__class_Onumber__of(_1377671), _1377673)), c_Groups_Oone__class_Oone(_1377671)) = hAPP(c_Int_Onumber__class_Onumber__of(_1377671), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1377673), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (6369 ^ _780119) ^ [_882803, _882805, _882807] : [hBOOL(hAPP(hAPP(c_member(_882803), _882805), hAPP(hAPP(c_Set_Oinsert(_882803), _882807), c_Orderings_Obot__class_Obot(tc_fun(_882803, tc_HOL_Obool))))), -(_882805 = _882807)], (19326 ^ _780119) ^ [_1131557, _1131559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131557)), 19329 ^ _780119 : [(19336 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131557), _1131559)), -(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), _1131559), _1131557))))], (19330 ^ _780119) ^ [] : [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), _1131559), _1131557))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131557), _1131559)))]]], (9364 ^ _780119) ^ [_941244, _941246, _941248] : [class_Lattices_Olattice(_941244), hBOOL(hAPP(c_Finite__Set_Ofinite(_941244), _941246)), -(_941246 = c_Orderings_Obot__class_Obot(tc_fun(_941244, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_941244, hAPP(hAPP(c_Set_Oinsert(_941244), _941248), _941246)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_941244), _941248), c_Big__Operators_Olattice__class_OSup__fin(_941244, _941246)))], (38850 ^ _780119) ^ [_1533143, _1533145, _1533147, _1533149, _1533151, _1533153] : [class_Groups_Ocomm__monoid__mult(_1533143), c_Fun_Oinj__on(_1533145, _1533147, _1533149, _1533151), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1533147, _1533143), _1533153), hAPP(c_Set_Oimage(_1533145, _1533147, _1533149), _1533151)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1533145, _1533143), hAPP(c_Fun_Ocomp(_1533147, _1533143, _1533145, _1533153), _1533149)), _1533151))], (39725 ^ _780119) ^ [_1554480, _1554482] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1554480, _1554480, _1554480), _1554482), c_Transitive__Closure_Ortrancl(_1554480, _1554482)) = hAPP(hAPP(c_Relation_Orel__comp(_1554480, _1554480, _1554480), c_Transitive__Closure_Ortrancl(_1554480, _1554482)), _1554482))], (23813 ^ _780119) ^ [_1215401, _1215403, _1215405, _1215407] : [class_Groups_Ocomm__monoid__add(_1215401), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215401), _1215403), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1215405), hAPP(c_Nat_OSuc, _1215407))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215401), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1215401, tc_Nat_Onat), _1215403), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1215405, _1215407)))], (27416 ^ _780119) ^ [_1286501, _1286503] : [-(_1286501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1286503, _1286501) = c_Nitpick_Onat__gcd(_1286501, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1286503, _1286501)))], (18099 ^ _780119) ^ [_1109788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1109788)), -(_1109788 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109788), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (1810 ^ _780119) ^ [_805468, _805470] : [-(class_Groups_Oone(_805468)), _805470 = _805468, class_Groups_Oone(_805470)], (46264 ^ _780119) ^ [_1712789, _1712791, _1712793] : [46265 ^ _780119 : [(46266 ^ _780119) ^ [_1712878, _1712880] : [_1712791 = hAPP(hAPP(c_List_Olist_OCons(_1712789), _1712880), _1712878)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712789), tc_List_Olist(_1712789))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712789), tc_List_Olist(_1712789)), c_List_Olist_ONil(_1712789)), _1712791)), c_List_Olexord(_1712789, _1712793))))], (37050 ^ _780119) ^ [_1486258, _1486260, _1486262, _1486264] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1486258, _1486260, _1486262), _1486264), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486260, _1486262), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486258, _1486262), tc_HOL_Obool)))], (15466 ^ _780119) ^ [_1062082, _1062084] : [class_Lattices_Obounded__lattice__top(_1062082), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1062082), _1062084), c_Orderings_Otop__class_Otop(_1062082)) = c_Orderings_Otop__class_Otop(_1062082))], (12569 ^ _780119) ^ [_1007800, _1007802, _1007804] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007800), _1007802)), 12572 ^ _780119 : [(12579 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1007800), _1007804), _1007802))), -(hAPP(c_Finite__Set_Ocard(_1007800), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007800, tc_HOL_Obool)), _1007802), hAPP(hAPP(c_Set_Oinsert(_1007800), _1007804), c_Orderings_Obot__class_Obot(tc_fun(_1007800, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1007800), _1007802))], (12573 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1007800), _1007804), _1007802)), -(hAPP(c_Finite__Set_Ocard(_1007800), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007800, tc_HOL_Obool)), _1007802), hAPP(hAPP(c_Set_Oinsert(_1007800), _1007804), c_Orderings_Obot__class_Obot(tc_fun(_1007800, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1007800), _1007802)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (51521 ^ _780119) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (40576 ^ _780119) ^ [_1575557, _1575559, _1575561, _1575563] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1575557, _1575559, _1575561), _1575563), c_Orderings_Obot__class_Obot(tc_fun(_1575557, tc_HOL_Obool))) = _1575563)], (22342 ^ _780119) ^ [_1187803, _1187805] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1187803, _1187805) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1187803), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1187803), _1187805)), _1187805)))], (21660 ^ _780119) ^ [_1175499, _1175501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175499)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175501)), -(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, _1175499, _1175501))))], (40648 ^ _780119) ^ [_1577147, _1577149, _1577151, _1577153, _1577155, _1577157] : [c_Finite__Set_Ofun__left__comm__idem(_1577147, _1577149, _1577151), hBOOL(hAPP(c_Finite__Set_Ofinite(_1577147), _1577153)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1577147, _1577149, _1577151), _1577155), hAPP(hAPP(c_Set_Oinsert(_1577147), _1577157), _1577153)) = hAPP(hAPP(c_Finite__Set_Ofold(_1577147, _1577149, _1577151), hAPP(hAPP(_1577151, _1577157), _1577155)), _1577153))], (42612 ^ _780119) ^ [_1623319] : [-(hAPP(c_List_Omap(_1623319, _1623319), c_COMBI(_1623319)) = c_Fun_Oid(tc_List_Olist(_1623319)))], (25510 ^ _780119) ^ [_1246672, _1246674] : [-(c_Int_Onat__aux(_1246672, _1246674) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1246672)), _1246674))], (27214 ^ _780119) ^ [_1282628, _1282630] : [-(c_Nitpick_Onat__lcm(_1282628, _1282630) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1282628), _1282630)), c_Nitpick_Onat__gcd(_1282628, _1282630)))], (32731 ^ _780119) ^ [_1390234, _1390236] : [class_Rings_Ocomm__semiring__1(_1390234), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390234), _1390236), _1390236) = hAPP(hAPP(c_Power_Opower__class_Opower(_1390234), _1390236), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (13658 ^ _780119) ^ [_1028499, _1028501] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028499)), _1028501) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028499), hAPP(c_Nat_OSuc, _1028501)))], (23072 ^ _780119) ^ [_1201481, _1201483, _1201485, _1201487] : [class_Rings_Osemiring__1(_1201481), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201481), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1201483, tc_Nat_Onat), _1201485), _1201487)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1201483, _1201481), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1201481, _1201483), c_Nat_Osemiring__1__class_Oof__nat(_1201481)), _1201485)), _1201487))], (51105 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (13913 ^ _780119) ^ [_1033132, _1033134] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1033132, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033132, tc_HOL_Obool)), _1033134)), _1033134) = c_Orderings_Obot__class_Obot(tc_fun(_1033132, tc_HOL_Obool)))], (35041 ^ _780119) ^ [_1438226, _1438228, _1438230, _1438232, _1438234, _1438236, _1438238, _1438240] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1438226, _1438228), tc_prod(_1438226, _1438228))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1438226, _1438228), tc_prod(_1438226, _1438228)), hAPP(hAPP(c_Product__Type_OPair(_1438226, _1438228), _1438230), _1438232)), hAPP(hAPP(c_Product__Type_OPair(_1438226, _1438228), _1438234), _1438236))), c_Wellfounded_Olex__prod(_1438226, _1438228, _1438238, _1438240))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1438226, _1438226)), hAPP(hAPP(c_Product__Type_OPair(_1438226, _1438226), _1438230), _1438234)), _1438238))), 35048 ^ _780119 : [(35051 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1438228, _1438228)), hAPP(hAPP(c_Product__Type_OPair(_1438228, _1438228), _1438232), _1438236)), _1438240)))], (35049 ^ _780119) ^ [] : [-(_1438230 = _1438234)]]], (48301 ^ _780119) ^ [_1756893, _1756895, _1756897, _1756899] : [class_Orderings_Olinorder(_1756893), 48304 ^ _780119 : [(48311 ^ _780119) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1756895), _1756899)), -(hBOOL(hAPP(c_List_Odistinct(_1756895), c_List_Olinorder__class_Osort__key(_1756895, _1756893, _1756897, _1756899))))], (48305 ^ _780119) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1756895), c_List_Olinorder__class_Osort__key(_1756895, _1756893, _1756897, _1756899))), -(hBOOL(hAPP(c_List_Odistinct(_1756895), _1756899)))]]], (51277 ^ _780119) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (9610 ^ _780119) ^ [_946251, _946253, _946255, _946257, _946259] : [class_Groups_Oab__semigroup__mult(_946251), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_946251, _946251, c_Groups_Otimes__class_Otimes(_946251), _946253, _946255), _946257)), hBOOL(hAPP(hAPP(c_member(_946251), _946259), _946255)), -(hBOOL(hAPP(hAPP(c_member(_946251), _946253), _946255))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_946251, _946251, c_Groups_Otimes__class_Otimes(_946251), _946259, hAPP(hAPP(c_Set_Oinsert(_946251), _946253), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946251, tc_HOL_Obool)), _946255), hAPP(hAPP(c_Set_Oinsert(_946251), _946259), c_Orderings_Obot__class_Obot(tc_fun(_946251, tc_HOL_Obool)))))), _946257)))], (28146 ^ _780119) ^ [_1300161, _1300163, _1300165, _1300167] : [class_Orderings_Olinorder(_1300161), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300161), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300161), _1300163), _1300165)), _1300167) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300161), _1300163), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300161), _1300165), _1300167)))], (40274 ^ _780119) ^ [_1568047, _1568049] : [-(hAPP(hAPP(c_Nat_Ocompow(_1568047, _1568047), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1568049) = c_Fun_Oid(_1568047))], (12715 ^ _780119) ^ [_1010533] : [-(c_Option_Oset(_1010533, c_Option_Ooption_ONone(_1010533)) = c_Orderings_Obot__class_Obot(tc_fun(_1010533, tc_HOL_Obool)))], (17029 ^ _780119) ^ [_1089443, _1089445, _1089447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1089443), _1089445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1089447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1089443), _1089447)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1089445), _1089447))))], (41782 ^ _780119) ^ [_1604209, _1604211] : [class_Complete__Lattice_Ocomplete__lattice(_1604209), -(c_Complete__Lattice_OInf__class_OInf(_1604209, _1604211) = c_Complete__Lattice_OSup__class_OSup(_1604209, hAPP(c_Set_OCollect(_1604209), hAPP(hAPP(c_COMBB(tc_fun(_1604209, tc_HOL_Obool), tc_HOL_Obool, _1604209), c_HOL_OAll(_1604209)), hAPP(hAPP(c_COMBB(tc_fun(_1604209, tc_HOL_Obool), tc_fun(_1604209, tc_HOL_Obool), _1604209), hAPP(c_COMBS(_1604209, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1604209), c_fimplies), hAPP(hAPP(c_COMBC(_1604209, tc_fun(_1604209, tc_HOL_Obool), tc_HOL_Obool), c_member(_1604209)), _1604211)))), c_Orderings_Oord__class_Oless__eq(_1604209))))))], (17760 ^ _780119) ^ [_1103011, _1103013, _1103015] : [17761 ^ _780119 : [(17764 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1103011), _1103015))], (17762 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1103013)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103011), _1103013)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103015), _1103013))))], (8082 ^ _780119) ^ [_918248, _918250] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_918248, _918250)], (40890 ^ _780119) ^ [_1581749, _1581751, _1581753] : [class_Orderings_Olinorder(_1581749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581749), _1581751)), -(hBOOL(hAPP(hAPP(c_member(_1581749), _1581753), _1581751))), -(c_Big__Operators_Olinorder__class_OMax(_1581749, hAPP(hAPP(c_Set_Oinsert(_1581749), _1581753), _1581751)) = hAPP(hAPP(c_Finite__Set_Ofold(_1581749, _1581749, c_Orderings_Oord__class_Omax(_1581749)), _1581753), _1581751))], (2982 ^ _780119) ^ [_824513, _824515, _824517, _824519, _824521, _824523, _824525, _824527, _824529, _824531] : [-(c_Finite__Set_Ofold__graph(_824531, _824527, _824523, _824519, _824515) = c_Finite__Set_Ofold__graph(_824529, _824525, _824521, _824517, _824513)), _824531 = _824529, _824527 = _824525, _824523 = _824521, _824519 = _824517, _824515 = _824513], (40213 ^ _780119) ^ [_1566310, _1566312] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566310, _1566310), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1566312) = _1566312)], (10286 ^ _780119) ^ [_960821, _960823, _960825, _960827] : [hBOOL(hAPP(hAPP(c_member(_960821), _960823), _960825)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960821, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_960821), _960823), _960827)), _960825) = hAPP(hAPP(c_Set_Oinsert(_960821), _960823), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960821, tc_HOL_Obool)), _960827), _960825)))], (50746 ^ _780119) ^ [_1809372, _1809374] : [hBOOL(hAPP(hAPP(c_List_Omember(_1809372), c_List_Olist_ONil(_1809372)), _1809374))], (51519 ^ _780119) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (15384 ^ _780119) ^ [_1060758, _1060760, _1060762] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060758), _1060760) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060758), _1060762), -(_1060760 = _1060762), -(_1060758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10404 ^ _780119) ^ [_963559, _963561, _963563, _963565, _963567] : [class_Groups_Oab__semigroup__mult(_963559), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_963559, _963559, c_Groups_Otimes__class_Otimes(_963559), _963561, _963563), _963565)), -(hBOOL(hAPP(hAPP(c_member(_963559), _963561), _963563))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_963559, _963559, c_Groups_Otimes__class_Otimes(_963559), _963567, hAPP(hAPP(c_Set_Oinsert(_963559), _963561), _963563)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963559), _963567), _963565))))], (46157 ^ _780119) ^ [_1710245, _1710247, _1710249] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710245)), _1710247), c_List_Olists(_1710245, c_Wellfounded_Oacc(_1710245, _1710249)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710245)), _1710247), c_Wellfounded_Oacc(tc_List_Olist(_1710245), c_List_Olistrel1(_1710245, _1710249)))))], (30381 ^ _780119) ^ [_1347879, _1347881, _1347883] : [class_Int_Onumber__ring(_1347879), -(hAPP(c_Int_Onumber__class_Onumber__of(_1347879), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1347881), _1347883)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347879), hAPP(c_Int_Onumber__class_Onumber__of(_1347879), _1347881)), hAPP(c_Int_Onumber__class_Onumber__of(_1347879), _1347883)))], (26485 ^ _780119) ^ [_1263430, _1263432] : [-(hAPP(c_Set_OCollect(_1263430), hAPP(hAPP(c_COMBC(_1263430, tc_fun(_1263430, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263430)), _1263432)) = _1263432)], (50027 ^ _780119) ^ [_1794447, _1794449] : [-(c_FunDef_Ois__measure(_1794447, _1794449))], (14536 ^ _780119) ^ [_1046684, _1046686, _1046688] : [class_Rings_Olinordered__semidom(_1046684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046684), c_Groups_Oone__class_Oone(_1046684)), _1046686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046684), c_Groups_Oone__class_Oone(_1046684)), hAPP(hAPP(c_Power_Opower__class_Opower(_1046684), _1046686), hAPP(c_Nat_OSuc, _1046688)))))], (47279 ^ _780119) ^ [_1732838, _1732840] : [class_Orderings_Olinorder(_1732838), hBOOL(hAPP(c_Finite__Set_Ofinite(_1732838), _1732840)), 47286 ^ _780119 : [(47289 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1732838, c_List_Olinorder__class_Osorted__list__of__set(_1732838, _1732840)))], (47291 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1732838), c_List_Olinorder__class_Osorted__list__of__set(_1732838, _1732840))))], (47287 ^ _780119) ^ [] : [-(hAPP(c_List_Oset(_1732838), c_List_Olinorder__class_Osorted__list__of__set(_1732838, _1732840)) = _1732840)]]], (37355 ^ _780119) ^ [_1494131, _1494133] : [hAPP(hAPP(c_Relation_Orel__comp(_1494131, _1494131, _1494131), _1494133), _1494133) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1494131, _1494131), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1494131, _1494133))], (21522 ^ _780119) ^ [_1172559, _1172561, _1172563, _1172565] : [class_Divides_Oring__div(_1172559), -(c_Divides_Odiv__class_Omod(_1172559, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1172559), _1172561), _1172563), _1172565) = c_Divides_Odiv__class_Omod(_1172559, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1172559), _1172561), c_Divides_Odiv__class_Omod(_1172559, _1172563, _1172565)), _1172565))], (43769 ^ _780119) ^ [_1654428, _1654430] : [-(c_Random_Oselect__weight(_1654428, _1654430) = 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(_1654428, 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, _1654428), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1654428)), _1654430)))), hAPP(hAPP(c_COMBB(_1654428, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1654428, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1654428, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1654428, _1654430))))], (3942 ^ _780119) ^ [_839651, _839653, _839655, _839657, _839659, _839661, _839663, _839665] : [-(c_Map_Omap__add(_839665, _839661, _839657, _839653) = c_Map_Omap__add(_839663, _839659, _839655, _839651)), _839665 = _839663, _839661 = _839659, _839657 = _839655, _839653 = _839651], (27932 ^ _780119) ^ [_1295795, _1295797, _1295799, _1295801] : [class_Orderings_Olinorder(_1295795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295795), _1295797), _1295799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295795), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1295795), _1295797), _1295801)), _1295799)))], (33495 ^ _780119) ^ [_1403712, _1403714] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1403712), hAPP(c_Int_Onumber__class_Onumber__of(_1403712), c_Int_OMin)), _1403714) = hAPP(c_Groups_Ouminus__class_Ouminus(_1403712), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1403712), c_Groups_Oone__class_Oone(_1403712)), _1403714))), class_Fields_Ofield__inverse__zero(_1403712), class_Int_Onumber__ring(_1403712)], (41623 ^ _780119) ^ [_1600602, _1600604, _1600606] : [-(hAPP(c_Relation_ODomain(_1600602, _1600604), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1600602, _1600604), tc_HOL_Obool), _1600606)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1600602, _1600604), tc_HOL_Obool), tc_fun(_1600602, tc_HOL_Obool)), _1600606), c_Relation_ODomain(_1600602, _1600604)))], (39567 ^ _780119) ^ [_1550132, _1550134, _1550136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1550132), _1550134)), -(c_Random_Ominus__shift(_1550136, _1550132, _1550134) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1550136), _1550132)), _1550134))], (35193 ^ _780119) ^ [_1442488, _1442490, _1442492, _1442494] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1442488), _1442490)), 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)), _1442488), _1442492)), 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)), _1442490), _1442494)), 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)), _1442490), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1442492), _1442494))), c_FunDef_Omin__strict)))], (45255 ^ _780119) ^ [_1687731, _1687733, _1687735, _1687737] : [-(hBOOL(hAPP(hAPP(c_member(_1687731), _1687733), hAPP(c_List_Oset(_1687731), _1687735)))), -(c_List_Oremove1(_1687731, _1687733, hAPP(hAPP(c_List_Oappend(_1687731), _1687735), _1687737)) = hAPP(hAPP(c_List_Oappend(_1687731), _1687735), c_List_Oremove1(_1687731, _1687733, _1687737)))], (5294 ^ _780119) ^ [_861091, _861093] : [_861093 = _861091, -(c_List_Olist_ONil(_861093) = c_List_Olist_ONil(_861091))], (50608 ^ _780119) ^ [_1806734, _1806736, _1806738, _1806740] : [50609 ^ _780119 : [(50612 ^ _780119) ^ [] : [_1806736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50610 ^ _780119) ^ [] : [hBOOL(hAPP(_1806740, _1806738))]], 50613 ^ _780119 : [(50614 ^ _780119) ^ [_1806859] : [hBOOL(hAPP(hAPP(c_member(_1806734), _1806859), hAPP(c_List_Oset(_1806734), c_List_Oreplicate(_1806734, _1806736, _1806738)))), -(hBOOL(hAPP(_1806740, _1806859)))]]], (40412 ^ _780119) ^ [_1571256, _1571258, _1571260, _1571262, _1571264] : [c_Relation_Osingle__valued(_1571256, _1571256, _1571258), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571256, _1571256)), hAPP(hAPP(c_Product__Type_OPair(_1571256, _1571256), _1571260), _1571262)), c_Transitive__Closure_Ortrancl(_1571256, _1571258))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571256, _1571256)), hAPP(hAPP(c_Product__Type_OPair(_1571256, _1571256), _1571260), _1571264)), c_Transitive__Closure_Ortrancl(_1571256, _1571258))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571256, _1571256)), hAPP(hAPP(c_Product__Type_OPair(_1571256, _1571256), _1571262), _1571264)), c_Transitive__Closure_Ortrancl(_1571256, _1571258)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571256, _1571256)), hAPP(hAPP(c_Product__Type_OPair(_1571256, _1571256), _1571264), _1571262)), c_Transitive__Closure_Ortrancl(_1571256, _1571258))))], (11937 ^ _780119) ^ [_995102, _995104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995102), _995104)), _995104))], (7392 ^ _780119) ^ [_904358, _904360, _904362, _904364, _904366] : [class_Lattices_Osemilattice__sup(_904358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904358), _904360), _904362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904358), _904364), _904366)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904358), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_904358), _904360), _904364)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_904358), _904362), _904366))))], (37526 ^ _780119) ^ [_1498266, _1498268, _1498270, _1498272, _1498274] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1498266, _1498268)), hAPP(hAPP(c_Product__Type_OPair(_1498266, _1498268), _1498270), _1498272)), _1498274)), -(hBOOL(hAPP(hAPP(c_member(_1498268), _1498272), hAPP(c_Relation_ORange(_1498266, _1498268), _1498274))))], (50021 ^ _780119) ^ [_1794370] : [class_Nat_Osize(_1794370), -(c_FunDef_Ois__measure(_1794370, c_Nat_Osize__class_Osize(_1794370)))], (21739 ^ _780119) ^ [_1177099, _1177101, _1177103] : [class_Divides_Osemiring__div(_1177099), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177099), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177099), _1177101), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1177099), _1177103), _1177101))), c_Divides_Odiv__class_Omod(_1177099, _1177103, _1177101)) = _1177103)], (18998 ^ _780119) ^ [_1126344, _1126346, _1126348] : [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), _1126344), _1126346)), _1126348))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126348), _1126344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126346)))], (22235 ^ _780119) ^ [_1185945, _1185947] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1185945, _1185947)) = _1185947, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1185945), _1185947) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50832 ^ _780119) ^ [_1811170, _1811172, _1811174] : [-(c_FunDef_OTHE__default(_1811172, _1811174, _1811170) = c_HOL_OThe(_1811172, _1811170)), 50833 ^ _780119 : [(50834 ^ _780119) ^ [_1811234] : [hBOOL(hAPP(_1811170, _1811234)), 50838 ^ _780119 : [(50841 ^ _780119) ^ [] : [50837 ^ [_1811170, _1811172, _1811174, _1811234] = _1811234], (50839 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1811170, 50837 ^ [_1811170, _1811172, _1811174, _1811234])))]]]]], (7253 ^ _780119) ^ [_901571] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _901571))), -(hAPP(c_Com_Obody, _901571) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 7256 ^ [_901571]))], (44798 ^ _780119) ^ [_1677304, _1677306, _1677308] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1677304), tc_List_Olist(_1677304))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1677304), tc_List_Olist(_1677304)), c_List_Olist_ONil(_1677304)), _1677306)), c_List_Olex(_1677304, _1677308)))], (7852 ^ _780119) ^ [_913807, _913809, _913811, _913813] : [hBOOL(hAPP(hAPP(c_member(_913807), _913809), _913811)), -(hBOOL(hAPP(hAPP(c_member(_913807), _913809), _913813))), -(hBOOL(hAPP(hAPP(c_member(_913807), _913809), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913807, tc_HOL_Obool)), _913811), _913813))))], (51291 ^ _780119) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (10368 ^ _780119) ^ [_962796, _962798, _962800, _962802] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_962796, tc_HOL_Obool)), _962798), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962796, tc_HOL_Obool)), _962800), _962802)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962796, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_962796, tc_HOL_Obool)), _962798), _962800)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_962796, tc_HOL_Obool)), _962798), _962802)))], (45588 ^ _780119) ^ [_1697479, _1697481, _1697483, _1697485] : [-(hAPP(hAPP(c_List_Odrop(_1697479), hAPP(c_Nat_OSuc, _1697481)), hAPP(hAPP(c_List_Olist_OCons(_1697479), _1697483), _1697485)) = hAPP(hAPP(c_List_Odrop(_1697479), _1697481), _1697485))], (29629 ^ _780119) ^ [_1330806, _1330808, _1330810, _1330812, _1330814, _1330816] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330806, tc_fun(_1330808, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330810, tc_fun(_1330806, tc_HOL_Obool)), _1330812), _1330814)), _1330816) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330810, tc_fun(_1330808, tc_HOL_Obool)), _1330812), hAPP(hAPP(c_COMBC(_1330810, tc_fun(_1330806, tc_fun(_1330808, tc_HOL_Obool)), tc_fun(_1330808, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1330806, tc_HOL_Obool), tc_fun(tc_fun(_1330806, tc_fun(_1330808, tc_HOL_Obool)), tc_fun(_1330808, tc_HOL_Obool)), _1330810), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330806, tc_fun(_1330808, tc_HOL_Obool))), _1330814)), _1330816)))], (5578 ^ _780119) ^ [_865565, _865567] : [_865567 = _865565, -(tc_Lazy__Sequence_Olazy__sequence(_865567) = tc_Lazy__Sequence_Olazy__sequence(_865565))], (35359 ^ _780119) ^ [_1446475, _1446477, _1446479, _1446481, _1446483] : [-(hAPP(c_Relation_OImage(_1446475, _1446477, _1446479), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446475, tc_HOL_Obool)), _1446481), _1446483)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446477, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446475, _1446477, _1446479), _1446481)), hAPP(c_Relation_OImage(_1446475, _1446477, _1446479), _1446483)))], (31485 ^ _780119) ^ [_1368443] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1368443), c_Int_OPls) = _1368443)], (36740 ^ _780119) ^ [_1478300, _1478302, _1478304, _1478306, _1478308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478300, tc_HOL_Obool)), _1478302), _1478304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478306, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1478306, _1478300, _1478308), _1478302)), hAPP(c_Set_Ovimage(_1478306, _1478300, _1478308), _1478304))))], (39619 ^ _780119) ^ [_1551832, _1551834] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1551832, _1551832)), hAPP(hAPP(c_Product__Type_OPair(_1551832, _1551832), _1551834), _1551834)), c_Relation_OId(_1551832))))], (17586 ^ _780119) ^ [_1099901, _1099903] : [hAPP(c_Finite__Set_Ocard(_1099901), _1099903) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1099903 = c_Orderings_Obot__class_Obot(tc_fun(_1099901, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099901), _1099903))], (2872 ^ _780119) ^ [_822880, _822882] : [_822882 = _822880, -(c_Nat_Ofunpow(_822882) = c_Nat_Ofunpow(_822880))], (27158 ^ _780119) ^ [_1280381, _1280383, _1280385] : [-(c_Map_Oran(_1280381, _1280383, _1280385) = hAPP(c_Set_OCollect(_1280383), hAPP(hAPP(c_COMBB(tc_fun(_1280381, tc_HOL_Obool), tc_HOL_Obool, _1280383), c_HOL_OEx(_1280381)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1280383), tc_fun(_1280381, tc_HOL_Obool), _1280383), hAPP(c_COMBC(_1280381, tc_Option_Ooption(_1280383), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1280383), tc_fun(tc_Option_Ooption(_1280383), tc_HOL_Obool), _1280381), c_fequal), _1280385))), c_Option_Ooption_OSome(_1280383)))))], (46028 ^ _780119) ^ [_1707159, _1707161] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1707159), _1707161) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46031 ^ _780119 : [(46034 ^ _780119) ^ [_1707273] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1707273), hAPP(c_List_Oset(tc_Nat_Onat), _1707161))), -(_1707273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46032 ^ _780119) ^ [] : [-(_1707159 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18804 ^ _780119) ^ [_1122968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122968), 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)), _1122968)), _1122968)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51173 ^ _780119) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (50620 ^ _780119) ^ [_1806982, _1806984, _1806986] : [-(_1806982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1806984, c_List_Oreplicate(_1806984, _1806982, _1806986)) = _1806986)], (14826 ^ _780119) ^ [_1052290] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052290), c_Orderings_Otop__class_Otop(tc_fun(_1052290, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1052290)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1052290), tc_HOL_Obool)))))], (12765 ^ _780119) ^ [_1011514, _1011516, _1011518] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1011514), _1011516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1011514, tc_HOL_Obool)), _1011518), _1011516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1011514), _1011518)), hAPP(c_Finite__Set_Ocard(_1011514), _1011516))))], (1490 ^ _780119) ^ [_801468, _801470] : [-(class_Groups_Ocancel__ab__semigroup__add(_801468)), _801470 = _801468, class_Groups_Ocancel__ab__semigroup__add(_801470)], (34303 ^ _780119) ^ [_1423926, _1423928] : [_1423926 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1423926, _1423928) = 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)))], (13244 ^ _780119) ^ [_1021177, _1021179, _1021181] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021177, tc_HOL_Obool)), _1021179) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021177, tc_HOL_Obool)), _1021181), -(_1021179 = _1021181)], (21582 ^ _780119) ^ [_1173853, _1173855, _1173857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1173853, tc_HOL_Obool)), _1173855), _1173857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1173853, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1173853), _1173855)), hAPP(c_Set_OPow(_1173853), _1173857))))], (45932 ^ _780119) ^ [_1705028, _1705030, _1705032] : [-(hAPP(c_List_Orotate(_1705028, hAPP(c_Nat_OSuc, _1705030)), _1705032) = hAPP(c_List_Orotate1(_1705028), hAPP(c_List_Orotate(_1705028, _1705030), _1705032)))], (42449 ^ _780119) ^ [_1619321, _1619323, _1619325, _1619327] : [c_Fun_Oinj__on(_1619321, tc_Option_Ooption(_1619323), _1619327, c_Map_Odom(_1619321, _1619323, _1619327)), -(c_Fun_Oinj__on(_1619321, tc_Option_Ooption(_1619323), c_Map_Omap__add(_1619321, _1619323, _1619325, _1619327), c_Map_Odom(_1619321, _1619323, _1619327)))], (20418 ^ _780119) ^ [_1151634, _1151636, _1151638] : [class_Fields_Olinordered__field(_1151634), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151634), c_Groups_Ozero__class_Ozero(_1151634)), _1151636)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151634), c_Groups_Ozero__class_Ozero(_1151634)), _1151638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151634), c_Groups_Ozero__class_Ozero(_1151634)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151634), _1151636), _1151638))))], (30203 ^ _780119) ^ [_1344285, _1344287, _1344289, _1344291] : [c_Com_Ocom_OLocal(_1344285, _1344287, _1344289) = hAPP(c_Com_Ocom_OBODY, _1344291)], (5781 ^ _780119) ^ [_871599, _871601, _871603, _871605] : [c_Hoare__Mirabelle_Ohoare__derivs(_871599, _871601, _871603), c_Hoare__Mirabelle_Ohoare__derivs(_871599, _871605, _871601), -(c_Hoare__Mirabelle_Ohoare__derivs(_871599, _871605, _871603))], (13746 ^ _780119) ^ [_1030017, _1030019, _1030021, _1030023, _1030025] : [class_Groups_Ocomm__monoid__mult(_1030017), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1030019, _1030017), hAPP(hAPP(c_COMBS(_1030019, _1030017, _1030017), hAPP(hAPP(c_COMBB(_1030017, tc_fun(_1030017, _1030017), _1030019), c_Groups_Otimes__class_Otimes(_1030017)), _1030021)), _1030023)), _1030025) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030017), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1030019, _1030017), _1030021), _1030025)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1030019, _1030017), _1030023), _1030025)))], (21614 ^ _780119) ^ [_1174593, _1174595, _1174597] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1174593, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1174593, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1174593), _1174595)), hAPP(c_Set_OPow(_1174593), _1174597))), hAPP(c_Set_OPow(_1174593), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1174593, tc_HOL_Obool)), _1174595), _1174597)))))], (24385 ^ _780119) ^ [_1226751, _1226753, _1226755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226751)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1226753), _1226755)), 24392 ^ _780119 : [(24393 ^ _780119) ^ [_1226947] : [24395 ^ _780119 : [(24399 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24397 ^ [_1226751, _1226753, _1226755, _1226947]), _1226755)))], (24401 ^ _780119) ^ [] : [-(_1226947 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24397 ^ [_1226751, _1226753, _1226755, _1226947]), 24394 ^ [_1226751, _1226753, _1226755, _1226947]))], (24396 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24394 ^ [_1226751, _1226753, _1226755, _1226947]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1226751))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226753), _1226947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226753), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226947), _1226751))))]]], (35619 ^ _780119) ^ [_1453427, _1453429, _1453431, _1453433] : [c_Equiv__Relations_Oequiv(_1453427, _1453429, _1453431), hBOOL(hAPP(hAPP(c_member(_1453427), _1453433), _1453429)), -(hBOOL(hAPP(hAPP(c_member(_1453427), _1453433), hAPP(c_Relation_OImage(_1453427, _1453427, _1453431), hAPP(hAPP(c_Set_Oinsert(_1453427), _1453433), c_Orderings_Obot__class_Obot(tc_fun(_1453427, tc_HOL_Obool)))))))], (28176 ^ _780119) ^ [_1300804, _1300806, _1300808, _1300810] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1300804), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300804), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300804), _1300806), _1300808)), _1300810) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300804), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300804), _1300806), _1300810)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300804), _1300808), _1300810)))], (7230 ^ _780119) ^ [_900545, _900547, _900549, _900551, _900553, _900555, _900557, _900559, _900561] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_900545), _900547)), 7236 ^ _780119 : [(7239 ^ _780119) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_900549, _900551, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_900549)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_900549), hAPP(_900559, 7235 ^ [_900545, _900547, _900549, _900551, _900553, _900555, _900557, _900559, _900561])), hAPP(_900555, 7235 ^ [_900545, _900547, _900549, _900551, _900553, _900555, _900557, _900559, _900561])), hAPP(_900561, 7235 ^ [_900545, _900547, _900549, _900551, _900553, _900555, _900557, _900559, _900561]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_900549), tc_HOL_Obool))))], (7237 ^ _780119) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_900549, _900551, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_900549)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_900549), hAPP(_900553, 7235 ^ [_900545, _900547, _900549, _900551, _900553, _900555, _900557, _900559, _900561])), hAPP(_900555, 7235 ^ [_900545, _900547, _900549, _900551, _900553, _900555, _900557, _900559, _900561])), hAPP(_900557, 7235 ^ [_900545, _900547, _900549, _900551, _900553, _900555, _900557, _900559, _900561]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_900549), tc_HOL_Obool)))))]], c_Hoare__Mirabelle_Ohoare__derivs(_900549, _900551, hAPP(c_Set_Oimage(_900545, tc_Hoare__Mirabelle_Otriple(_900549), hAPP(hAPP(c_COMBS(_900545, tc_fun(_900549, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_900549)), hAPP(hAPP(c_COMBS(_900545, tc_Com_Ocom, tc_fun(tc_fun(_900549, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_900549))), hAPP(hAPP(c_COMBB(tc_fun(_900549, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_900549, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_900549))), _900545), c_Hoare__Mirabelle_Otriple_Otriple(_900549)), _900553)), _900555)), _900557)), _900547)), -(c_Hoare__Mirabelle_Ohoare__derivs(_900549, _900551, hAPP(c_Set_Oimage(_900545, tc_Hoare__Mirabelle_Otriple(_900549), hAPP(hAPP(c_COMBS(_900545, tc_fun(_900549, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_900549)), hAPP(hAPP(c_COMBS(_900545, tc_Com_Ocom, tc_fun(tc_fun(_900549, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_900549))), hAPP(hAPP(c_COMBB(tc_fun(_900549, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_900549, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_900549))), _900545), c_Hoare__Mirabelle_Otriple_Otriple(_900549)), _900559)), _900555)), _900561)), _900547)))], (3662 ^ _780119) ^ [_835173, _835175, _835177, _835179] : [-(c_List_Olexord(_835179, _835175) = c_List_Olexord(_835177, _835173)), _835179 = _835177, _835175 = _835173], (28128 ^ _780119) ^ [_1299732, _1299734, _1299736, _1299738] : [class_Orderings_Olinorder(_1299732), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299732), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299732), _1299734), _1299736)), _1299738) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299732), _1299734), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299732), _1299736), _1299738)))], (18229 ^ _780119) ^ [_1112243, _1112245, _1112247, _1112249, _1112251] : [class_Groups_Ocomm__monoid__add(_1112243), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112245), _1112247)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112245), _1112249)), 18243 ^ _780119 : [(18246 ^ _780119) ^ [] : [hAPP(_1112251, 18242 ^ [_1112243, _1112245, _1112247, _1112249, _1112251]) = c_Groups_Ozero__class_Ozero(_1112243)], (18244 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112245), 18242 ^ [_1112243, _1112245, _1112247, _1112249, _1112251]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112245, tc_HOL_Obool)), _1112247), _1112249))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1112245, _1112243), _1112251), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1112245, tc_HOL_Obool)), _1112247), _1112249)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1112243), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1112245, _1112243), _1112251), _1112247)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1112245, _1112243), _1112251), _1112249)))], (25227 ^ _780119) ^ [_1241810, _1241812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241810)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241812)), 25234 ^ _780119 : [(25241 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241810), _1241812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1241810)), hAPP(c_Int_Onat, _1241812))))], (25235 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1241810)), hAPP(c_Int_Onat, _1241812))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241810), _1241812)))]]], (49323 ^ _780119) ^ [_1778327, _1778329, _1778331] : [hBOOL(hAPP(hAPP(c_member(_1778327), _1778329), hAPP(c_List_Oset(_1778327), _1778331))), -(c_List_Oinsert(_1778327, _1778329, _1778331) = _1778331)], (29807 ^ _780119) ^ [_1335712, _1335714, _1335716, _1335718, _1335720, _1335722] : [class_Complete__Lattice_Ocomplete__lattice(_1335712), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335714, tc_fun(_1335716, _1335712)), _1335718), _1335720), _1335722) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335714, _1335712), _1335718), hAPP(hAPP(c_COMBC(_1335714, _1335716, _1335712), _1335720), _1335722)))], (46231 ^ _780119) ^ [_1711901, _1711903, _1711905] : [46233 ^ _780119 : [(46236 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1711901), 46232 ^ [_1711901, _1711903, _1711905]), _1711905))], (46234 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1711901), 46232 ^ [_1711901, _1711903, _1711905]), hAPP(c_List_Oset(_1711901), _1711903))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1711901)), _1711903), c_List_Olists(_1711901, _1711905))))], (39373 ^ _780119) ^ [_1545869, _1545871, _1545873, _1545875, _1545877, _1545879, _1545881] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1545869, _1545871, _1545873, _1545875), _1545877), _1545879), _1545881) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1545871, _1545873, _1545875), _1545879), hAPP(_1545877, _1545881)))], (39022 ^ _780119) ^ [_1537249, _1537251, _1537253, _1537255, _1537257, _1537259] : [c_Finite__Set_Ofolding(_1537249, _1537251, _1537253, _1537255), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537249), _1537257)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537249), _1537259)), -(hAPP(c_Fun_Ocomp(_1537251, _1537251, _1537251, hAPP(_1537255, _1537259)), hAPP(_1537255, _1537257)) = hAPP(c_Fun_Ocomp(_1537251, _1537251, _1537251, hAPP(_1537255, _1537257)), hAPP(_1537255, _1537259)))], (40810 ^ _780119) ^ [_1580446, _1580448, _1580450, _1580452, _1580454] : [c_Finite__Set_Ofolding__one(_1580446, _1580448, _1580450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1580446), _1580452)), -(hBOOL(hAPP(hAPP(c_member(_1580446), _1580454), _1580452))), -(hAPP(_1580450, hAPP(hAPP(c_Set_Oinsert(_1580446), _1580454), _1580452)) = hAPP(hAPP(c_Finite__Set_Ofold(_1580446, _1580446, _1580448), _1580454), _1580452))], (31263 ^ _780119) ^ [_1364513, _1364515] : [class_Int_Onumber__ring(_1364513), -(hAPP(c_Int_Onumber__class_Onumber__of(_1364513), c_Int_OBit1(_1364515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364513), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364513), c_Groups_Oone__class_Oone(_1364513)), hAPP(c_Int_Onumber__class_Onumber__of(_1364513), _1364515))), hAPP(c_Int_Onumber__class_Onumber__of(_1364513), _1364515)))], (33221 ^ _780119) ^ [_1399702] : [c_Int_OMin = c_Int_OBit0(_1399702)], (13722 ^ _780119) ^ [_1029525, _1029527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029527)), _1029525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029525), _1029527))], (40098 ^ _780119) ^ [_1563208, _1563210, _1563212, _1563214] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563208, _1563208)), hAPP(hAPP(c_Product__Type_OPair(_1563208, _1563208), _1563210), _1563212)), hAPP(c_Relation_Oconverse(_1563208, _1563208), c_Transitive__Closure_Otrancl(_1563208, _1563214)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563208, _1563208)), hAPP(hAPP(c_Product__Type_OPair(_1563208, _1563208), _1563210), _1563212)), c_Transitive__Closure_Otrancl(_1563208, hAPP(c_Relation_Oconverse(_1563208, _1563208), _1563214)))))], (32649 ^ _780119) ^ [] : [-(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))))], (4400 ^ _780119) ^ [_846714, _846716] : [_846716 = _846714, -(c_Groups_Oabs__class_Oabs(_846716) = c_Groups_Oabs__class_Oabs(_846714))], (21050 ^ _780119) ^ [_1163011, _1163013, _1163015, _1163017] : [class_Fields_Ofield(_1163011), -(_1163013 = c_Groups_Ozero__class_Ozero(_1163011)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163011), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163011), _1163015), _1163013)), _1163017) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163011), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163011), _1163015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163011), _1163013), _1163017))), _1163013))], (46351 ^ _780119) ^ [_1714338, _1714340, _1714342, _1714344] : [-(_1714338 = c_List_Olist_ONil(_1714340)), -(c_List_Olast(_1714342, hAPP(hAPP(c_List_Omap(_1714340, _1714342), _1714344), _1714338)) = hAPP(_1714344, c_List_Olast(_1714340, _1714338)))], (34088 ^ _780119) ^ [_1420338, _1420340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420338), 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)), _1420340)), -(c_Divides_OnegDivAlg(_1420338, _1420340) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1420338), _1420340)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1420338, _1420340)))], (44546 ^ _780119) ^ [_1672534, _1672536] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1672534), _1672536) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1672534)), hAPP(c_Code__Numeral_Onat__of, _1672536))))], (42747 ^ _780119) ^ [_1626665, _1626667, _1626669, _1626671] : [-(hAPP(c_List_Oset(_1626665), hAPP(hAPP(c_List_Omap(_1626667, _1626665), _1626669), _1626671)) = hAPP(c_Set_Oimage(_1626667, _1626665, _1626669), hAPP(c_List_Oset(_1626667), _1626671)))], (16743 ^ _780119) ^ [_1084858, _1084860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1084858), hAPP(c_Nat_OSuc, _1084860))), -(_1084858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 16751 ^ _780119 : [(16754 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16750 ^ [_1084858, _1084860]), _1084860)))], (16752 ^ _780119) ^ [] : [-(_1084858 = hAPP(c_Nat_OSuc, 16750 ^ [_1084858, _1084860]))]]], (4092 ^ _780119) ^ [_841950, _841952, _841954, _841956] : [-(c_List_Olinorder__class_Osorted__list__of__set(_841956, _841952) = c_List_Olinorder__class_Osorted__list__of__set(_841954, _841950)), _841956 = _841954, _841952 = _841950], (42224 ^ _780119) ^ [_1614441, _1614443] : [-(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)))), _1614441)) = 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)))), _1614443))), 42226 ^ _780119 : [(42229 ^ _780119) ^ [] : [42230 ^ _780119 : [(42233 ^ _780119) ^ [] : [hBOOL(hAPP(_1614443, 42225 ^ [_1614441, _1614443]))], (42231 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1614441, 42225 ^ [_1614441, _1614443])))]], 42234 ^ _780119 : [(42237 ^ _780119) ^ [] : [hBOOL(hAPP(_1614441, 42225 ^ [_1614441, _1614443]))], (42235 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1614443, 42225 ^ [_1614441, _1614443])))]]], (42227 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 42225 ^ [_1614441, _1614443])))]]], (11563 ^ _780119) ^ [_987864, _987866, _987868, _987870] : [class_Rings_Ocomm__semiring(_987864), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987864), _987866), _987868)), _987870) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987864), _987866), _987870)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987864), _987868), _987870)))], (12483 ^ _780119) ^ [_1005621, _1005623, _1005625, _1005627, _1005629] : [hBOOL(hAPP(hAPP(c_member(_1005621), _1005623), _1005625)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1005621, tc_Option_Ooption(_1005627)), c_Map_Orestrict__map(_1005621, _1005627, _1005629, _1005625)), _1005623), c_Option_Ooption_ONone(_1005627)) = c_Map_Orestrict__map(_1005621, _1005627, _1005629, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005621, tc_HOL_Obool)), _1005625), hAPP(hAPP(c_Set_Oinsert(_1005621), _1005623), c_Orderings_Obot__class_Obot(tc_fun(_1005621, tc_HOL_Obool))))))], (28266 ^ _780119) ^ [_1302609, _1302611, _1302613, _1302615] : [class_Orderings_Olinorder(_1302609), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302609, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1302609, _1302611, _1302613)), hAPP(c_SetInterval_Oord__class_OatMost(_1302609), _1302615)) = c_SetInterval_Oord__class_OatLeastAtMost(_1302609, _1302611, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1302609), _1302613), _1302615)))], (17264 ^ _780119) ^ [_1093689, _1093691, _1093693, _1093695, _1093697] : [class_Rings_Olinordered__semiring__strict(_1093689), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093689), _1093691), _1093693)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093689), _1093695), _1093697)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093689), c_Groups_Ozero__class_Ozero(_1093689)), _1093693)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093689), c_Groups_Ozero__class_Ozero(_1093689)), _1093695)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093689), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093689), _1093691), _1093695)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093689), _1093693), _1093697))))], (32163 ^ _780119) ^ [_1379882, _1379884] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379882)), hAPP(c_Nat_OSuc, _1379884)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1379882))), 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, _1379884))), 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)), _1379884)))))], (6543 ^ _780119) ^ [_886360, _886362, _886364, _886366] : [6544 ^ _780119 : [(6547 ^ _780119) ^ [] : [hBOOL(hAPP(_886364, _886362))], (6545 ^ _780119) ^ [] : [hBOOL(hAPP(_886360, _886362))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886366, tc_HOL_Obool)), _886364), _886360), _886362)))], (4986 ^ _780119) ^ [_856277, _856279, _856281, _856283] : [-(c_Option_Omap(_856283, _856279) = c_Option_Omap(_856281, _856277)), _856283 = _856281, _856279 = _856277], (2368 ^ _780119) ^ [_815004, _815006, _815008, _815010] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_815010, _815006) = c_Code__Numeral_Odiv__mod__code__numeral(_815008, _815004)), _815010 = _815008, _815006 = _815004], (37235 ^ _780119) ^ [] : [-(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)))))], (41481 ^ _780119) ^ [] : [-(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)))], (25010 ^ _780119) ^ [_1238303] : [25012 ^ _780119 : [(25015 ^ _780119) ^ [] : [hBOOL(hAPP(_1238303, hAPP(c_Int_Onat, 25011 ^ [_1238303])))], (25013 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25011 ^ [_1238303])))]], 25016 ^ _780119 : [(25017 ^ _780119) ^ [_1238436] : [-(hBOOL(hAPP(_1238303, _1238436)))]]], (44460 ^ _780119) ^ [_1670990, _1670992, _1670994, _1670996, _1670998, _1671000, _1671002] : [-(hBOOL(hAPP(hAPP(c_member(_1670990), _1670992), hAPP(c_List_Oset(_1670990), hAPP(hAPP(c_List_Otake(_1670990), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670994)), _1670996)), _1670998))))), -(c_Map_Omap__upds(_1670990, _1670994, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1670990, tc_Option_Ooption(_1670994)), _1671000), _1670992), hAPP(c_Option_Ooption_OSome(_1670994), _1671002)), _1670998, _1670996) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1670990, tc_Option_Ooption(_1670994)), c_Map_Omap__upds(_1670990, _1670994, _1671000, _1670998, _1670996)), _1670992), hAPP(c_Option_Ooption_OSome(_1670994), _1671002)))], (18584 ^ _780119) ^ [_1119072, _1119074, _1119076, _1119078] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1119072, _1119074)), c_Sum__Type_OPlus(_1119072, _1119074, _1119076, _1119078))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1119072), _1119076)))], (50951 ^ _780119) ^ [_1813864, _1813866] : [class_Lattices_Obounded__lattice(_1813864), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1813866, _1813864)))], (28554 ^ _780119) ^ [_1307677, _1307679, _1307681] : [class_Orderings_Olinorder(_1307677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307677), _1307679)), -(hBOOL(hAPP(hAPP(c_member(_1307677), _1307681), _1307679))), -(_1307679 = c_Orderings_Obot__class_Obot(tc_fun(_1307677, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1307677, hAPP(hAPP(c_Set_Oinsert(_1307677), _1307681), _1307679)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1307677), _1307681), c_Big__Operators_Olinorder__class_OMax(_1307677, _1307679)))], (4820 ^ _780119) ^ [_853650, _853652] : [_853652 = _853650, -(c_New__Random__Sequence_Oneg__single(_853652) = c_New__Random__Sequence_Oneg__single(_853650))], (51133 ^ _780119) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (7536 ^ _780119) ^ [_906871, _906873, _906875] : [class_Lattices_Obounded__lattice__bot(_906871), 7539 ^ _780119 : [(7548 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_906871), _906873), _906875) = c_Orderings_Obot__class_Obot(_906871)), _906873 = c_Orderings_Obot__class_Obot(_906871), _906875 = c_Orderings_Obot__class_Obot(_906871)], (7540 ^ _780119) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_906871), _906873), _906875) = c_Orderings_Obot__class_Obot(_906871), 7543 ^ _780119 : [(7546 ^ _780119) ^ [] : [-(_906875 = c_Orderings_Obot__class_Obot(_906871))], (7544 ^ _780119) ^ [] : [-(_906873 = c_Orderings_Obot__class_Obot(_906871))]]]]], (27424 ^ _780119) ^ [_1286598, _1286600, _1286602] : [class_Orderings_Olinorder(_1286598), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286598), _1286600)), hBOOL(hAPP(hAPP(c_member(_1286598), _1286602), _1286600)), 27435 ^ _780119 : [(27442 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286598, tc_HOL_Obool)), _1286600), hAPP(hAPP(c_Set_Oinsert(_1286598), _1286602), c_Orderings_Obot__class_Obot(tc_fun(_1286598, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1286598, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1286598, _1286600) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1286598), _1286602), c_Big__Operators_Olinorder__class_OMin(_1286598, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286598, tc_HOL_Obool)), _1286600), hAPP(hAPP(c_Set_Oinsert(_1286598), _1286602), c_Orderings_Obot__class_Obot(tc_fun(_1286598, tc_HOL_Obool)))))))], (27436 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286598, tc_HOL_Obool)), _1286600), hAPP(hAPP(c_Set_Oinsert(_1286598), _1286602), c_Orderings_Obot__class_Obot(tc_fun(_1286598, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1286598, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1286598, _1286600) = _1286602)]]], (14926 ^ _780119) ^ [_1053966, _1053968] : [class_Groups_Olinordered__ab__group__add(_1053966), 14929 ^ _780119 : [(14936 ^ _780119) ^ [] : [_1053968 = c_Groups_Ozero__class_Ozero(_1053966), -(c_Groups_Ozero__class_Ozero(_1053966) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053966), _1053968), _1053968))], (14930 ^ _780119) ^ [] : [c_Groups_Ozero__class_Ozero(_1053966) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053966), _1053968), _1053968), -(_1053968 = c_Groups_Ozero__class_Ozero(_1053966))]]], (49864 ^ _780119) ^ [_1791213, _1791215, _1791217] : [c_List_Olist__all(_1791213, _1791217, _1791215), 49867 ^ _780119 : [(49868 ^ _780119) ^ [_1791294] : [hBOOL(hAPP(hAPP(c_member(_1791213), _1791294), hAPP(c_List_Oset(_1791213), _1791215))), -(hBOOL(hAPP(_1791217, _1791294)))]]], (44514 ^ _780119) ^ [_1671929, _1671931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1671929)), hAPP(c_Code__Numeral_Onat__of, _1671931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1671929), _1671931)))], (49816 ^ _780119) ^ [_1790328, _1790330, _1790332] : [49818 ^ _780119 : [(49821 ^ _780119) ^ [] : [hBOOL(hAPP(_1790330, 49817 ^ [_1790328, _1790330, _1790332]))], (49819 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790328), 49817 ^ [_1790328, _1790330, _1790332]), hAPP(c_List_Oset(_1790328), _1790332))))]], -(c_List_Olist__all(_1790328, _1790330, _1790332))], (19729 ^ _780119) ^ [_1139025, _1139027, _1139029] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1139025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1139027), _1139029)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1139025), _1139027)), _1139029))], (28002 ^ _780119) ^ [_1297055, _1297057, _1297059, _1297061] : [class_Orderings_Olinorder(_1297055), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297055), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1297055), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1297055), _1297057), _1297059)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1297055), _1297057), _1297061))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1297055), _1297057), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1297055), _1297059), _1297061)))))], (9846 ^ _780119) ^ [_951420, _951422, _951424] : [class_Lattices_Osemilattice__inf(_951420), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951420), _951422), _951424) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951420), _951424), _951422))], (16632 ^ _780119) ^ [_1082999, _1083001, _1083003] : [class_Groups_Ocomm__monoid__add(_1082999), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083001, _1082999), _1083003), c_Orderings_Obot__class_Obot(tc_fun(_1083001, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1082999))], (9708 ^ _780119) ^ [_948112, _948114, _948116] : [9709 ^ _780119 : [(9712 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_948112), _948116))], (9710 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_948112), _948114))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_948112), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_948112, tc_HOL_Obool)), _948114), _948116))))], (28608 ^ _780119) ^ [_1308477, _1308479, _1308481] : [class_Orderings_Olinorder(_1308477), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308477), _1308479)), 28615 ^ _780119 : [(28622 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308477, tc_HOL_Obool)), _1308479), hAPP(hAPP(c_Set_Oinsert(_1308477), _1308481), c_Orderings_Obot__class_Obot(tc_fun(_1308477, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1308477, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1308477, hAPP(hAPP(c_Set_Oinsert(_1308477), _1308481), _1308479)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1308477), _1308481), c_Big__Operators_Olinorder__class_OMax(_1308477, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308477, tc_HOL_Obool)), _1308479), hAPP(hAPP(c_Set_Oinsert(_1308477), _1308481), c_Orderings_Obot__class_Obot(tc_fun(_1308477, tc_HOL_Obool)))))))], (28616 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308477, tc_HOL_Obool)), _1308479), hAPP(hAPP(c_Set_Oinsert(_1308477), _1308481), c_Orderings_Obot__class_Obot(tc_fun(_1308477, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1308477, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1308477, hAPP(hAPP(c_Set_Oinsert(_1308477), _1308481), _1308479)) = _1308481)]]], (31285 ^ _780119) ^ [_1365025, _1365027] : [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), _1365025))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1365027), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1365025))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1365027), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365025))), 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), _1365027))), c_COMBI(tc_Int_Oint))))], (6363 ^ _780119) ^ [_882666, _882668, _882670] : [hBOOL(hAPP(hAPP(c_member(_882666), _882668), hAPP(hAPP(c_Set_Oinsert(_882666), _882670), c_Orderings_Obot__class_Obot(tc_fun(_882666, tc_HOL_Obool))))), -(_882668 = _882670)], (3738 ^ _780119) ^ [_836363, _836365, _836367, _836369] : [-(c_List_Oupto(_836369, _836365) = c_List_Oupto(_836367, _836363)), _836369 = _836367, _836365 = _836363], (34054 ^ _780119) ^ [_1419704, _1419706, _1419708, _1419710, _1419712] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1419704, _1419706)), hAPP(hAPP(c_Product__Type_OPair(_1419704, _1419706), _1419710), _1419712)), _1419708)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1419704, _1419706, _1419708), _1419710), _1419712)))], (34329 ^ _780119) ^ [_1424444] : [-(c_Divides_Odivmod__nat(_1424444, 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)), _1424444))], (29258 ^ _780119) ^ [_1322517, _1322519] : [class_Orderings_Olinorder(_1322517), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322517), _1322519)), -(_1322519 = c_Orderings_Obot__class_Obot(tc_fun(_1322517, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1322517), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322517), 29271 ^ [_1322517, _1322519]), 29272 ^ [_1322517, _1322519])), hAPP(hAPP(c_Set_Oinsert(_1322517), 29271 ^ [_1322517, _1322519]), hAPP(hAPP(c_Set_Oinsert(_1322517), 29272 ^ [_1322517, _1322519]), c_Orderings_Obot__class_Obot(tc_fun(_1322517, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1322517), c_Big__Operators_Olattice_OSup__fin(_1322517, c_Orderings_Oord__class_Omax(_1322517), _1322519)), _1322519)))], (17380 ^ _780119) ^ [_1095919, _1095921, _1095923, _1095925] : [class_Rings_Olinordered__semiring(_1095919), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095919), _1095921), _1095923)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095919), _1095921), _1095925))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095919), c_Groups_Ozero__class_Ozero(_1095919)), _1095921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095919), _1095923), _1095925)))], (18438 ^ _780119) ^ [_1116439, _1116441] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1116439)), _1116441) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116439), _1116441)))], (41830 ^ _780119) ^ [_1605506, _1605508, _1605510, _1605512] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1605506, tc_HOL_Obool), hAPP(c_Set_Oimage(_1605508, tc_fun(_1605506, tc_HOL_Obool), _1605510), _1605512)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1605508, tc_fun(_1605506, tc_HOL_Obool)), _1605512), _1605510))], (40774 ^ _780119) ^ [_1579612, _1579614, _1579616] : [class_Orderings_Olinorder(_1579612), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579612), _1579614)), -(c_Big__Operators_Olinorder__class_OMax(_1579612, hAPP(hAPP(c_Set_Oinsert(_1579612), _1579616), _1579614)) = hAPP(hAPP(c_Finite__Set_Ofold(_1579612, _1579612, c_Orderings_Oord__class_Omax(_1579612)), _1579616), _1579614))], (37278 ^ _780119) ^ [_1492670, _1492672, _1492674, _1492676, _1492678, _1492680, _1492682] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1492670, _1492672, _1492674, _1492676, _1492678), _1492680), _1492682))), 37279 ^ _780119 : [(37280 ^ _780119) ^ [_1492741] : [hBOOL(hAPP(hAPP(_1492676, _1492680), _1492741)), hBOOL(hAPP(hAPP(_1492678, _1492741), _1492682))]]], (40592 ^ _780119) ^ [_1575893, _1575895, _1575897] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1575893), _1575895)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1575893, tc_HOL_Obool)), _1575895), _1575897) = hAPP(hAPP(c_Finite__Set_Ofold(_1575893, tc_fun(_1575893, tc_HOL_Obool), c_Set_Oinsert(_1575893)), _1575897), _1575895))], (43491 ^ _780119) ^ [_1646820, _1646822, _1646824] : [-(hAPP(c_List_Oset(_1646820), hAPP(hAPP(c_List_Olist_OCons(_1646820), _1646822), _1646824)) = hAPP(hAPP(c_Set_Oinsert(_1646820), _1646822), hAPP(c_List_Oset(_1646820), _1646824)))], (43989 ^ _780119) ^ [_1659637, _1659639, _1659641] : [43991 ^ _780119 : [(43994 ^ _780119) ^ [] : [hBOOL(hAPP(_1659641, 43990 ^ [_1659637, _1659639, _1659641]))], (43992 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1659637), 43990 ^ [_1659637, _1659639, _1659641]), hAPP(c_List_Oset(_1659637), _1659639))))]], 43995 ^ _780119 : [(43996 ^ _780119) ^ [_1659821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659821), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659637)), _1659639))), -(hBOOL(hAPP(_1659641, hAPP(hAPP(c_List_Onth(_1659637), _1659639), _1659821))))]]], (48045 ^ _780119) ^ [_1750710, _1750712, _1750714] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750710)), c_List_OdropWhile(_1750710, _1750712, _1750714))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750710)), _1750714))))], (25586 ^ _780119) ^ [_1247826, _1247828] : [c_Nat__Transfer_Onat__set(_1247826), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1247828), _1247826)), -(c_Nat__Transfer_Ois__nat(_1247828))], (38247 ^ _780119) ^ [_1519383] : [-(c_Wellfounded_OwfP(_1519383, hAPP(c_COMBK(tc_fun(_1519383, tc_HOL_Obool), _1519383), hAPP(c_COMBK(tc_HOL_Obool, _1519383), c_fFalse))))], (22962 ^ _780119) ^ [_1199475, _1199477] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199475)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199477)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1199475), _1199477)))], (51089 ^ _780119) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (21060 ^ _780119) ^ [_1163189, _1163191, _1163193, _1163195] : [class_Fields_Ofield(_1163189), -(_1163191 = c_Groups_Ozero__class_Ozero(_1163189)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163189), _1163193), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163189), _1163195), _1163191)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163189), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163189), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163189), _1163191), _1163193)), _1163195)), _1163191))], (3316 ^ _780119) ^ [_829872, _829874, _829876, _829878] : [-(c_List_Olexn(_829878, _829874) = c_List_Olexn(_829876, _829872)), _829878 = _829876, _829874 = _829872], (45233 ^ _780119) ^ [_1687046, _1687048, _1687050, _1687052] : [-(hAPP(hAPP(c_List_Oappend(_1687046), hAPP(hAPP(c_List_Olist_OCons(_1687046), _1687048), _1687050)), _1687052) = hAPP(hAPP(c_List_Olist_OCons(_1687046), _1687048), hAPP(hAPP(c_List_Oappend(_1687046), _1687050), _1687052)))], (46000 ^ _780119) ^ [_1706495, _1706497, _1706499] : [class_Groups_Omonoid__add(_1706495), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1706495), _1706497), hAPP(c_List_Ofoldl(_1706495, _1706495, c_Groups_Oplus__class_Oplus(_1706495), c_Groups_Ozero__class_Ozero(_1706495)), _1706499)) = hAPP(c_List_Ofoldl(_1706495, _1706495, c_Groups_Oplus__class_Oplus(_1706495), _1706497), _1706499))], (44364 ^ _780119) ^ [_1668742, _1668744, _1668746, _1668748, _1668750] : [-(_1668742 = _1668744), -(hAPP(hAPP(c_List_Onth(_1668746), hAPP(hAPP(c_List_Olist__update(_1668746, _1668748), _1668742), _1668750)), _1668744) = hAPP(hAPP(c_List_Onth(_1668746), _1668748), _1668744))], (35363 ^ _780119) ^ [_1446633, _1446635, _1446637, _1446639, _1446641] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1446633, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446635, _1446633, _1446637), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446635, tc_HOL_Obool)), _1446639), _1446641))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446633, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446635, _1446633, _1446637), _1446639)), hAPP(c_Relation_OImage(_1446635, _1446633, _1446637), _1446641)))))], (23344 ^ _780119) ^ [_1206688, _1206690] : [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)), _1206688)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1206690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1206688), _1206690)))], (34551 ^ _780119) ^ [_1428542, _1428544, _1428546] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1428542, _1428544), _1428546)), 34554 ^ _780119 : [(34555 ^ _780119) ^ [_1428627] : [hBOOL(hAPP(hAPP(_1428544, _1428627), _1428546)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1428542, _1428544), _1428627)))]]], (13140 ^ _780119) ^ [_1019470, _1019472, _1019474, _1019476, _1019478] : [class_Groups_Ocomm__monoid__mult(_1019470), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019472), _1019474)), hBOOL(hAPP(hAPP(c_member(_1019472), _1019476), _1019474)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1019472, _1019470), _1019478), _1019474) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019470), hAPP(_1019478, _1019476)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1019472, _1019470), _1019478), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1019472, tc_HOL_Obool)), _1019474), hAPP(hAPP(c_Set_Oinsert(_1019472), _1019476), c_Orderings_Obot__class_Obot(tc_fun(_1019472, tc_HOL_Obool)))))))], (14671 ^ _780119) ^ [_1049395, _1049397, _1049399, _1049401, _1049403] : [class_Groups_Ocomm__monoid__mult(_1049395), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049397), _1049399)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1049397, tc_HOL_Obool)), _1049401), _1049399)), 14685 ^ _780119 : [(14688 ^ _780119) ^ [] : [hAPP(_1049403, 14684 ^ [_1049395, _1049397, _1049399, _1049401, _1049403]) = c_Groups_Oone__class_Oone(_1049395)], (14686 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1049397), 14684 ^ [_1049395, _1049397, _1049399, _1049401, _1049403]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049397, tc_HOL_Obool)), _1049399), _1049401))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1049397, _1049395), _1049403), _1049401) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1049397, _1049395), _1049403), _1049399))], (3424 ^ _780119) ^ [_831562, _831564, _831566, _831568] : [-(c_Random_Oselect(_831568, _831564) = c_Random_Oselect(_831566, _831562)), _831568 = _831566, _831564 = _831562], (42304 ^ _780119) ^ [_1616426, _1616428] : [-(c_Nitpick_Ouminus__frac(_1616426, _1616428) = c_Nitpick_OAbs__Frac(_1616426, 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(_1616426), _1616428))), hAPP(c_Nitpick_Odenom(_1616426), _1616428))))], (49028 ^ _780119) ^ [_1772165, _1772167, _1772169, _1772171, _1772173, _1772175, _1772177] : [c_List_Olist__all2(_1772165, _1772173, hAPP(hAPP(c_COMBC(_1772165, tc_fun(_1772173, _1772167), tc_fun(_1772173, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1772167, tc_HOL_Obool), tc_fun(tc_fun(_1772173, _1772167), tc_fun(_1772173, tc_HOL_Obool)), _1772165), c_COMBB(_1772167, tc_HOL_Obool, _1772173)), _1772169)), _1772175), _1772171, _1772177), -(c_List_Olist__all2(_1772165, _1772167, _1772169, _1772171, hAPP(hAPP(c_List_Omap(_1772173, _1772167), _1772175), _1772177)))], (1310 ^ _780119) ^ [_799218, _799220] : [-(class_Lattices_Osemilattice__inf(_799218)), _799220 = _799218, class_Lattices_Osemilattice__inf(_799220)], (21564 ^ _780119) ^ [_1173438] : [-(hAPP(c_Set_OPow(_1173438), c_Orderings_Obot__class_Obot(tc_fun(_1173438, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1173438, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1173438, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1173438, tc_HOL_Obool), tc_HOL_Obool))))], (8788 ^ _780119) ^ [_931912, _931914, _931916] : [class_Orderings_Olinorder(_931912), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931912), _931914), _931916))), -(_931914 = _931916), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931912), _931916), _931914)))], (29787 ^ _780119) ^ [_1334650, _1334652, _1334654, _1334656, _1334658, _1334660] : [-(hAPP(c_Set_Oimage(_1334650, _1334652, _1334654), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334656, tc_fun(_1334650, tc_HOL_Obool)), _1334658), _1334660)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334656, tc_fun(_1334652, tc_HOL_Obool)), _1334658), hAPP(hAPP(c_COMBB(tc_fun(_1334650, tc_HOL_Obool), tc_fun(_1334652, tc_HOL_Obool), _1334656), c_Set_Oimage(_1334650, _1334652, _1334654)), _1334660)))], (24916 ^ _780119) ^ [_1236767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236767), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1236767 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 24919 ^ [_1236767]))))], (51079 ^ _780119) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (5224 ^ _780119) ^ [_860040, _860042, _860044, _860046] : [-(c_List_Ofilter(_860046, _860042) = c_List_Ofilter(_860044, _860040)), _860046 = _860044, _860042 = _860040], (51097 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (48357 ^ _780119) ^ [_1757843, _1757845] : [class_Orderings_Olinorder(_1757843), -(c_List_Olinorder__class_Osorted(_1757843, c_List_Olinorder__class_Osort__key(_1757843, _1757843, c_COMBI(_1757843), _1757845)))], (47855 ^ _780119) ^ [_1746928, _1746930, _1746932, _1746934] : [-(hBOOL(hAPP(_1746928, _1746930))), -(c_List_OtakeWhile(_1746932, _1746928, hAPP(hAPP(c_List_Olist_OCons(_1746932), _1746930), _1746934)) = c_List_Olist_ONil(_1746932))], (23627 ^ _780119) ^ [_1212019, _1212021, _1212023] : [class_Orderings_Oorder(_1212019), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212019), _1212021), _1212023)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1212019, _1212023, _1212021) = c_Orderings_Obot__class_Obot(tc_fun(_1212019, tc_HOL_Obool)))], (5346 ^ _780119) ^ [_861905, _861907, _861909, _861911, _861913, _861915, _861917, _861919, _861921, _861923] : [-(c_Nitpick_Opair__box_Opair__box__case(_861923, _861919, _861915, _861911, _861907) = c_Nitpick_Opair__box_Opair__box__case(_861921, _861917, _861913, _861909, _861905)), _861923 = _861921, _861919 = _861917, _861915 = _861913, _861911 = _861909, _861907 = _861905], (32737 ^ _780119) ^ [_1390341, _1390343] : [class_Groups_Omonoid__mult(_1390341), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1390341), _1390343), 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(_1390341), _1390343), _1390343))], (51081 ^ _780119) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (6155 ^ _780119) ^ [_878283, _878285, _878287, _878289] : [hBOOL(hAPP(hAPP(c_member(_878283), _878285), _878287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878283, tc_HOL_Obool)), _878287), _878289)), -(hBOOL(hAPP(hAPP(c_member(_878283), _878285), _878289)))], (4206 ^ _780119) ^ [_843693, _843695] : [_843695 = _843693, -(c_Orderings_Otop__class_Otop(_843695) = c_Orderings_Otop__class_Otop(_843693))], (36309 ^ _780119) ^ [_1468732, _1468734, _1468736, _1468738, _1468740] : [c_Fun_Oinj__on(_1468732, _1468734, _1468736, c_Orderings_Otop__class_Otop(tc_fun(_1468732, tc_HOL_Obool))), 36312 ^ _780119 : [(36319 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1468732), _1468738), _1468740)), -(hBOOL(hAPP(hAPP(c_member(_1468734), hAPP(_1468736, _1468738)), hAPP(c_Set_Oimage(_1468732, _1468734, _1468736), _1468740))))], (36313 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1468734), hAPP(_1468736, _1468738)), hAPP(c_Set_Oimage(_1468732, _1468734, _1468736), _1468740))), -(hBOOL(hAPP(hAPP(c_member(_1468732), _1468738), _1468740)))]]], (50845 ^ _780119) ^ [_1811428, _1811430, _1811432] : [-(c_FunDef_OTHE__default(_1811430, _1811432, _1811428) = _1811432), 50847 ^ _780119 : [(50850 ^ _780119) ^ [_1811550] : [hBOOL(hAPP(_1811428, _1811550)), -(_1811550 = 50846 ^ [_1811428, _1811430, _1811432])], (50848 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1811428, 50846 ^ [_1811428, _1811430, _1811432])))]]], (29791 ^ _780119) ^ [_1334811, _1334813, _1334815, _1334817, _1334819] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334811, tc_fun(_1334813, tc_HOL_Obool)), _1334815), hAPP(hAPP(c_COMBS(_1334811, tc_fun(_1334813, tc_HOL_Obool), tc_fun(_1334813, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1334813, tc_HOL_Obool), tc_fun(tc_fun(_1334813, tc_HOL_Obool), tc_fun(_1334813, tc_HOL_Obool)), _1334811), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334813, tc_HOL_Obool))), _1334817)), _1334819)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334813, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334811, tc_fun(_1334813, tc_HOL_Obool)), _1334815), _1334817)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334811, tc_fun(_1334813, tc_HOL_Obool)), _1334815), _1334819)))], (41910 ^ _780119) ^ [_1607165, _1607167, _1607169] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1607165, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1607165, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1607165, tc_HOL_Obool), tc_HOL_Obool)), _1607167), _1607169))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607165, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1607165, tc_HOL_Obool), _1607167)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1607165, tc_HOL_Obool), _1607169)))))], (35829 ^ _780119) ^ [_1458011, _1458013, _1458015, _1458017, _1458019, _1458021, _1458023, _1458025, _1458027, _1458029] : [c_Equiv__Relations_Oequiv(_1458011, _1458013, _1458015), c_Equiv__Relations_Oequiv(_1458017, _1458019, _1458021), c_Equiv__Relations_Ocongruent2(_1458011, _1458017, tc_fun(_1458023, tc_HOL_Obool), _1458015, _1458021, _1458025), hBOOL(hAPP(hAPP(c_member(_1458011), _1458027), _1458013)), hBOOL(hAPP(hAPP(c_member(_1458017), _1458029), _1458019)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458011, tc_fun(_1458023, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1458011, _1458011, _1458015), hAPP(hAPP(c_Set_Oinsert(_1458011), _1458027), c_Orderings_Obot__class_Obot(tc_fun(_1458011, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1458017, tc_fun(_1458023, tc_HOL_Obool)), tc_fun(_1458023, tc_HOL_Obool), _1458011), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458017, tc_fun(_1458023, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1458017, _1458017, _1458021), hAPP(hAPP(c_Set_Oinsert(_1458017), _1458029), c_Orderings_Obot__class_Obot(tc_fun(_1458017, tc_HOL_Obool)))))), _1458025)) = hAPP(hAPP(_1458025, _1458027), _1458029))], (6487 ^ _780119) ^ [_885077, _885079, _885081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885077, tc_HOL_Obool)), _885079), _885081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885077, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_885077, tc_fun(_885077, tc_HOL_Obool), tc_HOL_Obool), c_member(_885077)), _885079)), hAPP(hAPP(c_COMBC(_885077, tc_fun(_885077, tc_HOL_Obool), tc_HOL_Obool), c_member(_885077)), _885081))))], (37692 ^ _780119) ^ [_1502605, _1502607] : [-(hAPP(c_Relation_OField(_1502605), _1502607) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1502605, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1502605, _1502605), _1502607)), hAPP(c_Relation_ORange(_1502605, _1502605), _1502607)))], (3004 ^ _780119) ^ [_824902, _824904, _824906, _824908, _824910, _824912] : [-(c_Relation_Orel__comp(_824912, _824908, _824904) = c_Relation_Orel__comp(_824910, _824906, _824902)), _824912 = _824910, _824908 = _824906, _824904 = _824902], (6007 ^ _780119) ^ [_875671, _875673, _875675] : [_875671 = _875673, 6010 ^ _780119 : [(6013 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875675, tc_HOL_Obool)), _875673), _875671)))], (6011 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875675, tc_HOL_Obool)), _875671), _875673)))]]], (26489 ^ _780119) ^ [_1263532, _1263534, _1263536] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1263532), hAPP(c_Set_OCollect(_1263532), hAPP(hAPP(c_COMBS(_1263532, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263532), c_fdisj), _1263534)), _1263536)))), 26492 ^ _780119 : [(26495 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1263532), hAPP(c_Set_OCollect(_1263532), _1263536))))], (26493 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1263532), hAPP(c_Set_OCollect(_1263532), _1263534))))]]], (1830 ^ _780119) ^ [_805718, _805720] : [-(class_Nat_Osize(_805718)), _805720 = _805718, class_Nat_Osize(_805720)], (36459 ^ _780119) ^ [_1471806, _1471808, _1471810, _1471812] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1471806), _1471808)), hAPP(c_Finite__Set_Ocard(_1471810), hAPP(c_Set_Oimage(_1471806, _1471810, _1471812), _1471808)) = hAPP(c_Finite__Set_Ocard(_1471806), _1471808), -(c_Fun_Oinj__on(_1471806, _1471810, _1471812, _1471808))], (27050 ^ _780119) ^ [_1276568, _1276570, _1276572, _1276574, _1276576, _1276578] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276568), _1276570)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276572), _1276574)), 27060 ^ _780119 : [(27063 ^ _780119) ^ [] : [hAPP(c_Finite__Set_Ocard(_1276568), hAPP(c_Set_OCollect(_1276568), hAPP(hAPP(c_COMBS(_1276568, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1276568), c_fconj), hAPP(hAPP(c_COMBC(_1276568, tc_fun(_1276568, tc_HOL_Obool), tc_HOL_Obool), c_member(_1276568)), _1276570))), hAPP(hAPP(c_COMBC(_1276568, _1276572, tc_HOL_Obool), _1276576), 27059 ^ [_1276568, _1276570, _1276572, _1276574, _1276576, _1276578])))) = hAPP(_1276578, 27059 ^ [_1276568, _1276570, _1276572, _1276574, _1276576, _1276578])], (27061 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1276572), 27059 ^ [_1276568, _1276570, _1276572, _1276574, _1276576, _1276578]), _1276574)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1276568, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1276572, tc_HOL_Obool), tc_Nat_Onat, _1276568), c_Finite__Set_Ocard(_1276572)), hAPP(hAPP(c_COMBB(tc_fun(_1276572, tc_HOL_Obool), tc_fun(_1276572, tc_HOL_Obool), _1276568), c_Set_OCollect(_1276572)), hAPP(hAPP(c_COMBB(tc_fun(_1276572, tc_HOL_Obool), tc_fun(_1276572, tc_HOL_Obool), _1276568), hAPP(c_COMBS(_1276572, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1276572), c_fconj), hAPP(hAPP(c_COMBC(_1276572, tc_fun(_1276572, tc_HOL_Obool), tc_HOL_Obool), c_member(_1276572)), _1276574)))), _1276576)))), _1276570) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1276572, tc_Nat_Onat), _1276578), _1276574))], (6513 ^ _780119) ^ [_885633, _885635, _885637, _885639, _885641] : [c_Finite__Set_Ofolding__one(_885633, _885635, _885637), hBOOL(hAPP(c_Finite__Set_Ofinite(_885633), _885639)), -(hBOOL(hAPP(hAPP(c_member(_885633), _885641), _885639))), -(_885639 = c_Orderings_Obot__class_Obot(tc_fun(_885633, tc_HOL_Obool))), -(hAPP(_885637, hAPP(hAPP(c_Set_Oinsert(_885633), _885641), _885639)) = hAPP(hAPP(_885635, _885641), hAPP(_885637, _885639)))], (26207 ^ _780119) ^ [_1258082, _1258084] : [class_Groups_Oordered__ab__group__add(_1258082), -(hAPP(c_Set_Oimage(_1258082, _1258082, c_Groups_Ouminus__class_Ouminus(_1258082)), hAPP(c_SetInterval_Oord__class_OatLeast(_1258082), _1258084)) = hAPP(c_SetInterval_Oord__class_OatMost(_1258082), hAPP(c_Groups_Ouminus__class_Ouminus(_1258082), _1258084)))], (22253 ^ _780119) ^ [_1186217, _1186219] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186217, _1186219) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1186217 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186219), 22256 ^ [_1186217, _1186219]))], (24869 ^ _780119) ^ [_1235834, _1235836, _1235838] : [class_Orderings_Olinorder(_1235834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235834), _1235836), _1235838)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235834, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1235834), _1235836), c_Orderings_Obot__class_Obot(tc_fun(_1235834, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1235834, _1235836, _1235838)) = c_SetInterval_Oord__class_OatLeastAtMost(_1235834, _1235836, _1235838))], (42913 ^ _780119) ^ [_1630575, _1630577, _1630579, _1630581, _1630583] : [hBOOL(hAPP(c_List_Odistinct(_1630575), hAPP(hAPP(c_List_Omap(tc_prod(_1630575, _1630577), _1630575), c_Product__Type_Ofst(_1630575, _1630577)), _1630579))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1630575, _1630577)), hAPP(hAPP(c_Product__Type_OPair(_1630575, _1630577), _1630581), _1630583)), hAPP(c_List_Oset(tc_prod(_1630575, _1630577)), _1630579))), -(hAPP(hAPP(c_Map_Omap__of(_1630575, _1630577), _1630579), _1630581) = hAPP(c_Option_Ooption_OSome(_1630577), _1630583))], (45088 ^ _780119) ^ [_1683752, _1683754, _1683756] : [hAPP(hAPP(c_List_Oappend(_1683752), _1683754), _1683756) = _1683754, -(_1683756 = c_List_Olist_ONil(_1683752))], (51073 ^ _780119) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (22394 ^ _780119) ^ [_1188847, _1188849, _1188851, _1188853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1188849), _1188851)), -(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), _1188851), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1188853, _1188847))), _1188849)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188851), _1188847))))], (9550 ^ _780119) ^ [_944814, _944816, _944818] : [class_Lattices_Olattice(_944814), hAPP(_944816, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944814), 9555 ^ [_944814, _944816, _944818]), 9556 ^ [_944814, _944816, _944818])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944814), hAPP(_944816, 9555 ^ [_944814, _944816, _944818])), hAPP(_944816, 9556 ^ [_944814, _944816, _944818])), hBOOL(hAPP(c_Finite__Set_Ofinite(_944814), _944818)), -(_944818 = c_Orderings_Obot__class_Obot(tc_fun(_944814, tc_HOL_Obool))), -(hAPP(_944816, c_Big__Operators_Olattice__class_OSup__fin(_944814, _944818)) = c_Big__Operators_Olattice__class_OSup__fin(_944814, hAPP(c_Set_Oimage(_944814, _944814, _944816), _944818)))], (35383 ^ _780119) ^ [_1447247, _1447249, _1447251, _1447253, _1447255, _1447257] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1447253, _1447253)), hAPP(hAPP(c_Product__Type_OPair(_1447253, _1447253), hAPP(_1447257, _1447249)), hAPP(_1447257, _1447251))), _1447255)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447247, _1447247)), hAPP(hAPP(c_Product__Type_OPair(_1447247, _1447247), _1447249), _1447251)), hAPP(hAPP(c_Relation_Oinv__image(_1447253, _1447247), _1447255), _1447257))))], (22958 ^ _780119) ^ [_1199383, _1199385] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199383)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199385)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1199383), _1199385)))], (1220 ^ _780119) ^ [_798093, _798095] : [-(class_Rings_Oring__1(_798093)), _798095 = _798093, class_Rings_Oring__1(_798095)], (27162 ^ _780119) ^ [_1280516] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1280516) = 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), _1280516), c_Int_Onat)))))], (48851 ^ _780119) ^ [_1768144, _1768146, _1768148] : [hBOOL(hAPP(c_List_Olistsp(_1768144, _1768146), _1768148)), 48854 ^ _780119 : [(48855 ^ _780119) ^ [_1768233] : [hBOOL(hAPP(hAPP(c_member(_1768144), _1768233), hAPP(c_List_Oset(_1768144), _1768148))), -(hBOOL(hAPP(_1768146, _1768233)))]]], (18055 ^ _780119) ^ [_1109014, _1109016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1109014), _1109016))), 18058 ^ _780119 : [(18061 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1109014), _1109016)))], (18059 ^ _780119) ^ [] : [_1109016 = c_Orderings_Obot__class_Obot(tc_fun(_1109014, tc_HOL_Obool))]]], (41024 ^ _780119) ^ [_1584369, _1584371, _1584373, _1584375, _1584377, _1584379, _1584381] : [c_Finite__Set_Ofun__left__comm(_1584369, _1584371, _1584373), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1584369, _1584371, _1584373, _1584375, _1584377), _1584379)), hBOOL(hAPP(hAPP(c_member(_1584369), _1584381), _1584377)), 41036 ^ _780119 : [(41039 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1584369, _1584371, _1584373, _1584375, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1584369, tc_HOL_Obool)), _1584377), hAPP(hAPP(c_Set_Oinsert(_1584369), _1584381), c_Orderings_Obot__class_Obot(tc_fun(_1584369, tc_HOL_Obool))))), 41035 ^ [_1584369, _1584371, _1584373, _1584375, _1584377, _1584379, _1584381])))], (41037 ^ _780119) ^ [] : [-(_1584379 = hAPP(hAPP(_1584373, _1584381), 41035 ^ [_1584369, _1584371, _1584373, _1584375, _1584377, _1584379, _1584381]))]]], (21544 ^ _780119) ^ [_1173002] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1173002) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19845 ^ _780119) ^ [_1140998, _1141000, _1141002] : [class_Rings_Odivision__ring(_1140998), -(_1141000 = c_Groups_Ozero__class_Ozero(_1140998)), 19852 ^ _780119 : [(19859 ^ _780119) ^ [] : [_1141002 = _1141000, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140998), _1141002), _1141000) = c_Groups_Oone__class_Oone(_1140998))], (19853 ^ _780119) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140998), _1141002), _1141000) = c_Groups_Oone__class_Oone(_1140998), -(_1141002 = _1141000)]]], (6264 ^ _780119) ^ [_880531, _880533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880531, tc_HOL_Obool)), _880533), c_Orderings_Obot__class_Obot(tc_fun(_880531, tc_HOL_Obool)))), -(_880533 = c_Orderings_Obot__class_Obot(tc_fun(_880531, tc_HOL_Obool)))], (46674 ^ _780119) ^ [_1721069, _1721071, _1721073, _1721075] : [hBOOL(hAPP(hAPP(c_member(_1721069), _1721071), hAPP(c_List_Oset(_1721069), _1721073))), -(hBOOL(hAPP(_1721075, _1721071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721069)), hAPP(c_List_Ofilter(_1721069, _1721075), _1721073))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721069)), _1721073))))], (27164 ^ _780119) ^ [_1280557, _1280559, _1280561] : [class_Lattices_Odistrib__lattice(_1280557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1280557), _1280559)), -(_1280559 = c_Orderings_Obot__class_Obot(tc_fun(_1280557, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280557), _1280561), c_Big__Operators_Olattice__class_OInf__fin(_1280557, _1280559)) = c_Big__Operators_Olattice__class_OInf__fin(_1280557, hAPP(c_Set_OCollect(_1280557), hAPP(hAPP(c_COMBB(tc_fun(_1280557, tc_HOL_Obool), tc_HOL_Obool, _1280557), c_HOL_OEx(_1280557)), hAPP(hAPP(c_COMBC(_1280557, tc_fun(_1280557, tc_HOL_Obool), tc_fun(_1280557, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1280557, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1280557, tc_HOL_Obool), tc_fun(_1280557, tc_HOL_Obool)), _1280557), c_COMBS(_1280557, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1280557, tc_HOL_Obool), tc_fun(_1280557, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1280557), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1280557), c_fconj)), hAPP(hAPP(c_COMBC(_1280557, tc_fun(_1280557, _1280557), tc_fun(_1280557, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1280557, tc_HOL_Obool), tc_fun(tc_fun(_1280557, _1280557), tc_fun(_1280557, tc_HOL_Obool)), _1280557), c_COMBB(_1280557, tc_HOL_Obool, _1280557)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280557), _1280561))))), hAPP(hAPP(c_COMBC(_1280557, tc_fun(_1280557, tc_HOL_Obool), tc_HOL_Obool), c_member(_1280557)), _1280559))))))], (4432 ^ _780119) ^ [_847182, _847184] : [_847184 = _847182, -(c_Nat_Osemiring__1__class_Oof__nat(_847184) = c_Nat_Osemiring__1__class_Oof__nat(_847182))], (2298 ^ _780119) ^ [_813921, _813923, _813925, _813927, _813929, _813931] : [-(c_Com_Ocom_OLocal(_813931, _813927, _813923) = c_Com_Ocom_OLocal(_813929, _813925, _813921)), _813931 = _813929, _813927 = _813925, _813923 = _813921], (19064 ^ _780119) ^ [_1127412, _1127414] : [class_Divides_Osemiring__div(_1127412), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1127412), c_Groups_Ozero__class_Ozero(_1127412)), _1127414) = c_Groups_Ozero__class_Ozero(_1127412))], (26453 ^ _780119) ^ [_1262855, _1262857] : [class_Groups_Oordered__ab__group__add__abs(_1262855), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262855), _1262857), hAPP(c_Groups_Oabs__class_Oabs(_1262855), _1262857))))], (29570 ^ _780119) ^ [_1329097, _1329099, _1329101, _1329103] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1329097, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1329099)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1329097, tc_HOL_Obool), tc_Nat_Onat), _1329101), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1329103))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1329097, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1329103, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1329099), _1329103))), _1329101))], (39134 ^ _780119) ^ [_1539945, _1539947, _1539949, _1539951, _1539953] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1539945, _1539947, _1539949), _1539951), _1539953))), hBOOL(hAPP(hAPP(_1539947, _1539951), _1539953)), hBOOL(hAPP(_1539949, _1539953))], (38030 ^ _780119) ^ [_1513893, _1513895] : [-(hAPP(c_Fun_Oid(_1513893), _1513895) = _1513895)], (39275 ^ _780119) ^ [_1543254, _1543256, _1543258] : [-(hBOOL(hAPP(hAPP(c_member(_1543254), _1543256), c_Wellfounded_Oacc(_1543254, _1543258)))), 39279 ^ _780119 : [(39282 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1543254), 39278 ^ [_1543254, _1543256, _1543258]), c_Wellfounded_Oacc(_1543254, _1543258)))], (39280 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1543254, _1543254)), hAPP(hAPP(c_Product__Type_OPair(_1543254, _1543254), 39278 ^ [_1543254, _1543256, _1543258]), _1543256)), _1543258)))]]], (2288 ^ _780119) ^ [_813772, _813774, _813776, _813778] : [-(c_Com_Ocom_OSemi(_813778, _813774) = c_Com_Ocom_OSemi(_813776, _813772)), _813778 = _813776, _813774 = _813772], (9180 ^ _780119) ^ [_937749, _937751, _937753, _937755] : [class_Lattices_Osemilattice__sup(_937749), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937749), _937751), _937753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937749), _937751), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_937749), _937755), _937753))))], (46447 ^ _780119) ^ [_1716360, _1716362, _1716364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1716360), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716362)), _1716364))), -(c_List_Obutlast(_1716362, hAPP(hAPP(c_List_Otake(_1716362), _1716360), _1716364)) = hAPP(hAPP(c_List_Otake(_1716362), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1716360), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1716364))], (31239 ^ _780119) ^ [_1364164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1364164), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1364164)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51463 ^ _780119) ^ [_1819295] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1819295)))], (13548 ^ _780119) ^ [_1026841, _1026843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1026841)), _1026843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026841), _1026843)))], (31503 ^ _780119) ^ [_1368658] : [class_Int_Onumber__ring(_1368658), -(hAPP(c_Int_Onumber__class_Onumber__of(_1368658), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1368658))], (40078 ^ _780119) ^ [_1562680, _1562682, _1562684] : [-(hAPP(c_Relation_ORange(_1562680, _1562682), hAPP(c_Relation_Oconverse(_1562682, _1562680), _1562684)) = hAPP(c_Relation_ODomain(_1562682, _1562680), _1562684))], (50250 ^ _780119) ^ [_1798511] : [-(c_Lazy__Sequence_Oyieldn(_1798511) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1798511), _1798511, c_Lazy__Sequence_Oyield(_1798511)))], (29911 ^ _780119) ^ [_1338420, _1338422, _1338424, _1338426, _1338428] : [-(_1338420 = c_Orderings_Obot__class_Obot(tc_fun(_1338422, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338424, tc_HOL_Obool)), _1338426), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338422, tc_fun(_1338424, tc_HOL_Obool)), _1338420), _1338428)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338422, tc_fun(_1338424, tc_HOL_Obool)), _1338420), hAPP(hAPP(c_COMBB(tc_fun(_1338424, tc_HOL_Obool), tc_fun(_1338424, tc_HOL_Obool), _1338422), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338424, tc_HOL_Obool)), _1338426)), _1338428)))], (45874 ^ _780119) ^ [_1703887, _1703889, _1703891] : [-(hAPP(hAPP(c_List_Odrop(_1703887), hAPP(c_Nat_OSuc, _1703889)), _1703891) = hAPP(hAPP(c_List_Odrop(_1703887), _1703889), hAPP(c_List_Otl(_1703887), _1703891)))], (928 ^ _780119) ^ [_794259, _794261, _794263, _794265, _794267, _794269, _794271, _794273] : [-(c_Nat__Transfer_Otransfer__morphism(_794271, _794267, _794263, _794259)), c_Nat__Transfer_Otransfer__morphism(_794273, _794269, _794265, _794261), _794273 = _794271, _794269 = _794267, _794265 = _794263, _794261 = _794259], (15532 ^ _780119) ^ [_1063184, _1063186, _1063188, _1063190] : [-(hBOOL(hAPP(hAPP(c_member(_1063184), hAPP(_1063186, _1063188)), hAPP(c_Set_Oimage(_1063190, _1063184, _1063186), c_Orderings_Otop__class_Otop(tc_fun(_1063190, tc_HOL_Obool))))))], (24895 ^ _780119) ^ [_1236355, _1236357, _1236359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236355)), 24901 ^ _780119 : [(24904 ^ _780119) ^ [] : [hBOOL(hAPP(_1236357, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24900 ^ [_1236355, _1236357, _1236359]), _1236355)))], (24902 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1236357, 24900 ^ [_1236355, _1236357, _1236359])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236359)), 24909 ^ _780119 : [(24910 ^ _780119) ^ [_1236644] : [hBOOL(hAPP(_1236357, _1236644)), -(hBOOL(hAPP(_1236357, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1236644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236359), _1236355)))))]]], (34859 ^ _780119) ^ [_1434497, _1434499, _1434501] : [-(hAPP(c_Product__Type_Ofst(_1434497, _1434499), _1434501) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1434497, _1434499, _1434497), c_COMBK(_1434497, _1434499)), _1434501))], (45323 ^ _780119) ^ [_1689431, _1689433, _1689435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689431), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689433)), _1689435))), -(hAPP(hAPP(c_List_Otake(_1689433), hAPP(c_Nat_OSuc, _1689431)), _1689435) = hAPP(hAPP(c_List_Oappend(_1689433), hAPP(hAPP(c_List_Otake(_1689433), _1689431), _1689435)), hAPP(hAPP(c_List_Olist_OCons(_1689433), hAPP(hAPP(c_List_Onth(_1689433), _1689435), _1689431)), c_List_Olist_ONil(_1689433))))], (41264 ^ _780119) ^ [_1590412, _1590414, _1590416, _1590418, _1590420, _1590422] : [hBOOL(hAPP(hAPP(c_member(_1590412), _1590414), _1590416)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590412, tc_fun(_1590418, tc_HOL_Obool)), _1590416), hAPP(hAPP(c_COMBB(tc_fun(_1590418, tc_HOL_Obool), tc_fun(_1590418, tc_HOL_Obool), _1590412), hAPP(c_Set_Oinsert(_1590418), _1590420)), _1590422)) = hAPP(hAPP(c_Set_Oinsert(_1590418), _1590420), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590412, tc_fun(_1590418, tc_HOL_Obool)), _1590416), _1590422)))], (36413 ^ _780119) ^ [_1470752, _1470754] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1470752), c_Orderings_Otop__class_Otop(tc_fun(_1470752, tc_HOL_Obool)))), c_Fun_Oinj__on(_1470752, _1470752, _1470754, c_Orderings_Otop__class_Otop(tc_fun(_1470752, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1470752, _1470752, _1470754), c_Orderings_Otop__class_Otop(tc_fun(_1470752, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1470752, tc_HOL_Obool)))], (36792 ^ _780119) ^ [_1479553, _1479555, _1479557, _1479559, _1479561] : [hAPP(c_Set_Oimage(_1479553, _1479555, _1479557), c_Orderings_Otop__class_Otop(tc_fun(_1479553, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1479555, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479553, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1479553, _1479555, _1479557), _1479559)), _1479561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479555, tc_HOL_Obool)), _1479559), hAPP(c_Set_Oimage(_1479553, _1479555, _1479557), _1479561))))], (37649 ^ _780119) ^ [_1501487, _1501489, _1501491] : [_1501491 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501487, _1501489), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1501487, _1501489), _1501491) = c_Orderings_Obot__class_Obot(tc_fun(_1501487, tc_HOL_Obool)))], (48489 ^ _780119) ^ [_1760715, _1760717, _1760719] : [class_Enum_Oenum(_1760715), class_Enum_Oenum(_1760717), 48496 ^ _780119 : [(48503 ^ _780119) ^ [] : [c_Enum_Oex__n__lists(_1760715, hAPP(hAPP(c_COMBB(tc_fun(_1760717, _1760715), tc_HOL_Obool, tc_List_Olist(_1760715)), _1760719), hAPP(hAPP(c_COMBB(tc_fun(_1760717, tc_Option_Ooption(_1760715)), tc_fun(_1760717, _1760715), tc_List_Olist(_1760715)), c_Fun_Ocomp(tc_Option_Ooption(_1760715), _1760715, _1760717, c_Option_Othe(_1760715))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1760717, _1760715)), tc_fun(_1760717, tc_Option_Ooption(_1760715)), tc_List_Olist(_1760715)), c_Map_Omap__of(_1760717, _1760715)), hAPP(c_List_Ozip(_1760717, _1760715), c_Enum_Oenum__class_Oenum(_1760717))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760717)), c_Enum_Oenum__class_Oenum(_1760717))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1760717, _1760715)), _1760719)))], (48497 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1760717, _1760715)), _1760719)), -(c_Enum_Oex__n__lists(_1760715, hAPP(hAPP(c_COMBB(tc_fun(_1760717, _1760715), tc_HOL_Obool, tc_List_Olist(_1760715)), _1760719), hAPP(hAPP(c_COMBB(tc_fun(_1760717, tc_Option_Ooption(_1760715)), tc_fun(_1760717, _1760715), tc_List_Olist(_1760715)), c_Fun_Ocomp(tc_Option_Ooption(_1760715), _1760715, _1760717, c_Option_Othe(_1760715))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1760717, _1760715)), tc_fun(_1760717, tc_Option_Ooption(_1760715)), tc_List_Olist(_1760715)), c_Map_Omap__of(_1760717, _1760715)), hAPP(c_List_Ozip(_1760717, _1760715), c_Enum_Oenum__class_Oenum(_1760717))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760717)), c_Enum_Oenum__class_Oenum(_1760717))))]]], (6165 ^ _780119) ^ [_878468, _878470, _878472, _878474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878468, tc_HOL_Obool)), _878470), _878472)), hBOOL(hAPP(hAPP(c_member(_878468), _878474), _878470)), -(hBOOL(hAPP(hAPP(c_member(_878468), _878474), _878472)))], (8450 ^ _780119) ^ [_926835, _926837, _926839, _926841] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_926835, _926837), _926839), _926841), hAPP(_926839, _926841)) = _926839)], (43422 ^ _780119) ^ [_1643910, _1643912, _1643914, _1643916] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643910), tc_List_Olist(_1643910))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643910), tc_List_Olist(_1643910)), _1643912), _1643914)), c_List_Olistrel(_1643910, _1643916)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643910)), _1643912) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643910)), _1643914), 43428 ^ _780119 : [(43431 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1643910, _1643910, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1643910, tc_fun(tc_prod(_1643910, _1643910), tc_HOL_Obool), tc_fun(_1643910, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1643910, tc_fun(tc_fun(tc_prod(_1643910, _1643910), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1643910, _1643910), tc_HOL_Obool), tc_fun(_1643910, tc_HOL_Obool)), _1643910), c_COMBC(_1643910, tc_fun(tc_prod(_1643910, _1643910), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1643910, tc_prod(_1643910, _1643910)), tc_fun(_1643910, tc_fun(tc_fun(tc_prod(_1643910, _1643910), tc_HOL_Obool), tc_HOL_Obool)), _1643910), hAPP(c_COMBB(tc_prod(_1643910, _1643910), tc_fun(tc_fun(tc_prod(_1643910, _1643910), tc_HOL_Obool), tc_HOL_Obool), _1643910), c_member(tc_prod(_1643910, _1643910)))), c_Product__Type_OPair(_1643910, _1643910)))), _1643916)), 43427 ^ [_1643910, _1643912, _1643914, _1643916]))], (43429 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643910, _1643910)), 43427 ^ [_1643910, _1643912, _1643914, _1643916]), hAPP(c_List_Oset(tc_prod(_1643910, _1643910)), hAPP(hAPP(c_List_Ozip(_1643910, _1643910), _1643912), _1643914)))))]]], (16312 ^ _780119) ^ [_1077465, _1077467, _1077469] : [class_Groups_Oordered__ab__group__add(_1077465), 16315 ^ _780119 : [(16322 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077465), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077465), _1077467), _1077469)), c_Groups_Ozero__class_Ozero(_1077465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077465), _1077467), _1077469)))], (16316 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077465), _1077467), _1077469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077465), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077465), _1077467), _1077469)), c_Groups_Ozero__class_Ozero(_1077465))))]]], (34277 ^ _780119) ^ [_1423478, _1423480] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1423478))), 34280 ^ _780119 : [(34287 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1423480))), -(c_Divides_Odivmod__int(_1423478, _1423480) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1423478), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1423480))))], (34281 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1423480)), -(c_Divides_Odivmod__int(_1423478, _1423480) = c_Divides_OnegDivAlg(_1423478, _1423480))]]], (44872 ^ _780119) ^ [_1678730, _1678732, _1678734, _1678736] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1678730) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1678732), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1678730)), hAPP(hAPP(c_List_Olist_OCons(_1678732), _1678734), _1678736)) = hAPP(hAPP(c_List_Olist_OCons(_1678732), _1678734), hAPP(hAPP(c_List_Otake(_1678732), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1678730)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1678736)))], (35489 ^ _780119) ^ [_1450127, _1450129, _1450131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1450127, _1450127), tc_HOL_Obool)), _1450129), _1450131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1450127, tc_HOL_Obool)), hAPP(c_Relation_OField(_1450127), _1450129)), hAPP(c_Relation_OField(_1450127), _1450131))))], (38515 ^ _780119) ^ [_1525125] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 38511 ^ [_1525125]), c_Int_OInteg)))], (44408 ^ _780119) ^ [_1669827, _1669829, _1669831, _1669833] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1669827, tc_HOL_Obool)), hAPP(c_List_Oset(_1669827), hAPP(hAPP(c_List_Olist__update(_1669827, _1669829), _1669831), _1669833))), hAPP(hAPP(c_Set_Oinsert(_1669827), _1669833), hAPP(c_List_Oset(_1669827), _1669829)))))], (22859 ^ _780119) ^ [_1197537, _1197539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197537), _1197539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197537)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197539))))], (51477 ^ _780119) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (42207 ^ _780119) ^ [_1613965, _1613967] : [-(c_Wellfounded_Owf(_1613965, _1613967)), 42210 ^ _780119 : [(42213 ^ _780119) ^ [_1614185] : [hBOOL(hAPP(hAPP(c_member(_1613965), _1614185), 42208 ^ [_1613965, _1613967])), 42217 ^ _780119 : [(42220 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613965), 42216 ^ [_1613965, _1613967, _1614185]), 42208 ^ [_1613965, _1613967])))], (42218 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613965, _1613965)), hAPP(hAPP(c_Product__Type_OPair(_1613965, _1613965), 42216 ^ [_1613965, _1613967, _1614185]), _1614185)), _1613967)))]]], (42211 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613965), 42209 ^ [_1613965, _1613967]), 42208 ^ [_1613965, _1613967])))]]], (2634 ^ _780119) ^ [_819137, _819139] : [_819139 = _819137, -(c_Nitpick_Oone__frac(_819139) = c_Nitpick_Oone__frac(_819137))], (22677 ^ _780119) ^ [_1194059, _1194061, _1194063, _1194065] : [class_Rings_Ocomm__semiring__1(_1194059), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194059), c_Groups_Oone__class_Oone(_1194059)), c_Groups_Oone__class_Oone(_1194059))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1194059), hAPP(hAPP(c_COMBB(_1194059, _1194059, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1194059), _1194061)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1194059, _1194059), hAPP(hAPP(c_COMBB(_1194059, tc_fun(_1194059, _1194059), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1194059)), c_Nat_Osemiring__1__class_Oof__nat(_1194059))), _1194063))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1194065))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194059), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1194059), _1194065)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194059), _1194061), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194059), _1194061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194059), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1194059), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1194065), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1194063)))))], (15126 ^ _780119) ^ [_1057015, _1057017] : [class_Groups_Ogroup__add(_1057015), 15129 ^ _780119 : [(15136 ^ _780119) ^ [] : [c_Groups_Ozero__class_Ozero(_1057015) = _1057017, -(c_Groups_Ozero__class_Ozero(_1057015) = hAPP(c_Groups_Ouminus__class_Ouminus(_1057015), _1057017))], (15130 ^ _780119) ^ [] : [c_Groups_Ozero__class_Ozero(_1057015) = hAPP(c_Groups_Ouminus__class_Ouminus(_1057015), _1057017), -(c_Groups_Ozero__class_Ozero(_1057015) = _1057017)]]], (51163 ^ _780119) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (3686 ^ _780119) ^ [_835543, _835545, _835547, _835549] : [-(c_Random_Opick(_835549, _835545) = c_Random_Opick(_835547, _835543)), _835549 = _835547, _835545 = _835543], (20706 ^ _780119) ^ [_1156609, _1156611, _1156613] : [class_Fields_Olinordered__field(_1156609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156609), _1156611), c_Groups_Ozero__class_Ozero(_1156609))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156609), c_Groups_Ozero__class_Ozero(_1156609)), _1156613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156609), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156609), _1156611), _1156613)), c_Groups_Ozero__class_Ozero(_1156609))))], (44914 ^ _780119) ^ [_1679855, _1679857, _1679859] : [-(c_List_Olistset(_1679855, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1679855, tc_HOL_Obool)), _1679857), _1679859)) = c_List_Oset__Cons(_1679855, _1679857, c_List_Olistset(_1679855, _1679859)))], (35355 ^ _780119) ^ [_1446190, _1446192, _1446194, _1446196] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1446190, _1446192), _1446194), _1446196) = hAPP(c_Set_OCollect(tc_prod(_1446192, _1446192)), hAPP(c_Product__Type_Oprod_Oprod__case(_1446192, _1446192, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1446192, tc_fun(tc_prod(_1446190, _1446190), tc_HOL_Obool), tc_fun(_1446192, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446192, tc_fun(tc_fun(tc_prod(_1446190, _1446190), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1446190, _1446190), tc_HOL_Obool), tc_fun(_1446192, tc_HOL_Obool)), _1446192), c_COMBC(_1446192, tc_fun(tc_prod(_1446190, _1446190), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446192, tc_prod(_1446190, _1446190)), tc_fun(_1446192, tc_fun(tc_fun(tc_prod(_1446190, _1446190), tc_HOL_Obool), tc_HOL_Obool)), _1446192), hAPP(c_COMBB(tc_prod(_1446190, _1446190), tc_fun(tc_fun(tc_prod(_1446190, _1446190), tc_HOL_Obool), tc_HOL_Obool), _1446192), c_member(tc_prod(_1446190, _1446190)))), hAPP(hAPP(c_COMBC(_1446192, tc_fun(_1446192, _1446190), tc_fun(_1446192, tc_prod(_1446190, _1446190))), hAPP(hAPP(c_COMBB(tc_fun(_1446190, tc_prod(_1446190, _1446190)), tc_fun(tc_fun(_1446192, _1446190), tc_fun(_1446192, tc_prod(_1446190, _1446190))), _1446192), c_COMBB(_1446190, tc_prod(_1446190, _1446190), _1446192)), hAPP(hAPP(c_COMBB(_1446190, tc_fun(_1446190, tc_prod(_1446190, _1446190)), _1446192), c_Product__Type_OPair(_1446190, _1446190)), _1446196))), _1446196)))), _1446194))))], (22451 ^ _780119) ^ [_1189903, _1189905, _1189907] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1189903), c_Map_Odom(_1189903, _1189905, _1189907))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1189903), c_Orderings_Otop__class_Otop(tc_fun(_1189903, tc_HOL_Obool))))), -(hAPP(_1189907, 22458 ^ [_1189903, _1189905, _1189907]) = c_Option_Ooption_ONone(_1189905))], (17308 ^ _780119) ^ [_1094535, _1094537, _1094539, _1094541, _1094543] : [class_Rings_Olinordered__semiring__strict(_1094535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094535), _1094537), _1094539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094535), _1094541), _1094543)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094535), c_Groups_Ozero__class_Ozero(_1094535)), _1094537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094535), c_Groups_Ozero__class_Ozero(_1094535)), _1094541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094535), _1094537), _1094541)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094535), _1094539), _1094543))))], (37688 ^ _780119) ^ [_1502441, _1502443, _1502445, _1502447] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502441, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1502441, _1502443), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1502441, _1502443), tc_HOL_Obool)), _1502445), _1502447))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1502441, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1502441, _1502443), _1502445)), hAPP(c_Relation_ODomain(_1502441, _1502443), _1502447)))))], (37542 ^ _780119) ^ [_1498660, _1498662, _1498664] : [_1498664 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1498660, _1498662), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1498660, _1498662), _1498664) = c_Orderings_Obot__class_Obot(tc_fun(_1498662, tc_HOL_Obool)))], (21276 ^ _780119) ^ [_1167412, _1167414, _1167416, _1167418, _1167420] : [class_Groups_Ocomm__monoid__add(_1167412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1167414), _1167416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1167414, tc_HOL_Obool)), _1167418), _1167416)), 21290 ^ _780119 : [(21293 ^ _780119) ^ [] : [hAPP(_1167420, 21289 ^ [_1167412, _1167414, _1167416, _1167418, _1167420]) = c_Groups_Ozero__class_Ozero(_1167412)], (21291 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1167414), 21289 ^ [_1167412, _1167414, _1167416, _1167418, _1167420]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1167414, tc_HOL_Obool)), _1167416), _1167418))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1167414, _1167412), _1167420), _1167418) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1167414, _1167412), _1167420), _1167416))], (19450 ^ _780119) ^ [_1133581, _1133583, _1133585] : [hBOOL(hAPP(_1133581, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1133583), _1133585))), 19453 ^ _780119 : [(19460 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133585)), 19463 ^ _780119 : [(19464 ^ _780119) ^ [_1133915] : [-(hBOOL(hAPP(_1133581, _1133915))), 19465 ^ _780119 : [(19466 ^ _780119) ^ [_1133986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133986), _1133585)), _1133583 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133585), _1133915)), _1133986)]]]]], (19478 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133585), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19481 ^ _780119 : [(19482 ^ _780119) ^ [_1134245] : [-(hBOOL(hAPP(_1133581, _1134245))), 19483 ^ _780119 : [(19484 ^ _780119) ^ [_1134319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133585), _1134319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1134319), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1133583 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133585), _1134245)), _1134319)]]]]], (19454 ^ _780119) ^ [] : [_1133585 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1133581, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (12159 ^ _780119) ^ [_999334, _999336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999334), _999336)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999334), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999336), _999334)) = _999336)], (34251 ^ _780119) ^ [_1423108, _1423110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1423108)), 34254 ^ _780119 : [(34261 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1423110))), 34264 ^ _780119 : [(34271 ^ _780119) ^ [] : [-(_1423108 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1423108, _1423110) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1423108), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1423110))))], (34265 ^ _780119) ^ [] : [_1423108 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1423108, _1423110) = 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)))]]], (34255 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1423110)), -(c_Divides_Odivmod__int(_1423108, _1423110) = c_Divides_OposDivAlg(_1423108, _1423110))]]], (18824 ^ _780119) ^ [_1123323, _1123325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1123323), _1123325)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123323), _1123325)))], (36712 ^ _780119) ^ [_1477628, _1477630, _1477632, _1477634, _1477636] : [hBOOL(hAPP(hAPP(c_member(_1477628), hAPP(_1477630, _1477632)), _1477634)), -(hBOOL(hAPP(hAPP(c_member(_1477636), _1477632), hAPP(c_Set_Ovimage(_1477636, _1477628, _1477630), _1477634))))], (51389 ^ _780119) ^ [_1818404] : [class_Enum_Oenum(_1818404), -(class_Enum_Oenum(tc_Option_Ooption(_1818404)))], (51101 ^ _780119) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (14774 ^ _780119) ^ [_1051454] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1051454)))], (27828 ^ _780119) ^ [_1293965, _1293967, _1293969, _1293971] : [class_Orderings_Olinorder(_1293965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293965), _1293967), _1293969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293965), _1293967), _1293971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293965), _1293967), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293965), _1293969), _1293971))))], (35067 ^ _780119) ^ [_1439004, _1439006, _1439008, _1439010, _1439012, _1439014] : [-(hAPP(c_Product__Type_Oapfst(_1439004, _1439006, _1439008, _1439010), hAPP(hAPP(c_Product__Type_OPair(_1439004, _1439008), _1439012), _1439014)) = hAPP(hAPP(c_Product__Type_OPair(_1439006, _1439008), hAPP(_1439010, _1439012)), _1439014))], (18212 ^ _780119) ^ [_1111899, _1111901, _1111903] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1111899), _1111901)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111899), _1111903)), 18222 ^ _780119 : [(18225 ^ _780119) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18223 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1111899), 18221 ^ [_1111899, _1111901, _1111903]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1111899, tc_HOL_Obool)), _1111901), _1111903))))]], -(hAPP(c_Finite__Set_Ocard(_1111899), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1111899, tc_HOL_Obool)), _1111901), _1111903)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1111899), _1111901)), hAPP(c_Finite__Set_Ocard(_1111899), _1111903)))], (3262 ^ _780119) ^ [_828937, _828939, _828941, _828943] : [-(c_Nitpick_Ocard_H(_828943, _828939) = c_Nitpick_Ocard_H(_828941, _828937)), _828943 = _828941, _828939 = _828937], (39573 ^ _780119) ^ [_1550247, _1550249, _1550251] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1550247), _1550249))), -(c_Random_Ominus__shift(_1550251, _1550247, _1550249) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1550247), _1550249))], (26811 ^ _780119) ^ [_1270193, _1270195, _1270197] : [-(hAPP(hAPP(c_Set_Oinsert(_1270193), _1270195), _1270197) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270193, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1270193), hAPP(hAPP(c_COMBC(_1270193, _1270193, tc_HOL_Obool), c_fequal), _1270195))), _1270197))], (51543 ^ _780119) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (31207 ^ _780119) ^ [_1363637, _1363639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1363637)), c_Int_OBit1(_1363639))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1363637), _1363639)))], (2408 ^ _780119) ^ [_815600, _815602] : [_815602 = _815600, -(c_Divides_Oadjust(_815602) = c_Divides_Oadjust(_815600))], (48949 ^ _780119) ^ [_1770357, _1770359] : [class_Orderings_Olinorder(_1770357), 48952 ^ _780119 : [(48973 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1770357, _1770359)), 48974 ^ _780119 : [(48977 ^ _780119) ^ [_1770917, _1770919] : [_1770359 = hAPP(hAPP(c_List_Olist_OCons(_1770357), _1770917), _1770919), 48983 ^ _780119 : [(48986 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1770357), _1770917), 48982 ^ [_1770357, _1770359, _1770917, _1770919]))], (48984 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770357), 48982 ^ [_1770357, _1770359, _1770917, _1770919]), hAPP(c_List_Oset(_1770357), _1770919))))]], c_List_Olinorder__class_Osorted(_1770357, _1770919)], (48975 ^ _780119) ^ [] : [_1770359 = c_List_Olist_ONil(_1770357)]]], (48953 ^ _780119) ^ [] : [c_List_Olinorder__class_Osorted(_1770357, _1770359), -(_1770359 = c_List_Olist_ONil(_1770357)), 48962 ^ _780119 : [(48971 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1770357, 48960 ^ [_1770357, _1770359]))], (48965 ^ _780119) ^ [_1770691] : [hBOOL(hAPP(hAPP(c_member(_1770357), _1770691), hAPP(c_List_Oset(_1770357), 48960 ^ [_1770357, _1770359]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1770357), 48961 ^ [_1770357, _1770359]), _1770691)))], (48963 ^ _780119) ^ [] : [-(_1770359 = hAPP(hAPP(c_List_Olist_OCons(_1770357), 48961 ^ [_1770357, _1770359]), 48960 ^ [_1770357, _1770359]))]]]]], (46509 ^ _780119) ^ [_1717562, _1717564, _1717566] : [-(c_List_Obutlast(_1717562, hAPP(hAPP(c_List_Oappend(_1717562), _1717564), hAPP(hAPP(c_List_Olist_OCons(_1717562), _1717566), c_List_Olist_ONil(_1717562)))) = _1717564)], (22719 ^ _780119) ^ [_1195138, _1195140, _1195142, _1195144] : [hBOOL(hAPP(hAPP(c_member(_1195138), _1195140), c_SetInterval_Oord_OgreaterThan(_1195138, _1195142, _1195144))), -(hBOOL(hAPP(hAPP(_1195142, _1195144), _1195140)))], (39383 ^ _780119) ^ [_1546116, _1546118, _1546120, _1546122, _1546124] : [-(_1546116 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1546118, _1546120, _1546116, _1546122), _1546124) = hAPP(hAPP(c_Product__Type_Oscomp(_1546120, _1546118, _1546120, tc_prod(_1546118, _1546120)), hAPP(_1546122, _1546124)), c_Random_Oiterate(_1546118, _1546120, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1546116), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1546122)))], (44993 ^ _780119) ^ [_1681976, _1681978, _1681980, _1681982, _1681984] : [hAPP(hAPP(c_List_Oappend(_1681976), _1681978), _1681980) = hAPP(hAPP(c_List_Olist_OCons(_1681976), _1681982), _1681984), 44998 ^ _780119 : [(45001 ^ _780119) ^ [] : [-(_1681980 = hAPP(hAPP(c_List_Olist_OCons(_1681976), _1681982), _1681984))], (44999 ^ _780119) ^ [] : [-(_1681978 = c_List_Olist_ONil(_1681976))]], 45003 ^ _780119 : [(45006 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1681976), 45002 ^ [_1681976, _1681978, _1681980, _1681982, _1681984]), _1681980) = _1681984)], (45004 ^ _780119) ^ [] : [-(_1681978 = hAPP(hAPP(c_List_Olist_OCons(_1681976), _1681982), 45002 ^ [_1681976, _1681978, _1681980, _1681982, _1681984]))]]], (49315 ^ _780119) ^ [_1778085, _1778087, _1778089, _1778091, _1778093] : [c_Fun_Oinj__on(_1778085, _1778087, _1778089, c_Orderings_Otop__class_Otop(tc_fun(_1778085, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1778085, _1778087), _1778089), hAPP(c_List_OremoveAll(_1778085, _1778091), _1778093)) = hAPP(c_List_OremoveAll(_1778087, hAPP(_1778089, _1778091)), hAPP(hAPP(c_List_Omap(_1778085, _1778087), _1778089), _1778093)))], (44710 ^ _780119) ^ [_1675771, _1675773] : [-(c_List_Oremove1(_1675771, _1675773, c_List_Olist_ONil(_1675771)) = c_List_Olist_ONil(_1675771))], (46438 ^ _780119) ^ [_1716110, _1716112, _1716114, _1716116] : [46440 ^ _780119 : [(46443 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1716114, 46439 ^ [_1716110, _1716112, _1716114, _1716116])), hAPP(_1716116, 46439 ^ [_1716110, _1716112, _1716114, _1716116])))], (46441 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1716110), 46439 ^ [_1716110, _1716112, _1716114, _1716116]), hAPP(c_List_Oset(_1716110), _1716112))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1716110, _1716114, _1716112)), c_List_Olist_Olist__size(_1716110, _1716116, _1716112))))], (49164 ^ _780119) ^ [_1774930, _1774932, _1774934, _1774936, _1774938] : [c_List_Olist__all2(_1774930, _1774932, _1774934, _1774936, _1774938), 49167 ^ _780119 : [(49170 ^ _780119) ^ [_1775093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1775093), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774930)), _1774936))), -(hBOOL(hAPP(hAPP(_1774934, hAPP(hAPP(c_List_Onth(_1774930), _1774936), _1775093)), hAPP(hAPP(c_List_Onth(_1774932), _1774938), _1775093))))], (49168 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774930)), _1774936) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774932)), _1774938))]]], (1720 ^ _780119) ^ [_804343, _804345] : [-(class_Rings_Osemiring__0(_804343)), _804345 = _804343, class_Rings_Osemiring__0(_804345)], (42675 ^ _780119) ^ [_1624956, _1624958, _1624960, _1624962, _1624964] : [-(c_Map_Odom(_1624956, _1624958, hAPP(hAPP(c_COMBS(_1624956, tc_Option_Ooption(_1624960), tc_Option_Ooption(_1624958)), hAPP(hAPP(c_COMBB(tc_fun(_1624960, _1624958), tc_fun(tc_Option_Ooption(_1624960), tc_Option_Ooption(_1624958)), _1624956), c_Option_Omap(_1624960, _1624958)), _1624962)), _1624964)) = c_Map_Odom(_1624956, _1624960, _1624964))], (32029 ^ _780119) ^ [_1377008, _1377010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1377008), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377008)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377010)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40498 ^ _780119) ^ [_1573956, _1573958, _1573960, _1573962] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573956, _1573956)), hAPP(hAPP(c_Product__Type_OPair(_1573956, _1573956), _1573958), _1573960)), c_Transitive__Closure_Otrancl(_1573956, _1573962))), 40502 ^ _780119 : [(40505 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573956, _1573956)), hAPP(hAPP(c_Product__Type_OPair(_1573956, _1573956), 40501 ^ [_1573956, _1573958, _1573960, _1573962]), _1573960)), c_Transitive__Closure_Ortrancl(_1573956, _1573962))))], (40503 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573956, _1573956)), hAPP(hAPP(c_Product__Type_OPair(_1573956, _1573956), _1573958), 40501 ^ [_1573956, _1573958, _1573960, _1573962])), _1573962)))]]], (12709 ^ _780119) ^ [_1010434, _1010436] : [_1010436 = c_Option_Ooption_ONone(_1010434), -(c_Option_Oset(_1010434, _1010436) = c_Orderings_Obot__class_Obot(tc_fun(_1010434, tc_HOL_Obool)))], (39689 ^ _780119) ^ [_1553520, _1553522, _1553524, _1553526, _1553528] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553520, _1553520)), hAPP(hAPP(c_Product__Type_OPair(_1553520, _1553520), _1553522), _1553524)), c_Transitive__Closure_Ortrancl(_1553520, _1553526))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1553520, _1553520)), hAPP(hAPP(c_Product__Type_OPair(_1553520, _1553520), _1553524), _1553528)), _1553526)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1553520, _1553520)), hAPP(hAPP(c_Product__Type_OPair(_1553520, _1553520), _1553522), _1553528)), c_Transitive__Closure_Ortrancl(_1553520, _1553526))))], (1510 ^ _780119) ^ [_801718, _801720] : [-(class_Rings_Oordered__comm__semiring(_801718)), _801720 = _801718, class_Rings_Oordered__comm__semiring(_801720)], (49034 ^ _780119) ^ [_1772368, _1772370, _1772372, _1772374, _1772376, _1772378, _1772380] : [c_List_Olist__all2(_1772368, _1772370, _1772372, _1772374, _1772376), c_List_Olist__all2(_1772368, _1772370, _1772372, _1772378, _1772380), -(c_List_Olist__all2(_1772368, _1772370, _1772372, hAPP(hAPP(c_List_Oappend(_1772368), _1772374), _1772378), hAPP(hAPP(c_List_Oappend(_1772370), _1772376), _1772380)))], (31559 ^ _780119) ^ [_1369504, _1369506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1369504)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1369506)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369504)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1369506), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1369504))))], (22793 ^ _780119) ^ [_1196452] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1196452) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1196452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33905 ^ _780119) ^ [_1416239, _1416241, _1416243, _1416245] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1416239, tc_fun(_1416241, tc_HOL_Obool))), _1416243), _1416245))], (31715 ^ _780119) ^ [_1371944, _1371946] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371944)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371946)))), 31718 ^ _780119 : [(31721 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1371946))], (31719 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371944), _1371946)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371944), _1371946))], (25145 ^ _780119) ^ [_1240439, _1240441] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1240439) = _1240441, 25148 ^ _780119 : [(25151 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240441)))], (25149 ^ _780119) ^ [] : [-(_1240439 = hAPP(c_Int_Onat, _1240441))]]], (1160 ^ _780119) ^ [_797343, _797345] : [-(class_Groups_Ogroup__add(_797343)), _797345 = _797343, class_Groups_Ogroup__add(_797345)], (19018 ^ _780119) ^ [_1126674, _1126676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126676)), -(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), _1126674), _1126676))))], (46179 ^ _780119) ^ [_1710774, _1710776, _1710778, _1710780] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710774)), hAPP(hAPP(c_List_Oappend(_1710774), _1710776), _1710778)), c_List_Olists(_1710774, _1710780)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710774)), _1710776), c_List_Olists(_1710774, _1710780))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710774)), _1710778), c_List_Olists(_1710774, _1710780)))], (10280 ^ _780119) ^ [_960648, _960650, _960652, _960654] : [class_Lattices_Olattice(_960648), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960648), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_960648), _960650), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960648), _960652), _960654))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960648), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_960648), _960650), _960652)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_960648), _960650), _960654)))))], (15290 ^ _780119) ^ [_1059339] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1059339) = _1059339)], (19691 ^ _780119) ^ [_1138181, _1138183, _1138185, _1138187] : [class_Rings_Odivision__ring(_1138181), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138181), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1138181), _1138183), _1138185)), _1138187) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1138181), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138181), _1138183), _1138187)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138181), _1138185), _1138187)))], (23873 ^ _780119) ^ [_1216779, _1216781, _1216783] : [class_Orderings_Olinorder(_1216779), 23876 ^ _780119 : [(23883 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1216779), _1216783), _1216781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1216779, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1216779), _1216781)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1216779), _1216783))))], (23877 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1216779, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1216779), _1216781)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1216779), _1216783))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1216779), _1216783), _1216781)))]]], (29418 ^ _780119) ^ [_1325940, _1325942, _1325944, _1325946] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1325940), _1325942))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325944), hAPP(c_Set_Oimage(_1325940, _1325944, _1325946), _1325942))), 29426 ^ _780119 : [(29429 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1325940), hAPP(c_Set_OCollect(_1325940), hAPP(hAPP(c_COMBS(_1325940, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1325940), c_fconj), hAPP(hAPP(c_COMBC(_1325940, tc_fun(_1325940, tc_HOL_Obool), tc_HOL_Obool), c_member(_1325940)), _1325942))), hAPP(hAPP(c_COMBC(_1325940, _1325944, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1325944, tc_fun(_1325944, tc_HOL_Obool), _1325940), c_fequal), _1325946)), hAPP(_1325946, 29425 ^ [_1325940, _1325942, _1325944, _1325946]))))))], (29427 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1325940), 29425 ^ [_1325940, _1325942, _1325944, _1325946]), _1325942)))]]], (33849 ^ _780119) ^ [_1414995, _1414997, _1414999] : [-(hAPP(c_Divides_Oadjust(_1414995), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1414997), _1414999)) = 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), _1414999), _1414995)), 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)))), _1414997)), 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)))), _1414997)), _1414999))))], (25901 ^ _780119) ^ [_1252779, _1252781] : [c_Nat__Transfer_Onat__set(_1252779), c_Nat__Transfer_Onat__set(_1252781), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1252779), _1252781) = 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), _1252779)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1252781))))], (40562 ^ _780119) ^ [_1575337, _1575339, _1575341] : [class_Orderings_Olinorder(_1575337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575337), _1575339)), -(hBOOL(hAPP(hAPP(c_member(_1575337), _1575341), _1575339))), -(c_Big__Operators_Olattice_OInf__fin(_1575337, c_Orderings_Oord__class_Omin(_1575337), hAPP(hAPP(c_Set_Oinsert(_1575337), _1575341), _1575339)) = hAPP(hAPP(c_Finite__Set_Ofold(_1575337, _1575337, c_Orderings_Oord__class_Omin(_1575337)), _1575341), _1575339))], (23133 ^ _780119) ^ [_1202599, _1202601, _1202603, _1202605] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1202599), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1202601, tc_Nat_Onat), _1202603), _1202605)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1202601, _1202599), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1202599, _1202601), c_Nat_Osemiring__1__class_Oof__nat(_1202599)), _1202603)), _1202605)), class_Groups_Ocomm__monoid__mult(_1202599), class_Rings_Osemiring__1(_1202599)], (25995 ^ _780119) ^ [_1254274, _1254276, _1254278] : [class_Groups_Ocomm__monoid__add(_1254274), class_Groups_Ocomm__monoid__mult(_1254274), c_Nat__Transfer_Onat__set(_1254276), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1254274), _1254278), _1254276) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1254274), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1254274, tc_Nat_Onat), _1254278), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1254276)))], (12829 ^ _780119) ^ [_1012681, _1012683, _1012685] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1012681), _1012683)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012681), _1012685)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1012681), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012681, tc_HOL_Obool)), _1012683), _1012685))), hAPP(c_Finite__Set_Ocard(_1012681), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1012681, tc_HOL_Obool)), _1012683), _1012685))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1012681), _1012683)), hAPP(c_Finite__Set_Ocard(_1012681), _1012685)))], (45394 ^ _780119) ^ [_1691469, _1691471] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1691469), tc_List_Olist(_1691469)), tc_HOL_Obool)), c_List_Olistrel(_1691469, _1691471)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1691469), c_List_Olistrel1(_1691469, _1691471)))))], (44015 ^ _780119) ^ [_1660267, _1660269, _1660271, _1660273, _1660275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1660267), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660269)), _1660271))), -(hAPP(hAPP(c_List_Onth(_1660273), hAPP(hAPP(c_List_Omap(_1660269, _1660273), _1660275), _1660271)), _1660267) = hAPP(_1660275, hAPP(hAPP(c_List_Onth(_1660269), _1660271), _1660267)))], (1240 ^ _780119) ^ [_798343, _798345] : [-(class_Rings_Oidom(_798343)), _798345 = _798343, class_Rings_Oidom(_798345)], (34899 ^ _780119) ^ [_1435414] : [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), _1435414))), -(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), _1435414)) = 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), _1435414))))], (10438 ^ _780119) ^ [_964338, _964340, _964342, _964344] : [-(hBOOL(hAPP(hAPP(c_member(_964338), _964340), _964342))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964338, tc_Nat_Onat), _964344), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964338, tc_HOL_Obool)), _964342), hAPP(hAPP(c_Set_Oinsert(_964338), _964340), c_Orderings_Obot__class_Obot(tc_fun(_964338, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964338, tc_Nat_Onat), _964344), _964342))], (42130 ^ _780119) ^ [_1612123, _1612125, _1612127, _1612129] : [class_Orderings_Olinorder(_1612123), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612123), _1612125)), 42140 ^ _780119 : [(42143 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612123), _1612127), 42139 ^ [_1612123, _1612125, _1612127, _1612129]))], (42141 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612123), 42139 ^ [_1612123, _1612125, _1612127, _1612129]), _1612125)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612123), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1612123), _1612127), _1612129)), hAPP(hAPP(c_Finite__Set_Ofold(_1612123, _1612123, c_Orderings_Oord__class_Omin(_1612123)), _1612129), _1612125))))], (49576 ^ _780119) ^ [_1785229, _1785231, _1785233, _1785235, _1785237] : [-(hAPP(hAPP(c_List_Olist_OCons(_1785229), _1785231), _1785233) = hAPP(c_List_Ofilter(_1785229, _1785235), _1785237)), 49577 ^ _780119 : [(49578 ^ _780119) ^ [_1785357, _1785359] : [_1785237 = hAPP(hAPP(c_List_Oappend(_1785229), _1785359), hAPP(hAPP(c_List_Olist_OCons(_1785229), _1785231), _1785357)), 49584 ^ _780119 : [(49587 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1785235, 49583 ^ [_1785229, _1785231, _1785233, _1785235, _1785237, _1785357, _1785359])))], (49585 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785229), 49583 ^ [_1785229, _1785231, _1785233, _1785235, _1785237, _1785357, _1785359]), hAPP(c_List_Oset(_1785229), _1785359))))]], hBOOL(hAPP(_1785235, _1785231)), _1785233 = hAPP(c_List_Ofilter(_1785229, _1785235), _1785357)]]], (5162 ^ _780119) ^ [_859147, _859149, _859151, _859153] : [-(c_List_Oconcat(_859153, _859149) = c_List_Oconcat(_859151, _859147)), _859153 = _859151, _859149 = _859147], (14042 ^ _780119) ^ [_1035772, _1035774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035772), _1035774)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1035774)), _1035772) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035774), _1035772)))], (46491 ^ _780119) ^ [_1717175, _1717177, _1717179] : [-(_1717175 = c_List_Olist_ONil(_1717177)), -(c_List_Obutlast(_1717177, hAPP(hAPP(c_List_Olist_OCons(_1717177), _1717179), _1717175)) = hAPP(hAPP(c_List_Olist_OCons(_1717177), _1717179), c_List_Obutlast(_1717177, _1717175)))], (6025 ^ _780119) ^ [_876017, _876019, _876021] : [_876017 = _876019, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876021, tc_HOL_Obool)), _876019), _876017)))], (42649 ^ _780119) ^ [_1624358, _1624360, _1624362, _1624364] : [hAPP(hAPP(c_Option_Omap(_1624358, _1624360), _1624362), _1624364) = c_Option_Ooption_ONone(_1624360), -(_1624364 = c_Option_Ooption_ONone(_1624358))], (17196 ^ _780119) ^ [_1092417, _1092419, _1092421] : [class_Groups_Oordered__comm__monoid__add(_1092417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092417), _1092419), c_Groups_Ozero__class_Ozero(_1092417))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092417), _1092421), c_Groups_Ozero__class_Ozero(_1092417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092417), _1092419), _1092421)), c_Groups_Ozero__class_Ozero(_1092417))))], (32863 ^ _780119) ^ [_1392562, _1392564] : [class_Rings_Olinordered__idom(_1392562), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1392562), c_Groups_Ozero__class_Ozero(_1392562)), hAPP(hAPP(c_Power_Opower__class_Opower(_1392562), _1392564), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (39337 ^ _780119) ^ [_1544879, _1544881, _1544883] : [c_Wellfounded_Owf(_1544879, _1544881), hBOOL(hAPP(hAPP(c_member(tc_prod(_1544879, _1544879)), hAPP(hAPP(c_Product__Type_OPair(_1544879, _1544879), hAPP(_1544883, hAPP(c_Nat_OSuc, 39340 ^ [_1544879, _1544881, _1544883]))), hAPP(_1544883, 39340 ^ [_1544879, _1544881, _1544883]))), _1544881))], (14516 ^ _780119) ^ [_1046309, _1046311, _1046313, _1046315] : [class_Rings_Olinordered__semidom(_1046309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046309), c_Groups_Oone__class_Oone(_1046309)), _1046311)), 14523 ^ _780119 : [(14530 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046313), _1046315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046309), hAPP(hAPP(c_Power_Opower__class_Opower(_1046309), _1046311), _1046313)), hAPP(hAPP(c_Power_Opower__class_Opower(_1046309), _1046311), _1046315))))], (14524 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046309), hAPP(hAPP(c_Power_Opower__class_Opower(_1046309), _1046311), _1046313)), hAPP(hAPP(c_Power_Opower__class_Opower(_1046309), _1046311), _1046315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046313), _1046315)))]]], (39422 ^ _780119) ^ [_1546945, _1546947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1546945), _1546947)), -(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), _1546945), _1546947)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (39585 ^ _780119) ^ [_1550388, _1550390] : [-(_1550388 = _1550390), -(c_Random_Oinc__shift(_1550388, _1550390) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1550390), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (33305 ^ _780119) ^ [_1400903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1400903))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1400903)))], (35438 ^ _780119) ^ [_1448719, _1448721, _1448723, _1448725] : [-(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), _1448719), _1448721)), 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), _1448723), _1448725)), 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), _1448719), _1448723)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1448721), _1448725))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (29658 ^ _780119) ^ [_1331657, _1331659, _1331661, _1331663, _1331665] : [class_Complete__Lattice_Ocomplete__lattice(_1331657), class_Orderings_Olinorder(_1331657), 29665 ^ _780119 : [(29675 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331657), _1331659), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331661, _1331657), _1331663), _1331665)))), 29676 ^ _780119 : [(29677 ^ _780119) ^ [_1332005] : [hBOOL(hAPP(hAPP(c_member(_1331661), _1332005), _1331663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331657), _1331659), hAPP(_1331665, _1332005)))]]], (29666 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331657), _1331659), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331661, _1331657), _1331663), _1331665))), 29670 ^ _780119 : [(29673 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331657), _1331659), hAPP(_1331665, 29669 ^ [_1331657, _1331659, _1331661, _1331663, _1331665]))))], (29671 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331661), 29669 ^ [_1331657, _1331659, _1331661, _1331663, _1331665]), _1331663)))]]]]], (50674 ^ _780119) ^ [_1807854, _1807856, _1807858] : [-(c_List_Oreplicate(_1807854, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807854)), hAPP(c_List_Ofilter(_1807854, hAPP(c_fequal, _1807856)), _1807858)), _1807856) = hAPP(c_List_Ofilter(_1807854, hAPP(c_fequal, _1807856)), _1807858))], (34589 ^ _780119) ^ [_1429304, _1429306, _1429308, _1429310] : [-(hAPP(c_Product__Type_Osnd(_1429304, _1429306), hAPP(hAPP(c_Product__Type_OPair(_1429304, _1429306), _1429308), _1429310)) = _1429310)], (42622 ^ _780119) ^ [_1623632, _1623634, _1623636, _1623638, _1623640] : [-(hAPP(c_Map_Omap__of(_1623632, _1623634), hAPP(hAPP(c_List_Omap(tc_prod(_1623632, _1623636), tc_prod(_1623632, _1623634)), hAPP(c_Product__Type_Oprod_Oprod__case(_1623632, _1623636, tc_prod(_1623632, _1623634)), hAPP(hAPP(c_COMBC(_1623632, tc_fun(_1623636, _1623634), tc_fun(_1623636, tc_prod(_1623632, _1623634))), hAPP(hAPP(c_COMBB(tc_fun(_1623634, tc_prod(_1623632, _1623634)), tc_fun(tc_fun(_1623636, _1623634), tc_fun(_1623636, tc_prod(_1623632, _1623634))), _1623632), c_COMBB(_1623634, tc_prod(_1623632, _1623634), _1623636)), c_Product__Type_OPair(_1623632, _1623634))), _1623638))), _1623640)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1623636), tc_Option_Ooption(_1623634), _1623632, hAPP(c_Option_Omap(_1623636, _1623634), _1623638)), hAPP(c_Map_Omap__of(_1623632, _1623636), _1623640)))], (47616 ^ _780119) ^ [_1740518, _1740520] : [-(hAPP(c_List_Oset(_1740518), c_List_Oconcat(_1740518, _1740520)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1740518), tc_fun(_1740518, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1740518)), _1740520)), c_List_Oset(_1740518)))], (12153 ^ _780119) ^ [_999211, _999213, _999215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999211), _999213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999215), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999213), _999215)), _999211))))], (27794 ^ _780119) ^ [_1293394, _1293396, _1293398] : [class_Orderings_Olinorder(_1293394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293394), _1293396), _1293398)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293394), _1293396), _1293398) = _1293396)], (29799 ^ _780119) ^ [_1335333, _1335335, _1335337, _1335339, _1335341] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335333, tc_HOL_Obool)), _1335335), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335337, tc_fun(_1335333, tc_HOL_Obool)), _1335339), _1335341)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335337, tc_fun(_1335333, tc_HOL_Obool)), _1335339), hAPP(hAPP(c_COMBB(tc_fun(_1335333, tc_HOL_Obool), tc_fun(_1335333, tc_HOL_Obool), _1335337), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335333, tc_HOL_Obool)), _1335335)), _1335341)))], (31653 ^ _780119) ^ [_1370944] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370944), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370944), c_Int_OPls)))], (12889 ^ _780119) ^ [_1014021, _1014023, _1014025] : [class_Lattices_Osemilattice__inf(_1014021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014021), _1014023)), -(_1014023 = c_Orderings_Obot__class_Obot(tc_fun(_1014021, tc_HOL_Obool))), 12900 ^ _780119 : [(12901 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014021), _1014025), hAPP(c_Finite__Set_Ofold1(_1014021, c_Lattices_Osemilattice__inf__class_Oinf(_1014021)), _1014023))), 12904 ^ _780119 : [(12905 ^ _780119) ^ [_1014314] : [hBOOL(hAPP(hAPP(c_member(_1014021), _1014314), _1014023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014021), _1014025), _1014314)))]]], (12911 ^ _780119) ^ [] : [12913 ^ _780119 : [(12916 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014021), _1014025), 12912 ^ [_1014021, _1014023, _1014025]))], (12914 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014021), 12912 ^ [_1014021, _1014023, _1014025]), _1014023)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014021), _1014025), hAPP(c_Finite__Set_Ofold1(_1014021, c_Lattices_Osemilattice__inf__class_Oinf(_1014021)), _1014023))))]]], (29514 ^ _780119) ^ [_1328066, _1328068, _1328070, _1328072] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1328066, tc_fun(_1328068, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1328066, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1328068, tc_HOL_Obool), tc_fun(_1328068, tc_HOL_Obool), _1328066), hAPP(c_COMBC(_1328068, tc_fun(_1328068, tc_HOL_Obool), tc_HOL_Obool), c_member(_1328068))), _1328070)), _1328072)), -(hBOOL(hAPP(hAPP(c_member(_1328068), _1328072), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1328066, tc_fun(_1328068, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1328066, tc_HOL_Obool))), _1328070))))], (18129 ^ _780119) ^ [_1110225, _1110227] : [-(_1110225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110225), _1110227) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110225), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1110227)))], (50542 ^ _780119) ^ [_1805425, _1805427] : [-(c_List_Oconcat(_1805425, c_List_Oreplicate(tc_List_Olist(_1805425), _1805427, c_List_Olist_ONil(_1805425))) = c_List_Olist_ONil(_1805425))], (36764 ^ _780119) ^ [_1478830, _1478832, _1478834, _1478836] : [-(hAPP(c_Set_Ovimage(_1478830, _1478832, _1478834), _1478836) = hAPP(c_Set_OCollect(_1478830), hAPP(hAPP(c_COMBC(_1478830, tc_fun(_1478832, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1478832, tc_fun(tc_fun(_1478832, tc_HOL_Obool), tc_HOL_Obool), _1478830), c_member(_1478832)), _1478834)), _1478836)))], (40369 ^ _780119) ^ [_1570182, _1570184] : [-(c_Relation_Osingle__valued(_1570182, _1570182, c_Relation_OId__on(_1570182, _1570184)))], (11213 ^ _780119) ^ [_979673, _979675] : [class_Lattices_Olattice(_979673), hBOOL(hAPP(c_Finite__Set_Ofinite(_979673), _979675)), -(_979675 = c_Orderings_Obot__class_Obot(tc_fun(_979673, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979673), c_Big__Operators_Olattice__class_OInf__fin(_979673, _979675)), c_Big__Operators_Olattice__class_OSup__fin(_979673, _979675))))], (46221 ^ _780119) ^ [_1711674, _1711676, _1711678] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1711674)), _1711676), c_List_Olists(_1711674, _1711678))), 46224 ^ _780119 : [(46225 ^ _780119) ^ [_1711782] : [hBOOL(hAPP(hAPP(c_member(_1711674), _1711782), hAPP(c_List_Oset(_1711674), _1711676))), -(hBOOL(hAPP(hAPP(c_member(_1711674), _1711782), _1711678)))]]], (37493 ^ _780119) ^ [] : [-(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))))], (47530 ^ _780119) ^ [_1738599, _1738601] : [-(c_List_Oconcat(_1738599, _1738601) = hAPP(c_List_Ofoldl(tc_List_Olist(_1738599), tc_List_Olist(_1738599), c_List_Oappend(_1738599), c_List_Olist_ONil(_1738599)), _1738601))], (32233 ^ _780119) ^ [_1381305, _1381307, _1381309] : [-(hAPP(c_Nat_Onat_Onat__rec(_1381305, _1381307, _1381309), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1381307)], (18574 ^ _780119) ^ [_1118895, _1118897, _1118899, _1118901] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1118895), _1118897)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1118899), _1118901)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1118895, _1118899)), c_Sum__Type_OPlus(_1118895, _1118899, _1118897, _1118901))))], (33929 ^ _780119) ^ [_1416744, _1416746, _1416748, _1416750, _1416752, _1416754] : [hBOOL(hAPP(hAPP(_1416744, _1416746), _1416748)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1416750, tc_fun(_1416752, tc_HOL_Obool))), _1416744), _1416754)), -(hBOOL(hAPP(hAPP(_1416754, _1416746), _1416748)))], (47430 ^ _780119) ^ [_1736491, _1736493, _1736495] : [hAPP(hAPP(c_List_Olist_OCons(_1736491), _1736493), c_List_Olist_ONil(_1736491)) = hAPP(c_List_Orev(_1736491), _1736495), -(_1736495 = hAPP(hAPP(c_List_Olist_OCons(_1736491), _1736493), c_List_Olist_ONil(_1736491)))], (37635 ^ _780119) ^ [_1501175, _1501177, _1501179, _1501181, _1501183] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1501175, _1501177)), hAPP(hAPP(c_Product__Type_OPair(_1501175, _1501177), _1501179), _1501181)), _1501183)), -(hBOOL(hAPP(hAPP(c_member(_1501175), _1501179), hAPP(c_Relation_ODomain(_1501175, _1501177), _1501183))))], (20234 ^ _780119) ^ [_1148178, _1148180, _1148182, _1148184, _1148186] : [class_Fields_Ofield__inverse__zero(_1148178), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148178), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148178), _1148180), _1148182)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148178), _1148184), _1148186)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148178), _1148180), _1148184)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148178), _1148182), _1148186)))], (9972 ^ _780119) ^ [_953796, _953798, _953800, _953802] : [class_Lattices_Osemilattice__inf(_953796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953796), _953798), _953800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953796), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_953796), _953798), _953802)), _953800)))], (41952 ^ _780119) ^ [_1608038, _1608040, _1608042] : [class_Complete__Lattice_Ocomplete__lattice(_1608038), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608038), _1608040)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1608038), _1608042), c_Complete__Lattice_OInf__class_OInf(_1608038, _1608040)) = hAPP(hAPP(c_Finite__Set_Ofold(_1608038, _1608038, c_Lattices_Osemilattice__inf__class_Oinf(_1608038)), _1608042), _1608040))], (4406 ^ _780119) ^ [_846799, _846801, _846803, _846805] : [-(c_Product__Type_Ofst(_846805, _846801) = c_Product__Type_Ofst(_846803, _846799)), _846805 = _846803, _846801 = _846799], (40201 ^ _780119) ^ [_1566023, _1566025, _1566027, _1566029] : [-(hAPP(hAPP(c_Nat_Ocompow(_1566023, _1566023), _1566025), hAPP(hAPP(c_Nat_Ocompow(_1566023, _1566023), _1566027), _1566029)) = hAPP(hAPP(c_Nat_Ocompow(_1566023, _1566023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1566027), _1566025)), _1566029))], (17224 ^ _780119) ^ [_1092927, _1092929, _1092931, _1092933] : [class_Rings_Olinordered__ring__strict(_1092927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092927), c_Groups_Ozero__class_Ozero(_1092927)), _1092929)), 17231 ^ _780119 : [(17238 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092927), _1092931), _1092933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092927), _1092929), _1092931)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092927), _1092929), _1092933))))], (17232 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092927), _1092929), _1092931)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092927), _1092929), _1092933))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092927), _1092931), _1092933)))]]], (33939 ^ _780119) ^ [_1416935, _1416937, _1416939, _1416941, _1416943, _1416945] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416935, tc_fun(_1416937, tc_HOL_Obool))), _1416939), _1416941), _1416943), _1416945)), -(hBOOL(hAPP(hAPP(_1416941, _1416943), _1416945)))], (38180 ^ _780119) ^ [_1517721, _1517723, _1517725, _1517727] : [c_Wellfounded_Owf(_1517721, _1517723), c_Fun_Oinj__on(_1517721, _1517725, _1517727, c_Orderings_Otop__class_Otop(tc_fun(_1517721, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1517725, hAPP(c_Set_Oimage(tc_prod(_1517721, _1517721), tc_prod(_1517725, _1517725), c_Product__Type_Omap__pair(_1517721, _1517725, _1517721, _1517725, _1517727, _1517727)), _1517723)))], (43028 ^ _780119) ^ [_1632970, _1632972, _1632974] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1632970, tc_HOL_Obool)), hAPP(c_List_Oset(_1632970), c_List_Oremove1(_1632970, _1632972, _1632974))), hAPP(c_List_Oset(_1632970), _1632974))))], (40692 ^ _780119) ^ [_1578061, _1578063, _1578065, _1578067] : [class_Lattices_Osemilattice__inf(_1578061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578061), _1578063)), hBOOL(hAPP(hAPP(c_member(_1578061), _1578065), _1578063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1578061), hAPP(hAPP(c_Finite__Set_Ofold(_1578061, _1578061, c_Lattices_Osemilattice__inf__class_Oinf(_1578061)), _1578067), _1578063)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1578061), _1578065), _1578067))))], (11698 ^ _780119) ^ [_990851, _990853, _990855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990851), _990853)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990853), _990851)), _990855) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990853), _990855)), _990851))], (41250 ^ _780119) ^ [_1590122, _1590124, _1590126, _1590128] : [-(_1590122 = c_Orderings_Obot__class_Obot(tc_fun(_1590124, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590124, tc_fun(_1590126, tc_HOL_Obool)), _1590122), hAPP(c_COMBK(tc_fun(_1590126, tc_HOL_Obool), _1590124), _1590128)) = _1590128)], (1918 ^ _780119) ^ [_807797, _807799, _807801, _807803, _807805, _807807, _807809, _807811, _807813, _807815] : [-(c_Option_Ooption_Ooption__rec(_807815, _807811, _807807, _807803, _807799) = c_Option_Ooption_Ooption__rec(_807813, _807809, _807805, _807801, _807797)), _807815 = _807813, _807811 = _807809, _807807 = _807805, _807803 = _807801, _807799 = _807797], (50336 ^ _780119) ^ [_1800805, _1800807, _1800809] : [-(hAPP(c_New__DSequence_Oneg__single(_1800805, _1800807), _1800809) = c_Lazy__Sequence_Ohb__single(_1800805, _1800807))], (51099 ^ _780119) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (25376 ^ _780119) ^ [_1244187, _1244189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244187)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244187), _1244189)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1244187)), hAPP(c_Int_Onat, _1244189)))], (39783 ^ _780119) ^ [_1555760, _1555762, _1555764, _1555766, _1555768] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1555760, _1555760)), hAPP(hAPP(c_Product__Type_OPair(_1555760, _1555760), _1555762), _1555764)), _1555766)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1555760, _1555760)), hAPP(hAPP(c_Product__Type_OPair(_1555760, _1555760), _1555764), _1555768)), c_Transitive__Closure_Ortrancl(_1555760, _1555766))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1555760, _1555760)), hAPP(hAPP(c_Product__Type_OPair(_1555760, _1555760), _1555762), _1555768)), c_Transitive__Closure_Otrancl(_1555760, _1555766))))], (50334 ^ _780119) ^ [_1800759, _1800761, _1800763, _1800765] : [-(hAPP(c_New__DSequence_Opos__union(_1800759, _1800761, _1800763), _1800765) = c_Lazy__Sequence_Oappend(_1800759, hAPP(_1800761, _1800765), hAPP(_1800763, _1800765)))], (37579 ^ _780119) ^ [_1499573, _1499575] : [-(c_Nitpick_Onumber__of__frac(_1499573, _1499575) = c_Nitpick_OAbs__Frac(_1499573, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1499575), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (10174 ^ _780119) ^ [_957762, _957764, _957766, _957768, _957770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957762, tc_HOL_Obool)), _957764), _957766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957762, tc_HOL_Obool)), _957768), _957770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957762, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957762, tc_HOL_Obool)), _957764), _957768)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957762, tc_HOL_Obool)), _957766), _957770))))], (11756 ^ _780119) ^ [_991751, _991753] : [11757 ^ _780119 : [(11760 ^ _780119) ^ [] : [_991751 = _991753], (11758 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991751), _991753))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991751), _991753)))], (47766 ^ _780119) ^ [_1744931, _1744933, _1744935, _1744937] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1744931), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1744931))), _1744933))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744935), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1744931))), c_List_Otranspose(_1744931, _1744933)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744937), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1744931))), hAPP(c_List_Ofilter(tc_List_Olist(_1744931), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1744931)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744935)), c_Nat_Osize__class_Osize(tc_List_Olist(_1744931)))), _1744933)))), -(hAPP(hAPP(c_List_Onth(_1744931), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1744931)), c_List_Otranspose(_1744931, _1744933)), _1744935)), _1744937) = hAPP(hAPP(c_List_Onth(_1744931), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1744931)), _1744933), _1744937)), _1744935))], (7844 ^ _780119) ^ [_913628, _913630, _913632, _913634] : [hBOOL(hAPP(hAPP(c_member(_913628), _913630), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913628, tc_HOL_Obool)), _913632), _913634))), 7847 ^ _780119 : [(7850 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_913628), _913630), _913634))], (7848 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_913628), _913630), _913632)))]]], (40270 ^ _780119) ^ [_1567921, _1567923, _1567925] : [-(hAPP(hAPP(c_Nat_Ocompow(_1567921, _1567921), hAPP(c_Nat_OSuc, _1567923)), _1567925) = hAPP(c_Fun_Ocomp(_1567921, _1567921, _1567921, _1567925), hAPP(hAPP(c_Nat_Ocompow(_1567921, _1567921), _1567923), _1567925)))], (44830 ^ _780119) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (35133 ^ _780119) ^ [_1440372, _1440374, _1440376, _1440378, _1440380, _1440382, _1440384] : [-(hAPP(c_Product__Type_Oapsnd(_1440372, _1440374, _1440376, _1440378), hAPP(c_Product__Type_Oapfst(_1440380, _1440376, _1440372, _1440382), _1440384)) = hAPP(hAPP(c_Product__Type_OPair(_1440376, _1440374), hAPP(_1440382, hAPP(c_Product__Type_Ofst(_1440380, _1440372), _1440384))), hAPP(_1440378, hAPP(c_Product__Type_Osnd(_1440380, _1440372), _1440384))))], (7812 ^ _780119) ^ [_912960, _912962, _912964, _912966, _912968, _912970, _912972, _912974] : [c_Finite__Set_Ofolding__image__simple__idem(_912960, _912962, _912964, _912966, _912968, _912970), hBOOL(hAPP(c_Finite__Set_Ofinite(_912962), _912972)), hBOOL(hAPP(c_Finite__Set_Ofinite(_912962), _912974)), -(hAPP(_912970, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912962, tc_HOL_Obool)), _912972), _912974)) = hAPP(hAPP(_912964, hAPP(_912970, _912972)), hAPP(_912970, _912974)))], (39743 ^ _780119) ^ [_1554889, _1554891] : [-(c_Transitive__Closure_Ortrancl(_1554889, c_Transitive__Closure_Otrancl(_1554889, _1554891)) = c_Transitive__Closure_Ortrancl(_1554889, _1554891))], (4908 ^ _780119) ^ [_855058, _855060, _855062, _855064] : [-(c_Lazy__Sequence_Osmall__lazy_H(_855064, _855060) = c_Lazy__Sequence_Osmall__lazy_H(_855062, _855058)), _855064 = _855062, _855060 = _855058], (31913 ^ _780119) ^ [_1375052, _1375054] : [class_Int_Onumber__ring(_1375052), -(hAPP(c_Int_Onumber__class_Onumber__of(_1375052), c_Int_Opred(_1375054)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1375052), hAPP(c_Groups_Ouminus__class_Ouminus(_1375052), c_Groups_Oone__class_Oone(_1375052))), hAPP(c_Int_Onumber__class_Onumber__of(_1375052), _1375054)))], (23068 ^ _780119) ^ [_1201395, _1201397] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1201395), _1201397)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201395)), _1201397))], (46626 ^ _780119) ^ [_1720013, _1720015, _1720017] : [hAPP(c_List_Ofilter(_1720013, _1720015), _1720017) = _1720017, 46629 ^ _780119 : [(46630 ^ _780119) ^ [_1720104] : [hBOOL(hAPP(hAPP(c_member(_1720013), _1720104), hAPP(c_List_Oset(_1720013), _1720017))), -(hBOOL(hAPP(_1720015, _1720104)))]]], (16606 ^ _780119) ^ [_1082528, _1082530, _1082532] : [class_Rings_Olinordered__semidom(_1082528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082528), c_Groups_Ozero__class_Ozero(_1082528)), _1082530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082528), c_Groups_Ozero__class_Ozero(_1082528)), hAPP(hAPP(c_Power_Opower__class_Opower(_1082528), _1082530), _1082532))))], (12391 ^ _780119) ^ [_1003990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003990), _1003990))], (41411 ^ _780119) ^ [_1595591, _1595593, _1595595, _1595597, _1595599] : [_1595591 = c_Orderings_Obot__class_Obot(tc_fun(_1595593, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595593, tc_fun(_1595595, tc_HOL_Obool)), _1595591), hAPP(hAPP(c_COMBC(_1595593, tc_fun(_1595595, tc_HOL_Obool), tc_fun(_1595595, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1595595, tc_HOL_Obool), tc_fun(tc_fun(_1595595, tc_HOL_Obool), tc_fun(_1595595, tc_HOL_Obool)), _1595593), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1595595, tc_HOL_Obool))), _1595597)), _1595599)) = c_Orderings_Otop__class_Otop(tc_fun(_1595595, tc_HOL_Obool)))], (10334 ^ _780119) ^ [_961827, _961829, _961831, _961833, _961835] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961827, tc_HOL_Obool)), hAPP(c_Set_Oimage(_961829, _961827, _961831), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961829, tc_HOL_Obool)), _961833), _961835))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961827, tc_HOL_Obool)), hAPP(c_Set_Oimage(_961829, _961827, _961831), _961833)), hAPP(c_Set_Oimage(_961829, _961827, _961831), _961835)))))], (44474 ^ _780119) ^ [_1671267, _1671269, _1671271, _1671273, _1671275, _1671277] : [-(c_Map_Omap__add(_1671267, _1671269, _1671271, c_Map_Omap__upds(_1671267, _1671269, _1671273, _1671275, _1671277)) = c_Map_Omap__upds(_1671267, _1671269, c_Map_Omap__add(_1671267, _1671269, _1671271, _1671273), _1671275, _1671277))], (32171 ^ _780119) ^ [_1380290, _1380292] : [class_Int_Onumber__ring(_1380290), 32174 ^ _780119 : [(32181 ^ _780119) ^ [] : [c_Int_Oiszero(_1380290, hAPP(c_Int_Onumber__class_Onumber__of(_1380290), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1380292), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1380290), _1380292) = c_Groups_Oone__class_Oone(_1380290))], (32175 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1380290), _1380292) = c_Groups_Oone__class_Oone(_1380290), -(c_Int_Oiszero(_1380290, hAPP(c_Int_Onumber__class_Onumber__of(_1380290), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1380292), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (15420 ^ _780119) ^ [_1061255] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061255), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33491 ^ _780119) ^ [_1403662] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1403662), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1403662))], (38984 ^ _780119) ^ [_1536228, _1536230, _1536232, _1536234, _1536236, _1536238] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536228, tc_fun(_1536230, tc_HOL_Obool)), _1536232), hAPP(c_Fun_Ocomp(_1536234, tc_fun(_1536230, tc_HOL_Obool), _1536228, _1536236), _1536238)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536234, tc_fun(_1536230, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1536228, _1536234, _1536238), _1536232)), _1536236))], (32781 ^ _780119) ^ [_1391098, _1391100] : [class_Rings_Olinordered__idom(_1391098), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1391098), hAPP(c_Groups_Oabs__class_Oabs(_1391098), _1391100)), 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(_1391098), _1391100), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (44494 ^ _780119) ^ [_1671613, _1671615] : [_1671613 = _1671615, -(hAPP(c_Code__Numeral_Onat__of, _1671613) = hAPP(c_Code__Numeral_Onat__of, _1671615))], (21875 ^ _780119) ^ [_1179455, _1179457, _1179459, _1179461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179457), _1179459)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179459), 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), _1179457), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179461, _1179455))), _1179459)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20094 ^ _780119) ^ [_1145510, _1145512, _1145514] : [-(hBOOL(hAPP(_1145510, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1145512), _1145514)))), 20095 ^ _780119 : [(20102 ^ _780119) ^ [_1145678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145514), _1145678)), _1145512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1145512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145514), hAPP(c_Nat_OSuc, _1145678)))), hBOOL(hAPP(_1145510, _1145678))], (20096 ^ _780119) ^ [] : [_1145514 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1145510, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (39717 ^ _780119) ^ [_1554255, _1554257, _1554259, _1554261] : [39718 ^ _780119 : [(39721 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554255, _1554255)), _1554257), c_Transitive__Closure_Ortrancl(_1554255, _1554261)))], (39719 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554255, _1554255)), _1554257), c_Transitive__Closure_Ortrancl(_1554255, _1554259)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1554255, _1554255)), _1554257), c_Transitive__Closure_Ortrancl(_1554255, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554255, _1554255), tc_HOL_Obool)), _1554259), _1554261)))))], (11463 ^ _780119) ^ [_985469, _985471, _985473, _985475] : [class_Rings_Ocomm__semiring__1(_985469), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985469), _985471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985469), _985473), _985475)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985469), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985469), _985471), _985473)), _985475))], (34325 ^ _780119) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (10184 ^ _780119) ^ [_958007, _958009, _958011, _958013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958007, tc_HOL_Obool)), _958009), _958011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958007, tc_HOL_Obool)), _958009), _958013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958007, tc_HOL_Obool)), _958009), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958007, tc_HOL_Obool)), _958011), _958013))))], (50108 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34541 ^ _780119) ^ [_1428357, _1428359, _1428361, _1428363] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1428357, _1428359), _1428361)), hBOOL(hAPP(hAPP(_1428359, _1428363), _1428361)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1428357, _1428359), _1428363)))], (35083 ^ _780119) ^ [_1439451, _1439453, _1439455, _1439457, _1439459] : [-(hAPP(c_Product__Type_Osnd(_1439451, _1439453), hAPP(c_Product__Type_Oapfst(_1439455, _1439451, _1439453, _1439457), _1439459)) = hAPP(c_Product__Type_Osnd(_1439455, _1439453), _1439459))], (15972 ^ _780119) ^ [_1071205, _1071207] : [class_Groups_Olinordered__ab__group__add(_1071205), 15975 ^ _780119 : [(15982 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071205), _1071207), c_Groups_Ozero__class_Ozero(_1071205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071205), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071205), _1071207), _1071207)), c_Groups_Ozero__class_Ozero(_1071205))))], (15976 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071205), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071205), _1071207), _1071207)), c_Groups_Ozero__class_Ozero(_1071205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071205), _1071207), c_Groups_Ozero__class_Ozero(_1071205))))]]], (46602 ^ _780119) ^ [_1719635, _1719637, _1719639, _1719641] : [-(hBOOL(hAPP(_1719635, _1719637))), -(c_List_Oremove1(_1719639, _1719637, hAPP(c_List_Ofilter(_1719639, _1719635), _1719641)) = hAPP(c_List_Ofilter(_1719639, _1719635), _1719641))], (35572 ^ _780119) ^ [_1452245, _1452247, _1452249, _1452251] : [_1452245 = _1452247, hBOOL(hAPP(hAPP(c_member(_1452249), _1452245), _1452251)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1452249, _1452249)), hAPP(hAPP(c_Product__Type_OPair(_1452249, _1452249), _1452245), _1452247)), c_Relation_OId__on(_1452249, _1452251))))], (43635 ^ _780119) ^ [_1650158, _1650160, _1650162, _1650164, _1650166, _1650168] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650158), tc_List_Olist(_1650158))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650158), tc_List_Olist(_1650158)), hAPP(hAPP(c_List_Olist_OCons(_1650158), _1650160), _1650162)), hAPP(hAPP(c_List_Olist_OCons(_1650158), _1650164), _1650166))), c_List_Olex(_1650158, _1650168)))), 43636 ^ _780119 : [(43643 ^ _780119) ^ [] : [_1650160 = _1650164, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650158), tc_List_Olist(_1650158))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650158), tc_List_Olist(_1650158)), _1650162), _1650166)), c_List_Olex(_1650158, _1650168)))], (43637 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1650158, _1650158)), hAPP(hAPP(c_Product__Type_OPair(_1650158, _1650158), _1650160), _1650164)), _1650168)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650158)), _1650162) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650158)), _1650166)]]], (11587 ^ _780119) ^ [_988534, _988536, _988538, _988540, _988542] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_988534), 11590 ^ _780119 : [(11591 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988534), _988536), _988538)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988534), _988540), _988542)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988534), _988536), _988542)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988534), _988540), _988538)), -(_988536 = _988540), -(_988538 = _988542)], (11601 ^ _780119) ^ [] : [11602 ^ _780119 : [(11605 ^ _780119) ^ [] : [_988538 = _988542], (11603 ^ _780119) ^ [] : [_988536 = _988540]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988534), _988536), _988538)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988534), _988540), _988542)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988534), _988536), _988542)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988534), _988540), _988538)))]]], (31771 ^ _780119) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (45906 ^ _780119) ^ [_1704590, _1704592, _1704594] : [hAPP(c_List_Orotate(_1704590, _1704592), _1704594) = c_List_Olist_ONil(_1704590), -(_1704594 = c_List_Olist_ONil(_1704590))], (25921 ^ _780119) ^ [_1253087, _1253089] : [class_Rings_Olinordered__idom(_1253087), 25924 ^ _780119 : [(25931 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253087), c_Groups_Ozero__class_Ozero(_1253087)), hAPP(c_Int_Oring__1__class_Oof__int(_1253087), _1253089))))], (25925 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253087), c_Groups_Ozero__class_Ozero(_1253087)), hAPP(c_Int_Oring__1__class_Oof__int(_1253087), _1253089))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253089)))]]], (32139 ^ _780119) ^ [_1379473, _1379475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379473)), hAPP(c_Nat_OSuc, _1379475))), -(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(_1379473))), 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)), _1379475)))))], (15452 ^ _780119) ^ [_1061802, _1061804, _1061806, _1061808, _1061810] : [-(hAPP(c_Set_Oimage(_1061802, _1061804, hAPP(hAPP(c_COMBB(_1061806, _1061804, _1061802), _1061808), _1061810)), c_Orderings_Otop__class_Otop(tc_fun(_1061802, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1061806, _1061804, _1061808), hAPP(c_Set_Oimage(_1061802, _1061806, _1061810), c_Orderings_Otop__class_Otop(tc_fun(_1061802, tc_HOL_Obool)))))], (42626 ^ _780119) ^ [_1623830, _1623832, _1623834, _1623836] : [-(hAPP(hAPP(c_Option_Omap(_1623830, _1623832), _1623834), hAPP(c_Option_Ooption_OSome(_1623830), _1623836)) = hAPP(c_Option_Ooption_OSome(_1623832), hAPP(_1623834, _1623836)))], (49673 ^ _780119) ^ [_1787217, _1787219, _1787221] : [-(c_List_Olist__ex(_1787217, _1787219, _1787221)), 49674 ^ _780119 : [(49675 ^ _780119) ^ [_1787274] : [hBOOL(hAPP(hAPP(c_member(_1787217), _1787274), hAPP(c_List_Oset(_1787217), _1787221))), hBOOL(hAPP(_1787219, _1787274))]]], (12495 ^ _780119) ^ [_1005889, _1005891, _1005893, _1005895, _1005897] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1005889, _1005891, hAPP(hAPP(c_Set_Oinsert(_1005889), _1005893), _1005895)), _1005897)), 12500 ^ _780119 : [(12503 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1005889, _1005889, _1005891, 12498 ^ [_1005889, _1005891, _1005893, _1005895, _1005897], 12499 ^ [_1005889, _1005891, _1005893, _1005895, _1005897]), _1005897)))], (12505 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1005889), 12498 ^ [_1005889, _1005891, _1005893, _1005895, _1005897]), 12499 ^ [_1005889, _1005891, _1005893, _1005895, _1005897]))], (12501 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1005889), _1005893), _1005895) = hAPP(hAPP(c_Set_Oinsert(_1005889), 12498 ^ [_1005889, _1005891, _1005893, _1005895, _1005897]), 12499 ^ [_1005889, _1005891, _1005893, _1005895, _1005897]))]]], (644 ^ _780119) ^ [_789951, _789953, _789955, _789957, _789959, _789961, _789963, _789965, _789967, _789969] : [-(c_Typedef_Otype__definition(_789967, _789963, _789959, _789955, _789951)), c_Typedef_Otype__definition(_789969, _789965, _789961, _789957, _789953), _789969 = _789967, _789965 = _789963, _789961 = _789959, _789957 = _789955, _789953 = _789951], (8044 ^ _780119) ^ [_917604, _917606] : [c_Com_Ocom_OWhile(_917604, _917606) = c_Com_Ocom_OSKIP], (21362 ^ _780119) ^ [_1169249, _1169251, _1169253] : [hAPP(c_Set_Oimage(_1169251, tc_fun(_1169251, tc_HOL_Obool), _1169249), _1169253) = hAPP(c_Set_OPow(_1169251), _1169253)], (33611 ^ _780119) ^ [_1407035, _1407037, _1407039, _1407041, _1407043, _1407045] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407035, tc_fun(_1407037, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1407035, tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_fun(_1407037, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407037, tc_fun(tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_fun(_1407037, tc_HOL_Obool)), _1407035), c_COMBC(_1407037, tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407037, tc_prod(_1407035, _1407037)), tc_fun(_1407037, tc_fun(tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_HOL_Obool)), _1407035), hAPP(c_COMBB(tc_prod(_1407035, _1407037), tc_fun(tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_HOL_Obool), _1407037), c_member(tc_prod(_1407035, _1407037)))), c_Product__Type_OPair(_1407035, _1407037)))), _1407039)), hAPP(hAPP(c_COMBC(_1407035, tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_fun(_1407037, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407037, tc_fun(tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_fun(_1407037, tc_HOL_Obool)), _1407035), c_COMBC(_1407037, tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407037, tc_prod(_1407035, _1407037)), tc_fun(_1407037, tc_fun(tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_HOL_Obool)), _1407035), hAPP(c_COMBB(tc_prod(_1407035, _1407037), tc_fun(tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool), tc_HOL_Obool), _1407037), c_member(tc_prod(_1407035, _1407037)))), c_Product__Type_OPair(_1407035, _1407037)))), _1407041)), _1407043), _1407045)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1407035, _1407037)), hAPP(hAPP(c_Product__Type_OPair(_1407035, _1407037), _1407043), _1407045)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1407035, _1407037), tc_HOL_Obool)), _1407039), _1407041))))], (3920 ^ _780119) ^ [_839262, _839264, _839266, _839268, _839270, _839272, _839274, _839276, _839278, _839280] : [-(c_Map_Omap__upds(_839280, _839276, _839272, _839268, _839264) = c_Map_Omap__upds(_839278, _839274, _839270, _839266, _839262)), _839280 = _839278, _839276 = _839274, _839272 = _839270, _839268 = _839266, _839264 = _839262], (47554 ^ _780119) ^ [_1739125, _1739127] : [-(hAPP(c_List_Orev(_1739125), hAPP(c_List_Orev(_1739125), _1739127)) = _1739127)], (35548 ^ _780119) ^ [_1451695, _1451697, _1451699, _1451701] : [hBOOL(hAPP(hAPP(c_member(_1451695), _1451697), _1451699)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1451695, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1451695, _1451695, _1451701), hAPP(hAPP(c_Set_Oinsert(_1451695), _1451697), c_Orderings_Obot__class_Obot(tc_fun(_1451695, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1451695), _1451699), _1451701))))], (13162 ^ _780119) ^ [_1019931, _1019933, _1019935] : [-(hBOOL(hAPP(hAPP(c_member(_1019931), _1019933), _1019935))), -(hBOOL(hAPP(hAPP(c_member(_1019931), _1019933), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019931, tc_HOL_Obool)), _1019935))))], (3640 ^ _780119) ^ [_834854, _834856, _834858, _834860] : [-(c_Wellfounded_Oacc(_834860, _834856) = c_Wellfounded_Oacc(_834858, _834854)), _834860 = _834858, _834856 = _834854], (6099 ^ _780119) ^ [_877267, _877269, _877271, _877273] : [hBOOL(hAPP(hAPP(c_member(_877267), _877269), _877271)), -(hBOOL(hAPP(hAPP(c_member(_877267), _877269), hAPP(hAPP(c_Set_Oinsert(_877267), _877273), _877271))))], (12209 ^ _780119) ^ [_1000241, _1000243, _1000245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000241), _1000243)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1000245), _1000243)), _1000241) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1000245), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000243), _1000241)))], (8116 ^ _780119) ^ [_919095, _919097, _919099, _919101] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919095, tc_HOL_Obool)), _919097), hAPP(hAPP(c_Set_Oinsert(_919095), _919099), _919101)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919095, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919095, tc_HOL_Obool)), _919097), _919101)), hAPP(hAPP(c_Set_Oinsert(_919095), _919099), c_Orderings_Obot__class_Obot(tc_fun(_919095, tc_HOL_Obool)))))], (49769 ^ _780119) ^ [_1789387, _1789389, _1789391] : [c_List_Olist__all(_1789387, _1789389, _1789391), 49772 ^ _780119 : [(49773 ^ _780119) ^ [_1789476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1789476), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789387)), _1789391))), -(hBOOL(hAPP(_1789389, hAPP(hAPP(c_List_Onth(_1789387), _1789391), _1789476))))]]], (21727 ^ _780119) ^ [_1176799, _1176801, _1176803, _1176805] : [class_Divides_Osemiring__div(_1176799), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176799), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176799), _1176801), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1176799), _1176803), _1176801))), c_Divides_Odiv__class_Omod(_1176799, _1176803, _1176801))), _1176805) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176799), _1176803), _1176805))], (24279 ^ _780119) ^ [_1224670, _1224672, _1224674] : [class_Orderings_Olinorder(_1224670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224670), _1224672), _1224674)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1224670, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1224670), _1224672), c_Orderings_Obot__class_Obot(tc_fun(_1224670, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1224670, _1224672, _1224674)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1224670, _1224672), _1224674))], (9900 ^ _780119) ^ [_952526, _952528, _952530, _952532, _952534] : [class_Lattices_Osemilattice__inf(_952526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952526), _952528), _952530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952526), _952532), _952534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952526), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952526), _952528), _952532)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952526), _952530), _952534))))], (45382 ^ _780119) ^ [_1691176, _1691178] : [-(c_List_Olistrel(_1691176, c_Transitive__Closure_Ortrancl(_1691176, _1691178)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1691176), c_List_Olistrel1(_1691176, _1691178)))], (51499 ^ _780119) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (41141 ^ _780119) ^ [_1587563, _1587565, _1587567, _1587569, _1587571] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587563, tc_fun(_1587565, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1587563, tc_HOL_Obool)), _1587567), _1587569)), _1587571) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1587565, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587563, tc_fun(_1587565, tc_HOL_Obool)), _1587567), _1587571)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587563, tc_fun(_1587565, tc_HOL_Obool)), _1587569), _1587571)))], (34437 ^ _780119) ^ [_1426354, _1426356] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1426354, _1426356), c_Divides_Odivmod__nat(_1426354, _1426356))))], (38754 ^ _780119) ^ [_1531009, _1531011, _1531013, _1531015, _1531017, _1531019] : [-(hAPP(c_Set_Ovimage(_1531009, _1531011, hAPP(c_Fun_Ocomp(_1531013, _1531011, _1531009, _1531015), _1531017)), _1531019) = hAPP(c_Set_Ovimage(_1531009, _1531013, _1531017), hAPP(c_Set_Ovimage(_1531013, _1531011, _1531015), _1531019)))], (22163 ^ _780119) ^ [_1184830] : [_1184830 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1184830) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17442 ^ _780119) ^ [_1097138, _1097140, _1097142] : [class_Rings_Olinordered__ring__strict(_1097138), 17445 ^ _780119 : [(17454 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097138), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097138), _1097140), _1097140)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097138), _1097142), _1097142))), c_Groups_Ozero__class_Ozero(_1097138)))), _1097140 = c_Groups_Ozero__class_Ozero(_1097138), _1097142 = c_Groups_Ozero__class_Ozero(_1097138)], (17446 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097138), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097138), _1097140), _1097140)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097138), _1097142), _1097142))), c_Groups_Ozero__class_Ozero(_1097138))), 17449 ^ _780119 : [(17452 ^ _780119) ^ [] : [-(_1097142 = c_Groups_Ozero__class_Ozero(_1097138))], (17450 ^ _780119) ^ [] : [-(_1097140 = c_Groups_Ozero__class_Ozero(_1097138))]]]]], (16780 ^ _780119) ^ [_1085452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1085452)), -(_1085452 = hAPP(c_Nat_OSuc, 16783 ^ [_1085452]))], (49519 ^ _780119) ^ [_1783643, _1783645, _1783647, _1783649, _1783651] : [hAPP(c_List_Ofilter(_1783643, _1783645), _1783647) = hAPP(hAPP(c_List_Olist_OCons(_1783643), _1783649), _1783651), 49524 ^ _780119 : [(49525 ^ _780119) ^ [] : [-(_1783647 = hAPP(hAPP(c_List_Oappend(_1783643), 49522 ^ [_1783643, _1783645, _1783647, _1783649, _1783651]), hAPP(hAPP(c_List_Olist_OCons(_1783643), _1783649), 49523 ^ [_1783643, _1783645, _1783647, _1783649, _1783651])))], (49533 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1783645, _1783649)))], (49527 ^ _780119) ^ [_1783957] : [hBOOL(hAPP(hAPP(c_member(_1783643), _1783957), hAPP(c_List_Oset(_1783643), 49522 ^ [_1783643, _1783645, _1783647, _1783649, _1783651]))), hBOOL(hAPP(_1783645, _1783957))], (49535 ^ _780119) ^ [] : [-(_1783651 = hAPP(c_List_Ofilter(_1783643, _1783645), 49523 ^ [_1783643, _1783645, _1783647, _1783649, _1783651]))]]], (43679 ^ _780119) ^ [_1652050, _1652052, _1652054] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652050)), c_List_Osublist(_1652050, _1652052, _1652054)) = 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(_1652050)), _1652052)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1652054)))))], (17732 ^ _780119) ^ [_1102477, _1102479, _1102481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102477), _1102479)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102477), _1102481))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102479), _1102481)))], (51301 ^ _780119) ^ [] : [-(class_HOL_Oequal(tc_Nat_Onat))], (10142 ^ _780119) ^ [_957120, _957122, _957124] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957120, tc_HOL_Obool)), _957122), _957124) = c_Orderings_Obot__class_Obot(tc_fun(_957120, tc_HOL_Obool)), 10145 ^ _780119 : [(10146 ^ _780119) ^ [_957244] : [hBOOL(hAPP(hAPP(c_member(_957120), _957244), _957122)), 10149 ^ _780119 : [(10150 ^ _780119) ^ [_957334] : [hBOOL(hAPP(hAPP(c_member(_957120), _957334), _957124)), _957244 = _957334]]]]], (45576 ^ _780119) ^ [_1697155, _1697157, _1697159, _1697161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697155), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697157)), _1697159))), -(hAPP(hAPP(c_List_Olist__update(_1697157, _1697159), _1697155), _1697161) = hAPP(hAPP(c_List_Oappend(_1697157), hAPP(hAPP(c_List_Otake(_1697157), _1697155), _1697159)), hAPP(hAPP(c_List_Olist_OCons(_1697157), _1697161), hAPP(hAPP(c_List_Odrop(_1697157), hAPP(c_Nat_OSuc, _1697155)), _1697159))))], (37453 ^ _780119) ^ [_1496556, _1496558] : [c_Wellfounded_Owf(_1496556, _1496558), -(c_Wellfounded_Owf(tc_List_Olist(_1496556), c_List_Olenlex(_1496556, _1496558)))], (18938 ^ _780119) ^ [_1125374, _1125376, _1125378, _1125380, _1125382] : [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), _1125374), _1125376)), _1125378)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1125374), _1125380)), _1125382))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125378), _1125374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125382), _1125374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125376), _1125380)))], (23010 ^ _780119) ^ [_1200271, _1200273, _1200275] : [class_Rings_Olinordered__semidom(_1200271), 23013 ^ _780119 : [(23020 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1200273), _1200275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1200271), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200271), _1200273)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200271), _1200275))))], (23014 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1200271), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200271), _1200273)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200271), _1200275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1200273), _1200275)))]]], (26925 ^ _780119) ^ [_1272591] : [_1272591 = 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), _1272591)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (3130 ^ _780119) ^ [_826807, _826809] : [_826809 = _826807, -(c_Nitpick_ORep__Frac(_826809) = c_Nitpick_ORep__Frac(_826807))], (7676 ^ _780119) ^ [_909777, _909779, _909781] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_909777, _909779, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909777)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909777), _909781), c_Com_Ocom_OSKIP), _909781)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909777), tc_HOL_Obool)))))], (11790 ^ _780119) ^ [_992397] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992397), _992397)))], (49261 ^ _780119) ^ [_1777206, _1777208, _1777210, _1777212] : [-(_1777206 = _1777208), -(hAPP(c_List_OremoveAll(_1777210, _1777206), hAPP(hAPP(c_List_Olist_OCons(_1777210), _1777208), _1777212)) = hAPP(hAPP(c_List_Olist_OCons(_1777210), _1777208), hAPP(c_List_OremoveAll(_1777210, _1777206), _1777212)))], (9828 ^ _780119) ^ [_951077, _951079, _951081] : [class_Lattices_Oab__semigroup__idem__mult(_951077), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951077), _951079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951077), _951079), _951081)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951077), _951079), _951081))], (8156 ^ _780119) ^ [_920196, _920198, _920200, _920202, _920204, _920206, _920208, _920210] : [c_Finite__Set_Ofolding__image__simple(_920196, _920198, _920200, _920202, _920204, _920206), hBOOL(hAPP(c_Finite__Set_Ofinite(_920198), _920208)), hBOOL(hAPP(hAPP(c_member(_920198), _920210), _920208)), -(hAPP(_920206, _920208) = hAPP(hAPP(_920200, hAPP(_920204, _920210)), hAPP(_920206, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920198, tc_HOL_Obool)), _920208), hAPP(hAPP(c_Set_Oinsert(_920198), _920210), c_Orderings_Obot__class_Obot(tc_fun(_920198, tc_HOL_Obool)))))))], (31451 ^ _780119) ^ [_1367867, _1367869] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367867))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367867)), _1367869)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1367869))], (41914 ^ _780119) ^ [_1607319, _1607321, _1607323] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1607319, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1607319, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1607319, tc_HOL_Obool), _1607321)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1607319, tc_HOL_Obool), _1607323))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1607319, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1607319, tc_HOL_Obool), tc_HOL_Obool)), _1607321), _1607323)))))], (50074 ^ _780119) ^ [_1795311] : [class_HOL_Oequal(_1795311), -(c_fequal = c_HOL_Oequal__class_Oequal(_1795311))], (34030 ^ _780119) ^ [_1418987, _1418989, _1418991, _1418993, _1418995, _1418997] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1418987, _1418989, _1418991), _1418993), hAPP(hAPP(c_Product__Type_OPair(_1418987, _1418989), _1418995), _1418997)) = hAPP(hAPP(_1418993, _1418995), _1418997))], (40066 ^ _780119) ^ [_1562460, _1562462] : [c_Wellfounded_Owf(_1562460, hAPP(c_Relation_Oconverse(_1562460, _1562460), _1562462)), -(c_Wellfounded_Owf(_1562460, hAPP(c_Relation_Oconverse(_1562460, _1562460), c_Transitive__Closure_Otrancl(_1562460, _1562462))))], (43952 ^ _780119) ^ [_1658724, _1658726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658724), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1658726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1658726), _1658724)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1658726))))], (46684 ^ _780119) ^ [_1721243, _1721245, _1721247] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1721243, tc_HOL_Obool)), hAPP(c_List_Oset(_1721243), _1721245)), hAPP(hAPP(c_Set_Oinsert(_1721243), _1721247), c_Orderings_Obot__class_Obot(tc_fun(_1721243, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1721243), hAPP(c_List_Ofilter(_1721243, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1721243), c_fNot), hAPP(hAPP(c_COMBC(_1721243, _1721243, tc_HOL_Obool), c_fequal), _1721247))), _1721245)))], (44804 ^ _780119) ^ [_1677535, _1677537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1677535), _1677537)), -(c_List_Oupto(_1677535, _1677537) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1677535), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1677535), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1677537)))], (12701 ^ _780119) ^ [_1010282, _1010284, _1010286, _1010288] : [-(hAPP(c_Map_Orestrict__map(_1010282, _1010284, _1010286, c_Orderings_Obot__class_Obot(tc_fun(_1010282, tc_HOL_Obool))), _1010288) = c_Option_Ooption_ONone(_1010284))], (39467 ^ _780119) ^ [_1547877, _1547879, _1547881] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547877, _1547877)), _1547879), _1547881)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547877, _1547877)), _1547879), c_Transitive__Closure_Otrancl(_1547877, _1547881))))], (47917 ^ _780119) ^ [_1748180, _1748182] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748180)), c_List_Oremdups(_1748180, _1748182))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748180)), _1748182))))], (15916 ^ _780119) ^ [_1070170, _1070172, _1070174] : [class_Rings_Oordered__ring(_1070170), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070170), c_Groups_Ozero__class_Ozero(_1070170)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070170), _1070172), _1070174)))), 15921 ^ _780119 : [(15928 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070170), _1070172), c_Groups_Ozero__class_Ozero(_1070170))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070170), _1070174), c_Groups_Ozero__class_Ozero(_1070170)))], (15922 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070170), c_Groups_Ozero__class_Ozero(_1070170)), _1070172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070170), c_Groups_Ozero__class_Ozero(_1070170)), _1070174))]]], (2 ^ _780119) ^ [_780146] : [-(_780146 = _780146)], (512 ^ _780119) ^ [_788003, _788005, _788007, _788009, _788011, _788013, _788015, _788017] : [-(c_Finite__Set_Ofolding(_788015, _788011, _788007, _788003)), c_Finite__Set_Ofolding(_788017, _788013, _788009, _788005), _788017 = _788015, _788013 = _788011, _788009 = _788007, _788005 = _788003], (11764 ^ _780119) ^ [_991886, _991888, _991890, _991892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991886), _991888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991890), _991892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991886), _991890)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991888), _991892))))], (29433 ^ _780119) ^ [_1326486, _1326488] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1326486)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1326488)), hAPP(c_Int_Onat, _1326486)) = hAPP(c_Int_Onat, _1326488))], (12519 ^ _780119) ^ [_1006697, _1006699, _1006701, _1006703, _1006705] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1006697, _1006699, hAPP(hAPP(c_Set_Oinsert(_1006697), _1006701), _1006703)), _1006705))), 12520 ^ _780119 : [(12521 ^ _780119) ^ [_1006801, _1006803] : [hAPP(hAPP(c_Set_Oinsert(_1006697), _1006701), _1006703) = hAPP(hAPP(c_Set_Oinsert(_1006697), _1006803), _1006801), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1006697, _1006697, _1006699, _1006803, _1006801), _1006705)), -(hBOOL(hAPP(hAPP(c_member(_1006697), _1006803), _1006801)))]]], (49305 ^ _780119) ^ [_1777884, _1777886, _1777888] : [hBOOL(hAPP(hAPP(c_member(_1777884), _1777886), hAPP(c_List_Oset(_1777884), _1777888))), -(c_List_Oinsert(_1777884, _1777886, _1777888) = _1777888)], (37237 ^ _780119) ^ [_1491944, _1491946, _1491948] : [c_Wellfounded_Owf(_1491944, _1491946), -(c_Wellfounded_Owf(_1491944, c_Wellfounded_Omlex__prod(_1491944, _1491948, _1491946)))], (29986 ^ _780119) ^ [_1340352, _1340354, _1340356] : [29988 ^ _780119 : [(29991 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1340354, 29987 ^ [_1340352, _1340354, _1340356])))], (29993 ^ _780119) ^ [] : [hBOOL(hAPP(_1340354, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 29987 ^ [_1340352, _1340354, _1340356]), _1340352)))], (29989 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29987 ^ [_1340352, _1340354, _1340356]), _1340352)))]], hBOOL(hAPP(_1340354, _1340356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1340356), _1340352)), -(hBOOL(hAPP(_1340354, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (13188 ^ _780119) ^ [_1020315] : [_1020315 = hAPP(c_Nat_OSuc, _1020315)], (40834 ^ _780119) ^ [_1580883, _1580885, _1580887] : [class_Groups_Oab__semigroup__mult(_1580883), hBOOL(hAPP(c_Finite__Set_Ofinite(_1580883), _1580885)), -(hBOOL(hAPP(hAPP(c_member(_1580883), _1580887), _1580885))), -(hAPP(c_Finite__Set_Ofold1(_1580883, c_Groups_Otimes__class_Otimes(_1580883)), hAPP(hAPP(c_Set_Oinsert(_1580883), _1580887), _1580885)) = hAPP(hAPP(c_Finite__Set_Ofold(_1580883, _1580883, c_Groups_Otimes__class_Otimes(_1580883)), _1580887), _1580885))], (42667 ^ _780119) ^ [_1624770, _1624772, _1624774, _1624776, _1624778] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1624770), tc_Option_Ooption(_1624772), tc_Option_Ooption(_1624774), hAPP(c_Option_Omap(_1624770, _1624772), _1624776)), hAPP(c_Option_Omap(_1624774, _1624770), _1624778)) = hAPP(c_Option_Omap(_1624774, _1624772), hAPP(c_Fun_Ocomp(_1624770, _1624772, _1624774, _1624776), _1624778)))], (10875 ^ _780119) ^ [_973066, _973068, _973070, _973072] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_973066), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973066), _973068), _973070)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973066), _973068), _973072))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973066), _973070), _973072)))], (43146 ^ _780119) ^ [_1636534, _1636536, _1636538, _1636540, _1636542] : [class_Orderings_Olinorder(_1636534), -(hAPP(c_List_Oset(_1636536), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1636536, _1636534, _1636538), _1636540), _1636542)) = hAPP(hAPP(c_Set_Oinsert(_1636536), _1636540), hAPP(c_List_Oset(_1636536), _1636542)))], (50672 ^ _780119) ^ [_1807816, _1807818, _1807820] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807816)), c_List_Oreplicate(_1807816, _1807818, _1807820)) = _1807818)], (31475 ^ _780119) ^ [_1368237, _1368239] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368237)), hAPP(c_Nat_OSuc, _1368239)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1368237))), 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)), _1368239)))))], (41790 ^ _780119) ^ [_1604478, _1604480, _1604482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1604478, tc_HOL_Obool), tc_HOL_Obool)), _1604480), _1604482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604478, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1604478, tc_HOL_Obool), _1604480)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1604478, tc_HOL_Obool), _1604482))))], (1978 ^ _780119) ^ [_808777, _808779, _808781, _808783, _808785, _808787] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_808787, _808783, _808779) = c_Hoare__Mirabelle_Otriple_Otriple__size(_808785, _808781, _808777)), _808787 = _808785, _808783 = _808781, _808779 = _808777], (25550 ^ _780119) ^ [_1247315, _1247317] : [c_Nat__Transfer_Onat__set(_1247315), c_Nat__Transfer_Onat__set(_1247317), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1247315), _1247317)))], (43216 ^ _780119) ^ [_1638034, _1638036] : [hBOOL(hAPP(c_List_Odistinct(_1638034), _1638036)), -(hAPP(c_Finite__Set_Ocard(_1638034), hAPP(c_List_Oset(_1638034), _1638036)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638034)), _1638036))], (50238 ^ _780119) ^ [_1798047] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1798047)), c_Int_OMin))], (30241 ^ _780119) ^ [_1345134, _1345136, _1345138] : [class_Int_Onumber(_1345134), class_Orderings_Olinorder(_1345134), 30248 ^ _780119 : [(30255 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345134), hAPP(c_Int_Onumber__class_Onumber__of(_1345134), _1345138)), hAPP(c_Int_Onumber__class_Onumber__of(_1345134), _1345136)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345134), hAPP(c_Int_Onumber__class_Onumber__of(_1345134), _1345136)), hAPP(c_Int_Onumber__class_Onumber__of(_1345134), _1345138))))], (30249 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345134), hAPP(c_Int_Onumber__class_Onumber__of(_1345134), _1345136)), hAPP(c_Int_Onumber__class_Onumber__of(_1345134), _1345138))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345134), hAPP(c_Int_Onumber__class_Onumber__of(_1345134), _1345138)), hAPP(c_Int_Onumber__class_Onumber__of(_1345134), _1345136)))]]], (31515 ^ _780119) ^ [_1368832, _1368834] : [class_Int_Onumber__ring(_1368832), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1368832), _1368834), hAPP(c_Int_Onumber__class_Onumber__of(_1368832), c_Int_OPls)) = _1368834)], (37342 ^ _780119) ^ [_1493896, _1493898] : [c_Wellfounded_Owf(_1493896, _1493898), 37345 ^ _780119 : [(37346 ^ _780119) ^ [_1493965] : [-(hBOOL(hAPP(hAPP(c_member(_1493896), _1493965), c_Wellfounded_Oacc(_1493896, _1493898))))]]], (35877 ^ _780119) ^ [_1459486, _1459488, _1459490, _1459492] : [c_Equiv__Relations_Oequivp(_1459486, _1459488), hBOOL(hAPP(hAPP(_1459488, _1459490), _1459492)), -(hBOOL(hAPP(hAPP(_1459488, _1459492), _1459490)))], (1480 ^ _780119) ^ [_801343, _801345] : [-(class_Groups_Oordered__comm__monoid__add(_801343)), _801345 = _801343, class_Groups_Oordered__comm__monoid__add(_801345)], (42397 ^ _780119) ^ [_1618224, _1618226, _1618228, _1618230, _1618232] : [hBOOL(hAPP(hAPP(c_member(_1618224), _1618226), c_Map_Odom(_1618224, _1618228, _1618230))), -(hAPP(c_Map_Omap__add(_1618224, _1618228, _1618232, _1618230), _1618226) = hAPP(_1618230, _1618226))], (39731 ^ _780119) ^ [_1554632, _1554634] : [-(c_Transitive__Closure_Ortrancl(_1554632, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1554632, _1554632), tc_HOL_Obool)), _1554634), c_Relation_OId(_1554632))) = c_Transitive__Closure_Ortrancl(_1554632, _1554634))], (4302 ^ _780119) ^ [_845197, _845199, _845201, _845203] : [-(c_Map_Omap__of(_845203, _845199) = c_Map_Omap__of(_845201, _845197)), _845203 = _845201, _845199 = _845197], (39643 ^ _780119) ^ [_1552455, _1552457, _1552459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552455, _1552455), tc_HOL_Obool)), _1552457), _1552459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552455, _1552455), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1552455, _1552457)), c_Transitive__Closure_Ortrancl(_1552455, _1552459))))], (39126 ^ _780119) ^ [_1539808, _1539810, _1539812, _1539814, _1539816] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1539808, _1539810, _1539812), _1539814), _1539816)), 39129 ^ _780119 : [(39132 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1539812, _1539816)))], (39130 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1539810, _1539814), _1539816)))]]], (44708 ^ _780119) ^ [_1675734, _1675736, _1675738, _1675740] : [-(c_List_Ofoldr(_1675734, _1675736, _1675738, c_List_Olist_ONil(_1675734), _1675740) = _1675740)], (49384 ^ _780119) ^ [_1779896, _1779898, _1779900, _1779902, _1779904] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779896, _1779896)), hAPP(hAPP(c_Product__Type_OPair(_1779896, _1779896), _1779898), _1779900)), c_List_Omeasures(_1779896, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1779896, tc_Nat_Onat)), _1779902), _1779904)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1779902, _1779898)), hAPP(_1779902, _1779900)))), 49391 ^ _780119 : [(49394 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779896, _1779896)), hAPP(hAPP(c_Product__Type_OPair(_1779896, _1779896), _1779898), _1779900)), c_List_Omeasures(_1779896, _1779904))))], (49392 ^ _780119) ^ [] : [-(hAPP(_1779902, _1779898) = hAPP(_1779902, _1779900))]]], (48077 ^ _780119) ^ [_1751266, _1751268, _1751270, _1751272] : [-(hBOOL(hAPP(_1751266, _1751268))), -(c_List_OdropWhile(_1751270, _1751266, hAPP(hAPP(c_List_Olist_OCons(_1751270), _1751268), _1751272)) = hAPP(hAPP(c_List_Olist_OCons(_1751270), _1751268), _1751272))], (49341 ^ _780119) ^ [_1778628, _1778630, _1778632, _1778634, _1778636] : [-(c_List_Omaps(_1778628, _1778630, _1778632, hAPP(hAPP(c_List_Olist_OCons(_1778628), _1778634), _1778636)) = hAPP(hAPP(c_List_Oappend(_1778630), hAPP(_1778632, _1778634)), c_List_Omaps(_1778628, _1778630, _1778632, _1778636)))], (51647 ^ _780119) ^ [_1821389, _1821391] : [hBOOL(hAPP(hAPP(c_fimplies, _1821389), _1821391)), hBOOL(_1821389), -(hBOOL(_1821391))], (11355 ^ _780119) ^ [_982989, _982991, _982993, _982995, _982997, _982999] : [class_Rings_Oordered__ring(_982989), 11358 ^ _780119 : [(11365 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982989), _982995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982989), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_982989), _982997), _982991)), _982993)), _982999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982989), _982991), _982993)), _982995)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982989), _982997), _982993)), _982999))))], (11359 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982989), _982991), _982993)), _982995)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982989), _982997), _982993)), _982999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982989), _982995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982989), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_982989), _982997), _982991)), _982993)), _982999))))]]], (46779 ^ _780119) ^ [_1723954, _1723956] : [class_Orderings_Olinorder(_1723954), -(c_List_Olinorder__class_Osorted(_1723954, hAPP(hAPP(c_List_Olist_OCons(_1723954), _1723956), c_List_Olist_ONil(_1723954))))], (10070 ^ _780119) ^ [_955496, _955498] : [class_Lattices_Obounded__lattice__bot(_955496), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955496), c_Orderings_Obot__class_Obot(_955496)), _955498) = c_Orderings_Obot__class_Obot(_955496))], (1620 ^ _780119) ^ [_803093, _803095] : [-(class_Groups_Osemigroup__add(_803093)), _803095 = _803093, class_Groups_Osemigroup__add(_803095)], (5664 ^ _780119) ^ [_866836, _866838, _866840, _866842, _866844, _866846] : [-(c_Set_Oimage(_866846, _866842, _866838) = c_Set_Oimage(_866844, _866840, _866836)), _866846 = _866844, _866842 = _866840, _866838 = _866836], (10304 ^ _780119) ^ [_961232, _961234, _961236, _961238] : [-(hBOOL(hAPP(hAPP(c_member(_961232), _961234), _961236))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961232, tc_HOL_Obool)), _961236), hAPP(hAPP(c_Set_Oinsert(_961232), _961234), _961238)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961232, tc_HOL_Obool)), _961236), _961238))], (4044 ^ _780119) ^ [_841202, _841204, _841206, _841208] : [-(c_Enum_Osublists(_841208, _841204) = c_Enum_Osublists(_841206, _841202)), _841208 = _841206, _841204 = _841202], (45329 ^ _780119) ^ [_1689624, _1689626, _1689628, _1689630] : [-(c_List_Osublist(_1689624, hAPP(hAPP(c_List_Olist_OCons(_1689624), _1689626), _1689628), _1689630) = hAPP(hAPP(c_List_Oappend(_1689624), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1689624)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1689630)), hAPP(hAPP(c_List_Olist_OCons(_1689624), _1689626), c_List_Olist_ONil(_1689624))), c_List_Olist_ONil(_1689624))), c_List_Osublist(_1689624, _1689628, 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)), _1689630)))))], (16983 ^ _780119) ^ [_1088588, _1088590] : [-(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), _1088588), _1088590)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1088588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1088590))], (31871 ^ _780119) ^ [_1374327, _1374329] : [class_Groups_Omonoid__mult(_1374327), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1374327), _1374329), 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(_1374327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374327), _1374329), _1374329)), _1374329))], (36820 ^ _780119) ^ [_1480181, _1480183, _1480185, _1480187] : [hBOOL(hAPP(hAPP(c_member(_1480181), _1480183), _1480185)), -(hAPP(c_Set_Ovimage(_1480187, _1480181, hAPP(c_COMBK(_1480181, _1480187), _1480183)), _1480185) = c_Orderings_Otop__class_Otop(tc_fun(_1480187, tc_HOL_Obool)))], (4610 ^ _780119) ^ [_850113, _850115, _850117, _850119, _850121, _850123, _850125, _850127] : [-(c_New__Random__Sequence_Opos__map(_850127, _850123, _850119, _850115) = c_New__Random__Sequence_Opos__map(_850125, _850121, _850117, _850113)), _850127 = _850125, _850123 = _850121, _850119 = _850117, _850115 = _850113], (50595 ^ _780119) ^ [_1806527, _1806529, _1806531, _1806533] : [50597 ^ _780119 : [(50600 ^ _780119) ^ [] : [hBOOL(hAPP(_1806533, 50596 ^ [_1806527, _1806529, _1806531, _1806533]))], (50598 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806527), 50596 ^ [_1806527, _1806529, _1806531, _1806533]), hAPP(c_List_Oset(_1806527), c_List_Oreplicate(_1806527, _1806529, _1806531)))))]], -(hBOOL(hAPP(_1806533, _1806531))), -(_1806529 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24807 ^ _780119) ^ [_1234559, _1234561, _1234563] : [class_Orderings_Oorder(_1234559), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1234559, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1234559, _1234561), _1234563)), hAPP(c_SetInterval_Oord__class_OatLeast(_1234559), _1234563)) = c_Orderings_Obot__class_Obot(tc_fun(_1234559, tc_HOL_Obool)))], (42628 ^ _780119) ^ [_1623905, _1623907, _1623909, _1623911, _1623913] : [hAPP(hAPP(c_Option_Omap(_1623905, _1623907), _1623909), _1623911) = hAPP(c_Option_Ooption_OSome(_1623907), _1623913), 42632 ^ _780119 : [(42635 ^ _780119) ^ [] : [-(hAPP(_1623909, 42631 ^ [_1623905, _1623907, _1623909, _1623911, _1623913]) = _1623913)], (42633 ^ _780119) ^ [] : [-(_1623911 = hAPP(c_Option_Ooption_OSome(_1623905), 42631 ^ [_1623905, _1623907, _1623909, _1623911, _1623913]))]]], (9418 ^ _780119) ^ [_942115, _942117, _942119, _942121, _942123] : [class_Groups_Oab__group__add(_942115), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_942115), _942117), _942119) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_942115), _942121), _942123), 9425 ^ _780119 : [(9432 ^ _780119) ^ [] : [_942121 = _942123, -(_942117 = _942119)], (9426 ^ _780119) ^ [] : [_942117 = _942119, -(_942121 = _942123)]]], (37534 ^ _780119) ^ [_1498447, _1498449, _1498451, _1498453] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498447, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1498447, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1498449, _1498447), _1498451)), hAPP(c_Relation_ORange(_1498449, _1498447), _1498453))), hAPP(c_Relation_ORange(_1498449, _1498447), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1498449, _1498447), tc_HOL_Obool)), _1498451), _1498453)))))], (9040 ^ _780119) ^ [_935645, _935647, _935649] : [class_Orderings_Opreorder(_935645), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935645), _935647), _935649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935645), _935647), _935649)))], (40335 ^ _780119) ^ [_1569532, _1569534, _1569536, _1569538, _1569540] : [c_Relation_Osingle__valued(_1569532, _1569534, hAPP(c_Relation_Oconverse(_1569534, _1569532), _1569536)), -(hAPP(c_Relation_OImage(_1569534, _1569532, _1569536), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1569534, tc_HOL_Obool)), _1569538), _1569540)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1569532, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1569534, _1569532, _1569536), _1569538)), hAPP(c_Relation_OImage(_1569534, _1569532, _1569536), _1569540)))], (5418 ^ _780119) ^ [_863133, _863135, _863137, _863139, _863141, _863143] : [-(c_FunDef_OTHE__default(_863143, _863139, _863135) = c_FunDef_OTHE__default(_863141, _863137, _863133)), _863143 = _863141, _863139 = _863137, _863135 = _863133], (39104 ^ _780119) ^ [_1538977, _1538979, _1538981, _1538983, _1538985] : [c_Hoare__Mirabelle_Ohoare__valids(_1538977, _1538979, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1538977)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1538977), c_Hoare__Mirabelle_Opeek__and(_1538977, _1538981, _1538983)), _1538985), _1538981)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1538977), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__valids(_1538977, _1538979, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1538977)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1538977), _1538981), c_Com_Ocom_OWhile(_1538983, _1538985)), c_Hoare__Mirabelle_Opeek__and(_1538977, _1538981, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1538983)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1538977), tc_HOL_Obool)))))], (19290 ^ _780119) ^ [_1130990, _1130992, _1130994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130992)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130992), _1130994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130990), _1130994)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130990), _1130992))))], (11786 ^ _780119) ^ [_992323] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992323), _992323)))))], (4700 ^ _780119) ^ [_851690, _851692, _851694, _851696] : [-(c_New__DSequence_Opos__single(_851696, _851692) = c_New__DSequence_Opos__single(_851694, _851690)), _851696 = _851694, _851692 = _851690], (33323 ^ _780119) ^ [_1401182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1401182), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1401182)), c_Int_OMin)))], (8320 ^ _780119) ^ [_923825] : [-(c_Finite__Set_Ofun__left__comm__idem(_923825, tc_fun(_923825, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_923825, tc_HOL_Obool), tc_fun(tc_fun(_923825, tc_HOL_Obool), tc_fun(_923825, tc_HOL_Obool)), _923825), hAPP(c_COMBC(tc_fun(_923825, tc_HOL_Obool), tc_fun(_923825, tc_HOL_Obool), tc_fun(_923825, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_923825, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_923825, tc_fun(_923825, tc_HOL_Obool), tc_fun(_923825, tc_HOL_Obool)), c_Set_Oinsert(_923825)), c_Orderings_Obot__class_Obot(tc_fun(_923825, tc_HOL_Obool))))))], (45524 ^ _780119) ^ [_1695493, _1695495, _1695497, _1695499, _1695501, _1695503] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1695493, _1695493)), hAPP(hAPP(c_Product__Type_OPair(_1695493, _1695493), _1695495), _1695497)), c_Transitive__Closure_Ortrancl(_1695493, _1695499))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695493), tc_List_Olist(_1695493))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695493), tc_List_Olist(_1695493)), _1695501), _1695503)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1695493), c_List_Olistrel1(_1695493, _1695499)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695493), tc_List_Olist(_1695493))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695493), tc_List_Olist(_1695493)), hAPP(hAPP(c_List_Olist_OCons(_1695493), _1695495), _1695501)), hAPP(hAPP(c_List_Olist_OCons(_1695493), _1695497), _1695503))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1695493), c_List_Olistrel1(_1695493, _1695499)))))], (24205 ^ _780119) ^ [_1223291, _1223293] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1223291, _1223293))))], (22577 ^ _780119) ^ [_1192139, _1192141, _1192143] : [class_Orderings_Oord(_1192139), 22580 ^ _780119 : [(22587 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192139), _1192141), _1192143)), -(hBOOL(hAPP(hAPP(c_member(_1192139), _1192141), hAPP(c_SetInterval_Oord__class_OlessThan(_1192139), _1192143))))], (22581 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1192139), _1192141), hAPP(c_SetInterval_Oord__class_OlessThan(_1192139), _1192143))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192139), _1192141), _1192143)))]]], (32451 ^ _780119) ^ [_1385121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1385121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1385121))))], (13680 ^ _780119) ^ [_1028855, _1028857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028855), _1028857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028855), hAPP(c_Nat_OSuc, _1028857))))], (18816 ^ _780119) ^ [_1123174] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123174), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1123174)], (6673 ^ _780119) ^ [_889122, _889124, _889126, _889128] : [hBOOL(hAPP(_889122, _889124)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889126, tc_HOL_Obool)), _889122), _889128), _889124)))], (19885 ^ _780119) ^ [_1141608, _1141610, _1141612] : [_1141608 = 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), _1141608), _1141610)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1141608), _1141612)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30005 ^ _780119) ^ [_1340714, _1340716, _1340718, _1340720, _1340722, _1340724] : [class_Groups_Oab__semigroup__mult(_1340714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340716), _1340718)), 30015 ^ _780119 : [(30018 ^ _780119) ^ [] : [hAPP(_1340720, 30014 ^ [_1340714, _1340716, _1340718, _1340720, _1340722, _1340724]) = hAPP(_1340722, 30014 ^ [_1340714, _1340716, _1340718, _1340720, _1340722, _1340724])], (30016 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1340716), 30014 ^ [_1340714, _1340716, _1340718, _1340720, _1340722, _1340724]), _1340718)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1340714, _1340716, c_Groups_Otimes__class_Otimes(_1340714)), _1340720), _1340724), _1340718) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1340714, _1340716, c_Groups_Otimes__class_Otimes(_1340714)), _1340722), _1340724), _1340718))], (45826 ^ _780119) ^ [_1703273, _1703275, _1703277] : [_1703273 = c_List_Olist_ONil(_1703275), -(hAPP(c_List_Ohd(_1703275), hAPP(hAPP(c_List_Oappend(_1703275), _1703273), _1703277)) = hAPP(c_List_Ohd(_1703275), _1703277))], (11704 ^ _780119) ^ [_991003, _991005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991003), _991005)), 11707 ^ _780119 : [(11710 ^ _780119) ^ [] : [_991003 = _991005], (11708 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991003), _991005)))]]], (42367 ^ _780119) ^ [_1617776, _1617778, _1617780, _1617782, _1617784] : [hAPP(c_Map_Omap__add(_1617776, _1617778, _1617780, _1617782), _1617784) = c_Option_Ooption_ONone(_1617778), 42370 ^ _780119 : [(42373 ^ _780119) ^ [] : [-(hAPP(_1617780, _1617784) = c_Option_Ooption_ONone(_1617778))], (42371 ^ _780119) ^ [] : [-(hAPP(_1617782, _1617784) = c_Option_Ooption_ONone(_1617778))]]], (42702 ^ _780119) ^ [_1625619, _1625621, _1625623, _1625625, _1625627, _1625629, _1625631] : [hAPP(_1625619, _1625621) = hAPP(c_Option_Ooption_OSome(_1625623), _1625625), -(c_Map_Omap__comp(_1625623, _1625627, _1625629, _1625631, _1625619, _1625621) = hAPP(_1625631, _1625625))], (9766 ^ _780119) ^ [_949671, _949673] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949671, tc_HOL_Obool)), _949673), _949673) = _949673)], (19532 ^ _780119) ^ [_1135255, _1135257, _1135259, _1135261] : [_1135255 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1135257), _1135259)), _1135261), -(_1135257 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1135255), _1135257) = _1135259), 19539 ^ _780119 : [(19542 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1135261), _1135257))], (19540 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135257)))]], 19547 ^ _780119 : [(19550 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1135257), _1135261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135261), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (19548 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135257))]]], (50396 ^ _780119) ^ [_1801968, _1801970, _1801972, _1801974, _1801976] : [-(c_Lazy__Sequence_Ohb__map(_1801968, _1801970, _1801972, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(_1801968), _1801974, _1801976)) = c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(_1801970), hAPP(hAPP(c_Option_Omap(_1801968, _1801970), _1801972), _1801974), c_Lazy__Sequence_Ohb__map(_1801968, _1801970, _1801972, _1801976)))], (13984 ^ _780119) ^ [_1034545, _1034547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034545), _1034547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1034545)), _1034547)))], (29724 ^ _780119) ^ [_1333040, _1333042, _1333044, _1333046] : [29726 ^ _780119 : [(29729 ^ _780119) ^ [] : [hAPP(_1333046, 29725 ^ [_1333040, _1333042, _1333044, _1333046]) = c_Orderings_Obot__class_Obot(tc_fun(_1333040, tc_HOL_Obool))], (29727 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333042), 29725 ^ [_1333040, _1333042, _1333044, _1333046]), _1333044)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1333040, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1333042, tc_fun(_1333040, tc_HOL_Obool)), _1333044), _1333046))], (3758 ^ _780119) ^ [_836661, _836663, _836665, _836667, _836669, _836671, _836673, _836675, _836677, _836679] : [-(c_List_Olinorder__class_Oinsort__insert__key(_836679, _836675, _836671, _836667, _836663) = c_List_Olinorder__class_Oinsort__insert__key(_836677, _836673, _836669, _836665, _836661)), _836679 = _836677, _836675 = _836673, _836671 = _836669, _836667 = _836665, _836663 = _836661], (24611 ^ _780119) ^ [_1231070, _1231072, _1231074] : [class_Orderings_Olinorder(_1231070), 24614 ^ _780119 : [(24621 ^ _780119) ^ [] : [_1231072 = _1231074, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1231070), _1231072) = hAPP(c_SetInterval_Oord__class_OatLeast(_1231070), _1231074))], (24615 ^ _780119) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1231070), _1231072) = hAPP(c_SetInterval_Oord__class_OatLeast(_1231070), _1231074), -(_1231072 = _1231074)]]], (44724 ^ _780119) ^ [_1676016, _1676018] : [hAPP(c_List_Oset(_1676016), _1676018) = c_Orderings_Obot__class_Obot(tc_fun(_1676016, tc_HOL_Obool)), -(_1676018 = c_List_Olist_ONil(_1676016))], (6449 ^ _780119) ^ [_884400] : [c_Hoare__Mirabelle_Ostate__not__singleton, c_Com_OWT__bodies, hBOOL(hAPP(c_Com_OWT, _884400)), -(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(c_Hoare__Mirabelle_OMGT, _884400)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (39976 ^ _780119) ^ [_1560367, _1560369] : [-(c_Transitive__Closure_Otrancl(_1560367, hAPP(c_Relation_Oconverse(_1560367, _1560367), _1560369)) = hAPP(c_Relation_Oconverse(_1560367, _1560367), c_Transitive__Closure_Otrancl(_1560367, _1560369)))], (44386 ^ _780119) ^ [_1669295, _1669297, _1669299, _1669301, _1669303] : [-(hAPP(hAPP(c_List_Olist__update(_1669295, hAPP(hAPP(c_List_Olist_OCons(_1669295), _1669297), _1669299)), hAPP(c_Nat_OSuc, _1669301)), _1669303) = hAPP(hAPP(c_List_Olist_OCons(_1669295), _1669297), hAPP(hAPP(c_List_Olist__update(_1669295, _1669299), _1669301), _1669303)))], (31547 ^ _780119) ^ [_1369308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1369308)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369308), c_Int_OPls)))], (51027 ^ _780119) ^ [_1814862, _1814864] : [class_Groups_Ouminus(_1814862), -(class_Groups_Ouminus(tc_fun(_1814864, _1814862)))], (49313 ^ _780119) ^ [_1778044, _1778046] : [-(c_List_Oinsert(_1778044, _1778046, c_List_Olist_ONil(_1778044)) = hAPP(hAPP(c_List_Olist_OCons(_1778044), _1778046), c_List_Olist_ONil(_1778044)))], (33311 ^ _780119) ^ [_1400986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1400986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1400986))))], (26599 ^ _780119) ^ [_1265739, _1265741, _1265743, _1265745, _1265747] : [class_Rings_Olinordered__idom(_1265739), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265739), hAPP(c_Groups_Oabs__class_Oabs(_1265739), _1265741)), _1265743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265739), hAPP(c_Groups_Oabs__class_Oabs(_1265739), _1265745)), _1265747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265739), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265739), hAPP(c_Groups_Oabs__class_Oabs(_1265739), _1265741)), hAPP(c_Groups_Oabs__class_Oabs(_1265739), _1265745))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265739), _1265743), _1265747))))], (35365 ^ _780119) ^ [_1446717, _1446719, _1446721, _1446723, _1446725, _1446727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1446717, _1446719), tc_HOL_Obool)), _1446721), _1446723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1446717, tc_HOL_Obool)), _1446725), _1446727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1446719, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446717, _1446719, _1446721), _1446725)), hAPP(c_Relation_OImage(_1446717, _1446719, _1446723), _1446727))))], (43376 ^ _780119) ^ [_1642275, _1642277, _1642279] : [-(hBOOL(hAPP(hAPP(c_member(_1642275), _1642277), hAPP(c_List_Oset(_1642275), _1642279)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642275)), c_List_Oremove1(_1642275, _1642277, _1642279)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642275)), _1642279))], (21432 ^ _780119) ^ [_1170598, _1170600, _1170602, _1170604, _1170606, _1170608] : [class_Divides_Osemiring__div(_1170598), c_Divides_Odiv__class_Omod(_1170598, _1170600, _1170602) = c_Divides_Odiv__class_Omod(_1170598, _1170604, _1170602), c_Divides_Odiv__class_Omod(_1170598, _1170606, _1170602) = c_Divides_Odiv__class_Omod(_1170598, _1170608, _1170602), -(c_Divides_Odiv__class_Omod(_1170598, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170598), _1170600), _1170606), _1170602) = c_Divides_Odiv__class_Omod(_1170598, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170598), _1170604), _1170608), _1170602))], (14302 ^ _780119) ^ [_1041574, _1041576, _1041578, _1041580, _1041582] : [c_Hoare__Mirabelle_Otriple__valid(_1041574, _1041576, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1041574), _1041578), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1041580))), _1041582)), -(c_Hoare__Mirabelle_Otriple__valid(_1041574, hAPP(c_Nat_OSuc, _1041576), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1041574), _1041578), hAPP(c_Com_Ocom_OBODY, _1041580)), _1041582)))], (9834 ^ _780119) ^ [_951202, _951204, _951206] : [class_Lattices_Osemilattice__inf(_951202), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951202), _951204), _951206) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951202), _951206), _951204))], (48912 ^ _780119) ^ [_1769383, _1769385, _1769387] : [hBOOL(hAPP(c_List_Olistsp(_1769383, hAPP(hAPP(c_COMBC(_1769383, tc_fun(_1769383, tc_HOL_Obool), tc_HOL_Obool), c_member(_1769383)), _1769385)), _1769387)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769383)), _1769387), c_List_Olists(_1769383, _1769385))))], (33893 ^ _780119) ^ [_1415963, _1415965, _1415967, _1415969, _1415971] : [hBOOL(hAPP(hAPP(_1415963, _1415965), _1415967)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1415969, _1415971, tc_HOL_Obool), _1415963), hAPP(hAPP(c_Product__Type_OPair(_1415969, _1415971), _1415965), _1415967))))], (51141 ^ _780119) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (38892 ^ _780119) ^ [_1534090, _1534092, _1534094, _1534096, _1534098, _1534100, _1534102] : [c_Fun_Oinj__on(_1534090, _1534092, _1534094, hAPP(c_Set_Oimage(_1534096, _1534090, _1534098), _1534100)), c_Fun_Oinj__on(_1534096, _1534090, _1534098, _1534100), hBOOL(hAPP(hAPP(c_member(_1534092), _1534102), hAPP(c_Set_Oimage(_1534090, _1534092, _1534094), hAPP(c_Set_Oimage(_1534096, _1534090, _1534098), _1534100)))), -(hAPP(c_Fun_Othe__inv__into(_1534096, _1534092, _1534100, hAPP(c_Fun_Ocomp(_1534090, _1534092, _1534096, _1534094), _1534098)), _1534102) = hAPP(hAPP(c_Fun_Ocomp(_1534090, _1534096, _1534092, c_Fun_Othe__inv__into(_1534096, _1534090, _1534100, _1534098)), c_Fun_Othe__inv__into(_1534090, _1534092, hAPP(c_Set_Oimage(_1534096, _1534090, _1534098), _1534100), _1534094)), _1534102))], (29843 ^ _780119) ^ [_1336686, _1336688, _1336690, _1336692, _1336694] : [hBOOL(hAPP(hAPP(c_member(_1336686), _1336688), _1336690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1336692, tc_HOL_Obool)), hAPP(_1336694, _1336688)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1336686, tc_fun(_1336692, tc_HOL_Obool)), _1336690), _1336694))))], (28938 ^ _780119) ^ [_1316393, _1316395, _1316397] : [class_Orderings_Olinorder(_1316393), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316393), _1316395)), -(_1316397 = c_Orderings_Obot__class_Obot(tc_fun(_1316393, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316393, tc_HOL_Obool)), _1316397), _1316395)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316393), c_Big__Operators_Olattice_OInf__fin(_1316393, c_Orderings_Oord__class_Omin(_1316393), _1316397)), c_Big__Operators_Olattice_OInf__fin(_1316393, c_Orderings_Oord__class_Omin(_1316393), _1316395)) = c_Big__Operators_Olattice_OInf__fin(_1316393, c_Orderings_Oord__class_Omin(_1316393), _1316395))], (7368 ^ _780119) ^ [_903919, _903921, _903923] : [hBOOL(hAPP(hAPP(c_member(_903919), _903921), c_Option_Oset(_903919, _903923))), -(_903923 = hAPP(c_Option_Ooption_OSome(_903919), _903921))], (28260 ^ _780119) ^ [_1302466, _1302468, _1302470, _1302472] : [class_Orderings_Olinorder(_1302466), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302466, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1302466), _1302468)), c_SetInterval_Oord__class_OatLeastAtMost(_1302466, _1302470, _1302472)) = c_SetInterval_Oord__class_OatLeastAtMost(_1302466, _1302470, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1302466), _1302468), _1302472)))], (7678 ^ _780119) ^ [_909833, _909835, _909837] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_909833, _909835, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909833)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909833), _909837), c_Com_Ocom_OSKIP), _909837)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909833), tc_HOL_Obool)))))], (27814 ^ _780119) ^ [_1293716, _1293718, _1293720, _1293722] : [class_Orderings_Olinorder(_1293716), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293716), _1293718), _1293720)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293716), _1293718), _1293722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293716), _1293718), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293716), _1293720), _1293722))))], (43398 ^ _780119) ^ [_1642878, _1642880] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1642878), _1642880)), -(c_Nitpick_Ocard_H(_1642878, _1642880) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642878)), c_Hilbert__Choice_OEps(tc_List_Olist(_1642878), hAPP(hAPP(c_COMBS(tc_List_Olist(_1642878), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1642878)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1642878), tc_fun(_1642878, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1642878, tc_HOL_Obool), tc_fun(tc_fun(_1642878, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1642878)), c_fequal), c_List_Oset(_1642878))), _1642880))), c_List_Odistinct(_1642878)))))], (39110 ^ _780119) ^ [_1539204, _1539206, _1539208, _1539210, _1539212, _1539214, _1539216] : [c_Hoare__Mirabelle_Ohoare__derivs(_1539204, _1539206, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1539204)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1539204), c_Hoare__Mirabelle_Opeek__and(_1539204, _1539208, _1539210)), _1539212), _1539214)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1539204), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1539204, _1539206, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1539204)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1539204), c_Hoare__Mirabelle_Opeek__and(_1539204, _1539208, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1539210))), _1539216), _1539214)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1539204), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1539204, _1539206, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1539204)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1539204), _1539208), c_Com_Ocom_OCond(_1539210, _1539212, _1539216)), _1539214)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1539204), tc_HOL_Obool)))))], (34010 ^ _780119) ^ [_1418457, _1418459, _1418461] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1418457, tc_HOL_Obool), tc_fun(_1418457, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1418457, tc_HOL_Obool), tc_fun(_1418457, tc_HOL_Obool)), _1418459), _1418461)), c_Wellfounded_Ofinite__psubset(_1418457))), 34013 ^ _780119 : [(34016 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1418457), _1418461)))], (34014 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1418457, tc_HOL_Obool)), _1418459), _1418461)))]]], (48560 ^ _780119) ^ [_1762001, _1762003] : [class_Enum_Oenum(_1762001), 48563 ^ _780119 : [(48571 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1762001), _1762003)), 48574 ^ _780119 : [(48575 ^ _780119) ^ [_1762219] : [-(hBOOL(hAPP(_1762003, _1762219)))]]], (48564 ^ _780119) ^ [] : [hBOOL(hAPP(_1762003, 48565 ^ [_1762001, _1762003])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1762001), _1762003)))]]], (37245 ^ _780119) ^ [_1492049] : [-(c_Wellfounded_Owf(tc_fun(_1492049, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1492049)))], (31247 ^ _780119) ^ [_1364299] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1364299)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1364299))], (33561 ^ _780119) ^ [_1404822, _1404824] : [-(c_Divides_Odivmod__int__rel(_1404822, _1404824) = 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, _1404822))), 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), _1404824)))))), 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)), _1404824))), 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)), _1404824))))), 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)), _1404824)))), 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), _1404824))), 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))))))))], (19939 ^ _780119) ^ [_1142661, _1142663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1142661)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1142661), _1142663)), _1142661) = _1142663)], (7584 ^ _780119) ^ [_907779, _907781, _907783, _907785, _907787] : [c_Finite__Set_Ofolding__one__idem(_907779, _907781, _907783), hBOOL(hAPP(c_Finite__Set_Ofinite(_907779), _907785)), -(_907785 = c_Orderings_Obot__class_Obot(tc_fun(_907779, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_907779), _907787)), -(_907787 = c_Orderings_Obot__class_Obot(tc_fun(_907779, tc_HOL_Obool))), -(hAPP(_907783, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907779, tc_HOL_Obool)), _907785), _907787)) = hAPP(hAPP(_907781, hAPP(_907783, _907785)), hAPP(_907783, _907787)))], (39921 ^ _780119) ^ [_1559076, _1559078] : [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), _1559076), _1559078)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1559076), _1559078)))], (4892 ^ _780119) ^ [_854824, _854826] : [_854826 = _854824, -(c_Lazy__Sequence_Osingle(_854826) = c_Lazy__Sequence_Osingle(_854824))], (22648 ^ _780119) ^ [_1193502] : [22650 ^ _780119 : [(22653 ^ _780119) ^ [_1193612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 22649 ^ [_1193502, _1193612]), _1193612))], (22651 ^ _780119) ^ [_1193578] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 22649 ^ [_1193502, _1193578]), _1193502)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1193502)))], (49876 ^ _780119) ^ [_1791455, _1791457, _1791459] : [c_List_Olist__all(_1791455, _1791457, _1791459), 49879 ^ _780119 : [(49880 ^ _780119) ^ [_1791536] : [hBOOL(hAPP(hAPP(c_member(_1791455), _1791536), hAPP(c_List_Oset(_1791455), _1791459))), -(hBOOL(hAPP(_1791457, _1791536)))]]], (5260 ^ _780119) ^ [_860572, _860574, _860576, _860578] : [-(c_List_Omap(_860578, _860574) = c_List_Omap(_860576, _860572)), _860578 = _860576, _860574 = _860572], (11945 ^ _780119) ^ [_995275, _995277, _995279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995277), _995279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995275), _995277)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995275), _995279))))], (22515 ^ _780119) ^ [_1190966, _1190968, _1190970, _1190972, _1190974, _1190976] : [-(c_Com_Ocom_OCond(_1190966, _1190968, _1190970) = c_Com_Ocom_OCond(_1190972, _1190974, _1190976)), _1190966 = _1190972, _1190968 = _1190974, _1190970 = _1190976], (47387 ^ _780119) ^ [_1734969, _1734971, _1734973, _1734975] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1734969, tc_Nat_Onat), _1734969), c_Product__Type_Ofst(_1734969, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1734969, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1734969, 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(_1734969, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1734969, tc_Nat_Onat))), _1734971)), hAPP(hAPP(c_List_Ozip(_1734969, tc_Nat_Onat), _1734973), c_List_Oupt(_1734975, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1734975), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734969)), _1734973)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1734969, tc_Nat_Onat), _1734969), c_Product__Type_Ofst(_1734969, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1734969, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1734969, 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(_1734969, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1734969, 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(_1734969, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1734969, tc_Nat_Onat))), _1734975))), _1734971)), hAPP(hAPP(c_List_Ozip(_1734969, tc_Nat_Onat), _1734973), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734969)), _1734973))))))], (43549 ^ _780119) ^ [_1648082, _1648084, _1648086, _1648088] : [_1648082 = _1648084, -(c_List_Oremove1(_1648086, _1648082, hAPP(hAPP(c_List_Olist_OCons(_1648086), _1648084), _1648088)) = _1648088)], (12193 ^ _780119) ^ [_999982, _999984, _999986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999982), _999984)), 12196 ^ _780119 : [(12203 ^ _780119) ^ [] : [_999984 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999986), _999982), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999984), _999982) = _999986)], (12197 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999984), _999982) = _999986, -(_999984 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999986), _999982))]]], (37850 ^ _780119) ^ [_1507781, _1507783] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1507781, _1507783), c_Orderings_Otop__class_Otop(tc_fun(_1507781, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1507783, tc_HOL_Obool), _1507781), c_Orderings_Otop__class_Otop(tc_fun(_1507783, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1507781, _1507783), tc_HOL_Obool)))], (13274 ^ _780119) ^ [_1021679, _1021681, _1021683, _1021685] : [class_Groups_Ouminus(_1021679), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021681, _1021679)), _1021683), _1021685) = hAPP(c_Groups_Ouminus__class_Ouminus(_1021679), hAPP(_1021683, _1021685)))], (22785 ^ _780119) ^ [_1196274] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1196274) = 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)), _1196274)))], (26963 ^ _780119) ^ [_1273757, _1273759, _1273761, _1273763, _1273765] : [-(c_Map_Odom(_1273757, _1273759, hAPP(hAPP(c_COMBS(_1273757, tc_Option_Ooption(_1273759), tc_Option_Ooption(_1273759)), hAPP(hAPP(c_COMBS(_1273757, tc_Option_Ooption(_1273759), tc_fun(tc_Option_Ooption(_1273759), tc_Option_Ooption(_1273759))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1273759), tc_fun(tc_Option_Ooption(_1273759), tc_Option_Ooption(_1273759))), _1273757), c_If(tc_Option_Ooption(_1273759))), _1273761)), _1273763)), _1273765)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273757, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1273757, tc_HOL_Obool)), c_Map_Odom(_1273757, _1273759, _1273763)), hAPP(c_Set_OCollect(_1273757), _1273761))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1273757, tc_HOL_Obool)), c_Map_Odom(_1273757, _1273759, _1273765)), hAPP(c_Set_OCollect(_1273757), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1273757), c_fNot), _1273761)))))], (26721 ^ _780119) ^ [_1268107, _1268109] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1268107), _1268109)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1268107) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (51461 ^ _780119) ^ [_1819271] : [-(class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(_1819271)))], (11569 ^ _780119) ^ [_988023, _988025, _988027, _988029] : [class_Rings_Ocomm__semiring__1(_988023), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988023), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988023), _988025), _988027)), _988029) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988023), _988025), _988029)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988023), _988027), _988029)))], (45446 ^ _780119) ^ [_1693206, _1693208, _1693210, _1693212] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693206), tc_List_Olist(_1693206))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693206), tc_List_Olist(_1693206)), _1693208), _1693210)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1693206), tc_List_Olist(_1693206)), c_List_Olistrel1(_1693206, _1693212)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693206), tc_List_Olist(_1693206))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693206), tc_List_Olist(_1693206)), _1693208), _1693210)), c_List_Olistrel1(_1693206, hAPP(c_Relation_Oconverse(_1693206, _1693206), _1693212)))))], (33957 ^ _780119) ^ [_1417334, _1417336, _1417338, _1417340, _1417342, _1417344] : [hBOOL(hAPP(hAPP(_1417334, _1417336), _1417338)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417340, tc_fun(_1417342, tc_HOL_Obool))), _1417334), _1417344), _1417336), _1417338)))], (31299 ^ _780119) ^ [_1365285] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365285))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365285) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13972 ^ _780119) ^ [_1034328, _1034330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1034328), _1034330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034328), hAPP(c_Nat_OSuc, _1034330))))], (26297 ^ _780119) ^ [_1259886, _1259888] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1259886)), -(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)), _1259886))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1259888))))) = 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)), _1259886))), 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, _1259888))))))], (4710 ^ _780119) ^ [_851839, _851841, _851843, _851845, _851847, _851849, _851851, _851853] : [-(c_New__DSequence_Oneg__bind(_851853, _851849, _851845, _851841) = c_New__DSequence_Oneg__bind(_851851, _851847, _851843, _851839)), _851853 = _851851, _851849 = _851847, _851845 = _851843, _851841 = _851839], (8554 ^ _780119) ^ [_928553, _928555, _928557] : [class_Orderings_Olinorder(_928553), 8557 ^ _780119 : [(8558 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928553), _928555), _928557))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928553), _928557), _928555))), -(_928555 = _928557)], (8568 ^ _780119) ^ [] : [8569 ^ _780119 : [(8572 ^ _780119) ^ [] : [_928555 = _928557], (8570 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928553), _928557), _928555))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928553), _928555), _928557))]]], (44134 ^ _780119) ^ [_1663025, _1663027, _1663029] : [-(hAPP(c_List_Oset(_1663025), c_List_Osublist(_1663025, _1663027, _1663029)) = hAPP(c_Set_OCollect(_1663025), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1663025), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1663025, 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)), _1663025), 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)), _1663025), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1663025, tc_fun(tc_Nat_Onat, _1663025), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1663025, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1663025), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1663025), c_COMBB(_1663025, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1663025), _1663027))))), 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(_1663025)), _1663027)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1663029))))))], (45064 ^ _780119) ^ [_1683323, _1683325, _1683327] : [_1683327 = c_List_Olist_ONil(_1683325), -(_1683323 = hAPP(hAPP(c_List_Oappend(_1683325), _1683327), _1683323))], (34347 ^ _780119) ^ [_1424785, _1424787] : [34348 ^ _780119 : [(34351 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1424787), _1424785))], (34349 ^ _780119) ^ [] : [_1424785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1424787, _1424785) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1424787))], (38687 ^ _780119) ^ [_1529574, _1529576] : [hBOOL(hAPP(_1529574, c_Hilbert__Choice_OEps(_1529576, _1529574))), -(hBOOL(hAPP(_1529574, 38690 ^ [_1529574, _1529576])))], (21554 ^ _780119) ^ [_1173209, _1173211, _1173213] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1173209), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1173211, _1173213)), _1173213) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1173209), _1173211), _1173213))], (36666 ^ _780119) ^ [_1476539, _1476541, _1476543, _1476545] : [c_Fun_Oinj__on(_1476539, _1476541, _1476543, c_Orderings_Otop__class_Otop(tc_fun(_1476539, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1476539, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1476539, _1476541, _1476543), hAPP(hAPP(c_Set_Oinsert(_1476541), _1476545), c_Orderings_Obot__class_Obot(tc_fun(_1476541, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1476539), c_HOL_OThe(_1476539, hAPP(hAPP(c_COMBC(_1476539, _1476541, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1476541, tc_fun(_1476541, tc_HOL_Obool), _1476539), c_fequal), _1476543)), _1476545))), c_Orderings_Obot__class_Obot(tc_fun(_1476539, tc_HOL_Obool))))))], (38816 ^ _780119) ^ [_1532302, _1532304, _1532306, _1532308, _1532310, _1532312, _1532314, _1532316, _1532318, _1532320, _1532322] : [-(hAPP(c_Product__Type_Omap__pair(_1532302, _1532304, _1532306, _1532308, _1532310, _1532312), hAPP(c_Product__Type_Omap__pair(_1532314, _1532302, _1532316, _1532306, _1532318, _1532320), _1532322)) = hAPP(c_Product__Type_Omap__pair(_1532314, _1532304, _1532316, _1532308, hAPP(c_Fun_Ocomp(_1532302, _1532304, _1532314, _1532310), _1532318), hAPP(c_Fun_Ocomp(_1532306, _1532308, _1532316, _1532312), _1532320)), _1532322))], (32187 ^ _780119) ^ [_1380549, _1380551] : [class_Int_Onumber__ring(_1380549), 32190 ^ _780119 : [(32197 ^ _780119) ^ [] : [c_Int_Oiszero(_1380549, hAPP(c_Int_Onumber__class_Onumber__of(_1380549), 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), _1380551)))), -(c_Groups_Oone__class_Oone(_1380549) = hAPP(c_Int_Onumber__class_Onumber__of(_1380549), _1380551))], (32191 ^ _780119) ^ [] : [c_Groups_Oone__class_Oone(_1380549) = hAPP(c_Int_Onumber__class_Onumber__of(_1380549), _1380551), -(c_Int_Oiszero(_1380549, hAPP(c_Int_Onumber__class_Onumber__of(_1380549), 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), _1380551)))))]]], (34877 ^ _780119) ^ [_1435005, _1435007, _1435009] : [-(c_HOL_OThe(tc_prod(_1435005, _1435007), hAPP(c_Product__Type_Oprod_Oprod__case(_1435005, _1435007, tc_HOL_Obool), _1435009)) = c_HOL_OThe(tc_prod(_1435005, _1435007), hAPP(hAPP(c_COMBS(tc_prod(_1435005, _1435007), _1435007, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1435005, tc_fun(_1435007, tc_HOL_Obool), tc_prod(_1435005, _1435007)), _1435009), c_Product__Type_Ofst(_1435005, _1435007))), c_Product__Type_Osnd(_1435005, _1435007))))], (43194 ^ _780119) ^ [_1637556, _1637558, _1637560, _1637562, _1637564, _1637566, _1637568] : [hAPP(hAPP(c_List_Omap(_1637556, _1637558), _1637560), _1637562) = hAPP(hAPP(c_List_Omap(_1637564, _1637558), _1637566), _1637568), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637556)), _1637562) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637564)), _1637568))], (39182 ^ _780119) ^ [_1541138, _1541140, _1541142, _1541144, _1541146, _1541148] : [c_Finite__Set_Ofolding__idem(_1541138, _1541140, _1541142, _1541144), hBOOL(hAPP(c_Finite__Set_Ofinite(_1541138), _1541146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1541138, tc_HOL_Obool)), _1541148), _1541146)), -(hAPP(c_Fun_Ocomp(_1541140, _1541140, _1541140, hAPP(_1541144, _1541146)), hAPP(_1541144, _1541148)) = hAPP(_1541144, _1541146))], (13889 ^ _780119) ^ [_1032595, _1032597, _1032599] : [class_Lattices_Oboolean__algebra(_1032595), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1032595), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1032595), _1032597), _1032599)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1032595), hAPP(c_Groups_Ouminus__class_Ouminus(_1032595), _1032597)), hAPP(c_Groups_Ouminus__class_Ouminus(_1032595), _1032599)))], (31647 ^ _780119) ^ [_1370845] : [class_Int_Onumber__ring(_1370845), -(hAPP(c_Int_Onumber__class_Onumber__of(_1370845), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1370845))], (25624 ^ _780119) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11931 ^ _780119) ^ [_994928, _994930, _994932] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994928), _994930)), _994932) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994928), _994932)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994930), _994932)))], (2506 ^ _780119) ^ [_817117, _817119, _817121, _817123, _817125, _817127, _817129, _817131, _817133, _817135] : [-(c_Product__Type_Oprod_Oprod__rec(_817135, _817131, _817127, _817123, _817119) = c_Product__Type_Oprod_Oprod__rec(_817133, _817129, _817125, _817121, _817117)), _817135 = _817133, _817131 = _817129, _817127 = _817125, _817123 = _817121, _817119 = _817117], (31399 ^ _780119) ^ [_1367062] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367062)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367062)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367062))], (43112 ^ _780119) ^ [_1635421, _1635423, _1635425, _1635427, _1635429, _1635431] : [-(hAPP(hAPP(c_List_Ozip(_1635421, _1635423), hAPP(hAPP(c_List_Omap(_1635425, _1635421), _1635427), _1635429)), _1635431) = hAPP(hAPP(c_List_Omap(tc_prod(_1635425, _1635423), tc_prod(_1635421, _1635423)), hAPP(c_Product__Type_Oprod_Oprod__case(_1635425, _1635423, tc_prod(_1635421, _1635423)), hAPP(hAPP(c_COMBB(_1635421, tc_fun(_1635423, tc_prod(_1635421, _1635423)), _1635425), c_Product__Type_OPair(_1635421, _1635423)), _1635427))), hAPP(hAPP(c_List_Ozip(_1635425, _1635423), _1635429), _1635431)))], (5280 ^ _780119) ^ [_860870, _860872, _860874, _860876, _860878, _860880] : [-(c_List_Oreplicate(_860880, _860876, _860872) = c_List_Oreplicate(_860878, _860874, _860870)), _860880 = _860878, _860876 = _860874, _860872 = _860870], (26777 ^ _780119) ^ [_1269448, _1269450, _1269452] : [hBOOL(hAPP(_1269448, _1269450)), -(hAPP(c_Set_OCollect(_1269452), hAPP(hAPP(c_COMBS(_1269452, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1269452), c_fconj), hAPP(c_fequal, _1269450))), _1269448)) = hAPP(hAPP(c_Set_Oinsert(_1269452), _1269450), c_Orderings_Obot__class_Obot(tc_fun(_1269452, tc_HOL_Obool))))], (41962 ^ _780119) ^ [_1608223, _1608225] : [class_Complete__Lattice_Ocomplete__lattice(_1608223), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608223), _1608225)), -(_1608225 = c_Orderings_Obot__class_Obot(tc_fun(_1608223, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1608223, _1608225) = c_Complete__Lattice_OInf__class_OInf(_1608223, _1608225))], (10242 ^ _780119) ^ [_959693] : [class_Lattices_Oab__semigroup__idem__mult(_959693), -(c_Finite__Set_Ofun__left__comm__idem(_959693, _959693, c_Groups_Otimes__class_Otimes(_959693)))], (6087 ^ _780119) ^ [_877042, _877044] : [_877044 = c_Orderings_Obot__class_Obot(tc_fun(_877042, tc_HOL_Obool)), 6090 ^ _780119 : [(6091 ^ _780119) ^ [_877122] : [hBOOL(hAPP(hAPP(c_member(_877042), _877122), _877044))]]], (36922 ^ _780119) ^ [_1482713, _1482715, _1482717, _1482719, _1482721] : [c_Fun_Oinj__on(_1482713, _1482715, _1482717, _1482719), hBOOL(hAPP(hAPP(c_member(_1482715), _1482721), hAPP(c_Set_Oimage(_1482713, _1482715, _1482717), _1482719))), -(hAPP(_1482717, hAPP(c_Fun_Othe__inv__into(_1482713, _1482715, _1482719, _1482717), _1482721)) = _1482721)], (28353 ^ _780119) ^ [_1304257, _1304259, _1304261] : [class_Orderings_Olinorder(_1304257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304257), _1304259)), -(_1304259 = c_Orderings_Obot__class_Obot(tc_fun(_1304257, tc_HOL_Obool))), 28364 ^ _780119 : [(28374 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304257), hAPP(c_Finite__Set_Ofold1(_1304257, c_Orderings_Oord__class_Omin(_1304257)), _1304259)), _1304261))), 28375 ^ _780119 : [(28376 ^ _780119) ^ [_1304646] : [hBOOL(hAPP(hAPP(c_member(_1304257), _1304646), _1304259)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304257), _1304646), _1304261))]]], (28365 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304257), hAPP(c_Finite__Set_Ofold1(_1304257, c_Orderings_Oord__class_Omin(_1304257)), _1304259)), _1304261)), 28369 ^ _780119 : [(28372 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304257), 28368 ^ [_1304257, _1304259, _1304261]), _1304261)))], (28370 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304257), 28368 ^ [_1304257, _1304259, _1304261]), _1304259)))]]]]], (41637 ^ _780119) ^ [_1601148, _1601150, _1601152, _1601154] : [-(hAPP(c_Set_Oimage(_1601148, _1601150, _1601152), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1601148, tc_HOL_Obool), _1601154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1601148, tc_HOL_Obool), tc_fun(_1601150, tc_HOL_Obool)), _1601154), c_Set_Oimage(_1601148, _1601150, _1601152)))], (51387 ^ _780119) ^ [_1818380] : [-(class_HOL_Oequal(tc_Option_Ooption(_1818380)))], (8972 ^ _780119) ^ [_934630, _934632, _934634] : [class_Orderings_Olinorder(_934630), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934630), _934632), _934634))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934630), _934634), _934632)))], (42893 ^ _780119) ^ [_1630140, _1630142, _1630144, _1630146] : [hBOOL(hAPP(c_List_Odistinct(_1630140), hAPP(hAPP(c_List_Omap(tc_prod(_1630140, _1630142), _1630140), c_Product__Type_Ofst(_1630140, _1630142)), _1630144))), hBOOL(hAPP(c_List_Odistinct(_1630140), hAPP(hAPP(c_List_Omap(tc_prod(_1630140, _1630142), _1630140), c_Product__Type_Ofst(_1630140, _1630142)), _1630146))), 42900 ^ _780119 : [(42907 ^ _780119) ^ [] : [hAPP(c_List_Oset(tc_prod(_1630140, _1630142)), _1630144) = hAPP(c_List_Oset(tc_prod(_1630140, _1630142)), _1630146), -(hAPP(c_Map_Omap__of(_1630140, _1630142), _1630144) = hAPP(c_Map_Omap__of(_1630140, _1630142), _1630146))], (42901 ^ _780119) ^ [] : [hAPP(c_Map_Omap__of(_1630140, _1630142), _1630144) = hAPP(c_Map_Omap__of(_1630140, _1630142), _1630146), -(hAPP(c_List_Oset(tc_prod(_1630140, _1630142)), _1630144) = hAPP(c_List_Oset(tc_prod(_1630140, _1630142)), _1630146))]]], (9798 ^ _780119) ^ [_950416, _950418, _950420, _950422] : [class_Lattices_Olattice(_950416), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950416), _950418), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950416), _950420), _950422)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950416), _950420), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950416), _950418), _950422)))], (44532 ^ _780119) ^ [_1672241, _1672243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1672241)), hAPP(c_Code__Numeral_Onat__of, _1672243))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1672241), _1672243)))], (18189 ^ _780119) ^ [_1111367, _1111369, _1111371, _1111373, _1111375] : [class_Groups_Oordered__comm__monoid__add(_1111367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111369), _1111371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1111369, tc_HOL_Obool)), _1111373), _1111371)), 18203 ^ _780119 : [(18206 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111367), c_Groups_Ozero__class_Ozero(_1111367)), hAPP(_1111375, 18202 ^ [_1111367, _1111369, _1111371, _1111373, _1111375])))], (18204 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1111369), 18202 ^ [_1111367, _1111369, _1111371, _1111373, _1111375]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1111369, tc_HOL_Obool)), _1111371), _1111373))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111367), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1111369, _1111367), _1111375), _1111373)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1111369, _1111367), _1111375), _1111371))))], (2006 ^ _780119) ^ [_809219, _809221, _809223, _809225, _809227, _809229, _809231, _809233] : [-(c_Sum__Type_OPlus(_809233, _809229, _809225, _809221) = c_Sum__Type_OPlus(_809231, _809227, _809223, _809219)), _809233 = _809231, _809229 = _809227, _809225 = _809223, _809221 = _809219], (35081 ^ _780119) ^ [_1439397, _1439399, _1439401, _1439403, _1439405] : [-(hAPP(c_Product__Type_Ofst(_1439397, _1439399), hAPP(c_Product__Type_Oapfst(_1439401, _1439397, _1439399, _1439403), _1439405)) = hAPP(_1439403, hAPP(c_Product__Type_Ofst(_1439401, _1439399), _1439405)))], (13670 ^ _780119) ^ [_1028731, _1028733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028731), hAPP(c_Nat_OSuc, _1028733))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028731), _1028733))), -(_1028731 = hAPP(c_Nat_OSuc, _1028733))], (21781 ^ _780119) ^ [_1177851, _1177853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177851), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 21784 ^ _780119 : [(21787 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177851), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1177853, _1177851))))], (21785 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1177853, _1177851)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (32793 ^ _780119) ^ [_1391314, _1391316] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1391314)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1391316))) = 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), _1391314), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1391316))))], (50308 ^ _780119) ^ [_1799833, _1799835, _1799837, _1799839, _1799841, _1799843, _1799845] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1799833, _1799835, _1799837, _1799839), _1799841), _1799843), _1799845) = c_New__DSequence_Oneg__bind(_1799833, _1799835, hAPP(hAPP(hAPP(_1799837, _1799841), _1799843), _1799845), hAPP(hAPP(c_COMBC(_1799833, 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(_1799835)))), hAPP(hAPP(c_COMBC(_1799833, 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(_1799835))))), hAPP(hAPP(c_COMBC(_1799833, 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(_1799835)))))), _1799839), _1799841)), _1799843)), _1799845)))], (39671 ^ _780119) ^ [_1553105, _1553107] : [-(hAPP(c_Relation_OImage(_1553105, _1553105, c_Relation_OId(_1553105)), _1553107) = _1553107)], (12215 ^ _780119) ^ [_1000378, _1000380, _1000382, _1000384, _1000386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000378), _1000380)), 12218 ^ _780119 : [(12225 ^ _780119) ^ [] : [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), _1000380), _1000378)), _1000382)), _1000384)), _1000386)), -(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), _1000380), _1000382)), _1000384)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000378), _1000382)), _1000386))))], (12219 ^ _780119) ^ [] : [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), _1000380), _1000382)), _1000384)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000378), _1000382)), _1000386))), -(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), _1000380), _1000378)), _1000382)), _1000384)), _1000386)))]]], (33367 ^ _780119) ^ [_1401784, _1401786] : [class_Int_Onumber__ring(_1401784), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401784), _1401786), hAPP(c_Int_Onumber__class_Onumber__of(_1401784), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1401784), _1401786))], (23709 ^ _780119) ^ [_1213407, _1213409] : [class_Orderings_Oorder(_1213407), -(c_SetInterval_Oord__class_OatLeastAtMost(_1213407, _1213409, _1213409) = hAPP(hAPP(c_Set_Oinsert(_1213407), _1213409), c_Orderings_Obot__class_Obot(tc_fun(_1213407, tc_HOL_Obool))))], (45936 ^ _780119) ^ [_1705161] : [-(c_List_Orotate(_1705161, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1705161)))], (47977 ^ _780119) ^ [_1749184, _1749186] : [hBOOL(hAPP(c_List_Odistinct(_1749184), _1749186)), -(c_List_Oremdups(_1749184, _1749186) = _1749186)], (31553 ^ _780119) ^ [_1369403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369403), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1369403)), c_Int_OPls)))], (51577 ^ _780119) ^ [] : [-(hBOOL(c_fTrue))], (22294 ^ _780119) ^ [_1186885, _1186887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186887, _1186885)), _1186885)))], (32415 ^ _780119) ^ [_1384569] : [c_Int_OPls = _1384569, -(c_Int_OPls = c_Int_OBit0(_1384569))], (28104 ^ _780119) ^ [_1299128, _1299130, _1299132, _1299134] : [class_Orderings_Olinorder(_1299128), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299128), _1299130), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299128), _1299132), _1299134)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299128), _1299132), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299128), _1299130), _1299134)))], (51313 ^ _780119) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (32687 ^ _780119) ^ [_1389519, _1389521] : [class_Int_Onumber__ring(_1389519), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389519), _1389521), hAPP(c_Int_Onumber__class_Onumber__of(_1389519), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389519), _1389521), _1389521))], (16875 ^ _780119) ^ [_1086857, _1086859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1086857)), -(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), _1086857), _1086859))))], (4212 ^ _780119) ^ [_843778, _843780, _843782, _843784] : [-(c_List_OremoveAll(_843784, _843780) = c_List_OremoveAll(_843782, _843778)), _843784 = _843782, _843780 = _843778], (9140 ^ _780119) ^ [_937046, _937048, _937050, _937052] : [class_Orderings_Opreorder(_937046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937046), _937048), _937050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937046), _937050), _937052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937046), _937048), _937052)))], (46913 ^ _780119) ^ [_1726323, _1726325, _1726327] : [class_Orderings_Olinorder(_1726323), c_List_Olinorder__class_Osorted(_1726323, _1726325), -(c_List_Olinorder__class_Osorted(_1726323, hAPP(hAPP(c_List_Odrop(_1726323), _1726327), _1726325)))], (47897 ^ _780119) ^ [_1747754, _1747756, _1747758, _1747760, _1747762] : [class_Orderings_Olinorder(_1747754), c_List_Olinorder__class_Osorted(_1747754, hAPP(c_List_Orev(_1747754), hAPP(hAPP(c_List_Omap(_1747756, _1747754), _1747758), _1747760))), -(hAPP(c_List_Ofilter(_1747756, hAPP(hAPP(c_COMBB(_1747754, tc_HOL_Obool, _1747756), hAPP(c_Orderings_Oord__class_Oless(_1747754), _1747762)), _1747758)), _1747760) = c_List_OtakeWhile(_1747756, hAPP(hAPP(c_COMBB(_1747754, tc_HOL_Obool, _1747756), hAPP(c_Orderings_Oord__class_Oless(_1747754), _1747762)), _1747758), _1747760))], (20404 ^ _780119) ^ [_1151379, _1151381, _1151383] : [class_Fields_Olinordered__field(_1151379), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151379), c_Groups_Ozero__class_Ozero(_1151379)), _1151381)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151379), _1151383), c_Groups_Ozero__class_Ozero(_1151379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151379), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151379), _1151381), _1151383)), c_Groups_Ozero__class_Ozero(_1151379))))], (37914 ^ _780119) ^ [_1509500, _1509502, _1509504, _1509506] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1509500, _1509502)), hAPP(hAPP(c_Product__Type_OSigma(_1509500, _1509502), _1509504), hAPP(c_COMBK(tc_fun(_1509502, tc_HOL_Obool), _1509500), _1509506)))), -(_1509506 = c_Orderings_Obot__class_Obot(tc_fun(_1509502, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1509500), _1509504)))], (7890 ^ _780119) ^ [_914436, _914438, _914440, _914442] : [-(c_Com_Ocom_OWhile(_914436, _914438) = c_Com_Ocom_OWhile(_914440, _914442)), _914436 = _914440, _914438 = _914442], (27524 ^ _780119) ^ [_1288636, _1288638, _1288640, _1288642, _1288644] : [class_Orderings_Olinorder(_1288636), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288636, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1288636, _1288638), _1288640)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1288636, _1288642), _1288644)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1288636, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288636), _1288638), _1288642)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288636), _1288640), _1288644)))], (42324 ^ _780119) ^ [_1616851, _1616853, _1616855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1616851), c_Nitpick_Oplus__frac(_1616851, _1616853, c_Nitpick_Ouminus__frac(_1616851, _1616855)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1616851, _1616853, _1616855))], (30341 ^ _780119) ^ [_1347095, _1347097, _1347099] : [class_Int_Onumber(_1347095), class_Orderings_Oord(_1347095), 30348 ^ _780119 : [(30355 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347095), hAPP(c_Int_Onumber__class_Onumber__of(_1347095), _1347097)), hAPP(c_Int_Onumber__class_Onumber__of(_1347095), _1347099)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1347095), hAPP(c_Int_Onumber__class_Onumber__of(_1347095), _1347097)), hAPP(c_Int_Onumber__class_Onumber__of(_1347095), _1347099)) = hAPP(c_Int_Onumber__class_Onumber__of(_1347095), _1347099))], (30349 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347095), hAPP(c_Int_Onumber__class_Onumber__of(_1347095), _1347097)), hAPP(c_Int_Onumber__class_Onumber__of(_1347095), _1347099))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1347095), hAPP(c_Int_Onumber__class_Onumber__of(_1347095), _1347097)), hAPP(c_Int_Onumber__class_Onumber__of(_1347095), _1347099)) = hAPP(c_Int_Onumber__class_Onumber__of(_1347095), _1347097))]]], (39978 ^ _780119) ^ [_1560425, _1560427] : [c_Wellfounded_Oacyclic(_1560425, hAPP(c_Relation_Oconverse(_1560425, _1560425), _1560427)), -(c_Wellfounded_Oacyclic(_1560425, _1560427))], (23394 ^ _780119) ^ [_1207563, _1207565, _1207567, _1207569] : [class_Rings_Osemiring__1(_1207563), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1207563, _1207565, hAPP(c_Nat_OSuc, _1207567), _1207569) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1207563, _1207565, _1207567, hAPP(_1207565, _1207569)))], (2544 ^ _780119) ^ [_817740, _817742, _817744, _817746, _817748, _817750, _817752, _817754] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_817754, _817750, _817746, _817742) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_817752, _817748, _817744, _817740)), _817754 = _817752, _817750 = _817748, _817746 = _817744, _817742 = _817740], (20612 ^ _780119) ^ [_1154830, _1154832, _1154834] : [class_Fields_Olinordered__field(_1154830), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154830), c_Groups_Ozero__class_Ozero(_1154830)), _1154832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154830), c_Groups_Ozero__class_Ozero(_1154830)), _1154834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154830), c_Groups_Ozero__class_Ozero(_1154830)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154830), _1154832), _1154834))))], (49044 ^ _780119) ^ [_1772567, _1772569, _1772571, _1772573, _1772575, _1772577, _1772579] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772567)), _1772569) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772571)), _1772573), 49047 ^ _780119 : [(49056 ^ _780119) ^ [] : [-(c_List_Olist__all2(_1772567, _1772571, _1772575, hAPP(hAPP(c_List_Oappend(_1772567), _1772569), _1772577), hAPP(hAPP(c_List_Oappend(_1772571), _1772573), _1772579))), c_List_Olist__all2(_1772567, _1772571, _1772575, _1772569, _1772573), c_List_Olist__all2(_1772567, _1772571, _1772575, _1772577, _1772579)], (49048 ^ _780119) ^ [] : [c_List_Olist__all2(_1772567, _1772571, _1772575, hAPP(hAPP(c_List_Oappend(_1772567), _1772569), _1772577), hAPP(hAPP(c_List_Oappend(_1772571), _1772573), _1772579)), 49051 ^ _780119 : [(49054 ^ _780119) ^ [] : [-(c_List_Olist__all2(_1772567, _1772571, _1772575, _1772577, _1772579))], (49052 ^ _780119) ^ [] : [-(c_List_Olist__all2(_1772567, _1772571, _1772575, _1772569, _1772573))]]]]], (47242 ^ _780119) ^ [_1732111, _1732113, _1732115] : [class_Orderings_Olinorder(_1732111), 47245 ^ _780119 : [(47258 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1732111, hAPP(hAPP(c_List_Olist_OCons(_1732111), _1732113), _1732115))), 47262 ^ _780119 : [(47265 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732111), _1732113), 47261 ^ [_1732111, _1732113, _1732115]))], (47263 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1732111), 47261 ^ [_1732111, _1732113, _1732115]), hAPP(c_List_Oset(_1732111), _1732115))))]], c_List_Olinorder__class_Osorted(_1732111, _1732115)], (47246 ^ _780119) ^ [] : [c_List_Olinorder__class_Osorted(_1732111, hAPP(hAPP(c_List_Olist_OCons(_1732111), _1732113), _1732115)), 47249 ^ _780119 : [(47250 ^ _780119) ^ [_1732279] : [hBOOL(hAPP(hAPP(c_member(_1732111), _1732279), hAPP(c_List_Oset(_1732111), _1732115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732111), _1732113), _1732279)))], (47256 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1732111, _1732115))]]]]], (33261 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (23677 ^ _780119) ^ [_1212898, _1212900, _1212902] : [class_Orderings_Oorder(_1212898), _1212900 = _1212902, -(c_SetInterval_Oord__class_OatLeastAtMost(_1212898, _1212900, _1212902) = hAPP(hAPP(c_Set_Oinsert(_1212898), _1212900), c_Orderings_Obot__class_Obot(tc_fun(_1212898, tc_HOL_Obool))))], (11025 ^ _780119) ^ [_975977, _975979, _975981, _975983, _975985] : [class_Groups_Oordered__cancel__ab__semigroup__add(_975977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975977), _975979), _975981)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975977), _975983), _975985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975977), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975977), _975979), _975983)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975977), _975981), _975985))))], (33563 ^ _780119) ^ [_1404933, _1404935] : [-(_1404933 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1404935, _1404933), c_Divides_Odivmod__int(_1404935, _1404933))))], (23090 ^ _780119) ^ [] : [-(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))], (9304 ^ _780119) ^ [_940195, _940197, _940199, _940201] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_940195, _940197, _940199, _940201, c_Orderings_Obot__class_Obot(tc_fun(_940195, tc_HOL_Obool))), _940201)))], (47638 ^ _780119) ^ [_1740919, _1740921, _1740923, _1740925] : [-(c_List_Otranspose(_1740919, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1740919)), hAPP(hAPP(c_List_Olist_OCons(_1740919), _1740921), _1740923)), _1740925)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1740919)), hAPP(hAPP(c_List_Olist_OCons(_1740919), _1740921), c_List_Oconcat(_1740919, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1740919), tc_List_Olist(_1740919)), c_List_Olist_Olist__case(tc_List_Olist(_1740919), _1740919, c_List_Olist_ONil(_1740919), hAPP(hAPP(c_COMBB(tc_List_Olist(_1740919), tc_fun(tc_List_Olist(_1740919), tc_List_Olist(_1740919)), _1740919), c_COMBK(tc_List_Olist(_1740919), tc_List_Olist(_1740919))), hAPP(hAPP(c_COMBC(_1740919, tc_List_Olist(_1740919), tc_List_Olist(_1740919)), c_List_Olist_OCons(_1740919)), c_List_Olist_ONil(_1740919))))), _1740925)))), c_List_Otranspose(_1740919, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1740919)), _1740923), c_List_Oconcat(tc_List_Olist(_1740919), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1740919), tc_List_Olist(tc_List_Olist(_1740919))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1740919)), _1740919, c_List_Olist_ONil(tc_List_Olist(_1740919)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1740919), tc_List_Olist(tc_List_Olist(_1740919))), _1740919), hAPP(hAPP(c_COMBC(tc_List_Olist(_1740919), tc_List_Olist(tc_List_Olist(_1740919)), tc_List_Olist(tc_List_Olist(_1740919))), c_List_Olist_OCons(tc_List_Olist(_1740919))), c_List_Olist_ONil(tc_List_Olist(_1740919)))))), _1740925))))))], (37425 ^ _780119) ^ [_1495834, _1495836] : [-(c_FunDef_Oreduction__pair(_1495834, _1495836)), c_Wellfounded_Owf(_1495834, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1495834, _1495834), tc_HOL_Obool), tc_fun(tc_prod(_1495834, _1495834), tc_HOL_Obool)), _1495836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1495834, _1495834), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1495834, _1495834, _1495834), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1495834, _1495834), tc_HOL_Obool), tc_fun(tc_prod(_1495834, _1495834), tc_HOL_Obool)), _1495836)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1495834, _1495834), tc_HOL_Obool), tc_fun(tc_prod(_1495834, _1495834), tc_HOL_Obool)), _1495836))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1495834, _1495834), tc_HOL_Obool), tc_fun(tc_prod(_1495834, _1495834), tc_HOL_Obool)), _1495836)))], (26235 ^ _780119) ^ [_1258666, _1258668, _1258670, _1258672, _1258674] : [class_Groups_Ocomm__monoid__add(_1258666), class_Groups_Ocomm__monoid__mult(_1258666), _1258668 = _1258670, c_Nat__Transfer_Onat__set(_1258670), 26253 ^ _780119 : [(26256 ^ _780119) ^ [] : [hAPP(_1258672, 26252 ^ [_1258666, _1258668, _1258670, _1258672, _1258674]) = hAPP(_1258674, 26252 ^ [_1258666, _1258668, _1258670, _1258672, _1258674])], (26254 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26252 ^ [_1258666, _1258668, _1258670, _1258672, _1258674])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1258666), _1258672), _1258668) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1258666), _1258674), _1258670))], (26715 ^ _780119) ^ [_1267968, _1267970, _1267972] : [class_Rings_Olinordered__idom(_1267968), -(hAPP(c_Groups_Oabs__class_Oabs(_1267968), hAPP(hAPP(c_Power_Opower__class_Opower(_1267968), hAPP(c_Groups_Ouminus__class_Ouminus(_1267968), _1267970)), _1267972)) = hAPP(c_Groups_Oabs__class_Oabs(_1267968), hAPP(hAPP(c_Power_Opower__class_Opower(_1267968), _1267970), _1267972)))], (3252 ^ _780119) ^ [_828788, _828790, _828792, _828794] : [-(c_List_Olenlex(_828794, _828790) = c_List_Olenlex(_828792, _828788)), _828794 = _828792, _828790 = _828788], (39284 ^ _780119) ^ [_1543481, _1543483, _1543485] : [39286 ^ _780119 : [(39289 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1543481), 39285 ^ [_1543481, _1543483, _1543485]), c_Wellfounded_Oacc(_1543481, _1543485)))], (39287 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1543481, _1543481)), hAPP(hAPP(c_Product__Type_OPair(_1543481, _1543481), 39285 ^ [_1543481, _1543483, _1543485]), _1543483)), _1543485)))]], -(hBOOL(hAPP(hAPP(c_member(_1543481), _1543483), c_Wellfounded_Oacc(_1543481, _1543485))))], (10038 ^ _780119) ^ [_954932, _954934, _954936] : [class_Lattices_Olattice(_954932), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954932), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954932), _954934), _954936)), _954934)))], (18814 ^ _780119) ^ [_1123148] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1123148) = _1123148)], (48227 ^ _780119) ^ [_1755048, _1755050, _1755052, _1755054, _1755056] : [c_List_Opartition(_1755048, _1755050, _1755052) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755048), tc_List_Olist(_1755048)), _1755054), _1755056), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1755048, tc_HOL_Obool)), hAPP(c_List_Oset(_1755048), _1755054)), hAPP(c_List_Oset(_1755048), _1755056)) = hAPP(c_List_Oset(_1755048), _1755052))], (44822 ^ _780119) ^ [_1677835, _1677837, _1677839] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1677835))), -(c_List_Osublist(_1677837, hAPP(hAPP(c_List_Olist_OCons(_1677837), _1677839), c_List_Olist_ONil(_1677837)), _1677835) = c_List_Olist_ONil(_1677837))], (19835 ^ _780119) ^ [_1140884, _1140886] : [class_Rings_Odivision__ring(_1140884), -(_1140886 = c_Groups_Ozero__class_Ozero(_1140884)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140884), _1140886), _1140886) = c_Groups_Oone__class_Oone(_1140884))], (15664 ^ _780119) ^ [_1065524, _1065526, _1065528] : [class_Rings_Olinordered__ring__strict(_1065524), 15667 ^ _780119 : [(15682 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065524), c_Groups_Ozero__class_Ozero(_1065524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065524), _1065526), _1065528)))), 15683 ^ _780119 : [(15690 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065524), _1065526), c_Groups_Ozero__class_Ozero(_1065524))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065524), _1065528), c_Groups_Ozero__class_Ozero(_1065524)))], (15684 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065524), c_Groups_Ozero__class_Ozero(_1065524)), _1065526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065524), c_Groups_Ozero__class_Ozero(_1065524)), _1065528))]]], (15668 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065524), c_Groups_Ozero__class_Ozero(_1065524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065524), _1065526), _1065528))), 15673 ^ _780119 : [(15676 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065524), c_Groups_Ozero__class_Ozero(_1065524)), _1065528)))], (15674 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065524), c_Groups_Ozero__class_Ozero(_1065524)), _1065526)))]], 15677 ^ _780119 : [(15680 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065524), _1065528), c_Groups_Ozero__class_Ozero(_1065524))))], (15678 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065524), _1065526), c_Groups_Ozero__class_Ozero(_1065524))))]]]]], (3886 ^ _780119) ^ [_838727, _838729] : [_838729 = _838727, -(c_List_Otranspose__rel(_838729) = c_List_Otranspose__rel(_838727))], (23191 ^ _780119) ^ [_1203728, _1203730] : [class_Rings_Olinordered__semidom(_1203728), 23194 ^ _780119 : [(23201 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203728), c_Groups_Ozero__class_Ozero(_1203728)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203728), _1203730))))], (23195 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203728), c_Groups_Ozero__class_Ozero(_1203728)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203728), _1203730))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203730)))]]], (44002 ^ _780119) ^ [_1659948, _1659950, _1659952] : [44004 ^ _780119 : [(44007 ^ _780119) ^ [] : [hBOOL(hAPP(_1659952, hAPP(hAPP(c_List_Onth(_1659948), _1659950), 44003 ^ [_1659948, _1659950, _1659952])))], (44005 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44003 ^ [_1659948, _1659950, _1659952]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659948)), _1659950))))]], 44008 ^ _780119 : [(44009 ^ _780119) ^ [_1660150] : [hBOOL(hAPP(hAPP(c_member(_1659948), _1660150), hAPP(c_List_Oset(_1659948), _1659950))), -(hBOOL(hAPP(_1659952, _1660150)))]]], (23431 ^ _780119) ^ [_1208358, _1208360, _1208362, _1208364] : [class_Groups_Oab__group__add(_1208358), 23434 ^ _780119 : [(23441 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1208360), _1208362))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1208358), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1208358, _1208358), hAPP(hAPP(c_COMBB(_1208358, tc_fun(_1208358, _1208358), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1208358)), _1208364)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1208358, tc_Nat_Onat), _1208364), 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, _1208360, _1208362)) = c_Groups_Ozero__class_Ozero(_1208358))], (23435 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1208360), _1208362)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1208358), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1208358, _1208358), hAPP(hAPP(c_COMBB(_1208358, tc_fun(_1208358, _1208358), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1208358)), _1208364)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1208358, tc_Nat_Onat), _1208364), 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, _1208360, _1208362)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1208358), hAPP(_1208364, _1208360)), hAPP(_1208364, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1208362), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (50080 ^ _780119) ^ [_1795388, _1795390, _1795392] : [class_HOL_Oequal(_1795388), 50083 ^ _780119 : [(50090 ^ _780119) ^ [] : [_1795390 = _1795392, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1795388), _1795390), _1795392)))], (50084 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1795388), _1795390), _1795392)), -(_1795390 = _1795392)]]], (8674 ^ _780119) ^ [_930090, _930092, _930094] : [class_Orderings_Opreorder(_930090), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930090), _930092), _930094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930090), _930094), _930092))], (48807 ^ _780119) ^ [_1767133, _1767135, _1767137, _1767139] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1767133)), _1767135), c_List_Olists(_1767133, _1767137))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1767133)), _1767135), c_List_Olists(_1767133, _1767139))), -(hBOOL(hAPP(c_List_Olistsp(_1767133, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1767133, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1767133, tc_fun(_1767133, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767133)), _1767137)), hAPP(hAPP(c_COMBC(_1767133, tc_fun(_1767133, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767133)), _1767139))), _1767135)))], (30231 ^ _780119) ^ [_1344883, _1344885, _1344887, _1344889, _1344891, _1344893] : [c_Com_Ocom_OCond(_1344883, _1344885, _1344887) = c_Com_Ocom_OLocal(_1344889, _1344891, _1344893)], (2598 ^ _780119) ^ [_818581, _818583] : [_818583 = _818581, -(c_Int_Oint__ge__less__than2(_818583) = c_Int_Oint__ge__less__than2(_818581))], (23805 ^ _780119) ^ [_1215224, _1215226, _1215228, _1215230] : [class_Orderings_Oorder(_1215224), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1215224, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1215224, _1215226), _1215228)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1215224, _1215228), _1215230)) = c_Orderings_Obot__class_Obot(tc_fun(_1215224, tc_HOL_Obool)))], (25808 ^ _780119) ^ [_1251165, _1251167] : [class_Rings_Oring__1(_1251165), -(hAPP(c_Int_Oring__1__class_Oof__int(_1251165), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1251167)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1251165), hAPP(c_Int_Oring__1__class_Oof__int(_1251165), _1251167)))], (24313 ^ _780119) ^ [_1225367, _1225369, _1225371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225367)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225369), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1225371)), 24320 ^ _780119 : [(24321 ^ _780119) ^ [_1225575] : [24323 ^ _780119 : [(24327 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24325 ^ [_1225367, _1225369, _1225371, _1225575]), _1225371)))], (24329 ^ _780119) ^ [] : [-(_1225575 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24325 ^ [_1225367, _1225369, _1225371, _1225575]), 24322 ^ [_1225367, _1225369, _1225371, _1225575]))], (24324 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24322 ^ [_1225367, _1225369, _1225371, _1225575]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1225367))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225575), _1225369)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225575), _1225367)), _1225369)))]]], (8242 ^ _780119) ^ [_922205, _922207, _922209, _922211, _922213, _922215, _922217, _922219] : [c_Finite__Set_Ofolding__image__simple__idem(_922205, _922207, _922209, _922211, _922213, _922215), hBOOL(hAPP(c_Finite__Set_Ofinite(_922207), _922217)), hBOOL(hAPP(hAPP(c_member(_922207), _922219), _922217)), -(hAPP(hAPP(_922209, hAPP(_922213, _922219)), hAPP(_922215, _922217)) = hAPP(_922215, _922217))], (46771 ^ _780119) ^ [_1723774, _1723776, _1723778] : [-(c_List_Osublist(_1723774, _1723776, _1723778) = hAPP(hAPP(c_List_Omap(tc_prod(_1723774, tc_Nat_Onat), _1723774), c_Product__Type_Ofst(_1723774, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1723774, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1723774, 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(_1723774, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1723774, tc_Nat_Onat))), _1723778)), hAPP(hAPP(c_List_Ozip(_1723774, tc_Nat_Onat), _1723776), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723774)), _1723776))))))], (26325 ^ _780119) ^ [_1260575] : [-(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)), _1260575)))))], (51535 ^ _780119) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (23457 ^ _780119) ^ [_1209061, _1209063] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209061), hAPP(c_Nat_OSuc, _1209063)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1209061, _1209063))], (29827 ^ _780119) ^ [_1336290, _1336292, _1336294, _1336296, _1336298] : [class_Complete__Lattice_Ocomplete__lattice(_1336290), hBOOL(hAPP(hAPP(c_member(_1336292), _1336294), _1336296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336290), hAPP(_1336298, _1336294)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1336292, _1336290), _1336296), _1336298))))], (26519 ^ _780119) ^ [_1264326, _1264328, _1264330] : [-(hAPP(c_Set_OCollect(_1264326), hAPP(hAPP(c_COMBS(_1264326, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1264326), c_fconj), _1264328)), _1264330)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1264326, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1264326), _1264328)), hAPP(c_Set_OCollect(_1264326), _1264330)))], (17352 ^ _780119) ^ [_1095381, _1095383, _1095385, _1095387] : [class_Rings_Olinordered__semiring(_1095381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095381), _1095383), _1095385)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095381), _1095387), _1095385))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095381), c_Groups_Ozero__class_Ozero(_1095381)), _1095385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095381), _1095383), _1095387)))], (33357 ^ _780119) ^ [_1401651] : [class_Int_Onumber__ring(_1401651), c_Int_Oiszero(_1401651, hAPP(c_Int_Onumber__class_Onumber__of(_1401651), c_Int_OMin))], (37306 ^ _780119) ^ [_1493186, _1493188, _1493190, _1493192] : [c_Wellfounded_Owf(_1493186, _1493188), hBOOL(hAPP(hAPP(c_member(tc_prod(_1493186, _1493186)), hAPP(hAPP(c_Product__Type_OPair(_1493186, _1493186), _1493190), _1493192)), _1493188)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1493186, _1493186)), hAPP(hAPP(c_Product__Type_OPair(_1493186, _1493186), _1493192), _1493190)), _1493188))], (4788 ^ _780119) ^ [_853128, _853130, _853132, _853134, _853136, _853138] : [-(c_Lazy__Sequence_Obind(_853138, _853134, _853130) = c_Lazy__Sequence_Obind(_853136, _853132, _853128)), _853138 = _853136, _853134 = _853132, _853130 = _853128], (37599 ^ _780119) ^ [_1500465, _1500467, _1500469, _1500471] : [hBOOL(hAPP(c_Predicate_ORangeP(_1500465, _1500467, _1500469), _1500471)), -(hBOOL(hAPP(hAPP(_1500469, 37602 ^ [_1500465, _1500467, _1500469, _1500471]), _1500471)))], (26539 ^ _780119) ^ [_1264756, _1264758] : [class_Groups_Oordered__ab__group__add__abs(_1264756), 26542 ^ _780119 : [(26549 ^ _780119) ^ [] : [_1264758 = c_Groups_Ozero__class_Ozero(_1264756), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264756), hAPP(c_Groups_Oabs__class_Oabs(_1264756), _1264758)), c_Groups_Ozero__class_Ozero(_1264756))))], (26543 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264756), hAPP(c_Groups_Oabs__class_Oabs(_1264756), _1264758)), c_Groups_Ozero__class_Ozero(_1264756))), -(_1264758 = c_Groups_Ozero__class_Ozero(_1264756))]]], (15490 ^ _780119) ^ [_1062470, _1062472, _1062474] : [class_Lattices_Obounded__lattice__top(_1062470), 15493 ^ _780119 : [(15502 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062470), _1062472), _1062474) = c_Orderings_Otop__class_Otop(_1062470)), _1062472 = c_Orderings_Otop__class_Otop(_1062470), _1062474 = c_Orderings_Otop__class_Otop(_1062470)], (15494 ^ _780119) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062470), _1062472), _1062474) = c_Orderings_Otop__class_Otop(_1062470), 15497 ^ _780119 : [(15500 ^ _780119) ^ [] : [-(_1062474 = c_Orderings_Otop__class_Otop(_1062470))], (15498 ^ _780119) ^ [] : [-(_1062472 = c_Orderings_Otop__class_Otop(_1062470))]]]]], (44977 ^ _780119) ^ [_1681605, _1681607, _1681609, _1681611, _1681613] : [-(hAPP(hAPP(c_List_Olist_OCons(_1681605), _1681607), _1681609) = hAPP(hAPP(c_List_Oappend(_1681605), _1681611), _1681613)), 44978 ^ _780119 : [(44985 ^ _780119) ^ [_1681788] : [hAPP(hAPP(c_List_Olist_OCons(_1681605), _1681607), _1681788) = _1681611, _1681609 = hAPP(hAPP(c_List_Oappend(_1681605), _1681788), _1681613)], (44979 ^ _780119) ^ [] : [_1681611 = c_List_Olist_ONil(_1681605), hAPP(hAPP(c_List_Olist_OCons(_1681605), _1681607), _1681609) = _1681613]]], (45598 ^ _780119) ^ [_1697742, _1697744, _1697746, _1697748, _1697750] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1697742, _1697744)), _1697746), hAPP(hAPP(c_List_Ozip(_1697742, _1697744), _1697748), _1697750)) = hAPP(hAPP(c_List_Ozip(_1697742, _1697744), hAPP(hAPP(c_List_Odrop(_1697742), _1697746), _1697748)), hAPP(hAPP(c_List_Odrop(_1697744), _1697746), _1697750)))], (26260 ^ _780119) ^ [_1259129, _1259131, _1259133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1259131), 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), _1259131), _1259133))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1259129))), _1259133)))], (25604 ^ _780119) ^ [_1248074, _1248076] : [c_Nat__Transfer_Onat__set(_1248074), c_Nat__Transfer_Onat__set(_1248076), 25611 ^ _780119 : [(25618 ^ _780119) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1248074) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1248076), -(_1248074 = _1248076)], (25612 ^ _780119) ^ [] : [_1248074 = _1248076, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1248074) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1248076))]]], (28200 ^ _780119) ^ [_1301324, _1301326, _1301328, _1301330] : [class_Groups_Oordered__ab__group__add(_1301324), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1301324), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1301324), _1301326), _1301328)), _1301330) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1301324), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1301324), _1301326), _1301330)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1301324), _1301328), _1301330)))], (32157 ^ _780119) ^ [_1379830] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379830)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379830)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1379830)))], (48345 ^ _780119) ^ [_1757637] : [class_Enum_Oenum(_1757637), -(hAPP(c_List_Oset(_1757637), c_Enum_Oenum__class_Oenum(_1757637)) = c_Orderings_Otop__class_Otop(tc_fun(_1757637, tc_HOL_Obool)))], (47618 ^ _780119) ^ [_1740570, _1740572] : [-(_1740570 = c_List_Olist_ONil(_1740572)), -(hAPP(c_List_Ohd(_1740572), hAPP(c_List_Orev(_1740572), _1740570)) = c_List_Olast(_1740572, _1740570))], (2040 ^ _780119) ^ [_809754, _809756, _809758, _809760] : [-(c_SMT_Oz3mod(_809760, _809756) = c_SMT_Oz3mod(_809758, _809754)), _809760 = _809758, _809756 = _809754], (36890 ^ _780119) ^ [_1481717, _1481719, _1481721, _1481723, _1481725, _1481727] : [hBOOL(hAPP(hAPP(c_member(_1481717), _1481719), _1481721)), 36893 ^ _780119 : [(36900 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1481717), _1481723), _1481721))), -(hAPP(c_Set_Ovimage(_1481725, _1481717, hAPP(hAPP(c_COMBC(_1481725, _1481717, _1481717), hAPP(hAPP(c_COMBC(_1481725, _1481717, tc_fun(_1481717, _1481717)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1481717, tc_fun(_1481717, _1481717)), _1481725), c_If(_1481717)), hAPP(hAPP(c_COMBC(_1481725, tc_fun(_1481725, tc_HOL_Obool), tc_HOL_Obool), c_member(_1481725)), _1481727))), _1481719)), _1481723)), _1481721) = _1481727)], (36894 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1481717), _1481723), _1481721)), -(hAPP(c_Set_Ovimage(_1481725, _1481717, hAPP(hAPP(c_COMBC(_1481725, _1481717, _1481717), hAPP(hAPP(c_COMBC(_1481725, _1481717, tc_fun(_1481717, _1481717)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1481717, tc_fun(_1481717, _1481717)), _1481725), c_If(_1481717)), hAPP(hAPP(c_COMBC(_1481725, tc_fun(_1481725, tc_HOL_Obool), tc_HOL_Obool), c_member(_1481725)), _1481727))), _1481719)), _1481723)), _1481721) = c_Orderings_Otop__class_Otop(tc_fun(_1481725, tc_HOL_Obool)))]]], (9236 ^ _780119) ^ [_938757, _938759, _938761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938757, tc_HOL_Obool)), _938759), _938761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938757, tc_HOL_Obool)), _938759), _938761)))], (39475 ^ _780119) ^ [_1548044, _1548046] : [-(hAPP(c_Relation_ODomain(_1548044, _1548044), c_Transitive__Closure_Otrancl(_1548044, _1548046)) = hAPP(c_Relation_ODomain(_1548044, _1548044), _1548046))], (29588 ^ _780119) ^ [_1329615, _1329617, _1329619, _1329621, _1329623] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1329615, tc_fun(_1329617, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1329615), _1329619), _1329621)), _1329623) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329617, tc_HOL_Obool)), hAPP(_1329623, _1329619)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1329615, tc_fun(_1329617, tc_HOL_Obool)), _1329621), _1329623)))], (32227 ^ _780119) ^ [_1381227] : [class_Rings_Osemiring__1(_1381227), c_Int_Oiszero(_1381227, c_Groups_Oone__class_Oone(_1381227))], (45698 ^ _780119) ^ [_1700041, _1700043, _1700045, _1700047] : [_1700041 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1700043), _1700041), hAPP(hAPP(c_List_Olist_OCons(_1700043), _1700045), _1700047)) = hAPP(hAPP(c_List_Olist_OCons(_1700043), _1700045), _1700047))], (16592 ^ _780119) ^ [_1082259, _1082261, _1082263, _1082265] : [class_Rings_Olinordered__semidom(_1082259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082259), _1082261), _1082263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082259), c_Groups_Ozero__class_Ozero(_1082259)), _1082261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082259), hAPP(hAPP(c_Power_Opower__class_Opower(_1082259), _1082261), _1082265)), hAPP(hAPP(c_Power_Opower__class_Opower(_1082259), _1082263), _1082265))))], (51195 ^ _780119) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (9328 ^ _780119) ^ [_940633] : [class_Lattices_Osemilattice__sup(_940633), -(c_Finite__Set_Ofun__left__comm__idem(_940633, _940633, c_Lattices_Osemilattice__sup__class_Osup(_940633)))], (34979 ^ _780119) ^ [_1436973, _1436975, _1436977] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1436973, _1436975), _1436977))), _1436973 = 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), _1436977)), _1436975)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1436977)), 34986 ^ _780119 : [(34989 ^ _780119) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1436977) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (34987 ^ _780119) ^ [] : [-(_1436975 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 34990 ^ _780119 : [(34993 ^ _780119) ^ [] : [34994 ^ _780119 : [(34997 ^ _780119) ^ [] : [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), _1436977))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1436977)), _1436975))], (34995 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1436975)))]], 35002 ^ _780119 : [(35005 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1436975), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1436977))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1436977)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35003 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1436975))]]], (34991 ^ _780119) ^ [] : [_1436975 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (25778 ^ _780119) ^ [_1250572, _1250574, _1250576] : [class_Rings_Oring__1(_1250572), -(hAPP(c_Int_Oring__1__class_Oof__int(_1250572), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1250574), _1250576)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1250572), hAPP(c_Int_Oring__1__class_Oof__int(_1250572), _1250574)), hAPP(c_Int_Oring__1__class_Oof__int(_1250572), _1250576)))], (20045 ^ _780119) ^ [_1144619, _1144621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1144619), _1144621)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144621), _1144619) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144621), _1144619)), _1144619)))], (7666 ^ _780119) ^ [_909355, _909357, _909359, _909361, _909363] : [7669 ^ _780119 : [(7672 ^ _780119) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_909357, _909359, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909357)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909357), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _909357), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 7668 ^ [_909355, _909357, _909359, _909361, _909363]))), _909361), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _909357), hAPP(_909363, 7667 ^ [_909355, _909357, _909359, _909361, _909363])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909357), tc_HOL_Obool))))], (7670 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_909355, 7667 ^ [_909355, _909357, _909359, _909361, _909363]), 7668 ^ [_909355, _909357, _909359, _909361, _909363])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_909357, _909359, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909357)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909357), _909355), _909361), _909363)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909357), tc_HOL_Obool)))))], (28460 ^ _780119) ^ [_1306143, _1306145, _1306147] : [class_Orderings_Olinorder(_1306143), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306143), _1306145)), -(_1306145 = c_Orderings_Obot__class_Obot(tc_fun(_1306143, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1306143, hAPP(hAPP(c_Set_Oinsert(_1306143), _1306147), _1306145)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1306143), _1306147), c_Big__Operators_Olinorder__class_OMin(_1306143, _1306145)))], (35941 ^ _780119) ^ [_1460648, _1460650, _1460652, _1460654, _1460656, _1460658, _1460660, _1460662, _1460664, _1460666] : [c_Equiv__Relations_Ocongruent2(_1460648, _1460650, _1460652, _1460654, _1460656, _1460658), hBOOL(hAPP(hAPP(c_member(tc_prod(_1460648, _1460648)), hAPP(hAPP(c_Product__Type_OPair(_1460648, _1460648), _1460660), _1460662)), _1460654)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1460650, _1460650)), hAPP(hAPP(c_Product__Type_OPair(_1460650, _1460650), _1460664), _1460666)), _1460656)), -(hAPP(hAPP(_1460658, _1460660), _1460664) = hAPP(hAPP(_1460658, _1460662), _1460666))], (11535 ^ _780119) ^ [_987287, _987289, _987291, _987293] : [class_Rings_Ocomm__semiring__1(_987287), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987287), _987289), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987287), _987291), _987293)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987287), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987287), _987289), _987291)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987287), _987289), _987293)))], (4254 ^ _780119) ^ [_844449, _844451, _844453, _844455] : [-(c_Relation_Oinv__image(_844455, _844451) = c_Relation_Oinv__image(_844453, _844449)), _844455 = _844453, _844451 = _844449], (11083 ^ _780119) ^ [_977263, _977265, _977267] : [class_Lattices_Olattice(_977263), hBOOL(hAPP(c_Finite__Set_Ofinite(_977263), _977265)), hBOOL(hAPP(hAPP(c_member(_977263), _977267), _977265)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_977263), _977267), c_Big__Operators_Olattice__class_OInf__fin(_977263, _977265)) = c_Big__Operators_Olattice__class_OInf__fin(_977263, _977265))], (31433 ^ _780119) ^ [_1367610, _1367612] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367610)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367610)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367612)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367610)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367612))))], (46666 ^ _780119) ^ [_1720780, _1720782, _1720784, _1720786] : [-(hAPP(c_List_Ofilter(_1720780, _1720782), hAPP(hAPP(c_List_Oappend(_1720780), _1720784), _1720786)) = hAPP(hAPP(c_List_Oappend(_1720780), hAPP(c_List_Ofilter(_1720780, _1720782), _1720784)), hAPP(c_List_Ofilter(_1720780, _1720782), _1720786)))], (32095 ^ _780119) ^ [_1378330, _1378332] : [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(_1378330))), 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)), _1378332))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1378330) = hAPP(c_Nat_OSuc, _1378332))], (48817 ^ _780119) ^ [_1767410, _1767412] : [-(hBOOL(hAPP(c_List_Olistsp(_1767410, _1767412), c_List_Olist_ONil(_1767410))))], (3124 ^ _780119) ^ [_826722, _826724] : [_826724 = _826722, -(c_Nitpick_Onum(_826724) = c_Nitpick_Onum(_826722))], (784 ^ _780119) ^ [_792075, _792077, _792079, _792081, _792083, _792085] : [-(c_Enum_Oall__n__lists(_792083, _792079, _792075)), c_Enum_Oall__n__lists(_792085, _792081, _792077), _792085 = _792083, _792081 = _792079, _792077 = _792075], (44276 ^ _780119) ^ [_1667134, _1667136, _1667138, _1667140, _1667142] : [-(hAPP(hAPP(c_List_Otake(_1667134), _1667136), hAPP(hAPP(c_List_Omap(_1667138, _1667134), _1667140), _1667142)) = hAPP(hAPP(c_List_Omap(_1667138, _1667134), _1667140), hAPP(hAPP(c_List_Otake(_1667138), _1667136), _1667142)))], (46469 ^ _780119) ^ [_1716776, _1716778] : [-(_1716776 = c_List_Olist_ONil(_1716778)), hBOOL(hAPP(c_List_Odistinct(_1716778), _1716776)), -(hBOOL(hAPP(c_List_Odistinct(_1716778), c_List_Obutlast(_1716778, _1716776))))], (28038 ^ _780119) ^ [_1297797, _1297799, _1297801] : [class_Orderings_Olinorder(_1297797), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1297797), _1297799), _1297801) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1297797), _1297801), _1297799))], (44866 ^ _780119) ^ [_1678607, _1678609, _1678611, _1678613] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1678607) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1678609), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1678607)), hAPP(hAPP(c_List_Olist_OCons(_1678609), _1678611), _1678613)) = c_List_Olist_ONil(_1678609))], (46333 ^ _780119) ^ [_1714115, _1714117, _1714119] : [-(_1714115 = c_List_Olist_ONil(_1714117)), -(c_List_Olast(_1714117, hAPP(hAPP(c_List_Oappend(_1714117), _1714119), _1714115)) = c_List_Olast(_1714117, _1714115))], (45878 ^ _780119) ^ [_1703978, _1703980, _1703982] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703978)), hAPP(c_List_Orotate(_1703978, _1703980), _1703982)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703978)), _1703982))], (27142 ^ _780119) ^ [_1280110, _1280112, _1280114, _1280116] : [-(c_Fun_Ooverride__on(_1280110, _1280112, _1280114, _1280116, c_Orderings_Obot__class_Obot(tc_fun(_1280110, tc_HOL_Obool))) = _1280114)], (4028 ^ _780119) ^ [_840968, _840970] : [_840970 = _840968, -(c_Power_Opower__class_Opower(_840970) = c_Power_Opower__class_Opower(_840968))], (51555 ^ _780119) ^ [_1820153, _1820155, _1820157, _1820159] : [-(hAPP(hAPP(c_COMBK(_1820153, _1820155), _1820157), _1820159) = _1820157)], (31183 ^ _780119) ^ [_1363191, _1363193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1363191)), c_Int_OBit1(_1363193))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1363191), _1363193)))], (12463 ^ _780119) ^ [_1005200, _1005202, _1005204] : [class_Lattices_Olattice(_1005200), hAPP(_1005202, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005200), 12468 ^ [_1005200, _1005202, _1005204]), 12469 ^ [_1005200, _1005202, _1005204])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005200), hAPP(_1005202, 12468 ^ [_1005200, _1005202, _1005204])), hAPP(_1005202, 12469 ^ [_1005200, _1005202, _1005204])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005200), _1005204)), -(_1005204 = c_Orderings_Obot__class_Obot(tc_fun(_1005200, tc_HOL_Obool))), -(hAPP(_1005202, c_Big__Operators_Olattice__class_OInf__fin(_1005200, _1005204)) = c_Big__Operators_Olattice__class_OInf__fin(_1005200, hAPP(c_Set_Oimage(_1005200, _1005200, _1005202), _1005204)))], (23099 ^ _780119) ^ [_1201974, _1201976] : [23100 ^ _780119 : [(23101 ^ _780119) ^ [_1202030] : [_1201976 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201974), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1202030)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201974), _1201976)))], (40188 ^ _780119) ^ [_1565744, _1565746, _1565748] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565744, _1565744)), _1565746), c_Transitive__Closure_Ortrancl(_1565744, _1565748))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565744, _1565744)), _1565746), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1565744, _1565744), 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(_1565744, _1565744), tc_HOL_Obool), tc_fun(tc_prod(_1565744, _1565744), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1565744, _1565744), tc_HOL_Obool)), _1565748)))))], (46067 ^ _780119) ^ [_1707887, _1707889] : [class_Complete__Lattice_Ocomplete__lattice(_1707887), -(c_Complete__Lattice_OInf__class_OInf(_1707887, hAPP(c_List_Oset(_1707887), _1707889)) = hAPP(c_List_Ofoldl(_1707887, _1707887, c_Lattices_Osemilattice__inf__class_Oinf(_1707887), c_Orderings_Otop__class_Otop(_1707887)), _1707889))], (17330 ^ _780119) ^ [_1094958, _1094960, _1094962, _1094964, _1094966] : [class_Rings_Olinordered__semiring__strict(_1094958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094958), _1094960), _1094962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094958), _1094964), _1094966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094958), c_Groups_Ozero__class_Ozero(_1094958)), _1094960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094958), c_Groups_Ozero__class_Ozero(_1094958)), _1094964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094958), _1094960), _1094964)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094958), _1094962), _1094966))))], (15858 ^ _780119) ^ [_1069055, _1069057, _1069059, _1069061] : [class_Rings_Oordered__ring(_1069055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069055), _1069057), _1069059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069055), _1069061), c_Groups_Ozero__class_Ozero(_1069055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069055), _1069061), _1069059)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069055), _1069061), _1069057))))], (7344 ^ _780119) ^ [_903329, _903331, _903333, _903335] : [class_Lattices_Osemilattice__sup(_903329), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903329), _903331), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903329), _903333), _903335)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903329), _903333), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903329), _903331), _903335)))], (47436 ^ _780119) ^ [_1736616, _1736618, _1736620] : [_1736620 = hAPP(hAPP(c_List_Olist_OCons(_1736616), _1736618), c_List_Olist_ONil(_1736616)), -(hAPP(hAPP(c_List_Olist_OCons(_1736616), _1736618), c_List_Olist_ONil(_1736616)) = hAPP(c_List_Orev(_1736616), _1736620))], (23731 ^ _780119) ^ [_1213741, _1213743, _1213745] : [class_Orderings_Oorder(_1213741), 23734 ^ _780119 : [(23741 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213741), _1213743), _1213745))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1213741, _1213743), _1213745) = c_Orderings_Obot__class_Obot(tc_fun(_1213741, tc_HOL_Obool)))], (23735 ^ _780119) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1213741, _1213743), _1213745) = c_Orderings_Obot__class_Obot(tc_fun(_1213741, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213741), _1213743), _1213745))]]], (50480 ^ _780119) ^ [_1803848, _1803850, _1803852, _1803854, _1803856] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1803848, _1803850, hAPP(hAPP(c_COMBC(_1803848, tc_fun(tc_prod(_1803848, _1803850), tc_HOL_Obool), tc_fun(_1803850, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1803850, tc_fun(tc_fun(tc_prod(_1803848, _1803850), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1803848, _1803850), tc_HOL_Obool), tc_fun(_1803850, tc_HOL_Obool)), _1803848), c_COMBC(_1803850, tc_fun(tc_prod(_1803848, _1803850), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1803850, tc_prod(_1803848, _1803850)), tc_fun(_1803850, tc_fun(tc_fun(tc_prod(_1803848, _1803850), tc_HOL_Obool), tc_HOL_Obool)), _1803848), hAPP(c_COMBB(tc_prod(_1803848, _1803850), tc_fun(tc_fun(tc_prod(_1803848, _1803850), tc_HOL_Obool), tc_HOL_Obool), _1803850), c_member(tc_prod(_1803848, _1803850)))), c_Product__Type_OPair(_1803848, _1803850)))), _1803852)), _1803854), _1803856)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1803850, _1803848)), hAPP(hAPP(c_Product__Type_OPair(_1803850, _1803848), _1803854), _1803856)), hAPP(c_Relation_Oconverse(_1803848, _1803850), _1803852))))], (25341 ^ _780119) ^ [_1243566, _1243568] : [-(hBOOL(hAPP(_1243566, hAPP(c_Int_Onat, _1243568)))), 25345 ^ _780119 : [(25348 ^ _780119) ^ [] : [hBOOL(hAPP(_1243566, 25344 ^ [_1243566, _1243568]))], (25346 ^ _780119) ^ [] : [-(_1243568 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 25344 ^ [_1243566, _1243568]))]], 25349 ^ _780119 : [(25352 ^ _780119) ^ [] : [hBOOL(hAPP(_1243566, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25350 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243568), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25111 ^ _780119) ^ [_1239956, _1239958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239958)), 25118 ^ _780119 : [(25125 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239956), _1239958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1239956)), hAPP(c_Int_Onat, _1239958))))], (25119 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1239956)), hAPP(c_Int_Onat, _1239958))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239956), _1239958)))]]], (43896 ^ _780119) ^ [_1657142, _1657144, _1657146, _1657148, _1657150] : [class_Orderings_Olinorder(_1657142), hBOOL(hAPP(hAPP(c_member(_1657142), hAPP(_1657144, _1657146)), hAPP(c_Set_Oimage(_1657148, _1657142, _1657144), hAPP(c_List_Oset(_1657148), _1657150)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1657148, _1657142, _1657144, _1657146, _1657150) = _1657150)], (38523 ^ _780119) ^ [_1525285, _1525287, _1525289] : [hBOOL(hAPP(c_Predicate_OPowp(_1525285, _1525287), _1525289)), 38526 ^ _780119 : [(38527 ^ _780119) ^ [_1525369] : [hBOOL(hAPP(hAPP(c_member(_1525285), _1525369), _1525289)), -(hBOOL(hAPP(_1525287, _1525369)))]]], (51553 ^ _780119) ^ [_1820123, _1820125] : [-(hAPP(c_COMBI(_1820123), _1820125) = _1820125)], (28836 ^ _780119) ^ [_1314709, _1314711] : [class_Orderings_Olinorder(_1314709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314709), _1314711)), -(_1314711 = c_Orderings_Obot__class_Obot(tc_fun(_1314709, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314709), c_Big__Operators_Olattice_OInf__fin(_1314709, c_Orderings_Oord__class_Omin(_1314709), _1314711)), c_Big__Operators_Olattice_OSup__fin(_1314709, c_Orderings_Oord__class_Omax(_1314709), _1314711))))], (51049 ^ _780119) ^ [_1815149, _1815151] : [-(class_Enum_Oenum(tc_fun(_1815149, _1815151))), class_Enum_Oenum(_1815149), class_Enum_Oenum(_1815151)], (46875 ^ _780119) ^ [_1725639, _1725641, _1725643, _1725645] : [class_Orderings_Olinorder(_1725639), 46878 ^ _780119 : [(46887 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1725639, hAPP(hAPP(c_List_Olist_OCons(_1725639), _1725641), hAPP(hAPP(c_List_Olist_OCons(_1725639), _1725643), _1725645)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1725639), _1725641), _1725643)), c_List_Olinorder__class_Osorted(_1725639, hAPP(hAPP(c_List_Olist_OCons(_1725639), _1725643), _1725645))], (46879 ^ _780119) ^ [] : [c_List_Olinorder__class_Osorted(_1725639, hAPP(hAPP(c_List_Olist_OCons(_1725639), _1725641), hAPP(hAPP(c_List_Olist_OCons(_1725639), _1725643), _1725645))), 46882 ^ _780119 : [(46885 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1725639, hAPP(hAPP(c_List_Olist_OCons(_1725639), _1725643), _1725645)))], (46883 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1725639), _1725641), _1725643)))]]]]], (36423 ^ _780119) ^ [_1470947, _1470949, _1470951, _1470953, _1470955] : [c_Fun_Oinj__on(_1470947, _1470949, _1470951, c_Orderings_Otop__class_Otop(tc_fun(_1470947, tc_HOL_Obool))), 36426 ^ _780119 : [(36433 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470947, tc_HOL_Obool)), _1470953), _1470955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470949, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470947, _1470949, _1470951), _1470953)), hAPP(c_Set_Oimage(_1470947, _1470949, _1470951), _1470955))))], (36427 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470949, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470947, _1470949, _1470951), _1470953)), hAPP(c_Set_Oimage(_1470947, _1470949, _1470951), _1470955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470947, tc_HOL_Obool)), _1470953), _1470955)))]]], (49279 ^ _780119) ^ [_1777486, _1777488, _1777490, _1777492] : [-(hAPP(c_List_OremoveAll(_1777486, _1777488), hAPP(hAPP(c_List_Oappend(_1777486), _1777490), _1777492)) = hAPP(hAPP(c_List_Oappend(_1777486), hAPP(c_List_OremoveAll(_1777486, _1777488), _1777490)), hAPP(c_List_OremoveAll(_1777486, _1777488), _1777492)))], (51297 ^ _780119) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (50789 ^ _780119) ^ [_1810266, _1810268, _1810270] : [-(c_List_Olist__ex1(_1810266, _1810268, _1810270)), 50790 ^ _780119 : [(50791 ^ _780119) ^ [_1810360] : [hBOOL(hAPP(hAPP(c_member(_1810266), _1810360), hAPP(c_List_Oset(_1810266), _1810270))), hBOOL(hAPP(_1810268, _1810360)), 50799 ^ _780119 : [(50802 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1810268, 50798 ^ [_1810266, _1810268, _1810270, _1810360])))], (50804 ^ _780119) ^ [] : [50798 ^ [_1810266, _1810268, _1810270, _1810360] = _1810360], (50800 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810266), 50798 ^ [_1810266, _1810268, _1810270, _1810360]), hAPP(c_List_Oset(_1810266), _1810270))))]]]]], (22683 ^ _780119) ^ [_1194403, _1194405, _1194407, _1194409] : [hBOOL(hAPP(hAPP(c_member(_1194403), _1194405), c_SetInterval_Oord_OatMost(_1194403, _1194407, _1194409))), -(hBOOL(hAPP(hAPP(_1194407, _1194405), _1194409)))], (35327 ^ _780119) ^ [_1445416, _1445418] : [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)), _1445416), 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)), _1445418), 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)), _1445416), _1445418)), c_Int_Ointrel)))], (29538 ^ _780119) ^ [_1328648] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1328648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328648), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (38312 ^ _780119) ^ [_1520545, _1520547, _1520549, _1520551, _1520553] : [c_Relation_Orefl__on(_1520545, _1520547, _1520549), hBOOL(hAPP(hAPP(c_member(tc_prod(_1520545, _1520545)), hAPP(hAPP(c_Product__Type_OPair(_1520545, _1520545), _1520551), _1520553)), _1520549)), -(hBOOL(hAPP(hAPP(c_member(_1520545), _1520553), _1520547)))], (33749 ^ _780119) ^ [_1413048, _1413050] : [-(c_Divides_Odivmod__int(_1413048, _1413050) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1413048), _1413050)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1413048, _1413050)))], (6005 ^ _780119) ^ [_875620, _875622, _875624] : [-(hAPP(hAPP(c_Set_Oinsert(_875620), _875622), hAPP(hAPP(c_Set_Oinsert(_875620), _875622), _875624)) = hAPP(hAPP(c_Set_Oinsert(_875620), _875622), _875624))], (34379 ^ _780119) ^ [_1425194, _1425196] : [_1425194 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1425194, _1425196) = 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)))], (11271 ^ _780119) ^ [_980979, _980981, _980983, _980985, _980987] : [class_Groups_Ocomm__monoid__mult(_980979), hBOOL(hAPP(c_Finite__Set_Ofinite(_980981), _980983)), hBOOL(hAPP(c_Finite__Set_Ofinite(_980981), _980985)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980979), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_980979, _980981, c_Groups_Otimes__class_Otimes(_980979)), _980987), c_Groups_Oone__class_Oone(_980979)), _980983)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_980979, _980981, c_Groups_Otimes__class_Otimes(_980979)), _980987), c_Groups_Oone__class_Oone(_980979)), _980985)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980979), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_980979, _980981, c_Groups_Otimes__class_Otimes(_980979)), _980987), c_Groups_Oone__class_Oone(_980979)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980981, tc_HOL_Obool)), _980983), _980985))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_980979, _980981, c_Groups_Otimes__class_Otimes(_980979)), _980987), c_Groups_Oone__class_Oone(_980979)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980981, tc_HOL_Obool)), _980983), _980985))))], (45946 ^ _780119) ^ [_1705360, _1705362, _1705364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705360)), _1705362)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1705360, _1705364), _1705362) = _1705362)], (36782 ^ _780119) ^ [_1479352, _1479354, _1479356, _1479358] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1479352), hAPP(c_Set_Ovimage(_1479352, _1479354, _1479356), _1479358))), hAPP(c_Set_Oimage(_1479352, _1479354, _1479356), c_Orderings_Otop__class_Otop(tc_fun(_1479352, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1479354, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1479354), _1479358)))], (15058 ^ _780119) ^ [_1055960, _1055962] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055960, tc_HOL_Obool)), _1055962), c_Orderings_Otop__class_Otop(tc_fun(_1055960, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1055960, tc_HOL_Obool)))], (44274 ^ _780119) ^ [_1667092, _1667094, _1667096] : [-(c_List_Osublist(_1667092, _1667094, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1667096)) = hAPP(hAPP(c_List_Otake(_1667092), _1667096), _1667094))], (37612 ^ _780119) ^ [_1500698, _1500700, _1500702] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1500698), _1500700), _1500702) = c_Nitpick_OAbs__Frac(_1500698, c_Nitpick_Onorm__frac(_1500700, _1500702)))], (8896 ^ _780119) ^ [_933519, _933521, _933523] : [class_Orderings_Oorder(_933519), 8899 ^ _780119 : [(8908 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933519), _933521), _933523))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933519), _933521), _933523)), -(_933521 = _933523)], (8900 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933519), _933521), _933523)), 8903 ^ _780119 : [(8906 ^ _780119) ^ [] : [_933521 = _933523], (8904 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933519), _933521), _933523)))]]]]], (18534 ^ _780119) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46584 ^ _780119) ^ [_1719230, _1719232, _1719234] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719230)), hAPP(c_List_Ofilter(_1719230, _1719232), _1719234))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719230)), _1719234))))], (39557 ^ _780119) ^ [_1550050, _1550052] : [-(c_Random_Olog(_1550050, _1550052) = 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(_1550050, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1550052), _1550050)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1550050), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1550052), _1550050)))], (14772 ^ _780119) ^ [_1051426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051426), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10661 ^ _780119) ^ [_969185, _969187, _969189] : [class_Lattices_Olattice(_969185), hBOOL(hAPP(c_Finite__Set_Ofinite(_969185), _969187)), -(_969187 = c_Orderings_Obot__class_Obot(tc_fun(_969185, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_969185), _969189)), -(_969189 = c_Orderings_Obot__class_Obot(tc_fun(_969185, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_969185, tc_HOL_Obool)), _969187), _969189) = c_Orderings_Obot__class_Obot(tc_fun(_969185, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_969185, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_969185, tc_HOL_Obool)), _969187), _969189)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_969185), c_Big__Operators_Olattice__class_OInf__fin(_969185, _969187)), c_Big__Operators_Olattice__class_OInf__fin(_969185, _969189)))], (30411 ^ _780119) ^ [_1348588, _1348590, _1348592, _1348594] : [class_Int_Onumber__ring(_1348588), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348588), hAPP(c_Int_Onumber__class_Onumber__of(_1348588), _1348590)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348588), hAPP(c_Int_Onumber__class_Onumber__of(_1348588), _1348592)), _1348594)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348588), hAPP(c_Int_Onumber__class_Onumber__of(_1348588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1348590), _1348592))), _1348594))], (21757 ^ _780119) ^ [_1177458, _1177460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177458)), 21760 ^ _780119 : [(21763 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1177460, _1177458)), _1177458)))], (21761 ^ _780119) ^ [] : [-(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, _1177460, _1177458))))]]], (17408 ^ _780119) ^ [_1096457, _1096459, _1096461, _1096463] : [class_Rings_Olinordered__semiring__strict(_1096457), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096457), _1096459), _1096461)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096457), _1096463), _1096461))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096457), c_Groups_Ozero__class_Ozero(_1096457)), _1096461)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096457), _1096459), _1096463)))], (33105 ^ _780119) ^ [_1397091, _1397093, _1397095] : [class_Rings_Olinordered__idom(_1397091), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397091), c_Groups_Ozero__class_Ozero(_1397091)), hAPP(hAPP(c_Power_Opower__class_Opower(_1397091), _1397093), 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)))), _1397095))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397091), c_Groups_Ozero__class_Ozero(_1397091)), _1397093)))], (42570 ^ _780119) ^ [_1622500, _1622502, _1622504] : [c_Fun_Oinj__on(_1622500, _1622502, _1622504, c_Orderings_Otop__class_Otop(tc_fun(_1622500, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1622500), tc_List_Olist(_1622502), hAPP(c_List_Omap(_1622500, _1622502), _1622504), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1622500), tc_HOL_Obool))))], (3656 ^ _780119) ^ [_835088, _835090] : [_835090 = _835088, -(c_Groups_Otimes__class_Otimes(_835090) = c_Groups_Otimes__class_Otimes(_835088))], (24889 ^ _780119) ^ [_1236252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236252)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236252) = 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, _1236252))))], (29184 ^ _780119) ^ [_1320974, _1320976, _1320978] : [class_Orderings_Olinorder(_1320974), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320974), _1320976)), -(_1320976 = c_Orderings_Obot__class_Obot(tc_fun(_1320974, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320974), _1320978)), -(_1320978 = c_Orderings_Obot__class_Obot(tc_fun(_1320974, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320974, tc_HOL_Obool)), _1320976), _1320978) = c_Orderings_Obot__class_Obot(tc_fun(_1320974, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1320974, c_Orderings_Oord__class_Omax(_1320974), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320974, tc_HOL_Obool)), _1320976), _1320978)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320974), c_Big__Operators_Olattice_OSup__fin(_1320974, c_Orderings_Oord__class_Omax(_1320974), _1320976)), c_Big__Operators_Olattice_OSup__fin(_1320974, c_Orderings_Oord__class_Omax(_1320974), _1320978)))], (32375 ^ _780119) ^ [_1383868] : [-(c_Int_OBit0(_1383868) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1383868), _1383868))], (28760 ^ _780119) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (38655 ^ _780119) ^ [_1528913, _1528915, _1528917] : [-(hAPP(c_Fun_Ocomp(_1528913, _1528913, _1528915, c_Fun_Oid(_1528913)), _1528917) = _1528917)], (30393 ^ _780119) ^ [_1348149, _1348151, _1348153, _1348155] : [class_Int_Onumber__ring(_1348149), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348149), hAPP(c_Int_Onumber__class_Onumber__of(_1348149), _1348151)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348149), hAPP(c_Int_Onumber__class_Onumber__of(_1348149), _1348153)), _1348155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348149), hAPP(c_Int_Onumber__class_Onumber__of(_1348149), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1348151), _1348153))), _1348155))], (26515 ^ _780119) ^ [_1264214] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1264214, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1264214), hAPP(c_COMBK(tc_HOL_Obool, _1264214), c_fTrue)))], (39665 ^ _780119) ^ [_1552950, _1552952, _1552954] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552950, _1552950), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552950, _1552950), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1552950, _1552952)), c_Transitive__Closure_Ortrancl(_1552950, _1552954))), c_Transitive__Closure_Ortrancl(_1552950, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552950, _1552950), tc_HOL_Obool)), _1552952), _1552954)))))], (13033 ^ _780119) ^ [_1016941, _1016943, _1016945, _1016947] : [13034 ^ _780119 : [(13035 ^ _780119) ^ [_1017030] : [_1016945 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1016941, tc_Option_Ooption(_1016943)), hAPP(c_COMBK(tc_Option_Ooption(_1016943), _1016941), c_Option_Ooption_ONone(_1016943))), _1016947), hAPP(c_Option_Ooption_OSome(_1016943), _1017030))]], -(c_Map_Odom(_1016941, _1016943, _1016945) = hAPP(hAPP(c_Set_Oinsert(_1016941), _1016947), c_Orderings_Obot__class_Obot(tc_fun(_1016941, tc_HOL_Obool))))], (10929 ^ _780119) ^ [_974117, _974119, _974121, _974123] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_974117), 10932 ^ _780119 : [(10939 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974117), _974121), _974123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974117), _974119), _974121)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974117), _974119), _974123))))], (10933 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974117), _974119), _974121)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974117), _974119), _974123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974117), _974121), _974123)))]]], (396 ^ _780119) ^ [_786205, _786207, _786209, _786211, _786213, _786215] : [-(c_Hoare__Mirabelle_Otriple__valid(_786213, _786209, _786205)), c_Hoare__Mirabelle_Otriple__valid(_786215, _786211, _786207), _786215 = _786213, _786211 = _786209, _786207 = _786205], (40548 ^ _780119) ^ [_1575117, _1575119, _1575121] : [class_Orderings_Olinorder(_1575117), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575117), _1575119)), -(hBOOL(hAPP(hAPP(c_member(_1575117), _1575121), _1575119))), -(c_Big__Operators_Olattice_OSup__fin(_1575117, c_Orderings_Oord__class_Omax(_1575117), hAPP(hAPP(c_Set_Oinsert(_1575117), _1575121), _1575119)) = hAPP(hAPP(c_Finite__Set_Ofold(_1575117, _1575117, c_Orderings_Oord__class_Omax(_1575117)), _1575121), _1575119))], (13865 ^ _780119) ^ [_1032151, _1032153] : [class_Rings_Ocomm__ring__1(_1032151), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1032151), _1032153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032151), hAPP(c_Groups_Ouminus__class_Ouminus(_1032151), c_Groups_Oone__class_Oone(_1032151))), _1032153))], (21036 ^ _780119) ^ [_1162764, _1162766, _1162768, _1162770, _1162772] : [class_Fields_Ofield(_1162764), -(_1162766 = c_Groups_Ozero__class_Ozero(_1162764)), -(_1162768 = c_Groups_Ozero__class_Ozero(_1162764)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1162764), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162764), _1162770), _1162766)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162764), _1162772), _1162768)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162764), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1162764), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162764), _1162770), _1162768)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162764), _1162772), _1162766))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162764), _1162766), _1162768)))], (32493 ^ _780119) ^ [_1385876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1385876))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1385876)))], (17610 ^ _780119) ^ [_1100299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100299)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1100299), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1100299)], (44816 ^ _780119) ^ [_1677710, _1677712, _1677714] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1677710)), -(c_List_Osublist(_1677712, hAPP(hAPP(c_List_Olist_OCons(_1677712), _1677714), c_List_Olist_ONil(_1677712)), _1677710) = hAPP(hAPP(c_List_Olist_OCons(_1677712), _1677714), c_List_Olist_ONil(_1677712)))], (1120 ^ _780119) ^ [_796843, _796845] : [-(class_Rings_Olinordered__idom(_796843)), _796845 = _796843, class_Rings_Olinordered__idom(_796845)], (44938 ^ _780119) ^ [_1680621, _1680623, _1680625, _1680627, _1680629, _1680631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680621)), _1680623)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680625)), _1680627))), -(c_Map_Omap__upds(_1680621, _1680625, _1680629, hAPP(hAPP(c_List_Oappend(_1680621), _1680623), hAPP(hAPP(c_List_Olist_OCons(_1680621), _1680631), c_List_Olist_ONil(_1680621))), _1680627) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1680621, tc_Option_Ooption(_1680625)), c_Map_Omap__upds(_1680621, _1680625, _1680629, _1680623, _1680627)), _1680631), hAPP(c_Option_Ooption_OSome(_1680625), hAPP(hAPP(c_List_Onth(_1680625), _1680627), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680621)), _1680623)))))], (50206 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (50264 ^ _780119) ^ [_1798901, _1798903, _1798905, _1798907, _1798909, _1798911] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1798901, _1798903, _1798905, _1798907, c_Lazy__Sequence_Olazy__sequence_OInsert(_1798903, _1798909, _1798911)) = hAPP(hAPP(_1798907, _1798909), _1798911))], (28220 ^ _780119) ^ [_1301778] : [class_Orderings_Olinorder(_1301778), -(c_Finite__Set_Ofun__left__comm__idem(_1301778, _1301778, c_Orderings_Oord__class_Omin(_1301778)))], (47989 ^ _780119) ^ [_1749403, _1749405] : [c_List_Oremdups(_1749403, _1749405) = _1749405, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749403)), c_List_Oremdups(_1749403, _1749405)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749403)), _1749405))], (21566 ^ _780119) ^ [_1173495, _1173497] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1173495, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1173495, tc_HOL_Obool))), hAPP(c_Set_OPow(_1173495), _1173497))))], (11682 ^ _780119) ^ [_990487, _990489] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990487), _990489)), _990489) = _990487)], (35647 ^ _780119) ^ [_1453952, _1453954, _1453956, _1453958, _1453960] : [c_Equiv__Relations_Oequiv(_1453952, _1453954, _1453956), hBOOL(hAPP(hAPP(c_member(tc_prod(_1453952, _1453952)), hAPP(hAPP(c_Product__Type_OPair(_1453952, _1453952), _1453958), _1453960)), _1453956)), -(hAPP(c_Relation_OImage(_1453952, _1453952, _1453956), hAPP(hAPP(c_Set_Oinsert(_1453952), _1453958), c_Orderings_Obot__class_Obot(tc_fun(_1453952, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1453952, _1453952, _1453956), hAPP(hAPP(c_Set_Oinsert(_1453952), _1453960), c_Orderings_Obot__class_Obot(tc_fun(_1453952, tc_HOL_Obool)))))], (47600 ^ _780119) ^ [_1740077, _1740079, _1740081] : [-(hAPP(c_List_Orev(_1740077), hAPP(hAPP(c_List_Olist_OCons(_1740077), _1740079), _1740081)) = hAPP(hAPP(c_List_Oappend(_1740077), hAPP(c_List_Orev(_1740077), _1740081)), hAPP(hAPP(c_List_Olist_OCons(_1740077), _1740079), c_List_Olist_ONil(_1740077))))], (37263 ^ _780119) ^ [_1492343, _1492345, _1492347] : [c_Wellfounded_Owf(_1492343, _1492345), -(c_Wellfounded_Owf(_1492343, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1492343, _1492343), tc_HOL_Obool)), _1492345), _1492347)))], (6334 ^ _780119) ^ [_881933, _881935, _881937] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881933, tc_HOL_Obool)), _881935), hAPP(hAPP(c_Set_Oinsert(_881933), _881937), _881935))))], (35165 ^ _780119) ^ [_1441351, _1441353, _1441355, _1441357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1441351), _1441353)), -(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), _1441351), _1441355)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1441353), _1441357))), c_FunDef_Opair__less)))], (14570 ^ _780119) ^ [_1047411, _1047413] : [class_Groups_Omonoid__mult(_1047411), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1047411), _1047413), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1047413)], (35377 ^ _780119) ^ [_1447060, _1447062, _1447064, _1447066, _1447068, _1447070] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1447060, _1447060)), hAPP(hAPP(c_Product__Type_OPair(_1447060, _1447060), _1447062), _1447064)), hAPP(hAPP(c_Relation_Oinv__image(_1447066, _1447060), _1447068), _1447070))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447066, _1447066)), hAPP(hAPP(c_Product__Type_OPair(_1447066, _1447066), hAPP(_1447070, _1447062)), hAPP(_1447070, _1447064))), _1447068)))], (21889 ^ _780119) ^ [_1179714, _1179716, _1179718, _1179720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179716), _1179718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179718), 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), _1179716), _1179714)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179716), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179720, _1179714))), _1179718))))], (50 ^ _780119) ^ [_780924, _780926, _780928, _780930, _780932, _780934, _780936, _780938, _780940, _780942, _780944, _780946] : [-(c_Nitpick_Ofold__graph_H(_780944, _780940, _780936, _780932, _780928, _780924)), c_Nitpick_Ofold__graph_H(_780946, _780942, _780938, _780934, _780930, _780926), _780946 = _780944, _780942 = _780940, _780938 = _780936, _780934 = _780932, _780930 = _780928, _780926 = _780924], (552 ^ _780119) ^ [_788625, _788627, _788629, _788631, _788633, _788635] : [-(c_Finite__Set_Ofolding__one(_788633, _788629, _788625)), c_Finite__Set_Ofolding__one(_788635, _788631, _788627), _788635 = _788633, _788631 = _788629, _788627 = _788625], (26783 ^ _780119) ^ [_1269607, _1269609, _1269611] : [-(hBOOL(hAPP(_1269607, _1269609))), -(hAPP(c_Set_OCollect(_1269611), hAPP(hAPP(c_COMBS(_1269611, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1269611), c_fconj), hAPP(c_fequal, _1269609))), _1269607)) = c_Orderings_Obot__class_Obot(tc_fun(_1269611, tc_HOL_Obool)))], (22701 ^ _780119) ^ [_1194757, _1194759, _1194761, _1194763] : [hBOOL(hAPP(hAPP(_1194761, _1194763), _1194759)), -(hBOOL(hAPP(hAPP(c_member(_1194757), _1194759), c_SetInterval_Oord_OatLeast(_1194757, _1194761, _1194763))))], (14084 ^ _780119) ^ [_1036783, _1036785, _1036787, _1036789, _1036791] : [class_Groups_Ocomm__monoid__mult(_1036783), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036785), _1036787)), 14091 ^ _780119 : [(14098 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1036785), _1036789), _1036787))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1036785, _1036783), hAPP(hAPP(c_COMBC(_1036785, _1036783, _1036783), hAPP(hAPP(c_COMBS(_1036785, _1036783, tc_fun(_1036783, _1036783)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1036783, tc_fun(_1036783, _1036783)), _1036785), c_If(_1036783)), hAPP(c_fequal, _1036789))), _1036791)), c_Groups_Oone__class_Oone(_1036783))), _1036787) = c_Groups_Oone__class_Oone(_1036783))], (14092 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1036785), _1036789), _1036787)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1036785, _1036783), hAPP(hAPP(c_COMBC(_1036785, _1036783, _1036783), hAPP(hAPP(c_COMBS(_1036785, _1036783, tc_fun(_1036783, _1036783)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1036783, tc_fun(_1036783, _1036783)), _1036785), c_If(_1036783)), hAPP(c_fequal, _1036789))), _1036791)), c_Groups_Oone__class_Oone(_1036783))), _1036787) = hAPP(_1036791, _1036789))]]], (12956 ^ _780119) ^ [_1015248, _1015250, _1015252, _1015254] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1015248), _1015250)), hBOOL(hAPP(hAPP(c_member(_1015248), _1015252), _1015250)), -(hBOOL(hAPP(hAPP(c_member(_1015248), _1015252), _1015254))), -(hAPP(c_Finite__Set_Ocard(_1015248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1015248, tc_HOL_Obool)), _1015250), hAPP(hAPP(c_Set_Oinsert(_1015248), _1015252), _1015254))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1015248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1015248, tc_HOL_Obool)), _1015250), _1015254))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (22487 ^ _780119) ^ [] : [-(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)))], (26887 ^ _780119) ^ [_1271930, _1271932] : [class_Groups_Oabs__if(_1271930), 26890 ^ _780119 : [(26897 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271930), _1271932), c_Groups_Ozero__class_Ozero(_1271930)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1271930), _1271932) = _1271932)], (26891 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271930), _1271932), c_Groups_Ozero__class_Ozero(_1271930))), -(hAPP(c_Groups_Oabs__class_Oabs(_1271930), _1271932) = hAPP(c_Groups_Ouminus__class_Ouminus(_1271930), _1271932))]]], (29869 ^ _780119) ^ [_1337367, _1337369, _1337371, _1337373, _1337375] : [_1337367 = c_Orderings_Obot__class_Obot(tc_fun(_1337369, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1337371), _1337373), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337369, tc_fun(_1337371, tc_HOL_Obool)), _1337367), _1337375)) = hAPP(hAPP(c_Set_Oinsert(_1337371), _1337373), c_Orderings_Obot__class_Obot(tc_fun(_1337371, tc_HOL_Obool))))], (5306 ^ _780119) ^ [_861261, _861263] : [_861263 = _861261, -(c_List_Omember(_861263) = c_List_Omember(_861261))], (24959 ^ _780119) ^ [_1237487, _1237489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237489)), 24966 ^ _780119 : [(24973 ^ _780119) ^ [] : [_1237487 = _1237489, -(hAPP(c_Int_Onat, _1237487) = hAPP(c_Int_Onat, _1237489))], (24967 ^ _780119) ^ [] : [hAPP(c_Int_Onat, _1237487) = hAPP(c_Int_Onat, _1237489), -(_1237487 = _1237489)]]], (49010 ^ _780119) ^ [_1771654, _1771656, _1771658, _1771660, _1771662, _1771664, _1771666] : [c_List_Olist__all2(_1771654, _1771656, _1771658, hAPP(hAPP(c_List_Omap(_1771660, _1771654), _1771662), _1771664), _1771666), -(c_List_Olist__all2(_1771660, _1771656, hAPP(hAPP(c_COMBB(_1771654, tc_fun(_1771656, tc_HOL_Obool), _1771660), _1771658), _1771662), _1771664, _1771666))], (21799 ^ _780119) ^ [_1178166, _1178168] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178166, _1178168) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178166, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178168)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13698 ^ _780119) ^ [_1029204, _1029206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029204), hAPP(c_Nat_OSuc, _1029206))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029204), _1029206))), -(_1029204 = hAPP(c_Nat_OSuc, _1029206))], (46973 ^ _780119) ^ [_1727231, _1727233] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1727231, _1727233))))], (26631 ^ _780119) ^ [_1266519, _1266521, _1266523] : [class_Groups_Oordered__ab__group__add__abs(_1266519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266519), hAPP(c_Groups_Oabs__class_Oabs(_1266519), _1266521)), _1266523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266519), hAPP(c_Groups_Ouminus__class_Ouminus(_1266519), _1266521)), _1266523)))], (6065 ^ _780119) ^ [_876764, _876766] : [hBOOL(hAPP(hAPP(c_member(_876764), _876766), c_Orderings_Obot__class_Obot(tc_fun(_876764, tc_HOL_Obool))))], (12719 ^ _780119) ^ [_1010647, _1010649, _1010651, _1010653] : [c_Finite__Set_Ofolding__one(_1010647, _1010649, _1010651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010647), _1010653)), -(hAPP(_1010651, _1010653) = hAPP(c_Finite__Set_Ofold1(_1010647, _1010649), _1010653))], (35269 ^ _780119) ^ [_1443903] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1443903)), -(_1443903 = 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))), _1443903)), c_FunDef_Omax__strict)))], (30405 ^ _780119) ^ [_1348453, _1348455, _1348457] : [class_Int_Onumber__ring(_1348453), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348453), hAPP(c_Int_Onumber__class_Onumber__of(_1348453), _1348455)), hAPP(c_Int_Onumber__class_Onumber__of(_1348453), _1348457)) = hAPP(c_Int_Onumber__class_Onumber__of(_1348453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1348455), _1348457)))], (34459 ^ _780119) ^ [_1426742, _1426744] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1426742, _1426744), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1426742), _1426744)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1426742, _1426744)))))], (44242 ^ _780119) ^ [_1666454, _1666456, _1666458] : [hBOOL(hAPP(c_List_Odistinct(_1666454), _1666456)), -(hBOOL(hAPP(c_List_Odistinct(_1666454), hAPP(hAPP(c_List_Otake(_1666454), _1666458), _1666456))))], (41284 ^ _780119) ^ [_1591035, _1591037, _1591039, _1591041] : [41286 ^ _780119 : [(41289 ^ _780119) ^ [] : [hAPP(_1591041, 41285 ^ [_1591035, _1591037, _1591039, _1591041]) = c_Orderings_Otop__class_Otop(tc_fun(_1591035, tc_HOL_Obool))], (41287 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591037), 41285 ^ [_1591035, _1591037, _1591039, _1591041]), _1591039)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1591035, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591037, tc_fun(_1591035, tc_HOL_Obool)), _1591039), _1591041))], (34463 ^ _780119) ^ [_1426806, _1426808, _1426810, _1426812, _1426814, _1426816, _1426818] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1426806, _1426808), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1426810), _1426812))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1426814, _1426808), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1426816), _1426818))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1426808)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1426806), _1426814), _1426808), 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), _1426810), _1426816)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1426812), _1426818)), _1426808))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1426812), _1426818), _1426808)))))], (44630 ^ _780119) ^ [_1674273, _1674275, _1674277] : [-(hAPP(hAPP(c_List_Olist__update(_1674273, c_List_Olist_ONil(_1674273)), _1674275), _1674277) = c_List_Olist_ONil(_1674273))], (7464 ^ _780119) ^ [_905628, _905630, _905632, _905634] : [class_Lattices_Osemilattice__sup(_905628), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905628), _905630), _905632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905628), _905630), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_905628), _905632), _905634))))], (41818 ^ _780119) ^ [_1605106] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1605106, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1605106, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1605106, tc_HOL_Obool)))], (46517 ^ _780119) ^ [_1717751, _1717753] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717751)), c_List_Obutlast(_1717751, _1717753)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717751)), _1717753)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (51085 ^ _780119) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (13692 ^ _780119) ^ [_1029078, _1029080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029078), _1029080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029078)), hAPP(c_Nat_OSuc, _1029080))))], (27730 ^ _780119) ^ [_1292293, _1292295, _1292297] : [class_Orderings_Olinorder(_1292293), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292293), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292293), _1292295), _1292297)), _1292297)))], (41242 ^ _780119) ^ [_1589893, _1589895, _1589897, _1589899, _1589901] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589893, tc_fun(_1589895, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1589893), _1589897), _1589899)), _1589901) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589895, tc_HOL_Obool)), hAPP(_1589901, _1589897)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589893, tc_fun(_1589895, tc_HOL_Obool)), _1589899), _1589901)))], (49154 ^ _780119) ^ [_1774689, _1774691, _1774693, _1774695, _1774697, _1774699] : [c_List_Olist__all2(_1774689, _1774691, _1774693, _1774695, _1774697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1774699), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774689)), _1774695))), -(hBOOL(hAPP(hAPP(_1774693, hAPP(hAPP(c_List_Onth(_1774689), _1774695), _1774699)), hAPP(hAPP(c_List_Onth(_1774691), _1774697), _1774699))))], (19610 ^ _780119) ^ [_1136576, _1136578, _1136580, _1136582, _1136584, _1136586] : [class_Groups_Oordered__ab__group__add(_1136576), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136578), _1136580)), 19620 ^ _780119 : [(19623 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136576), c_Groups_Ozero__class_Ozero(_1136576)), hAPP(_1136582, 19619 ^ [_1136576, _1136578, _1136580, _1136582, _1136584, _1136586])))], (19621 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1136578), 19619 ^ [_1136576, _1136578, _1136580, _1136582, _1136584, _1136586]), _1136580)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1136578, _1136576), _1136582), _1136580) = _1136584, hBOOL(hAPP(hAPP(c_member(_1136578), _1136586), _1136580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136576), hAPP(_1136582, _1136586)), _1136584)))], (48233 ^ _780119) ^ [_1755217, _1755219, _1755221] : [-(hAPP(c_List_Oset(tc_List_Olist(_1755217)), c_Enum_On__lists(_1755217, _1755219, _1755221)) = hAPP(c_Set_OCollect(tc_List_Olist(_1755217)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1755217), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1755217)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1755217), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1755217)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1755217)))), _1755219))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1755217), tc_fun(_1755217, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1755217, tc_HOL_Obool), tc_fun(tc_fun(_1755217, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1755217)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1755217, tc_HOL_Obool))), c_List_Oset(_1755217))), hAPP(c_List_Oset(_1755217), _1755221)))))], (41125 ^ _780119) ^ [_1586646, _1586648, _1586650, _1586652, _1586654] : [-(hAPP(c_Relation_Oconverse(_1586646, _1586648), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586650, tc_fun(tc_prod(_1586646, _1586648), tc_HOL_Obool)), _1586652), _1586654)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586650, tc_fun(tc_prod(_1586648, _1586646), tc_HOL_Obool)), _1586652), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1586646, _1586648), tc_HOL_Obool), tc_fun(tc_prod(_1586648, _1586646), tc_HOL_Obool), _1586650), c_Relation_Oconverse(_1586646, _1586648)), _1586654)))], (43174 ^ _780119) ^ [_1637127, _1637129, _1637131, _1637133, _1637135] : [class_Orderings_Olinorder(_1637127), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637129)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1637129, _1637127, _1637131), _1637133), _1637135)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637129)), _1637135)))], (39436 ^ _780119) ^ [_1547172, _1547174] : [c_Wellfounded_Oacyclic(_1547172, _1547174), 39439 ^ _780119 : [(39440 ^ _780119) ^ [_1547257] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547172, _1547172)), hAPP(hAPP(c_Product__Type_OPair(_1547172, _1547172), _1547257), _1547257)), c_Transitive__Closure_Otrancl(_1547172, _1547174)))]]], (8176 ^ _780119) ^ [_920674, _920676, _920678] : [-(hBOOL(hAPP(hAPP(c_member(_920674), _920676), _920678))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920674, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_920674), _920676), _920678)), hAPP(hAPP(c_Set_Oinsert(_920674), _920676), c_Orderings_Obot__class_Obot(tc_fun(_920674, tc_HOL_Obool)))) = _920678)], (26185 ^ _780119) ^ [_1257633, _1257635, _1257637] : [class_Orderings_Olinorder(_1257633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257633), _1257635), _1257637)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257633, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1257633), _1257635)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1257633, _1257635, _1257637)) = hAPP(c_SetInterval_Oord__class_OatMost(_1257633), _1257637))], (50246 ^ _780119) ^ [_1798419] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1798419), _1798419)))], (45884 ^ _780119) ^ [_1704143, _1704145, _1704147, _1704149] : [-(hAPP(c_List_Orotate(_1704143, _1704145), hAPP(c_List_Orotate(_1704143, _1704147), _1704149)) = hAPP(c_List_Orotate(_1704143, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704145), _1704147)), _1704149))], (25426 ^ _780119) ^ [_1245120, _1245122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245122)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1245120)), hAPP(c_Int_Onat, _1245122)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1245120), _1245122)))], (29445 ^ _780119) ^ [_1326655, _1326657, _1326659] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1326655, _1326657) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1326659, _1326657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1326659), _1326655)), -(_1326655 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1326659), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1326657), 29452 ^ [_1326655, _1326657, _1326659])))], (40211 ^ _780119) ^ [_1566247, _1566249, _1566251, _1566253] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1566247, _1566249), tc_fun(_1566247, _1566249)), _1566251), c_Fun_Ocomp(_1566249, _1566249, _1566247, _1566253)) = c_Fun_Ocomp(_1566249, _1566249, _1566247, hAPP(hAPP(c_Nat_Ocompow(_1566249, _1566249), _1566251), _1566253)))], (36081 ^ _780119) ^ [_1464311, _1464313, _1464315] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1464311), _1464313)), c_Fun_Oinj__on(_1464311, tc_fun(tc_fun(_1464311, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1464311, tc_fun(tc_prod(_1464311, _1464311), tc_HOL_Obool), tc_fun(tc_fun(_1464311, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464311, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1464311, _1464311), tc_HOL_Obool), tc_fun(tc_fun(_1464311, tc_HOL_Obool), tc_HOL_Obool)), _1464311), c_Equiv__Relations_Oquotient(_1464311)), hAPP(hAPP(c_COMBC(_1464311, tc_fun(_1464311, tc_HOL_Obool), tc_fun(_1464311, tc_HOL_Obool)), c_Set_Oinsert(_1464311)), c_Orderings_Obot__class_Obot(tc_fun(_1464311, tc_HOL_Obool))))), _1464315), _1464313), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1464311, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464311), _1464313), _1464315)) = hAPP(c_Finite__Set_Ocard(_1464311), _1464313))], (23326 ^ _780119) ^ [_1206392, _1206394] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206392) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206394), -(_1206392 = _1206394)], (37978 ^ _780119) ^ [_1511034, _1511036, _1511038, _1511040, _1511042, _1511044, _1511046, _1511048] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1511034, _1511036), tc_fun(tc_prod(_1511038, _1511040), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1511034, _1511036), _1511042), hAPP(c_COMBK(tc_fun(_1511036, tc_HOL_Obool), _1511034), _1511044))), hAPP(c_Product__Type_Oprod_Oprod__case(_1511034, _1511036, tc_fun(tc_prod(_1511038, _1511040), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1511034, tc_fun(_1511036, tc_fun(_1511038, tc_fun(_1511040, tc_HOL_Obool))), tc_fun(_1511036, tc_fun(tc_prod(_1511038, _1511040), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1511038, tc_fun(_1511040, tc_HOL_Obool)), tc_fun(tc_prod(_1511038, _1511040), tc_HOL_Obool)), tc_fun(tc_fun(_1511036, tc_fun(_1511038, tc_fun(_1511040, tc_HOL_Obool))), tc_fun(_1511036, tc_fun(tc_prod(_1511038, _1511040), tc_HOL_Obool))), _1511034), c_COMBB(tc_fun(_1511038, tc_fun(_1511040, tc_HOL_Obool)), tc_fun(tc_prod(_1511038, _1511040), tc_HOL_Obool), _1511036)), hAPP(hAPP(c_COMBB(tc_fun(_1511038, tc_HOL_Obool), tc_fun(tc_fun(_1511038, tc_fun(_1511040, tc_HOL_Obool)), tc_fun(tc_prod(_1511038, _1511040), tc_HOL_Obool)), _1511034), c_Product__Type_OSigma(_1511038, _1511040)), _1511046))), hAPP(hAPP(c_COMBB(tc_fun(_1511040, tc_HOL_Obool), tc_fun(_1511038, tc_fun(_1511040, tc_HOL_Obool)), _1511036), c_COMBK(tc_fun(_1511040, tc_HOL_Obool), _1511038)), _1511048)))) = hAPP(hAPP(c_Product__Type_OSigma(_1511038, _1511040), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1511034, tc_fun(_1511038, tc_HOL_Obool)), _1511042), _1511046)), hAPP(c_COMBK(tc_fun(_1511040, tc_HOL_Obool), _1511038), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1511036, tc_fun(_1511040, tc_HOL_Obool)), _1511044), _1511048))))], (24739 ^ _780119) ^ [_1233178] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1233178)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1233178))], (44154 ^ _780119) ^ [_1663749, _1663751, _1663753, _1663755] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663749), tc_List_Olist(_1663749))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663749), tc_List_Olist(_1663749)), _1663751), _1663753)), c_List_Olistrel(_1663749, _1663755))), 44157 ^ _780119 : [(44160 ^ _780119) ^ [_1663978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663978), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663749)), _1663751))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1663749, _1663749)), hAPP(hAPP(c_Product__Type_OPair(_1663749, _1663749), hAPP(hAPP(c_List_Onth(_1663749), _1663751), _1663978)), hAPP(hAPP(c_List_Onth(_1663749), _1663753), _1663978))), _1663755)))], (44158 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663749)), _1663751) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663749)), _1663753))]]], (35863 ^ _780119) ^ [_1459257, _1459259, _1459261, _1459263, _1459265] : [c_Equiv__Relations_Oequivp(_1459257, _1459259), hBOOL(hAPP(hAPP(_1459259, _1459261), _1459263)), hBOOL(hAPP(hAPP(_1459259, _1459263), _1459265)), -(hBOOL(hAPP(hAPP(_1459259, _1459261), _1459265)))], (18742 ^ _780119) ^ [_1121912, _1121914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121912), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1121914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121912), _1121914)))], (28628 ^ _780119) ^ [_1308947, _1308949, _1308951] : [class_Orderings_Olinorder(_1308947), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308947), _1308949)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308947), _1308951)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308947, tc_HOL_Obool)), _1308949), _1308951) = c_Orderings_Obot__class_Obot(tc_fun(_1308947, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1308947), c_Big__Operators_Olinorder__class_OMax(_1308947, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308947, tc_HOL_Obool)), _1308949), _1308951))), c_Big__Operators_Olinorder__class_OMax(_1308947, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308947, tc_HOL_Obool)), _1308949), _1308951))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1308947), c_Big__Operators_Olinorder__class_OMax(_1308947, _1308949)), c_Big__Operators_Olinorder__class_OMax(_1308947, _1308951)))], (34735 ^ _780119) ^ [_1432000, _1432002] : [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), _1432000), _1432002))), 34738 ^ _780119 : [(34745 ^ _780119) ^ [] : [-(_1432002 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1432000, _1432002) = c_Nitpick_Onat__gcd(_1432002, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1432000, _1432002)))], (34739 ^ _780119) ^ [] : [_1432002 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1432000, _1432002) = _1432000)]]], (11451 ^ _780119) ^ [_985217, _985219, _985221] : [class_Rings_Ocomm__semiring__1(_985217), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985217), _985219), _985221) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985217), _985221), _985219))], (43304 ^ _780119) ^ [_1640375, _1640377] : [-(c_List_Olenlex(_1640375, _1640377) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1640375)), tc_List_Olist(_1640375)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1640375), c_Wellfounded_Oless__than, c_List_Olex(_1640375, _1640377))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1640375), tc_List_Olist(_1640375), tc_prod(tc_Nat_Onat, tc_List_Olist(_1640375))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1640375), tc_prod(tc_Nat_Onat, tc_List_Olist(_1640375))), tc_List_Olist(_1640375)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1640375))), c_Nat_Osize__class_Osize(tc_List_Olist(_1640375)))), c_COMBI(tc_List_Olist(_1640375)))))], (32637 ^ _780119) ^ [_1388447, _1388449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1388447)), c_Int_OBit0(_1388449))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1388447), _1388449)))], (45052 ^ _780119) ^ [_1683109, _1683111, _1683113] : [_1683113 = c_List_Olist_ONil(_1683111), -(_1683109 = hAPP(hAPP(c_List_Oappend(_1683111), _1683109), _1683113))], (20246 ^ _780119) ^ [_1148484, _1148486, _1148488] : [class_Fields_Ofield__inverse__zero(_1148484), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1148484), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148484), _1148486), _1148488)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148484), _1148486), hAPP(c_Groups_Ouminus__class_Ouminus(_1148484), _1148488)))], (24429 ^ _780119) ^ [_1227562, _1227564, _1227566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227562)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1227564), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1227566)), 24439 ^ _780119 : [(24443 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24441 ^ [_1227562, _1227564, _1227566]), _1227566)))], (24445 ^ _780119) ^ [] : [-(_1227564 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24441 ^ [_1227562, _1227564, _1227566]), 24438 ^ [_1227562, _1227564, _1227566]))], (24440 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24438 ^ [_1227562, _1227564, _1227566]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1227562))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1227564), _1227562) = _1227564)], (1850 ^ _780119) ^ [_805964, _805966, _805968, _805970, _805972, _805974] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_805972, _805968, _805964)), c_Hoare__Mirabelle_Ohoare__derivs(_805974, _805970, _805966), _805974 = _805972, _805970 = _805968, _805966 = _805964], (13258 ^ _780119) ^ [_1021438, _1021440, _1021442] : [class_Lattices_Oboolean__algebra(_1021438), 13261 ^ _780119 : [(13268 ^ _780119) ^ [] : [_1021440 = _1021442, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1021438), _1021440) = hAPP(c_Groups_Ouminus__class_Ouminus(_1021438), _1021442))], (13262 ^ _780119) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1021438), _1021440) = hAPP(c_Groups_Ouminus__class_Ouminus(_1021438), _1021442), -(_1021440 = _1021442)]]], (44596 ^ _780119) ^ [_1673598, _1673600] : [-(_1673598 = c_List_Olist_ONil(_1673600)), -(c_Random_Oselect__weight(_1673600, hAPP(hAPP(c_List_Omap(_1673600, tc_prod(tc_Code__Numeral_Ocode__numeral, _1673600)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1673600), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1673598)) = c_Random_Oselect(_1673600, _1673598))], (41365 ^ _780119) ^ [_1594060] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594060, tc_HOL_Obool) = c_Set_OBall(_1594060))], (14040 ^ _780119) ^ [_1035726, _1035728] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1035726)), _1035728) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1035726), _1035728)))], (38934 ^ _780119) ^ [_1535077, _1535079, _1535081, _1535083, _1535085, _1535087, _1535089, _1535091] : [c_Finite__Set_Ofolding__image(_1535077, _1535079, _1535081, _1535083, _1535085), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535079), _1535087)), c_Fun_Oinj__on(_1535079, _1535079, _1535089, _1535087), -(hAPP(hAPP(_1535085, _1535091), hAPP(c_Set_Oimage(_1535079, _1535079, _1535089), _1535087)) = hAPP(hAPP(_1535085, hAPP(c_Fun_Ocomp(_1535079, _1535077, _1535079, _1535091), _1535089)), _1535087))], (47522 ^ _780119) ^ [_1738366, _1738368] : [-(hAPP(c_List_Orev(_1738366), c_List_Oconcat(_1738366, _1738368)) = c_List_Oconcat(_1738366, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738366), tc_List_Olist(_1738366)), c_List_Orev(_1738366)), hAPP(c_List_Orev(tc_List_Olist(_1738366)), _1738368))))], (43459 ^ _780119) ^ [_1645388, _1645390, _1645392, _1645394] : [c_List_Olistrelp(_1645388, hAPP(hAPP(c_COMBC(_1645388, tc_fun(tc_prod(_1645388, _1645388), tc_HOL_Obool), tc_fun(_1645388, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1645388, tc_fun(tc_fun(tc_prod(_1645388, _1645388), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1645388, _1645388), tc_HOL_Obool), tc_fun(_1645388, tc_HOL_Obool)), _1645388), c_COMBC(_1645388, tc_fun(tc_prod(_1645388, _1645388), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1645388, tc_prod(_1645388, _1645388)), tc_fun(_1645388, tc_fun(tc_fun(tc_prod(_1645388, _1645388), tc_HOL_Obool), tc_HOL_Obool)), _1645388), hAPP(c_COMBB(tc_prod(_1645388, _1645388), tc_fun(tc_fun(tc_prod(_1645388, _1645388), tc_HOL_Obool), tc_HOL_Obool), _1645388), c_member(tc_prod(_1645388, _1645388)))), c_Product__Type_OPair(_1645388, _1645388)))), _1645390), _1645392, _1645394), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645388), tc_List_Olist(_1645388))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645388), tc_List_Olist(_1645388)), _1645392), _1645394)), c_List_Olistrel(_1645388, _1645390))))], (10026 ^ _780119) ^ [_954718, _954720, _954722] : [class_Lattices_Olattice(_954718), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954718), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954718), _954720), _954722)), _954722)))], (5979 ^ _780119) ^ [_875196, _875198] : [class_Finite__Set_Ofinite(_875196), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_875196), _875198)))], (33759 ^ _780119) ^ [_1413176, _1413178, _1413180, _1413182, _1413184, _1413186, _1413188] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1413176, _1413178), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1413180), _1413182))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1413184, _1413178), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1413186), _1413188))), -(_1413178 = 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), _1413176), _1413184), _1413178), 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), _1413180), _1413186)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413182), _1413188)), _1413178))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413182), _1413188), _1413178)))))], (40008 ^ _780119) ^ [_1561065, _1561067, _1561069] : [c_Relation_Ototal__on(_1561065, _1561067, hAPP(c_Relation_Oconverse(_1561065, _1561065), _1561069)), -(c_Relation_Ototal__on(_1561065, _1561067, _1561069))], (5568 ^ _780119) ^ [_865416, _865418, _865420, _865422] : [-(tc_prod(_865422, _865418) = tc_prod(_865420, _865416)), _865422 = _865420, _865418 = _865416], (37111 ^ _780119) ^ [_1487958, _1487960, _1487962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1487958, _1487958), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1487958, _1487958, _1487958), _1487960), _1487962)), _1487960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1487958, tc_HOL_Obool), tc_fun(_1487958, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1487958, tc_HOL_Obool), tc_fun(_1487958, tc_HOL_Obool), tc_fun(_1487958, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1487958, _1487960)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1487958, tc_HOL_Obool), tc_fun(_1487958, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1487958, _1487962)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1487958, tc_HOL_Obool), tc_fun(_1487958, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1487958, tc_HOL_Obool), tc_fun(_1487958, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1487958, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1487958, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1487958, tc_HOL_Obool), tc_fun(_1487958, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1487958, _1487960))))], (3108 ^ _780119) ^ [_826488, _826490, _826492, _826494] : [-(c_Nitpick_Ouminus__frac(_826494, _826490) = c_Nitpick_Ouminus__frac(_826492, _826488)), _826494 = _826492, _826490 = _826488], (45882 ^ _780119) ^ [_1704086, _1704088, _1704090, _1704092] : [-(hAPP(hAPP(c_List_Omap(_1704086, _1704088), _1704090), hAPP(c_List_Otl(_1704086), _1704092)) = hAPP(c_List_Otl(_1704088), hAPP(hAPP(c_List_Omap(_1704086, _1704088), _1704090), _1704092)))], (10985 ^ _780119) ^ [_975139, _975141] : [class_Groups_Omonoid__mult(_975139), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975139), _975141), c_Groups_Oone__class_Oone(_975139)) = _975141)], (50120 ^ _780119) ^ [_1796035, _1796037, _1796039, _1796041, _1796043] : [-(_1796035 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1796037, _1796039, _1796041, _1796043), _1796035) = hAPP(c_Lazy__Sequence_Obind(_1796037, _1796039, hAPP(_1796041, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1796035), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1796037, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1796039)), _1796043), _1796035)))], (22350 ^ _780119) ^ [_1188005, _1188007, _1188009] : [hBOOL(hAPP(_1188005, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1188007, _1188009))), 22353 ^ _780119 : [(22360 ^ _780119) ^ [] : [-(_1188009 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22363 ^ _780119 : [(22364 ^ _780119) ^ [_1188253, _1188255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1188253), _1188009)), _1188007 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188009), _1188255)), _1188253), -(hBOOL(hAPP(_1188005, _1188253)))]]], (22354 ^ _780119) ^ [] : [_1188009 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1188005, _1188007)))]]], (1070 ^ _780119) ^ [_796218, _796220] : [-(class_Rings_Oring__no__zero__divisors(_796218)), _796220 = _796218, class_Rings_Oring__no__zero__divisors(_796220)], (8822 ^ _780119) ^ [_932402, _932404, _932406, _932408, _932410] : [c_Finite__Set_Ofun__left__comm__idem(_932402, _932404, _932406), -(c_Finite__Set_Ofun__left__comm__idem(_932408, _932404, hAPP(hAPP(c_COMBB(_932402, tc_fun(_932404, _932404), _932408), _932406), _932410)))], (32337 ^ _780119) ^ [_1383198, _1383200] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1383198)), _1383200) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1383198), _1383200)))], (35893 ^ _780119) ^ [_1459747, _1459749] : [c_Equiv__Relations_Oequivp(_1459747, _1459749), 35896 ^ _780119 : [(35903 ^ _780119) ^ [_1459940, _1459942] : [hAPP(_1459749, _1459942) = hAPP(_1459749, _1459940), -(hBOOL(hAPP(hAPP(_1459749, _1459942), _1459940)))], (35897 ^ _780119) ^ [_1459841, _1459843] : [hBOOL(hAPP(hAPP(_1459749, _1459843), _1459841)), -(hAPP(_1459749, _1459843) = hAPP(_1459749, _1459841))]]], (25472 ^ _780119) ^ [_1245984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1245984)), -(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, _1245984))))], (38651 ^ _780119) ^ [_1528718, _1528720, _1528722, _1528724, _1528726, _1528728] : [-(hAPP(c_Set_Ovimage(_1528718, tc_prod(_1528720, _1528722), _1528724), hAPP(hAPP(c_Product__Type_OSigma(_1528720, _1528722), _1528726), hAPP(c_COMBK(tc_fun(_1528722, tc_HOL_Obool), _1528720), _1528728))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1528718, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1528718, _1528720, hAPP(c_Fun_Ocomp(tc_prod(_1528720, _1528722), _1528720, _1528718, c_Product__Type_Ofst(_1528720, _1528722)), _1528724)), _1528726)), hAPP(c_Set_Ovimage(_1528718, _1528722, hAPP(c_Fun_Ocomp(tc_prod(_1528720, _1528722), _1528722, _1528718, c_Product__Type_Osnd(_1528720, _1528722)), _1528724)), _1528728)))], (33653 ^ _780119) ^ [_1410887, _1410889, _1410891, _1410893] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1410887, _1410889)), hAPP(hAPP(c_Product__Type_OPair(_1410887, _1410889), _1410891), _1410893)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1410887, _1410889), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1410887, tc_fun(_1410889, tc_HOL_Obool))), _1410891), _1410893)))], (41860 ^ _780119) ^ [_1606028, _1606030, _1606032] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1606028, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1606028, tc_HOL_Obool), tc_HOL_Obool)), _1606030), _1606032)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606028, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1606028, tc_HOL_Obool), _1606030)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1606028, tc_HOL_Obool), _1606032)))], (50012 ^ _780119) ^ [_1794192, _1794194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50013 ^ [_1794192, _1794194]), hAPP(_1794192, 50013 ^ [_1794192, _1794194]))), -(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)), _1794192)), _1794194)))))], (13574 ^ _780119) ^ [_1027231, _1027233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027231), _1027233)), -(hAPP(c_Nat_OSuc, _1027231) = _1027233), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027231)), _1027233)))], (13059 ^ _780119) ^ [_1017527, _1017529, _1017531, _1017533, _1017535] : [hAPP(_1017527, _1017529) = c_Option_Ooption_ONone(_1017531), -(c_Map_Oran(_1017533, _1017531, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1017533, tc_Option_Ooption(_1017531)), _1017527), _1017529), hAPP(c_Option_Ooption_OSome(_1017531), _1017535))) = hAPP(hAPP(c_Set_Oinsert(_1017531), _1017535), c_Map_Oran(_1017533, _1017531, _1017527)))], (27244 ^ _780119) ^ [_1283658, _1283660] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283658), _1283660)), -(_1283660 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1283658, 27248 ^ [_1283658, _1283660]), 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)), 27247 ^ [_1283658, _1283660]))))], (18398 ^ _780119) ^ [_1115857, _1115859, _1115861, _1115863] : [18399 ^ _780119 : [(18402 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1115861), _1115863)))], (18400 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1115857), _1115859)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1115857, _1115861)), c_Sum__Type_OPlus(_1115857, _1115861, _1115859, _1115863)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25047 ^ _780119) ^ [_1238888, _1238890, _1238892] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1238888), _1238890), _1238892) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1238888), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1238888, tc_Int_Oint), _1238890), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238892))), class_Groups_Ocomm__monoid__add(_1238888), class_Groups_Ocomm__monoid__mult(_1238888)], (45058 ^ _780119) ^ [_1683228, _1683230, _1683232] : [_1683228 = hAPP(hAPP(c_List_Oappend(_1683230), _1683232), _1683228), -(_1683232 = c_List_Olist_ONil(_1683230))], (33225 ^ _780119) ^ [] : [c_Int_OMin = c_Int_OPls], (50306 ^ _780119) ^ [_1799772, _1799774, _1799776, _1799778, _1799780] : [-(hAPP(c_New__DSequence_Oneg__bind(_1799772, _1799774, _1799776, _1799778), _1799780) = c_Lazy__Sequence_Ohb__bind(_1799772, _1799774, hAPP(_1799776, _1799780), hAPP(hAPP(c_COMBC(_1799772, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1799774))), _1799778), _1799780)))], (28206 ^ _780119) ^ [_1301483, _1301485, _1301487, _1301489] : [class_Groups_Oordered__ab__group__add(_1301483), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1301483), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1301483), _1301485), _1301487)), _1301489) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1301483), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1301483), _1301485), _1301489)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1301483), _1301487), _1301489)))], (45868 ^ _780119) ^ [_1703731, _1703733, _1703735] : [-(hAPP(c_List_Otl(_1703731), hAPP(hAPP(c_List_Odrop(_1703731), _1703733), _1703735)) = hAPP(hAPP(c_List_Odrop(_1703731), _1703733), hAPP(c_List_Otl(_1703731), _1703735)))], (43964 ^ _780119) ^ [_1659017, _1659019, _1659021] : [_1659017 = _1659019, 43967 ^ _780119 : [(43970 ^ _780119) ^ [_1659165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659165), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659021)), _1659017))), -(hAPP(hAPP(c_List_Onth(_1659021), _1659017), _1659165) = hAPP(hAPP(c_List_Onth(_1659021), _1659019), _1659165))], (43968 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659021)), _1659017) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659021)), _1659019))]]], (26089 ^ _780119) ^ [_1255896] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1255896) = 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), _1255896))))], (50668 ^ _780119) ^ [_1807715, _1807717, _1807719] : [-(c_List_Oreplicate(_1807715, hAPP(c_Nat_OSuc, _1807717), _1807719) = hAPP(hAPP(c_List_Olist_OCons(_1807715), _1807719), c_List_Oreplicate(_1807715, _1807717, _1807719)))], (24009 ^ _780119) ^ [_1219413, _1219415] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1219413), _1219415))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1219413), hAPP(c_Nat_OSuc, _1219415)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (40480 ^ _780119) ^ [_1573384, _1573386, _1573388, _1573390, _1573392] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573384, _1573384)), hAPP(hAPP(c_Product__Type_OPair(_1573384, _1573384), _1573386), _1573388)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1573384, _1573384), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1573390)), _1573392))), 40484 ^ _780119 : [(40487 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573384, _1573384)), hAPP(hAPP(c_Product__Type_OPair(_1573384, _1573384), 40483 ^ [_1573384, _1573386, _1573388, _1573390, _1573392]), _1573388)), _1573392)))], (40485 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573384, _1573384)), hAPP(hAPP(c_Product__Type_OPair(_1573384, _1573384), _1573386), 40483 ^ [_1573384, _1573386, _1573388, _1573390, _1573392])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1573384, _1573384), tc_HOL_Obool), _1573390), _1573392))))]]], (18444 ^ _780119) ^ [_1116537, _1116539, _1116541] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1116539), _1116541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116537), _1116539)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116537), _1116541)))], (33437 ^ _780119) ^ [_1402925] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1402925)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1402925)))], (13448 ^ _780119) ^ [_1024863, _1024865, _1024867] : [class_Rings_Oidom(_1024863), 13451 ^ _780119 : [(13452 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024863), _1024865), _1024865) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024863), _1024867), _1024867), -(_1024865 = _1024867), -(_1024865 = hAPP(c_Groups_Ouminus__class_Ouminus(_1024863), _1024867))], (13462 ^ _780119) ^ [] : [13463 ^ _780119 : [(13466 ^ _780119) ^ [] : [_1024865 = hAPP(c_Groups_Ouminus__class_Ouminus(_1024863), _1024867)], (13464 ^ _780119) ^ [] : [_1024865 = _1024867]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024863), _1024865), _1024865) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024863), _1024867), _1024867))]]], (46791 ^ _780119) ^ [_1724164, _1724166, _1724168, _1724170, _1724172] : [class_Orderings_Olinorder(_1724164), -(c_List_Olinorder__class_Osorted(_1724164, hAPP(hAPP(c_List_Omap(_1724166, _1724164), _1724168), hAPP(c_List_Ofilter(_1724166, hAPP(hAPP(c_COMBC(_1724166, _1724164, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1724164, tc_fun(_1724164, tc_HOL_Obool), _1724166), c_fequal), _1724168)), hAPP(_1724170, _1724172))), _1724172))))], (46751 ^ _780119) ^ [_1723269, _1723271, _1723273, _1723275, _1723277] : [-(hAPP(hAPP(c_List_Omap(_1723269, _1723271), _1723273), hAPP(c_List_Ofilter(_1723269, _1723275), _1723277)) = c_List_Omap__filter(_1723269, _1723271, hAPP(hAPP(c_COMBC(_1723269, tc_Option_Ooption(_1723271), tc_Option_Ooption(_1723271)), hAPP(hAPP(c_COMBS(_1723269, tc_Option_Ooption(_1723271), tc_fun(tc_Option_Ooption(_1723271), tc_Option_Ooption(_1723271))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1723271), tc_fun(tc_Option_Ooption(_1723271), tc_Option_Ooption(_1723271))), _1723269), c_If(tc_Option_Ooption(_1723271))), _1723275)), hAPP(hAPP(c_COMBB(_1723271, tc_Option_Ooption(_1723271), _1723269), c_Option_Ooption_OSome(_1723271)), _1723273))), c_Option_Ooption_ONone(_1723271)), _1723277))], (35361 ^ _780119) ^ [_1446549, _1446551, _1446553, _1446555, _1446557, _1446559] : [-(hAPP(c_Relation_OImage(_1446549, _1446551, _1446553), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446555, tc_fun(_1446549, tc_HOL_Obool)), _1446557), _1446559)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446555, tc_fun(_1446551, tc_HOL_Obool)), _1446557), hAPP(hAPP(c_COMBB(tc_fun(_1446549, tc_HOL_Obool), tc_fun(_1446551, tc_HOL_Obool), _1446555), c_Relation_OImage(_1446549, _1446551, _1446553)), _1446559)))], (48245 ^ _780119) ^ [_1755605] : [-(c_Enum_Osublists(_1755605, c_List_Olist_ONil(_1755605)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1755605)), c_List_Olist_ONil(_1755605)), c_List_Olist_ONil(tc_List_Olist(_1755605))))], (4582 ^ _780119) ^ [_849639, _849641, _849643, _849645, _849647, _849649, _849651, _849653, _849655, _849657] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_849657, _849653, _849649, _849645, _849641) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_849655, _849651, _849647, _849643, _849639)), _849657 = _849655, _849653 = _849651, _849649 = _849647, _849645 = _849643, _849641 = _849639], (25660 ^ _780119) ^ [_1248809, _1248811] : [c_Nat__Transfer_Ois__nat(_1248809), c_Nat__Transfer_Ois__nat(_1248811), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1248809), _1248811)))], (42241 ^ _780119) ^ [_1614762, _1614764, _1614766, _1614768, _1614770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1614762, tc_HOL_Obool)), _1614764), _1614766)), 42247 ^ _780119 : [(42250 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1614768, 42246 ^ [_1614762, _1614764, _1614766, _1614768, _1614770])))], (42252 ^ _780119) ^ [] : [hBOOL(hAPP(_1614770, 42246 ^ [_1614762, _1614764, _1614766, _1614768, _1614770]))], (42248 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614762), 42246 ^ [_1614762, _1614764, _1614766, _1614768, _1614770]), _1614764)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1614762, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614762, tc_HOL_Obool)), _1614764), hAPP(c_Set_OCollect(_1614762), _1614768))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614762, tc_HOL_Obool)), _1614766), hAPP(c_Set_OCollect(_1614762), _1614770)))))], (5172 ^ _780119) ^ [_859296, _859298] : [_859298 = _859296, -(c_List_Orev(_859298) = c_List_Orev(_859296))], (6749 ^ _780119) ^ [_890844, _890846, _890848] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890844, tc_HOL_Obool)), _890846), _890848) = c_Orderings_Obot__class_Obot(tc_fun(_890844, tc_HOL_Obool)), 6752 ^ _780119 : [(6755 ^ _780119) ^ [] : [-(_890848 = c_Orderings_Obot__class_Obot(tc_fun(_890844, tc_HOL_Obool)))], (6753 ^ _780119) ^ [] : [-(_890846 = c_Orderings_Obot__class_Obot(tc_fun(_890844, tc_HOL_Obool)))]]], (47562 ^ _780119) ^ [_1739273, _1739275, _1739277] : [_1739275 = hAPP(c_List_Orev(_1739273), _1739277), -(hAPP(c_List_Orev(_1739273), _1739275) = _1739277)], (29607 ^ _780119) ^ [_1330152, _1330154, _1330156, _1330158, _1330160] : [29609 ^ _780119 : [(29613 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330152), 29611 ^ [_1330152, _1330154, _1330156, _1330158, _1330160]), hAPP(_1330158, 29608 ^ [_1330152, _1330154, _1330156, _1330158, _1330160]))))], (29615 ^ _780119) ^ [] : [hBOOL(hAPP(_1330160, 29611 ^ [_1330152, _1330154, _1330156, _1330158, _1330160]))], (29610 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330154), 29608 ^ [_1330152, _1330154, _1330156, _1330158, _1330160]), _1330156)))]], 29616 ^ _780119 : [(29617 ^ _780119) ^ [_1330462] : [hBOOL(hAPP(hAPP(c_member(_1330152), _1330462), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330154, tc_fun(_1330152, tc_HOL_Obool)), _1330156), _1330158))), -(hBOOL(hAPP(_1330160, _1330462)))]]], (40022 ^ _780119) ^ [_1561292, _1561294, _1561296, _1561298] : [-(hAPP(c_Relation_Oconverse(_1561292, _1561294), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1561292, _1561294), tc_HOL_Obool)), _1561296), _1561298)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1561294, _1561292), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1561292, _1561294), _1561296)), hAPP(c_Relation_Oconverse(_1561292, _1561294), _1561298)))], (8526 ^ _780119) ^ [_928209, _928211] : [class_Orderings_Opreorder(_928209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928209), _928211), _928211))], (43493 ^ _780119) ^ [_1646873, _1646875, _1646877] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646873, tc_HOL_Obool)), hAPP(c_List_Oset(_1646873), _1646875)), hAPP(c_List_Oset(_1646873), hAPP(hAPP(c_List_Olist_OCons(_1646873), _1646877), _1646875)))))], (3238 ^ _780119) ^ [_828567, _828569, _828571, _828573, _828575, _828577] : [-(c_Map_Oran(_828577, _828573, _828569) = c_Map_Oran(_828575, _828571, _828567)), _828577 = _828575, _828573 = _828571, _828569 = _828567], (44810 ^ _780119) ^ [_1677652, _1677654] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1677652), _1677654))), -(c_List_Oupto(_1677652, _1677654) = c_List_Olist_ONil(tc_Int_Oint))], (964 ^ _780119) ^ [_794805, _794807] : [-(class_Fields_Olinordered__field(_794805)), _794807 = _794805, class_Fields_Olinordered__field(_794807)], (33713 ^ _780119) ^ [_1412187, _1412189, _1412191, _1412193, _1412195, _1412197] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1412189, _1412191)), hAPP(hAPP(c_Product__Type_OPair(_1412189, _1412191), _1412195), _1412197)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412187, tc_fun(tc_prod(_1412189, _1412191), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1412187, tc_HOL_Obool))), _1412193))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412187, tc_fun(_1412189, tc_fun(_1412191, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1412187, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1412189, _1412191), tc_HOL_Obool), tc_fun(_1412189, tc_fun(_1412191, tc_HOL_Obool)), _1412187), hAPP(c_COMBC(_1412189, tc_fun(tc_prod(_1412189, _1412191), tc_HOL_Obool), tc_fun(_1412191, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412191, tc_fun(tc_fun(tc_prod(_1412189, _1412191), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1412189, _1412191), tc_HOL_Obool), tc_fun(_1412191, tc_HOL_Obool)), _1412189), c_COMBC(_1412191, tc_fun(tc_prod(_1412189, _1412191), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412191, tc_prod(_1412189, _1412191)), tc_fun(_1412191, tc_fun(tc_fun(tc_prod(_1412189, _1412191), tc_HOL_Obool), tc_HOL_Obool)), _1412189), hAPP(c_COMBB(tc_prod(_1412189, _1412191), tc_fun(tc_fun(tc_prod(_1412189, _1412191), tc_HOL_Obool), tc_HOL_Obool), _1412191), c_member(tc_prod(_1412189, _1412191)))), c_Product__Type_OPair(_1412189, _1412191))))), _1412193)), _1412195), _1412197)))], (25602 ^ _780119) ^ [_1248042] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1248042)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1248042))], (23611 ^ _780119) ^ [_1211800, _1211802, _1211804] : [class_Orderings_Oorder(_1211800), 23614 ^ _780119 : [(23621 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211800), _1211802), _1211804))), -(c_Orderings_Obot__class_Obot(tc_fun(_1211800, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1211800, _1211802, _1211804))], (23615 ^ _780119) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1211800, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1211800, _1211802, _1211804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211800), _1211802), _1211804))]]], (28590 ^ _780119) ^ [_1308151, _1308153, _1308155] : [class_Orderings_Olinorder(_1308151), -(_1308153 = c_Orderings_Obot__class_Obot(tc_fun(_1308151, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1308151, tc_HOL_Obool)), _1308153), _1308155)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308151), _1308155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308151), hAPP(c_Finite__Set_Ofold1(_1308151, c_Orderings_Oord__class_Omin(_1308151)), _1308155)), hAPP(c_Finite__Set_Ofold1(_1308151, c_Orderings_Oord__class_Omin(_1308151)), _1308153))))], (5408 ^ _780119) ^ [_862984, _862986, _862988, _862990] : [-(c_HOL_OThe(_862990, _862986) = c_HOL_OThe(_862988, _862984)), _862990 = _862988, _862986 = _862984], (45838 ^ _780119) ^ [_1703442, _1703444, _1703446] : [-(_1703442 = c_List_Olist_ONil(_1703444)), -(hAPP(c_List_Ohd(_1703444), hAPP(hAPP(c_List_Oappend(_1703444), _1703442), _1703446)) = hAPP(c_List_Ohd(_1703444), _1703442))], (9208 ^ _780119) ^ [_938274, _938276, _938278] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938274, tc_HOL_Obool)), _938276), _938278))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938274, tc_HOL_Obool)), _938276), _938278)), -(_938276 = _938278)], (35315 ^ _780119) ^ [_1444689, _1444691, _1444693, _1444695] : [c_FunDef_Oreduction__pair(_1444689, _1444691), -(c_FunDef_Oreduction__pair(_1444693, hAPP(hAPP(c_FunDef_Orp__inv__image(_1444689, _1444693), _1444691), _1444695)))], (5600 ^ _780119) ^ [_865884, _865886, _865888, _865890, _865892, _865894] : [-(c_COMBC(_865894, _865890, _865886) = c_COMBC(_865892, _865888, _865884)), _865894 = _865892, _865890 = _865888, _865886 = _865884], (41129 ^ _780119) ^ [_1586828, _1586830, _1586832, _1586834, _1586836] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586828, tc_fun(_1586830, tc_HOL_Obool)), _1586832), hAPP(hAPP(c_COMBC(_1586828, tc_fun(_1586830, tc_HOL_Obool), tc_fun(_1586830, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586830, tc_HOL_Obool), tc_fun(tc_fun(_1586830, tc_HOL_Obool), tc_fun(_1586830, tc_HOL_Obool)), _1586828), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1586830, tc_HOL_Obool))), _1586834)), _1586836)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1586830, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586828, tc_fun(_1586830, tc_HOL_Obool)), _1586832), _1586834)), _1586836))], (38064 ^ _780119) ^ [_1514513, _1514515, _1514517, _1514519, _1514521, _1514523] : [class_Groups_Ocomm__monoid__mult(_1514513), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514515), _1514517)), 38074 ^ _780119 : [(38077 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514519), hAPP(_1514521, 38073 ^ [_1514513, _1514515, _1514517, _1514519, _1514521, _1514523])))], (38075 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514515), 38073 ^ [_1514513, _1514515, _1514517, _1514519, _1514521, _1514523]), _1514517)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514515, _1514513), hAPP(hAPP(c_COMBS(_1514515, tc_fun(_1514519, tc_HOL_Obool), _1514513), hAPP(hAPP(c_COMBB(tc_fun(_1514519, _1514513), tc_fun(tc_fun(_1514519, tc_HOL_Obool), _1514513), _1514515), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514519, _1514513)), _1514523)), _1514521)), _1514517) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1514515, _1514519), _1514513), hAPP(c_Product__Type_Oprod_Oprod__case(_1514515, _1514519, _1514513), _1514523)), hAPP(hAPP(c_Product__Type_OSigma(_1514515, _1514519), _1514517), _1514521)))], (6679 ^ _780119) ^ [_889263, _889265, _889267, _889269, _889271, _889273, _889275] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_889263), _889265), _889267), _889269) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_889263), _889271), _889273), _889275), 6682 ^ _780119 : [(6685 ^ _780119) ^ [] : [-(_889267 = _889273)], (6687 ^ _780119) ^ [] : [-(_889269 = _889275)], (6683 ^ _780119) ^ [] : [-(_889265 = _889271)]]], (45926 ^ _780119) ^ [_1704880, _1704882, _1704884] : [-(hAPP(hAPP(c_List_Otake(_1704880), _1704882), hAPP(c_List_Otl(_1704880), _1704884)) = hAPP(c_List_Otl(_1704880), hAPP(hAPP(c_List_Otake(_1704880), hAPP(c_Nat_OSuc, _1704882)), _1704884)))], (19819 ^ _780119) ^ [_1140662, _1140664] : [class_Rings_Odivision__ring__inverse__zero(_1140662), 19822 ^ _780119 : [(19829 ^ _780119) ^ [] : [-(_1140664 = c_Groups_Ozero__class_Ozero(_1140662)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140662), _1140664), _1140664) = c_Groups_Oone__class_Oone(_1140662))], (19823 ^ _780119) ^ [] : [_1140664 = c_Groups_Ozero__class_Ozero(_1140662), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140662), _1140664), _1140664) = c_Groups_Ozero__class_Ozero(_1140662))]]], (11788 ^ _780119) ^ [_992363] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992363), _992363))))], (38752 ^ _780119) ^ [_1530942, _1530944, _1530946, _1530948, _1530950, _1530952, _1530954] : [-(hAPP(c_Product__Type_Oapsnd(_1530942, _1530944, _1530946, _1530948), hAPP(c_Product__Type_Oapsnd(_1530950, _1530942, _1530946, _1530952), _1530954)) = hAPP(c_Product__Type_Oapsnd(_1530950, _1530944, _1530946, hAPP(c_Fun_Ocomp(_1530942, _1530944, _1530950, _1530948), _1530952)), _1530954))], (15246 ^ _780119) ^ [_1058734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1058734), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34847 ^ _780119) ^ [_1434321, _1434323] : [hAPP(c_Int_ORep__Integ, _1434321) = hAPP(c_Int_ORep__Integ, _1434323), -(_1434321 = _1434323)], (30417 ^ _780119) ^ [_1348757, _1348759, _1348761] : [class_Int_Onumber__ring(_1348757), -(hAPP(c_Int_Onumber__class_Onumber__of(_1348757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1348759), _1348761)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1348757), hAPP(c_Int_Onumber__class_Onumber__of(_1348757), _1348759)), hAPP(c_Int_Onumber__class_Onumber__of(_1348757), _1348761)))], (43495 ^ _780119) ^ [_1646943, _1646945, _1646947] : [_1646943 = hAPP(hAPP(c_List_Olist_OCons(_1646945), _1646947), _1646943)], (27146 ^ _780119) ^ [_1280199, _1280201, _1280203, _1280205, _1280207, _1280209] : [hBOOL(hAPP(hAPP(c_member(_1280199), _1280201), _1280203)), -(hAPP(c_Fun_Ooverride__on(_1280199, _1280205, _1280207, _1280209, _1280203), _1280201) = hAPP(_1280209, _1280201))], (32057 ^ _780119) ^ [_1377467, _1377469] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377467))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377469)) = 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)))), _1377467), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377469)))], (19054 ^ _780119) ^ [_1127227, _1127229] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1127227)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1127229)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127227), _1127229))], (47568 ^ _780119) ^ [_1739392, _1739394, _1739396] : [hAPP(c_List_Orev(_1739392), _1739394) = hAPP(c_List_Orev(_1739392), _1739396), -(_1739394 = _1739396)], (43499 ^ _780119) ^ [_1647052, _1647054, _1647056, _1647058, _1647060] : [hAPP(hAPP(c_List_Olist_OCons(_1647052), _1647054), _1647056) = hAPP(hAPP(c_List_Olist_OCons(_1647052), _1647058), _1647060), 43502 ^ _780119 : [(43505 ^ _780119) ^ [] : [-(_1647056 = _1647060)], (43503 ^ _780119) ^ [] : [-(_1647054 = _1647058)]]], (31231 ^ _780119) ^ [_1364028] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1364028) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1364028))], (47821 ^ _780119) ^ [_1746347, _1746349, _1746351] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746347)), c_List_OtakeWhile(_1746347, _1746349, _1746351))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746347)), _1746351))))], (44053 ^ _780119) ^ [_1661337, _1661339, _1661341, _1661343] : [hBOOL(hAPP(c_List_Odistinct(_1661337), _1661339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661341), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661337)), _1661339))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661343), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661337)), _1661339))), 44064 ^ _780119 : [(44071 ^ _780119) ^ [] : [_1661341 = _1661343, -(hAPP(hAPP(c_List_Onth(_1661337), _1661339), _1661341) = hAPP(hAPP(c_List_Onth(_1661337), _1661339), _1661343))], (44065 ^ _780119) ^ [] : [hAPP(hAPP(c_List_Onth(_1661337), _1661339), _1661341) = hAPP(hAPP(c_List_Onth(_1661337), _1661339), _1661343), -(_1661341 = _1661343)]]], (29803 ^ _780119) ^ [_1335513, _1335515, _1335517, _1335519, _1335521] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335513, tc_fun(_1335515, tc_HOL_Obool)), _1335517), hAPP(hAPP(c_COMBC(_1335513, tc_fun(_1335515, tc_HOL_Obool), tc_fun(_1335515, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1335515, tc_HOL_Obool), tc_fun(tc_fun(_1335515, tc_HOL_Obool), tc_fun(_1335515, tc_HOL_Obool)), _1335513), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335515, tc_HOL_Obool))), _1335519)), _1335521)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335515, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335513, tc_fun(_1335515, tc_HOL_Obool)), _1335517), _1335519)), _1335521))], (37805 ^ _780119) ^ [_1506405, _1506407, _1506409, _1506411] : [-(hAPP(c_Set_Oimage(tc_prod(_1506405, _1506407), tc_prod(_1506407, _1506405), hAPP(c_Product__Type_Oprod_Oprod__case(_1506405, _1506407, tc_prod(_1506407, _1506405)), hAPP(c_COMBC(_1506407, _1506405, tc_prod(_1506407, _1506405)), c_Product__Type_OPair(_1506407, _1506405)))), hAPP(hAPP(c_Product__Type_OSigma(_1506405, _1506407), _1506409), hAPP(c_COMBK(tc_fun(_1506407, tc_HOL_Obool), _1506405), _1506411))) = hAPP(hAPP(c_Product__Type_OSigma(_1506407, _1506405), _1506411), hAPP(c_COMBK(tc_fun(_1506405, tc_HOL_Obool), _1506407), _1506409)))], (25857 ^ _780119) ^ [_1251985] : [-(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)), _1251985)))], (36722 ^ _780119) ^ [_1477849, _1477851, _1477853, _1477855, _1477857] : [-(hAPP(c_Set_Ovimage(_1477849, _1477851, _1477853), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1477851, tc_HOL_Obool)), _1477855), _1477857)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1477849, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1477849, _1477851, _1477853), _1477855)), hAPP(c_Set_Ovimage(_1477849, _1477851, _1477853), _1477857)))], (46211 ^ _780119) ^ [_1711439, _1711441, _1711443, _1711445] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1711439)), hAPP(hAPP(c_List_Olist_OCons(_1711439), _1711441), _1711443)), c_List_Olists(_1711439, _1711445)))), hBOOL(hAPP(hAPP(c_member(_1711439), _1711441), _1711445)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1711439)), _1711443), c_List_Olists(_1711439, _1711445)))], (14976 ^ _780119) ^ [_1054733, _1054735] : [class_Rings_Ocomm__semiring__1(_1054733), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054733), c_Groups_Ozero__class_Ozero(_1054733)), _1054735) = _1054735)], (13154 ^ _780119) ^ [_1019795, _1019797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1019795), _1019797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1019795)), hAPP(c_Nat_OSuc, _1019797))))], (27009 ^ _780119) ^ [_1275147, _1275149, _1275151, _1275153, _1275155, _1275157] : [class_Groups_Ocomm__monoid__add(_1275147), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275149), _1275151)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1275149, _1275147), hAPP(hAPP(c_COMBS(_1275149, _1275147, _1275147), hAPP(hAPP(c_COMBS(_1275149, _1275147, tc_fun(_1275147, _1275147)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1275147, tc_fun(_1275147, _1275147)), _1275149), c_If(_1275147)), _1275153)), _1275155)), _1275157)), _1275151) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1275147), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1275149, _1275147), _1275155), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1275149, tc_HOL_Obool)), _1275151), hAPP(c_Set_OCollect(_1275149), _1275153)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1275149, _1275147), _1275157), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1275149, tc_HOL_Obool)), _1275151), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1275149, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1275149), _1275153))))))], (2582 ^ _780119) ^ [_818347, _818349] : [_818349 = _818347, -(c_Wellfounded_Ofinite__psubset(_818349) = c_Wellfounded_Ofinite__psubset(_818347))], (51327 ^ _780119) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (44270 ^ _780119) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6809 ^ _780119) ^ [_892074, _892076, _892078] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892074, tc_HOL_Obool)), _892076), _892078) = _892078, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892074, tc_HOL_Obool)), _892076), _892078)))], (6080 ^ _780119) ^ [_876991, _876993] : [-(hBOOL(hAPP(hAPP(c_member(_876991), 6081 ^ [_876991, _876993]), _876993))), -(_876993 = c_Orderings_Obot__class_Obot(tc_fun(_876991, tc_HOL_Obool)))], (39972 ^ _780119) ^ [_1560291] : [-(hAPP(c_Relation_Oconverse(_1560291, _1560291), c_Relation_OId(_1560291)) = c_Relation_OId(_1560291))], (33573 ^ _780119) ^ [_1405172, _1405174, _1405176, _1405178, _1405180] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1405172, _1405174), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1405176), _1405178))), -(_1405174 = 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)), _1405180)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1405172, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1405174), _1405180)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1405176), _1405180)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1405174), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1405176, _1405180))), _1405178)))))], (31127 ^ _780119) ^ [_1362130, _1362132] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362130)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362132)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1362130), _1362132)))], (24571 ^ _780119) ^ [_1230291, _1230293, _1230295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230291)), 24574 ^ _780119 : [(24575 ^ _780119) ^ [_1230425] : [24577 ^ _780119 : [(24581 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24579 ^ [_1230291, _1230293, _1230295, _1230425]), _1230293)))], (24583 ^ _780119) ^ [] : [-(_1230425 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24579 ^ [_1230291, _1230293, _1230295, _1230425]), 24576 ^ [_1230291, _1230293, _1230295, _1230425]))], (24578 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24576 ^ [_1230291, _1230293, _1230295, _1230425]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1230291))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230425), _1230295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1230425), _1230291)), _1230295)))]]], (35608 ^ _780119) ^ [_1453181, _1453183, _1453185, _1453187] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1453181, tc_HOL_Obool)), _1453183), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1453181), _1453185), _1453187))), 35612 ^ _780119 : [(35615 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1453181), 35611 ^ [_1453181, _1453183, _1453185, _1453187]), _1453185)))], (35613 ^ _780119) ^ [] : [-(_1453183 = hAPP(c_Relation_OImage(_1453181, _1453181, _1453187), hAPP(hAPP(c_Set_Oinsert(_1453181), 35611 ^ [_1453181, _1453183, _1453185, _1453187]), c_Orderings_Obot__class_Obot(tc_fun(_1453181, tc_HOL_Obool)))))]]], (31567 ^ _780119) ^ [_1369661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369661), 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), _1369661)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (35093 ^ _780119) ^ [_1439664, _1439666, _1439668] : [class_Rings_Osemiring__1(_1439664), hBOOL(hAPP(hAPP(c_member(_1439664), _1439666), c_Nat_Osemiring__1__class_ONats(_1439664))), hBOOL(hAPP(hAPP(c_member(_1439664), _1439668), c_Nat_Osemiring__1__class_ONats(_1439664))), -(hBOOL(hAPP(hAPP(c_member(_1439664), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1439664), _1439666), _1439668)), c_Nat_Osemiring__1__class_ONats(_1439664))))], (31479 ^ _780119) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (13883 ^ _780119) ^ [_1032476, _1032478, _1032480] : [class_Lattices_Oboolean__algebra(_1032476), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032476), _1032478), _1032480) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1032476), _1032478), hAPP(c_Groups_Ouminus__class_Ouminus(_1032476), _1032480)))], (31527 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (27878 ^ _780119) ^ [_1294887, _1294889, _1294891, _1294893] : [class_Orderings_Olinorder(_1294887), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294887), _1294889), _1294891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294887), _1294889), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1294887), _1294893), _1294891))))], (47552 ^ _780119) ^ [_1739081, _1739083] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739081)), hAPP(c_List_Orev(_1739081), _1739083)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739081)), _1739083))], (33347 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (17011 ^ _780119) ^ [_1089111, _1089113, _1089115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1089111), _1089113)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1089115), _1089113))), 17014 ^ _780119 : [(17017 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1089111), _1089115)))], (17015 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1089113)))]]], (47624 ^ _780119) ^ [_1740617, _1740619] : [-(_1740617 = c_List_Olist_ONil(_1740619)), -(c_List_Olast(_1740619, hAPP(c_List_Orev(_1740619), _1740617)) = hAPP(c_List_Ohd(_1740619), _1740617))], (30399 ^ _780119) ^ [_1348318, _1348320, _1348322] : [class_Int_Onumber__ring(_1348318), -(hAPP(c_Int_Onumber__class_Onumber__of(_1348318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1348320), _1348322)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348318), hAPP(c_Int_Onumber__class_Onumber__of(_1348318), _1348320)), hAPP(c_Int_Onumber__class_Onumber__of(_1348318), _1348322)))], (1540 ^ _780119) ^ [_802093, _802095] : [-(class_Rings_Olinordered__semidom(_802093)), _802095 = _802093, class_Rings_Olinordered__semidom(_802095)], (42556 ^ _780119) ^ [_1622157, _1622159, _1622161] : [c_Fun_Oinj__on(_1622157, _1622159, _1622161, c_Orderings_Otop__class_Otop(tc_fun(_1622157, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1622157), tc_List_Olist(_1622159), hAPP(c_List_Omap(_1622157, _1622159), _1622161), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1622157), tc_HOL_Obool))))], (49558 ^ _780119) ^ [_1784711, _1784713, _1784715, _1784717, _1784719] : [hAPP(hAPP(c_List_Olist_OCons(_1784711), _1784713), _1784715) = hAPP(c_List_Ofilter(_1784711, _1784717), _1784719), 49563 ^ _780119 : [(49564 ^ _780119) ^ [] : [-(_1784719 = hAPP(hAPP(c_List_Oappend(_1784711), 49561 ^ [_1784711, _1784713, _1784715, _1784717, _1784719]), hAPP(hAPP(c_List_Olist_OCons(_1784711), _1784713), 49562 ^ [_1784711, _1784713, _1784715, _1784717, _1784719])))], (49572 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1784717, _1784713)))], (49566 ^ _780119) ^ [_1785025] : [hBOOL(hAPP(hAPP(c_member(_1784711), _1785025), hAPP(c_List_Oset(_1784711), 49561 ^ [_1784711, _1784713, _1784715, _1784717, _1784719]))), hBOOL(hAPP(_1784717, _1785025))], (49574 ^ _780119) ^ [] : [-(_1784715 = hAPP(c_List_Ofilter(_1784711, _1784717), 49562 ^ [_1784711, _1784713, _1784715, _1784717, _1784719]))]]], (23967 ^ _780119) ^ [_1218503, _1218505, _1218507] : [class_Orderings_Oorder(_1218503), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1218503, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1218503), _1218505)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218503, _1218505), _1218507)) = c_Orderings_Obot__class_Obot(tc_fun(_1218503, tc_HOL_Obool)))], (31531 ^ _780119) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27558 ^ _780119) ^ [_1289315, _1289317, _1289319] : [class_Orderings_Olinorder(_1289315), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289315), _1289317), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289315), _1289317), _1289319))))], (6739 ^ _780119) ^ [_890613, _890615, _890617, _890619] : [hBOOL(hAPP(hAPP(c_member(_890613), _890615), _890617)), -(hBOOL(hAPP(hAPP(c_member(_890613), _890615), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890613, tc_HOL_Obool)), _890619), _890617))))], (51511 ^ _780119) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (21366 ^ _780119) ^ [_1169331, _1169333, _1169335] : [class_Divides_Osemiring__div(_1169331), -(c_Divides_Odiv__class_Omod(_1169331, c_Divides_Odiv__class_Omod(_1169331, _1169333, _1169335), _1169335) = c_Divides_Odiv__class_Omod(_1169331, _1169333, _1169335))], (37908 ^ _780119) ^ [_1509319, _1509321, _1509323, _1509325, _1509327, _1509329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509319, _1509321), tc_HOL_Obool)), _1509323), hAPP(hAPP(c_Product__Type_OSigma(_1509319, _1509321), _1509325), hAPP(c_COMBK(tc_fun(_1509321, tc_HOL_Obool), _1509319), _1509327)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509321, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1509319, _1509321, _1509323), _1509329)), _1509327)))], (40462 ^ _780119) ^ [_1572764, _1572766, _1572768, _1572770, _1572772] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572764, _1572764)), hAPP(hAPP(c_Product__Type_OPair(_1572764, _1572764), _1572766), _1572768)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1572764, _1572764), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1572770)), _1572772))), 40466 ^ _780119 : [(40469 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572764, _1572764)), hAPP(hAPP(c_Product__Type_OPair(_1572764, _1572764), 40465 ^ [_1572764, _1572766, _1572768, _1572770, _1572772]), _1572768)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1572764, _1572764), tc_HOL_Obool), _1572770), _1572772))))], (40467 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572764, _1572764)), hAPP(hAPP(c_Product__Type_OPair(_1572764, _1572764), _1572766), 40465 ^ [_1572764, _1572766, _1572768, _1572770, _1572772])), _1572772)))]]], (25670 ^ _780119) ^ [_1248944, _1248946] : [c_Nat__Transfer_Ois__nat(_1248944), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1248944), _1248946)))], (38210 ^ _780119) ^ [_1518490, _1518492, _1518494] : [c_Relation_Orefl__on(_1518490, _1518492, _1518494), 38213 ^ _780119 : [(38216 ^ _780119) ^ [_1518672] : [hBOOL(hAPP(hAPP(c_member(_1518490), _1518672), _1518492)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1518490, _1518490)), hAPP(hAPP(c_Product__Type_OPair(_1518490, _1518490), _1518672), _1518672)), _1518494)))], (38214 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518490, _1518490), tc_HOL_Obool)), _1518494), hAPP(hAPP(c_Product__Type_OSigma(_1518490, _1518490), _1518492), hAPP(c_COMBK(tc_fun(_1518490, tc_HOL_Obool), _1518490), _1518492)))))]]], (51137 ^ _780119) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (41581 ^ _780119) ^ [_1599510, _1599512, _1599514, _1599516, _1599518] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599510, tc_fun(_1599512, tc_HOL_Obool)), _1599514), _1599516), _1599518)), 41584 ^ _780119 : [(41585 ^ _780119) ^ [_1599619] : [hBOOL(hAPP(hAPP(c_member(_1599510), _1599619), _1599514)), -(hBOOL(hAPP(hAPP(_1599516, _1599619), _1599518)))]]], (16664 ^ _780119) ^ [_1083465] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1083465, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1083465, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1083465, tc_HOL_Obool)))], (6057 ^ _780119) ^ [_876584, _876586, _876588, _876590, _876592, _876594] : [-(hAPP(c_Set_Oimage(_876584, _876586, _876588), hAPP(c_Set_Oimage(_876590, _876584, _876592), _876594)) = hAPP(c_Set_Oimage(_876590, _876586, hAPP(hAPP(c_COMBB(_876584, _876586, _876590), _876588), _876592)), _876594))], (26071 ^ _780119) ^ [_1255436, _1255438, _1255440] : [26073 ^ _780119 : [(26076 ^ _780119) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1255440, 26072 ^ [_1255436, _1255438, _1255440]))], (26074 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1255436), 26072 ^ [_1255436, _1255438, _1255440]), _1255438)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1255436, tc_Int_Oint), _1255440), _1255438) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1255436, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1255436), c_Int_Onat), _1255440)), _1255438)))], (48992 ^ _780119) ^ [_1771256, _1771258, _1771260, _1771262, _1771264, _1771266, _1771268] : [c_List_Olist__all2(_1771256, _1771258, _1771260, hAPP(hAPP(c_List_Olist_OCons(_1771256), _1771262), _1771264), hAPP(hAPP(c_List_Olist_OCons(_1771258), _1771266), _1771268)), 48995 ^ _780119 : [(48998 ^ _780119) ^ [] : [-(c_List_Olist__all2(_1771256, _1771258, _1771260, _1771264, _1771268))], (48996 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1771260, _1771262), _1771266)))]]], (7974 ^ _780119) ^ [_916127, _916129] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916127, tc_HOL_Obool)), _916129), c_Orderings_Obot__class_Obot(tc_fun(_916127, tc_HOL_Obool))) = _916129)], (6821 ^ _780119) ^ [_892318, _892320, _892322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892318, tc_HOL_Obool)), _892320), _892322)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892318, tc_HOL_Obool)), _892322), _892320) = _892322)], (32761 ^ _780119) ^ [_1390747] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1390747), 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), _1390747), _1390747))], (47790 ^ _780119) ^ [_1745630, _1745632, _1745634, _1745636, _1745638] : [-(hAPP(hAPP(c_List_Ozip(_1745630, _1745632), c_List_OtakeWhile(_1745630, _1745634, _1745636)), _1745638) = c_List_OtakeWhile(tc_prod(_1745630, _1745632), hAPP(c_Fun_Ocomp(_1745630, tc_HOL_Obool, tc_prod(_1745630, _1745632), _1745634), c_Product__Type_Ofst(_1745630, _1745632)), hAPP(hAPP(c_List_Ozip(_1745630, _1745632), _1745636), _1745638)))], (39667 ^ _780119) ^ [_1553027, _1553029, _1553031] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1553027, _1553027, _1553029), c_Relation_OId(_1553027)), _1553031) = _1553031)], (31939 ^ _780119) ^ [_1375495, _1375497] : [class_Int_Onumber__ring(_1375495), class_Rings_Olinordered__idom(_1375495), 31946 ^ _780119 : [(31953 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1375497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375495), c_Groups_Oone__class_Oone(_1375495)), hAPP(c_Int_Onumber__class_Onumber__of(_1375495), _1375497))))], (31947 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375495), c_Groups_Oone__class_Oone(_1375495)), hAPP(c_Int_Onumber__class_Onumber__of(_1375495), _1375497))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1375497)))]]], (51665 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), v_F), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), 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))), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))))], (26425 ^ _780119) ^ [_1262293, _1262295, _1262297] : [class_Groups_Oordered__ab__group__add__abs(_1262293), -(hAPP(c_Groups_Oabs__class_Oabs(_1262293), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1262293), hAPP(c_Groups_Oabs__class_Oabs(_1262293), _1262295)), hAPP(c_Groups_Oabs__class_Oabs(_1262293), _1262297))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1262293), hAPP(c_Groups_Oabs__class_Oabs(_1262293), _1262295)), hAPP(c_Groups_Oabs__class_Oabs(_1262293), _1262297)))], (47945 ^ _780119) ^ [_1748664, _1748666] : [c_List_Olist_ONil(_1748664) = c_List_Oremdups(_1748664, _1748666), -(_1748666 = c_List_Olist_ONil(_1748664))], (18135 ^ _780119) ^ [_1110287, _1110289, _1110291, _1110293, _1110295] : [class_Groups_Ocomm__monoid__add(_1110287), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110289), _1110291)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1110289, _1110287), _1110293), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1110289, tc_HOL_Obool)), _1110291), _1110295)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1110289, _1110287), hAPP(hAPP(c_COMBC(_1110289, _1110287, _1110287), hAPP(hAPP(c_COMBS(_1110289, _1110287, tc_fun(_1110287, _1110287)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1110287, tc_fun(_1110287, _1110287)), _1110289), c_If(_1110287)), hAPP(hAPP(c_COMBC(_1110289, tc_fun(_1110289, tc_HOL_Obool), tc_HOL_Obool), c_member(_1110289)), _1110295))), _1110293)), c_Groups_Ozero__class_Ozero(_1110287))), _1110291))], (1690 ^ _780119) ^ [_803968, _803970] : [-(class_Groups_Omonoid__mult(_803968)), _803970 = _803968, class_Groups_Omonoid__mult(_803970)], (10032 ^ _780119) ^ [_954825, _954827, _954829] : [class_Lattices_Osemilattice__inf(_954825), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954825), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954825), _954827), _954829)), _954827)))], (6899 ^ _780119) ^ [_894147, _894149, _894151] : [class_Orderings_Oorder(_894147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894147), _894149), _894151)), 6906 ^ _780119 : [(6913 ^ _780119) ^ [] : [_894151 = _894149, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894147), _894151), _894149)))], (6907 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894147), _894151), _894149)), -(_894151 = _894149)]]], (22203 ^ _780119) ^ [_1185416, _1185418, _1185420] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185416), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1185418, _1185420)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185416), _1185418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185416), _1185420)))], (154 ^ _780119) ^ [_782728, _782730] : [-(class_Rings_Odivision__ring__inverse__zero(_782728)), _782730 = _782728, class_Rings_Odivision__ring__inverse__zero(_782730)], (3724 ^ _780119) ^ [_836142, _836144, _836146, _836148, _836150, _836152] : [-(c_List_Osublist(_836152, _836148, _836144) = c_List_Osublist(_836150, _836146, _836142)), _836152 = _836150, _836148 = _836146, _836144 = _836142], (51209 ^ _780119) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (32061 ^ _780119) ^ [_1377567, _1377569] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377567)))), _1377569) = 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)))), _1377567)), _1377569))], (51601 ^ _780119) ^ [_1820820, _1820822] : [hBOOL(hAPP(hAPP(c_fconj, _1820820), _1820822)), -(hBOOL(_1820820))], (9914 ^ _780119) ^ [_952797, _952799, _952801, _952803] : [class_Lattices_Osemilattice__inf(_952797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952797), _952799), _952801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952797), _952799), _952803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952797), _952799), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952797), _952801), _952803))))], (42741 ^ _780119) ^ [_1626528, _1626530, _1626532, _1626534] : [-(hAPP(c_Map_Omap__of(_1626528, _1626530), hAPP(hAPP(c_List_Omap(_1626528, tc_prod(_1626528, _1626530)), hAPP(hAPP(c_COMBS(_1626528, _1626530, tc_prod(_1626528, _1626530)), c_Product__Type_OPair(_1626528, _1626530)), _1626532)), _1626534)) = c_Map_Orestrict__map(_1626528, _1626530, hAPP(c_Fun_Ocomp(_1626530, tc_Option_Ooption(_1626530), _1626528, c_Option_Ooption_OSome(_1626530)), _1626532), hAPP(c_List_Oset(_1626528), _1626534)))], (48247 ^ _780119) ^ [_1755649, _1755651, _1755653] : [-(c_Enum_Osublists(_1755649, hAPP(hAPP(c_List_Olist_OCons(_1755649), _1755651), _1755653)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1755649)), tc_List_Olist(tc_List_Olist(_1755649))), c_Enum_Osublists(_1755649, _1755653)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1755649)), tc_List_Olist(tc_List_Olist(_1755649)), tc_List_Olist(tc_List_Olist(_1755649))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1755649)), tc_fun(tc_List_Olist(tc_List_Olist(_1755649)), tc_List_Olist(tc_List_Olist(_1755649))), tc_List_Olist(tc_List_Olist(_1755649))), c_List_Oappend(tc_List_Olist(_1755649))), hAPP(c_List_Omap(tc_List_Olist(_1755649), tc_List_Olist(_1755649)), hAPP(c_List_Olist_OCons(_1755649), _1755651)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1755649))))))], (38756 ^ _780119) ^ [_1531071, _1531073, _1531075, _1531077, _1531079, _1531081] : [c_Fun_Oinj__on(_1531071, _1531073, hAPP(c_Fun_Ocomp(_1531075, _1531073, _1531071, _1531077), _1531079), _1531081), -(c_Fun_Oinj__on(_1531071, _1531075, _1531079, _1531081))], (21835 ^ _780119) ^ [_1178815, _1178817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178815), _1178817)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178815, _1178817) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178815), _1178817))], (41820 ^ _780119) ^ [_1605148, _1605150] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1605148, tc_HOL_Obool), _1605150) = hAPP(c_Set_OCollect(_1605148), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1605148, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1605148), c_HOL_OAll(tc_fun(_1605148, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1605148, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1605148, tc_HOL_Obool), tc_HOL_Obool), _1605148), hAPP(c_COMBS(tc_fun(_1605148, 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(_1605148, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1605148, tc_HOL_Obool), tc_fun(tc_fun(_1605148, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1605148, tc_HOL_Obool))), _1605150)))), c_member(_1605148)))))], (24988 ^ _780119) ^ [_1237927] : [-(hBOOL(hAPP(_1237927, 24995 ^ [_1237927]))), 24989 ^ _780119 : [(24990 ^ _780119) ^ [_1237979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237979)), hBOOL(hAPP(_1237927, hAPP(c_Int_Onat, _1237979)))]]], (36017 ^ _780119) ^ [_1462581, _1462583, _1462585, _1462587, _1462589, _1462591, _1462593, _1462595, _1462597, _1462599, _1462601] : [c_Equiv__Relations_Oequiv(_1462581, _1462583, _1462585), c_Equiv__Relations_Oequiv(_1462587, _1462589, _1462591), c_Equiv__Relations_Ocongruent2(_1462581, _1462587, tc_fun(_1462593, tc_HOL_Obool), _1462585, _1462591, _1462595), hBOOL(hAPP(hAPP(c_member(tc_fun(_1462581, tc_HOL_Obool)), _1462597), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462581), _1462583), _1462585))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1462587, tc_HOL_Obool)), _1462599), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462587), _1462589), _1462591))), 36039 ^ _780119 : [(36043 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1462587), 36041 ^ [_1462581, _1462583, _1462585, _1462587, _1462589, _1462591, _1462593, _1462595, _1462597, _1462599, _1462601]), _1462589)))], (36045 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1462593, tc_HOL_Obool)), hAPP(hAPP(_1462595, 36038 ^ [_1462581, _1462583, _1462585, _1462587, _1462589, _1462591, _1462593, _1462595, _1462597, _1462599, _1462601]), 36041 ^ [_1462581, _1462583, _1462585, _1462587, _1462589, _1462591, _1462593, _1462595, _1462597, _1462599, _1462601])), _1462601))], (36040 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1462581), 36038 ^ [_1462581, _1462583, _1462585, _1462587, _1462589, _1462591, _1462593, _1462595, _1462597, _1462599, _1462601]), _1462583)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1462593, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1462581, tc_fun(_1462593, tc_HOL_Obool)), _1462597), hAPP(hAPP(c_COMBB(tc_fun(_1462587, tc_fun(_1462593, tc_HOL_Obool)), tc_fun(_1462593, tc_HOL_Obool), _1462581), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1462587, tc_fun(_1462593, tc_HOL_Obool)), _1462599)), _1462595))), _1462601)))], (30301 ^ _780119) ^ [_1346433, _1346435, _1346437] : [class_Int_Onumber__ring(_1346433), class_Rings_Olinordered__idom(_1346433), 30308 ^ _780119 : [(30315 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1346435), _1346437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346433), hAPP(c_Int_Onumber__class_Onumber__of(_1346433), _1346435)), hAPP(c_Int_Onumber__class_Onumber__of(_1346433), _1346437))))], (30309 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346433), hAPP(c_Int_Onumber__class_Onumber__of(_1346433), _1346435)), hAPP(c_Int_Onumber__class_Onumber__of(_1346433), _1346437))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1346435), _1346437)))]]], (25560 ^ _780119) ^ [_1247450, _1247452, _1247454] : [class_Int_Oring__char__0(_1247450), 25563 ^ _780119 : [(25570 ^ _780119) ^ [] : [_1247452 = _1247454, -(hAPP(c_Int_Oring__1__class_Oof__int(_1247450), _1247452) = hAPP(c_Int_Oring__1__class_Oof__int(_1247450), _1247454))], (25564 ^ _780119) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1247450), _1247452) = hAPP(c_Int_Oring__1__class_Oof__int(_1247450), _1247454), -(_1247452 = _1247454)]]], (25494 ^ _780119) ^ [_1246334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246334)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1246334)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1246334)))], (5761 ^ _780119) ^ [_871269, _871271, _871273, _871275] : [c_Hoare__Mirabelle_Ohoare__derivs(_871269, _871271, _871273), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_871269), tc_HOL_Obool)), _871275), _871273)), -(c_Hoare__Mirabelle_Ohoare__derivs(_871269, _871271, _871275))], (3042 ^ _780119) ^ [_825493, _825495, _825497, _825499, _825501, _825503] : [-(c_Nitpick_Oof__frac(_825503, _825499, _825495) = c_Nitpick_Oof__frac(_825501, _825497, _825493)), _825503 = _825501, _825499 = _825497, _825495 = _825493], (45195 ^ _780119) ^ [_1686023, _1686025, _1686027, _1686029] : [-(hAPP(c_Map_Omap__of(_1686023, _1686025), hAPP(hAPP(c_List_Oappend(tc_prod(_1686023, _1686025)), _1686027), _1686029)) = c_Map_Omap__add(_1686023, _1686025, hAPP(c_Map_Omap__of(_1686023, _1686025), _1686029), hAPP(c_Map_Omap__of(_1686023, _1686025), _1686027)))], (17880 ^ _780119) ^ [_1105278, _1105280, _1105282, _1105284, _1105286] : [class_Groups_Ocomm__monoid__add(_1105278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105280), _1105282)), 17887 ^ _780119 : [(17894 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1105280), _1105284), _1105282))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105280, _1105278), hAPP(hAPP(c_COMBC(_1105280, _1105278, _1105278), hAPP(hAPP(c_COMBS(_1105280, _1105278, tc_fun(_1105278, _1105278)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1105278, tc_fun(_1105278, _1105278)), _1105280), c_If(_1105278)), hAPP(c_fequal, _1105284))), _1105286)), c_Groups_Ozero__class_Ozero(_1105278))), _1105282) = c_Groups_Ozero__class_Ozero(_1105278))], (17888 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1105280), _1105284), _1105282)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105280, _1105278), hAPP(hAPP(c_COMBC(_1105280, _1105278, _1105278), hAPP(hAPP(c_COMBS(_1105280, _1105278, tc_fun(_1105278, _1105278)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1105278, tc_fun(_1105278, _1105278)), _1105280), c_If(_1105278)), hAPP(c_fequal, _1105284))), _1105286)), c_Groups_Ozero__class_Ozero(_1105278))), _1105282) = hAPP(_1105286, _1105284))]]], (37548 ^ _780119) ^ [_1498779, _1498781] : [-(hAPP(c_Relation_ORange(_1498779, _1498781), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1498779, _1498781), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1498781, tc_HOL_Obool)))], (46670 ^ _780119) ^ [_1720912, _1720914, _1720916] : [-(hAPP(c_List_Oset(_1720912), hAPP(c_List_Ofilter(_1720912, _1720914), _1720916)) = hAPP(c_Set_OCollect(_1720912), hAPP(hAPP(c_COMBS(_1720912, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1720912), c_fconj), hAPP(hAPP(c_COMBC(_1720912, tc_fun(_1720912, tc_HOL_Obool), tc_HOL_Obool), c_member(_1720912)), hAPP(c_List_Oset(_1720912), _1720916)))), _1720914)))], (18796 ^ _780119) ^ [] : [-(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))))], (31141 ^ _780119) ^ [_1362403, _1362405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1362403), _1362405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362403)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362405))))], (49016 ^ _780119) ^ [_1771793, _1771795, _1771797, _1771799, _1771801, _1771803, _1771805] : [c_List_Olist__all2(_1771799, _1771795, hAPP(hAPP(c_COMBB(_1771793, tc_fun(_1771795, tc_HOL_Obool), _1771799), _1771797), _1771801), _1771803, _1771805), -(c_List_Olist__all2(_1771793, _1771795, _1771797, hAPP(hAPP(c_List_Omap(_1771799, _1771793), _1771801), _1771803), _1771805))], (22137 ^ _780119) ^ [_1184397, _1184399] : [class_Rings_Olinordered__idom(_1184397), 22140 ^ _780119 : [(22147 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184397), _1184399), c_Groups_Ozero__class_Ozero(_1184397))), -(c_Groups_Osgn__class_Osgn(_1184397, _1184399) = hAPP(c_Groups_Ouminus__class_Ouminus(_1184397), c_Groups_Oone__class_Oone(_1184397)))], (22141 ^ _780119) ^ [] : [c_Groups_Osgn__class_Osgn(_1184397, _1184399) = hAPP(c_Groups_Ouminus__class_Ouminus(_1184397), c_Groups_Oone__class_Oone(_1184397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184397), _1184399), c_Groups_Ozero__class_Ozero(_1184397))))]]], (47182 ^ _780119) ^ [_1730893, _1730895, _1730897, _1730899] : [-(c_List_Oupt(_1730893, _1730895) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1730897), _1730899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730893), _1730895)), _1730893 = _1730897, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1730893), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1730895) = _1730899], (12323 ^ _780119) ^ [_1003066, _1003068, _1003070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003066), _1003068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003070), _1003068))))], (5919 ^ _780119) ^ [_874216, _874218, _874220, _874222] : [_874216 = _874218, hBOOL(hAPP(hAPP(c_member(_874220), _874218), _874222)), -(hBOOL(hAPP(hAPP(c_member(_874220), _874216), _874222)))], (5877 ^ _780119) ^ [_873455, _873457, _873459, _873461] : [_873455 = c_Orderings_Obot__class_Obot(tc_fun(_873457, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_873457, _873459, hAPP(c_COMBK(_873459, _873457), _873461)), _873455) = c_Orderings_Obot__class_Obot(tc_fun(_873459, tc_HOL_Obool)))], (19660 ^ _780119) ^ [_1137593, _1137595] : [-(hBOOL(hAPP(_1137593, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1137593, _1137595)), 19668 ^ _780119 : [(19677 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1137593, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19667 ^ [_1137593, _1137595]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (19671 ^ _780119) ^ [_1137831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1137831), 19667 ^ [_1137593, _1137595])), hBOOL(hAPP(_1137593, _1137831))], (19669 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19667 ^ [_1137593, _1137595]), _1137595)))]]], (14048 ^ _780119) ^ [_1035913, _1035915, _1035917] : [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, _1035913)), _1035915)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1035913)), _1035917))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035915), _1035917)))], (49713 ^ _780119) ^ [_1787903, _1787905] : [c_List_Olist__ex(_1787903, _1787905, c_List_Olist_ONil(_1787903))], (34040 ^ _780119) ^ [_1419232, _1419234, _1419236, _1419238] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1419232, _1419234, _1419236), hAPP(hAPP(c_COMBB(tc_fun(_1419234, tc_prod(_1419232, _1419234)), tc_fun(_1419234, _1419236), _1419232), hAPP(c_COMBB(tc_prod(_1419232, _1419234), _1419236, _1419234), _1419238)), c_Product__Type_OPair(_1419232, _1419234))) = _1419238)], (51205 ^ _780119) ^ [] : [-(class_HOL_Oequal(tc_Int_Oint))], (16756 ^ _780119) ^ [_1085038, _1085040] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1085038), hAPP(c_Nat_OSuc, _1085040)))), 16757 ^ _780119 : [(16760 ^ _780119) ^ [_1085126] : [_1085038 = hAPP(c_Nat_OSuc, _1085126), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1085126), _1085040))], (16758 ^ _780119) ^ [] : [_1085038 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (45237 ^ _780119) ^ [_1687167, _1687169, _1687171, _1687173] : [-(hAPP(hAPP(c_List_Onth(_1687167), hAPP(hAPP(c_List_Oappend(_1687167), _1687169), _1687171)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687167)), _1687169)), _1687173)) = hAPP(hAPP(c_List_Onth(_1687167), _1687171), _1687173))], (42972 ^ _780119) ^ [_1631981, _1631983] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1631981, _1631983) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1631981), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1631983)))], (9262 ^ _780119) ^ [_939300, _939302, _939304, _939306, _939308, _939310, _939312] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_939300, tc_Option_Ooption(_939302)), _939304), _939306), hAPP(c_Option_Ooption_OSome(_939302), _939308)), _939310) = hAPP(c_Option_Ooption_OSome(_939302), _939312), 9267 ^ _780119 : [(9270 ^ _780119) ^ [] : [-(_939308 = _939312)], (9268 ^ _780119) ^ [] : [-(_939310 = _939306)]], 9271 ^ _780119 : [(9274 ^ _780119) ^ [] : [-(hAPP(_939304, _939310) = hAPP(c_Option_Ooption_OSome(_939302), _939312))], (9272 ^ _780119) ^ [] : [_939310 = _939306]]], (34355 ^ _780119) ^ [_1424916, _1424918] : [-(c_Divides_Odivmod__nat(_1424918, _1424916) = 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), _1424918), _1424916), _1424916))), -(_1424916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1424918), _1424916)))], (51279 ^ _780119) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (37793 ^ _780119) ^ [_1505931, _1505933, _1505935, _1505937, _1505939] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1505931, _1505933), _1505935), hAPP(hAPP(c_COMBS(_1505931, tc_fun(_1505933, tc_HOL_Obool), tc_fun(_1505933, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505933, tc_HOL_Obool), tc_fun(tc_fun(_1505933, tc_HOL_Obool), tc_fun(_1505933, tc_HOL_Obool)), _1505931), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1505933, tc_HOL_Obool))), _1505937)), _1505939)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1505931, _1505933), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1505931, _1505933), _1505935), _1505937)), hAPP(hAPP(c_Product__Type_OSigma(_1505931, _1505933), _1505935), _1505939)))], (37825 ^ _780119) ^ [_1506967, _1506969, _1506971, _1506973, _1506975] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1506967, _1506969), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506967, tc_HOL_Obool)), _1506971), _1506973)), hAPP(c_COMBK(tc_fun(_1506969, tc_HOL_Obool), _1506967), _1506975)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1506967, _1506969), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1506967, _1506969), _1506971), hAPP(c_COMBK(tc_fun(_1506969, tc_HOL_Obool), _1506967), _1506975))), hAPP(hAPP(c_Product__Type_OSigma(_1506967, _1506969), _1506973), hAPP(c_COMBK(tc_fun(_1506969, tc_HOL_Obool), _1506967), _1506975))))], (35289 ^ _780119) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (26765 ^ _780119) ^ [_1269181, _1269183, _1269185] : [hBOOL(hAPP(_1269181, _1269183)), -(hAPP(c_Set_OCollect(_1269185), hAPP(hAPP(c_COMBS(_1269185, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1269185), c_fconj), hAPP(hAPP(c_COMBC(_1269185, _1269185, tc_HOL_Obool), c_fequal), _1269183))), _1269181)) = hAPP(hAPP(c_Set_Oinsert(_1269185), _1269183), c_Orderings_Obot__class_Obot(tc_fun(_1269185, tc_HOL_Obool))))], (37934 ^ _780119) ^ [_1509828, _1509830, _1509832, _1509834] : [-(hAPP(c_Set_OCollect(tc_prod(_1509828, _1509830)), hAPP(c_Product__Type_Oprod_Oprod__case(_1509828, _1509830, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1509828, tc_fun(_1509830, tc_HOL_Obool), tc_fun(_1509830, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1509830, tc_HOL_Obool), tc_fun(_1509830, tc_HOL_Obool)), _1509828), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1509830)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509828), c_fconj), _1509832))), _1509834))) = hAPP(hAPP(c_Product__Type_OSigma(_1509828, _1509830), hAPP(c_Set_OCollect(_1509828), _1509832)), hAPP(c_COMBK(tc_fun(_1509830, tc_HOL_Obool), _1509828), hAPP(c_Set_OCollect(_1509830), _1509834))))], (46073 ^ _780119) ^ [_1708002, _1708004, _1708006] : [class_Lattices_Olattice(_1708002), -(c_Big__Operators_Olattice__class_OSup__fin(_1708002, hAPP(c_List_Oset(_1708002), hAPP(hAPP(c_List_Olist_OCons(_1708002), _1708004), _1708006))) = hAPP(c_List_Ofoldl(_1708002, _1708002, c_Lattices_Osemilattice__sup__class_Osup(_1708002), _1708004), _1708006))], (15050 ^ _780119) ^ [_1055815, _1055817] : [class_Rings_Omult__zero(_1055815), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055815), c_Groups_Ozero__class_Ozero(_1055815)), _1055817) = c_Groups_Ozero__class_Ozero(_1055815))], (27888 ^ _780119) ^ [_1295066, _1295068, _1295070, _1295072] : [class_Orderings_Olinorder(_1295066), 27891 ^ _780119 : [(27892 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295066), _1295068), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1295066), _1295070), _1295072))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295066), _1295068), _1295070))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295066), _1295068), _1295072)))], (27902 ^ _780119) ^ [] : [27903 ^ _780119 : [(27906 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295066), _1295068), _1295072))], (27904 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295066), _1295068), _1295070))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295066), _1295068), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1295066), _1295070), _1295072))))]]], (598 ^ _780119) ^ [_789288, _789290, _789292, _789294, _789296, _789298] : [-(c_Nitpick_Oless__frac(_789296, _789292, _789288)), c_Nitpick_Oless__frac(_789298, _789294, _789290), _789298 = _789296, _789294 = _789292, _789290 = _789288], (51443 ^ _780119) ^ [_1819100, _1819102] : [-(class_Nat_Osize(tc_prod(_1819100, _1819102)))], (17790 ^ _780119) ^ [_1103548, _1103550] : [-(_1103548 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1103550), _1103548) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103550), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1103550), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103548), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (44562 ^ _780119) ^ [_1672857, _1672859, _1672861, _1672863, _1672865, _1672867, _1672869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672857)), _1672859)), _1672861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672861), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672863)), _1672865))), -(c_Map_Omap__upds(_1672857, _1672863, _1672867, _1672859, hAPP(hAPP(c_List_Olist__update(_1672863, _1672865), _1672861), _1672869)) = c_Map_Omap__upds(_1672857, _1672863, _1672867, _1672859, _1672865))], (10170 ^ _780119) ^ [_957641, _957643] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957641, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_957641, tc_HOL_Obool))), _957643) = c_Orderings_Obot__class_Obot(tc_fun(_957641, tc_HOL_Obool)))], (8392 ^ _780119) ^ [_925492, _925494, _925496, _925498, _925500, _925502, _925504] : [hBOOL(hAPP(hAPP(c_member(_925492), _925494), _925496)), c_Nitpick_Ofold__graph_H(_925492, _925498, _925500, _925502, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925492, tc_HOL_Obool)), _925496), hAPP(hAPP(c_Set_Oinsert(_925492), _925494), c_Orderings_Obot__class_Obot(tc_fun(_925492, tc_HOL_Obool)))), _925504), -(c_Nitpick_Ofold__graph_H(_925492, _925498, _925500, _925502, _925496, hAPP(hAPP(_925500, _925494), _925504)))], (23489 ^ _780119) ^ [_1209609, _1209611, _1209613, _1209615] : [class_Orderings_Oorder(_1209609), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1209609, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1209609, _1209611), _1209613)), c_SetInterval_Oord__class_OatLeastAtMost(_1209609, _1209613, _1209615)) = c_Orderings_Obot__class_Obot(tc_fun(_1209609, tc_HOL_Obool)))], (20534 ^ _780119) ^ [_1153563, _1153565, _1153567, _1153569] : [class_Fields_Ofield__inverse__zero(_1153563), 20537 ^ _780119 : [(20538 ^ _780119) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153563), _1153565), _1153567) = _1153569, 20541 ^ _780119 : [(20548 ^ _780119) ^ [] : [_1153567 = c_Groups_Ozero__class_Ozero(_1153563), -(_1153569 = c_Groups_Ozero__class_Ozero(_1153563))], (20542 ^ _780119) ^ [] : [-(_1153567 = c_Groups_Ozero__class_Ozero(_1153563)), -(_1153565 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153563), _1153569), _1153567))]]], (20554 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153563), _1153565), _1153567) = _1153569), 20557 ^ _780119 : [(20560 ^ _780119) ^ [] : [_1153565 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153563), _1153569), _1153567)], (20558 ^ _780119) ^ [] : [_1153567 = c_Groups_Ozero__class_Ozero(_1153563)]], 20561 ^ _780119 : [(20564 ^ _780119) ^ [] : [_1153569 = c_Groups_Ozero__class_Ozero(_1153563)], (20562 ^ _780119) ^ [] : [-(_1153567 = c_Groups_Ozero__class_Ozero(_1153563))]]]]], (41635 ^ _780119) ^ [_1601058, _1601060, _1601062, _1601064] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1601058, _1601060), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1601058, tc_HOL_Obool), _1601062)), _1601064) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1601058, tc_HOL_Obool), tc_fun(tc_prod(_1601058, _1601060), tc_HOL_Obool)), _1601062), hAPP(hAPP(c_COMBC(tc_fun(_1601058, tc_HOL_Obool), tc_fun(_1601058, tc_fun(_1601060, tc_HOL_Obool)), tc_fun(tc_prod(_1601058, _1601060), tc_HOL_Obool)), c_Product__Type_OSigma(_1601058, _1601060)), _1601064)))], (7826 ^ _780119) ^ [_913253, _913255, _913257, _913259, _913261] : [-(c_Option_Ooption_Ooption__rec(_913253, _913255, _913257, _913259, hAPP(c_Option_Ooption_OSome(_913255), _913261)) = hAPP(_913259, _913261))], (49431 ^ _780119) ^ [_1781450, _1781452, _1781454, _1781456] : [hAPP(c_List_Oset(_1781450), hAPP(hAPP(c_List_Omap(tc_prod(_1781450, _1781452), _1781450), c_Product__Type_Ofst(_1781450, _1781452)), _1781454)) = hAPP(c_List_Oset(_1781450), hAPP(hAPP(c_List_Omap(tc_prod(_1781450, _1781452), _1781450), c_Product__Type_Ofst(_1781450, _1781452)), _1781456)), 49437 ^ _780119 : [(49440 ^ _780119) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1781450, _1781452), _1781454), 49436 ^ [_1781450, _1781452, _1781454, _1781456]) = hAPP(hAPP(c_Map_Omap__of(_1781450, _1781452), _1781456), 49436 ^ [_1781450, _1781452, _1781454, _1781456])], (49438 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781450), 49436 ^ [_1781450, _1781452, _1781454, _1781456]), hAPP(c_List_Oset(_1781450), hAPP(hAPP(c_List_Omap(tc_prod(_1781450, _1781452), _1781450), c_Product__Type_Ofst(_1781450, _1781452)), _1781454)))))]], -(hAPP(c_Map_Omap__of(_1781450, _1781452), _1781454) = hAPP(c_Map_Omap__of(_1781450, _1781452), _1781456))], (30611 ^ _780119) ^ [_1352082, _1352084, _1352086, _1352088] : [class_Fields_Olinordered__field__inverse__zero(_1352082), class_Int_Onumber(_1352082), 30618 ^ _780119 : [(30619 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352082), _1352084), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086))), _1352088)), 30622 ^ _780119 : [(30629 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), c_Groups_Ozero__class_Ozero(_1352082)), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086)))), 30632 ^ _780119 : [(30639 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086)), c_Groups_Ozero__class_Ozero(_1352082)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), c_Groups_Ozero__class_Ozero(_1352082)), _1352088)))], (30633 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086)), c_Groups_Ozero__class_Ozero(_1352082))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1352082), _1352088), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086))), _1352084)))]]], (30623 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), c_Groups_Ozero__class_Ozero(_1352082)), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), _1352084), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1352082), _1352088), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086)))))]]], (30645 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352082), _1352084), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086))), _1352088))), 30648 ^ _780119 : [(30651 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), _1352084), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1352082), _1352088), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086))))], (30649 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), c_Groups_Ozero__class_Ozero(_1352082)), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086))))]], 30652 ^ _780119 : [(30655 ^ _780119) ^ [] : [30656 ^ _780119 : [(30659 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1352082), _1352088), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086))), _1352084))], (30657 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086)), c_Groups_Ozero__class_Ozero(_1352082))))]], 30660 ^ _780119 : [(30663 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), c_Groups_Ozero__class_Ozero(_1352082)), _1352088))], (30661 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086)), c_Groups_Ozero__class_Ozero(_1352082)))]]], (30653 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352082), c_Groups_Ozero__class_Ozero(_1352082)), hAPP(c_Int_Onumber__class_Onumber__of(_1352082), _1352086)))]]]]], (6767 ^ _780119) ^ [_891202, _891204, _891206] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_891202), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891202, tc_HOL_Obool)), _891204), _891206))), 6770 ^ _780119 : [(6773 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_891202), _891206)))], (6771 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_891202), _891204)))]]], (49610 ^ _780119) ^ [_1786041, _1786043, _1786045] : [class_Orderings_Olinorder(_1786041), 49616 ^ _780119 : [(49619 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1786041), _1786045), 49615 ^ [_1786041, _1786043, _1786045]))], (49617 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786041), 49615 ^ [_1786041, _1786043, _1786045]), hAPP(c_List_Oset(_1786041), _1786043))))]], c_List_Olinorder__class_Osorted(_1786041, _1786043), -(c_List_Olinorder__class_Osorted(_1786041, hAPP(hAPP(c_List_Olist_OCons(_1786041), _1786045), _1786043)))], (46286 ^ _780119) ^ [_1713262, _1713264, _1713266, _1713268, _1713270] : [class_Groups_Omonoid__add(_1713262), class_Groups_Oordered__ab__semigroup__add(_1713262), 46296 ^ _780119 : [(46299 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713262), hAPP(_1713268, 46295 ^ [_1713262, _1713264, _1713266, _1713268, _1713270])), hAPP(_1713270, 46295 ^ [_1713262, _1713264, _1713266, _1713268, _1713270])))], (46297 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1713264), 46295 ^ [_1713262, _1713264, _1713266, _1713268, _1713270]), hAPP(c_List_Oset(_1713264), _1713266))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713262), hAPP(c_List_Omonoid__add__class_Olistsum(_1713262), hAPP(hAPP(c_List_Omap(_1713264, _1713262), _1713268), _1713266))), hAPP(c_List_Omonoid__add__class_Olistsum(_1713262), hAPP(hAPP(c_List_Omap(_1713264, _1713262), _1713270), _1713266)))))], (32643 ^ _780119) ^ [_1388548, _1388550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1388548), _1388550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1388548)), c_Int_OBit0(_1388550))))], (33283 ^ _780119) ^ [_1400552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1400552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1400552))))], (15212 ^ _780119) ^ [_1058254, _1058256] : [15213 ^ _780119 : [(15216 ^ _780119) ^ [] : [_1058254 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15214 ^ _780119) ^ [] : [_1058256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1058254), _1058256) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21831 ^ _780119) ^ [_1178721, _1178723] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178721, _1178723) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178721), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1178721), _1178723)), _1178723)))], (42825 ^ _780119) ^ [_1628301, _1628303, _1628305, _1628307, _1628309] : [hAPP(hAPP(c_Map_Omap__of(_1628301, _1628303), _1628305), _1628307) = hAPP(c_Option_Ooption_OSome(_1628303), _1628309), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628301, _1628303)), hAPP(hAPP(c_Product__Type_OPair(_1628301, _1628303), _1628307), _1628309)), hAPP(c_List_Oset(tc_prod(_1628301, _1628303)), _1628305))))], (15568 ^ _780119) ^ [_1063870, _1063872, _1063874, _1063876] : [class_Groups_Oordered__comm__monoid__add(_1063870), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063870), c_Groups_Ozero__class_Ozero(_1063870)), _1063872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063870), _1063874), _1063876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063870), _1063874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063870), _1063872), _1063876))))], (43306 ^ _780119) ^ [_1640483, _1640485, _1640487] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1640483), _1640485)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1640483)), hAPP(c_Set_OCollect(tc_List_Olist(_1640483)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1640483), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1640483)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1640483), tc_fun(_1640483, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1640483, tc_HOL_Obool), tc_fun(tc_fun(_1640483, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1640483)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1640483, tc_HOL_Obool))), c_List_Oset(_1640483))), _1640485))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1640483), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1640483)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1640483)))), _1640487))))))], (33411 ^ _780119) ^ [_1402518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1402518)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1402518), c_Int_OMin)))], (22970 ^ _780119) ^ [_1199608, _1199610, _1199612] : [class_Rings_Olinordered__semidom(_1199608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199608), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1199608), _1199610)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1199608), _1199612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1199610), _1199612)))], (47849 ^ _780119) ^ [_1746801, _1746803, _1746805, _1746807] : [hBOOL(hAPP(_1746801, _1746803)), -(c_List_OtakeWhile(_1746805, _1746801, hAPP(hAPP(c_List_Olist_OCons(_1746805), _1746803), _1746807)) = hAPP(hAPP(c_List_Olist_OCons(_1746805), _1746803), c_List_OtakeWhile(_1746805, _1746801, _1746807)))], (44800 ^ _780119) ^ [_1677378, _1677380, _1677382] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1677378), tc_List_Olist(_1677378))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1677378), tc_List_Olist(_1677378)), _1677380), c_List_Olist_ONil(_1677378))), c_List_Olex(_1677378, _1677382)))], (4 ^ _780119) ^ [_780169, _780171] : [_780171 = _780169, -(_780169 = _780171)], (32017 ^ _780119) ^ [_1376802, _1376804, _1376806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376802), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376802)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376804)), _1376806)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34078 ^ _780119) ^ [_1420179, _1420181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420179), 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)), _1420181)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1420179, _1420181), c_Divides_OnegDivAlg(_1420179, _1420181))))], (6322 ^ _780119) ^ [_881643, _881645, _881647, _881649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881643, tc_HOL_Obool)), _881645), _881647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881643, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_881643), _881649), _881645)), hAPP(hAPP(c_Set_Oinsert(_881643), _881649), _881647))))], (41429 ^ _780119) ^ [_1596112, _1596114, _1596116, _1596118, _1596120] : [-(_1596112 = c_Orderings_Obot__class_Obot(tc_fun(_1596114, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596114, tc_fun(_1596116, tc_HOL_Obool)), _1596112), hAPP(hAPP(c_COMBB(tc_fun(_1596116, tc_HOL_Obool), tc_fun(_1596116, tc_HOL_Obool), _1596114), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1596116, tc_HOL_Obool)), _1596118)), _1596120)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1596116, tc_HOL_Obool)), _1596118), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596114, tc_fun(_1596116, tc_HOL_Obool)), _1596112), _1596120)))], (7136 ^ _780119) ^ [_898314, _898316, _898318] : [hAPP(hAPP(c_COMBC(_898314, tc_fun(_898314, tc_HOL_Obool), tc_HOL_Obool), c_member(_898314)), _898316) = hAPP(hAPP(c_COMBC(_898314, tc_fun(_898314, tc_HOL_Obool), tc_HOL_Obool), c_member(_898314)), _898318), -(_898316 = _898318)], (9752 ^ _780119) ^ [_949305, _949307, _949309, _949311] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949305, tc_HOL_Obool)), _949307), _949309), _949311)), -(hBOOL(hAPP(_949307, _949311)))], (37779 ^ _780119) ^ [_1505309, _1505311, _1505313] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1505309, _1505311), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1505309, _1505311), c_Orderings_Otop__class_Otop(tc_fun(_1505309, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1505311, tc_HOL_Obool), _1505309), _1505313))) = hAPP(hAPP(c_Product__Type_OSigma(_1505309, _1505311), c_Orderings_Otop__class_Otop(tc_fun(_1505309, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1505311, tc_HOL_Obool), _1505309), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1505311, tc_HOL_Obool)), _1505313))))], (46085 ^ _780119) ^ [_1708260, _1708262, _1708264] : [class_Orderings_Olinorder(_1708260), -(c_Big__Operators_Olinorder__class_OMin(_1708260, hAPP(c_List_Oset(_1708260), hAPP(hAPP(c_List_Olist_OCons(_1708260), _1708262), _1708264))) = hAPP(c_List_Ofoldl(_1708260, _1708260, c_Orderings_Oord__class_Omin(_1708260), _1708262), _1708264))], (44234 ^ _780119) ^ [_1666280, _1666282, _1666284] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1666280, tc_HOL_Obool)), hAPP(c_List_Oset(_1666280), hAPP(hAPP(c_List_Otake(_1666280), _1666282), _1666284))), hAPP(c_List_Oset(_1666280), _1666284))))], (31405 ^ _780119) ^ [_1367121, _1367123] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367121))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367121), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367123)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14298 ^ _780119) ^ [_1041489] : [-(hAPP(c_Nat_OSuc, _1041489) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1041489))], (31171 ^ _780119) ^ [_1362968, _1362970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1362968)), c_Int_OBit1(_1362970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1362968), _1362970)))], (42509 ^ _780119) ^ [_1620776, _1620778] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1620776), _1620778) = c_Smallcheck_Osmall_H(_1620776, hAPP(c_Code__Numeral_Oint__of, _1620778), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1620778))))], (1090 ^ _780119) ^ [_796468, _796470] : [-(class_Groups_Oordered__ab__group__add(_796468)), _796470 = _796468, class_Groups_Oordered__ab__group__add(_796470)], (33485 ^ _780119) ^ [_1403569] : [class_Int_Onumber__ring(_1403569), -(hAPP(c_Int_Oring__1__class_Oof__int(_1403569), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1403569), c_Int_OMin))], (2820 ^ _780119) ^ [_822060, _822062, _822064, _822066, _822068, _822070, _822072, _822074] : [-(c_Random_Oiterate(_822074, _822070, _822066, _822062) = c_Random_Oiterate(_822072, _822068, _822064, _822060)), _822074 = _822072, _822070 = _822068, _822066 = _822064, _822062 = _822060], (51539 ^ _780119) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (37513 ^ _780119) ^ [_1497978, _1497980, _1497982, _1497984] : [37515 ^ _780119 : [(37518 ^ _780119) ^ [] : [c_Wellfounded_Owf(_1497980, hAPP(_1497982, 37514 ^ [_1497978, _1497980, _1497982, _1497984]))], (37516 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1497978, 37514 ^ [_1497978, _1497980, _1497982, _1497984])))]], -(c_Wellfounded_Owf(tc_prod(_1497984, _1497980), c_Recdef_Osame__fst(_1497984, _1497980, _1497978, _1497982)))], (48237 ^ _780119) ^ [_1755421, _1755423] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1755421))), c_Enum_Osublists(_1755421, _1755423)) = 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(_1755421)), _1755423)))], (17949 ^ _780119) ^ [_1106963, _1106965, _1106967, _1106969] : [-(c_Hoare__Mirabelle_Otriple__valid(_1106963, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1106963), _1106965), hAPP(c_Com_Ocom_OBODY, _1106967)), _1106969)))], (19134 ^ _780119) ^ [_1128475, _1128477, _1128479, _1128481] : [class_Divides_Osemiring__div(_1128475), 19137 ^ _780119 : [(19144 ^ _780119) ^ [] : [-(_1128477 = c_Groups_Ozero__class_Ozero(_1128475)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128475), _1128477), _1128479)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128475), _1128477), _1128481)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128475), _1128479), _1128481))], (19138 ^ _780119) ^ [] : [_1128477 = c_Groups_Ozero__class_Ozero(_1128475), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128475), _1128477), _1128479)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128475), _1128477), _1128481)) = c_Groups_Ozero__class_Ozero(_1128475))]]], (23113 ^ _780119) ^ [_1202242, _1202244] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202242)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202244))))), _1202242 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1202244 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48918 ^ _780119) ^ [_1769522, _1769524, _1769526] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769522)), _1769526), c_List_Olists(_1769522, _1769524))), -(hBOOL(hAPP(c_List_Olistsp(_1769522, hAPP(hAPP(c_COMBC(_1769522, tc_fun(_1769522, tc_HOL_Obool), tc_HOL_Obool), c_member(_1769522)), _1769524)), _1769526)))], (3094 ^ _780119) ^ [_826267, _826269, _826271, _826273, _826275, _826277] : [-(c_Nitpick_Oplus__frac(_826277, _826273, _826269) = c_Nitpick_Oplus__frac(_826275, _826271, _826267)), _826277 = _826275, _826273 = _826271, _826269 = _826267], (10945 ^ _780119) ^ [_974424, _974426, _974428, _974430] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_974424), 10948 ^ _780119 : [(10955 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974424), _974426), _974430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974424), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974424), _974426), _974428)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974424), _974430), _974428))))], (10949 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974424), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974424), _974426), _974428)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974424), _974430), _974428))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974424), _974426), _974430)))]]], (40876 ^ _780119) ^ [_1581535, _1581537, _1581539] : [class_Orderings_Olinorder(_1581535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581535), _1581537)), -(hBOOL(hAPP(hAPP(c_member(_1581535), _1581539), _1581537))), -(c_Big__Operators_Olinorder__class_OMin(_1581535, hAPP(hAPP(c_Set_Oinsert(_1581535), _1581539), _1581537)) = hAPP(hAPP(c_Finite__Set_Ofold(_1581535, _1581535, c_Orderings_Oord__class_Omin(_1581535)), _1581539), _1581537))], (45297 ^ _780119) ^ [_1688722, _1688724, _1688726, _1688728] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688722), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688724)), _1688726)))), -(hAPP(hAPP(c_List_Onth(_1688724), hAPP(hAPP(c_List_Oappend(_1688724), _1688726), _1688728)), _1688722) = hAPP(hAPP(c_List_Onth(_1688724), _1688728), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1688722), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688724)), _1688726))))], (33345 ^ _780119) ^ [_1401509] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1401509) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1401509))], (31533 ^ _780119) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (11057 ^ _780119) ^ [_976688, _976690, _976692, _976694] : [-(c_Map_Odom(_976688, _976690, c_Map_Orestrict__map(_976688, _976690, _976692, _976694)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976688, tc_HOL_Obool)), c_Map_Odom(_976688, _976690, _976692)), _976694))], (14840 ^ _780119) ^ [_1052591, _1052593] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1052591, _1052593)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1052591, _1052593), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052591), c_Orderings_Otop__class_Otop(tc_fun(_1052591, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052593), c_Orderings_Otop__class_Otop(tc_fun(_1052593, tc_HOL_Obool))))], (37833 ^ _780119) ^ [_1507302, _1507304, _1507306, _1507308, _1507310] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1507302, _1507304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1507302, tc_HOL_Obool)), _1507306), _1507308)), hAPP(c_COMBK(tc_fun(_1507304, tc_HOL_Obool), _1507302), _1507310)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1507302, _1507304), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1507302, _1507304), _1507306), hAPP(c_COMBK(tc_fun(_1507304, tc_HOL_Obool), _1507302), _1507310))), hAPP(hAPP(c_Product__Type_OSigma(_1507302, _1507304), _1507308), hAPP(c_COMBK(tc_fun(_1507304, tc_HOL_Obool), _1507302), _1507310))))], (45534 ^ _780119) ^ [_1695875, _1695877, _1695879, _1695881] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695875), tc_List_Olist(_1695875))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695875), tc_List_Olist(_1695875)), _1695877), _1695879)), c_List_Olistrel1(_1695875, _1695881))), 45539 ^ _780119 : [(45542 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45538 ^ [_1695875, _1695877, _1695879, _1695881]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695875)), _1695877))))], (45544 ^ _780119) ^ [] : [-(_1695879 = hAPP(hAPP(c_List_Olist__update(_1695875, _1695877), 45538 ^ [_1695875, _1695877, _1695879, _1695881]), 45537 ^ [_1695875, _1695877, _1695879, _1695881]))], (45540 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1695875, _1695875)), hAPP(hAPP(c_Product__Type_OPair(_1695875, _1695875), hAPP(hAPP(c_List_Onth(_1695875), _1695877), 45538 ^ [_1695875, _1695877, _1695879, _1695881])), 45537 ^ [_1695875, _1695877, _1695879, _1695881])), _1695881)))]]], (4996 ^ _780119) ^ [_856426, _856428, _856430, _856432, _856434, _856436, _856438, _856440, _856442, _856444, _856446, _856448] : [-(c_New__Random__Sequence_Oneg__union(_856448, _856444, _856440, _856436, _856432, _856428) = c_New__Random__Sequence_Oneg__union(_856446, _856442, _856438, _856434, _856430, _856426)), _856448 = _856446, _856444 = _856442, _856440 = _856438, _856436 = _856434, _856432 = _856430, _856428 = _856426], (45386 ^ _780119) ^ [_1691262, _1691264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1691262), tc_List_Olist(_1691262)), tc_HOL_Obool)), c_List_Olistrel1(_1691262, c_Transitive__Closure_Ortrancl(_1691262, _1691264))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1691262), c_List_Olistrel1(_1691262, _1691264)))))], (50728 ^ _780119) ^ [_1808991, _1808993, _1808995] : [hBOOL(hAPP(hAPP(c_List_Omember(_1808991), _1808995), _1808993)), -(hBOOL(hAPP(hAPP(c_member(_1808991), _1808993), hAPP(c_List_Oset(_1808991), _1808995))))], (48021 ^ _780119) ^ [_1750036, _1750038] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1750036), _1750038) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1750036)), c_List_Oembed__list(_1750038))))], (15080 ^ _780119) ^ [_1056329, _1056331, _1056333] : [class_Groups_Oab__group__add(_1056329), 15083 ^ _780119 : [(15090 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056329), _1056331), _1056333) = c_Groups_Ozero__class_Ozero(_1056329), -(_1056331 = _1056333)], (15084 ^ _780119) ^ [] : [_1056331 = _1056333, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056329), _1056331), _1056333) = c_Groups_Ozero__class_Ozero(_1056329))]]], (50172 ^ _780119) ^ [_1796858] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1796858)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1796858))))], (14194 ^ _780119) ^ [_1039318, _1039320, _1039322, _1039324] : [class_Groups_Ocomm__monoid__mult(_1039318), 14197 ^ _780119 : [(14204 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039320), _1039322))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1039320, _1039318), _1039324), _1039322) = c_Groups_Oone__class_Oone(_1039318))], (14198 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039320), _1039322)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1039320, _1039318), _1039324), _1039322) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1039318, _1039320, c_Groups_Otimes__class_Otimes(_1039318)), _1039324), c_Groups_Oone__class_Oone(_1039318)), _1039322))]]], (37735 ^ _780119) ^ [_1504206, _1504208, _1504210, _1504212, _1504214, _1504216] : [hBOOL(hAPP(hAPP(c_member(_1504206), _1504208), _1504210)), 37738 ^ _780119 : [(37745 ^ _780119) ^ [] : [_1504214 = _1504216, -(hAPP(hAPP(c_Product__Type_OSigma(_1504212, _1504206), _1504214), hAPP(c_COMBK(tc_fun(_1504206, tc_HOL_Obool), _1504212), _1504210)) = hAPP(hAPP(c_Product__Type_OSigma(_1504212, _1504206), _1504216), hAPP(c_COMBK(tc_fun(_1504206, tc_HOL_Obool), _1504212), _1504210)))], (37739 ^ _780119) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1504212, _1504206), _1504214), hAPP(c_COMBK(tc_fun(_1504206, tc_HOL_Obool), _1504212), _1504210)) = hAPP(hAPP(c_Product__Type_OSigma(_1504212, _1504206), _1504216), hAPP(c_COMBK(tc_fun(_1504206, tc_HOL_Obool), _1504212), _1504210)), -(_1504214 = _1504216)]]], (9242 ^ _780119) ^ [_938876, _938878, _938880, _938882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938876, tc_HOL_Obool)), _938878), _938880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938876, tc_HOL_Obool)), _938880), _938882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938876, tc_HOL_Obool)), _938878), _938882)))], (10759 ^ _780119) ^ [_970900, _970902, _970904, _970906] : [class_Groups_Ocancel__semigroup__add(_970900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970900), _970902), _970904) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970900), _970902), _970906), -(_970904 = _970906)], (41828 ^ _780119) ^ [_1605449, _1605451, _1605453, _1605455] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1605449, tc_fun(_1605451, tc_HOL_Obool)), _1605453), _1605455) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1605451, tc_HOL_Obool), hAPP(c_Set_Oimage(_1605449, tc_fun(_1605451, tc_HOL_Obool), _1605455), _1605453)))], (3078 ^ _780119) ^ [_826033, _826035] : [_826035 = _826033, -(c_Nitpick_Ofrac(_826035) = c_Nitpick_Ofrac(_826033))], (46563 ^ _780119) ^ [_1718591, _1718593, _1718595, _1718597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718591), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718593)), _1718595))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718591), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718593)), _1718597))), 46573 ^ _780119 : [(46576 ^ _780119) ^ [] : [hAPP(hAPP(c_List_Onth(_1718593), _1718595), 46572 ^ [_1718591, _1718593, _1718595, _1718597]) = hAPP(hAPP(c_List_Onth(_1718593), _1718597), 46572 ^ [_1718591, _1718593, _1718595, _1718597])], (46574 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46572 ^ [_1718591, _1718593, _1718595, _1718597]), _1718591)))]], -(hAPP(hAPP(c_List_Otake(_1718593), _1718591), _1718595) = hAPP(hAPP(c_List_Otake(_1718593), _1718591), _1718597))], (37056 ^ _780119) ^ [_1486549, _1486551, _1486553, _1486555] : [hAPP(hAPP(c_Relation_Orel__comp(_1486549, _1486549, _1486549), _1486551), _1486553) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486549, _1486549), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1486549, _1486549, _1486549), _1486555), _1486553) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486549, _1486549), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1486549, _1486549, _1486549), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1486549, _1486549), tc_HOL_Obool)), _1486551), _1486555)), _1486553) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486549, _1486549), tc_HOL_Obool)))], (45918 ^ _780119) ^ [_1704786] : [-(hAPP(c_List_Otl(_1704786), c_List_Olist_ONil(_1704786)) = c_List_Olist_ONil(_1704786))], (7290 ^ _780119) ^ [_902250, _902252] : [class_Lattices_Osemilattice__sup(_902250), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902250), _902252), _902252) = _902252)], (39729 ^ _780119) ^ [_1554575, _1554577] : [-(c_Transitive__Closure_Ortrancl(_1554575, _1554577) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554575, _1554575), tc_HOL_Obool)), c_Relation_OId(_1554575)), hAPP(hAPP(c_Relation_Orel__comp(_1554575, _1554575, _1554575), c_Transitive__Closure_Ortrancl(_1554575, _1554577)), _1554577)))], (32313 ^ _780119) ^ [_1382655, _1382657] : [-(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), _1382655)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1382657)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1382655))) = 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), _1382657)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1382655)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (46737 ^ _780119) ^ [_1722696, _1722698, _1722700, _1722702] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1722696, tc_Nat_Onat), _1722696), c_Product__Type_Ofst(_1722696, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1722696, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1722696, tc_Nat_Onat)), _1722698), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1722696, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1722696, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1722696, tc_Nat_Onat), _1722700), _1722702))) = hAPP(hAPP(c_List_Omap(tc_prod(_1722696, tc_Nat_Onat), _1722696), c_Product__Type_Ofst(_1722696, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1722696, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1722696, tc_Nat_Onat)), _1722698), c_Product__Type_Osnd(_1722696, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1722696, tc_Nat_Onat), _1722700), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1722702)))))], (40542 ^ _780119) ^ [_1574984, _1574986, _1574988] : [class_Divides_Osemiring__div(_1574984), -(_1574986 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1574984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1574984), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1574984), _1574986), _1574988)), _1574988)), c_Divides_Odiv__class_Omod(_1574984, _1574986, _1574988)))], (5712 ^ _780119) ^ [_867584, _867586, _867588, _867590] : [-(hAPP(_867590, _867586) = hAPP(_867588, _867584)), _867590 = _867588, _867586 = _867584], (21364 ^ _780119) ^ [_1169291, _1169293] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1169291, tc_HOL_Obool)), _1169293), hAPP(c_Set_OPow(_1169291), _1169293))))], (36109 ^ _780119) ^ [_1464946, _1464948, _1464950, _1464952, _1464954] : [c_Fun_Oinj__on(_1464946, _1464948, _1464950, _1464952), c_Fun_Oinj__on(_1464946, _1464948, _1464950, _1464954), -(c_Fun_Oinj__on(_1464946, _1464948, _1464950, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464946, tc_HOL_Obool)), _1464952), _1464954)))], (44770 ^ _780119) ^ [_1676759, _1676761, _1676763] : [44771 ^ _780119 : [(44774 ^ _780119) ^ [] : [_1676763 = c_List_Olist_ONil(_1676759)], (44772 ^ _780119) ^ [] : [_1676761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1676759), _1676761), _1676763) = c_List_Olist_ONil(_1676759))], (31483 ^ _780119) ^ [_1368418] : [c_Int_OBit1(_1368418) = c_Int_OPls], (46371 ^ _780119) ^ [_1714622, _1714624] : [-(_1714622 = c_List_Olist_ONil(_1714624)), -(c_List_Olast(_1714624, _1714622) = hAPP(hAPP(c_List_Onth(_1714624), _1714622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714624)), _1714622)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (46773 ^ _780119) ^ [_1723877] : [class_Orderings_Olinorder(_1723877), -(c_List_Olinorder__class_Osorted(_1723877, c_List_Olist_ONil(_1723877)))], (42332 ^ _780119) ^ [_1617003] : [-(c_Nitpick_Onum(_1617003) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1617003, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1617003)))], (11421 ^ _780119) ^ [_984685, _984687, _984689, _984691, _984693, _984695] : [class_Rings_Oring(_984685), 11424 ^ _780119 : [(11431 ^ _780119) ^ [] : [_984691 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984685), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_984685), _984693), _984687)), _984689)), _984695), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984685), _984687), _984689)), _984691) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984685), _984693), _984689)), _984695))], (11425 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984685), _984687), _984689)), _984691) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984685), _984693), _984689)), _984695), -(_984691 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984685), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_984685), _984693), _984687)), _984689)), _984695))]]], (49339 ^ _780119) ^ [_1778592, _1778594, _1778596] : [-(c_List_Omaps(_1778592, _1778594, _1778596, c_List_Olist_ONil(_1778592)) = c_List_Olist_ONil(_1778594))], (33773 ^ _780119) ^ [_1413486, _1413488, _1413490, _1413492] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1413486, _1413488), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1413490), _1413492))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1413486), _1413488), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1413492), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1413490)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1413490)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1413492), 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), _1413488), _1413492))))))], (15348 ^ _780119) ^ [_1060212, _1060214, _1060216] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060212), _1060214) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060212), _1060216), -(_1060212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1060214 = _1060216)], (48209 ^ _780119) ^ [_1754366, _1754368] : [_1754366 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1754368, _1754366, c_List_Olist_ONil(_1754368)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1754368)), c_List_Olist_ONil(_1754368)), c_List_Olist_ONil(tc_List_Olist(_1754368))))], (46616 ^ _780119) ^ [_1719849, _1719851, _1719853, _1719855, _1719857, _1719859] : [class_Orderings_Olinorder(_1719849), -(hBOOL(hAPP(_1719851, _1719853))), -(hAPP(c_List_Ofilter(_1719855, _1719851), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1719855, _1719849, _1719857), _1719853), _1719859)) = hAPP(c_List_Ofilter(_1719855, _1719851), _1719859))], (37191 ^ _780119) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (22956 ^ _780119) ^ [_1199344, _1199346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199344)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199346))))], (15200 ^ _780119) ^ [_1058115] : [hAPP(c_Nat_OSuc, _1058115) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44628 ^ _780119) ^ [_1674233, _1674235, _1674237] : [-(hAPP(hAPP(c_List_Olist__update(_1674233, c_List_Olist_ONil(_1674233)), _1674235), _1674237) = c_List_Olist_ONil(_1674233))], (49468 ^ _780119) ^ [_1782509, _1782511] : [class_Orderings_Olinorder(_1782509), hBOOL(hAPP(c_Finite__Set_Ofinite(_1782509), _1782511)), 49476 ^ _780119 : [(49477 ^ _780119) ^ [] : [-(hAPP(c_List_Oset(_1782509), 49475 ^ [_1782509, _1782511]) = _1782511)], (49479 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1782509, 49475 ^ [_1782509, _1782511]))], (49483 ^ _780119) ^ [_1782835] : [-(_1782835 = 49475 ^ [_1782509, _1782511]), hAPP(c_List_Oset(_1782509), _1782835) = _1782511, c_List_Olinorder__class_Osorted(_1782509, _1782835), hBOOL(hAPP(c_List_Odistinct(_1782509), _1782835))], (49481 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1782509), 49475 ^ [_1782509, _1782511])))]]], (13424 ^ _780119) ^ [_1024347, _1024349, _1024351] : [class_Groups_Ogroup__add(_1024347), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024347), hAPP(c_Groups_Ouminus__class_Ouminus(_1024347), _1024349)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024347), _1024349), _1024351)) = _1024351)], (47887 ^ _780119) ^ [_1747557, _1747559] : [-(_1747557 = c_List_Olist_ONil(_1747559)), hBOOL(hAPP(c_List_Odistinct(_1747559), _1747557)), -(c_List_OtakeWhile(_1747559, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1747559), c_fNot), hAPP(hAPP(c_COMBC(_1747559, _1747559, tc_HOL_Obool), c_fequal), c_List_Olast(_1747559, _1747557))), _1747557) = c_List_Obutlast(_1747559, _1747557))], (16927 ^ _780119) ^ [_1087650, _1087652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1087652), _1087650)), -(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), _1087650), _1087652))))], (44700 ^ _780119) ^ [_1675598, _1675600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1675598), _1675600)), -(c_List_Oupto(_1675600, _1675598) = c_List_Olist_ONil(tc_Int_Oint))], (34293 ^ _780119) ^ [_1423706, _1423708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1423706)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1423706), _1423708)), -(c_Divides_Odivmod__nat(_1423708, _1423706) = 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), _1423708), _1423706)), _1423706))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1423708), _1423706), _1423706)))], (16328 ^ _780119) ^ [_1077748, _1077750, _1077752] : [class_Groups_Oordered__ab__group__add(_1077748), 16331 ^ _780119 : [(16338 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077748), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077748), _1077750), _1077752)), c_Groups_Ozero__class_Ozero(_1077748))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077748), _1077750), _1077752)))], (16332 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077748), _1077750), _1077752)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077748), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077748), _1077750), _1077752)), c_Groups_Ozero__class_Ozero(_1077748))))]]], (42745 ^ _780119) ^ [_1626631, _1626633] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1626631), hAPP(c_List_Oset(_1626631), _1626633))))], (4264 ^ _780119) ^ [_844598, _844600, _844602, _844604] : [-(c_List_Olex(_844604, _844600) = c_List_Olex(_844602, _844598)), _844604 = _844602, _844600 = _844598], (12417 ^ _780119) ^ [_1004419, _1004421] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004419), _1004421), 12420 ^ _780119 : [(12423 ^ _780119) ^ [] : [-(_1004421 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12421 ^ _780119) ^ [] : [-(_1004419 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (49664 ^ _780119) ^ [_1787063, _1787065, _1787067] : [c_List_Olist__ex(_1787063, _1787065, _1787067), 49668 ^ _780119 : [(49671 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1787065, 49667 ^ [_1787063, _1787065, _1787067])))], (49669 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1787063), 49667 ^ [_1787063, _1787065, _1787067]), hAPP(c_List_Oset(_1787063), _1787067))))]]], (41710 ^ _780119) ^ [_1602786, _1602788, _1602790] : [class_Complete__Lattice_Ocomplete__lattice(_1602786), class_Orderings_Olinorder(_1602786), 41717 ^ _780119 : [(41727 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1602786), c_Complete__Lattice_OInf__class_OInf(_1602786, _1602788)), _1602790))), 41728 ^ _780119 : [(41729 ^ _780119) ^ [_1603092] : [hBOOL(hAPP(hAPP(c_member(_1602786), _1603092), _1602788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1602786), _1603092), _1602790))]]], (41718 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1602786), c_Complete__Lattice_OInf__class_OInf(_1602786, _1602788)), _1602790)), 41722 ^ _780119 : [(41725 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1602786), 41721 ^ [_1602786, _1602788, _1602790]), _1602790)))], (41723 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602786), 41721 ^ [_1602786, _1602788, _1602790]), _1602788)))]]]]], (9840 ^ _780119) ^ [_951311, _951313, _951315] : [class_Lattices_Olattice(_951311), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951311), _951313), _951315) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951311), _951315), _951313))], (32325 ^ _780119) ^ [_1382888, _1382890, _1382892] : [-(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), _1382888)), 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))), _1382890))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1382892))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1382892)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382888), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382888), 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), _1382892), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1382890)))))], (39202 ^ _780119) ^ [_1541566, _1541568, _1541570, _1541572, _1541574] : [c_Finite__Set_Ofolding__idem(_1541566, _1541568, _1541570, _1541572), -(hAPP(c_Fun_Ocomp(_1541568, _1541568, _1541568, hAPP(_1541570, _1541574)), hAPP(_1541570, _1541574)) = hAPP(_1541570, _1541574))], (51471 ^ _780119) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (21823 ^ _780119) ^ [_1178479, _1178481, _1178483] : [-(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), _1178479), _1178481)), _1178481)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178479, _1178481))), _1178483) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178479), _1178483))], (7332 ^ _780119) ^ [_903043, _903045, _903047, _903049] : [class_Lattices_Osemilattice__sup(_903043), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903043), _903045), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903043), _903047), _903049)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903043), _903047), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903043), _903045), _903049)))], (6463 ^ _780119) ^ [_884587, _884589] : [-(c_Set_Othe__elem(_884587, hAPP(hAPP(c_Set_Oinsert(_884587), _884589), c_Orderings_Obot__class_Obot(tc_fun(_884587, tc_HOL_Obool)))) = _884589)], (44730 ^ _780119) ^ [_1676113, _1676115] : [_1676115 = c_List_Olist_ONil(_1676113), -(hAPP(c_List_Oset(_1676113), _1676115) = c_Orderings_Obot__class_Obot(tc_fun(_1676113, tc_HOL_Obool)))], (51171 ^ _780119) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (26101 ^ _780119) ^ [_1256127, _1256129] : [class_Orderings_Oorder(_1256127), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1256127, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1256127), _1256129)), hAPP(c_SetInterval_Oord__class_OatLeast(_1256127), _1256129)) = hAPP(hAPP(c_Set_Oinsert(_1256127), _1256129), c_Orderings_Obot__class_Obot(tc_fun(_1256127, tc_HOL_Obool))))], (7302 ^ _780119) ^ [_902450, _902452, _902454] : [class_Lattices_Olattice(_902450), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902450), _902452), _902454) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902450), _902454), _902452))], (41149 ^ _780119) ^ [_1587823, _1587825, _1587827, _1587829, _1587831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1587823, tc_HOL_Obool)), _1587825), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587827, tc_fun(_1587823, tc_HOL_Obool)), _1587829), _1587831))), 41152 ^ _780119 : [(41153 ^ _780119) ^ [_1587956] : [hBOOL(hAPP(hAPP(c_member(_1587827), _1587956), _1587829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1587823, tc_HOL_Obool)), _1587825), hAPP(_1587831, _1587956))))]]], (28232 ^ _780119) ^ [_1301996, _1301998, _1302000] : [class_Orderings_Olinorder(_1301996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301996), _1301998)), hBOOL(hAPP(hAPP(c_member(_1301996), _1302000), _1301998)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1301996), _1302000), c_Big__Operators_Olinorder__class_OMax(_1301996, _1301998)) = c_Big__Operators_Olinorder__class_OMax(_1301996, _1301998))], (10841 ^ _780119) ^ [_972405, _972407, _972409, _972411, _972413] : [class_Groups_Oordered__ab__semigroup__add(_972405), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972405), _972407), _972409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972405), _972411), _972413)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972405), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972405), _972407), _972411)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972405), _972409), _972413))))], (37014 ^ _780119) ^ [_1484597, _1484599, _1484601] : [hBOOL(hAPP(hAPP(c_member(_1484597), _1484601), c_Wellfounded_Oacc(_1484597, _1484599))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1484597, hAPP(hAPP(c_COMBC(_1484597, tc_fun(tc_prod(_1484597, _1484597), tc_HOL_Obool), tc_fun(_1484597, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484597, tc_fun(tc_fun(tc_prod(_1484597, _1484597), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484597, _1484597), tc_HOL_Obool), tc_fun(_1484597, tc_HOL_Obool)), _1484597), c_COMBC(_1484597, tc_fun(tc_prod(_1484597, _1484597), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484597, tc_prod(_1484597, _1484597)), tc_fun(_1484597, tc_fun(tc_fun(tc_prod(_1484597, _1484597), tc_HOL_Obool), tc_HOL_Obool)), _1484597), hAPP(c_COMBB(tc_prod(_1484597, _1484597), tc_fun(tc_fun(tc_prod(_1484597, _1484597), tc_HOL_Obool), tc_HOL_Obool), _1484597), c_member(tc_prod(_1484597, _1484597)))), c_Product__Type_OPair(_1484597, _1484597)))), _1484599)), _1484601)))], (17436 ^ _780119) ^ [_1096995, _1096997, _1096999] : [class_Rings_Olinordered__ring(_1096995), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096995), c_Groups_Ozero__class_Ozero(_1096995)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096995), _1096997), _1096997)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096995), _1096999), _1096999)))))], (37892 ^ _780119) ^ [_1508897, _1508899, _1508901, _1508903, _1508905, _1508907] : [hBOOL(hAPP(hAPP(c_member(_1508897), _1508899), _1508901)), 37895 ^ _780119 : [(37902 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508903, tc_HOL_Obool)), _1508905), _1508907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1508903, _1508897), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1508903, _1508897), _1508905), hAPP(c_COMBK(tc_fun(_1508897, tc_HOL_Obool), _1508903), _1508901))), hAPP(hAPP(c_Product__Type_OSigma(_1508903, _1508897), _1508907), hAPP(c_COMBK(tc_fun(_1508897, tc_HOL_Obool), _1508903), _1508901)))))], (37896 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1508903, _1508897), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1508903, _1508897), _1508905), hAPP(c_COMBK(tc_fun(_1508897, tc_HOL_Obool), _1508903), _1508901))), hAPP(hAPP(c_Product__Type_OSigma(_1508903, _1508897), _1508907), hAPP(c_COMBK(tc_fun(_1508897, tc_HOL_Obool), _1508903), _1508901)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508903, tc_HOL_Obool)), _1508905), _1508907)))]]], (38710 ^ 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tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1275739, tc_HOL_Obool)), c_Map_Odom(_1275739, _1275741, _1275743)), hAPP(c_Set_OCollect(_1275739), hAPP(hAPP(c_COMBC(_1275739, tc_fun(_1275739, tc_HOL_Obool), tc_HOL_Obool), c_member(_1275739)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1275739, tc_HOL_Obool)), _1275747), c_Map_Odom(_1275739, _1275741, _1275745)))))), hAPP(c_Set_OCollect(_1275739), hAPP(hAPP(c_COMBC(_1275739, tc_fun(_1275739, tc_HOL_Obool), tc_HOL_Obool), c_member(_1275739)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1275739, tc_HOL_Obool)), _1275747), c_Map_Odom(_1275739, _1275741, _1275745))))))], (39735 ^ _780119) ^ [_1554713, _1554715] : [-(c_Transitive__Closure_Otrancl(_1554713, _1554715) = hAPP(hAPP(c_Relation_Orel__comp(_1554713, _1554713, _1554713), c_Transitive__Closure_Ortrancl(_1554713, _1554715)), _1554715))], (26821 ^ _780119) ^ [_1270517, _1270519, _1270521] : [class_Rings_Oordered__ring__abs(_1270517), -(hAPP(c_Groups_Oabs__class_Oabs(_1270517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270517), _1270519), _1270521)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270517), hAPP(c_Groups_Oabs__class_Oabs(_1270517), _1270519)), hAPP(c_Groups_Oabs__class_Oabs(_1270517), _1270521))), 26828 ^ _780119 : [(26831 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270517), _1270519), c_Groups_Ozero__class_Ozero(_1270517)))], (26829 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270517), c_Groups_Ozero__class_Ozero(_1270517)), _1270519))]], 26832 ^ _780119 : [(26835 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270517), _1270521), c_Groups_Ozero__class_Ozero(_1270517)))], (26833 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270517), c_Groups_Ozero__class_Ozero(_1270517)), _1270521))]]], (43337 ^ _780119) ^ [_1641429, _1641431, _1641433, _1641435, _1641437] : 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c_Orderings_Oord__class_Omin(_1315953), hAPP(hAPP(c_Set_Oinsert(_1315953), _1315957), _1315955)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315953), _1315957), c_Big__Operators_Olattice_OInf__fin(_1315953, c_Orderings_Oord__class_Omin(_1315953), _1315955)))], (50236 ^ _780119) ^ [_1798011] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1798011)))], (36972 ^ _780119) ^ [_1483609, _1483611, _1483613, _1483615, _1483617, _1483619, _1483621] : [c_Typedef_Otype__definition(_1483609, _1483611, _1483613, _1483615, _1483617), hBOOL(hAPP(hAPP(c_member(_1483611), _1483619), _1483617)), hBOOL(hAPP(hAPP(c_member(_1483611), _1483621), _1483617)), 36983 ^ _780119 : [(36990 ^ _780119) ^ [] : [_1483619 = _1483621, -(hAPP(_1483615, _1483619) = hAPP(_1483615, _1483621))], (36984 ^ _780119) ^ [] : [hAPP(_1483615, _1483619) = hAPP(_1483615, _1483621), -(_1483619 = _1483621)]]], (31493 ^ _780119) ^ [_1368532] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1368532) = _1368532)], (37733 ^ _780119) ^ [_1504157, _1504159, _1504161] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1504157, _1504159), c_Orderings_Obot__class_Obot(tc_fun(_1504157, tc_HOL_Obool))), _1504161) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1504157, _1504159), tc_HOL_Obool)))], (29584 ^ _780119) ^ [_1329430, _1329432, _1329434, _1329436] : [-(hAPP(c_Set_Oimage(_1329430, _1329432, _1329434), _1329436) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1329430, tc_fun(_1329432, tc_HOL_Obool)), _1329436), hAPP(hAPP(c_COMBC(_1329430, tc_fun(_1329432, tc_HOL_Obool), tc_fun(_1329432, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1329432, tc_fun(tc_fun(_1329432, tc_HOL_Obool), tc_fun(_1329432, tc_HOL_Obool)), _1329430), c_Set_Oinsert(_1329432)), _1329434)), c_Orderings_Obot__class_Obot(tc_fun(_1329432, tc_HOL_Obool)))))], (28110 ^ _780119) ^ [_1299271, _1299273, _1299275, _1299277] : [class_Orderings_Olinorder(_1299271), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299271), _1299273), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299271), _1299275), _1299277)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299271), _1299275), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299271), _1299273), _1299277)))], (26791 ^ _780119) ^ [_1269735, _1269737] : [-(hAPP(c_Set_OCollect(_1269735), hAPP(c_fequal, _1269737)) = hAPP(hAPP(c_Set_Oinsert(_1269735), _1269737), c_Orderings_Obot__class_Obot(tc_fun(_1269735, tc_HOL_Obool))))], (35485 ^ _780119) ^ [_1449995, _1449997, _1449999, _1450001] : [-(hAPP(c_Relation_OField(_1449995), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1449995, _1449995)), hAPP(hAPP(c_Product__Type_OPair(_1449995, _1449995), _1449997), _1449999)), _1450001)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1449995, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1449995), _1449997), hAPP(hAPP(c_Set_Oinsert(_1449995), _1449999), c_Orderings_Obot__class_Obot(tc_fun(_1449995, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1449995), _1450001)))], (47754 ^ _780119) ^ [_1744470, _1744472, _1744474] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1744470), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1744470))), _1744472))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744474), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1744470))), _1744472))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1744470))), hAPP(c_List_Ofilter(tc_List_Olist(_1744470), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1744470)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744474)), c_Nat_Osize__class_Osize(tc_List_Olist(_1744470)))), c_List_Otranspose(_1744470, _1744472))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744470)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1744470)), _1744472), _1744474)))], (31099 ^ _780119) ^ [_1361536, _1361538, _1361540] : [class_Int_Onumber__ring(_1361536), 31102 ^ _780119 : [(31109 ^ _780119) ^ [] : [-(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), _1361538)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1361536), hAPP(c_Int_Onumber__class_Onumber__of(_1361536), _1361540)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1361538))) = c_Groups_Oone__class_Oone(_1361536))], (31103 ^ _780119) ^ [] : [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), _1361538))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1361536), hAPP(c_Int_Onumber__class_Onumber__of(_1361536), _1361540)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1361538))) = hAPP(hAPP(c_HOL_OLet(_1361536, _1361536), hAPP(hAPP(c_Power_Opower__class_Opower(_1361536), hAPP(c_Int_Onumber__class_Onumber__of(_1361536), _1361540)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1361538))), hAPP(hAPP(c_COMBS(_1361536, _1361536, _1361536), hAPP(hAPP(c_COMBB(_1361536, tc_fun(_1361536, _1361536), _1361536), c_Groups_Otimes__class_Otimes(_1361536)), hAPP(c_Groups_Otimes__class_Otimes(_1361536), hAPP(c_Int_Onumber__class_Onumber__of(_1361536), _1361540)))), c_COMBI(_1361536))))]]], (49683 ^ _780119) ^ [_1787431, _1787433, _1787435] : [c_List_Olist__ex(_1787431, _1787433, hAPP(c_List_Orev(_1787431), _1787435)), -(c_List_Olist__ex(_1787431, _1787433, _1787435))], (26219 ^ _780119) ^ [_1258328, _1258330] : [class_Orderings_Olinorder(_1258328), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258328, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1258328), _1258330)), hAPP(hAPP(c_Set_Oinsert(_1258328), _1258330), c_Orderings_Obot__class_Obot(tc_fun(_1258328, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1258328), _1258330))], (13584 ^ _780119) ^ [_1027355, _1027357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027355), _1027357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027355), hAPP(c_Nat_OSuc, _1027357))))], (6210 ^ _780119) ^ [_879403] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_879403), c_Orderings_Obot__class_Obot(tc_fun(_879403, tc_HOL_Obool)))))], (8684 ^ _780119) ^ [_930250, _930252, _930254] : [class_Orderings_Oorder(_930250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930250), _930252), _930254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930250), _930254), _930252))], (29498 ^ _780119) ^ [_1327736, _1327738, _1327740, _1327742, _1327744] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1327736, tc_fun(_1327738, tc_HOL_Obool)), _1327740), _1327742), _1327744))), 29499 ^ _780119 : [(29500 ^ _780119) ^ [_1327808] : [hBOOL(hAPP(hAPP(c_member(_1327736), _1327808), _1327740)), hBOOL(hAPP(hAPP(_1327742, _1327808), _1327744))]]], (6571 ^ _780119) ^ [_886805, _886807, _886809, _886811] : [6572 ^ _780119 : [(6575 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886805), _886807), _886811))], (6573 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886805), _886807), _886809))]], -(hBOOL(hAPP(hAPP(c_member(_886805), _886807), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886805, tc_HOL_Obool)), _886811), _886809))))], (39120 ^ _780119) ^ [_1539557, _1539559, _1539561, _1539563, _1539565] : [c_Hoare__Mirabelle_Ohoare__derivs(_1539557, _1539559, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1539557)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1539557), c_Hoare__Mirabelle_Opeek__and(_1539557, _1539561, _1539563)), _1539565), _1539561)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1539557), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1539557, _1539559, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1539557)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1539557), _1539561), c_Com_Ocom_OWhile(_1539563, _1539565)), c_Hoare__Mirabelle_Opeek__and(_1539557, _1539561, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1539563)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1539557), tc_HOL_Obool)))))], (7060 ^ _780119) ^ [_896664] : [7061 ^ _780119 : [(7062 ^ _780119) ^ [_896712] : [hAPP(c_Com_Obody, _896664) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _896712)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _896664))))], (17019 ^ _780119) ^ [_1089260, _1089262, _1089264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1089260), _1089262)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1089264), _1089262)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1089262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1089260), _1089264))], (5084 ^ _780119) ^ [_857912, _857914] : [_857914 = _857912, -(c_Lattices_Osemilattice__inf__class_Oinf(_857914) = c_Lattices_Osemilattice__inf__class_Oinf(_857912))], (7518 ^ _780119) ^ [_906550, _906552, _906554] : [class_Lattices_Olattice(_906550), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906550), _906552), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_906550), _906554), _906552))))], (11874 ^ _780119) ^ [_993822, _993824, _993826, _993828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993822), _993824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993826), _993828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993822), _993826)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993824), _993828))))], (12626 ^ _780119) ^ [_1009006, _1009008] : [-(_1009006 = c_Option_Ooption_ONone(_1009008)), -(_1009006 = hAPP(c_Option_Ooption_OSome(_1009008), 12629 ^ [_1009006, _1009008]))], (21701 ^ _780119) ^ [_1176173, _1176175] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176173, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176175)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176173, _1176175) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (35285 ^ _780119) ^ [] : [-(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)))], (38722 ^ _780119) ^ [_1530162, _1530164, _1530166, _1530168, _1530170, _1530172, _1530174, _1530176, _1530178, _1530180, _1530182] : [hAPP(_1530162, hAPP(_1530164, _1530166)) = hAPP(_1530168, hAPP(_1530170, _1530172)), -(hAPP(hAPP(c_Fun_Ocomp(_1530174, _1530176, _1530178, _1530162), _1530164), _1530166) = hAPP(hAPP(c_Fun_Ocomp(_1530180, _1530176, _1530182, _1530168), _1530170), _1530172))], (1600 ^ _780119) ^ [_802843, _802845] : [-(class_Groups_Ocomm__monoid__add(_802843)), _802845 = _802843, class_Groups_Ocomm__monoid__add(_802845)], (49287 ^ _780119) ^ [_1777601, _1777603] : [-(hAPP(c_List_OremoveAll(_1777601, _1777603), c_List_Olist_ONil(_1777601)) = c_List_Olist_ONil(_1777601))], (14502 ^ _780119) ^ [_1046044, _1046046, _1046048, _1046050] : [class_Rings_Olinordered__semidom(_1046044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046044), c_Groups_Oone__class_Oone(_1046044)), _1046046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046044), hAPP(hAPP(c_Power_Opower__class_Opower(_1046044), _1046046), _1046048)), hAPP(hAPP(c_Power_Opower__class_Opower(_1046044), _1046046), _1046050))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046048), _1046050)))], (5312 ^ _780119) ^ [_861346, _861348, _861350, _861352, _861354, _861356, _861358, _861360, _861362, _861364] : [-(c_Nitpick_Opair__box_Opair__box__size(_861364, _861360, _861356, _861352, _861348) = c_Nitpick_Opair__box_Opair__box__size(_861362, _861358, _861354, _861350, _861346)), _861364 = _861362, _861360 = _861358, _861356 = _861354, _861352 = _861350, _861348 = _861346], (48829 ^ _780119) ^ [_1767631, _1767633, _1767635] : [-(c_List_Olistsp(_1767631, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1767631, tc_HOL_Obool)), _1767633), _1767635)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1767631), tc_HOL_Obool)), c_List_Olistsp(_1767631, _1767633)), c_List_Olistsp(_1767631, _1767635)))], (13942 ^ _780119) ^ [_1033842, _1033844] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033842), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1033842), _1033844)))))], (10743 ^ _780119) ^ [_970635, _970637, _970639, _970641] : [class_Groups_Ocancel__semigroup__add(_970635), 10746 ^ _780119 : [(10753 ^ _780119) ^ [] : [_970637 = _970641, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970635), _970637), _970639) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970635), _970641), _970639))], (10747 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970635), _970637), _970639) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970635), _970641), _970639), -(_970637 = _970641)]]], (6851 ^ _780119) ^ [_893036, _893038, _893040, _893042, _893044] : [c_Hoare__Mirabelle_Ohoare__derivs(_893036, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_893036), tc_HOL_Obool)), _893038), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_893036), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_893036)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_893036))), hAPP(hAPP(c_COMBB(tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_893036))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_893036)), _893040)), c_Com_Ocom_OBODY)), _893042)), _893044)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_893036), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_893036)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_893036))), hAPP(hAPP(c_COMBB(tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_893036))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_893036)), _893040)), 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))), _893042)), _893044)), -(c_Hoare__Mirabelle_Ohoare__derivs(_893036, _893038, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_893036), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_893036)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_893036))), hAPP(hAPP(c_COMBB(tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_893036, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_893036))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_893036)), _893040)), c_Com_Ocom_OBODY)), _893042)), _893044)))], (9326 ^ _780119) ^ [_940604] : [-(c_Finite__Set_Ofun__left__comm__idem(_940604, tc_fun(_940604, tc_HOL_Obool), c_Set_Oinsert(_940604)))], (4236 ^ _780119) ^ [_844148, _844150, _844152, _844154, _844156, _844158, _844160, _844162] : [-(c_List_Omaps(_844162, _844158, _844154, _844150) = c_List_Omaps(_844160, _844156, _844152, _844148)), _844162 = _844160, _844158 = _844156, _844154 = _844152, _844150 = _844148], (49289 ^ _780119) ^ [_1777632, _1777634, _1777636, _1777638] : [-(hBOOL(hAPP(_1777632, _1777634))), -(hAPP(c_List_OremoveAll(_1777636, _1777634), hAPP(c_List_Ofilter(_1777636, _1777632), _1777638)) = hAPP(c_List_Ofilter(_1777636, _1777632), _1777638))], (50634 ^ _780119) ^ [_1807121, _1807123, _1807125, _1807127] : [-(hAPP(hAPP(c_List_Odrop(_1807121), _1807123), c_List_Oreplicate(_1807121, _1807125, _1807127)) = c_List_Oreplicate(_1807121, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1807125), _1807123), _1807127))], (44346 ^ _780119) ^ [_1668323, _1668325, _1668327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668323), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1668325))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1668325), _1668323), _1668327)) = 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), _1668325)), _1668327)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1668325), _1668323)))], (37137 ^ _780119) ^ [_1490038, _1490040, _1490042] : [c_Wellfounded_Owf(_1490038, _1490040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1490038, _1490038), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1490038, _1490038, _1490038), _1490040), _1490042)), _1490040)), -(c_FunDef_Oreduction__pair(_1490038, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1490038, _1490038), tc_HOL_Obool), tc_fun(tc_prod(_1490038, _1490038), tc_HOL_Obool)), _1490040), _1490042)))], (3562 ^ _780119) ^ [_833667, _833669, _833671, _833673] : [-(c_Big__Operators_Olinorder__class_OMin(_833673, _833669) = c_Big__Operators_Olinorder__class_OMin(_833671, _833667)), _833673 = _833671, _833669 = _833667], (35507 ^ _780119) ^ [_1450728, _1450730, _1450732, _1450734, _1450736] : [hBOOL(hAPP(hAPP(c_member(_1450728), _1450730), hAPP(c_Relation_OImage(_1450732, _1450728, _1450734), _1450736))), 35511 ^ _780119 : [(35514 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450732), 35510 ^ [_1450728, _1450730, _1450732, _1450734, _1450736]), _1450736)))], (35512 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1450732, _1450728)), hAPP(hAPP(c_Product__Type_OPair(_1450732, _1450728), 35510 ^ [_1450728, _1450730, _1450732, _1450734, _1450736]), _1450730)), _1450734)))]]], (40297 ^ _780119) ^ [_1568620] : [-(c_Nat_Ofunpow(_1568620) = c_Nat_Ocompow(_1568620, _1568620))], (23243 ^ _780119) ^ [_1204690, _1204692, _1204694, _1204696, _1204698] : [class_Groups_Oordered__ab__semigroup__add(_1204690), class_Rings_Osemiring__1(_1204690), 23253 ^ _780119 : [(23256 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204690), hAPP(_1204696, 23252 ^ [_1204690, _1204692, _1204694, _1204696, _1204698])), _1204698))], (23254 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1204692), 23252 ^ [_1204690, _1204692, _1204694, _1204696, _1204698]), _1204694)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204690), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1204692, _1204690), _1204696), _1204694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204690), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1204690), hAPP(c_Finite__Set_Ocard(_1204692), _1204694))), _1204698))))], (40966 ^ _780119) ^ [_1583276, _1583278, _1583280, _1583282, _1583284, _1583286] : [c_Finite__Set_Ofun__left__comm(_1583276, _1583278, _1583280), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583276), _1583282)), -(hAPP(hAPP(_1583280, _1583284), hAPP(hAPP(c_Finite__Set_Ofold(_1583276, _1583278, _1583280), _1583286), _1583282)) = hAPP(hAPP(c_Finite__Set_Ofold(_1583276, _1583278, _1583280), hAPP(hAPP(_1583280, _1583284), _1583286)), _1583282))], (39815 ^ _780119) ^ [_1556556, _1556558, _1556560, _1556562, _1556564] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1556556, _1556556)), hAPP(hAPP(c_Product__Type_OPair(_1556556, _1556556), _1556558), _1556560)), c_Transitive__Closure_Otrancl(_1556556, _1556562))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1556556, _1556556)), hAPP(hAPP(c_Product__Type_OPair(_1556556, _1556556), _1556560), _1556564)), c_Transitive__Closure_Ortrancl(_1556556, _1556562))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556556, _1556556)), hAPP(hAPP(c_Product__Type_OPair(_1556556, _1556556), _1556558), _1556564)), c_Transitive__Closure_Otrancl(_1556556, _1556562))))], (21670 ^ _780119) ^ [_1175648, _1175650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1175650, _1175648)), _1175648)))], (8032 ^ _780119) ^ [_917408, _917410] : [hBOOL(hAPP(c_Com_OWT, _917410)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_917408, _917410))))], (30281 ^ _780119) ^ [_1345947, _1345949, _1345951, _1345953] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345947), hAPP(c_Int_Onumber__class_Onumber__of(_1345947), _1345949)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1345947), _1345951), _1345953)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1345947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345947), hAPP(c_Int_Onumber__class_Onumber__of(_1345947), _1345949)), _1345951)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345947), hAPP(c_Int_Onumber__class_Onumber__of(_1345947), _1345949)), _1345953))), class_Int_Onumber(_1345947), class_Rings_Oring(_1345947)], (42471 ^ _780119) ^ [_1619854, _1619856, _1619858] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1619854)), hAPP(c_Set_Oimage(_1619856, tc_Option_Ooption(_1619854), hAPP(c_Map_Omap__of(_1619856, _1619854), _1619858)), c_Orderings_Otop__class_Otop(tc_fun(_1619856, tc_HOL_Obool))))))], (51087 ^ _780119) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (20432 ^ _780119) ^ [_1151889, _1151891, _1151893] : [class_Fields_Olinordered__field__inverse__zero(_1151889), 20435 ^ _780119 : [(20450 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151889), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151889), _1151891), _1151893)), c_Groups_Ozero__class_Ozero(_1151889)))), 20451 ^ _780119 : [(20458 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151889), _1151891), c_Groups_Ozero__class_Ozero(_1151889))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151889), c_Groups_Ozero__class_Ozero(_1151889)), _1151893))], (20452 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151889), c_Groups_Ozero__class_Ozero(_1151889)), _1151891)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151889), _1151893), c_Groups_Ozero__class_Ozero(_1151889)))]]], (20436 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151889), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151889), _1151891), _1151893)), c_Groups_Ozero__class_Ozero(_1151889))), 20441 ^ _780119 : [(20444 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151889), _1151893), c_Groups_Ozero__class_Ozero(_1151889))))], (20442 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151889), c_Groups_Ozero__class_Ozero(_1151889)), _1151891)))]], 20445 ^ _780119 : [(20448 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151889), c_Groups_Ozero__class_Ozero(_1151889)), _1151893)))], (20446 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151889), _1151891), c_Groups_Ozero__class_Ozero(_1151889))))]]]]], (44376 ^ _780119) ^ [_1668932, _1668934, _1668936, _1668938] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668932)), hAPP(hAPP(c_List_Olist__update(_1668932, _1668934), _1668936), _1668938)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668932)), _1668934))], (30239 ^ _780119) ^ [_1345103, _1345105, _1345107] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_1345103, _1345105, _1345107)], (30091 ^ _780119) ^ [_1342520, _1342522, _1342524] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_1342520, _1342522, _1342524)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1342524)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6551 ^ _780119) ^ [_886515, _886517, _886519, _886521] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886515, tc_HOL_Obool)), _886517), _886519), _886521)), -(hBOOL(hAPP(_886517, _886521))), -(hBOOL(hAPP(_886519, _886521)))], (34179 ^ _780119) ^ [_1421977, _1421979] : [34180 ^ _780119 : [(34183 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1421979), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34181 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421977), _1421979))]], -(c_Divides_OposDivAlg(_1421977, _1421979) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1421977))], (34477 ^ _780119) ^ [_1427167, _1427169] : [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), _1427167), _1427169))), 34480 ^ _780119 : [(34489 ^ _780119) ^ [] : [-(c_Divides_OnegDivAlg(_1427167, _1427169) = hAPP(c_Divides_Oadjust(_1427169), c_Divides_OnegDivAlg(_1427167, 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)))), _1427169)))), -(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), _1427167), _1427169)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427169), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34481 ^ _780119) ^ [] : [34482 ^ _780119 : [(34485 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427169), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34483 ^ _780119) ^ [] : [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), _1427167), _1427169)))]], -(c_Divides_OnegDivAlg(_1427167, _1427169) = 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), _1427167), _1427169)))]]], (46197 ^ _780119) ^ [_1711138, _1711140, _1711142] : [c_Relation_Orefl__on(_1711138, _1711140, _1711142), -(c_Relation_Orefl__on(tc_List_Olist(_1711138), c_List_Olists(_1711138, _1711140), c_List_Olistrel(_1711138, _1711142)))], (36575 ^ _780119) ^ [_1474359, _1474361, _1474363, _1474365, _1474367] : [c_Fun_Oinj__on(_1474359, _1474361, _1474363, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474359, tc_HOL_Obool)), _1474365), _1474367)), 36578 ^ _780119 : [(36581 ^ _780119) ^ [] : [-(c_Fun_Oinj__on(_1474359, _1474361, _1474363, _1474367))], (36583 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474361, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1474359, _1474361, _1474363), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474359, tc_HOL_Obool)), _1474365), _1474367))), hAPP(c_Set_Oimage(_1474359, _1474361, _1474363), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474359, tc_HOL_Obool)), _1474367), _1474365))) = c_Orderings_Obot__class_Obot(tc_fun(_1474361, tc_HOL_Obool)))], (36579 ^ _780119) ^ [] : [-(c_Fun_Oinj__on(_1474359, _1474361, _1474363, _1474365))]]], (13923 ^ _780119) ^ [_1033441, _1033443, _1033445] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1033441, tc_HOL_Obool)), _1033443), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033441, tc_HOL_Obool)), _1033445)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1033441, tc_HOL_Obool)), _1033443), _1033445))], (29398 ^ _780119) ^ [_1325538, _1325540, _1325542] : [class_Orderings_Olinorder(_1325538), hAPP(_1325540, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1325538), 29403 ^ [_1325538, _1325540, _1325542]), 29404 ^ [_1325538, _1325540, _1325542])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1325538), hAPP(_1325540, 29403 ^ [_1325538, _1325540, _1325542])), hAPP(_1325540, 29404 ^ [_1325538, _1325540, _1325542])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325538), _1325542)), -(_1325542 = c_Orderings_Obot__class_Obot(tc_fun(_1325538, tc_HOL_Obool))), -(hAPP(_1325540, c_Big__Operators_Olinorder__class_OMin(_1325538, _1325542)) = c_Big__Operators_Olinorder__class_OMin(_1325538, hAPP(c_Set_Oimage(_1325538, _1325538, _1325540), _1325542)))], (10831 ^ _780119) ^ [_972210, _972212, _972214, _972216] : [class_Groups_Oordered__ab__semigroup__add(_972210), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972210), _972212), _972214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972210), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972210), _972216), _972212)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972210), _972216), _972214))))], (36730 ^ _780119) ^ [_1478054, _1478056, _1478058, _1478060, _1478062] : [hBOOL(hAPP(_1478060, hAPP(_1478058, _1478062))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1478054, _1478056, _1478058), _1478060), _1478062)))], (30213 ^ _780119) ^ [_1344484, _1344486, _1344488] : [hBOOL(hAPP(c_Com_OWT, _1344488)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1344484, _1344486, _1344488))))], (51077 ^ _780119) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (33996 ^ _780119) ^ [_1418136, _1418138, _1418140] : [hBOOL(hAPP(_1418136, hAPP(hAPP(c_Product__Type_OPair(_1418138, _1418140), 33997 ^ [_1418136, _1418138, _1418140]), 33998 ^ [_1418136, _1418138, _1418140]))), 34001 ^ _780119 : [(34002 ^ _780119) ^ [_1418283] : [-(hBOOL(hAPP(_1418136, _1418283)))]]], (31349 ^ _780119) ^ [_1366089, _1366091] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366089) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366091)), 31352 ^ _780119 : [(31355 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366091)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (31353 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366089))))]], 31356 ^ _780119 : [(31359 ^ _780119) ^ [] : [31360 ^ _780119 : [(31363 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366089) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (31361 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366091))))]], 31364 ^ _780119 : [(31367 ^ _780119) ^ [] : [_1366089 = _1366091], (31365 ^ _780119) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366091)))]]], (31357 ^ _780119) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366089)))]]], (5815 ^ _780119) ^ [_872265, _872267, _872269, _872271] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_872265), _872267)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_872269), hAPP(c_Set_Oimage(_872265, _872269, _872271), _872267))))], (16626 ^ _780119) ^ [_1082894, _1082896] : [class_Groups_Ogroup__add(_1082894), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082894), c_Groups_Ozero__class_Ozero(_1082894)), _1082896) = hAPP(c_Groups_Ouminus__class_Ouminus(_1082894), _1082896))], (32083 ^ _780119) ^ [_1378063, _1378065] : [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(_1378065))), 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)), _1378063))))), -(hAPP(c_Nat_OSuc, _1378063) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1378065))], (38249 ^ _780119) ^ [_1519421, _1519423] : [-(c_Relation_Orefl__on(_1519421, _1519423, c_Relation_OId__on(_1519421, _1519423)))], (3844 ^ _780119) ^ [_838032, _838034, _838036, _838038, _838040, _838042] : [-(c_Divides_Odiv__class_Omod(_838042, _838038, _838034) = c_Divides_Odiv__class_Omod(_838040, _838036, _838032)), _838042 = _838040, _838038 = _838036, _838034 = _838032], (49102 ^ _780119) ^ [_1773723, _1773725, _1773727, _1773729] : [c_List_Olist__all2(_1773723, _1773725, _1773727, c_List_Olist_ONil(_1773723), _1773729), -(_1773729 = c_List_Olist_ONil(_1773725))], (35851 ^ _780119) ^ [_1458609, _1458611] : [c_Equiv__Relations_Oequiv(_1458609, c_Orderings_Otop__class_Otop(tc_fun(_1458609, tc_HOL_Obool)), _1458611), -(c_Equiv__Relations_Oequivp(_1458609, hAPP(hAPP(c_COMBC(_1458609, tc_fun(tc_prod(_1458609, _1458609), tc_HOL_Obool), tc_fun(_1458609, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458609, tc_fun(tc_fun(tc_prod(_1458609, _1458609), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1458609, _1458609), tc_HOL_Obool), tc_fun(_1458609, tc_HOL_Obool)), _1458609), c_COMBC(_1458609, tc_fun(tc_prod(_1458609, _1458609), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458609, tc_prod(_1458609, _1458609)), tc_fun(_1458609, tc_fun(tc_fun(tc_prod(_1458609, _1458609), tc_HOL_Obool), tc_HOL_Obool)), _1458609), hAPP(c_COMBB(tc_prod(_1458609, _1458609), tc_fun(tc_fun(tc_prod(_1458609, _1458609), tc_HOL_Obool), tc_HOL_Obool), _1458609), c_member(tc_prod(_1458609, _1458609)))), c_Product__Type_OPair(_1458609, _1458609)))), _1458611)))], (35503 ^ _780119) ^ [_1450448, _1450450] : [-(c_Relation_OId__on(_1450448, _1450450) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1450448, tc_fun(tc_prod(_1450448, _1450448), tc_HOL_Obool)), _1450450), hAPP(hAPP(c_COMBC(_1450448, tc_fun(tc_prod(_1450448, _1450448), tc_HOL_Obool), tc_fun(tc_prod(_1450448, _1450448), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1450448, _1450448), tc_fun(tc_fun(tc_prod(_1450448, _1450448), tc_HOL_Obool), tc_fun(tc_prod(_1450448, _1450448), tc_HOL_Obool)), _1450448), c_Set_Oinsert(tc_prod(_1450448, _1450448))), hAPP(hAPP(c_COMBS(_1450448, _1450448, tc_prod(_1450448, _1450448)), c_Product__Type_OPair(_1450448, _1450448)), c_COMBI(_1450448)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1450448, _1450448), tc_HOL_Obool)))))], (47933 ^ _780119) ^ [_1748469, _1748471] : [c_List_Oremdups(_1748469, _1748471) = c_List_Olist_ONil(_1748469), -(_1748471 = c_List_Olist_ONil(_1748469))], (45138 ^ _780119) ^ [_1684750, _1684752, _1684754, _1684756] : [hAPP(hAPP(c_List_Oappend(_1684750), _1684752), _1684754) = hAPP(hAPP(c_List_Oappend(_1684750), _1684756), _1684754), -(_1684752 = _1684756)], (4074 ^ _780119) ^ [_841649, _841651, _841653, _841655, _841657, _841659, _841661, _841663] : [-(c_Enum_Oproduct(_841663, _841659, _841655, _841651) = c_Enum_Oproduct(_841661, _841657, _841653, _841649)), _841663 = _841661, _841659 = _841657, _841655 = _841653, _841651 = _841649], (36906 ^ _780119) ^ [_1482208, _1482210, _1482212, _1482214, _1482216, _1482218] : [-(hBOOL(hAPP(hAPP(c_member(_1482208), _1482210), _1482212))), 36909 ^ _780119 : [(36916 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482208), _1482214), _1482212))), -(hAPP(c_Set_Ovimage(_1482216, _1482208, hAPP(hAPP(c_COMBC(_1482216, _1482208, _1482208), hAPP(hAPP(c_COMBC(_1482216, _1482208, tc_fun(_1482208, _1482208)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1482208, tc_fun(_1482208, _1482208)), _1482216), c_If(_1482208)), hAPP(hAPP(c_COMBC(_1482216, tc_fun(_1482216, tc_HOL_Obool), tc_HOL_Obool), c_member(_1482216)), _1482218))), _1482210)), _1482214)), _1482212) = c_Orderings_Obot__class_Obot(tc_fun(_1482216, tc_HOL_Obool)))], (36910 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1482208), _1482214), _1482212)), -(hAPP(c_Set_Ovimage(_1482216, _1482208, hAPP(hAPP(c_COMBC(_1482216, _1482208, _1482208), hAPP(hAPP(c_COMBC(_1482216, _1482208, tc_fun(_1482208, _1482208)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1482208, tc_fun(_1482208, _1482208)), _1482216), c_If(_1482208)), hAPP(hAPP(c_COMBC(_1482216, tc_fun(_1482216, tc_HOL_Obool), tc_HOL_Obool), c_member(_1482216)), _1482218))), _1482210)), _1482214)), _1482212) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1482216, tc_HOL_Obool)), _1482218))]]], (18023 ^ _780119) ^ [_1108419, _1108421, _1108423, _1108425] : [class_Rings_Olinordered__semidom(_1108419), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1108421), _1108423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108419), c_Groups_Ozero__class_Ozero(_1108419)), _1108425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108419), _1108425), c_Groups_Oone__class_Oone(_1108419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108419), hAPP(hAPP(c_Power_Opower__class_Opower(_1108419), _1108425), _1108423)), hAPP(hAPP(c_Power_Opower__class_Opower(_1108419), _1108425), _1108421))))], (39477 ^ _780119) ^ [_1548084, _1548086] : [-(hAPP(c_Relation_ORange(_1548084, _1548084), c_Transitive__Closure_Otrancl(_1548084, _1548086)) = hAPP(c_Relation_ORange(_1548084, _1548084), _1548086))], (21194 ^ _780119) ^ [_1165703, _1165705, _1165707, _1165709] : [class_Fields_Olinordered__field(_1165703), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165703), c_Groups_Ozero__class_Ozero(_1165703)), _1165705)), 21201 ^ _780119 : [(21208 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165703), _1165707), _1165705)), _1165709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165703), _1165707), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165703), _1165709), _1165705))))], (21202 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165703), _1165707), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165703), _1165709), _1165705))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165703), _1165707), _1165705)), _1165709)))]]], (4976 ^ _780119) ^ [_856128, _856130, _856132, _856134] : [-(c_Lazy__Sequence_Ohb__flat(_856134, _856130) = c_Lazy__Sequence_Ohb__flat(_856132, _856128)), _856134 = _856132, _856130 = _856128], (47454 ^ _780119) ^ [_1737036, _1737038] : [c_List_Oconcat(_1737036, _1737038) = c_List_Olist_ONil(_1737036), 47457 ^ _780119 : [(47458 ^ _780119) ^ [_1737127] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1737036)), _1737127), hAPP(c_List_Oset(tc_List_Olist(_1737036)), _1737038))), -(_1737127 = c_List_Olist_ONil(_1737036))]]], (28020 ^ _780119) ^ [_1297506, _1297508] : [class_Orderings_Olinorder(_1297506), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1297506), _1297508), _1297508) = _1297508)], (8624 ^ _780119) ^ [_929332, _929334, _929336] : [class_Orderings_Oorder(_929332), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929332), _929334), _929336)), _929334 = _929336], (12443 ^ _780119) ^ [_1004810, _1004812, _1004814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004810), _1004812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004810), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1004812), _1004814))))], (30151 ^ _780119) ^ [_1343491, _1343493, _1343495] : [class_Int_Onumber__ring(_1343491), class_Int_Oring__char__0(_1343491), 30158 ^ _780119 : [(30165 ^ _780119) ^ [] : [_1343493 = _1343495, -(hAPP(c_Int_Onumber__class_Onumber__of(_1343491), _1343493) = hAPP(c_Int_Onumber__class_Onumber__of(_1343491), _1343495))], (30159 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1343491), _1343493) = hAPP(c_Int_Onumber__class_Onumber__of(_1343491), _1343495), -(_1343493 = _1343495)]]], (18838 ^ _780119) ^ [_1123517, _1123519] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1123517, _1123519)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1123519)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45976 ^ _780119) ^ [_1705956, _1705958, _1705960, _1705962, _1705964, _1705966] : [-(hAPP(c_List_Ofoldl(_1705956, _1705958, _1705960, _1705962), hAPP(hAPP(c_List_Oappend(_1705958), _1705964), _1705966)) = hAPP(c_List_Ofoldl(_1705956, _1705958, _1705960, hAPP(c_List_Ofoldl(_1705956, _1705958, _1705960, _1705962), _1705964)), _1705966))], (15358 ^ _780119) ^ [_1060324, _1060326, _1060328] : [15359 ^ _780119 : [(15362 ^ _780119) ^ [] : [_1060326 = _1060328], (15360 ^ _780119) ^ [] : [_1060324 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060324), _1060326) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060324), _1060328))], (51507 ^ _780119) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (45199 ^ _780119) ^ [_1686160, _1686162, _1686164, _1686166, _1686168, _1686170] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686160)), _1686162) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686164)), _1686166), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686160)), _1686168) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686164)), _1686170), -(hAPP(hAPP(c_List_Ozip(_1686160, _1686164), hAPP(hAPP(c_List_Oappend(_1686160), _1686162), _1686168)), hAPP(hAPP(c_List_Oappend(_1686164), _1686166), _1686170)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1686160, _1686164)), hAPP(hAPP(c_List_Ozip(_1686160, _1686164), _1686162), _1686166)), hAPP(hAPP(c_List_Ozip(_1686160, _1686164), _1686168), _1686170)))], (42475 ^ _780119) ^ [_1619965, _1619967, _1619969, _1619971] : [-(c_Map_Omap__add(_1619965, _1619967, _1619969, hAPP(c_Map_Omap__of(_1619965, _1619967), _1619971)) = c_List_Ofoldr(tc_prod(_1619965, _1619967), tc_fun(_1619965, tc_Option_Ooption(_1619967)), hAPP(c_Product__Type_Oprod_Oprod__case(_1619965, _1619967, tc_fun(tc_fun(_1619965, tc_Option_Ooption(_1619967)), tc_fun(_1619965, tc_Option_Ooption(_1619967)))), hAPP(hAPP(c_COMBC(_1619965, tc_fun(_1619967, tc_Option_Ooption(_1619967)), tc_fun(_1619967, tc_fun(tc_fun(_1619965, tc_Option_Ooption(_1619967)), tc_fun(_1619965, tc_Option_Ooption(_1619967))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1619967), tc_fun(tc_fun(_1619965, tc_Option_Ooption(_1619967)), tc_fun(_1619965, tc_Option_Ooption(_1619967)))), tc_fun(tc_fun(_1619967, tc_Option_Ooption(_1619967)), tc_fun(_1619967, tc_fun(tc_fun(_1619965, tc_Option_Ooption(_1619967)), tc_fun(_1619965, tc_Option_Ooption(_1619967))))), _1619965), c_COMBB(tc_Option_Ooption(_1619967), tc_fun(tc_fun(_1619965, tc_Option_Ooption(_1619967)), tc_fun(_1619965, tc_Option_Ooption(_1619967))), _1619967)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1619965, tc_Option_Ooption(_1619967)), tc_fun(tc_Option_Ooption(_1619967), tc_fun(_1619965, tc_Option_Ooption(_1619967)))), tc_fun(tc_Option_Ooption(_1619967), tc_fun(tc_fun(_1619965, tc_Option_Ooption(_1619967)), tc_fun(_1619965, tc_Option_Ooption(_1619967)))), _1619965), c_COMBC(tc_fun(_1619965, tc_Option_Ooption(_1619967)), tc_Option_Ooption(_1619967), tc_fun(_1619965, tc_Option_Ooption(_1619967)))), hAPP(c_COMBC(tc_fun(_1619965, tc_Option_Ooption(_1619967)), _1619965, tc_fun(tc_Option_Ooption(_1619967), tc_fun(_1619965, tc_Option_Ooption(_1619967)))), c_Fun_Ofun__upd(_1619965, tc_Option_Ooption(_1619967)))))), c_Option_Ooption_OSome(_1619967))), _1619971, _1619969))], (46521 ^ _780119) ^ [_1717863, _1717865, _1717867, _1717869] : [_1717863 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717865)), _1717867)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1717865, hAPP(hAPP(c_List_Olist__update(_1717865, _1717867), _1717863), _1717869)) = c_List_Obutlast(_1717865, _1717867))], (37696 ^ _780119) ^ [_1502747, _1502749, _1502751, _1502753] : [hBOOL(hAPP(c_Predicate_ODomainP(_1502747, _1502749, hAPP(hAPP(c_COMBC(_1502747, tc_fun(tc_prod(_1502747, _1502749), tc_HOL_Obool), tc_fun(_1502749, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502749, tc_fun(tc_fun(tc_prod(_1502747, _1502749), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1502747, _1502749), tc_HOL_Obool), tc_fun(_1502749, tc_HOL_Obool)), _1502747), c_COMBC(_1502749, tc_fun(tc_prod(_1502747, _1502749), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502749, tc_prod(_1502747, _1502749)), tc_fun(_1502749, tc_fun(tc_fun(tc_prod(_1502747, _1502749), tc_HOL_Obool), tc_HOL_Obool)), _1502747), hAPP(c_COMBB(tc_prod(_1502747, _1502749), tc_fun(tc_fun(tc_prod(_1502747, _1502749), tc_HOL_Obool), tc_HOL_Obool), _1502749), c_member(tc_prod(_1502747, _1502749)))), c_Product__Type_OPair(_1502747, _1502749)))), _1502751)), _1502753)), -(hBOOL(hAPP(hAPP(c_member(_1502747), _1502753), hAPP(c_Relation_ODomain(_1502747, _1502749), _1502751))))], (24755 ^ _780119) ^ [_1233475, _1233477] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1233475), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1233477) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1233475, _1233477))], (51059 ^ _780119) ^ [] : [-(class_HOL_Oequal(tc_Com_Ocom))], (44832 ^ _780119) ^ [_1677963, _1677965, _1677967, _1677969] : [_1677963 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1677965), _1677963), hAPP(hAPP(c_List_Olist_OCons(_1677965), _1677967), _1677969)) = c_List_Olist_ONil(_1677965))], (31499 ^ _780119) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44128 ^ _780119) ^ [_1662892, _1662894] : [class_Groups_Ocomm__monoid__add(_1662892), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1662892), _1662894) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1662892), hAPP(c_List_Onth(_1662892), _1662894)), 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(_1662892)), _1662894))))], (39617 ^ _780119) ^ [_1551783, _1551785, _1551787] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1551783, _1551783)), hAPP(hAPP(c_Product__Type_OPair(_1551783, _1551783), _1551785), _1551785)), c_Transitive__Closure_Ortrancl(_1551783, _1551787))))], (14468 ^ _780119) ^ [_1045349, _1045351, _1045353] : [class_Rings_Oring__1(_1045349), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1045349), hAPP(c_Groups_Ouminus__class_Ouminus(_1045349), _1045351)), _1045353) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045349), hAPP(hAPP(c_Power_Opower__class_Opower(_1045349), hAPP(c_Groups_Ouminus__class_Ouminus(_1045349), c_Groups_Oone__class_Oone(_1045349))), _1045353)), hAPP(hAPP(c_Power_Opower__class_Opower(_1045349), _1045351), _1045353)))], (2186 ^ _780119) ^ [_812167, _812169, _812171, _812173, _812175, _812177, _812179, _812181] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_812181, _812177, _812173, _812169) = c_Nat_Osemiring__1__class_Oof__nat__aux(_812179, _812175, _812171, _812167)), _812181 = _812179, _812177 = _812175, _812173 = _812171, _812169 = _812167], (42562 ^ _780119) ^ [_1622288, _1622290, _1622292, _1622294, _1622296, _1622298, _1622300] : [-(c_List_Ofoldr(_1622288, _1622290, _1622292, hAPP(hAPP(c_List_Omap(_1622294, _1622288), _1622296), _1622298), _1622300) = c_List_Ofoldr(_1622294, _1622290, hAPP(c_Fun_Ocomp(_1622288, tc_fun(_1622290, _1622290), _1622294, _1622292), _1622296), _1622298, _1622300))], (1650 ^ _780119) ^ [_803468, _803470] : [-(class_Nat_Osemiring__char__0(_803468)), _803470 = _803468, class_Nat_Osemiring__char__0(_803470)], (25506 ^ _780119) ^ [_1246578, _1246580] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1246578, _1246580)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246580), _1246578)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (15394 ^ _780119) ^ [_1060870, _1060872, _1060874] : [15395 ^ _780119 : [(15398 ^ _780119) ^ [] : [_1060870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15396 ^ _780119) ^ [] : [_1060872 = _1060874]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060870), _1060872) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060870), _1060874))], (24813 ^ _780119) ^ [_1234690, _1234692, _1234694] : [class_Orderings_Oorder(_1234690), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1234690, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1234690, _1234692, _1234694)), hAPP(c_SetInterval_Oord__class_OatLeast(_1234690), _1234694)) = c_Orderings_Obot__class_Obot(tc_fun(_1234690, tc_HOL_Obool)))], (12819 ^ _780119) ^ [_1012424, _1012426, _1012428] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1012424), _1012426)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012424), _1012428)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1012424), _1012426)), hAPP(c_Finite__Set_Ocard(_1012424), _1012428)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1012424), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012424, tc_HOL_Obool)), _1012426), _1012428))), hAPP(c_Finite__Set_Ocard(_1012424), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1012424, tc_HOL_Obool)), _1012426), _1012428))))], (38038 ^ _780119) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (47873 ^ _780119) ^ [_1747172, _1747174, _1747176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747172)), c_List_OtakeWhile(_1747172, _1747174, _1747176))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747172)), _1747176))), hBOOL(hAPP(_1747174, hAPP(hAPP(c_List_Onth(_1747172), _1747176), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747172)), c_List_OtakeWhile(_1747172, _1747174, _1747176)))))], (44506 ^ _780119) ^ [] : [-(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))))], (43655 ^ _780119) ^ [_1651272, _1651274, _1651276, _1651278, _1651280] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651272), tc_List_Olist(_1651272))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651272), tc_List_Olist(_1651272)), _1651274), hAPP(hAPP(c_List_Olist_OCons(_1651272), _1651276), _1651278))), c_List_Olistrel(_1651272, _1651280))), 43660 ^ _780119 : [(43663 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651272, _1651272)), hAPP(hAPP(c_Product__Type_OPair(_1651272, _1651272), 43658 ^ [_1651272, _1651274, _1651276, _1651278, _1651280]), _1651276)), _1651280)))], (43665 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651272), tc_List_Olist(_1651272))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651272), tc_List_Olist(_1651272)), 43659 ^ [_1651272, _1651274, _1651276, _1651278, _1651280]), _1651278)), c_List_Olistrel(_1651272, _1651280))))], (43661 ^ _780119) ^ [] : [-(_1651274 = hAPP(hAPP(c_List_Olist_OCons(_1651272), 43658 ^ [_1651272, _1651274, _1651276, _1651278, _1651280]), 43659 ^ [_1651272, _1651274, _1651276, _1651278, _1651280]))]]], (17182 ^ _780119) ^ [_1092164, _1092166, _1092168, _1092170] : [class_Groups_Oordered__comm__monoid__add(_1092164), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092164), c_Groups_Ozero__class_Ozero(_1092164)), _1092166)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092164), _1092168), _1092170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092164), _1092168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092164), _1092166), _1092170))))], (45796 ^ _780119) ^ [_1702571, _1702573, _1702575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702571), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702573)), _1702575))), -(_1702575 = hAPP(hAPP(c_List_Oappend(_1702573), hAPP(hAPP(c_List_Otake(_1702573), _1702571), _1702575)), hAPP(hAPP(c_List_Olist_OCons(_1702573), hAPP(hAPP(c_List_Onth(_1702573), _1702575), _1702571)), hAPP(hAPP(c_List_Odrop(_1702573), hAPP(c_Nat_OSuc, _1702571)), _1702575))))], (32935 ^ _780119) ^ [_1393683, _1393685] : [class_Rings_Oring__1__no__zero__divisors(_1393683), 32938 ^ _780119 : [(32939 ^ _780119) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1393683), _1393685), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1393683), -(_1393685 = c_Groups_Oone__class_Oone(_1393683)), -(_1393685 = hAPP(c_Groups_Ouminus__class_Ouminus(_1393683), c_Groups_Oone__class_Oone(_1393683)))], (32949 ^ _780119) ^ [] : [32950 ^ _780119 : [(32953 ^ _780119) ^ [] : [_1393685 = hAPP(c_Groups_Ouminus__class_Ouminus(_1393683), c_Groups_Oone__class_Oone(_1393683))], (32951 ^ _780119) ^ [] : [_1393685 = c_Groups_Oone__class_Oone(_1393683)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1393683), _1393685), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1393683))]]], (36521 ^ _780119) ^ [_1473081] : [-(c_Fun_Oinj__on(_1473081, tc_fun(_1473081, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1473081, tc_fun(_1473081, tc_HOL_Obool), tc_fun(_1473081, tc_HOL_Obool)), c_Set_Oinsert(_1473081)), c_Orderings_Obot__class_Obot(tc_fun(_1473081, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1473081, tc_HOL_Obool))))], (19586 ^ _780119) ^ [_1136035, _1136037, _1136039, _1136041, _1136043] : [class_Fields_Ofield(_1136035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136037), _1136039)), -(hAPP(_1136041, _1136043) = c_Groups_Ozero__class_Ozero(_1136035)), 19597 ^ _780119 : [(19604 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1136037), _1136043), _1136039))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1136037, _1136035), _1136041), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1136037, tc_HOL_Obool)), _1136039), hAPP(hAPP(c_Set_Oinsert(_1136037), _1136043), c_Orderings_Obot__class_Obot(tc_fun(_1136037, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1136037, _1136035), _1136041), _1136039))], (19598 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1136037), _1136043), _1136039)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1136037, _1136035), _1136041), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1136037, tc_HOL_Obool)), _1136039), hAPP(hAPP(c_Set_Oinsert(_1136037), _1136043), c_Orderings_Obot__class_Obot(tc_fun(_1136037, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136035), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1136037, _1136035), _1136041), _1136039)), hAPP(_1136041, _1136043)))]]], (5548 ^ _780119) ^ [_865118, _865120, _865122, _865124] : [-(tc_sum(_865124, _865120) = tc_sum(_865122, _865118)), _865124 = _865122, _865120 = _865118], (46963 ^ _780119) ^ [_1727092, _1727094, _1727096] : [class_Orderings_Olinorder(_1727092), c_List_Olinorder__class_Osorted(_1727092, _1727094), -(c_List_Olinorder__class_Osorted(_1727092, c_List_Oremove1(_1727092, _1727096, _1727094)))], (25077 ^ _780119) ^ [_1239380, _1239382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239380)), 25080 ^ _780119 : [(25087 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239382), _1239380)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1239382)), hAPP(c_Int_Onat, _1239380))))], (25081 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1239382)), hAPP(c_Int_Onat, _1239380))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239382), _1239380)))]]], (25448 ^ _780119) ^ [_1245539, _1245541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245539)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1245539), _1245541)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1245539)), _1245541))], (39715 ^ _780119) ^ [_1554208, _1554210] : [-(c_Transitive__Closure_Ortrancl(_1554208, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554208, _1554208), tc_HOL_Obool)), _1554210), c_Relation_OId(_1554208))) = c_Transitive__Closure_Ortrancl(_1554208, _1554210))], (24691 ^ _780119) ^ [_1232340, _1232342, _1232344] : [class_Orderings_Oord(_1232340), 24694 ^ _780119 : [(24701 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232340), _1232344), _1232342)), -(hBOOL(hAPP(hAPP(c_member(_1232340), _1232342), hAPP(c_SetInterval_Oord__class_OatLeast(_1232340), _1232344))))], (24695 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1232340), _1232342), hAPP(c_SetInterval_Oord__class_OatLeast(_1232340), _1232344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232340), _1232344), _1232342)))]]], (44864 ^ _780119) ^ [_1678517, _1678519] : [-(c_List_Oset__Cons(_1678517, _1678519, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1678517)), c_List_Olist_ONil(_1678517)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1678517), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1678517, tc_List_Olist(_1678517), hAPP(hAPP(c_COMBC(_1678517, tc_List_Olist(_1678517), tc_List_Olist(_1678517)), c_List_Olist_OCons(_1678517)), c_List_Olist_ONil(_1678517))), _1678519))], (24361 ^ _780119) ^ [_1226301, _1226303, _1226305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226301)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1226303), _1226305)), 24368 ^ _780119 : [(24369 ^ _780119) ^ [_1226491] : [24371 ^ _780119 : [(24375 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24373 ^ [_1226301, _1226303, _1226305, _1226491]), _1226305)))], (24377 ^ _780119) ^ [] : [-(_1226491 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24373 ^ [_1226301, _1226303, _1226305, _1226491]), 24370 ^ [_1226301, _1226303, _1226305, _1226491]))], (24372 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24370 ^ [_1226301, _1226303, _1226305, _1226491]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1226301))))]], -(_1226491 = _1226303), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226491), _1226301) = _1226303]]], (7266 ^ _780119) ^ [_901844, _901846, _901848, _901850, _901852] : [class_Lattices_Olattice(_901844), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901846, _901844)), _901848), _901850), _901852) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901844), hAPP(_901848, _901852)), hAPP(_901850, _901852)))], (37717 ^ _780119) ^ [_1503817, _1503819, _1503821, _1503823, _1503825] : [hBOOL(hAPP(hAPP(_1503817, _1503819), _1503821)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1503823, _1503825, _1503817), _1503819)))], (22964 ^ _780119) ^ [_1199521] : [class_Rings_Osemiring__1(_1199521), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1199521), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1199521))], (51211 ^ _780119) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11780 ^ _780119) ^ [_992200, _992202, _992204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992200), _992202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992200), _992204)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992202), _992204))))], (44398 ^ _780119) ^ [_1669594, _1669596, _1669598, _1669600, _1669602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1669594, tc_HOL_Obool)), hAPP(c_List_Oset(_1669594), _1669596)), _1669598)), hBOOL(hAPP(hAPP(c_member(_1669594), _1669600), _1669598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1669594, tc_HOL_Obool)), hAPP(c_List_Oset(_1669594), hAPP(hAPP(c_List_Olist__update(_1669594, _1669596), _1669602), _1669600))), _1669598)))], (33617 ^ _780119) ^ [_1407692, _1407694, _1407696, _1407698, _1407700, _1407702] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1407692, _1407694)), hAPP(hAPP(c_Product__Type_OPair(_1407692, _1407694), _1407700), _1407702)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool)), _1407696), _1407698))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407692, tc_fun(_1407694, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1407692, tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_fun(_1407694, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407694, tc_fun(tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_fun(_1407694, tc_HOL_Obool)), _1407692), c_COMBC(_1407694, tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407694, tc_prod(_1407692, _1407694)), tc_fun(_1407694, tc_fun(tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_HOL_Obool)), _1407692), hAPP(c_COMBB(tc_prod(_1407692, _1407694), tc_fun(tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_HOL_Obool), _1407694), c_member(tc_prod(_1407692, _1407694)))), c_Product__Type_OPair(_1407692, _1407694)))), _1407696)), hAPP(hAPP(c_COMBC(_1407692, tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_fun(_1407694, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407694, tc_fun(tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_fun(_1407694, tc_HOL_Obool)), _1407692), c_COMBC(_1407694, tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407694, tc_prod(_1407692, _1407694)), tc_fun(_1407694, tc_fun(tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_HOL_Obool)), _1407692), hAPP(c_COMBB(tc_prod(_1407692, _1407694), tc_fun(tc_fun(tc_prod(_1407692, _1407694), tc_HOL_Obool), tc_HOL_Obool), _1407694), c_member(tc_prod(_1407692, _1407694)))), c_Product__Type_OPair(_1407692, _1407694)))), _1407698)), _1407700), _1407702)))], (14721 ^ _780119) ^ [_1050401, _1050403] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050401), _1050403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1050401)), _1050403)))], (1190 ^ _780119) ^ [_797718, _797720] : [-(class_Int_Onumber__ring(_797718)), _797720 = _797718, class_Int_Onumber__ring(_797720)], (7882 ^ _780119) ^ [_914321, _914323, _914325, _914327] : [c_Com_Ocom_OWhile(_914321, _914323) = c_Com_Ocom_OWhile(_914325, _914327), 7885 ^ _780119 : [(7888 ^ _780119) ^ [] : [-(_914323 = _914327)], (7886 ^ _780119) ^ [] : [-(_914321 = _914325)]]], (9942 ^ _780119) ^ [_953295, _953297, _953299] : [class_Lattices_Osemilattice__inf(_953295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953295), _953297), _953299)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_953295), _953299), _953297) = _953297)], (39947 ^ _780119) ^ [_1559566, _1559568, _1559570] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1559566, _1559566), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1559566, _1559566), _1559568)), c_Transitive__Closure_Ortrancl(_1559566, _1559568)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1559566, _1559566), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1559566, _1559566)), hAPP(hAPP(c_Product__Type_OPair(_1559566, _1559566), _1559570), _1559570)), c_Transitive__Closure_Otrancl(_1559566, _1559568)))], (49537 ^ _780119) ^ [_1784161, _1784163, _1784165, _1784167, _1784169] : [-(hAPP(c_List_Ofilter(_1784161, _1784163), _1784165) = hAPP(hAPP(c_List_Olist_OCons(_1784161), _1784167), _1784169)), 49538 ^ _780119 : [(49539 ^ _780119) ^ [_1784289, _1784291] : [_1784165 = hAPP(hAPP(c_List_Oappend(_1784161), _1784291), hAPP(hAPP(c_List_Olist_OCons(_1784161), _1784167), _1784289)), 49545 ^ _780119 : [(49548 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1784163, 49544 ^ [_1784161, _1784163, _1784165, _1784167, _1784169, _1784289, _1784291])))], (49546 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1784161), 49544 ^ [_1784161, _1784163, _1784165, _1784167, _1784169, _1784289, _1784291]), hAPP(c_List_Oset(_1784161), _1784291))))]], hBOOL(hAPP(_1784163, _1784167)), _1784169 = hAPP(c_List_Ofilter(_1784161, _1784163), _1784289)]]], (51213 ^ _780119) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (40042 ^ _780119) ^ [_1561778, _1561780, _1561782, _1561784, _1561786] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561778, _1561780)), hAPP(hAPP(c_Product__Type_OPair(_1561778, _1561780), _1561782), _1561784)), hAPP(c_Relation_Oconverse(_1561780, _1561778), _1561786))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561780, _1561778)), hAPP(hAPP(c_Product__Type_OPair(_1561780, _1561778), _1561784), _1561782)), _1561786)))], (37131 ^ _780119) ^ [_1489397, _1489399, _1489401, _1489403, _1489405, _1489407, _1489409] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1489397, _1489401)), hAPP(hAPP(c_Product__Type_OPair(_1489397, _1489401), _1489407), _1489409)), hAPP(hAPP(c_Relation_Orel__comp(_1489397, _1489399, _1489401), _1489403), _1489405))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1489397, _1489399, _1489401, hAPP(hAPP(c_COMBC(_1489397, tc_fun(tc_prod(_1489397, _1489399), tc_HOL_Obool), tc_fun(_1489399, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1489399, tc_fun(tc_fun(tc_prod(_1489397, _1489399), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1489397, _1489399), tc_HOL_Obool), tc_fun(_1489399, tc_HOL_Obool)), _1489397), c_COMBC(_1489399, tc_fun(tc_prod(_1489397, _1489399), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1489399, tc_prod(_1489397, _1489399)), tc_fun(_1489399, tc_fun(tc_fun(tc_prod(_1489397, _1489399), tc_HOL_Obool), tc_HOL_Obool)), _1489397), hAPP(c_COMBB(tc_prod(_1489397, _1489399), tc_fun(tc_fun(tc_prod(_1489397, _1489399), tc_HOL_Obool), tc_HOL_Obool), _1489399), c_member(tc_prod(_1489397, _1489399)))), c_Product__Type_OPair(_1489397, _1489399)))), _1489403), hAPP(hAPP(c_COMBC(_1489399, tc_fun(tc_prod(_1489399, _1489401), tc_HOL_Obool), tc_fun(_1489401, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1489401, tc_fun(tc_fun(tc_prod(_1489399, _1489401), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1489399, _1489401), tc_HOL_Obool), tc_fun(_1489401, tc_HOL_Obool)), _1489399), c_COMBC(_1489401, tc_fun(tc_prod(_1489399, _1489401), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1489401, tc_prod(_1489399, _1489401)), tc_fun(_1489401, tc_fun(tc_fun(tc_prod(_1489399, _1489401), tc_HOL_Obool), tc_HOL_Obool)), _1489399), hAPP(c_COMBB(tc_prod(_1489399, _1489401), tc_fun(tc_fun(tc_prod(_1489399, _1489401), tc_HOL_Obool), tc_HOL_Obool), _1489401), c_member(tc_prod(_1489399, _1489401)))), c_Product__Type_OPair(_1489399, _1489401)))), _1489405)), _1489407), _1489409)))], (17548 ^ _780119) ^ [_1099083, _1099085, _1099087, _1099089] : [class_Rings_Olinordered__semidom(_1099083), hAPP(hAPP(c_Power_Opower__class_Opower(_1099083), _1099085), hAPP(c_Nat_OSuc, _1099087)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1099083), _1099089), hAPP(c_Nat_OSuc, _1099087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099083), c_Groups_Ozero__class_Ozero(_1099083)), _1099085)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099083), c_Groups_Ozero__class_Ozero(_1099083)), _1099089)), -(_1099085 = _1099089)], (39839 ^ _780119) ^ [_1557174] : [-(c_Relation_Orefl__on(_1557174, c_Orderings_Otop__class_Otop(tc_fun(_1557174, tc_HOL_Obool)), c_Relation_OId(_1557174)))], (44838 ^ _780119) ^ [_1678074, _1678076, _1678078, _1678080] : [-(_1678074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1678076), _1678074), hAPP(hAPP(c_List_Olist_OCons(_1678076), _1678078), _1678080)) = hAPP(hAPP(c_List_Olist_OCons(_1678076), _1678078), hAPP(hAPP(c_List_Otake(_1678076), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1678074), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1678080)))], (40862 ^ _780119) ^ [_1581321, _1581323, _1581325] : [class_Lattices_Olattice(_1581321), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581321), _1581323)), -(hBOOL(hAPP(hAPP(c_member(_1581321), _1581325), _1581323))), -(c_Big__Operators_Olattice__class_OInf__fin(_1581321, hAPP(hAPP(c_Set_Oinsert(_1581321), _1581325), _1581323)) = hAPP(hAPP(c_Finite__Set_Ofold(_1581321, _1581321, c_Lattices_Osemilattice__inf__class_Oinf(_1581321)), _1581325), _1581323))], (11854 ^ _780119) ^ [_993449, _993451, _993453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993449), _993451)), _993453)), 11857 ^ _780119 : [(11860 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993451), _993453)))], (11858 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993449), _993453)))]]], (44648 ^ _780119) ^ [_1674590] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674590)), c_List_Olist_ONil(_1674590)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32421 ^ _780119) ^ [_1384662] : [c_Int_OBit0(_1384662) = c_Int_OPls, -(_1384662 = c_Int_OPls)], (26741 ^ _780119) ^ [_1268507, _1268509, _1268511] : [-(hAPP(hAPP(c_Set_Oinsert(_1268507), _1268509), _1268511) = hAPP(c_Set_OCollect(_1268507), hAPP(hAPP(c_COMBS(_1268507, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268507), c_fdisj), hAPP(hAPP(c_COMBC(_1268507, _1268507, tc_HOL_Obool), c_fequal), _1268509))), hAPP(hAPP(c_COMBC(_1268507, tc_fun(_1268507, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268507)), _1268511))))], (46315 ^ _780119) ^ [_1713853, _1713855, _1713857] : [_1713853 = c_List_Olist_ONil(_1713855), -(c_List_Olast(_1713855, hAPP(hAPP(c_List_Olist_OCons(_1713855), _1713857), _1713853)) = _1713857)], (43851 ^ _780119) ^ [_1656351] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1656351) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43854 ^ _780119 : [(43855 ^ _780119) ^ [_1656426] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1656426), hAPP(c_List_Oset(tc_Nat_Onat), _1656351))), -(_1656426 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42330 ^ _780119) ^ [_1616968] : [-(c_Nitpick_Odenom(_1616968) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1616968, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1616968)))], (18450 ^ _780119) ^ [_1116688, _1116690, _1116692] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116688), _1116690)), _1116692) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116688), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116690), _1116692)))], (13871 ^ _780119) ^ [_1032266, _1032268] : [class_Lattices_Oboolean__algebra(_1032266), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1032266), hAPP(c_Groups_Ouminus__class_Ouminus(_1032266), _1032268)), _1032268) = c_Orderings_Obot__class_Obot(_1032266))], (30479 ^ _780119) ^ [_1349827, _1349829, _1349831, _1349833] : [class_Fields_Ofield__inverse__zero(_1349827), class_Int_Onumber(_1349827), 30486 ^ _780119 : [(30487 ^ _780119) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349827), _1349829), _1349831) = hAPP(c_Int_Onumber__class_Onumber__of(_1349827), _1349833), 30490 ^ _780119 : [(30497 ^ _780119) ^ [] : [_1349831 = c_Groups_Ozero__class_Ozero(_1349827), -(hAPP(c_Int_Onumber__class_Onumber__of(_1349827), _1349833) = c_Groups_Ozero__class_Ozero(_1349827))], (30491 ^ _780119) ^ [] : [-(_1349831 = c_Groups_Ozero__class_Ozero(_1349827)), -(_1349829 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349827), hAPP(c_Int_Onumber__class_Onumber__of(_1349827), _1349833)), _1349831))]]], (30503 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349827), _1349829), _1349831) = hAPP(c_Int_Onumber__class_Onumber__of(_1349827), _1349833)), 30506 ^ _780119 : [(30509 ^ _780119) ^ [] : [_1349829 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349827), hAPP(c_Int_Onumber__class_Onumber__of(_1349827), _1349833)), _1349831)], (30507 ^ _780119) ^ [] : [_1349831 = c_Groups_Ozero__class_Ozero(_1349827)]], 30510 ^ _780119 : [(30513 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1349827), _1349833) = c_Groups_Ozero__class_Ozero(_1349827)], (30511 ^ _780119) ^ [] : [-(_1349831 = c_Groups_Ozero__class_Ozero(_1349827))]]]]], (29510 ^ _780119) ^ [_1327993] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1327993)))], (9672 ^ _780119) ^ [_947420, _947422, _947424, _947426] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947420, tc_HOL_Obool)), _947422), _947424), _947426)), 9675 ^ _780119 : [(9678 ^ _780119) ^ [] : [-(hBOOL(hAPP(_947424, _947426)))], (9676 ^ _780119) ^ [] : [-(hBOOL(hAPP(_947422, _947426)))]]], (12809 ^ _780119) ^ [_1012266, _1012268, _1012270] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1012266), _1012268)), -(hBOOL(hAPP(hAPP(c_member(_1012266), _1012270), _1012268))), -(hAPP(c_Finite__Set_Ocard(_1012266), hAPP(hAPP(c_Set_Oinsert(_1012266), _1012270), _1012268)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1012266), _1012268)))], (33271 ^ _780119) ^ [_1400356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400356), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1400356)), c_Int_OMin)))], (44910 ^ _780119) ^ [_1679761, _1679763, _1679765, _1679767, _1679769, _1679771] : [-(hAPP(c_List_Olist_Olist__case(_1679761, _1679763, _1679765, _1679767), hAPP(hAPP(c_List_Olist_OCons(_1679763), _1679769), _1679771)) = hAPP(hAPP(_1679767, _1679769), _1679771))], (18854 ^ _780119) ^ [_1123786, _1123788, _1123790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1123786)), _1123786 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123786), _1123790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123788), _1123786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1123790)))], (44526 ^ _780119) ^ [_1672136, _1672138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1672136), _1672138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1672136)), hAPP(c_Code__Numeral_Onat__of, _1672138))))], (49022 ^ _780119) ^ [_1771968, _1771970, _1771972, _1771974, _1771976, _1771978, _1771980] : [c_List_Olist__all2(_1771968, _1771970, _1771972, _1771974, hAPP(hAPP(c_List_Omap(_1771976, _1771970), _1771978), _1771980)), -(c_List_Olist__all2(_1771968, _1771976, hAPP(hAPP(c_COMBC(_1771968, tc_fun(_1771976, _1771970), tc_fun(_1771976, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1771970, tc_HOL_Obool), tc_fun(tc_fun(_1771976, _1771970), tc_fun(_1771976, tc_HOL_Obool)), _1771968), c_COMBB(_1771970, tc_HOL_Obool, _1771976)), _1771972)), _1771978), _1771974, _1771980))], (6191 ^ _780119) ^ [_879001, _879003, _879005, _879007, _879009] : [hBOOL(hAPP(hAPP(c_member(_879001), _879003), hAPP(c_Set_Oimage(_879005, _879001, _879007), _879009))), 6195 ^ _780119 : [(6198 ^ _780119) ^ [] : [-(_879003 = hAPP(_879007, 6194 ^ [_879001, _879003, _879005, _879007, _879009]))], (6196 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_879005), 6194 ^ [_879001, _879003, _879005, _879007, _879009]), _879009)))]]], (13686 ^ _780119) ^ [_1028973, _1028975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028973)), hAPP(c_Nat_OSuc, _1028975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028973), _1028975)))], (16368 ^ _780119) ^ [_1078452, _1078454, _1078456, _1078458, _1078460, _1078462] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1078452), -(_1078454 = c_Groups_Ozero__class_Ozero(_1078452)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078452), _1078456), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078452), _1078454), _1078460)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078452), _1078458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078452), _1078454), _1078462)), _1078456 = _1078458, -(_1078460 = _1078462)], (25879 ^ _780119) ^ [_1252404, _1252406, _1252408, _1252410] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1252404), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1252406, tc_Int_Oint), _1252408), _1252410)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1252406, _1252404), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1252404, _1252406), c_Int_Oring__1__class_Oof__int(_1252404)), _1252408)), _1252410)), class_Groups_Ocomm__monoid__mult(_1252404), class_Rings_Oring__1(_1252404)], (22555 ^ _780119) ^ [_1191656, _1191658, _1191660] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1191656, _1191658, _1191660)))), hBOOL(hAPP(c_Com_OWT, _1191658)), hBOOL(hAPP(c_Com_OWT, _1191660))], (24683 ^ _780119) ^ [_1232177, _1232179, _1232181, _1232183] : [class_Orderings_Oorder(_1232177), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1232177, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1232177, _1232179, _1232181)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1232177, _1232181, _1232183)) = c_Orderings_Obot__class_Obot(tc_fun(_1232177, tc_HOL_Obool)))], (26619 ^ _780119) ^ [_1266203, _1266205, _1266207] : [class_Groups_Oordered__ab__group__add__abs(_1266203), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1266203), hAPP(c_Groups_Oabs__class_Oabs(_1266203), _1266205)), hAPP(c_Groups_Oabs__class_Oabs(_1266203), _1266207))), hAPP(c_Groups_Oabs__class_Oabs(_1266203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1266203), _1266205), _1266207)))))], (43601 ^ _780119) ^ [_1649176, _1649178, _1649180, _1649182, _1649184, _1649186] : [-(_1649176 = _1649178), -(hAPP(hAPP(c_Map_Omap__of(_1649180, _1649182), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1649180, _1649182)), hAPP(hAPP(c_Product__Type_OPair(_1649180, _1649182), _1649176), _1649184)), _1649186)), _1649178) = hAPP(hAPP(c_Map_Omap__of(_1649180, _1649182), _1649186), _1649178))], (39679 ^ _780119) ^ [_1553253, _1553255, _1553257, _1553259, _1553261] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553253, _1553253)), hAPP(hAPP(c_Product__Type_OPair(_1553253, _1553253), _1553255), _1553257)), _1553259)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1553253, _1553253)), hAPP(hAPP(c_Product__Type_OPair(_1553253, _1553253), _1553257), _1553261)), c_Transitive__Closure_Ortrancl(_1553253, _1553259))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1553253, _1553253)), hAPP(hAPP(c_Product__Type_OPair(_1553253, _1553253), _1553255), _1553261)), c_Transitive__Closure_Ortrancl(_1553253, _1553259))))], (11929 ^ _780119) ^ [_994892, _994894] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994892), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994894), _994892))))], (39659 ^ _780119) ^ [_1552801, _1552803, _1552805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552801, _1552801), tc_HOL_Obool)), _1552803), c_Transitive__Closure_Ortrancl(_1552801, _1552805))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552801, _1552801), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1552801, _1552803)), c_Transitive__Closure_Ortrancl(_1552801, _1552805))))], (11627 ^ _780119) ^ [_989245, _989247, _989249] : [class_Rings_Olinordered__semidom(_989245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989245), c_Groups_Oone__class_Oone(_989245)), _989247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989245), c_Groups_Oone__class_Oone(_989245)), _989249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989245), c_Groups_Oone__class_Oone(_989245)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989245), _989247), _989249))))], (47202 ^ _780119) ^ [_1731245, _1731247, _1731249, _1731251, _1731253, _1731255] : [class_Orderings_Olinorder(_1731245), c_List_Olinorder__class_Osorted(_1731245, hAPP(hAPP(c_List_Omap(_1731247, _1731245), _1731249), _1731251)), hBOOL(hAPP(_1731253, _1731255)), -(hAPP(c_List_Ofilter(_1731247, _1731253), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1731247, _1731245, _1731249), _1731255), _1731251)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1731247, _1731245, _1731249), _1731255), hAPP(c_List_Ofilter(_1731247, _1731253), _1731251)))], (22169 ^ _780119) ^ [_1184906] : [-(_1184906 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22172 ^ _780119 : [(22179 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184906))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1184906) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22173 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184906)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1184906) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (9596 ^ _780119) ^ [_945926, _945928, _945930, _945932, _945934] : [class_Rings_Oring(_945926), hBOOL(hAPP(c_Finite__Set_Ofinite(_945928), _945930)), hBOOL(hAPP(hAPP(c_member(_945928), _945932), _945930)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_945928, _945926), _945934), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_945928, tc_HOL_Obool)), _945930), hAPP(hAPP(c_Set_Oinsert(_945928), _945932), c_Orderings_Obot__class_Obot(tc_fun(_945928, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_945926), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_945928, _945926), _945934), _945930)), hAPP(_945934, _945932)))], (6441 ^ _780119) ^ [_884261, _884263, _884265, _884267, _884269] : [hAPP(_884261, _884263) = hAPP(c_Option_Ooption_OSome(_884265), _884267), -(hBOOL(hAPP(hAPP(c_member(_884269), _884263), c_Map_Odom(_884269, _884265, _884261))))], (8870 ^ _780119) ^ [_933192, _933194, _933196] : [class_Orderings_Olinorder(_933192), 8873 ^ _780119 : [(8880 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933192), _933196), _933194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933192), _933194), _933196))], (8874 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933192), _933194), _933196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933192), _933196), _933194)))]]], (22336 ^ _780119) ^ [_1187636, _1187638, _1187640] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1187636), _1187638)), _1187640) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1187636), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1187638), _1187640))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1187636), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1187638, _1187640))), _1187640)))], (22725 ^ _780119) ^ [_1195247, _1195249, _1195251, _1195253] : [hBOOL(hAPP(hAPP(_1195251, _1195253), _1195249)), -(hBOOL(hAPP(hAPP(c_member(_1195247), _1195249), c_SetInterval_Oord_OgreaterThan(_1195247, _1195251, _1195253))))], (51245 ^ _780119) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (33379 ^ _780119) ^ [_1402006] : [class_Int_Onumber__ring(_1402006), -(hAPP(c_Int_Onumber__class_Onumber__of(_1402006), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1402006), c_Groups_Oone__class_Oone(_1402006)))], (36261 ^ _780119) ^ [_1467826, _1467828, _1467830, _1467832, _1467834] : [c_Fun_Oinj__on(_1467826, _1467828, _1467830, c_Orderings_Otop__class_Otop(tc_fun(_1467826, tc_HOL_Obool))), 36264 ^ _780119 : [(36271 ^ _780119) ^ [] : [_1467832 = _1467834, -(hAPP(c_Set_Oimage(_1467826, _1467828, _1467830), _1467832) = hAPP(c_Set_Oimage(_1467826, _1467828, _1467830), _1467834))], (36265 ^ _780119) ^ [] : [hAPP(c_Set_Oimage(_1467826, _1467828, _1467830), _1467832) = hAPP(c_Set_Oimage(_1467826, _1467828, _1467830), _1467834), -(_1467832 = _1467834)]]], (49925 ^ _780119) ^ [_1792432, _1792434, _1792436, _1792438] : [class_Rings_Olinordered__semidom(_1792432), 49931 ^ _780119 : [(49934 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1792432), c_Groups_Ozero__class_Ozero(_1792432)), hAPP(_1792438, 49930 ^ [_1792432, _1792434, _1792436, _1792438])))], (49932 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1792434), 49930 ^ [_1792432, _1792434, _1792436, _1792438]), _1792436)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1792432), c_Groups_Ozero__class_Ozero(_1792432)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1792434, _1792432), _1792438), _1792436))))], (12053 ^ _780119) ^ [_997339, _997341, _997343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997339), _997341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997339), _997343)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997341), _997343))))], (20720 ^ _780119) ^ [_1156864, _1156866, _1156868] : [class_Fields_Olinordered__field(_1156864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156864), _1156866), c_Groups_Ozero__class_Ozero(_1156864))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156864), _1156868), c_Groups_Ozero__class_Ozero(_1156864))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156864), c_Groups_Ozero__class_Ozero(_1156864)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156864), _1156866), _1156868))))], (13470 ^ _780119) ^ [_1025182, _1025184, _1025186] : [class_Rings_Oring(_1025182), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025182), hAPP(c_Groups_Ouminus__class_Ouminus(_1025182), _1025184)), hAPP(c_Groups_Ouminus__class_Ouminus(_1025182), _1025186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025182), _1025184), _1025186))], (39549 ^ _780119) ^ [_1549915, _1549917] : [39550 ^ _780119 : [(39553 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1549917), _1549915))], (39551 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1549915), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1549915, _1549917) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (28900 ^ _780119) ^ [_1315790, _1315792] : [class_Orderings_Olinorder(_1315790), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315790), _1315792)), -(c_Big__Operators_Olattice_OSup__fin(_1315790, c_Orderings_Oord__class_Omax(_1315790), _1315792) = hAPP(c_Finite__Set_Ofold1(_1315790, c_Orderings_Oord__class_Omax(_1315790)), _1315792))], (45704 ^ _780119) ^ [_1700164, _1700166, _1700168, _1700170] : [-(_1700164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1700166), _1700164), hAPP(hAPP(c_List_Olist_OCons(_1700166), _1700168), _1700170)) = hAPP(hAPP(c_List_Odrop(_1700166), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1700164), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1700170))], (51453 ^ _780119) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (31861 ^ _780119) ^ [_1374200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1374200)), -(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), _1374200))))], (29358 ^ _780119) ^ [_1324720, _1324722, _1324724] : [class_Orderings_Olinorder(_1324720), hAPP(_1324722, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1324720), 29363 ^ [_1324720, _1324722, _1324724]), 29364 ^ [_1324720, _1324722, _1324724])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1324720), hAPP(_1324722, 29363 ^ [_1324720, _1324722, _1324724])), hAPP(_1324722, 29364 ^ [_1324720, _1324722, _1324724])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324720), _1324724)), -(_1324724 = c_Orderings_Obot__class_Obot(tc_fun(_1324720, tc_HOL_Obool))), -(hAPP(_1324722, c_Big__Operators_Olattice_OInf__fin(_1324720, c_Orderings_Oord__class_Omin(_1324720), _1324724)) = c_Big__Operators_Olattice_OInf__fin(_1324720, c_Orderings_Oord__class_Omin(_1324720), hAPP(c_Set_Oimage(_1324720, _1324720, _1324722), _1324724)))], (40295 ^ _780119) ^ [_1568549, _1568551] : [-(c_Transitive__Closure_Ortrancl(_1568549, _1568551) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1568549, _1568549), 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(_1568549, _1568549), tc_HOL_Obool), tc_fun(tc_prod(_1568549, _1568549), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1568549, _1568549), tc_HOL_Obool)), _1568551)))], (28026 ^ _780119) ^ [_1297597, _1297599] : [class_Orderings_Olinorder(_1297597), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1297597), _1297599), _1297599) = _1297599)], (6531 ^ _780119) ^ [_885878, _885880, _885882, _885884, _885886] : [c_Hoare__Mirabelle_Ohoare__derivs(_885878, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_885878)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_885878), _885880), hAPP(c_Com_Ocom_OBODY, _885882)), _885884)), _885886), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_885878)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_885878), _885880), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _885882))), _885884)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_885878), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_885878, _885886, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_885878)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_885878), _885880), hAPP(c_Com_Ocom_OBODY, _885882)), _885884)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_885878), tc_HOL_Obool)))))], (21496 ^ _780119) ^ [_1171998, _1172000, _1172002, _1172004, _1172006, _1172008] : [class_Divides_Oring__div(_1171998), c_Divides_Odiv__class_Omod(_1171998, _1172000, _1172002) = c_Divides_Odiv__class_Omod(_1171998, _1172004, _1172002), c_Divides_Odiv__class_Omod(_1171998, _1172006, _1172002) = c_Divides_Odiv__class_Omod(_1171998, _1172008, _1172002), -(c_Divides_Odiv__class_Omod(_1171998, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1171998), _1172000), _1172006), _1172002) = c_Divides_Odiv__class_Omod(_1171998, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1171998), _1172004), _1172008), _1172002))], (3434 ^ _780119) ^ [_831711, _831713, _831715, _831717, _831719, _831721] : [-(c_Relation_OImage(_831721, _831717, _831713) = c_Relation_OImage(_831719, _831715, _831711)), _831721 = _831719, _831717 = _831715, _831713 = _831711], (37783 ^ _780119) ^ [_1505493, _1505495, _1505497, _1505499, _1505501, _1505503] : [class_Groups_Ocomm__monoid__mult(_1505493), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1505495, _1505493), hAPP(hAPP(c_COMBC(_1505495, tc_fun(_1505497, tc_HOL_Obool), _1505493), hAPP(hAPP(c_COMBB(tc_fun(_1505497, _1505493), tc_fun(tc_fun(_1505497, tc_HOL_Obool), _1505493), _1505495), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1505497, _1505493)), _1505499)), _1505501)), _1505503) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1505495, _1505497), _1505493), hAPP(c_Product__Type_Oprod_Oprod__case(_1505495, _1505497, _1505493), _1505499)), hAPP(hAPP(c_Product__Type_OSigma(_1505495, _1505497), _1505503), hAPP(c_COMBK(tc_fun(_1505497, tc_HOL_Obool), _1505495), _1505501))))], (31815 ^ _780119) ^ [_1373484, _1373486] : [class_Int_Onumber__ring(_1373484), class_Rings_Olinordered__idom(_1373484), 31822 ^ _780119 : [(31829 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1373486), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373484), hAPP(c_Int_Onumber__class_Onumber__of(_1373484), _1373486)), c_Groups_Ozero__class_Ozero(_1373484))))], (31823 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373484), hAPP(c_Int_Onumber__class_Onumber__of(_1373484), _1373486)), c_Groups_Ozero__class_Ozero(_1373484))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1373486), c_Int_OPls)))]]], (37397 ^ _780119) ^ [_1495162, _1495164, _1495166] : [c_Wellfounded_Owf(_1495162, _1495164), c_Wellfounded_Owf(_1495162, _1495166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1495162, _1495162), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1495162, _1495162, _1495162), _1495164), _1495166)), _1495164)), -(c_Wellfounded_Owf(_1495162, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1495162, _1495162), tc_HOL_Obool)), _1495164), _1495166)))], (33349 ^ _780119) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (16002 ^ _780119) ^ [_1071743, _1071745, _1071747] : [class_Groups_Oordered__comm__monoid__add(_1071743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071743), _1071745), c_Groups_Ozero__class_Ozero(_1071743))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071743), _1071747), c_Groups_Ozero__class_Ozero(_1071743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071743), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071743), _1071745), _1071747)), c_Groups_Ozero__class_Ozero(_1071743))))], (9962 ^ _780119) ^ [_953617, _953619, _953621, _953623] : [class_Lattices_Osemilattice__inf(_953617), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953617), _953619), _953621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953617), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_953617), _953623), _953619)), _953621)))], (45696 ^ _780119) ^ [_1699950, _1699952, _1699954, _1699956] : [-(hAPP(hAPP(c_List_Odrop(_1699950), _1699952), hAPP(hAPP(c_List_Olist_OCons(_1699950), _1699954), _1699956)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1699950), hAPP(hAPP(c_List_Olist_OCons(_1699950), _1699954), _1699956), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1699950), tc_List_Olist(_1699950)), c_List_Odrop(_1699950)), _1699956), _1699952))], (23475 ^ _780119) ^ [_1209340, _1209342, _1209344, _1209346] : [class_Orderings_Olinorder(_1209340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209340), _1209342), _1209344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209340), _1209344), _1209346)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1209340, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1209340, _1209342), _1209344)), c_SetInterval_Oord__class_OatLeastAtMost(_1209340, _1209344, _1209346)) = c_SetInterval_Oord__class_OatLeastAtMost(_1209340, _1209342, _1209346))], (40276 ^ _780119) ^ [_1568101, _1568103, _1568105] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568101, _1568101)), _1568103), c_Transitive__Closure_Otrancl(_1568101, _1568105))), 40280 ^ _780119 : [(40283 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568101, _1568101)), _1568103), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1568101, _1568101), tc_HOL_Obool), 40279 ^ [_1568101, _1568103, _1568105]), _1568105))))], (40281 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 40279 ^ [_1568101, _1568103, _1568105])))]]], (45594 ^ _780119) ^ [_1697622, _1697624, _1697626] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697622)), hAPP(hAPP(c_List_Odrop(_1697622), _1697624), _1697626)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697622)), _1697626)), _1697624))], (51579 ^ _780119) ^ [_1820570] : [hBOOL(hAPP(c_fNot, _1820570)), hBOOL(_1820570)], (33587 ^ _780119) ^ [_1405493, _1405495] : [c_Code__Numeral_OSuc__code__numeral(_1405493) = c_Code__Numeral_OSuc__code__numeral(_1405495), -(_1405493 = _1405495)], (50923 ^ _780119) ^ [_1813442, _1813444, _1813446] : [-(c_Lazy__Sequence_Ohb__map(_1813442, _1813444, _1813446, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(_1813442))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(_1813444)))], (10220 ^ _780119) ^ [_959039, _959041, _959043, _959045] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959039, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959039, tc_HOL_Obool)), _959041), _959043)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959039, tc_HOL_Obool)), _959045), _959043)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959039, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959039, tc_HOL_Obool)), _959041), _959043)), _959045))], (33351 ^ _780119) ^ [_1401574] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1401574), c_Int_OMin) = c_Int_Opred(_1401574))], (22787 ^ _780119) ^ [_1196306, _1196308, _1196310] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1196306, tc_Nat_Onat), _1196308), _1196310)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1196306, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1196306), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1196308)), _1196310))], (34163 ^ _780119) ^ [_1421708] : [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), _1421708))), 34166 ^ _780119 : [(34173 ^ _780119) ^ [] : [-(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), _1421708)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421708)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421708)), 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), _1421708)))))], (34167 ^ _780119) ^ [] : [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), _1421708))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421708)) = 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)))]]], (43016 ^ _780119) ^ [_1632796, _1632798, _1632800, _1632802] : [-(hBOOL(hAPP(hAPP(c_member(_1632796), _1632798), hAPP(c_List_Oset(_1632796), _1632800)))), hBOOL(hAPP(hAPP(c_member(_1632796), _1632798), hAPP(c_List_Oset(_1632796), c_List_Oremove1(_1632796, _1632802, _1632800))))], (21546 ^ _780119) ^ [_1173029] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1173029, _1173029) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (41353 ^ _780119) ^ [_1593333, _1593335, _1593337, _1593339, _1593341, _1593343] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593335, _1593337)), hAPP(hAPP(c_Product__Type_OPair(_1593335, _1593337), _1593341), _1593343)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593333, tc_fun(tc_prod(_1593335, _1593337), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1593333, tc_HOL_Obool))), _1593339))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593333, tc_fun(_1593335, tc_fun(_1593337, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1593333, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1593335, _1593337), tc_HOL_Obool), tc_fun(_1593335, tc_fun(_1593337, tc_HOL_Obool)), _1593333), hAPP(c_COMBC(_1593335, tc_fun(tc_prod(_1593335, _1593337), tc_HOL_Obool), tc_fun(_1593337, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1593337, tc_fun(tc_fun(tc_prod(_1593335, _1593337), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1593335, _1593337), tc_HOL_Obool), tc_fun(_1593337, tc_HOL_Obool)), _1593335), c_COMBC(_1593337, tc_fun(tc_prod(_1593335, _1593337), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1593337, tc_prod(_1593335, _1593337)), tc_fun(_1593337, tc_fun(tc_fun(tc_prod(_1593335, _1593337), tc_HOL_Obool), tc_HOL_Obool)), _1593335), hAPP(c_COMBB(tc_prod(_1593335, _1593337), tc_fun(tc_fun(tc_prod(_1593335, _1593337), tc_HOL_Obool), tc_HOL_Obool), _1593337), c_member(tc_prod(_1593335, _1593337)))), c_Product__Type_OPair(_1593335, _1593337))))), _1593339)), _1593341), _1593343)))], (47837 ^ _780119) ^ [_1746614, _1746616] : [-(c_List_OtakeWhile(_1746614, _1746616, c_List_Olist_ONil(_1746614)) = c_List_Olist_ONil(_1746614))], (17120 ^ _780119) ^ [_1091040] : [class_Lattices_Oboolean__algebra(_1091040), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1091040), c_Orderings_Otop__class_Otop(_1091040)) = c_Orderings_Obot__class_Obot(_1091040))], (47951 ^ _780119) ^ [_1748751, _1748753] : [_1748753 = c_List_Olist_ONil(_1748751), -(c_List_Olist_ONil(_1748751) = c_List_Oremdups(_1748751, _1748753))], (17114 ^ _780119) ^ [_1090949] : [class_Lattices_Oboolean__algebra(_1090949), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1090949), c_Orderings_Obot__class_Obot(_1090949)) = c_Orderings_Otop__class_Otop(_1090949))], (23189 ^ _780119) ^ [_1203691] : [-(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, _1203691)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (46519 ^ _780119) ^ [_1717799, _1717801] : [-(c_List_Obutlast(_1717799, _1717801) = hAPP(hAPP(c_List_Otake(_1717799), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717799)), _1717801)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1717801))], (20166 ^ _780119) ^ [_1146878, _1146880, _1146882, _1146884] : [class_Fields_Olinordered__field(_1146878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146878), _1146880), c_Groups_Ozero__class_Ozero(_1146878))), 20173 ^ _780119 : [(20180 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146878), _1146884), _1146880)), _1146882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146878), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146878), _1146882), _1146880)), _1146884)))], (20174 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146878), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146878), _1146882), _1146880)), _1146884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146878), _1146884), _1146880)), _1146882)))]]], (48249 ^ _780119) ^ [_1755783, _1755785, _1755787, _1755789, _1755791] : [-(c_Enum_Oproduct(_1755783, _1755785, hAPP(hAPP(c_List_Olist_OCons(_1755783), _1755787), _1755789), _1755791) = hAPP(hAPP(c_List_Oappend(tc_prod(_1755783, _1755785)), hAPP(hAPP(c_List_Omap(_1755785, tc_prod(_1755783, _1755785)), hAPP(c_Product__Type_OPair(_1755783, _1755785), _1755787)), _1755791)), c_Enum_Oproduct(_1755783, _1755785, _1755789, _1755791)))], (14220 ^ _780119) ^ [_1039748, _1039750, _1039752] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039748), _1039750)), 14223 ^ _780119 : [(14230 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1039748), _1039752), _1039750))), -(hAPP(c_Finite__Set_Ocard(_1039748), hAPP(hAPP(c_Set_Oinsert(_1039748), _1039752), _1039750)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1039748), _1039750)))], (14224 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1039748), _1039752), _1039750)), -(hAPP(c_Finite__Set_Ocard(_1039748), hAPP(hAPP(c_Set_Oinsert(_1039748), _1039752), _1039750)) = hAPP(c_Finite__Set_Ocard(_1039748), _1039750))]]], (5584 ^ _780119) ^ [_865650, _865652] : [_865652 = _865650, -(c_COMBI(_865652) = c_COMBI(_865650))], (51159 ^ _780119) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (7284 ^ _780119) ^ [_902159, _902161] : [class_Lattices_Osemilattice__sup(_902159), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902159), _902161), _902161) = _902161)], (40122 ^ _780119) ^ [_1564006, _1564008, _1564010] : [c_Relation_Orefl__on(_1564006, _1564008, _1564010), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564006, _1564006), tc_HOL_Obool)), _1564010), hAPP(hAPP(c_Relation_Orel__comp(_1564006, _1564006, _1564006), hAPP(c_Relation_Oconverse(_1564006, _1564006), _1564010)), _1564010))))], (33263 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (14210 ^ _780119) ^ [_1039590, _1039592, _1039594] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039590), _1039592)), -(hBOOL(hAPP(hAPP(c_member(_1039590), _1039594), _1039592))), -(hAPP(c_Finite__Set_Ocard(_1039590), hAPP(hAPP(c_Set_Oinsert(_1039590), _1039594), _1039592)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1039590), _1039592)))], (50492 ^ _780119) ^ [_1804620, _1804622, _1804624] : [-(c_List_Osplice(_1804620, hAPP(hAPP(c_List_Olist_OCons(_1804620), _1804622), _1804624), c_List_Olist_ONil(_1804620)) = hAPP(hAPP(c_List_Olist_OCons(_1804620), _1804622), _1804624))], (49396 ^ _780119) ^ [_1780175, _1780177, _1780179, _1780181, _1780183] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780175, _1780175)), hAPP(hAPP(c_Product__Type_OPair(_1780175, _1780175), _1780177), _1780179)), c_List_Omeasures(_1780175, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1780175, tc_Nat_Onat)), _1780181), _1780183))))), 49397 ^ _780119 : [(49400 ^ _780119) ^ [] : [hAPP(_1780181, _1780177) = hAPP(_1780181, _1780179), hBOOL(hAPP(hAPP(c_member(tc_prod(_1780175, _1780175)), hAPP(hAPP(c_Product__Type_OPair(_1780175, _1780175), _1780177), _1780179)), c_List_Omeasures(_1780175, _1780183)))], (49398 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1780181, _1780177)), hAPP(_1780181, _1780179)))]]], (42415 ^ _780119) ^ [_1618583, _1618585, _1618587, _1618589, _1618591, _1618593] : [-(hAPP(c_Map_Omap__add(_1618583, _1618585, _1618587, _1618589), _1618591) = hAPP(c_Option_Ooption_OSome(_1618585), _1618593)), 42416 ^ _780119 : [(42419 ^ _780119) ^ [] : [hAPP(_1618589, _1618591) = c_Option_Ooption_ONone(_1618585), hAPP(_1618587, _1618591) = hAPP(c_Option_Ooption_OSome(_1618585), _1618593)], (42417 ^ _780119) ^ [] : [hAPP(_1618589, _1618591) = hAPP(c_Option_Ooption_OSome(_1618585), _1618593)]]], (17138 ^ _780119) ^ [_1091341, _1091343, _1091345, _1091347, _1091349] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1091341, _1091343, _1091345), _1091347), hAPP(c_Nat_OSuc, _1091349)) = hAPP(hAPP(_1091345, _1091347), hAPP(hAPP(c_Power_Opower_Opower(_1091341, _1091343, _1091345), _1091347), _1091349)))], (32601 ^ _780119) ^ [_1387778, _1387780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1387778)), c_Int_OBit1(_1387780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1387778), _1387780)))], (15422 ^ _780119) ^ [_1061284] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1061284) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3384 ^ _780119) ^ [_830942, _830944, _830946, _830948] : [-(c_Code__Numeral_Onat__of__aux(_830948, _830944) = c_Code__Numeral_Onat__of__aux(_830946, _830942)), _830948 = _830946, _830944 = _830942], (26945 ^ _780119) ^ [_1272880, _1272882] : [-(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), _1272880)), _1272882))))], (36746 ^ _780119) ^ [_1478451, _1478453, _1478455, _1478457, _1478459, _1478461] : [-(hAPP(c_Set_Ovimage(_1478451, _1478453, _1478455), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478457, tc_fun(_1478453, tc_HOL_Obool)), _1478459), _1478461)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478457, tc_fun(_1478451, tc_HOL_Obool)), _1478459), hAPP(hAPP(c_COMBB(tc_fun(_1478453, tc_HOL_Obool), tc_fun(_1478451, tc_HOL_Obool), _1478457), c_Set_Ovimage(_1478451, _1478453, _1478455)), _1478461)))], (38241 ^ _780119) ^ [_1519274, _1519276] : [c_Wellfounded_Owf(_1519274, hAPP(c_Set_OCollect(tc_prod(_1519274, _1519274)), hAPP(c_Product__Type_Oprod_Oprod__case(_1519274, _1519274, tc_HOL_Obool), _1519276))), -(c_Wellfounded_OwfP(_1519274, _1519276))], (39208 ^ _780119) ^ [_1541687, _1541689, _1541691, _1541693, _1541695, _1541697] : [c_Finite__Set_Ofolding__idem(_1541687, _1541689, _1541691, _1541693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1541687), _1541695)), hBOOL(hAPP(hAPP(c_member(_1541687), _1541697), _1541695)), -(hAPP(c_Fun_Ocomp(_1541689, _1541689, _1541689, hAPP(_1541693, _1541695)), hAPP(_1541691, _1541697)) = hAPP(_1541693, _1541695))], (8486 ^ _780119) ^ [_927500, _927502, _927504, _927506, _927508, _927510] : [-(_927500 = _927502), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927504, _927506), _927508), _927502), _927510), _927500) = hAPP(_927508, _927500))], (6405 ^ _780119) ^ [_883540, _883542, _883544, _883546] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883540, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_883540), _883542), _883544)), _883546))), hBOOL(hAPP(hAPP(c_member(_883540), _883542), _883546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883540, tc_HOL_Obool)), _883544), _883546))], (46270 ^ _780119) ^ [_1712972, _1712974, _1712976, _1712978] : [-(_1712972 = c_List_Olist_ONil(_1712974)), 46273 ^ _780119 : [(46280 ^ _780119) ^ [] : [-(_1712976 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712974)), _1712972)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1712974, hAPP(hAPP(c_List_Olist__update(_1712974, _1712972), _1712976), _1712978)) = c_List_Olast(_1712974, _1712972))], (46274 ^ _780119) ^ [] : [_1712976 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712974)), _1712972)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1712974, hAPP(hAPP(c_List_Olist__update(_1712974, _1712972), _1712976), _1712978)) = _1712978)]]], (42710 ^ _780119) ^ [_1625854, _1625856, _1625858, _1625860, _1625862] : [-(c_Map_Omap__comp(_1625854, _1625856, _1625858, _1625860, hAPP(c_COMBK(tc_Option_Ooption(_1625854), _1625858), c_Option_Ooption_ONone(_1625854)), _1625862) = c_Option_Ooption_ONone(_1625856))], (42265 ^ _780119) ^ [_1615354, _1615356, _1615358, _1615360] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615354, _1615356)), _1615358), hAPP(c_Relation_Oconverse(_1615356, _1615354), _1615360))), 42270 ^ _780119 : [(42273 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615356, _1615354)), hAPP(hAPP(c_Product__Type_OPair(_1615356, _1615354), 42268 ^ [_1615354, _1615356, _1615358, _1615360]), 42269 ^ [_1615354, _1615356, _1615358, _1615360])), _1615360)))], (42271 ^ _780119) ^ [] : [-(_1615358 = hAPP(hAPP(c_Product__Type_OPair(_1615354, _1615356), 42269 ^ [_1615354, _1615356, _1615358, _1615360]), 42268 ^ [_1615354, _1615356, _1615358, _1615360]))]]], (8512 ^ _780119) ^ [_927892, _927894, _927896, _927898, _927900, _927902] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927892, _927894), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927892, _927894), _927896), _927898), _927900)), _927898), _927902) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927892, _927894), _927896), _927898), _927902))], (39491 ^ _780119) ^ [_1548359, _1548361, _1548363, _1548365, _1548367] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548359, _1548359)), hAPP(hAPP(c_Product__Type_OPair(_1548359, _1548359), _1548361), _1548363)), c_Transitive__Closure_Otrancl(_1548359, _1548365))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1548359, _1548359)), hAPP(hAPP(c_Product__Type_OPair(_1548359, _1548359), _1548363), _1548367)), c_Transitive__Closure_Otrancl(_1548359, _1548365))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548359, _1548359)), hAPP(hAPP(c_Product__Type_OPair(_1548359, _1548359), _1548361), _1548367)), c_Transitive__Closure_Otrancl(_1548359, _1548365))))], (17838 ^ _780119) ^ [_1104444, _1104446, _1104448] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1104444), _1104446)), 17841 ^ _780119 : [(17861 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104444, tc_Nat_Onat), _1104448), _1104446) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 17862 ^ _780119 : [(17863 ^ _780119) ^ [_1104925] : [hBOOL(hAPP(hAPP(c_member(_1104444), _1104925), _1104446)), hAPP(_1104448, _1104925) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 17871 ^ _780119 : [(17874 ^ _780119) ^ [] : [_1104925 = 17870 ^ [_1104444, _1104446, _1104448, _1104925]], (17876 ^ _780119) ^ [] : [hAPP(_1104448, 17870 ^ [_1104444, _1104446, _1104448, _1104925]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17872 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1104444), 17870 ^ [_1104444, _1104446, _1104448, _1104925]), _1104446)))]]]]], (17842 ^ _780119) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104444, tc_Nat_Onat), _1104448), _1104446) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 17846 ^ _780119 : [(17849 ^ _780119) ^ [] : [-(hAPP(_1104448, 17845 ^ [_1104444, _1104446, _1104448]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17851 ^ _780119) ^ [_1104764] : [hBOOL(hAPP(hAPP(c_member(_1104444), _1104764), _1104446)), -(17845 ^ [_1104444, _1104446, _1104448] = _1104764), -(hAPP(_1104448, _1104764) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17847 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1104444), 17845 ^ [_1104444, _1104446, _1104448]), _1104446)))]]]]], (41515 ^ _780119) ^ [_1598102, _1598104] : [class_Complete__Lattice_Ocomplete__lattice(_1598102), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598102), _1598104)), -(c_Complete__Lattice_OInf__class_OInf(_1598102, _1598104) = hAPP(hAPP(c_Finite__Set_Ofold(_1598102, _1598102, c_Lattices_Osemilattice__inf__class_Oinf(_1598102)), c_Orderings_Otop__class_Otop(_1598102)), _1598104))], (48225 ^ _780119) ^ [_1754993, _1754995, _1754997] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1754993), tc_List_Olist(_1754993)), c_List_Opartition(_1754993, _1754995, _1754997)) = hAPP(c_List_Ofilter(_1754993, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1754993, c_fNot), _1754995)), _1754997))], (7994 ^ _780119) ^ [_916492, _916494, _916496, _916498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916492, tc_HOL_Obool)), _916494), _916496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916492, tc_HOL_Obool)), _916496), _916498)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916492, tc_HOL_Obool)), _916496), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916492, tc_HOL_Obool)), _916498), _916494)) = _916494)], (37524 ^ _780119) ^ [_1498191, _1498193, _1498195] : [-(hAPP(c_Relation_ORange(_1498191, _1498193), hAPP(c_Set_OCollect(tc_prod(_1498191, _1498193)), hAPP(c_Product__Type_Oprod_Oprod__case(_1498191, _1498193, tc_HOL_Obool), _1498195))) = hAPP(c_Set_OCollect(_1498193), hAPP(hAPP(c_COMBB(tc_fun(_1498191, tc_HOL_Obool), tc_HOL_Obool, _1498193), c_HOL_OEx(_1498191)), hAPP(c_COMBC(_1498191, _1498193, tc_HOL_Obool), _1498195))))], (20348 ^ _780119) ^ [_1150331, _1150333, _1150335, _1150337] : [class_Fields_Olinordered__field(_1150331), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150331), _1150333), _1150335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150331), _1150337), c_Groups_Ozero__class_Ozero(_1150331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150331), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150331), _1150335), _1150337)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150331), _1150333), _1150337))))], (40060 ^ _780119) ^ [_1562289, _1562291, _1562293, _1562295, _1562297] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562289, _1562291)), hAPP(hAPP(c_Product__Type_OPair(_1562289, _1562291), _1562293), _1562295)), hAPP(c_Relation_Oconverse(_1562291, _1562289), _1562297))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562291, _1562289)), hAPP(hAPP(c_Product__Type_OPair(_1562291, _1562289), _1562295), _1562293)), _1562297)))], (48599 ^ _780119) ^ [_1762615, _1762617] : [class_Enum_Oenum(_1762615), 48602 ^ _780119 : [(48603 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1762615)), _1762617)), -(hBOOL(hAPP(_1762617, c_Option_Ooption_ONone(_1762615)))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1762615), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1762615), tc_HOL_Obool, _1762615), _1762617), c_Option_Ooption_OSome(_1762615)))))], (48613 ^ _780119) ^ [] : [48614 ^ _780119 : [(48617 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1762615), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1762615), tc_HOL_Obool, _1762615), _1762617), c_Option_Ooption_OSome(_1762615))))], (48615 ^ _780119) ^ [] : [hBOOL(hAPP(_1762617, c_Option_Ooption_ONone(_1762615)))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1762615)), _1762617)))]]], (49989 ^ _780119) ^ [_1793727, _1793729, _1793731] : [-(c_List_Olist__ex1(_1793727, _1793729, _1793731)), 49990 ^ _780119 : [(49991 ^ _780119) ^ [_1793821] : [hBOOL(hAPP(hAPP(c_member(_1793727), _1793821), hAPP(c_List_Oset(_1793727), _1793731))), hBOOL(hAPP(_1793729, _1793821)), 49999 ^ _780119 : [(50002 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1793729, 49998 ^ [_1793727, _1793729, _1793731, _1793821])))], (50004 ^ _780119) ^ [] : [49998 ^ [_1793727, _1793729, _1793731, _1793821] = _1793821], (50000 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1793727), 49998 ^ [_1793727, _1793729, _1793731, _1793821]), hAPP(c_List_Oset(_1793727), _1793731))))]]]]], (47792 ^ _780119) ^ [_1745704, _1745706, _1745708, _1745710, _1745712] : [-(hAPP(hAPP(c_List_Ozip(_1745704, _1745706), _1745708), c_List_OtakeWhile(_1745706, _1745710, _1745712)) = c_List_OtakeWhile(tc_prod(_1745704, _1745706), hAPP(c_Fun_Ocomp(_1745706, tc_HOL_Obool, tc_prod(_1745704, _1745706), _1745710), c_Product__Type_Osnd(_1745704, _1745706)), hAPP(hAPP(c_List_Ozip(_1745704, _1745706), _1745708), _1745712)))], (16484 ^ _780119) ^ [_1080443, _1080445] : [class_Groups_Olinordered__ab__group__add(_1080443), 16487 ^ _780119 : [(16494 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080443), c_Groups_Ozero__class_Ozero(_1080443)), _1080445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080443), hAPP(c_Groups_Ouminus__class_Ouminus(_1080443), _1080445)), _1080445)))], (16488 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080443), hAPP(c_Groups_Ouminus__class_Ouminus(_1080443), _1080445)), _1080445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080443), c_Groups_Ozero__class_Ozero(_1080443)), _1080445)))]]], (10721 ^ _780119) ^ [_970227, _970229, _970231, _970233] : [class_Groups_Oab__semigroup__add(_970227), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970227), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970227), _970229), _970231)), _970233) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970227), _970229), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970227), _970231), _970233)))], (33545 ^ _780119) ^ [] : [-(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))], (7191 ^ _780119) ^ [_899399, _899401, _899403] : [class_Orderings_Obot(_899399), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_899401, _899399)), _899403) = c_Orderings_Obot__class_Obot(_899399))], (49132 ^ _780119) ^ [_1774304, _1774306, _1774308] : [_1774304 = _1774306, -(c_List_Olist__all2(_1774308, _1774308, c_fequal, _1774304, _1774306))], (43200 ^ _780119) ^ [_1637707, _1637709, _1637711, _1637713] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637707)), hAPP(hAPP(c_List_Omap(_1637709, _1637707), _1637711), _1637713)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637709)), _1637713))], (40794 ^ _780119) ^ [_1579988, _1579990, _1579992] : [class_Orderings_Olinorder(_1579988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579988), _1579990)), -(c_Big__Operators_Olattice_OSup__fin(_1579988, c_Orderings_Oord__class_Omax(_1579988), hAPP(hAPP(c_Set_Oinsert(_1579988), _1579992), _1579990)) = hAPP(hAPP(c_Finite__Set_Ofold(_1579988, _1579988, c_Orderings_Oord__class_Omax(_1579988)), _1579992), _1579990))], (50476 ^ _780119) ^ [_1803762, _1803764] : [-(c_List_Osplice(_1803762, _1803764, c_List_Olist_ONil(_1803762)) = _1803764)], (42845 ^ _780119) ^ [_1628859, _1628861, _1628863, _1628865] : [hAPP(hAPP(c_Map_Omap__of(_1628859, _1628861), _1628863), _1628865) = c_Option_Ooption_ONone(_1628861), hBOOL(hAPP(hAPP(c_member(_1628859), _1628865), hAPP(c_Set_Oimage(tc_prod(_1628859, _1628861), _1628859, c_Product__Type_Ofst(_1628859, _1628861)), hAPP(c_List_Oset(tc_prod(_1628859, _1628861)), _1628863))))], (34439 ^ _780119) ^ [_1426387, _1426389, _1426391] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1426387, _1426389), _1426391)), -(c_Divides_Odivmod__nat(_1426387, _1426389) = _1426391)], (44292 ^ _780119) ^ [_1667448, _1667450] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1667448), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1667450), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 44299 ^ _780119 : [(44306 ^ _780119) ^ [] : [_1667448 = _1667450, -(hAPP(c_Code__Numeral_Oof__nat, _1667448) = hAPP(c_Code__Numeral_Oof__nat, _1667450))], (44300 ^ _780119) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1667448) = hAPP(c_Code__Numeral_Oof__nat, _1667450), -(_1667448 = _1667450)]]], (23040 ^ _780119) ^ [_1200860, _1200862] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200860), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200862)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1200860, _1200862)))], (47520 ^ _780119) ^ [_1738315, _1738317, _1738319] : [-(c_List_Oconcat(_1738315, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1738315)), _1738317), _1738319)) = hAPP(hAPP(c_List_Oappend(_1738315), _1738317), c_List_Oconcat(_1738315, _1738319)))], (39521 ^ _780119) ^ [_1549166, _1549168, _1549170, _1549172, _1549174] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549166, _1549166)), hAPP(hAPP(c_Product__Type_OPair(_1549166, _1549166), _1549168), _1549170)), _1549172)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1549166, _1549166)), hAPP(hAPP(c_Product__Type_OPair(_1549166, _1549166), _1549170), _1549174)), _1549172)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549166, _1549166)), hAPP(hAPP(c_Product__Type_OPair(_1549166, _1549166), _1549168), _1549174)), c_Transitive__Closure_Otrancl(_1549166, _1549172))))], (42288 ^ _780119) ^ [_1615985, _1615987, _1615989] : [-(c_Nitpick_Oplus__frac(_1615985, _1615987, _1615989) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1615985), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1615985), _1615987), hAPP(c_Nitpick_Odenom(_1615985), _1615989))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1615985), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1615985), tc_Int_Oint), c_Nitpick_Ofrac(_1615985)), 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(_1615985), _1615987))), 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(_1615985), _1615987))))), 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(_1615985), _1615989))), 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(_1615985), _1615989)))))), c_COMBI(tc_Int_Oint))))], (12653 ^ _780119) ^ [_1009481, _1009483, _1009485, _1009487] : [-(hAPP(_1009487, _1009483) = c_Option_Ooption_ONone(_1009485)), -(hBOOL(hAPP(hAPP(c_member(_1009481), _1009483), c_Map_Odom(_1009481, _1009485, _1009487))))], (46735 ^ _780119) ^ [_1722613, _1722615, _1722617, _1722619, _1722621] : [-(c_List_Omap__filter(_1722613, _1722615, _1722617, hAPP(hAPP(c_List_Olist_OCons(_1722613), _1722619), _1722621)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1722615), _1722615, c_List_Omap__filter(_1722613, _1722615, _1722617, _1722621), hAPP(hAPP(c_COMBC(_1722615, tc_List_Olist(_1722615), tc_List_Olist(_1722615)), c_List_Olist_OCons(_1722615)), c_List_Omap__filter(_1722613, _1722615, _1722617, _1722621))), hAPP(_1722617, _1722619)))], (36469 ^ _780119) ^ [_1471989, _1471991, _1471993, _1471995] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1471989), _1471991)), 36472 ^ _780119 : [(36479 ^ _780119) ^ [] : [hAPP(c_Finite__Set_Ocard(_1471993), hAPP(c_Set_Oimage(_1471989, _1471993, _1471995), _1471991)) = hAPP(c_Finite__Set_Ocard(_1471989), _1471991), -(c_Fun_Oinj__on(_1471989, _1471993, _1471995, _1471991))], (36473 ^ _780119) ^ [] : [c_Fun_Oinj__on(_1471989, _1471993, _1471995, _1471991), -(hAPP(c_Finite__Set_Ocard(_1471993), hAPP(c_Set_Oimage(_1471989, _1471993, _1471995), _1471991)) = hAPP(c_Finite__Set_Ocard(_1471989), _1471991))]]], (38162 ^ _780119) ^ [_1517170, _1517172, _1517174, _1517176] : [-(c_Product__Type_Oapfst(_1517170, _1517172, _1517174, _1517176) = c_Product__Type_Omap__pair(_1517170, _1517172, _1517174, _1517174, _1517176, c_Fun_Oid(_1517174)))], (24211 ^ _780119) ^ [_1223404] : [-(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)), _1223404))))], (2698 ^ _780119) ^ [_820111, _820113, _820115, _820117, _820119, _820121] : [-(c_Predicate_ORangeP(_820121, _820117, _820113) = c_Predicate_ORangeP(_820119, _820115, _820111)), _820121 = _820119, _820117 = _820115, _820113 = _820111], (9768 ^ _780119) ^ [_949707, _949709, _949711, _949713, _949715] : [class_Lattices_Olattice(_949707), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949709, _949707)), _949711), _949713), _949715) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949707), hAPP(_949711, _949715)), hAPP(_949713, _949715)))], (18063 ^ _780119) ^ [_1109155, _1109157] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1109155), _1109157)))), -(_1109157 = c_Orderings_Obot__class_Obot(tc_fun(_1109155, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109155), _1109157))], (51273 ^ _780119) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (50228 ^ _780119) ^ [_1797856, _1797858] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1797856), _1797858)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1797856)), c_Int_OBit0(_1797858))))], (22099 ^ _780119) ^ [_1183704, _1183706, _1183708] : [hBOOL(hAPP(c_Predicate_OPowp(_1183704, hAPP(hAPP(c_COMBC(_1183704, tc_fun(_1183704, tc_HOL_Obool), tc_HOL_Obool), c_member(_1183704)), _1183706)), _1183708)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1183704, tc_HOL_Obool)), _1183708), hAPP(c_Set_OPow(_1183704), _1183706))))], (25500 ^ _780119) ^ [_1246437, _1246439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1246437), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1246437), _1246439)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246437))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246439))))], (14236 ^ _780119) ^ [_1040042, _1040044, _1040046, _1040048, _1040050] : [hAPP(_1040042, _1040044) = hAPP(c_Option_Ooption_OSome(_1040046), _1040048), -(hBOOL(hAPP(hAPP(c_member(_1040046), _1040048), c_Map_Oran(_1040050, _1040046, _1040042))))], (10292 ^ _780119) ^ [_960992, _960994, _960996, _960998] : [hBOOL(hAPP(hAPP(c_member(_960992), _960994), _960996)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960992, tc_HOL_Obool)), _960996), hAPP(hAPP(c_Set_Oinsert(_960992), _960994), _960998)) = hAPP(hAPP(c_Set_Oinsert(_960992), _960994), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960992, tc_HOL_Obool)), _960996), _960998)))], (12595 ^ _780119) ^ [_1008393, _1008395, _1008397, _1008399] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1008393), _1008395)), hBOOL(hAPP(hAPP(c_member(_1008393), _1008397), _1008395)), hBOOL(hAPP(hAPP(c_member(_1008393), _1008399), _1008395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1008393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008393, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008393, tc_HOL_Obool)), _1008395), hAPP(hAPP(c_Set_Oinsert(_1008393), _1008397), c_Orderings_Obot__class_Obot(tc_fun(_1008393, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1008393), _1008399), c_Orderings_Obot__class_Obot(tc_fun(_1008393, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1008393), _1008395))))], (40976 ^ _780119) ^ [_1583495, _1583497, _1583499, _1583501, _1583503, _1583505] : [c_Finite__Set_Ofun__left__comm(_1583495, _1583497, _1583499), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1583495, _1583497, _1583499, _1583501, _1583503), _1583505)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1583495, _1583497, _1583499), _1583501), _1583503) = _1583505)], (45422 ^ _780119) ^ [_1692449, _1692451, _1692453] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692449), tc_List_Olist(_1692449))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692449), tc_List_Olist(_1692449)), c_List_Olist_ONil(_1692449)), _1692451)), c_List_Olistrel1(_1692449, _1692453)))], (4554 ^ _780119) ^ [_849189, _849191, _849193, _849195, _849197, _849199, _849201, _849203] : [-(c_New__DSequence_Opos__bind(_849203, _849199, _849195, _849191) = c_New__DSequence_Opos__bind(_849201, _849197, _849193, _849189)), _849203 = _849201, _849199 = _849197, _849195 = _849193, _849191 = _849189], (34032 ^ _780119) ^ [_1419045, _1419047, _1419049, _1419051, _1419053, _1419055] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1419045, _1419047, _1419049), _1419051), hAPP(hAPP(c_Product__Type_OPair(_1419045, _1419047), _1419053), _1419055)) = hAPP(hAPP(_1419051, _1419053), _1419055))], (33257 ^ _780119) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (24653 ^ _780119) ^ [_1231693, _1231695, _1231697] : [class_Orderings_Oorder(_1231693), 24656 ^ _780119 : [(24663 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231693), _1231695), _1231697))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1231693, _1231695, _1231697) = c_Orderings_Obot__class_Obot(tc_fun(_1231693, tc_HOL_Obool)))], (24657 ^ _780119) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1231693, _1231695, _1231697) = c_Orderings_Obot__class_Obot(tc_fun(_1231693, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231693), _1231695), _1231697))]]], (33131 ^ _780119) ^ [_1397612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1397612)), -(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), _1397612), 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)))))))], (50997 ^ _780119) ^ [_1814467, _1814469] : [class_Lattices_Olattice(_1814467), -(class_Lattices_Olattice(tc_fun(_1814469, _1814467)))], (33971 ^ _780119) ^ [_1417645, _1417647, _1417649, _1417651, _1417653, _1417655] : [hAPP(hAPP(c_Product__Type_OPair(_1417645, _1417647), _1417649), _1417651) = hAPP(hAPP(c_Product__Type_OPair(_1417645, _1417647), _1417653), _1417655), 33974 ^ _780119 : [(33977 ^ _780119) ^ [] : [-(_1417651 = _1417655)], (33975 ^ _780119) ^ [] : [-(_1417649 = _1417653)]]], (1330 ^ _780119) ^ [_799468, _799470] : [-(class_Lattices_Oboolean__algebra(_799468)), _799470 = _799468, class_Lattices_Oboolean__algebra(_799470)], (41641 ^ _780119) ^ [_1601270, _1601272] : [-(hAPP(c_Relation_OField(_1601270), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1601270, _1601270), tc_HOL_Obool), _1601272)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1601270, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1601270, _1601270), tc_HOL_Obool), tc_fun(_1601270, tc_HOL_Obool), c_Relation_OField(_1601270)), _1601272)))], (22849 ^ _780119) ^ [_1197349] : [-(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), _1197349))))], (32035 ^ _780119) ^ [_1377113, _1377115] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1377113), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377113)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377115)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1377113), _1377115)))], (36692 ^ _780119) ^ [_1477139, _1477141, _1477143, _1477145, _1477147] : [-(hAPP(c_Set_Ovimage(_1477139, _1477141, _1477143), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477141, tc_HOL_Obool)), _1477145), _1477147)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477139, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1477139, _1477141, _1477143), _1477145)), hAPP(c_Set_Ovimage(_1477139, _1477141, _1477143), _1477147)))], (50314 ^ _780119) ^ [_1800142, _1800144] : [class_Lazy__Sequence_Osmall__lazy(_1800142), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1800142), _1800144) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1800142), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1800142)), c_List_Olist_ONil(_1800142)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1800142))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1800144)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1800142, tc_List_Olist(_1800142)), tc_List_Olist(_1800142), c_Lazy__Sequence_Oproduct(_1800142, tc_List_Olist(_1800142), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1800142, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1800144), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1800142), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1800144), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1800142, tc_List_Olist(_1800142), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1800142))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1800142), tc_List_Olist(_1800142)), tc_fun(tc_List_Olist(_1800142), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1800142))), _1800142), hAPP(c_COMBB(tc_List_Olist(_1800142), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1800142)), tc_List_Olist(_1800142)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1800142)))), c_List_Olist_OCons(_1800142))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1800142)))))], (6248 ^ _780119) ^ [_880183, _880185, _880187] : [hAPP(hAPP(c_Set_Oinsert(_880183), _880185), _880187) = c_Orderings_Obot__class_Obot(tc_fun(_880183, tc_HOL_Obool))], (32145 ^ _780119) ^ [_1379600, _1379602] : [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(_1379600))), 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)), _1379602)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379600)), hAPP(c_Nat_OSuc, _1379602))))], (50418 ^ _780119) ^ [_1802569, _1802571, _1802573, _1802575, _1802577] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1802569, _1802571, _1802573), _1802575), _1802577)), -(hBOOL(hAPP(hAPP(_1802573, _1802577), _1802575)))], (45642 ^ _780119) ^ [_1698720, _1698722] : [_1698722 = c_List_Olist_ONil(_1698720), -(hAPP(c_List_Orotate1(_1698720), _1698722) = c_List_Olist_ONil(_1698720))], (2050 ^ _780119) ^ [_809903, _809905, _809907, _809909, _809911, _809913] : [-(c_SetInterval_Oord_OatMost(_809913, _809909, _809905) = c_SetInterval_Oord_OatMost(_809911, _809907, _809903)), _809913 = _809911, _809909 = _809907, _809905 = _809903], (45786 ^ _780119) ^ [_1702246, _1702248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702246)), _1702248)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1702246), _1702248) = _1702248)], (42427 ^ _780119) ^ [_1618834, _1618836, _1618838, _1618840, _1618842, _1618844] : [hAPP(c_Map_Omap__add(_1618834, _1618836, _1618838, _1618840), _1618842) = hAPP(c_Option_Ooption_OSome(_1618836), _1618844), -(hAPP(_1618840, _1618842) = hAPP(c_Option_Ooption_OSome(_1618836), _1618844)), 42434 ^ _780119 : [(42437 ^ _780119) ^ [] : [-(hAPP(_1618838, _1618842) = hAPP(c_Option_Ooption_OSome(_1618836), _1618844))], (42435 ^ _780119) ^ [] : [-(hAPP(_1618840, _1618842) = c_Option_Ooption_ONone(_1618836))]]], (50312 ^ _780119) ^ [_1800077, _1800079, _1800081, _1800083] : [-(c_New__Random__Sequence_Oneg__map(_1800077, _1800079, _1800081, _1800083) = c_New__Random__Sequence_Oneg__bind(_1800077, _1800079, _1800083, hAPP(c_Fun_Ocomp(_1800079, 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(_1800079)))))), _1800077, c_New__Random__Sequence_Oneg__single(_1800079)), _1800081)))], (51123 ^ _780119) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (41312 ^ _780119) ^ [_1591745, _1591747, _1591749, _1591751, _1591753] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591745, tc_fun(_1591747, tc_HOL_Obool)), _1591749), hAPP(hAPP(c_COMBS(_1591745, tc_fun(_1591747, tc_HOL_Obool), tc_fun(_1591747, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1591747, tc_HOL_Obool), tc_fun(tc_fun(_1591747, tc_HOL_Obool), tc_fun(_1591747, tc_HOL_Obool)), _1591745), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1591747, tc_HOL_Obool))), _1591751)), _1591753)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1591747, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591745, tc_fun(_1591747, tc_HOL_Obool)), _1591749), _1591751)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591745, tc_fun(_1591747, tc_HOL_Obool)), _1591749), _1591753)))], (41631 ^ _780119) ^ [_1600908, _1600910, _1600912] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1600908, tc_HOL_Obool)), _1600910), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1600908, tc_HOL_Obool), _1600912)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1600908, tc_HOL_Obool), tc_fun(_1600908, tc_HOL_Obool)), _1600912), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1600908, tc_HOL_Obool)), _1600910)))], (50987 ^ _780119) ^ [_1814338, _1814340] : [-(class_Finite__Set_Ofinite(tc_fun(_1814338, _1814340))), class_Finite__Set_Ofinite(_1814338), class_Finite__Set_Ofinite(_1814340)], (8370 ^ _780119) ^ [_925005, _925007, _925009] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_925005), _925007)), hBOOL(hAPP(_925009, c_Orderings_Obot__class_Obot(tc_fun(_925005, tc_HOL_Obool)))), 8381 ^ _780119 : [(8382 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_925005), 8380 ^ [_925005, _925007, _925009])))], (8384 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_925005), 8379 ^ [_925005, _925007, _925009]), 8380 ^ [_925005, _925007, _925009]))], (8388 ^ _780119) ^ [] : [hBOOL(hAPP(_925009, hAPP(hAPP(c_Set_Oinsert(_925005), 8379 ^ [_925005, _925007, _925009]), 8380 ^ [_925005, _925007, _925009])))], (8386 ^ _780119) ^ [] : [-(hBOOL(hAPP(_925009, 8380 ^ [_925005, _925007, _925009])))]], -(hBOOL(hAPP(_925009, _925007)))], (2246 ^ _780119) ^ [_813155, _813157, _813159, _813161] : [-(c_Nitpick_Onat__lcm(_813161, _813157) = c_Nitpick_Onat__lcm(_813159, _813155)), _813161 = _813159, _813157 = _813155], (18145 ^ _780119) ^ [_1110617, _1110619] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1110617), _1110619)), -(hAPP(c_Finite__Set_Ocard(_1110617), _1110619) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1110617, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1110617), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1110619))], (8322 ^ _780119) ^ [_923939, _923941, _923943, _923945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_923939, tc_HOL_Obool)), _923941), hAPP(hAPP(c_Set_Oinsert(_923939), _923943), _923945))), 8325 ^ _780119 : [(8332 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_923939), _923943), _923945))), 8335 ^ _780119 : [(8342 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_923939), _923943), _923941))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_923939, tc_HOL_Obool)), _923941), _923945)))], (8336 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_923939), _923943), _923941)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_923939, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923939, tc_HOL_Obool)), _923941), hAPP(hAPP(c_Set_Oinsert(_923939), _923943), c_Orderings_Obot__class_Obot(tc_fun(_923939, tc_HOL_Obool))))), _923945)))]]], (8326 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_923939), _923943), _923945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_923939, tc_HOL_Obool)), _923941), _923945)))]]], (23092 ^ _780119) ^ [_1201855, _1201857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201855), _1201857)), -(_1201857 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201855), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 23095 ^ [_1201855, _1201857]))))], (11862 ^ _780119) ^ [_993600, _993602, _993604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993600), _993602)), _993604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993600), _993604)))], (10328 ^ _780119) ^ [_961748, _961750, _961752, _961754] : [-(hBOOL(hAPP(hAPP(c_member(_961748), _961750), _961752))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961748, tc_HOL_Obool)), _961752), hAPP(hAPP(c_Set_Oinsert(_961748), _961750), _961754)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961748, tc_HOL_Obool)), _961752), _961754))], (18668 ^ _780119) ^ [_1120687, _1120689] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120687), _1120689))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120687), _1120689)), -(_1120687 = _1120689)], (25508 ^ _780119) ^ [_1246625, _1246627] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1246625, _1246627)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246627), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246625), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (45510 ^ _780119) ^ [_1695114, _1695116, _1695118, _1695120, _1695122, _1695124, _1695126, _1695128] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1695114, _1695114)), hAPP(hAPP(c_Product__Type_OPair(_1695114, _1695114), _1695116), _1695118)), _1695120)), _1695122 = hAPP(hAPP(c_List_Oappend(_1695114), _1695124), hAPP(hAPP(c_List_Olist_OCons(_1695114), _1695116), _1695126)), _1695128 = hAPP(hAPP(c_List_Oappend(_1695114), _1695124), hAPP(hAPP(c_List_Olist_OCons(_1695114), _1695118), _1695126)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695114), tc_List_Olist(_1695114))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695114), tc_List_Olist(_1695114)), _1695122), _1695128)), c_List_Olistrel1(_1695114, _1695120))))], (19811 ^ _780119) ^ [_1140534] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1140534), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1140534)], (49788 ^ _780119) ^ [_1789830, _1789832, _1789834, _1789836] : [c_List_Olist__all(_1789830, _1789832, hAPP(hAPP(c_List_Olist_OCons(_1789830), _1789834), _1789836)), 49791 ^ _780119 : [(49794 ^ _780119) ^ [] : [-(c_List_Olist__all(_1789830, _1789832, _1789836))], (49792 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1789832, _1789834)))]]], (44482 ^ _780119) ^ [_1671422, _1671424] : [_1671422 = _1671424, -(hAPP(c_Code__Numeral_Onat__of, _1671422) = hAPP(c_Code__Numeral_Onat__of, _1671424))], (33245 ^ _780119) ^ [_1400015] : [c_Int_OMin = c_Int_OBit1(_1400015), -(c_Int_OMin = _1400015)], (47538 ^ _780119) ^ [_1738822, _1738824] : [hBOOL(hAPP(c_List_Odistinct(_1738822), hAPP(c_List_Orev(_1738822), _1738824))), -(hBOOL(hAPP(c_List_Odistinct(_1738822), _1738824)))], (8272 ^ _780119) ^ [_922836, _922838, _922840] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922836, tc_HOL_Obool)), _922838), hAPP(hAPP(c_Set_Oinsert(_922836), _922840), c_Orderings_Obot__class_Obot(tc_fun(_922836, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_922836, _922840, _922838) = c_HOL_OThe(_922836, hAPP(hAPP(c_COMBC(_922836, tc_fun(_922836, tc_HOL_Obool), tc_HOL_Obool), c_member(_922836)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922836, tc_HOL_Obool)), _922838), hAPP(hAPP(c_Set_Oinsert(_922836), _922840), c_Orderings_Obot__class_Obot(tc_fun(_922836, tc_HOL_Obool)))))))], (27910 ^ _780119) ^ [_1295415, _1295417, _1295419, _1295421] : [class_Orderings_Olinorder(_1295415), 27913 ^ _780119 : [(27922 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295415), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1295415), _1295417), _1295419)), _1295421))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295415), _1295417), _1295421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295415), _1295419), _1295421))], (27914 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295415), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1295415), _1295417), _1295419)), _1295421)), 27917 ^ _780119 : [(27920 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295415), _1295419), _1295421)))], (27918 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295415), _1295417), _1295421)))]]]]], (40590 ^ _780119) ^ [_1575843, _1575845, _1575847, _1575849, _1575851] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1575843, _1575845, _1575847), _1575849), _1575851) = c_HOL_OThe(_1575845, c_Finite__Set_Ofold__graph(_1575843, _1575845, _1575847, _1575849, _1575851)))], (1640 ^ _780119) ^ [_803343, _803345] : [-(class_Rings_Ocomm__semiring(_803343)), _803345 = _803343, class_Rings_Ocomm__semiring(_803345)], (44228 ^ _780119) ^ [_1666141, _1666143, _1666145, _1666147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1666141), _1666143)), -(hAPP(hAPP(c_List_Onth(_1666145), hAPP(hAPP(c_List_Otake(_1666145), _1666143), _1666147)), _1666141) = hAPP(hAPP(c_List_Onth(_1666145), _1666147), _1666141))], (50178 ^ _780119) ^ [_1796959, _1796961] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1796959)), c_Int_OBit0(_1796961)))], (13085 ^ _780119) ^ [_1018144, _1018146, _1018148] : [class_Lattices_Oab__semigroup__idem__mult(_1018144), hAPP(_1018146, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018144), 13090 ^ [_1018144, _1018146, _1018148]), 13091 ^ [_1018144, _1018146, _1018148])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018144), hAPP(_1018146, 13090 ^ [_1018144, _1018146, _1018148])), hAPP(_1018146, 13091 ^ [_1018144, _1018146, _1018148])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018144), _1018148)), -(_1018148 = c_Orderings_Obot__class_Obot(tc_fun(_1018144, tc_HOL_Obool))), -(hAPP(_1018146, hAPP(c_Finite__Set_Ofold1(_1018144, c_Groups_Otimes__class_Otimes(_1018144)), _1018148)) = hAPP(c_Finite__Set_Ofold1(_1018144, c_Groups_Otimes__class_Otimes(_1018144)), hAPP(c_Set_Oimage(_1018144, _1018144, _1018146), _1018148)))], (35791 ^ _780119) ^ [_1457156, _1457158, _1457160, _1457162, _1457164] : [c_Equiv__Relations_Oequiv(_1457156, _1457158, _1457160), hBOOL(hAPP(hAPP(c_member(_1457156), _1457162), _1457158)), hBOOL(hAPP(hAPP(c_member(_1457156), _1457164), _1457158)), 35802 ^ _780119 : [(35809 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1457156, _1457156)), hAPP(hAPP(c_Product__Type_OPair(_1457156, _1457156), _1457162), _1457164)), _1457160)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457156), hAPP(hAPP(c_Set_Oinsert(_1457156), _1457162), c_Orderings_Obot__class_Obot(tc_fun(_1457156, tc_HOL_Obool)))), _1457160) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457156), hAPP(hAPP(c_Set_Oinsert(_1457156), _1457164), c_Orderings_Obot__class_Obot(tc_fun(_1457156, tc_HOL_Obool)))), _1457160))], (35803 ^ _780119) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457156), hAPP(hAPP(c_Set_Oinsert(_1457156), _1457162), c_Orderings_Obot__class_Obot(tc_fun(_1457156, tc_HOL_Obool)))), _1457160) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457156), hAPP(hAPP(c_Set_Oinsert(_1457156), _1457164), c_Orderings_Obot__class_Obot(tc_fun(_1457156, tc_HOL_Obool)))), _1457160), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1457156, _1457156)), hAPP(hAPP(c_Product__Type_OPair(_1457156, _1457156), _1457162), _1457164)), _1457160)))]]], (21396 ^ _780119) ^ [_1169806, _1169808, _1169810] : [class_Divides_Osemiring__div(_1169806), -(c_Divides_Odiv__class_Omod(_1169806, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169806), _1169808), _1169810), _1169808) = c_Divides_Odiv__class_Omod(_1169806, _1169810, _1169808))], (44878 ^ _780119) ^ [_1678819, _1678821] : [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), _1678819), _1678821))), 44881 ^ _780119 : [(44888 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1678819), _1678821))), -(c_List_Oupto(_1678819, _1678821) = c_List_Olist_ONil(tc_Int_Oint))], (44882 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1678819), _1678821)), -(c_List_Oupto(_1678819, _1678821) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1678819), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1678819), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1678821)))]]], (51473 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (13940 ^ _780119) ^ [_1033803, _1033805] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033803), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1033805), _1033803)))))], (42692 ^ _780119) ^ [_1625379, _1625381, _1625383, _1625385, _1625387, _1625389, _1625391] : [-(c_Map_Omap__comp(_1625379, _1625381, _1625383, _1625385, _1625387, _1625389) = hAPP(c_Option_Ooption_OSome(_1625381), _1625391)), 42693 ^ _780119 : [(42694 ^ _780119) ^ [_1625457] : [hAPP(_1625387, _1625389) = hAPP(c_Option_Ooption_OSome(_1625379), _1625457), hAPP(_1625385, _1625457) = hAPP(c_Option_Ooption_OSome(_1625381), _1625391)]]], (47732 ^ _780119) ^ [_1743627, _1743629, _1743631, _1743633] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1743627)), c_List_Otranspose__rel(_1743627)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1743627)), hAPP(hAPP(c_List_Olist_OCons(_1743627), _1743629), _1743631)), _1743633))), -(c_List_Otranspose(_1743627, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1743627)), hAPP(hAPP(c_List_Olist_OCons(_1743627), _1743629), _1743631)), _1743633)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1743627)), hAPP(hAPP(c_List_Olist_OCons(_1743627), _1743629), c_List_Oconcat(_1743627, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1743627), tc_List_Olist(_1743627)), c_List_Olist_Olist__case(tc_List_Olist(_1743627), _1743627, c_List_Olist_ONil(_1743627), hAPP(hAPP(c_COMBB(tc_List_Olist(_1743627), tc_fun(tc_List_Olist(_1743627), tc_List_Olist(_1743627)), _1743627), c_COMBK(tc_List_Olist(_1743627), tc_List_Olist(_1743627))), hAPP(hAPP(c_COMBC(_1743627, tc_List_Olist(_1743627), tc_List_Olist(_1743627)), c_List_Olist_OCons(_1743627)), c_List_Olist_ONil(_1743627))))), _1743633)))), c_List_Otranspose(_1743627, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1743627)), _1743631), c_List_Oconcat(tc_List_Olist(_1743627), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1743627), tc_List_Olist(tc_List_Olist(_1743627))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1743627)), _1743627, c_List_Olist_ONil(tc_List_Olist(_1743627)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1743627), tc_List_Olist(tc_List_Olist(_1743627))), _1743627), hAPP(hAPP(c_COMBC(tc_List_Olist(_1743627), tc_List_Olist(tc_List_Olist(_1743627)), tc_List_Olist(tc_List_Olist(_1743627))), c_List_Olist_OCons(tc_List_Olist(_1743627))), c_List_Olist_ONil(tc_List_Olist(_1743627)))))), _1743633))))))], (27312 ^ _780119) ^ [_1284882, _1284884] : [class_Orderings_Olinorder(_1284882), -(c_Big__Operators_Olinorder__class_OMax(_1284882, hAPP(hAPP(c_Set_Oinsert(_1284882), _1284884), c_Orderings_Obot__class_Obot(tc_fun(_1284882, tc_HOL_Obool)))) = _1284884)], (38146 ^ _780119) ^ [_1516678, _1516680, _1516682, _1516684, _1516686, _1516688, _1516690, _1516692, _1516694] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516678, _1516680)), hAPP(hAPP(c_Product__Type_OPair(_1516678, _1516680), _1516682), _1516684)), _1516686)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516688, _1516690)), hAPP(hAPP(c_Product__Type_OPair(_1516688, _1516690), hAPP(_1516692, _1516682)), hAPP(_1516694, _1516684))), hAPP(c_Set_Oimage(tc_prod(_1516678, _1516680), tc_prod(_1516688, _1516690), c_Product__Type_Omap__pair(_1516678, _1516688, _1516680, _1516690, _1516692, _1516694)), _1516686))))], (39966 ^ _780119) ^ [_1560174, _1560176, _1560178] : [c_Relation_Ototal__on(_1560174, _1560176, _1560178), -(c_Relation_Ototal__on(_1560174, _1560176, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1560174, _1560174), tc_HOL_Obool)), _1560178), c_Relation_OId(_1560174))))], (27392 ^ _780119) ^ [_1286109, _1286111, _1286113] : [class_Orderings_Olinorder(_1286109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286109, tc_HOL_Obool)), _1286111), _1286113)), -(_1286111 = c_Orderings_Obot__class_Obot(tc_fun(_1286109, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286109), _1286113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286109), c_Big__Operators_Olinorder__class_OMax(_1286109, _1286111)), c_Big__Operators_Olinorder__class_OMax(_1286109, _1286113))))], (21711 ^ _780119) ^ [_1176323] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176323, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1176323)], (39253 ^ _780119) ^ [_1542667, _1542669] : [39255 ^ _780119 : [(39258 ^ _780119) ^ [] : [39254 ^ [_1542667, _1542669] = c_Orderings_Obot__class_Obot(tc_fun(_1542667, tc_HOL_Obool))], (39256 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1542667, tc_HOL_Obool)), 39254 ^ [_1542667, _1542669]), hAPP(c_Relation_OImage(_1542667, _1542667, _1542669), 39254 ^ [_1542667, _1542669]))))]], -(c_Wellfounded_Owf(_1542667, _1542669))], (5140 ^ _780119) ^ [_858758, _858760, _858762, _858764, _858766, _858768, _858770, _858772, _858774, _858776] : [-(c_Predicate_Opred__comp(_858776, _858772, _858768, _858764, _858760) = c_Predicate_Opred__comp(_858774, _858770, _858766, _858762, _858758)), _858776 = _858774, _858772 = _858770, _858768 = _858766, _858764 = _858762, _858760 = _858758], (46957 ^ _780119) ^ [_1726999, _1727001] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1726999), _1727001)) = c_List_Oupt(_1726999, _1727001))], (25706 ^ _780119) ^ [_1249461, _1249463] : [class_Int_Oring__char__0(_1249461), 25709 ^ _780119 : [(25716 ^ _780119) ^ [] : [_1249463 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1249461), _1249463) = c_Groups_Ozero__class_Ozero(_1249461))], (25710 ^ _780119) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1249461), _1249463) = c_Groups_Ozero__class_Ozero(_1249461), -(_1249463 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (27702 ^ _780119) ^ [_1291837, _1291839, _1291841, _1291843] : [class_Orderings_Olinorder(_1291837), 27705 ^ _780119 : [(27706 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291837), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291837), _1291839), _1291841)), _1291843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291837), _1291839), _1291843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291837), _1291841), _1291843)))], (27716 ^ _780119) ^ [] : [27717 ^ _780119 : [(27720 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291837), _1291841), _1291843))], (27718 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291837), _1291839), _1291843))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291837), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291837), _1291839), _1291841)), _1291843)))]]], (38778 ^ _780119) ^ [_1531502, _1531504, _1531506, _1531508, _1531510, _1531512] : [c_Fun_Oinj__on(_1531502, _1531504, _1531506, _1531508), c_Fun_Oinj__on(_1531504, _1531510, _1531512, hAPP(c_Set_Oimage(_1531502, _1531504, _1531506), _1531508)), -(c_Fun_Oinj__on(_1531502, _1531510, hAPP(c_Fun_Ocomp(_1531504, _1531510, _1531502, _1531512), _1531506), _1531508))], (15288 ^ _780119) ^ [] : [-(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))], (11387 ^ _780119) ^ [_983867, _983869] : [class_Rings_Ocomm__semiring__1(_983867), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983867), _983869), _983869) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983867), c_Groups_Oone__class_Oone(_983867)), c_Groups_Oone__class_Oone(_983867))), _983869))], (51215 ^ _780119) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (31457 ^ _780119) ^ [_1367978, _1367980] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367978)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367978)), _1367980)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1367978))), _1367980))], (27306 ^ _780119) ^ [_1284775, _1284777] : [class_Orderings_Olinorder(_1284775), -(c_Big__Operators_Olinorder__class_OMin(_1284775, hAPP(hAPP(c_Set_Oinsert(_1284775), _1284777), c_Orderings_Obot__class_Obot(tc_fun(_1284775, tc_HOL_Obool)))) = _1284777)], (47794 ^ _780119) ^ [_1745796, _1745798, _1745800] : [c_List_OtakeWhile(_1745796, _1745798, _1745800) = _1745800, 47797 ^ _780119 : [(47798 ^ _780119) ^ [_1745883] : [hBOOL(hAPP(hAPP(c_member(_1745796), _1745883), hAPP(c_List_Oset(_1745796), _1745800))), -(hBOOL(hAPP(_1745798, _1745883)))]]], (33719 ^ _780119) ^ [_1412676, _1412678, _1412680] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1412676, _1412676), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1412678), _1412680))), -(_1412676 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1412678 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (38381 ^ _780119) ^ [_1522364, _1522366, _1522368] : [c_Wellfounded_Oacyclic(_1522364, _1522366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522364, _1522364), tc_HOL_Obool)), _1522368), _1522366)), -(c_Wellfounded_Oacyclic(_1522364, _1522368))], (27067 ^ _780119) ^ [_1277278, _1277280] : [-(c_Nitpick_Oint__lcm(_1277278, _1277280) = 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), _1277278)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1277280)))))], (8962 ^ _780119) ^ [_934510, _934512, _934514] : [class_Orderings_Olinorder(_934510), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934510), _934512), _934514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934510), _934514), _934512)))], (31477 ^ _780119) ^ [_1368294, _1368296] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1368294)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368296)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1368296))), 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), _1368294)), c_Int_Onat)))))], (18532 ^ _780119) ^ [_1118195] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _1118195)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48047 ^ _780119) ^ [_1750759, _1750761, _1750763] : [-(c_List_OdropWhile(_1750759, _1750761, _1750763) = c_List_Olist_ONil(_1750759)), hBOOL(hAPP(_1750761, hAPP(c_List_Ohd(_1750759), c_List_OdropWhile(_1750759, _1750761, _1750763))))], (37992 ^ _780119) ^ [_1511821, _1511823, _1511825, _1511827, _1511829, _1511831, _1511833] : [class_Rings_Osemiring__0(_1511821), c_Fun_Oinj__on(tc_prod(_1511823, _1511825), _1511821, hAPP(c_Product__Type_Oprod_Oprod__case(_1511823, _1511825, _1511821), hAPP(hAPP(c_COMBC(_1511823, tc_fun(_1511825, _1511821), tc_fun(_1511825, _1511821)), hAPP(hAPP(c_COMBB(tc_fun(_1511821, _1511821), tc_fun(tc_fun(_1511825, _1511821), tc_fun(_1511825, _1511821)), _1511823), c_COMBB(_1511821, _1511821, _1511825)), hAPP(hAPP(c_COMBB(_1511821, tc_fun(_1511821, _1511821), _1511823), c_Groups_Otimes__class_Otimes(_1511821)), _1511827))), _1511829)), hAPP(hAPP(c_Product__Type_OSigma(_1511823, _1511825), _1511831), hAPP(c_COMBK(tc_fun(_1511825, tc_HOL_Obool), _1511823), _1511833))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1511821), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511823, _1511821), _1511827), _1511831)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511825, _1511821), _1511829), _1511833)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511821, _1511821), c_Fun_Oid(_1511821)), hAPP(c_Set_OCollect(_1511821), hAPP(hAPP(c_COMBB(tc_fun(_1511823, tc_HOL_Obool), tc_HOL_Obool, _1511821), c_HOL_OEx(_1511823)), hAPP(hAPP(c_COMBB(tc_fun(_1511823, tc_fun(_1511825, tc_HOL_Obool)), tc_fun(_1511823, tc_HOL_Obool), _1511821), hAPP(c_COMBB(tc_fun(_1511825, tc_HOL_Obool), tc_HOL_Obool, _1511823), c_HOL_OEx(_1511825))), hAPP(hAPP(c_COMBC(_1511821, tc_fun(_1511823, tc_fun(_1511825, tc_HOL_Obool)), tc_fun(_1511823, tc_fun(_1511825, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511823, tc_fun(tc_fun(_1511825, tc_HOL_Obool), tc_fun(_1511825, tc_HOL_Obool))), tc_fun(tc_fun(_1511823, tc_fun(_1511825, tc_HOL_Obool)), tc_fun(_1511823, tc_fun(_1511825, tc_HOL_Obool))), _1511821), c_COMBS(_1511823, tc_fun(_1511825, tc_HOL_Obool), tc_fun(_1511825, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511823, tc_fun(_1511825, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1511823, tc_fun(tc_fun(_1511825, tc_HOL_Obool), tc_fun(_1511825, tc_HOL_Obool))), _1511821), hAPP(c_COMBB(tc_fun(_1511825, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1511825, tc_HOL_Obool), tc_fun(_1511825, tc_HOL_Obool)), _1511823), c_COMBS(_1511825, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511823, tc_fun(_1511825, tc_HOL_Obool)), tc_fun(_1511823, tc_fun(_1511825, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1511821), hAPP(c_COMBB(tc_fun(_1511825, tc_HOL_Obool), tc_fun(_1511825, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1511823), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511825), c_fconj))), hAPP(hAPP(c_COMBC(_1511821, tc_fun(_1511823, tc_fun(_1511825, _1511821)), tc_fun(_1511823, tc_fun(_1511825, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1511825, _1511821), tc_fun(_1511825, tc_HOL_Obool)), tc_fun(tc_fun(_1511823, tc_fun(_1511825, _1511821)), tc_fun(_1511823, tc_fun(_1511825, tc_HOL_Obool))), _1511821), c_COMBB(tc_fun(_1511825, _1511821), tc_fun(_1511825, tc_HOL_Obool), _1511823)), hAPP(hAPP(c_COMBB(tc_fun(_1511821, tc_HOL_Obool), tc_fun(tc_fun(_1511825, _1511821), tc_fun(_1511825, tc_HOL_Obool)), _1511821), c_COMBB(_1511821, tc_HOL_Obool, _1511825)), c_fequal))), hAPP(hAPP(c_COMBC(_1511823, tc_fun(_1511825, _1511821), tc_fun(_1511825, _1511821)), hAPP(hAPP(c_COMBB(tc_fun(_1511821, _1511821), tc_fun(tc_fun(_1511825, _1511821), tc_fun(_1511825, _1511821)), _1511823), c_COMBB(_1511821, _1511821, _1511825)), hAPP(hAPP(c_COMBB(_1511821, tc_fun(_1511821, _1511821), _1511823), c_Groups_Otimes__class_Otimes(_1511821)), _1511827))), _1511829)))))), hAPP(hAPP(c_COMBC(_1511823, tc_fun(_1511825, tc_HOL_Obool), tc_fun(_1511825, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1511825, tc_HOL_Obool), tc_fun(_1511825, tc_HOL_Obool)), _1511823), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1511825)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511823), c_fconj), hAPP(hAPP(c_COMBC(_1511823, tc_fun(_1511823, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511823)), _1511831)))), hAPP(hAPP(c_COMBC(_1511825, tc_fun(_1511825, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511825)), _1511833))))))))], (26497 ^ _780119) ^ [_1263727, _1263729, _1263731] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1263727), hAPP(c_Set_OCollect(_1263727), hAPP(hAPP(c_COMBS(_1263727, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263727), c_fdisj), _1263729)), _1263731))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263727), hAPP(c_Set_OCollect(_1263727), _1263729))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263727), hAPP(c_Set_OCollect(_1263727), _1263731)))], (26931 ^ _780119) ^ [_1272690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1272690), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1272690) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1272690))], (45632 ^ _780119) ^ [_1698480, _1698482, _1698484, _1698486] : [-(hAPP(hAPP(c_List_Otake(_1698480), _1698482), hAPP(hAPP(c_List_Odrop(_1698480), _1698484), _1698486)) = hAPP(hAPP(c_List_Odrop(_1698480), _1698484), hAPP(hAPP(c_List_Otake(_1698480), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1698482), _1698484)), _1698486)))], (37980 ^ _780119) ^ [_1511308, _1511310, _1511312, _1511314] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1511308, _1511310), _1511312), _1511314) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1511308, tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool)), _1511312), hAPP(hAPP(c_COMBS(_1511308, tc_fun(_1511310, tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool)), tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511310, tc_HOL_Obool), tc_fun(tc_fun(_1511310, tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool)), tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool)), _1511308), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1511310, tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool))), _1511314)), hAPP(hAPP(c_COMBC(_1511308, tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool), tc_fun(_1511310, tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511310, tc_fun(tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool), tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool), tc_fun(_1511310, tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool))), _1511308), c_COMBC(_1511310, tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool), tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511310, tc_prod(_1511308, _1511310)), tc_fun(_1511310, tc_fun(tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool), tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool))), _1511308), hAPP(c_COMBB(tc_prod(_1511308, _1511310), tc_fun(tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool), tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool)), _1511310), c_Set_Oinsert(tc_prod(_1511308, _1511310)))), c_Product__Type_OPair(_1511308, _1511310)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1511308, _1511310), tc_HOL_Obool))))))], (48239 ^ _780119) ^ [_1755468, _1755470] : [hBOOL(hAPP(c_List_Odistinct(_1755468), _1755470)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1755468, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1755468), tc_fun(_1755468, tc_HOL_Obool)), c_List_Oset(_1755468)), c_Enum_Osublists(_1755468, _1755470)))))], (30291 ^ _780119) ^ [_1346190, _1346192, _1346194, _1346196] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346190), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346190), _1346192), _1346194)), hAPP(c_Int_Onumber__class_Onumber__of(_1346190), _1346196)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346190), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346190), _1346192), hAPP(c_Int_Onumber__class_Onumber__of(_1346190), _1346196))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346190), _1346194), hAPP(c_Int_Onumber__class_Onumber__of(_1346190), _1346196)))), class_Int_Onumber(_1346190), class_Rings_Oring(_1346190)], (44742 ^ _780119) ^ [_1676328, _1676330] : [_1676330 = c_List_Olist_ONil(_1676328), -(c_Orderings_Obot__class_Obot(tc_fun(_1676328, tc_HOL_Obool)) = hAPP(c_List_Oset(_1676328), _1676330))], (8708 ^ _780119) ^ [_930629, _930631, _930633, _930635] : [class_Orderings_Oorder(_930629), _930631 = _930633, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930629), _930635), _930633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930629), _930635), _930631)))], (43960 ^ _780119) ^ [_1658888, _1658890, _1658892, _1658894] : [-(hAPP(hAPP(c_List_Onth(_1658888), hAPP(hAPP(c_List_Olist_OCons(_1658888), _1658890), _1658892)), hAPP(c_Nat_OSuc, _1658894)) = hAPP(hAPP(c_List_Onth(_1658888), _1658892), _1658894))], (48351 ^ _780119) ^ [_1757734, _1757736, _1757738, _1757740] : [class_Orderings_Olinorder(_1757734), -(hAPP(c_List_Oset(_1757736), c_List_Olinorder__class_Osort__key(_1757736, _1757734, _1757738, _1757740)) = hAPP(c_List_Oset(_1757736), _1757740))], (44432 ^ _780119) ^ [_1670326, _1670328, _1670330, _1670332, _1670334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670326), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670328)), _1670330))), 44435 ^ _780119 : [(44442 ^ _780119) ^ [] : [-(_1670326 = _1670332), -(hAPP(hAPP(c_List_Onth(_1670328), hAPP(hAPP(c_List_Olist__update(_1670328, _1670330), _1670326), _1670334)), _1670332) = hAPP(hAPP(c_List_Onth(_1670328), _1670330), _1670332))], (44436 ^ _780119) ^ [] : [_1670326 = _1670332, -(hAPP(hAPP(c_List_Onth(_1670328), hAPP(hAPP(c_List_Olist__update(_1670328, _1670330), _1670326), _1670334)), _1670332) = _1670334)]]], (25366 ^ _780119) ^ [_1244008, _1244010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244008)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244010)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1244008)), hAPP(c_Int_Onat, _1244010)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244008), _1244010)))], (20568 ^ _780119) ^ [_1154057, _1154059, _1154061, _1154063] : [class_Fields_Ofield__inverse__zero(_1154057), -(_1154059 = c_Groups_Ozero__class_Ozero(_1154057)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154057), _1154061), _1154059)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154057), _1154063), _1154059)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154057), _1154061), _1154063))], (21695 ^ _780119) ^ [_1176083, _1176085] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176083), _1176085) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176083, _1176085) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (43102 ^ _780119) ^ [_1635015, _1635017, _1635019, _1635021, _1635023, _1635025] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635015, _1635017)), hAPP(hAPP(c_Product__Type_OPair(_1635015, _1635017), _1635019), _1635021)), hAPP(c_List_Oset(tc_prod(_1635015, _1635017)), hAPP(hAPP(c_List_Ozip(_1635015, _1635017), _1635023), _1635025)))), 43105 ^ _780119 : [(43108 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1635017), _1635021), hAPP(c_List_Oset(_1635017), _1635025))))], (43106 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1635015), _1635019), hAPP(c_List_Oset(_1635015), _1635023))))]]], (42669 ^ _780119) ^ [_1624841] : [-(hAPP(c_Option_Omap(_1624841, _1624841), c_COMBI(_1624841)) = c_Fun_Oid(tc_Option_Ooption(_1624841)))], (1440 ^ _780119) ^ [_800843, _800845] : [-(class_Rings_Olinordered__comm__semiring__strict(_800843)), _800845 = _800843, class_Rings_Olinordered__comm__semiring__strict(_800845)], (51271 ^ _780119) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (39990 ^ _780119) ^ [_1560601, _1560603, _1560605, _1560607, _1560609] : [-(hAPP(c_Relation_Oconverse(_1560601, _1560603), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1560605, tc_fun(tc_prod(_1560601, _1560603), tc_HOL_Obool)), _1560607), _1560609)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1560605, tc_fun(tc_prod(_1560603, _1560601), tc_HOL_Obool)), _1560607), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1560601, _1560603), tc_HOL_Obool), tc_fun(tc_prod(_1560603, _1560601), tc_HOL_Obool), _1560605), c_Relation_Oconverse(_1560601, _1560603)), _1560609)))], (35283 ^ _780119) ^ [] : [-(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)))))], (42455 ^ _780119) ^ [_1619446, _1619448, _1619450, _1619452] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1619446, tc_HOL_Obool)), c_Map_Odom(_1619446, _1619448, _1619450)), c_Map_Odom(_1619446, _1619448, _1619452)) = c_Orderings_Obot__class_Obot(tc_fun(_1619446, tc_HOL_Obool)), -(c_Map_Omap__add(_1619446, _1619448, _1619450, _1619452) = c_Map_Omap__add(_1619446, _1619448, _1619452, _1619450))], (26411 ^ _780119) ^ [_1261997, _1261999] : [-(hAPP(c_Set_OCollect(_1261997), _1261999) = _1261999)], (51347 ^ _780119) ^ [_1817870] : [class_Lazy__Sequence_Osmall__lazy(_1817870), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1817870)))], (4182 ^ _780119) ^ [_843323, _843325, _843327, _843329] : [-(c_List_Oremdups(_843329, _843325) = c_List_Oremdups(_843327, _843323)), _843329 = _843327, _843325 = _843323], (50442 ^ _780119) ^ [_1803059, _1803061, _1803063, _1803065, _1803067] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1803059, _1803061, _1803063), _1803065), _1803067)), -(hBOOL(hAPP(hAPP(_1803063, _1803067), _1803065)))], (16725 ^ _780119) ^ [_1084513, _1084515, _1084517, _1084519] : [class_Rings_Ocomm__semiring__1(_1084513), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084515), _1084517)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084515, _1084513), _1084519), _1084517) = c_Groups_Ozero__class_Ozero(_1084513)), 16734 ^ _780119 : [(16735 ^ _780119) ^ [_1084694] : [hBOOL(hAPP(hAPP(c_member(_1084515), _1084694), _1084517)), hAPP(_1084519, _1084694) = c_Groups_Ozero__class_Ozero(_1084513)]]], (6328 ^ _780119) ^ [_881796, _881798, _881800, _881802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881796, tc_HOL_Obool)), _881798), _881800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881796, tc_HOL_Obool)), _881798), hAPP(hAPP(c_Set_Oinsert(_881796), _881802), _881800))))], (37532 ^ _780119) ^ [_1498413, _1498415] : [-(hAPP(c_Relation_ORange(_1498413, _1498413), c_Relation_OId__on(_1498413, _1498415)) = _1498415)], (27069 ^ _780119) ^ [_1277324, _1277326, _1277328] : [class_Lattices_Odistrib__lattice(_1277324), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277324), _1277326)), -(_1277326 = c_Orderings_Obot__class_Obot(tc_fun(_1277324, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277324), _1277328)), -(_1277328 = c_Orderings_Obot__class_Obot(tc_fun(_1277324, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1277324), c_Big__Operators_Olattice__class_OSup__fin(_1277324, _1277326)), c_Big__Operators_Olattice__class_OSup__fin(_1277324, _1277328)) = c_Big__Operators_Olattice__class_OSup__fin(_1277324, hAPP(c_Set_OCollect(_1277324), hAPP(hAPP(c_COMBB(tc_fun(_1277324, tc_HOL_Obool), tc_HOL_Obool, _1277324), c_HOL_OEx(_1277324)), hAPP(hAPP(c_COMBB(tc_fun(_1277324, tc_fun(_1277324, tc_HOL_Obool)), tc_fun(_1277324, tc_HOL_Obool), _1277324), hAPP(c_COMBB(tc_fun(_1277324, tc_HOL_Obool), tc_HOL_Obool, _1277324), c_HOL_OEx(_1277324))), hAPP(hAPP(c_COMBC(_1277324, tc_fun(_1277324, tc_fun(_1277324, tc_HOL_Obool)), tc_fun(_1277324, tc_fun(_1277324, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1277324, tc_fun(tc_fun(_1277324, tc_HOL_Obool), tc_fun(_1277324, tc_HOL_Obool))), tc_fun(tc_fun(_1277324, tc_fun(_1277324, tc_HOL_Obool)), tc_fun(_1277324, tc_fun(_1277324, tc_HOL_Obool))), _1277324), c_COMBS(_1277324, tc_fun(_1277324, tc_HOL_Obool), tc_fun(_1277324, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1277324, tc_fun(_1277324, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1277324, tc_fun(tc_fun(_1277324, tc_HOL_Obool), tc_fun(_1277324, tc_HOL_Obool))), _1277324), hAPP(c_COMBB(tc_fun(_1277324, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1277324, tc_HOL_Obool), tc_fun(_1277324, tc_HOL_Obool)), _1277324), c_COMBS(_1277324, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1277324, tc_fun(_1277324, tc_HOL_Obool)), tc_fun(_1277324, tc_fun(_1277324, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1277324), hAPP(c_COMBB(tc_fun(_1277324, tc_HOL_Obool), tc_fun(_1277324, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1277324), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1277324), c_fconj))), hAPP(hAPP(c_COMBC(_1277324, tc_fun(_1277324, tc_fun(_1277324, _1277324)), tc_fun(_1277324, tc_fun(_1277324, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1277324, _1277324), tc_fun(_1277324, tc_HOL_Obool)), tc_fun(tc_fun(_1277324, tc_fun(_1277324, _1277324)), tc_fun(_1277324, tc_fun(_1277324, tc_HOL_Obool))), _1277324), c_COMBB(tc_fun(_1277324, _1277324), tc_fun(_1277324, tc_HOL_Obool), _1277324)), hAPP(hAPP(c_COMBB(tc_fun(_1277324, tc_HOL_Obool), tc_fun(tc_fun(_1277324, _1277324), tc_fun(_1277324, tc_HOL_Obool)), _1277324), c_COMBB(_1277324, tc_HOL_Obool, _1277324)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1277324)))))), hAPP(hAPP(c_COMBC(_1277324, tc_fun(_1277324, tc_HOL_Obool), tc_fun(_1277324, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1277324, tc_HOL_Obool), tc_fun(_1277324, tc_HOL_Obool)), _1277324), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1277324)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1277324), c_fconj), hAPP(hAPP(c_COMBC(_1277324, tc_fun(_1277324, tc_HOL_Obool), tc_HOL_Obool), c_member(_1277324)), _1277326)))), hAPP(hAPP(c_COMBC(_1277324, tc_fun(_1277324, tc_HOL_Obool), tc_HOL_Obool), c_member(_1277324)), _1277328))))))))], (36565 ^ _780119) ^ [_1474083, _1474085, _1474087, _1474089, _1474091] : [-(c_Fun_Oinj__on(_1474083, _1474085, _1474087, hAPP(hAPP(c_Set_Oinsert(_1474083), _1474089), _1474091))), c_Fun_Oinj__on(_1474083, _1474085, _1474087, _1474091), -(hBOOL(hAPP(hAPP(c_member(_1474085), hAPP(_1474087, _1474089)), hAPP(c_Set_Oimage(_1474083, _1474085, _1474087), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474083, tc_HOL_Obool)), _1474091), hAPP(hAPP(c_Set_Oinsert(_1474083), _1474089), c_Orderings_Obot__class_Obot(tc_fun(_1474083, tc_HOL_Obool))))))))], (40110 ^ _780119) ^ [_1563618, _1563620, _1563622, _1563624, _1563626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1563618, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1563620, _1563618, _1563622), _1563624)), _1563626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1563620, tc_HOL_Obool)), _1563624), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1563620, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1563618, _1563620, hAPP(c_Relation_Oconverse(_1563620, _1563618), _1563622)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1563618, tc_HOL_Obool)), _1563626))))))], (35127 ^ _780119) ^ [_1440269, _1440271] : [class_Rings_Osemiring__1(_1440269), -(hBOOL(hAPP(hAPP(c_member(_1440269), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1440269), _1440271)), c_Nat_Osemiring__1__class_ONats(_1440269))))], (8828 ^ _780119) ^ [_932515, _932517, _932519, _932521] : [-(c_Nitpick_Ofold__graph_H(_932515, _932517, _932519, _932521, c_Orderings_Obot__class_Obot(tc_fun(_932515, tc_HOL_Obool)), _932521))], (22013 ^ _780119) ^ [_1182104, _1182106, _1182108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182104)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182106, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182108), _1182104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182108), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182106), _1182108), _1182104))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182106, _1182108)))], (51497 ^ _780119) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (37708 ^ _780119) ^ [_1503455, _1503457, _1503459, _1503461] : [hBOOL(hAPP(hAPP(c_member(_1503455), _1503457), hAPP(c_Relation_ODomain(_1503455, _1503459), _1503461))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1503455, _1503459)), hAPP(hAPP(c_Product__Type_OPair(_1503455, _1503459), _1503457), 37711 ^ [_1503455, _1503457, _1503459, _1503461])), _1503461)))], (25826 ^ _780119) ^ [_1251516] : [c_Nat__Transfer_Onat__set(_1251516), 25829 ^ _780119 : [(25830 ^ _780119) ^ [_1251582] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1251582), _1251516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251582)))]]], (18894 ^ _780119) ^ [_1124520, _1124522, _1124524, _1124526, _1124528] : [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), _1124520), _1124522)), _1124524)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1124520), _1124526)), _1124528))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124528), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124520), _1124528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124520), _1124524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124526), _1124522)))], (22739 ^ _780119) ^ [_1195535, _1195537, _1195539, _1195541, _1195543] : [-(hBOOL(hAPP(hAPP(c_member(_1195535), _1195537), c_SetInterval_Oord_OatLeastAtMost(_1195535, _1195539, _1195541, _1195543)))), hBOOL(hAPP(hAPP(_1195539, _1195541), _1195537)), hBOOL(hAPP(hAPP(_1195539, _1195537), _1195543))], (21676 ^ _780119) ^ [_1175747, _1175749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175747), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175747), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1175749, _1175747))))], (41328 ^ _780119) ^ [_1592332, _1592334, _1592336, _1592338, _1592340] : [hBOOL(hAPP(hAPP(c_member(_1592332), _1592334), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592336, tc_fun(_1592332, tc_HOL_Obool)), _1592338), _1592340))), 41331 ^ _780119 : [(41332 ^ _780119) ^ [_1592456] : [hBOOL(hAPP(hAPP(c_member(_1592336), _1592456), _1592338)), -(hBOOL(hAPP(hAPP(c_member(_1592332), _1592334), hAPP(_1592340, _1592456))))]]], (440 ^ _780119) ^ [_786919, _786921, _786923, _786925, _786927, _786929] : [-(c_Hoare__Mirabelle_Ohoare__valids(_786927, _786923, _786919)), c_Hoare__Mirabelle_Ohoare__valids(_786929, _786925, _786921), _786929 = _786927, _786925 = _786923, _786921 = _786919], (51557 ^ _780119) ^ [_1820191, _1820193, _1820195, _1820197, _1820199, _1820201] : [-(hAPP(hAPP(hAPP(c_COMBB(_1820191, _1820193, _1820195), _1820197), _1820199), _1820201) = hAPP(_1820197, hAPP(_1820199, _1820201)))], (22019 ^ _780119) ^ [_1182258, _1182260] : [-(_1182258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22022 ^ _780119 : [(22029 ^ _780119) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182260, _1182258) = 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), _1182260)), _1182258) = 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), _1182260), _1182258))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22023 ^ _780119) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182260, _1182258) = 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), _1182260)), _1182258) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182260), _1182258)))]]], (13730 ^ _780119) ^ [_1029671, _1029673] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029671)), hAPP(c_Nat_OSuc, _1029673)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029671), _1029673))], (45624 ^ _780119) ^ [_1698295, _1698297] : [-(hAPP(c_List_Oset(_1698295), hAPP(c_List_Orotate1(_1698295), _1698297)) = hAPP(c_List_Oset(_1698295), _1698297))], (46941 ^ _780119) ^ [_1726735, _1726737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726735), _1726737)), -(c_List_Oupt(_1726735, _1726737) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1726735), c_List_Oupt(hAPP(c_Nat_OSuc, _1726735), _1726737)))], (17104 ^ _780119) ^ [_1090692, _1090694, _1090696, _1090698, _1090700] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1090692), hAPP(c_Set_Oimage(_1090694, _1090692, _1090696), c_Orderings_Otop__class_Otop(tc_fun(_1090694, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1090698), hAPP(c_Set_Oimage(_1090694, _1090698, hAPP(hAPP(c_COMBB(_1090692, _1090698, _1090694), _1090700), _1090696)), c_Orderings_Otop__class_Otop(tc_fun(_1090694, tc_HOL_Obool))))))], (50114 ^ _780119) ^ [_1795938, _1795940, _1795942, _1795944, _1795946] : [_1795938 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1795940, _1795942, _1795944, _1795946), _1795938) = c_Lazy__Sequence_Oempty(_1795942))], (12855 ^ _780119) ^ [_1013358, _1013360, _1013362] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1013358), _1013360)), -(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(_1013358), _1013362)), hAPP(c_Finite__Set_Ocard(_1013358), _1013360))), hAPP(c_Finite__Set_Ocard(_1013358), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013358, tc_HOL_Obool)), _1013362), _1013360)))))], (42147 ^ _780119) ^ [_1612487, _1612489, _1612491] : [42149 ^ _780119 : [(42152 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1612487), _1612491), 42148 ^ [_1612487, _1612489, _1612491]))], (42150 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1612487, tc_HOL_Obool)), 42148 ^ [_1612487, _1612489, _1612491]), _1612489)))]], -(hBOOL(hAPP(hAPP(c_member(_1612487), _1612491), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1612487, tc_HOL_Obool), _1612489))))], (29082 ^ _780119) ^ [_1318759, _1318761, _1318763] : [class_Orderings_Olinorder(_1318759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318759), _1318761)), 29089 ^ _780119 : [(29096 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318759, tc_HOL_Obool)), _1318761), hAPP(hAPP(c_Set_Oinsert(_1318759), _1318763), c_Orderings_Obot__class_Obot(tc_fun(_1318759, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1318759, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1318759, c_Orderings_Oord__class_Omin(_1318759), hAPP(hAPP(c_Set_Oinsert(_1318759), _1318763), _1318761)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318759), _1318763), c_Big__Operators_Olattice_OInf__fin(_1318759, c_Orderings_Oord__class_Omin(_1318759), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318759, tc_HOL_Obool)), _1318761), hAPP(hAPP(c_Set_Oinsert(_1318759), _1318763), c_Orderings_Obot__class_Obot(tc_fun(_1318759, tc_HOL_Obool)))))))], (29090 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318759, tc_HOL_Obool)), _1318761), hAPP(hAPP(c_Set_Oinsert(_1318759), _1318763), c_Orderings_Obot__class_Obot(tc_fun(_1318759, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1318759, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1318759, c_Orderings_Oord__class_Omin(_1318759), hAPP(hAPP(c_Set_Oinsert(_1318759), _1318763), _1318761)) = _1318763)]]], (35781 ^ _780119) ^ [_1456875, _1456877, _1456879, _1456881, _1456883] : [c_Equiv__Relations_Oequiv(_1456875, _1456877, _1456879), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456875, _1456875)), hAPP(hAPP(c_Product__Type_OPair(_1456875, _1456875), _1456881), _1456883)), _1456879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456875, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1456875, _1456875, _1456879), hAPP(hAPP(c_Set_Oinsert(_1456875), _1456881), c_Orderings_Obot__class_Obot(tc_fun(_1456875, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1456875, _1456875, _1456879), hAPP(hAPP(c_Set_Oinsert(_1456875), _1456883), c_Orderings_Obot__class_Obot(tc_fun(_1456875, tc_HOL_Obool)))))))], (31233 ^ _780119) ^ [_1364069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1364069)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1364069), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26165 ^ _780119) ^ [_1257234, _1257236] : [class_Orderings_Olinorder(_1257234), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1257234, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257234), _1257236)) = hAPP(c_SetInterval_Oord__class_OatMost(_1257234), _1257236))], (11939 ^ _780119) ^ [_995156, _995158, _995160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995156), _995158)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995156), _995160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995158), _995160)))], (15312 ^ _780119) ^ [_1059663, _1059665] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1059663), _1059665) = _1059663, -(_1059665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49299 ^ _780119) ^ [_1777777, _1777779, _1777781] : [hBOOL(hAPP(c_List_Odistinct(_1777777), _1777779)), -(c_List_Oremove1(_1777777, _1777781, _1777779) = hAPP(c_List_OremoveAll(_1777777, _1777781), _1777779))], (36379 ^ _780119) ^ [_1470131, _1470133, _1470135] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1470131), _1470133)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470131, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470131, _1470131, _1470135), _1470133)), _1470133)), c_Fun_Oinj__on(_1470131, _1470131, _1470135, _1470133), -(hAPP(c_Set_Oimage(_1470131, _1470131, _1470135), _1470133) = _1470133)], (13360 ^ _780119) ^ [_1023215, _1023217, _1023219] : [class_Groups_Oordered__ab__group__add(_1023215), 13363 ^ _780119 : [(13370 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023215), _1023219), hAPP(c_Groups_Ouminus__class_Ouminus(_1023215), _1023217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023215), _1023217), hAPP(c_Groups_Ouminus__class_Ouminus(_1023215), _1023219))))], (13364 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023215), _1023217), hAPP(c_Groups_Ouminus__class_Ouminus(_1023215), _1023219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023215), _1023219), hAPP(c_Groups_Ouminus__class_Ouminus(_1023215), _1023217))))]]], (21318 ^ _780119) ^ [_1168339, _1168341, _1168343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1168339)), 21321 ^ _780119 : [(21322 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1168341, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1168343), _1168339)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1168343, _1168339))), 21325 ^ _780119 : [(21326 ^ _780119) ^ [_1168540, _1168542] : [-(hBOOL(hAPP(hAPP(_1168341, _1168542), _1168540))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1168540)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1168540), _1168339)), _1168343 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1168339), _1168542)), _1168540)]]], (21340 ^ _780119) ^ [] : [21343 ^ _780119 : [(21344 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21342 ^ [_1168339, _1168341, _1168343])))], (21346 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 21342 ^ [_1168339, _1168341, _1168343]), _1168339)))], (21350 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1168341, 21341 ^ [_1168339, _1168341, _1168343]), 21342 ^ [_1168339, _1168341, _1168343]))], (21348 ^ _780119) ^ [] : [-(_1168343 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1168339), 21341 ^ [_1168339, _1168341, _1168343])), 21342 ^ [_1168339, _1168341, _1168343]))]], -(hBOOL(hAPP(hAPP(_1168341, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1168343), _1168339)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1168343, _1168339))))]]], (43791 ^ _780119) ^ [_1654888, _1654890, _1654892, _1654894] : [class_Groups_Ocomm__monoid__add(_1654888), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1654888), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1654888), _1654890), c_List_Oupto(_1654892, _1654894))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1654888), _1654890), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1654892, _1654894))))], (29905 ^ _780119) ^ [_1338287, _1338289, _1338291, _1338293, _1338295] : [_1338287 = c_Orderings_Obot__class_Obot(tc_fun(_1338289, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338291, tc_HOL_Obool)), _1338293), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338289, tc_fun(_1338291, tc_HOL_Obool)), _1338287), _1338295)) = _1338293)], (31135 ^ _780119) ^ [_1362298, _1362300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362298)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362300))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1362298), _1362300)))], (26383 ^ _780119) ^ [_1261569] : [class_Groups_Oordered__ab__group__add__abs(_1261569), -(hAPP(c_Groups_Oabs__class_Oabs(_1261569), c_Groups_Ozero__class_Ozero(_1261569)) = c_Groups_Ozero__class_Ozero(_1261569))], (37536 ^ _780119) ^ [_1498547, _1498549, _1498551] : [hAPP(c_Relation_ORange(_1498547, _1498549), _1498551) = c_Orderings_Obot__class_Obot(tc_fun(_1498549, tc_HOL_Obool)), -(_1498551 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1498547, _1498549), tc_HOL_Obool)))], (24043 ^ _780119) ^ [_1220041] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220041)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1220041)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220041)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (8458 ^ _780119) ^ [_927000, _927002, _927004, _927006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927000, tc_HOL_Obool)), _927002), _927004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927000, tc_HOL_Obool)), _927004), _927006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927000, tc_HOL_Obool)), _927002), _927006)))], (40580 ^ _780119) ^ [_1575654, _1575656, _1575658, _1575660, _1575662, _1575664] : [c_Finite__Set_Ofolding(_1575654, _1575656, _1575658, _1575660), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575654), _1575662)), -(hAPP(hAPP(_1575660, _1575662), _1575664) = hAPP(hAPP(c_Finite__Set_Ofold(_1575654, _1575656, _1575658), _1575664), _1575662))], (28246 ^ _780119) ^ [_1302231, _1302233, _1302235] : [class_Orderings_Olinorder(_1302231), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302231), _1302233)), hBOOL(hAPP(hAPP(c_member(_1302231), _1302235), _1302233)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1302231), _1302235), c_Big__Operators_Olinorder__class_OMin(_1302231, _1302233)) = c_Big__Operators_Olinorder__class_OMin(_1302231, _1302233))], (6933 ^ _780119) ^ [_894666, _894668, _894670, _894672] : [class_Orderings_Oorder(_894666), _894668 = _894670, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894666), _894672), _894670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894666), _894672), _894668)))], (2976 ^ _780119) ^ [_824428, _824430] : [_824430 = _824428, -(c_HOL_OAll(_824430) = c_HOL_OAll(_824428))], (41409 ^ _780119) ^ [_1595408, _1595410, _1595412, _1595414] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595408, tc_fun(_1595410, tc_HOL_Obool)), _1595412), _1595414) = hAPP(c_Set_OCollect(_1595410), hAPP(hAPP(c_COMBB(tc_fun(_1595408, tc_HOL_Obool), tc_HOL_Obool, _1595410), c_HOL_OAll(_1595408)), hAPP(hAPP(c_COMBB(tc_fun(_1595408, tc_HOL_Obool), tc_fun(_1595408, tc_HOL_Obool), _1595410), hAPP(c_COMBS(_1595408, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1595408), c_fimplies), hAPP(hAPP(c_COMBC(_1595408, tc_fun(_1595408, tc_HOL_Obool), tc_HOL_Obool), c_member(_1595408)), _1595412)))), hAPP(hAPP(c_COMBC(_1595410, tc_fun(_1595408, tc_fun(_1595410, tc_HOL_Obool)), tc_fun(_1595408, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1595410, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1595408, tc_fun(_1595410, tc_HOL_Obool)), tc_fun(_1595408, tc_HOL_Obool)), _1595410), c_COMBB(tc_fun(_1595410, tc_HOL_Obool), tc_HOL_Obool, _1595408)), c_member(_1595410))), _1595414)))))], (44828 ^ _780119) ^ [_1677893, _1677895] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1677893), _1677895) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1677893), _1677895))], (43114 ^ _780119) ^ [_1635525, _1635527, _1635529, _1635531, _1635533, _1635535] : [-(hAPP(hAPP(c_List_Ozip(_1635525, _1635527), _1635529), hAPP(hAPP(c_List_Omap(_1635531, _1635527), _1635533), _1635535)) = hAPP(hAPP(c_List_Omap(tc_prod(_1635525, _1635531), tc_prod(_1635525, _1635527)), hAPP(c_Product__Type_Oprod_Oprod__case(_1635525, _1635531, tc_prod(_1635525, _1635527)), hAPP(hAPP(c_COMBC(_1635525, tc_fun(_1635531, _1635527), tc_fun(_1635531, tc_prod(_1635525, _1635527))), hAPP(hAPP(c_COMBB(tc_fun(_1635527, tc_prod(_1635525, _1635527)), tc_fun(tc_fun(_1635531, _1635527), tc_fun(_1635531, tc_prod(_1635525, _1635527))), _1635525), c_COMBB(_1635527, tc_prod(_1635525, _1635527), _1635531)), c_Product__Type_OPair(_1635525, _1635527))), _1635533))), hAPP(hAPP(c_List_Ozip(_1635525, _1635531), _1635529), _1635535)))], (2214 ^ _780119) ^ [_812617, _812619, _812621, _812623] : [-(c_Nat__Transfer_Otsub(_812623, _812619) = c_Nat__Transfer_Otsub(_812621, _812617)), _812623 = _812621, _812619 = _812617], (44680 ^ _780119) ^ [_1675192, _1675194, _1675196, _1675198] : [class_Orderings_Olinorder(_1675192), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1675194, _1675192, _1675196), _1675198), c_List_Olist_ONil(_1675194)) = hAPP(hAPP(c_List_Olist_OCons(_1675194), _1675198), c_List_Olist_ONil(_1675194)))], (7444 ^ _780119) ^ [_905288, _905290, _905292] : [class_Lattices_Osemilattice__sup(_905288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905288), _905290), _905292)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_905288), _905290), _905292) = _905292)], (31371 ^ _780119) ^ [_1366502, _1366504, _1366506] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366502))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366502)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366504)), _1366506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366504)), _1366506))], (44476 ^ _780119) ^ [_1671337, _1671339] : [hAPP(c_Code__Numeral_Onat__of, _1671337) = hAPP(c_Code__Numeral_Onat__of, _1671339), -(_1671337 = _1671339)], (37166 ^ _780119) ^ [_1490680, _1490682, _1490684, _1490686] : [-(c_Wellfounded_Omax__extp(_1490680, _1490682, _1490684, _1490686)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490680), _1490684)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490680), _1490686)), -(_1490686 = c_Orderings_Obot__class_Obot(tc_fun(_1490680, tc_HOL_Obool))), 37180 ^ _780119 : [(37183 ^ _780119) ^ [_1491025] : [hBOOL(hAPP(hAPP(c_member(_1490680), _1491025), _1490686)), hBOOL(hAPP(hAPP(_1490682, 37179 ^ [_1490680, _1490682, _1490684, _1490686]), _1491025))], (37181 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490680), 37179 ^ [_1490680, _1490682, _1490684, _1490686]), _1490684)))]]], (13652 ^ _780119) ^ [_1028393, _1028395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028395), hAPP(c_Nat_OSuc, _1028393))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028393), _1028395))], (42439 ^ _780119) ^ [_1619043, _1619045, _1619047, _1619049] : [-(c_Map_Odom(_1619043, _1619045, c_Map_Omap__add(_1619043, _1619045, _1619047, _1619049)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1619043, tc_HOL_Obool)), c_Map_Odom(_1619043, _1619045, _1619049)), c_Map_Odom(_1619043, _1619045, _1619047)))], (11269 ^ _780119) ^ [_980884, _980886, _980888, _980890, _980892, _980894] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_980884, tc_Option_Ooption(_980886)), c_Map_Orestrict__map(_980884, _980886, _980888, _980890)), _980892), _980894) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_980884, tc_Option_Ooption(_980886)), c_Map_Orestrict__map(_980884, _980886, _980888, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980884, tc_HOL_Obool)), _980890), hAPP(hAPP(c_Set_Oinsert(_980884), _980892), c_Orderings_Obot__class_Obot(tc_fun(_980884, tc_HOL_Obool)))))), _980892), _980894))], (12861 ^ _780119) ^ [_1013519, _1013521, _1013523] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1013519), _1013521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013519, tc_HOL_Obool)), _1013523), _1013521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1013519), _1013523)), hAPP(c_Finite__Set_Ocard(_1013519), _1013521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013519, tc_HOL_Obool)), _1013523), _1013521)))], (47907 ^ _780119) ^ [_1748001] : [c_List_Onat__list(_1748001), -(c_List_Oembed__list(c_List_Oreturn__list(_1748001)) = _1748001)], (7047 ^ _780119) ^ [_896448, _896450, _896452] : [_896450 = _896452, -(hBOOL(hAPP(hAPP(c_member(_896448), _896450), hAPP(c_fequal, _896452))))], (17622 ^ _780119) ^ [_1100505, _1100507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1100505)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1100507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100507), _1100505))))], (26745 ^ _780119) ^ [_1268685, _1268687, _1268689] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1268685, tc_HOL_Obool)), _1268687), _1268689) = hAPP(c_Set_OCollect(_1268685), hAPP(hAPP(c_COMBS(_1268685, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268685), c_fconj), hAPP(hAPP(c_COMBC(_1268685, tc_fun(_1268685, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268685)), _1268687))), hAPP(hAPP(c_COMBC(_1268685, tc_fun(_1268685, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268685)), _1268689))))], (38517 ^ _780119) ^ [_1525160, _1525162, _1525164] : [hBOOL(hAPP(hAPP(c_member(_1525162), _1525160), c_Orderings_Obot__class_Obot(tc_fun(_1525162, tc_HOL_Obool)))), -(hBOOL(hAPP(_1525164, _1525160)))], (42819 ^ _780119) ^ [_1628112, _1628114, _1628116, _1628118] : [hAPP(c_Map_Omap__of(_1628112, _1628114), _1628116) = hAPP(c_Map_Omap__of(_1628112, _1628114), _1628118), -(hAPP(c_Set_Oimage(tc_prod(_1628112, _1628114), _1628112, c_Product__Type_Ofst(_1628112, _1628114)), hAPP(c_List_Oset(tc_prod(_1628112, _1628114)), _1628116)) = hAPP(c_Set_Oimage(tc_prod(_1628112, _1628114), _1628112, c_Product__Type_Ofst(_1628112, _1628114)), hAPP(c_List_Oset(tc_prod(_1628112, _1628114)), _1628118)))], (9576 ^ _780119) ^ [_945456, _945458, _945460, _945462, _945464] : [class_Groups_Oab__group__add(_945456), hBOOL(hAPP(c_Finite__Set_Ofinite(_945458), _945460)), 9583 ^ _780119 : [(9590 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_945458), _945462), _945460))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_945458, _945456), _945464), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_945458, tc_HOL_Obool)), _945460), hAPP(hAPP(c_Set_Oinsert(_945458), _945462), c_Orderings_Obot__class_Obot(tc_fun(_945458, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_945458, _945456), _945464), _945460))], (9584 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_945458), _945462), _945460)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_945458, _945456), _945464), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_945458, tc_HOL_Obool)), _945460), hAPP(hAPP(c_Set_Oinsert(_945458), _945462), c_Orderings_Obot__class_Obot(tc_fun(_945458, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_945456), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_945458, _945456), _945464), _945460)), hAPP(_945464, _945462)))]]], (33251 ^ _780119) ^ [_1400090] : [c_Int_OMin = _1400090, -(c_Int_OMin = c_Int_OBit1(_1400090))], (44670 ^ _780119) ^ [_1675019, _1675021, _1675023, _1675025] : [_1675025 = c_List_Olist_ONil(_1675021), -(c_List_Olist_ONil(_1675019) = hAPP(hAPP(c_List_Omap(_1675021, _1675019), _1675023), _1675025))], (3976 ^ _780119) ^ [_840186, _840188, _840190, _840192, _840194, _840196] : [-(c_Finite__Set_Ofold(_840196, _840192, _840188) = c_Finite__Set_Ofold(_840194, _840190, _840186)), _840196 = _840194, _840192 = _840190, _840188 = _840186], (48831 ^ _780119) ^ [_1767712, _1767714, _1767716, _1767718] : [hBOOL(hAPP(c_List_Olistsp(_1767712, hAPP(hAPP(c_COMBS(_1767712, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1767712), c_fconj), _1767714)), _1767716)), _1767718)), 48834 ^ _780119 : [(48837 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1767712, _1767716), _1767718)))], (48835 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1767712, _1767714), _1767718)))]]], (45774 ^ _780119) ^ [_1701956, _1701958, _1701960, _1701962] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1701956) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1701958), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1701956)), hAPP(hAPP(c_List_Olist_OCons(_1701958), _1701960), _1701962)) = hAPP(hAPP(c_List_Odrop(_1701958), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1701956)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1701962))], (28864 ^ _780119) ^ [_1315154, _1315156, _1315158] : [class_Orderings_Olinorder(_1315154), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315154), _1315156)), hBOOL(hAPP(hAPP(c_member(_1315154), _1315158), _1315156)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1315154), _1315158), c_Big__Operators_Olattice_OSup__fin(_1315154, c_Orderings_Oord__class_Omax(_1315154), _1315156)) = c_Big__Operators_Olattice_OSup__fin(_1315154, c_Orderings_Oord__class_Omax(_1315154), _1315156))], (5022 ^ _780119) ^ [_856911, _856913, _856915, _856917, _856919, _856921] : [-(c_New__DSequence_Oneg__union(_856921, _856917, _856913) = c_New__DSequence_Oneg__union(_856919, _856915, _856911)), _856921 = _856919, _856917 = _856915, _856913 = _856911], (534 ^ _780119) ^ [_788356, _788358, _788360, _788362, _788364, _788366] : [-(c_Finite__Set_Ofolding__one__idem(_788364, _788360, _788356)), c_Finite__Set_Ofolding__one__idem(_788366, _788362, _788358), _788366 = _788364, _788362 = _788360, _788358 = _788356], (23501 ^ _780119) ^ [_1209867, _1209869, _1209871, _1209873, _1209875] : [class_Orderings_Olinorder(_1209867), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209867), _1209869), _1209871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209867), _1209873), _1209875)), 23512 ^ _780119 : [(23521 ^ _780119) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1209867, _1209869), _1209871) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1209867, _1209873), _1209875)), _1209869 = _1209873, _1209871 = _1209875], (23513 ^ _780119) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1209867, _1209869), _1209871) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1209867, _1209873), _1209875), 23516 ^ _780119 : [(23519 ^ _780119) ^ [] : [-(_1209871 = _1209875)], (23517 ^ _780119) ^ [] : [-(_1209869 = _1209873)]]]]], (34875 ^ _780119) ^ [_1434946, _1434948, _1434950, _1434952, _1434954] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1434946, _1434948, _1434950), _1434952), _1434954) = hAPP(hAPP(_1434952, hAPP(c_Product__Type_Ofst(_1434946, _1434948), _1434954)), hAPP(c_Product__Type_Osnd(_1434946, _1434948), _1434954)))], (30233 ^ _780119) ^ [_1344945, _1344947, _1344949, _1344951, _1344953] : [c_Com_Ocom_OLocal(_1344945, _1344947, _1344949) = c_Com_Ocom_OSemi(_1344951, _1344953)], (31159 ^ _780119) ^ [_1362757] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1362757)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362757))))], (23795 ^ _780119) ^ [_1215017, _1215019, _1215021, _1215023] : [class_Orderings_Olinorder(_1215017), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215017), _1215019), _1215021)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1215017, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1215017, _1215019), _1215023)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1215017, _1215019), _1215021)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1215017, _1215021), _1215023))], (38375 ^ _780119) ^ [_1522257, _1522259] : [c_Wellfounded_OwfP(_1522257, _1522259), -(c_Wellfounded_Oacyclic(_1522257, hAPP(c_Set_OCollect(tc_prod(_1522257, _1522257)), hAPP(c_Product__Type_Oprod_Oprod__case(_1522257, _1522257, tc_HOL_Obool), _1522259))))], (10274 ^ _780119) ^ [_960475, _960477, _960479, _960481] : [class_Lattices_Olattice(_960475), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960475), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_960475), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960475), _960477), _960479)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960475), _960477), _960481))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960475), _960477), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_960475), _960479), _960481)))))], (21384 ^ _780119) ^ [_1169610, _1169612] : [class_Divides_Osemiring__div(_1169610), -(c_Divides_Odiv__class_Omod(_1169610, _1169612, _1169612) = c_Groups_Ozero__class_Ozero(_1169610))], (2496 ^ _780119) ^ [_816968, _816970, _816972, _816974] : [-(c_Divides_Odivmod__nat__rel(_816974, _816970) = c_Divides_Odivmod__nat__rel(_816972, _816968)), _816974 = _816972, _816970 = _816968], (22749 ^ _780119) ^ [_1195722, _1195724] : [-(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), _1195722))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1195724))))], (51115 ^ _780119) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (39056 ^ _780119) ^ [_1537960, _1537962, _1537964, _1537966, _1537968, _1537970, _1537972] : [c_Finite__Set_Ofolding__image(_1537960, _1537962, _1537964, _1537966, _1537968), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537962), _1537970)), -(hAPP(hAPP(_1537968, _1537972), _1537970) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1537960, _1537962, _1537964), _1537972), _1537966), _1537970))], (31029 ^ _780119) ^ [_1360227, _1360229, _1360231, _1360233] : [class_Fields_Olinordered__field__inverse__zero(_1360227), class_Int_Onumber(_1360227), 31036 ^ _780119 : [(31037 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360227), _1360229), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360227), _1360231), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233)))), 31040 ^ _780119 : [(31047 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360227), c_Groups_Ozero__class_Ozero(_1360227)), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233)))), 31050 ^ _780119 : [(31057 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360227), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233)), c_Groups_Ozero__class_Ozero(_1360227)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360227), _1360229), c_Groups_Ozero__class_Ozero(_1360227))))], (31051 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360227), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233)), c_Groups_Ozero__class_Ozero(_1360227))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360227), _1360231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360227), _1360229), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233)))))]]], (31041 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360227), c_Groups_Ozero__class_Ozero(_1360227)), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360227), _1360229), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233))), _1360231)))]]], (31063 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360227), _1360229), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360227), _1360231), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233))))), 31066 ^ _780119 : [(31069 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360227), _1360229), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233))), _1360231))], (31067 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360227), c_Groups_Ozero__class_Ozero(_1360227)), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233))))]], 31070 ^ _780119 : [(31073 ^ _780119) ^ [] : [31074 ^ _780119 : [(31077 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360227), _1360231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360227), _1360229), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233))))], (31075 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360227), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233)), c_Groups_Ozero__class_Ozero(_1360227))))]], 31078 ^ _780119 : [(31081 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360227), _1360229), c_Groups_Ozero__class_Ozero(_1360227)))], (31079 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360227), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233)), c_Groups_Ozero__class_Ozero(_1360227)))]]], (31071 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360227), c_Groups_Ozero__class_Ozero(_1360227)), hAPP(c_Int_Onumber__class_Onumber__of(_1360227), _1360233)))]]]]], (50338 ^ _780119) ^ [_1800841, _1800843, _1800845, _1800847, _1800849, _1800851] : [-(c_New__Random__Sequence_Opos__union(_1800841, _1800843, _1800845, _1800847, _1800849, _1800851) = c_New__DSequence_Opos__union(_1800841, hAPP(hAPP(hAPP(_1800843, _1800847), _1800849), _1800851), hAPP(hAPP(hAPP(_1800845, _1800847), _1800849), _1800851)))], (51287 ^ _780119) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (50808 ^ _780119) ^ [_1810695, _1810697, _1810699, _1810701] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1810695, _1810697)), c_Nitpick_Opair__box_OPairBox(_1810695, _1810697, _1810699, _1810701)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25969 ^ _780119) ^ [_1253864, _1253866] : [class_Rings_Olinordered__idom(_1253864), 25972 ^ _780119 : [(25979 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253864), c_Groups_Ozero__class_Ozero(_1253864)), hAPP(c_Int_Oring__1__class_Oof__int(_1253864), _1253866))))], (25973 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253864), c_Groups_Ozero__class_Ozero(_1253864)), hAPP(c_Int_Oring__1__class_Oof__int(_1253864), _1253866))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253866)))]]], (29002 ^ _780119) ^ [_1317527, _1317529, _1317531] : [class_Orderings_Olinorder(_1317527), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317527), _1317529)), -(_1317529 = c_Orderings_Obot__class_Obot(tc_fun(_1317527, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317527), _1317531)), -(_1317531 = c_Orderings_Obot__class_Obot(tc_fun(_1317527, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1317527, c_Orderings_Oord__class_Omin(_1317527), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317527, tc_HOL_Obool)), _1317529), _1317531)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317527), c_Big__Operators_Olattice_OInf__fin(_1317527, c_Orderings_Oord__class_Omin(_1317527), _1317529)), c_Big__Operators_Olattice_OInf__fin(_1317527, c_Orderings_Oord__class_Omin(_1317527), _1317531)))], (11712 ^ _780119) ^ [_991130, _991132] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991130), _991132))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991130), _991132)), -(_991130 = _991132)], (17920 ^ 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-(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(_1106326, tc_Nat_Onat), _1106330), _1106328))))]]], (48839 ^ _780119) ^ [_1767885, _1767887, _1767889, _1767891] : [-(hBOOL(hAPP(c_List_Olistsp(_1767885, hAPP(hAPP(c_COMBS(_1767885, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1767885), c_fconj), _1767887)), _1767889)), _1767891))), hBOOL(hAPP(c_List_Olistsp(_1767885, _1767887), _1767891)), hBOOL(hAPP(c_List_Olistsp(_1767885, _1767889), _1767891))], (27374 ^ _780119) ^ [_1285803, _1285805, _1285807] : [class_Orderings_Olinorder(_1285803), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1285803, tc_HOL_Obool)), _1285805), _1285807)), -(_1285805 = c_Orderings_Obot__class_Obot(tc_fun(_1285803, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285803), _1285807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285803), c_Big__Operators_Olinorder__class_OMin(_1285803, _1285807)), c_Big__Operators_Olinorder__class_OMin(_1285803, _1285805))))], (10979 ^ _780119) ^ [_975044, _975046] : [class_Groups_Ocomm__monoid__mult(_975044), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975044), c_Groups_Oone__class_Oone(_975044)), _975046) = _975046)], (51305 ^ _780119) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (45024 ^ _780119) ^ [_1682616, _1682618] : [-(hAPP(hAPP(c_List_Oappend(_1682616), c_List_Olist_ONil(_1682616)), _1682618) = _1682618)], (40024 ^ _780119) ^ [_1561367, _1561369] : [-(hAPP(c_Relation_Oconverse(_1561367, _1561367), c_Relation_OId__on(_1561367, _1561369)) = c_Relation_OId__on(_1561367, _1561369))], (40080 ^ _780119) ^ [_1562725, _1562727, _1562729] : [-(hAPP(c_Relation_ODomain(_1562725, _1562727), hAPP(c_Relation_Oconverse(_1562727, _1562725), _1562729)) = hAPP(c_Relation_ORange(_1562727, _1562725), _1562729))], (12095 ^ _780119) ^ [_998097, _998099, _998101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998097), _998099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998097), _998101)), 12102 ^ _780119 : [(12109 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998099), _998101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998099), _998097)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998101), _998097))))], (12103 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998099), _998097)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998101), _998097))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998099), _998101)))]]], (46839 ^ _780119) ^ [_1725016, _1725018, _1725020] : 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-(hBOOL(hAPP(hAPP(c_member(_885370), _885372), c_Orderings_Obot__class_Obot(tc_fun(_885370, tc_HOL_Obool)))))], (47473 ^ _780119) ^ [_1737448, _1737450] : [c_List_Olist_ONil(_1737448) = c_List_Oconcat(_1737448, _1737450), 47476 ^ _780119 : [(47477 ^ _780119) ^ [_1737539] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1737448)), _1737539), hAPP(c_List_Oset(tc_List_Olist(_1737448)), _1737450))), -(_1737539 = c_List_Olist_ONil(_1737448))]]], (11997 ^ _780119) ^ [_996285, _996287, _996289] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996285), _996287)), _996289) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996285), _996289)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996287), _996289)))], (51181 ^ _780119) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (16811 ^ _780119) ^ [_1085940, _1085942] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085940), _1085942)), 16812 ^ _780119 : [(16819 ^ _780119) ^ [] : [_1085940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1085942 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16813 ^ _780119) ^ [] : [_1085940 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1085942 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (38429 ^ _780119) ^ [_1523068, _1523070] : [c_Nitpick_Owf_H(_1523068, _1523070), 38432 ^ _780119 : [(38435 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523068, _1523068)), _1523070))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (38433 ^ _780119) ^ [] : [-(c_Wellfounded_Oacyclic(_1523068, _1523070))]]], (35483 ^ _780119) ^ [_1449944] : [-(_1449944 = 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), 35480 ^ [_1449944]), 35481 ^ [_1449944])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (44102 ^ _780119) ^ [_1662372, _1662374, _1662376, _1662378] : [_1662372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1662374), hAPP(hAPP(c_List_Olist_OCons(_1662374), _1662376), _1662378)), _1662372) = _1662376)], (8222 ^ _780119) ^ [_921723, _921725, _921727, _921729, _921731] : [c_Finite__Set_Ofolding__one(_921723, _921725, _921727), hBOOL(hAPP(c_Finite__Set_Ofinite(_921723), _921729)), 8229 ^ _780119 : [(8236 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921723, tc_HOL_Obool)), _921729), hAPP(hAPP(c_Set_Oinsert(_921723), _921731), c_Orderings_Obot__class_Obot(tc_fun(_921723, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_921723, tc_HOL_Obool))), -(hAPP(_921727, hAPP(hAPP(c_Set_Oinsert(_921723), _921731), _921729)) = hAPP(hAPP(_921725, _921731), hAPP(_921727, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921723, tc_HOL_Obool)), _921729), hAPP(hAPP(c_Set_Oinsert(_921723), _921731), c_Orderings_Obot__class_Obot(tc_fun(_921723, tc_HOL_Obool)))))))], (8230 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921723, tc_HOL_Obool)), _921729), hAPP(hAPP(c_Set_Oinsert(_921723), _921731), c_Orderings_Obot__class_Obot(tc_fun(_921723, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_921723, tc_HOL_Obool)), -(hAPP(_921727, hAPP(hAPP(c_Set_Oinsert(_921723), _921731), _921729)) = _921731)]]], (46753 ^ _780119) ^ [_1723395, _1723397, _1723399, _1723401, _1723403] : [class_Orderings_Olinorder(_1723395), hBOOL(hAPP(hAPP(c_member(_1723397), _1723399), hAPP(c_List_Oset(_1723397), _1723401))), c_List_Olinorder__class_Osorted(_1723395, hAPP(hAPP(c_List_Omap(_1723397, _1723395), _1723403), _1723401)), hAPP(c_List_Ohd(_1723397), hAPP(c_List_Ofilter(_1723397, hAPP(hAPP(c_COMBB(_1723395, tc_HOL_Obool, _1723397), hAPP(c_fequal, hAPP(_1723403, _1723399))), _1723403)), _1723401)) = _1723399, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1723397, _1723395, _1723403), _1723399), c_List_Oremove1(_1723397, _1723399, _1723401)) = _1723401)], (28068 ^ _780119) ^ [_1298342, _1298344, _1298346] : [class_Orderings_Olinorder(_1298342), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298342), _1298344), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298342), _1298344), _1298346)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298342), _1298344), _1298346))], (23747 ^ _780119) ^ [_1213966, _1213968, _1213970, _1213972, _1213974] : [class_Orderings_Olinorder(_1213966), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1213966, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1213966, _1213968), _1213970)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1213966, _1213972), _1213974))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213966), _1213970), _1213968))), 23758 ^ _780119 : [(23761 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213966), _1213970), _1213974)))], (23759 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213966), _1213972), _1213968)))]]], (18041 ^ _780119) ^ [_1108758, _1108760, _1108762] : [class_Rings_Olinordered__semidom(_1108758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108758), c_Groups_Oone__class_Oone(_1108758)), _1108760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108758), c_Groups_Oone__class_Oone(_1108758)), hAPP(hAPP(c_Power_Opower__class_Opower(_1108758), _1108760), _1108762))))], (18304 ^ _780119) ^ [_1113935, _1113937] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1113935), hAPP(c_Nat_OSuc, _1113937)) = 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), _1113935), _1113937)))], (51225 ^ _780119) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (15302 ^ _780119) ^ [_1059520, _1059522] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1059520), _1059522) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1059520 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1059522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22851 ^ _780119) ^ [_1197386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197386)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20578 ^ _780119) ^ [_1154219, _1154221, _1154223, _1154225] : [class_Fields_Ofield__inverse__zero(_1154219), -(_1154221 = c_Groups_Ozero__class_Ozero(_1154219)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154219), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154219), _1154221), _1154223)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154219), _1154221), _1154225)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154219), _1154223), _1154225))], (46807 ^ _780119) ^ [_1724514, _1724516] : [class_Orderings_Olinorder(_1724514), -(_1724516 = c_List_Olist_ONil(_1724514)), c_List_Olinorder__class_Osorted(_1724514, _1724516), -(c_List_Olinorder__class_Osorted(_1724514, c_List_Obutlast(_1724514, _1724516)))], (2124 ^ _780119) ^ [_811088, _811090, _811092, _811094, _811096, _811098, _811100, _811102, _811104, _811106] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_811106, _811102, _811098, _811094, _811090) = c_SetInterval_Oord_OgreaterThanAtMost(_811104, _811100, _811096, _811092, _811088)), _811106 = _811104, _811102 = _811100, _811098 = _811096, _811094 = _811092, _811090 = _811088], (46242 ^ _780119) ^ [_1712199] : [-(c_List_Olists(_1712199, c_Orderings_Obot__class_Obot(tc_fun(_1712199, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1712199)), c_List_Olist_ONil(_1712199)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1712199), tc_HOL_Obool))))], (49705 ^ _780119) ^ [_1787748, _1787750, _1787752, _1787754] : [49706 ^ _780119 : [(49709 ^ _780119) ^ [] : [c_List_Olist__ex(_1787748, _1787750, _1787754)], (49707 ^ _780119) ^ [] : [c_List_Olist__ex(_1787748, _1787750, _1787752)]], -(c_List_Olist__ex(_1787748, _1787750, hAPP(hAPP(c_List_Oappend(_1787748), _1787752), _1787754)))], (33963 ^ _780119) ^ [_1417467, _1417469, _1417471, _1417473, _1417475, _1417477] : [hAPP(hAPP(c_Product__Type_OPair(_1417467, _1417469), _1417471), _1417473) = hAPP(hAPP(c_Product__Type_OPair(_1417467, _1417469), _1417475), _1417477), 33966 ^ _780119 : [(33969 ^ _780119) ^ [] : [-(_1417473 = _1417477)], (33967 ^ _780119) ^ [] : [-(_1417471 = _1417475)]]], (7278 ^ _780119) ^ [_902076, _902078, _902080] : [c_Hoare__Mirabelle_Ohoare__derivs(_902076, _902078, _902080), -(c_Hoare__Mirabelle_Ohoare__valids(_902076, _902078, _902080))], (6709 ^ _780119) ^ [_889917, _889919, _889921, _889923] : [hBOOL(hAPP(hAPP(c_member(_889917), _889923), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889917, tc_HOL_Obool)), _889919), _889921))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889917, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_889917, tc_fun(_889917, tc_HOL_Obool), tc_HOL_Obool), c_member(_889917)), _889919)), hAPP(hAPP(c_COMBC(_889917, tc_fun(_889917, tc_HOL_Obool), tc_HOL_Obool), c_member(_889917)), _889921)), _889923)))], (23165 ^ _780119) ^ [_1203279] : [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), _1203279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203279)))], (48766 ^ _780119) ^ [_1766168, _1766170, _1766172] : [48768 ^ _780119 : [(48771 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1766170, 48767 ^ [_1766168, _1766170, _1766172])))], (48769 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766168), 48767 ^ [_1766168, _1766170, _1766172]), hAPP(c_List_Oset(_1766168), c_List_OdropWhile(_1766168, _1766170, _1766172)))))]], -(c_List_OtakeWhile(_1766168, _1766170, _1766172) = hAPP(c_List_Ofilter(_1766168, _1766170), _1766172))], (49368 ^ _780119) ^ [_1779405, _1779407, _1779409, _1779411, _1779413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1779405, _1779407)), hAPP(_1779405, _1779409))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1779411, _1779411)), hAPP(hAPP(c_Product__Type_OPair(_1779411, _1779411), _1779407), _1779409)), c_List_Omeasures(_1779411, _1779413))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779411, _1779411)), hAPP(hAPP(c_Product__Type_OPair(_1779411, _1779411), _1779407), _1779409)), c_List_Omeasures(_1779411, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1779411, tc_Nat_Onat)), _1779405), _1779413)))))], (21789 ^ _780119) ^ [_1178000, _1178002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178000), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178002), _1178000)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178000, _1178002) = _1178000)], (22533 ^ _780119) ^ [_1191274, _1191276, _1191278, _1191280] : [hAPP(c_Com_Ocom_OBODY, _1191274) = c_Com_Ocom_OCond(_1191276, _1191278, _1191280)], (44108 ^ _780119) ^ [_1662479, _1662481, _1662483, _1662485] : [-(_1662479 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1662481), hAPP(hAPP(c_List_Olist_OCons(_1662481), _1662483), _1662485)), _1662479) = hAPP(hAPP(c_List_Onth(_1662481), _1662485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1662479), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (24213 ^ _780119) ^ [_1223432, _1223434, _1223436] : [class_Orderings_Oorder(_1223432), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223432), _1223434), _1223436)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1223432, _1223436, _1223434) = c_Orderings_Obot__class_Obot(tc_fun(_1223432, tc_HOL_Obool)))], (37243 ^ _780119) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (18250 ^ _780119) ^ [_1112738, _1112740, _1112742, _1112744, _1112746] : [class_Groups_Ocomm__monoid__add(_1112738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112740), _1112742)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112740), _1112744)), 18264 ^ _780119 : [(18267 ^ _780119) ^ [] : [hAPP(_1112746, 18263 ^ [_1112738, _1112740, _1112742, _1112744, _1112746]) = c_Groups_Ozero__class_Ozero(_1112738)], (18265 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112740), 18263 ^ [_1112738, _1112740, _1112742, _1112744, _1112746]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112740, tc_HOL_Obool)), _1112742), _1112744))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1112740, _1112738), _1112746), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1112740, tc_HOL_Obool)), _1112742), _1112744)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1112738), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1112740, _1112738), _1112746), _1112742)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1112740, _1112738), _1112746), _1112744)))], (41258 ^ _780119) ^ [_1590239, _1590241, _1590243, _1590245, _1590247] : [hBOOL(hAPP(hAPP(c_member(_1590239), _1590241), _1590243)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1590245, tc_HOL_Obool)), hAPP(_1590247, _1590241)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590239, tc_fun(_1590245, tc_HOL_Obool)), _1590243), _1590247)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590239, tc_fun(_1590245, tc_HOL_Obool)), _1590243), _1590247))], (42477 ^ _780119) ^ [_1620232, _1620234, _1620236] : [-(c_Smallcheck_Oorelse(_1620232, _1620234, _1620236) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1620232), _1620232, _1620236, c_Option_Ooption_OSome(_1620232)), _1620234))], (51515 ^ _780119) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (47839 ^ _780119) ^ [_1746647, _1746649, _1746651] : [class_Orderings_Olinorder(_1746647), c_List_Olinorder__class_Osorted(_1746647, _1746649), -(c_List_Olinorder__class_Osorted(_1746647, c_List_OtakeWhile(_1746647, _1746651, _1746649)))], (50670 ^ _780119) ^ [_1807761, _1807763, _1807765, _1807767] : [-(hAPP(hAPP(c_List_Omap(_1807761, _1807763), hAPP(c_COMBK(_1807763, _1807761), _1807765)), _1807767) = c_List_Oreplicate(_1807763, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807761)), _1807767), _1807765))], (41131 ^ _780119) ^ [_1586937, _1586939, _1586941, _1586943, _1586945] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1586937, tc_HOL_Obool)), _1586939), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586941, tc_fun(_1586937, tc_HOL_Obool)), _1586943), _1586945)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586941, tc_fun(_1586937, tc_HOL_Obool)), _1586943), hAPP(hAPP(c_COMBB(tc_fun(_1586937, tc_HOL_Obool), tc_fun(_1586937, tc_HOL_Obool), _1586941), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1586937, tc_HOL_Obool)), _1586939)), _1586945)))], (42624 ^ _780119) ^ [_1623775, _1623777, _1623779, _1623781, _1623783, _1623785] : [-(c_Map_Omap__comp(_1623775, _1623777, _1623779, _1623781, _1623783, _1623785) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1623777), _1623775, c_Option_Ooption_ONone(_1623777), _1623781), hAPP(_1623783, _1623785)))], (41441 ^ _780119) ^ [_1596403, _1596405, _1596407, _1596409, _1596411] : [-(_1596403 = c_Orderings_Obot__class_Obot(tc_fun(_1596405, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1596407, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596405, tc_fun(_1596407, tc_HOL_Obool)), _1596403), _1596409)), _1596411) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596405, tc_fun(_1596407, tc_HOL_Obool)), _1596403), hAPP(hAPP(c_COMBC(_1596405, tc_fun(_1596407, tc_HOL_Obool), tc_fun(_1596407, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1596407, tc_HOL_Obool), tc_fun(tc_fun(_1596407, tc_HOL_Obool), tc_fun(_1596407, tc_HOL_Obool)), _1596405), c_Groups_Ominus__class_Ominus(tc_fun(_1596407, tc_HOL_Obool))), _1596409)), _1596411)))], (43392 ^ _780119) ^ [_1642566, _1642568, _1642570] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1642566), _1642568)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1642566)), hAPP(c_Set_OCollect(tc_List_Olist(_1642566)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1642566), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1642566)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1642566), tc_fun(_1642566, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1642566, tc_HOL_Obool), tc_fun(tc_fun(_1642566, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1642566)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1642566, tc_HOL_Obool))), c_List_Oset(_1642566))), _1642568))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1642566), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1642566)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1642566)))), _1642570))))))], (36706 ^ _780119) ^ [_1477497, _1477499, _1477501, _1477503, _1477505] : [hBOOL(hAPP(hAPP(c_member(_1477497), _1477499), hAPP(c_Set_Ovimage(_1477497, _1477501, _1477503), _1477505))), -(hBOOL(hAPP(hAPP(c_member(_1477501), hAPP(_1477503, _1477499)), _1477505)))], (10222 ^ _780119) ^ [_959123, _959125, _959127, _959129] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959123, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959123, tc_HOL_Obool)), _959125), _959127)), _959129) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959123, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959123, tc_HOL_Obool)), _959125), _959129)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959123, tc_HOL_Obool)), _959127), _959129)))], (33593 ^ _780119) ^ [_1405574, _1405576] : [_1405574 = _1405576, -(c_Code__Numeral_OSuc__code__numeral(_1405574) = c_Code__Numeral_OSuc__code__numeral(_1405576))], (22111 ^ _780119) ^ [_1184000, _1184002] : [class_Groups_Osgn__if(_1184000), 22114 ^ _780119 : [(22121 ^ _780119) ^ [] : [-(_1184002 = c_Groups_Ozero__class_Ozero(_1184000)), 22124 ^ _780119 : [(22131 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184000), c_Groups_Ozero__class_Ozero(_1184000)), _1184002))), -(c_Groups_Osgn__class_Osgn(_1184000, _1184002) = hAPP(c_Groups_Ouminus__class_Ouminus(_1184000), c_Groups_Oone__class_Oone(_1184000)))], (22125 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184000), c_Groups_Ozero__class_Ozero(_1184000)), _1184002)), -(c_Groups_Osgn__class_Osgn(_1184000, _1184002) = c_Groups_Oone__class_Oone(_1184000))]]], (22115 ^ _780119) ^ [] : [_1184002 = c_Groups_Ozero__class_Ozero(_1184000), -(c_Groups_Osgn__class_Osgn(_1184000, _1184002) = c_Groups_Ozero__class_Ozero(_1184000))]]], (1210 ^ _780119) ^ [_797968, _797970] : [-(class_Groups_Oabs__if(_797968)), _797970 = _797968, class_Groups_Oabs__if(_797970)], (38160 ^ _780119) ^ [_1517129, _1517131] : [-(c_Product__Type_Omap__pair(_1517129, _1517129, _1517131, _1517131, c_COMBI(_1517129), c_COMBI(_1517131)) = c_Fun_Oid(tc_prod(_1517129, _1517131)))], (45716 ^ _780119) ^ [_1700437, _1700439, _1700441, _1700443, _1700445] : [hAPP(hAPP(c_List_Oappend(_1700437), _1700439), _1700441) = hAPP(hAPP(c_List_Oappend(_1700437), _1700443), _1700445), 45719 ^ _780119 : [(45728 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700437)), _1700439)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700437)), _1700443)))), 45731 ^ _780119 : [(45734 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1700437), hAPP(hAPP(c_List_Odrop(_1700437), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700437)), _1700443)), _1700439)), _1700441) = _1700445)], (45732 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1700437), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700437)), _1700443)), _1700439) = _1700443)]]], (45720 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700437)), _1700439)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700437)), _1700443))), 45723 ^ _780119 : [(45726 ^ _780119) ^ [] : [-(_1700441 = hAPP(hAPP(c_List_Oappend(_1700437), hAPP(hAPP(c_List_Odrop(_1700437), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700437)), _1700439)), _1700443)), _1700445))], (45724 ^ _780119) ^ [] : [-(_1700439 = hAPP(hAPP(c_List_Otake(_1700437), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700437)), _1700439)), _1700443))]]]]], (18970 ^ _780119) ^ [_1125962] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125962), _1125962)))], (6252 ^ _780119) ^ [_880296, _880298, _880300] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_880296), hAPP(hAPP(c_Set_Oinsert(_880296), _880298), _880300))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_880296), _880300)))], (17422 ^ _780119) ^ [_1096726, _1096728, _1096730, _1096732] : [class_Rings_Olinordered__semiring__strict(_1096726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096726), _1096728), _1096730)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096726), _1096728), _1096732))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096726), c_Groups_Ozero__class_Ozero(_1096726)), _1096728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096726), _1096730), _1096732)))], (44862 ^ _780119) ^ [_1678440, _1678442] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1678440), tc_List_Olist(_1678440), c_List_Olistrel(_1678440, _1678442)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1678440)), c_List_Olist_ONil(_1678440)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1678440), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1678440)), c_List_Olist_ONil(_1678440)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1678440), tc_HOL_Obool))))], (43916 ^ _780119) ^ [_1657520, _1657522, _1657524, _1657526, _1657528, _1657530] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657520), tc_List_Olist(_1657520))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657520), tc_List_Olist(_1657520)), hAPP(hAPP(c_List_Olist_OCons(_1657520), _1657522), _1657524)), hAPP(hAPP(c_List_Olist_OCons(_1657520), _1657526), _1657528))), c_List_Olexord(_1657520, _1657530))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1657520, _1657520)), hAPP(hAPP(c_Product__Type_OPair(_1657520, _1657520), _1657522), _1657526)), _1657530))), 43923 ^ _780119 : [(43926 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657520), tc_List_Olist(_1657520))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657520), tc_List_Olist(_1657520)), _1657524), _1657528)), c_List_Olexord(_1657520, _1657530))))], (43924 ^ _780119) ^ [] : [-(_1657522 = _1657526)]]], (19394 ^ _780119) ^ [_1132589, _1132591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1132591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132589), _1132591)), _1132589)))], (3400 ^ _780119) ^ [_831176, _831178] : [_831178 = _831176, -(c_Divides_Odiv__class_Odiv(_831178) = c_Divides_Odiv__class_Odiv(_831176))], (7558 ^ _780119) ^ [_907198, _907200] : [class_Lattices_Obounded__lattice__bot(_907198), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_907198), _907200), c_Orderings_Obot__class_Obot(_907198)) = _907200)], (48469 ^ _780119) ^ [_1760168, _1760170, _1760172] : [class_Enum_Oenum(_1760168), class_Enum_Oenum(_1760170), 48476 ^ _780119 : [(48483 ^ _780119) ^ [] : [c_Enum_Oall__n__lists(_1760168, hAPP(hAPP(c_COMBB(tc_fun(_1760170, _1760168), tc_HOL_Obool, tc_List_Olist(_1760168)), _1760172), hAPP(hAPP(c_COMBB(tc_fun(_1760170, tc_Option_Ooption(_1760168)), tc_fun(_1760170, _1760168), tc_List_Olist(_1760168)), c_Fun_Ocomp(tc_Option_Ooption(_1760168), _1760168, _1760170, c_Option_Othe(_1760168))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1760170, _1760168)), tc_fun(_1760170, tc_Option_Ooption(_1760168)), tc_List_Olist(_1760168)), c_Map_Omap__of(_1760170, _1760168)), hAPP(c_List_Ozip(_1760170, _1760168), c_Enum_Oenum__class_Oenum(_1760170))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760170)), c_Enum_Oenum__class_Oenum(_1760170))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1760170, _1760168)), _1760172)))], (48477 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1760170, _1760168)), _1760172)), -(c_Enum_Oall__n__lists(_1760168, hAPP(hAPP(c_COMBB(tc_fun(_1760170, _1760168), tc_HOL_Obool, tc_List_Olist(_1760168)), _1760172), hAPP(hAPP(c_COMBB(tc_fun(_1760170, tc_Option_Ooption(_1760168)), tc_fun(_1760170, _1760168), tc_List_Olist(_1760168)), c_Fun_Ocomp(tc_Option_Ooption(_1760168), _1760168, _1760170, c_Option_Othe(_1760168))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1760170, _1760168)), tc_fun(_1760170, tc_Option_Ooption(_1760168)), tc_List_Olist(_1760168)), c_Map_Omap__of(_1760170, _1760168)), hAPP(c_List_Ozip(_1760170, _1760168), c_Enum_Oenum__class_Oenum(_1760170))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760170)), c_Enum_Oenum__class_Oenum(_1760170))))]]], (21414 ^ _780119) ^ [_1170185, _1170187, _1170189, _1170191] : [class_Divides_Osemiring__div(_1170185), -(c_Divides_Odiv__class_Omod(_1170185, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170185), _1170187), _1170189), _1170191) = c_Divides_Odiv__class_Omod(_1170185, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170185), c_Divides_Odiv__class_Omod(_1170185, _1170187, _1170191)), c_Divides_Odiv__class_Omod(_1170185, _1170189, _1170191)), _1170191))], (12675 ^ _780119) ^ [_1009796, _1009798] : [-(c_Map_Odom(_1009796, _1009798, hAPP(c_COMBK(tc_Option_Ooption(_1009798), _1009796), c_Option_Ooption_ONone(_1009798))) = c_Orderings_Obot__class_Obot(tc_fun(_1009796, tc_HOL_Obool)))], (45856 ^ _780119) ^ [_1703594, _1703596] : [-(_1703594 = c_List_Olist_ONil(_1703596)), -(hAPP(c_List_Orotate1(_1703596), _1703594) = hAPP(hAPP(c_List_Oappend(_1703596), hAPP(c_List_Otl(_1703596), _1703594)), hAPP(hAPP(c_List_Olist_OCons(_1703596), hAPP(c_List_Ohd(_1703596), _1703594)), c_List_Olist_ONil(_1703596))))], (48819 ^ _780119) ^ [_1767442, _1767444, _1767446, _1767448] : [hBOOL(hAPP(c_List_Olistsp(_1767442, _1767444), _1767446)), hBOOL(hAPP(c_List_Olistsp(_1767442, _1767448), _1767446)), -(hBOOL(hAPP(c_List_Olistsp(_1767442, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1767442, tc_HOL_Obool)), _1767444), _1767448)), _1767446)))], (17063 ^ _780119) ^ [_1090053, _1090055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1090053), _1090055)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1090053), _1090055) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42759 ^ _780119) ^ [_1626988, _1626990, _1626992, _1626994, _1626996] : [42761 ^ _780119 : [(42764 ^ _780119) ^ [] : [hAPP(_1626992, 42760 ^ [_1626988, _1626990, _1626992, _1626994, _1626996]) = hAPP(_1626996, 42760 ^ [_1626988, _1626990, _1626992, _1626994, _1626996])], (42762 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626988), 42760 ^ [_1626988, _1626990, _1626992, _1626994, _1626996]), hAPP(c_List_Oset(_1626988), _1626994))))]], -(hAPP(hAPP(c_List_Omap(_1626988, _1626990), _1626992), _1626994) = hAPP(hAPP(c_List_Omap(_1626988, _1626990), _1626996), _1626994))], (51661 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), v_F)))], (39066 ^ _780119) ^ [_1538161, _1538163, _1538165, _1538167, _1538169, _1538171] : [c_Finite__Set_Ofolding(_1538161, _1538163, _1538165, _1538167), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538161), _1538169)), -(hBOOL(hAPP(hAPP(c_member(_1538161), _1538171), _1538169))), -(hAPP(_1538167, hAPP(hAPP(c_Set_Oinsert(_1538161), _1538171), _1538169)) = hAPP(c_Fun_Ocomp(_1538163, _1538163, _1538163, hAPP(_1538167, _1538169)), hAPP(_1538165, _1538171)))], (22889 ^ _780119) ^ [_1198125, _1198127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198125)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198125), _1198127)))], (41303 ^ _780119) ^ [_1591515, _1591517, _1591519, _1591521] : [41305 ^ _780119 : [(41308 ^ _780119) ^ [] : [hAPP(_1591521, 41304 ^ [_1591515, _1591517, _1591519, _1591521]) = c_Orderings_Otop__class_Otop(tc_fun(_1591517, tc_HOL_Obool))], (41306 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591515), 41304 ^ [_1591515, _1591517, _1591519, _1591521]), _1591519)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591515, tc_fun(_1591517, tc_HOL_Obool)), _1591519), _1591521) = c_Orderings_Otop__class_Otop(tc_fun(_1591517, tc_HOL_Obool)))], (34373 ^ _780119) ^ [_1425135, _1425137] : [-(_1425135 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1425137, _1425135) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1425137), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1425135)))], (21648 ^ _780119) ^ [_1175295, _1175297, _1175299] : [class_Divides_Osemiring__div(_1175295), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175295), c_Divides_Odiv__class_Omod(_1175295, _1175297, _1175299)), _1175299) = c_Groups_Ozero__class_Ozero(_1175295))], (10488 ^ _780119) ^ [_965392, _965394, _965396, _965398, _965400] : [c_Finite__Set_Ofolding__one(_965392, _965394, _965396), hBOOL(hAPP(c_Finite__Set_Ofinite(_965392), _965398)), -(_965398 = c_Orderings_Obot__class_Obot(tc_fun(_965392, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_965392), _965400)), -(_965400 = c_Orderings_Obot__class_Obot(tc_fun(_965392, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965392, tc_HOL_Obool)), _965398), _965400) = c_Orderings_Obot__class_Obot(tc_fun(_965392, tc_HOL_Obool)), -(hAPP(_965396, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_965392, tc_HOL_Obool)), _965398), _965400)) = hAPP(hAPP(_965394, hAPP(_965396, _965398)), hAPP(_965396, _965400)))], (6947 ^ _780119) ^ [_894885, _894887, _894889, _894891] : [class_Orderings_Oord(_894885), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894885), _894887), _894889)), _894889 = _894891, 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c_Orderings_Obot__class_Obot(tc_fun(_912438, tc_HOL_Obool))), -(hAPP(_912442, _912444) = hAPP(hAPP(_912440, _912446), hAPP(_912442, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912438, tc_HOL_Obool)), _912444), hAPP(hAPP(c_Set_Oinsert(_912438), _912446), c_Orderings_Obot__class_Obot(tc_fun(_912438, tc_HOL_Obool)))))))], (7800 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912438, tc_HOL_Obool)), _912444), hAPP(hAPP(c_Set_Oinsert(_912438), _912446), c_Orderings_Obot__class_Obot(tc_fun(_912438, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_912438, tc_HOL_Obool)), -(hAPP(_912442, _912444) = _912446)]]], (11836 ^ _780119) ^ [_993122, _993124, _993126] : [_993124 = _993126, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993122), _993124) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993122), _993126))], (51613 ^ _780119) ^ [_1820994, _1820996] : [hBOOL(_1820994), -(hBOOL(hAPP(hAPP(c_fdisj, _1820994), _1820996)))], (50410 ^ _780119) ^ [_1802351, _1802353] : [c_Wellfounded_Oacyclic(_1802351, hAPP(c_Set_OCollect(tc_prod(_1802351, _1802351)), hAPP(c_Product__Type_Oprod_Oprod__case(_1802351, _1802351, tc_HOL_Obool), _1802353))), -(c_Wellfounded_Oacyclic(_1802351, hAPP(c_Set_OCollect(tc_prod(_1802351, _1802351)), hAPP(c_Product__Type_Oprod_Oprod__case(_1802351, _1802351, tc_HOL_Obool), c_Predicate_Oconversep(_1802351, _1802351, _1802353)))))], (38702 ^ _780119) ^ [_1529817, _1529819] : [-(c_Hilbert__Choice_OEps(_1529817, hAPP(c_fequal, _1529819)) = _1529819)], (18646 ^ _780119) ^ [_1120279, _1120281] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_1120279, _1120281)) = 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), _1120279)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1120281))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47712 ^ _780119) ^ [_1743313, _1743315, _1743317] : [class_Orderings_Olinorder(_1743313), c_List_Olinorder__class_Osorted(_1743313, hAPP(c_List_Orev(_1743313), _1743315)), 47719 ^ _780119 : [(47726 ^ _780119) ^ [] : [-(_1743315 = c_List_Olist_ONil(_1743313)), -(c_List_Ofoldr(_1743313, _1743313, c_Orderings_Oord__class_Omax(_1743313), _1743315, _1743317) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1743313), hAPP(hAPP(c_List_Onth(_1743313), _1743315), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1743317))], (47720 ^ _780119) ^ [] : [_1743315 = c_List_Olist_ONil(_1743313), -(c_List_Ofoldr(_1743313, _1743313, c_Orderings_Oord__class_Omax(_1743313), _1743315, _1743317) = _1743317)]]], (24849 ^ _780119) ^ [_1235444, _1235446, _1235448] : [class_Orderings_Olinorder(_1235444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235444), _1235446), _1235448)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235444, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1235444, _1235446, _1235448)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1235444), _1235448)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1235444), _1235446))], (29685 ^ _780119) ^ [_1332199, _1332201, _1332203, _1332205, _1332207] : [hBOOL(hAPP(hAPP(c_member(_1332199), _1332201), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1332203, tc_fun(_1332199, tc_HOL_Obool)), _1332205), _1332207))), 29689 ^ _780119 : [(29692 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1332199), _1332201), hAPP(_1332207, 29688 ^ [_1332199, _1332201, _1332203, _1332205, _1332207]))))], (29690 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1332203), 29688 ^ [_1332199, _1332201, _1332203, _1332205, _1332207]), _1332205)))]]], (35562 ^ _780119) ^ [_1452048, _1452050, _1452052, _1452054] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1452048, _1452048)), hAPP(hAPP(c_Product__Type_OPair(_1452048, _1452048), _1452050), _1452052)), c_Relation_OId__on(_1452048, _1452054)))), _1452050 = _1452052, hBOOL(hAPP(hAPP(c_member(_1452048), _1452050), _1452054))], (3164 ^ _780119) ^ [_827334, _827336, _827338, _827340, _827342, _827344] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_827344, _827340, _827336) = c_Smallcheck_Ofull__small__class_Ofull__small(_827342, _827338, _827334)), _827344 = _827342, _827340 = _827338, _827336 = _827334], (16787 ^ _780119) ^ [_1085543] : [16788 ^ _780119 : [(16789 ^ _780119) ^ [_1085585] : [_1085543 = hAPP(c_Nat_OSuc, _1085585)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1085543)))], (1750 ^ _780119) ^ [_804718, _804720] : [-(class_Rings_Osemiring(_804718)), _804720 = _804718, class_Rings_Osemiring(_804720)], (32607 ^ _780119) ^ [_1387879, _1387881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1387879), _1387881)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1387879)), c_Int_OBit1(_1387881))))], (37835 ^ _780119) ^ [_1507412, _1507414, _1507416, _1507418, _1507420] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1507412, _1507414), _1507416), hAPP(hAPP(c_COMBS(_1507412, tc_fun(_1507414, tc_HOL_Obool), tc_fun(_1507414, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507414, tc_HOL_Obool), tc_fun(tc_fun(_1507414, tc_HOL_Obool), tc_fun(_1507414, tc_HOL_Obool)), _1507412), c_Groups_Ominus__class_Ominus(tc_fun(_1507414, tc_HOL_Obool))), _1507418)), _1507420)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1507412, _1507414), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1507412, _1507414), _1507416), _1507418)), hAPP(hAPP(c_Product__Type_OSigma(_1507412, _1507414), _1507416), _1507420)))], (11826 ^ _780119) ^ [_992903, _992905, _992907] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _992903), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _992905), _992907)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _992905), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _992903), _992907)))], (40036 ^ _780119) ^ [_1561657, _1561659, _1561661] : [c_Relation_Orefl__on(_1561657, _1561659, _1561661), -(c_Relation_Orefl__on(_1561657, _1561659, hAPP(c_Relation_Oconverse(_1561657, _1561657), _1561661)))], (18406 ^ _780119) ^ [_1115957, _1115959, _1115961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1115957), _1115959)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1115961), _1115957)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1115961), _1115959))))], (5078 ^ _780119) ^ [_857827, _857829] : [_857829 = _857827, -(c_Lattices_Osemilattice__sup__class_Osup(_857829) = c_Lattices_Osemilattice__sup__class_Osup(_857827))], (20206 ^ _780119) ^ [_1147640, _1147642, _1147644, _1147646] : [class_Fields_Olinordered__field(_1147640), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147640), c_Groups_Ozero__class_Ozero(_1147640)), _1147642)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147640), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147640), _1147644), _1147642)), _1147646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147640), _1147644), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147640), _1147646), _1147642))))], (38750 ^ _780119) ^ [_1530864, _1530866, _1530868, _1530870, _1530872, _1530874, _1530876] : [-(hAPP(c_Fun_Ocomp(_1530864, _1530866, _1530868, _1530870), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1530868, _1530864), _1530872), _1530874), _1530876)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1530868, _1530866), hAPP(c_Fun_Ocomp(_1530864, _1530866, _1530868, _1530870), _1530872)), _1530874), hAPP(_1530870, _1530876)))], (1530 ^ _780119) ^ [_801968, _801970] : [-(class_Rings_Olinordered__semiring(_801968)), _801970 = _801968, class_Rings_Olinordered__semiring(_801970)], (40186 ^ _780119) ^ [_1565568, _1565570, _1565572] : [-(hAPP(c_Relation_Oconverse(_1565568, _1565570), _1565572) = hAPP(c_Set_OCollect(tc_prod(_1565570, _1565568)), hAPP(c_Product__Type_Oprod_Oprod__case(_1565570, _1565568, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1565570, tc_fun(tc_prod(_1565568, _1565570), tc_HOL_Obool), tc_fun(_1565568, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565568, tc_fun(tc_fun(tc_prod(_1565568, _1565570), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1565568, _1565570), tc_HOL_Obool), tc_fun(_1565568, tc_HOL_Obool)), _1565570), c_COMBC(_1565568, tc_fun(tc_prod(_1565568, _1565570), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565568, tc_prod(_1565568, _1565570)), tc_fun(_1565568, tc_fun(tc_fun(tc_prod(_1565568, _1565570), tc_HOL_Obool), tc_HOL_Obool)), _1565570), hAPP(c_COMBB(tc_prod(_1565568, _1565570), tc_fun(tc_fun(tc_prod(_1565568, _1565570), tc_HOL_Obool), tc_HOL_Obool), _1565568), c_member(tc_prod(_1565568, _1565570)))), hAPP(c_COMBC(_1565568, _1565570, tc_prod(_1565568, _1565570)), c_Product__Type_OPair(_1565568, _1565570))))), _1565572))))], (27804 ^ _780119) ^ [_1293555, _1293557, _1293559] : [class_Orderings_Olinorder(_1293555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293555), _1293557), _1293559)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293555), _1293559), _1293557) = _1293557)], (7434 ^ _780119) ^ [_905127, _905129, _905131] : [class_Lattices_Osemilattice__sup(_905127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905127), _905129), _905131)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_905127), _905131), _905129) = _905131)], (634 ^ _780119) ^ [_789826, _789828] : [-(c_Nat__Transfer_Onat__set(_789826)), _789828 = _789826, c_Nat__Transfer_Onat__set(_789828)], (37336 ^ _780119) ^ [_1493782, _1493784, _1493786] : [c_Wellfounded_Owf(_1493782, _1493784), -(hBOOL(hAPP(hAPP(c_member(_1493782), _1493786), c_Wellfounded_Oacc(_1493782, _1493784))))], (2640 ^ _780119) ^ [_819222, _819224, _819226, _819228] : [-(c_Nitpick_Onumber__of__frac(_819228, _819224) = c_Nitpick_Onumber__of__frac(_819226, _819222)), _819228 = _819226, _819224 = _819222], (49739 ^ _780119) ^ [_1788541, _1788543, _1788545] : [-(hBOOL(hAPP(hAPP(c_member(_1788541), _1788543), hAPP(c_List_Oset(_1788541), _1788545)))), 49740 ^ _780119 : [(49741 ^ _780119) ^ [_1788630, _1788632] : [_1788545 = hAPP(hAPP(c_List_Oappend(_1788541), _1788632), hAPP(hAPP(c_List_Olist_OCons(_1788541), _1788543), _1788630)), -(hBOOL(hAPP(hAPP(c_member(_1788541), _1788543), hAPP(c_List_Oset(_1788541), _1788630))))]]], (42614 ^ _780119) ^ [_1623354, _1623356, _1623358, _1623360, _1623362] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1623354), tc_List_Olist(_1623356), tc_List_Olist(_1623358), hAPP(c_List_Omap(_1623354, _1623356), _1623360)), hAPP(c_List_Omap(_1623358, _1623354), _1623362)) = hAPP(c_List_Omap(_1623358, _1623356), hAPP(c_Fun_Ocomp(_1623354, _1623356, _1623358, _1623360), _1623362)))], (1550 ^ _780119) ^ [_802218, _802220] : [-(class_Groups_Oab__semigroup__mult(_802218)), _802220 = _802218, class_Groups_Oab__semigroup__mult(_802220)], (42493 ^ _780119) ^ [_1620490, _1620492, _1620494] : [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)), _1620490), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1620492), _1620494)))), 42496 ^ _780119 : [(42503 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1620492), _1620494))), -(c_Smallcheck_Osmall_H(_1620490, _1620492, _1620494) = 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(_1620490, _1620492, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1620494), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1620490, _1620494)))], (42497 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1620492), _1620494)), -(c_Smallcheck_Osmall_H(_1620490, _1620492, _1620494) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))]]], (33181 ^ _780119) ^ [_1398512, _1398514] : [class_Rings_Oring__1(_1398512), 33184 ^ _780119 : [(33191 ^ _780119) ^ [] : [-(_1398514 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 33194 ^ _780119 : [(33201 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1398514), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1398512), _1398514) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1398512), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1398512, _1398512)), tc_fun(tc_Int_Oint, _1398512)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1398512, _1398512), _1398512), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1398512, _1398512)), tc_fun(tc_Int_Oint, _1398512)), tc_Int_Oint), c_COMBB(tc_fun(_1398512, _1398512), _1398512, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1398512, tc_fun(tc_fun(_1398512, _1398512), _1398512), tc_Int_Oint), c_HOL_OLet(_1398512, _1398512)), c_Int_Oring__1__class_Oof__int(_1398512)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1398512, _1398512), tc_fun(_1398512, _1398512)), hAPP(hAPP(c_COMBB(tc_fun(_1398512, tc_fun(_1398512, _1398512)), tc_fun(tc_fun(_1398512, _1398512), tc_fun(_1398512, _1398512)), tc_Int_Oint), c_COMBS(_1398512, _1398512, _1398512)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1398512, _1398512), tc_fun(_1398512, tc_fun(_1398512, _1398512))), hAPP(hAPP(c_COMBB(tc_fun(_1398512, tc_fun(_1398512, _1398512)), tc_fun(tc_fun(_1398512, _1398512), tc_fun(_1398512, tc_fun(_1398512, _1398512))), tc_Int_Oint), c_COMBB(_1398512, tc_fun(_1398512, _1398512), _1398512)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1398512, tc_fun(_1398512, _1398512)), tc_Int_Oint), c_If(_1398512)), 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(_1398512, _1398512, _1398512), c_Groups_Oplus__class_Oplus(_1398512)), c_COMBI(_1398512))))), hAPP(hAPP(c_COMBC(_1398512, _1398512, _1398512), hAPP(hAPP(c_COMBB(_1398512, tc_fun(_1398512, _1398512), _1398512), c_Groups_Oplus__class_Oplus(_1398512)), hAPP(hAPP(c_COMBS(_1398512, _1398512, _1398512), c_Groups_Oplus__class_Oplus(_1398512)), c_COMBI(_1398512)))), c_Groups_Oone__class_Oone(_1398512))))), c_Divides_Odivmod__int(_1398514, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (33195 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1398514), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1398512), _1398514) = hAPP(c_Groups_Ouminus__class_Ouminus(_1398512), hAPP(c_Int_Oring__1__class_Oof__int(_1398512), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1398514))))]]], (33185 ^ _780119) ^ [] : [_1398514 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1398512), _1398514) = c_Groups_Ozero__class_Ozero(_1398512))]]], (33343 ^ _780119) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34499 ^ _780119) ^ [_1427514, _1427516] : [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), _1427514), _1427516))), 34502 ^ _780119 : [(34511 ^ _780119) ^ [] : [-(c_Divides_OposDivAlg(_1427514, _1427516) = hAPP(c_Divides_Oadjust(_1427516), c_Divides_OposDivAlg(_1427514, 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)))), _1427516)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427514), _1427516))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427516), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34503 ^ _780119) ^ [] : [34504 ^ _780119 : [(34507 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427516), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34505 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427514), _1427516))]], -(c_Divides_OposDivAlg(_1427514, _1427516) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427514))]]], (45912 ^ _780119) ^ [_1704685, _1704687, _1704689] : [_1704689 = c_List_Olist_ONil(_1704685), -(hAPP(c_List_Orotate(_1704685, _1704687), _1704689) = c_List_Olist_ONil(_1704685))], (21682 ^ _780119) ^ [_1175867, _1175869] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1175867, _1175869) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1175867 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175869), 21685 ^ [_1175867, _1175869]))], (9774 ^ _780119) ^ [_949844, _949846, _949848, _949850] : [class_Lattices_Osemilattice__inf(_949844), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949844), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949844), _949846), _949848)), _949850) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949844), _949846), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949844), _949848), _949850)))], (47271 ^ _780119) ^ [_1732637, _1732639] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1732637, _1732639) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1732637), _1732639)))], (42620 ^ _780119) ^ [_1623564, _1623566, _1623568, _1623570, _1623572, _1623574] : [-(hAPP(hAPP(c_List_Omap(_1623564, _1623566), _1623568), hAPP(hAPP(c_List_Omap(_1623570, _1623564), _1623572), _1623574)) = hAPP(hAPP(c_List_Omap(_1623570, _1623566), hAPP(c_Fun_Ocomp(_1623564, _1623566, _1623570, _1623568), _1623572)), _1623574))], (42576 ^ _780119) ^ [_1622633, _1622635, _1622637, _1622639, _1622641] : [c_Fun_Oinj__on(_1622633, _1622635, _1622637, c_Orderings_Otop__class_Otop(tc_fun(_1622633, tc_HOL_Obool))), 42579 ^ _780119 : [(42586 ^ _780119) ^ [] : [_1622639 = _1622641, -(hAPP(hAPP(c_List_Omap(_1622633, _1622635), _1622637), _1622639) = hAPP(hAPP(c_List_Omap(_1622633, _1622635), _1622637), _1622641))], (42580 ^ _780119) ^ [] : [hAPP(hAPP(c_List_Omap(_1622633, _1622635), _1622637), _1622639) = hAPP(hAPP(c_List_Omap(_1622633, _1622635), _1622637), _1622641), -(_1622639 = _1622641)]]], (14912 ^ _780119) ^ [_1053736, _1053738] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1053736, tc_HOL_Obool)), _1053738), c_Orderings_Otop__class_Otop(tc_fun(_1053736, tc_HOL_Obool)))))], (29694 ^ _780119) ^ [_1332407, _1332409, _1332411, _1332413, _1332415] : [-(hBOOL(hAPP(hAPP(c_member(_1332407), _1332409), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1332411, tc_fun(_1332407, tc_HOL_Obool)), _1332413), _1332415)))), 29695 ^ _780119 : [(29696 ^ _780119) ^ [_1332489] : [hBOOL(hAPP(hAPP(c_member(_1332411), _1332489), _1332413)), hBOOL(hAPP(hAPP(c_member(_1332407), _1332409), hAPP(_1332415, _1332489)))]]], (6465 ^ _780119) ^ [_884628, _884630] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), _884628), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), _884630)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), 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))), _884630)), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), _884630)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _884628, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), _884630)))], (45124 ^ _780119) ^ [_1684400, _1684402, _1684404] : [-(hAPP(c_List_Oset(_1684400), hAPP(hAPP(c_List_Oappend(_1684400), _1684402), _1684404)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1684400, tc_HOL_Obool)), hAPP(c_List_Oset(_1684400), _1684402)), hAPP(c_List_Oset(_1684400), _1684404)))], (4162 ^ _780119) ^ [_843025, _843027, _843029, _843031] : [-(c_List_Olists(_843031, _843027) = c_List_Olists(_843029, _843025)), _843031 = _843029, _843027 = _843025], (41600 ^ _780119) ^ [_1599981, _1599983, _1599985, _1599987, _1599989, _1599991, _1599993] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599981, tc_fun(_1599983, tc_fun(_1599985, tc_HOL_Obool))), _1599987), _1599989), _1599991), _1599993)), 41603 ^ _780119 : [(41604 ^ _780119) ^ [_1600109] : [hBOOL(hAPP(hAPP(c_member(_1599981), _1600109), _1599987)), -(hBOOL(hAPP(hAPP(hAPP(_1599989, _1600109), _1599991), _1599993)))]]], (13728 ^ _780119) ^ [_1029640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029640)), _1029640))], (25738 ^ _780119) ^ [_1249913] : [class_Rings_Oring__1(_1249913), -(hAPP(c_Int_Oring__1__class_Oof__int(_1249913), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1249913))], (3748 ^ _780119) ^ [_836512, _836514, _836516, _836518] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_836518, _836514) = c_SetInterval_Oord__class_OatLeastLessThan(_836516, _836512)), _836518 = _836516, _836514 = _836512], (51289 ^ _780119) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (49343 ^ _780119) ^ [_1778688, _1778690] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1778688)), _1778690)), 49349 ^ _780119 : [(49352 ^ _780119) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1778688), 49348 ^ [_1778688, _1778690]))], (49350 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1778688)), 49348 ^ [_1778688, _1778690]), hAPP(c_List_Oset(tc_List_Olist(_1778688)), _1778690))))]], 49356 ^ _780119 : [(49357 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1778688)), 49355 ^ [_1778688, _1778690]), hAPP(c_List_Oset(tc_List_Olist(_1778688)), _1778690))))], (49360 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1778688)), 49358 ^ [_1778688, _1778690]), hAPP(c_List_Oset(tc_List_Olist(_1778688)), _1778690))))], (49364 ^ _780119) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1778688, tc_HOL_Obool)), hAPP(c_List_Oset(_1778688), 49355 ^ [_1778688, _1778690])), hAPP(c_List_Oset(_1778688), 49358 ^ [_1778688, _1778690])) = c_Orderings_Obot__class_Obot(tc_fun(_1778688, tc_HOL_Obool))], (49362 ^ _780119) ^ [] : [49355 ^ [_1778688, _1778690] = 49358 ^ [_1778688, _1778690]]], -(hBOOL(hAPP(c_List_Odistinct(_1778688), c_List_Oconcat(_1778688, _1778690))))], (18724 ^ _780119) ^ [_1121572, _1121574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121572), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1121574), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121572), _1121574)))], (12253 ^ _780119) ^ [_1001361, _1001363, _1001365, _1001367, _1001369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001361), _1001363)), 12256 ^ _780119 : [(12263 ^ _780119) ^ [] : [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), _1001363), _1001361)), _1001365)), _1001367) = _1001369, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001363), _1001365)), _1001367) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001361), _1001365)), _1001369))], (12257 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001363), _1001365)), _1001367) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001361), _1001365)), _1001369), -(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), _1001363), _1001361)), _1001365)), _1001367) = _1001369)]]], (28974 ^ _780119) ^ [_1317057, _1317059, _1317061] : [class_Orderings_Olinorder(_1317057), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317057), _1317059)), hBOOL(hAPP(hAPP(c_member(_1317057), _1317061), _1317059)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1317057), _1317061), c_Big__Operators_Olattice_OInf__fin(_1317057, c_Orderings_Oord__class_Omin(_1317057), _1317059)) = _1317061)], (2562 ^ _780119) ^ [_818041, _818043] : [_818043 = _818041, -(c_Wellfounded_Omeasure(_818043) = c_Wellfounded_Omeasure(_818041))], (7830 ^ _780119) ^ [_913345, _913347, _913349, _913351, _913353, _913355, _913357, _913359] : [c_Finite__Set_Ofolding__image__simple__idem(_913345, _913347, _913349, _913351, _913353, _913355), hBOOL(hAPP(c_Finite__Set_Ofinite(_913347), _913357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913347, tc_HOL_Obool)), _913359), _913357)), -(hAPP(hAPP(_913349, hAPP(_913355, _913359)), hAPP(_913355, _913357)) = hAPP(_913355, _913357))], (5390 ^ _780119) ^ [_862683, _862685, _862687, _862689, _862691, _862693, _862695, _862697] : [-(c_Nitpick_Opair__box_OPairBox(_862697, _862693, _862689, _862685) = c_Nitpick_Opair__box_OPairBox(_862695, _862691, _862687, _862683)), _862697 = _862695, _862693 = _862691, _862689 = _862687, _862685 = _862683], (41798 ^ _780119) ^ [_1604688, _1604690, _1604692] : [c_Equiv__Relations_Oequiv(_1604688, _1604690, _1604692), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1604688, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1604688), _1604690), _1604692)) = _1604690)], (47428 ^ _780119) ^ [_1736440, _1736442] : [-(c_Fun_Oinj__on(tc_List_Olist(_1736440), tc_List_Olist(_1736440), c_List_Orev(_1736440), _1736442))], (49796 ^ _780119) ^ [_1789957, _1789959, _1789961, _1789963] : [-(c_List_Olist__all(_1789957, _1789959, hAPP(hAPP(c_List_Olist_OCons(_1789957), _1789961), _1789963))), hBOOL(hAPP(_1789959, _1789961)), c_List_Olist__all(_1789957, _1789959, _1789963)], (14424 ^ _780119) ^ [_1044510, _1044512, _1044514, _1044516] : [class_Groups_Ocomm__monoid__mult(_1044510), hBOOL(hAPP(c_Finite__Set_Ofinite(_1044512), _1044514)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1044512, _1044510), hAPP(c_COMBK(_1044510, _1044512), _1044516)), _1044514) = hAPP(hAPP(c_Power_Opower__class_Opower(_1044510), _1044516), hAPP(c_Finite__Set_Ocard(_1044512), _1044514)))], (27752 ^ _780119) ^ [_1292656, _1292658, _1292660, _1292662] : [class_Orderings_Olinorder(_1292656), 27755 ^ _780119 : [(27764 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292656), _1292658), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292656), _1292660), _1292662)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292656), _1292658), _1292660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292656), _1292658), _1292662))], (27756 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292656), _1292658), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292656), _1292660), _1292662))), 27759 ^ _780119 : [(27762 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292656), _1292658), _1292662)))], (27760 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292656), _1292658), _1292660)))]]]]], (5945 ^ _780119) ^ [_874642, _874644, _874646, _874648] : [_874642 = _874644, 5948 ^ _780119 : [(5955 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874646), _874648), _874644)), -(hBOOL(hAPP(hAPP(c_member(_874646), _874648), _874642)))], (5949 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874646), _874648), _874642)), -(hBOOL(hAPP(hAPP(c_member(_874646), _874648), _874644)))]]], (9098 ^ _780119) ^ [_936406, _936408, _936410] : [class_Orderings_Oorder(_936406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936406), _936408), _936410)), -(_936410 = _936408), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936406), _936408), _936410)))], (49378 ^ _780119) ^ [_1779678, _1779680] : [-(c_Wellfounded_Owf(_1779678, c_List_Omeasures(_1779678, _1779680)))], (13292 ^ _780119) ^ [_1022008, _1022010, _1022012] : [class_Lattices_Oboolean__algebra(_1022008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022008), _1022010), _1022012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022008), hAPP(c_Groups_Ouminus__class_Ouminus(_1022008), _1022012)), hAPP(c_Groups_Ouminus__class_Ouminus(_1022008), _1022010))))], (44794 ^ _780119) ^ [_1677156, _1677158] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1677156), tc_List_Olist(_1677156))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1677156), tc_List_Olist(_1677156)), c_List_Olist_ONil(_1677156)), c_List_Olist_ONil(_1677156))), c_List_Olistrel(_1677156, _1677158))))], (44572 ^ _780119) ^ [_1673092, _1673094, _1673096, _1673098, _1673100, _1673102, _1673104] : [-(hBOOL(hAPP(hAPP(c_member(_1673092), _1673094), hAPP(c_List_Oset(_1673092), _1673096)))), -(c_Map_Omap__upds(_1673092, _1673098, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1673092, tc_Option_Ooption(_1673098)), _1673100), _1673094), hAPP(c_Option_Ooption_OSome(_1673098), _1673102)), _1673096, _1673104) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1673092, tc_Option_Ooption(_1673098)), c_Map_Omap__upds(_1673092, _1673098, _1673100, _1673096, _1673104)), _1673094), hAPP(c_Option_Ooption_OSome(_1673098), _1673102)))], (1180 ^ _780119) ^ [_797593, _797595] : [-(class_Int_Oring__char__0(_797593)), _797595 = _797593, class_Int_Oring__char__0(_797595)], (44320 ^ _780119) ^ [_1667926, _1667928] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1667926)), hAPP(c_Code__Numeral_Oof__nat, _1667928)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1667926), _1667928)))], (11921 ^ _780119) ^ [_994742, _994744] : [11922 ^ _780119 : [(11923 ^ _780119) ^ [_994792] : [_994744 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994742), _994792)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994742), _994744)))], (29923 ^ _780119) ^ [_1338679, _1338681, _1338683, _1338685, _1338687] : [-(_1338679 = c_Orderings_Obot__class_Obot(tc_fun(_1338681, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338683, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338681, tc_fun(_1338683, tc_HOL_Obool)), _1338679), _1338685)), _1338687) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338681, tc_fun(_1338683, tc_HOL_Obool)), _1338679), hAPP(hAPP(c_COMBC(_1338681, tc_fun(_1338683, tc_HOL_Obool), tc_fun(_1338683, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1338683, tc_HOL_Obool), tc_fun(tc_fun(_1338683, tc_HOL_Obool), tc_fun(_1338683, tc_HOL_Obool)), _1338681), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338683, tc_HOL_Obool))), _1338685)), _1338687)))], (37435 ^ _780119) ^ [_1496155, _1496157, _1496159, _1496161] : [c_FunDef_Oreduction__pair(_1496155, _1496157), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1496155, _1496155), tc_HOL_Obool)), _1496159), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1496155, _1496155), tc_HOL_Obool), tc_fun(tc_prod(_1496155, _1496155), tc_HOL_Obool)), _1496157))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1496155, _1496155), tc_HOL_Obool)), _1496161), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1496155, _1496155), tc_HOL_Obool), tc_fun(tc_prod(_1496155, _1496155), tc_HOL_Obool)), _1496157))), c_Wellfounded_Owf(_1496155, _1496161), -(c_Wellfounded_Owf(_1496155, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1496155, _1496155), tc_HOL_Obool)), _1496159), _1496161)))], (2838 ^ _780119) ^ [_822361, _822363, _822365, _822367] : [-(c_Random_Olog(_822367, _822363) = c_Random_Olog(_822365, _822361)), _822367 = _822365, _822363 = _822361], (37361 ^ _780119) ^ [_1494262, _1494264, _1494266] : [c_Wellfounded_Owf(_1494262, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1494262, _1494262), tc_HOL_Obool)), _1494264), _1494266)), -(c_Wellfounded_Owf(_1494262, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1494262, _1494262), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1494262, _1494262), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1494262, _1494262, _1494262), _1494264), _1494264)), hAPP(hAPP(c_Relation_Orel__comp(_1494262, _1494262, _1494262), _1494266), _1494264))), _1494266)))], (46203 ^ _780119) ^ [_1711258, _1711260, _1711262, _1711264] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1711258)), hAPP(hAPP(c_List_Olist_OCons(_1711258), _1711260), _1711262)), c_List_Olists(_1711258, _1711264))), 46206 ^ _780119 : [(46209 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1711258)), _1711262), c_List_Olists(_1711258, _1711264))))], (46207 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1711258), _1711260), _1711264)))]]], (21476 ^ _780119) ^ [_1171580, _1171582, _1171584, _1171586] : [class_Divides_Osemiring__div(_1171580), -(c_Divides_Odiv__class_Omod(_1171580, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171580), c_Divides_Odiv__class_Omod(_1171580, _1171582, _1171584)), _1171586), _1171584) = c_Divides_Odiv__class_Omod(_1171580, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171580), _1171582), _1171586), _1171584))], (7116 ^ _780119) ^ [_897626, _897628] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _897626) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _897628), -(hBOOL(hAPP(c_Com_OWT, _897628)))], (47879 ^ _780119) ^ [_1747340, _1747342, _1747344, _1747346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747340), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747342)), c_List_OtakeWhile(_1747342, _1747344, _1747346)))), -(hAPP(hAPP(c_List_Onth(_1747342), c_List_OtakeWhile(_1747342, _1747344, _1747346)), _1747340) = hAPP(hAPP(c_List_Onth(_1747342), _1747346), _1747340))], (25045 ^ _780119) ^ [_1238847, _1238849] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1238847, _1238849)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1238849), _1238847)))], (29929 ^ _780119) ^ [_1338806, _1338808, _1338810, _1338812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338806, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1338806, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29930 ^ [_1338806, _1338808, _1338810, _1338812])), _1338808)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1338806, 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), 29930 ^ [_1338806, _1338808, _1338810, _1338812]), _1338810))), _1338812))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338806, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1338806, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1338808)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1338806, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1338812))))], (41844 ^ _780119) ^ [_1605770, _1605772, _1605774] : [class_Complete__Lattice_Ocomplete__lattice(_1605770), hBOOL(hAPP(hAPP(c_member(_1605770), _1605772), _1605774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1605770), c_Complete__Lattice_OInf__class_OInf(_1605770, _1605774)), _1605772)))], (838 ^ _780119) ^ [_792890, _792892, _792894, _792896, _792898, _792900, _792902, _792904, _792906, _792908] : [-(c_List_Olist__all2(_792906, _792902, _792898, _792894, _792890)), c_List_Olist__all2(_792908, _792904, _792900, _792896, _792892), _792908 = _792906, _792904 = _792902, _792900 = _792898, _792896 = _792894, _792892 = _792890], (46851 ^ _780119) ^ [_1725267, _1725269] : [c_List_Oupt(_1725267, _1725269) = c_List_Olist_ONil(tc_Nat_Onat), -(_1725269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1725269), _1725267)))], (32933 ^ _780119) ^ [] : [-(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))))], (1780 ^ _780119) ^ [_805093, _805095] : [-(class_Power_Opower(_805093)), _805095 = _805093, class_Power_Opower(_805095)], (34197 ^ _780119) ^ [_1422187] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1422187) = 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)))], (47536 ^ _780119) ^ [_1738749, _1738751, _1738753] : [-(hAPP(c_List_Orev(_1738749), hAPP(hAPP(c_List_Oappend(_1738749), _1738751), _1738753)) = hAPP(hAPP(c_List_Oappend(_1738749), hAPP(c_List_Orev(_1738749), _1738753)), hAPP(c_List_Orev(_1738749), _1738751)))], (48661 ^ _780119) ^ [_1763827, _1763829, _1763831, _1763833] : [class_Orderings_Oorder(_1763827), class_Enum_Oenum(_1763829), 48668 ^ _780119 : [(48675 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1763829), hAPP(hAPP(c_COMBS(_1763829, _1763827, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1763827, tc_fun(_1763827, tc_HOL_Obool), _1763829), c_Orderings_Oord__class_Oless__eq(_1763827)), _1763831)), _1763833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1763829, _1763827)), _1763831), _1763833)))], (48669 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1763829, _1763827)), _1763831), _1763833)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1763829), hAPP(hAPP(c_COMBS(_1763829, _1763827, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1763827, tc_fun(_1763827, tc_HOL_Obool), _1763829), c_Orderings_Oord__class_Oless__eq(_1763827)), _1763831)), _1763833))))]]], (19568 ^ _780119) ^ [_1135826, _1135828] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135826))), -(c_SMT_Oz3div(_1135828, _1135826) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1135828), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1135826))))], (4426 ^ _780119) ^ [_847097, _847099] : [_847099 = _847097, -(c_Enum_Oenum__class_Oenum(_847099) = c_Enum_Oenum__class_Oenum(_847097))], (38332 ^ _780119) ^ [_1520935, _1520937] : [c_Wellfounded_Owf(_1520935, _1520937), -(c_Wellfounded_OwfP(_1520935, c_FunDef_Oin__rel(_1520935, _1520935, _1520937)))], (37076 ^ _780119) ^ [_1487095, _1487097, _1487099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1487095, _1487095), tc_HOL_Obool)), _1487097), _1487099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487095, tc_HOL_Obool)), c_Wellfounded_Oacc(_1487095, _1487099)), c_Wellfounded_Oacc(_1487095, _1487097))))], (43096 ^ _780119) ^ [_1634834, _1634836, _1634838, _1634840, _1634842, _1634844] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634834, _1634836)), hAPP(hAPP(c_Product__Type_OPair(_1634834, _1634836), _1634838), _1634840)), hAPP(c_List_Oset(tc_prod(_1634834, _1634836)), hAPP(hAPP(c_List_Ozip(_1634834, _1634836), _1634842), _1634844)))), -(hBOOL(hAPP(hAPP(c_member(_1634836), _1634840), hAPP(c_List_Oset(_1634836), _1634844))))], (28492 ^ _780119) ^ [_1306665, _1306667, _1306669] : [class_Orderings_Olinorder(_1306665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306665), _1306667)), -(_1306669 = c_Orderings_Obot__class_Obot(tc_fun(_1306665, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306665, tc_HOL_Obool)), _1306669), _1306667)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1306665), c_Big__Operators_Olinorder__class_OMin(_1306665, _1306669)), c_Big__Operators_Olinorder__class_OMin(_1306665, _1306667)) = c_Big__Operators_Olinorder__class_OMin(_1306665, _1306667))], (46189 ^ _780119) ^ [_1711001] : [-(c_List_Olists(_1711001, c_Orderings_Otop__class_Otop(tc_fun(_1711001, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1711001), tc_HOL_Obool)))], (29867 ^ _780119) ^ [_1337289, _1337291] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337289, tc_fun(_1337289, tc_HOL_Obool)), _1337291), hAPP(hAPP(c_COMBC(_1337289, tc_fun(_1337289, tc_HOL_Obool), tc_fun(_1337289, tc_HOL_Obool)), c_Set_Oinsert(_1337289)), c_Orderings_Obot__class_Obot(tc_fun(_1337289, tc_HOL_Obool)))) = _1337291)], (24953 ^ _780119) ^ [_1237422] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1237422)) = _1237422)], (22489 ^ _780119) ^ [_1190551, _1190553, _1190555] : [class_Orderings_Olinorder(_1190551), 22492 ^ _780119 : [(22499 ^ _780119) ^ [] : [_1190553 = _1190555, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1190551), _1190553) = hAPP(c_SetInterval_Oord__class_OlessThan(_1190551), _1190555))], (22493 ^ _780119) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1190551), _1190553) = hAPP(c_SetInterval_Oord__class_OlessThan(_1190551), _1190555), -(_1190553 = _1190555)]]], (33483 ^ _780119) ^ [_1403536] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1403536)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1403536)))], (47017 ^ _780119) ^ [_1727891, _1727893, _1727895] : [class_Orderings_Olinorder(_1727891), c_List_Olinorder__class_Osorted(_1727891, _1727893), -(c_List_Olinorder__class_Osorted(_1727891, hAPP(hAPP(c_List_Otake(_1727891), _1727895), _1727893)))], (38024 ^ _780119) ^ [_1513793, _1513795] : [-(hAPP(c_Set_Oimage(_1513793, _1513793, c_Fun_Oid(_1513793)), _1513795) = _1513795)], (20055 ^ _780119) ^ [_1144804, _1144806, _1144808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144804)), 20058 ^ _780119 : [(20059 ^ _780119) ^ [] : [-(_1144806 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144808), _1144804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144804), _1144806)), _1144808)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144804), hAPP(c_Nat_OSuc, _1144806))))], (20069 ^ _780119) ^ [] : [_1144806 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144808), _1144804), 20072 ^ _780119 : [(20075 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144804), hAPP(c_Nat_OSuc, _1144806)))))], (20073 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144804), _1144806)), _1144808)))]]]]], (47965 ^ _780119) ^ [_1749004, _1749006] : [c_List_Oremdups(_1749004, _1749006) = _1749006, -(hBOOL(hAPP(c_List_Odistinct(_1749004), _1749006)))], (11868 ^ _780119) ^ [_993711, _993713, _993715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993711), _993713)), _993715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993713), _993715)))], (16016 ^ _780119) ^ [_1071998, _1072000, _1072002, _1072004] : [class_Rings_Olinordered__semidom(_1071998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071998), c_Groups_Ozero__class_Ozero(_1071998)), _1072000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071998), _1072002), _1072004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071998), _1072002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071998), _1072000), _1072004))))], (8048 ^ _780119) ^ [_917687, _917689, _917691] : [c_Com_Ocom_OSemi(_917687, _917689) = hAPP(c_Com_Ocom_OBODY, _917691)], (36832 ^ _780119) ^ [_1480373, _1480375, _1480377, _1480379] : [-(hAPP(c_Set_Ovimage(_1480373, _1480375, _1480377), _1480379) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480375, tc_fun(_1480373, tc_HOL_Obool)), _1480379), hAPP(hAPP(c_COMBB(tc_fun(_1480375, tc_HOL_Obool), tc_fun(_1480373, tc_HOL_Obool), _1480375), c_Set_Ovimage(_1480373, _1480375, _1480377)), hAPP(hAPP(c_COMBC(_1480375, tc_fun(_1480375, tc_HOL_Obool), tc_fun(_1480375, tc_HOL_Obool)), c_Set_Oinsert(_1480375)), c_Orderings_Obot__class_Obot(tc_fun(_1480375, tc_HOL_Obool))))))], (44370 ^ _780119) ^ [_1668809, _1668811, _1668813, _1668815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668809)), _1668811)), _1668813)), -(hAPP(hAPP(c_List_Olist__update(_1668809, _1668811), _1668813), _1668815) = _1668811)], (8918 ^ _780119) ^ [_933855, _933857, _933859] : [class_Orderings_Opreorder(_933855), 8921 ^ _780119 : [(8930 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933855), _933857), _933859))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933855), _933857), _933859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933855), _933859), _933857)))], (8922 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933855), _933857), _933859)), 8925 ^ _780119 : [(8928 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933855), _933859), _933857))], (8926 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933855), _933857), _933859)))]]]]], (33515 ^ _780119) ^ [_1404058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1404058)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1404058) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36505 ^ _780119) ^ [_1472791, _1472793, _1472795, _1472797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1472791), hAPP(c_Set_Oimage(_1472793, _1472791, _1472795), _1472797))), hAPP(c_Finite__Set_Ocard(_1472793), _1472797))), c_Fun_Oinj__on(_1472793, _1472791, _1472795, _1472797)], (30441 ^ _780119) ^ [_1349217, _1349219, _1349221, _1349223] : [class_Fields_Ofield__inverse__zero(_1349217), class_Int_Onumber(_1349217), 30448 ^ _780119 : [(30449 ^ _780119) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349217), _1349219), hAPP(c_Int_Onumber__class_Onumber__of(_1349217), _1349221)) = _1349223, 30452 ^ _780119 : [(30459 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1349217), _1349221) = c_Groups_Ozero__class_Ozero(_1349217), -(_1349223 = c_Groups_Ozero__class_Ozero(_1349217))], (30453 ^ _780119) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1349217), _1349221) = c_Groups_Ozero__class_Ozero(_1349217)), -(_1349219 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349217), _1349223), hAPP(c_Int_Onumber__class_Onumber__of(_1349217), _1349221)))]]], (30465 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349217), _1349219), hAPP(c_Int_Onumber__class_Onumber__of(_1349217), _1349221)) = _1349223), 30468 ^ _780119 : [(30471 ^ _780119) ^ [] : [_1349219 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349217), _1349223), hAPP(c_Int_Onumber__class_Onumber__of(_1349217), _1349221))], (30469 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1349217), _1349221) = c_Groups_Ozero__class_Ozero(_1349217)]], 30472 ^ _780119 : [(30475 ^ _780119) ^ [] : [_1349223 = c_Groups_Ozero__class_Ozero(_1349217)], (30473 ^ _780119) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1349217), _1349221) = c_Groups_Ozero__class_Ozero(_1349217))]]]]], (23143 ^ _780119) ^ [_1202802, _1202804] : [class_Rings_Osemiring__1(_1202802), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1202802), hAPP(c_Nat_OSuc, _1202804)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1202802), c_Groups_Oone__class_Oone(_1202802)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1202802), _1202804)))], (14920 ^ _780119) ^ [_1053871, _1053873] : [class_Groups_Ocomm__monoid__add(_1053871), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053871), c_Groups_Ozero__class_Ozero(_1053871)), _1053873) = _1053873)], (5200 ^ _780119) ^ [_859700, _859702] : [_859702 = _859700, -(c_List_Odrop(_859702) = c_List_Odrop(_859700))], (47196 ^ _780119) ^ [_1731134, _1731136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731134), _1731136)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1731134, _1731136)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1731136), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (22338 ^ _780119) ^ [_1187709, _1187711] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1187709), _1187711)), _1187711) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1187709), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1187709, _1187711)))], (42743 ^ _780119) ^ [] : [-(c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))], (4284 ^ _780119) ^ [_844896, _844898, _844900, _844902, _844904, _844906, _844908, _844910] : [-(c_List_Ofoldl(_844910, _844906, _844902, _844898) = c_List_Ofoldl(_844908, _844904, _844900, _844896)), _844910 = _844908, _844906 = _844904, _844902 = _844900, _844898 = _844896], (2964 ^ _780119) ^ [_824258, _824260] : [_824260 = _824258, -(c_Relation_OField(_824260) = c_Relation_OField(_824258))], (45384 ^ _780119) ^ [_1691215, _1691217] : [-(c_List_Olistrel1(_1691215, hAPP(c_Relation_Oconverse(_1691215, _1691215), _1691217)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1691215), tc_List_Olist(_1691215)), c_List_Olistrel1(_1691215, _1691217)))], (24245 ^ _780119) ^ [_1224068, _1224070, _1224072, _1224074] : [class_Orderings_Oorder(_1224068), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1224068, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1224068, _1224070, _1224072)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1224068, _1224072), _1224074)) = c_Orderings_Obot__class_Obot(tc_fun(_1224068, tc_HOL_Obool)))], (50136 ^ _780119) ^ [_1796270] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1796270), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1796270)), c_Int_OMin)))], (14062 ^ _780119) ^ [_1036213] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036213) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1036213)))], (50722 ^ _780119) ^ [_1808878, _1808880, _1808882] : [hBOOL(hAPP(hAPP(c_member(_1808878), _1808880), hAPP(c_List_Oset(_1808878), _1808882))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1808878), _1808882), _1808880)))], (12703 ^ _780119) ^ [_1010341, _1010343] : [c_Option_Oset(_1010341, _1010343) = c_Orderings_Obot__class_Obot(tc_fun(_1010341, tc_HOL_Obool)), -(_1010343 = c_Option_Ooption_ONone(_1010341))], (46592 ^ _780119) ^ [_1719432, _1719434, _1719436, _1719438] : [-(hBOOL(hAPP(_1719432, _1719434))), -(hAPP(c_List_Ofilter(_1719436, _1719432), hAPP(hAPP(c_List_Olist_OCons(_1719436), _1719434), _1719438)) = hAPP(c_List_Ofilter(_1719436, _1719432), _1719438))], (19951 ^ _780119) ^ [_1142897, _1142899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1142897)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1142899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142899), _1142897)), _1142899)))], (43382 ^ _780119) ^ [_1642345, _1642347, _1642349, _1642351] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642345)), _1642347) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642349)), _1642351), hBOOL(hAPP(c_List_Odistinct(_1642345), _1642347)), -(c_Map_Odom(_1642345, _1642349, hAPP(c_Map_Omap__of(_1642345, _1642349), hAPP(hAPP(c_List_Ozip(_1642345, _1642349), _1642347), _1642351))) = hAPP(c_List_Oset(_1642345), _1642347))], (5871 ^ _780119) ^ [_873291, _873293, _873295, _873297, _873299] : [hBOOL(hAPP(hAPP(c_member(_873291), _873293), _873295)), -(hAPP(c_Set_Oimage(_873291, _873297, hAPP(c_COMBK(_873297, _873291), _873299)), _873295) = hAPP(hAPP(c_Set_Oinsert(_873297), _873299), c_Orderings_Obot__class_Obot(tc_fun(_873297, tc_HOL_Obool))))], (35544 ^ _780119) ^ [_1451608] : [-(c_Relation_OId__on(_1451608, c_Orderings_Obot__class_Obot(tc_fun(_1451608, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1451608, _1451608), tc_HOL_Obool)))], (38641 ^ _780119) ^ [_1528393, _1528395, _1528397, _1528399, _1528401, _1528403] : [38644 ^ _780119 : [(38647 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1528399), _1528401), hAPP(hAPP(_1528403, 38642 ^ [_1528393, _1528395, _1528397, _1528399, _1528401, _1528403]), 38643 ^ [_1528393, _1528395, _1528397, _1528399, _1528401, _1528403])))], (38645 ^ _780119) ^ [] : [-(_1528393 = hAPP(hAPP(c_Product__Type_OPair(_1528395, _1528397), 38642 ^ [_1528393, _1528395, _1528397, _1528399, _1528401, _1528403]), 38643 ^ [_1528393, _1528395, _1528397, _1528399, _1528401, _1528403]))]], -(hBOOL(hAPP(hAPP(c_member(_1528399), _1528401), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1528395, _1528397, tc_fun(_1528399, tc_HOL_Obool)), _1528403), _1528393))))], (37560 ^ _780119) ^ [_1499075, _1499077, _1499079, _1499081] : [hBOOL(hAPP(hAPP(c_member(_1499075), _1499077), hAPP(c_Relation_ORange(_1499079, _1499075), _1499081))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1499079, _1499075)), hAPP(hAPP(c_Product__Type_OPair(_1499079, _1499075), 37563 ^ [_1499075, _1499077, _1499079, _1499081]), _1499077)), _1499081)))], (44548 ^ _780119) ^ [_1672580] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1672580), 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, _1672580)) = _1672580)], (41399 ^ _780119) ^ [_1595199, _1595201, _1595203, _1595205, _1595207] : [class_Complete__Lattice_Ocomplete__lattice(_1595199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1595201, tc_HOL_Obool)), _1595203), _1595205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1595199), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595201, _1595199), _1595205), _1595207)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595201, _1595199), _1595203), _1595207))))], (33423 ^ _780119) ^ [_1402726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1402726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1402726)))], (37587 ^ _780119) ^ [_1499982, _1499984, _1499986, _1499988] : [hBOOL(hAPP(hAPP(c_member(_1499984), _1499988), hAPP(c_Relation_ORange(_1499982, _1499984), _1499986))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1499982, _1499984, hAPP(hAPP(c_COMBC(_1499982, tc_fun(tc_prod(_1499982, _1499984), tc_HOL_Obool), tc_fun(_1499984, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499984, tc_fun(tc_fun(tc_prod(_1499982, _1499984), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499982, _1499984), tc_HOL_Obool), tc_fun(_1499984, tc_HOL_Obool)), _1499982), c_COMBC(_1499984, tc_fun(tc_prod(_1499982, _1499984), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499984, tc_prod(_1499982, _1499984)), tc_fun(_1499984, tc_fun(tc_fun(tc_prod(_1499982, _1499984), tc_HOL_Obool), tc_HOL_Obool)), _1499982), hAPP(c_COMBB(tc_prod(_1499982, _1499984), tc_fun(tc_fun(tc_prod(_1499982, _1499984), tc_HOL_Obool), tc_HOL_Obool), _1499984), c_member(tc_prod(_1499982, _1499984)))), c_Product__Type_OPair(_1499982, _1499984)))), _1499986)), _1499988)))], (3084 ^ _780119) ^ [_826118, _826120, _826122, _826124] : [-(c_Nitpick_OAbs__Frac(_826124, _826120) = c_Nitpick_OAbs__Frac(_826122, _826118)), _826124 = _826122, _826120 = _826118], (14270 ^ _780119) ^ [_1040827, _1040829, _1040831, _1040833, _1040835] : [class_Groups_Ocomm__monoid__mult(_1040827), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040829), _1040831)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040829), _1040833)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040829, tc_HOL_Obool)), _1040831), _1040833) = c_Orderings_Obot__class_Obot(tc_fun(_1040829, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1040829, _1040827), _1040835), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040829, tc_HOL_Obool)), _1040831), _1040833)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040827), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1040829, _1040827), _1040835), _1040831)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1040829, _1040827), _1040835), _1040833)))], (51331 ^ _780119) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (46379 ^ _780119) ^ [_1714721, _1714723, _1714725] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1714721, _1714721)), hAPP(hAPP(c_Product__Type_OPair(_1714721, _1714721), 46380 ^ [_1714721, _1714723, _1714725]), 46380 ^ [_1714721, _1714723, _1714725])), _1714723))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714721), tc_List_Olist(_1714721))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714721), tc_List_Olist(_1714721)), _1714725), _1714725)), c_List_Olexord(_1714721, _1714723)))], (45267 ^ _780119) ^ [_1688062, _1688064, _1688066] : [hBOOL(hAPP(c_List_Odistinct(_1688062), hAPP(hAPP(c_List_Oappend(_1688062), _1688064), _1688066))), 45270 ^ _780119 : [(45273 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1688062), _1688066)))], (45275 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1688062, tc_HOL_Obool)), hAPP(c_List_Oset(_1688062), _1688064)), hAPP(c_List_Oset(_1688062), _1688066)) = c_Orderings_Obot__class_Obot(tc_fun(_1688062, tc_HOL_Obool)))], (45271 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1688062), _1688064)))]]], (49886 ^ _780119) ^ [_1791645, _1791647, _1791649] : [49888 ^ _780119 : [(49891 ^ _780119) ^ [] : [hBOOL(hAPP(_1791647, 49887 ^ [_1791645, _1791647, _1791649]))], (49889 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791645), 49887 ^ [_1791645, _1791647, _1791649]), hAPP(c_List_Oset(_1791645), _1791649))))]], -(c_List_Olist__all(_1791645, _1791647, _1791649))], (48323 ^ _780119) ^ [_1757284, _1757286] : [-(c_Enum_Oenum__class_Oenum(tc_prod(_1757284, _1757286)) = c_Enum_Oproduct(_1757284, _1757286, c_Enum_Oenum__class_Oenum(_1757284), c_Enum_Oenum__class_Oenum(_1757286))), class_Enum_Oenum(_1757284), class_Enum_Oenum(_1757286)], (21977 ^ _780119) ^ [_1181392, _1181394, _1181396] : [-(hBOOL(hAPP(_1181392, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181394, _1181396)))), 21980 ^ _780119 : [(21983 ^ _780119) ^ [] : [hBOOL(hAPP(_1181392, _1181394))], (21981 ^ _780119) ^ [] : [-(_1181396 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 21986 ^ _780119 : [(21995 ^ _780119) ^ [] : [-(_1181394 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181396), 21988 ^ [_1181392, _1181394, _1181396])), 21989 ^ [_1181392, _1181394, _1181396]))], (21993 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 21989 ^ [_1181392, _1181394, _1181396]), _1181396)))], (21991 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21989 ^ [_1181392, _1181394, _1181396])))], (21987 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181396)))], (21997 ^ _780119) ^ [] : [hBOOL(hAPP(_1181392, 21989 ^ [_1181392, _1181394, _1181396]))]], 21998 ^ _780119 : [(22007 ^ _780119) ^ [] : [-(_1181394 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181396), 22000 ^ [_1181392, _1181394, _1181396])), 22001 ^ [_1181392, _1181394, _1181396]))], (22005 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 22001 ^ [_1181392, _1181394, _1181396]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22003 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181396), 22001 ^ [_1181392, _1181394, _1181396])))], (21999 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181396), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22009 ^ _780119) ^ [] : [hBOOL(hAPP(_1181392, 22001 ^ [_1181392, _1181394, _1181396]))]]], (41908 ^ _780119) ^ [_1607036, _1607038, _1607040, _1607042, _1607044] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1607036, tc_fun(_1607038, tc_HOL_Obool)), _1607040), hAPP(hAPP(c_COMBS(_1607036, tc_fun(_1607038, tc_HOL_Obool), tc_fun(_1607038, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1607038, tc_HOL_Obool), tc_fun(tc_fun(_1607038, tc_HOL_Obool), tc_fun(_1607038, tc_HOL_Obool)), _1607036), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1607038, tc_HOL_Obool))), _1607042)), _1607044)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1607038, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1607038, tc_HOL_Obool), hAPP(c_Set_Oimage(_1607036, tc_fun(_1607038, tc_HOL_Obool), _1607042), _1607040))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1607038, tc_HOL_Obool), hAPP(c_Set_Oimage(_1607036, tc_fun(_1607038, tc_HOL_Obool), _1607044), _1607040))))], (50939 ^ _780119) ^ [_1813706, _1813708] : [class_Complete__Lattice_Ocomplete__lattice(_1813706), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1813708, _1813706)))], (41373 ^ _780119) ^ [_1594328, _1594330, _1594332, _1594334] : [hBOOL(hAPP(hAPP(c_member(_1594330), _1594334), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594328, tc_fun(_1594330, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1594328, tc_HOL_Obool))), _1594332))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594328, tc_fun(_1594330, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1594328, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1594330, tc_HOL_Obool), tc_fun(_1594330, tc_HOL_Obool), _1594328), hAPP(c_COMBC(_1594330, tc_fun(_1594330, tc_HOL_Obool), tc_HOL_Obool), c_member(_1594330))), _1594332)), _1594334)))], (50304 ^ _780119) ^ [_1799734, _1799736, _1799738] : [-(hAPP(c_New__DSequence_Opos__single(_1799734, _1799736), _1799738) = hAPP(c_Lazy__Sequence_Osingle(_1799734), _1799736))], (32655 ^ _780119) ^ [_1388765, _1388767] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1388765)), c_Int_OBit1(_1388767)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1388765), c_Int_Osucc(_1388767))))], (28098 ^ _780119) ^ [_1298985, _1298987, _1298989, _1298991] : [class_Orderings_Olinorder(_1298985), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298985), _1298987), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298985), _1298989), _1298991)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298985), _1298989), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298985), _1298987), _1298991)))], (48393 ^ _780119) ^ [_1758513, _1758515] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1758513, _1758515)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1758515), tc_fun(_1758513, _1758515)), hAPP(hAPP(c_COMBB(tc_fun(_1758513, tc_Option_Ooption(_1758515)), tc_fun(_1758513, _1758515), tc_List_Olist(_1758515)), c_Fun_Ocomp(tc_Option_Ooption(_1758515), _1758515, _1758513, c_Option_Othe(_1758515))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1758513, _1758515)), tc_fun(_1758513, tc_Option_Ooption(_1758515)), tc_List_Olist(_1758515)), c_Map_Omap__of(_1758513, _1758515)), hAPP(c_List_Ozip(_1758513, _1758515), c_Enum_Oenum__class_Oenum(_1758513))))), c_Enum_On__lists(_1758515, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758513)), c_Enum_Oenum__class_Oenum(_1758513)), c_Enum_Oenum__class_Oenum(_1758515)))), class_Enum_Oenum(_1758513), class_Enum_Oenum(_1758515)], (29813 ^ _780119) ^ [_1335863, _1335865, _1335867, _1335869, _1335871] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335863, tc_fun(_1335865, tc_HOL_Obool)), _1335867), hAPP(hAPP(c_COMBC(_1335863, tc_fun(_1335865, tc_HOL_Obool), tc_fun(_1335865, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1335865, tc_HOL_Obool), tc_fun(tc_fun(_1335865, tc_HOL_Obool), tc_fun(_1335865, tc_HOL_Obool)), _1335863), c_Groups_Ominus__class_Ominus(tc_fun(_1335865, tc_HOL_Obool))), _1335869)), _1335871)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335865, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335863, tc_fun(_1335865, tc_HOL_Obool)), _1335867), _1335869)), _1335871))], (36720 ^ _780119) ^ [_1477793, _1477795, _1477797, _1477799] : [-(hAPP(c_Set_Ovimage(_1477793, _1477795, _1477797), hAPP(c_Set_OCollect(_1477795), _1477799)) = hAPP(c_Set_OCollect(_1477793), hAPP(hAPP(c_COMBB(_1477795, tc_HOL_Obool, _1477793), _1477799), _1477797)))], (17750 ^ _780119) ^ [_1102834, _1102836, _1102838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102834), _1102836)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102838), _1102836))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102834), _1102838)))], (5909 ^ _780119) ^ [_874043, _874045, _874047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874043, tc_HOL_Obool)), _874045), _874047)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874043, tc_HOL_Obool)), _874047), _874045)), -(_874045 = _874047)], (36834 ^ _780119) ^ [_1480464, _1480466, _1480468, _1480470, _1480472, _1480474] : [c_Fun_Oinj__on(_1480464, _1480466, _1480468, _1480470), hAPP(_1480468, _1480472) = _1480474, hBOOL(hAPP(hAPP(c_member(_1480464), _1480472), _1480470)), -(hAPP(c_Fun_Othe__inv__into(_1480464, _1480466, _1480470, _1480468), _1480474) = _1480472)], (3136 ^ _780119) ^ [_826892, _826894, _826896, _826898, _826900, _826902] : [-(c_Product__Type_Ointernal__split(_826902, _826898, _826894) = c_Product__Type_Ointernal__split(_826900, _826896, _826892)), _826902 = _826900, _826898 = _826896, _826894 = _826892], (13934 ^ _780119) ^ [_1033683, _1033685] : [13935 ^ _780119 : [(13936 ^ _780119) ^ [_1033736] : [_1033685 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1033683), _1033736))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033683), _1033685)))], (39531 ^ _780119) ^ [_1549427, _1549429, _1549431, _1549433] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549427, _1549427)), _1549429), c_Transitive__Closure_Otrancl(_1549427, _1549431))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1549427, _1549427), tc_HOL_Obool)), _1549431), _1549433)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549427, _1549427)), _1549429), c_Transitive__Closure_Otrancl(_1549427, _1549433))))], (40430 ^ _780119) ^ [_1571646, _1571648, _1571650, _1571652, _1571654] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571646, _1571646)), hAPP(hAPP(c_Product__Type_OPair(_1571646, _1571646), _1571648), _1571650)), c_Transitive__Closure_Ortrancl(_1571646, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571646, _1571646), tc_HOL_Obool)), _1571652), _1571654)))), 40436 ^ _780119 : [(40440 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571646, _1571646)), hAPP(hAPP(c_Product__Type_OPair(_1571646, _1571646), 40438 ^ [_1571646, _1571648, _1571650, _1571652, _1571654]), 40435 ^ [_1571646, _1571648, _1571650, _1571652, _1571654])), _1571654)))], (40442 ^ _780119) ^ [] : [40438 ^ [_1571646, _1571648, _1571650, _1571652, _1571654] = 40435 ^ [_1571646, _1571648, _1571650, _1571652, _1571654]], (40437 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571646, _1571646)), hAPP(hAPP(c_Product__Type_OPair(_1571646, _1571646), 40435 ^ [_1571646, _1571648, _1571650, _1571652, _1571654]), _1571650)), c_Transitive__Closure_Ortrancl(_1571646, _1571652))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571646, _1571646)), hAPP(hAPP(c_Product__Type_OPair(_1571646, _1571646), _1571648), _1571650)), c_Transitive__Closure_Ortrancl(_1571646, _1571652))))], (42831 ^ _780119) ^ [_1628466, _1628468, _1628470, _1628472, _1628474] : [hAPP(hAPP(c_Map_Omap__of(_1628466, _1628468), _1628470), _1628472) = hAPP(c_Option_Ooption_OSome(_1628468), _1628474), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628466, _1628468)), hAPP(hAPP(c_Product__Type_OPair(_1628466, _1628468), _1628472), _1628474)), hAPP(c_List_Oset(tc_prod(_1628466, _1628468)), _1628470))))], (47923 ^ _780119) ^ [_1748321, _1748323] : [class_Orderings_Olinorder(_1748321), c_List_Olinorder__class_Osorted(_1748321, _1748323), -(c_List_Olinorder__class_Osorted(_1748321, c_List_Oremdups(_1748321, _1748323)))], (32657 ^ _780119) ^ [_1388810, _1388812, _1388814] : [class_Int_Onumber__ring(_1388810), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1388810), _1388812), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1388814))) = hAPP(hAPP(c_HOL_OLet(_1388810, _1388810), hAPP(hAPP(c_Power_Opower__class_Opower(_1388810), _1388812), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1388814))), hAPP(hAPP(c_COMBS(_1388810, _1388810, _1388810), c_Groups_Otimes__class_Otimes(_1388810)), c_COMBI(_1388810))))], (10228 ^ _780119) ^ [_959364, _959366, _959368, _959370, _959372] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_959364, _959366, _959368), _959370), _959372), c_Orderings_Obot__class_Obot(tc_fun(_959366, tc_HOL_Obool))) = _959372)], (31679 ^ _780119) ^ [_1371346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1371346)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371346), c_Int_OPls)))], (13901 ^ _780119) ^ [_1032888, _1032890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1032888, tc_HOL_Obool)), _1032890), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1032888, tc_HOL_Obool)), _1032890))), -(_1032890 = c_Orderings_Obot__class_Obot(tc_fun(_1032888, tc_HOL_Obool)))], (42869 ^ _780119) ^ [_1629468, _1629470, _1629472] : [hBOOL(hAPP(c_List_Odistinct(_1629468), hAPP(hAPP(c_List_Omap(tc_prod(_1629468, _1629470), _1629468), c_Product__Type_Ofst(_1629468, _1629470)), _1629472))), -(hAPP(c_List_Oset(tc_prod(_1629468, _1629470)), _1629472) = hAPP(c_Set_OCollect(tc_prod(_1629468, _1629470)), hAPP(c_Product__Type_Oprod_Oprod__case(_1629468, _1629470, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1629468, tc_fun(_1629470, tc_Option_Ooption(_1629470)), tc_fun(_1629470, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1629470), tc_HOL_Obool), tc_fun(tc_fun(_1629470, tc_Option_Ooption(_1629470)), tc_fun(_1629470, tc_HOL_Obool)), _1629468), c_COMBB(tc_Option_Ooption(_1629470), tc_HOL_Obool, _1629470)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1629470), tc_fun(tc_Option_Ooption(_1629470), tc_HOL_Obool), _1629468), c_fequal), hAPP(c_Map_Omap__of(_1629468, _1629470), _1629472)))), c_Option_Ooption_OSome(_1629470)))))], (32055 ^ _780119) ^ [_1377422, _1377424] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377422))), _1377424) = 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)))), _1377422), _1377424))], (41071 ^ _780119) ^ [_1585406, _1585408, _1585410, _1585412, _1585414, _1585416] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1585406, tc_fun(_1585408, tc_HOL_Obool)), _1585410), _1585412), _1585414)), hBOOL(hAPP(hAPP(c_member(_1585406), _1585416), _1585410)), -(hBOOL(hAPP(hAPP(_1585412, _1585416), _1585414)))], (44378 ^ _780119) ^ [_1668984, _1668986, _1668988, _1668990, _1668992, _1668994] : [-(hAPP(hAPP(c_List_Omap(_1668984, _1668986), _1668988), hAPP(hAPP(c_List_Olist__update(_1668984, _1668990), _1668992), _1668994)) = hAPP(hAPP(c_List_Olist__update(_1668986, hAPP(hAPP(c_List_Omap(_1668984, _1668986), _1668988), _1668990)), _1668992), hAPP(_1668988, _1668994)))], (48369 ^ _780119) ^ [_1758027, _1758029, _1758031, _1758033] : [class_Orderings_Olinorder(_1758027), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758029)), c_List_Olinorder__class_Osort__key(_1758029, _1758027, _1758031, _1758033)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758029)), _1758033))], (19440 ^ _780119) ^ [_1133399, _1133401, _1133403] : [class_Divides_Osemiring__div(_1133399), -(_1133401 = c_Groups_Ozero__class_Ozero(_1133399)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133399), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133399), _1133401), _1133403)), _1133401) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133399), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133399), _1133403), _1133401)), c_Groups_Oone__class_Oone(_1133399)))], (49295 ^ _780119) ^ [_1777692, _1777694] : [-(c_List_OremoveAll(_1777692, _1777694) = c_List_Ofilter(_1777692, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1777692), c_fNot), hAPP(c_fequal, _1777694))))], (41776 ^ _780119) ^ [_1603968, _1603970] : [class_Complete__Lattice_Ocomplete__lattice(_1603968), -(c_Complete__Lattice_OSup__class_OSup(_1603968, _1603970) = c_Complete__Lattice_OInf__class_OInf(_1603968, hAPP(c_Set_OCollect(_1603968), hAPP(hAPP(c_COMBB(tc_fun(_1603968, tc_HOL_Obool), tc_HOL_Obool, _1603968), c_HOL_OAll(_1603968)), hAPP(hAPP(c_COMBB(tc_fun(_1603968, tc_HOL_Obool), tc_fun(_1603968, tc_HOL_Obool), _1603968), hAPP(c_COMBS(_1603968, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1603968), c_fimplies), hAPP(hAPP(c_COMBC(_1603968, tc_fun(_1603968, tc_HOL_Obool), tc_HOL_Obool), c_member(_1603968)), _1603970)))), hAPP(c_COMBC(_1603968, _1603968, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1603968)))))))], (28032 ^ _780119) ^ [_1297688, _1297690, _1297692] : [class_Orderings_Olinorder(_1297688), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1297688), _1297690), _1297692) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1297688), _1297692), _1297690))], (31573 ^ _780119) ^ [_1369752] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369752), 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), _1369752)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1369752)))], (29899 ^ _780119) ^ [_1338142, _1338144, _1338146, _1338148, _1338150] : [-(_1338142 = c_Orderings_Obot__class_Obot(tc_fun(_1338144, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338144, tc_fun(_1338146, tc_HOL_Obool)), _1338142), hAPP(hAPP(c_COMBC(_1338144, tc_fun(_1338146, tc_HOL_Obool), tc_fun(_1338146, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1338146, tc_HOL_Obool), tc_fun(tc_fun(_1338146, tc_HOL_Obool), tc_fun(_1338146, tc_HOL_Obool)), _1338144), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338146, tc_HOL_Obool))), _1338148)), _1338150)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338146, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338144, tc_fun(_1338146, tc_HOL_Obool)), _1338142), _1338148)), _1338150))], (15454 ^ _780119) ^ [_1061874, _1061876, _1061878] : [class_Groups_Ocomm__monoid__add(_1061874), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1061876, _1061874), hAPP(c_COMBK(_1061874, _1061876), c_Groups_Ozero__class_Ozero(_1061874))), _1061878) = c_Groups_Ozero__class_Ozero(_1061874))], (51083 ^ _780119) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (23177 ^ _780119) ^ [_1203455, _1203457, _1203459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203455), _1203457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203459)), -(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), _1203459)), _1203455)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203459)), _1203457))))], (25466 ^ _780119) ^ [_1245899] : [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, _1245899))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1245899)))], (29623 ^ _780119) ^ [_1330597, _1330599, _1330601, _1330603, _1330605, _1330607] : [class_Complete__Lattice_Ocomplete__lattice(_1330597), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330599, _1330597), _1330601), hAPP(hAPP(c_COMBB(tc_fun(_1330603, _1330597), _1330597, _1330599), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330603, _1330597), _1330605)), _1330607)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330603, _1330597), _1330605), hAPP(hAPP(c_COMBB(tc_fun(_1330599, _1330597), _1330597, _1330603), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330599, _1330597), _1330601)), hAPP(c_COMBC(_1330599, _1330603, _1330597), _1330607))))], (48175 ^ _780119) ^ [_1753585, _1753587, _1753589] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1753585), tc_List_Olist(_1753585)), c_List_Opartition(_1753585, _1753587, _1753589)) = hAPP(c_List_Ofilter(_1753585, _1753587), _1753589))], (2106 ^ _780119) ^ [_810787, _810789, _810791, _810793, _810795, _810797, _810799, _810801] : [-(c_SetInterval_Oord_OatLeastAtMost(_810801, _810797, _810793, _810789) = c_SetInterval_Oord_OatLeastAtMost(_810799, _810795, _810791, _810787)), _810801 = _810799, _810797 = _810795, _810793 = _810791, _810789 = _810787], (1150 ^ _780119) ^ [_797218, _797220] : [-(class_Rings_Ocomm__ring__1(_797218)), _797220 = _797218, class_Rings_Ocomm__ring__1(_797220)], (19342 ^ _780119) ^ [_1131807, _1131809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131807)), 19345 ^ _780119 : [(19352 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131809)), -(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), _1131809), _1131807))))], (19346 ^ _780119) ^ [] : [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), _1131809), _1131807))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131809)))]]], (1630 ^ _780119) ^ [_803218, _803220] : [-(class_Divides_Osemiring__div(_803218)), _803220 = _803218, class_Divides_Osemiring__div(_803220)], (16993 ^ _780119) ^ [_1088761, _1088763, _1088765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1088761), _1088763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1088761), _1088765))), 16996 ^ _780119 : [(16999 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1088763), _1088765)))], (16997 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1088761)))]]], (46961 ^ _780119) ^ [_1727064, _1727066] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1727064, _1727066)))], (47049 ^ _780119) ^ [_1728352, _1728354, _1728356, _1728358, _1728360] : [class_Orderings_Olinorder(_1728352), c_List_Olinorder__class_Osorted(_1728352, hAPP(hAPP(c_List_Omap(_1728354, _1728352), _1728356), _1728358)), -(c_List_Olinorder__class_Osorted(_1728352, hAPP(hAPP(c_List_Omap(_1728354, _1728352), _1728356), c_List_Olinorder__class_Oinsort__insert__key(_1728354, _1728352, _1728356, _1728360, _1728358))))], (42708 ^ _780119) ^ [_1625742, _1625744, _1625746, _1625748, _1625750, _1625752, _1625754] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1625742), tc_Option_Ooption(_1625744), _1625746, hAPP(c_Option_Omap(_1625742, _1625744), _1625748)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1625746, tc_Option_Ooption(_1625742)), _1625750), _1625752), hAPP(c_Option_Ooption_OSome(_1625742), _1625754))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1625746, tc_Option_Ooption(_1625744)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1625742), tc_Option_Ooption(_1625744), _1625746, hAPP(c_Option_Omap(_1625742, _1625744), _1625748)), _1625750)), _1625752), hAPP(c_Option_Ooption_OSome(_1625744), hAPP(_1625748, _1625754))))], (21458 ^ _780119) ^ [_1171151, _1171153, _1171155, _1171157] : [class_Divides_Osemiring__div(_1171151), -(c_Divides_Odiv__class_Omod(_1171151, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171151), _1171153), _1171155), _1171157) = c_Divides_Odiv__class_Omod(_1171151, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171151), c_Divides_Odiv__class_Omod(_1171151, _1171153, _1171157)), c_Divides_Odiv__class_Omod(_1171151, _1171155, _1171157)), _1171157))], (5985 ^ _780119) ^ [_875300, _875302, _875304, _875306] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_875300), _875302), _875304), _875306)), -(_875302 = _875306), -(hBOOL(hAPP(_875304, _875306)))], (15366 ^ _780119) ^ [_1060485, _1060487, _1060489] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060485), _1060487) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060489), _1060487), -(_1060485 = _1060489), -(_1060487 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37781 ^ _780119) ^ [_1505401, _1505403, _1505405] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1505401, _1505403), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1505401, _1505403), _1505405), hAPP(c_COMBK(tc_fun(_1505403, tc_HOL_Obool), _1505401), c_Orderings_Otop__class_Otop(tc_fun(_1505403, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1505401, _1505403), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1505401, tc_HOL_Obool)), _1505405)), hAPP(c_COMBK(tc_fun(_1505403, tc_HOL_Obool), _1505401), c_Orderings_Otop__class_Otop(tc_fun(_1505403, tc_HOL_Obool)))))], (39974 ^ _780119) ^ [_1560324, _1560326] : [-(c_Transitive__Closure_Ortrancl(_1560324, hAPP(c_Relation_Oconverse(_1560324, _1560324), _1560326)) = hAPP(c_Relation_Oconverse(_1560324, _1560324), c_Transitive__Closure_Ortrancl(_1560324, _1560326)))], (34533 ^ _780119) ^ [_1428148, _1428150, _1428152, _1428154, _1428156, _1428158] : [hAPP(_1428154, hAPP(c_Product__Type_Osnd(_1428152, _1428148), _1428156)) = hAPP(_1428158, hAPP(c_Product__Type_Osnd(_1428152, _1428148), _1428156)), -(hAPP(c_Product__Type_Oapsnd(_1428148, _1428150, _1428152, _1428154), _1428156) = hAPP(c_Product__Type_Oapsnd(_1428148, _1428150, _1428152, _1428158), _1428156))], (16270 ^ _780119) ^ [_1076658, _1076660, _1076662, _1076664] : [class_Rings_Olinordered__comm__semiring__strict(_1076658), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076658), _1076660), _1076662)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076658), c_Groups_Ozero__class_Ozero(_1076658)), _1076664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076658), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076658), _1076664), _1076660)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076658), _1076664), _1076662))))], (18440 ^ _780119) ^ [_1116482] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1116482) = _1116482)], (37125 ^ _780119) ^ [_1488762, _1488764, _1488766, _1488768, _1488770, _1488772, _1488774] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1488762, _1488764, _1488766, hAPP(hAPP(c_COMBC(_1488762, tc_fun(tc_prod(_1488762, _1488764), tc_HOL_Obool), tc_fun(_1488764, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488764, tc_fun(tc_fun(tc_prod(_1488762, _1488764), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1488762, _1488764), tc_HOL_Obool), tc_fun(_1488764, tc_HOL_Obool)), _1488762), c_COMBC(_1488764, tc_fun(tc_prod(_1488762, _1488764), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488764, tc_prod(_1488762, _1488764)), tc_fun(_1488764, tc_fun(tc_fun(tc_prod(_1488762, _1488764), tc_HOL_Obool), tc_HOL_Obool)), _1488762), hAPP(c_COMBB(tc_prod(_1488762, _1488764), tc_fun(tc_fun(tc_prod(_1488762, _1488764), tc_HOL_Obool), tc_HOL_Obool), _1488764), c_member(tc_prod(_1488762, _1488764)))), c_Product__Type_OPair(_1488762, _1488764)))), _1488768), hAPP(hAPP(c_COMBC(_1488764, tc_fun(tc_prod(_1488764, _1488766), tc_HOL_Obool), tc_fun(_1488766, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488766, tc_fun(tc_fun(tc_prod(_1488764, _1488766), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1488764, _1488766), tc_HOL_Obool), tc_fun(_1488766, tc_HOL_Obool)), _1488764), c_COMBC(_1488766, tc_fun(tc_prod(_1488764, _1488766), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488766, tc_prod(_1488764, _1488766)), tc_fun(_1488766, tc_fun(tc_fun(tc_prod(_1488764, _1488766), tc_HOL_Obool), tc_HOL_Obool)), _1488764), hAPP(c_COMBB(tc_prod(_1488764, _1488766), tc_fun(tc_fun(tc_prod(_1488764, _1488766), tc_HOL_Obool), tc_HOL_Obool), _1488766), c_member(tc_prod(_1488764, _1488766)))), c_Product__Type_OPair(_1488764, _1488766)))), _1488770)), _1488772), _1488774)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1488762, _1488766)), hAPP(hAPP(c_Product__Type_OPair(_1488762, _1488766), _1488772), _1488774)), hAPP(hAPP(c_Relation_Orel__comp(_1488762, _1488764, _1488766), _1488768), _1488770))))], (25043 ^ _780119) ^ [_1238818] : [-(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)), _1238818)) = _1238818)], (43110 ^ _780119) ^ [_1635250, _1635252, _1635254, _1635256, _1635258, _1635260, _1635262, _1635264] : [-(hAPP(hAPP(c_List_Ozip(_1635250, _1635252), hAPP(hAPP(c_List_Omap(_1635254, _1635250), _1635256), _1635258)), hAPP(hAPP(c_List_Omap(_1635260, _1635252), _1635262), _1635264)) = hAPP(hAPP(c_List_Omap(tc_prod(_1635254, _1635260), tc_prod(_1635250, _1635252)), hAPP(c_Product__Type_Oprod_Oprod__case(_1635254, _1635260, tc_prod(_1635250, _1635252)), hAPP(hAPP(c_COMBC(_1635254, tc_fun(_1635260, _1635252), tc_fun(_1635260, tc_prod(_1635250, _1635252))), hAPP(hAPP(c_COMBB(tc_fun(_1635252, tc_prod(_1635250, _1635252)), tc_fun(tc_fun(_1635260, _1635252), tc_fun(_1635260, tc_prod(_1635250, _1635252))), _1635254), c_COMBB(_1635252, tc_prod(_1635250, _1635252), _1635260)), hAPP(hAPP(c_COMBB(_1635250, tc_fun(_1635252, tc_prod(_1635250, _1635252)), _1635254), c_Product__Type_OPair(_1635250, _1635252)), _1635256))), _1635262))), hAPP(hAPP(c_List_Ozip(_1635254, _1635260), _1635258), _1635264)))], (49096 ^ _780119) ^ [_1773605, _1773607, _1773609, _1773611] : [_1773611 = c_List_Olist_ONil(_1773605), -(c_List_Olist__all2(_1773605, _1773607, _1773609, _1773611, c_List_Olist_ONil(_1773607)))], (48289 ^ _780119) ^ [_1756661, _1756663] : [class_Orderings_Olinorder(_1756661), -(c_List_Olinorder__class_Osort__key(_1756661, _1756661, c_COMBI(_1756661), _1756663) = hAPP(c_List_Ofoldl(tc_List_Olist(_1756661), _1756661, hAPP(c_COMBC(_1756661, tc_List_Olist(_1756661), tc_List_Olist(_1756661)), c_List_Olinorder__class_Oinsort__key(_1756661, _1756661, c_COMBI(_1756661))), c_List_Olist_ONil(_1756661)), _1756663))], (45650 ^ _780119) ^ [_1698854, _1698856, _1698858] : [-(hAPP(hAPP(c_List_Oappend(_1698854), hAPP(hAPP(c_List_Otake(_1698854), _1698856), _1698858)), hAPP(hAPP(c_List_Odrop(_1698854), _1698856), _1698858)) = _1698858)], (2930 ^ _780119) ^ [_823739, _823741, _823743, _823745] : [-(c_Relation_ODomain(_823745, _823741) = c_Relation_ODomain(_823743, _823739)), _823745 = _823743, _823741 = _823739], (27996 ^ _780119) ^ [_1296882, _1296884, _1296886, _1296888] : [class_Orderings_Olinorder(_1296882), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296882), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1296882), _1296884), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1296882), _1296886), _1296888))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1296882), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1296882), _1296884), _1296886)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1296882), _1296884), _1296888)))))], (28140 ^ _780119) ^ [_1300018, _1300020, _1300022, _1300024] : [class_Orderings_Olinorder(_1300018), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300018), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300018), _1300020), _1300022)), _1300024) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300018), _1300020), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300018), _1300022), _1300024)))], (51311 ^ _780119) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (33877 ^ _780119) ^ [_1415589, _1415591, _1415593, _1415595, _1415597, _1415599] : [hBOOL(hAPP(hAPP(_1415589, _1415591), _1415593)), hBOOL(hAPP(hAPP(_1415595, _1415591), _1415593)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415597, tc_fun(_1415599, tc_HOL_Obool))), _1415589), _1415595), _1415591), _1415593)))], (16933 ^ _780119) ^ [_1087755, _1087757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1087755)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1087757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1087757), _1087755)), _1087757)))], (8052 ^ _780119) ^ [_917783, _917785] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_917783, _917785))), 8055 ^ _780119 : [(8058 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _917785)))], (8056 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _917783)))]]], (33851 ^ _780119) ^ [_1415075, _1415077, _1415079, _1415081, _1415083, _1415085] : [33852 ^ _780119 : [(33855 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1415081, _1415077), _1415079))], (33853 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1415075, _1415077), _1415079))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415083, tc_fun(_1415085, tc_HOL_Obool))), _1415081), _1415075), _1415077), _1415079)))], (12849 ^ _780119) ^ [_1013163, _1013165, _1013167] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1013163), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013163, tc_HOL_Obool)), _1013165), _1013167))), -(hAPP(c_Finite__Set_Ocard(_1013163), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013163, tc_HOL_Obool)), _1013165), _1013167)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1013163), _1013165)), hAPP(c_Finite__Set_Ocard(_1013163), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013163, tc_HOL_Obool)), _1013165), _1013167))))], (45934 ^ _780119) ^ [_1705075, _1705077, _1705079] : [-(hAPP(c_List_Otl(_1705075), hAPP(hAPP(c_List_Oappend(_1705075), _1705077), _1705079)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1705075), _1705075, hAPP(c_List_Otl(_1705075), _1705079), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1705075), tc_List_Olist(_1705075)), _1705075), hAPP(hAPP(c_COMBC(tc_List_Olist(_1705075), tc_List_Olist(_1705075), tc_List_Olist(_1705075)), c_List_Oappend(_1705075)), _1705079))), _1705077))], (34401 ^ _780119) ^ [_1425584] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1425584)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1425584)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51309 ^ _780119) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (19961 ^ _780119) ^ [_1143056, _1143058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1143056)), 19964 ^ _780119 : [(19971 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143058), _1143056))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143058), _1143056) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1143058), _1143056)), _1143056)))], (19965 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143058), _1143056)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143058), _1143056) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5270 ^ _780119) ^ [_860721, _860723, _860725, _860727] : [-(c_List_Oupt(_860727, _860723) = c_List_Oupt(_860725, _860721)), _860727 = _860725, _860723 = _860721], (12677 ^ _780119) ^ [_1009858, _1009860, _1009862] : [c_Map_Odom(_1009858, _1009860, _1009862) = c_Orderings_Obot__class_Obot(tc_fun(_1009858, tc_HOL_Obool)), -(_1009862 = hAPP(c_COMBK(tc_Option_Ooption(_1009860), _1009858), c_Option_Ooption_ONone(_1009860)))], (43547 ^ _780119) ^ [_1647999, _1648001, _1648003, _1648005, _1648007] : [-(hAPP(hAPP(c_List_Omap(_1647999, _1648001), _1648003), hAPP(hAPP(c_List_Olist_OCons(_1647999), _1648005), _1648007)) = hAPP(hAPP(c_List_Olist_OCons(_1648001), hAPP(_1648003, _1648005)), hAPP(hAPP(c_List_Omap(_1647999, _1648001), _1648003), _1648007)))], (7972 ^ _780119) ^ [_916086, _916088] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916086, tc_HOL_Obool)), _916088), _916088) = c_Orderings_Obot__class_Obot(tc_fun(_916086, tc_HOL_Obool)))], (23769 ^ _780119) ^ [_1214418, _1214420, _1214422, _1214424] : [class_Orderings_Olinorder(_1214418), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214418), _1214420), _1214422)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214418), _1214422), _1214424)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1214418, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1214418, _1214420), _1214422)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1214418, _1214422), _1214424)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1214418, _1214420), _1214424))], (6185 ^ _780119) ^ [_878846, _878848, _878850, _878852, _878854] : [hBOOL(hAPP(hAPP(c_member(_878846), _878848), _878850)), -(hBOOL(hAPP(hAPP(c_member(_878852), hAPP(_878854, _878848)), hAPP(c_Set_Oimage(_878846, _878852, _878854), _878850))))], (10895 ^ _780119) ^ [_973456, _973458, _973460, _973462, _973464] : [class_Groups_Oordered__cancel__ab__semigroup__add(_973456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973456), _973458), _973460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973456), _973462), _973464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973456), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973456), _973458), _973462)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973456), _973460), _973464))))], (39367 ^ _780119) ^ [_1545645, _1545647, _1545649, _1545651, _1545653] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1545645, _1545647, _1545645, _1545649), hAPP(c_Product__Type_OPair(_1545647, _1545645), _1545651)), _1545653) = hAPP(_1545653, _1545651))], (51321 ^ _780119) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (4764 ^ _780119) ^ [_852742, _852744, _852746, _852748, _852750, _852752, _852754, _852756] : [-(c_Fun_Ocomp(_852756, _852752, _852748, _852744) = c_Fun_Ocomp(_852754, _852750, _852746, _852742)), _852756 = _852754, _852752 = _852750, _852748 = _852746, _852744 = _852742], (31959 ^ _780119) ^ [_1375800, _1375802] : [class_Int_Onumber__ring(_1375800), class_Rings_Olinordered__idom(_1375800), 31966 ^ _780119 : [(31973 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1375802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1375800), c_Groups_Oone__class_Oone(_1375800)), hAPP(c_Int_Onumber__class_Onumber__of(_1375800), _1375802))))], (31967 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1375800), c_Groups_Oone__class_Oone(_1375800)), hAPP(c_Int_Onumber__class_Onumber__of(_1375800), _1375802))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1375802)))]]], (37817 ^ _780119) ^ [_1506709, _1506711, _1506713] : [c_Equiv__Relations_Oequiv(_1506709, _1506711, _1506713), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1506709, _1506709), tc_HOL_Obool)), _1506713), hAPP(hAPP(c_Product__Type_OSigma(_1506709, _1506709), _1506711), hAPP(c_COMBK(tc_fun(_1506709, tc_HOL_Obool), _1506709), _1506711)))))], (2332 ^ _780119) ^ [_814448, _814450] : [_814450 = _814448, -(c_Int_Opred(_814450) = c_Int_Opred(_814448))], (41272 ^ _780119) ^ [_1590701, _1590703, _1590705, _1590707, _1590709] : [-(hAPP(hAPP(c_Set_Oinsert(_1590701), _1590703), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590705, tc_fun(_1590701, tc_HOL_Obool)), _1590707), _1590709)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590705, tc_fun(_1590701, tc_HOL_Obool)), _1590707), hAPP(hAPP(c_COMBB(tc_fun(_1590701, tc_HOL_Obool), tc_fun(_1590701, tc_HOL_Obool), _1590705), hAPP(c_Set_Oinsert(_1590701), _1590703)), _1590709)))], (27498 ^ _780119) ^ [_1288219] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1288219) = c_Orderings_Oord__class_Omax(_1288219)), class_Lattices_Osemilattice__sup(_1288219), class_Orderings_Olinorder(_1288219)], (2168 ^ _780119) ^ [_811866, _811868, _811870, _811872, _811874, _811876, _811878, _811880] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_811880, _811876, _811872, _811868) = c_SetInterval_Oord_OgreaterThanLessThan(_811878, _811874, _811870, _811866)), _811880 = _811878, _811876 = _811874, _811872 = _811870, _811868 = _811866], (38814 ^ _780119) ^ [_1532240, _1532242, _1532244, _1532246, _1532248, _1532250] : [-(hAPP(c_Set_Oimage(_1532240, _1532242, hAPP(c_Fun_Ocomp(_1532244, _1532242, _1532240, _1532246), _1532248)), _1532250) = hAPP(c_Set_Oimage(_1532244, _1532242, _1532246), hAPP(c_Set_Oimage(_1532240, _1532244, _1532248), _1532250)))], (23531 ^ _780119) ^ [_1210348, _1210350, _1210352, _1210354, _1210356] : [class_Orderings_Olinorder(_1210348), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1210348, _1210350), _1210352) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1210348, _1210354), _1210356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210348), _1210350), _1210352)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210348), _1210354), _1210356)), -(_1210350 = _1210354)], (28924 ^ _780119) ^ [_1316173, _1316175, _1316177] : [class_Orderings_Olinorder(_1316173), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316173), _1316175)), -(_1316175 = c_Orderings_Obot__class_Obot(tc_fun(_1316173, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1316173, c_Orderings_Oord__class_Omax(_1316173), hAPP(hAPP(c_Set_Oinsert(_1316173), _1316177), _1316175)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1316173), _1316177), c_Big__Operators_Olattice_OSup__fin(_1316173, c_Orderings_Oord__class_Omax(_1316173), _1316175)))], (24957 ^ _780119) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11792 ^ _780119) ^ [_992421, _992423] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992421), _992423))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992423), _992421)))], (51187 ^ _780119) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (50370 ^ _780119) ^ [_1801349, _1801351, _1801353] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1801349), _1801351))), -(hBOOL(hAPP(hAPP(_1801353, _1801349), _1801351))), 50377 ^ _780119 : [(50386 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1801353, 50375 ^ [_1801349, _1801351, _1801353]), 50376 ^ [_1801349, _1801351, _1801353]))], (50380 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 50375 ^ [_1801349, _1801351, _1801353]), 50376 ^ [_1801349, _1801351, _1801353]))), -(hBOOL(hAPP(hAPP(_1801353, 50375 ^ [_1801349, _1801351, _1801353]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 50376 ^ [_1801349, _1801351, _1801353]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50378 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 50375 ^ [_1801349, _1801351, _1801353]), 50376 ^ [_1801349, _1801351, _1801353]))))]]], (47498 ^ _780119) ^ [_1737951, _1737953] : [_1737953 = c_List_Olist_ONil(_1737951), -(hAPP(c_List_Orev(_1737951), _1737953) = c_List_Olist_ONil(_1737951))], (29298 ^ _780119) ^ [_1323417, _1323419] : [class_Orderings_Olinorder(_1323417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323417), _1323419)), -(_1323419 = c_Orderings_Obot__class_Obot(tc_fun(_1323417, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1323417), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1323417), 29311 ^ [_1323417, _1323419]), 29312 ^ [_1323417, _1323419])), hAPP(hAPP(c_Set_Oinsert(_1323417), 29311 ^ [_1323417, _1323419]), hAPP(hAPP(c_Set_Oinsert(_1323417), 29312 ^ [_1323417, _1323419]), c_Orderings_Obot__class_Obot(tc_fun(_1323417, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1323417), c_Big__Operators_Olinorder__class_OMax(_1323417, _1323419)), _1323419)))], (8114 ^ _780119) ^ [_919012, _919014, _919016, _919018] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919012, tc_HOL_Obool)), _919014), hAPP(hAPP(c_Set_Oinsert(_919012), _919016), _919018)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919012, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919012, tc_HOL_Obool)), _919014), hAPP(hAPP(c_Set_Oinsert(_919012), _919016), c_Orderings_Obot__class_Obot(tc_fun(_919012, tc_HOL_Obool))))), _919018))], (33659 ^ _780119) ^ [_1411059] : [c_Code__Numeral_OSuc__code__numeral(_1411059) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (29574 ^ _780119) ^ [_1329213, _1329215, _1329217, _1329219, _1329221, _1329223] : [hBOOL(hAPP(hAPP(c_member(_1329213), _1329215), _1329217)), hBOOL(hAPP(hAPP(c_member(_1329219), _1329221), hAPP(_1329223, _1329215))), -(hBOOL(hAPP(hAPP(c_member(_1329219), _1329221), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1329213, tc_fun(_1329219, tc_HOL_Obool)), _1329217), _1329223))))], (46947 ^ _780119) ^ [_1726852, _1726854, _1726856] : [class_Orderings_Olinorder(_1726852), c_List_Olinorder__class_Osorted(_1726852, _1726854), -(c_List_Olinorder__class_Osorted(_1726852, c_List_Olinorder__class_Oinsort__insert__key(_1726852, _1726852, c_COMBI(_1726852), _1726856, _1726854)))], (16897 ^ _780119) ^ [_1087222, _1087224] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1087222), _1087224))), -(hAPP(c_Finite__Set_Ocard(_1087222), _1087224) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29318 ^ _780119) ^ [_1323861, _1323863] : [class_Orderings_Olinorder(_1323861), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323861), _1323863)), -(_1323863 = c_Orderings_Obot__class_Obot(tc_fun(_1323861, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1323861), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1323861), 29331 ^ [_1323861, _1323863]), 29332 ^ [_1323861, _1323863])), hAPP(hAPP(c_Set_Oinsert(_1323861), 29331 ^ [_1323861, _1323863]), hAPP(hAPP(c_Set_Oinsert(_1323861), 29332 ^ [_1323861, _1323863]), c_Orderings_Obot__class_Obot(tc_fun(_1323861, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1323861), c_Big__Operators_Olinorder__class_OMin(_1323861, _1323863)), _1323863)))], (1470 ^ _780119) ^ [_801218, _801220] : [-(class_Groups_Oordered__ab__semigroup__add(_801218)), _801220 = _801218, class_Groups_Oordered__ab__semigroup__add(_801220)], (26819 ^ _780119) ^ [_1270475, _1270477] : [-(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), _1270475)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1270477))))))], (12489 ^ _780119) ^ [_1005812, _1005814, _1005816, _1005818, _1005820] : [-(hBOOL(hAPP(hAPP(c_member(_1005812), _1005814), _1005816))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1005812, tc_Option_Ooption(_1005818)), c_Map_Orestrict__map(_1005812, _1005818, _1005820, _1005816)), _1005814), c_Option_Ooption_ONone(_1005818)) = c_Map_Orestrict__map(_1005812, _1005818, _1005820, _1005816))], (39709 ^ _780119) ^ [_1554060, _1554062] : [-(c_Transitive__Closure_Ortrancl(_1554060, c_Transitive__Closure_Ortrancl(_1554060, _1554062)) = c_Transitive__Closure_Ortrancl(_1554060, _1554062))], (40299 ^ _780119) ^ [_1568648, _1568650, _1568652, _1568654, _1568656] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568648, _1568648)), hAPP(hAPP(c_Product__Type_OPair(_1568648, _1568648), _1568650), _1568652)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1568648, _1568648), tc_HOL_Obool), _1568654), _1568656))), 40304 ^ _780119 : [(40307 ^ _780119) ^ [] : [-(_1568650 = _1568652)], (40305 ^ _780119) ^ [] : [-(_1568654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 40310 ^ _780119 : [(40313 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568648, _1568648)), hAPP(hAPP(c_Product__Type_OPair(_1568648, _1568648), _1568650), 40308 ^ [_1568648, _1568650, _1568652, _1568654, _1568656])), _1568656)))], (40315 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568648, _1568648)), hAPP(hAPP(c_Product__Type_OPair(_1568648, _1568648), 40308 ^ [_1568648, _1568650, _1568652, _1568654, _1568656]), _1568652)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1568648, _1568648), tc_HOL_Obool), 40309 ^ [_1568648, _1568650, _1568652, _1568654, _1568656]), _1568656))))], (40311 ^ _780119) ^ [] : [-(_1568654 = hAPP(c_Nat_OSuc, 40309 ^ [_1568648, _1568650, _1568652, _1568654, _1568656]))]]], (36219 ^ _780119) ^ [_1467084, _1467086, _1467088, _1467090] : [c_Fun_Oinj__on(_1467084, _1467086, _1467088, c_Orderings_Otop__class_Otop(tc_fun(_1467084, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1467084, tc_fun(_1467090, _1467086), hAPP(hAPP(c_COMBB(_1467086, tc_fun(_1467090, _1467086), _1467084), c_COMBK(_1467086, _1467090)), _1467088), c_Orderings_Otop__class_Otop(tc_fun(_1467084, tc_HOL_Obool))))], (37944 ^ _780119) ^ [_1510246, _1510248, _1510250, _1510252] : [-(_1510246 = c_Orderings_Obot__class_Obot(tc_fun(_1510248, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1510250, _1510248), _1510250, c_Product__Type_Ofst(_1510250, _1510248)), hAPP(hAPP(c_Product__Type_OSigma(_1510250, _1510248), _1510252), hAPP(c_COMBK(tc_fun(_1510248, tc_HOL_Obool), _1510250), _1510246))) = _1510252)], (17642 ^ _780119) ^ [_1100823, _1100825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1100823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1100825)), -(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), _1100825), _1100823))))], (15108 ^ _780119) ^ [_1056760] : [class_Rings_Ozero__neq__one(_1056760), c_Groups_Ozero__class_Ozero(_1056760) = c_Groups_Oone__class_Oone(_1056760)], (43595 ^ _780119) ^ [_1649029, _1649031, _1649033, _1649035, _1649037, _1649039] : [_1649029 = _1649031, -(hAPP(hAPP(c_Map_Omap__of(_1649033, _1649035), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1649033, _1649035)), hAPP(hAPP(c_Product__Type_OPair(_1649033, _1649035), _1649029), _1649037)), _1649039)), _1649031) = hAPP(c_Option_Ooption_OSome(_1649035), _1649037))], (21482 ^ _780119) ^ [_1171715, _1171717, _1171719, _1171721, _1171723, _1171725] : [class_Divides_Osemiring__div(_1171715), c_Divides_Odiv__class_Omod(_1171715, _1171717, _1171719) = c_Divides_Odiv__class_Omod(_1171715, _1171721, _1171719), c_Divides_Odiv__class_Omod(_1171715, _1171723, _1171719) = c_Divides_Odiv__class_Omod(_1171715, _1171725, _1171719), -(c_Divides_Odiv__class_Omod(_1171715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171715), _1171717), _1171723), _1171719) = c_Divides_Odiv__class_Omod(_1171715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171715), _1171721), _1171725), _1171719))], (45802 ^ _780119) ^ [_1702760, _1702762, _1702764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702760), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702762)), _1702764))), -(hAPP(hAPP(c_List_Oappend(_1702762), hAPP(hAPP(c_List_Otake(_1702762), _1702760), _1702764)), hAPP(hAPP(c_List_Olist_OCons(_1702762), hAPP(c_List_Ohd(_1702762), hAPP(hAPP(c_List_Odrop(_1702762), _1702760), _1702764))), c_List_Olist_ONil(_1702762))) = hAPP(hAPP(c_List_Otake(_1702762), hAPP(c_Nat_OSuc, _1702760)), _1702764))], (1500 ^ _780119) ^ [_801593, _801595] : [-(class_Rings_Oordered__cancel__semiring(_801593)), _801595 = _801593, class_Rings_Oordered__cancel__semiring(_801595)], (13482 ^ _780119) ^ [_1025440, _1025442, _1025444] : [class_Rings_Oring(_1025440), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1025440), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025440), _1025442), _1025444)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025440), hAPP(c_Groups_Ouminus__class_Ouminus(_1025440), _1025442)), _1025444))], (2424 ^ _780119) ^ [_815834, _815836, _815838, _815840] : [-(c_Set_Othe__elem(_815840, _815836) = c_Set_Othe__elem(_815838, _815834)), _815840 = _815838, _815836 = _815834], (51335 ^ _780119) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (44416 ^ _780119) ^ [_1670032, _1670034, _1670036, _1670038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670032), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670034)), _1670036))), 44419 ^ _780119 : [(44426 ^ _780119) ^ [] : [hAPP(hAPP(c_List_Onth(_1670034), _1670036), _1670032) = _1670038, -(hAPP(hAPP(c_List_Olist__update(_1670034, _1670036), _1670032), _1670038) = _1670036)], (44420 ^ _780119) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1670034, _1670036), _1670032), _1670038) = _1670036, -(hAPP(hAPP(c_List_Onth(_1670034), _1670036), _1670032) = _1670038)]]], (41687 ^ _780119) ^ [_1602352, _1602354, _1602356] : [class_Complete__Lattice_Ocomplete__lattice(_1602352), 41690 ^ _780119 : [(41691 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1602352), c_Complete__Lattice_OSup__class_OSup(_1602352, _1602354)), _1602356)), 41694 ^ _780119 : [(41695 ^ _780119) ^ [_1602510] : [hBOOL(hAPP(hAPP(c_member(_1602352), _1602510), _1602354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1602352), _1602510), _1602356)))]]], (41701 ^ _780119) ^ [] : [41703 ^ _780119 : [(41706 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1602352), 41702 ^ [_1602352, _1602354, _1602356]), _1602356))], (41704 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602352), 41702 ^ [_1602352, _1602354, _1602356]), _1602354)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1602352), c_Complete__Lattice_OSup__class_OSup(_1602352, _1602354)), _1602356)))]]], (25744 ^ _780119) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (25169 ^ _780119) ^ [_1240807, _1240809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1240807), hAPP(c_Int_Onat, _1240809))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1240807)), _1240809)))], (29887 ^ _780119) ^ [_1337809, _1337811, _1337813, _1337815, _1337817] : [-(_1337809 = c_Orderings_Obot__class_Obot(tc_fun(_1337811, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337811, tc_fun(_1337813, tc_HOL_Obool)), _1337809), hAPP(hAPP(c_COMBB(tc_fun(_1337813, tc_HOL_Obool), tc_fun(_1337813, tc_HOL_Obool), _1337811), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337813, tc_HOL_Obool)), _1337815)), _1337817)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337813, tc_HOL_Obool)), _1337815), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337811, tc_fun(_1337813, tc_HOL_Obool)), _1337809), _1337817)))], (22940 ^ _780119) ^ [_1199079, _1199081] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199079)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199081)), _1199079 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1199081 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43721 ^ _780119) ^ [_1653020, _1653022, _1653024] : [class_Groups_Omonoid__add(_1653020), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1653020), hAPP(hAPP(c_List_Olist_OCons(_1653020), _1653022), _1653024)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1653020), _1653022), hAPP(c_List_Omonoid__add__class_Olistsum(_1653020), _1653024)))], (28272 ^ _780119) ^ [_1302752, _1302754, _1302756, _1302758] : [class_Orderings_Olinorder(_1302752), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302752, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1302752, _1302754, _1302756)), hAPP(c_SetInterval_Oord__class_OatLeast(_1302752), _1302758)) = c_SetInterval_Oord__class_OatLeastAtMost(_1302752, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1302752), _1302754), _1302758), _1302756))], (50424 ^ _780119) ^ [_1802680, _1802682, _1802684, _1802686, _1802688] : [hBOOL(hAPP(hAPP(_1802680, _1802682), _1802684)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1802686, _1802688, _1802680), _1802684), _1802682)))], (45648 ^ _780119) ^ [_1698817, _1698819] : [-(hAPP(hAPP(c_List_Odrop(_1698817), _1698819), c_List_Olist_ONil(_1698817)) = c_List_Olist_ONil(_1698817))], (8452 ^ _780119) ^ [_926879, _926881, _926883, _926885, _926887] : [c_Finite__Set_Ofun__left__comm__idem(_926879, _926881, _926883), -(hAPP(hAPP(_926883, _926885), hAPP(hAPP(_926883, _926885), _926887)) = hAPP(hAPP(_926883, _926885), _926887))], (10004 ^ _780119) ^ [_954355, _954357, _954359] : [class_Lattices_Osemilattice__inf(_954355), 10007 ^ _780119 : [(10014 ^ _780119) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954355), _954357), _954359) = _954357, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954355), _954357), _954359)))], (10008 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954355), _954357), _954359)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954355), _954357), _954359) = _954357)]]], (12996 ^ _780119) ^ [_1016187, _1016189, _1016191, _1016193, _1016195] : [_1016187 = c_Option_Ooption_ONone(_1016189), -(c_Map_Odom(_1016191, _1016189, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1016191, tc_Option_Ooption(_1016189)), _1016193), _1016195), _1016187)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016191, tc_HOL_Obool)), c_Map_Odom(_1016191, _1016189, _1016193)), hAPP(hAPP(c_Set_Oinsert(_1016191), _1016195), c_Orderings_Obot__class_Obot(tc_fun(_1016191, tc_HOL_Obool)))))], (41393 ^ _780119) ^ [_1594871, _1594873, _1594875, _1594877, _1594879] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1594871, tc_fun(_1594873, tc_HOL_Obool)), _1594875), hAPP(hAPP(c_COMBB(tc_fun(_1594873, tc_HOL_Obool), tc_fun(_1594873, tc_HOL_Obool), _1594871), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1594873, tc_HOL_Obool)), _1594877)), _1594879)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1594873, tc_HOL_Obool)), _1594877), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594871, tc_fun(_1594873, tc_HOL_Obool)), _1594875), _1594879)))], (20588 ^ _780119) ^ [_1154381, _1154383, _1154385, _1154387, _1154389] : [class_Fields_Ofield(_1154381), -(_1154383 = c_Groups_Ozero__class_Ozero(_1154381)), -(_1154385 = c_Groups_Ozero__class_Ozero(_1154381)), 20599 ^ _780119 : [(20606 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154381), _1154387), _1154385) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154381), _1154389), _1154383), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154381), _1154387), _1154383) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154381), _1154389), _1154385))], (20600 ^ _780119) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154381), _1154387), _1154383) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154381), _1154389), _1154385), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154381), _1154387), _1154385) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154381), _1154389), _1154383))]]], (44778 ^ _780119) ^ [_1676902, _1676904, _1676906] : [-(hAPP(hAPP(c_Map_Omap__of(_1676902, _1676904), c_List_Olist_ONil(tc_prod(_1676902, _1676904))), _1676906) = c_Option_Ooption_ONone(_1676904))], (41655 ^ _780119) ^ [_1601655, _1601657, _1601659] : [41657 ^ _780119 : [(41660 ^ _780119) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1601655, tc_HOL_Obool)), 41656 ^ [_1601655, _1601657, _1601659]), _1601659) = c_Orderings_Obot__class_Obot(tc_fun(_1601655, tc_HOL_Obool))], (41658 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1601655, tc_HOL_Obool)), 41656 ^ [_1601655, _1601657, _1601659]), _1601657)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1601655, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1601655, tc_HOL_Obool), _1601657)), _1601659) = c_Orderings_Obot__class_Obot(tc_fun(_1601655, tc_HOL_Obool)))], (35542 ^ _780119) ^ [_1451514, _1451516] : [-(c_Relation_OId__on(_1451514, _1451516) = hAPP(c_Product__Type_Oprod_Oprod__case(_1451514, _1451514, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1451514, tc_HOL_Obool, tc_fun(_1451514, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451514, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1451514, tc_HOL_Obool)), _1451514), c_COMBC(_1451514, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451514, tc_HOL_Obool), tc_fun(_1451514, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1451514), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1451514), c_fconj)), c_fequal))), _1451516)))], (22865 ^ _780119) ^ [_1197663, _1197665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197663)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197663), _1197665)))], (41619 ^ _780119) ^ [_1600488, _1600490, _1600492, _1600494] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600488, tc_fun(_1600490, tc_HOL_Obool)), _1600492), _1600494) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1600490, tc_HOL_Obool), hAPP(c_Set_Oimage(_1600488, tc_fun(_1600490, tc_HOL_Obool), _1600494), _1600492)))], (31887 ^ _780119) ^ [_1374624, _1374626] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374624), c_Int_OPls))), 31890 ^ _780119 : [(31897 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374626), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374624)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374626)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1374624), _1374626)))], (31891 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374626), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374624)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374626)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374624))]]], (9308 ^ _780119) ^ [_940279, _940281, _940283, _940285, _940287] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_940279, _940281, _940283, _940285, c_Orderings_Obot__class_Obot(tc_fun(_940279, tc_HOL_Obool))), _940287)), -(_940287 = _940285)], (692 ^ _780119) ^ [_790749, _790751] : [-(class_Lattices_Oab__semigroup__idem__mult(_790749)), _790751 = _790749, class_Lattices_Oab__semigroup__idem__mult(_790751)], (12363 ^ _780119) ^ [_1003732, _1003734] : [-(_1003732 = _1003734), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003732), _1003734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003734), _1003732)))], (29735 ^ _780119) ^ [_1333343, _1333345, _1333347, _1333349] : [_1333343 = c_Orderings_Obot__class_Obot(tc_fun(_1333345, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1333345, tc_fun(_1333347, tc_HOL_Obool)), _1333343), hAPP(c_COMBK(tc_fun(_1333347, tc_HOL_Obool), _1333345), _1333349)) = c_Orderings_Obot__class_Obot(tc_fun(_1333347, tc_HOL_Obool)))], (7784 ^ _780119) ^ [_912311, _912313] : [-(c_HOL_OThe(_912311, hAPP(c_fequal, _912313)) = _912313)], (31469 ^ _780119) ^ [_1368164, _1368166] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368164), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368166)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368164)) = 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), _1368166), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1368164)))), 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)))], (37938 ^ _780119) ^ [_1510089, _1510091, _1510093, _1510095] : [_1510089 = c_Orderings_Obot__class_Obot(tc_fun(_1510091, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1510093, _1510091), _1510093, c_Product__Type_Ofst(_1510093, _1510091)), hAPP(hAPP(c_Product__Type_OSigma(_1510093, _1510091), _1510095), hAPP(c_COMBK(tc_fun(_1510091, tc_HOL_Obool), _1510093), _1510089))) = c_Orderings_Obot__class_Obot(tc_fun(_1510093, tc_HOL_Obool)))], (31677 ^ _780119) ^ [] : [-(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))))], (15816 ^ _780119) ^ [_1068248, _1068250, _1068252, _1068254] : [class_Rings_Oordered__semiring(_1068248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068248), _1068250), _1068252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068248), c_Groups_Ozero__class_Ozero(_1068248)), _1068254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068248), _1068254), _1068250)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068248), _1068254), _1068252))))], (3532 ^ _780119) ^ [_833220, _833222, _833224, _833226] : [-(c_Complete__Lattice_OInf__class_OInf(_833226, _833222) = c_Complete__Lattice_OInf__class_OInf(_833224, _833220)), _833226 = _833224, _833222 = _833220], (49497 ^ _780119) ^ [_1783066, _1783068, _1783070, _1783072] : [49499 ^ _780119 : [(49502 ^ _780119) ^ [] : [hBOOL(hAPP(_1783070, 49498 ^ [_1783066, _1783068, _1783070, _1783072]))], (49500 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1783066), 49498 ^ [_1783066, _1783068, _1783070, _1783072]), hAPP(c_List_Oset(_1783066), _1783068))))]], -(c_List_OtakeWhile(_1783066, _1783070, hAPP(hAPP(c_List_Oappend(_1783066), _1783068), _1783072)) = hAPP(hAPP(c_List_Oappend(_1783066), _1783068), c_List_OtakeWhile(_1783066, _1783070, _1783072)))], (38744 ^ _780119) ^ [_1530743, _1530745, _1530747, _1530749, _1530751, _1530753, _1530755] : [hAPP(c_Fun_Ocomp(_1530743, _1530745, _1530747, _1530749), _1530751) = _1530753, -(hAPP(_1530749, hAPP(_1530751, _1530755)) = hAPP(_1530753, _1530755))], (41361 ^ _780119) ^ [_1593899, _1593901, _1593903, _1593905, _1593907, _1593909] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593899, tc_fun(_1593901, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1593903, _1593899, _1593905), _1593907)), _1593909) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593903, tc_fun(_1593901, tc_HOL_Obool)), _1593907), hAPP(hAPP(c_COMBB(_1593899, tc_fun(_1593901, tc_HOL_Obool), _1593903), _1593909), _1593905)))], (10572 ^ _780119) ^ [_967023, _967025, _967027, _967029, _967031, _967033] : [hBOOL(hAPP(hAPP(c_member(_967023), _967025), _967027)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_967023, tc_Option_Ooption(_967029)), c_Map_Orestrict__map(_967023, _967029, _967031, _967027)), _967025), _967033) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_967023, tc_Option_Ooption(_967029)), c_Map_Orestrict__map(_967023, _967029, _967031, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967023, tc_HOL_Obool)), _967027), hAPP(hAPP(c_Set_Oinsert(_967023), _967025), c_Orderings_Obot__class_Obot(tc_fun(_967023, tc_HOL_Obool)))))), _967025), _967033))], (37221 ^ _780119) ^ [_1491689, _1491691] : [-(c_Wellfounded_Owf(_1491689, hAPP(c_Wellfounded_Omeasure(_1491689), _1491691)))], (35444 ^ _780119) ^ [_1448931, _1448933, _1448935, _1448937] : [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), _1448931), _1448933)), 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), _1448935), _1448937)), 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), _1448931), _1448937)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1448935), _1448933))))], (40628 ^ _780119) ^ [_1576701, _1576703, _1576705, _1576707] : [class_Orderings_Olinorder(_1576701), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576701), _1576703)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1576701, _1576701, c_Orderings_Oord__class_Omax(_1576701)), _1576705), hAPP(hAPP(c_Set_Oinsert(_1576701), _1576707), _1576703)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1576701), _1576707), hAPP(hAPP(c_Finite__Set_Ofold(_1576701, _1576701, c_Orderings_Oord__class_Omax(_1576701)), _1576705), _1576703)))], (31905 ^ _780119) ^ [] : [-(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)))))], (12667 ^ _780119) ^ [_1009631, _1009633, _1009635] : [-(hAPP(c_Finite__Set_Ofold1(_1009631, _1009633), hAPP(hAPP(c_Set_Oinsert(_1009631), _1009635), c_Orderings_Obot__class_Obot(tc_fun(_1009631, tc_HOL_Obool)))) = _1009635)], (24265 ^ _780119) ^ [_1224401, _1224403, _1224405, _1224407] : [class_Orderings_Olinorder(_1224401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224401), _1224403), _1224405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224401), _1224405), _1224407)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1224401, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1224401, _1224403, _1224405)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1224401, _1224405), _1224407)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1224401, _1224403, _1224407))], (40489 ^ _780119) ^ [_1573696, _1573698, _1573700, _1573702] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573696, _1573696)), hAPP(hAPP(c_Product__Type_OPair(_1573696, _1573696), _1573698), _1573700)), c_Transitive__Closure_Otrancl(_1573696, _1573702))), 40493 ^ _780119 : [(40496 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573696, _1573696)), hAPP(hAPP(c_Product__Type_OPair(_1573696, _1573696), 40492 ^ [_1573696, _1573698, _1573700, _1573702]), _1573700)), _1573702)))], (40494 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573696, _1573696)), hAPP(hAPP(c_Product__Type_OPair(_1573696, _1573696), _1573698), 40492 ^ [_1573696, _1573698, _1573700, _1573702])), c_Transitive__Closure_Ortrancl(_1573696, _1573702))))]]], (7512 ^ _780119) ^ [_906443, _906445, _906447] : [class_Lattices_Osemilattice__sup(_906443), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906443), _906445), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_906443), _906447), _906445))))], (43164 ^ _780119) ^ [_1636937, _1636939, _1636941, _1636943, _1636945, _1636947] : [class_Orderings_Olinorder(_1636937), -(hAPP(_1636939, _1636941) = hAPP(_1636939, _1636943)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1636945, _1636937, _1636939), _1636943), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1636945, _1636937, _1636939), _1636941), _1636947)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1636945, _1636937, _1636939), _1636941), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1636945, _1636937, _1636939), _1636943), _1636947)))], (18988 ^ _780119) ^ [_1126195, _1126197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126195), _1126197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126197), _1126195)), -(_1126195 = _1126197)], (26813 ^ _780119) ^ [_1270254, _1270256] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1270254, tc_HOL_Obool)), _1270256) = hAPP(c_Set_OCollect(_1270254), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1270254), c_fNot), hAPP(hAPP(c_COMBC(_1270254, tc_fun(_1270254, tc_HOL_Obool), tc_HOL_Obool), c_member(_1270254)), _1270256))))], (50686 ^ _780119) ^ [_1808099, _1808101, _1808103] : [_1808099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1808101), c_List_Oreplicate(_1808101, _1808099, _1808103)) = c_Orderings_Obot__class_Obot(tc_fun(_1808101, tc_HOL_Obool)))], (22344 ^ _780119) ^ [_1187850, _1187852, _1187854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1187850, tc_HOL_Obool)), _1187852), _1187854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1187850, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1187850, _1187852)), c_Predicate_OPowp(_1187850, _1187854))))], (12559 ^ _780119) ^ [_1007565, _1007567, _1007569] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007565), _1007567)), hBOOL(hAPP(hAPP(c_member(_1007565), _1007569), _1007567)), -(hAPP(c_Finite__Set_Ocard(_1007565), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007565, tc_HOL_Obool)), _1007567), hAPP(hAPP(c_Set_Oinsert(_1007565), _1007569), c_Orderings_Obot__class_Obot(tc_fun(_1007565, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1007565), _1007567)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (33465 ^ _780119) ^ [_1403277, _1403279] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1403277), _1403279) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 33466 ^ _780119 : [(33473 ^ _780119) ^ [] : [_1403277 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1403279 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (33467 ^ _780119) ^ [] : [_1403277 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1403279 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (24107 ^ _780119) ^ [_1221457, _1221459] : [24115 ^ _780119 : [(24118 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1221459, 24114 ^ [_1221457, _1221459])))], (24116 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24114 ^ [_1221457, _1221459]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1221457))))]], 24108 ^ _780119 : [(24109 ^ _780119) ^ [_1221526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221526), _1221457)), hBOOL(hAPP(_1221459, _1221526))]]], (23368 ^ _780119) ^ [_1207110, _1207112] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207110)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1207112))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1207110), _1207112)))], (15102 ^ _780119) ^ [_1056665, _1056667] : [class_Groups_Ogroup__add(_1056665), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056665), _1056667), c_Groups_Ozero__class_Ozero(_1056665)) = _1056667)], (11908 ^ _780119) ^ [_994495, _994497, _994499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994497), _994499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994495), _994497)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994495), _994499))))], (39713 ^ _780119) ^ [_1554141, _1554143, _1554145] : [-(c_Transitive__Closure_Ortrancl(_1554141, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554141, _1554141), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1554141, _1554143)), c_Transitive__Closure_Ortrancl(_1554141, _1554145))) = c_Transitive__Closure_Ortrancl(_1554141, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554141, _1554141), tc_HOL_Obool)), _1554143), _1554145)))], (47813 ^ _780119) ^ [_1746180, _1746182, _1746184, _1746186] : [hBOOL(hAPP(hAPP(c_member(_1746180), _1746182), hAPP(c_List_Oset(_1746180), c_List_OtakeWhile(_1746180, _1746184, _1746186)))), 47816 ^ _780119 : [(47819 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1746184, _1746182)))], (47817 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1746180), _1746182), hAPP(c_List_Oset(_1746180), _1746186))))]]], (16242 ^ _780119) ^ [_1076120, _1076122, _1076124, _1076126] : [class_Rings_Olinordered__semiring__strict(_1076120), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076120), _1076122), _1076124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076120), c_Groups_Ozero__class_Ozero(_1076120)), _1076126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076120), _1076122), _1076126)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076120), _1076124), _1076126))))], (39677 ^ _780119) ^ [_1553214, _1553216] : [-(hAPP(c_Relation_ORange(_1553214, _1553214), c_Transitive__Closure_Ortrancl(_1553214, _1553216)) = c_Orderings_Otop__class_Otop(tc_fun(_1553214, tc_HOL_Obool)))], (16214 ^ _780119) ^ [_1075610, _1075612, _1075614] : [class_Rings_Olinordered__semiring__strict(_1075610), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075610), _1075612), c_Groups_Ozero__class_Ozero(_1075610))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075610), c_Groups_Ozero__class_Ozero(_1075610)), _1075614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075610), _1075612), _1075614)), c_Groups_Ozero__class_Ozero(_1075610))))], (48878 ^ _780119) ^ [_1768702, _1768704, _1768706, _1768708] : [-(hBOOL(hAPP(c_List_Olistsp(_1768702, _1768704), hAPP(hAPP(c_List_Oappend(_1768702), _1768706), _1768708)))), hBOOL(hAPP(c_List_Olistsp(_1768702, _1768704), _1768706)), hBOOL(hAPP(c_List_Olistsp(_1768702, _1768704), _1768708))], (46467 ^ _780119) ^ [_1716747] : [-(c_List_Obutlast(_1716747, c_List_Olist_ONil(_1716747)) = c_List_Olist_ONil(_1716747))], (30227 ^ _780119) ^ [_1344756, _1344758, _1344760, _1344762, _1344764] : [c_Com_Ocom_OWhile(_1344756, _1344758) = c_Com_Ocom_OLocal(_1344760, _1344762, _1344764)], (24337 ^ _780119) ^ [_1225851, _1225853, _1225855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225851)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1225853), _1225855)), 24344 ^ _780119 : [(24345 ^ _780119) ^ [_1226041] : [24347 ^ _780119 : [(24351 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24349 ^ [_1225851, _1225853, _1225855, _1226041]), _1225855)))], (24353 ^ _780119) ^ [] : [-(_1226041 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24349 ^ [_1225851, _1225853, _1225855, _1226041]), 24346 ^ [_1225851, _1225853, _1225855, _1226041]))], (24348 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24346 ^ [_1225851, _1225853, _1225855, _1226041]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1225851))))]], -(_1226041 = _1225853), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226041), _1225851) = _1225853]]], (33355 ^ _780119) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (19987 ^ _780119) ^ [_1143476, _1143478, _1143480] : [hBOOL(hAPP(_1143476, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143478), _1143480))), 19990 ^ _780119 : [(19997 ^ _780119) ^ [] : [-(_1143480 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20000 ^ _780119 : [(20001 ^ _780119) ^ [_1143728, _1143730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143728), _1143480)), _1143478 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143480), _1143730)), _1143728), -(hBOOL(hAPP(_1143476, _1143730)))]]], (19991 ^ _780119) ^ [] : [_1143480 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1143476, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (51591 ^ _780119) ^ [_1820681, _1820683] : [hBOOL(_1820681), hBOOL(_1820683), -(hBOOL(hAPP(hAPP(c_fconj, _1820681), _1820683)))], (37982 ^ _780119) ^ [_1511588, _1511590, _1511592] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1511588), _1511590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511588, _1511588), tc_HOL_Obool)), _1511592), hAPP(hAPP(c_Product__Type_OSigma(_1511588, _1511588), _1511590), hAPP(c_COMBK(tc_fun(_1511588, tc_HOL_Obool), _1511588), _1511590)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1511588, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1511588), _1511590), _1511592))))], (34783 ^ _780119) ^ [_1433012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1433012)), 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), _1433012)) = 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), _1433012))))))], (35965 ^ _780119) ^ [_1461184, _1461186, _1461188, _1461190, _1461192, _1461194, _1461196, _1461198, _1461200] : [c_Equiv__Relations_Oequiv(_1461184, _1461186, _1461188), c_Equiv__Relations_Oequiv(_1461190, _1461192, _1461194), c_Equiv__Relations_Ocongruent2(_1461184, _1461190, tc_fun(_1461196, tc_HOL_Obool), _1461188, _1461194, _1461198), hBOOL(hAPP(hAPP(c_member(_1461190), _1461200), _1461192)), -(c_Equiv__Relations_Ocongruent(_1461184, tc_fun(_1461196, tc_HOL_Obool), _1461188, hAPP(hAPP(c_COMBB(tc_fun(_1461190, tc_fun(_1461196, tc_HOL_Obool)), tc_fun(_1461196, tc_HOL_Obool), _1461184), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1461190, tc_fun(_1461196, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1461190, _1461190, _1461194), hAPP(hAPP(c_Set_Oinsert(_1461190), _1461200), c_Orderings_Obot__class_Obot(tc_fun(_1461190, tc_HOL_Obool)))))), _1461198)))], (15248 ^ _780119) ^ [_1058762, _1058764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1058762), _1058764)), _1058764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41135 ^ _780119) ^ [_1587117, _1587119, _1587121, _1587123, _1587125] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1587117, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587119, tc_fun(_1587117, tc_HOL_Obool)), _1587121), _1587123)), _1587125) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587119, tc_fun(_1587117, tc_HOL_Obool)), _1587121), hAPP(hAPP(c_COMBC(_1587119, tc_fun(_1587117, tc_HOL_Obool), tc_fun(_1587117, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1587117, tc_HOL_Obool), tc_fun(tc_fun(_1587117, tc_HOL_Obool), tc_fun(_1587117, tc_HOL_Obool)), _1587119), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1587117, tc_HOL_Obool))), _1587123)), _1587125)))], (48849 ^ _780119) ^ [_1768094, _1768096] : [-(hBOOL(hAPP(c_List_Olistsp(_1768094, _1768096), c_List_Olist_ONil(_1768094))))], (39377 ^ _780119) ^ [_1546011, _1546013, _1546015, _1546017, _1546019] : [_1546011 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1546013, _1546015, _1546011, _1546017), _1546019) = hAPP(c_Product__Type_OPair(_1546013, _1546015), _1546019))], (44554 ^ _780119) ^ [_1672677, _1672679] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1672677), _1672679) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1672677)), hAPP(c_Code__Numeral_Onat__of, _1672679))))], (22657 ^ _780119) ^ [_1193693] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1193693)), 22661 ^ _780119 : [(22662 ^ _780119) ^ [_1193773] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1193773), _1193693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1193773), 22660 ^ [_1193693])))]]], (42340 ^ _780119) ^ [_1617137, _1617139, _1617141, _1617143] : [class_Rings_Olinordered__semidom(_1617137), 42346 ^ _780119 : [(42349 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1617137), c_Groups_Ozero__class_Ozero(_1617137)), hAPP(_1617143, 42345 ^ [_1617137, _1617139, _1617141, _1617143])))], (42347 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617139), 42345 ^ [_1617137, _1617139, _1617141, _1617143]), _1617141)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1617137), c_Groups_Ozero__class_Ozero(_1617137)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1617139, _1617137), _1617143), _1617141))))], (39673 ^ _780119) ^ [_1553139, _1553141] : [-(hAPP(c_Relation_ODomain(_1553139, _1553139), c_Transitive__Closure_Ortrancl(_1553139, _1553141)) = c_Orderings_Otop__class_Otop(tc_fun(_1553139, tc_HOL_Obool)))], (44906 ^ _780119) ^ [_1679510] : [-(c_List_Olistset(_1679510, c_List_Olist_ONil(tc_fun(_1679510, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1679510)), c_List_Olist_ONil(_1679510)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1679510), tc_HOL_Obool))))], (38585 ^ _780119) ^ [_1527035, _1527037, _1527039, _1527041, _1527043, _1527045] : [hBOOL(hAPP(hAPP(c_member(_1527035), _1527037), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1527039, _1527041, tc_fun(_1527035, tc_HOL_Obool)), _1527043), _1527045))), 38590 ^ _780119 : [(38593 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527035), _1527037), hAPP(hAPP(_1527043, 38588 ^ [_1527035, _1527037, _1527039, _1527041, _1527043, _1527045]), 38589 ^ [_1527035, _1527037, _1527039, _1527041, _1527043, _1527045]))))], (38591 ^ _780119) ^ [] : [-(_1527045 = hAPP(hAPP(c_Product__Type_OPair(_1527039, _1527041), 38588 ^ [_1527035, _1527037, _1527039, _1527041, _1527043, _1527045]), 38589 ^ [_1527035, _1527037, _1527039, _1527041, _1527043, _1527045]))]]], (36814 ^ _780119) ^ [_1480043, _1480045, _1480047, _1480049] : [c_Fun_Oinj__on(_1480043, _1480045, _1480047, c_Orderings_Otop__class_Otop(tc_fun(_1480043, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1480043, _1480045, _1480047), hAPP(c_Set_Oimage(_1480043, _1480045, _1480047), _1480049)) = _1480049)], (33751 ^ _780119) ^ [_1413092] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1413092)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1413092)], (13518 ^ _780119) ^ [_1026144, _1026146, _1026148] : [class_Groups_Oab__group__add(_1026144), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1026144), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026144), _1026146), _1026148)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026144), _1026148), _1026146))], (2660 ^ _780119) ^ [_819520, _819522, _819524, _819526, _819528, _819530] : [-(c_FunDef_Oin__rel(_819530, _819526, _819522) = c_FunDef_Oin__rel(_819528, _819524, _819520)), _819530 = _819528, _819526 = _819524, _819522 = _819520], (30593 ^ _780119) ^ [_1351627, _1351629, _1351631, _1351633] : [class_Int_Onumber__ring(_1351627), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351627), hAPP(c_Int_Onumber__class_Onumber__of(_1351627), _1351629)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351627), hAPP(c_Int_Onumber__class_Onumber__of(_1351627), _1351631)), _1351633)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351627), hAPP(c_Int_Onumber__class_Onumber__of(_1351627), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1351629), _1351631))), _1351633))], (46151 ^ _780119) ^ [_1710000, _1710002, _1710004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1710000, _1710000), tc_HOL_Obool)), _1710002), hAPP(hAPP(c_Product__Type_OSigma(_1710000, _1710000), _1710004), hAPP(c_COMBK(tc_fun(_1710000, tc_HOL_Obool), _1710000), _1710004)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1710000), tc_List_Olist(_1710000)), tc_HOL_Obool)), c_List_Olistrel(_1710000, _1710002)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1710000), tc_List_Olist(_1710000)), c_List_Olists(_1710000, _1710004)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1710000), tc_HOL_Obool), tc_List_Olist(_1710000)), c_List_Olists(_1710000, _1710004))))))], (41061 ^ _780119) ^ [_1585189, _1585191, _1585193, _1585195, _1585197, _1585199] : [hBOOL(hAPP(hAPP(c_member(_1585189), _1585191), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1585193, tc_fun(_1585189, tc_HOL_Obool)), _1585195), _1585197))), hBOOL(hAPP(hAPP(c_member(_1585193), _1585199), _1585195)), -(hBOOL(hAPP(hAPP(c_member(_1585189), _1585191), hAPP(_1585197, _1585199))))], (31177 ^ _780119) ^ [_1363069, _1363071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1363069), _1363071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1363069)), c_Int_OBit1(_1363071))))], (41459 ^ _780119) ^ [_1596900, _1596902, _1596904, _1596906, _1596908] : [_1596900 = c_Orderings_Obot__class_Obot(tc_fun(_1596902, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1596904, tc_HOL_Obool)), _1596906), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1596902, tc_fun(_1596904, tc_HOL_Obool)), _1596900), _1596908)) = _1596906)], (19783 ^ _780119) ^ [_1140074, _1140076, _1140078, _1140080] : [class_Rings_Odivision__ring(_1140074), -(_1140076 = c_Groups_Ozero__class_Ozero(_1140074)), _1140078 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140074), _1140080), _1140076), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140074), _1140078), _1140076) = _1140080)], (32059 ^ _780119) ^ [_1377518, _1377520] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377518), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377520)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377518), 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)))), _1377520)))], (43715 ^ _780119) ^ [_1652829, _1652831, _1652833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1652829), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1652831), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1652831)), _1652833)))), -(hBOOL(hAPP(hAPP(c_member(_1652831), hAPP(c_Random_Opick(_1652831, _1652833), _1652829)), hAPP(c_List_Oset(_1652831), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1652831), _1652831), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1652831)), _1652833)))))], (39222 ^ _780119) ^ [_1541952, _1541954, _1541956, _1541958, _1541960, _1541962] : [c_Finite__Set_Ofolding__idem(_1541952, _1541954, _1541956, _1541958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1541952), _1541960)), -(hAPP(_1541958, hAPP(hAPP(c_Set_Oinsert(_1541952), _1541962), _1541960)) = hAPP(c_Fun_Ocomp(_1541954, _1541954, _1541954, hAPP(_1541958, _1541960)), hAPP(_1541956, _1541962)))], (34617 ^ _780119) ^ [_1429850, _1429852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1429850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1429852)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1429850, _1429852) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1429850, _1429852)))], (38948 ^ _780119) ^ [_1535366, _1535368, _1535370, _1535372, _1535374, _1535376] : [c_Finite__Set_Ofolding(_1535366, _1535368, _1535370, _1535372), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535366), _1535374)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535366), _1535376)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535366, tc_HOL_Obool)), _1535374), _1535376) = c_Orderings_Obot__class_Obot(tc_fun(_1535366, tc_HOL_Obool)), -(hAPP(_1535372, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1535366, tc_HOL_Obool)), _1535374), _1535376)) = hAPP(c_Fun_Ocomp(_1535368, _1535368, _1535368, hAPP(_1535372, _1535374)), hAPP(_1535372, _1535376)))], (48053 ^ _780119) ^ [_1750865, _1750867, _1750869] : [hBOOL(hAPP(c_List_Odistinct(_1750865), _1750867)), -(hBOOL(hAPP(c_List_Odistinct(_1750865), c_List_OdropWhile(_1750865, _1750869, _1750867))))], (32505 ^ _780119) ^ [_1386060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1386060)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1386060), c_Int_OPls)))], (50180 ^ _780119) ^ [_1797005, _1797007] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1797005)), c_Int_OBit1(_1797007)))], (39036 ^ _780119) ^ [_1537530, _1537532, _1537534, _1537536, _1537538, _1537540, _1537542, _1537544] : [c_Finite__Set_Ofolding(_1537530, _1537532, _1537534, _1537536), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537530), _1537538)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537530), _1537540)), -(hAPP(c_Fun_Ocomp(_1537532, _1537532, _1537542, hAPP(_1537536, _1537540)), hAPP(c_Fun_Ocomp(_1537532, _1537532, _1537542, hAPP(_1537536, _1537538)), _1537544)) = hAPP(c_Fun_Ocomp(_1537532, _1537532, _1537542, hAPP(_1537536, _1537538)), hAPP(c_Fun_Ocomp(_1537532, _1537532, _1537542, hAPP(_1537536, _1537540)), _1537544)))], (10338 ^ _780119) ^ [_961965, _961967, _961969] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961965, tc_HOL_Obool)), _961967), _961969) = c_Orderings_Obot__class_Obot(tc_fun(_961965, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_961965, tc_HOL_Obool)), _961967), _961969) = _961967)], (49597 ^ _780119) ^ [_1785755, _1785757, _1785759, _1785761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1785755), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1785757)), _1785759))), 49603 ^ _780119 : [(49606 ^ _780119) ^ [] : [hBOOL(hAPP(_1785761, 49602 ^ [_1785755, _1785757, _1785759, _1785761]))], (49604 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785757), 49602 ^ [_1785755, _1785757, _1785759, _1785761]), hAPP(c_List_Oset(_1785757), _1785759))))]], -(hBOOL(hAPP(_1785761, hAPP(hAPP(c_List_Onth(_1785757), _1785759), _1785755))))], (9084 ^ _780119) ^ [_936232, _936234, _936236] : [class_Orderings_Oorder(_936232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936232), _936234), _936236)), -(_936234 = _936236), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936232), _936234), _936236)))], (37936 ^ _780119) ^ [_1509949, _1509951, _1509953, _1509955] : [-(hAPP(c_Set_OCollect(tc_prod(_1509949, _1509951)), hAPP(c_Product__Type_Oprod_Oprod__case(_1509949, _1509951, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1509949, tc_fun(_1509951, tc_HOL_Obool), tc_fun(_1509951, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1509951, tc_HOL_Obool), tc_fun(_1509951, tc_HOL_Obool)), _1509949), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1509951)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509949), c_fconj), _1509953))), _1509955))) = hAPP(hAPP(c_Product__Type_OSigma(_1509949, _1509951), hAPP(c_Set_OCollect(_1509949), _1509953)), hAPP(hAPP(c_COMBB(tc_fun(_1509951, tc_HOL_Obool), tc_fun(_1509951, tc_HOL_Obool), _1509949), c_Set_OCollect(_1509951)), _1509955)))], (4646 ^ _780119) ^ [_850715, _850717, _850719, _850721, _850723, _850725, _850727, _850729, _850731, _850733, _850735, _850737, _850739, _850741] : [-(c_New__Random__Sequence_Oneg__decr__bind(_850741, _850737, _850733, _850729, _850725, _850721, _850717) = c_New__Random__Sequence_Oneg__decr__bind(_850739, _850735, _850731, _850727, _850723, _850719, _850715)), _850741 = _850739, _850737 = _850735, _850733 = _850731, _850729 = _850727, _850725 = _850723, _850721 = _850719, _850717 = _850715], (26351 ^ _780119) ^ [_1261119, _1261121] : [c_Orderings_Obot__class_Obot(tc_fun(_1261119, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1261119), _1261121), 26354 ^ _780119 : [(26355 ^ _780119) ^ [_1261204] : [hBOOL(hAPP(_1261121, _1261204))]]], (35023 ^ _780119) ^ [_1437829, _1437831, _1437833, _1437835, _1437837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1437829, _1437831)), hAPP(_1437829, _1437833))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1437835, _1437835)), hAPP(hAPP(c_Product__Type_OPair(_1437835, _1437835), _1437831), _1437833)), c_Wellfounded_Omlex__prod(_1437835, _1437829, _1437837))))], (33401 ^ _780119) ^ [_1402345, _1402347] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1402345), _1402347), hAPP(c_Int_Onumber__class_Onumber__of(_1402345), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1402345), _1402347)), class_Fields_Ofield__inverse__zero(_1402345), class_Int_Onumber__ring(_1402345)], (22260 ^ _780119) ^ [_1186322, _1186324] : [22261 ^ _780119 : [(22262 ^ _780119) ^ [_1186371] : [_1186322 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186324), _1186371)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186322, _1186324) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51185 ^ _780119) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (50500 ^ _780119) ^ [_1804722, _1804724] : [-(c_Predicate_Opred__comp(_1804722, _1804722, _1804722, c_fequal, c_Predicate_Opred__comp(_1804722, _1804722, _1804722, _1804724, c_fequal)) = _1804724)], (46357 ^ _780119) ^ [_1714394, _1714396] : [-(_1714394 = c_List_Olist_ONil(_1714396)), -(hBOOL(hAPP(hAPP(c_member(_1714396), c_List_Olast(_1714396, _1714394)), hAPP(c_List_Oset(_1714396), _1714394))))], (36996 ^ _780119) ^ [_1484022, _1484024, _1484026, _1484028, _1484030, _1484032] : [c_Typedef_Otype__definition(_1484022, _1484024, _1484026, _1484028, _1484030), hBOOL(hAPP(hAPP(c_member(_1484024), _1484032), _1484030)), -(hAPP(_1484026, hAPP(_1484028, _1484032)) = _1484032)], (14982 ^ _780119) ^ [_1054828, _1054830, _1054832] : [class_Rings_Ono__zero__divisors(_1054828), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054828), _1054830), _1054832) = c_Groups_Ozero__class_Ozero(_1054828), -(_1054830 = c_Groups_Ozero__class_Ozero(_1054828)), -(_1054832 = c_Groups_Ozero__class_Ozero(_1054828))], (2486 ^ _780119) ^ [_816819, _816821, _816823, _816825] : [-(c_Divides_Odivmod__nat(_816825, _816821) = c_Divides_Odivmod__nat(_816823, _816819)), _816825 = _816823, _816821 = _816819], (44216 ^ _780119) ^ [_1665823, _1665825, _1665827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665823), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665825)), _1665827))), -(hAPP(c_Random_Opick(_1665825, hAPP(hAPP(c_List_Omap(_1665825, tc_prod(tc_Code__Numeral_Ocode__numeral, _1665825)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1665825), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1665827)), hAPP(c_Code__Numeral_Oof__nat, _1665823)) = hAPP(hAPP(c_List_Onth(_1665825), _1665827), _1665823))], (41256 ^ _780119) ^ [_1590190, _1590192, _1590194] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590190, tc_fun(_1590192, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1590190, tc_HOL_Obool))), _1590194) = c_Orderings_Otop__class_Otop(tc_fun(_1590192, tc_HOL_Obool)))], (3780 ^ _780119) ^ [_837050, _837052, _837054, _837056, _837058, _837060] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_837060, _837056, _837052) = c_SetInterval_Oord__class_OatLeastAtMost(_837058, _837054, _837050)), _837060 = _837058, _837056 = _837054, _837052 = _837050], (32699 ^ _780119) ^ [_1389753] : [class_Int_Onumber__ring(_1389753), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389753), c_Groups_Oone__class_Oone(_1389753)), c_Groups_Oone__class_Oone(_1389753)) = hAPP(c_Int_Onumber__class_Onumber__of(_1389753), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (28672 ^ _780119) ^ [_1309772, _1309774, _1309776] : [class_Orderings_Olinorder(_1309772), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309772), _1309774)), 28679 ^ _780119 : [(28686 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309772, tc_HOL_Obool)), _1309774), hAPP(hAPP(c_Set_Oinsert(_1309772), _1309776), c_Orderings_Obot__class_Obot(tc_fun(_1309772, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1309772, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1309772, hAPP(hAPP(c_Set_Oinsert(_1309772), _1309776), _1309774)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1309772), _1309776), c_Big__Operators_Olinorder__class_OMin(_1309772, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309772, tc_HOL_Obool)), _1309774), hAPP(hAPP(c_Set_Oinsert(_1309772), _1309776), c_Orderings_Obot__class_Obot(tc_fun(_1309772, tc_HOL_Obool)))))))], (28680 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309772, tc_HOL_Obool)), _1309774), hAPP(hAPP(c_Set_Oinsert(_1309772), _1309776), c_Orderings_Obot__class_Obot(tc_fun(_1309772, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1309772, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1309772, hAPP(hAPP(c_Set_Oinsert(_1309772), _1309776), _1309774)) = _1309776)]]], (9218 ^ _780119) ^ [_938470, _938472, _938474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938470, tc_HOL_Obool)), _938472), _938474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938470, tc_HOL_Obool)), _938472), _938474))), -(_938472 = _938474)], (13186 ^ _780119) ^ [_1020280] : [hAPP(c_Nat_OSuc, _1020280) = _1020280], (34044 ^ _780119) ^ [_1419406, _1419408, _1419410] : [-(c_HOL_OThe(tc_prod(_1419406, _1419408), _1419410) = c_HOL_OThe(tc_prod(_1419406, _1419408), hAPP(c_Product__Type_Oprod_Oprod__case(_1419406, _1419408, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1419408, tc_prod(_1419406, _1419408)), tc_fun(_1419408, tc_HOL_Obool), _1419406), hAPP(c_COMBB(tc_prod(_1419406, _1419408), tc_HOL_Obool, _1419408), _1419410)), c_Product__Type_OPair(_1419406, _1419408)))))], (37831 ^ _780119) ^ [_1507219, _1507221, _1507223, _1507225, _1507227] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1507219, _1507221), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1507219, tc_HOL_Obool)), _1507223), _1507225)), _1507227) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1507219, _1507221), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1507219, _1507221), _1507223), _1507227)), hAPP(hAPP(c_Product__Type_OSigma(_1507219, _1507221), _1507225), _1507227)))], (30219 ^ _780119) ^ [_1344581, _1344583, _1344585] : [hBOOL(hAPP(c_Com_OWT, _1344581)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1344583, _1344585, _1344581))))], (25514 ^ _780119) ^ [_1246727, _1246729] : [c_Nat__Transfer_Ois__nat(_1246727), c_Nat__Transfer_Ois__nat(_1246729), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1246727, _1246729) = 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, _1246727), hAPP(c_Int_Onat, _1246729))))], (22901 ^ _780119) ^ [_1198341, _1198343] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198341)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198343)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198341), _1198343)))], (23825 ^ _780119) ^ [_1215747, _1215749, _1215751] : [-(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)), _1215747)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1215749), _1215751)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1215749), _1215747)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1215751), _1215747)))], (40092 ^ _780119) ^ [_1563027, _1563029, _1563031, _1563033] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563027, _1563027)), hAPP(hAPP(c_Product__Type_OPair(_1563027, _1563027), _1563029), _1563031)), c_Transitive__Closure_Ortrancl(_1563027, _1563033))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563027, _1563027)), hAPP(hAPP(c_Product__Type_OPair(_1563027, _1563027), _1563031), _1563029)), c_Transitive__Closure_Ortrancl(_1563027, hAPP(c_Relation_Oconverse(_1563027, _1563027), _1563033)))))], (37665 ^ _780119) ^ [_1501873, _1501875, _1501877] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1501873, _1501875)), _1501877)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1501873), hAPP(c_Relation_ODomain(_1501873, _1501875), _1501877))))], (45636 ^ _780119) ^ [_1698629, _1698631] : [hAPP(c_List_Orotate1(_1698629), _1698631) = c_List_Olist_ONil(_1698629), -(_1698631 = c_List_Olist_ONil(_1698629))], (38350 ^ _780119) ^ [_1521674, _1521676] : [c_Predicate_Oreflp(_1521674, _1521676), -(c_Relation_Orefl__on(_1521674, c_Orderings_Otop__class_Otop(tc_fun(_1521674, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1521674, _1521674)), hAPP(c_Product__Type_Oprod_Oprod__case(_1521674, _1521674, tc_HOL_Obool), _1521676))))], (11255 ^ _780119) ^ [_980523, _980525, _980527, _980529, _980531] : [class_Groups_Oab__group__add(_980523), hBOOL(hAPP(c_Finite__Set_Ofinite(_980525), _980527)), hBOOL(hAPP(c_Finite__Set_Ofinite(_980525), _980529)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_980525, _980523), _980531), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980525, tc_HOL_Obool)), _980527), _980529)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_980523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980523), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_980525, _980523), _980531), _980527)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_980525, _980523), _980531), _980529))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_980525, _980523), _980531), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980525, tc_HOL_Obool)), _980527), _980529))))], (46250 ^ _780119) ^ [_1712392, _1712394, _1712396, _1712398] : [46251 ^ _780119 : [(46252 ^ _780119) ^ [_1712489, _1712491] : [_1712392 = hAPP(hAPP(c_List_Olist_OCons(_1712394), _1712491), _1712489)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712394), tc_List_Olist(_1712394))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712394), tc_List_Olist(_1712394)), _1712396), hAPP(hAPP(c_List_Oappend(_1712394), _1712396), _1712392))), c_List_Olexord(_1712394, _1712398))))], (48681 ^ _780119) ^ [_1764217, _1764219, _1764221, _1764223] : [class_Orderings_Oorder(_1764217), class_Enum_Oenum(_1764219), 48688 ^ _780119 : [(48697 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1764219, _1764217)), _1764221), _1764223))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1764219, _1764217)), _1764221), _1764223)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1764219), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1764219), c_fNot), hAPP(hAPP(c_COMBS(_1764219, _1764217, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1764217, tc_fun(_1764217, tc_HOL_Obool), _1764219), c_fequal), _1764221)), _1764223))))], (48689 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1764219, _1764217)), _1764221), _1764223)), 48692 ^ _780119 : [(48695 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1764219), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1764219), c_fNot), hAPP(hAPP(c_COMBS(_1764219, _1764217, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1764217, tc_fun(_1764217, tc_HOL_Obool), _1764219), c_fequal), _1764221)), _1764223)))))], (48693 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1764219, _1764217)), _1764221), _1764223)))]]]]], (15774 ^ _780119) ^ [_1067469, _1067471, _1067473] : [class_Rings_Oordered__cancel__semiring(_1067469), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067469), _1067471), c_Groups_Ozero__class_Ozero(_1067469))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067469), c_Groups_Ozero__class_Ozero(_1067469)), _1067473)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067469), _1067471), _1067473)), c_Groups_Ozero__class_Ozero(_1067469))))], (15142 ^ _780119) ^ [_1057247, _1057249] : [class_Groups_Olinordered__ab__group__add(_1057247), 15145 ^ _780119 : [(15152 ^ _780119) ^ [] : [_1057249 = c_Groups_Ozero__class_Ozero(_1057247), -(_1057249 = hAPP(c_Groups_Ouminus__class_Ouminus(_1057247), _1057249))], (15146 ^ _780119) ^ [] : [_1057249 = hAPP(c_Groups_Ouminus__class_Ouminus(_1057247), _1057249), -(_1057249 = c_Groups_Ozero__class_Ozero(_1057247))]]], (33635 ^ _780119) ^ [_1409605, _1409607, _1409609, _1409611] : [hAPP(hAPP(c_COMBC(_1409605, tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_fun(_1409607, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409607, tc_fun(tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_fun(_1409607, tc_HOL_Obool)), _1409605), c_COMBC(_1409607, tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409607, tc_prod(_1409605, _1409607)), tc_fun(_1409607, tc_fun(tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_HOL_Obool)), _1409605), hAPP(c_COMBB(tc_prod(_1409605, _1409607), tc_fun(tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_HOL_Obool), _1409607), c_member(tc_prod(_1409605, _1409607)))), c_Product__Type_OPair(_1409605, _1409607)))), _1409609) = hAPP(hAPP(c_COMBC(_1409605, tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_fun(_1409607, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409607, tc_fun(tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_fun(_1409607, tc_HOL_Obool)), _1409605), c_COMBC(_1409607, tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409607, tc_prod(_1409605, _1409607)), tc_fun(_1409607, tc_fun(tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_HOL_Obool)), _1409605), hAPP(c_COMBB(tc_prod(_1409605, _1409607), tc_fun(tc_fun(tc_prod(_1409605, _1409607), tc_HOL_Obool), tc_HOL_Obool), _1409607), c_member(tc_prod(_1409605, _1409607)))), c_Product__Type_OPair(_1409605, _1409607)))), _1409611), -(_1409609 = _1409611)], (25478 ^ _780119) ^ [_1246075, _1246077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246075)), 25481 ^ _780119 : [(25488 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246075), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1246077))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1246075)), _1246077)))], (25482 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1246075)), _1246077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246075), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1246077))))]]], (38156 ^ _780119) ^ [_1517009, _1517011, _1517013, _1517015, _1517017, _1517019, _1517021] : [-(hAPP(c_Product__Type_Ofst(_1517009, _1517011), hAPP(c_Product__Type_Omap__pair(_1517013, _1517009, _1517015, _1517011, _1517017, _1517019), _1517021)) = hAPP(_1517017, hAPP(c_Product__Type_Ofst(_1517013, _1517015), _1517021)))], (45904 ^ _780119) ^ [_1704529, _1704531, _1704533] : [-(hAPP(c_List_Oset(_1704529), hAPP(c_List_Orotate(_1704529, _1704531), _1704533)) = hAPP(c_List_Oset(_1704529), _1704533))], (51217 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (12393 ^ _780119) ^ [_1004018, _1004020] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004018), _1004020) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004020), _1004018))], (32765 ^ _780119) ^ [_1390814, _1390816, _1390818] : [class_Groups_Omonoid__mult(_1390814), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1390814), _1390816), 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)))), _1390818)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1390814), hAPP(hAPP(c_Power_Opower__class_Opower(_1390814), _1390816), _1390818)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (29532 ^ _780119) ^ [_1328550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328550)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1328550))], (23715 ^ _780119) ^ [_1213516, _1213518, _1213520] : [class_Orderings_Oorder(_1213516), 23718 ^ _780119 : [(23725 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213516), _1213518), _1213520))), -(c_Orderings_Obot__class_Obot(tc_fun(_1213516, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1213516, _1213518), _1213520))], (23719 ^ _780119) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1213516, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1213516, _1213518), _1213520), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213516), _1213518), _1213520))]]], (11842 ^ _780119) ^ [_993245, _993247, _993249] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993245), _993247) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993249), _993247), -(_993245 = _993249)], (37507 ^ _780119) ^ [_1497867, _1497869] : [-(c_List_Olex(_1497867, _1497869) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1497867), tc_List_Olist(_1497867)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1497867, _1497869)))], (46694 ^ _780119) ^ [_1721565, _1721567, _1721569, _1721571] : [-(c_List_Omap__filter(_1721565, _1721567, _1721569, _1721571) = hAPP(hAPP(c_List_Omap(_1721565, _1721567), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1721567), _1721567, _1721565, c_Option_Othe(_1721567)), _1721569)), hAPP(c_List_Ofilter(_1721565, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1721565), c_fNot), hAPP(hAPP(c_COMBC(_1721565, tc_Option_Ooption(_1721567), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1721567), tc_fun(tc_Option_Ooption(_1721567), tc_HOL_Obool), _1721565), c_fequal), _1721569)), c_Option_Ooption_ONone(_1721567)))), _1721571)))], (27033 ^ _780119) ^ [_1275878, _1275880, _1275882, _1275884, _1275886, _1275888] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1275878), _1275880)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275882), _1275884)), 27043 ^ _780119 : [(27046 ^ _780119) ^ [] : [hAPP(c_Finite__Set_Ocard(_1275878), hAPP(c_Set_OCollect(_1275878), hAPP(hAPP(c_COMBS(_1275878, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1275878), c_fconj), hAPP(hAPP(c_COMBC(_1275878, tc_fun(_1275878, tc_HOL_Obool), tc_HOL_Obool), c_member(_1275878)), _1275880))), hAPP(hAPP(c_COMBC(_1275878, _1275882, tc_HOL_Obool), _1275886), 27042 ^ [_1275878, _1275880, _1275882, _1275884, _1275886, _1275888])))) = _1275888], (27044 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1275882), 27042 ^ [_1275878, _1275880, _1275882, _1275884, _1275886, _1275888]), _1275884)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1275878, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1275882, tc_HOL_Obool), tc_Nat_Onat, _1275878), c_Finite__Set_Ocard(_1275882)), hAPP(hAPP(c_COMBB(tc_fun(_1275882, tc_HOL_Obool), tc_fun(_1275882, tc_HOL_Obool), _1275878), c_Set_OCollect(_1275882)), hAPP(hAPP(c_COMBB(tc_fun(_1275882, tc_HOL_Obool), tc_fun(_1275882, tc_HOL_Obool), _1275878), hAPP(c_COMBS(_1275882, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1275882), c_fconj), hAPP(hAPP(c_COMBC(_1275882, tc_fun(_1275882, tc_HOL_Obool), tc_HOL_Obool), c_member(_1275882)), _1275884)))), _1275886)))), _1275880) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1275888), hAPP(c_Finite__Set_Ocard(_1275882), _1275884)))], (5058 ^ _780119) ^ [_857521, _857523] : [_857523 = _857521, -(c_Set_OCollect(_857523) = c_Set_OCollect(_857521))], (48333 ^ _780119) ^ [_1757437, _1757439] : [class_Enum_Oenum(_1757437), -(hBOOL(hAPP(hAPP(c_member(_1757437), _1757439), hAPP(c_List_Oset(_1757437), c_Enum_Oenum__class_Oenum(_1757437)))))], (22615 ^ _780119) ^ [_1192852, _1192854, _1192856] : [class_Orderings_Olinorder(_1192852), 22618 ^ _780119 : [(22625 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192852), _1192854), _1192856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1192852, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1192852), _1192854)), hAPP(c_SetInterval_Oord__class_OlessThan(_1192852), _1192856))))], (22619 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1192852, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1192852), _1192854)), hAPP(c_SetInterval_Oord__class_OlessThan(_1192852), _1192856))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192852), _1192854), _1192856)))]]], (41577 ^ _780119) ^ [_1599306, _1599308, _1599310, _1599312] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599306, tc_fun(_1599308, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1599306, tc_HOL_Obool), _1599310)), _1599312) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1599306, tc_HOL_Obool), tc_fun(_1599308, tc_HOL_Obool)), _1599310), hAPP(hAPP(c_COMBC(tc_fun(_1599306, tc_HOL_Obool), tc_fun(_1599306, tc_fun(_1599308, tc_HOL_Obool)), tc_fun(_1599308, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599306, tc_fun(_1599308, tc_HOL_Obool))), _1599312)))], (23857 ^ _780119) ^ [_1216511, _1216513, _1216515] : [class_Orderings_Oord(_1216511), 23860 ^ _780119 : [(23867 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216511), _1216515), _1216513)), -(hBOOL(hAPP(hAPP(c_member(_1216511), _1216513), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1216511), _1216515))))], (23861 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1216511), _1216513), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1216511), _1216515))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216511), _1216515), _1216513)))]]], (50530 ^ _780119) ^ [_1805262, _1805264, _1805266, _1805268] : [hBOOL(hAPP(_1805262, _1805264)), -(hAPP(c_List_Ofilter(_1805266, _1805262), c_List_Oreplicate(_1805266, _1805268, _1805264)) = c_List_Oreplicate(_1805266, _1805268, _1805264))], (32345 ^ _780119) ^ [_1383355, _1383357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383355), _1383357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1383355)), c_Int_OBit0(_1383357))))], (17110 ^ _780119) ^ [_1090859, _1090861, _1090863, _1090865] : [-(c_Nat_Onat_Onat__case(_1090859, _1090861, _1090863, hAPP(c_Nat_OSuc, _1090865)) = hAPP(_1090863, _1090865))], (5558 ^ _780119) ^ [_865267, _865269, _865271, _865273] : [-(tc_Nitpick_Opair__box(_865273, _865269) = tc_Nitpick_Opair__box(_865271, _865267)), _865273 = _865271, _865269 = _865267], (3510 ^ _780119) ^ [_832901, _832903] : [_832903 = _832901, -(c_List_Orotate1(_832903) = c_List_Orotate1(_832901))], (322 ^ _780119) ^ [_785148, _785150, _785152, _785154] : [-(c_Predicate_Oreflp(_785152, _785148)), c_Predicate_Oreflp(_785154, _785150), _785154 = _785152, _785150 = _785148], (19128 ^ _780119) ^ [_1128435] : [-(_1128435 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1128435), _1128435) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35085 ^ _780119) ^ [_1439502, _1439504, _1439506, _1439508, _1439510, _1439512, _1439514] : [-(hAPP(c_Product__Type_Oapsnd(_1439502, _1439504, _1439506, _1439508), hAPP(c_Product__Type_Oapfst(_1439510, _1439506, _1439502, _1439512), _1439514)) = hAPP(c_Product__Type_Oapfst(_1439510, _1439506, _1439504, _1439512), hAPP(c_Product__Type_Oapsnd(_1439502, _1439504, _1439510, _1439508), _1439514)))], (34108 ^ _780119) ^ [_1420722, _1420724] : [-(c_Divides_OnegDivAlg(_1420722, _1420724) = hAPP(c_Divides_Oadjust(_1420724), c_Divides_OnegDivAlg(_1420722, 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)))), _1420724)))), -(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), _1420722), _1420724)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420724), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31463 ^ _780119) ^ [_1368053, _1368055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368053), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368055)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368053)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368055))], (41326 ^ _780119) ^ [_1592226, _1592228, _1592230, _1592232] : [-(hAPP(c_Set_OPow(_1592226), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592228, tc_fun(_1592226, tc_HOL_Obool)), _1592230), _1592232)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592228, tc_fun(tc_fun(_1592226, tc_HOL_Obool), tc_HOL_Obool)), _1592230), hAPP(hAPP(c_COMBB(tc_fun(_1592226, tc_HOL_Obool), tc_fun(tc_fun(_1592226, tc_HOL_Obool), tc_HOL_Obool), _1592228), c_Set_OPow(_1592226)), _1592232)))], (26131 ^ _780119) ^ [_1256633] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1256633)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1256633)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1256633)))], (19042 ^ _780119) ^ [_1127016, _1127018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1127016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127018)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1127018), _1127016)), _1127018) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1127018), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1127016), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (6827 ^ _780119) ^ [_892439, _892441, _892443, _892445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892439, tc_HOL_Obool)), _892441), _892443)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892439, tc_HOL_Obool)), _892445), _892443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892439, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892439, tc_HOL_Obool)), _892441), _892445)), _892443)))], (37054 ^ _780119) ^ [_1486417, _1486419, _1486421, _1486423, _1486425, _1486427, _1486429] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1486417, _1486419, _1486421), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486423, tc_fun(tc_prod(_1486417, _1486419), tc_HOL_Obool)), _1486425), _1486427)), _1486429) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486423, tc_fun(tc_prod(_1486417, _1486421), tc_HOL_Obool)), _1486425), hAPP(hAPP(c_COMBC(_1486423, tc_fun(tc_prod(_1486419, _1486421), tc_HOL_Obool), tc_fun(tc_prod(_1486417, _1486421), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1486417, _1486419), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1486419, _1486421), tc_HOL_Obool), tc_fun(tc_prod(_1486417, _1486421), tc_HOL_Obool)), _1486423), c_Relation_Orel__comp(_1486417, _1486419, _1486421)), _1486427)), _1486429)))], (31727 ^ _780119) ^ [_1372154, _1372156] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1372154), _1372156), hAPP(c_Int_Onumber__class_Onumber__of(_1372154), c_Int_OBit1(c_Int_OPls))) = _1372156), class_Fields_Ofield(_1372154), class_Int_Onumber__ring(_1372154)], (19404 ^ _780119) ^ [_1132748, _1132750, _1132752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132748)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132752), _1132748)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132750), _1132752)), _1132748))], (22471 ^ _780119) ^ [_1190237, _1190239, _1190241] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_1190237, _1190239, _1190241)) = 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), _1190239)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1190241))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (40934 ^ _780119) ^ [_1582704, _1582706, _1582708, _1582710, _1582712, _1582714] : [c_Finite__Set_Ofun__left__comm(_1582704, _1582706, _1582708), -(hAPP(hAPP(_1582708, _1582710), hAPP(hAPP(_1582708, _1582712), _1582714)) = hAPP(hAPP(_1582708, _1582712), hAPP(hAPP(_1582708, _1582710), _1582714)))], (46704 ^ _780119) ^ [_1721922, _1721924] : [c_List_Otranspose(_1721922, _1721924) = c_List_Olist_ONil(tc_List_Olist(_1721922)), 46707 ^ _780119 : [(46708 ^ _780119) ^ [_1722017] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1721922)), _1722017), hAPP(c_List_Oset(tc_List_Olist(_1721922)), _1721924))), -(_1722017 = c_List_Olist_ONil(_1721922))]]], (33137 ^ _780119) ^ [_1397719, _1397721] : [class_Rings_Osemiring__1(_1397719), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1397721)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1397719), 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)))), _1397721))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1397719), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1397719), hAPP(c_Int_Onat, _1397721))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1397719), hAPP(c_Int_Onat, _1397721))))], (34062 ^ _780119) ^ [_1419889] : [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), _1419889))), 34065 ^ _780119 : [(34072 ^ _780119) ^ [] : [-(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), _1419889))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419889)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419889)), 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), _1419889)))))], (34066 ^ _780119) ^ [] : [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), _1419889)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419889)) = 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), _1419889))))]]], (5472 ^ _780119) ^ [_863950, _863952] : [_863952 = _863950, -(c_Orderings_Oord__class_Oless(_863952) = c_Orderings_Oord__class_Oless(_863950))], (45112 ^ _780119) ^ [_1684162, _1684164, _1684166] : [_1684162 = _1684164, -(_1684162 = hAPP(hAPP(c_List_Oappend(_1684166), c_List_Olist_ONil(_1684166)), _1684164))], (18748 ^ _780119) ^ [_1122017, _1122019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122017), _1122019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122017), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1122019)))], (15240 ^ _780119) ^ [_1058643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1058643)), _1058643 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23891 ^ _780119) ^ [_1217112, _1217114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1217112), hAPP(c_Nat_OSuc, _1217114))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1217112, hAPP(c_Nat_OSuc, _1217114)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1217114)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1217112, _1217114)))], (32791 ^ _780119) ^ [_1391270] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1391270))), 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), _1391270), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (49455 ^ _780119) ^ [_1782151, _1782153, _1782155, _1782157, _1782159] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782151)), _1782153) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782155)), _1782157), 49461 ^ _780119 : [(49464 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1782159, hAPP(hAPP(c_List_Onth(_1782151), _1782153), 49460 ^ [_1782151, _1782153, _1782155, _1782157, _1782159])), hAPP(hAPP(c_List_Onth(_1782155), _1782157), 49460 ^ [_1782151, _1782153, _1782155, _1782157, _1782159])))], (49462 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49460 ^ [_1782151, _1782153, _1782155, _1782157, _1782159]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782151)), _1782153))))]], -(c_List_Olist__all2(_1782151, _1782155, _1782159, _1782153, _1782157))], (22807 ^ _780119) ^ [_1196642] : [22809 ^ _780119 : [(22812 ^ _780119) ^ [] : [hBOOL(hAPP(_1196642, 22808 ^ [_1196642]))], (22810 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22808 ^ [_1196642])))]], 22813 ^ _780119 : [(22814 ^ _780119) ^ [_1196769] : [-(hBOOL(hAPP(_1196642, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1196769))))]]], (50404 ^ _780119) ^ [_1802210, _1802212] : [c_Wellfounded_Oacyclic(_1802210, hAPP(c_Set_OCollect(tc_prod(_1802210, _1802210)), hAPP(c_Product__Type_Oprod_Oprod__case(_1802210, _1802210, tc_HOL_Obool), c_Predicate_Oconversep(_1802210, _1802210, _1802212)))), -(c_Wellfounded_Oacyclic(_1802210, hAPP(c_Set_OCollect(tc_prod(_1802210, _1802210)), hAPP(c_Product__Type_Oprod_Oprod__case(_1802210, _1802210, tc_HOL_Obool), _1802212))))], (40116 ^ _780119) ^ [_1563809, _1563811, _1563813, _1563815, _1563817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1563811, tc_HOL_Obool)), _1563815), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1563811, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1563809, _1563811, hAPP(c_Relation_Oconverse(_1563811, _1563809), _1563813)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1563809, tc_HOL_Obool)), _1563817))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1563809, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1563811, _1563809, _1563813), _1563815)), _1563817)))], (8438 ^ _780119) ^ [_926547, _926549, _926551, _926553, _926555, _926557] : [hBOOL(hAPP(hAPP(c_member(_926547), _926549), _926551)), -(hAPP(c_Set_Oimage(_926547, _926553, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_926547, _926553), _926555), _926549), _926557)), _926551) = hAPP(hAPP(c_Set_Oinsert(_926553), _926557), hAPP(c_Set_Oimage(_926547, _926553, _926555), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926547, tc_HOL_Obool)), _926551), hAPP(hAPP(c_Set_Oinsert(_926547), _926549), c_Orderings_Obot__class_Obot(tc_fun(_926547, tc_HOL_Obool)))))))], (46833 ^ _780119) ^ [_1724887, _1724889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724887), _1724889)), -(c_List_Oupt(_1724887, hAPP(c_Nat_OSuc, _1724889)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1724887, _1724889)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1724889), c_List_Olist_ONil(tc_Nat_Onat))))], (42026 ^ _780119) ^ [_1609768, _1609770] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1609768, tc_HOL_Obool)), _1609770)), 42032 ^ _780119 : [(42035 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1609768), 42031 ^ [_1609768, _1609770]))], (42033 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1609768, tc_HOL_Obool)), 42031 ^ [_1609768, _1609770]), _1609770)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1609768), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1609768, tc_HOL_Obool), _1609770))))], (48015 ^ _780119) ^ [_1749885, _1749887, _1749889, _1749891, _1749893] : [c_Finite__Set_Ofun__left__comm(_1749885, _1749887, _1749889), -(hAPP(hAPP(c_Finite__Set_Ofold(_1749885, _1749887, _1749889), _1749891), hAPP(c_List_Oset(_1749885), _1749893)) = hAPP(c_List_Ofoldl(_1749887, _1749885, hAPP(c_COMBC(_1749885, _1749887, _1749887), _1749889), _1749891), c_List_Oremdups(_1749885, _1749893)))], (27618 ^ _780119) ^ [_1290344, _1290346, _1290348, _1290350] : [class_Orderings_Olinorder(_1290344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290344), _1290346), _1290348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290344), _1290346), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290344), _1290350), _1290348))))], (8532 ^ _780119) ^ [_928299, _928301, _928303] : [class_Orderings_Olinorder(_928299), 8535 ^ _780119 : [(8536 ^ _780119) ^ [] : [-(_928301 = _928303), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928299), _928301), _928303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928299), _928303), _928301)))], (8546 ^ _780119) ^ [] : [8547 ^ _780119 : [(8550 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928299), _928303), _928301))], (8548 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928299), _928301), _928303))]], _928301 = _928303]]], (35349 ^ _780119) ^ [_1446013, _1446015, _1446017, _1446019, _1446021] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1446017, _1446013)), hAPP(hAPP(c_Product__Type_OPair(_1446017, _1446013), _1446021), _1446015)), _1446019)), -(hBOOL(hAPP(hAPP(c_member(_1446013), _1446015), hAPP(c_Relation_OImage(_1446017, _1446013, _1446019), hAPP(hAPP(c_Set_Oinsert(_1446017), _1446021), c_Orderings_Obot__class_Obot(tc_fun(_1446017, tc_HOL_Obool)))))))], (8576 ^ _780119) ^ [_928807, _928809, _928811] : [class_Orderings_Olinorder(_928807), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928807), _928809), _928811))), -(_928809 = _928811), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928807), _928811), _928809)))], (5829 ^ _780119) ^ [_872527] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_872527), c_Orderings_Obot__class_Obot(tc_fun(_872527, tc_HOL_Obool)))))], (45758 ^ _780119) ^ [_1701538, _1701540, _1701542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701538), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701540)), _1701542))), -(hAPP(hAPP(c_List_Olist_OCons(_1701540), hAPP(hAPP(c_List_Onth(_1701540), _1701542), _1701538)), hAPP(hAPP(c_List_Odrop(_1701540), hAPP(c_Nat_OSuc, _1701538)), _1701542)) = hAPP(hAPP(c_List_Odrop(_1701540), _1701538), _1701542))], (13915 ^ _780119) ^ [_1033181, _1033183] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1033181, tc_HOL_Obool)), _1033183), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033181, tc_HOL_Obool)), _1033183)) = c_Orderings_Obot__class_Obot(tc_fun(_1033181, tc_HOL_Obool)))], (51247 ^ _780119) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (44544 ^ _780119) ^ [_1672500] : [-(c_Code__Numeral_OSuc__code__numeral(_1672500) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1672500))))], (18716 ^ _780119) ^ [_1121408, _1121410] : [18717 ^ _780119 : [(18720 ^ _780119) ^ [] : [_1121408 = _1121410], (18718 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121408), _1121410))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121408), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121410), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (14546 ^ _780119) ^ [_1046873, _1046875, _1046877] : [class_Groups_Omonoid__mult(_1046873), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046873), hAPP(hAPP(c_Power_Opower__class_Opower(_1046873), _1046875), _1046877)), _1046875) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046873), _1046875), hAPP(hAPP(c_Power_Opower__class_Opower(_1046873), _1046875), _1046877)))], (47823 ^ _780119) ^ [_1746397, _1746399, _1746401] : [-(c_List_OtakeWhile(_1746397, _1746399, _1746401) = hAPP(hAPP(c_List_Otake(_1746397), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746397)), c_List_OtakeWhile(_1746397, _1746399, _1746401))), _1746401))], (10260 ^ _780119) ^ [_960197, _960199, _960201, _960203, _960205, _960207] : [class_Groups_Oab__semigroup__mult(_960197), hBOOL(hAPP(c_Finite__Set_Ofinite(_960199), _960201)), -(hBOOL(hAPP(hAPP(c_member(_960199), _960203), _960201))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_960197, _960199, c_Groups_Otimes__class_Otimes(_960197)), _960205), _960207), hAPP(hAPP(c_Set_Oinsert(_960199), _960203), _960201)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960197), hAPP(_960205, _960203)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_960197, _960199, c_Groups_Otimes__class_Otimes(_960197)), _960205), _960207), _960201)))], (33729 ^ _780119) ^ [_1412792, _1412794, _1412796, _1412798] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1412792, _1412794), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1412796), _1412798))), -(_1412794 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1412792, _1412794) = _1412798)], (49329 ^ _780119) ^ [_1778432, _1778434, _1778436] : [-(hBOOL(hAPP(hAPP(c_member(_1778432), _1778434), hAPP(c_List_Oset(_1778432), _1778436)))), -(c_List_Oinsert(_1778432, _1778434, _1778436) = hAPP(hAPP(c_List_Olist_OCons(_1778432), _1778434), _1778436))], (42663 ^ _780119) ^ [_1624634, _1624636, _1624638, _1624640, _1624642, _1624644] : [-(hAPP(hAPP(c_Option_Omap(_1624634, _1624636), _1624638), hAPP(hAPP(c_Option_Omap(_1624640, _1624634), _1624642), _1624644)) = hAPP(hAPP(c_Option_Omap(_1624640, _1624636), hAPP(c_Fun_Ocomp(_1624634, _1624636, _1624640, _1624638), _1624642)), _1624644))], (16420 ^ _780119) ^ [_1079359, _1079361] : [class_Groups_Oordered__ab__group__add(_1079359), 16423 ^ _780119 : [(16430 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079359), _1079361), c_Groups_Ozero__class_Ozero(_1079359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079359), c_Groups_Ozero__class_Ozero(_1079359)), hAPP(c_Groups_Ouminus__class_Ouminus(_1079359), _1079361))))], (16424 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079359), c_Groups_Ozero__class_Ozero(_1079359)), hAPP(c_Groups_Ouminus__class_Ouminus(_1079359), _1079361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079359), _1079361), c_Groups_Ozero__class_Ozero(_1079359))))]]], (6847 ^ _780119) ^ [_892903, _892905, _892907, _892909, _892911] : [-(hAPP(c_Set_Oimage(_892903, _892905, _892907), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892903, tc_HOL_Obool)), _892909), _892911)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892905, tc_HOL_Obool)), hAPP(c_Set_Oimage(_892903, _892905, _892907), _892909)), hAPP(c_Set_Oimage(_892903, _892905, _892907), _892911)))], (42966 ^ _780119) ^ [_1631873, _1631875] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1631873, _1631875)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1631873, _1631875))], (19096 ^ _780119) ^ [_1127924, _1127926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1127924), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19099 ^ _780119 : [(19106 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127926), _1127924)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19100 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127926), _1127924)), 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)), _1127926)))]]], (34865 ^ _780119) ^ [_1434642, _1434644, _1434646] : [-(_1434642 = hAPP(hAPP(c_Product__Type_OPair(_1434644, _1434646), hAPP(c_Product__Type_Ofst(_1434644, _1434646), _1434642)), hAPP(c_Product__Type_Osnd(_1434644, _1434646), _1434642)))], (19945 ^ _780119) ^ [_1142766, _1142768, _1142770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1142766)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1142766), _1142768)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1142766), _1142770)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142768), _1142770))], (17510 ^ _780119) ^ [_1098376, _1098378, _1098380] : [class_Rings_Olinordered__idom(_1098376), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098376), c_Groups_Ozero__class_Ozero(_1098376)), _1098378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098376), c_Groups_Ozero__class_Ozero(_1098376)), _1098380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098376), _1098380), c_Groups_Oone__class_Oone(_1098376))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098376), _1098380), _1098378)), _1098378)))], (18163 ^ _780119) ^ [_1110924, _1110926] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1110924, _1110926)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1110924, _1110926), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1110926), c_Orderings_Otop__class_Otop(tc_fun(_1110926, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1110924), c_Orderings_Otop__class_Otop(tc_fun(_1110924, tc_HOL_Obool)))))], (5961 ^ _780119) ^ [_874921, _874923, _874925] : [hBOOL(hAPP(hAPP(c_member(_874921), _874923), _874925)), -(hBOOL(hAPP(_874925, _874923)))], (42312 ^ _780119) ^ [_1616605, _1616607, _1616609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1616605), c_Nitpick_Oplus__frac(_1616605, _1616607, c_Nitpick_Ouminus__frac(_1616605, _1616609)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1616605, _1616607, _1616609))], (39605 ^ _780119) ^ [_1551231, _1551233, _1551235, _1551237] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1551231, _1551231)), hAPP(hAPP(c_Product__Type_OPair(_1551231, _1551231), _1551235), _1551237)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551231, _1551231), tc_HOL_Obool)), _1551233), c_Relation_OId(_1551231)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1551231, tc_fun(_1551231, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1551231, tc_fun(tc_prod(_1551231, _1551231), tc_HOL_Obool), tc_fun(_1551231, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551231, tc_fun(tc_fun(tc_prod(_1551231, _1551231), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1551231, _1551231), tc_HOL_Obool), tc_fun(_1551231, tc_HOL_Obool)), _1551231), c_COMBC(_1551231, tc_fun(tc_prod(_1551231, _1551231), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551231, tc_prod(_1551231, _1551231)), tc_fun(_1551231, tc_fun(tc_fun(tc_prod(_1551231, _1551231), tc_HOL_Obool), tc_HOL_Obool)), _1551231), hAPP(c_COMBB(tc_prod(_1551231, _1551231), tc_fun(tc_fun(tc_prod(_1551231, _1551231), tc_HOL_Obool), tc_HOL_Obool), _1551231), c_member(tc_prod(_1551231, _1551231)))), c_Product__Type_OPair(_1551231, _1551231)))), _1551233)), c_fequal), _1551235), _1551237)))], (6045 ^ _780119) ^ [_876374, _876376, _876378] : [-(_876374 = _876376), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876378, tc_HOL_Obool)), _876374), _876376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876378, tc_HOL_Obool)), _876376), _876374))], (14701 ^ _780119) ^ [_1050048, _1050050, _1050052] : [class_Lattices_Oboolean__algebra(_1050048), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1050048), _1050050), _1050052) = c_Orderings_Obot__class_Obot(_1050048), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1050048), _1050050), _1050052) = c_Orderings_Otop__class_Otop(_1050048), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1050048), _1050050) = _1050052)], (30779 ^ _780119) ^ [_1355334, _1355336, _1355338, _1355340] : [class_Fields_Olinordered__field__inverse__zero(_1355334), class_Int_Onumber(_1355334), 30786 ^ _780119 : [(30787 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), _1355336), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355334), _1355338), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340)))), 30790 ^ _780119 : [(30797 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), c_Groups_Ozero__class_Ozero(_1355334)), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340)))), 30800 ^ _780119 : [(30807 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340)), c_Groups_Ozero__class_Ozero(_1355334)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), _1355336), c_Groups_Ozero__class_Ozero(_1355334))))], (30801 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340)), c_Groups_Ozero__class_Ozero(_1355334))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), _1355338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355334), _1355336), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340)))))]]], (30791 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), c_Groups_Ozero__class_Ozero(_1355334)), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355334), _1355336), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340))), _1355338)))]]], (30813 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), _1355336), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355334), _1355338), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340))))), 30816 ^ _780119 : [(30819 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355334), _1355336), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340))), _1355338))], (30817 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), c_Groups_Ozero__class_Ozero(_1355334)), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340))))]], 30820 ^ _780119 : [(30823 ^ _780119) ^ [] : [30824 ^ _780119 : [(30827 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), _1355338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355334), _1355336), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340))))], (30825 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340)), c_Groups_Ozero__class_Ozero(_1355334))))]], 30828 ^ _780119 : [(30831 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), _1355336), c_Groups_Ozero__class_Ozero(_1355334)))], (30829 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340)), c_Groups_Ozero__class_Ozero(_1355334)))]]], (30821 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355334), c_Groups_Ozero__class_Ozero(_1355334)), hAPP(c_Int_Onumber__class_Onumber__of(_1355334), _1355340)))]]]]], (22105 ^ _780119) ^ [_1183849, _1183851, _1183853] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1183849, tc_HOL_Obool)), _1183853), hAPP(c_Set_OPow(_1183849), _1183851))), -(hBOOL(hAPP(c_Predicate_OPowp(_1183849, hAPP(hAPP(c_COMBC(_1183849, tc_fun(_1183849, tc_HOL_Obool), tc_HOL_Obool), c_member(_1183849)), _1183851)), _1183853)))], (20734 ^ _780119) ^ [_1157119, _1157121, _1157123, _1157125] : [class_Fields_Olinordered__field__inverse__zero(_1157119), 20737 ^ _780119 : [(20738 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), _1157121), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157119), _1157123), _1157125))), 20741 ^ _780119 : [(20748 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), c_Groups_Ozero__class_Ozero(_1157119)), _1157125))), 20751 ^ _780119 : [(20758 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), _1157125), c_Groups_Ozero__class_Ozero(_1157119)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), _1157121), c_Groups_Ozero__class_Ozero(_1157119))))], (20752 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), _1157125), c_Groups_Ozero__class_Ozero(_1157119))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), _1157123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157119), _1157121), _1157125))))]]], (20742 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), c_Groups_Ozero__class_Ozero(_1157119)), _1157125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157119), _1157121), _1157125)), _1157123)))]]], (20764 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), _1157121), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157119), _1157123), _1157125)))), 20767 ^ _780119 : [(20770 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157119), _1157121), _1157125)), _1157123))], (20768 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), c_Groups_Ozero__class_Ozero(_1157119)), _1157125)))]], 20771 ^ _780119 : [(20774 ^ _780119) ^ [] : [20775 ^ _780119 : [(20778 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), _1157123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157119), _1157121), _1157125)))], (20776 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), _1157125), c_Groups_Ozero__class_Ozero(_1157119))))]], 20779 ^ _780119 : [(20782 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), _1157121), c_Groups_Ozero__class_Ozero(_1157119)))], (20780 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), _1157125), c_Groups_Ozero__class_Ozero(_1157119)))]]], (20772 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157119), c_Groups_Ozero__class_Ozero(_1157119)), _1157125))]]]]], (44021 ^ _780119) ^ [_1660445, _1660447] : [hBOOL(hAPP(c_List_Odistinct(_1660445), _1660447)), 44024 ^ _780119 : [(44025 ^ _780119) ^ [_1660577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1660577), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660445)), _1660447))), 44028 ^ _780119 : [(44029 ^ _780119) ^ [_1660704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1660704), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660445)), _1660447))), -(_1660577 = _1660704), hAPP(hAPP(c_List_Onth(_1660445), _1660447), _1660577) = hAPP(hAPP(c_List_Onth(_1660445), _1660447), _1660704)]]]]], (414 ^ _780119) ^ [_786474, _786476, _786478, _786480, _786482, _786484, _786486, _786488, _786490, _786492] : [-(c_Finite__Set_Ofolding__image(_786490, _786486, _786482, _786478, _786474)), c_Finite__Set_Ofolding__image(_786492, _786488, _786484, _786480, _786476), _786492 = _786490, _786488 = _786486, _786484 = _786482, _786480 = _786478, _786476 = _786474], (8504 ^ _780119) ^ [_927782, _927784, _927786, _927788, _927790, _927792] : [-(_927782 = _927784), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927786, _927788), _927790), _927784), _927792), _927782) = hAPP(_927790, _927782))], (8050 ^ _780119) ^ [_917735, _917737, _917739] : [hAPP(c_Com_Ocom_OBODY, _917735) = c_Com_Ocom_OSemi(_917737, _917739)], (19430 ^ _780119) ^ [_1133235, _1133237, _1133239] : [class_Divides_Osemiring__div(_1133235), -(_1133237 = c_Groups_Ozero__class_Ozero(_1133235)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133235), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133235), _1133239), _1133237)), _1133237) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133235), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133235), _1133239), _1133237)), c_Groups_Oone__class_Oone(_1133235)))], (45261 ^ _780119) ^ [_1687809, _1687811, _1687813, _1687815, _1687817] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1687809), tc_List_Olist(_1687809))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1687809), tc_List_Olist(_1687809)), _1687811), _1687813)), c_List_Olexord(_1687809, _1687815))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1687809), tc_List_Olist(_1687809))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1687809), tc_List_Olist(_1687809)), hAPP(hAPP(c_List_Oappend(_1687809), _1687817), _1687811)), hAPP(hAPP(c_List_Oappend(_1687809), _1687817), _1687813))), c_List_Olexord(_1687809, _1687815))))], (8106 ^ _780119) ^ [_918858, _918860, _918862, _918864] : [-(hBOOL(hAPP(hAPP(c_member(_918858), _918860), _918862))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918858, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_918858), _918860), _918864)), _918862) = hAPP(hAPP(c_Set_Oinsert(_918858), _918860), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918858, tc_HOL_Obool)), _918864), _918862)))], (41159 ^ _780119) ^ [_1588081, _1588083, _1588085, _1588087, _1588089] : [41161 ^ _780119 : [(41164 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1588081, tc_HOL_Obool)), _1588083), hAPP(_1588089, 41160 ^ [_1588081, _1588083, _1588085, _1588087, _1588089])))], (41162 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588085), 41160 ^ [_1588081, _1588083, _1588085, _1588087, _1588089]), _1588087)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1588081, tc_HOL_Obool)), _1588083), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1588085, tc_fun(_1588081, tc_HOL_Obool)), _1588087), _1588089))))], (14412 ^ _780119) ^ [_1044266, _1044268, _1044270, _1044272] : [class_Rings_Ocomm__semiring__1(_1044266), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044266), hAPP(hAPP(c_Power_Opower__class_Opower(_1044266), _1044268), _1044270)), hAPP(hAPP(c_Power_Opower__class_Opower(_1044266), _1044268), _1044272)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1044266), _1044268), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044270), _1044272)))], (7680 ^ _780119) ^ [_909889, _909891] : [-(c_Set_Othe__elem(_909889, _909891) = c_HOL_OThe(_909889, hAPP(hAPP(c_COMBB(tc_fun(_909889, tc_HOL_Obool), tc_HOL_Obool, _909889), hAPP(c_fequal, _909891)), hAPP(hAPP(c_COMBC(_909889, tc_fun(_909889, tc_HOL_Obool), tc_fun(_909889, tc_HOL_Obool)), c_Set_Oinsert(_909889)), c_Orderings_Obot__class_Obot(tc_fun(_909889, tc_HOL_Obool))))))], (16346 ^ _780119) ^ [_1078077, _1078079, _1078081] : [class_Rings_Olinordered__ring__strict(_1078077), 16349 ^ _780119 : [(16358 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078077), _1078079), _1078079)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078077), _1078081), _1078081)) = c_Groups_Ozero__class_Ozero(_1078077)), _1078079 = c_Groups_Ozero__class_Ozero(_1078077), _1078081 = c_Groups_Ozero__class_Ozero(_1078077)], (16350 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078077), _1078079), _1078079)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078077), _1078081), _1078081)) = c_Groups_Ozero__class_Ozero(_1078077), 16353 ^ _780119 : [(16356 ^ _780119) ^ [] : [-(_1078081 = c_Groups_Ozero__class_Ozero(_1078077))], (16354 ^ _780119) ^ [] : [-(_1078079 = c_Groups_Ozero__class_Ozero(_1078077))]]]]], (34789 ^ _780119) ^ [_1433145] : [-(hAPP(c_Int_Onat, _1433145) = 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, _1433145)), 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)))))))], (50398 ^ _780119) ^ [_1802030, _1802032, _1802034, _1802036, _1802038, _1802040] : [-(c_New__Random__Sequence_Oneg__union(_1802030, _1802032, _1802034, _1802036, _1802038, _1802040) = c_New__DSequence_Oneg__union(_1802030, hAPP(hAPP(hAPP(_1802032, _1802036), _1802038), _1802040), hAPP(hAPP(hAPP(_1802034, _1802036), _1802038), _1802040)))], (11902 ^ _780119) ^ [_994376, _994378, _994380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994376), _994378)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994376), _994380))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994378), _994380)))], (15056 ^ _780119) ^ [_1055914, _1055916] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055914, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1055914, tc_HOL_Obool))), _1055916) = c_Orderings_Otop__class_Otop(tc_fun(_1055914, tc_HOL_Obool)))], (45317 ^ _780119) ^ [_1689182, _1689184, _1689186, _1689188, _1689190, _1689192, _1689194] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1689182, _1689182)), hAPP(hAPP(c_Product__Type_OPair(_1689182, _1689182), _1689184), _1689186)), _1689188)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1689182), tc_List_Olist(_1689182))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689182), tc_List_Olist(_1689182)), hAPP(hAPP(c_List_Oappend(_1689182), _1689190), hAPP(hAPP(c_List_Olist_OCons(_1689182), _1689184), _1689192))), hAPP(hAPP(c_List_Oappend(_1689182), _1689190), hAPP(hAPP(c_List_Olist_OCons(_1689182), _1689186), _1689194)))), c_List_Olexord(_1689182, _1689188))))], (46321 ^ _780119) ^ [_1713952, _1713954, _1713956] : [-(_1713952 = c_List_Olist_ONil(_1713954)), -(c_List_Olast(_1713954, hAPP(hAPP(c_List_Olist_OCons(_1713954), _1713956), _1713952)) = c_List_Olast(_1713954, _1713952))], (51295 ^ _780119) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (44196 ^ _780119) ^ [_1665162, _1665164, _1665166, _1665168] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665162), tc_List_Olist(_1665162))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665162), tc_List_Olist(_1665162)), _1665164), _1665166)), c_List_Olexord(_1665162, _1665168)))), 44197 ^ _780119 : [(44204 ^ _780119) ^ [_1665469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665469), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665162)), _1665164)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665162)), _1665166)))), hAPP(hAPP(c_List_Otake(_1665162), _1665469), _1665164) = hAPP(hAPP(c_List_Otake(_1665162), _1665469), _1665166), hBOOL(hAPP(hAPP(c_member(tc_prod(_1665162, _1665162)), hAPP(hAPP(c_Product__Type_OPair(_1665162, _1665162), hAPP(hAPP(c_List_Onth(_1665162), _1665164), _1665469)), hAPP(hAPP(c_List_Onth(_1665162), _1665166), _1665469))), _1665168))], (44198 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665162)), _1665164)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665162)), _1665166))), hAPP(hAPP(c_List_Otake(_1665162), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665162)), _1665164)), _1665166) = _1665164]]], (34235 ^ _780119) ^ [_1422781, _1422783] : [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), _1422781))), 34238 ^ _780119 : [(34245 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422783)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422781)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422783), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422781)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422781)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422783), 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), _1422781)))))], (34239 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422783)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422781))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422783), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422781)) = 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), _1422783)))]]], (39793 ^ _780119) ^ [_1556027, _1556029, _1556031, _1556033] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1556027, _1556027)), hAPP(hAPP(c_Product__Type_OPair(_1556027, _1556027), _1556029), _1556031)), c_Transitive__Closure_Ortrancl(_1556027, _1556033))), -(_1556029 = _1556031), 39800 ^ _780119 : [(39803 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556027, _1556027)), hAPP(hAPP(c_Product__Type_OPair(_1556027, _1556027), _1556029), _1556031)), c_Transitive__Closure_Otrancl(_1556027, _1556033))))], (39801 ^ _780119) ^ [] : [_1556029 = _1556031]]], (41133 ^ _780119) ^ [_1587027, _1587029, _1587031, _1587033, _1587035] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1587027, tc_HOL_Obool)), _1587029), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587031, tc_fun(_1587027, tc_HOL_Obool)), _1587033), _1587035)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587031, tc_fun(_1587027, tc_HOL_Obool)), _1587033), hAPP(hAPP(c_COMBB(tc_fun(_1587027, tc_HOL_Obool), tc_fun(_1587027, tc_HOL_Obool), _1587031), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1587027, tc_HOL_Obool)), _1587029)), _1587035)))], (51659 ^ _780119) ^ [] : [-(c_Com_OWT__bodies)], (24741 ^ _780119) ^ [_1233210, _1233212, _1233214, _1233216] : [class_Orderings_Olinorder(_1233210), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233210), _1233212), _1233214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233210), _1233214), _1233216)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1233210, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1233210, _1233212, _1233214)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1233210, _1233214, _1233216)) = c_SetInterval_Oord__class_OatLeastAtMost(_1233210, _1233212, _1233216))], (11237 ^ _780119) ^ [_980128, _980130, _980132, _980134, _980136] : [class_Groups_Ocomm__monoid__add(_980128), hBOOL(hAPP(c_Finite__Set_Ofinite(_980130), _980132)), hBOOL(hAPP(c_Finite__Set_Ofinite(_980130), _980134)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980130, tc_HOL_Obool)), _980132), _980134) = c_Orderings_Obot__class_Obot(tc_fun(_980130, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_980130, _980128), _980136), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980130, tc_HOL_Obool)), _980132), _980134)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980128), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_980130, _980128), _980136), _980132)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_980130, _980128), _980136), _980134)))], (30599 ^ _780119) ^ [_1351796, _1351798, _1351800] : [class_Int_Onumber__ring(_1351796), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351796), hAPP(c_Groups_Ouminus__class_Ouminus(_1351796), hAPP(c_Int_Onumber__class_Onumber__of(_1351796), _1351798))), _1351800) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351796), hAPP(c_Int_Onumber__class_Onumber__of(_1351796), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1351798))), _1351800))], (51379 ^ _780119) ^ [_1818278, _1818280] : [-(class_Nat_Osize(tc_sum(_1818278, _1818280)))], (32011 ^ _780119) ^ [_1376667, _1376669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1376667)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1376669)), _1376667) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1376669), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1376667), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (17714 ^ _780119) ^ [_1102181, _1102183] : [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), _1102181), _1102183))), 17717 ^ _780119 : [(17720 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1102183)))], (17718 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1102181)))]]], (45424 ^ _780119) ^ [_1692508, _1692510, _1692512, _1692514, _1692516, _1692518] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692508), tc_List_Olist(_1692508))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692508), tc_List_Olist(_1692508)), hAPP(hAPP(c_List_Oappend(_1692508), _1692510), _1692516)), 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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(_1391992), c_Groups_Ozero__class_Ozero(_1391992)), _1391994)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391992), c_Groups_Ozero__class_Ozero(_1391992)), _1391996)), -(_1391994 = _1391996)], (3542 ^ _780119) ^ [_833369, _833371, _833373, _833375] : [-(c_Big__Operators_Olattice__class_OSup__fin(_833375, _833371) = c_Big__Operators_Olattice__class_OSup__fin(_833373, _833369)), _833375 = _833373, _833371 = _833369], (50142 ^ _780119) ^ [_1796383] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1796383))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1796383)))], (50810 ^ _780119) ^ [_1810764, _1810766, _1810768, _1810770, _1810772, _1810774] : [c_Nitpick_Opair__box_OPairBox(_1810764, _1810766, _1810768, _1810770) = c_Nitpick_Opair__box_OPairBox(_1810764, _1810766, _1810772, _1810774), 50813 ^ _780119 : [(50816 ^ _780119) ^ [] : [-(_1810770 = _1810774)], (50814 ^ _780119) ^ [] : [-(_1810768 = _1810772)]]], (46700 ^ _780119) ^ [_1721837] : [-(c_List_Otranspose(_1721837, c_List_Olist_ONil(tc_List_Olist(_1721837))) = c_List_Olist_ONil(tc_List_Olist(_1721837)))], (43880 ^ _780119) ^ [_1656842, _1656844, _1656846] : [class_Orderings_Olinorder(_1656842), hBOOL(hAPP(hAPP(c_member(_1656842), _1656844), hAPP(c_List_Oset(_1656842), _1656846))), -(c_List_Olinorder__class_Oinsort__insert__key(_1656842, _1656842, c_COMBI(_1656842), _1656844, _1656846) = _1656846)], (5114 ^ _780119) ^ [_858367, _858369, _858371, _858373, _858375, _858377] : [-(c_List_Osplice(_858377, _858373, _858369) = c_List_Osplice(_858375, _858371, _858367)), _858377 = _858375, _858373 = _858371, _858369 = _858367], (45794 ^ _780119) ^ [_1702464, _1702466, _1702468, _1702470, _1702472] : [-(hAPP(hAPP(c_List_Ozip(_1702464, _1702466), hAPP(hAPP(c_List_Oappend(_1702464), _1702468), _1702470)), 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hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1567295, _1567295), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1567301)), _1567303))))], (26370 ^ _780119) ^ [_1261407, _1261409] : [-(hBOOL(hAPP(_1261409, 26371 ^ [_1261407, _1261409]))), -(hAPP(c_Set_OCollect(_1261407), _1261409) = c_Orderings_Obot__class_Obot(tc_fun(_1261407, tc_HOL_Obool)))], (19709 ^ _780119) ^ [_1138642, _1138644, _1138646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1138642), _1138644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1138642), _1138646)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1138644), _1138646))))], (5590 ^ _780119) ^ [_865735, _865737, _865739, _865741] : [-(c_COMBK(_865741, _865737) = c_COMBK(_865739, _865735)), _865741 = _865739, _865737 = _865735], (45592 ^ _780119) ^ [_1697578, _1697580] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697578)), hAPP(c_List_Orotate1(_1697578), _1697580)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697578)), _1697580))], (6867 ^ _780119) ^ [_893675, _893677, _893679] : [class_Orderings_Oorder(_893675), 6870 ^ _780119 : [(6879 ^ _780119) ^ [] : [-(_893677 = _893679), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893675), _893677), _893679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893675), _893679), _893677))], (6871 ^ _780119) ^ [] : [_893677 = _893679, 6874 ^ _780119 : [(6877 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893675), _893679), _893677)))], (6875 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893675), _893677), _893679)))]]]]], (33115 ^ _780119) ^ [_1397286, _1397288, _1397290] : [class_Rings_Olinordered__idom(_1397286), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397286), _1397288), c_Groups_Ozero__class_Ozero(_1397286))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397286), hAPP(hAPP(c_Power_Opower__class_Opower(_1397286), _1397288), 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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)), _1444013), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (31659 ^ _780119) ^ [_1371031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371031), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371031))], (30062 ^ _780119) ^ [_1341992, _1341994, _1341996] : [class_Orderings_Olinorder(_1341992), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341992), _1341994)), 30072 ^ _780119 : [(30075 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341992), _1341996), 30071 ^ [_1341992, _1341994, _1341996]))], (30073 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1341992), 30071 ^ [_1341992, _1341994, _1341996]), _1341994)))]], hBOOL(hAPP(hAPP(c_member(_1341992), _1341996), _1341994)), -(c_Big__Operators_Olinorder__class_OMin(_1341992, _1341994) = _1341996)], (10106 ^ _780119) ^ [_956290, _956292, _956294, _956296] : [class_Lattices_Odistrib__lattice(_956290), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_956290), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956290), _956292), _956294)), _956296) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956290), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_956290), _956292), _956296)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_956290), _956294), _956296)))], (43555 ^ _780119) ^ [_1648181, _1648183, _1648185, _1648187] : [-(_1648181 = _1648183), -(c_List_Oremove1(_1648185, _1648181, hAPP(hAPP(c_List_Olist_OCons(_1648185), _1648183), _1648187)) = hAPP(hAPP(c_List_Olist_OCons(_1648185), _1648183), c_List_Oremove1(_1648185, _1648181, _1648187)))], (41629 ^ _780119) ^ [_1600818, _1600820, _1600822, _1600824] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1600818, tc_HOL_Obool), tc_fun(_1600820, tc_HOL_Obool)), _1600822), hAPP(hAPP(c_COMBC(tc_fun(_1600818, tc_HOL_Obool), tc_fun(_1600818, tc_fun(_1600820, tc_HOL_Obool)), tc_fun(_1600820, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1600818, tc_fun(_1600820, tc_HOL_Obool))), _1600824)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1600818, tc_fun(_1600820, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1600818, tc_HOL_Obool), _1600822)), _1600824))], (22300 ^ _780119) ^ [_1186984, _1186986, _1186988] : [-(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), _1186984), _1186986)), _1186988)), _1186986) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1186988), _1186986))], (21360 ^ _780119) ^ [_1169195, _1169197] : [hAPP(c_Set_OPow(_1169195), _1169197) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1169195, tc_HOL_Obool), tc_HOL_Obool))], (48253 ^ _780119) ^ [_1755892, _1755894, _1755896] : [-(c_Enum_Oproduct(_1755892, _1755894, c_List_Olist_ONil(_1755892), _1755896) = c_List_Olist_ONil(tc_prod(_1755892, _1755894)))], (3610 ^ _780119) ^ [_834407, _834409, _834411, _834413] : [-(c_Fun_Ofun__upd(_834413, _834409) = c_Fun_Ofun__upd(_834411, _834407)), _834413 = _834411, _834409 = _834407], (51561 ^ _780119) ^ [_1820295, _1820297, _1820299, _1820301, _1820303, _1820305] : [-(hAPP(hAPP(hAPP(c_COMBS(_1820295, _1820297, _1820299), _1820301), _1820303), _1820305) = hAPP(hAPP(_1820301, _1820305), hAPP(_1820303, _1820305)))], (21745 ^ _780119) ^ [_1177232, _1177234, _1177236] : [class_Divides_Osemiring__div(_1177232), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177232), c_Divides_Odiv__class_Omod(_1177232, _1177234, _1177236)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177232), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1177232), _1177234), _1177236)), _1177236)) = _1177234)], (22751 ^ _780119) ^ [_1195761, _1195763] : [-(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, _1195761)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1195763))))], (49311 ^ _780119) ^ [_1777995, _1777997, _1777999] : [-(hAPP(c_List_Oset(_1777995), c_List_Oinsert(_1777995, _1777997, _1777999)) = hAPP(hAPP(c_Set_Oinsert(_1777995), _1777997), hAPP(c_List_Oset(_1777995), _1777999)))], (51093 ^ _780119) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (38270 ^ _780119) ^ [_1519764, _1519766, _1519768] : [c_Wellfounded_OwfP(_1519764, _1519766), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519764, tc_fun(_1519764, tc_HOL_Obool))), _1519768), _1519766)), -(c_Wellfounded_OwfP(_1519764, _1519768))], (26177 ^ _780119) ^ [_1257456, _1257458, _1257460] : [class_Groups_Ocomm__monoid__add(_1257456), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1257456), _1257458), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1257460))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1257456), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1257456), _1257458), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1257460))), hAPP(_1257458, hAPP(c_Nat_OSuc, _1257460))))], (51505 ^ _780119) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (39960 ^ _780119) ^ [_1560063, _1560065, _1560067] : [c_Relation_Ototal__on(_1560063, _1560065, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1560063, _1560063), tc_HOL_Obool)), _1560067), c_Relation_OId(_1560063))), -(c_Relation_Ototal__on(_1560063, _1560065, _1560067))], (15460 ^ _780119) ^ [_1061989, _1061991] : [class_Orderings_Otop(_1061989), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061989), _1061991), c_Orderings_Otop__class_Otop(_1061989))))], (22637 ^ _780119) ^ [_1193315] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1193315)), 22641 ^ _780119 : [(22642 ^ _780119) ^ [_1193395] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1193395), _1193315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1193395), 22640 ^ [_1193315])))]]], (18700 ^ _780119) ^ [_1121152, _1121154, _1121156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121152), _1121154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121156), _1121152)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121156), _1121154))))], (31605 ^ _780119) ^ [_1370212] : [-(c_Int_Opred(_1370212) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1370212), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36091 ^ _780119) ^ [_1464660, _1464662, _1464664] : [-(c_Fun_Oinj__on(_1464660, _1464662, _1464664, c_Orderings_Obot__class_Obot(tc_fun(_1464660, tc_HOL_Obool))))], (14488 ^ _780119) ^ [_1045779, _1045781, _1045783, _1045785] : [class_Rings_Olinordered__semidom(_1045779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045781), _1045783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045779), c_Groups_Oone__class_Oone(_1045779)), _1045785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045779), hAPP(hAPP(c_Power_Opower__class_Opower(_1045779), _1045785), _1045781)), hAPP(hAPP(c_Power_Opower__class_Opower(_1045779), _1045785), _1045783))))], (38036 ^ _780119) ^ [_1513990, _1513992] : [-(hAPP(c_Set_Ovimage(_1513990, _1513990, c_Fun_Oid(_1513990)), _1513992) = _1513992)], (22871 ^ _780119) ^ [_1197768, _1197770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197768), _1197770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197768)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197770))))], (27628 ^ _780119) ^ [_1290523, _1290525, _1290527] : [class_Orderings_Olinorder(_1290523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290523), _1290525), _1290527)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290523), _1290525), _1290527) = _1290527)], (27292 ^ _780119) ^ [_1284575, _1284577] : [class_Groups_Olinordered__ab__group__add(_1284575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284575), _1284577)), -(_1284577 = c_Orderings_Obot__class_Obot(tc_fun(_1284575, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1284575), c_Big__Operators_Olinorder__class_OMax(_1284575, _1284577)) = c_Big__Operators_Olinorder__class_OMin(_1284575, hAPP(c_Set_Oimage(_1284575, _1284575, c_Groups_Ouminus__class_Ouminus(_1284575)), _1284577)))], (19763 ^ _780119) ^ [_1139746, _1139748, _1139750, _1139752] : [class_Rings_Odivision__ring(_1139746), -(_1139748 = c_Groups_Ozero__class_Ozero(_1139746)), 19770 ^ _780119 : [(19777 ^ _780119) ^ [] : [_1139750 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139746), _1139752), _1139748), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139746), _1139750), _1139748) = _1139752)], (19771 ^ _780119) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139746), _1139750), _1139748) = _1139752, -(_1139750 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139746), _1139752), _1139748))]]], (51493 ^ _780119) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (14060 ^ _780119) ^ [_1036181] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1036181)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1036181)], (14814 ^ _780119) ^ [_1052038, _1052040] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1052038, _1052040)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1052038, _1052040), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052040), c_Orderings_Otop__class_Otop(tc_fun(_1052040, tc_HOL_Obool)))))], (51319 ^ _780119) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (42375 ^ _780119) ^ [_1617921, _1617923, _1617925, _1617927, _1617929] : [-(hAPP(c_Map_Omap__add(_1617921, _1617923, _1617925, _1617927), _1617929) = c_Option_Ooption_ONone(_1617923)), hAPP(_1617927, _1617929) = c_Option_Ooption_ONone(_1617923), hAPP(_1617925, _1617929) = c_Option_Ooption_ONone(_1617923)], (32369 ^ _780119) ^ [_1383781, _1383783] : [_1383781 = _1383783, -(c_Int_OBit0(_1383781) = c_Int_OBit0(_1383783))], (15044 ^ _780119) ^ [_1055716, _1055718] : [class_Rings_Ocomm__semiring__1(_1055716), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055716), c_Groups_Ozero__class_Ozero(_1055716)), _1055718) = c_Groups_Ozero__class_Ozero(_1055716))], (5706 ^ _780119) ^ [_867499, _867501] : [_867501 = _867499, -(c_Set_Oinsert(_867501) = c_Set_Oinsert(_867499))], (17081 ^ _780119) ^ [_1090272, _1090274, _1090276] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1090272), _1090274)), 17084 ^ _780119 : [(17085 ^ _780119) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1090272, tc_Nat_Onat), _1090276), _1090274) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 17088 ^ _780119 : [(17089 ^ _780119) ^ [_1090434] : [hBOOL(hAPP(hAPP(c_member(_1090272), _1090434), _1090274)), -(hAPP(_1090276, _1090434) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (17095 ^ _780119) ^ [] : [17097 ^ _780119 : [(17100 ^ _780119) ^ [] : [hAPP(_1090276, 17096 ^ [_1090272, _1090274, _1090276]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17098 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1090272), 17096 ^ [_1090272, _1090274, _1090276]), _1090274)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1090272, tc_Nat_Onat), _1090276), _1090274) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (26877 ^ _780119) ^ [_1271765, _1271767] : [class_Groups_Oordered__ab__group__add__abs(_1271765), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271765), _1271767), c_Groups_Ozero__class_Ozero(_1271765))), -(hAPP(c_Groups_Oabs__class_Oabs(_1271765), _1271767) = hAPP(c_Groups_Ouminus__class_Ouminus(_1271765), _1271767))], (45128 ^ _780119) ^ [_1684520, _1684522, _1684524, _1684526, _1684528, _1684530] : [hAPP(hAPP(c_List_Oappend(_1684520), _1684522), _1684524) = _1684526, _1684528 = hAPP(hAPP(c_List_Oappend(_1684520), _1684524), _1684530), -(hAPP(hAPP(c_List_Oappend(_1684520), _1684522), _1684528) = hAPP(hAPP(c_List_Oappend(_1684520), _1684526), _1684530))], (45844 ^ _780119) ^ [_1703496, _1703498] : [-(_1703496 = c_List_Olist_ONil(_1703498)), -(hBOOL(hAPP(hAPP(c_member(_1703498), hAPP(c_List_Ohd(_1703498), _1703496)), hAPP(c_List_Oset(_1703498), _1703496))))], (27097 ^ _780119) ^ [_1278580, _1278582] : [-(hAPP(c_Set_OPow(_1278580), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1278580, tc_HOL_Obool)), _1278582)) = hAPP(c_Set_OCollect(tc_fun(_1278580, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1278580, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1278580, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1278580, tc_HOL_Obool), tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1278580, tc_HOL_Obool)), c_COMBS(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1278580, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1278580, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1278580, tc_HOL_Obool), tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_fun(_1278580, tc_HOL_Obool)), tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_fun(_1278580, tc_HOL_Obool)), tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1278580, tc_HOL_Obool)), c_COMBB(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1278580, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1278580, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1278580, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1278580, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1278580, tc_HOL_Obool)), _1278582)), c_Set_OPow(_1278580))))))], (44328 ^ _780119) ^ [_1668092, _1668094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1668092), _1668094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1668092)), hAPP(c_Code__Numeral_Oof__nat, _1668094))))], (6589 ^ _780119) ^ [_887302, _887304, _887306, _887308] : [6590 ^ _780119 : [(6591 ^ _780119) ^ [_887412] : [hBOOL(hAPP(hAPP(c_member(_887302), _887412), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887302, tc_HOL_Obool)), _887304), _887306))), hBOOL(hAPP(_887308, _887412))]], 6599 ^ _780119 : [(6602 ^ _780119) ^ [] : [-(hBOOL(hAPP(_887308, 6598 ^ [_887302, _887304, _887306, _887308])))], (6600 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887302), 6598 ^ [_887302, _887304, _887306, _887308]), _887304)))]], 6604 ^ _780119 : [(6607 ^ _780119) ^ [] : [-(hBOOL(hAPP(_887308, 6603 ^ [_887302, _887304, _887306, _887308])))], (6605 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887302), 6603 ^ [_887302, _887304, _887306, _887308]), _887306)))]]], (1730 ^ _780119) ^ [_804468, _804470] : [-(class_Rings_Omult__zero(_804468)), _804470 = _804468, class_Rings_Omult__zero(_804470)], (1710 ^ _780119) ^ [_804218, _804220] : [-(class_Rings_Osemiring__1(_804218)), _804220 = _804218, class_Rings_Osemiring__1(_804220)], (26201 ^ _780119) ^ [_1257955, _1257957, _1257959] : [class_Orderings_Oorder(_1257955), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1257955, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1257955), _1257957)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1257955, _1257957, _1257959)) = c_Orderings_Obot__class_Obot(tc_fun(_1257955, tc_HOL_Obool)))], (14308 ^ _780119) ^ [_1041725, _1041727, _1041729, _1041731, _1041733] : [c_Hoare__Mirabelle_Otriple__valid(_1041725, hAPP(c_Nat_OSuc, _1041727), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1041725), _1041729), hAPP(c_Com_Ocom_OBODY, _1041731)), _1041733)), -(c_Hoare__Mirabelle_Otriple__valid(_1041725, _1041727, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1041725), _1041729), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1041731))), _1041733)))], (43090 ^ _780119) ^ [_1634653, _1634655, _1634657, _1634659, _1634661, _1634663] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634653, _1634655)), hAPP(hAPP(c_Product__Type_OPair(_1634653, _1634655), _1634657), _1634659)), hAPP(c_List_Oset(tc_prod(_1634653, _1634655)), hAPP(hAPP(c_List_Ozip(_1634653, _1634655), _1634661), _1634663)))), -(hBOOL(hAPP(hAPP(c_member(_1634653), _1634657), hAPP(c_List_Oset(_1634653), _1634661))))], (41143 ^ _780119) ^ [_1587652, _1587654, _1587656, _1587658, _1587660] : [hBOOL(hAPP(hAPP(c_member(_1587652), _1587654), _1587656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1587658, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587652, tc_fun(_1587658, tc_HOL_Obool)), _1587656), _1587660)), hAPP(_1587660, _1587654))))], (6381 ^ _780119) ^ [_883038, _883040, _883042, _883044] : [-(hBOOL(hAPP(hAPP(c_member(_883038), _883040), _883042))), 6384 ^ _780119 : [(6391 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883038, tc_HOL_Obool)), _883042), _883044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883038, tc_HOL_Obool)), _883042), hAPP(hAPP(c_Set_Oinsert(_883038), _883040), _883044))))], (6385 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883038, tc_HOL_Obool)), _883042), hAPP(hAPP(c_Set_Oinsert(_883038), _883040), _883044))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883038, tc_HOL_Obool)), _883042), _883044)))]]], (25686 ^ _780119) ^ [_1249158, _1249160] : [c_Nat__Transfer_Ois__nat(_1249158), c_Nat__Transfer_Onat__set(_1249160), 25693 ^ _780119 : [(25700 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1249158)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1249160))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1249158), _1249160)))], (25694 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1249158), _1249160)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1249158)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1249160))))]]], (31671 ^ _780119) ^ [_1371223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371223), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371223) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1740 ^ _780119) ^ [_804593, _804595] : [-(class_Orderings_Oorder(_804593)), _804595 = _804593, class_Orderings_Oorder(_804595)], (24081 ^ _780119) ^ [_1220932, _1220934] : [24083 ^ _780119 : [(24086 ^ _780119) ^ [] : [hBOOL(hAPP(_1220934, 24082 ^ [_1220932, _1220934]))], (24084 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 24082 ^ [_1220932, _1220934]), _1220932)))]], 24087 ^ _780119 : [(24088 ^ _780119) ^ [_1221083] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1221083), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1220932))), -(hBOOL(hAPP(_1220934, _1221083)))]]], (28878 ^ _780119) ^ [_1315401, _1315403] : [class_Orderings_Olinorder(_1315401), -(c_Big__Operators_Olattice_OInf__fin(_1315401, c_Orderings_Oord__class_Omin(_1315401), hAPP(hAPP(c_Set_Oinsert(_1315401), _1315403), c_Orderings_Obot__class_Obot(tc_fun(_1315401, tc_HOL_Obool)))) = _1315403)], (38081 ^ _780119) ^ [_1514990, _1514992, _1514994, _1514996, _1514998, _1515000] : [class_Groups_Ocomm__monoid__add(_1514990), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514992), _1514994)), 38091 ^ _780119 : [(38094 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514996), hAPP(_1514998, 38090 ^ [_1514990, _1514992, _1514994, _1514996, _1514998, _1515000])))], (38092 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514992), 38090 ^ [_1514990, _1514992, _1514994, _1514996, _1514998, _1515000]), _1514994)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514992, _1514990), hAPP(hAPP(c_COMBS(_1514992, tc_fun(_1514996, tc_HOL_Obool), _1514990), hAPP(hAPP(c_COMBB(tc_fun(_1514996, _1514990), tc_fun(tc_fun(_1514996, tc_HOL_Obool), _1514990), _1514992), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514996, _1514990)), _1515000)), _1514998)), _1514994) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1514992, _1514996), _1514990), hAPP(c_Product__Type_Oprod_Oprod__case(_1514992, _1514996, _1514990), _1515000)), hAPP(hAPP(c_Product__Type_OSigma(_1514992, _1514996), _1514994), _1514998)))], (29544 ^ _780119) ^ [_1328733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328733), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1328733)))], (17366 ^ _780119) ^ [_1095650, _1095652, _1095654, _1095656] : [class_Rings_Olinordered__semiring__strict(_1095650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095650), _1095652), _1095654)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095650), _1095656), _1095654))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095650), c_Groups_Ozero__class_Ozero(_1095650)), _1095654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095650), _1095652), _1095656)))], (36956 ^ _780119) ^ [_1483348, _1483350, _1483352, _1483354, _1483356, _1483358, _1483360] : [c_Typedef_Otype__definition(_1483348, _1483350, _1483352, _1483354, _1483356), 36959 ^ _780119 : [(36966 ^ _780119) ^ [] : [_1483358 = _1483360, -(hAPP(_1483352, _1483358) = hAPP(_1483352, _1483360))], (36960 ^ _780119) ^ [] : [hAPP(_1483352, _1483358) = hAPP(_1483352, _1483360), -(_1483358 = _1483360)]]], (5744 ^ _780119) ^ [_870972, _870974] : [hAPP(_870972, 5745 ^ [_870972, _870974]) = hAPP(_870974, 5745 ^ [_870972, _870974]), -(_870972 = _870974)], (32405 ^ _780119) ^ [_1384421, _1384423] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1384421)), c_Int_OBit0(_1384423)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1384421), _1384423)))], (308 ^ _780119) ^ [_784955, _784957, _784959, _784961] : [-(c_FunDef_Oreduction__pair(_784959, _784955)), c_FunDef_Oreduction__pair(_784961, _784957), _784961 = _784959, _784957 = _784955], (50700 ^ _780119) ^ [_1808314, _1808316, _1808318] : [class_Fields_Olinordered__field(_1808314), 50706 ^ _780119 : [(50709 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1808314), _1808316), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808314), _1808318), 50705 ^ [_1808314, _1808316, _1808318])))], (50707 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1808314), c_Groups_Ozero__class_Ozero(_1808314)), 50705 ^ [_1808314, _1808316, _1808318])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1808314), _1808316), _1808318)))], (22960 ^ _780119) ^ [_1199429, _1199431] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1199429), _1199431)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199429)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199431)))], (47357 ^ _780119) ^ [_1734386, _1734388, _1734390, _1734392, _1734394] : [class_Orderings_Olinorder(_1734386), c_Fun_Oinj__on(_1734388, _1734386, _1734390, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1734388, tc_HOL_Obool)), hAPP(c_List_Oset(_1734388), _1734392)), hAPP(c_List_Oset(_1734388), _1734394))), c_List_Olinorder__class_Osorted(_1734386, hAPP(hAPP(c_List_Omap(_1734388, _1734386), _1734390), _1734392)), hBOOL(hAPP(c_List_Odistinct(_1734386), hAPP(hAPP(c_List_Omap(_1734388, _1734386), _1734390), _1734392))), c_List_Olinorder__class_Osorted(_1734386, hAPP(hAPP(c_List_Omap(_1734388, _1734386), _1734390), _1734394)), hBOOL(hAPP(c_List_Odistinct(_1734386), hAPP(hAPP(c_List_Omap(_1734388, _1734386), _1734390), _1734394))), hAPP(c_List_Oset(_1734388), _1734392) = hAPP(c_List_Oset(_1734388), _1734394), -(_1734392 = _1734394)], (48183 ^ _780119) ^ [_1753739, _1753741, _1753743] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753739))), c_Enum_On__lists(_1753739, _1753741, _1753743)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753739)), _1753743)), _1753741))], (45026 ^ _780119) ^ [_1682669, _1682671, _1682673] : [c_List_Olist_ONil(_1682669) = hAPP(hAPP(c_List_Oappend(_1682669), _1682671), _1682673), 45029 ^ _780119 : [(45032 ^ _780119) ^ [] : [-(_1682673 = c_List_Olist_ONil(_1682669))], (45030 ^ _780119) ^ [] : [-(_1682671 = c_List_Olist_ONil(_1682669))]]], (45670 ^ _780119) ^ [_1699328, _1699330, _1699332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699328)), _1699332)), _1699330)), -(hAPP(hAPP(c_List_Odrop(_1699328), _1699330), _1699332) = c_List_Olist_ONil(_1699328))], (34150 ^ _780119) ^ [_1421421, _1421423] : [c_Nitpick_Orefl_H(_1421421, _1421423), 34153 ^ _780119 : [(34154 ^ _780119) ^ [_1421499] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1421421, _1421421)), hAPP(hAPP(c_Product__Type_OPair(_1421421, _1421421), _1421499), _1421499)), _1421423)))]]], (39727 ^ _780119) ^ [_1554531, _1554533] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1554531, _1554531, _1554531), c_Transitive__Closure_Ortrancl(_1554531, _1554533)), c_Transitive__Closure_Ortrancl(_1554531, _1554533)) = c_Transitive__Closure_Ortrancl(_1554531, _1554533))], (48007 ^ _780119) ^ [_1749766, _1749768, _1749770] : [-(hBOOL(hAPP(hAPP(c_member(_1749766), _1749768), hAPP(c_List_Oset(_1749766), _1749770)))), -(c_List_Oremdups(_1749766, hAPP(hAPP(c_List_Olist_OCons(_1749766), _1749768), _1749770)) = hAPP(hAPP(c_List_Olist_OCons(_1749766), _1749768), c_List_Oremdups(_1749766, _1749770)))], (8038 ^ _780119) ^ [_917501, _917503] : [hBOOL(hAPP(c_Com_OWT, _917501)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_917503, _917501))))], (23687 ^ _780119) ^ [_1213063, _1213065, _1213067, _1213069] : [class_Orderings_Oorder(_1213063), 23690 ^ _780119 : [(23699 ^ _780119) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1213063, _1213065, _1213067) = hAPP(hAPP(c_Set_Oinsert(_1213063), _1213069), c_Orderings_Obot__class_Obot(tc_fun(_1213063, tc_HOL_Obool)))), _1213065 = _1213067, _1213067 = _1213069], (23691 ^ _780119) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1213063, _1213065, _1213067) = hAPP(hAPP(c_Set_Oinsert(_1213063), _1213069), c_Orderings_Obot__class_Obot(tc_fun(_1213063, tc_HOL_Obool))), 23694 ^ _780119 : [(23697 ^ _780119) ^ [] : [-(_1213067 = _1213069)], (23695 ^ _780119) ^ [] : [-(_1213065 = _1213067)]]]]], (17051 ^ _780119) ^ [_1089857, _1089859] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1089857), _1089859) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1089857), _1089859)))], (49646 ^ _780119) ^ [_1786786, _1786788, _1786790, _1786792] : [c_List_Olist__ex(_1786786, _1786788, hAPP(hAPP(c_List_Olist_OCons(_1786786), _1786790), _1786792)), -(hBOOL(hAPP(_1786788, _1786790))), -(c_List_Olist__ex(_1786786, _1786788, _1786792))], (10789 ^ _780119) ^ [_971401, _971403, _971405, _971407] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_971401), 10792 ^ _780119 : [(10799 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971401), _971403), _971407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971401), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971401), _971403), _971405)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971401), _971407), _971405))))], (10793 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971401), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971401), _971403), _971405)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971401), _971407), _971405))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971401), _971403), _971407)))]]], (32535 ^ _780119) ^ [_1386595, _1386597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1386595), _1386597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1386595)), c_Int_OBit0(_1386597))))], (3360 ^ _780119) ^ [_830556, _830558, _830560, _830562, _830564, _830566, _830568, _830570] : [-(c_Product__Type_Oscomp(_830570, _830566, _830562, _830558) = c_Product__Type_Oscomp(_830568, _830564, _830560, _830556)), _830570 = _830568, _830566 = _830564, _830562 = _830560, _830558 = _830556], (27346 ^ _780119) ^ [_1285443, _1285445] : [class_Orderings_Olinorder(_1285443), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285443), _1285445)), -(_1285445 = c_Orderings_Obot__class_Obot(tc_fun(_1285443, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1285443), c_Big__Operators_Olinorder__class_OMin(_1285443, _1285445)), _1285445)))], (18640 ^ _780119) ^ [_1120172] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120172)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1120172)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (3118 ^ _780119) ^ [_826637, _826639] : [_826639 = _826637, -(c_Nitpick_Odenom(_826639) = c_Nitpick_Odenom(_826637))], (50474 ^ _780119) ^ [_1803693, _1803695, _1803697, _1803699] : [-(c_Predicate_Oconversep(_1803693, _1803695, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803693, tc_fun(_1803695, tc_HOL_Obool))), _1803697), _1803699)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803695, tc_fun(_1803693, tc_HOL_Obool))), c_Predicate_Oconversep(_1803693, _1803695, _1803697)), c_Predicate_Oconversep(_1803693, _1803695, _1803699)))], (37459 ^ _780119) ^ [_1496643, _1496645, _1496647, _1496649] : [37461 ^ _780119 : [(37464 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1496645, hAPP(_1496647, 37460 ^ [_1496643, _1496645, _1496647, _1496649]))), hAPP(_1496645, 37460 ^ [_1496643, _1496645, _1496647, _1496649])))], (37462 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1496643, 37460 ^ [_1496643, _1496645, _1496647, _1496649])))]], -(c_Wellfounded_Owf(_1496649, hAPP(c_Set_OCollect(tc_prod(_1496649, _1496649)), hAPP(c_Product__Type_Oprod_Oprod__case(_1496649, _1496649, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1496649, tc_HOL_Obool), tc_fun(_1496649, tc_HOL_Obool), _1496649), hAPP(c_COMBS(_1496649, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1496649), c_fconj), _1496643))), hAPP(hAPP(c_COMBC(_1496649, tc_fun(_1496649, _1496649), tc_fun(_1496649, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1496649, tc_HOL_Obool), tc_fun(tc_fun(_1496649, _1496649), tc_fun(_1496649, tc_HOL_Obool)), _1496649), c_COMBB(_1496649, tc_HOL_Obool, _1496649)), c_fequal)), _1496647))))))], (20320 ^ _780119) ^ [_1149793, _1149795, _1149797, _1149799] : [class_Fields_Olinordered__field__inverse__zero(_1149793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149793), _1149795), _1149797)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149793), c_Groups_Ozero__class_Ozero(_1149793)), _1149799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149793), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149793), _1149795), _1149799)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149793), _1149797), _1149799))))], (47634 ^ _780119) ^ [_1740780, _1740782, _1740784] : [-(hAPP(c_List_Orev(_1740780), hAPP(hAPP(c_List_Odrop(_1740780), _1740782), _1740784)) = hAPP(hAPP(c_List_Otake(_1740780), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740780)), _1740784)), _1740782)), hAPP(c_List_Orev(_1740780), _1740784)))], (48526 ^ _780119) ^ [_1761505, _1761507] : [class_Enum_Oenum(_1761505), 48529 ^ _780119 : [(48536 ^ _780119) ^ [] : [hBOOL(hAPP(_1761507, 48537 ^ [_1761505, _1761507])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1761505), _1761507)))], (48530 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1761505), _1761507)), 48533 ^ _780119 : [(48534 ^ _780119) ^ [_1761631] : [-(hBOOL(hAPP(_1761507, _1761631)))]]]]], (37468 ^ _780119) ^ [_1497036, _1497038, _1497040, _1497042] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497036), _1497038)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497036), _1497040)), -(_1497040 = c_Orderings_Obot__class_Obot(tc_fun(_1497036, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1497036, tc_HOL_Obool), tc_fun(_1497036, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1497036, tc_HOL_Obool), tc_fun(_1497036, tc_HOL_Obool)), _1497038), _1497040)), c_Wellfounded_Omax__ext(_1497036, _1497042)))), 37482 ^ _780119 : [(37485 ^ _780119) ^ [_1497441] : [hBOOL(hAPP(hAPP(c_member(_1497036), _1497441), _1497040)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1497036, _1497036)), hAPP(hAPP(c_Product__Type_OPair(_1497036, _1497036), 37481 ^ [_1497036, _1497038, _1497040, _1497042]), _1497441)), _1497042))], (37483 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497036), 37481 ^ [_1497036, _1497038, _1497040, _1497042]), _1497038)))]]], (44900 ^ _780119) ^ [_1679214, _1679216, _1679218, _1679220, _1679222] : [-(_1679214 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1679216, _1679218, _1679220), _1679214), _1679222) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1679218), _1679216), tc_prod(_1679218, _1679216), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679218), _1679216), c_List_Olist_ONil(_1679218)), _1679222), hAPP(c_Product__Type_Oprod_Oprod__case(_1679218, _1679216, tc_prod(tc_List_Olist(_1679218), _1679216)), hAPP(hAPP(c_COMBC(_1679218, tc_fun(_1679216, tc_prod(tc_List_Olist(_1679218), _1679216)), tc_fun(_1679216, tc_prod(tc_List_Olist(_1679218), _1679216))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1679218), _1679216), tc_prod(tc_List_Olist(_1679218), _1679216)), tc_fun(tc_fun(_1679216, tc_prod(tc_List_Olist(_1679218), _1679216)), tc_fun(_1679216, tc_prod(tc_List_Olist(_1679218), _1679216))), _1679218), c_COMBB(tc_prod(tc_List_Olist(_1679218), _1679216), tc_prod(tc_List_Olist(_1679218), _1679216), _1679216)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1679218), tc_fun(_1679216, tc_prod(tc_List_Olist(_1679218), _1679216))), tc_fun(tc_prod(tc_List_Olist(_1679218), _1679216), tc_prod(tc_List_Olist(_1679218), _1679216)), _1679218), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1679218), _1679216, tc_prod(tc_List_Olist(_1679218), _1679216))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1679218), tc_List_Olist(_1679218)), tc_fun(tc_List_Olist(_1679218), tc_fun(_1679216, tc_prod(tc_List_Olist(_1679218), _1679216))), _1679218), hAPP(c_COMBB(tc_List_Olist(_1679218), tc_fun(_1679216, tc_prod(tc_List_Olist(_1679218), _1679216)), tc_List_Olist(_1679218)), c_Product__Type_OPair(tc_List_Olist(_1679218), _1679216))), c_List_Olist_OCons(_1679218))))), hAPP(c_Lazy__Sequence_Oanamorph(_1679216, _1679218, _1679220), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1679214), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1679220, _1679222)))], (34309 ^ _780119) ^ [_1424004, _1424006] : [-(_1424004 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34312 ^ _780119 : [(34319 ^ _780119) ^ [] : [-(_1424006 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1424004, _1424006) = 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, _1424006))), 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)), _1424006)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1424004))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1424006), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1424004), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1424004, _1424006)), 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), _1424006))))), c_Divides_Opdivmod(_1424004, _1424006)))))], (34313 ^ _780119) ^ [] : [_1424006 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1424004, _1424006) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1424004))]]], (45994 ^ _780119) ^ [_1706344, _1706346, _1706348, _1706350] : [class_Groups_Osemigroup__add(_1706344), -(hAPP(c_List_Ofoldl(_1706344, _1706344, c_Groups_Oplus__class_Oplus(_1706344), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1706344), _1706346), _1706348)), _1706350) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1706344), _1706346), hAPP(c_List_Ofoldl(_1706344, _1706344, c_Groups_Oplus__class_Oplus(_1706344), _1706348), _1706350)))], (14156 ^ _780119) ^ [_1038401, _1038403, _1038405, _1038407, _1038409] : [class_Groups_Ocomm__monoid__mult(_1038401), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038403), _1038405)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038403), _1038407)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038401), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038403, _1038401), _1038409), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1038403, tc_HOL_Obool)), _1038405), _1038407))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038403, _1038401), _1038409), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1038403, tc_HOL_Obool)), _1038405), _1038407))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038401), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038403, _1038401), _1038409), _1038405)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038403, _1038401), _1038409), _1038407)))], (43489 ^ _780119) ^ [_1646733, _1646735, _1646737, _1646739, _1646741, _1646743] : [-(hAPP(hAPP(c_List_Ozip(_1646733, _1646735), hAPP(hAPP(c_List_Olist_OCons(_1646733), _1646737), _1646739)), hAPP(hAPP(c_List_Olist_OCons(_1646735), _1646741), _1646743)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1646733, _1646735)), hAPP(hAPP(c_Product__Type_OPair(_1646733, _1646735), _1646737), _1646741)), hAPP(hAPP(c_List_Ozip(_1646733, _1646735), _1646739), _1646743)))], (588 ^ _780119) ^ [_789163, _789165] : [-(class_Rings_Oinverse(_789163)), _789165 = _789163, class_Rings_Oinverse(_789165)], (48023 ^ _780119) ^ [_1750079, _1750081, _1750083] : [hBOOL(hAPP(c_List_Odistinct(_1750079), _1750081)), hBOOL(hAPP(hAPP(c_member(_1750079), _1750083), hAPP(c_List_Oset(_1750079), _1750081))), -(c_List_OtakeWhile(_1750079, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1750079), c_fNot), hAPP(hAPP(c_COMBC(_1750079, _1750079, tc_HOL_Obool), c_fequal), _1750083)), hAPP(c_List_Orev(_1750079), _1750081)) = hAPP(c_List_Orev(_1750079), hAPP(c_List_Otl(_1750079), c_List_OdropWhile(_1750079, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1750079), c_fNot), hAPP(hAPP(c_COMBC(_1750079, _1750079, tc_HOL_Obool), c_fequal), _1750083)), _1750081))))], (40341 ^ _780119) ^ [_1569715, _1569717, _1569719] : [c_Relation_Osingle__valued(_1569715, _1569715, _1569717), -(c_Relation_Osingle__valued(_1569715, _1569715, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1569715, _1569715), tc_HOL_Obool), _1569719), _1569717)))], (50160 ^ _780119) ^ [_1796662] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1796662), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1796662)), c_Int_OPls)))], (44758 ^ _780119) ^ [_1676594, _1676596] : [-(hAPP(hAPP(c_List_Otake(_1676594), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1676596) = c_List_Olist_ONil(_1676594))], (21012 ^ _780119) ^ [_1162339, _1162341, _1162343, _1162345] : [class_Fields_Ofield(_1162339), -(_1162341 = c_Groups_Ozero__class_Ozero(_1162339)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162339), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162339), _1162343), _1162341)), _1162345) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162339), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162339), _1162343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162339), _1162341), _1162345))), _1162341))], (25576 ^ _780119) ^ [_1247691, _1247693] : [c_Nat__Transfer_Onat__set(_1247691), c_Nat__Transfer_Onat__set(_1247693), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1247691), _1247693)))], (39649 ^ _780119) ^ [_1552598, _1552600, _1552602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552598, _1552598), tc_HOL_Obool)), _1552600), _1552602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552598, _1552598), tc_HOL_Obool)), _1552602), c_Transitive__Closure_Ortrancl(_1552598, _1552600))), -(c_Transitive__Closure_Ortrancl(_1552598, _1552602) = c_Transitive__Closure_Ortrancl(_1552598, _1552600))], (45223 ^ _780119) ^ [_1686837, _1686839, _1686841, _1686843, _1686845, _1686847] : [hAPP(hAPP(c_List_Olist_OCons(_1686837), _1686839), _1686841) = _1686843, _1686845 = hAPP(hAPP(c_List_Oappend(_1686837), _1686841), _1686847), -(hAPP(hAPP(c_List_Olist_OCons(_1686837), _1686839), _1686845) = hAPP(hAPP(c_List_Oappend(_1686837), _1686843), _1686847))], (5128 ^ _780119) ^ [_858588, _858590] : [_858590 = _858588, -(c_List_Otl(_858590) = c_List_Otl(_858588))], (6785 ^ _780119) ^ [_891530, _891532, _891534] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_891530), _891532)), hBOOL(hAPP(c_Finite__Set_Ofinite(_891530), _891534)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_891530), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891530, tc_HOL_Obool)), _891532), _891534))))], (26051 ^ _780119) ^ [_1255133, _1255135] : [c_Nat__Transfer_Onat__set(_1255133), c_Nat__Transfer_Onat__set(_1255135), 26058 ^ _780119 : [(26065 ^ _780119) ^ [] : [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), _1255133)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1255135))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1255133), _1255135)))], (26059 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1255133), _1255135)), -(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), _1255133)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1255135))))]]], (32469 ^ _780119) ^ [_1385433, _1385435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1385433)), c_Int_OBit1(_1385435))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1385433), _1385435)))], (9822 ^ _780119) ^ [_950952, _950954, _950956] : [class_Lattices_Osemilattice__inf(_950952), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950952), _950954), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950952), _950954), _950956)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950952), _950954), _950956))], (44664 ^ _780119) ^ [_1674916, _1674918, _1674920, _1674922] : [c_List_Olist_ONil(_1674916) = hAPP(hAPP(c_List_Omap(_1674918, _1674916), _1674920), _1674922), -(_1674922 = c_List_Olist_ONil(_1674918))], (37641 ^ _780119) ^ [_1501322, _1501324] : [-(hAPP(c_Relation_ODomain(_1501322, _1501322), c_Relation_OId__on(_1501322, _1501324)) = _1501324)], (27638 ^ _780119) ^ [_1290684, _1290686, _1290688] : [class_Orderings_Olinorder(_1290684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290684), _1290686), _1290688)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290684), _1290688), _1290686) = _1290688)], (11069 ^ _780119) ^ [_977034, _977036, _977038] : [class_Lattices_Olattice(_977034), hBOOL(hAPP(c_Finite__Set_Ofinite(_977034), _977036)), hBOOL(hAPP(hAPP(c_member(_977034), _977038), _977036)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977034), _977038), c_Big__Operators_Olattice__class_OInf__fin(_977034, _977036)) = _977038)], (40824 ^ _780119) ^ [_1580668, _1580670, _1580672, _1580674] : [class_Complete__Lattice_Ocomplete__lattice(_1580668), hBOOL(hAPP(c_Finite__Set_Ofinite(_1580670), _1580672)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1580670, _1580668), _1580672), _1580674) = hAPP(hAPP(c_Finite__Set_Ofold(_1580670, _1580668, hAPP(hAPP(c_COMBB(_1580668, tc_fun(_1580668, _1580668), _1580670), c_Lattices_Osemilattice__sup__class_Osup(_1580668)), _1580674)), c_Orderings_Obot__class_Obot(_1580668)), _1580672))], (7454 ^ _780119) ^ [_905449, _905451, _905453, _905455] : [class_Lattices_Osemilattice__sup(_905449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905449), _905451), _905453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905449), _905451), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_905449), _905455), _905453))))], (30127 ^ _780119) ^ [_1343121, _1343123, _1343125, _1343127, _1343129, _1343131] : [c_Com_Ocom_OLocal(_1343121, _1343123, _1343125) = c_Com_Ocom_OLocal(_1343127, _1343129, _1343131), 30130 ^ _780119 : [(30133 ^ _780119) ^ [] : [-(_1343123 = _1343129)], (30135 ^ _780119) ^ [] : [-(_1343125 = _1343131)], (30131 ^ _780119) ^ [] : [-(_1343121 = _1343127)]]], (11609 ^ _780119) ^ [_988946, _988948] : [class_Rings_Ocomm__semiring__1(_988946), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988946), c_Groups_Oone__class_Oone(_988946)), _988948) = _988948)], (16532 ^ _780119) ^ [_1081259, _1081261] : [class_Rings_Olinordered__idom(_1081259), 16535 ^ _780119 : [(16542 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081259), _1081261), c_Groups_Ozero__class_Ozero(_1081259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081259), _1081261), hAPP(c_Groups_Ouminus__class_Ouminus(_1081259), _1081261))))], (16536 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081259), _1081261), hAPP(c_Groups_Ouminus__class_Ouminus(_1081259), _1081261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081259), _1081261), c_Groups_Ozero__class_Ozero(_1081259))))]]], (37552 ^ _780119) ^ [_1498895, _1498897, _1498899] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1498895, _1498897)), _1498899)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1498897), hAPP(c_Relation_ORange(_1498895, _1498897), _1498899))))], (42787 ^ _780119) ^ [_1627482, _1627484, _1627486, _1627488, _1627490] : [c_Fun_Oinj__on(_1627482, _1627484, _1627486, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1627482, tc_HOL_Obool)), hAPP(c_List_Oset(_1627482), _1627488)), hAPP(c_List_Oset(_1627482), _1627490))), 42790 ^ _780119 : [(42797 ^ _780119) ^ [] : [_1627488 = _1627490, -(hAPP(hAPP(c_List_Omap(_1627482, _1627484), _1627486), _1627488) = hAPP(hAPP(c_List_Omap(_1627482, _1627484), _1627486), _1627490))], (42791 ^ _780119) ^ [] : [hAPP(hAPP(c_List_Omap(_1627482, _1627484), _1627486), _1627488) = hAPP(hAPP(c_List_Omap(_1627482, _1627484), _1627486), _1627490), -(_1627488 = _1627490)]]], (4054 ^ _780119) ^ [_841351, _841353, _841355, _841357] : [-(c_Enum_Oenum__the(_841357, _841353) = c_Enum_Oenum__the(_841355, _841351)), _841357 = _841355, _841353 = _841351], (30237 ^ _780119) ^ [_1345057, _1345059, _1345061] : [c_Com_Ocom_OLocal(_1345057, _1345059, _1345061) = c_Com_Ocom_OSKIP], (29278 ^ _780119) ^ [_1322967, _1322969] : [class_Orderings_Olinorder(_1322967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322967), _1322969)), -(_1322969 = c_Orderings_Obot__class_Obot(tc_fun(_1322967, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1322967), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1322967), 29291 ^ [_1322967, _1322969]), 29292 ^ [_1322967, _1322969])), hAPP(hAPP(c_Set_Oinsert(_1322967), 29291 ^ [_1322967, _1322969]), hAPP(hAPP(c_Set_Oinsert(_1322967), 29292 ^ [_1322967, _1322969]), c_Orderings_Obot__class_Obot(tc_fun(_1322967, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1322967), c_Big__Operators_Olattice_OInf__fin(_1322967, c_Orderings_Oord__class_Omin(_1322967), _1322969)), _1322969)))], (2684 ^ _780119) ^ [_819890, _819892, _819894, _819896, _819898, _819900] : [-(c_Predicate_ODomainP(_819900, _819896, _819892) = c_Predicate_ODomainP(_819898, _819894, _819890)), _819900 = _819898, _819896 = _819894, _819892 = _819890], (51341 ^ _780119) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (42357 ^ _780119) ^ [_1617532, _1617534, _1617536] : [-(c_Map_Omap__add(_1617532, _1617534, _1617536, hAPP(c_COMBK(tc_Option_Ooption(_1617534), _1617532), c_Option_Ooption_ONone(_1617534))) = _1617536)], (15582 ^ _780119) ^ [_1064123, _1064125, _1064127] : [class_Groups_Oordered__comm__monoid__add(_1064123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064123), c_Groups_Ozero__class_Ozero(_1064123)), _1064125)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064123), c_Groups_Ozero__class_Ozero(_1064123)), _1064127)), 15593 ^ _780119 : [(15602 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064123), _1064125), _1064127) = c_Groups_Ozero__class_Ozero(_1064123)), _1064125 = c_Groups_Ozero__class_Ozero(_1064123), _1064127 = c_Groups_Ozero__class_Ozero(_1064123)], (15594 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064123), _1064125), _1064127) = c_Groups_Ozero__class_Ozero(_1064123), 15597 ^ _780119 : [(15600 ^ _780119) ^ [] : [-(_1064127 = c_Groups_Ozero__class_Ozero(_1064123))], (15598 ^ _780119) ^ [] : [-(_1064125 = c_Groups_Ozero__class_Ozero(_1064123))]]]]], (29861 ^ _780119) ^ [_1337187, _1337189, _1337191, _1337193, _1337195] : [-(_1337187 = c_Orderings_Obot__class_Obot(tc_fun(_1337189, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337189, tc_fun(_1337191, tc_HOL_Obool)), _1337187), hAPP(hAPP(c_COMBB(tc_fun(_1337191, tc_HOL_Obool), tc_fun(_1337191, tc_HOL_Obool), _1337189), hAPP(c_Set_Oinsert(_1337191), _1337193)), _1337195)) = hAPP(hAPP(c_Set_Oinsert(_1337191), _1337193), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337189, tc_fun(_1337191, tc_HOL_Obool)), _1337187), _1337195)))], (36686 ^ _780119) ^ [_1477021, _1477023] : [-(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)), _1477021), _1477023))], (9734 ^ _780119) ^ [_948940, _948942, _948944, _948946, _948948] : [class_Rings_Osemiring__0(_948940), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948940), _948942), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_948944, _948940), _948946), _948948)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_948944, _948940), hAPP(hAPP(c_COMBB(_948940, _948940, _948944), hAPP(c_Groups_Otimes__class_Otimes(_948940), _948942)), _948946)), _948948))], (33099 ^ _780119) ^ [_1396876, _1396878, _1396880] : [class_Int_Onumber__ring(_1396876), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1396876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1396876), _1396878), _1396880)), 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(_1396876), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1396876), hAPP(hAPP(c_Power_Opower__class_Opower(_1396876), _1396878), 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(_1396876), _1396880), 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(_1396876), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396876), hAPP(c_Int_Onumber__class_Onumber__of(_1396876), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1396878)), _1396880)))], (5640 ^ _780119) ^ [_866496, _866498] : [_866498 = _866496, -(c_Orderings_Oord__class_Oless__eq(_866498) = c_Orderings_Oord__class_Oless__eq(_866496))], (22193 ^ _780119) ^ [_1185234, _1185236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185234), _1185236)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1185234, _1185236) = _1185234)], (12141 ^ _780119) ^ [_998967, _998969, _998971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998967), _998969)), _998971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998967), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998971), _998969))))], (40082 ^ _780119) ^ [_1562770, _1562772, _1562774] : [-(hAPP(c_Relation_ORange(_1562770, _1562772), _1562774) = hAPP(c_Relation_ODomain(_1562772, _1562770), hAPP(c_Relation_Oconverse(_1562770, _1562772), _1562774)))], (4064 ^ _780119) ^ [_841500, _841502, _841504, _841506] : [-(c_Product__Type_OSigma(_841506, _841502) = c_Product__Type_OSigma(_841504, _841500)), _841506 = _841504, _841502 = _841500], (42883 ^ _780119) ^ [_1629953, _1629955, _1629957, _1629959] : [-(hBOOL(hAPP(c_List_Odistinct(_1629953), hAPP(hAPP(c_List_Omap(_1629955, _1629953), _1629957), _1629959)))), hBOOL(hAPP(c_List_Odistinct(_1629955), _1629959)), c_Fun_Oinj__on(_1629955, _1629953, _1629957, hAPP(c_List_Oset(_1629955), _1629959))], (45420 ^ _780119) ^ [_1692375, _1692377, _1692379] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692375), tc_List_Olist(_1692375))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692375), tc_List_Olist(_1692375)), _1692377), c_List_Olist_ONil(_1692375))), c_List_Olistrel1(_1692375, _1692379)))], (24225 ^ _780119) ^ [_1223633, _1223635, _1223637] : [class_Groups_Oordered__ab__group__add(_1223633), -(hAPP(c_Set_Oimage(_1223633, _1223633, c_Groups_Ouminus__class_Ouminus(_1223633)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1223633, _1223635, _1223637)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1223633, hAPP(c_Groups_Ouminus__class_Ouminus(_1223633), _1223637), hAPP(c_Groups_Ouminus__class_Ouminus(_1223633), _1223635)))], (14026 ^ _780119) ^ [_1035412, _1035414, _1035416] : [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, _1035412)), _1035414)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1035412)), _1035416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035414), _1035416)))], (34863 ^ _780119) ^ [_1434594, _1434596, _1434598] : [-(hAPP(hAPP(c_Product__Type_OPair(_1434594, _1434596), hAPP(c_Product__Type_Ofst(_1434594, _1434596), _1434598)), hAPP(c_Product__Type_Osnd(_1434594, _1434596), _1434598)) = _1434598)], (39050 ^ _780119) ^ [_1537855, _1537857, _1537859, _1537861] : [c_Finite__Set_Ofolding(_1537855, _1537857, _1537859, _1537861), -(hAPP(_1537861, c_Orderings_Obot__class_Obot(tc_fun(_1537855, tc_HOL_Obool))) = c_Fun_Oid(_1537857))], (48295 ^ _780119) ^ [_1756808] : [class_Enum_Oenum(_1756808), -(hBOOL(hAPP(c_List_Odistinct(_1756808), c_Enum_Oenum__class_Oenum(_1756808))))], (8024 ^ _780119) ^ [_917273, _917275, _917277] : [hAPP(c_Com_Ocom_OBODY, _917273) = c_Com_Ocom_OWhile(_917275, _917277)], (50830 ^ _780119) ^ [_1811108, _1811110, _1811112, _1811114, _1811116, _1811118] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1811108, _1811110, _1811112, _1811114, c_Nitpick_Opair__box_OPairBox(_1811108, _1811110, _1811116, _1811118)) = hAPP(hAPP(_1811114, _1811116), _1811118))], (32591 ^ _780119) ^ [_1387550] : [-(c_Int_Osucc(c_Int_OBit1(_1387550)) = c_Int_OBit0(c_Int_Osucc(_1387550)))], (1040 ^ _780119) ^ [_795843, _795845] : [-(class_Groups_Olinordered__ab__group__add(_795843)), _795845 = _795843, class_Groups_Olinordered__ab__group__add(_795845)], (17699 ^ _780119) ^ [_1101881, _1101883, _1101885] : [-(hBOOL(hAPP(_1101881, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1101883), _1101885)))), 17702 ^ _780119 : [(17705 ^ _780119) ^ [] : [hBOOL(hAPP(_1101881, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17703 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101883), _1101885)))]], 17707 ^ _780119 : [(17710 ^ _780119) ^ [] : [hBOOL(hAPP(_1101881, 17706 ^ [_1101881, _1101883, _1101885]))], (17708 ^ _780119) ^ [] : [-(_1101883 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101885), 17706 ^ [_1101881, _1101883, _1101885]))]]], (41314 ^ _780119) ^ [_1591866, _1591868, _1591870, _1591872, _1591874, _1591876] : [class_Complete__Lattice_Ocomplete__lattice(_1591866), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591868, tc_fun(_1591870, _1591866)), _1591872), _1591874), _1591876) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591868, _1591866), _1591872), hAPP(hAPP(c_COMBC(_1591868, _1591870, _1591866), _1591874), _1591876)))], (38966 ^ _780119) ^ [_1535739, _1535741, _1535743, _1535745, _1535747, _1535749, _1535751, _1535753, _1535755, _1535757, _1535759] : [c_Finite__Set_Ofolding(_1535739, _1535741, _1535743, _1535745), -(hAPP(c_Fun_Ocomp(_1535747, _1535749, _1535751, _1535753), hAPP(c_Fun_Ocomp(_1535755, _1535747, _1535751, _1535757), _1535759)) = hAPP(c_Fun_Ocomp(_1535755, _1535749, _1535751, hAPP(c_Fun_Ocomp(_1535747, _1535749, _1535755, _1535753), _1535757)), _1535759))], (51281 ^ _780119) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (24763 ^ _780119) ^ [_1233641, _1233643, _1233645] : [class_Groups_Oordered__ab__group__add(_1233641), -(hAPP(c_Set_Oimage(_1233641, _1233641, c_Groups_Ouminus__class_Ouminus(_1233641)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1233641, _1233643, _1233645)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1233641, hAPP(c_Groups_Ouminus__class_Ouminus(_1233641), _1233645)), hAPP(c_Groups_Ouminus__class_Ouminus(_1233641), _1233643)))], (46827 ^ _780119) ^ [_1724838, _1724840] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724838), _1724840))), -(c_List_Oupt(_1724838, hAPP(c_Nat_OSuc, _1724840)) = c_List_Olist_ONil(tc_Nat_Onat))], (10210 ^ _780119) ^ [_958564, _958566, _958568, _958570] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958564, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958564, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958564, tc_HOL_Obool)), _958566), _958568)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958564, tc_HOL_Obool)), _958568), _958570))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958564, tc_HOL_Obool)), _958570), _958566)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958564, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958564, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958564, tc_HOL_Obool)), _958566), _958568)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958564, tc_HOL_Obool)), _958568), _958570))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958564, tc_HOL_Obool)), _958570), _958566)))], (44760 ^ _780119) ^ [_1676647, _1676649, _1676651] : [hAPP(hAPP(c_List_Otake(_1676647), _1676649), _1676651) = c_List_Olist_ONil(_1676647), -(_1676649 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1676651 = c_List_Olist_ONil(_1676647))], (11581 ^ _780119) ^ [_988341, _988343, _988345, _988347, _988349] : [class_Rings_Osemiring(_988341), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988341), _988343), _988345)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988341), _988347), _988345)), _988349)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988341), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988341), _988343), _988347)), _988345)), _988349))], (14376 ^ _780119) ^ [_1043484, _1043486, _1043488, _1043490] : [class_Rings_Ocomm__semiring__1(_1043484), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1043484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043484), _1043486), _1043488)), _1043490) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043484), hAPP(hAPP(c_Power_Opower__class_Opower(_1043484), _1043486), _1043490)), hAPP(hAPP(c_Power_Opower__class_Opower(_1043484), _1043488), _1043490)))], (42306 ^ _780119) ^ [_1616494, _1616496, _1616498] : [c_Nitpick_Oless__frac(_1616494, _1616496, _1616498), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1616494), c_Nitpick_Oplus__frac(_1616494, _1616496, c_Nitpick_Ouminus__frac(_1616494, _1616498)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (44468 ^ _780119) ^ [_1671199, _1671201, _1671203, _1671205, _1671207, _1671209] : [-(hBOOL(hAPP(hAPP(c_member(_1671199), _1671201), hAPP(c_List_Oset(_1671199), _1671203)))), -(hAPP(c_Map_Omap__upds(_1671199, _1671205, _1671207, _1671203, _1671209), _1671201) = hAPP(_1671207, _1671201))], (6312 ^ _780119) ^ [_881474, _881476, _881478] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_881474), _881476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881474, tc_HOL_Obool)), _881478), _881476)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_881474), _881478)))], (10687 ^ _780119) ^ [_969662, _969664, _969666] : [class_Lattices_Olattice(_969662), hBOOL(hAPP(c_Finite__Set_Ofinite(_969662), _969664)), hBOOL(hAPP(c_Finite__Set_Ofinite(_969662), _969666)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_969662, tc_HOL_Obool)), _969664), _969666) = c_Orderings_Obot__class_Obot(tc_fun(_969662, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_969662), c_Big__Operators_Olattice__class_OInf__fin(_969662, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_969662, tc_HOL_Obool)), _969664), _969666))), c_Big__Operators_Olattice__class_OInf__fin(_969662, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_969662, tc_HOL_Obool)), _969664), _969666))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_969662), c_Big__Operators_Olattice__class_OInf__fin(_969662, _969664)), c_Big__Operators_Olattice__class_OInf__fin(_969662, _969666)))], (37962 ^ _780119) ^ [_1510574, _1510576, _1510578, _1510580, _1510582, _1510584] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1510574, _1510576), hAPP(hAPP(c_Set_Oinsert(_1510574), _1510578), _1510580)), hAPP(c_COMBK(tc_fun(_1510576, tc_HOL_Obool), _1510574), hAPP(hAPP(c_Set_Oinsert(_1510576), _1510582), _1510584))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1510574, _1510576)), hAPP(hAPP(c_Product__Type_OPair(_1510574, _1510576), _1510578), _1510582)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1510574, _1510576), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1510574, _1510576), _1510580), hAPP(c_COMBK(tc_fun(_1510576, tc_HOL_Obool), _1510574), hAPP(hAPP(c_Set_Oinsert(_1510576), _1510582), _1510584)))), hAPP(hAPP(c_Product__Type_OSigma(_1510574, _1510576), hAPP(hAPP(c_Set_Oinsert(_1510574), _1510578), _1510580)), hAPP(c_COMBK(tc_fun(_1510576, tc_HOL_Obool), _1510574), _1510584)))))], (37193 ^ _780119) ^ [_1491211, _1491213, _1491215, _1491217, _1491219, _1491221, _1491223, _1491225] : [hBOOL(hAPP(hAPP(_1491211, _1491213), _1491215)), hBOOL(hAPP(hAPP(_1491217, _1491215), _1491219)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1491221, _1491223, _1491225, _1491211, _1491217), _1491213), _1491219)))], (33779 ^ _780119) ^ [_1413713, _1413715, _1413717, _1413719] : [_1413713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1413715), _1413717)), _1413719), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1413713, _1413715), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1413717), _1413719)))), 33786 ^ _780119 : [(33789 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1413719)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413719), _1413715))], (33787 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1413715)))]], 33794 ^ _780119 : [(33797 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413715), _1413719)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1413719), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33795 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1413715))]]], (32475 ^ _780119) ^ [_1385534, _1385536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1385534), _1385536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1385534)), c_Int_OBit1(_1385536))))], (39428 ^ _780119) ^ [_1547056, _1547058] : [c_Wellfounded_Owf(_1547056, _1547058), -(c_Wellfounded_Owf(_1547056, c_Transitive__Closure_Otrancl(_1547056, _1547058)))], (10094 ^ _780119) ^ [_955972, _955974, _955976, _955978] : [class_Lattices_Odistrib__lattice(_955972), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955972), _955974), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955972), _955976), _955978)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955972), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955972), _955974), _955976)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955972), _955974), _955978)))], (18832 ^ _780119) ^ [_1123452] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _1123452)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3630 ^ _780119) ^ [_834705, _834707, _834709, _834711] : [-(c_List_Olistrel1(_834711, _834707) = c_List_Olistrel1(_834709, _834705)), _834711 = _834709, _834707 = _834705], (31619 ^ _780119) ^ [_1370401, _1370403] : [class_Int_Onumber__ring(_1370401), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1370401), hAPP(c_Int_Onumber__class_Onumber__of(_1370401), c_Int_OBit1(c_Int_OPls))), _1370403) = _1370403)], (31631 ^ _780119) ^ [_1370603, _1370605] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1370603), _1370605), hAPP(c_Int_Onumber__class_Onumber__of(_1370603), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1370603)), class_Fields_Ofield__inverse__zero(_1370603), class_Int_Onumber__ring(_1370603)], (48870 ^ _780119) ^ [_1768553, _1768555, _1768557, _1768559] : [hBOOL(hAPP(c_List_Olistsp(_1768553, _1768555), hAPP(hAPP(c_List_Oappend(_1768553), _1768557), _1768559))), 48873 ^ _780119 : [(48876 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1768553, _1768555), _1768559)))], (48874 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1768553, _1768555), _1768557)))]]], (29102 ^ _780119) ^ [_1319247, _1319249, _1319251] : [class_Orderings_Olinorder(_1319247), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319247), _1319249)), 29109 ^ _780119 : [(29116 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319247, tc_HOL_Obool)), _1319249), hAPP(hAPP(c_Set_Oinsert(_1319247), _1319251), c_Orderings_Obot__class_Obot(tc_fun(_1319247, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1319247, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1319247, c_Orderings_Oord__class_Omax(_1319247), hAPP(hAPP(c_Set_Oinsert(_1319247), _1319251), _1319249)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1319247), _1319251), c_Big__Operators_Olattice_OSup__fin(_1319247, c_Orderings_Oord__class_Omax(_1319247), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319247, tc_HOL_Obool)), _1319249), hAPP(hAPP(c_Set_Oinsert(_1319247), _1319251), c_Orderings_Obot__class_Obot(tc_fun(_1319247, tc_HOL_Obool)))))))], (29110 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319247, tc_HOL_Obool)), _1319249), hAPP(hAPP(c_Set_Oinsert(_1319247), _1319251), c_Orderings_Obot__class_Obot(tc_fun(_1319247, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1319247, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1319247, c_Orderings_Oord__class_Omax(_1319247), hAPP(hAPP(c_Set_Oinsert(_1319247), _1319251), _1319249)) = _1319251)]]], (41922 ^ _780119) ^ [_1607540, _1607542, _1607544] : [class_Complete__Lattice_Ocomplete__lattice(_1607540), -(c_Complete__Lattice_OInf__class_OInf(_1607540, hAPP(hAPP(c_Set_Oinsert(_1607540), _1607542), hAPP(hAPP(c_Set_Oinsert(_1607540), _1607544), c_Orderings_Obot__class_Obot(tc_fun(_1607540, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1607540), _1607542), _1607544))], (20362 ^ _780119) ^ [_1150600, _1150602, _1150604, _1150606] : [class_Fields_Olinordered__field(_1150600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150600), _1150602), _1150604)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150600), c_Groups_Ozero__class_Ozero(_1150600)), _1150606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150600), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150600), _1150602), _1150606)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150600), _1150604), _1150606))))], (40104 ^ _780119) ^ [_1563401, _1563403, _1563405, _1563407] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563401, _1563401)), hAPP(hAPP(c_Product__Type_OPair(_1563401, _1563401), _1563403), _1563405)), c_Transitive__Closure_Otrancl(_1563401, hAPP(c_Relation_Oconverse(_1563401, _1563401), _1563407)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563401, _1563401)), hAPP(hAPP(c_Product__Type_OPair(_1563401, _1563401), _1563403), _1563405)), hAPP(c_Relation_Oconverse(_1563401, _1563401), c_Transitive__Closure_Otrancl(_1563401, _1563407)))))], (2848 ^ _780119) ^ [_822510, _822512, _822514, _822516, _822518, _822520] : [-(c_Random_Ominus__shift(_822520, _822516, _822512) = c_Random_Ominus__shift(_822518, _822514, _822510)), _822520 = _822518, _822516 = _822514, _822512 = _822510], (24797 ^ _780119) ^ [_1234360, _1234362, _1234364] : [class_Orderings_Olinorder(_1234360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234360), _1234362), _1234364)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234360, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1234360, _1234362), _1234364)), hAPP(c_SetInterval_Oord__class_OatLeast(_1234360), _1234364)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1234360), _1234362))], (26727 ^ _780119) ^ [_1268208, _1268210] : [class_Rings_Olinordered__idom(_1268208), -(hAPP(c_Groups_Oabs__class_Oabs(_1268208), _1268210) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1268208), _1268210), c_Groups_Osgn__class_Osgn(_1268208, _1268210)))], (8080 ^ _780119) ^ [_918208, _918210] : [c_Com_Ocom_OSemi(_918208, _918210) = c_Com_Ocom_OSKIP], (15260 ^ _780119) ^ [_1058882, _1058884, _1058886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1058882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1058882), _1058884)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1058882), _1058886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1058884), _1058886)))], (15844 ^ _780119) ^ [_1068786, _1068788, _1068790, _1068792] : [class_Rings_Oordered__ring(_1068786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068786), _1068788), _1068790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068786), _1068792), c_Groups_Ozero__class_Ozero(_1068786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068786), _1068790), _1068792)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068786), _1068788), _1068792))))], (35065 ^ _780119) ^ [_1438926, _1438928, _1438930, _1438932, _1438934, _1438936, _1438938] : [-(hAPP(c_Product__Type_Oapfst(_1438926, _1438928, _1438930, _1438932), hAPP(c_Product__Type_Oapsnd(_1438934, _1438930, _1438926, _1438936), _1438938)) = hAPP(hAPP(c_Product__Type_OPair(_1438928, _1438930), hAPP(_1438932, hAPP(c_Product__Type_Ofst(_1438926, _1438934), _1438938))), hAPP(_1438936, hAPP(c_Product__Type_Osnd(_1438926, _1438934), _1438938))))], (14904 ^ _780119) ^ [_1053612] : [c_Orderings_Otop__class_Otop(tc_fun(_1053612, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1053612, tc_HOL_Obool))], (38860 ^ _780119) ^ [_1533356, _1533358, _1533360, _1533362] : [-(c_Hilbert__Choice_OEps(tc_prod(_1533356, _1533358), hAPP(c_Product__Type_Oprod_Oprod__case(_1533356, _1533358, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1533356, tc_fun(_1533358, tc_HOL_Obool), tc_fun(_1533358, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1533358, tc_HOL_Obool), tc_fun(_1533358, tc_HOL_Obool)), _1533356), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1533358)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533356), c_fconj), hAPP(c_fequal, _1533360)))), hAPP(c_fequal, _1533362)))) = hAPP(hAPP(c_Product__Type_OPair(_1533356, _1533358), _1533360), _1533362))], (26641 ^ _780119) ^ [_1266698, _1266700, _1266702] : [class_Groups_Oordered__ab__group__add__abs(_1266698), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266698), _1266700), _1266702)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266698), hAPP(c_Groups_Ouminus__class_Ouminus(_1266698), _1266700)), _1266702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266698), hAPP(c_Groups_Oabs__class_Oabs(_1266698), _1266700)), _1266702)))], (47995 ^ _780119) ^ [_1749522, _1749524] : [-(c_List_Oremdups(_1749522, c_List_Oremdups(_1749522, _1749524)) = c_List_Oremdups(_1749522, _1749524))], (17001 ^ _780119) ^ [_1088910, _1088912, _1088914] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1088910), _1088912)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1088910), _1088914)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1088910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1088912), _1088914))], (13660 ^ _780119) ^ [_1028542, _1028544] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028542)), _1028544) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028542), _1028544)))], (2378 ^ _780119) ^ [_815153, _815155, _815157, _815159] : [-(c_Divides_Odivmod__int__rel(_815159, _815155) = c_Divides_Odivmod__int__rel(_815157, _815153)), _815159 = _815157, _815155 = _815153], (42712 ^ _780119) ^ [_1625904, _1625906, _1625908, _1625910, _1625912] : [-(c_Map_Omap__comp(_1625904, _1625906, _1625908, hAPP(c_COMBK(tc_Option_Ooption(_1625906), _1625904), c_Option_Ooption_ONone(_1625906)), _1625910, _1625912) = c_Option_Ooption_ONone(_1625906))], (11935 ^ _780119) ^ [_995054, _995056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995054), _995056)), _995054))], (9760 ^ _780119) ^ [_949489, _949491, _949493, _949495] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949489, tc_HOL_Obool)), _949491), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949489, tc_HOL_Obool)), _949493), _949495)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949489, tc_HOL_Obool)), _949493), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949489, tc_HOL_Obool)), _949491), _949495)))], (49267 ^ _780119) ^ [_1777276, _1777278, _1777280] : [hBOOL(hAPP(c_List_Odistinct(_1777276), _1777278)), -(hBOOL(hAPP(c_List_Odistinct(_1777276), c_List_Oinsert(_1777276, _1777280, _1777278))))], (45978 ^ _780119) ^ [_1706021, _1706023, _1706025, _1706027] : [-(hAPP(c_List_Ofoldl(_1706021, _1706023, _1706025, _1706027), c_List_Olist_ONil(_1706023)) = _1706027)], (16166 ^ _780119) ^ [_1074719, _1074721, _1074723] : [class_Rings_Olinordered__semiring__strict(_1074719), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074719), c_Groups_Ozero__class_Ozero(_1074719)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074719), _1074721), _1074723))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074719), c_Groups_Ozero__class_Ozero(_1074719)), _1074721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074719), c_Groups_Ozero__class_Ozero(_1074719)), _1074723)))], (40014 ^ _780119) ^ [_1561156, _1561158, _1561160] : [c_Relation_Ototal__on(_1561156, _1561158, _1561160), -(c_Relation_Ototal__on(_1561156, _1561158, hAPP(c_Relation_Oconverse(_1561156, _1561156), _1561160)))], (45658 ^ _780119) ^ [_1699068, _1699070, _1699072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699068)), _1699070)), _1699072)), -(hAPP(hAPP(c_List_Odrop(_1699068), _1699072), _1699070) = c_List_Olist_ONil(_1699068))], (44636 ^ _780119) ^ [_1674402, _1674404] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674402)), _1674404) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1674404 = c_List_Olist_ONil(_1674402))], (46668 ^ _780119) ^ [_1720843, _1720845, _1720847, _1720849, _1720851] : [-(hAPP(c_List_Ofilter(_1720843, _1720845), hAPP(hAPP(c_List_Omap(_1720847, _1720843), _1720849), _1720851)) = hAPP(hAPP(c_List_Omap(_1720847, _1720843), _1720849), hAPP(c_List_Ofilter(_1720847, hAPP(c_Fun_Ocomp(_1720843, tc_HOL_Obool, _1720847, _1720845), _1720849)), _1720851)))], (37844 ^ _780119) ^ [_1507663, _1507665, _1507667, _1507669] : [37845 ^ _780119 : [(37846 ^ _780119) ^ [_1507717] : [hBOOL(hAPP(hAPP(_1507667, _1507669), _1507717))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1507663, _1507665, _1507667), _1507669)))], (22278 ^ _780119) ^ [_1186585, _1186587] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186585), _1186587))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186585, _1186587) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1186585), _1186587), _1186587))], (4604 ^ _780119) ^ [_850028, _850030] : [_850030 = _850028, -(c_Lazy__Sequence_Oyield(_850030) = c_Lazy__Sequence_Oyield(_850028))], (26323 ^ _780119) ^ [_1260544] : [-(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)), _1260544)))))], (32625 ^ _780119) ^ [_1388224, _1388226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1388224)), c_Int_OBit0(_1388226))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1388224), _1388226)))], (19797 ^ _780119) ^ [_1140304, _1140306, _1140308, _1140310] : [class_Rings_Odivision__ring(_1140304), -(_1140306 = c_Groups_Ozero__class_Ozero(_1140304)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140304), _1140308), _1140306) = _1140310, -(_1140308 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140304), _1140310), _1140306))], (14104 ^ _780119) ^ [_1037311, _1037313, _1037315] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1037311, tc_HOL_Obool)), _1037313), _1037315) = c_Orderings_Obot__class_Obot(tc_fun(_1037311, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1037311, tc_HOL_Obool)), _1037313), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1037311, tc_HOL_Obool)), _1037315))))], (14634 ^ _780119) ^ [_1048652, _1048654, _1048656] : [class_Rings_Olinordered__semidom(_1048652), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048652), c_Groups_Oone__class_Oone(_1048652)), _1048654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048652), c_Groups_Oone__class_Oone(_1048652)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048652), _1048654), hAPP(hAPP(c_Power_Opower__class_Opower(_1048652), _1048654), _1048656)))))], (43781 ^ _780119) ^ [_1654689, _1654691, _1654693, _1654695] : [class_Groups_Ocomm__monoid__add(_1654689), hBOOL(hAPP(c_List_Odistinct(_1654691), _1654693)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1654689), hAPP(hAPP(c_List_Omap(_1654691, _1654689), _1654695), _1654693)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1654691, _1654689), _1654695), hAPP(c_List_Oset(_1654691), _1654693)))], (25937 ^ _780119) ^ [_1253340, _1253342] : [class_Rings_Olinordered__idom(_1253340), 25940 ^ _780119 : [(25947 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1253342), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253340), hAPP(c_Int_Oring__1__class_Oof__int(_1253340), _1253342)), c_Groups_Ozero__class_Ozero(_1253340))))], (25941 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253340), hAPP(c_Int_Oring__1__class_Oof__int(_1253340), _1253342)), c_Groups_Ozero__class_Ozero(_1253340))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1253342), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23897 ^ _780119) ^ [_1217245] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1217245), hAPP(c_Nat_OSuc, _1217245)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1217245), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51293 ^ _780119) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (38675 ^ _780119) ^ [_1529288, _1529290, _1529292, _1529294, _1529296, _1529298, _1529300] : [-(hAPP(c_Product__Type_Oapfst(_1529288, _1529290, _1529292, _1529294), hAPP(c_Product__Type_Oapfst(_1529296, _1529288, _1529292, _1529298), _1529300)) = hAPP(c_Product__Type_Oapfst(_1529296, _1529290, _1529292, hAPP(c_Fun_Ocomp(_1529288, _1529290, _1529296, _1529294), _1529298)), _1529300))], (39675 ^ _780119) ^ [_1553178] : [-(c_Transitive__Closure_Ortrancl(_1553178, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1553178, _1553178), tc_HOL_Obool))) = c_Relation_OId(_1553178))], (46115 ^ _780119) ^ [_1708959, _1708961, _1708963, _1708965] : [class_Complete__Lattice_Ocomplete__lattice(_1708959), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708961, _1708959), hAPP(c_List_Oset(_1708961), _1708963)), _1708965) = hAPP(c_List_Ofoldl(_1708959, _1708961, hAPP(c_COMBC(_1708961, _1708959, _1708959), hAPP(hAPP(c_COMBB(_1708959, tc_fun(_1708959, _1708959), _1708961), c_Lattices_Osemilattice__inf__class_Oinf(_1708959)), _1708965)), c_Orderings_Otop__class_Otop(_1708959)), _1708963))], (12117 ^ _780119) ^ [_998519, _998521, _998523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _998519), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998521), _998523))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998519), _998523)), _998521)))], (43803 ^ _780119) ^ [_1655174, _1655176, _1655178, _1655180] : [class_Rings_Osemiring__1(_1655174), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1655174), hAPP(hAPP(c_List_Omap(_1655176, _1655174), hAPP(c_COMBK(_1655174, _1655176), _1655178)), _1655180)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1655174), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1655174), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655176)), _1655180))), _1655178))], (32275 ^ _780119) ^ [_1381981, _1381983] : [class_Int_Onumber__ring(_1381981), 32278 ^ _780119 : [(32285 ^ _780119) ^ [] : [c_Int_Oiszero(_1381981, hAPP(c_Int_Onumber__class_Onumber__of(_1381981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1381983)))), -(c_Groups_Ozero__class_Ozero(_1381981) = hAPP(c_Int_Onumber__class_Onumber__of(_1381981), _1381983))], (32279 ^ _780119) ^ [] : [c_Groups_Ozero__class_Ozero(_1381981) = hAPP(c_Int_Onumber__class_Onumber__of(_1381981), _1381983), -(c_Int_Oiszero(_1381981, hAPP(c_Int_Onumber__class_Onumber__of(_1381981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1381983)))))]]], (36864 ^ _780119) ^ [_1481013, _1481015, _1481017, _1481019] : [c_Fun_Oinj__on(_1481013, _1481015, _1481017, _1481019), -(c_Fun_Oinj__on(_1481015, _1481013, c_Fun_Othe__inv__into(_1481013, _1481015, _1481019, _1481017), hAPP(c_Set_Oimage(_1481013, _1481015, _1481017), _1481019)))], (13318 ^ _780119) ^ [_1022470, _1022472, _1022474] : [class_Groups_Oordered__ab__group__add(_1022470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022470), _1022472), _1022474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022470), hAPP(c_Groups_Ouminus__class_Ouminus(_1022470), _1022474)), hAPP(c_Groups_Ouminus__class_Ouminus(_1022470), _1022472))))], (51525 ^ _780119) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (31147 ^ _780119) ^ [_1362529, _1362531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362529)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1362529), _1362531)))], (6059 ^ _780119) ^ [_876648, _876650, _876652] : [_876648 = c_Orderings_Obot__class_Obot(tc_fun(_876650, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_876650), _876652), _876648))], (24037 ^ _780119) ^ [_1219918, _1219920] : [class_Groups_Oordered__ab__group__add(_1219918), -(hAPP(c_Set_Oimage(_1219918, _1219918, c_Groups_Ouminus__class_Ouminus(_1219918)), hAPP(c_SetInterval_Oord__class_OlessThan(_1219918), _1219920)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1219918), hAPP(c_Groups_Ouminus__class_Ouminus(_1219918), _1219920)))], (38453 ^ _780119) ^ [_1523365, _1523367] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1523365), c_Int_OInteg)), hBOOL(hAPP(_1523367, hAPP(c_Int_ORep__Integ, 38458 ^ [_1523365, _1523367]))), -(hBOOL(hAPP(_1523367, _1523365)))], (44236 ^ _780119) ^ [_1666335, _1666337, _1666339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666335)), _1666337)), _1666339)), -(hAPP(hAPP(c_List_Otake(_1666335), _1666339), _1666337) = _1666337)], (1940 ^ _780119) ^ [_808186, _808188, _808190, _808192] : [-(c_Option_Oset(_808192, _808188) = c_Option_Oset(_808190, _808186)), _808192 = _808190, _808188 = _808186], (8192 ^ _780119) ^ [_921027, _921029, _921031, _921033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921027, tc_HOL_Obool)), _921029), hAPP(hAPP(c_Set_Oinsert(_921027), _921031), _921033))), 8195 ^ _780119 : [(8202 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_921027), _921031), _921029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921027, tc_HOL_Obool)), _921029), _921033)))], (8196 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_921027), _921031), _921029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921027, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921027, tc_HOL_Obool)), _921029), hAPP(hAPP(c_Set_Oinsert(_921027), _921031), c_Orderings_Obot__class_Obot(tc_fun(_921027, tc_HOL_Obool))))), _921033)))]]], (34327 ^ _780119) ^ [_1424382, _1424384, _1424386, _1424388, _1424390, _1424392] : [-(hAPP(c_Product__Type_Oapsnd(_1424382, _1424384, _1424386, _1424388), hAPP(hAPP(c_Product__Type_OPair(_1424386, _1424382), _1424390), _1424392)) = hAPP(hAPP(c_Product__Type_OPair(_1424386, _1424384), _1424390), hAPP(_1424388, _1424392)))], (45560 ^ _780119) ^ [_1696656, _1696658, _1696660, _1696662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1696656), tc_List_Olist(_1696656))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1696656), tc_List_Olist(_1696656)), _1696658), _1696660)), c_List_Olistrel1(_1696656, _1696662))), 45565 ^ _780119 : [(45570 ^ _780119) ^ [] : [-(_1696658 = hAPP(hAPP(c_List_Oappend(_1696656), 45567 ^ [_1696656, _1696658, _1696660, _1696662]), hAPP(hAPP(c_List_Olist_OCons(_1696656), 45563 ^ [_1696656, _1696658, _1696660, _1696662]), 45568 ^ [_1696656, _1696658, _1696660, _1696662])))], (45572 ^ _780119) ^ [] : [-(_1696660 = hAPP(hAPP(c_List_Oappend(_1696656), 45567 ^ [_1696656, _1696658, _1696660, _1696662]), hAPP(hAPP(c_List_Olist_OCons(_1696656), 45564 ^ [_1696656, _1696658, _1696660, _1696662]), 45568 ^ [_1696656, _1696658, _1696660, _1696662])))], (45566 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1696656, _1696656)), hAPP(hAPP(c_Product__Type_OPair(_1696656, _1696656), 45563 ^ [_1696656, _1696658, _1696660, _1696662]), 45564 ^ [_1696656, _1696658, _1696660, _1696662])), _1696662)))]]], (16436 ^ _780119) ^ [_1079633, _1079635] : [class_Groups_Olinordered__ab__group__add(_1079633), 16439 ^ _780119 : [(16446 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079633), _1079635), c_Groups_Ozero__class_Ozero(_1079633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079633), _1079635), hAPP(c_Groups_Ouminus__class_Ouminus(_1079633), _1079635))))], (16440 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079633), _1079635), hAPP(c_Groups_Ouminus__class_Ouminus(_1079633), _1079635))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079633), _1079635), c_Groups_Ozero__class_Ozero(_1079633))))]]], (23356 ^ _780119) ^ [_1206899, _1206901] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1206899) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1206901), -(_1206899 = _1206901)], (33869 ^ _780119) ^ [_1415416, _1415418, _1415420, _1415422, _1415424, _1415426] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415416, tc_fun(_1415418, tc_HOL_Obool))), _1415420), _1415422), _1415424), _1415426)), 33872 ^ _780119 : [(33875 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1415422, _1415424), _1415426)))], (33873 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1415420, _1415424), _1415426)))]]], (22575 ^ _780119) ^ [_1192108, _1192110, _1192112] : [c_Com_Ocom_OCond(_1192108, _1192110, _1192112) = c_Com_Ocom_OSKIP], (25199 ^ _780119) ^ [_1241375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1241375))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241375)))], (32543 ^ _780119) ^ [_1386745, _1386747] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1386745)), c_Int_OBit0(_1386747)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1386745), _1386747)))], (32291 ^ _780119) ^ [_1382240, _1382242] : [class_Int_Onumber__ring(_1382240), 32294 ^ _780119 : [(32301 ^ _780119) ^ [] : [c_Int_Oiszero(_1382240, hAPP(c_Int_Onumber__class_Onumber__of(_1382240), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382242), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1382240), _1382242) = c_Groups_Ozero__class_Ozero(_1382240))], (32295 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1382240), _1382242) = c_Groups_Ozero__class_Ozero(_1382240), -(c_Int_Oiszero(_1382240, hAPP(c_Int_Onumber__class_Onumber__of(_1382240), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382242), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (49446 ^ _780119) ^ [_1781933, _1781935, _1781937, _1781939] : [49448 ^ _780119 : [(49451 ^ _780119) ^ [] : [hBOOL(hAPP(_1781937, 49447 ^ [_1781933, _1781935, _1781937, _1781939]))], (49449 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781933), 49447 ^ [_1781933, _1781935, _1781937, _1781939]), hAPP(c_List_Oset(_1781933), _1781935))))]], -(c_List_OdropWhile(_1781933, _1781937, hAPP(hAPP(c_List_Oappend(_1781933), _1781935), _1781939)) = c_List_OdropWhile(_1781933, _1781937, _1781939))], (41495 ^ _780119) ^ [_1597645, _1597647, _1597649, _1597651, _1597653, _1597655] : [c_Relation_Osingle__valued(_1597645, _1597647, hAPP(c_Relation_Oconverse(_1597647, _1597645), _1597649)), -(_1597651 = c_Orderings_Obot__class_Obot(tc_fun(_1597653, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1597647, _1597645, _1597649), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597653, tc_fun(_1597647, tc_HOL_Obool)), _1597651), _1597655)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597653, tc_fun(_1597645, tc_HOL_Obool)), _1597651), hAPP(hAPP(c_COMBB(tc_fun(_1597647, tc_HOL_Obool), tc_fun(_1597645, tc_HOL_Obool), _1597653), c_Relation_OImage(_1597647, _1597645, _1597649)), _1597655)))], (43667 ^ _780119) ^ [_1651661, _1651663, _1651665, _1651667, _1651669] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651661), tc_List_Olist(_1651661))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651661), tc_List_Olist(_1651661)), hAPP(hAPP(c_List_Olist_OCons(_1651661), _1651663), _1651665)), _1651667)), c_List_Olistrel(_1651661, _1651669))), 43672 ^ _780119 : [(43675 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651661, _1651661)), hAPP(hAPP(c_Product__Type_OPair(_1651661, _1651661), _1651663), 43670 ^ [_1651661, _1651663, _1651665, _1651667, _1651669])), _1651669)))], (43677 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651661), tc_List_Olist(_1651661))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651661), tc_List_Olist(_1651661)), _1651665), 43671 ^ [_1651661, _1651663, _1651665, _1651667, _1651669])), c_List_Olistrel(_1651661, _1651669))))], (43673 ^ _780119) ^ [] : [-(_1651667 = hAPP(hAPP(c_List_Olist_OCons(_1651661), 43670 ^ [_1651661, _1651663, _1651665, _1651667, _1651669]), 43671 ^ [_1651661, _1651663, _1651665, _1651667, _1651669]))]]], (9378 ^ _780119) ^ [_941452, _941454, _941456] : [class_Lattices_Olattice(_941452), hBOOL(hAPP(c_Finite__Set_Ofinite(_941452), _941454)), -(_941456 = c_Orderings_Obot__class_Obot(tc_fun(_941452, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941452, tc_HOL_Obool)), _941456), _941454)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_941452), c_Big__Operators_Olattice__class_OSup__fin(_941452, _941456)), c_Big__Operators_Olattice__class_OSup__fin(_941452, _941454)) = c_Big__Operators_Olattice__class_OSup__fin(_941452, _941454))], (13238 ^ _780119) ^ [_1021064, _1021066] : [class_Groups_Ogroup__add(_1021064), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1021064), hAPP(c_Groups_Ouminus__class_Ouminus(_1021064), _1021066)) = _1021066)], (41621 ^ _780119) ^ [_1600545, _1600547, _1600549, _1600551] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1600545, tc_HOL_Obool), hAPP(c_Set_Oimage(_1600547, tc_fun(_1600545, tc_HOL_Obool), _1600549), _1600551)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600547, tc_fun(_1600545, tc_HOL_Obool)), _1600551), _1600549))], (13590 ^ _780119) ^ [_1027457, _1027459] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027457), _1027459))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027457), hAPP(c_Nat_OSuc, _1027459))), -(_1027459 = _1027457)], (28646 ^ _780119) ^ [_1309295, _1309297, _1309299] : [class_Orderings_Olinorder(_1309295), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309295), _1309297)), -(_1309297 = c_Orderings_Obot__class_Obot(tc_fun(_1309295, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309295), _1309299)), -(_1309299 = c_Orderings_Obot__class_Obot(tc_fun(_1309295, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309295, tc_HOL_Obool)), _1309297), _1309299) = c_Orderings_Obot__class_Obot(tc_fun(_1309295, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1309295, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309295, tc_HOL_Obool)), _1309297), _1309299)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309295), c_Big__Operators_Olinorder__class_OMax(_1309295, _1309297)), c_Big__Operators_Olinorder__class_OMax(_1309295, _1309299)))], (27564 ^ _780119) ^ [_1289422, _1289424, _1289426] : [class_Orderings_Olinorder(_1289422), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289422), _1289424), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289422), _1289426), _1289424))))], (28062 ^ _780119) ^ [_1298233, _1298235, _1298237] : [class_Orderings_Olinorder(_1298233), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298233), _1298235), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298233), _1298235), _1298237)) = _1298235)], (47831 ^ _780119) ^ [_1746546, _1746548, _1746550, _1746552, _1746554] : [-(hBOOL(hAPP(_1746546, _1746548))), -(c_List_OtakeWhile(_1746550, _1746546, hAPP(hAPP(c_List_Oappend(_1746550), _1746552), hAPP(hAPP(c_List_Olist_OCons(_1746550), _1746548), _1746554))) = c_List_OtakeWhile(_1746550, _1746546, _1746552))], (42521 ^ _780119) ^ [_1621105, _1621107, _1621109, _1621111] : [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)), _1621105), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1621107), _1621109)))), -(hBOOL(hAPP(hAPP(hAPP(_1621111, _1621105), _1621107), _1621109))), 42529 ^ _780119 : [(42542 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1621111, 42526 ^ [_1621105, _1621107, _1621109, _1621111]), 42527 ^ [_1621105, _1621107, _1621109, _1621111]), 42528 ^ [_1621105, _1621107, _1621109, _1621111]))], (42532 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 42527 ^ [_1621105, _1621107, _1621109, _1621111]), 42528 ^ [_1621105, _1621107, _1621109, _1621111]))), hAPP(42526 ^ [_1621105, _1621107, _1621109, _1621111], 42528 ^ [_1621105, _1621107, _1621109, _1621111]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1621111, 42526 ^ [_1621105, _1621107, _1621109, _1621111]), 42527 ^ [_1621105, _1621107, _1621109, _1621111]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 42528 ^ [_1621105, _1621107, _1621109, _1621111]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42530 ^ _780119) ^ [] : [-(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)), 42526 ^ [_1621105, _1621107, _1621109, _1621111]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 42527 ^ [_1621105, _1621107, _1621109, _1621111]), 42528 ^ [_1621105, _1621107, _1621109, _1621111])))))]]], (41137 ^ _780119) ^ [_1587226, _1587228, _1587230, _1587232, _1587234, _1587236, _1587238] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1587226, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587228, tc_fun(_1587226, tc_HOL_Obool)), _1587230), _1587232)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587234, tc_fun(_1587226, tc_HOL_Obool)), _1587236), _1587238)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587228, tc_fun(_1587226, tc_HOL_Obool)), _1587230), hAPP(hAPP(c_COMBB(tc_fun(_1587234, tc_fun(_1587226, tc_HOL_Obool)), tc_fun(_1587226, tc_HOL_Obool), _1587228), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587234, tc_fun(_1587226, tc_HOL_Obool)), _1587236)), hAPP(hAPP(c_COMBC(_1587228, tc_fun(_1587234, tc_fun(_1587226, tc_HOL_Obool)), tc_fun(_1587234, tc_fun(_1587226, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1587226, tc_HOL_Obool), tc_fun(_1587226, tc_HOL_Obool)), tc_fun(tc_fun(_1587234, tc_fun(_1587226, tc_HOL_Obool)), tc_fun(_1587234, tc_fun(_1587226, tc_HOL_Obool))), _1587228), c_COMBB(tc_fun(_1587226, tc_HOL_Obool), tc_fun(_1587226, tc_HOL_Obool), _1587234)), hAPP(hAPP(c_COMBB(tc_fun(_1587226, tc_HOL_Obool), tc_fun(tc_fun(_1587226, tc_HOL_Obool), tc_fun(_1587226, tc_HOL_Obool)), _1587228), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1587226, tc_HOL_Obool))), _1587232))), _1587238))))], (29757 ^ _780119) ^ [_1333798, _1333800, _1333802, _1333804] : [29759 ^ _780119 : [(29762 ^ _780119) ^ [] : [hAPP(_1333804, 29758 ^ [_1333798, _1333800, _1333802, _1333804]) = c_Orderings_Obot__class_Obot(tc_fun(_1333800, tc_HOL_Obool))], (29760 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333798), 29758 ^ [_1333798, _1333800, _1333802, _1333804]), _1333802)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1333798, tc_fun(_1333800, tc_HOL_Obool)), _1333802), _1333804) = c_Orderings_Obot__class_Obot(tc_fun(_1333800, tc_HOL_Obool)))], (38694 ^ _780119) ^ [_1529673, _1529675] : [38695 ^ _780119 : [(38696 ^ _780119) ^ [_1529719] : [hBOOL(hAPP(_1529673, _1529719))]], -(hBOOL(hAPP(_1529673, c_Hilbert__Choice_OEps(_1529675, _1529673))))], (5244 ^ _780119) ^ [_860338, _860340] : [_860340 = _860338, -(c_Orderings_Oord__class_Omin(_860340) = c_Orderings_Oord__class_Omin(_860338))], (40026 ^ _780119) ^ [_1561404, _1561406, _1561408, _1561410] : [-(hAPP(c_Relation_Oconverse(_1561404, _1561406), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1561404, _1561406), tc_HOL_Obool)), _1561408), _1561410)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1561406, _1561404), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1561404, _1561406), _1561408)), hAPP(c_Relation_Oconverse(_1561404, _1561406), _1561410)))], (21234 ^ _780119) ^ [_1166465, _1166467, _1166469, _1166471, _1166473] : [class_Fields_Ofield(_1166465), hBOOL(hAPP(c_Finite__Set_Ofinite(_1166467), _1166469)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1166467), _1166471)), 21248 ^ _780119 : [(21251 ^ _780119) ^ [] : [-(hAPP(_1166473, 21247 ^ [_1166465, _1166467, _1166469, _1166471, _1166473]) = c_Groups_Ozero__class_Ozero(_1166465))], (21249 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1166467), 21247 ^ [_1166465, _1166467, _1166469, _1166471, _1166473]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1166467, tc_HOL_Obool)), _1166469), _1166471))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166467, _1166465), _1166473), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1166467, tc_HOL_Obool)), _1166469), _1166471)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166465), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166467, _1166465), _1166473), _1166469)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166467, _1166465), _1166473), _1166471))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166467, _1166465), _1166473), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1166467, tc_HOL_Obool)), _1166469), _1166471))))], (29508 ^ _780119) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (46121 ^ _780119) ^ [_1709130, _1709132, _1709134, _1709136, _1709138] : [hBOOL(hAPP(hAPP(c_member(_1709130), _1709132), hAPP(c_List_Oset(_1709130), _1709134))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709136), hAPP(_1709138, _1709132))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709136), c_List_Olist_Olist__size(_1709130, _1709138, _1709134))))], (50258 ^ _780119) ^ [_1798673, _1798675, _1798677, _1798679, _1798681, _1798683, _1798685] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1798673, _1798675, _1798677, _1798679), _1798681), _1798683), _1798685) = c_New__DSequence_Opos__bind(_1798673, _1798675, hAPP(hAPP(hAPP(_1798677, _1798681), _1798683), _1798685), hAPP(hAPP(c_COMBC(_1798673, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1798675))), hAPP(hAPP(c_COMBC(_1798673, 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(_1798675)))), hAPP(hAPP(c_COMBC(_1798673, 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(_1798675))))), _1798679), _1798681)), _1798683)), _1798685)))], (20684 ^ _780119) ^ [_1156186, _1156188, _1156190, _1156192, _1156194] : [class_Fields_Olinordered__field(_1156186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156186), c_Groups_Ozero__class_Ozero(_1156186)), _1156188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156186), _1156188), _1156190)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156186), c_Groups_Ozero__class_Ozero(_1156186)), _1156192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156186), _1156192), _1156194)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156186), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156186), _1156188), _1156194)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156186), _1156190), _1156192))))], (10124 ^ _780119) ^ [_956732, _956734, _956736, _956738] : [hBOOL(hAPP(hAPP(c_member(_956732), _956734), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956732, tc_HOL_Obool)), _956736), _956738))), 10127 ^ _780119 : [(10130 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_956732), _956734), _956738)))], (10128 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_956732), _956734), _956736)))]]], (31189 ^ _780119) ^ [_1363292, _1363294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1363292), _1363294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1363292)), c_Int_OBit1(_1363294))))], (14832 ^ _780119) ^ [_1052426, _1052428] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1052426, _1052428)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1052426, _1052428), tc_HOL_Obool)))), 14835 ^ _780119 : [(14838 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052428), c_Orderings_Otop__class_Otop(tc_fun(_1052428, tc_HOL_Obool)))))], (14836 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052426), c_Orderings_Otop__class_Otop(tc_fun(_1052426, tc_HOL_Obool)))))]]], (51353 ^ _780119) ^ [_1817945] : [-(class_HOL_Oequal(tc_List_Olist(_1817945)))], (2970 ^ _780119) ^ [_824343, _824345] : [_824345 = _824343, -(c_Equiv__Relations_Oquotient(_824345) = c_Equiv__Relations_Oquotient(_824343))], (42334 ^ _780119) ^ [_1617034, _1617036, _1617038, _1617040, _1617042, _1617044] : [-(hBOOL(hAPP(hAPP(c_member(_1617034), _1617036), c_Map_Odom(_1617034, _1617038, _1617040)))), -(c_Map_Omap__add(_1617034, _1617038, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1617034, tc_Option_Ooption(_1617038)), _1617042), _1617036), hAPP(c_Option_Ooption_OSome(_1617038), _1617044)), _1617040) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1617034, tc_Option_Ooption(_1617038)), c_Map_Omap__add(_1617034, _1617038, _1617042, _1617040)), _1617036), hAPP(c_Option_Ooption_OSome(_1617038), _1617044)))], (14142 ^ _780119) ^ [_1038151, _1038153, _1038155, _1038157, _1038159] : [class_Groups_Ocomm__monoid__mult(_1038151), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038153), _1038155)), -(hBOOL(hAPP(hAPP(c_member(_1038153), _1038157), _1038155))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038153, _1038151), _1038159), hAPP(hAPP(c_Set_Oinsert(_1038153), _1038157), _1038155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038151), hAPP(_1038159, _1038157)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038153, _1038151), _1038159), _1038155)))], (41822 ^ _780119) ^ [_1605276] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1605276, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1605276, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1605276, tc_HOL_Obool)))], (29789 ^ _780119) ^ [_1334734, _1334736, _1334738, _1334740, _1334742, _1334744] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334734, tc_fun(_1334736, tc_HOL_Obool)), _1334738), hAPP(hAPP(c_COMBB(_1334740, tc_fun(_1334736, tc_HOL_Obool), _1334734), _1334742), _1334744)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334740, tc_fun(_1334736, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1334734, _1334740, _1334744), _1334738)), _1334742))], (18384 ^ _780119) ^ [_1115554, _1115556] : [-(hBOOL(hAPP(hAPP(c_member(_1115554), _1115556), c_Orderings_Otop__class_Otop(tc_fun(_1115554, tc_HOL_Obool)))))], (19170 ^ _780119) ^ [_1129037, _1129039, _1129041, _1129043] : [class_Divides_Osemiring__div(_1129037), -(_1129039 = c_Groups_Ozero__class_Ozero(_1129037)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129037), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129037), _1129041), _1129039)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129037), _1129043), _1129039)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129037), _1129041), _1129043))], (7320 ^ _780119) ^ [_902793, _902795, _902797] : [class_Lattices_Olattice(_902793), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902793), _902795), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902793), _902795), _902797)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902793), _902795), _902797))], (36950 ^ _780119) ^ [_1483245, _1483247, _1483249, _1483251, _1483253, _1483255] : [c_Typedef_Otype__definition(_1483245, _1483247, _1483249, _1483251, _1483253), -(hAPP(_1483251, hAPP(_1483249, _1483255)) = _1483255)], (31737 ^ _780119) ^ [_1372305, _1372307] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1372305), _1372307), hAPP(c_Int_Onumber__class_Onumber__of(_1372305), c_Int_OBit1(c_Int_OPls))) = _1372307), class_Fields_Ofield(_1372305), class_Int_Onumber__ring(_1372305)], (1430 ^ _780119) ^ [_800718, _800720] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_800718)), _800720 = _800718, class_Groups_Oordered__ab__semigroup__add__imp__le(_800720)], (2256 ^ _780119) ^ [_813304, _813306, _813308, _813310] : [-(c_Orderings_Oord_Omax(_813310, _813306) = c_Orderings_Oord_Omax(_813308, _813304)), _813310 = _813308, _813306 = _813304], (10967 ^ _780119) ^ [_974840, _974842, _974844] : [class_Groups_Ogroup__add(_974840), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974840), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974840), _974842), _974844)), _974844) = _974842)], (48387 ^ _780119) ^ [_1758376, _1758378, _1758380, _1758382, _1758384] : [class_Orderings_Olinorder(_1758376), -(c_List_Olinorder__class_Osort__key(_1758378, _1758376, _1758380, hAPP(hAPP(c_List_Olist_OCons(_1758378), _1758382), _1758384)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1758378, _1758376, _1758380), _1758382), c_List_Olinorder__class_Osort__key(_1758378, _1758376, _1758380, _1758384)))], (47031 ^ _780119) ^ [_1728112] : [-(c_List_Oupt(_1728112, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (37791 ^ _780119) ^ [_1505821, _1505823, _1505825, _1505827, _1505829] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1505821, _1505823), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1505821, tc_HOL_Obool)), _1505825), _1505827)), hAPP(c_COMBK(tc_fun(_1505823, tc_HOL_Obool), _1505821), _1505829)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1505821, _1505823), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1505821, _1505823), _1505825), hAPP(c_COMBK(tc_fun(_1505823, tc_HOL_Obool), _1505821), _1505829))), hAPP(hAPP(c_Product__Type_OSigma(_1505821, _1505823), _1505827), hAPP(c_COMBK(tc_fun(_1505823, tc_HOL_Obool), _1505821), _1505829))))], (51091 ^ _780119) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (13554 ^ _780119) ^ [_1026944, _1026946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026944), hAPP(c_Nat_OSuc, _1026946))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026944), _1026946))), -(_1026944 = _1026946)], (35815 ^ _780119) ^ [_1457710, _1457712, _1457714, _1457716, _1457718, _1457720] : [c_Equiv__Relations_Oequiv(_1457710, _1457712, _1457714), c_Equiv__Relations_Ocongruent(_1457710, tc_fun(_1457716, tc_HOL_Obool), _1457714, _1457718), hBOOL(hAPP(hAPP(c_member(_1457710), _1457720), _1457712)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1457710, tc_fun(_1457716, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1457710, _1457710, _1457714), hAPP(hAPP(c_Set_Oinsert(_1457710), _1457720), c_Orderings_Obot__class_Obot(tc_fun(_1457710, tc_HOL_Obool))))), _1457718) = hAPP(_1457718, _1457720))], (18678 ^ _780119) ^ [_1120837, _1120839] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120837), _1120839))), -(_1120837 = _1120839), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120839), _1120837)))], (458 ^ _780119) ^ [_787188, _787190, _787192, _787194, _787196, _787198, _787200, _787202] : [-(c_Finite__Set_Ofolding__idem(_787200, _787196, _787192, _787188)), c_Finite__Set_Ofolding__idem(_787202, _787198, _787194, _787190), _787202 = _787200, _787198 = _787196, _787194 = _787192, _787190 = _787188], (28192 ^ _780119) ^ [_1301214] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1301214) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5090 ^ _780119) ^ [_857997, _857999, _858001, _858003, _858005, _858007] : [-(c_Predicate_Oconversep(_858007, _858003, _857999) = c_Predicate_Oconversep(_858005, _858001, _857997)), _858007 = _858005, _858003 = _858001, _857999 = _857997], (21556 ^ _780119) ^ [_1173260, _1173262] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1173260, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1173262)) = 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), _1173260), _1173262)))], (32595 ^ _780119) ^ [_1387618, _1387620] : [class_Int_Onumber__ring(_1387618), -(hAPP(c_Int_Onumber__class_Onumber__of(_1387618), c_Int_OBit0(_1387620)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387618), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387618), c_Groups_Ozero__class_Ozero(_1387618)), hAPP(c_Int_Onumber__class_Onumber__of(_1387618), _1387620))), hAPP(c_Int_Onumber__class_Onumber__of(_1387618), _1387620)))], (39835 ^ _780119) ^ [_1557102] : [-(hAPP(c_Relation_ODomain(_1557102, _1557102), c_Relation_OId(_1557102)) = c_Orderings_Otop__class_Otop(tc_fun(_1557102, tc_HOL_Obool)))], (47669 ^ _780119) ^ [_1742049, _1742051, _1742053] : [c_List_Oconcat(_1742049, _1742051) = c_List_Oconcat(_1742049, _1742053), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1742049))), _1742051) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1742049))), _1742053), 47679 ^ _780119 : [(47682 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1742049), tc_List_Olist(_1742049), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1742049), tc_fun(tc_List_Olist(_1742049), tc_Nat_Onat), tc_fun(tc_List_Olist(_1742049), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1742049), tc_Nat_Onat), tc_fun(tc_List_Olist(_1742049), tc_HOL_Obool)), tc_List_Olist(_1742049)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1742049))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1742049)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1742049))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1742049)))), 47678 ^ [_1742049, _1742051, _1742053]))], (47680 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742049), tc_List_Olist(_1742049))), 47678 ^ [_1742049, _1742051, _1742053]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1742049), tc_List_Olist(_1742049))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1742049), tc_List_Olist(_1742049)), _1742051), _1742053)))))]], -(_1742051 = _1742053)], (50256 ^ _780119) ^ [_1798637, _1798639, _1798641, _1798643] : [-(c_New__Random__Sequence_Opos__empty(_1798637, _1798639, _1798641, _1798643) = c_New__DSequence_Opos__empty(_1798637))], (41123 ^ _780119) ^ [_1586564, _1586566, _1586568, _1586570] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1586564, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586566, tc_fun(_1586564, tc_HOL_Obool)), _1586568), _1586570)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1586566, tc_fun(_1586564, tc_HOL_Obool)), _1586568), hAPP(hAPP(c_COMBB(tc_fun(_1586564, tc_HOL_Obool), tc_fun(_1586564, tc_HOL_Obool), _1586566), c_Groups_Ouminus__class_Ouminus(tc_fun(_1586564, tc_HOL_Obool))), _1586570)))], (6125 ^ _780119) ^ [_877757, _877759, _877761, _877763] : [hBOOL(hAPP(hAPP(c_member(_877757), _877759), hAPP(hAPP(c_Set_Oinsert(_877757), _877761), _877763))), -(_877759 = _877761), -(hBOOL(hAPP(hAPP(c_member(_877757), _877759), _877763)))], (13136 ^ _780119) ^ [_1019297, _1019299, _1019301, _1019303, _1019305] : [-(c_Map_Orestrict__map(_1019297, _1019299, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1019297, tc_Option_Ooption(_1019299)), _1019301), _1019303), hAPP(c_Option_Ooption_OSome(_1019299), _1019305)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019297, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1019297), _1019303), c_Orderings_Obot__class_Obot(tc_fun(_1019297, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1019297, _1019299, _1019301, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019297, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1019297), _1019303), c_Orderings_Obot__class_Obot(tc_fun(_1019297, tc_HOL_Obool))))))], (38344 ^ _780119) ^ [_1521344, _1521346] : [c_Wellfounded_Owf(_1521344, _1521346), -(c_Wellfounded_OwfP(_1521344, hAPP(hAPP(c_COMBC(_1521344, tc_fun(tc_prod(_1521344, _1521344), tc_HOL_Obool), tc_fun(_1521344, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1521344, tc_fun(tc_fun(tc_prod(_1521344, _1521344), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1521344, _1521344), tc_HOL_Obool), tc_fun(_1521344, tc_HOL_Obool)), _1521344), c_COMBC(_1521344, tc_fun(tc_prod(_1521344, _1521344), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1521344, tc_prod(_1521344, _1521344)), tc_fun(_1521344, tc_fun(tc_fun(tc_prod(_1521344, _1521344), tc_HOL_Obool), tc_HOL_Obool)), _1521344), hAPP(c_COMBB(tc_prod(_1521344, _1521344), tc_fun(tc_fun(tc_prod(_1521344, _1521344), tc_HOL_Obool), tc_HOL_Obool), _1521344), c_member(tc_prod(_1521344, _1521344)))), c_Product__Type_OPair(_1521344, _1521344)))), _1521346)))], (21552 ^ _780119) ^ [_1173158, _1173160, _1173162] : [-(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, _1173158, _1173160)), _1173162), _1173160) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1173158), _1173162), _1173160))], (8402 ^ _780119) ^ [_925731, _925733, _925735] : [class_Lattices_Olattice(_925731), hBOOL(hAPP(c_Finite__Set_Ofinite(_925731), _925733)), hBOOL(hAPP(hAPP(c_member(_925731), _925735), _925733)), 8413 ^ _780119 : [(8420 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925731, tc_HOL_Obool)), _925733), hAPP(hAPP(c_Set_Oinsert(_925731), _925735), c_Orderings_Obot__class_Obot(tc_fun(_925731, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_925731, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_925731, _925733) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925731), _925735), c_Big__Operators_Olattice__class_OSup__fin(_925731, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925731, tc_HOL_Obool)), _925733), hAPP(hAPP(c_Set_Oinsert(_925731), _925735), c_Orderings_Obot__class_Obot(tc_fun(_925731, tc_HOL_Obool)))))))], (8414 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925731, tc_HOL_Obool)), _925733), hAPP(hAPP(c_Set_Oinsert(_925731), _925735), c_Orderings_Obot__class_Obot(tc_fun(_925731, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_925731, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_925731, _925733) = _925735)]]], (40170 ^ _780119) ^ [_1564986, _1564988, _1564990] : [40172 ^ _780119 : [(40180 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564986, _1564986)), hAPP(hAPP(c_Product__Type_OPair(_1564986, _1564986), 40171 ^ [_1564986, _1564988, _1564990]), 40174 ^ [_1564986, _1564988, _1564990])), _1564990))], (40178 ^ _780119) ^ [] : [40171 ^ [_1564986, _1564988, _1564990] = 40174 ^ [_1564986, _1564988, _1564990]], (40176 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1564986), 40174 ^ [_1564986, _1564988, _1564990]), _1564988)))], (40173 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1564986), 40171 ^ [_1564986, _1564988, _1564990]), _1564988)))], (40182 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564986, _1564986)), hAPP(hAPP(c_Product__Type_OPair(_1564986, _1564986), 40174 ^ [_1564986, _1564988, _1564990]), 40171 ^ [_1564986, _1564988, _1564990])), _1564990))]], -(c_Relation_Ototal__on(_1564986, _1564988, _1564990))], (25247 ^ _780119) ^ [_1242140, _1242142] : [hAPP(c_Int_Onat, _1242140) = _1242142, 25250 ^ _780119 : [(25257 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242140))), -(_1242142 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25251 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242140)), -(_1242140 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1242142))]]], (19685 ^ _780119) ^ [_1138082, _1138084] : [class_Rings_Odivision__ring__inverse__zero(_1138082), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138082), _1138084), c_Groups_Ozero__class_Ozero(_1138082)) = c_Groups_Ozero__class_Ozero(_1138082))], (19715 ^ _780119) ^ [_1138765, _1138767] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1138765), _1138767)), _1138765)))], (7314 ^ _780119) ^ [_902668, _902670, _902672] : [class_Lattices_Osemilattice__sup(_902668), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902668), _902670), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902668), _902670), _902672)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902668), _902670), _902672))], (51061 ^ _780119) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (28092 ^ _780119) ^ [_1298842, _1298844, _1298846, _1298848] : [class_Orderings_Olinorder(_1298842), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298842), _1298844), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298842), _1298846), _1298848)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298842), _1298846), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298842), _1298844), _1298848)))], (6989 ^ _780119) ^ [_895536, _895538, _895540, _895542] : [class_Orderings_Opreorder(_895536), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895536), _895538), _895540)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895536), _895540), _895542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895536), _895538), _895542)))], (32665 ^ _780119) ^ [_1389032, _1389034] : [class_Int_Onumber__ring(_1389032), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389032), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389032), c_Groups_Oone__class_Oone(_1389032)), c_Groups_Oone__class_Oone(_1389032))), hAPP(c_Int_Onumber__class_Onumber__of(_1389032), _1389034)) = hAPP(c_Int_Onumber__class_Onumber__of(_1389032), c_Int_OBit0(_1389034)))], (33159 ^ _780119) ^ [_1398176] : [_1398176 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1398176) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43443 ^ _780119) ^ [_1644877, _1644879, _1644881, _1644883, _1644885] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644877), tc_List_Olist(_1644877))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644877), tc_List_Olist(_1644877)), _1644879), _1644881)), c_List_Olistrel(_1644877, c_Transitive__Closure_Ortrancl(_1644877, _1644883)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644877), tc_List_Olist(_1644877))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644877), tc_List_Olist(_1644877)), _1644881), _1644885)), c_List_Olistrel(_1644877, c_Transitive__Closure_Ortrancl(_1644877, _1644883)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644877), tc_List_Olist(_1644877))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644877), tc_List_Olist(_1644877)), _1644879), _1644885)), c_List_Olistrel(_1644877, c_Transitive__Closure_Ortrancl(_1644877, _1644883)))))], (10855 ^ _780119) ^ [_972676, _972678, _972680, _972682] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_972676), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972676), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972676), _972678), _972680)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972676), _972682), _972680))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972676), _972678), _972682)))], (23207 ^ _780119) ^ [_1203999, _1204001, _1204003] : [hBOOL(hAPP(_1203999, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1204001), _1204003)))), 23210 ^ _780119 : [(23217 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204001), _1204003)), -(hBOOL(hAPP(_1203999, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23211 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204003), _1204001)), -(hBOOL(hAPP(_1203999, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204001)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204003)))))]]], (19562 ^ _780119) ^ [_1135733, _1135735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135733)), -(c_SMT_Oz3div(_1135735, _1135733) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1135735), _1135733))], (27842 ^ _780119) ^ [_1294214, _1294216, _1294218, _1294220, _1294222] : [class_Orderings_Olinorder(_1294214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294214), _1294216), _1294218)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294214), _1294220), _1294222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294214), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1294214), _1294216), _1294220)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1294214), _1294218), _1294222))))], (34048 ^ _780119) ^ [_1419569, _1419571, _1419573, _1419575, _1419577] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1419569, _1419571, _1419573), _1419575), _1419577)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1419569, _1419571)), hAPP(hAPP(c_Product__Type_OPair(_1419569, _1419571), _1419575), _1419577)), _1419573)))], (31907 ^ _780119) ^ [_1374933, _1374935] : [class_Int_Onumber__ring(_1374933), -(hAPP(c_Int_Onumber__class_Onumber__of(_1374933), c_Int_Osucc(_1374935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1374933), c_Groups_Oone__class_Oone(_1374933)), hAPP(c_Int_Onumber__class_Onumber__of(_1374933), _1374935)))], (10336 ^ _780119) ^ [_961911, _961913, _961915] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961911, tc_HOL_Obool)), _961913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_961911, tc_HOL_Obool)), _961915), _961913)) = c_Orderings_Obot__class_Obot(tc_fun(_961911, tc_HOL_Obool)))], (15936 ^ _780119) ^ [_1070546, _1070548, _1070550] : [class_Rings_Oordered__cancel__semiring(_1070546), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070546), _1070548), _1070550)), c_Groups_Ozero__class_Ozero(_1070546)))), 15941 ^ _780119 : [(15948 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070546), _1070548), c_Groups_Ozero__class_Ozero(_1070546))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070546), c_Groups_Ozero__class_Ozero(_1070546)), _1070550))], (15942 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070546), c_Groups_Ozero__class_Ozero(_1070546)), _1070548)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070546), _1070550), c_Groups_Ozero__class_Ozero(_1070546)))]]], (44502 ^ _780119) ^ [_1671733] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1671733)) = _1671733)], (35442 ^ _780119) ^ [_1448872] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1448872) = 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, _1448872)), 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))))))))], (10054 ^ _780119) ^ [_955218, _955220, _955222, _955224] : [class_Lattices_Osemilattice__inf(_955218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955218), _955220), _955222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955218), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955218), _955220), _955224)), _955222)))], (43471 ^ _780119) ^ [_1646148, _1646150, _1646152] : [-(hAPP(c_List_Olexn(_1646148, _1646150), hAPP(c_Nat_OSuc, _1646152)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1646148), tc_List_Olist(_1646148)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1646148, tc_List_Olist(_1646148)), tc_prod(_1646148, tc_List_Olist(_1646148))), tc_prod(tc_List_Olist(_1646148), tc_List_Olist(_1646148)), c_Product__Type_Omap__pair(tc_prod(_1646148, tc_List_Olist(_1646148)), tc_List_Olist(_1646148), tc_prod(_1646148, tc_List_Olist(_1646148)), tc_List_Olist(_1646148), hAPP(c_Product__Type_Oprod_Oprod__case(_1646148, tc_List_Olist(_1646148), tc_List_Olist(_1646148)), c_List_Olist_OCons(_1646148)), hAPP(c_Product__Type_Oprod_Oprod__case(_1646148, tc_List_Olist(_1646148), tc_List_Olist(_1646148)), c_List_Olist_OCons(_1646148)))), c_Wellfounded_Olex__prod(_1646148, tc_List_Olist(_1646148), _1646150, hAPP(c_List_Olexn(_1646148, _1646150), _1646152)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1646148), tc_List_Olist(_1646148))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1646148), tc_List_Olist(_1646148), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1646148), tc_fun(tc_List_Olist(_1646148), tc_HOL_Obool), tc_fun(tc_List_Olist(_1646148), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1646148), tc_HOL_Obool), tc_fun(tc_List_Olist(_1646148), tc_HOL_Obool)), tc_List_Olist(_1646148)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1646148))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1646148)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1646148), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1646148)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1646148)))), hAPP(c_Nat_OSuc, _1646152))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1646148), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1646148)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1646148)))), hAPP(c_Nat_OSuc, _1646152)))))))], (44720 ^ _780119) ^ [_1675939, _1675941] : [-(c_List_Olistrelp(_1675939, _1675941, c_List_Olist_ONil(_1675939), c_List_Olist_ONil(_1675939)))], (51125 ^ _780119) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (39919 ^ _780119) ^ [_1559020, _1559022] : [-(c_Relation_Oirrefl(_1559020, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1559020, _1559020), tc_HOL_Obool)), _1559022), c_Relation_OId(_1559020))))], (50925 ^ _780119) ^ [_1813497, _1813499, _1813501] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1813497) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1813497, _1813499, _1813501)], (50464 ^ _780119) ^ [_1803497, _1803499, _1803501] : [-(_1803499 = _1803501), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1803497, _1803497, hAPP(hAPP(c_COMBB(tc_fun(_1803497, tc_HOL_Obool), tc_fun(_1803497, tc_HOL_Obool), _1803497), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1803497), c_fNot)), c_fequal)), _1803499), _1803501)))], (9680 ^ _780119) ^ [_947565, _947567, _947569, _947571] : [hBOOL(hAPP(_947565, _947567)), hBOOL(hAPP(_947569, _947567)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947571, tc_HOL_Obool)), _947565), _947569), _947567)))], (30137 ^ _780119) ^ [_1343268, _1343270, _1343272, _1343274, _1343276, _1343278] : [-(c_Com_Ocom_OLocal(_1343268, _1343270, _1343272) = c_Com_Ocom_OLocal(_1343274, _1343276, _1343278)), _1343268 = _1343274, _1343270 = _1343276, _1343272 = _1343278], (34527 ^ _780119) ^ [_1427999, _1428001, _1428003, _1428005, _1428007, _1428009] : [hAPP(c_Product__Type_Oapsnd(_1427999, _1428001, _1428003, _1428005), _1428007) = hAPP(c_Product__Type_Oapsnd(_1427999, _1428001, _1428003, _1428009), _1428007), -(hAPP(_1428005, hAPP(c_Product__Type_Osnd(_1428003, _1427999), _1428007)) = hAPP(_1428009, hAPP(c_Product__Type_Osnd(_1428003, _1427999), _1428007)))], (38464 ^ _780119) ^ [_1523547] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1523547), c_Int_OInteg)), -(_1523547 = hAPP(c_Int_ORep__Integ, 38467 ^ [_1523547]))], (24923 ^ _780119) ^ [_1236880, _1236882, _1236884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236880)), 24929 ^ _780119 : [(24932 ^ _780119) ^ [] : [hBOOL(hAPP(_1236882, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24928 ^ [_1236880, _1236882, _1236884]), _1236880)))], (24930 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1236882, 24928 ^ [_1236880, _1236882, _1236884])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236884)), 24937 ^ _780119 : [(24938 ^ _780119) ^ [_1237169] : [hBOOL(hAPP(_1236882, _1237169)), -(hBOOL(hAPP(_1236882, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1237169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236884), _1236880)))))]]], (19058 ^ _780119) ^ [_1127313, _1127315] : [class_Divides_Osemiring__div(_1127313), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1127313), _1127315), c_Groups_Ozero__class_Ozero(_1127313)) = c_Groups_Ozero__class_Ozero(_1127313))], (32775 ^ _780119) ^ [_1390981, _1390983] : [class_Rings_Olinordered__idom(_1390981), -(hAPP(c_Groups_Oabs__class_Oabs(_1390981), hAPP(hAPP(c_Power_Opower__class_Opower(_1390981), _1390983), 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(_1390981), _1390983), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (2780 ^ _780119) ^ [_821456, _821458] : [_821458 = _821456, -(c_Hoare__Mirabelle_Otriple_Otriple(_821458) = c_Hoare__Mirabelle_Otriple_Otriple(_821456))], (25133 ^ _780119) ^ [_1240295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240295)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1240295)) = _1240295)], (802 ^ _780119) ^ [_792344, _792346, _792348, _792350, _792352, _792354, _792356, _792358] : [-(c_Fun_Oinj__on(_792356, _792352, _792348, _792344)), c_Fun_Oinj__on(_792358, _792354, _792350, _792346), _792358 = _792356, _792354 = _792352, _792350 = _792348, _792346 = _792344], (38625 ^ _780119) ^ [_1527992, _1527994, _1527996] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1527992, _1527994, _1527996)), 38627 ^ _780119 : [(38637 ^ _780119) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1527992, 38626 ^ [_1527992, _1527994, _1527996], 38633 ^ [_1527992, _1527994, _1527996])], (38628 ^ _780119) ^ [_1528138] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1527992)), _1528138), _1527994)), -(c_Hoare__Mirabelle_Otriple__valid(_1527992, 38626 ^ [_1527992, _1527994, _1527996], _1528138))], (38635 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1527992)), 38633 ^ [_1527992, _1527994, _1527996]), _1527996)))]]], (29875 ^ _780119) ^ [_1337520, _1337522, _1337524, _1337526, _1337528] : [-(_1337520 = c_Orderings_Obot__class_Obot(tc_fun(_1337522, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1337524), _1337526), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337522, tc_fun(_1337524, tc_HOL_Obool)), _1337520), _1337528)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337522, tc_fun(_1337524, tc_HOL_Obool)), _1337520), hAPP(hAPP(c_COMBB(tc_fun(_1337524, tc_HOL_Obool), tc_fun(_1337524, tc_HOL_Obool), _1337522), hAPP(c_Set_Oinsert(_1337524), _1337526)), _1337528)))], (28044 ^ _780119) ^ [_1297906, _1297908, _1297910] : [class_Orderings_Olinorder(_1297906), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1297906), _1297908), _1297910) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1297906), _1297910), _1297908))], (43681 ^ _780119) ^ [_1652131, _1652133, _1652135, _1652137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1652131), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1652133), _1652135))), -(hAPP(c_Random_Opick(_1652133, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1652133)), _1652135), _1652137)), _1652131) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1652133), _1652135))], (22227 ^ _780119) ^ [_1185782, _1185784, _1185786] : [class_Rings_Olinordered__idom(_1185782), -(c_Groups_Osgn__class_Osgn(_1185782, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185782), _1185784), _1185786)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185782), c_Groups_Osgn__class_Osgn(_1185782, _1185784)), c_Groups_Osgn__class_Osgn(_1185782, _1185786)))], (37657 ^ _780119) ^ [_1501650, _1501652, _1501654, _1501656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501650, _1501652), tc_HOL_Obool)), _1501654), _1501656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501650, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1501650, _1501652), _1501654)), hAPP(c_Relation_ODomain(_1501650, _1501652), _1501656))))], (19977 ^ _780119) ^ [_1143310, _1143312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1143310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143312), _1143310))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143312), _1143310) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1143312), _1143310)), _1143310)))], (51075 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (4192 ^ _780119) ^ [_843472, _843474, _843476, _843478, _843480, _843482] : [-(c_List_Oremove1(_843482, _843478, _843474) = c_List_Oremove1(_843480, _843476, _843472)), _843482 = _843480, _843478 = _843476, _843474 = _843472], (33259 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (49321 ^ _780119) ^ [_1778248, _1778250, _1778252] : [-(hAPP(c_List_Oset(_1778248), hAPP(c_List_OremoveAll(_1778248, _1778250), _1778252)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1778248, tc_HOL_Obool)), hAPP(c_List_Oset(_1778248), _1778252)), hAPP(hAPP(c_Set_Oinsert(_1778248), _1778250), c_Orderings_Obot__class_Obot(tc_fun(_1778248, tc_HOL_Obool)))))], (38822 ^ _780119) ^ [_1532581, _1532583, _1532585, _1532587, _1532589, _1532591] : [class_Groups_Ocomm__monoid__add(_1532581), c_Fun_Oinj__on(_1532583, _1532585, _1532587, _1532589), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1532585, _1532581), _1532591), hAPP(c_Set_Oimage(_1532583, _1532585, _1532587), _1532589)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1532583, _1532581), hAPP(c_Fun_Ocomp(_1532585, _1532581, _1532583, _1532591), _1532587)), _1532589))], (32121 ^ _780119) ^ [_1379014, _1379016] : [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(_1379014))), 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)), _1379016)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379014)), hAPP(c_Nat_OSuc, _1379016))))], (35287 ^ _780119) ^ [] : [-(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)))], (6703 ^ _780119) ^ [_889718, _889720, _889722, _889724] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889718, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_889718, tc_fun(_889718, tc_HOL_Obool), tc_HOL_Obool), c_member(_889718)), _889720)), hAPP(hAPP(c_COMBC(_889718, tc_fun(_889718, tc_HOL_Obool), tc_HOL_Obool), c_member(_889718)), _889722)), _889724)), -(hBOOL(hAPP(hAPP(c_member(_889718), _889724), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889718, tc_HOL_Obool)), _889720), _889722))))], (41900 ^ _780119) ^ [_1606841, _1606843, _1606845] : [class_Complete__Lattice_Ocomplete__lattice(_1606841), -(c_Complete__Lattice_OInf__class_OInf(_1606841, hAPP(hAPP(c_Set_Oinsert(_1606841), _1606843), _1606845)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1606841), _1606843), c_Complete__Lattice_OInf__class_OInf(_1606841, _1606845)))], (41788 ^ _780119) ^ [_1604436] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1604436, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1604436, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1604436, tc_HOL_Obool)))], (46580 ^ _780119) ^ [_1719008, _1719010, _1719012, _1719014] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719008)), _1719010))), c_List_Ofoldr(tc_List_Olist(_1719012), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1719012)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1719012))), _1719014, 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(_1719008)), _1719010)), c_List_Ofoldr(tc_List_Olist(_1719012), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1719012)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719012), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1719012)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1719012)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1719012), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1719012)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719012), tc_List_Olist(_1719012), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1719012)))), _1719014), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (41639 ^ _780119) ^ [_1601209, _1601211, _1601213, _1601215] : [-(hAPP(c_Set_Ovimage(_1601209, _1601211, _1601213), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1601211, tc_HOL_Obool), _1601215)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1601211, tc_HOL_Obool), tc_fun(_1601209, tc_HOL_Obool)), _1601215), c_Set_Ovimage(_1601209, _1601211, _1601213)))], (27200 ^ _780119) ^ [_1282142, _1282144, _1282146] : [class_Lattices_Odistrib__lattice(_1282142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282142), _1282144)), -(_1282144 = c_Orderings_Obot__class_Obot(tc_fun(_1282142, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282142), _1282146), c_Big__Operators_Olattice__class_OSup__fin(_1282142, _1282144)) = c_Big__Operators_Olattice__class_OSup__fin(_1282142, hAPP(c_Set_OCollect(_1282142), hAPP(hAPP(c_COMBB(tc_fun(_1282142, tc_HOL_Obool), tc_HOL_Obool, _1282142), c_HOL_OEx(_1282142)), hAPP(hAPP(c_COMBC(_1282142, tc_fun(_1282142, tc_HOL_Obool), tc_fun(_1282142, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1282142, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1282142, tc_HOL_Obool), tc_fun(_1282142, tc_HOL_Obool)), _1282142), c_COMBS(_1282142, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1282142, tc_HOL_Obool), tc_fun(_1282142, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1282142), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1282142), c_fconj)), hAPP(hAPP(c_COMBC(_1282142, tc_fun(_1282142, _1282142), tc_fun(_1282142, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1282142, tc_HOL_Obool), tc_fun(tc_fun(_1282142, _1282142), tc_fun(_1282142, tc_HOL_Obool)), _1282142), c_COMBB(_1282142, tc_HOL_Obool, _1282142)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282142), _1282146))))), hAPP(hAPP(c_COMBC(_1282142, tc_fun(_1282142, tc_HOL_Obool), tc_HOL_Obool), c_member(_1282142)), _1282144))))))], (51127 ^ _780119) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (38251 ^ _780119) ^ [_1519465, _1519467] : [c_Wellfounded_OwfP(_1519465, _1519467), 38254 ^ _780119 : [(38255 ^ _780119) ^ [_1519529] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1519465, _1519467), _1519529)))]]], (31999 ^ _780119) ^ [_1376419, _1376421] : [class_Int_Onumber__ring(_1376419), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376419), hAPP(c_Int_Onumber__class_Onumber__of(_1376419), _1376421)), c_Groups_Oone__class_Oone(_1376419)) = hAPP(c_Int_Onumber__class_Onumber__of(_1376419), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1376421), c_Int_OBit1(c_Int_OPls))))], (33075 ^ _780119) ^ [_1396504, _1396506] : [-(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), _1396504)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1396506))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1396504))) = 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), _1396506)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396504)))], (48906 ^ _780119) ^ [_1769230, _1769232, _1769234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1769230, tc_HOL_Obool)), _1769232), _1769234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1769230), tc_HOL_Obool)), c_List_Olistsp(_1769230, _1769232)), c_List_Olistsp(_1769230, _1769234))))], (14770 ^ _780119) ^ [_1051380, _1051382] : [-(hBOOL(hAPP(hAPP(c_member(_1051380), _1051382), c_Orderings_Otop__class_Otop(tc_fun(_1051380, tc_HOL_Obool)))))], (24859 ^ _780119) ^ [_1235639, _1235641, _1235643] : [class_Orderings_Olinorder(_1235639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235639), _1235641), _1235643)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235639, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1235639, _1235641, _1235643)), hAPP(c_SetInterval_Oord__class_OatLeast(_1235639), _1235643)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1235639), _1235641))], (29714 ^ _780119) ^ [_1332811, _1332813, _1332815, _1332817] : [c_Orderings_Obot__class_Obot(tc_fun(_1332811, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1332813, tc_fun(_1332811, tc_HOL_Obool)), _1332815), _1332817), 29717 ^ _780119 : [(29718 ^ _780119) ^ [_1332927] : [hBOOL(hAPP(hAPP(c_member(_1332813), _1332927), _1332815)), -(hAPP(_1332817, _1332927) = c_Orderings_Obot__class_Obot(tc_fun(_1332811, tc_HOL_Obool)))]]], (34561 ^ _780119) ^ [_1428728, _1428730, _1428732] : [34563 ^ _780119 : [(34566 ^ _780119) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1428728, _1428730), 34562 ^ [_1428728, _1428730, _1428732]))], (34564 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1428730, 34562 ^ [_1428728, _1428730, _1428732]), _1428732)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1428728, _1428730), _1428732)))], (48207 ^ _780119) ^ [_1754309, _1754311] : [-(c_List_Opartition(_1754309, _1754311, c_List_Olist_ONil(_1754309)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754309), tc_List_Olist(_1754309)), c_List_Olist_ONil(_1754309)), c_List_Olist_ONil(_1754309)))], (2362 ^ _780119) ^ [_814919, _814921] : [_814921 = _814919, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_814921) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_814919))], (8150 ^ _780119) ^ [_920087, _920089, _920091, _920093, _920095, _920097] : [c_Finite__Set_Ofolding__image__simple(_920087, _920089, _920091, _920093, _920095, _920097), -(hAPP(_920097, c_Orderings_Obot__class_Obot(tc_fun(_920089, tc_HOL_Obool))) = _920093)], (51197 ^ _780119) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (31495 ^ _780119) ^ [_1368558] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1368558), c_Int_OPls) = _1368558)], (14850 ^ _780119) ^ [_1052788, _1052790] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052788), c_Orderings_Otop__class_Otop(tc_fun(_1052788, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052790), c_Orderings_Otop__class_Otop(tc_fun(_1052790, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1052788, _1052790)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1052788, _1052790), tc_HOL_Obool)))))], (30605 ^ _780119) ^ [_1351941, _1351943, _1351945] : [class_Int_Onumber__ring(_1351941), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351941), hAPP(c_Int_Onumber__class_Onumber__of(_1351941), _1351943)), hAPP(c_Int_Onumber__class_Onumber__of(_1351941), _1351945)) = hAPP(c_Int_Onumber__class_Onumber__of(_1351941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1351943), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1351945))))], (10298 ^ _780119) ^ [_961159, _961161, _961163, _961165] : [-(hBOOL(hAPP(hAPP(c_member(_961159), _961161), _961163))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961159, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_961159), _961161), _961165)), _961163) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961159, tc_HOL_Obool)), _961165), _961163))], (12045 ^ _780119) ^ [_997180, _997182] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997180), _997182)), _997180)))], (8664 ^ _780119) ^ [_929944, _929946, _929948] : [class_Orderings_Oorder(_929944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929944), _929946), _929948)), _929948 = _929946], (11774 ^ _780119) ^ [_992077, _992079, _992081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992077), _992079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992081), _992077)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992081), _992079))))], (40514 ^ _780119) ^ [_1574358, _1574360, _1574362, _1574364] : [40516 ^ _780119 : [(40519 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40515 ^ [_1574358, _1574360, _1574362, _1574364]), _1574360)))], (40521 ^ _780119) ^ [] : [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(_1574362, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 40515 ^ [_1574358, _1574360, _1574362, _1574364]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1574362, 40515 ^ [_1574358, _1574360, _1574362, _1574364])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (40517 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1574358), 40515 ^ [_1574358, _1574360, _1574362, _1574364])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1574358), _1574360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1574362, _1574358)), _1574364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1574364), hAPP(_1574362, _1574360))), 40535 ^ _780119 : [(40538 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 40534 ^ [_1574358, _1574360, _1574362, _1574364]), _1574360)))], (40540 ^ _780119) ^ [] : [-(hAPP(_1574362, 40534 ^ [_1574358, _1574360, _1574362, _1574364]) = _1574364)], (40536 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1574358), 40534 ^ [_1574358, _1574360, _1574362, _1574364])))]]], (3552 ^ _780119) ^ [_833518, _833520, _833522, _833524] : [-(c_Big__Operators_Olattice__class_OInf__fin(_833524, _833520) = c_Big__Operators_Olattice__class_OInf__fin(_833522, _833518)), _833524 = _833522, _833520 = _833518], (950 ^ _780119) ^ [_794612, _794614, _794616, _794618] : [-(c_Wellfounded_Oacyclic(_794616, _794612)), c_Wellfounded_Oacyclic(_794618, _794614), _794618 = _794616, _794614 = _794612], (16152 ^ _780119) ^ [_1074464, _1074466, _1074468] : [class_Rings_Olinordered__semiring__strict(_1074464), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074464), c_Groups_Ozero__class_Ozero(_1074464)), _1074466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074464), _1074468), c_Groups_Ozero__class_Ozero(_1074464))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074464), _1074468), _1074466)), c_Groups_Ozero__class_Ozero(_1074464))))], (7098 ^ _780119) ^ [_897320, _897322, _897324, _897326] : [c_Finite__Set_Ofolding__one(_897320, _897322, _897324), -(hAPP(_897324, hAPP(hAPP(c_Set_Oinsert(_897320), _897326), c_Orderings_Obot__class_Obot(tc_fun(_897320, tc_HOL_Obool)))) = _897326)], (51265 ^ _780119) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (44962 ^ _780119) ^ [_1681312, _1681314, _1681316, _1681318, _1681320] : [hAPP(hAPP(c_List_Olist_OCons(_1681312), _1681314), _1681316) = hAPP(hAPP(c_List_Oappend(_1681312), _1681318), _1681320), 44967 ^ _780119 : [(44970 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1681312), _1681314), _1681316) = _1681320)], (44968 ^ _780119) ^ [] : [-(_1681318 = c_List_Olist_ONil(_1681312))]], 44972 ^ _780119 : [(44975 ^ _780119) ^ [] : [-(_1681316 = hAPP(hAPP(c_List_Oappend(_1681312), 44971 ^ [_1681312, _1681314, _1681316, _1681318, _1681320]), _1681320))], (44973 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1681312), _1681314), 44971 ^ [_1681312, _1681314, _1681316, _1681318, _1681320]) = _1681318)]]], (41882 ^ _780119) ^ [_1606562] : [class_Complete__Lattice_Ocomplete__lattice(_1606562), -(c_Complete__Lattice_OSup__class_OSup(_1606562, c_Orderings_Otop__class_Otop(tc_fun(_1606562, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1606562))], (7696 ^ _780119) ^ [_910388, _910390, _910392, _910394, _910396, _910398] : [c_Hoare__Mirabelle_Ohoare__derivs(_910388, _910390, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_910388)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_910388), _910392), _910394), _910396)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_910388), tc_HOL_Obool)))), 7703 ^ _780119 : [(7706 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_910398, 7701 ^ [_910388, _910390, _910392, _910394, _910396, _910398]), 7702 ^ [_910388, _910390, _910392, _910394, _910396, _910398]))], (7704 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_910396, 7701 ^ [_910388, _910390, _910392, _910394, _910396, _910398]), 7702 ^ [_910388, _910390, _910392, _910394, _910396, _910398])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_910388, _910390, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_910388)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_910388), _910392), _910394), _910398)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_910388), tc_HOL_Obool)))))], (4486 ^ _780119) ^ [_848111, _848113, _848115, _848117, _848119, _848121, _848123, _848125] : [-(c_New__DSequence_Opos__decr__bind(_848125, _848121, _848117, _848113) = c_New__DSequence_Opos__decr__bind(_848123, _848119, _848115, _848111)), _848125 = _848123, _848121 = _848119, _848117 = _848115, _848113 = _848111], (47222 ^ _780119) ^ [_1731653, _1731655, _1731657, _1731659] : [class_Groups_Ocomm__monoid__add(_1731653), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1731653), _1731655), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1731657, _1731659))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1731653), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1731653), _1731655), c_List_Oupt(_1731657, _1731659))))], (28532 ^ _780119) ^ [_1307328, _1307330, _1307332] : [class_Orderings_Olinorder(_1307328), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307328), _1307330)), -(_1307330 = c_Orderings_Obot__class_Obot(tc_fun(_1307328, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307328), _1307332)), -(_1307332 = c_Orderings_Obot__class_Obot(tc_fun(_1307328, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1307328, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307328, tc_HOL_Obool)), _1307330), _1307332)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1307328), c_Big__Operators_Olinorder__class_OMin(_1307328, _1307330)), c_Big__Operators_Olinorder__class_OMin(_1307328, _1307332)))], (43819 ^ _780119) ^ [_1655582, _1655584, _1655586] : [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, _1655582), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1655582)), _1655584)))), -(hBOOL(hAPP(hAPP(c_member(_1655582), hAPP(c_Product__Type_Ofst(_1655582, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1655582, _1655584), _1655586))), hAPP(c_List_Oset(_1655582), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1655582), _1655582), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1655582)), _1655584)))))], (46010 ^ _780119) ^ [_1706797] : [class_Groups_Omonoid__add(_1706797), -(c_List_Omonoid__add__class_Olistsum(_1706797) = c_List_Ofoldl(_1706797, _1706797, c_Groups_Oplus__class_Oplus(_1706797), c_Groups_Ozero__class_Ozero(_1706797)))], (26091 ^ _780119) ^ [_1255932, _1255934, _1255936] : [class_Orderings_Olinorder(_1255932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255932), _1255934), _1255936)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255932, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1255932), _1255934)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1255932, _1255934, _1255936)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1255932), _1255936))], (14948 ^ _780119) ^ [_1054302, _1054304] : [class_Groups_Ocomm__monoid__add(_1054302), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054302), _1054304), c_Groups_Ozero__class_Ozero(_1054302)) = _1054304)], (31497 ^ _780119) ^ [_1368587] : [-(c_Int_Osucc(c_Int_Opred(_1368587)) = _1368587)], (24689 ^ _780119) ^ [_1232304, _1232306] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1232304), _1232306) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1232304, _1232306))], (26747 ^ _780119) ^ [_1268799, _1268801, _1268803, _1268805] : [hBOOL(hAPP(hAPP(c_member(_1268799), _1268801), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1268799, tc_HOL_Obool)), _1268803), hAPP(c_Set_OCollect(_1268799), _1268805)))), 26750 ^ _780119 : [(26753 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1268805, _1268801)))], (26751 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1268799), _1268801), _1268803)))]]], (35436 ^ _780119) ^ [_1448675] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1448675) = 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), _1448675), 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))))))], (29166 ^ _780119) ^ [_1320602, _1320604, _1320606] : [class_Orderings_Olinorder(_1320602), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320602), _1320604)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320602), _1320606)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320602, tc_HOL_Obool)), _1320604), _1320606) = c_Orderings_Obot__class_Obot(tc_fun(_1320602, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320602), c_Big__Operators_Olattice_OSup__fin(_1320602, c_Orderings_Oord__class_Omax(_1320602), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320602, tc_HOL_Obool)), _1320604), _1320606))), c_Big__Operators_Olattice_OSup__fin(_1320602, c_Orderings_Oord__class_Omax(_1320602), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320602, tc_HOL_Obool)), _1320604), _1320606))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320602), c_Big__Operators_Olattice_OSup__fin(_1320602, c_Orderings_Oord__class_Omax(_1320602), _1320604)), c_Big__Operators_Olattice_OSup__fin(_1320602, c_Orderings_Oord__class_Omax(_1320602), _1320606)))], (25845 ^ _780119) ^ [_1251833] : [c_Nat__Transfer_Ois__nat(_1251833), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251833)))], (19254 ^ _780119) ^ [_1130414, _1130416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130414), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19257 ^ _780119 : [(19264 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130416), 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), _1130416), _1130414))))], (19258 ^ _780119) ^ [] : [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), _1130416), _1130414))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130416), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29817 ^ _780119) ^ [_1336081, _1336083, _1336085, _1336087, _1336089] : [class_Complete__Lattice_Ocomplete__lattice(_1336081), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1336083, tc_HOL_Obool)), _1336085), _1336087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336081), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1336083, _1336081), _1336085), _1336089)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1336083, _1336081), _1336087), _1336089))))], (13662 ^ _780119) ^ [_1028585, _1028587] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028585), hAPP(c_Nat_OSuc, _1028587)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028585), _1028587)))], (31835 ^ _780119) ^ [_1373798, _1373800] : [class_Int_Onumber__ring(_1373798), class_Rings_Olinordered__idom(_1373798), 31842 ^ _780119 : [(31849 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1373800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373798), c_Groups_Ozero__class_Ozero(_1373798)), hAPP(c_Int_Onumber__class_Onumber__of(_1373798), _1373800))))], (31843 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373798), c_Groups_Ozero__class_Ozero(_1373798)), hAPP(c_Int_Onumber__class_Onumber__of(_1373798), _1373800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1373800)))]]], (174 ^ _780119) ^ [_782978, _782980] : [-(class_Fields_Ofield(_782978)), _782980 = _782978, class_Fields_Ofield(_782980)], (16668 ^ _780119) ^ [_1083547, _1083549] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1083547), _1083549)), 16671 ^ _780119 : [(16678 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1083547), c_Orderings_Otop__class_Otop(tc_fun(_1083547, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1083547), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1083547, tc_HOL_Obool)), _1083549))))], (16672 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1083547), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1083547, tc_HOL_Obool)), _1083549))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1083547), c_Orderings_Otop__class_Otop(tc_fun(_1083547, tc_HOL_Obool)))))]]], (23495 ^ _780119) ^ [_1209740, _1209742, _1209744] : [class_Orderings_Oorder(_1209740), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1209740, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1209740, _1209742, _1209744)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1209740), _1209744)) = c_Orderings_Obot__class_Obot(tc_fun(_1209740, tc_HOL_Obool)))], (49176 ^ _780119) ^ [_1775246, _1775248, _1775250, _1775252, _1775254] : [-(c_List_Olist__all2(_1775246, _1775248, _1775250, _1775252, _1775254)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775246)), _1775252) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775248)), _1775254), 49182 ^ _780119 : [(49185 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1775250, hAPP(hAPP(c_List_Onth(_1775246), _1775252), 49181 ^ [_1775246, _1775248, _1775250, _1775252, _1775254])), hAPP(hAPP(c_List_Onth(_1775248), _1775254), 49181 ^ [_1775246, _1775248, _1775250, _1775252, _1775254])))], (49183 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49181 ^ [_1775246, _1775248, _1775250, _1775252, _1775254]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775246)), _1775252))))]]], (24781 ^ _780119) ^ [_1234038, _1234040, _1234042] : [class_Orderings_Olinorder(_1234038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234038), _1234040), _1234042)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234038, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1234038, _1234040, _1234042)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1234038), _1234042)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1234038), _1234040))], (10344 ^ _780119) ^ [_962119, _962121, _962123, _962125] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962119, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962119, tc_HOL_Obool)), _962121), _962123)), _962125) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962119, tc_HOL_Obool)), _962121), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962119, tc_HOL_Obool)), _962123), _962125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962119, tc_HOL_Obool)), _962125), _962121)))], (34337 ^ _780119) ^ [_1424572, _1424574] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1424572), _1424574)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1424572), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1424574)))], (29586 ^ _780119) ^ [_1329520, _1329522, _1329524, _1329526] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1329520, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1329522, tc_fun(tc_fun(_1329520, tc_HOL_Obool), tc_HOL_Obool)), _1329524), hAPP(hAPP(c_COMBB(tc_fun(_1329520, tc_HOL_Obool), tc_fun(tc_fun(_1329520, tc_HOL_Obool), tc_HOL_Obool), _1329522), c_Set_OPow(_1329520)), _1329526))), hAPP(c_Set_OPow(_1329520), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1329522, tc_fun(_1329520, tc_HOL_Obool)), _1329524), _1329526)))))], (26377 ^ _780119) ^ [_1261464, _1261466] : [class_Groups_Oordered__ab__group__add__abs(_1261464), -(hAPP(c_Groups_Oabs__class_Oabs(_1261464), hAPP(c_Groups_Ouminus__class_Ouminus(_1261464), _1261466)) = hAPP(c_Groups_Oabs__class_Oabs(_1261464), _1261466))], (24159 ^ _780119) ^ [_1222422, _1222424] : [24161 ^ _780119 : [(24164 ^ _780119) ^ [] : [hBOOL(hAPP(_1222424, 24160 ^ [_1222422, _1222424]))], (24162 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24160 ^ [_1222422, _1222424]), _1222422)))]], 24165 ^ _780119 : [(24166 ^ _780119) ^ [_1222572] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1222572), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1222422))), -(hBOOL(hAPP(_1222424, _1222572)))]]], (9070 ^ _780119) ^ [_936060, _936062, _936064] : [class_Orderings_Oorder(_936060), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936060), _936062), _936064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936060), _936062), _936064))), -(_936062 = _936064)], (47410 ^ _780119) ^ [_1735843] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1735843)), c_List_Otranspose__rel(_1735843)), c_List_Olist_ONil(tc_List_Olist(_1735843)))), -(c_List_Otranspose(_1735843, c_List_Olist_ONil(tc_List_Olist(_1735843))) = c_List_Olist_ONil(tc_List_Olist(_1735843)))], (6919 ^ _780119) ^ [_894447, _894449, _894451, _894453] : [class_Orderings_Oord(_894447), _894449 = _894451, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894447), _894451), _894453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894447), _894449), _894453)))], (32235 ^ _780119) ^ [_1381339, _1381341, _1381343, _1381345] : [-(hAPP(c_Nat_Onat_Onat__rec(_1381339, _1381341, _1381343), hAPP(c_Nat_OSuc, _1381345)) = hAPP(hAPP(_1381343, _1381345), hAPP(c_Nat_Onat_Onat__rec(_1381339, _1381341, _1381343), _1381345)))], (46163 ^ _780119) ^ [_1710388, _1710390] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710388)), c_List_Olist_ONil(_1710388)), c_List_Olists(_1710388, _1710390))))], (13512 ^ _780119) ^ [_1026082, _1026084, _1026086] : [-(hBOOL(hAPP(hAPP(c_member(_1026082), _1026084), _1026086))), -(hBOOL(hAPP(hAPP(c_member(_1026082), _1026084), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026082, tc_HOL_Obool)), _1026086))))], (40764 ^ _780119) ^ [_1579427, _1579429, _1579431] : [class_Orderings_Olinorder(_1579427), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579427), _1579429)), -(c_Big__Operators_Olinorder__class_OMin(_1579427, hAPP(hAPP(c_Set_Oinsert(_1579427), _1579431), _1579429)) = hAPP(hAPP(c_Finite__Set_Ofold(_1579427, _1579427, c_Orderings_Oord__class_Omin(_1579427)), _1579431), _1579429))], (19270 ^ _780119) ^ [_1130670, _1130672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130670), _1130672)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130670), _1130672) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22477 ^ _780119) ^ [_1190366, _1190368, _1190370] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1190366, _1190368, _1190370))), 22480 ^ _780119 : [(22483 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1190370)))], (22481 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1190368)))]]], (26625 ^ _780119) ^ [_1266356, _1266358, _1266360] : [class_Groups_Oordered__ab__group__add__abs(_1266356), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266356), hAPP(c_Groups_Oabs__class_Oabs(_1266356), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1266356), hAPP(c_Groups_Oabs__class_Oabs(_1266356), _1266358)), hAPP(c_Groups_Oabs__class_Oabs(_1266356), _1266360)))), hAPP(c_Groups_Oabs__class_Oabs(_1266356), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1266356), _1266358), _1266360)))))], (3596 ^ _780119) ^ [_834186, _834188, _834190, _834192, _834194, _834196] : [-(c_Big__Operators_Olattice_OSup__fin(_834196, _834192, _834188) = c_Big__Operators_Olattice_OSup__fin(_834194, _834190, _834186)), _834196 = _834194, _834192 = _834190, _834188 = _834186], (51411 ^ _780119) ^ [_1818686, _1818688] : [-(class_Finite__Set_Ofinite(tc_prod(_1818686, _1818688))), class_Finite__Set_Ofinite(_1818686), class_Finite__Set_Ofinite(_1818688)], (45876 ^ _780119) ^ [_1703938, _1703940, _1703942] : [-(hAPP(c_List_Otl(_1703938), hAPP(hAPP(c_List_Olist_OCons(_1703938), _1703940), _1703942)) = _1703942)], (50506 ^ _780119) ^ [_1804869, _1804871, _1804873] : [c_List_Olist_ONil(_1804869) = c_List_Oreplicate(_1804869, _1804871, _1804873), -(_1804871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22707 ^ _780119) ^ [_1194893, _1194895, _1194897, _1194899] : [hBOOL(hAPP(hAPP(c_member(_1194893), _1194895), c_SetInterval_Oord_OlessThan(_1194893, _1194897, _1194899))), -(hBOOL(hAPP(hAPP(_1194897, _1194895), _1194899)))], (40240 ^ _780119) ^ [_1567055, _1567057] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1567055, _1567055), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1567057) = c_Relation_OId(_1567055))], (40148 ^ _780119) ^ [_1564497, _1564499, _1564501] : [c_Relation_Ototal__on(_1564497, _1564499, _1564501), 40151 ^ _780119 : [(40152 ^ _780119) ^ [_1564641] : [hBOOL(hAPP(hAPP(c_member(_1564497), _1564641), _1564499)), 40155 ^ _780119 : [(40156 ^ _780119) ^ [_1564781] : [hBOOL(hAPP(hAPP(c_member(_1564497), _1564781), _1564499)), -(_1564641 = _1564781), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564497, _1564497)), hAPP(hAPP(c_Product__Type_OPair(_1564497, _1564497), _1564641), _1564781)), _1564501))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564497, _1564497)), hAPP(hAPP(c_Product__Type_OPair(_1564497, _1564497), _1564781), _1564641)), _1564501)))]]]]], (11979 ^ _780119) ^ [_995936, _995938, _995940, _995942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995936), _995938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995940), _995938) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995936), _995942), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995940), _995942)))], (21420 ^ _780119) ^ [_1170328, _1170330, _1170332, _1170334] : [class_Divides_Osemiring__div(_1170328), -(c_Divides_Odiv__class_Omod(_1170328, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170328), _1170330), c_Divides_Odiv__class_Omod(_1170328, _1170332, _1170334)), _1170334) = c_Divides_Odiv__class_Omod(_1170328, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170328), _1170330), _1170332), _1170334))], (32565 ^ _780119) ^ [_1387168] : [-(c_Int_Opred(c_Int_OBit1(_1387168)) = c_Int_OBit0(_1387168))], (42024 ^ _780119) ^ [_1609717, _1609719] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1609717, tc_HOL_Obool), _1609719) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1609717, tc_HOL_Obool), tc_fun(_1609717, tc_HOL_Obool)), _1609719), c_COMBI(tc_fun(_1609717, tc_HOL_Obool))))], (22895 ^ _780119) ^ [_1198230, _1198232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198230), _1198232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198230)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198232))))], (1380 ^ _780119) ^ [_800093, _800095] : [-(class_Lazy__Sequence_Osmall__lazy(_800093)), _800095 = _800093, class_Lazy__Sequence_Osmall__lazy(_800095)], (878 ^ _780119) ^ [_793528, _793530, _793532, _793534, _793536, _793538] : [-(c_List_Olist__ex(_793536, _793532, _793528)), c_List_Olist__ex(_793538, _793534, _793530), _793538 = _793536, _793534 = _793532, _793530 = _793528], (44780 ^ _780119) ^ [_1676960, _1676962] : [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(_1676960)), _1676962))), _1676962 = c_List_Olist_ONil(_1676960)], (10647 ^ _780119) ^ [_968860, _968862, _968864, _968866, _968868] : [class_Groups_Ocomm__monoid__add(_968860), hBOOL(hAPP(c_Finite__Set_Ofinite(_968862), _968864)), hBOOL(hAPP(hAPP(c_member(_968862), _968866), _968864)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_968862, _968860), _968868), _968864) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968860), hAPP(_968868, _968866)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_968862, _968860), _968868), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968862, tc_HOL_Obool)), _968864), hAPP(hAPP(c_Set_Oinsert(_968862), _968866), c_Orderings_Obot__class_Obot(tc_fun(_968862, tc_HOL_Obool)))))))], (42057 ^ _780119) ^ [_1610619, _1610621, _1610623, _1610625] : [-(_1610619 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1610621, tc_HOL_Obool), tc_HOL_Obool))), 42063 ^ _780119 : [(42066 ^ _780119) ^ [] : [c_Fun_Oinj__on(_1610621, _1610623, _1610625, 42062 ^ [_1610619, _1610621, _1610623, _1610625])], (42064 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1610621, tc_HOL_Obool)), 42062 ^ [_1610619, _1610621, _1610623, _1610625]), _1610619)))]], -(c_Fun_Oinj__on(_1610621, _1610623, _1610625, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1610621, tc_HOL_Obool), _1610619)))], (21903 ^ _780119) ^ [_1179985, _1179987, _1179989, _1179991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179987), _1179989)), -(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), _1179989), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179991, _1179985))), _1179987)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179989), _1179985))))], (15038 ^ _780119) ^ [_1055617, _1055619] : [class_Rings_Omult__zero(_1055617), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055617), _1055619), c_Groups_Ozero__class_Ozero(_1055617)) = c_Groups_Ozero__class_Ozero(_1055617))], (5895 ^ _780119) ^ [_873780, _873782, _873784, _873786] : [_873780 = _873782, 5900 ^ _780119 : [(5903 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_873784), _873786), _873782)))], (5901 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_873784), _873786), _873780)))]], 5904 ^ _780119 : [(5907 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873784), _873786), _873782))], (5905 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873784), _873786), _873780))]]], (18302 ^ _780119) ^ [_1113884, _1113886, _1113888] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1113884), _1113886)), _1113888) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1113884), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113886), _1113888)))], (11121 ^ _780119) ^ [_978063, _978065, _978067, _978069, _978071] : [class_Groups_Ocomm__monoid__add(_978063), hBOOL(hAPP(c_Finite__Set_Ofinite(_978065), _978067)), -(hBOOL(hAPP(hAPP(c_member(_978065), _978069), _978067))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_978065, _978063), _978071), hAPP(hAPP(c_Set_Oinsert(_978065), _978069), _978067)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978063), hAPP(_978071, _978069)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_978065, _978063), _978071), _978067)))], (26527 ^ _780119) ^ [_1264548, _1264550] : [-(hAPP(c_Set_OCollect(_1264548), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1264548), c_fNot), _1264550)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264548, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1264548), _1264550)))], (32205 ^ _780119) ^ [_1380939, _1380941] : [class_Rings_Osemiring__1(_1380939), 32208 ^ _780119 : [(32215 ^ _780119) ^ [] : [_1380941 = c_Groups_Ozero__class_Ozero(_1380939), -(c_Int_Oiszero(_1380939, _1380941))], (32209 ^ _780119) ^ [] : [c_Int_Oiszero(_1380939, _1380941), -(_1380941 = c_Groups_Ozero__class_Ozero(_1380939))]]], (41575 ^ _780119) ^ [_1599239, _1599241, _1599243] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1599239, tc_HOL_Obool)), _1599241), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1599239, tc_HOL_Obool), _1599243)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1599239, tc_HOL_Obool), tc_fun(_1599239, tc_HOL_Obool)), _1599243), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1599239, tc_HOL_Obool)), _1599241)))], (45315 ^ _780119) ^ [_1689103, _1689105, _1689107, _1689109] : [-(c_List_Osublist(_1689103, hAPP(hAPP(c_List_Oappend(_1689103), _1689105), _1689107), _1689109) = hAPP(hAPP(c_List_Oappend(_1689103), c_List_Osublist(_1689103, _1689105, _1689109)), c_List_Osublist(_1689103, _1689107, 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(_1689103)), _1689105)))), _1689109)))))], (17071 ^ _780119) ^ [_1090170, _1090172] : [_1090170 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1090170), _1090172), -(_1090172 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1090170 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50254 ^ _780119) ^ [_1798576, _1798578, _1798580, _1798582, _1798584] : [-(hAPP(c_New__DSequence_Opos__bind(_1798576, _1798578, _1798580, _1798582), _1798584) = hAPP(c_Lazy__Sequence_Obind(_1798576, _1798578, hAPP(_1798580, _1798584)), hAPP(hAPP(c_COMBC(_1798576, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1798578)), _1798582), _1798584)))], (51241 ^ _780119) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (50148 ^ _780119) ^ [_1796466] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1796466)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1796466))))], (1868 ^ _780119) ^ [_806974, _806976, _806978, _806980, _806982, _806984, _806986, _806988] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_806988, _806984, _806980, _806976) = c_Hoare__Mirabelle_Otriple_Otriple__case(_806986, _806982, _806978, _806974)), _806988 = _806986, _806984 = _806982, _806980 = _806978, _806976 = _806974], (22199 ^ _780119) ^ [_1185329, _1185331] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1185329, _1185331)), _1185329)))], (50430 ^ _780119) ^ [_1802815, _1802817, _1802819, _1802821, _1802823] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1802815, _1802817, _1802819), _1802821), _1802823)), -(hBOOL(hAPP(hAPP(_1802819, _1802823), _1802821)))], (35389 ^ _780119) ^ [_1447464, _1447466, _1447468, _1447470, _1447472] : [hBOOL(hAPP(hAPP(c_member(_1447464), _1447466), hAPP(c_Relation_OImage(_1447468, _1447464, _1447470), _1447472))), 35393 ^ _780119 : [(35396 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447468, _1447464)), hAPP(hAPP(c_Product__Type_OPair(_1447468, _1447464), 35392 ^ [_1447464, _1447466, _1447468, _1447470, _1447472]), _1447466)), _1447470)))], (35394 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1447468), 35392 ^ [_1447464, _1447466, _1447468, _1447470, _1447472]), _1447472)))]]], (23374 ^ _780119) ^ [_1207236, _1207238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1207236), _1207238)), -(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)), _1207236)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1207238))))], (7828 ^ _780119) ^ [_913298, _913300, _913302, _913304, _913306] : [-(hAPP(c_Option_Ooption_Ooption__case(_913298, _913300, _913302, _913304), hAPP(c_Option_Ooption_OSome(_913300), _913306)) = hAPP(_913304, _913306))], (37387 ^ _780119) ^ [_1494985, _1494987, _1494989] : [c_Wellfounded_Owf(_1494985, _1494987), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494985, tc_HOL_Obool)), _1494989), hAPP(c_Relation_OImage(_1494985, _1494985, _1494987), _1494989))), -(_1494989 = c_Orderings_Obot__class_Obot(tc_fun(_1494985, tc_HOL_Obool)))], (44756 ^ _780119) ^ [_1676557, _1676559] : [-(hAPP(hAPP(c_List_Otake(_1676557), _1676559), c_List_Olist_ONil(_1676557)) = c_List_Olist_ONil(_1676557))], (11684 ^ _780119) ^ [_990524, _990526] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990524), _990526)), _990524) = _990526)], (16298 ^ _780119) ^ [_1077196, _1077198, _1077200, _1077202] : [class_Rings_Olinordered__ring__strict(_1077196), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077196), _1077198), _1077200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077196), _1077202), c_Groups_Ozero__class_Ozero(_1077196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077196), _1077202), _1077200)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077196), _1077202), _1077198))))], (34403 ^ _780119) ^ [_1425621, _1425623, _1425625, _1425627, _1425629] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1425621, _1425623), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1425625), _1425627))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1425623)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1425629)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1425621, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1425623), _1425629)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1425625), _1425629)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1425623), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1425625, _1425629))), _1425627)))))], (43607 ^ _780119) ^ [_1649260, _1649262, _1649264] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649260)), hAPP(hAPP(c_List_Olist_OCons(_1649260), _1649262), _1649264)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649260)), _1649264)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43745 ^ _780119) ^ [_1653688, _1653690, _1653692, _1653694, _1653696] : [class_Rings_Osemiring__0(_1653688), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1653688), hAPP(hAPP(c_List_Omap(_1653690, _1653688), hAPP(hAPP(c_COMBC(_1653690, _1653688, _1653688), hAPP(hAPP(c_COMBB(_1653688, tc_fun(_1653688, _1653688), _1653690), c_Groups_Otimes__class_Otimes(_1653688)), _1653692)), _1653694)), _1653696)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1653688), hAPP(c_List_Omonoid__add__class_Olistsum(_1653688), hAPP(hAPP(c_List_Omap(_1653690, _1653688), _1653692), _1653696))), _1653694))], (40244 ^ _780119) ^ [_1567152, _1567154, _1567156, _1567158] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567152, _1567152)), hAPP(hAPP(c_Product__Type_OPair(_1567152, _1567152), _1567154), _1567156)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1567152, _1567152), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1567158))), -(_1567154 = _1567156)], (36355 ^ _780119) ^ [_1469673, _1469675, _1469677, _1469679] : [-(_1469673 = c_Orderings_Obot__class_Obot(tc_fun(_1469675, tc_HOL_Obool))), 36358 ^ _780119 : [(36359 ^ _780119) ^ [] : [-(hAPP(c_Set_Oimage(_1469677, _1469675, 36366 ^ [_1469673, _1469675, _1469677, _1469679]), _1469679) = _1469673), 36360 ^ _780119 : [(36361 ^ _780119) ^ [_1469814] : [c_Fun_Oinj__on(_1469675, _1469677, _1469814, _1469673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469677, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469675, _1469677, _1469814), _1469673)), _1469679))]]], (36370 ^ _780119) ^ [] : [36371 ^ _780119 : [(36372 ^ _780119) ^ [_1470006] : [hAPP(c_Set_Oimage(_1469677, _1469675, _1470006), _1469679) = _1469673]], 36374 ^ _780119 : [(36377 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469677, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469675, _1469677, 36373 ^ [_1469673, _1469675, _1469677, _1469679]), _1469673)), _1469679)))], (36375 ^ _780119) ^ [] : [-(c_Fun_Oinj__on(_1469675, _1469677, 36373 ^ [_1469673, _1469675, _1469677, _1469679], _1469673))]]]]], (49831 ^ _780119) ^ [_1790617, _1790619, _1790621] : [c_List_Olist__all(_1790617, _1790619, _1790621), -(c_List_Olist__all(_1790617, _1790619, hAPP(c_List_Orev(_1790617), _1790621)))], (50931 ^ _780119) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (32989 ^ _780119) ^ [_1394674, _1394676, _1394678] : [class_Rings_Olinordered__idom(_1394674), 32992 ^ _780119 : [(33001 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394674), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1394674), hAPP(hAPP(c_Power_Opower__class_Opower(_1394674), _1394676), 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(_1394674), _1394678), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1394674)))), _1394676 = c_Groups_Ozero__class_Ozero(_1394674), _1394678 = c_Groups_Ozero__class_Ozero(_1394674)], (32993 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394674), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1394674), hAPP(hAPP(c_Power_Opower__class_Opower(_1394674), _1394676), 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(_1394674), _1394678), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1394674))), 32996 ^ _780119 : [(32999 ^ _780119) ^ [] : [-(_1394678 = c_Groups_Ozero__class_Ozero(_1394674))], (32997 ^ _780119) ^ [] : [-(_1394676 = c_Groups_Ozero__class_Ozero(_1394674))]]]]], (4918 ^ _780119) ^ [_855207, _855209] : [_855209 = _855207, -(c_Groups_Ouminus__class_Ouminus(_855209) = c_Groups_Ouminus__class_Ouminus(_855207))], (18660 ^ _780119) ^ [_1120560, _1120562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120560), _1120562)), 18663 ^ _780119 : [(18666 ^ _780119) ^ [] : [_1120560 = _1120562], (18664 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120560), _1120562)))]]], (49203 ^ _780119) ^ [_1775905, _1775907, _1775909, _1775911, _1775913, _1775915, _1775917, _1775919] : [c_List_Olist__all2(_1775905, _1775907, _1775909, _1775911, _1775913), hBOOL(hAPP(hAPP(_1775909, _1775915), _1775917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1775919), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775907)), _1775913))), -(c_List_Olist__all2(_1775905, _1775907, _1775909, hAPP(hAPP(c_List_Olist__update(_1775905, _1775911), _1775919), _1775915), hAPP(hAPP(c_List_Olist__update(_1775907, _1775913), _1775919), _1775917)))], (10470 ^ _780119) ^ [_965003, _965005, _965007, _965009, _965011, _965013, _965015, _965017] : [c_Finite__Set_Ofolding__image__simple(_965003, _965005, _965007, _965009, _965011, _965013), hBOOL(hAPP(c_Finite__Set_Ofinite(_965005), _965015)), hBOOL(hAPP(c_Finite__Set_Ofinite(_965005), _965017)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965005, tc_HOL_Obool)), _965015), _965017) = c_Orderings_Obot__class_Obot(tc_fun(_965005, tc_HOL_Obool)), -(hAPP(_965013, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_965005, tc_HOL_Obool)), _965015), _965017)) = hAPP(hAPP(_965007, hAPP(_965013, _965015)), hAPP(_965013, _965017)))], (10885 ^ _780119) ^ [_973261, _973263, _973265, _973267] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_973261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973261), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973261), _973263), _973265)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973261), _973267), _973265))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973261), _973263), _973267)))], (14612 ^ _780119) ^ [_1048155, _1048157, _1048159] : [class_Groups_Omonoid__mult(_1048155), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1048155), _1048157), hAPP(c_Nat_OSuc, _1048159)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048155), hAPP(hAPP(c_Power_Opower__class_Opower(_1048155), _1048157), _1048159)), _1048157))], (44796 ^ _780119) ^ [_1677230, _1677232, _1677234] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1677230), tc_List_Olist(_1677230))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1677230), tc_List_Olist(_1677230)), _1677232), c_List_Olist_ONil(_1677230))), c_List_Olexord(_1677230, _1677234)))], (36652 ^ _780119) ^ [_1476252, _1476254, _1476256, _1476258, _1476260, _1476262] : [c_Fun_Oinj__on(_1476252, _1476254, _1476256, _1476258), hBOOL(hAPP(hAPP(c_member(_1476254), _1476260), hAPP(c_Set_Oimage(_1476252, _1476254, _1476256), _1476258))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1476252, tc_HOL_Obool)), _1476258), _1476262)), -(hBOOL(hAPP(hAPP(c_member(_1476252), hAPP(c_Fun_Othe__inv__into(_1476252, _1476254, _1476258, _1476256), _1476260)), _1476262)))], (9292 ^ _780119) ^ [_939895, _939897, _939899, _939901, _939903] : [hAPP(_939895, _939897) = hAPP(c_Option_Ooption_OSome(_939899), _939901), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_939903, tc_Option_Ooption(_939899)), _939895), _939897), hAPP(c_Option_Ooption_OSome(_939899), _939901)) = _939895)], (21713 ^ _780119) ^ [_1176352, _1176354, _1176356] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176352), _1176354)), _1176356) = 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), _1176352), _1176356)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1176354), _1176356))), 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, _1176352, _1176356)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176354, _1176356))), _1176356)))], (31129 ^ _780119) ^ [_1362176] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362176)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1362176)))], (738 ^ _780119) ^ [_791412, _791414] : [-(c_List_Onat__list(_791412)), _791414 = _791412, c_List_Onat__list(_791414)], (1560 ^ _780119) ^ [_802343, _802345] : [-(class_Groups_Ocomm__monoid__mult(_802343)), _802345 = _802343, class_Groups_Ocomm__monoid__mult(_802345)], (12247 ^ _780119) ^ [_1001160, _1001162, _1001164, _1001166, _1001168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001160), _1001162)), -(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), _1001162), _1001164)), _1001166)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001160), _1001164)), _1001168)) = 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), _1001162), _1001160)), _1001164)), _1001166)), _1001168))], (18324 ^ _780119) ^ [_1114286, _1114288, _1114290] : [hAPP(c_Finite__Set_Ocard(_1114286), _1114288) = hAPP(c_Nat_OSuc, _1114290), 18329 ^ _780119 : [(18330 ^ _780119) ^ [] : [-(_1114288 = hAPP(hAPP(c_Set_Oinsert(_1114286), 18327 ^ [_1114286, _1114288, _1114290]), 18328 ^ [_1114286, _1114288, _1114290]))], (18332 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1114286), 18327 ^ [_1114286, _1114288, _1114290]), 18328 ^ [_1114286, _1114288, _1114290]))], (18336 ^ _780119) ^ [] : [_1114290 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(18328 ^ [_1114286, _1114288, _1114290] = c_Orderings_Obot__class_Obot(tc_fun(_1114286, tc_HOL_Obool)))], (18334 ^ _780119) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1114286), 18328 ^ [_1114286, _1114288, _1114290]) = _1114290)]]], (21618 ^ _780119) ^ [_1174740, _1174742, _1174744] : [class_Divides_Osemiring__div(_1174740), -(c_Divides_Odiv__class_Omod(_1174740, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174740), _1174742), _1174744), _1174742) = c_Groups_Ozero__class_Ozero(_1174740))], (33951 ^ _780119) ^ [_1417201, _1417203, _1417205, _1417207, _1417209, _1417211] : [hBOOL(hAPP(hAPP(_1417201, _1417203), _1417205)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417207, tc_fun(_1417209, tc_HOL_Obool))), _1417211), _1417201), _1417203), _1417205)))], (23577 ^ _780119) ^ [_1211181, _1211183, _1211185] : [class_Orderings_Olinorder(_1211181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211181), _1211183), _1211185)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1211181, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1211181, _1211183), _1211185)), hAPP(hAPP(c_Set_Oinsert(_1211181), _1211185), c_Orderings_Obot__class_Obot(tc_fun(_1211181, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1211181, _1211183, _1211185))], (41423 ^ _780119) ^ [_1595943, _1595945, _1595947, _1595949, _1595951] : [_1595943 = c_Orderings_Obot__class_Obot(tc_fun(_1595945, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595945, tc_fun(_1595947, tc_HOL_Obool)), _1595943), hAPP(hAPP(c_COMBB(tc_fun(_1595947, tc_HOL_Obool), tc_fun(_1595947, tc_HOL_Obool), _1595945), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1595947, tc_HOL_Obool)), _1595949)), _1595951)) = c_Orderings_Otop__class_Otop(tc_fun(_1595947, tc_HOL_Obool)))], (12451 ^ _780119) ^ [_1004992, _1004994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004992), _1004994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004992), _1004994)))], (45766 ^ _780119) ^ [_1701744, _1701746, _1701748, _1701750] : [-(hAPP(c_List_Orotate1(_1701746), hAPP(hAPP(c_List_Olist_OCons(_1701746), _1701748), _1701750)) = hAPP(hAPP(c_List_Oappend(_1701746), _1701750), hAPP(hAPP(c_List_Olist_OCons(_1701746), _1701748), c_List_Olist_ONil(_1701746))))], (15114 ^ _780119) ^ [_1056842] : [class_Rings_Ozero__neq__one(_1056842), c_Groups_Oone__class_Oone(_1056842) = c_Groups_Ozero__class_Ozero(_1056842)], (35983 ^ _780119) ^ [_1461611, _1461613, _1461615, _1461617, _1461619, _1461621, _1461623] : [c_Equiv__Relations_Oequiv(_1461611, _1461613, _1461615), c_Equiv__Relations_Ocongruent(_1461611, tc_fun(_1461617, tc_HOL_Obool), _1461615, _1461619), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1461611, tc_fun(_1461617, tc_HOL_Obool)), _1461621), _1461619) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1461611, tc_fun(_1461617, tc_HOL_Obool)), _1461623), _1461619), hBOOL(hAPP(hAPP(c_member(tc_fun(_1461611, tc_HOL_Obool)), _1461621), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1461611), _1461613), _1461615))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1461611, tc_HOL_Obool)), _1461623), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1461611), _1461613), _1461615))), 36005 ^ _780119 : [(36006 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1461611), 36004 ^ [_1461611, _1461613, _1461615, _1461617, _1461619, _1461621, _1461623]), _1461613)))], (36009 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1461611), 36007 ^ [_1461611, _1461613, _1461615, _1461617, _1461619, _1461621, _1461623]), _1461613)))], (36013 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1461611, _1461611)), hAPP(hAPP(c_Product__Type_OPair(_1461611, _1461611), 36004 ^ [_1461611, _1461613, _1461615, _1461617, _1461619, _1461621, _1461623]), 36007 ^ [_1461611, _1461613, _1461615, _1461617, _1461619, _1461621, _1461623])), _1461615))], (36011 ^ _780119) ^ [] : [-(hAPP(_1461619, 36004 ^ [_1461611, _1461613, _1461615, _1461617, _1461619, _1461621, _1461623]) = hAPP(_1461619, 36007 ^ [_1461611, _1461613, _1461615, _1461617, _1461619, _1461621, _1461623]))]], -(_1461621 = _1461623)], (3272 ^ _780119) ^ [_829086, _829088, _829090, _829092, _829094, _829096, _829098, _829100, _829102, _829104, _829106, _829108] : [-(c_Product__Type_Omap__pair(_829108, _829104, _829100, _829096, _829092, _829088) = c_Product__Type_Omap__pair(_829106, _829102, _829098, _829094, _829090, _829086)), _829108 = _829106, _829104 = _829102, _829100 = _829098, _829096 = _829094, _829092 = _829090, _829088 = _829086], (11499 ^ _780119) ^ [_986327, _986329, _986331, _986333] : [class_Rings_Ocomm__semiring__1(_986327), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986327), _986329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986327), _986331), _986333)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986327), _986329), _986331)), _986333))], (1340 ^ _780119) ^ [_799593, _799595] : [-(class_Lattices_Olattice(_799593)), _799595 = _799593, class_Lattices_Olattice(_799595)], (40349 ^ _780119) ^ [_1569848, _1569850, _1569852, _1569854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569848, _1569850), tc_HOL_Obool)), _1569852), _1569854)), c_Relation_Osingle__valued(_1569848, _1569850, _1569854), -(c_Relation_Osingle__valued(_1569848, _1569850, _1569852))], (8520 ^ _780119) ^ [_928094, _928096, _928098, _928100, _928102] : [hAPP(_928098, _928100) = _928102, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928094, _928096), _928098), _928100), _928102) = _928098)], (30052 ^ _780119) ^ [_1341739, _1341741, _1341743, _1341745, _1341747, _1341749, _1341751] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1341739, tc_fun(_1341741, tc_fun(_1341743, tc_HOL_Obool))), _1341745), _1341747), _1341749), _1341751))), 30053 ^ _780119 : [(30054 ^ _780119) ^ [_1341824] : [hBOOL(hAPP(hAPP(c_member(_1341739), _1341824), _1341745)), hBOOL(hAPP(hAPP(hAPP(_1341747, _1341824), _1341749), _1341751))]]], (21568 ^ _780119) ^ [_1173555, _1173557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1173555, tc_HOL_Obool)), hAPP(c_Set_OPow(_1173555), _1173557))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1173555), _1173557)))], (49273 ^ _780119) ^ [_1777379, _1777381, _1777383] : [hBOOL(hAPP(c_List_Odistinct(_1777379), _1777381)), -(hBOOL(hAPP(c_List_Odistinct(_1777379), hAPP(c_List_OremoveAll(_1777379, _1777383), _1777381))))], (16392 ^ _780119) ^ [_1078886] : [class_Rings_Olinordered__semidom(_1078886), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078886), c_Groups_Ozero__class_Ozero(_1078886)), c_Groups_Oone__class_Oone(_1078886))))], (28164 ^ _780119) ^ [_1300622, _1300624] : [class_Orderings_Olinorder(_1300622), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300622), _1300624), _1300624) = _1300624)], (41842 ^ _780119) ^ [_1605728] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1605728, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1605728, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1605728, tc_HOL_Obool)))], (51179 ^ _780119) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (30043 ^ _780119) ^ [_1341521, _1341523, _1341525, _1341527, _1341529, _1341531, _1341533] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1341521, tc_fun(_1341523, tc_fun(_1341525, tc_HOL_Obool))), _1341527), _1341529), _1341531), _1341533)), 30047 ^ _780119 : [(30050 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1341529, 30046 ^ [_1341521, _1341523, _1341525, _1341527, _1341529, _1341531, _1341533]), _1341531), _1341533)))], (30048 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1341521), 30046 ^ [_1341521, _1341523, _1341525, _1341527, _1341529, _1341531, _1341533]), _1341527)))]]], (47590 ^ _780119) ^ [_1739807, _1739809] : [-(hAPP(c_List_Oset(_1739807), hAPP(c_List_Orev(_1739807), _1739809)) = hAPP(c_List_Oset(_1739807), _1739809))], (38026 ^ _780119) ^ [_1513827, _1513829] : [-(c_Fun_Oinj__on(_1513827, _1513827, c_Fun_Oid(_1513827), _1513829))], (12507 ^ _780119) ^ [_1006306, _1006308, _1006310, _1006312, _1006314] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1006306, _1006308, hAPP(hAPP(c_Set_Oinsert(_1006306), _1006310), _1006312)), _1006314)), 12512 ^ _780119 : [(12515 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1006306, _1006306, _1006308, 12510 ^ [_1006306, _1006308, _1006310, _1006312, _1006314], 12511 ^ [_1006306, _1006308, _1006310, _1006312, _1006314]), _1006314)))], (12517 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1006306), 12510 ^ [_1006306, _1006308, _1006310, _1006312, _1006314]), 12511 ^ [_1006306, _1006308, _1006310, _1006312, _1006314]))], (12513 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1006306), _1006310), _1006312) = hAPP(hAPP(c_Set_Oinsert(_1006306), 12510 ^ [_1006306, _1006308, _1006310, _1006312, _1006314]), 12511 ^ [_1006306, _1006308, _1006310, _1006312, _1006314]))]]], (44714 ^ _780119) ^ [_1675833, _1675835, _1675837, _1675839, _1675841] : [class_Orderings_Olinorder(_1675833), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1675835, _1675833, _1675837), _1675839), _1675841) = c_List_Olist_ONil(_1675835)], (2312 ^ _780119) ^ [_814142, _814144] : [_814144 = _814142, -(c_Int_Oring__1__class_OInts(_814144) = c_Int_Oring__1__class_OInts(_814142))], (45478 ^ _780119) ^ [_1694256, _1694258, _1694260, _1694262, _1694264, _1694266] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694256), tc_List_Olist(_1694256))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694256), tc_List_Olist(_1694256)), hAPP(hAPP(c_List_Olist_OCons(_1694256), _1694258), _1694260)), hAPP(hAPP(c_List_Olist_OCons(_1694256), _1694262), _1694264))), c_List_Olistrel1(_1694256, _1694266)))), 45479 ^ _780119 : [(45486 ^ _780119) ^ [] : [_1694258 = _1694262, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694256), tc_List_Olist(_1694256))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694256), tc_List_Olist(_1694256)), _1694260), _1694264)), c_List_Olistrel1(_1694256, _1694266)))], (45480 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1694256, _1694256)), hAPP(hAPP(c_Product__Type_OPair(_1694256, _1694256), _1694258), _1694262)), _1694266)), _1694260 = _1694264]]], (32327 ^ _780119) ^ [_1382975, _1382977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1382975), 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)))), _1382977))), 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)))), _1382975)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382977), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1382975))], (23042 ^ _780119) ^ [_1200902, _1200904] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1200902), _1200904)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200902)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200904)))], (21811 ^ _780119) ^ [_1178327, _1178329] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178327, _1178329) = 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), _1178327), _1178329) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21612 ^ _780119) ^ [_1174552] : [-(hAPP(c_Set_OPow(_1174552), c_Orderings_Otop__class_Otop(tc_fun(_1174552, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1174552, tc_HOL_Obool), tc_HOL_Obool)))], (45345 ^ _780119) ^ [_1690148, _1690150, _1690152, _1690154, _1690156, _1690158] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1690148), tc_List_Olist(_1690148))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690148), tc_List_Olist(_1690148)), hAPP(hAPP(c_List_Oappend(_1690148), _1690150), hAPP(hAPP(c_List_Olist_OCons(_1690148), _1690152), c_List_Olist_ONil(_1690148)))), hAPP(hAPP(c_List_Oappend(_1690148), _1690154), hAPP(hAPP(c_List_Olist_OCons(_1690148), _1690156), c_List_Olist_ONil(_1690148))))), c_List_Olistrel1(_1690148, _1690158)))), 45346 ^ _780119 : [(45353 ^ _780119) ^ [] : [_1690150 = _1690154, hBOOL(hAPP(hAPP(c_member(tc_prod(_1690148, _1690148)), hAPP(hAPP(c_Product__Type_OPair(_1690148, _1690148), _1690152), _1690156)), _1690158))], (45347 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1690148), tc_List_Olist(_1690148))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690148), tc_List_Olist(_1690148)), _1690150), _1690154)), c_List_Olistrel1(_1690148, _1690158))), _1690152 = _1690156]]], (22980 ^ _780119) ^ [_1199783, _1199785, _1199787] : [class_Rings_Olinordered__semidom(_1199783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1199785), _1199787)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199783), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1199783), _1199785)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1199783), _1199787))))], (6093 ^ _780119) ^ [_877158, _877160, _877162] : [hBOOL(hAPP(hAPP(c_member(_877158), _877160), _877162)), -(hAPP(hAPP(c_Set_Oinsert(_877158), _877160), _877162) = _877162)], (51231 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (45622 ^ _780119) ^ [_1698240, _1698242, _1698244] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1698240, tc_HOL_Obool)), hAPP(c_List_Oset(_1698240), hAPP(hAPP(c_List_Odrop(_1698240), _1698242), _1698244))), hAPP(c_List_Oset(_1698240), _1698244))))], (42968 ^ _780119) ^ [_1631908, _1631910] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1631908, _1631910))))], (47526 ^ _780119) ^ [_1738481, _1738483, _1738485, _1738487] : [-(hAPP(hAPP(c_List_Omap(_1738481, _1738483), _1738485), c_List_Oconcat(_1738481, _1738487)) = c_List_Oconcat(_1738483, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738481), tc_List_Olist(_1738483)), hAPP(c_List_Omap(_1738481, _1738483), _1738485)), _1738487)))], (22449 ^ _780119) ^ [_1189822, _1189824, _1189826] : [-(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), _1189822)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1189824))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1189826))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1189826), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1189822), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1189822), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1189826), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1189824)))))], (24707 ^ _780119) ^ [_1232608, _1232610, _1232612] : [class_Orderings_Oorder(_1232608), 24710 ^ _780119 : [(24717 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232608), _1232612), _1232610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1232608, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1232608), _1232610)), hAPP(c_SetInterval_Oord__class_OatLeast(_1232608), _1232612))))], (24711 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1232608, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1232608), _1232610)), hAPP(c_SetInterval_Oord__class_OatLeast(_1232608), _1232612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232608), _1232612), _1232610)))]]], (10865 ^ _780119) ^ [_972871, _972873, _972875, _972877] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_972871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972871), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972871), _972873), _972875)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972871), _972873), _972877))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972871), _972875), _972877)))], (32787 ^ _780119) ^ [] : [-(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))))], (19244 ^ _780119) ^ [_1130249, _1130251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130249), 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)), _1130251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130249), _1130251)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35155 ^ _780119) ^ [_1440958, _1440960, _1440962, _1440964, _1440966, _1440968] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1440958, tc_HOL_Obool), tc_fun(_1440958, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1440958, tc_HOL_Obool), tc_fun(_1440958, tc_HOL_Obool)), _1440960), _1440962)), c_Wellfounded_Omax__ext(_1440958, _1440964))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1440958, tc_HOL_Obool), tc_fun(_1440958, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1440958, tc_HOL_Obool), tc_fun(_1440958, tc_HOL_Obool)), _1440966), _1440968)), c_Wellfounded_Omax__ext(_1440958, _1440964))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1440958, tc_HOL_Obool), tc_fun(_1440958, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1440958, tc_HOL_Obool), tc_fun(_1440958, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440958, tc_HOL_Obool)), _1440960), _1440966)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440958, tc_HOL_Obool)), _1440962), _1440968))), c_Wellfounded_Omax__ext(_1440958, _1440964))))], (49627 ^ _780119) ^ [_1786375, _1786377, _1786379] : [c_List_Olist__ex(_1786375, _1786377, _1786379), 49631 ^ _780119 : [(49634 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1786377, hAPP(hAPP(c_List_Onth(_1786375), _1786379), 49630 ^ [_1786375, _1786377, _1786379]))))], (49632 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49630 ^ [_1786375, _1786377, _1786379]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786375)), _1786379))))]]], (41081 ^ _780119) ^ [_1585603, _1585605, _1585607, _1585609, _1585611, _1585613] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1585603, tc_fun(_1585605, tc_HOL_Obool)), _1585607), _1585609), _1585611)), -(hBOOL(hAPP(hAPP(_1585609, _1585613), _1585611))), hBOOL(hAPP(hAPP(c_member(_1585603), _1585613), _1585607))], (14335 ^ _780119) ^ [_1042377, _1042379, _1042381, _1042383, _1042385] : [class_Groups_Ocomm__monoid__mult(_1042377), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042379), _1042381)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042379), _1042383)), 14349 ^ _780119 : [(14352 ^ _780119) ^ [] : [hAPP(_1042385, 14348 ^ [_1042377, _1042379, _1042381, _1042383, _1042385]) = c_Groups_Oone__class_Oone(_1042377)], (14350 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1042379), 14348 ^ [_1042377, _1042379, _1042381, _1042383, _1042385]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1042379, tc_HOL_Obool)), _1042381), _1042383))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1042379, _1042377), _1042385), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042379, tc_HOL_Obool)), _1042381), _1042383)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042377), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1042379, _1042377), _1042385), _1042381)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1042379, _1042377), _1042385), _1042383)))], (23386 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (26133 ^ _780119) ^ [_1256674, _1256676, _1256678] : [class_Orderings_Oord(_1256674), 26136 ^ _780119 : [(26143 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256674), _1256676), _1256678)), -(hBOOL(hAPP(hAPP(c_member(_1256674), _1256676), hAPP(c_SetInterval_Oord__class_OatMost(_1256674), _1256678))))], (26137 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1256674), _1256676), hAPP(c_SetInterval_Oord__class_OatMost(_1256674), _1256678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256674), _1256676), _1256678)))]]], (43870 ^ _780119) ^ [_1656675, _1656677, _1656679, _1656681, _1656683] : [class_Orderings_Olinorder(_1656675), hBOOL(hAPP(c_List_Odistinct(_1656677), _1656679)), -(hBOOL(hAPP(c_List_Odistinct(_1656677), c_List_Olinorder__class_Oinsort__insert__key(_1656677, _1656675, _1656681, _1656683, _1656679))))], (32593 ^ _780119) ^ [_1387581] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1387581)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1387581)), 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))))], (23044 ^ _780119) ^ [_1200948, _1200950] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200948)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200950)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1200948), _1200950)))], (28050 ^ _780119) ^ [_1298015, _1298017, _1298019] : [class_Orderings_Olinorder(_1298015), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298015), _1298017), _1298019) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298015), _1298019), _1298017))], (6336 ^ _780119) ^ [_881978, _881980, _881982, _881984, _881986] : [-(hAPP(c_Set_Oimage(_881978, _881980, _881982), hAPP(hAPP(c_Set_Oinsert(_881978), _881984), _881986)) = hAPP(hAPP(c_Set_Oinsert(_881980), hAPP(_881982, _881984)), hAPP(c_Set_Oimage(_881978, _881980, _881982), _881986)))], (48013 ^ _780119) ^ [_1749840, _1749842] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749840)), c_List_Oremdups(_1749840, _1749842)) = hAPP(c_Finite__Set_Ocard(_1749840), hAPP(c_List_Oset(_1749840), _1749842)))], (27676 ^ _780119) ^ [_1291343, _1291345, _1291347, _1291349, _1291351] : [class_Orderings_Olinorder(_1291343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291343), _1291345), _1291347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291343), _1291349), _1291351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291343), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291343), _1291345), _1291349)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291343), _1291347), _1291351))))], (42671 ^ _780119) ^ [_1624876] : [-(hAPP(c_Option_Omap(_1624876, _1624876), c_Fun_Oid(_1624876)) = c_Fun_Oid(tc_Option_Ooption(_1624876)))], (31427 ^ _780119) ^ [_1367505, _1367507] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367505))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367505)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367507)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41367 ^ _780119) ^ [_1594109, _1594111, _1594113, _1594115] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594109, tc_fun(_1594111, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1594109, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1594111, tc_HOL_Obool), tc_fun(_1594111, tc_HOL_Obool), _1594109), hAPP(c_COMBC(_1594111, tc_fun(_1594111, tc_HOL_Obool), tc_HOL_Obool), c_member(_1594111))), _1594113)), _1594115)), -(hBOOL(hAPP(hAPP(c_member(_1594111), _1594115), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594109, tc_fun(_1594111, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1594109, tc_HOL_Obool))), _1594113))))], (49825 ^ _780119) ^ [_1790528, _1790530, _1790532] : [c_List_Olist__all(_1790528, _1790530, hAPP(c_List_Orev(_1790528), _1790532)), -(c_List_Olist__all(_1790528, _1790530, _1790532))], (51475 ^ _780119) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (27124 ^ _780119) ^ [_1279567, _1279569, _1279571, _1279573] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279567), hAPP(c_Set_OCollect(_1279567), _1279569))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279571), hAPP(c_Set_OCollect(_1279571), hAPP(hAPP(c_COMBB(tc_fun(_1279567, tc_HOL_Obool), tc_HOL_Obool, _1279571), c_HOL_OEx(_1279567)), hAPP(hAPP(c_COMBC(_1279571, tc_fun(_1279567, tc_HOL_Obool), tc_fun(_1279567, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279567, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1279567, tc_HOL_Obool), tc_fun(_1279567, tc_HOL_Obool)), _1279571), c_COMBS(_1279567, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279567, tc_HOL_Obool), tc_fun(_1279567, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1279571), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1279567), c_fconj)), hAPP(hAPP(c_COMBC(_1279571, tc_fun(_1279567, _1279571), tc_fun(_1279567, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279571, tc_HOL_Obool), tc_fun(tc_fun(_1279567, _1279571), tc_fun(_1279567, tc_HOL_Obool)), _1279571), c_COMBB(_1279571, tc_HOL_Obool, _1279567)), c_fequal)), _1279573)))), _1279569))))))], (50262 ^ _780119) ^ [_1798841, _1798843, _1798845, _1798847] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1798841, _1798843), c_Lazy__Sequence_Olazy__sequence_OInsert(_1798841, _1798845, _1798847)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1798843, _1798845)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1798841, _1798843), _1798847))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51143 ^ _780119) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (18590 ^ _780119) ^ [_1119185, _1119187, _1119189, _1119191] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1119185, _1119187)), c_Sum__Type_OPlus(_1119185, _1119187, _1119189, _1119191))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1119187), _1119191)))], (40086 ^ _780119) ^ [_1562846, _1562848, _1562850, _1562852] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562846, _1562846)), hAPP(hAPP(c_Product__Type_OPair(_1562846, _1562846), _1562848), _1562850)), c_Transitive__Closure_Ortrancl(_1562846, hAPP(c_Relation_Oconverse(_1562846, _1562846), _1562852)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562846, _1562846)), hAPP(hAPP(c_Product__Type_OPair(_1562846, _1562846), _1562850), _1562848)), c_Transitive__Closure_Ortrancl(_1562846, _1562852))))], (10044 ^ _780119) ^ [_955039, _955041, _955043, _955045] : [class_Lattices_Osemilattice__inf(_955039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955039), _955041), _955043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955039), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955039), _955045), _955041)), _955043)))], (17604 ^ _780119) ^ [_1100200, _1100202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1100200), _1100202))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1100200), _1100202)))], (49297 ^ _780119) ^ [_1777736, _1777738, _1777740] : [-(c_List_Oinsert(_1777736, _1777738, c_List_Oremdups(_1777736, _1777740)) = c_List_Oremdups(_1777736, c_List_Oinsert(_1777736, _1777738, _1777740)))], (35430 ^ _780119) ^ [_1448564] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1448564)) = _1448564)], (7954 ^ _780119) ^ [_915705, _915707, _915709, _915711] : [hBOOL(hAPP(hAPP(c_member(_915705), _915707), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915705, tc_HOL_Obool)), _915709), _915711))), 7957 ^ _780119 : [(7960 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_915705), _915707), _915711))], (7958 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_915705), _915707), _915709)))]]], (24120 ^ _780119) ^ [_1221687, _1221689] : [24128 ^ _780119 : [(24131 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1221689, 24127 ^ [_1221687, _1221689])))], (24129 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 24127 ^ [_1221687, _1221689]), _1221687)))]], 24121 ^ _780119 : [(24122 ^ _780119) ^ [_1221756] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1221756), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1221687))), hBOOL(hAPP(_1221689, _1221756))]]], (41389 ^ _780119) ^ [_1594687, _1594689, _1594691, _1594693, _1594695, _1594697] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1594687, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1594689, _1594687, _1594691), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594693, tc_fun(_1594689, tc_HOL_Obool)), _1594695), _1594697))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594693, tc_fun(_1594687, tc_HOL_Obool)), _1594695), hAPP(hAPP(c_COMBB(tc_fun(_1594689, tc_HOL_Obool), tc_fun(_1594687, tc_HOL_Obool), _1594693), c_Relation_OImage(_1594689, _1594687, _1594691)), _1594697)))))], (43435 ^ _780119) ^ [_1644648, _1644650, _1644652] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644648), tc_List_Olist(_1644648))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644648), tc_List_Olist(_1644648)), _1644650), _1644650)), c_List_Olistrel(_1644648, c_Transitive__Closure_Ortrancl(_1644648, _1644652)))))], (36070 ^ _780119) ^ [] : [-(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))], (39745 ^ _780119) ^ [_1554923, _1554925] : [-(c_Transitive__Closure_Otrancl(_1554923, c_Transitive__Closure_Ortrancl(_1554923, _1554925)) = c_Transitive__Closure_Ortrancl(_1554923, _1554925))], (33979 ^ _780119) ^ [_1417788, _1417790, _1417792, _1417794, _1417796, _1417798] : [-(hAPP(hAPP(c_Product__Type_OPair(_1417788, _1417790), _1417792), _1417794) = hAPP(hAPP(c_Product__Type_OPair(_1417788, _1417790), _1417796), _1417798)), _1417792 = _1417796, _1417794 = _1417798], (42837 ^ _780119) ^ [_1628631, _1628633, _1628635] : [-(c_Map_Odom(_1628631, _1628633, hAPP(c_Map_Omap__of(_1628631, _1628633), _1628635)) = hAPP(c_Set_Oimage(tc_prod(_1628631, _1628633), _1628631, c_Product__Type_Ofst(_1628631, _1628633)), hAPP(c_List_Oset(tc_prod(_1628631, _1628633)), _1628635)))], (45277 ^ _780119) ^ [_1688279, _1688281, _1688283] : [-(hBOOL(hAPP(c_List_Odistinct(_1688279), hAPP(hAPP(c_List_Oappend(_1688279), _1688281), _1688283)))), hBOOL(hAPP(c_List_Odistinct(_1688279), _1688281)), hBOOL(hAPP(c_List_Odistinct(_1688279), _1688283)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1688279, tc_HOL_Obool)), hAPP(c_List_Oset(_1688279), _1688281)), hAPP(c_List_Oset(_1688279), _1688283)) = c_Orderings_Obot__class_Obot(tc_fun(_1688279, tc_HOL_Obool))], (26080 ^ _780119) ^ [_1255666, _1255668, _1255670] : [26082 ^ _780119 : [(26085 ^ _780119) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1255670, 26081 ^ [_1255666, _1255668, _1255670]))], (26083 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1255666), 26081 ^ [_1255666, _1255668, _1255670]), _1255668)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1255666, tc_Int_Oint), _1255670), _1255668) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1255666, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1255666), c_Int_Onat), _1255670)), _1255668)))], (7782 ^ _780119) ^ [_912273, _912275] : [-(c_HOL_OThe(_912273, hAPP(hAPP(c_COMBC(_912273, _912273, tc_HOL_Obool), c_fequal), _912275)) = _912275)], (10206 ^ _780119) ^ [_958468, _958470, _958472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958468, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958468, tc_HOL_Obool)), _958470), _958472)), _958472)))], (15698 ^ _780119) ^ [_1066114, _1066116, _1066118] : [class_Rings_Olinordered__ring__strict(_1066114), 15701 ^ _780119 : [(15716 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066114), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066114), _1066116), _1066118)), c_Groups_Ozero__class_Ozero(_1066114)))), 15717 ^ _780119 : [(15724 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066114), _1066116), c_Groups_Ozero__class_Ozero(_1066114))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066114), c_Groups_Ozero__class_Ozero(_1066114)), _1066118))], (15718 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066114), c_Groups_Ozero__class_Ozero(_1066114)), _1066116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066114), _1066118), c_Groups_Ozero__class_Ozero(_1066114)))]]], (15702 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066114), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066114), _1066116), _1066118)), c_Groups_Ozero__class_Ozero(_1066114))), 15707 ^ _780119 : [(15710 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066114), _1066118), c_Groups_Ozero__class_Ozero(_1066114))))], (15708 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066114), c_Groups_Ozero__class_Ozero(_1066114)), _1066116)))]], 15711 ^ _780119 : [(15714 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066114), c_Groups_Ozero__class_Ozero(_1066114)), _1066118)))], (15712 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066114), _1066116), c_Groups_Ozero__class_Ozero(_1066114))))]]]]], (22689 ^ _780119) ^ [_1194512, _1194514, _1194516, _1194518] : [hBOOL(hAPP(hAPP(_1194516, _1194514), _1194518)), -(hBOOL(hAPP(hAPP(c_member(_1194512), _1194514), c_SetInterval_Oord_OatMost(_1194512, _1194516, _1194518))))], (29635 ^ _780119) ^ [_1331163, _1331165, _1331167, _1331169, _1331171] : [class_Complete__Lattice_Ocomplete__lattice(_1331163), 29638 ^ _780119 : [(29639 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331163), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331165, _1331163), _1331167), _1331169)), _1331171)), 29642 ^ _780119 : [(29643 ^ _780119) ^ [_1331344] : [hBOOL(hAPP(hAPP(c_member(_1331165), _1331344), _1331167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331163), hAPP(_1331169, _1331344)), _1331171)))]]], (29649 ^ _780119) ^ [] : [29651 ^ _780119 : [(29654 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331163), hAPP(_1331169, 29650 ^ [_1331163, _1331165, _1331167, _1331169, _1331171])), _1331171))], (29652 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331165), 29650 ^ [_1331163, _1331165, _1331167, _1331169, _1331171]), _1331167)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331163), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331165, _1331163), _1331167), _1331169)), _1331171)))]]], (32101 ^ _780119) ^ [_1378459, _1378461, _1378463, _1378465] : [-(c_Nat_Onat_Onat__case(_1378459, _1378461, _1378463, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1378465)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1378459), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1378465))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1378459, _1378459), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1378459, tc_fun(_1378459, _1378459)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1378459, tc_fun(_1378459, _1378459)), tc_Int_Oint), c_If(_1378459)), c_Nat__Numeral_Oneg)), _1378461)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1378459, tc_Int_Oint), _1378463), c_Int_Onat))))], (46479 ^ _780119) ^ [_1716927, _1716929, _1716931] : [hBOOL(hAPP(hAPP(c_member(_1716927), _1716929), hAPP(c_List_Oset(_1716927), c_List_Obutlast(_1716927, _1716931)))), -(hBOOL(hAPP(hAPP(c_member(_1716927), _1716929), hAPP(c_List_Oset(_1716927), _1716931))))], (46696 ^ _780119) ^ [_1721667, _1721669] : [-(c_List_Ofoldr(tc_List_Olist(_1721667), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1721667)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1721667))), c_List_Otranspose(_1721667, _1721669), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1721667))), hAPP(c_List_Ofilter(tc_List_Olist(_1721667), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1721667)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1721667), tc_List_Olist(_1721667), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1721667)))), _1721669)))], (2748 ^ _780119) ^ [_820934, _820936, _820938, _820940, _820942, _820944, _820946, _820948] : [-(c_Fun_Othe__inv__into(_820948, _820944, _820940, _820936) = c_Fun_Othe__inv__into(_820946, _820942, _820938, _820934)), _820948 = _820946, _820944 = _820942, _820940 = _820938, _820936 = _820934], (19913 ^ _780119) ^ [_1142108, _1142110, _1142112, _1142114, _1142116] : [class_Fields_Ofield__inverse__zero(_1142108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1142110), _1142112)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1142110, _1142108), hAPP(hAPP(c_COMBS(_1142110, _1142108, _1142108), hAPP(hAPP(c_COMBB(_1142108, tc_fun(_1142108, _1142108), _1142110), c_Rings_Oinverse__class_Odivide(_1142108)), _1142114)), _1142116)), _1142112) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142108), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1142110, _1142108), _1142114), _1142112)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1142110, _1142108), _1142116), _1142112)))], (2204 ^ _780119) ^ [_812468, _812470, _812472, _812474] : [-(c_Int_Onat__aux(_812474, _812470) = c_Int_Onat__aux(_812472, _812468)), _812474 = _812472, _812470 = _812468], (13065 ^ _780119) ^ [_1017690, _1017692] : [class_Groups_Oab__semigroup__mult(_1017690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017690), _1017692)), -(_1017692 = c_Orderings_Obot__class_Obot(tc_fun(_1017690, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1017690), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017690), 13078 ^ [_1017690, _1017692]), 13079 ^ [_1017690, _1017692])), hAPP(hAPP(c_Set_Oinsert(_1017690), 13078 ^ [_1017690, _1017692]), hAPP(hAPP(c_Set_Oinsert(_1017690), 13079 ^ [_1017690, _1017692]), c_Orderings_Obot__class_Obot(tc_fun(_1017690, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1017690), hAPP(c_Finite__Set_Ofold1(_1017690, c_Groups_Otimes__class_Otimes(_1017690)), _1017692)), _1017692)))], (9462 ^ _780119) ^ [_942756, _942758, _942760] : [class_Lattices_Olattice(_942756), hBOOL(hAPP(c_Finite__Set_Ofinite(_942756), _942758)), 9469 ^ _780119 : [(9476 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942756, tc_HOL_Obool)), _942758), hAPP(hAPP(c_Set_Oinsert(_942756), _942760), c_Orderings_Obot__class_Obot(tc_fun(_942756, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_942756, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_942756, hAPP(hAPP(c_Set_Oinsert(_942756), _942760), _942758)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_942756), _942760), c_Big__Operators_Olattice__class_OSup__fin(_942756, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942756, tc_HOL_Obool)), _942758), hAPP(hAPP(c_Set_Oinsert(_942756), _942760), c_Orderings_Obot__class_Obot(tc_fun(_942756, tc_HOL_Obool)))))))], (9470 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942756, tc_HOL_Obool)), _942758), hAPP(hAPP(c_Set_Oinsert(_942756), _942760), c_Orderings_Obot__class_Obot(tc_fun(_942756, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_942756, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_942756, hAPP(hAPP(c_Set_Oinsert(_942756), _942760), _942758)) = _942760)]]], (6415 ^ _780119) ^ [_883749, _883751, _883753, _883755, _883757] : [hBOOL(hAPP(hAPP(c_member(_883749), _883751), _883753)), -(hAPP(hAPP(c_Set_Oinsert(_883755), hAPP(_883757, _883751)), hAPP(c_Set_Oimage(_883749, _883755, _883757), _883753)) = hAPP(c_Set_Oimage(_883749, _883755, _883757), _883753))], (24551 ^ _780119) ^ [_1229883, _1229885, _1229887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229883)), 24554 ^ _780119 : [(24555 ^ _780119) ^ [_1230017] : [24557 ^ _780119 : [(24561 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24559 ^ [_1229883, _1229885, _1229887, _1230017]), _1229885)))], (24563 ^ _780119) ^ [] : [-(_1230017 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24559 ^ [_1229883, _1229885, _1229887, _1230017]), 24556 ^ [_1229883, _1229885, _1229887, _1230017]))], (24558 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24556 ^ [_1229883, _1229885, _1229887, _1230017]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1229883))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229887), _1230017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229887), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1230017), _1229883))))]]], (36756 ^ _780119) ^ [_1478634, _1478636, _1478638, _1478640] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478634, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1478636, _1478634, _1478638), hAPP(c_Set_Ovimage(_1478636, _1478634, _1478638), _1478640))), _1478640)))], (32259 ^ _780119) ^ [_1381698, _1381700, _1381702] : [class_Int_Onumber__ring(_1381698), 32262 ^ _780119 : [(32269 ^ _780119) ^ [] : [c_Int_Oiszero(_1381698, hAPP(c_Int_Onumber__class_Onumber__of(_1381698), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1381700), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1381702)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1381698), _1381700) = hAPP(c_Int_Onumber__class_Onumber__of(_1381698), _1381702))], (32263 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1381698), _1381700) = hAPP(c_Int_Onumber__class_Onumber__of(_1381698), _1381702), -(c_Int_Oiszero(_1381698, hAPP(c_Int_Onumber__class_Onumber__of(_1381698), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1381700), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1381702)))))]]], (31269 ^ _780119) ^ [_1364658, _1364660, _1364662] : [class_Int_Onumber__ring(_1364658), 31272 ^ _780119 : [(31279 ^ _780119) ^ [] : [-(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), _1364660)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1364658), _1364662), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1364660))) = c_Groups_Oone__class_Oone(_1364658))], (31273 ^ _780119) ^ [] : [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), _1364660))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1364658), _1364662), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1364660))) = hAPP(hAPP(c_HOL_OLet(_1364658, _1364658), hAPP(hAPP(c_Power_Opower__class_Opower(_1364658), _1364662), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1364660))), hAPP(hAPP(c_COMBS(_1364658, _1364658, _1364658), hAPP(hAPP(c_COMBB(_1364658, tc_fun(_1364658, _1364658), _1364658), c_Groups_Otimes__class_Otimes(_1364658)), hAPP(c_Groups_Otimes__class_Otimes(_1364658), _1364662))), c_COMBI(_1364658))))]]], (6015 ^ _780119) ^ [_875820, _875822, _875824, _875826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875820, tc_HOL_Obool)), _875822), _875824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875820, tc_HOL_Obool)), _875824), _875826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875820, tc_HOL_Obool)), _875822), _875826)))], (47636 ^ _780119) ^ [_1740846, _1740848, _1740850] : [-(hAPP(c_List_Orotate(_1740846, _1740848), hAPP(c_List_Orev(_1740846), _1740850)) = hAPP(c_List_Orev(_1740846), hAPP(c_List_Orotate(_1740846, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740846)), _1740850)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1740848, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740846)), _1740850)))), _1740850)))], (38804 ^ _780119) ^ [_1531981, _1531983, _1531985, _1531987, _1531989] : [hAPP(c_Set_Oimage(_1531981, _1531983, _1531985), c_Orderings_Otop__class_Otop(tc_fun(_1531981, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1531983, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1531983, _1531987, _1531989), c_Orderings_Otop__class_Otop(tc_fun(_1531983, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1531987, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1531981, _1531987, hAPP(c_Fun_Ocomp(_1531983, _1531987, _1531981, _1531989), _1531985)), c_Orderings_Otop__class_Otop(tc_fun(_1531981, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1531987, tc_HOL_Obool)))], (10821 ^ _780119) ^ [_972015, _972017, _972019, _972021] : [class_Groups_Oordered__ab__semigroup__add(_972015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972015), _972017), _972019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972015), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972015), _972017), _972021)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972015), _972019), _972021))))], (27101 ^ _780119) ^ [_1278919, _1278921, _1278923, _1278925] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278919), hAPP(c_Set_OCollect(_1278919), _1278921))), 27104 ^ _780119 : [(27105 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278923), hAPP(c_Set_OCollect(_1278923), hAPP(hAPP(c_COMBB(tc_fun(_1278919, tc_HOL_Obool), tc_HOL_Obool, _1278923), c_HOL_OEx(_1278919)), hAPP(hAPP(c_COMBB(tc_fun(_1278919, tc_HOL_Obool), tc_fun(_1278919, tc_HOL_Obool), _1278923), hAPP(c_COMBS(_1278919, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1278919), c_fconj), _1278921))), _1278925))))), 27108 ^ _780119 : [(27109 ^ _780119) ^ [_1279202] : [hBOOL(hAPP(_1278921, _1279202)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1278923), hAPP(c_Set_OCollect(_1278923), hAPP(hAPP(c_COMBC(_1278923, _1278919, tc_HOL_Obool), _1278925), _1279202)))))]]], (27115 ^ _780119) ^ [] : [27117 ^ _780119 : [(27120 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278923), hAPP(c_Set_OCollect(_1278923), hAPP(hAPP(c_COMBC(_1278923, _1278919, tc_HOL_Obool), _1278925), 27116 ^ [_1278919, _1278921, _1278923, _1278925]))))], (27118 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1278921, 27116 ^ [_1278919, _1278921, _1278923, _1278925])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1278923), hAPP(c_Set_OCollect(_1278923), hAPP(hAPP(c_COMBB(tc_fun(_1278919, tc_HOL_Obool), tc_HOL_Obool, _1278923), c_HOL_OEx(_1278919)), hAPP(hAPP(c_COMBB(tc_fun(_1278919, tc_HOL_Obool), tc_fun(_1278919, tc_HOL_Obool), _1278923), hAPP(c_COMBS(_1278919, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1278919), c_fconj), _1278921))), _1278925))))))]]], (26795 ^ _780119) ^ [_1269884, _1269886] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1269884), hAPP(c_Set_OCollect(_1269884), _1269886))), 26798 ^ _780119 : [(26805 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1269884), c_Orderings_Otop__class_Otop(tc_fun(_1269884, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1269884), hAPP(c_Set_OCollect(_1269884), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1269884), c_fNot), _1269886)))))], (26799 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1269884), hAPP(c_Set_OCollect(_1269884), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1269884), c_fNot), _1269886)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1269884), c_Orderings_Otop__class_Otop(tc_fun(_1269884, tc_HOL_Obool)))))]]], (13174 ^ _780119) ^ [_1020095, _1020097] : [hAPP(c_Nat_OSuc, _1020095) = hAPP(c_Nat_OSuc, _1020097), -(_1020095 = _1020097)], (33207 ^ _780119) ^ [_1399425, _1399427] : [class_Int_Onumber__ring(_1399425), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1399425), hAPP(c_Int_Onumber__class_Onumber__of(_1399425), 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)))), _1399427))) = hAPP(c_Int_Onumber__class_Onumber__of(_1399425), c_Int_OMin))], (46785 ^ _780119) ^ [_1724049, _1724051, _1724053] : [class_Orderings_Olinorder(_1724049), -(c_List_Olinorder__class_Osorted(_1724049, hAPP(c_List_Ofilter(_1724049, hAPP(hAPP(c_COMBC(_1724049, _1724049, tc_HOL_Obool), c_fequal), hAPP(_1724051, _1724053))), _1724053)))], (42290 ^ _780119) ^ [_1616116, _1616118, _1616120] : [-(c_Nitpick_Otimes__frac(_1616116, _1616118, _1616120) = hAPP(hAPP(c_Nitpick_Ofrac(_1616116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1616116), _1616118)), hAPP(c_Nitpick_Onum(_1616116), _1616120))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1616116), _1616118)), hAPP(c_Nitpick_Odenom(_1616116), _1616120))))], (22087 ^ _780119) ^ [_1183547, _1183549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183547)), -(c_SMT_Oz3mod(_1183549, _1183547) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183549, _1183547))], (32041 ^ _780119) ^ [_1377189] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1377189)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377189) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2810 ^ _780119) ^ [_821911, _821913, _821915, _821917] : [-(c_Wellfounded_Omax__ext(_821917, _821913) = c_Wellfounded_Omax__ext(_821915, _821911)), _821917 = _821915, _821913 = _821911], (22926 ^ _780119) ^ [_1198844, _1198846] : [class_Rings_Olinordered__semidom(_1198844), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198844), c_Groups_Ozero__class_Ozero(_1198844)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1198844), _1198846))))], (8100 ^ _780119) ^ [_918709, _918711, _918713, _918715] : [hBOOL(hAPP(hAPP(c_member(_918709), _918711), _918713)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918709, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_918709), _918711), _918715)), _918713) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918709, tc_HOL_Obool)), _918715), _918713))], (9438 ^ _780119) ^ [_942428, _942430] : [class_Lattices_Olattice(_942428), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_942428), _942430), _942430) = _942430)], (26345 ^ _780119) ^ [_1261013] : [class_Rings_Olinordered__idom(_1261013), -(hAPP(c_Groups_Oabs__class_Oabs(_1261013), c_Groups_Oone__class_Oone(_1261013)) = c_Groups_Oone__class_Oone(_1261013))], (13494 ^ _780119) ^ [_1025698, _1025700, _1025702] : [hBOOL(hAPP(hAPP(c_member(_1025698), _1025700), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025698, tc_HOL_Obool)), _1025702))), hBOOL(hAPP(hAPP(c_member(_1025698), _1025700), _1025702))], (33569 ^ _780119) ^ [_1404977] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1404977)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1404977)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17951 ^ _780119) ^ [_1107007, _1107009, _1107011, _1107013, _1107015, _1107017] : [class_Rings_Olinordered__semiring__1(_1107007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107007), _1107009), _1107011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107007), _1107013), _1107011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107007), c_Groups_Ozero__class_Ozero(_1107007)), _1107015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107007), c_Groups_Ozero__class_Ozero(_1107007)), _1107017)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107007), _1107015), _1107017) = c_Groups_Oone__class_Oone(_1107007), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107007), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107007), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107007), _1107015), _1107009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107007), _1107017), _1107013))), _1107011)))], (37411 ^ _780119) ^ [_1495423] : [class_Orderings_Owellorder(_1495423), -(c_Wellfounded_Owf(_1495423, hAPP(c_Set_OCollect(tc_prod(_1495423, _1495423)), hAPP(c_Product__Type_Oprod_Oprod__case(_1495423, _1495423, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1495423)))))], (19358 ^ _780119) ^ [_1132063, _1132065] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132063), _1132065) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1132065 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19367 ^ _780119 : [(19370 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132063), _1132065)))], (19368 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132063)))]], 19371 ^ _780119 : [(19374 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132065), _1132063)))], (19372 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132063), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (32749 ^ _780119) ^ [_1390533] : [class_Rings_Osemiring__1(_1390533), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1390533), c_Groups_Oone__class_Oone(_1390533)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1390533))], (7948 ^ _780119) ^ [_915553, _915555, _915557, _915559] : [hBOOL(hAPP(hAPP(c_member(_915553), _915555), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915553, tc_HOL_Obool)), _915557), _915559))), -(hBOOL(hAPP(hAPP(c_member(_915553), _915555), _915557)))], (45331 ^ _780119) ^ [_1689738, _1689740, _1689742, _1689744, _1689746, _1689748] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1689738), tc_List_Olist(_1689738))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689738), tc_List_Olist(_1689738)), hAPP(hAPP(c_List_Oappend(_1689738), _1689740), hAPP(hAPP(c_List_Olist_OCons(_1689738), _1689742), c_List_Olist_ONil(_1689738)))), hAPP(hAPP(c_List_Oappend(_1689738), _1689744), hAPP(hAPP(c_List_Olist_OCons(_1689738), _1689746), c_List_Olist_ONil(_1689738))))), c_List_Olistrel1(_1689738, _1689748))), 45336 ^ _780119 : [(45339 ^ _780119) ^ [] : [-(_1689742 = _1689746)], (45337 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1689738), tc_List_Olist(_1689738))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689738), tc_List_Olist(_1689738)), _1689740), _1689744)), c_List_Olistrel1(_1689738, _1689748))))]], 45340 ^ _780119 : [(45343 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1689738, _1689738)), hAPP(hAPP(c_Product__Type_OPair(_1689738, _1689738), _1689742), _1689746)), _1689748)))], (45341 ^ _780119) ^ [] : [-(_1689740 = _1689744)]]], (47788 ^ _780119) ^ [_1745565, _1745567, _1745569, _1745571, _1745573] : [-(c_List_OtakeWhile(_1745565, _1745567, hAPP(hAPP(c_List_Omap(_1745569, _1745565), _1745571), _1745573)) = hAPP(hAPP(c_List_Omap(_1745569, _1745565), _1745571), c_List_OtakeWhile(_1745569, hAPP(c_Fun_Ocomp(_1745565, tc_HOL_Obool, _1745569, _1745567), _1745571), _1745573)))], (5889 ^ _780119) ^ [_873649, _873651, _873653, _873655, _873657] : [hAPP(_873649, _873651) = hAPP(c_Option_Ooption_OSome(_873653), _873655), -(hAPP(hAPP(c_Set_Oinsert(_873657), _873651), c_Map_Odom(_873657, _873653, _873649)) = c_Map_Odom(_873657, _873653, _873649))], (42479 ^ _780119) ^ [_1620275, _1620277] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1620275, _1620277) = c_Smallcheck_Ofull__small_H(_1620275, hAPP(c_Code__Numeral_Oint__of, _1620277), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1620277))))], (6475 ^ _780119) ^ [_884795, _884797] : [class_Orderings_Opreorder(_884795), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884795), _884797), _884797)))], (7086 ^ _780119) ^ [_897124, _897126, _897128] : [hAPP(c_Option_Ooption_OSome(_897124), _897126) = hAPP(c_Option_Ooption_OSome(_897124), _897128), -(_897126 = _897128)], (44558 ^ _780119) ^ [_1672769, _1672771] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1672769), _1672771) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1672769)), hAPP(c_Code__Numeral_Onat__of, _1672771))))], (38003 ^ _780119) ^ [_1513096, _1513098, _1513100, _1513102] : [-(c_Fun_Oinj__on(_1513096, tc_prod(_1513098, _1513096), 38001 ^ [_1513096, _1513098, _1513100, _1513102], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1513098, tc_fun(_1513096, tc_HOL_Obool)), _1513100), _1513102)))], (37334 ^ _780119) ^ [_1493757] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1493757)))], (29849 ^ _780119) ^ [_1336833, _1336835, _1336837, _1336839, _1336841] : [hBOOL(hAPP(hAPP(c_member(_1336833), _1336835), _1336837)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1336839, tc_HOL_Obool)), hAPP(_1336841, _1336835)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1336833, tc_fun(_1336839, tc_HOL_Obool)), _1336837), _1336841)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1336833, tc_fun(_1336839, tc_HOL_Obool)), _1336837), _1336841))], (37288 ^ _780119) ^ [_1492890, _1492892] : [c_Wellfounded_Owf(_1492890, _1492892), -(c_Wellfounded_Owf(tc_fun(_1492890, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1492890, _1492892)))], (38441 ^ _780119) ^ [_1523188, _1523190] : [-(c_Nitpick_Owf_H(_1523188, _1523190)), c_Wellfounded_Oacyclic(_1523188, _1523190), 38446 ^ _780119 : [(38449 ^ _780119) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (38447 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523188, _1523188)), _1523190))]]], (10064 ^ _780119) ^ [_955397, _955399] : [class_Lattices_Obounded__lattice__bot(_955397), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955397), _955399), c_Orderings_Obot__class_Obot(_955397)) = c_Orderings_Obot__class_Obot(_955397))], (51269 ^ _780119) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (18836 ^ _780119) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47029 ^ _780119) ^ [_1728075, _1728077] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1728075), _1728077) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1728075, _1728077)))], (49729 ^ _780119) ^ [_1788286, _1788288, _1788290] : [hBOOL(hAPP(hAPP(c_member(_1788286), _1788288), hAPP(c_List_Oset(_1788286), _1788290))), 49734 ^ _780119 : [(49737 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1788286), _1788288), hAPP(c_List_Oset(_1788286), 49733 ^ [_1788286, _1788288, _1788290])))], (49735 ^ _780119) ^ [] : [-(_1788290 = hAPP(hAPP(c_List_Oappend(_1788286), 49732 ^ [_1788286, _1788288, _1788290]), hAPP(hAPP(c_List_Olist_OCons(_1788286), _1788288), 49733 ^ [_1788286, _1788288, _1788290])))]]], (12329 ^ _780119) ^ [_1003177, _1003179, _1003181] : [12330 ^ _780119 : [(12333 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1003181, _1003179), _1003177))], (12331 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003177), _1003179)))]], 12336 ^ _780119 : [(12339 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1003181, _1003179), _1003177))], (12337 ^ _780119) ^ [] : [-(_1003177 = _1003179)]], 12342 ^ _780119 : [(12345 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1003181, _1003179), _1003177))], (12343 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003179), _1003177)))]], -(hBOOL(hAPP(hAPP(_1003181, _1003179), _1003177)))], (34791 ^ _780119) ^ [_1433183, _1433185, _1433187] : [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), _1433183), _1433185))), -(hBOOL(hAPP(hAPP(_1433187, _1433183), _1433185))), 34798 ^ _780119 : [(34807 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1433187, 34796 ^ [_1433183, _1433185, _1433187]), 34797 ^ [_1433183, _1433185, _1433187]))], (34801 ^ _780119) ^ [] : [-(34797 ^ [_1433183, _1433185, _1433187] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1433187, 34797 ^ [_1433183, _1433185, _1433187]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 34796 ^ [_1433183, _1433185, _1433187], 34797 ^ [_1433183, _1433185, _1433187]))))], (34799 ^ _780119) ^ [] : [-(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), 34796 ^ [_1433183, _1433185, _1433187]), 34797 ^ [_1433183, _1433185, _1433187]))))]]], (21825 ^ _780119) ^ [_1178540, _1178542, _1178544] : [-(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), _1178540), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1178542), _1178540))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178542, _1178540))), _1178544) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178542), _1178544))], (9050 ^ _780119) ^ [_935804, _935806, _935808] : [class_Orderings_Olinorder(_935804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935804), _935806), _935808)), 9057 ^ _780119 : [(9064 ^ _780119) ^ [] : [_935806 = _935808, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935804), _935806), _935808))], (9058 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935804), _935806), _935808))), -(_935806 = _935808)]]], (13115 ^ _780119) ^ [_1018796, _1018798, _1018800, _1018802, _1018804, _1018806, _1018808, _1018810] : [c_Finite__Set_Ofolding__image__simple(_1018796, _1018798, _1018800, _1018802, _1018804, _1018806), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018798), _1018808)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018798), _1018810)), 13129 ^ _780119 : [(13132 ^ _780119) ^ [] : [hAPP(_1018804, 13128 ^ [_1018796, _1018798, _1018800, _1018802, _1018804, _1018806, _1018808, _1018810]) = _1018802], (13130 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1018798), 13128 ^ [_1018796, _1018798, _1018800, _1018802, _1018804, _1018806, _1018808, _1018810]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1018798, tc_HOL_Obool)), _1018808), _1018810))))]], -(hAPP(_1018806, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1018798, tc_HOL_Obool)), _1018808), _1018810)) = hAPP(hAPP(_1018800, hAPP(_1018806, _1018808)), hAPP(_1018806, _1018810)))], (45303 ^ _780119) ^ [_1688831, _1688833, _1688835, _1688837, _1688839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688831), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688833)), _1688835))), -(hAPP(hAPP(c_List_Olist__update(_1688833, hAPP(hAPP(c_List_Oappend(_1688833), _1688835), _1688837)), _1688831), _1688839) = hAPP(hAPP(c_List_Oappend(_1688833), hAPP(hAPP(c_List_Olist__update(_1688833, _1688835), _1688831), _1688839)), _1688837))], (18630 ^ _780119) ^ [_1119987, _1119989, _1119991, _1119993] : [-(c_Sum__Type_OPlus(_1119987, _1119989, _1119991, _1119993) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1119987, _1119989), tc_HOL_Obool))), _1119991 = c_Orderings_Obot__class_Obot(tc_fun(_1119987, tc_HOL_Obool)), _1119993 = c_Orderings_Obot__class_Obot(tc_fun(_1119989, tc_HOL_Obool))], (49695 ^ _780119) ^ [_1787636, _1787638, _1787640, _1787642] : [c_List_Olist__ex(_1787636, _1787638, hAPP(hAPP(c_List_Oappend(_1787636), _1787640), _1787642)), -(c_List_Olist__ex(_1787636, _1787638, _1787640)), -(c_List_Olist__ex(_1787636, _1787638, _1787642))], (42677 ^ _780119) ^ [_1625032, _1625034, _1625036, _1625038, _1625040, _1625042] : [hAPP(_1625032, _1625034) = c_Option_Ooption_ONone(_1625036), -(c_Map_Omap__comp(_1625036, _1625038, _1625040, _1625042, _1625032, _1625034) = c_Option_Ooption_ONone(_1625038))], (33913 ^ _780119) ^ [_1416432, _1416434, _1416436] : [_1416432 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1416434, _1416434), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1416434, _1416434), tc_HOL_Obool)), _1416432), _1416436)))], (3696 ^ _780119) ^ [_835692, _835694, _835696, _835698] : [-(c_Random_Oselect__weight(_835698, _835694) = c_Random_Oselect__weight(_835696, _835692)), _835698 = _835696, _835694 = _835692], (26613 ^ _780119) ^ [_1266050, _1266052, _1266054] : [class_Groups_Oordered__ab__group__add__abs(_1266050), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266050), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1266050), hAPP(c_Groups_Oabs__class_Oabs(_1266050), _1266052)), hAPP(c_Groups_Oabs__class_Oabs(_1266050), _1266054))), hAPP(c_Groups_Oabs__class_Oabs(_1266050), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1266050), _1266054), _1266052)))))], (33481 ^ _780119) ^ [_1403503] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1403503)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1403503)))], (45832 ^ _780119) ^ [_1703386, _1703388, _1703390] : [-(_1703386 = c_List_Olist_ONil(_1703388)), -(hAPP(c_List_Ohd(_1703388), hAPP(hAPP(c_List_Oappend(_1703388), _1703386), _1703390)) = hAPP(c_List_Ohd(_1703388), _1703386))], (38403 ^ _780119) ^ [_1522689, _1522691] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1522689, _1522689)), _1522691)), c_Wellfounded_Oacyclic(_1522689, _1522691), -(c_Wellfounded_Owf(_1522689, _1522691))], (31603 ^ _780119) ^ [_1370177] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1370177)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1370177))))], (20186 ^ _780119) ^ [_1147259, _1147261, _1147263, _1147265] : [class_Fields_Olinordered__field(_1147259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147259), _1147261), c_Groups_Ozero__class_Ozero(_1147259))), 20193 ^ _780119 : [(20200 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147259), _1147265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147259), _1147263), _1147261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147259), _1147263), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147259), _1147265), _1147261))))], (20194 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147259), _1147263), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147259), _1147265), _1147261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147259), _1147265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147259), _1147263), _1147261))))]]], (12115 ^ _780119) ^ [_998450, _998452, _998454] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998450), _998452)), _998454) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998450), _998454)), _998452))], (33623 ^ _780119) ^ [_1408376, _1408378, _1408380, _1408382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408376, tc_fun(_1408378, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1408376, tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_fun(_1408378, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408378, tc_fun(tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_fun(_1408378, tc_HOL_Obool)), _1408376), c_COMBC(_1408378, tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408378, tc_prod(_1408376, _1408378)), tc_fun(_1408378, tc_fun(tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_HOL_Obool)), _1408376), hAPP(c_COMBB(tc_prod(_1408376, _1408378), tc_fun(tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_HOL_Obool), _1408378), c_member(tc_prod(_1408376, _1408378)))), c_Product__Type_OPair(_1408376, _1408378)))), _1408380)), hAPP(hAPP(c_COMBC(_1408376, tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_fun(_1408378, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408378, tc_fun(tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_fun(_1408378, tc_HOL_Obool)), _1408376), c_COMBC(_1408378, tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408378, tc_prod(_1408376, _1408378)), tc_fun(_1408378, tc_fun(tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_HOL_Obool)), _1408376), hAPP(c_COMBB(tc_prod(_1408376, _1408378), tc_fun(tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool), tc_HOL_Obool), _1408378), c_member(tc_prod(_1408376, _1408378)))), c_Product__Type_OPair(_1408376, _1408378)))), _1408382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1408376, _1408378), tc_HOL_Obool)), _1408380), _1408382)))], (26771 ^ _780119) ^ [_1269354, _1269356, _1269358] : [-(hBOOL(hAPP(_1269354, _1269356))), -(hAPP(c_Set_OCollect(_1269358), hAPP(hAPP(c_COMBS(_1269358, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1269358), c_fconj), hAPP(hAPP(c_COMBC(_1269358, _1269358, tc_HOL_Obool), c_fequal), _1269356))), _1269354)) = c_Orderings_Obot__class_Obot(tc_fun(_1269358, tc_HOL_Obool)))], (11746 ^ _780119) ^ [_991639, _991641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991639), _991641)), -(_991639 = _991641), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991639), _991641)))], (51641 ^ _780119) ^ [_1821302, _1821304] : [hBOOL(_1821302), -(hBOOL(hAPP(hAPP(c_fimplies, _1821304), _1821302)))], (47492 ^ _780119) ^ [_1737860, _1737862] : [hAPP(c_List_Orev(_1737860), _1737862) = c_List_Olist_ONil(_1737860), -(_1737862 = c_List_Olist_ONil(_1737860))], (49444 ^ _780119) ^ [_1781888, _1781890, _1781892, _1781894] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1781888, _1781890, _1781892, _1781894) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1781888, _1781890), _1781892), _1781894)))], (44466 ^ _780119) ^ [_1671115, _1671117] : [-(c_Random_Oselect(_1671115, _1671117) = 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(_1671115, 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(_1671115)), _1671117)))), hAPP(hAPP(c_COMBB(_1671115, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1671115, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1671115, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1671115, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1671115), _1671117)), c_Code__Numeral_Onat__of))))], (46191 ^ _780119) ^ [_1711039, _1711041, _1711043] : [c_Equiv__Relations_Oequiv(_1711039, _1711041, _1711043), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1711039), c_List_Olists(_1711039, _1711041), c_List_Olistrel(_1711039, _1711043)))], (1200 ^ _780119) ^ [_797843, _797845] : [-(class_Groups_Osgn__if(_797843)), _797845 = _797843, class_Groups_Osgn__if(_797845)], (19580 ^ _780119) ^ [_1135989, _1135991] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135989), _1135991))), -(c_Nat__Transfer_Otsub(_1135991, _1135989) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43651 ^ _780119) ^ [_1650614, _1650616, _1650618, _1650620] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1650614), tc_List_Olist(_1650614), c_List_Olistrel(_1650614, _1650616)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1650614)), hAPP(hAPP(c_List_Olist_OCons(_1650614), _1650618), _1650620)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1650614), tc_HOL_Obool)))) = c_List_Oset__Cons(_1650614, hAPP(c_Relation_OImage(_1650614, _1650614, _1650616), hAPP(hAPP(c_Set_Oinsert(_1650614), _1650618), c_Orderings_Obot__class_Obot(tc_fun(_1650614, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1650614), tc_List_Olist(_1650614), c_List_Olistrel(_1650614, _1650616)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1650614)), _1650620), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1650614), tc_HOL_Obool))))))], (9722 ^ _780119) ^ [_948614, _948616, _948618, _948620, _948622] : [class_Rings_Osemiring__0(_948614), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948614), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_948616, _948614), _948618), _948620)), _948622) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_948616, _948614), hAPP(hAPP(c_COMBC(_948616, _948614, _948614), hAPP(hAPP(c_COMBB(_948614, tc_fun(_948614, _948614), _948616), c_Groups_Otimes__class_Otimes(_948614)), _948618)), _948622)), _948620))], (11481 ^ _780119) ^ [_985898, _985900, _985902, _985904, _985906] : [class_Rings_Ocomm__semiring__1(_985898), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985898), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985898), _985900), _985902)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985898), _985904), _985906)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985898), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985898), _985900), _985904)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985898), _985902), _985906)))], (17596 ^ _780119) ^ [_1100056, _1100058] : [17597 ^ _780119 : [(17600 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1100056), _1100058)))], (17598 ^ _780119) ^ [] : [_1100058 = c_Orderings_Obot__class_Obot(tc_fun(_1100056, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1100056), _1100058) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43517 ^ _780119) ^ [_1647391, _1647393, _1647395, _1647397, _1647399, _1647401] : [c_List_Olistrelp(_1647391, _1647393, hAPP(hAPP(c_List_Olist_OCons(_1647391), _1647395), _1647397), hAPP(hAPP(c_List_Olist_OCons(_1647391), _1647399), _1647401)), 43520 ^ _780119 : [(43523 ^ _780119) ^ [] : [-(c_List_Olistrelp(_1647391, _1647393, _1647397, _1647401))], (43521 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1647393, _1647395), _1647399)))]]], (37807 ^ _780119) ^ [_1506506, _1506508, _1506510, _1506512] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506506), _1506508)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1506510), _1506512)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1506506, _1506510)), hAPP(hAPP(c_Product__Type_OSigma(_1506506, _1506510), _1506508), hAPP(c_COMBK(tc_fun(_1506510, tc_HOL_Obool), _1506506), _1506512)))))], (51337 ^ _780119) ^ [] : [-(class_HOL_Oequal(tc_HOL_Obool))], (48641 ^ _780119) ^ [_1763388, _1763390, _1763392] : [class_Enum_Oenum(_1763388), class_Enum_Oenum(_1763390), 48648 ^ _780119 : [(48655 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1763390), hAPP(hAPP(c_COMBB(tc_fun(_1763388, tc_HOL_Obool), tc_HOL_Obool, _1763390), c_Enum_Oenum__class_Oenum__ex(_1763388)), hAPP(hAPP(c_COMBB(tc_fun(_1763388, tc_prod(_1763390, _1763388)), tc_fun(_1763388, tc_HOL_Obool), _1763390), hAPP(c_COMBB(tc_prod(_1763390, _1763388), tc_HOL_Obool, _1763388), _1763392)), c_Product__Type_OPair(_1763390, _1763388))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1763390, _1763388)), _1763392)))], (48649 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1763390, _1763388)), _1763392)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1763390), hAPP(hAPP(c_COMBB(tc_fun(_1763388, tc_HOL_Obool), tc_HOL_Obool, _1763390), c_Enum_Oenum__class_Oenum__ex(_1763388)), hAPP(hAPP(c_COMBB(tc_fun(_1763388, tc_prod(_1763390, _1763388)), tc_fun(_1763388, tc_HOL_Obool), _1763390), hAPP(c_COMBB(tc_prod(_1763390, _1763388), tc_HOL_Obool, _1763388), _1763392)), c_Product__Type_OPair(_1763390, _1763388))))))]]], (18698 ^ _780119) ^ [_1121115, _1121117] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121115), _1121117) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121117), _1121115))], (44334 ^ _780119) ^ [_1668209] : [-(_1668209 = 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)), _1668209)))], (25039 ^ _780119) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19230 ^ _780119) ^ [_1130004, _1130006, _1130008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130004), 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)), _1130006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130006), _1130008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130004), _1130006)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130004), _1130008))))], (13008 ^ _780119) ^ [_1016436, _1016438, _1016440] : [class_Groups_Oab__semigroup__mult(_1016436), -(_1016438 = c_Orderings_Obot__class_Obot(tc_fun(_1016436, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016436), _1016438)), -(hBOOL(hAPP(hAPP(c_member(_1016436), _1016440), _1016438))), -(hAPP(c_Finite__Set_Ofold1(_1016436, c_Groups_Otimes__class_Otimes(_1016436)), hAPP(hAPP(c_Set_Oinsert(_1016436), _1016440), _1016438)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016436), _1016440), hAPP(c_Finite__Set_Ofold1(_1016436, c_Groups_Otimes__class_Otimes(_1016436)), _1016438)))], (7530 ^ _780119) ^ [_906764, _906766, _906768] : [class_Lattices_Olattice(_906764), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906764), _906766), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_906764), _906766), _906768))))], (33033 ^ _780119) ^ [_1395445, _1395447, _1395449] : [class_Rings_Olinordered__idom(_1395445), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395445), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1395445), hAPP(hAPP(c_Power_Opower__class_Opower(_1395445), _1395447), 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(_1395445), _1395449), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1395445)))], (26529 ^ _780119) ^ [_1264601, _1264603] : [class_Groups_Oordered__ab__group__add__abs(_1264601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264601), c_Groups_Ozero__class_Ozero(_1264601)), _1264603)), -(hAPP(c_Groups_Oabs__class_Oabs(_1264601), _1264603) = _1264603)], (36439 ^ _780119) ^ [_1471288, _1471290, _1471292, _1471294, _1471296, _1471298] : [c_Fun_Oinj__on(_1471288, _1471290, _1471292, _1471294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471288, tc_HOL_Obool)), _1471296), _1471294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471288, tc_HOL_Obool)), _1471298), _1471294)), -(hAPP(c_Set_Oimage(_1471288, _1471290, _1471292), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471288, tc_HOL_Obool)), _1471296), _1471298)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471290, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471288, _1471290, _1471292), _1471296)), hAPP(c_Set_Oimage(_1471288, _1471290, _1471292), _1471298)))], (23957 ^ _780119) ^ [_1218304, _1218306, _1218308] : [class_Orderings_Olinorder(_1218304), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218304), _1218306), _1218308)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1218304, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1218304), _1218306)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218304, _1218306), _1218308)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1218304), _1218308))], (7976 ^ _780119) ^ [_916168, _916170] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916168, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_916168, tc_HOL_Obool))), _916170) = c_Orderings_Obot__class_Obot(tc_fun(_916168, tc_HOL_Obool)))], (34521 ^ _780119) ^ [_1427837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427837)), 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), _1427837)) = 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), _1427837))))))], (21516 ^ _780119) ^ [_1172424, _1172426, _1172428, _1172430] : [class_Divides_Oring__div(_1172424), -(c_Divides_Odiv__class_Omod(_1172424, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1172424), _1172426), _1172428), _1172430) = c_Divides_Odiv__class_Omod(_1172424, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1172424), c_Divides_Odiv__class_Omod(_1172424, _1172426, _1172430)), _1172428), _1172430))], (32165 ^ _780119) ^ [_1379948, _1379950] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1379948)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379950)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1379950))), 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, _1379948))), 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), _1379948)), c_Int_Onat)))))], (43000 ^ _780119) ^ [_1632496, _1632498, _1632500, _1632502] : [-(_1632496 = _1632498), 43003 ^ _780119 : [(43010 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1632500), _1632496), hAPP(c_List_Oset(_1632500), _1632502))), -(hBOOL(hAPP(hAPP(c_member(_1632500), _1632496), hAPP(c_List_Oset(_1632500), c_List_Oremove1(_1632500, _1632498, _1632502)))))], (43004 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1632500), _1632496), hAPP(c_List_Oset(_1632500), c_List_Oremove1(_1632500, _1632498, _1632502)))), -(hBOOL(hAPP(hAPP(c_member(_1632500), _1632496), hAPP(c_List_Oset(_1632500), _1632502))))]]], (40706 ^ _780119) ^ [_1578328, _1578330, _1578332, _1578334] : [class_Orderings_Olinorder(_1578328), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578328), _1578330)), hBOOL(hAPP(hAPP(c_member(_1578328), _1578332), _1578330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1578328), hAPP(hAPP(c_Finite__Set_Ofold(_1578328, _1578328, c_Orderings_Oord__class_Omin(_1578328)), _1578334), _1578330)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1578328), _1578332), _1578334))))], (47483 ^ _780119) ^ [_1737654, _1737656] : [47485 ^ _780119 : [(47488 ^ _780119) ^ [] : [47484 ^ [_1737654, _1737656] = c_List_Olist_ONil(_1737654)], (47486 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1737654)), 47484 ^ [_1737654, _1737656]), hAPP(c_List_Oset(tc_List_Olist(_1737654)), _1737656))))]], -(c_List_Olist_ONil(_1737654) = c_List_Oconcat(_1737654, _1737656))], (44114 ^ _780119) ^ [_1662551, _1662553] : [-(hAPP(c_List_Oset(_1662551), _1662553) = hAPP(c_Set_OCollect(_1662551), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1662551), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1662551, 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)), _1662551), 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)), _1662551), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1662551, tc_fun(tc_Nat_Onat, _1662551), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1662551, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1662551), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1662551), c_COMBB(_1662551, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1662551), _1662553))))), 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(_1662551)), _1662553))))))], (16576 ^ _780119) ^ [_1081993, _1081995] : [class_Groups_Oab__group__add(_1081993), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081993), hAPP(c_Groups_Ouminus__class_Ouminus(_1081993), _1081995)), _1081995) = c_Groups_Ozero__class_Ozero(_1081993))], (48221 ^ _780119) ^ [_1754529, _1754531] : [-(c_Enum_On__lists(_1754529, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1754531) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1754529)), c_List_Olist_ONil(_1754529)), c_List_Olist_ONil(tc_List_Olist(_1754529))))], (49072 ^ _780119) ^ [_1773124, _1773126, _1773128, _1773130, _1773132] : [c_List_Olist__all2(_1773124, _1773126, _1773128, _1773130, hAPP(c_List_Orev(_1773126), _1773132)), -(c_List_Olist__all2(_1773124, _1773126, _1773128, hAPP(c_List_Orev(_1773124), _1773130), _1773132))], (46533 ^ _780119) ^ [_1718069, _1718071] : [-(_1718069 = c_List_Olist_ONil(_1718071)), -(hAPP(hAPP(c_List_Oappend(_1718071), c_List_Obutlast(_1718071, _1718069)), hAPP(hAPP(c_List_Olist_OCons(_1718071), c_List_Olast(_1718071, _1718069)), c_List_Olist_ONil(_1718071))) = _1718069)], (31769 ^ _780119) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (42637 ^ _780119) ^ [_1624085, _1624087, _1624089, _1624091, _1624093] : [-(hAPP(hAPP(c_Option_Omap(_1624085, _1624087), _1624089), _1624091) = hAPP(c_Option_Ooption_OSome(_1624087), _1624093)), 42638 ^ _780119 : [(42639 ^ _780119) ^ [_1624153] : [_1624091 = hAPP(c_Option_Ooption_OSome(_1624085), _1624153), hAPP(_1624089, _1624153) = _1624093]]], (45880 ^ _780119) ^ [_1704025, _1704027, _1704029, _1704031, _1704033] : [-(hAPP(c_List_Orotate(_1704025, _1704027), hAPP(hAPP(c_List_Omap(_1704029, _1704025), _1704031), _1704033)) = hAPP(hAPP(c_List_Omap(_1704029, _1704025), _1704031), hAPP(c_List_Orotate(_1704029, _1704027), _1704033)))], (51267 ^ _780119) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (43144 ^ _780119) ^ [_1636466, _1636468, _1636470, _1636472] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1636466, _1636468))), hAPP(hAPP(c_List_Ozip(_1636466, _1636468), _1636470), _1636472)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636466)), _1636470)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636468)), _1636472)))], (12415 ^ _780119) ^ [_1004375] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004375), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1004375)], (8182 ^ _780119) ^ [_920751, _920753, _920755, _920757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920751, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920751, tc_HOL_Obool)), _920753), hAPP(hAPP(c_Set_Oinsert(_920751), _920755), c_Orderings_Obot__class_Obot(tc_fun(_920751, tc_HOL_Obool))))), _920757)), hBOOL(hAPP(hAPP(c_member(_920751), _920755), _920753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920751, tc_HOL_Obool)), _920753), hAPP(hAPP(c_Set_Oinsert(_920751), _920755), _920757))))], (42739 ^ _780119) ^ [_1626472, _1626474, _1626476] : [-(hAPP(c_Option_Omap(_1626472, _1626474), _1626476) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1626474), _1626472, c_Option_Ooption_ONone(_1626474), hAPP(hAPP(c_COMBB(_1626474, tc_Option_Ooption(_1626474), _1626472), c_Option_Ooption_OSome(_1626474)), _1626476)))], (7420 ^ _780119) ^ [_904878, _904880, _904882, _904884] : [class_Lattices_Osemilattice__sup(_904878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904878), _904880), _904882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904878), _904884), _904882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_904878), _904880), _904884)), _904882)))], (26861 ^ _780119) ^ [_1271487, _1271489] : [class_Groups_Oordered__ab__group__add__abs(_1271487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271487), _1271489), c_Groups_Ozero__class_Ozero(_1271487))), -(hAPP(c_Groups_Oabs__class_Oabs(_1271487), _1271489) = hAPP(c_Groups_Ouminus__class_Ouminus(_1271487), _1271489))], (34945 ^ _780119) ^ [_1436382, _1436384] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1436382), _1436384) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1436382, _1436384)))], (38653 ^ _780119) ^ [_1528832, _1528834, _1528836] : [-(c_Hilbert__Choice_OEps(tc_prod(_1528832, _1528834), hAPP(c_Product__Type_Oprod_Oprod__case(_1528832, _1528834, tc_HOL_Obool), _1528836)) = c_Hilbert__Choice_OEps(tc_prod(_1528832, _1528834), hAPP(hAPP(c_COMBS(tc_prod(_1528832, _1528834), _1528834, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1528832, tc_fun(_1528834, tc_HOL_Obool), tc_prod(_1528832, _1528834)), _1528836), c_Product__Type_Ofst(_1528832, _1528834))), c_Product__Type_Osnd(_1528832, _1528834))))], (29556 ^ _780119) ^ [_1328905] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1328905))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1328905)) = _1328905)], (14038 ^ _780119) ^ [_1035680, _1035682] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1035680), hAPP(c_Nat_OSuc, _1035682)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1035680), _1035682)))], (34118 ^ _780119) ^ [_1420794, _1420796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1420794)), 34121 ^ _780119 : [(34128 ^ _780119) ^ [] : [-(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), _1420796), _1420794)))), -(c_Divides_OnegDivAlg(_1420796, _1420794) = hAPP(c_Divides_Oadjust(_1420794), c_Divides_OnegDivAlg(_1420796, 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)))), _1420794))))], (34122 ^ _780119) ^ [] : [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), _1420796), _1420794))), -(c_Divides_OnegDivAlg(_1420796, _1420794) = 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), _1420796), _1420794)))]]], (50154 ^ _780119) ^ [_1796567] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1796567)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1796567), c_Int_OPls)))], (50352 ^ _780119) ^ [_1801061, _1801063] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1801061), _1801063))), 50355 ^ _780119 : [(50362 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1801061), _1801063))), -(c_Lazy__Sequence_Osmall__lazy_H(_1801061, _1801063) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1801063), c_Lazy__Sequence_Osmall__lazy_H(_1801061, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1801063), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50356 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1801061), _1801063)), -(c_Lazy__Sequence_Osmall__lazy_H(_1801061, _1801063) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (1170 ^ _780119) ^ [_797468, _797470] : [-(class_Divides_Oring__div(_797468)), _797470 = _797468, class_Divides_Oring__div(_797470)], (11303 ^ _780119) ^ [_981641, _981643, _981645] : [class_Lattices_Olattice(_981641), hBOOL(hAPP(c_Finite__Set_Ofinite(_981641), _981643)), 11310 ^ _780119 : [(11317 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981641, tc_HOL_Obool)), _981643), hAPP(hAPP(c_Set_Oinsert(_981641), _981645), c_Orderings_Obot__class_Obot(tc_fun(_981641, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_981641, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_981641, hAPP(hAPP(c_Set_Oinsert(_981641), _981645), _981643)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981641), _981645), c_Big__Operators_Olattice__class_OInf__fin(_981641, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981641, tc_HOL_Obool)), _981643), hAPP(hAPP(c_Set_Oinsert(_981641), _981645), c_Orderings_Obot__class_Obot(tc_fun(_981641, tc_HOL_Obool)))))))], (11311 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981641, tc_HOL_Obool)), _981643), hAPP(hAPP(c_Set_Oinsert(_981641), _981645), c_Orderings_Obot__class_Obot(tc_fun(_981641, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_981641, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_981641, hAPP(hAPP(c_Set_Oinsert(_981641), _981645), _981643)) = _981645)]]], (45686 ^ _780119) ^ [_1699735, _1699737, _1699739, _1699741] : [-(hAPP(hAPP(c_List_Oappend(_1699735), _1699737), _1699739) = _1699741), _1699737 = hAPP(hAPP(c_List_Otake(_1699735), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699735)), _1699737)), _1699741), _1699739 = hAPP(hAPP(c_List_Odrop(_1699735), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699735)), _1699737)), _1699741)], (2078 ^ _780119) ^ [_810345, _810347, _810349, _810351, _810353, _810355] : [-(c_SetInterval_Oord_OlessThan(_810355, _810351, _810347) = c_SetInterval_Oord_OlessThan(_810353, _810349, _810345)), _810355 = _810353, _810351 = _810349, _810347 = _810345], (42039 ^ _780119) ^ [_1610026, _1610028, _1610030] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1610026, tc_HOL_Obool)), _1610028), _1610030))), 42045 ^ _780119 : [(42046 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1610026, tc_HOL_Obool)), 42044 ^ [_1610026, _1610028, _1610030]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1610026, tc_HOL_Obool)), _1610028), _1610030))))], (42049 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1610026, tc_HOL_Obool)), 42047 ^ [_1610026, _1610028, _1610030]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1610026, tc_HOL_Obool)), _1610028), _1610030))))], (42053 ^ _780119) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610026, tc_HOL_Obool)), 42044 ^ [_1610026, _1610028, _1610030]), 42047 ^ [_1610026, _1610028, _1610030]) = c_Orderings_Obot__class_Obot(tc_fun(_1610026, tc_HOL_Obool))], (42051 ^ _780119) ^ [] : [42044 ^ [_1610026, _1610028, _1610030] = 42047 ^ [_1610026, _1610028, _1610030]]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610026, tc_HOL_Obool)), _1610028), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1610026, tc_HOL_Obool), _1610030)) = c_Orderings_Obot__class_Obot(tc_fun(_1610026, tc_HOL_Obool)))], (29815 ^ _780119) ^ [_1335972, _1335974, _1335976, _1335978, _1335980] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335972, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335974, tc_fun(_1335972, tc_HOL_Obool)), _1335976), _1335978)), _1335980) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335974, tc_fun(_1335972, tc_HOL_Obool)), _1335976), hAPP(hAPP(c_COMBC(_1335974, tc_fun(_1335972, tc_HOL_Obool), tc_fun(_1335972, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1335972, tc_HOL_Obool), tc_fun(tc_fun(_1335972, tc_HOL_Obool), tc_fun(_1335972, tc_HOL_Obool)), _1335974), c_Groups_Ominus__class_Ominus(tc_fun(_1335972, tc_HOL_Obool))), _1335978)), _1335980)))], (51251 ^ _780119) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (40578 ^ _780119) ^ [_1575601, _1575603, _1575605, _1575607] : [-(hAPP(c_Finite__Set_Ofold__image(_1575601, _1575603, _1575605), _1575607) = c_Finite__Set_Ofold(_1575603, _1575601, hAPP(hAPP(c_COMBB(_1575601, tc_fun(_1575601, _1575601), _1575603), _1575605), _1575607)))], (24591 ^ _780119) ^ [_1230699] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1230699)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1230699)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1230699), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (25873 ^ _780119) ^ [_1252255, _1252257, _1252259, _1252261] : [class_Rings_Oring__1(_1252255), -(hAPP(c_Int_Oring__1__class_Oof__int(_1252255), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1252257, tc_Int_Oint), _1252259), _1252261)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1252257, _1252255), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1252255, _1252257), c_Int_Oring__1__class_Oof__int(_1252255)), _1252259)), _1252261))], (29805 ^ _780119) ^ [_1335622, _1335624, _1335626, _1335628, _1335630] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335622, tc_fun(_1335624, tc_HOL_Obool)), _1335626), hAPP(hAPP(c_COMBB(tc_fun(_1335624, tc_HOL_Obool), tc_fun(_1335624, tc_HOL_Obool), _1335622), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335624, tc_HOL_Obool)), _1335628)), _1335630)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335624, tc_HOL_Obool)), _1335628), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335622, tc_fun(_1335624, tc_HOL_Obool)), _1335626), _1335630)))], (28122 ^ _780119) ^ [_1299573, _1299575, _1299577, _1299579] : [class_Orderings_Olinorder(_1299573), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299573), _1299575), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299573), _1299577), _1299579)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299573), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299573), _1299575), _1299577)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299573), _1299575), _1299579)))], (32755 ^ _780119) ^ [_1390630, _1390632] : [class_Rings_Oring__1(_1390630), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1390630), hAPP(c_Groups_Ouminus__class_Ouminus(_1390630), _1390632)), 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(_1390630), _1390632), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (32433 ^ _780119) ^ [_1384830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1384830)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384830), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26437 ^ _780119) ^ [_1262581, _1262583] : [class_Rings_Olinordered__idom(_1262581), -(hAPP(c_Groups_Oabs__class_Oabs(_1262581), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1262581), _1262583)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1262581), _1262583))], (3354 ^ _780119) ^ [_830471, _830473] : [_830473 = _830471, -(c_HOL_OEx(_830473) = c_HOL_OEx(_830471))], (37655 ^ _780119) ^ [_1501606, _1501608] : [-(hAPP(c_Relation_ODomain(_1501606, _1501608), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501606, _1501608), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1501606, tc_HOL_Obool)))], (5823 ^ _780119) ^ [_872416, _872418, _872420] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_872416), _872418)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_872416), hAPP(hAPP(c_Set_Oinsert(_872416), _872420), _872418))))], (45872 ^ _780119) ^ [_1703837, _1703839, _1703841] : [-(hAPP(c_List_Orotate(_1703837, _1703839), _1703841) = hAPP(c_List_Orotate(_1703837, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1703839, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703837)), _1703841))), _1703841))], (4022 ^ _780119) ^ [_840883, _840885] : [_840885 = _840883, -(c_Set_OPow(_840885) = c_Set_OPow(_840883))], (25512 ^ _780119) ^ [] : [-(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))))], (24727 ^ _780119) ^ [_1232956, _1232958] : [class_Orderings_Olinorder(_1232956), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1232956, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1232956), _1232958)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1232956), _1232958))], (5206 ^ _780119) ^ [_859785, _859787] : [_859787 = _859785, -(c_Groups_Ominus__class_Ominus(_859787) = c_Groups_Ominus__class_Ominus(_859785))], (48423 ^ _780119) ^ [_1759308, _1759310, _1759312] : [class_Enum_Oenum(_1759308), 48426 ^ _780119 : [(48436 ^ _780119) ^ [] : [-(c_Enum_Oex__n__lists(_1759308, _1759310, _1759312)), 48437 ^ _780119 : [(48438 ^ _780119) ^ [_1759564] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1759308)), _1759564), hAPP(c_List_Oset(tc_List_Olist(_1759308)), c_Enum_On__lists(_1759308, _1759312, c_Enum_Oenum__class_Oenum(_1759308))))), hBOOL(hAPP(_1759310, _1759564))]]], (48427 ^ _780119) ^ [] : [c_Enum_Oex__n__lists(_1759308, _1759310, _1759312), 48431 ^ _780119 : [(48434 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1759310, 48430 ^ [_1759308, _1759310, _1759312])))], (48432 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1759308)), 48430 ^ [_1759308, _1759310, _1759312]), hAPP(c_List_Oset(tc_List_Olist(_1759308)), c_Enum_On__lists(_1759308, _1759312, c_Enum_Oenum__class_Oenum(_1759308))))))]]]]], (8094 ^ _780119) ^ [_918539, _918541, _918543, _918545] : [hBOOL(hAPP(hAPP(c_member(_918539), _918541), _918543)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918539, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_918539), _918541), _918545)), _918543) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918539, tc_HOL_Obool)), _918545), _918543))], (18448 ^ _780119) ^ [_1116651, _1116653] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116651), _1116653) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116653), _1116651))], (45780 ^ _780119) ^ [_1702037, _1702039, _1702041, _1702043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702037), _1702039)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702041)), _1702043))), -(hAPP(hAPP(c_List_Otake(_1702041), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702037), _1702039)), _1702043) = hAPP(hAPP(c_List_Oappend(_1702041), hAPP(hAPP(c_List_Otake(_1702041), _1702037), _1702043)), hAPP(hAPP(c_List_Otake(_1702041), _1702039), hAPP(hAPP(c_List_Odrop(_1702041), _1702037), _1702043))))], (51431 ^ _780119) ^ [_1818944, _1818946] : [-(class_HOL_Oequal(tc_prod(_1818944, _1818946)))], (7326 ^ _780119) ^ [_902918, _902920, _902922] : [class_Lattices_Osemilattice__sup(_902918), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902918), _902920), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902918), _902920), _902922)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902918), _902920), _902922))], (15032 ^ _780119) ^ [_1055518, _1055520] : [class_Rings_Ocomm__semiring__1(_1055518), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055518), _1055520), c_Groups_Ozero__class_Ozero(_1055518)) = c_Groups_Ozero__class_Ozero(_1055518))], (24593 ^ _780119) ^ [_1230743, _1230745, _1230747, _1230749] : [class_Orderings_Olinorder(_1230743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230743), _1230745), _1230747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230743), _1230747), _1230749)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1230743, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1230743, _1230745, _1230747)), c_SetInterval_Oord__class_OatLeastAtMost(_1230743, _1230747, _1230749)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1230743, _1230745, _1230749))], (12647 ^ _780119) ^ [_1009373, _1009375, _1009377, _1009379] : [hBOOL(hAPP(hAPP(c_member(_1009373), _1009375), c_Map_Odom(_1009373, _1009377, _1009379))), hAPP(_1009379, _1009375) = c_Option_Ooption_ONone(_1009377)], (11191 ^ _780119) ^ [_979324, _979326, _979328] : [class_Lattices_Olattice(_979324), hBOOL(hAPP(c_Finite__Set_Ofinite(_979324), _979326)), -(_979326 = c_Orderings_Obot__class_Obot(tc_fun(_979324, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_979324), _979328)), -(_979328 = c_Orderings_Obot__class_Obot(tc_fun(_979324, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_979324, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979324, tc_HOL_Obool)), _979326), _979328)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_979324), c_Big__Operators_Olattice__class_OInf__fin(_979324, _979326)), c_Big__Operators_Olattice__class_OInf__fin(_979324, _979328)))], (51395 ^ _780119) ^ [_1818479] : [-(class_Nat_Osize(tc_Option_Ooption(_1818479)))], (48104 ^ _780119) ^ [_1751805, _1751807, _1751809, _1751811, _1751813] : [hBOOL(hAPP(hAPP(c_member(_1751805), _1751807), hAPP(c_List_Oset(_1751805), _1751809))), -(hBOOL(hAPP(_1751811, _1751807))), -(c_List_OdropWhile(_1751805, _1751811, hAPP(hAPP(c_List_Oappend(_1751805), _1751809), _1751813)) = hAPP(hAPP(c_List_Oappend(_1751805), c_List_OdropWhile(_1751805, _1751811, _1751809)), _1751813))], (10230 ^ _780119) ^ [_959413, _959415, _959417, _959419, _959421] : [class_Groups_Oab__group__add(_959413), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_959415, _959413), hAPP(hAPP(c_COMBS(_959415, _959413, _959413), hAPP(hAPP(c_COMBB(_959413, tc_fun(_959413, _959413), _959415), c_Groups_Ominus__class_Ominus(_959413)), _959417)), _959419)), _959421) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959413), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_959415, _959413), _959417), _959421)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_959415, _959413), _959419), _959421)))], (12641 ^ _780119) ^ [_1009198, _1009200] : [-(hAPP(c_Finite__Set_Ocard(_1009198), _1009200) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009198, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1009198), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1009200))], (16554 ^ _780119) ^ [_1081632, _1081634, _1081636] : [class_Groups_Ogroup__add(_1081632), 16557 ^ _780119 : [(16564 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081632), _1081634), _1081636) = c_Groups_Ozero__class_Ozero(_1081632), -(_1081634 = hAPP(c_Groups_Ouminus__class_Ouminus(_1081632), _1081636))], (16558 ^ _780119) ^ [] : [_1081634 = hAPP(c_Groups_Ouminus__class_Ouminus(_1081632), _1081636), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081632), _1081634), _1081636) = c_Groups_Ozero__class_Ozero(_1081632))]]], (16694 ^ _780119) ^ [_1083980, _1083982, _1083984, _1083986] : [class_Rings_Ocomm__semiring__1(_1083980), class_Rings_Ono__zero__divisors(_1083980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083982), _1083984)), 16705 ^ _780119 : [(16715 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1083982, _1083980), _1083986), _1083984) = c_Groups_Ozero__class_Ozero(_1083980)), 16716 ^ _780119 : [(16717 ^ _780119) ^ [_1084358] : [hBOOL(hAPP(hAPP(c_member(_1083982), _1084358), _1083984)), hAPP(_1083986, _1084358) = c_Groups_Ozero__class_Ozero(_1083980)]]], (16706 ^ _780119) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1083982, _1083980), _1083986), _1083984) = c_Groups_Ozero__class_Ozero(_1083980), 16710 ^ _780119 : [(16713 ^ _780119) ^ [] : [-(hAPP(_1083986, 16709 ^ [_1083980, _1083982, _1083984, _1083986]) = c_Groups_Ozero__class_Ozero(_1083980))], (16711 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1083982), 16709 ^ [_1083980, _1083982, _1083984, _1083986]), _1083984)))]]]]], (46455 ^ _780119) ^ [_1716578, _1716580, _1716582] : [_1716578 = c_List_Olist_ONil(_1716580), -(c_List_Obutlast(_1716580, hAPP(hAPP(c_List_Oappend(_1716580), _1716582), _1716578)) = c_List_Obutlast(_1716580, _1716582))], (35075 ^ _780119) ^ [_1439242, _1439244, _1439246, _1439248, _1439250, _1439252] : [hAPP(_1439248, hAPP(c_Product__Type_Ofst(_1439242, _1439246), _1439250)) = hAPP(_1439252, hAPP(c_Product__Type_Ofst(_1439242, _1439246), _1439250)), -(hAPP(c_Product__Type_Oapfst(_1439242, _1439244, _1439246, _1439248), _1439250) = hAPP(c_Product__Type_Oapfst(_1439242, _1439244, _1439246, _1439252), _1439250))], (49255 ^ _780119) ^ [_1777091, _1777093, _1777095, _1777097] : [_1777091 = _1777093, -(hAPP(c_List_OremoveAll(_1777095, _1777091), hAPP(hAPP(c_List_Olist_OCons(_1777095), _1777093), _1777097)) = hAPP(c_List_OremoveAll(_1777095, _1777091), _1777097))], (17528 ^ _780119) ^ [_1098699] : [class_Rings_Olinordered__semidom(_1098699), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098699), c_Groups_Ozero__class_Ozero(_1098699)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098699), c_Groups_Oone__class_Oone(_1098699)), c_Groups_Oone__class_Oone(_1098699)))))], (12171 ^ _780119) ^ [_999582, _999584, _999586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999582), _999584)), 12174 ^ _780119 : [(12181 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999586), _999582)), _999584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999586), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999584), _999582))))], (12175 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999586), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999584), _999582))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999586), _999582)), _999584)))]]], (6715 ^ _780119) ^ [_890143, _890145, _890147, _890149] : [hBOOL(hAPP(hAPP(c_member(_890143), _890145), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890143, tc_HOL_Obool)), _890147), _890149))), -(hBOOL(hAPP(hAPP(c_member(_890143), _890145), _890147))), -(hBOOL(hAPP(hAPP(c_member(_890143), _890145), _890149)))], (26755 ^ _780119) ^ [_1268966, _1268968, _1268970, _1268972] : [-(hBOOL(hAPP(hAPP(c_member(_1268966), _1268968), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1268966, tc_HOL_Obool)), _1268970), hAPP(c_Set_OCollect(_1268966), _1268972))))), hBOOL(hAPP(hAPP(c_member(_1268966), _1268968), _1268970)), hBOOL(hAPP(_1268972, _1268968))], (25676 ^ _780119) ^ [_1249029, _1249031] : [c_Nat__Transfer_Ois__nat(_1249029), c_Nat__Transfer_Ois__nat(_1249031), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1249029, _1249031)))], (256 ^ _780119) ^ [_784057, _784059, _784061, _784063, _784065, _784067, _784069, _784071, _784073, _784075, _784077, _784079] : [-(c_Equiv__Relations_Ocongruent2(_784077, _784073, _784069, _784065, _784061, _784057)), c_Equiv__Relations_Ocongruent2(_784079, _784075, _784071, _784067, _784063, _784059), _784079 = _784077, _784075 = _784073, _784071 = _784069, _784067 = _784065, _784063 = _784061, _784059 = _784057], (7092 ^ _780119) ^ [_897219, _897221, _897223] : [_897221 = _897223, -(hAPP(c_Option_Ooption_OSome(_897219), _897221) = hAPP(c_Option_Ooption_OSome(_897219), _897223))], (47220 ^ _780119) ^ [_1731621] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1731621) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1731621)))], (51527 ^ _780119) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (46109 ^ _780119) ^ [_1708788, _1708790, _1708792, _1708794] : [class_Complete__Lattice_Ocomplete__lattice(_1708788), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1708790, _1708788), hAPP(c_List_Oset(_1708790), _1708792)), _1708794) = hAPP(c_List_Ofoldl(_1708788, _1708790, hAPP(c_COMBC(_1708790, _1708788, _1708788), hAPP(hAPP(c_COMBB(_1708788, tc_fun(_1708788, _1708788), _1708790), c_Lattices_Osemilattice__sup__class_Osup(_1708788)), _1708794)), c_Orderings_Obot__class_Obot(_1708788)), _1708792))], (9016 ^ _780119) ^ [_935269, _935271, _935273] : [class_Orderings_Oorder(_935269), -(_935271 = _935273), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935269), _935273), _935271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935269), _935273), _935271)))], (47957 ^ _780119) ^ [_1748844] : [-(c_List_Oremdups(_1748844, c_List_Olist_ONil(_1748844)) = c_List_Olist_ONil(_1748844))], (6561 ^ _780119) ^ [_886645, _886647, _886649, _886651] : [hBOOL(hAPP(hAPP(c_member(_886645), _886647), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886645, tc_HOL_Obool)), _886649), _886651))), -(hBOOL(hAPP(hAPP(c_member(_886645), _886647), _886649))), -(hBOOL(hAPP(hAPP(c_member(_886645), _886647), _886651)))], (32071 ^ _780119) ^ [_1377798, _1377800] : [class_Int_Onumber__ring(_1377798), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1377798), c_Groups_Oone__class_Oone(_1377798)), hAPP(c_Int_Onumber__class_Onumber__of(_1377798), _1377800)) = hAPP(c_Int_Onumber__class_Onumber__of(_1377798), 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), _1377800))))], (25195 ^ _780119) ^ [_1241288] : [-(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)), _1241288)) = hAPP(c_Int_Onat, _1241288))], (18117 ^ _780119) ^ [_1110074, _1110076] : [-(_1110074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110074), _1110076) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110074), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1110076)))], (31439 ^ _780119) ^ [_1367689, _1367691] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367689))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367689)), _1367691) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1367691))], (32957 ^ _780119) ^ [_1393990, _1393992, _1393994] : [class_Rings_Ocomm__semiring__1(_1393990), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1393990), _1393992), 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)))), _1393994)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393990), hAPP(hAPP(c_Power_Opower__class_Opower(_1393990), _1393992), _1393994)), hAPP(hAPP(c_Power_Opower__class_Opower(_1393990), _1393992), _1393994)))], (19933 ^ _780119) ^ [_1142556, _1142558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1142556)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1142558), _1142556)), _1142556) = _1142558)], (44856 ^ _780119) ^ [_1678376, _1678378, _1678380] : [-(_1678376 = c_List_Olist_ONil(_1678378)), -(hBOOL(hAPP(hAPP(c_member(_1678378), hAPP(c_Product__Type_Ofst(_1678378, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1678378, _1678376), _1678380))), hAPP(c_List_Oset(_1678378), _1678376))))], (5995 ^ _780119) ^ [_875414, _875416, _875418, _875420] : [5996 ^ _780119 : [(5999 ^ _780119) ^ [] : [hBOOL(hAPP(_875418, _875420))], (5997 ^ _780119) ^ [] : [_875416 = _875420]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_875414), _875416), _875418), _875420)))], (14860 ^ _780119) ^ [_1052983, _1052985, _1052987] : [class_Orderings_Otop(_1052983), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1052985, _1052983)), _1052987) = c_Orderings_Otop__class_Otop(_1052983))], (5678 ^ _780119) ^ [_867057, _867059, _867061, _867063, _867065, _867067] : [-(c_COMBB(_867067, _867063, _867059) = c_COMBB(_867065, _867061, _867057)), _867067 = _867065, _867063 = _867061, _867059 = _867057], (51667 ^ _780119) ^ [] : [-(hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))], (38280 ^ _780119) ^ [_1519923] : [-(c_Relation_Orefl__on(_1519923, c_Orderings_Obot__class_Obot(tc_fun(_1519923, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519923, _1519923), tc_HOL_Obool))))], (51503 ^ _780119) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (12395 ^ _780119) ^ [_1004055, _1004057, _1004059] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004055), _1004057)), _1004059) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004057), _1004059)))], (39599 ^ _780119) ^ [_1550810, _1550812, _1550814, _1550816] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1550810, tc_fun(_1550810, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1550810, tc_fun(tc_prod(_1550810, _1550810), tc_HOL_Obool), tc_fun(_1550810, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550810, tc_fun(tc_fun(tc_prod(_1550810, _1550810), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1550810, _1550810), tc_HOL_Obool), tc_fun(_1550810, tc_HOL_Obool)), _1550810), c_COMBC(_1550810, tc_fun(tc_prod(_1550810, _1550810), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550810, tc_prod(_1550810, _1550810)), tc_fun(_1550810, tc_fun(tc_fun(tc_prod(_1550810, _1550810), tc_HOL_Obool), tc_HOL_Obool)), _1550810), hAPP(c_COMBB(tc_prod(_1550810, _1550810), tc_fun(tc_fun(tc_prod(_1550810, _1550810), tc_HOL_Obool), tc_HOL_Obool), _1550810), c_member(tc_prod(_1550810, _1550810)))), c_Product__Type_OPair(_1550810, _1550810)))), _1550812)), c_fequal), _1550814), _1550816)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1550810, _1550810)), hAPP(hAPP(c_Product__Type_OPair(_1550810, _1550810), _1550814), _1550816)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1550810, _1550810), tc_HOL_Obool)), _1550812), c_Relation_OId(_1550810)))))], (50921 ^ _780119) ^ [_1813410] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1813410)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1813410)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33363 ^ _780119) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (12129 ^ _780119) ^ [_998759, _998761] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _998759), _998761))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998759), _998761)) = _998759)], (22537 ^ _780119) ^ [_1191364, _1191366, _1191368] : [hBOOL(hAPP(c_Com_OWT, _1191364)), hBOOL(hAPP(c_Com_OWT, _1191366)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1191368, _1191364, _1191366))))], (44122 ^ _780119) ^ [_1662811, _1662813, _1662815, _1662817] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662811) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1662813), hAPP(hAPP(c_List_Olist_OCons(_1662813), _1662815), _1662817)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662811)) = hAPP(hAPP(c_List_Onth(_1662813), _1662817), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662811)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (14624 ^ _780119) ^ [_1048441, _1048443, _1048445] : [class_Rings_Olinordered__semidom(_1048441), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048441), c_Groups_Oone__class_Oone(_1048441)), _1048443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048441), hAPP(hAPP(c_Power_Opower__class_Opower(_1048441), _1048443), _1048445)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048441), _1048443), hAPP(hAPP(c_Power_Opower__class_Opower(_1048441), _1048443), _1048445)))))], (43906 ^ _780119) ^ [_1657337, _1657339, _1657341] : [class_Orderings_Olinorder(_1657337), -(hBOOL(hAPP(hAPP(c_member(_1657337), _1657339), hAPP(c_List_Oset(_1657337), _1657341)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1657337, _1657337, c_COMBI(_1657337), _1657339, _1657341) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1657337, _1657337, c_COMBI(_1657337)), _1657339), _1657341))], (45808 ^ _780119) ^ [_1702962, _1702964, _1702966] : [-(_1702962 = c_List_Olist_ONil(_1702964)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702966), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702964)), _1702962))), -(hAPP(c_List_Ohd(_1702964), hAPP(hAPP(c_List_Odrop(_1702964), _1702966), _1702962)) = hAPP(hAPP(c_List_Onth(_1702964), _1702962), _1702966))], (14388 ^ _780119) ^ [_1043782, _1043784] : [class_Rings_Ocomm__semiring__1(_1043782), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1043782), _1043784), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1043784)], (14753 ^ _780119) ^ [_1051039, _1051041, _1051043, _1051045] : [class_Groups_Ocomm__monoid__mult(_1051039), hBOOL(hAPP(c_Finite__Set_Ofinite(_1051041), _1051043)), 14763 ^ _780119 : [(14766 ^ _780119) ^ [] : [hAPP(_1051045, 14762 ^ [_1051039, _1051041, _1051043, _1051045]) = c_Groups_Oone__class_Oone(_1051039)], (14764 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1051041), 14762 ^ [_1051039, _1051041, _1051043, _1051045]), _1051043)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1051039, _1051041, c_Groups_Otimes__class_Otimes(_1051039)), _1051045), c_Groups_Oone__class_Oone(_1051039)), _1051043) = c_Groups_Oone__class_Oone(_1051039))], (46303 ^ _780119) ^ [_1713686, _1713688, _1713690] : [_1713686 = c_List_Olist_ONil(_1713688), -(c_List_Olast(_1713688, hAPP(hAPP(c_List_Olist_OCons(_1713688), _1713690), _1713686)) = _1713690)], (37795 ^ _780119) ^ [_1506046, _1506048, _1506050, _1506052, _1506054, _1506056, _1506058, _1506060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1506046, _1506048), tc_HOL_Obool)), _1506050), hAPP(hAPP(c_Product__Type_OSigma(_1506046, _1506048), _1506052), hAPP(c_COMBK(tc_fun(_1506048, tc_HOL_Obool), _1506046), _1506054)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1506048, _1506056), tc_HOL_Obool)), _1506058), hAPP(hAPP(c_Product__Type_OSigma(_1506048, _1506056), _1506054), hAPP(c_COMBK(tc_fun(_1506056, tc_HOL_Obool), _1506048), _1506060)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1506046, _1506056), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1506046, _1506048, _1506056), _1506050), _1506058)), hAPP(hAPP(c_Product__Type_OSigma(_1506046, _1506056), _1506052), hAPP(c_COMBK(tc_fun(_1506056, tc_HOL_Obool), _1506046), _1506060)))))], (51113 ^ _780119) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (1060 ^ _780119) ^ [_796093, _796095] : [-(class_Rings_Olinordered__ring__strict(_796093)), _796095 = _796093, class_Rings_Olinordered__ring__strict(_796095)], (7718 ^ _780119) ^ [_910956] : [hAPP(c_Com_Ocom_OBODY, _910956) = c_Com_Ocom_OSKIP], (11914 ^ _780119) ^ [_994635, _994637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994635), _994637)), -(_994637 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994635), 11917 ^ [_994635, _994637]))], (26171 ^ _780119) ^ [_1257345, _1257347] : [class_Orderings_Olinorder(_1257345), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1257345, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1257345), _1257347)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257345), _1257347))], (19028 ^ _780119) ^ [] : [-(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))))], (37048 ^ _780119) ^ [_1486203, _1486205, _1486207, _1486209] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1486203, _1486205, _1486207), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486203, _1486205), tc_HOL_Obool))), _1486209) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486203, _1486207), tc_HOL_Obool)))], (41270 ^ _780119) ^ [_1590617, _1590619, _1590621, _1590623, _1590625] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590617, tc_fun(_1590619, tc_HOL_Obool)), _1590621), hAPP(hAPP(c_COMBB(tc_fun(_1590619, tc_HOL_Obool), tc_fun(_1590619, tc_HOL_Obool), _1590617), hAPP(c_Set_Oinsert(_1590619), _1590623)), _1590625)) = hAPP(hAPP(c_Set_Oinsert(_1590619), _1590623), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590617, tc_fun(_1590619, tc_HOL_Obool)), _1590621), _1590625)))], (10390 ^ _780119) ^ [_963330, _963332, _963334] : [class_Lattices_Olattice(_963330), hBOOL(hAPP(c_Finite__Set_Ofinite(_963330), _963332)), hBOOL(hAPP(hAPP(c_member(_963330), _963334), _963332)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963330), _963334), c_Big__Operators_Olattice__class_OSup__fin(_963330, _963332)) = _963334)], (44712 ^ _780119) ^ [_1675804] : [-(hBOOL(hAPP(c_List_Odistinct(_1675804), c_List_Olist_ONil(_1675804))))], (43066 ^ _780119) ^ [_1633808, _1633810, _1633812] : [-(hAPP(hAPP(c_List_Ozip(_1633808, _1633810), hAPP(hAPP(c_List_Omap(tc_prod(_1633808, _1633810), _1633808), c_Product__Type_Ofst(_1633808, _1633810)), _1633812)), hAPP(hAPP(c_List_Omap(tc_prod(_1633808, _1633810), _1633810), c_Product__Type_Osnd(_1633808, _1633810)), _1633812)) = _1633812)], (33299 ^ _780119) ^ [_1400790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400790), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1400790)), c_Int_OMin)))], (8022 ^ _780119) ^ [_917225, _917227, _917229] : [c_Com_Ocom_OWhile(_917225, _917227) = hAPP(c_Com_Ocom_OBODY, _917229)], (29793 ^ _780119) ^ [_1334932, _1334934, _1334936, _1334938, _1334940] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334932, tc_fun(_1334934, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334932, tc_HOL_Obool)), _1334936), _1334938)), _1334940) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334934, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334932, tc_fun(_1334934, tc_HOL_Obool)), _1334936), _1334940)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334932, tc_fun(_1334934, tc_HOL_Obool)), _1334938), _1334940)))], (22668 ^ _780119) ^ [_1193880] : [22670 ^ _780119 : [(22673 ^ _780119) ^ [_1193990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 22669 ^ [_1193880, _1193990]), _1193990))], (22671 ^ _780119) ^ [_1193956] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 22669 ^ [_1193880, _1193956]), _1193880)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1193880)))], (51537 ^ _780119) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (25101 ^ _780119) ^ [_1239789, _1239791] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1239789)), hAPP(c_Int_Onat, _1239791)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239789), _1239791))], (29456 ^ _780119) ^ [_1326852, _1326854, _1326856, _1326858, _1326860, _1326862] : [hBOOL(hAPP(hAPP(c_member(_1326852), _1326854), _1326856)), hBOOL(hAPP(hAPP(_1326858, _1326854), _1326860)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326852, tc_fun(_1326862, tc_HOL_Obool)), _1326856), _1326858), _1326860)))], (6397 ^ _780119) ^ [_883367, _883369, _883371, _883373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883367, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_883367), _883369), _883371)), _883373)), 6400 ^ _780119 : [(6403 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883367, tc_HOL_Obool)), _883371), _883373)))], (6401 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_883367), _883369), _883373)))]]], (37380 ^ _780119) ^ [_1494884, _1494886] : [37382 ^ _780119 : [(37383 ^ _780119) ^ [_1494909] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494884, _1494884)), hAPP(hAPP(c_Product__Type_OPair(_1494884, _1494884), hAPP(37381 ^ [_1494884, _1494886], hAPP(c_Nat_OSuc, _1494909))), hAPP(37381 ^ [_1494884, _1494886], _1494909))), _1494886)))]], -(c_Wellfounded_Owf(_1494884, _1494886))], (37066 ^ _780119) ^ [_1486822, _1486824, _1486826, _1486828] : [hAPP(hAPP(c_Relation_Orel__comp(_1486822, _1486822, _1486822), _1486824), _1486826) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486822, _1486822), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1486822, _1486822, _1486822), _1486824), _1486828) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486822, _1486822), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1486822, _1486822, _1486822), _1486824), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1486822, _1486822), tc_HOL_Obool)), _1486826), _1486828)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486822, _1486822), tc_HOL_Obool)))], (38005 ^ _780119) ^ [_1513150, _1513152, _1513154, _1513156] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1513152, _1513150), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1513150, tc_prod(_1513152, _1513150), 38001 ^ [_1513150, _1513152, _1513154, _1513156]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1513152, tc_fun(_1513150, tc_HOL_Obool)), _1513154), _1513156))), hAPP(hAPP(c_Product__Type_OSigma(_1513152, _1513150), _1513154), _1513156))))], (51467 ^ _780119) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (27736 ^ _780119) ^ [_1292400, _1292402, _1292404] : [class_Orderings_Olinorder(_1292400), 27739 ^ _780119 : [(27746 ^ _780119) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292400), _1292402), _1292404) = _1292402, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292400), _1292402), _1292404)))], (27740 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292400), _1292402), _1292404)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292400), _1292402), _1292404) = _1292402)]]], (18271 ^ _780119) ^ [_1113233, _1113235, _1113237, _1113239, _1113241] : [class_Groups_Ocomm__monoid__add(_1113233), class_Groups_Oordered__ab__semigroup__add(_1113233), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113235), _1113237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1113235, tc_HOL_Obool)), _1113239), _1113237)), 18289 ^ _780119 : [(18292 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113233), c_Groups_Ozero__class_Ozero(_1113233)), hAPP(_1113241, 18288 ^ [_1113233, _1113235, _1113237, _1113239, _1113241])))], (18290 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1113235), 18288 ^ [_1113233, _1113235, _1113237, _1113239, _1113241]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1113235, tc_HOL_Obool)), _1113237), _1113239))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113233), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1113235, _1113233), _1113241), _1113239)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1113235, _1113233), _1113241), _1113237))))], (50628 ^ _780119) ^ [_1807074, _1807076, _1807078] : [-(_1807074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1807076), c_List_Oreplicate(_1807076, _1807074, _1807078)) = _1807078)], (8854 ^ _780119) ^ [_932983, _932985, _932987] : [class_Orderings_Olinorder(_932983), 8857 ^ _780119 : [(8864 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932983), _932987), _932985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932983), _932985), _932987))], (8858 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932983), _932985), _932987))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932983), _932987), _932985)))]]], (17210 ^ _780119) ^ [_1092672, _1092674, _1092676] : [class_Groups_Oordered__comm__monoid__add(_1092672), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092672), _1092674), c_Groups_Ozero__class_Ozero(_1092672))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092672), _1092676), c_Groups_Ozero__class_Ozero(_1092672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092672), _1092674), _1092676)), c_Groups_Ozero__class_Ozero(_1092672))))], (13831 ^ _780119) ^ [_1031606, _1031608, _1031610] : [class_Groups_Oab__group__add(_1031606), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031606), _1031608), _1031610) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031606), _1031608), hAPP(c_Groups_Ouminus__class_Ouminus(_1031606), _1031610)))], (21548 ^ _780119) ^ [_1173056, _1173058, _1173060] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1173056), _1173058), _1173060) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1173056), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1173058, _1173060)), _1173060))], (13344 ^ _780119) ^ [_1022932, _1022934, _1022936] : [class_Groups_Oordered__ab__group__add(_1022932), 13347 ^ _780119 : [(13354 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022932), hAPP(c_Groups_Ouminus__class_Ouminus(_1022932), _1022936)), _1022934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022932), hAPP(c_Groups_Ouminus__class_Ouminus(_1022932), _1022934)), _1022936)))], (13348 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022932), hAPP(c_Groups_Ouminus__class_Ouminus(_1022932), _1022934)), _1022936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022932), hAPP(c_Groups_Ouminus__class_Ouminus(_1022932), _1022936)), _1022934)))]]], (30261 ^ _780119) ^ [_1345461, _1345463, _1345465, _1345467] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345461), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1345461), _1345463), _1345465)), hAPP(c_Int_Onumber__class_Onumber__of(_1345461), _1345467)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1345461), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345461), _1345463), hAPP(c_Int_Onumber__class_Onumber__of(_1345461), _1345467))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345461), _1345465), hAPP(c_Int_Onumber__class_Onumber__of(_1345461), _1345467)))), class_Int_Onumber(_1345461), class_Rings_Osemiring(_1345461)], (22473 ^ _780119) ^ [_1190289, _1190291, _1190293] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_1190289, _1190291, _1190293)) = 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(_1190291)), c_Com_Ocom_Ocom__size(_1190293))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18830 ^ _780119) ^ [] : [-(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))], (36640 ^ _780119) ^ [_1475767, _1475769, _1475771, _1475773] : [c_Fun_Oinj__on(_1475767, tc_fun(tc_fun(_1475767, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1475767, tc_fun(tc_prod(_1475767, _1475767), tc_HOL_Obool), tc_fun(tc_fun(_1475767, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1475767, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1475767, _1475767), tc_HOL_Obool), tc_fun(tc_fun(_1475767, tc_HOL_Obool), tc_HOL_Obool)), _1475767), c_Equiv__Relations_Oquotient(_1475767)), hAPP(hAPP(c_COMBC(_1475767, tc_fun(_1475767, tc_HOL_Obool), tc_fun(_1475767, tc_HOL_Obool)), c_Set_Oinsert(_1475767)), c_Orderings_Obot__class_Obot(tc_fun(_1475767, tc_HOL_Obool))))), _1475769), _1475771), hBOOL(hAPP(hAPP(c_member(_1475767), _1475773), _1475771)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1475767), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1475767, tc_HOL_Obool)), _1475771), hAPP(hAPP(c_Set_Oinsert(_1475767), _1475773), c_Orderings_Obot__class_Obot(tc_fun(_1475767, tc_HOL_Obool))))), _1475769) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1475767, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1475767), _1475771), _1475769)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1475767), hAPP(hAPP(c_Set_Oinsert(_1475767), _1475773), c_Orderings_Obot__class_Obot(tc_fun(_1475767, tc_HOL_Obool)))), _1475769)))], (31795 ^ _780119) ^ [_1373170, _1373172] : [class_Int_Onumber__ring(_1373170), class_Rings_Olinordered__idom(_1373170), 31802 ^ _780119 : [(31809 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1373172), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373170), hAPP(c_Int_Onumber__class_Onumber__of(_1373170), _1373172)), c_Groups_Ozero__class_Ozero(_1373170))))], (31803 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373170), hAPP(c_Int_Onumber__class_Onumber__of(_1373170), _1373172)), c_Groups_Ozero__class_Ozero(_1373170))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1373172), c_Int_OPls)))]]], (27942 ^ _780119) ^ [_1295974, _1295976, _1295978, _1295980] : [class_Orderings_Olinorder(_1295974), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295974), _1295976), _1295978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295974), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1295974), _1295980), _1295976)), _1295978)))], (3582 ^ _780119) ^ [_833965, _833967, _833969, _833971, _833973, _833975] : [-(c_Big__Operators_Olattice_OInf__fin(_833975, _833971, _833967) = c_Big__Operators_Olattice_OInf__fin(_833973, _833969, _833965)), _833975 = _833973, _833971 = _833969, _833967 = _833965], (33537 ^ _780119) ^ [] : [-(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)))], (39621 ^ _780119) ^ [_1551878, _1551880, _1551882, _1551884] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1551878, _1551878)), hAPP(hAPP(c_Product__Type_OPair(_1551878, _1551878), _1551880), _1551882)), c_Transitive__Closure_Otrancl(_1551878, _1551884))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1551878, _1551878)), hAPP(hAPP(c_Product__Type_OPair(_1551878, _1551878), _1551880), _1551882)), c_Transitive__Closure_Ortrancl(_1551878, _1551884))))], (18536 ^ _780119) ^ [_1118241, _1118243] : [class_Int_Oring__char__0(_1118241), hBOOL(hAPP(hAPP(c_member(_1118241), _1118243), c_Int_Oring__1__class_OInts(_1118241))), 18543 ^ _780119 : [(18550 ^ _780119) ^ [] : [_1118243 = c_Groups_Ozero__class_Ozero(_1118241), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118241), _1118243), _1118243) = c_Groups_Ozero__class_Ozero(_1118241))], (18544 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118241), _1118243), _1118243) = c_Groups_Ozero__class_Ozero(_1118241), -(_1118243 = c_Groups_Ozero__class_Ozero(_1118241))]]], (50740 ^ _780119) ^ [_1809241, _1809243, _1809245] : [hBOOL(hAPP(hAPP(c_member(_1809241), _1809245), hAPP(c_List_Oset(_1809241), _1809243))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1809241), _1809243), _1809245)))], (48621 ^ _780119) ^ [_1762949, _1762951, _1762953] : [class_Enum_Oenum(_1762949), class_Enum_Oenum(_1762951), 48628 ^ _780119 : [(48635 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1762951), hAPP(hAPP(c_COMBB(tc_fun(_1762949, tc_HOL_Obool), tc_HOL_Obool, _1762951), c_Enum_Oenum__class_Oenum__all(_1762949)), hAPP(hAPP(c_COMBB(tc_fun(_1762949, tc_prod(_1762951, _1762949)), tc_fun(_1762949, tc_HOL_Obool), _1762951), hAPP(c_COMBB(tc_prod(_1762951, _1762949), tc_HOL_Obool, _1762949), _1762953)), c_Product__Type_OPair(_1762951, _1762949))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1762951, _1762949)), _1762953)))], (48629 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1762951, _1762949)), _1762953)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1762951), hAPP(hAPP(c_COMBB(tc_fun(_1762949, tc_HOL_Obool), tc_HOL_Obool, _1762951), c_Enum_Oenum__class_Oenum__all(_1762949)), hAPP(hAPP(c_COMBB(tc_fun(_1762949, tc_prod(_1762951, _1762949)), tc_fun(_1762949, tc_HOL_Obool), _1762951), hAPP(c_COMBB(tc_prod(_1762951, _1762949), tc_HOL_Obool, _1762949), _1762953)), c_Product__Type_OPair(_1762951, _1762949))))))]]], (51189 ^ _780119) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (6801 ^ _780119) ^ [_891891, _891893, _891895] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891891, tc_HOL_Obool)), _891893), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891891, tc_HOL_Obool)), _891895), _891893))))], (10156 ^ _780119) ^ [_957434, _957436, _957438] : [10158 ^ _780119 : [(10162 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_957434), 10160 ^ [_957434, _957436, _957438]), _957438)))], (10164 ^ _780119) ^ [] : [-(10157 ^ [_957434, _957436, _957438] = 10160 ^ [_957434, _957436, _957438])], (10159 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_957434), 10157 ^ [_957434, _957436, _957438]), _957436)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957434, tc_HOL_Obool)), _957436), _957438) = c_Orderings_Obot__class_Obot(tc_fun(_957434, tc_HOL_Obool)))], (42957 ^ _780119) ^ [_1631655, _1631657, _1631659, _1631661, _1631663] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631655, _1631657)), hAPP(hAPP(c_Product__Type_OPair(_1631655, _1631657), _1631659), _1631661)), hAPP(c_List_Oset(tc_prod(_1631655, _1631657)), _1631663))), -(hAPP(hAPP(c_Map_Omap__of(_1631655, _1631657), _1631663), _1631659) = hAPP(c_Option_Ooption_OSome(_1631657), 42960 ^ [_1631655, _1631657, _1631659, _1631661, _1631663]))], (43274 ^ _780119) ^ [_1639250, _1639252, _1639254] : 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c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12349 ^ _780119) ^ [_1003523, _1003525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003523), _1003525)), _1003523 = _1003525], (33707 ^ _780119) ^ [_1411704, _1411706, _1411708, _1411710, _1411712, _1411714] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411704, tc_fun(_1411706, tc_fun(_1411708, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1411704, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1411706, _1411708), tc_HOL_Obool), tc_fun(_1411706, tc_fun(_1411708, tc_HOL_Obool)), _1411704), hAPP(c_COMBC(_1411706, tc_fun(tc_prod(_1411706, _1411708), tc_HOL_Obool), tc_fun(_1411708, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411708, tc_fun(tc_fun(tc_prod(_1411706, _1411708), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1411706, _1411708), tc_HOL_Obool), tc_fun(_1411708, tc_HOL_Obool)), _1411706), c_COMBC(_1411708, tc_fun(tc_prod(_1411706, _1411708), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411708, tc_prod(_1411706, _1411708)), tc_fun(_1411708, tc_fun(tc_fun(tc_prod(_1411706, _1411708), tc_HOL_Obool), tc_HOL_Obool)), _1411706), hAPP(c_COMBB(tc_prod(_1411706, _1411708), tc_fun(tc_fun(tc_prod(_1411706, _1411708), tc_HOL_Obool), tc_HOL_Obool), _1411708), c_member(tc_prod(_1411706, _1411708)))), c_Product__Type_OPair(_1411706, _1411708))))), _1411710)), _1411712), _1411714)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1411706, _1411708)), hAPP(hAPP(c_Product__Type_OPair(_1411706, _1411708), _1411712), _1411714)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411704, tc_fun(tc_prod(_1411706, _1411708), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1411704, tc_HOL_Obool))), _1411710))))], (13002 ^ _780119) ^ [_1016360, _1016362, _1016364, _1016366, _1016368] : [-(_1016360 = c_Option_Ooption_ONone(_1016362)), -(c_Map_Odom(_1016364, _1016362, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1016364, tc_Option_Ooption(_1016362)), _1016366), _1016368), _1016360)) = hAPP(hAPP(c_Set_Oinsert(_1016364), _1016368), c_Map_Odom(_1016364, _1016362, _1016366)))], (3212 ^ _780119) ^ [_828082, _828084, _828086, _828088, _828090, _828092, _828094, _828096, _828098, _828100, _828102, _828104] : [-(c_Map_Omap__comp(_828104, _828100, _828096, _828092, _828088, _828084) = c_Map_Omap__comp(_828102, _828098, _828094, _828090, _828086, _828082)), _828104 = _828102, _828100 = _828098, _828096 = _828094, _828092 = _828090, _828088 = _828086, _828084 = _828082], (26327 ^ _780119) ^ [_1260606, _1260608, _1260610, _1260612] : [class_Groups_Oordered__ab__group__add__abs(_1260606), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260606), c_Groups_Ozero__class_Ozero(_1260606)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1260608, _1260606), hAPP(hAPP(c_COMBB(_1260606, _1260606, _1260608), c_Groups_Oabs__class_Oabs(_1260606)), _1260610)), _1260612))))], (7272 ^ _780119) ^ [_901981, _901983] : 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[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148613), c_Groups_Ozero__class_Ozero(_1148613)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148613), _1148615), _1148617)))), 20271 ^ _780119 : [(20278 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148613), _1148615), c_Groups_Ozero__class_Ozero(_1148613))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148613), _1148617), c_Groups_Ozero__class_Ozero(_1148613)))], (20272 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148613), c_Groups_Ozero__class_Ozero(_1148613)), _1148615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148613), c_Groups_Ozero__class_Ozero(_1148613)), _1148617))]]], (20256 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148613), c_Groups_Ozero__class_Ozero(_1148613)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148613), _1148615), _1148617))), 20261 ^ _780119 : [(20264 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148613), c_Groups_Ozero__class_Ozero(_1148613)), _1148617)))], (20262 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148613), c_Groups_Ozero__class_Ozero(_1148613)), _1148615)))]], 20265 ^ _780119 : [(20268 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148613), _1148617), c_Groups_Ozero__class_Ozero(_1148613))))], (20266 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148613), _1148615), c_Groups_Ozero__class_Ozero(_1148613))))]]]]], (5064 ^ _780119) ^ [_857606, _857608, _857610, _857612, _857614, _857616] : [-(c_Product__Type_Oprod_Oprod__case(_857616, _857612, _857608) = c_Product__Type_Oprod_Oprod__case(_857614, _857610, _857606)), _857616 = _857614, _857612 = _857610, _857608 = _857606], (45494 ^ _780119) ^ [_1694684, _1694686, _1694688, _1694690, _1694692] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1694684, _1694684)), hAPP(hAPP(c_Product__Type_OPair(_1694684, _1694684), _1694686), _1694688)), _1694690)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694684), tc_List_Olist(_1694684))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694684), tc_List_Olist(_1694684)), hAPP(hAPP(c_List_Olist_OCons(_1694684), _1694686), _1694692)), hAPP(hAPP(c_List_Olist_OCons(_1694684), _1694688), _1694692))), c_List_Olistrel1(_1694684, _1694690))))], (48177 ^ _780119) ^ [_1753632, _1753634, _1753636] : [hBOOL(hAPP(c_List_Odistinct(_1753632), _1753634)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1753632)), c_Enum_On__lists(_1753632, _1753636, _1753634))))], (6105 ^ _780119) ^ [_877391, _877393, _877395, _877397] : [-(hBOOL(hAPP(hAPP(c_member(_877391), _877393), _877395))), -(hBOOL(hAPP(hAPP(c_member(_877391), _877393), _877397))), 6112 ^ _780119 : [(6119 ^ _780119) ^ [] : [_877395 = _877397, -(hAPP(hAPP(c_Set_Oinsert(_877391), _877393), _877395) = hAPP(hAPP(c_Set_Oinsert(_877391), _877393), _877397))], (6113 ^ _780119) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_877391), _877393), _877395) = hAPP(hAPP(c_Set_Oinsert(_877391), _877393), _877397), -(_877395 = _877397)]]], (11814 ^ _780119) ^ [_992717, _992719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992717), _992719)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992719), _992717)), -(_992717 = _992719)], (40020 ^ _780119) ^ [_1561253, _1561255, _1561257] : [-(hAPP(c_Relation_Oconverse(_1561253, _1561255), hAPP(c_Relation_Oconverse(_1561255, _1561253), _1561257)) = _1561257)], (17057 ^ _780119) ^ [_1089952, _1089954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1089952), _1089954)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1089952), _1089954) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40242 ^ _780119) ^ [_1567094, _1567096, _1567098] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567094, _1567094)), hAPP(hAPP(c_Product__Type_OPair(_1567094, _1567094), _1567096), _1567096)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1567094, _1567094), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1567098))))], (50518 ^ _780119) ^ [_1805067, _1805069, _1805071] : [c_List_Oreplicate(_1805067, _1805069, _1805071) = c_List_Olist_ONil(_1805067), -(_1805069 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51343 ^ _780119) ^ [] : [-(class_HOL_Oequal(tc_Com_Ostate))], (12285 ^ _780119) ^ [_1002113, _1002115, _1002117, _1002119, _1002121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002113), _1002115)), 12288 ^ _780119 : [(12295 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002119), 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), _1002115), _1002113)), _1002117)), _1002121))), -(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), _1002113), _1002117)), _1002119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002115), _1002117)), _1002121))))], (12289 ^ _780119) ^ [] : [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), _1002113), _1002117)), _1002119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002115), _1002117)), _1002121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002119), 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), _1002115), _1002113)), _1002117)), _1002121))))]]], (23105 ^ _780119) ^ [_1202115, _1202117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202115)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202117)))), 23108 ^ _780119 : [(23111 ^ _780119) ^ [] : [-(_1202117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23109 ^ _780119) ^ [] : [-(_1202115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (34445 ^ _780119) ^ [_1426482, _1426484] : [-(c_Divides_Odivmod__nat(_1426482, _1426484) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1426482, _1426484)))], (21588 ^ _780119) ^ [_1173998, _1174000, _1174002] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1173998, tc_HOL_Obool)), _1174000), hAPP(c_Set_OPow(_1173998), _1174002))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1173998, tc_HOL_Obool)), _1174000), _1174002)))], (38730 ^ _780119) ^ [_1530392, _1530394, _1530396, _1530398, _1530400, _1530402] : [-(hAPP(hAPP(c_Fun_Ocomp(_1530392, _1530394, _1530396, _1530398), _1530400), _1530402) = hAPP(_1530398, hAPP(_1530400, _1530402)))], (11285 ^ _780119) ^ [_981404, _981406, _981408] : [class_Lattices_Olattice(_981404), hBOOL(hAPP(c_Finite__Set_Ofinite(_981404), _981406)), -(hBOOL(hAPP(hAPP(c_member(_981404), _981408), _981406))), -(_981406 = c_Orderings_Obot__class_Obot(tc_fun(_981404, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_981404, hAPP(hAPP(c_Set_Oinsert(_981404), _981408), _981406)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981404), _981408), c_Big__Operators_Olattice__class_OInf__fin(_981404, _981406)))], (27091 ^ _780119) ^ [_1278423, _1278425] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278423), _1278425)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1278423, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1278423, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1278423, tc_HOL_Obool), tc_fun(_1278423, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1278423, tc_HOL_Obool))), _1278425)))))], (9758 ^ _780119) ^ [_949416, _949418, _949420, _949422] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949416, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949416, tc_HOL_Obool)), _949418), _949420)), _949422) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949416, tc_HOL_Obool)), _949418), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949416, tc_HOL_Obool)), _949420), _949422)))], (29837 ^ _780119) ^ [_1336481, _1336483, _1336485, _1336487, _1336489, _1336491] : [hBOOL(hAPP(hAPP(c_member(_1336481), _1336483), _1336485)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1336481, tc_fun(_1336487, tc_HOL_Obool)), _1336485), hAPP(hAPP(c_COMBB(tc_fun(_1336487, tc_HOL_Obool), tc_fun(_1336487, tc_HOL_Obool), _1336481), hAPP(c_Set_Oinsert(_1336487), _1336489)), _1336491)) = hAPP(hAPP(c_Set_Oinsert(_1336487), _1336489), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1336481, tc_fun(_1336487, tc_HOL_Obool)), _1336485), _1336491)))], (43958 ^ _780119) ^ [_1658845, _1658847, _1658849] : [-(hAPP(hAPP(c_List_Onth(_1658845), hAPP(hAPP(c_List_Olist_OCons(_1658845), _1658847), _1658849)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1658847)], (18362 ^ _780119) ^ [_1115126, _1115128, _1115130] : [-(c_Option_Ooption_Ooption__size(_1115126, _1115128, hAPP(c_Option_Ooption_OSome(_1115126), _1115130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1115128, _1115130)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16887 ^ _780119) ^ [_1087049, _1087051] : [class_Power_Opower(_1087049), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1087049), _1087051), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1087049))], (39843 ^ _780119) ^ [_1557222, _1557224, _1557226, _1557228] : [-(hBOOL(hAPP(hAPP(c_member(_1557222), _1557224), hAPP(c_Relation_ODomain(_1557222, _1557222), _1557226)))), 39846 ^ _780119 : [(39853 ^ _780119) ^ [] : [_1557224 = _1557228, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1557222, _1557222)), hAPP(hAPP(c_Product__Type_OPair(_1557222, _1557222), _1557224), _1557228)), c_Transitive__Closure_Ortrancl(_1557222, _1557226))))], (39847 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1557222, _1557222)), hAPP(hAPP(c_Product__Type_OPair(_1557222, _1557222), _1557224), _1557228)), c_Transitive__Closure_Ortrancl(_1557222, _1557226))), -(_1557224 = _1557228)]]], (37964 ^ _780119) ^ [_1510727, _1510729, _1510731, _1510733] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1510727), _1510729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1510727, _1510727), tc_HOL_Obool)), _1510731), hAPP(hAPP(c_Product__Type_OSigma(_1510727, _1510727), _1510729), hAPP(c_COMBK(tc_fun(_1510727, tc_HOL_Obool), _1510727), _1510729)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1510727, tc_HOL_Obool)), _1510733), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510727), _1510729), _1510731))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1510727), _1510733)))], (5753 ^ _780119) ^ [_871131, _871133] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871131, _871133, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871131), tc_HOL_Obool))))], (38222 ^ _780119) ^ [_1518807, _1518809, _1518811] : [-(c_Relation_Orefl__on(_1518807, _1518809, _1518811)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518807, _1518807), tc_HOL_Obool)), _1518811), hAPP(hAPP(c_Product__Type_OSigma(_1518807, _1518807), _1518809), hAPP(c_COMBK(tc_fun(_1518807, tc_HOL_Obool), _1518807), _1518809)))), 38228 ^ _780119 : [(38231 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1518807, _1518807)), hAPP(hAPP(c_Product__Type_OPair(_1518807, _1518807), 38227 ^ [_1518807, _1518809, _1518811]), 38227 ^ [_1518807, _1518809, _1518811])), _1518811))], (38229 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1518807), 38227 ^ [_1518807, _1518809, _1518811]), _1518809)))]]], (51487 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (49723 ^ _780119) ^ [_1788108, _1788110, _1788112] : [49724 ^ _780119 : [(49725 ^ _780119) ^ [_1788185, _1788187] : [_1788112 = hAPP(hAPP(c_List_Oappend(_1788108), _1788187), hAPP(hAPP(c_List_Olist_OCons(_1788108), _1788110), _1788185))]], -(hBOOL(hAPP(hAPP(c_member(_1788108), _1788110), hAPP(c_List_Oset(_1788108), _1788112))))], (37123 ^ _780119) ^ [_1488700, _1488702, _1488704] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1488700, _1488702, _1488704, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1488702)], (41555 ^ _780119) ^ [_1598845, _1598847, _1598849, _1598851] : [hBOOL(hAPP(hAPP(c_member(_1598845), _1598847), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1598845, tc_HOL_Obool), _1598849))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1598845, tc_HOL_Obool)), _1598851), _1598849)), -(hBOOL(hAPP(hAPP(c_member(_1598845), _1598847), _1598851)))], (37671 ^ _780119) ^ [_1501986, _1501988, _1501990] : [-(hAPP(c_Set_Oimage(tc_prod(_1501986, _1501988), _1501986, c_Product__Type_Ofst(_1501986, _1501988)), _1501990) = hAPP(c_Relation_ODomain(_1501986, _1501988), _1501990))], (24723 ^ _780119) ^ [_1232900, _1232902] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1232900, _1232902)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1232902), _1232900))], (37606 ^ _780119) ^ [_1500580, _1500582, _1500584, _1500586] : [37607 ^ _780119 : [(37608 ^ _780119) ^ [_1500634] : [hBOOL(hAPP(hAPP(_1500584, _1500634), _1500586))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1500580, _1500582, _1500584), _1500586)))], (336 ^ _780119) ^ [_785341, _785343, _785345, _785347] : [-(c_Nitpick_Owf_H(_785345, _785341)), c_Nitpick_Owf_H(_785347, _785343), _785347 = _785345, _785343 = _785341], (33887 ^ _780119) ^ [_1415792, _1415794, _1415796, _1415798, _1415800, _1415802, _1415804] : [hBOOL(hAPP(hAPP(c_member(_1415792), _1415794), hAPP(hAPP(_1415796, _1415798), _1415800))), -(hBOOL(hAPP(hAPP(c_member(_1415792), _1415794), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1415802, _1415804, tc_fun(_1415792, tc_HOL_Obool)), _1415796), hAPP(hAPP(c_Product__Type_OPair(_1415802, _1415804), _1415798), _1415800)))))], (45892 ^ _780119) ^ [_1704317, _1704319, _1704321] : [hBOOL(hAPP(c_List_Odistinct(_1704317), hAPP(c_List_Orotate(_1704317, _1704319), _1704321))), -(hBOOL(hAPP(c_List_Odistinct(_1704317), _1704321)))], (23296 ^ _780119) ^ [_1205850, _1205852, _1205854, _1205856, _1205858] : [hBOOL(hAPP(hAPP(c_member(_1205850), _1205852), c_SetInterval_Oord_OgreaterThanLessThan(_1205850, _1205854, _1205856, _1205858))), 23299 ^ _780119 : [(23302 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1205854, _1205852), _1205858)))], (23300 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1205854, _1205856), _1205852)))]]], (42974 ^ _780119) ^ [_1632034] : [c_List_Onat__list(_1632034), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1632034)))], (5967 ^ _780119) ^ [_875014, _875016, _875018] : [hBOOL(hAPP(_875018, _875016)), -(hBOOL(hAPP(hAPP(c_member(_875014), _875016), _875018)))], (6288 ^ _780119) ^ [_881012, _881014, _881016] : [-(hAPP(c_Set_Oimage(_881012, _881014, _881016), c_Orderings_Obot__class_Obot(tc_fun(_881012, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_881014, tc_HOL_Obool)))], (1140 ^ _780119) ^ [_797093, _797095] : [-(class_Rings_Oordered__ring(_797093)), _797095 = _797093, class_Rings_Oordered__ring(_797095)], (25889 ^ _780119) ^ [_1252607, _1252609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252607)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1252607, _1252609)))], (43465 ^ _780119) ^ [_1645765, _1645767, _1645769, _1645771] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645765), tc_List_Olist(_1645765))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645765), tc_List_Olist(_1645765)), _1645769), _1645771)), c_List_Olistrel(_1645765, _1645767))), -(c_List_Olistrelp(_1645765, hAPP(hAPP(c_COMBC(_1645765, tc_fun(tc_prod(_1645765, _1645765), tc_HOL_Obool), tc_fun(_1645765, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1645765, tc_fun(tc_fun(tc_prod(_1645765, _1645765), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1645765, _1645765), tc_HOL_Obool), tc_fun(_1645765, tc_HOL_Obool)), _1645765), c_COMBC(_1645765, tc_fun(tc_prod(_1645765, _1645765), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1645765, tc_prod(_1645765, _1645765)), tc_fun(_1645765, tc_fun(tc_fun(tc_prod(_1645765, _1645765), tc_HOL_Obool), tc_HOL_Obool)), _1645765), hAPP(c_COMBB(tc_prod(_1645765, _1645765), tc_fun(tc_fun(tc_prod(_1645765, _1645765), tc_HOL_Obool), tc_HOL_Obool), _1645765), c_member(tc_prod(_1645765, _1645765)))), c_Product__Type_OPair(_1645765, _1645765)))), _1645767), _1645769, _1645771))], (42673 ^ _780119) ^ [_1624920] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1624920)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1624920), tc_HOL_Obool))))], (48775 ^ _780119) ^ [_1766289, _1766291, _1766293, _1766295] : [48777 ^ _780119 : [(48780 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48776 ^ [_1766289, _1766291, _1766293, _1766295]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766291)), _1766293))))], (48782 ^ _780119) ^ [] : [hBOOL(hAPP(_1766295, hAPP(hAPP(c_List_Onth(_1766291), _1766293), 48776 ^ [_1766289, _1766291, _1766293, _1766295])))], (48778 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48776 ^ [_1766289, _1766291, _1766293, _1766295]), _1766289)))]], 48785 ^ _780119 : [(48788 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1766295, hAPP(hAPP(c_List_Onth(_1766291), _1766293), _1766289))))], (48786 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1766289), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766291)), _1766293))))]], -(c_List_OtakeWhile(_1766291, _1766295, _1766293) = hAPP(hAPP(c_List_Otake(_1766291), _1766289), _1766293))], (51329 ^ _780119) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (45664 ^ _780119) ^ [_1699209, _1699211, _1699213] : [hAPP(hAPP(c_List_Odrop(_1699209), _1699211), _1699213) = c_List_Olist_ONil(_1699209), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699209)), _1699213)), _1699211)))], (50666 ^ _780119) ^ [_1807646, _1807648, _1807650, _1807652] : [-(hAPP(hAPP(c_List_Oappend(_1807646), c_List_Oreplicate(_1807646, _1807648, _1807650)), hAPP(hAPP(c_List_Olist_OCons(_1807646), _1807650), _1807652)) = hAPP(hAPP(c_List_Olist_OCons(_1807646), _1807650), hAPP(hAPP(c_List_Oappend(_1807646), c_List_Oreplicate(_1807646, _1807648, _1807650)), _1807652)))], (44632 ^ _780119) ^ [_1674313, _1674315, _1674317, _1674319] : [-(c_Map_Omap__upds(_1674313, _1674315, _1674317, _1674319, c_List_Olist_ONil(_1674315)) = _1674317)], (26871 ^ _780119) ^ [_1271652, _1271654] : [class_Groups_Oordered__ab__group__add__abs(_1271652), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271652), hAPP(c_Groups_Ouminus__class_Ouminus(_1271652), hAPP(c_Groups_Oabs__class_Oabs(_1271652), _1271654))), c_Groups_Ozero__class_Ozero(_1271652))))], (30083 ^ _780119) ^ [_1342364] : [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), _1342364))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1342364) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1342364)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (33945 ^ _780119) ^ [_1417068, _1417070, _1417072, _1417074, _1417076, _1417078] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417068, tc_fun(_1417070, tc_HOL_Obool))), _1417072), _1417074), _1417076), _1417078)), -(hBOOL(hAPP(hAPP(_1417072, _1417076), _1417078)))], (34871 ^ _780119) ^ [_1434786, _1434788, _1434790, _1434792, _1434794, _1434796] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1434786, _1434788), _1434788, _1434790), hAPP(hAPP(c_COMBB(_1434792, tc_fun(_1434788, _1434790), tc_prod(_1434786, _1434788)), _1434794), hAPP(hAPP(c_COMBB(_1434786, _1434792, tc_prod(_1434786, _1434788)), _1434796), c_Product__Type_Ofst(_1434786, _1434788)))), c_Product__Type_Osnd(_1434786, _1434788)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1434786, _1434788, _1434790), hAPP(hAPP(c_COMBB(_1434792, tc_fun(_1434788, _1434790), _1434786), _1434794), _1434796)))], (22791 ^ _780119) ^ [] : [-(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)))], (22233 ^ _780119) ^ [_1185909] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1185909, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47033 ^ _780119) ^ [_1728138] : [class_Orderings_Olinorder(_1728138), -(c_List_Olinorder__class_Osorted(_1728138, c_List_Olist_ONil(_1728138)))], (12661 ^ _780119) ^ [_1009572, _1009574, _1009576, _1009578, _1009580] : [-(hBOOL(hAPP(hAPP(c_member(_1009572), _1009574), _1009576))), -(hAPP(c_Map_Orestrict__map(_1009572, _1009578, _1009580, _1009576), _1009574) = c_Option_Ooption_ONone(_1009578))], (6757 ^ _780119) ^ [_890997, _890999, _891001] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890997, tc_HOL_Obool)), _890999), _891001) = c_Orderings_Obot__class_Obot(tc_fun(_890997, tc_HOL_Obool))), _890999 = c_Orderings_Obot__class_Obot(tc_fun(_890997, tc_HOL_Obool)), _891001 = c_Orderings_Obot__class_Obot(tc_fun(_890997, tc_HOL_Obool))], (44254 ^ _780119) ^ [_1666665, _1666667] : [_1666665 = _1666667, -(hAPP(c_Code__Numeral_Oof__nat, _1666665) = hAPP(c_Code__Numeral_Oof__nat, _1666667))], (37680 ^ _780119) ^ [_1502210, _1502212, _1502214, _1502216] : [37681 ^ _780119 : [(37682 ^ _780119) ^ [_1502285] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1502210, _1502214)), hAPP(hAPP(c_Product__Type_OPair(_1502210, _1502214), _1502212), _1502285)), _1502216))]], -(hBOOL(hAPP(hAPP(c_member(_1502210), _1502212), hAPP(c_Relation_ODomain(_1502210, _1502214), _1502216))))], (42473 ^ _780119) ^ [_1619907, _1619909, _1619911, _1619913, _1619915, _1619917] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1619907, _1619909, _1619911), _1619913), hAPP(hAPP(c_Product__Type_OPair(_1619907, _1619909), _1619915), _1619917)) = hAPP(hAPP(_1619913, _1619915), _1619917))], (13180 ^ _780119) ^ [_1020180, _1020182] : [_1020180 = _1020182, -(hAPP(c_Nat_OSuc, _1020180) = hAPP(c_Nat_OSuc, _1020182))], (38906 ^ _780119) ^ [_1534453, _1534455, _1534457, _1534459, _1534461, _1534463, _1534465] : [class_Groups_Oab__semigroup__mult(_1534453), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534455), _1534457)), c_Fun_Oinj__on(_1534455, _1534459, _1534461, _1534457), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1534453, _1534459, c_Groups_Otimes__class_Otimes(_1534453)), _1534463), _1534465), hAPP(c_Set_Oimage(_1534455, _1534459, _1534461), _1534457)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1534453, _1534455, c_Groups_Otimes__class_Otimes(_1534453)), hAPP(c_Fun_Ocomp(_1534459, _1534453, _1534455, _1534463), _1534461)), _1534465), _1534457))], (22334 ^ _780119) ^ [_1187573, _1187575, _1187577] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1187573, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1187575), _1187577)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1187575), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1187573), _1187575), _1187577))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1187573, _1187575)))], (49281 ^ _780119) ^ [_1777545, _1777547, _1777549] : [-(hBOOL(hAPP(hAPP(c_member(_1777545), _1777547), hAPP(c_List_Oset(_1777545), _1777549)))), -(hAPP(c_List_OremoveAll(_1777545, _1777547), _1777549) = _1777549)], (44662 ^ _780119) ^ [_1674855, _1674857, _1674859] : [-(hAPP(hAPP(c_List_Omap(_1674855, _1674857), _1674859), c_List_Olist_ONil(_1674855)) = c_List_Olist_ONil(_1674857))], (46141 ^ _780119) ^ [_1709528, _1709530, _1709532, _1709534, _1709536] : [-(c_Map_Omap__upds(_1709528, _1709530, _1709532, _1709534, _1709536) = hAPP(c_List_Ofoldl(tc_fun(_1709528, tc_Option_Ooption(_1709530)), tc_prod(_1709528, _1709530), hAPP(hAPP(c_COMBB(tc_fun(_1709528, tc_fun(_1709530, tc_fun(_1709528, tc_Option_Ooption(_1709530)))), tc_fun(tc_prod(_1709528, _1709530), tc_fun(_1709528, tc_Option_Ooption(_1709530))), tc_fun(_1709528, tc_Option_Ooption(_1709530))), c_Product__Type_Oprod_Oprod__case(_1709528, _1709530, tc_fun(_1709528, tc_Option_Ooption(_1709530)))), hAPP(hAPP(c_COMBC(tc_fun(_1709528, tc_Option_Ooption(_1709530)), tc_fun(_1709530, tc_Option_Ooption(_1709530)), tc_fun(_1709528, tc_fun(_1709530, tc_fun(_1709528, tc_Option_Ooption(_1709530))))), hAPP(hAPP(c_COMBB(tc_fun(_1709528, tc_fun(tc_fun(_1709530, tc_Option_Ooption(_1709530)), tc_fun(_1709530, tc_fun(_1709528, tc_Option_Ooption(_1709530))))), tc_fun(tc_fun(_1709530, tc_Option_Ooption(_1709530)), tc_fun(_1709528, tc_fun(_1709530, tc_fun(_1709528, tc_Option_Ooption(_1709530))))), tc_fun(_1709528, tc_Option_Ooption(_1709530))), c_COMBC(_1709528, tc_fun(_1709530, tc_Option_Ooption(_1709530)), tc_fun(_1709530, tc_fun(_1709528, tc_Option_Ooption(_1709530))))), hAPP(hAPP(c_COMBB(tc_fun(_1709528, tc_fun(tc_Option_Ooption(_1709530), tc_fun(_1709528, tc_Option_Ooption(_1709530)))), tc_fun(_1709528, tc_fun(tc_fun(_1709530, tc_Option_Ooption(_1709530)), tc_fun(_1709530, tc_fun(_1709528, tc_Option_Ooption(_1709530))))), tc_fun(_1709528, tc_Option_Ooption(_1709530))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1709530), tc_fun(_1709528, tc_Option_Ooption(_1709530))), tc_fun(tc_fun(_1709530, tc_Option_Ooption(_1709530)), tc_fun(_1709530, tc_fun(_1709528, tc_Option_Ooption(_1709530)))), _1709528), c_COMBB(tc_Option_Ooption(_1709530), tc_fun(_1709528, tc_Option_Ooption(_1709530)), _1709530))), c_Fun_Ofun__upd(_1709528, tc_Option_Ooption(_1709530))))), c_Option_Ooption_OSome(_1709530))), _1709532), hAPP(hAPP(c_List_Ozip(_1709528, _1709530), _1709534), _1709536)))], (16398 ^ _780119) ^ [_1078981] : [class_Rings_Olinordered__semidom(_1078981), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078981), c_Groups_Ozero__class_Ozero(_1078981)), c_Groups_Oone__class_Oone(_1078981))))], (32511 ^ _780119) ^ [_1386155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1386155), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1386155)), c_Int_OPls)))], (36780 ^ _780119) ^ [_1479268, _1479270, _1479272, _1479274, _1479276] : [-(hAPP(c_Set_Ovimage(_1479268, _1479270, _1479272), hAPP(hAPP(c_Set_Oinsert(_1479270), _1479274), _1479276)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1479268, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1479268, _1479270, _1479272), hAPP(hAPP(c_Set_Oinsert(_1479270), _1479274), c_Orderings_Obot__class_Obot(tc_fun(_1479270, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1479268, _1479270, _1479272), _1479276)))], (50346 ^ _780119) ^ [_1800999, _1801001] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1800999), _1801001))), -(c_Lazy__Sequence_Osmall__lazy_H(_1800999, _1801001) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1801001), c_Lazy__Sequence_Osmall__lazy_H(_1800999, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1801001), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (32439 ^ _780119) ^ [_1384925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384925), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1384925)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (42302 ^ _780119) ^ [_1616380, _1616382] : [-(c_Nitpick_Oinverse__frac(_1616380, _1616382) = hAPP(hAPP(c_Nitpick_Ofrac(_1616380), hAPP(c_Nitpick_Odenom(_1616380), _1616382)), hAPP(c_Nitpick_Onum(_1616380), _1616382)))], (2766 ^ _780119) ^ [_821235, _821237, _821239, _821241, _821243, _821245] : [-(c_Com_Ocom_OCond(_821245, _821241, _821237) = c_Com_Ocom_OCond(_821243, _821239, _821235)), _821245 = _821243, _821241 = _821239, _821237 = _821235], (35462 ^ _780119) ^ [_1449537, _1449539, _1449541, _1449543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1449537), _1449543)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1449541), _1449539))), -(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), _1449537), _1449539)), 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), _1449541), _1449543)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (4450 ^ _780119) ^ [_847437, _847439] : [_847439 = _847437, -(c_Int_OBit0(_847439) = c_Int_OBit0(_847437))], (36585 ^ _780119) ^ [_1474626, _1474628, _1474630, _1474632, _1474634] : [-(c_Fun_Oinj__on(_1474626, _1474628, _1474630, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474626, tc_HOL_Obool)), _1474632), _1474634))), c_Fun_Oinj__on(_1474626, _1474628, _1474630, _1474632), c_Fun_Oinj__on(_1474626, _1474628, _1474630, _1474634), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474628, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1474626, _1474628, _1474630), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474626, tc_HOL_Obool)), _1474632), _1474634))), hAPP(c_Set_Oimage(_1474626, _1474628, _1474630), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474626, tc_HOL_Obool)), _1474634), _1474632))) = c_Orderings_Obot__class_Obot(tc_fun(_1474628, tc_HOL_Obool))], (9690 ^ _780119) ^ [_947736, _947738, _947740, _947742] : [hBOOL(hAPP(hAPP(c_member(_947736), _947738), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947736, tc_HOL_Obool)), _947740), _947742))), 9693 ^ _780119 : [(9696 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_947736), _947738), _947742)))], (9694 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_947736), _947738), _947740)))]]], (44676 ^ _780119) ^ [_1675128, _1675130] : [-(c_List_Osublist(_1675128, c_List_Olist_ONil(_1675128), _1675130) = c_List_Olist_ONil(_1675128))], (8060 ^ _780119) ^ [_917900, _917902] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_917900, _917902)))), hBOOL(hAPP(c_Com_OWT, _917900)), hBOOL(hAPP(c_Com_OWT, _917902))], (46672 ^ _780119) ^ [_1720995, _1720997, _1720999, _1721001, _1721003] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720995)), hAPP(c_List_Ofilter(_1720995, _1720997), hAPP(hAPP(c_List_Omap(_1720999, _1720995), _1721001), _1721003))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720999)), hAPP(c_List_Ofilter(_1720999, hAPP(c_Fun_Ocomp(_1720995, tc_HOL_Obool, _1720999, _1720997), _1721001)), _1721003)))], (33989 ^ _780119) ^ [_1417989, _1417991, _1417993] : [hBOOL(hAPP(_1417989, 33990 ^ [_1417989, _1417991, _1417993])), 33993 ^ _780119 : [(33994 ^ _780119) ^ [_1418100, _1418102] : [-(hBOOL(hAPP(_1417989, hAPP(hAPP(c_Product__Type_OPair(_1417991, _1417993), _1418102), _1418100))))]]], (44322 ^ _780119) ^ [_1667987, _1667989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1667987)), hAPP(c_Code__Numeral_Oof__nat, _1667989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667987), _1667989)))], (45736 ^ _780119) ^ [_1700950, _1700952, _1700954, _1700956, _1700958] : [-(hAPP(hAPP(c_List_Oappend(_1700950), _1700952), _1700954) = hAPP(hAPP(c_List_Oappend(_1700950), _1700956), _1700958)), 45739 ^ _780119 : [(45742 ^ _780119) ^ [] : [_1700952 = hAPP(hAPP(c_List_Otake(_1700950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700950)), _1700952)), _1700956), _1700954 = hAPP(hAPP(c_List_Oappend(_1700950), hAPP(hAPP(c_List_Odrop(_1700950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700950)), _1700952)), _1700956)), _1700958)], (45740 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700950)), _1700952)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700950)), _1700956))))]], 45747 ^ _780119 : [(45750 ^ _780119) ^ [] : [hAPP(hAPP(c_List_Otake(_1700950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700950)), _1700956)), _1700952) = _1700956, hAPP(hAPP(c_List_Oappend(_1700950), hAPP(hAPP(c_List_Odrop(_1700950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700950)), _1700956)), _1700952)), _1700954) = _1700958], (45748 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700950)), _1700952)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700950)), _1700956)))]]], (29489 ^ _780119) ^ [_1327548, _1327550, _1327552, _1327554, _1327556] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1327548, tc_fun(_1327550, tc_HOL_Obool)), _1327552), _1327554), _1327556)), 29493 ^ _780119 : [(29496 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1327554, 29492 ^ [_1327548, _1327550, _1327552, _1327554, _1327556]), _1327556)))], (29494 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327548), 29492 ^ [_1327548, _1327550, _1327552, _1327554, _1327556]), _1327552)))]]], (11969 ^ _780119) ^ [_995745, _995747, _995749, _995751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995745), _995747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995749), _995751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995745), _995749)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995747), _995751))))], (48936 ^ _780119) ^ [_1770016, _1770018, _1770020, _1770022, _1770024] : [-(c_List_Olist__all2(_1770016, _1770018, _1770020, _1770022, _1770024)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770016)), _1770022) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770018)), _1770024), 48942 ^ _780119 : [(48945 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1770016, _1770018, tc_HOL_Obool), _1770020), 48941 ^ [_1770016, _1770018, _1770020, _1770022, _1770024]))], (48943 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1770016, _1770018)), 48941 ^ [_1770016, _1770018, _1770020, _1770022, _1770024]), hAPP(c_List_Oset(tc_prod(_1770016, _1770018)), hAPP(hAPP(c_List_Ozip(_1770016, _1770018), _1770022), _1770024)))))]]], (46499 ^ _780119) ^ [_1717288, _1717290, _1717292] : [-(c_List_Obutlast(_1717288, hAPP(hAPP(c_List_Odrop(_1717288), _1717290), _1717292)) = hAPP(hAPP(c_List_Odrop(_1717288), _1717290), c_List_Obutlast(_1717288, _1717292)))], (47234 ^ _780119) ^ [_1731939, _1731941, _1731943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1731939), _1731941)), _1731943)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1731939, _1731943)), _1731941) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1731939), _1731941))], (16654 ^ _780119) ^ [_1083341, _1083343, _1083345, _1083347] : [class_Groups_Ocomm__monoid__add(_1083341), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1083343), _1083345))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083343, _1083341), _1083347), _1083345) = c_Groups_Ozero__class_Ozero(_1083341))], (11437 ^ _780119) ^ [_985082, _985084, _985086] : [class_Rings_Olinordered__idom(_985082), -(_985084 = _985086), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985082), _985084), _985086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985082), _985086), _985084)))], (10322 ^ _780119) ^ [_961583, _961585, _961587, _961589] : [hBOOL(hAPP(hAPP(c_member(_961583), _961585), _961587)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961583, tc_HOL_Obool)), _961587), hAPP(hAPP(c_Set_Oinsert(_961583), _961585), _961589)) = hAPP(hAPP(c_Set_Oinsert(_961583), _961585), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961583, tc_HOL_Obool)), _961587), _961589)))], (48059 ^ _780119) ^ [_1750968, _1750970] : [-(c_List_OdropWhile(_1750968, _1750970, c_List_Olist_ONil(_1750968)) = c_List_Olist_ONil(_1750968))], (28198 ^ _780119) ^ [_1301295] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1301295), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1301295)], (7104 ^ _780119) ^ [_897450, _897452] : [hAPP(c_Com_Ocom_OBODY, _897450) = hAPP(c_Com_Ocom_OBODY, _897452), -(_897450 = _897452)], (41417 ^ _780119) ^ [_1595798, _1595800, _1595802, _1595804, _1595806] : [-(_1595798 = c_Orderings_Obot__class_Obot(tc_fun(_1595800, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595800, tc_fun(_1595802, tc_HOL_Obool)), _1595798), hAPP(hAPP(c_COMBC(_1595800, tc_fun(_1595802, tc_HOL_Obool), tc_fun(_1595802, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1595802, tc_HOL_Obool), tc_fun(tc_fun(_1595802, tc_HOL_Obool), tc_fun(_1595802, tc_HOL_Obool)), _1595800), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1595802, tc_HOL_Obool))), _1595804)), _1595806)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1595802, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595800, tc_fun(_1595802, tc_HOL_Obool)), _1595798), _1595804)), _1595806))], (51129 ^ _780119) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (8138 ^ _780119) ^ [_919777, _919779, _919781, _919783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919777, tc_HOL_Obool)), _919779), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_919777, tc_HOL_Obool)), _919781), _919783))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919777, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919777, tc_HOL_Obool)), _919779), _919781)), _919783)))], (10464 ^ _780119) ^ [_964882, _964884, _964886, _964888] : [_964886 = _964888, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_964882, _964884, hAPP(hAPP(c_Set_Oinsert(_964882), _964886), c_Orderings_Obot__class_Obot(tc_fun(_964882, tc_HOL_Obool)))), _964888)))], (43561 ^ _780119) ^ [_1648247, _1648249, _1648251, _1648253, _1648255, _1648257] : [class_Orderings_Olinorder(_1648247), 43564 ^ _780119 : [(43571 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1648247), hAPP(_1648249, _1648251)), hAPP(_1648249, _1648253)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1648255, _1648247, _1648249), _1648251), hAPP(hAPP(c_List_Olist_OCons(_1648255), _1648253), _1648257)) = hAPP(hAPP(c_List_Olist_OCons(_1648255), _1648253), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1648255, _1648247, _1648249), _1648251), _1648257)))], (43565 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1648247), hAPP(_1648249, _1648251)), hAPP(_1648249, _1648253))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1648255, _1648247, _1648249), _1648251), hAPP(hAPP(c_List_Olist_OCons(_1648255), _1648253), _1648257)) = hAPP(hAPP(c_List_Olist_OCons(_1648255), _1648251), hAPP(hAPP(c_List_Olist_OCons(_1648255), _1648253), _1648257)))]]], (9928 ^ _780119) ^ [_953046, _953048, _953050, _953052] : [class_Lattices_Osemilattice__inf(_953046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953046), _953048), _953050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953046), _953048), _953052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953046), _953048), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_953046), _953050), _953052))))], (18089 ^ _780119) ^ [_1109593, _1109595, _1109597, _1109599] : [class_Groups_Ocomm__monoid__add(_1109593), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109595), _1109597)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1109595, _1109593), _1109599), _1109597) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1109593, _1109595, c_Groups_Oplus__class_Oplus(_1109593)), _1109599), c_Groups_Ozero__class_Ozero(_1109593)), _1109597))], (24449 ^ _780119) ^ [_1227901, _1227903, _1227905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227901)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1227903), _1227905)), 24456 ^ _780119 : [(24457 ^ _780119) ^ [_1228097] : [24459 ^ _780119 : [(24463 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24461 ^ [_1227901, _1227903, _1227905, _1228097]), _1227905)))], (24465 ^ _780119) ^ [] : [-(_1228097 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24461 ^ [_1227901, _1227903, _1227905, _1228097]), 24458 ^ [_1227901, _1227903, _1227905, _1228097]))], (24460 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24458 ^ [_1227901, _1227903, _1227905, _1228097]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1227901))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228097), _1227903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228097), _1227901)), _1227903)))]]], (35505 ^ _780119) ^ [_1450572, _1450574, _1450576] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1450572), _1450574), _1450576) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1450572, tc_fun(tc_fun(_1450572, tc_HOL_Obool), tc_HOL_Obool)), _1450574), hAPP(hAPP(c_COMBC(_1450572, tc_fun(tc_fun(_1450572, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1450572, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450572, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1450572, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1450572, tc_HOL_Obool), tc_HOL_Obool)), _1450572), c_Set_Oinsert(tc_fun(_1450572, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1450572, tc_HOL_Obool), tc_fun(_1450572, tc_HOL_Obool), _1450572), c_Relation_OImage(_1450572, _1450572, _1450576)), hAPP(hAPP(c_COMBC(_1450572, tc_fun(_1450572, tc_HOL_Obool), tc_fun(_1450572, tc_HOL_Obool)), c_Set_Oinsert(_1450572)), c_Orderings_Obot__class_Obot(tc_fun(_1450572, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1450572, tc_HOL_Obool), tc_HOL_Obool)))))], (22340 ^ _780119) ^ [_1187756, _1187758] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1187756), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1187758), _1187756)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1187758), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1187758, _1187756)))], (50504 ^ _780119) ^ [_1804820, _1804822] : [-(c_List_Oreplicate(_1804820, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1804822) = c_List_Olist_ONil(_1804820))], (23350 ^ _780119) ^ [_1206814, _1206816] : [_1206814 = _1206816, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1206814) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1206816))], (3018 ^ _780119) ^ [_825123, _825125, _825127, _825129] : [-(c_Nitpick_Oint__lcm(_825129, _825125) = c_Nitpick_Oint__lcm(_825127, _825123)), _825129 = _825127, _825125 = _825123], (51501 ^ _780119) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (43058 ^ _780119) ^ [_1633623, _1633625, _1633627, _1633629] : [hBOOL(hAPP(c_List_Odistinct(_1633623), _1633625)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1633623, _1633627)), hAPP(hAPP(c_List_Ozip(_1633623, _1633627), _1633625), _1633629))))], (38098 ^ _780119) ^ [_1515467, _1515469, _1515471, _1515473] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515467), _1515469)), 38104 ^ _780119 : [(38107 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515471), hAPP(_1515473, 38103 ^ [_1515467, _1515469, _1515471, _1515473])))], (38105 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515467), 38103 ^ [_1515467, _1515469, _1515471, _1515473]), _1515469)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1515467, _1515471)), hAPP(hAPP(c_Product__Type_OSigma(_1515467, _1515471), _1515469), _1515473)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1515467, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1515471, tc_HOL_Obool), tc_Nat_Onat, _1515467), c_Finite__Set_Ocard(_1515471)), _1515473)), _1515469))], (46053 ^ _780119) ^ [_1707596, _1707598] : [-(c_List_Olist_Olist__size(_1707596, _1707598, c_List_Olist_ONil(_1707596)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12920 ^ _780119) ^ [_1014599, _1014601, _1014603] : [class_Lattices_Oab__semigroup__idem__mult(_1014599), -(_1014601 = c_Orderings_Obot__class_Obot(tc_fun(_1014599, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014599), _1014601)), -(hAPP(c_Finite__Set_Ofold1(_1014599, c_Groups_Otimes__class_Otimes(_1014599)), hAPP(hAPP(c_Set_Oinsert(_1014599), _1014603), _1014601)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014599), _1014603), hAPP(c_Finite__Set_Ofold1(_1014599, c_Groups_Otimes__class_Otimes(_1014599)), _1014601)))], (13708 ^ _780119) ^ [_1029322, _1029324] : [13709 ^ _780119 : [(13712 ^ _780119) ^ [] : [_1029322 = hAPP(c_Nat_OSuc, _1029324)], (13710 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029322), _1029324))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029322), hAPP(c_Nat_OSuc, _1029324))))], (38391 ^ _780119) ^ [_1522523, _1522525] : [c_Wellfounded_Owf(_1522523, _1522525), -(c_Wellfounded_Oacyclic(_1522523, _1522525))], (28304 ^ _780119) ^ [_1303352, _1303354] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1303352)), _1303354) = 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), _1303352)), _1303354))], (16570 ^ _780119) ^ [_1081888, _1081890] : [class_Groups_Ogroup__add(_1081888), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081888), hAPP(c_Groups_Ouminus__class_Ouminus(_1081888), _1081890)), _1081890) = c_Groups_Ozero__class_Ozero(_1081888))], (2610 ^ _780119) ^ [_818751, _818753, _818755, _818757, _818759, _818761, _818763, _818765] : [-(c_Recdef_Osame__fst(_818765, _818761, _818757, _818753) = c_Recdef_Osame__fst(_818763, _818759, _818755, _818751)), _818765 = _818763, _818761 = _818759, _818757 = _818755, _818753 = _818751], (42467 ^ _780119) ^ [_1619778, _1619780, _1619782] : [-(c_Product__Type_Ointernal__split(_1619778, _1619780, _1619782) = c_Product__Type_Oprod_Oprod__case(_1619778, _1619780, _1619782))], (2282 ^ _780119) ^ [_813687, _813689] : [_813689 = _813687, -(c_Com_Ocom_Ocom__size(_813689) = c_Com_Ocom_Ocom__size(_813687))], (12231 ^ _780119) ^ [_1000769, _1000771, _1000773, _1000775, _1000777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000769), _1000771)), 12234 ^ _780119 : [(12241 ^ _780119) ^ [] : [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), _1000771), _1000769)), _1000773)), _1000775)), _1000777)), -(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), _1000771), _1000773)), _1000775)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000769), _1000773)), _1000777))))], (12235 ^ _780119) ^ [] : [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), _1000771), _1000773)), _1000775)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000769), _1000773)), _1000777))), -(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), _1000771), _1000769)), _1000773)), _1000775)), _1000777)))]]], (16959 ^ _780119) ^ [_1088197, _1088199, _1088201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1088197)), 16962 ^ _780119 : [(16969 ^ _780119) ^ [] : [_1088199 = _1088201, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1088197), _1088199) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1088197), _1088201))], (16963 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1088197), _1088199) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1088197), _1088201), -(_1088199 = _1088201)]]], (40678 ^ _780119) ^ [_1577794, _1577796, _1577798, _1577800] : [class_Lattices_Osemilattice__sup(_1577794), hBOOL(hAPP(c_Finite__Set_Ofinite(_1577794), _1577796)), hBOOL(hAPP(hAPP(c_member(_1577794), _1577798), _1577796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577794), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1577794), _1577798), _1577800)), hAPP(hAPP(c_Finite__Set_Ofold(_1577794, _1577794, c_Lattices_Osemilattice__sup__class_Osup(_1577794)), _1577800), _1577796))))], (32109 ^ _780119) ^ [_1378721, _1378723] : [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(_1378723))), 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), _1378721)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1378721)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1378723))))], (31757 ^ _780119) ^ [_1372601, _1372603] : [31758 ^ _780119 : [(31761 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372601), c_Int_OPls))], (31759 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372601), _1372603))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372601)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372603))))], (27422 ^ _780119) ^ [_1286549, _1286551] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1286549), _1286551) = 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), _1286549)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1286551)))))], (36650 ^ _780119) ^ [] : [-(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))], (2024 ^ _780119) ^ [_809520, _809522] : [_809522 = _809520, -(c_Nat_Onat_Onat__size(_809522) = c_Nat_Onat_Onat__size(_809520))], (24133 ^ _780119) ^ [_1221942, _1221944] : [24141 ^ _780119 : [(24144 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1221944, 24140 ^ [_1221942, _1221944])))], (24142 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24140 ^ [_1221942, _1221944]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1221942))))]], 24134 ^ _780119 : [(24135 ^ _780119) ^ [_1222010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1222010), _1221942)), hBOOL(hAPP(_1221944, _1222010))]]], (8348 ^ _780119) ^ [_924466, _924468, _924470, _924472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_924466, tc_HOL_Obool)), _924468), hAPP(hAPP(c_Set_Oinsert(_924466), _924470), _924472)))), 8351 ^ _780119 : [(8354 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_924466, tc_HOL_Obool)), _924468), _924472))], (8352 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_924466), _924470), _924472)))]], 8355 ^ _780119 : [(8358 ^ _780119) ^ [] : [8359 ^ _780119 : [(8362 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_924466, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924466, tc_HOL_Obool)), _924468), hAPP(hAPP(c_Set_Oinsert(_924466), _924470), c_Orderings_Obot__class_Obot(tc_fun(_924466, tc_HOL_Obool))))), _924472))], (8360 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_924466), _924470), _924468)))]], 8363 ^ _780119 : [(8366 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_924466, tc_HOL_Obool)), _924468), _924472))], (8364 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_924466), _924470), _924468))]]], (8356 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_924466), _924470), _924472))]]], (26561 ^ _780119) ^ [_1265112, _1265114] : [class_Groups_Oordered__ab__group__add__abs(_1265112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265112), c_Groups_Ozero__class_Ozero(_1265112)), _1265114)), -(hAPP(c_Groups_Oabs__class_Oabs(_1265112), _1265114) = _1265114)], (35213 ^ _780119) ^ [_1442810, _1442812, _1442814, _1442816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1442810), _1442812)), -(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), _1442810), _1442814)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1442812), _1442816))), c_FunDef_Opair__leq)))], (49423 ^ _780119) ^ [_1781038, _1781040, _1781042, _1781044, _1781046] : [49424 ^ _780119 : [(49427 ^ _780119) ^ [] : [hBOOL(hAPP(_1781046, hAPP(hAPP(c_List_Ozip(_1781038, _1781042), hAPP(hAPP(c_List_Otake(_1781038), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781038)), _1781040)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781042)), _1781044))), _1781040)), hAPP(hAPP(c_List_Otake(_1781042), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781038)), _1781040)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781042)), _1781044))), _1781044))))], (49425 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781038)), hAPP(hAPP(c_List_Otake(_1781038), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781038)), _1781040)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781042)), _1781044))), _1781040)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781042)), hAPP(hAPP(c_List_Otake(_1781042), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781038)), _1781040)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781042)), _1781044))), _1781044)))]], -(hBOOL(hAPP(_1781046, hAPP(hAPP(c_List_Ozip(_1781038, _1781042), _1781040), _1781044))))], (37348 ^ _780119) ^ [_1493998, _1494000] : [hBOOL(hAPP(hAPP(c_member(_1493998), 37349 ^ [_1493998, _1494000]), c_Wellfounded_Oacc(_1493998, _1494000))), -(c_Wellfounded_Owf(_1493998, _1494000))], (39196 ^ _780119) ^ [_1541409, _1541411, _1541413, _1541415, _1541417, _1541419, _1541421] : [c_Finite__Set_Ofolding__idem(_1541409, _1541411, _1541413, _1541415), -(hAPP(c_Fun_Ocomp(_1541411, _1541411, _1541417, hAPP(_1541413, _1541419)), hAPP(c_Fun_Ocomp(_1541411, _1541411, _1541417, hAPP(_1541413, _1541419)), _1541421)) = hAPP(c_Fun_Ocomp(_1541411, _1541411, _1541417, hAPP(_1541413, _1541419)), _1541421))], (218 ^ _780119) ^ [_783546, _783548] : [-(class_Fields_Ofield__inverse__zero(_783546)), _783548 = _783546, class_Fields_Ofield__inverse__zero(_783548)], (1950 ^ _780119) ^ [_808335, _808337, _808339, _808341, _808343, _808345] : [-(c_Finite__Set_Ofold1Set(_808345, _808341, _808337) = c_Finite__Set_Ofold1Set(_808343, _808339, _808335)), _808345 = _808343, _808341 = _808339, _808337 = _808335], (14576 ^ _780119) ^ [_1047502, _1047504, _1047506] : [class_Rings_Olinordered__semidom(_1047502), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047502), c_Groups_Oone__class_Oone(_1047502)), _1047504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047502), c_Groups_Oone__class_Oone(_1047502)), hAPP(hAPP(c_Power_Opower__class_Opower(_1047502), _1047504), _1047506))))], (14474 ^ _780119) ^ [_1045514, _1045516, _1045518, _1045520] : [class_Rings_Olinordered__semidom(_1045514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045516), _1045518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045514), c_Groups_Oone__class_Oone(_1045514)), _1045520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045514), hAPP(hAPP(c_Power_Opower__class_Opower(_1045514), _1045520), _1045516)), hAPP(hAPP(c_Power_Opower__class_Opower(_1045514), _1045520), _1045518))))], (39312 ^ _780119) ^ [_1544246, _1544248, _1544250, _1544252] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1544246, tc_HOL_Obool), tc_fun(_1544246, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1544246, tc_HOL_Obool), tc_fun(_1544246, tc_HOL_Obool)), _1544248), _1544250)), c_Wellfounded_Omax__ext(_1544246, _1544252)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544246), _1544248)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544246), _1544250)), -(_1544250 = c_Orderings_Obot__class_Obot(tc_fun(_1544246, tc_HOL_Obool))), 39326 ^ _780119 : [(39329 ^ _780119) ^ [_1544651] : [hBOOL(hAPP(hAPP(c_member(_1544246), _1544651), _1544250)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1544246, _1544246)), hAPP(hAPP(c_Product__Type_OPair(_1544246, _1544246), 39325 ^ [_1544246, _1544248, _1544250, _1544252]), _1544651)), _1544252))], (39327 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544246), 39325 ^ [_1544246, _1544248, _1544250, _1544252]), _1544248)))]]], (32651 ^ _780119) ^ [_1388673, _1388675] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1388673)), _1388675) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1388673), _1388675))), _1388675))], (43116 ^ _780119) ^ [_1635667, _1635669, _1635671] : [class_Orderings_Olinorder(_1635667), hBOOL(hAPP(c_Finite__Set_Ofinite(_1635667), _1635669)), -(c_List_Olinorder__class_Osorted__list__of__set(_1635667, hAPP(hAPP(c_Set_Oinsert(_1635667), _1635671), _1635669)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1635667, _1635667, c_COMBI(_1635667)), _1635671), c_List_Olinorder__class_Osorted__list__of__set(_1635667, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1635667, tc_HOL_Obool)), _1635669), hAPP(hAPP(c_Set_Oinsert(_1635667), _1635671), c_Orderings_Obot__class_Obot(tc_fun(_1635667, tc_HOL_Obool)))))))], (35281 ^ _780119) ^ [] : [-(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)))))], (14394 ^ _780119) ^ [_1043873, _1043875, _1043877] : [class_Rings_Ocomm__semiring__1(_1043873), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1043873), _1043875), hAPP(c_Nat_OSuc, _1043877)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043873), _1043875), hAPP(hAPP(c_Power_Opower__class_Opower(_1043873), _1043875), _1043877)))], (4394 ^ _780119) ^ [_846629, _846631] : [_846631 = _846629, -(c_HOL_Obool_Obool__size(_846631) = c_HOL_Obool_Obool__size(_846629))], (1020 ^ _780119) ^ [_795593, _795595] : [-(class_Rings_Olinordered__semiring__1__strict(_795593)), _795595 = _795593, class_Rings_Olinordered__semiring__1__strict(_795595)], (31775 ^ _780119) ^ [_1372865, _1372867] : [class_Int_Onumber__ring(_1372865), class_Rings_Olinordered__idom(_1372865), 31782 ^ _780119 : [(31789 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1372867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372865), c_Groups_Ozero__class_Ozero(_1372865)), hAPP(c_Int_Onumber__class_Onumber__of(_1372865), _1372867))))], (31783 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372865), c_Groups_Ozero__class_Ozero(_1372865)), hAPP(c_Int_Onumber__class_Onumber__of(_1372865), _1372867))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1372867)))]]], (36804 ^ _780119) ^ [_1479862, _1479864, _1479866, _1479868] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1479862), _1479864)), c_Fun_Oinj__on(_1479866, _1479862, _1479868, c_Orderings_Otop__class_Otop(tc_fun(_1479866, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1479866), hAPP(c_Set_Ovimage(_1479866, _1479862, _1479868), _1479864))))], (11487 ^ _780119) ^ [_986075, _986077, _986079] : [class_Rings_Ocomm__semiring__1(_986075), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986075), _986077), _986079) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986075), _986079), _986077))], (18644 ^ _780119) ^ [_1120247] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1120247)), c_Option_Ooption_ONone(_1120247)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51199 ^ _780119) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (51663 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, v_y)), v_F))], (44384 ^ _780119) ^ [_1669241, _1669243, _1669245, _1669247] : [-(hAPP(hAPP(c_List_Olist__update(_1669241, hAPP(hAPP(c_List_Olist_OCons(_1669241), _1669243), _1669245)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1669247) = hAPP(hAPP(c_List_Olist_OCons(_1669241), _1669247), _1669245))], (38040 ^ _780119) ^ [_1514042] : [-(hAPP(c_Set_Oimage(_1514042, _1514042, c_Fun_Oid(_1514042)), c_Orderings_Otop__class_Otop(tc_fun(_1514042, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1514042, tc_HOL_Obool)))], (49189 ^ _780119) ^ [_1775606, _1775608, _1775610, _1775612, _1775614, _1775616, _1775618, _1775620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1775606), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775608)), _1775610))), c_List_Olist__all2(_1775608, _1775612, _1775614, _1775610, _1775616), hBOOL(hAPP(hAPP(_1775614, _1775618), _1775620)), -(c_List_Olist__all2(_1775608, _1775612, _1775614, hAPP(hAPP(c_List_Olist__update(_1775608, _1775610), _1775606), _1775618), hAPP(hAPP(c_List_Olist__update(_1775612, _1775616), _1775606), _1775620)))], (24094 ^ _780119) ^ [_1221186, _1221188] : [24096 ^ _780119 : [(24099 ^ _780119) ^ [] : [hBOOL(hAPP(_1221188, 24095 ^ [_1221186, _1221188]))], (24097 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24095 ^ [_1221186, _1221188]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1221186))))]], 24100 ^ _780119 : [(24101 ^ _780119) ^ [_1221341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221341), _1221186)), -(hBOOL(hAPP(_1221188, _1221341)))]]], (33451 ^ _780119) ^ [_1403093, _1403095] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1403093), _1403095) = c_Groups_Oone__class_Oone(tc_Int_Oint), 33456 ^ _780119 : [(33459 ^ _780119) ^ [] : [-(_1403095 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (33457 ^ _780119) ^ [] : [-(_1403093 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 33460 ^ _780119 : [(33463 ^ _780119) ^ [] : [-(_1403095 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (33461 ^ _780119) ^ [] : [-(_1403093 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (34365 ^ _780119) ^ [_1424981, _1424983] : [-(c_Divides_Opdivmod(_1424981, _1424983) = 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), _1424981)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1424983))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1424981), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1424983))))], (13752 ^ _780119) ^ [_1030218, _1030220, _1030222] : [class_Groups_Ocomm__monoid__mult(_1030218), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1030220, _1030218), hAPP(c_COMBK(_1030218, _1030220), c_Groups_Oone__class_Oone(_1030218))), _1030222) = c_Groups_Oone__class_Oone(_1030218))], (15202 ^ _780119) ^ [_1058156, _1058158] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1058156), _1058158) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1058158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1058156 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5851 ^ _780119) ^ [_872937, _872939, _872941, _872943] : [hBOOL(hAPP(hAPP(c_member(_872937), _872939), hAPP(hAPP(c_Set_Oinsert(_872937), _872941), _872943))), -(_872939 = _872941), -(hBOOL(hAPP(hAPP(c_member(_872937), _872939), _872943)))], (37205 ^ _780119) ^ [_1491437, _1491439, _1491441, _1491443] : [c_Wellfounded_Owf(_1491437, _1491439), -(c_Wellfounded_Owf(_1491441, hAPP(hAPP(c_Relation_Oinv__image(_1491437, _1491441), _1491439), _1491443)))], (38978 ^ _780119) ^ [_1536047, _1536049, _1536051, _1536053, _1536055, _1536057, _1536059, _1536061] : [c_Finite__Set_Ofolding(_1536047, _1536049, _1536051, _1536053), -(hAPP(c_Fun_Ocomp(_1536049, _1536049, _1536055, hAPP(_1536051, _1536057)), hAPP(c_Fun_Ocomp(_1536049, _1536049, _1536055, hAPP(_1536051, _1536059)), _1536061)) = hAPP(c_Fun_Ocomp(_1536049, _1536049, _1536055, hAPP(_1536051, _1536059)), hAPP(c_Fun_Ocomp(_1536049, _1536049, _1536055, hAPP(_1536051, _1536057)), _1536061)))], (45898 ^ _780119) ^ [_1704420, _1704422, _1704424] : [hBOOL(hAPP(c_List_Odistinct(_1704420), _1704424)), -(hBOOL(hAPP(c_List_Odistinct(_1704420), hAPP(c_List_Orotate(_1704420, _1704422), _1704424))))], (25057 ^ _780119) ^ [] : [-(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))))], (32047 ^ _780119) ^ [_1377280] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377280) = 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(_1377280)))))], (35341 ^ _780119) ^ [_1445715, _1445717, _1445719, _1445721] : [-(hAPP(c_Relation_OImage(_1445715, _1445717, _1445719), hAPP(hAPP(c_Set_Oinsert(_1445715), _1445721), c_Orderings_Obot__class_Obot(tc_fun(_1445715, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1445717), hAPP(hAPP(c_COMBC(_1445717, tc_fun(tc_prod(_1445715, _1445717), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1445715, _1445717), tc_fun(tc_fun(tc_prod(_1445715, _1445717), tc_HOL_Obool), tc_HOL_Obool), _1445717), c_member(tc_prod(_1445715, _1445717))), hAPP(c_Product__Type_OPair(_1445715, _1445717), _1445721))), _1445719)))], (26195 ^ _780119) ^ [_1257828, _1257830, _1257832] : [class_Orderings_Oorder(_1257828), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1257828, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1257828), _1257830)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1257828, _1257830, _1257832)) = c_Orderings_Obot__class_Obot(tc_fun(_1257828, tc_HOL_Obool)))], (44166 ^ _780119) ^ [_1664157, _1664159, _1664161, _1664163] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664157), tc_List_Olist(_1664157))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664157), tc_List_Olist(_1664157)), _1664159), _1664161)), c_List_Olistrel(_1664157, _1664163)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664157)), _1664159) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664157)), _1664161), 44172 ^ _780119 : [(44175 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1664157, _1664157)), hAPP(hAPP(c_Product__Type_OPair(_1664157, _1664157), hAPP(hAPP(c_List_Onth(_1664157), _1664159), 44171 ^ [_1664157, _1664159, _1664161, _1664163])), hAPP(hAPP(c_List_Onth(_1664157), _1664161), 44171 ^ [_1664157, _1664159, _1664161, _1664163]))), _1664163))], (44173 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44171 ^ [_1664157, _1664159, _1664161, _1664163]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664157)), _1664159))))]]], (50828 ^ _780119) ^ [_1811058, _1811060, _1811062, _1811064, _1811066, _1811068] : [-(c_Nitpick_Opair__box_Opair__box__case(_1811058, _1811060, _1811062, _1811064, c_Nitpick_Opair__box_OPairBox(_1811058, _1811060, _1811066, _1811068)) = hAPP(hAPP(_1811064, _1811066), _1811068))], (38168 ^ _780119) ^ [_1517297, _1517299, _1517301, _1517303, _1517305, _1517307] : [-(c_Product__Type_Omap__pair(_1517297, _1517299, _1517301, _1517303, _1517305, _1517307) = hAPP(c_Product__Type_Oprod_Oprod__case(_1517297, _1517301, tc_prod(_1517299, _1517303)), hAPP(hAPP(c_COMBC(_1517297, tc_fun(_1517301, _1517303), tc_fun(_1517301, tc_prod(_1517299, _1517303))), hAPP(hAPP(c_COMBB(tc_fun(_1517303, tc_prod(_1517299, _1517303)), tc_fun(tc_fun(_1517301, _1517303), tc_fun(_1517301, tc_prod(_1517299, _1517303))), _1517297), c_COMBB(_1517303, tc_prod(_1517299, _1517303), _1517301)), hAPP(hAPP(c_COMBB(_1517299, tc_fun(_1517303, tc_prod(_1517299, _1517303)), _1517297), c_Product__Type_OPair(_1517299, _1517303)), _1517305))), _1517307)))], (32547 ^ _780119) ^ [_1386821, _1386823] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1386821)), c_Int_OBit0(_1386823)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1386821), _1386823)))], (45408 ^ _780119) ^ [_1692012, _1692014, _1692016, _1692018] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692012), tc_List_Olist(_1692012))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692012), tc_List_Olist(_1692012)), _1692014), _1692016)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1692012), c_List_Olistrel1(_1692012, _1692018)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692012)), _1692014) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692012)), _1692016))], (51203 ^ _780119) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (4336 ^ _780119) ^ [_845732, _845734, _845736, _845738, _845740, _845742] : [-(c_List_OdropWhile(_845742, _845738, _845734) = c_List_OdropWhile(_845740, _845736, _845732)), _845742 = _845740, _845738 = _845736, _845734 = _845732], (40507 ^ _780119) ^ [_1574216, _1574218] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574216, _1574216)), _1574218), c_Relation_OId(_1574216))), -(_1574218 = hAPP(hAPP(c_Product__Type_OPair(_1574216, _1574216), 40510 ^ [_1574216, _1574218]), 40510 ^ [_1574216, _1574218]))], (3056 ^ _780119) ^ [_825714, _825716] : [_825716 = _825714, -(c_Rings_Oinverse__class_Odivide(_825716) = c_Rings_Oinverse__class_Odivide(_825714))], (26793 ^ _780119) ^ [_1269781, _1269783, _1269785] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1269781, tc_HOL_Obool)), _1269783), _1269785) = hAPP(c_Set_OCollect(_1269781), hAPP(hAPP(c_COMBS(_1269781, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1269781), c_fconj), hAPP(hAPP(c_COMBC(_1269781, tc_fun(_1269781, tc_HOL_Obool), tc_HOL_Obool), c_member(_1269781)), _1269783))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1269781), c_fNot), hAPP(hAPP(c_COMBC(_1269781, tc_fun(_1269781, tc_HOL_Obool), tc_HOL_Obool), c_member(_1269781)), _1269785)))))], (31625 ^ _780119) ^ [_1370502, _1370504] : [class_Int_Onumber__ring(_1370502), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1370502), _1370504), hAPP(c_Int_Onumber__class_Onumber__of(_1370502), c_Int_OBit1(c_Int_OPls))) = _1370504)], (15802 ^ _780119) ^ [_1067979, _1067981, _1067983, _1067985] : [class_Rings_Oordered__semiring(_1067979), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067979), _1067981), _1067983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067979), c_Groups_Ozero__class_Ozero(_1067979)), _1067985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067979), _1067981), _1067985)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067979), _1067983), _1067985))))], (6338 ^ _780119) ^ [_882042, _882044, _882046, _882048, _882050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882042, tc_HOL_Obool)), _882044), _882046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882048, tc_HOL_Obool)), hAPP(c_Set_Oimage(_882042, _882048, _882050), _882044)), hAPP(c_Set_Oimage(_882042, _882048, _882050), _882046))))], (51433 ^ _780119) ^ [_1818971, _1818973] : [-(class_Enum_Oenum(tc_prod(_1818971, _1818973))), class_Enum_Oenum(_1818971), class_Enum_Oenum(_1818973)], (3192 ^ _780119) ^ [_827776, _827778, _827780, _827782, _827784, _827786] : [-(c_Smallcheck_Osmall_H(_827786, _827782, _827778) = c_Smallcheck_Osmall_H(_827784, _827780, _827776)), _827786 = _827784, _827782 = _827780, _827778 = _827776], (38704 ^ _780119) ^ [_1529848, _1529850, _1529852, _1529854] : [c_Finite__Set_Ofun__left__comm__idem(_1529848, _1529850, _1529852), -(hAPP(c_Fun_Ocomp(_1529850, _1529850, _1529850, hAPP(_1529852, _1529854)), hAPP(_1529852, _1529854)) = hAPP(_1529852, _1529854))], (31219 ^ _780119) ^ [_1363860, _1363862] : [c_Int_OBit1(_1363860) = c_Int_OBit1(_1363862), -(_1363860 = _1363862)], (40260 ^ _780119) ^ [_1567608, _1567610, _1567612, _1567614, _1567616, _1567618] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567608, _1567608)), hAPP(hAPP(c_Product__Type_OPair(_1567608, _1567608), _1567610), _1567612)), _1567614)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567608, _1567608)), hAPP(hAPP(c_Product__Type_OPair(_1567608, _1567608), _1567612), _1567616)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1567608, _1567608), tc_HOL_Obool), _1567618), _1567614))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567608, _1567608)), hAPP(hAPP(c_Product__Type_OPair(_1567608, _1567608), _1567610), _1567616)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1567608, _1567608), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1567618)), _1567614))))], (21080 ^ _780119) ^ [_1163582, _1163584, _1163586] : [class_Fields_Olinordered__field(_1163582), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163582), _1163584), _1163586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163582), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163582), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163582), _1163584), _1163586)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163582), c_Groups_Oone__class_Oone(_1163582)), c_Groups_Oone__class_Oone(_1163582)))), _1163586)))], (33239 ^ _780119) ^ [_1399922] : [_1399922 = c_Int_OMin, -(c_Int_OBit1(_1399922) = c_Int_OMin)], (50194 ^ _780119) ^ [_1797265, _1797267] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1797265)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1797267))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1797265), _1797267)))], (8510 ^ _780119) ^ [_927846, _927848, _927850, _927852, _927854] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927846, _927848), _927850), _927852), _927854), _927852) = _927854)], (22631 ^ _780119) ^ [_1193144, _1193146] : [class_Orderings_Oorder(_1193144), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1193144, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1193144), _1193146), c_Orderings_Obot__class_Obot(tc_fun(_1193144, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1193144), _1193146)) = hAPP(hAPP(c_Set_Oinsert(_1193144), _1193146), c_Orderings_Obot__class_Obot(tc_fun(_1193144, tc_HOL_Obool))))], (5432 ^ _780119) ^ [_863354, _863356, _863358, _863360] : [-(c_Complete__Lattice_OSup__class_OSup(_863360, _863356) = c_Complete__Lattice_OSup__class_OSup(_863358, _863354)), _863360 = _863358, _863356 = _863354], (51585 ^ _780119) ^ [_1820646] : [-(hBOOL(_1820646)), -(hBOOL(hAPP(c_fNot, _1820646)))], (44604 ^ _780119) ^ [_1673706, _1673708, _1673710] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1673706), tc_List_Olist(_1673706))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1673706), tc_List_Olist(_1673706)), _1673708), c_List_Olist_ONil(_1673706))), c_List_Olistrel(_1673706, _1673710))), -(_1673708 = c_List_Olist_ONil(_1673706))], (43699 ^ _780119) ^ [_1652465, _1652467, _1652469, _1652471] : [hBOOL(hAPP(hAPP(c_member(_1652465), _1652467), hAPP(c_List_Oset(_1652465), c_List_Osublist(_1652465, _1652469, _1652471)))), -(hBOOL(hAPP(hAPP(c_member(_1652465), _1652467), hAPP(c_List_Oset(_1652465), _1652469))))], (33701 ^ _780119) ^ [_1411638] : [-(_1411638 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1411638), 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)))))], (22695 ^ _780119) ^ [_1194648, _1194650, _1194652, _1194654] : [hBOOL(hAPP(hAPP(c_member(_1194648), _1194650), c_SetInterval_Oord_OatLeast(_1194648, _1194652, _1194654))), -(hBOOL(hAPP(hAPP(_1194652, _1194654), _1194650)))], (12457 ^ _780119) ^ [_1005089, _1005091, _1005093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005089), _1005091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005089), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005091), _1005093))))], (12147 ^ _780119) ^ [_999086, _999088, _999090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999090), _999088))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999086), _999088)), _999090)))], (18105 ^ _780119) ^ [_1109885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1109885)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109885), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1109885)], (31501 ^ _780119) ^ [_1368632] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1368632) = c_Int_OPls)], (38665 ^ _780119) ^ [_1529128, _1529130, _1529132] : [38666 ^ _780119 : [(38667 ^ _780119) ^ [_1529182] : [hBOOL(hAPP(_1529128, _1529182))]], _1529130 = c_Hilbert__Choice_OEps(_1529132, _1529128), -(hBOOL(hAPP(_1529128, _1529130)))], (7722 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (39611 ^ _780119) ^ [_1551658, _1551660, _1551662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1551658, _1551658)), _1551660), _1551662)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1551658, _1551658)), _1551660), c_Transitive__Closure_Ortrancl(_1551658, _1551662))))], (2796 ^ _780119) ^ [_821690, _821692, _821694, _821696, _821698, _821700] : [-(c_Hoare__Mirabelle_Opeek__and(_821700, _821696, _821692) = c_Hoare__Mirabelle_Opeek__and(_821698, _821694, _821690)), _821700 = _821698, _821696 = _821694, _821692 = _821690], (51401 ^ _780119) ^ [_1818557, _1818559] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1818557, _1818559))), class_Lazy__Sequence_Osmall__lazy(_1818557), class_Lazy__Sequence_Osmall__lazy(_1818559)], (15956 ^ _780119) ^ [_1070922, _1070924] : [class_Groups_Olinordered__ab__group__add(_1070922), 15959 ^ _780119 : [(15966 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070922), c_Groups_Ozero__class_Ozero(_1070922)), _1070924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070922), c_Groups_Ozero__class_Ozero(_1070922)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070922), _1070924), _1070924))))], (15960 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070922), c_Groups_Ozero__class_Ozero(_1070922)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070922), _1070924), _1070924))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070922), c_Groups_Ozero__class_Ozero(_1070922)), _1070924)))]]], (24203 ^ _780119) ^ [_1223258, _1223260] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1223258), _1223260))))], (48102 ^ _780119) ^ [_1751740, _1751742, _1751744, _1751746, _1751748] : [-(c_List_OdropWhile(_1751740, _1751742, hAPP(hAPP(c_List_Omap(_1751744, _1751740), _1751746), _1751748)) = hAPP(hAPP(c_List_Omap(_1751744, _1751740), _1751746), c_List_OdropWhile(_1751744, hAPP(c_Fun_Ocomp(_1751740, tc_HOL_Obool, _1751744, _1751742), _1751746), _1751748)))], (45156 ^ _780119) ^ [_1685104, _1685106, _1685108, _1685110] : [_1685108 = _1685110, -(hAPP(hAPP(c_List_Oappend(_1685104), _1685106), _1685108) = hAPP(hAPP(c_List_Oappend(_1685104), _1685106), _1685110))], (35518 ^ _780119) ^ [_1451016, _1451018, _1451020] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1451016, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1451016), _1451018), _1451020), -(_1451018 = c_Orderings_Obot__class_Obot(tc_fun(_1451016, tc_HOL_Obool)))], (22905 ^ _780119) ^ [_1198433, _1198435, _1198437] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198433)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198435)), _1198437)) = 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), _1198433), _1198435))), _1198437))], (32795 ^ _780119) ^ [_1391366] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1391366), _1391366)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1391366)], (30723 ^ _780119) ^ [_1354265, _1354267, _1354269, _1354271] : [class_Fields_Olinordered__field__inverse__zero(_1354265), class_Int_Onumber(_1354265), 30730 ^ _780119 : [(30731 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), hAPP(c_Int_Onumber__class_Onumber__of(_1354265), _1354267)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354265), _1354269), _1354271))), 30734 ^ _780119 : [(30741 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), c_Groups_Ozero__class_Ozero(_1354265)), _1354271))), 30744 ^ _780119 : [(30751 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), _1354271), c_Groups_Ozero__class_Ozero(_1354265)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), hAPP(c_Int_Onumber__class_Onumber__of(_1354265), _1354267)), c_Groups_Ozero__class_Ozero(_1354265))))], (30745 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), _1354271), c_Groups_Ozero__class_Ozero(_1354265))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), _1354269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354265), hAPP(c_Int_Onumber__class_Onumber__of(_1354265), _1354267)), _1354271))))]]], (30735 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), c_Groups_Ozero__class_Ozero(_1354265)), _1354271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354265), hAPP(c_Int_Onumber__class_Onumber__of(_1354265), _1354267)), _1354271)), _1354269)))]]], (30757 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), hAPP(c_Int_Onumber__class_Onumber__of(_1354265), _1354267)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354265), _1354269), _1354271)))), 30760 ^ _780119 : [(30763 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354265), hAPP(c_Int_Onumber__class_Onumber__of(_1354265), _1354267)), _1354271)), _1354269))], (30761 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), c_Groups_Ozero__class_Ozero(_1354265)), _1354271)))]], 30764 ^ _780119 : [(30767 ^ _780119) ^ [] : [30768 ^ _780119 : [(30771 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), _1354269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354265), hAPP(c_Int_Onumber__class_Onumber__of(_1354265), _1354267)), _1354271)))], (30769 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), _1354271), c_Groups_Ozero__class_Ozero(_1354265))))]], 30772 ^ _780119 : [(30775 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), hAPP(c_Int_Onumber__class_Onumber__of(_1354265), _1354267)), c_Groups_Ozero__class_Ozero(_1354265)))], (30773 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), _1354271), c_Groups_Ozero__class_Ozero(_1354265)))]]], (30765 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354265), c_Groups_Ozero__class_Ozero(_1354265)), _1354271))]]]]], (30387 ^ _780119) ^ [_1348014, _1348016, _1348018] : [class_Int_Onumber__ring(_1348014), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348014), hAPP(c_Int_Onumber__class_Onumber__of(_1348014), _1348016)), hAPP(c_Int_Onumber__class_Onumber__of(_1348014), _1348018)) = hAPP(c_Int_Onumber__class_Onumber__of(_1348014), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1348016), _1348018)))], (40002 ^ _780119) ^ [_1560926, _1560928, _1560930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560928, _1560926)), _1560930)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560926, _1560928)), hAPP(c_Relation_Oconverse(_1560928, _1560926), _1560930))))], (9876 ^ _780119) ^ [_951939, _951941] : [class_Lattices_Oab__semigroup__idem__mult(_951939), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951939), _951941), _951941) = _951941)], (51261 ^ _780119) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (2064 ^ _780119) ^ [_810124, _810126, _810128, _810130, _810132, _810134] : [-(c_SetInterval_Oord_OatLeast(_810134, _810130, _810126) = c_SetInterval_Oord_OatLeast(_810132, _810128, _810124)), _810134 = _810132, _810130 = _810128, _810126 = _810124], (47218 ^ _780119) ^ [_1731583, _1731585] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1731583, _1731585) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1731583, hAPP(c_Nat_OSuc, _1731585))))], (47646 ^ _780119) ^ [_1741322, _1741324, _1741326] : [47648 ^ _780119 : [(47651 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1741322), tc_List_Olist(_1741322), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1741322), tc_fun(tc_List_Olist(_1741322), tc_Nat_Onat), tc_fun(tc_List_Olist(_1741322), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1741322), tc_Nat_Onat), tc_fun(tc_List_Olist(_1741322), tc_HOL_Obool)), tc_List_Olist(_1741322)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1741322))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1741322)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1741322))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1741322)))), 47647 ^ [_1741322, _1741324, _1741326]))], (47649 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741322), tc_List_Olist(_1741322))), 47647 ^ [_1741322, _1741324, _1741326]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1741322), tc_List_Olist(_1741322))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1741322), tc_List_Olist(_1741322)), _1741324), _1741326)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1741322))), _1741324) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1741322))), _1741326), 47656 ^ _780119 : [(47663 ^ _780119) ^ [] : [_1741324 = _1741326, -(c_List_Oconcat(_1741322, _1741324) = c_List_Oconcat(_1741322, _1741326))], (47657 ^ _780119) ^ [] : [c_List_Oconcat(_1741322, _1741324) = c_List_Oconcat(_1741322, _1741326), -(_1741324 = _1741326)]]], (11457 ^ _780119) ^ [_985326, _985328, _985330, _985332] : [class_Rings_Ocomm__semiring__1(_985326), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985326), _985328), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985326), _985330), _985332)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985326), _985330), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985326), _985328), _985332)))], (45574 ^ _780119) ^ [_1697061, _1697063] : [-(hAPP(c_List_Orotate1(_1697061), _1697063) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1697061), _1697061, c_List_Olist_ONil(_1697061), hAPP(hAPP(c_COMBB(tc_List_Olist(_1697061), tc_fun(tc_List_Olist(_1697061), tc_List_Olist(_1697061)), _1697061), hAPP(c_COMBC(tc_List_Olist(_1697061), tc_List_Olist(_1697061), tc_List_Olist(_1697061)), c_List_Oappend(_1697061))), hAPP(hAPP(c_COMBC(_1697061, tc_List_Olist(_1697061), tc_List_Olist(_1697061)), c_List_Olist_OCons(_1697061)), c_List_Olist_ONil(_1697061)))), _1697063))], (32481 ^ _780119) ^ [_1385656, _1385658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1385656)), c_Int_OBit1(_1385658))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1385656), _1385658)))], (3482 ^ _780119) ^ [_832451, _832453, _832455, _832457, _832459, _832461, _832463, _832465] : [-(c_Nat_Onat_Onat__case(_832465, _832461, _832457, _832453) = c_Nat_Onat_Onat__case(_832463, _832459, _832455, _832451)), _832465 = _832463, _832461 = _832459, _832457 = _832455, _832453 = _832451], (50486 ^ _780119) ^ [_1804231, _1804233, _1804235, _1804237, _1804239] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1804233, _1804231)), hAPP(hAPP(c_Product__Type_OPair(_1804233, _1804231), _1804237), _1804239)), hAPP(c_Relation_Oconverse(_1804231, _1804233), _1804235))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1804231, _1804233, hAPP(hAPP(c_COMBC(_1804231, tc_fun(tc_prod(_1804231, _1804233), tc_HOL_Obool), tc_fun(_1804233, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1804233, tc_fun(tc_fun(tc_prod(_1804231, _1804233), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1804231, _1804233), tc_HOL_Obool), tc_fun(_1804233, tc_HOL_Obool)), _1804231), c_COMBC(_1804233, tc_fun(tc_prod(_1804231, _1804233), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1804233, tc_prod(_1804231, _1804233)), tc_fun(_1804233, tc_fun(tc_fun(tc_prod(_1804231, _1804233), tc_HOL_Obool), tc_HOL_Obool)), _1804231), hAPP(c_COMBB(tc_prod(_1804231, _1804233), tc_fun(tc_fun(tc_prod(_1804231, _1804233), tc_HOL_Obool), tc_HOL_Obool), _1804233), c_member(tc_prod(_1804231, _1804233)))), c_Product__Type_OPair(_1804231, _1804233)))), _1804235)), _1804237), _1804239)))], (9764 ^ _780119) ^ [_949622, _949624, _949626] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949622, tc_HOL_Obool)), _949624), _949626) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949622, tc_HOL_Obool)), _949626), _949624))], (8480 ^ _780119) ^ [_927391, _927393, _927395, _927397, _927399] : [hAPP(_927391, _927393) = _927395, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927397, _927399), _927391), _927393), _927395) = _927391)], (14618 ^ _780119) ^ [_1048286, _1048288, _1048290, _1048292] : [class_Groups_Omonoid__mult(_1048286), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1048286), _1048288), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048290), _1048292)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048286), hAPP(hAPP(c_Power_Opower__class_Opower(_1048286), _1048288), _1048290)), hAPP(hAPP(c_Power_Opower__class_Opower(_1048286), _1048288), _1048292)))], (51177 ^ _780119) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (6609 ^ _780119) ^ [_887701, _887703, _887705, _887707] : [6623 ^ _780119 : [(6626 ^ _780119) ^ [] : [-(hBOOL(hAPP(_887707, 6622 ^ [_887701, _887703, _887705, _887707])))], (6624 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887701), 6622 ^ [_887701, _887703, _887705, _887707]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887701, tc_HOL_Obool)), _887703), _887705))))]], 6610 ^ _780119 : [(6617 ^ _780119) ^ [_887910] : [hBOOL(hAPP(hAPP(c_member(_887701), _887910), _887705)), hBOOL(hAPP(_887707, _887910))], (6611 ^ _780119) ^ [_887814] : [hBOOL(hAPP(hAPP(c_member(_887701), _887814), _887703)), hBOOL(hAPP(_887707, _887814))]]], (44278 ^ _780119) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (15292 ^ _780119) ^ [_1059365] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1059365), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1059365)], (10590 ^ _780119) ^ [_967561, _967563, _967565, _967567, _967569] : [class_Groups_Ocomm__monoid__mult(_967561), hBOOL(hAPP(c_Finite__Set_Ofinite(_967563), _967565)), hBOOL(hAPP(c_Finite__Set_Ofinite(_967563), _967567)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_967563, tc_HOL_Obool)), _967565), _967567) = c_Orderings_Obot__class_Obot(tc_fun(_967563, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_967561, _967563, c_Groups_Otimes__class_Otimes(_967561)), _967569), c_Groups_Oone__class_Oone(_967561)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_967563, tc_HOL_Obool)), _967565), _967567)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967561), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_967561, _967563, c_Groups_Otimes__class_Otimes(_967561)), _967569), c_Groups_Oone__class_Oone(_967561)), _967565)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_967561, _967563, c_Groups_Otimes__class_Otimes(_967561)), _967569), c_Groups_Oone__class_Oone(_967561)), _967567)))], (34879 ^ _780119) ^ [_1435086, _1435088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435086), 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)), _1435088)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1435086), _1435088) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1435086, _1435088)))], (25796 ^ _780119) ^ [_1250929, _1250931, _1250933] : [class_Rings_Oring__1(_1250929), -(hAPP(c_Int_Oring__1__class_Oof__int(_1250929), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1250931), _1250933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1250929), hAPP(c_Int_Oring__1__class_Oof__int(_1250929), _1250931)), hAPP(c_Int_Oring__1__class_Oof__int(_1250929), _1250933)))], (40224 ^ _780119) ^ [_1566595, _1566597, _1566599] : [40225 ^ _780119 : [(40226 ^ _780119) ^ [_1566671] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566595, _1566595)), _1566597), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566595, _1566595), tc_HOL_Obool), _1566671), _1566599)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566595, _1566595)), _1566597), c_Transitive__Closure_Ortrancl(_1566595, _1566599))))], (22799 ^ _780119) ^ [_1196529] : [_1196529 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1196529) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18416 ^ _780119) ^ [_1116138, _1116140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116138)), 18419 ^ _780119 : [(18428 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116138), _1116140) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1116138 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1116140 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (18420 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116138), _1116140) = c_Groups_Oone__class_Oone(tc_Int_Oint), 18423 ^ _780119 : [(18426 ^ _780119) ^ [] : [-(_1116140 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (18424 ^ _780119) ^ [] : [-(_1116138 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (42173 ^ _780119) ^ [_1613067, _1613069, _1613071, _1613073] : [class_Lattices_Osemilattice__sup(_1613067), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613067), _1613069)), 42183 ^ _780119 : [(42186 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1613067), 42182 ^ [_1613067, _1613069, _1613071, _1613073]), _1613071))], (42184 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613067), 42182 ^ [_1613067, _1613069, _1613071, _1613073]), _1613069)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1613067), hAPP(hAPP(c_Finite__Set_Ofold(_1613067, _1613067, c_Lattices_Osemilattice__sup__class_Osup(_1613067)), _1613073), _1613069)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1613067), _1613071), _1613073))))], (41525 ^ _780119) ^ [_1598271, _1598273] : [class_Complete__Lattice_Ocomplete__lattice(_1598271), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598271), _1598273)), -(c_Complete__Lattice_OSup__class_OSup(_1598271, _1598273) = hAPP(hAPP(c_Finite__Set_Ofold(_1598271, _1598271, c_Lattices_Osemilattice__sup__class_Osup(_1598271)), c_Orderings_Obot__class_Obot(_1598271)), _1598273))], (48122 ^ _780119) ^ [_1752184, _1752186, _1752188, _1752190, _1752192] : [-(c_List_OdropWhile(_1752184, _1752186, _1752188) = hAPP(hAPP(c_List_Olist_OCons(_1752184), _1752190), _1752192)), _1752188 = hAPP(hAPP(c_List_Oappend(_1752184), c_List_OtakeWhile(_1752184, _1752186, _1752188)), hAPP(hAPP(c_List_Olist_OCons(_1752184), _1752190), _1752192)), -(hBOOL(hAPP(_1752186, _1752190)))], (18300 ^ _780119) ^ [_1113827, _1113829, _1113831] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1113827), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113829), _1113831)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1113827), _1113829)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1113827), _1113831)))], (35375 ^ _780119) ^ [_1446956, _1446958, _1446960, _1446962, _1446964] : [-(hAPP(c_Relation_OImage(_1446956, _1446958, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1446956, _1446958), tc_HOL_Obool)), _1446960), _1446962)), _1446964) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446958, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446956, _1446958, _1446960), _1446964)), hAPP(c_Relation_OImage(_1446956, _1446958, _1446962), _1446964)))], (15096 ^ _780119) ^ [_1056570, _1056572] : [class_Groups_Ogroup__add(_1056570), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056570), _1056572), _1056572) = c_Groups_Ozero__class_Ozero(_1056570))], (2338 ^ _780119) ^ [_814533, _814535] : [_814535 = _814533, -(c_Int_Osucc(_814535) = c_Int_Osucc(_814533))], (29431 ^ _780119) ^ [_1326405, _1326407, _1326409] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1326405, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1326407)), _1326409) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326405, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1326405, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1326407)), _1326409)), hAPP(_1326409, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10236 ^ _780119) ^ [_959614] : [class_Lattices_Osemilattice__inf(_959614), -(c_Finite__Set_Ofun__left__comm__idem(_959614, _959614, c_Lattices_Osemilattice__inf__class_Oinf(_959614)))], (35013 ^ _780119) ^ [_1437582, _1437584, _1437586, _1437588, _1437590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1437582, _1437584)), hAPP(_1437582, _1437586))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1437588, _1437588)), hAPP(hAPP(c_Product__Type_OPair(_1437588, _1437588), _1437584), _1437586)), _1437590)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1437588, _1437588)), hAPP(hAPP(c_Product__Type_OPair(_1437588, _1437588), _1437584), _1437586)), c_Wellfounded_Omlex__prod(_1437588, _1437582, _1437590))))], (22241 ^ _780119) ^ [_1186044, _1186046] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186044, _1186046)) = _1186046), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1186044), _1186046) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186044, _1186046)))], (34633 ^ _780119) ^ [_1430124, _1430126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1430124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430126), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1430124, _1430126) = 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), _1430124), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1430126)))))], (16548 ^ _780119) ^ [_1081527, _1081529] : [class_Groups_Ogroup__add(_1081527), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081527), _1081529), hAPP(c_Groups_Ouminus__class_Ouminus(_1081527), _1081529)) = c_Groups_Ozero__class_Ozero(_1081527))], (50368 ^ _780119) ^ [_1801317] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1801317) = c_Lazy__Sequence_Osmall__lazy_H(_1801317, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1801317)))], (43890 ^ _780119) ^ [_1657013, _1657015, _1657017] : [class_Orderings_Olinorder(_1657013), -(hAPP(c_List_Oset(_1657013), c_List_Olinorder__class_Oinsort__insert__key(_1657013, _1657013, c_COMBI(_1657013), _1657015, _1657017)) = hAPP(hAPP(c_Set_Oinsert(_1657013), _1657015), hAPP(c_List_Oset(_1657013), _1657017)))], (2712 ^ _780119) ^ [_820332, _820334, _820336, _820338, _820340, _820342, _820344, _820346] : [-(c_Product__Type_Oapfst(_820346, _820342, _820338, _820334) = c_Product__Type_Oapfst(_820344, _820340, _820336, _820332)), _820346 = _820344, _820342 = _820340, _820338 = _820336, _820334 = _820332], (20838 ^ _780119) ^ [_1159025, _1159027, _1159029, _1159031] : [class_Fields_Olinordered__field(_1159025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159025), c_Groups_Ozero__class_Ozero(_1159025)), _1159027)), 20845 ^ _780119 : [(20852 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159025), _1159029), _1159027)), _1159031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159025), _1159029), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159025), _1159031), _1159027))))], (20846 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159025), _1159029), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159025), _1159031), _1159027))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159025), _1159029), _1159027)), _1159031)))]]], (6537 ^ _780119) ^ [_886143, _886145, _886147, _886149, _886151] : [c_Hoare__Mirabelle_Ohoare__derivs(_886143, _886145, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_886143)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_886143), _886147), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _886149))), _886151)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_886143), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_886143, _886145, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_886143)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_886143), _886147), hAPP(c_Com_Ocom_OBODY, _886149)), _886151)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_886143), tc_HOL_Obool)))))], (19574 ^ _780119) ^ [_1135890, _1135892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135890), _1135892)), -(c_Nat__Transfer_Otsub(_1135892, _1135890) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1135892), _1135890))], (1320 ^ _780119) ^ [_799343, _799345] : [-(class_Lattices_Odistrib__lattice(_799343)), _799345 = _799343, class_Lattices_Odistrib__lattice(_799345)], (47295 ^ _780119) ^ [_1733094, _1733096, _1733098] : [class_Orderings_Olinorder(_1733094), hBOOL(hAPP(hAPP(c_member(_1733094), _1733096), hAPP(c_List_Oset(_1733094), _1733098))), c_List_Olinorder__class_Osorted(_1733094, _1733098), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733094, _1733094, c_COMBI(_1733094)), _1733096), c_List_Oremove1(_1733094, _1733096, _1733098)) = _1733098)], (43302 ^ _780119) ^ [_1639819, _1639821] : [-(c_List_Olenlex(_1639819, _1639821) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1639819), tc_List_Olist(_1639819))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1639819), tc_List_Olist(_1639819), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1639819), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1639819), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool)), tc_List_Olist(_1639819)), c_COMBS(tc_List_Olist(_1639819), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool), tc_fun(tc_List_Olist(_1639819), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1639819)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1639819)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1639819), tc_fun(tc_List_Olist(_1639819), tc_Nat_Onat), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1639819), tc_Nat_Onat), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool)), tc_List_Olist(_1639819)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1639819))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1639819)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1639819))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1639819)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1639819), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1639819), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool)), tc_List_Olist(_1639819)), c_COMBS(tc_List_Olist(_1639819), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool), tc_fun(tc_List_Olist(_1639819), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1639819)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1639819)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1639819), tc_fun(tc_List_Olist(_1639819), tc_Nat_Onat), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1639819), tc_Nat_Onat), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool)), tc_List_Olist(_1639819)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1639819))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1639819)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1639819))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1639819)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1639819), tc_fun(tc_prod(tc_List_Olist(_1639819), tc_List_Olist(_1639819)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1639819), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1639819), tc_List_Olist(_1639819)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1639819), tc_List_Olist(_1639819)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1639819), tc_HOL_Obool)), tc_List_Olist(_1639819)), c_COMBC(tc_List_Olist(_1639819), tc_fun(tc_prod(tc_List_Olist(_1639819), tc_List_Olist(_1639819)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1639819), tc_prod(tc_List_Olist(_1639819), tc_List_Olist(_1639819))), tc_fun(tc_List_Olist(_1639819), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1639819), tc_List_Olist(_1639819)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1639819)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1639819), tc_List_Olist(_1639819)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1639819), tc_List_Olist(_1639819)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1639819)), c_member(tc_prod(tc_List_Olist(_1639819), tc_List_Olist(_1639819))))), c_Product__Type_OPair(tc_List_Olist(_1639819), tc_List_Olist(_1639819))))), c_List_Olex(_1639819, _1639821)))))))], (26937 ^ _780119) ^ [_1272781] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1272781), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1272781) = _1272781)], (43942 ^ _780119) ^ [_1658445, _1658447, _1658449, _1658451, _1658453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658445), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658447)), _1658449))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658445), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658451)), _1658453))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1658447, _1658451)), hAPP(hAPP(c_List_Ozip(_1658447, _1658451), _1658449), _1658453)), _1658445) = hAPP(hAPP(c_Product__Type_OPair(_1658447, _1658451), hAPP(hAPP(c_List_Onth(_1658447), _1658449), _1658445)), hAPP(hAPP(c_List_Onth(_1658451), _1658453), _1658445)))], (20878 ^ _780119) ^ [_1159787, _1159789, _1159791, _1159793] : [class_Fields_Olinordered__field(_1159787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159787), c_Groups_Ozero__class_Ozero(_1159787)), _1159789)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159787), _1159791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159787), _1159793), _1159789))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159787), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159787), _1159791), _1159789)), _1159793)))], (50130 ^ _780119) ^ [_1796175] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1796175)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1796175), c_Int_OMin)))], (32711 ^ _780119) ^ [_1389957, _1389959] : [class_Rings_Oring__1__no__zero__divisors(_1389957), 32714 ^ _780119 : [(32721 ^ _780119) ^ [] : [_1389959 = c_Groups_Ozero__class_Ozero(_1389957), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1389957), _1389959), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1389957))], (32715 ^ _780119) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1389957), _1389959), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1389957), -(_1389959 = c_Groups_Ozero__class_Ozero(_1389957))]]], (1460 ^ _780119) ^ [_801093, _801095] : [-(class_Rings_Olinordered__semiring__strict(_801093)), _801095 = _801093, class_Rings_Olinordered__semiring__strict(_801095)], (12361 ^ _780119) ^ [_1003708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003708), _1003708))], (37567 ^ _780119) ^ [_1499232, _1499234, _1499236, _1499238] : [37568 ^ _780119 : [(37569 ^ _780119) ^ [_1499307] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1499236, _1499232)), hAPP(hAPP(c_Product__Type_OPair(_1499236, _1499232), _1499307), _1499234)), _1499238))]], -(hBOOL(hAPP(hAPP(c_member(_1499232), _1499234), hAPP(c_Relation_ORange(_1499236, _1499232), _1499238))))], (26989 ^ _780119) ^ [_1274327, _1274329, _1274331, _1274333, _1274335] : [class_Groups_Ocomm__monoid__add(_1274327), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274329), _1274331)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1274329, _1274327), _1274333), hAPP(c_Set_OCollect(_1274329), hAPP(hAPP(c_COMBS(_1274329, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1274329), c_fconj), hAPP(hAPP(c_COMBC(_1274329, tc_fun(_1274329, tc_HOL_Obool), tc_HOL_Obool), c_member(_1274329)), _1274331))), hAPP(hAPP(c_COMBC(_1274329, tc_fun(_1274329, tc_HOL_Obool), tc_HOL_Obool), c_member(_1274329)), _1274335)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1274329, _1274327), hAPP(hAPP(c_COMBC(_1274329, _1274327, _1274327), hAPP(hAPP(c_COMBS(_1274329, _1274327, tc_fun(_1274327, _1274327)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1274327, tc_fun(_1274327, _1274327)), _1274329), c_If(_1274327)), hAPP(hAPP(c_COMBC(_1274329, tc_fun(_1274329, tc_HOL_Obool), tc_HOL_Obool), c_member(_1274329)), _1274335))), _1274333)), c_Groups_Ozero__class_Ozero(_1274327))), _1274331))], (7406 ^ _780119) ^ [_904629, _904631, _904633, _904635] : [class_Lattices_Osemilattice__sup(_904629), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904629), _904631), _904633)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904629), _904635), _904633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904629), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_904629), _904631), _904635)), _904633)))], (7350 ^ _780119) ^ [_903472, _903474, _903476, _903478] : [class_Lattices_Osemilattice__sup(_903472), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903472), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903472), _903474), _903476)), _903478) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903472), _903474), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903472), _903476), _903478)))], (11227 ^ _780119) ^ [_979859, _979861, _979863, _979865, _979867] : [class_Groups_Ocomm__monoid__add(_979859), hBOOL(hAPP(c_Finite__Set_Ofinite(_979861), _979863)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979861, _979859), _979865), hAPP(hAPP(c_Set_Oinsert(_979861), _979867), _979863)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979859), hAPP(_979865, _979867)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979861, _979859), _979865), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979861, tc_HOL_Obool)), _979863), hAPP(hAPP(c_Set_Oinsert(_979861), _979867), c_Orderings_Obot__class_Obot(tc_fun(_979861, tc_HOL_Obool)))))))], (41505 ^ _780119) ^ [_1597871, _1597873, _1597875, _1597877, _1597879] : [class_Complete__Lattice_Ocomplete__lattice(_1597871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597873), _1597875)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1597871), _1597877), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597873, _1597871), _1597875), _1597879)) = hAPP(hAPP(c_Finite__Set_Ofold(_1597873, _1597871, hAPP(hAPP(c_COMBB(_1597871, tc_fun(_1597871, _1597871), _1597873), c_Lattices_Osemilattice__inf__class_Oinf(_1597871)), _1597879)), _1597877), _1597875))], (28890 ^ _780119) ^ [_1315627, _1315629] : [class_Orderings_Olinorder(_1315627), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315627), _1315629)), -(c_Big__Operators_Olattice_OInf__fin(_1315627, c_Orderings_Oord__class_Omin(_1315627), _1315629) = hAPP(c_Finite__Set_Ofold1(_1315627, c_Orderings_Oord__class_Omin(_1315627)), _1315629))], (18812 ^ _780119) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (24609 ^ _780119) ^ [_1231039, _1231041] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1231039, _1231041))))], (31297 ^ _780119) ^ [_1365236, _1365238] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365236)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365238)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1365236), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1365238))))], (29520 ^ _780119) ^ [_1328285, _1328287, _1328289, _1328291] : [hBOOL(hAPP(hAPP(c_member(_1328287), _1328291), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1328285, tc_fun(_1328287, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1328285, tc_HOL_Obool))), _1328289))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1328285, tc_fun(_1328287, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1328285, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1328287, tc_HOL_Obool), tc_fun(_1328287, tc_HOL_Obool), _1328285), hAPP(c_COMBC(_1328287, tc_fun(_1328287, tc_HOL_Obool), tc_HOL_Obool), c_member(_1328287))), _1328289)), _1328291)))], (5542 ^ _780119) ^ [_865033, _865035] : [_865035 = _865033, -(tc_List_Olist(_865035) = tc_List_Olist(_865033))], (46698 ^ _780119) ^ [_1721764, _1721766, _1721768, _1721770] : [-(c_List_Otranspose(_1721764, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1721766), tc_List_Olist(_1721764)), hAPP(c_List_Omap(_1721766, _1721764), _1721768)), _1721770)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1721766), tc_List_Olist(_1721764)), hAPP(c_List_Omap(_1721766, _1721764), _1721768)), c_List_Otranspose(_1721766, _1721770)))], (47630 ^ _780119) ^ [_1740668, _1740670] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1740668), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1740668))), c_List_Otranspose(_1740668, _1740670)))))], (35887 ^ _780119) ^ [_1459643, _1459645, _1459647] : [c_Equiv__Relations_Oequivp(_1459643, _1459645), -(hBOOL(hAPP(hAPP(_1459645, _1459647), _1459647)))], (51147 ^ _780119) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (31305 ^ _780119) ^ [_1365391, _1365393] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1365391) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365393), 31308 ^ _780119 : [(31311 ^ _780119) ^ [] : [-(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), _1365393))))], (31309 ^ _780119) ^ [] : [-(_1365391 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365393)))]]], (30111 ^ _780119) ^ [_1342854, _1342856] : [class_Int_Onumber__ring(_1342854), 30114 ^ _780119 : [(30121 ^ _780119) ^ [] : [-(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), _1342856)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1342854), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1342856)) = c_Groups_Ozero__class_Ozero(_1342854))], (30115 ^ _780119) ^ [] : [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), _1342856))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1342854), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1342856)) = hAPP(c_Int_Onumber__class_Onumber__of(_1342854), _1342856))]]], (26655 ^ _780119) ^ [_1266945, _1266947, _1266949] : [class_Groups_Oordered__ab__group__add__abs(_1266945), 26658 ^ _780119 : [(26667 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266945), hAPP(c_Groups_Oabs__class_Oabs(_1266945), _1266947)), _1266949))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266945), _1266947), _1266949)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266945), hAPP(c_Groups_Ouminus__class_Ouminus(_1266945), _1266947)), _1266949))], (26659 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266945), hAPP(c_Groups_Oabs__class_Oabs(_1266945), _1266947)), _1266949)), 26662 ^ _780119 : [(26665 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266945), hAPP(c_Groups_Ouminus__class_Ouminus(_1266945), _1266947)), _1266949)))], (26663 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266945), _1266947), _1266949)))]]]]], (46598 ^ _780119) ^ [_1719496, _1719498, _1719500] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719496)), hAPP(c_List_Ofilter(_1719496, _1719498), _1719500))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719496)), hAPP(c_List_Ofilter(_1719496, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1719496), c_fNot), _1719498)), _1719500))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719496)), _1719500))], (42481 ^ _780119) ^ [_1620329, _1620331, _1620333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1620329), _1620331)), -(c_Smallcheck_Osmall_H(_1620333, _1620329, _1620331) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (51451 ^ _780119) ^ [] : [-(class_HOL_Oequal(tc_Product__Type_Ounit))], (36724 ^ _780119) ^ [_1477947, _1477949, _1477951, _1477953, _1477955] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1477947, _1477949, _1477951), _1477953), _1477955)), -(hBOOL(hAPP(_1477953, hAPP(_1477951, _1477955))))], (16036 ^ _780119) ^ [_1072361, _1072363, _1072365, _1072367] : [class_Rings_Olinordered__ring__strict(_1072361), 16039 ^ _780119 : [(16054 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072361), _1072363), _1072365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072361), _1072367), _1072365)))), 16055 ^ _780119 : [(16062 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), _1072365), c_Groups_Ozero__class_Ozero(_1072361))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), _1072367), _1072363))], (16056 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), c_Groups_Ozero__class_Ozero(_1072361)), _1072365)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), _1072363), _1072367))]]], (16040 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072361), _1072363), _1072365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072361), _1072367), _1072365))), 16045 ^ _780119 : [(16048 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), _1072363), _1072367)))], (16046 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), c_Groups_Ozero__class_Ozero(_1072361)), _1072365)))]], 16049 ^ _780119 : [(16052 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), _1072367), _1072363)))], (16050 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), _1072365), c_Groups_Ozero__class_Ozero(_1072361))))]]]]], (14002 ^ _780119) ^ [_1034884, _1034886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034884), _1034886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1034884)), _1034886)))], (41391 ^ _780119) ^ [_1594781, _1594783, _1594785, _1594787, _1594789] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1594781, tc_HOL_Obool)), _1594783), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594785, tc_fun(_1594781, tc_HOL_Obool)), _1594787), _1594789)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1594785, tc_fun(_1594781, tc_HOL_Obool)), _1594787), hAPP(hAPP(c_COMBB(tc_fun(_1594781, tc_HOL_Obool), tc_fun(_1594781, tc_HOL_Obool), _1594785), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1594781, tc_HOL_Obool)), _1594783)), _1594789)))], (49138 ^ _780119) ^ [_1774385, _1774387, _1774389] : [c_List_Olist__all2(_1774389, _1774389, c_fequal, _1774385, _1774387), -(_1774385 = _1774387)], (32923 ^ _780119) ^ [_1393567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1393567), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1393567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1393567 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46610 ^ _780119) ^ [_1719742, _1719744, _1719746] : [hBOOL(hAPP(c_List_Odistinct(_1719742), _1719744)), -(hBOOL(hAPP(c_List_Odistinct(_1719742), hAPP(c_List_Ofilter(_1719742, _1719746), _1719744))))], (48543 ^ _780119) ^ [_1761758, _1761760] : [class_Enum_Oenum(_1761758), 48546 ^ _780119 : [(48553 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1761758), _1761760)), -(hBOOL(hAPP(_1761760, 48556 ^ [_1761758, _1761760])))], (48547 ^ _780119) ^ [] : [48548 ^ _780119 : [(48549 ^ _780119) ^ [_1761860] : [hBOOL(hAPP(_1761760, _1761860))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1761758), _1761760)))]]], (616 ^ _780119) ^ [_789557, _789559, _789561, _789563, _789565, _789567] : [-(c_Nitpick_Oless__eq__frac(_789565, _789561, _789557)), c_Nitpick_Oless__eq__frac(_789567, _789563, _789559), _789567 = _789565, _789563 = _789561, _789559 = _789557], (43497 ^ _780119) ^ [_1646993, _1646995, _1646997] : [hAPP(hAPP(c_List_Olist_OCons(_1646993), _1646995), _1646997) = _1646997], (21817 ^ _780119) ^ [_1178420, _1178422] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178420, _1178422) = 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), _1178420), _1178422) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178422), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178420, _1178422)))], (26909 ^ _780119) ^ [_1272291, _1272293, _1272295] : [class_Fields_Olinordered__field__inverse__zero(_1272291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272291), c_Groups_Ozero__class_Ozero(_1272291)), _1272293)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272291), hAPP(c_Groups_Oabs__class_Oabs(_1272291), _1272295)), _1272293) = hAPP(c_Groups_Oabs__class_Oabs(_1272291), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272291), _1272295), _1272293)))], (41625 ^ _780119) ^ [_1600665, _1600667, _1600669] : [-(hAPP(c_Relation_ORange(_1600665, _1600667), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1600665, _1600667), tc_HOL_Obool), _1600669)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1600665, _1600667), tc_HOL_Obool), tc_fun(_1600667, tc_HOL_Obool)), _1600669), c_Relation_ORange(_1600665, _1600667)))], (10548 ^ _780119) ^ [_966517, _966519, _966521] : [class_Lattices_Olattice(_966517), hBOOL(hAPP(c_Finite__Set_Ofinite(_966517), _966519)), hBOOL(hAPP(hAPP(c_member(_966517), _966521), _966519)), 10559 ^ _780119 : [(10566 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966517, tc_HOL_Obool)), _966519), hAPP(hAPP(c_Set_Oinsert(_966517), _966521), c_Orderings_Obot__class_Obot(tc_fun(_966517, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_966517, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_966517, _966519) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_966517), _966521), c_Big__Operators_Olattice__class_OInf__fin(_966517, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966517, tc_HOL_Obool)), _966519), hAPP(hAPP(c_Set_Oinsert(_966517), _966521), c_Orderings_Obot__class_Obot(tc_fun(_966517, tc_HOL_Obool)))))))], (10560 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966517, tc_HOL_Obool)), _966519), hAPP(hAPP(c_Set_Oinsert(_966517), _966521), c_Orderings_Obot__class_Obot(tc_fun(_966517, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_966517, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_966517, _966519) = _966521)]]], (7716 ^ _780119) ^ [_910921] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _910921)], (6135 ^ _780119) ^ [_877891, _877893, _877895, _877897] : [6136 ^ _780119 : [(6139 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_877891), _877893), _877897))], (6137 ^ _780119) ^ [] : [_877893 = _877895]], -(hBOOL(hAPP(hAPP(c_member(_877891), _877893), hAPP(hAPP(c_Set_Oinsert(_877891), _877895), _877897))))], (51513 ^ _780119) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (11740 ^ _780119) ^ [_991542, _991544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991542), _991544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991542), _991544)))], (6837 ^ _780119) ^ [_892658, _892660, _892662, _892664, _892666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892658, tc_HOL_Obool)), _892660), _892662)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892658, tc_HOL_Obool)), _892664), _892666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892658, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892658, tc_HOL_Obool)), _892660), _892664)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892658, tc_HOL_Obool)), _892662), _892666))))], (32379 ^ _780119) ^ [_1383957, _1383959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1383957)), c_Int_OBit0(_1383959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1383957), _1383959)))], (50564 ^ _780119) ^ [_1805852, _1805854, _1805856, _1805858] : [-(hAPP(hAPP(c_List_Oappend(_1805852), c_List_Oreplicate(_1805852, _1805854, _1805856)), c_List_Oreplicate(_1805852, _1805858, _1805856)) = hAPP(hAPP(c_List_Oappend(_1805852), c_List_Oreplicate(_1805852, _1805858, _1805856)), c_List_Oreplicate(_1805852, _1805854, _1805856)))], (7076 ^ _780119) ^ [_896941, _896943, _896945, _896947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896941, tc_HOL_Obool)), _896943), _896945)), hBOOL(hAPP(_896943, _896947)), -(hBOOL(hAPP(_896945, _896947)))], (43771 ^ _780119) ^ [_1654512, _1654514] : [class_Groups_Ocomm__monoid__add(_1654512), hBOOL(hAPP(c_List_Odistinct(_1654512), _1654514)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1654512), _1654514) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1654512, _1654512), c_COMBI(_1654512)), hAPP(c_List_Oset(_1654512), _1654514)))], (26733 ^ _780119) ^ [_1268315, _1268317] : [class_Rings_Olinordered__idom(_1268315), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1268315), c_Groups_Osgn__class_Osgn(_1268315, _1268317)), hAPP(c_Groups_Oabs__class_Oabs(_1268315), _1268317)) = _1268317)], (47039 ^ _780119) ^ [_1728215, _1728217] : [class_Orderings_Olinorder(_1728215), c_List_Olinorder__class_Osorted(_1728215, _1728217), -(c_List_Olinorder__class_Osorted(_1728215, hAPP(c_List_Otl(_1728215), _1728217)))], (42863 ^ _780119) ^ [_1629289, _1629291, _1629293] : [hBOOL(hAPP(c_List_Odistinct(_1629289), hAPP(hAPP(c_List_Omap(tc_prod(_1629289, _1629291), _1629289), c_Product__Type_Ofst(_1629289, _1629291)), _1629293))), -(c_Map_Oran(_1629289, _1629291, hAPP(c_Map_Omap__of(_1629289, _1629291), _1629293)) = hAPP(c_Set_Oimage(tc_prod(_1629289, _1629291), _1629291, c_Product__Type_Osnd(_1629289, _1629291)), hAPP(c_List_Oset(tc_prod(_1629289, _1629291)), _1629293)))], (51465 ^ _780119) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (10370 ^ _780119) ^ [_962880, _962882, _962884, _962886, _962888, _962890, _962892] : [c_Finite__Set_Ofolding__image__simple(_962880, _962882, _962884, _962886, _962888, _962890), hBOOL(hAPP(c_Finite__Set_Ofinite(_962882), _962892)), -(hAPP(_962890, _962892) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_962880, _962882, _962884), _962888), _962886), _962892))], (45870 ^ _780119) ^ [_1703784, _1703786, _1703788] : [-(hAPP(hAPP(c_List_Odrop(_1703784), _1703786), hAPP(c_List_Otl(_1703784), _1703788)) = hAPP(c_List_Otl(_1703784), hAPP(hAPP(c_List_Odrop(_1703784), _1703786), _1703788)))], (13716 ^ _780119) ^ [_1029480, _1029482] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029480), _1029482))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029482)), _1029480)))], (32891 ^ _780119) ^ [_1393005, _1393007, _1393009] : [class_Rings_Olinordered__idom(_1393005), 32894 ^ _780119 : [(32903 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1393005), hAPP(hAPP(c_Power_Opower__class_Opower(_1393005), _1393007), 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(_1393005), _1393009), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1393005)), _1393007 = c_Groups_Ozero__class_Ozero(_1393005), _1393009 = c_Groups_Ozero__class_Ozero(_1393005)], (32895 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1393005), hAPP(hAPP(c_Power_Opower__class_Opower(_1393005), _1393007), 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(_1393005), _1393009), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1393005), 32898 ^ _780119 : [(32901 ^ _780119) ^ [] : [-(_1393009 = c_Groups_Ozero__class_Ozero(_1393005))], (32899 ^ _780119) ^ [] : [-(_1393007 = c_Groups_Ozero__class_Ozero(_1393005))]]]]], (3800 ^ _780119) ^ [_837356, _837358, _837360, _837362, _837364, _837366] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_837366, _837362, _837358) = c_SetInterval_Oord__class_OgreaterThanAtMost(_837364, _837360, _837356)), _837366 = _837364, _837362 = _837360, _837358 = _837356], (47464 ^ _780119) ^ [_1737242, _1737244] : [47466 ^ _780119 : [(47469 ^ _780119) ^ [] : [47465 ^ [_1737242, _1737244] = c_List_Olist_ONil(_1737242)], (47467 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1737242)), 47465 ^ [_1737242, _1737244]), hAPP(c_List_Oset(tc_List_Olist(_1737242)), _1737244))))]], -(c_List_Oconcat(_1737242, _1737244) = c_List_Olist_ONil(_1737242))], (45850 ^ _780119) ^ [_1703547, _1703549] : [-(_1703547 = c_List_Olist_ONil(_1703549)), -(hAPP(c_List_Ohd(_1703549), _1703547) = hAPP(hAPP(c_List_Onth(_1703549), _1703547), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24031 ^ _780119) ^ [_1219795, _1219797] : [class_Groups_Oordered__ab__group__add(_1219795), -(hAPP(c_Set_Oimage(_1219795, _1219795, c_Groups_Ouminus__class_Ouminus(_1219795)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1219795), _1219797)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1219795), hAPP(c_Groups_Ouminus__class_Ouminus(_1219795), _1219797)))], (10514 ^ _780119) ^ [_965893, _965895, _965897, _965899, _965901] : [c_Finite__Set_Ofolding__one(_965893, _965895, _965897), hBOOL(hAPP(c_Finite__Set_Ofinite(_965893), _965899)), hBOOL(hAPP(c_Finite__Set_Ofinite(_965893), _965901)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965893, tc_HOL_Obool)), _965899), _965901) = c_Orderings_Obot__class_Obot(tc_fun(_965893, tc_HOL_Obool))), -(hAPP(hAPP(_965895, hAPP(_965897, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_965893, tc_HOL_Obool)), _965899), _965901))), hAPP(_965897, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965893, tc_HOL_Obool)), _965899), _965901))) = hAPP(hAPP(_965895, hAPP(_965897, _965899)), hAPP(_965897, _965901)))], (35925 ^ _780119) ^ [_1460374] : [-(c_Equiv__Relations_Oequivp(_1460374, c_fequal))], (39859 ^ _780119) ^ [_1557518, _1557520, _1557522, _1557524] : [hBOOL(hAPP(hAPP(c_member(_1557518), _1557520), c_Wellfounded_Oacc(_1557518, _1557522))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1557518, _1557518)), hAPP(hAPP(c_Product__Type_OPair(_1557518, _1557518), _1557524), _1557520)), c_Transitive__Closure_Ortrancl(_1557518, _1557522))), -(hBOOL(hAPP(hAPP(c_member(_1557518), _1557524), c_Wellfounded_Oacc(_1557518, _1557522))))], (6431 ^ _780119) ^ [_884070, _884072, _884074, _884076, _884078] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_884070), _884072)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884074, tc_HOL_Obool)), _884076), hAPP(c_Set_Oimage(_884070, _884074, _884078), _884072))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_884074), _884076)))], (7868 ^ _780119) ^ [_914084, _914086] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_914084, _914086))), -(hBOOL(hAPP(c_Com_OWT, _914086)))], (34845 ^ _780119) ^ [_1434262, _1434264, _1434266, _1434268] : [-(hAPP(c_Product__Type_Ofst(_1434262, _1434264), hAPP(hAPP(c_Product__Type_OPair(_1434262, _1434264), _1434266), _1434268)) = _1434266)], (50524 ^ _780119) ^ [_1805154, _1805156, _1805158] : [_1805156 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1805154, _1805156, _1805158) = c_List_Olist_ONil(_1805154))], (21917 ^ _780119) ^ [_1180250, _1180252, _1180254, _1180256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180252), _1180254)), -(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), _1180254), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1180256, _1180250))), _1180252))))], (32763 ^ _780119) ^ [_1390782] : [-(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)))), _1390782) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1390782), _1390782))], (27662 ^ _780119) ^ [_1291094, _1291096, _1291098, _1291100] : [class_Orderings_Olinorder(_1291094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291094), _1291096), _1291098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291094), _1291100), _1291098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291094), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291094), _1291096), _1291100)), _1291098)))], (3572 ^ _780119) ^ [_833816, _833818, _833820, _833822] : [-(c_Big__Operators_Olinorder__class_OMax(_833822, _833818) = c_Big__Operators_Olinorder__class_OMax(_833820, _833816)), _833822 = _833820, _833818 = _833816], (32167 ^ _780119) ^ [_1380020, _1380022, _1380024, _1380026, _1380028] : [-(c_Nat_Onat_Onat__case(_1380020, _1380022, _1380024, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1380026)), _1380028)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1380020), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1380026))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1380020, _1380020), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1380020, tc_fun(_1380020, _1380020)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1380020, tc_fun(_1380020, _1380020)), tc_Int_Oint), c_If(_1380020)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1380020, _1380022, _1380024, _1380028))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1380020, tc_Int_Oint), _1380024), 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)), _1380028)))))], (7053 ^ _780119) ^ [_896561] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _896561))), -(hAPP(c_Com_Obody, _896561) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 7056 ^ [_896561]))], (35398 ^ _780119) ^ [_1447680, _1447682, _1447684, _1447686, _1447688] : [-(hBOOL(hAPP(hAPP(c_member(_1447680), _1447682), hAPP(c_Relation_OImage(_1447684, _1447680, _1447686), _1447688)))), 35399 ^ _780119 : [(35400 ^ _780119) ^ [_1447766] : [hBOOL(hAPP(hAPP(c_member(_1447684), _1447766), _1447688)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1447684, _1447680)), hAPP(hAPP(c_Product__Type_OPair(_1447684, _1447680), _1447766), _1447682)), _1447686))]]], (3794 ^ _780119) ^ [_837271, _837273] : [_837273 = _837271, -(c_SetInterval_Oord__class_OlessThan(_837273) = c_SetInterval_Oord__class_OlessThan(_837271))], (21562 ^ _780119) ^ [_1173387, _1173389, _1173391] : [-(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, _1173387, _1173389)), _1173391), _1173389) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1173387), _1173391), _1173389))], (39917 ^ _780119) ^ [_1558891] : [-(c_Relation_OId(_1558891) = hAPP(c_Set_OCollect(tc_prod(_1558891, _1558891)), hAPP(hAPP(c_COMBB(tc_fun(_1558891, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1558891, _1558891)), c_HOL_OEx(_1558891)), hAPP(hAPP(c_COMBC(tc_prod(_1558891, _1558891), tc_fun(_1558891, tc_prod(_1558891, _1558891)), tc_fun(_1558891, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1558891, _1558891), tc_HOL_Obool), tc_fun(tc_fun(_1558891, tc_prod(_1558891, _1558891)), tc_fun(_1558891, tc_HOL_Obool)), tc_prod(_1558891, _1558891)), c_COMBB(tc_prod(_1558891, _1558891), tc_HOL_Obool, _1558891)), c_fequal)), hAPP(hAPP(c_COMBS(_1558891, _1558891, tc_prod(_1558891, _1558891)), c_Product__Type_OPair(_1558891, _1558891)), c_COMBI(_1558891))))))], (13776 ^ _780119) ^ [_1030700, _1030702, _1030704, _1030706] : [class_Groups_Ocomm__monoid__mult(_1030700), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1030702), _1030704))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1030702, _1030700), _1030706), _1030704) = c_Groups_Oone__class_Oone(_1030700))], (14778 ^ _780119) ^ [_1051507, _1051509, _1051511] : [class_Power_Opower(_1051507), class_Rings_Omult__zero(_1051507), class_Rings_Ono__zero__divisors(_1051507), class_Rings_Ozero__neq__one(_1051507), 14793 ^ _780119 : [(14802 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1051507), _1051509), _1051511) = c_Groups_Ozero__class_Ozero(_1051507)), _1051509 = c_Groups_Ozero__class_Ozero(_1051507), -(_1051511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14794 ^ _780119) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1051507), _1051509), _1051511) = c_Groups_Ozero__class_Ozero(_1051507), 14797 ^ _780119 : [(14800 ^ _780119) ^ [] : [_1051511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14798 ^ _780119) ^ [] : [-(_1051509 = c_Groups_Ozero__class_Ozero(_1051507))]]]]], (4350 ^ _780119) ^ [_845953, _845955] : [_845955 = _845953, -(c_List_Odistinct(_845955) = c_List_Odistinct(_845953))], (8590 ^ _780119) ^ [_928938, _928940, _928942] : [class_Orderings_Olinorder(_928938), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928938), _928940), _928942))), 8597 ^ _780119 : [(8604 ^ _780119) ^ [] : [_928942 = _928940, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928938), _928942), _928940))], (8598 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928938), _928942), _928940))), -(_928942 = _928940)]]], (13764 ^ _780119) ^ [_1030482, _1030484, _1030486] : [class_Groups_Ocomm__monoid__mult(_1030482), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1030484, _1030482), _1030486), c_Orderings_Obot__class_Obot(tc_fun(_1030484, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1030482))], (36137 ^ _780119) ^ [_1465527, _1465529, _1465531, _1465533] : [36139 ^ _780119 : [(36140 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1465527), 36138 ^ [_1465527, _1465529, _1465531, _1465533]), _1465533)))], (36143 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1465527), 36141 ^ [_1465527, _1465529, _1465531, _1465533]), _1465533)))], (36147 ^ _780119) ^ [] : [36138 ^ [_1465527, _1465529, _1465531, _1465533] = 36141 ^ [_1465527, _1465529, _1465531, _1465533]], (36145 ^ _780119) ^ [] : [-(hAPP(_1465531, 36138 ^ [_1465527, _1465529, _1465531, _1465533]) = hAPP(_1465531, 36141 ^ [_1465527, _1465529, _1465531, _1465533]))]], -(c_Fun_Oinj__on(_1465527, _1465529, _1465531, _1465533))], (21378 ^ _780119) ^ [_1169523, _1169525] : [class_Divides_Osemiring__div(_1169523), -(c_Divides_Odiv__class_Omod(_1169523, _1169525, c_Groups_Ozero__class_Ozero(_1169523)) = _1169525)], (31133 ^ _780119) ^ [_1362237, _1362239] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362237)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362239)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1362237), _1362239)))], (41397 ^ _780119) ^ [_1595080, _1595082, _1595084, _1595086, _1595088, _1595090] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595080, tc_fun(_1595082, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1595084, tc_fun(_1595080, tc_HOL_Obool)), _1595086), _1595088)), _1595090) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595084, tc_fun(_1595082, tc_HOL_Obool)), _1595086), hAPP(hAPP(c_COMBC(_1595084, tc_fun(_1595080, tc_fun(_1595082, tc_HOL_Obool)), tc_fun(_1595082, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1595080, tc_HOL_Obool), tc_fun(tc_fun(_1595080, tc_fun(_1595082, tc_HOL_Obool)), tc_fun(_1595082, tc_HOL_Obool)), _1595084), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595080, tc_fun(_1595082, tc_HOL_Obool))), _1595088)), _1595090)))], (25985 ^ _780119) ^ [_1254117, _1254119] : [class_Rings_Oring__1(_1254117), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254119)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1254117), hAPP(c_Int_Onat, _1254119)) = hAPP(c_Int_Oring__1__class_Oof__int(_1254117), _1254119))], (50110 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15194 ^ _780119) ^ [_1058010] : [hAPP(c_Nat_OSuc, _1058010) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41812 ^ _780119) ^ [_1604957, _1604959, _1604961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1604957, tc_HOL_Obool), tc_HOL_Obool)), _1604959), _1604961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604957, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1604957, tc_HOL_Obool), _1604961)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1604957, tc_HOL_Obool), _1604959))))], (34751 ^ _780119) ^ [_1432239, _1432241, _1432243, _1432245] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1432239, _1432239)), hAPP(hAPP(c_Product__Type_OPair(_1432239, _1432239), _1432241), _1432243)), hAPP(c_Wellfounded_Omeasure(_1432239), _1432245))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1432245, _1432241)), hAPP(_1432245, _1432243))))], (51237 ^ _780119) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (43825 ^ _780119) ^ [_1655779, _1655781, _1655783, _1655785] : [class_Groups_Ocomm__monoid__add(_1655779), 43828 ^ _780119 : [(43835 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1655781), _1655783))), -(c_Nitpick_Osetsum_H(_1655781, _1655779, _1655785, _1655783) = c_Groups_Ozero__class_Ozero(_1655779))], (43829 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1655781), _1655783)), -(c_Nitpick_Osetsum_H(_1655781, _1655779, _1655785, _1655783) = hAPP(c_List_Omonoid__add__class_Olistsum(_1655779), hAPP(hAPP(c_List_Omap(_1655781, _1655779), _1655785), c_Hilbert__Choice_OEps(tc_List_Olist(_1655781), hAPP(hAPP(c_COMBS(tc_List_Olist(_1655781), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1655781)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1655781), tc_fun(_1655781, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1655781, tc_HOL_Obool), tc_fun(tc_fun(_1655781, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1655781)), c_fequal), c_List_Oset(_1655781))), _1655783))), c_List_Odistinct(_1655781))))))]]], (37511 ^ _780119) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (22569 ^ _780119) ^ [_1191950, _1191952, _1191954, _1191956, _1191958] : [c_Com_Ocom_OSemi(_1191950, _1191952) = c_Com_Ocom_OCond(_1191954, _1191956, _1191958)], (37829 ^ _780119) ^ [_1507160, _1507162] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507160, _1507160), tc_HOL_Obool)), c_Relation_OId__on(_1507160, _1507162)), hAPP(hAPP(c_Product__Type_OSigma(_1507160, _1507160), _1507162), hAPP(c_COMBK(tc_fun(_1507160, tc_HOL_Obool), _1507160), _1507162)))))], (18760 ^ _780119) ^ [_1122248, _1122250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1122248), _1122250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122250), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (31393 ^ _780119) ^ [_1366971] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366971))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366971)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10362 ^ _780119) ^ [_962614, _962616, _962618] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_962614, _962616, c_Orderings_Obot__class_Obot(tc_fun(_962614, tc_HOL_Obool))), _962618))], (50470 ^ _780119) ^ [_1803569, _1803571, _1803573, _1803575, _1803577] : [-(c_Predicate_Oconversep(_1803569, _1803571, c_Predicate_Opred__comp(_1803569, _1803573, _1803571, _1803575, _1803577)) = c_Predicate_Opred__comp(_1803571, _1803573, _1803569, c_Predicate_Oconversep(_1803573, _1803571, _1803577), c_Predicate_Oconversep(_1803569, _1803573, _1803575)))], (44944 ^ _780119) ^ [_1680896, _1680898, _1680900, _1680902, _1680904] : [hAPP(hAPP(c_List_Oappend(_1680896), _1680898), hAPP(hAPP(c_List_Olist_OCons(_1680896), _1680900), c_List_Olist_ONil(_1680896))) = hAPP(hAPP(c_List_Oappend(_1680896), _1680902), hAPP(hAPP(c_List_Olist_OCons(_1680896), _1680904), c_List_Olist_ONil(_1680896))), 44947 ^ _780119 : [(44950 ^ _780119) ^ [] : [-(_1680900 = _1680904)], (44948 ^ _780119) ^ [] : [-(_1680898 = _1680902)]]], (2318 ^ _780119) ^ [_814227, _814229, _814231, _814233, _814235, _814237] : [-(c_Nat_Onat_Onat__rec(_814237, _814233, _814229) = c_Nat_Onat_Onat__rec(_814235, _814231, _814227)), _814237 = _814235, _814233 = _814231, _814229 = _814227], (9728 ^ _780119) ^ [_948797, _948799, _948801, _948803] : [class_Groups_Oab__semigroup__mult(_948797), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948797), _948799), _948801)), _948803) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948797), _948799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948797), _948801), _948803)))], (6857 ^ _780119) ^ [_893557, _893559, _893561] : [class_Orderings_Olinorder(_893557), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893557), _893559), _893561))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893557), _893561), _893559)))], (10973 ^ _780119) ^ [_974949, _974951] : [class_Groups_Omonoid__mult(_974949), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974949), c_Groups_Oone__class_Oone(_974949)), _974951) = _974951)], (40194 ^ _780119) ^ [_1565951, _1565953] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565951, _1565951)), hAPP(hAPP(c_Product__Type_OPair(_1565951, _1565951), 40195 ^ [_1565951, _1565953]), 40195 ^ [_1565951, _1565953])), c_Transitive__Closure_Otrancl(_1565951, _1565953)))), -(c_Wellfounded_Oacyclic(_1565951, _1565953))], (29140 ^ _780119) ^ [_1320107, _1320109, _1320111] : [class_Orderings_Olinorder(_1320107), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320107), _1320109)), -(_1320109 = c_Orderings_Obot__class_Obot(tc_fun(_1320107, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320107), _1320111)), -(_1320111 = c_Orderings_Obot__class_Obot(tc_fun(_1320107, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320107, tc_HOL_Obool)), _1320109), _1320111) = c_Orderings_Obot__class_Obot(tc_fun(_1320107, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1320107, c_Orderings_Oord__class_Omin(_1320107), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320107, tc_HOL_Obool)), _1320109), _1320111)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1320107), c_Big__Operators_Olattice_OInf__fin(_1320107, c_Orderings_Oord__class_Omin(_1320107), _1320109)), c_Big__Operators_Olattice_OInf__fin(_1320107, c_Orderings_Oord__class_Omin(_1320107), _1320111)))], (45546 ^ _780119) ^ [_1696223, _1696225, _1696227, _1696229] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1696223), tc_List_Olist(_1696223))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1696223), tc_List_Olist(_1696223)), _1696225), _1696227)), c_List_Olistrel1(_1696223, _1696229)))), 45547 ^ _780119 : [(45548 ^ _780119) ^ [_1696356, _1696358] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1696223, _1696223)), hAPP(hAPP(c_Product__Type_OPair(_1696223, _1696223), hAPP(hAPP(c_List_Onth(_1696223), _1696225), _1696356)), _1696358)), _1696229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1696356), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696223)), _1696225))), _1696227 = hAPP(hAPP(c_List_Olist__update(_1696223, _1696225), _1696356), _1696358)]]], (37117 ^ _780119) ^ [_1488329, _1488331, _1488333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1488329, _1488329), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1488329, _1488329, _1488329), _1488331), _1488333)), _1488331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1488329, tc_HOL_Obool), tc_fun(_1488329, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1488329, tc_HOL_Obool), tc_fun(_1488329, tc_HOL_Obool), tc_fun(_1488329, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1488329, _1488331)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1488329, tc_HOL_Obool), tc_fun(_1488329, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1488329, _1488333)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1488329, tc_HOL_Obool), tc_fun(_1488329, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1488329, tc_HOL_Obool), tc_fun(_1488329, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1488329, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1488329, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1488329, tc_HOL_Obool), tc_fun(_1488329, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1488329, _1488331))))], (34869 ^ _780119) ^ [_1434749, _1434751] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1434749), _1434751) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1434749, _1434751)))], (13917 ^ _780119) ^ [_1033230, _1033232, _1033234] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033230, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1033230, tc_HOL_Obool)), _1033232), _1033234)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1033230, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033230, tc_HOL_Obool)), _1033232)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033230, tc_HOL_Obool)), _1033234)))], (43687 ^ _780119) ^ [_1652274, _1652276, _1652278, _1652280] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1652274), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1652276), _1652278)))), -(hAPP(c_Random_Opick(_1652276, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1652276)), _1652278), _1652280)), _1652274) = hAPP(c_Random_Opick(_1652276, _1652280), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1652274), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1652276), _1652278))))], (32203 ^ _780119) ^ [_1380808, _1380810, _1380812, _1380814] : [-(hAPP(c_Nat_Onat_Onat__rec(_1380808, _1380810, _1380812), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1380814)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1380808), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1380814))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1380808, _1380808), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1380808, tc_fun(_1380808, _1380808)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1380808, tc_fun(_1380808, _1380808)), tc_Int_Oint), c_If(_1380808)), c_Nat__Numeral_Oneg)), _1380810)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1380808, _1380808), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1380808, _1380808), tc_Int_Oint), _1380812), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1380808, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1380808, _1380810, _1380812)), c_Int_Onat)))))], (11995 ^ _780119) ^ [_996228, _996230, _996232] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996230), _996232)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996228), _996230)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996228), _996232)))], (43080 ^ _780119) ^ [_1634418, _1634420, _1634422, _1634424] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634418, _1634418)), hAPP(hAPP(c_Product__Type_OPair(_1634418, _1634418), _1634420), _1634422)), hAPP(c_List_Oset(tc_prod(_1634418, _1634418)), hAPP(hAPP(c_List_Ozip(_1634418, _1634418), _1634424), _1634424))))), hBOOL(hAPP(hAPP(c_member(_1634418), _1634420), hAPP(c_List_Oset(_1634418), _1634424))), _1634420 = _1634422], (25836 ^ _780119) ^ [_1251673] : [25838 ^ _780119 : [(25841 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25837 ^ [_1251673]))], (25839 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 25837 ^ [_1251673]), _1251673)))]], -(c_Nat__Transfer_Onat__set(_1251673))], (21510 ^ _780119) ^ [_1172281, _1172283, _1172285, _1172287] : [class_Divides_Oring__div(_1172281), -(c_Divides_Odiv__class_Omod(_1172281, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1172281), _1172283), _1172285), _1172287) = c_Divides_Odiv__class_Omod(_1172281, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1172281), c_Divides_Odiv__class_Omod(_1172281, _1172283, _1172287)), c_Divides_Odiv__class_Omod(_1172281, _1172285, _1172287)), _1172287))], (51155 ^ _780119) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (8298 ^ _780119) ^ [_923300, _923302, _923304] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_923300), _923302)), hBOOL(hAPP(_923304, _923302)), 8309 ^ _780119 : [(8310 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_923300), 8308 ^ [_923300, _923302, _923304])))], (8312 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_923300), 8307 ^ [_923300, _923302, _923304]), 8308 ^ [_923300, _923302, _923304])))], (8316 ^ _780119) ^ [] : [hBOOL(hAPP(_923304, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923300, tc_HOL_Obool)), 8308 ^ [_923300, _923302, _923304]), hAPP(hAPP(c_Set_Oinsert(_923300), 8307 ^ [_923300, _923302, _923304]), c_Orderings_Obot__class_Obot(tc_fun(_923300, tc_HOL_Obool))))))], (8314 ^ _780119) ^ [] : [-(hBOOL(hAPP(_923304, 8308 ^ [_923300, _923302, _923304])))]], -(hBOOL(hAPP(_923304, c_Orderings_Obot__class_Obot(tc_fun(_923300, tc_HOL_Obool)))))], (4384 ^ _780119) ^ [_846480, _846482, _846484, _846486] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_846486, _846482) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_846484, _846480)), _846486 = _846484, _846482 = _846480], (26127 ^ _780119) ^ [_1256569] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1256569)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1256569))], (9190 ^ _780119) ^ [_937928, _937930, _937932, _937934] : [class_Lattices_Osemilattice__sup(_937928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937928), _937930), _937932)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937928), _937930), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_937928), _937932), _937934))))], (37022 ^ _780119) ^ [_1485392, _1485394, _1485396, _1485398, _1485400, _1485402, _1485404, _1485406] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1485392, _1485394)), hAPP(hAPP(c_Product__Type_OPair(_1485392, _1485394), _1485396), _1485398)), _1485400)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1485394, _1485402)), hAPP(hAPP(c_Product__Type_OPair(_1485394, _1485402), _1485398), _1485404)), _1485406)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1485392, _1485402)), hAPP(hAPP(c_Product__Type_OPair(_1485392, _1485402), _1485396), _1485404)), hAPP(hAPP(c_Relation_Orel__comp(_1485392, _1485394, _1485402), _1485400), _1485406))))], (40238 ^ _780119) ^ [_1566974, _1566976, _1566978, _1566980] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566974, _1566974), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1566976), _1566978)), _1566980) = hAPP(hAPP(c_Relation_Orel__comp(_1566974, _1566974, _1566974), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566974, _1566974), tc_HOL_Obool), _1566976), _1566980)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566974, _1566974), tc_HOL_Obool), _1566978), _1566980)))], (29747 ^ _780119) ^ [_1333569, _1333571, _1333573, _1333575] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1333569, tc_fun(_1333571, tc_HOL_Obool)), _1333573), _1333575) = c_Orderings_Obot__class_Obot(tc_fun(_1333571, tc_HOL_Obool)), 29750 ^ _780119 : [(29751 ^ _780119) ^ [_1333685] : [hBOOL(hAPP(hAPP(c_member(_1333569), _1333685), _1333573)), -(hAPP(_1333575, _1333685) = c_Orderings_Obot__class_Obot(tc_fun(_1333571, tc_HOL_Obool)))]]], (38397 ^ _780119) ^ [_1522600, _1522602, _1522604] : [c_Predicate_Oreflp(_1522600, _1522602), -(hBOOL(hAPP(hAPP(_1522602, _1522604), _1522604)))], (25394 ^ _780119) ^ [_1244535, _1244537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1244535), _1244537)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1244537), _1244535)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1244537)), hAPP(c_Int_Onat, _1244535)))], (17534 ^ _780119) ^ [_1098814, _1098816, _1098818, _1098820] : [class_Rings_Olinordered__semidom(_1098814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098814), hAPP(hAPP(c_Power_Opower__class_Opower(_1098814), _1098816), _1098818)), hAPP(hAPP(c_Power_Opower__class_Opower(_1098814), _1098820), _1098818))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098814), c_Groups_Ozero__class_Ozero(_1098814)), _1098820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098814), _1098816), _1098820)))], (16841 ^ _780119) ^ [_1086365, _1086367] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086365), _1086367) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 16842 ^ _780119 : [(16849 ^ _780119) ^ [] : [_1086365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1086367 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16843 ^ _780119) ^ [] : [_1086365 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1086367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (5771 ^ _780119) ^ [_871434, _871436, _871438, _871440] : [c_Hoare__Mirabelle_Ohoare__derivs(_871434, _871436, _871438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_871434), tc_HOL_Obool)), _871436), _871440)), -(c_Hoare__Mirabelle_Ohoare__derivs(_871434, _871440, _871438))], (43158 ^ _780119) ^ [_1636762, _1636764, _1636766, _1636768] : [class_Orderings_Olinorder(_1636762), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1636762, _1636762, c_COMBI(_1636762)), _1636764), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1636762, _1636762, c_COMBI(_1636762)), _1636766), _1636768)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1636762, _1636762, c_COMBI(_1636762)), _1636766), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1636762, _1636762, c_COMBI(_1636762)), _1636764), _1636768)))], (1790 ^ _780119) ^ [_805218, _805220] : [-(class_Groups_Ozero(_805218)), _805220 = _805218, class_Groups_Ozero(_805220)], (25442 ^ _780119) ^ [_1245422, _1245424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245422)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1245422)), _1245424) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1245422), _1245424)))], (50234 ^ _780119) ^ [_1797972] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1797972)), c_Int_OPls))], (49970 ^ _780119) ^ [_1793294, _1793296, _1793298] : [c_List_Olist__ex1(_1793294, _1793296, _1793298), 49974 ^ _780119 : [(49977 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1793296, 49973 ^ [_1793294, _1793296, _1793298])))], (49979 ^ _780119) ^ [_1793540] : [-(_1793540 = 49973 ^ [_1793294, _1793296, _1793298]), hBOOL(hAPP(hAPP(c_member(_1793294), _1793540), hAPP(c_List_Oset(_1793294), _1793298))), hBOOL(hAPP(_1793296, _1793540))], (49975 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1793294), 49973 ^ [_1793294, _1793296, _1793298]), hAPP(c_List_Oset(_1793294), _1793298))))]]], (40138 ^ _780119) ^ [_1564324, _1564326] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564324, _1564324)), _1564326)), c_Wellfounded_Oacyclic(_1564324, _1564326), -(c_Wellfounded_Owf(_1564324, hAPP(c_Relation_Oconverse(_1564324, _1564324), _1564326)))], (47166 ^ _780119) ^ [_1730641, _1730643] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730641)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730643)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730641), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730643)) = c_List_Olist_ONil(tc_Nat_Onat))], (32553 ^ _780119) ^ [_1386972] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1386972)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1386972))))], (36688 ^ _780119) ^ [_1477051, _1477053, _1477055] : [-(hAPP(c_Set_Ovimage(_1477051, _1477053, _1477055), c_Orderings_Otop__class_Otop(tc_fun(_1477053, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1477051, tc_HOL_Obool)))], (33231 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (26025 ^ _780119) ^ [_1254739] : [c_Nat__Transfer_Onat__set(_1254739), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1254739) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1254739)))], (38878 ^ _780119) ^ [_1533815, _1533817, _1533819, _1533821, _1533823] : [class_Groups_Ocomm__monoid__mult(_1533815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533817), _1533819)), c_Fun_Oinj__on(_1533817, _1533817, _1533821, _1533819), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1533817, _1533815), _1533823), hAPP(c_Set_Oimage(_1533817, _1533817, _1533821), _1533819)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1533817, _1533815), hAPP(c_Fun_Ocomp(_1533817, _1533815, _1533817, _1533823), _1533821)), _1533819))], (51657 ^ _780119) ^ [] : [-(c_Hoare__Mirabelle_Ostate__not__singleton)], (47997 ^ _780119) ^ [_1749556, _1749558, _1749560] : [-(c_List_Oremdups(_1749556, hAPP(c_List_Ofilter(_1749556, _1749558), _1749560)) = hAPP(c_List_Ofilter(_1749556, _1749558), c_List_Oremdups(_1749556, _1749560)))], (43208 ^ _780119) ^ [_1637868, _1637870] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1637868), hAPP(c_List_Oset(_1637868), _1637870))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637868)), _1637870))))], (10132 ^ _780119) ^ [_956899, _956901, _956903, _956905] : [-(hBOOL(hAPP(hAPP(c_member(_956899), _956901), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956899, tc_HOL_Obool)), _956903), _956905)))), hBOOL(hAPP(hAPP(c_member(_956899), _956901), _956903)), hBOOL(hAPP(hAPP(c_member(_956899), _956901), _956905))], (48731 ^ _780119) ^ [_1765338, _1765340, _1765342] : [class_Enum_Oenum(_1765338), class_Enum_Oenum(_1765340), class_HOL_Oequal(_1765340), 48742 ^ _780119 : [(48749 ^ _780119) ^ [] : [c_Enum_Oall__n__lists(_1765338, hAPP(hAPP(c_COMBB(tc_fun(_1765340, _1765338), tc_HOL_Obool, tc_List_Olist(_1765338)), _1765342), hAPP(hAPP(c_COMBB(tc_fun(_1765340, tc_Option_Ooption(_1765338)), tc_fun(_1765340, _1765338), tc_List_Olist(_1765338)), c_Fun_Ocomp(tc_Option_Ooption(_1765338), _1765338, _1765340, c_Option_Othe(_1765338))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1765340, _1765338)), tc_fun(_1765340, tc_Option_Ooption(_1765338)), tc_List_Olist(_1765338)), c_Map_Omap__of(_1765340, _1765338)), hAPP(c_List_Ozip(_1765340, _1765338), c_Enum_Oenum__class_Oenum(_1765340))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765340)), c_Enum_Oenum__class_Oenum(_1765340))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1765340, _1765338)), _1765342)))], (48743 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1765340, _1765338)), _1765342)), -(c_Enum_Oall__n__lists(_1765338, hAPP(hAPP(c_COMBB(tc_fun(_1765340, _1765338), tc_HOL_Obool, tc_List_Olist(_1765338)), _1765342), hAPP(hAPP(c_COMBB(tc_fun(_1765340, tc_Option_Ooption(_1765338)), tc_fun(_1765340, _1765338), tc_List_Olist(_1765338)), c_Fun_Ocomp(tc_Option_Ooption(_1765338), _1765338, _1765340, c_Option_Othe(_1765338))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1765340, _1765338)), tc_fun(_1765340, tc_Option_Ooption(_1765338)), tc_List_Olist(_1765338)), c_Map_Omap__of(_1765340, _1765338)), hAPP(c_List_Ozip(_1765340, _1765338), c_Enum_Oenum__class_Oenum(_1765340))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765340)), c_Enum_Oenum__class_Oenum(_1765340))))]]], (32541 ^ _780119) ^ [_1386702, _1386704] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1386702)), c_Int_OBit1(_1386704)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1386702), _1386704)))], (25382 ^ _780119) ^ [_1244310, _1244312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244312)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1244310)), hAPP(c_Int_Onat, _1244312)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244310), _1244312)))], (24607 ^ _780119) ^ [_1231008, _1231010] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1231008, _1231010))))], (31535 ^ _780119) ^ [_1369124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1369124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1369124)))], (41127 ^ _780119) ^ [_1586738, _1586740, _1586742, _1586744, _1586746] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586738, tc_fun(_1586740, tc_HOL_Obool)), _1586742), hAPP(hAPP(c_COMBB(tc_fun(_1586740, tc_HOL_Obool), tc_fun(_1586740, tc_HOL_Obool), _1586738), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1586740, tc_HOL_Obool)), _1586744)), _1586746)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1586740, tc_HOL_Obool)), _1586744), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586738, tc_fun(_1586740, tc_HOL_Obool)), _1586742), _1586746)))], (24473 ^ _780119) ^ [_1228373, _1228375, _1228377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228373)), 24476 ^ _780119 : [(24477 ^ _780119) ^ [_1228507] : [24479 ^ _780119 : [(24483 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24481 ^ [_1228373, _1228375, _1228377, _1228507]), _1228375)))], (24485 ^ _780119) ^ [] : [-(_1228507 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24481 ^ [_1228373, _1228375, _1228377, _1228507]), 24478 ^ [_1228373, _1228375, _1228377, _1228507]))], (24480 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24478 ^ [_1228373, _1228375, _1228377, _1228507]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1228373))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228507), _1228377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1228507), _1228373)), _1228377)))]]], (9762 ^ _780119) ^ [_949562, _949564, _949566] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949562, tc_HOL_Obool)), _949564), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949562, tc_HOL_Obool)), _949564), _949566)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949562, tc_HOL_Obool)), _949564), _949566))], (33549 ^ _780119) ^ [_1404692, _1404694] : [_1404692 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1404692, _1404694) = _1404694)], (33541 ^ _780119) ^ [_1404445] : [-(c_Int_Oint__ge__less__than(_1404445) = 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), _1404445)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (12307 ^ _780119) ^ [_1002705, _1002707, _1002709, _1002711, _1002713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002705), _1002707)), 12310 ^ _780119 : [(12317 ^ _780119) ^ [] : [_1002711 = 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), _1002707), _1002705)), _1002709)), _1002713), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002705), _1002709)), _1002711) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002707), _1002709)), _1002713))], (12311 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002705), _1002709)), _1002711) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002707), _1002709)), _1002713), -(_1002711 = 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), _1002707), _1002705)), _1002709)), _1002713))]]], (51131 ^ _780119) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (29733 ^ _780119) ^ [_1333270, _1333272, _1333274] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1333270, tc_fun(_1333272, tc_HOL_Obool)), _1333274), hAPP(c_COMBK(tc_fun(_1333272, tc_HOL_Obool), _1333270), c_Orderings_Obot__class_Obot(tc_fun(_1333272, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1333272, tc_HOL_Obool)))], (32339 ^ _780119) ^ [_1383254, _1383256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1383254)), c_Int_OBit0(_1383256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383254), _1383256)))], (12449 ^ 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[class_Orderings_Olinorder(_1341119), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341119), _1341121)), 30032 ^ _780119 : [(30035 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341119), 30031 ^ [_1341119, _1341121, _1341123]), _1341123))], (30033 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1341119), 30031 ^ [_1341119, _1341121, _1341123]), _1341121)))]], hBOOL(hAPP(hAPP(c_member(_1341119), _1341123), _1341121)), -(c_Big__Operators_Olinorder__class_OMax(_1341119, _1341121) = _1341123)], (26317 ^ _780119) ^ [_1260381, _1260383, _1260385, _1260387] : [class_Groups_Oordered__ab__group__add__abs(_1260381), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260381), hAPP(c_Groups_Oabs__class_Oabs(_1260381), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1260383, _1260381), _1260385), _1260387))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1260383, _1260381), hAPP(hAPP(c_COMBB(_1260381, _1260381, _1260383), c_Groups_Oabs__class_Oabs(_1260381)), _1260385)), _1260387))))], (13049 ^ _780119) ^ [_1017362, _1017364, _1017366, _1017368] : [c_Big__Operators_Osemilattice__big(_1017362, _1017364, _1017366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017362), _1017368)), -(hAPP(_1017366, _1017368) = hAPP(c_Finite__Set_Ofold1(_1017362, _1017364), _1017368))], (1260 ^ _780119) ^ [_798593, _798595] : [-(class_Orderings_Owellorder(_798593)), _798595 = _798593, class_Orderings_Owellorder(_798595)], (37558 ^ _780119) ^ [_1499008, _1499010, _1499012] : [-(hAPP(c_Set_Oimage(tc_prod(_1499008, _1499010), _1499010, c_Product__Type_Osnd(_1499008, _1499010)), _1499012) = hAPP(c_Relation_ORange(_1499008, _1499010), _1499012))], (31153 ^ _780119) ^ [_1362634, _1362636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1362634), _1362636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362634)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362636))))], (42096 ^ _780119) ^ [_1611433, _1611435, _1611437, _1611439, _1611441, _1611443, _1611445] : [c_Finite__Set_Ofun__left__comm(_1611433, _1611435, _1611437), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1611433, _1611435, _1611437, _1611439, hAPP(hAPP(c_Set_Oinsert(_1611433), _1611441), _1611443)), _1611445)), -(hBOOL(hAPP(hAPP(c_member(_1611433), _1611441), _1611443))), 42108 ^ _780119 : [(42111 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1611433, _1611435, _1611437, _1611439, _1611443), 42107 ^ [_1611433, _1611435, _1611437, _1611439, _1611441, _1611443, _1611445])))], (42109 ^ _780119) ^ [] : [-(_1611445 = hAPP(hAPP(_1611437, _1611441), 42107 ^ [_1611433, _1611435, _1611437, _1611439, _1611441, _1611443, _1611445]))]]], (21464 ^ _780119) ^ [_1171294, _1171296, _1171298, _1171300] : [class_Divides_Osemiring__div(_1171294), -(c_Divides_Odiv__class_Omod(_1171294, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171294), _1171296), _1171298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171294), _1171296), _1171300)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171294), _1171296), c_Divides_Odiv__class_Omod(_1171294, _1171298, _1171300)))], (21707 ^ _780119) ^ [_1176264, _1176266] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176264, _1176266)), _1176266) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18296 ^ _780119) ^ [_1113777, _1113779] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1113777, tc_HOL_Obool)), _1113779)))], (7142 ^ _780119) ^ [_898449, _898451, _898453] : [_898451 = _898453, -(hAPP(hAPP(c_COMBC(_898449, tc_fun(_898449, tc_HOL_Obool), tc_HOL_Obool), c_member(_898449)), _898451) = hAPP(hAPP(c_COMBC(_898449, tc_fun(_898449, tc_HOL_Obool), tc_HOL_Obool), c_member(_898449)), _898453))], (50010 ^ _780119) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30917 ^ _780119) ^ [_1358089, _1358091, _1358093, _1358095] : [class_Fields_Olinordered__field__inverse__zero(_1358089), class_Int_Onumber(_1358089), 30924 ^ _780119 : [(30925 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358089), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358089), _1358091), _1358093)), hAPP(c_Int_Onumber__class_Onumber__of(_1358089), _1358095))), 30928 ^ _780119 : [(30935 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358089), c_Groups_Ozero__class_Ozero(_1358089)), _1358093))), 30938 ^ _780119 : [(30945 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358089), _1358093), c_Groups_Ozero__class_Ozero(_1358089)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358089), c_Groups_Ozero__class_Ozero(_1358089)), hAPP(c_Int_Onumber__class_Onumber__of(_1358089), _1358095))))], (30939 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358089), _1358093), c_Groups_Ozero__class_Ozero(_1358089))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358089), hAPP(c_Int_Onumber__class_Onumber__of(_1358089), _1358095)), _1358093)), _1358091)))]]], (30929 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358089), c_Groups_Ozero__class_Ozero(_1358089)), _1358093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358089), _1358091), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358089), hAPP(c_Int_Onumber__class_Onumber__of(_1358089), _1358095)), _1358093))))]]], (30951 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358089), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358089), _1358091), _1358093)), hAPP(c_Int_Onumber__class_Onumber__of(_1358089), _1358095)))), 30954 ^ _780119 : [(30957 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358089), _1358091), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358089), hAPP(c_Int_Onumber__class_Onumber__of(_1358089), _1358095)), _1358093)))], (30955 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358089), c_Groups_Ozero__class_Ozero(_1358089)), _1358093)))]], 30958 ^ _780119 : [(30961 ^ _780119) ^ [] : [30962 ^ _780119 : [(30965 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358089), hAPP(c_Int_Onumber__class_Onumber__of(_1358089), _1358095)), _1358093)), _1358091))], (30963 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358089), _1358093), c_Groups_Ozero__class_Ozero(_1358089))))]], 30966 ^ _780119 : [(30969 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358089), c_Groups_Ozero__class_Ozero(_1358089)), hAPP(c_Int_Onumber__class_Onumber__of(_1358089), _1358095)))], (30967 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358089), _1358093), c_Groups_Ozero__class_Ozero(_1358089)))]]], (30959 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358089), c_Groups_Ozero__class_Ozero(_1358089)), _1358093))]]]]], (10364 ^ _780119) ^ [_962652, _962654, _962656] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962652, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_962652, tc_HOL_Obool)), _962654), _962656)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962652, tc_HOL_Obool)), _962654), _962656)) = _962654)], (5652 ^ _780119) ^ [_866666, _866668] : [_866668 = _866666, -(c_Option_Othe(_866668) = c_Option_Othe(_866666))], (10194 ^ _780119) ^ [_958226, _958228, _958230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958226, tc_HOL_Obool)), _958228), _958230)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958226, tc_HOL_Obool)), _958230), _958228) = _958228)], (23993 ^ _780119) ^ [_1219056, _1219058, _1219060, _1219062] : [class_Groups_Ocomm__monoid__add(_1219056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1219058), _1219060)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219056), _1219062), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1219058, _1219060)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219056), hAPP(_1219062, _1219058)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219056), _1219062), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1219058), _1219060))))], (47172 ^ _780119) ^ [_1730720, _1730722, _1730724, _1730726] : [c_List_Oupt(_1730720, _1730722) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1730724), _1730726), 47175 ^ _780119 : [(47178 ^ _780119) ^ [] : [-(_1730720 = _1730724)], (47180 ^ _780119) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1730720), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1730722) = _1730726)], (47176 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730720), _1730722)))]]], (1610 ^ _780119) ^ [_802968, _802970] : [-(class_Rings_Ocomm__semiring__1(_802968)), _802970 = _802968, class_Rings_Ocomm__semiring__1(_802970)], (25636 ^ _780119) ^ [_1248500] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1248500)))], (8694 ^ _780119) ^ [_930410, _930412, _930414, _930416] : [class_Orderings_Oord(_930410), _930412 = _930414, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930410), _930414), _930416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930410), _930412), _930416)))], (9126 ^ _780119) ^ [_936813, _936815, _936817, _936819] : [class_Orderings_Oorder(_936813), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936813), _936815), _936817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936813), _936819), _936815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936813), _936819), _936817)))], (1700 ^ _780119) ^ [_804093, _804095] : [-(class_Groups_Omonoid__add(_804093)), _804095 = _804093, class_Groups_Omonoid__add(_804095)], (17394 ^ _780119) ^ [_1096188, _1096190, _1096192, _1096194] : [class_Rings_Olinordered__semiring__strict(_1096188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096188), _1096190), _1096192)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096188), _1096190), _1096194))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096188), c_Groups_Ozero__class_Ozero(_1096188)), _1096190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096188), _1096192), _1096194)))], (35689 ^ _780119) ^ [_1454857, _1454859, _1454861, _1454863, _1454865, _1454867, _1454869] : [c_Equiv__Relations_Oequiv(_1454857, _1454859, _1454861), hBOOL(hAPP(hAPP(c_member(tc_fun(_1454857, tc_HOL_Obool)), _1454863), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1454857), _1454859), _1454861))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1454857, tc_HOL_Obool)), _1454865), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1454857), _1454859), _1454861))), hBOOL(hAPP(hAPP(c_member(_1454857), _1454867), _1454863)), hBOOL(hAPP(hAPP(c_member(_1454857), _1454869), _1454865)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1454857, _1454857)), hAPP(hAPP(c_Product__Type_OPair(_1454857, _1454857), _1454867), _1454869)), _1454861)), -(_1454863 = _1454865)], (7768 ^ _780119) ^ [_912029, _912031, _912033, _912035, _912037, _912039, _912041, _912043] : [c_Finite__Set_Ofolding__image__simple(_912029, _912031, _912033, _912035, _912037, _912039), hBOOL(hAPP(c_Finite__Set_Ofinite(_912031), _912041)), -(hBOOL(hAPP(hAPP(c_member(_912031), _912043), _912041))), -(hAPP(_912039, hAPP(hAPP(c_Set_Oinsert(_912031), _912043), _912041)) = hAPP(hAPP(_912033, hAPP(_912037, _912043)), hAPP(_912039, _912041)))], (16256 ^ _780119) ^ [_1076389, _1076391, _1076393, _1076395] : [class_Rings_Olinordered__semiring__strict(_1076389), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076389), _1076391), _1076393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076389), c_Groups_Ozero__class_Ozero(_1076389)), _1076395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076389), _1076395), _1076391)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076389), _1076395), _1076393))))], (39879 ^ _780119) ^ [_1557981, _1557983, _1557985, _1557987] : [c_Wellfounded_Owf(_1557981, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1557981, _1557981)), hAPP(hAPP(c_Product__Type_OPair(_1557981, _1557981), _1557983), _1557985)), _1557987)), 39882 ^ _780119 : [(39885 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1557981, _1557981)), hAPP(hAPP(c_Product__Type_OPair(_1557981, _1557981), _1557985), _1557983)), c_Transitive__Closure_Ortrancl(_1557981, _1557987)))], (39883 ^ _780119) ^ [] : [-(c_Wellfounded_Owf(_1557981, _1557987))]]], (34733 ^ _780119) ^ [_1431965, _1431967] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1431965, _1431967) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1431965, _1431967)))], (13105 ^ _780119) ^ [_1018567, _1018569, _1018571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018567), _1018569)), hBOOL(hAPP(hAPP(c_member(_1018567), _1018571), _1018569)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1018567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018567, tc_HOL_Obool)), _1018569), hAPP(hAPP(c_Set_Oinsert(_1018567), _1018571), c_Orderings_Obot__class_Obot(tc_fun(_1018567, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1018567), _1018569))], (23052 ^ _780119) ^ [_1201081, _1201083] : [class_Rings_Oring__1(_1201081), -(hBOOL(hAPP(hAPP(c_member(_1201081), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201081), _1201083)), c_Int_Oring__1__class_OInts(_1201081))))], (17652 ^ _780119) ^ [_1100994, _1100996, _1100998] : [hBOOL(hAPP(_1100994, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1100996), _1100998))), 17655 ^ _780119 : [(17662 ^ _780119) ^ [_1101185] : [_1100996 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1100998), _1101185), -(hBOOL(hAPP(_1100994, _1101185)))], (17656 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100996), _1100998)), -(hBOOL(hAPP(_1100994, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (14866 ^ _780119) ^ [_1053080, _1053082] : [class_Groups_Ozero(_1053080), 14869 ^ _780119 : [(14876 ^ _780119) ^ [] : [_1053082 = c_Groups_Ozero__class_Ozero(_1053080), -(c_Groups_Ozero__class_Ozero(_1053080) = _1053082)], (14870 ^ _780119) ^ [] : [c_Groups_Ozero__class_Ozero(_1053080) = _1053082, -(_1053082 = c_Groups_Ozero__class_Ozero(_1053080))]]], (46386 ^ _780119) ^ [_1714896, _1714898, _1714900, _1714902] : [46389 ^ _780119 : [(46392 ^ _780119) ^ [] : [46387 ^ [_1714896, _1714898, _1714900, _1714902] = 46388 ^ [_1714896, _1714898, _1714900, _1714902]], (46394 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1714896, _1714896)), hAPP(hAPP(c_Product__Type_OPair(_1714896, _1714896), 46388 ^ [_1714896, _1714898, _1714900, _1714902]), 46387 ^ [_1714896, _1714898, _1714900, _1714902])), _1714898))], (46390 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1714896, _1714896)), hAPP(hAPP(c_Product__Type_OPair(_1714896, _1714896), 46387 ^ [_1714896, _1714898, _1714900, _1714902]), 46388 ^ [_1714896, _1714898, _1714900, _1714902])), _1714898))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714896), tc_List_Olist(_1714896))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714896), tc_List_Olist(_1714896)), _1714900), _1714902)), c_List_Olexord(_1714896, _1714898)))), -(_1714900 = _1714902), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714896), tc_List_Olist(_1714896))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714896), tc_List_Olist(_1714896)), _1714902), _1714900)), c_List_Olexord(_1714896, _1714898))))], (48043 ^ _780119) ^ [_1750667, _1750669, _1750671] : [-(hAPP(hAPP(c_List_Oappend(_1750667), c_List_OtakeWhile(_1750667, _1750669, _1750671)), c_List_OdropWhile(_1750667, _1750669, _1750671)) = _1750671)], (40754 ^ _780119) ^ [_1579242, _1579244, _1579246] : [class_Lattices_Olattice(_1579242), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579242), _1579244)), -(c_Big__Operators_Olattice__class_OInf__fin(_1579242, hAPP(hAPP(c_Set_Oinsert(_1579242), _1579246), _1579244)) = hAPP(hAPP(c_Finite__Set_Ofold(_1579242, _1579242, c_Lattices_Osemilattice__inf__class_Oinf(_1579242)), _1579246), _1579244))], (22816 ^ _780119) ^ [_1196799] : [hBOOL(hAPP(_1196799, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 22817 ^ [_1196799]))), 22820 ^ _780119 : [(22821 ^ _780119) ^ [_1196899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196899)), -(hBOOL(hAPP(_1196799, _1196899)))]]], (47592 ^ _780119) ^ [_1739847, _1739849, _1739851, _1739853] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739847)), _1739849) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739851)), _1739853), -(hAPP(hAPP(c_List_Ozip(_1739847, _1739851), hAPP(c_List_Orev(_1739847), _1739849)), hAPP(c_List_Orev(_1739851), _1739853)) = hAPP(c_List_Orev(tc_prod(_1739847, _1739851)), hAPP(hAPP(c_List_Ozip(_1739847, _1739851), _1739849), _1739853)))], (45616 ^ _780119) ^ [_1698135, _1698137] : [hBOOL(hAPP(c_List_Odistinct(_1698135), _1698137)), -(hBOOL(hAPP(c_List_Odistinct(_1698135), hAPP(c_List_Orotate1(_1698135), _1698137))))], (46363 ^ _780119) ^ [_1714447, _1714449, _1714451] : [-(c_List_Olast(_1714447, hAPP(hAPP(c_List_Oappend(_1714447), _1714449), hAPP(hAPP(c_List_Olist_OCons(_1714447), _1714451), c_List_Olist_ONil(_1714447)))) = _1714451)], (23338 ^ _780119) ^ [_1206583, _1206585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1206583), _1206585)), -(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)), _1206583)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1206585))))], (50031 ^ _780119) ^ [_1794497, _1794499] : [-(c_FunDef_Ois__measure(_1794497, _1794499))], (50494 ^ _780119) ^ [_1804665, _1804667, _1804669] : [-(_1804665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1804667), c_List_Oreplicate(_1804667, _1804665, _1804669)) = c_List_Oreplicate(_1804667, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1804665), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1804669))], (3706 ^ _780119) ^ [_835841, _835843, _835845, _835847, _835849, _835851, _835853, _835855] : [-(c_List_Omap__filter(_835855, _835851, _835847, _835843) = c_List_Omap__filter(_835853, _835849, _835845, _835841)), _835855 = _835853, _835851 = _835849, _835847 = _835845, _835843 = _835841], (7920 ^ _780119) ^ [_914945, _914947, _914949, _914951] : [c_Com_Ocom_OSemi(_914945, _914947) = c_Com_Ocom_OWhile(_914949, _914951)], (40918 ^ _780119) ^ [_1582292, _1582294, _1582296, _1582298, _1582300, _1582302] : [c_Finite__Set_Ofun__left__comm(_1582292, _1582294, _1582296), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582292), _1582298)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1582292, _1582294, _1582296), _1582300), hAPP(hAPP(c_Set_Oinsert(_1582292), _1582302), _1582298)) = hAPP(hAPP(_1582296, _1582302), hAPP(hAPP(c_Finite__Set_Ofold(_1582292, _1582294, _1582296), _1582300), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1582292, tc_HOL_Obool)), _1582298), hAPP(hAPP(c_Set_Oinsert(_1582292), _1582302), c_Orderings_Obot__class_Obot(tc_fun(_1582292, tc_HOL_Obool)))))))], (41627 ^ _780119) ^ [_1600728, _1600730, _1600732, _1600734] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1600728, tc_fun(_1600730, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1600728, tc_HOL_Obool), _1600732)), _1600734) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1600728, tc_HOL_Obool), tc_fun(_1600730, tc_HOL_Obool)), _1600732), hAPP(hAPP(c_COMBC(tc_fun(_1600728, tc_HOL_Obool), tc_fun(_1600728, tc_fun(_1600730, tc_HOL_Obool)), tc_fun(_1600730, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1600728, tc_fun(_1600730, tc_HOL_Obool))), _1600734)))], (8026 ^ _780119) ^ [_917321, _917323] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_917321, _917323))), -(hBOOL(hAPP(c_Com_OWT, _917323)))], (494 ^ _780119) ^ [_787734, _787736, _787738, _787740, _787742, _787744] : [-(c_Relation_Ototal__on(_787742, _787738, _787734)), c_Relation_Ototal__on(_787744, _787740, _787736), _787744 = _787742, _787740 = _787738, _787736 = _787734], (3814 ^ _780119) ^ [_837577, _837579, _837581, _837583, _837585, _837587] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_837587, _837583, _837579) = c_SetInterval_Oord__class_OgreaterThanLessThan(_837585, _837581, _837577)), _837587 = _837585, _837583 = _837581, _837579 = _837577], (41359 ^ _780119) ^ [_1593822, _1593824, _1593826, _1593828, _1593830, _1593832] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593822, tc_fun(_1593824, tc_HOL_Obool)), _1593826), hAPP(hAPP(c_COMBB(_1593828, tc_fun(_1593824, tc_HOL_Obool), _1593822), _1593830), _1593832)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593828, tc_fun(_1593824, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1593822, _1593828, _1593832), _1593826)), _1593830))], (31085 ^ _780119) ^ [_1361347] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1361347))), -(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), _1361347)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15626 ^ _780119) ^ [_1064849, _1064851] : [class_Groups_Olinordered__ab__group__add(_1064849), 15629 ^ _780119 : [(15636 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064849), _1064851), c_Groups_Ozero__class_Ozero(_1064849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064849), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064849), _1064851), _1064851)), c_Groups_Ozero__class_Ozero(_1064849))))], (15630 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064849), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064849), _1064851), _1064851)), c_Groups_Ozero__class_Ozero(_1064849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064849), _1064851), c_Groups_Ozero__class_Ozero(_1064849))))]]], (824 ^ _780119) ^ [_792697, _792699, _792701, _792703] : [-(c_Wellfounded_Owf(_792701, _792697)), c_Wellfounded_Owf(_792703, _792699), _792703 = _792701, _792699 = _792697], (18978 ^ _780119) ^ [_1126032, _1126034, _1126036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126032), _1126034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126034), _1126036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126032), _1126036)))], (27648 ^ _780119) ^ [_1290845, _1290847, _1290849, _1290851] : [class_Orderings_Olinorder(_1290845), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290845), _1290847), _1290849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290845), _1290851), _1290849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290845), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290845), _1290847), _1290851)), _1290849)))], (35031 ^ _780119) ^ [_1438034, _1438036] : [class_Int_Onumber__ring(_1438034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1438036)), -(hBOOL(hAPP(hAPP(c_member(_1438034), hAPP(c_Int_Onumber__class_Onumber__of(_1438034), _1438036)), c_Nat_Osemiring__1__class_ONats(_1438034))))], (32357 ^ _780119) ^ [_1383578, _1383580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383578), _1383580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1383578)), c_Int_OBit0(_1383580))))], (26739 ^ _780119) ^ [_1268422, _1268424, _1268426] : [-(hAPP(hAPP(c_Set_Oinsert(_1268422), _1268424), _1268426) = hAPP(c_Set_OCollect(_1268422), hAPP(hAPP(c_COMBS(_1268422, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268422), c_fdisj), hAPP(hAPP(c_COMBC(_1268422, _1268422, tc_HOL_Obool), c_fequal), _1268424))), hAPP(hAPP(c_COMBC(_1268422, tc_fun(_1268422, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268422)), _1268426))))], (19717 ^ _780119) ^ [_1138801, _1138803] : [class_Rings_Odivision__ring(_1138801), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138801), _1138803), c_Groups_Oone__class_Oone(_1138801)) = _1138803)], (3834 ^ _780119) ^ [_837883, _837885, _837887, _837889] : [-(c_List_Orotate(_837889, _837885) = c_List_Orotate(_837887, _837883)), _837889 = _837887, _837885 = _837883], (24239 ^ _780119) ^ [_1223941, _1223943, _1223945, _1223947] : [class_Orderings_Oorder(_1223941), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1223941, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1223941, _1223943, _1223945)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1223941, _1223945, _1223947)) = c_Orderings_Obot__class_Obot(tc_fun(_1223941, tc_HOL_Obool)))], (49779 ^ _780119) ^ [_1789601, _1789603, _1789605] : [49781 ^ _780119 : [(49784 ^ _780119) ^ [] : [hBOOL(hAPP(_1789603, hAPP(hAPP(c_List_Onth(_1789601), _1789605), 49780 ^ [_1789601, _1789603, _1789605])))], (49782 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49780 ^ [_1789601, _1789603, _1789605]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789601)), _1789605))))]], -(c_List_Olist__all(_1789601, _1789603, _1789605))], (18778 ^ _780119) ^ [_1122564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122564)), -(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)), _1122564))))], (47293 ^ _780119) ^ [_1733059] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1733059) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1733059))))], (13190 ^ _780119) ^ [_1020341, _1020343, _1020345] : [class_Groups_Ogroup__add(_1020341), 13193 ^ _780119 : [(13200 ^ _780119) ^ [] : [_1020343 = _1020345, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1020341), _1020343) = hAPP(c_Groups_Ouminus__class_Ouminus(_1020341), _1020345))], (13194 ^ _780119) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1020341), _1020343) = hAPP(c_Groups_Ouminus__class_Ouminus(_1020341), _1020345), -(_1020343 = _1020345)]]], (30555 ^ _780119) ^ [_1351017, _1351019, _1351021, _1351023] : [class_Fields_Ofield__inverse__zero(_1351017), class_Int_Onumber(_1351017), 30562 ^ _780119 : [(30563 ^ _780119) ^ [] : [_1351019 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351017), _1351021), hAPP(c_Int_Onumber__class_Onumber__of(_1351017), _1351023)), 30566 ^ _780119 : [(30573 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1351017), _1351023) = c_Groups_Ozero__class_Ozero(_1351017), -(_1351019 = c_Groups_Ozero__class_Ozero(_1351017))], (30567 ^ _780119) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1351017), _1351023) = c_Groups_Ozero__class_Ozero(_1351017)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351017), _1351019), hAPP(c_Int_Onumber__class_Onumber__of(_1351017), _1351023)) = _1351021)]]], (30579 ^ _780119) ^ [] : [-(_1351019 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351017), _1351021), hAPP(c_Int_Onumber__class_Onumber__of(_1351017), _1351023))), 30582 ^ _780119 : [(30585 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351017), _1351019), hAPP(c_Int_Onumber__class_Onumber__of(_1351017), _1351023)) = _1351021], (30583 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1351017), _1351023) = c_Groups_Ozero__class_Ozero(_1351017)]], 30586 ^ _780119 : [(30589 ^ _780119) ^ [] : [_1351019 = c_Groups_Ozero__class_Ozero(_1351017)], (30587 ^ _780119) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1351017), _1351023) = c_Groups_Ozero__class_Ozero(_1351017))]]]]], (43280 ^ _780119) ^ [_1639371, _1639373, _1639375, _1639377, _1639379] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639371)), _1639373) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639375)), _1639377), 43283 ^ _780119 : [(43292 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1639371, _1639375), _1639373), _1639377) = _1639379), hAPP(hAPP(c_List_Omap(tc_prod(_1639371, _1639375), _1639371), c_Product__Type_Ofst(_1639371, _1639375)), _1639379) = _1639373, hAPP(hAPP(c_List_Omap(tc_prod(_1639371, _1639375), _1639375), c_Product__Type_Osnd(_1639371, _1639375)), _1639379) = _1639377], (43284 ^ _780119) ^ [] : [hAPP(hAPP(c_List_Ozip(_1639371, _1639375), _1639373), _1639377) = _1639379, 43287 ^ _780119 : [(43290 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1639371, _1639375), _1639375), c_Product__Type_Osnd(_1639371, _1639375)), _1639379) = _1639377)], (43288 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1639371, _1639375), _1639371), c_Product__Type_Ofst(_1639371, _1639375)), _1639379) = _1639373)]]]]], (1390 ^ _780119) ^ [_800218, _800220] : [-(class_Finite__Set_Ofinite(_800218)), _800220 = _800218, class_Finite__Set_Ofinite(_800220)], (720 ^ _780119) ^ [_791143, _791145, _791147, _791149, _791151, _791153] : [-(c_Equiv__Relations_Oequiv(_791151, _791147, _791143)), c_Equiv__Relations_Oequiv(_791153, _791149, _791145), _791153 = _791151, _791149 = _791147, _791145 = _791143], (34219 ^ _780119) ^ [_1422541, _1422543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1422541)), 34222 ^ _780119 : [(34229 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422543), _1422541))), -(c_Divides_OposDivAlg(_1422543, _1422541) = hAPP(c_Divides_Oadjust(_1422541), c_Divides_OposDivAlg(_1422543, 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)))), _1422541))))], (34223 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422543), _1422541)), -(c_Divides_OposDivAlg(_1422543, _1422541) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1422543))]]], (6302 ^ _780119) ^ [_881305, _881307, _881309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881305, tc_HOL_Obool)), _881307), _881309)), hBOOL(hAPP(c_Finite__Set_Ofinite(_881305), _881309)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_881305), _881307)))], (42980 ^ _780119) ^ [_1632107] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1632107)), -(c_List_Onat__list(_1632107))], (22535 ^ _780119) ^ [_1191328, _1191330, _1191332, _1191334] : [c_Com_Ocom_OCond(_1191328, _1191330, _1191332) = hAPP(c_Com_Ocom_OBODY, _1191334)], (38533 ^ _780119) ^ [_1525468, _1525470, _1525472] : [38535 ^ _780119 : [(38538 ^ _780119) ^ [] : [hBOOL(hAPP(_1525470, 38534 ^ [_1525468, _1525470, _1525472]))], (38536 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525468), 38534 ^ [_1525468, _1525470, _1525472]), _1525472)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1525468, _1525470), _1525472)))], (16124 ^ _780119) ^ [_1073954, _1073956, _1073958] : [class_Rings_Olinordered__semiring__strict(_1073954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073954), c_Groups_Ozero__class_Ozero(_1073954)), _1073956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073954), c_Groups_Ozero__class_Ozero(_1073954)), _1073958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073954), c_Groups_Ozero__class_Ozero(_1073954)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073954), _1073956), _1073958))))], (37269 ^ _780119) ^ [_1492480, _1492482, _1492484, _1492486, _1492488, _1492490, _1492492] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1492480, _1492482, _1492484, _1492486, _1492488), _1492490), _1492492)), 37273 ^ _780119 : [(37276 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1492488, 37272 ^ [_1492480, _1492482, _1492484, _1492486, _1492488, _1492490, _1492492]), _1492492)))], (37274 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1492486, _1492490), 37272 ^ [_1492480, _1492482, _1492484, _1492486, _1492488, _1492490, _1492492])))]]], (7874 ^ _780119) ^ [_914175, _914177] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_914175, _914177))), 7877 ^ _780119 : [(7880 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _914177)))], (7878 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _914175)))]]], (26431 ^ _780119) ^ [_1262452, _1262454, _1262456] : [class_Rings_Olinordered__idom(_1262452), -(hAPP(c_Groups_Oabs__class_Oabs(_1262452), hAPP(hAPP(c_Power_Opower__class_Opower(_1262452), _1262454), _1262456)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1262452), hAPP(c_Groups_Oabs__class_Oabs(_1262452), _1262454)), _1262456))], (32169 ^ _780119) ^ [_1380138, _1380140, _1380142, _1380144, _1380146] : [-(hAPP(c_Nat_Onat_Onat__rec(_1380138, _1380140, _1380142), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1380144)), _1380146)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1380138), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1380144))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1380138, _1380138), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1380138, tc_fun(_1380138, _1380138)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1380138, tc_fun(_1380138, _1380138)), tc_Int_Oint), c_If(_1380138)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1380138, _1380140, _1380142), _1380146))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1380138, _1380138), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1380138, _1380138), tc_Int_Oint), _1380142), 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)), _1380146))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1380138, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1380138, _1380140, _1380142)), 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)), _1380146))))))], (16895 ^ _780119) ^ [_1087193] : [-(hAPP(c_Finite__Set_Ocard(_1087193), c_Orderings_Obot__class_Obot(tc_fun(_1087193, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38972 ^ _780119) ^ [_1535902, _1535904, _1535906, _1535908, _1535910, _1535912] : [c_Finite__Set_Ofolding(_1535902, _1535904, _1535906, _1535908), -(hAPP(c_Fun_Ocomp(_1535904, _1535904, _1535904, hAPP(_1535906, _1535910)), hAPP(_1535906, _1535912)) = hAPP(c_Fun_Ocomp(_1535904, _1535904, _1535904, hAPP(_1535906, _1535912)), hAPP(_1535906, _1535910)))], (43324 ^ _780119) ^ [_1641115, _1641117, _1641119] : [-(_1641115 = _1641117), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641119)), _1641115) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641119)), _1641117), 43330 ^ _780119 : [(43333 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1641119, _1641119, tc_HOL_Obool), c_fequal), 43329 ^ [_1641115, _1641117, _1641119]))], (43331 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641119, _1641119)), 43329 ^ [_1641115, _1641117, _1641119]), hAPP(c_List_Oset(tc_prod(_1641119, _1641119)), hAPP(hAPP(c_List_Ozip(_1641119, _1641119), _1641115), _1641117)))))]]], (38034 ^ _780119) ^ [_1513953, _1513955] : [-(c_Product__Type_Oapsnd(_1513953, _1513953, _1513955, c_Fun_Oid(_1513953)) = c_Fun_Oid(tc_prod(_1513955, _1513953)))], (48235 ^ _780119) ^ [_1755362, _1755364] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1755362), tc_fun(_1755362, tc_HOL_Obool), c_List_Oset(_1755362)), hAPP(c_List_Oset(tc_List_Olist(_1755362)), c_Enum_Osublists(_1755362, _1755364))) = hAPP(c_Set_OPow(_1755362), hAPP(c_List_Oset(_1755362), _1755364)))], (16768 ^ _780119) ^ [_1085272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1085272), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1085272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33521 ^ _780119) ^ [_1404143, _1404145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1404143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1404143), _1404145)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1404143), _1404145) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (37777 ^ _780119) ^ [_1505251, _1505253, _1505255] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1505251, _1505253), _1505255), hAPP(c_COMBK(tc_fun(_1505253, tc_HOL_Obool), _1505251), c_Orderings_Obot__class_Obot(tc_fun(_1505253, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1505251, _1505253), tc_HOL_Obool)))], (24979 ^ _780119) ^ [_1237784] : [24980 ^ _780119 : [(24981 ^ _780119) ^ [_1237841] : [hBOOL(hAPP(_1237784, _1237841))]], 24983 ^ _780119 : [(24986 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1237784, hAPP(c_Int_Onat, 24982 ^ [_1237784]))))], (24984 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24982 ^ [_1237784])))]]], (21829 ^ _780119) ^ [_1178674, _1178676] : [-(_1178674 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178676), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1178674), _1178676))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178674, _1178676)))], (22201 ^ _780119) ^ [_1185363, _1185365, _1185367] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1185363, _1185365)), _1185367) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185363), _1185367), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185365), _1185367)))], (10584 ^ _780119) ^ [_967484, _967486, _967488, _967490, _967492, _967494] : [-(hBOOL(hAPP(hAPP(c_member(_967484), _967486), _967488))), -(c_Map_Orestrict__map(_967484, _967490, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_967484, tc_Option_Ooption(_967490)), _967492), _967486), _967494), _967488) = c_Map_Orestrict__map(_967484, _967490, _967492, _967488))], (38338 ^ _780119) ^ [_1521035, _1521037] : [c_Wellfounded_OwfP(_1521035, hAPP(hAPP(c_COMBC(_1521035, tc_fun(tc_prod(_1521035, _1521035), tc_HOL_Obool), tc_fun(_1521035, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1521035, tc_fun(tc_fun(tc_prod(_1521035, _1521035), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1521035, _1521035), tc_HOL_Obool), tc_fun(_1521035, tc_HOL_Obool)), _1521035), c_COMBC(_1521035, tc_fun(tc_prod(_1521035, _1521035), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1521035, tc_prod(_1521035, _1521035)), tc_fun(_1521035, tc_fun(tc_fun(tc_prod(_1521035, _1521035), tc_HOL_Obool), tc_HOL_Obool)), _1521035), hAPP(c_COMBB(tc_prod(_1521035, _1521035), tc_fun(tc_fun(tc_prod(_1521035, _1521035), tc_HOL_Obool), tc_HOL_Obool), _1521035), c_member(tc_prod(_1521035, _1521035)))), c_Product__Type_OPair(_1521035, _1521035)))), _1521037)), -(c_Wellfounded_Owf(_1521035, _1521037))], (43072 ^ _780119) ^ [_1634219, _1634221, _1634223, _1634225] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634219, _1634219)), hAPP(hAPP(c_Product__Type_OPair(_1634219, _1634219), _1634221), _1634223)), hAPP(c_List_Oset(tc_prod(_1634219, _1634219)), hAPP(hAPP(c_List_Ozip(_1634219, _1634219), _1634225), _1634225)))), 43075 ^ _780119 : [(43078 ^ _780119) ^ [] : [-(_1634221 = _1634223)], (43076 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1634219), _1634221), hAPP(c_List_Oset(_1634219), _1634225))))]]], (49938 ^ _780119) ^ [_1792740, _1792742] : [c_List_Olist__ex1(_1792740, _1792742, c_List_Olist_ONil(_1792740))], (17126 ^ _780119) ^ [_1091131, _1091133] : [class_Lattices_Oboolean__algebra(_1091131), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1091131), hAPP(c_Groups_Ouminus__class_Ouminus(_1091131), _1091133)), _1091133) = c_Orderings_Otop__class_Otop(_1091131))], (37367 ^ _780119) ^ [_1494461, _1494463, _1494465] : [c_Wellfounded_Owf(_1494461, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1494461, _1494461), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1494461, _1494461), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1494461, _1494461, _1494461), _1494463), _1494463)), hAPP(hAPP(c_Relation_Orel__comp(_1494461, _1494461, _1494461), _1494465), _1494463))), _1494465)), -(c_Wellfounded_Owf(_1494461, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1494461, _1494461), tc_HOL_Obool)), _1494463), _1494465)))], (28284 ^ _780119) ^ [_1303038, _1303040] : [class_Orderings_Olinorder(_1303038), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303038), _1303040)), -(c_Big__Operators_Olinorder__class_OMax(_1303038, _1303040) = hAPP(c_Finite__Set_Ofold1(_1303038, c_Orderings_Oord__class_Omax(_1303038)), _1303040))], (22853 ^ _780119) ^ [_1197432, _1197434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197432)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197432), _1197434)))], (5522 ^ _780119) ^ [_864727, _864729, _864731, _864733, _864735, _864737] : [-(c_Lazy__Sequence_Oappend(_864737, _864733, _864729) = c_Lazy__Sequence_Oappend(_864735, _864731, _864727)), _864737 = _864735, _864733 = _864731, _864729 = _864727], (15332 ^ _780119) ^ [_1059957, _1059959] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1059957), _1059959) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1059959), _1059957) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1059957 = _1059959)], (39000 ^ _780119) ^ [_1536706, _1536708, _1536710, _1536712, _1536714, _1536716, _1536718] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1536706, _1536708, _1536710), hAPP(c_Fun_Ocomp(_1536712, tc_fun(_1536708, _1536710), _1536706, _1536714), _1536716)), _1536718) = hAPP(hAPP(_1536714, hAPP(_1536716, hAPP(c_Product__Type_Ofst(_1536706, _1536708), _1536718))), hAPP(c_Product__Type_Osnd(_1536706, _1536708), _1536718)))], (51317 ^ _780119) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (24513 ^ _780119) ^ [_1229189, _1229191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229189)), 24522 ^ _780119 : [(24525 ^ _780119) ^ [] : [hBOOL(hAPP(_1229191, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24518 ^ [_1229189, _1229191]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 24519 ^ [_1229189, _1229191]), _1229189))))], (24523 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1229191, 24518 ^ [_1229189, _1229191])))]], 24526 ^ _780119 : [(24529 ^ _780119) ^ [] : [hBOOL(hAPP(_1229191, 24518 ^ [_1229189, _1229191]))], (24527 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1229191, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24518 ^ [_1229189, _1229191]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 24519 ^ [_1229189, _1229191]), _1229189)))))]], 24530 ^ _780119 : [(24540 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1229191, 24547 ^ [_1229189, _1229191]))), 24541 ^ _780119 : [(24542 ^ _780119) ^ [_1229736] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1229736), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1229189))), hBOOL(hAPP(_1229191, _1229736))]]], (24531 ^ _780119) ^ [] : [24532 ^ _780119 : [(24533 ^ _780119) ^ [_1229621] : [hBOOL(hAPP(_1229191, _1229621))]], 24535 ^ _780119 : [(24538 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1229191, 24534 ^ [_1229189, _1229191])))], (24536 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24534 ^ [_1229189, _1229191]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1229189))))]]]]], (19040 ^ _780119) ^ [] : [-(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))))], (7978 ^ _780119) ^ [_916214, _916216, _916218] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_916214), _916216)), 7981 ^ _780119 : [(7988 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_916214), _916218)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_916214), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916214, tc_HOL_Obool)), _916218), _916216))))], (7982 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_916214), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916214, tc_HOL_Obool)), _916218), _916216))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_916214), _916218)))]]], (43739 ^ _780119) ^ [_1653505, _1653507, _1653509, _1653511, _1653513] : [class_Rings_Osemiring__0(_1653505), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1653505), hAPP(hAPP(c_List_Omap(_1653507, _1653505), hAPP(hAPP(c_COMBB(_1653505, _1653505, _1653507), hAPP(c_Groups_Otimes__class_Otimes(_1653505), _1653509)), _1653511)), _1653513)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1653505), _1653509), hAPP(c_List_Omonoid__add__class_Olistsum(_1653505), hAPP(hAPP(c_List_Omap(_1653507, _1653505), _1653511), _1653513))))], (5628 ^ _780119) ^ [_866326, _866328] : [_866328 = _866326, -(c_Finite__Set_Ofinite(_866328) = c_Finite__Set_Ofinite(_866326))], (12799 ^ _780119) ^ [_1012109, _1012111] : [class_Lattices_Olattice(_1012109), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012109), _1012111)), -(c_Big__Operators_Olattice__class_OInf__fin(_1012109, _1012111) = hAPP(c_Finite__Set_Ofold1(_1012109, c_Lattices_Osemilattice__inf__class_Oinf(_1012109)), _1012111))], (13786 ^ _780119) ^ [_1030824, _1030826, _1030828, _1030830] : [class_Groups_Ocomm__monoid__mult(_1030824), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1030826), _1030828))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1030826, _1030824), _1030830), _1030828) = c_Groups_Oone__class_Oone(_1030824))], (16194 ^ _780119) ^ [_1075229, _1075231, _1075233, _1075235] : [class_Rings_Olinordered__ring__strict(_1075229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075229), _1075231), c_Groups_Ozero__class_Ozero(_1075229))), 16201 ^ _780119 : [(16208 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075229), _1075235), _1075233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075229), _1075231), _1075233)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075229), _1075231), _1075235))))], (16202 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075229), _1075231), _1075233)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075229), _1075231), _1075235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075229), _1075235), _1075233)))]]], (6628 ^ _780119) ^ [_888125, _888127, _888129, _888131] : [6630 ^ _780119 : [(6633 ^ _780119) ^ [] : [hBOOL(hAPP(_888131, 6629 ^ [_888125, _888127, _888129, _888131]))], (6631 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_888125), 6629 ^ [_888125, _888127, _888129, _888131]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888125, tc_HOL_Obool)), _888127), _888129))))]], 6634 ^ _780119 : [(6641 ^ _780119) ^ [_888442] : [hBOOL(hAPP(hAPP(c_member(_888125), _888442), _888129)), -(hBOOL(hAPP(_888131, _888442)))], (6635 ^ _780119) ^ [_888345] : [hBOOL(hAPP(hAPP(c_member(_888125), _888345), _888127)), -(hBOOL(hAPP(_888131, _888345)))]]], (17168 ^ _780119) ^ [_1091911, _1091913, _1091915, _1091917] : [class_Groups_Oordered__comm__monoid__add(_1091911), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091911), c_Groups_Ozero__class_Ozero(_1091911)), _1091913)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091911), _1091915), _1091917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091911), _1091915), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091911), _1091913), _1091917))))], (25540 ^ _780119) ^ [_1247148, _1247150] : [c_Nat__Transfer_Onat__set(_1247148), c_Nat__Transfer_Onat__set(_1247150), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1247148), _1247150) = 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), _1247148)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1247150))))], (35333 ^ _780119) ^ [_1445547, _1445549] : [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)), _1445547), _1445549)), 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)), _1445547), 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)), _1445549), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (35207 ^ _780119) ^ [_1442765] : [-(_1442765 = 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)), _1442765), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (41916 ^ _780119) ^ [_1607399, _1607401, _1607403] : [class_Complete__Lattice_Ocomplete__lattice(_1607399), -(c_Complete__Lattice_OSup__class_OSup(_1607399, hAPP(hAPP(c_Set_Oinsert(_1607399), _1607401), hAPP(hAPP(c_Set_Oinsert(_1607399), _1607403), c_Orderings_Obot__class_Obot(tc_fun(_1607399, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1607399), _1607401), _1607403))], (13622 ^ _780119) ^ [_1027958, _1027960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027958), _1027960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027958)), hAPP(c_Nat_OSuc, _1027960))))], (45820 ^ _780119) ^ [_1703197, _1703199, _1703201, _1703203] : [-(_1703197 = c_List_Olist_ONil(_1703199)), -(hAPP(c_List_Ohd(_1703201), hAPP(hAPP(c_List_Omap(_1703199, _1703201), _1703203), _1703197)) = hAPP(_1703203, hAPP(c_List_Ohd(_1703199), _1703197)))], (5722 ^ _780119) ^ [_867733, _867735] : [_867735 = _867733, -(c_Orderings_Obot__class_Obot(_867735) = c_Orderings_Obot__class_Obot(_867733))], (45177 ^ _780119) ^ [_1685574, _1685576, _1685578, _1685580, _1685582] : [-(hAPP(hAPP(c_List_Oappend(_1685574), _1685576), _1685578) = hAPP(hAPP(c_List_Oappend(_1685574), _1685580), _1685582)), 45178 ^ _780119 : [(45185 ^ _780119) ^ [_1685798] : [hAPP(hAPP(c_List_Oappend(_1685574), _1685576), _1685798) = _1685580, _1685578 = hAPP(hAPP(c_List_Oappend(_1685574), _1685798), _1685582)], (45179 ^ _780119) ^ [_1685686] : [_1685576 = hAPP(hAPP(c_List_Oappend(_1685574), _1685580), _1685686), hAPP(hAPP(c_List_Oappend(_1685574), _1685686), _1685578) = _1685582]]], (13628 ^ _780119) ^ [_1028084, _1028086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028084), hAPP(c_Nat_OSuc, _1028086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028084), _1028086))), -(_1028084 = _1028086)], (22505 ^ _780119) ^ [_1190819, _1190821, _1190823, _1190825, _1190827, _1190829] : [c_Com_Ocom_OCond(_1190819, _1190821, _1190823) = c_Com_Ocom_OCond(_1190825, _1190827, _1190829), 22508 ^ _780119 : [(22511 ^ _780119) ^ [] : [-(_1190821 = _1190827)], (22513 ^ _780119) ^ [] : [-(_1190823 = _1190829)], (22509 ^ _780119) ^ [] : [-(_1190819 = _1190825)]]], (47632 ^ _780119) ^ [_1740714, _1740716, _1740718] : [-(hAPP(c_List_Orev(_1740714), hAPP(hAPP(c_List_Otake(_1740714), _1740716), _1740718)) = hAPP(hAPP(c_List_Odrop(_1740714), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740714)), _1740718)), _1740716)), hAPP(c_List_Orev(_1740714), _1740718)))], (51121 ^ _780119) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (47588 ^ _780119) ^ [_1739750, _1739752, _1739754, _1739756, _1739758] : [-(hAPP(c_List_Ofoldl(_1739750, _1739752, _1739754, _1739756), _1739758) = c_List_Ofoldr(_1739752, _1739750, hAPP(c_COMBC(_1739750, _1739752, _1739750), _1739754), hAPP(c_List_Orev(_1739752), _1739758), _1739756))], (32005 ^ _780119) ^ [_1376546, _1376548] : [class_Int_Onumber__ring(_1376546), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376546), c_Groups_Oone__class_Oone(_1376546)), hAPP(c_Int_Onumber__class_Onumber__of(_1376546), _1376548)) = hAPP(c_Int_Onumber__class_Onumber__of(_1376546), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1376548)))], (26571 ^ _780119) ^ [_1265267, _1265269] : [class_Groups_Oordered__ab__group__add__abs(_1265267), 26574 ^ _780119 : [(26581 ^ _780119) ^ [] : [-(_1265269 = c_Groups_Ozero__class_Ozero(_1265267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265267), c_Groups_Ozero__class_Ozero(_1265267)), hAPP(c_Groups_Oabs__class_Oabs(_1265267), _1265269))))], (26575 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265267), c_Groups_Ozero__class_Ozero(_1265267)), hAPP(c_Groups_Oabs__class_Oabs(_1265267), _1265269))), _1265269 = c_Groups_Ozero__class_Ozero(_1265267)]]], (11163 ^ _780119) ^ [_978882, _978884, _978886] : [class_Lattices_Olattice(_978882), hBOOL(hAPP(c_Finite__Set_Ofinite(_978882), _978884)), -(_978886 = c_Orderings_Obot__class_Obot(tc_fun(_978882, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978882, tc_HOL_Obool)), _978886), _978884)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978882), c_Big__Operators_Olattice__class_OInf__fin(_978882, _978886)), c_Big__Operators_Olattice__class_OInf__fin(_978882, _978884)) = c_Big__Operators_Olattice__class_OInf__fin(_978882, _978884))], (21558 ^ _780119) ^ [_1173302, _1173304] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1173302), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1173304)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1173302, _1173304)))], (4444 ^ _780119) ^ [_847352, _847354] : [_847354 = _847352, -(c_Int_OBit1(_847354) = c_Int_OBit1(_847352))], (45361 ^ _780119) ^ [_1690616, _1690618, _1690620, _1690622, _1690624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1690616), tc_List_Olist(_1690616))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690616), tc_List_Olist(_1690616)), hAPP(hAPP(c_List_Oappend(_1690616), _1690618), _1690620)), hAPP(hAPP(c_List_Oappend(_1690616), _1690618), _1690622))), c_List_Olexord(_1690616, _1690624))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1690616, _1690616)), hAPP(hAPP(c_Product__Type_OPair(_1690616, _1690616), 45366 ^ [_1690616, _1690618, _1690620, _1690622, _1690624]), 45366 ^ [_1690616, _1690618, _1690620, _1690622, _1690624])), _1690624))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1690616), tc_List_Olist(_1690616))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690616), tc_List_Olist(_1690616)), _1690620), _1690622)), c_List_Olexord(_1690616, _1690624))))], (9334 ^ _780119) ^ [_940708, _940710, _940712, _940714, _940716, _940718] : [-(hBOOL(hAPP(hAPP(c_member(_940708), _940710), _940712))), -(hAPP(c_Set_Oimage(_940708, tc_Option_Ooption(_940714), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_940708, tc_Option_Ooption(_940714)), _940716), _940710), hAPP(c_Option_Ooption_OSome(_940714), _940718))), _940712) = hAPP(c_Set_Oimage(_940708, tc_Option_Ooption(_940714), _940716), _940712))], (5134 ^ _780119) ^ [_858673, _858675] : [_858675 = _858673, -(c_Groups_Oone__class_Oone(_858675) = c_Groups_Oone__class_Oone(_858673))], (15988 ^ _780119) ^ [_1071488, _1071490, _1071492] : [class_Groups_Oordered__comm__monoid__add(_1071488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071488), c_Groups_Ozero__class_Ozero(_1071488)), _1071490)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071488), c_Groups_Ozero__class_Ozero(_1071488)), _1071492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071488), c_Groups_Ozero__class_Ozero(_1071488)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071488), _1071490), _1071492))))], (31445 ^ _780119) ^ [_1367794, _1367796] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367794)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367794)), _1367796) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367794)), _1367796)))], (31195 ^ _780119) ^ [_1363414, _1363416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1363414)), c_Int_OBit1(_1363416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1363414), _1363416)))], (24185 ^ _780119) ^ [_1222927, _1222929, _1222931, _1222933] : [class_Orderings_Olinorder(_1222927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222927), _1222929), _1222931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222927), _1222931), _1222933)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222927, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1222927, _1222929, _1222931)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1222927, _1222931, _1222933)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222927, _1222929), _1222933))], (11989 ^ _780119) ^ [_996117, _996119, _996121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996117), _996119)), _996121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996117), _996121)))], (26817 ^ _780119) ^ [_1270398, _1270400, _1270402] : [-(c_Map_Odom(_1270398, _1270400, _1270402) = hAPP(c_Set_OCollect(_1270398), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1270398), c_fNot), hAPP(hAPP(c_COMBC(_1270398, tc_Option_Ooption(_1270400), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1270400), tc_fun(tc_Option_Ooption(_1270400), tc_HOL_Obool), _1270398), c_fequal), _1270402)), c_Option_Ooption_ONone(_1270400)))))], (22185 ^ _780119) ^ [_1185098, _1185100] : [class_Rings_Olinordered__idom(_1185098), -(c_Groups_Osgn__class_Osgn(_1185098, c_Groups_Osgn__class_Osgn(_1185098, _1185100)) = c_Groups_Osgn__class_Osgn(_1185098, _1185100))], (10076 ^ _780119) ^ [_955595, _955597, _955599] : [class_Lattices_Olattice(_955595), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955595), _955597), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955595), _955597), _955599)) = _955597)], (45974 ^ _780119) ^ [_1705896, _1705898, _1705900, _1705902] : [-(c_List_Olist_Olist__size(_1705896, _1705898, hAPP(hAPP(c_List_Olist_OCons(_1705896), _1705900), _1705902)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1705898, _1705900)), c_List_Olist_Olist__size(_1705896, _1705898, _1705902))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18810 ^ _780119) ^ [_1123092] : [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)), _1123092)), _1123092) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (18596 ^ _780119) ^ [_1119298, _1119300, _1119302, _1119304] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1119298), _1119300)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119302), _1119304)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1119298, _1119302)), c_Sum__Type_OPlus(_1119298, _1119302, _1119300, _1119304)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1119298), _1119300)), hAPP(c_Finite__Set_Ocard(_1119302), _1119304)))], (23819 ^ _780119) ^ [_1215564, _1215566, _1215568, _1215570, _1215572] : [class_Groups_Ocomm__monoid__add(_1215564), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215564), _1215566), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1215568), _1215570), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1215572), _1215570))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215564), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1215564, tc_Nat_Onat), _1215566), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1215570))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1215568, _1215572)))], (19376 ^ _780119) ^ [_1132294, _1132296] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132294), _1132296) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19377 ^ _780119 : [(19380 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132294), _1132296))], (19386 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132294), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132296), _1132294))], (19378 ^ _780119) ^ [] : [_1132296 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (50750 ^ _780119) ^ [_1809454, _1809456, _1809458, _1809460] : [hBOOL(hAPP(hAPP(c_List_Omember(_1809454), hAPP(hAPP(c_List_Olist_OCons(_1809454), _1809456), _1809458)), _1809460)), -(_1809456 = _1809460), -(hBOOL(hAPP(hAPP(c_List_Omember(_1809454), _1809458), _1809460)))], (22573 ^ _780119) ^ [_1192062, _1192064, _1192066] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_1192062, _1192064, _1192066)], (26031 ^ _780119) ^ [_1254830, _1254832] : [c_Nat__Transfer_Onat__set(_1254830), c_Nat__Transfer_Onat__set(_1254832), 26038 ^ _780119 : [(26045 ^ _780119) ^ [] : [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), _1254830)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1254832))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1254830), _1254832)))], (26039 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1254830), _1254832)), -(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), _1254830)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1254832))))]]], (10168 ^ _780119) ^ [_957595, _957597] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957595, tc_HOL_Obool)), _957597), c_Orderings_Obot__class_Obot(tc_fun(_957595, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_957595, tc_HOL_Obool)))], (21303 ^ _780119) ^ [_1167990, _1167992, _1167994] : [class_Fields_Olinordered__field__inverse__zero(_1167990), 21309 ^ _780119 : [(21312 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167990), 21308 ^ [_1167990, _1167992, _1167994]), c_Groups_Oone__class_Oone(_1167990))))], (21314 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167990), 21308 ^ [_1167990, _1167992, _1167994]), _1167992)), _1167994))], (21310 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167990), c_Groups_Ozero__class_Ozero(_1167990)), 21308 ^ [_1167990, _1167992, _1167994])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167990), _1167992), _1167994)))], (30187 ^ _780119) ^ [_1344027, _1344029] : [class_Int_Onumber__ring(_1344027), 30190 ^ _780119 : [(30197 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1344029)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1344027), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1344029)) = hAPP(c_Int_Onumber__class_Onumber__of(_1344027), _1344029))], (30191 ^ _780119) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1344029))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1344027), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1344029)) = c_Groups_Ozero__class_Ozero(_1344027))]]], (21733 ^ _780119) ^ [_1176966, _1176968, _1176970] : [class_Divides_Osemiring__div(_1176966), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176966), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1176966), _1176968), _1176970)), _1176970)), c_Divides_Odiv__class_Omod(_1176966, _1176968, _1176970)) = _1176968)], (28384 ^ _780119) ^ [_1304807, _1304809, _1304811] : [class_Orderings_Olinorder(_1304807), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304807), _1304809)), -(_1304809 = c_Orderings_Obot__class_Obot(tc_fun(_1304807, tc_HOL_Obool))), 28395 ^ _780119 : [(28405 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304807), hAPP(c_Finite__Set_Ofold1(_1304807, c_Orderings_Oord__class_Omin(_1304807)), _1304809)), _1304811))), 28406 ^ _780119 : [(28407 ^ _780119) ^ [_1305196] : [hBOOL(hAPP(hAPP(c_member(_1304807), _1305196), _1304809)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304807), _1305196), _1304811))]]], (28396 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304807), hAPP(c_Finite__Set_Ofold1(_1304807, c_Orderings_Oord__class_Omin(_1304807)), _1304809)), _1304811)), 28400 ^ _780119 : [(28403 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304807), 28399 ^ [_1304807, _1304809, _1304811]), _1304811)))], (28401 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304807), 28399 ^ [_1304807, _1304809, _1304811]), _1304809)))]]]]], (36072 ^ _780119) ^ [_1464112, _1464114, _1464116] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1464112, _1464112)), _1464114), c_Relation_OId__on(_1464112, _1464116))), 36076 ^ _780119 : [(36079 ^ _780119) ^ [] : [-(_1464114 = hAPP(hAPP(c_Product__Type_OPair(_1464112, _1464112), 36075 ^ [_1464112, _1464114, _1464116]), 36075 ^ [_1464112, _1464114, _1464116]))], (36077 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1464112), 36075 ^ [_1464112, _1464114, _1464116]), _1464116)))]]], (46345 ^ _780119) ^ [_1714286, _1714288, _1714290] : [-(_1714286 = c_List_Olist_ONil(_1714288)), -(c_List_Olast(_1714288, hAPP(hAPP(c_List_Oappend(_1714288), _1714290), _1714286)) = c_List_Olast(_1714288, _1714286))], (15198 ^ _780119) ^ [_1058080] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1058080)], (51191 ^ _780119) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (40608 ^ _780119) ^ [_1576255, _1576257, _1576259, _1576261] : [class_Lattices_Osemilattice__inf(_1576255), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576255), _1576257)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1576255, _1576255, c_Lattices_Osemilattice__inf__class_Oinf(_1576255)), _1576259), hAPP(hAPP(c_Set_Oinsert(_1576255), _1576261), _1576257)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1576255), _1576261), hAPP(hAPP(c_Finite__Set_Ofold(_1576255, _1576255, c_Lattices_Osemilattice__inf__class_Oinf(_1576255)), _1576259), _1576257)))], (32397 ^ _780119) ^ [_1384281, _1384283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384281), _1384283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1384281)), c_Int_OBit0(_1384283))))], (10705 ^ _780119) ^ [_970010, _970012] : [class_Groups_Oone(_970010), 10708 ^ _780119 : [(10715 ^ _780119) ^ [] : [_970012 = c_Groups_Oone__class_Oone(_970010), -(c_Groups_Oone__class_Oone(_970010) = _970012)], (10709 ^ _780119) ^ [] : [c_Groups_Oone__class_Oone(_970010) = _970012, -(_970012 = c_Groups_Oone__class_Oone(_970010))]]], (44382 ^ _780119) ^ [_1669148, _1669150, _1669152, _1669154, _1669156, _1669158] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1669148, _1669150), hAPP(hAPP(c_List_Ozip(_1669148, _1669150), _1669152), _1669154)), _1669156), _1669158) = hAPP(hAPP(c_List_Ozip(_1669148, _1669150), hAPP(hAPP(c_List_Olist__update(_1669148, _1669152), _1669156), hAPP(c_Product__Type_Ofst(_1669148, _1669150), _1669158))), hAPP(hAPP(c_List_Olist__update(_1669150, _1669154), _1669156), hAPP(c_Product__Type_Osnd(_1669148, _1669150), _1669158))))], (46327 ^ _780119) ^ [_1714008, _1714010, _1714012] : [_1714008 = c_List_Olist_ONil(_1714010), -(c_List_Olast(_1714010, hAPP(hAPP(c_List_Oappend(_1714010), _1714012), _1714008)) = c_List_Olast(_1714010, _1714012))], (29024 ^ _780119) ^ [_1317894, _1317896, _1317898] : [class_Orderings_Olinorder(_1317894), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317894), _1317896)), -(_1317896 = c_Orderings_Obot__class_Obot(tc_fun(_1317894, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317894), _1317898)), -(_1317898 = c_Orderings_Obot__class_Obot(tc_fun(_1317894, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1317894, c_Orderings_Oord__class_Omax(_1317894), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317894, tc_HOL_Obool)), _1317896), _1317898)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1317894), c_Big__Operators_Olattice_OSup__fin(_1317894, c_Orderings_Oord__class_Omax(_1317894), _1317896)), c_Big__Operators_Olattice_OSup__fin(_1317894, c_Orderings_Oord__class_Omax(_1317894), _1317898)))], (10727 ^ _780119) ^ [_970370, _970372, _970374, _970376] : [class_Groups_Ocancel__semigroup__add(_970370), 10730 ^ _780119 : [(10737 ^ _780119) ^ [] : [_970374 = _970376, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970370), _970372), _970374) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970370), _970372), _970376))], (10731 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970370), _970372), _970374) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970370), _970372), _970376), -(_970374 = _970376)]]], (49715 ^ _780119) ^ [_1787949, _1787951, _1787953] : [hBOOL(hAPP(hAPP(c_member(_1787949), _1787951), hAPP(c_List_Oset(_1787949), _1787953))), -(_1787953 = hAPP(hAPP(c_List_Oappend(_1787949), 49718 ^ [_1787949, _1787951, _1787953]), hAPP(hAPP(c_List_Olist_OCons(_1787949), _1787951), 49719 ^ [_1787949, _1787951, _1787953])))], (43246 ^ _780119) ^ [_1638691, _1638693, _1638695, _1638697] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638691)), _1638693) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638695)), _1638697), -(hAPP(hAPP(c_List_Omap(tc_prod(_1638691, _1638695), _1638695), c_Product__Type_Osnd(_1638691, _1638695)), hAPP(hAPP(c_List_Ozip(_1638691, _1638695), _1638693), _1638697)) = _1638697)], (18446 ^ _780119) ^ [_1116594, _1116596, _1116598] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1116594), _1116596)), _1116598) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116594), _1116598)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116596), _1116598)))], (1410 ^ _780119) ^ [_800468, _800470] : [-(class_Enum_Oenum(_800468)), _800470 = _800468, class_Enum_Oenum(_800470)], (32849 ^ _780119) ^ [_1392299, _1392301, _1392303] : [class_Rings_Olinordered__semidom(_1392299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1392299), hAPP(hAPP(c_Power_Opower__class_Opower(_1392299), _1392301), 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(_1392299), _1392303), 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(_1392299), c_Groups_Ozero__class_Ozero(_1392299)), _1392303)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1392299), _1392301), _1392303)))], (11045 ^ _780119) ^ [_976355, _976357, _976359, _976361, _976363] : [class_Groups_Ocomm__monoid__add(_976355), hBOOL(hAPP(c_Finite__Set_Ofinite(_976357), _976359)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_976357, _976355), hAPP(hAPP(c_COMBS(_976357, _976355, _976355), hAPP(hAPP(c_COMBB(_976355, tc_fun(_976355, _976355), _976357), c_Groups_Oplus__class_Oplus(_976355)), _976361)), _976363)), _976359) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976355), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_976357, _976355), _976361), _976359)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_976357, _976355), _976363), _976359)))], (32457 ^ _780119) ^ [_1385222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1385222)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1385222), c_Int_OPls)))], (29785 ^ _780119) ^ [_1334573, _1334575, _1334577, _1334579, _1334581, _1334583] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334573, tc_fun(_1334575, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1334577, _1334573, _1334579), _1334581)), _1334583) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334577, tc_fun(_1334575, tc_HOL_Obool)), _1334581), hAPP(hAPP(c_COMBB(_1334573, tc_fun(_1334575, tc_HOL_Obool), _1334577), _1334583), _1334579)))], (50544 ^ _780119) ^ [_1805463, _1805465, _1805467, _1805469, _1805471] : [-(hAPP(hAPP(c_List_Omap(_1805463, _1805465), _1805467), c_List_Oreplicate(_1805463, _1805469, _1805471)) = c_List_Oreplicate(_1805465, _1805469, hAPP(_1805467, _1805471)))], (33691 ^ _780119) ^ [_1411526, _1411528, _1411530] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1411526, _1411526), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1411528), _1411530))), -(_1411526 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1411530 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42256 ^ _780119) ^ [_1615162, _1615164, _1615166] : [hBOOL(hAPP(hAPP(c_member(_1615162), _1615164), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1615162, tc_HOL_Obool), _1615166))), 42260 ^ _780119 : [(42263 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1615162, tc_HOL_Obool)), 42259 ^ [_1615162, _1615164, _1615166]), _1615166)))], (42261 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1615162), _1615164), 42259 ^ [_1615162, _1615164, _1615166])))]]], (13138 ^ _780119) ^ [_1019399, _1019401, _1019403, _1019405] : [-(c_Map_Orestrict__map(_1019399, _1019401, _1019403, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019399, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1019399), _1019405), c_Orderings_Obot__class_Obot(tc_fun(_1019399, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1019399, tc_Option_Ooption(_1019401)), _1019403), _1019405), c_Option_Ooption_ONone(_1019401)))], (22302 ^ _780119) ^ [_1187037, _1187039] : [class_Rings_Olinordered__idom(_1187037), 22305 ^ _780119 : [(22312 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187037), _1187039), c_Groups_Ozero__class_Ozero(_1187037))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187037), c_Groups_Osgn__class_Osgn(_1187037, _1187039)), c_Groups_Ozero__class_Ozero(_1187037))))], (22306 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187037), c_Groups_Osgn__class_Osgn(_1187037, _1187039)), c_Groups_Ozero__class_Ozero(_1187037))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187037), _1187039), c_Groups_Ozero__class_Ozero(_1187037))))]]], (18956 ^ _780119) ^ [_1125723, _1125725, _1125727] : [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), _1125723), _1125725)), _1125727)), 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)), _1125727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125725), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47516 ^ _780119) ^ [_1738251] : [-(c_List_Oconcat(_1738251, c_List_Olist_ONil(tc_List_Olist(_1738251))) = c_List_Olist_ONil(_1738251))], (37008 ^ _780119) ^ [_1484256, _1484258, _1484260] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1484256, hAPP(hAPP(c_COMBC(_1484256, tc_fun(tc_prod(_1484256, _1484256), tc_HOL_Obool), tc_fun(_1484256, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484256, tc_fun(tc_fun(tc_prod(_1484256, _1484256), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484256, _1484256), tc_HOL_Obool), tc_fun(_1484256, tc_HOL_Obool)), _1484256), c_COMBC(_1484256, tc_fun(tc_prod(_1484256, _1484256), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484256, tc_prod(_1484256, _1484256)), tc_fun(_1484256, tc_fun(tc_fun(tc_prod(_1484256, _1484256), tc_HOL_Obool), tc_HOL_Obool)), _1484256), hAPP(c_COMBB(tc_prod(_1484256, _1484256), tc_fun(tc_fun(tc_prod(_1484256, _1484256), tc_HOL_Obool), tc_HOL_Obool), _1484256), c_member(tc_prod(_1484256, _1484256)))), c_Product__Type_OPair(_1484256, _1484256)))), _1484258)), _1484260)), -(hBOOL(hAPP(hAPP(c_member(_1484256), _1484260), c_Wellfounded_Oacc(_1484256, _1484258))))], (38136 ^ _780119) ^ [_1516393, _1516395, _1516397, _1516399, _1516401, _1516403] : [hAPP(c_Set_Oimage(_1516393, _1516395, _1516397), c_Orderings_Otop__class_Otop(tc_fun(_1516393, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1516395, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1516399, _1516401, _1516403), c_Orderings_Otop__class_Otop(tc_fun(_1516399, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1516401, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1516393, _1516399), tc_prod(_1516395, _1516401), c_Product__Type_Omap__pair(_1516393, _1516395, _1516399, _1516401, _1516397, _1516403)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1516393, _1516399), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1516395, _1516401), tc_HOL_Obool)))], (46821 ^ _780119) ^ [_1724715, _1724717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724715), _1724717)), -(c_List_Oupt(_1724715, hAPP(c_Nat_OSuc, _1724717)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1724715, _1724717)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1724717), c_List_Olist_ONil(tc_Nat_Onat))))], (36826 ^ _780119) ^ [_1480306, _1480308, _1480310, _1480312] : [-(hBOOL(hAPP(hAPP(c_member(_1480306), _1480308), _1480310))), -(hAPP(c_Set_Ovimage(_1480312, _1480306, hAPP(c_COMBK(_1480306, _1480312), _1480308)), _1480310) = c_Orderings_Obot__class_Obot(tc_fun(_1480312, tc_HOL_Obool)))], (31879 ^ _780119) ^ [_1374468] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1374468))) = 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)))), _1374468))], (7908 ^ _780119) ^ [_914723, _914725, _914727, _914729] : [-(c_Com_Ocom_OSemi(_914723, _914725) = c_Com_Ocom_OSemi(_914727, _914729)), _914723 = _914727, _914725 = _914729], (36738 ^ _780119) ^ [_1478226, _1478228, _1478230, _1478232, _1478234] : [-(hAPP(c_Set_Ovimage(_1478226, _1478228, _1478230), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478228, tc_HOL_Obool)), _1478232), _1478234)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478226, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1478226, _1478228, _1478230), _1478232)), hAPP(c_Set_Ovimage(_1478226, _1478228, _1478230), _1478234)))], (28056 ^ _780119) ^ [_1298124, _1298126, _1298128] : [class_Orderings_Olinorder(_1298124), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298124), _1298126), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298124), _1298126), _1298128)) = _1298126)], (4172 ^ _780119) ^ [_843174, _843176, _843178, _843180] : [-(c_List_Olist__update(_843180, _843176) = c_List_Olist__update(_843178, _843174)), _843180 = _843178, _843176 = _843174], (25181 ^ _780119) ^ [_1241023] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241023))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38762 ^ _780119) ^ [_1531180, _1531182, _1531184, _1531186, _1531188] : [c_Fun_Oinj__on(_1531180, _1531182, _1531184, c_Orderings_Otop__class_Otop(tc_fun(_1531180, tc_HOL_Obool))), c_Fun_Oinj__on(_1531186, _1531180, _1531188, c_Orderings_Otop__class_Otop(tc_fun(_1531186, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1531186, _1531182, hAPP(c_Fun_Ocomp(_1531180, _1531182, _1531186, _1531184), _1531188), c_Orderings_Otop__class_Otop(tc_fun(_1531186, tc_HOL_Obool))))], (38111 ^ _780119) ^ [_1515804, _1515806, _1515808, _1515810] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515804), _1515806)), 38117 ^ _780119 : [(38120 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515808), hAPP(_1515810, 38116 ^ [_1515804, _1515806, _1515808, _1515810])))], (38118 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515804), 38116 ^ [_1515804, _1515806, _1515808, _1515810]), _1515806)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1515804, _1515808)), hAPP(hAPP(c_Product__Type_OSigma(_1515804, _1515808), _1515806), _1515810))))], (11135 ^ _780119) ^ [_978313, _978315, _978317, _978319, _978321] : [class_Groups_Ocomm__monoid__add(_978313), hBOOL(hAPP(c_Finite__Set_Ofinite(_978315), _978317)), hBOOL(hAPP(c_Finite__Set_Ofinite(_978315), _978319)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978313), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_978315, _978313), _978321), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978315, tc_HOL_Obool)), _978317), _978319))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_978315, _978313), _978321), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978315, tc_HOL_Obool)), _978317), _978319))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978313), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_978315, _978313), _978321), _978317)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_978315, _978313), _978321), _978319)))], (6481 ^ _780119) ^ [_884902, _884904, _884906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884902, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_884902, tc_fun(_884902, tc_HOL_Obool), tc_HOL_Obool), c_member(_884902)), _884904)), hAPP(hAPP(c_COMBC(_884902, tc_fun(_884902, tc_HOL_Obool), tc_HOL_Obool), c_member(_884902)), _884906))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884902, tc_HOL_Obool)), _884904), _884906)))], (13476 ^ _780119) ^ [_1025311, _1025313, _1025315] : [class_Rings_Oring(_1025311), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025311), hAPP(c_Groups_Ouminus__class_Ouminus(_1025311), _1025313)), _1025315) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025311), _1025313), hAPP(c_Groups_Ouminus__class_Ouminus(_1025311), _1025315)))], (27178 ^ _780119) ^ [_1281043, _1281045, _1281047] : [class_Lattices_Odistrib__lattice(_1281043), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281043), _1281045)), -(_1281045 = c_Orderings_Obot__class_Obot(tc_fun(_1281043, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281043), _1281047)), -(_1281047 = c_Orderings_Obot__class_Obot(tc_fun(_1281043, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281043), c_Big__Operators_Olattice__class_OInf__fin(_1281043, _1281045)), c_Big__Operators_Olattice__class_OInf__fin(_1281043, _1281047)) = c_Big__Operators_Olattice__class_OInf__fin(_1281043, hAPP(c_Set_OCollect(_1281043), hAPP(hAPP(c_COMBB(tc_fun(_1281043, tc_HOL_Obool), tc_HOL_Obool, _1281043), c_HOL_OEx(_1281043)), hAPP(hAPP(c_COMBB(tc_fun(_1281043, tc_fun(_1281043, tc_HOL_Obool)), tc_fun(_1281043, tc_HOL_Obool), _1281043), hAPP(c_COMBB(tc_fun(_1281043, tc_HOL_Obool), tc_HOL_Obool, _1281043), c_HOL_OEx(_1281043))), hAPP(hAPP(c_COMBC(_1281043, tc_fun(_1281043, tc_fun(_1281043, tc_HOL_Obool)), tc_fun(_1281043, tc_fun(_1281043, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1281043, tc_fun(tc_fun(_1281043, tc_HOL_Obool), tc_fun(_1281043, tc_HOL_Obool))), tc_fun(tc_fun(_1281043, tc_fun(_1281043, tc_HOL_Obool)), tc_fun(_1281043, tc_fun(_1281043, tc_HOL_Obool))), _1281043), c_COMBS(_1281043, tc_fun(_1281043, tc_HOL_Obool), tc_fun(_1281043, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1281043, tc_fun(_1281043, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1281043, tc_fun(tc_fun(_1281043, tc_HOL_Obool), tc_fun(_1281043, tc_HOL_Obool))), _1281043), hAPP(c_COMBB(tc_fun(_1281043, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1281043, tc_HOL_Obool), tc_fun(_1281043, tc_HOL_Obool)), _1281043), c_COMBS(_1281043, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1281043, tc_fun(_1281043, tc_HOL_Obool)), tc_fun(_1281043, tc_fun(_1281043, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1281043), hAPP(c_COMBB(tc_fun(_1281043, tc_HOL_Obool), tc_fun(_1281043, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1281043), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1281043), c_fconj))), hAPP(hAPP(c_COMBC(_1281043, tc_fun(_1281043, tc_fun(_1281043, _1281043)), tc_fun(_1281043, tc_fun(_1281043, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1281043, _1281043), tc_fun(_1281043, tc_HOL_Obool)), tc_fun(tc_fun(_1281043, tc_fun(_1281043, _1281043)), tc_fun(_1281043, tc_fun(_1281043, tc_HOL_Obool))), _1281043), c_COMBB(tc_fun(_1281043, _1281043), tc_fun(_1281043, tc_HOL_Obool), _1281043)), hAPP(hAPP(c_COMBB(tc_fun(_1281043, tc_HOL_Obool), tc_fun(tc_fun(_1281043, _1281043), tc_fun(_1281043, tc_HOL_Obool)), _1281043), c_COMBB(_1281043, tc_HOL_Obool, _1281043)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1281043)))))), hAPP(hAPP(c_COMBC(_1281043, tc_fun(_1281043, tc_HOL_Obool), tc_fun(_1281043, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1281043, tc_HOL_Obool), tc_fun(_1281043, tc_HOL_Obool)), _1281043), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1281043)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1281043), c_fconj), hAPP(hAPP(c_COMBC(_1281043, tc_fun(_1281043, tc_HOL_Obool), tc_HOL_Obool), c_member(_1281043)), _1281045)))), hAPP(hAPP(c_COMBC(_1281043, tc_fun(_1281043, tc_HOL_Obool), tc_HOL_Obool), c_member(_1281043)), _1281047))))))))], (43976 ^ _780119) ^ [_1659304, _1659306, _1659308] : [-(_1659304 = _1659306), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659308)), _1659304) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659308)), _1659306), 43982 ^ _780119 : [(43985 ^ _780119) ^ [] : [hAPP(hAPP(c_List_Onth(_1659308), _1659304), 43981 ^ [_1659304, _1659306, _1659308]) = hAPP(hAPP(c_List_Onth(_1659308), _1659306), 43981 ^ [_1659304, _1659306, _1659308])], (43983 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43981 ^ [_1659304, _1659306, _1659308]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659308)), _1659304))))]]], (22593 ^ _780119) ^ [_1192407, _1192409, _1192411] : [class_Orderings_Olinorder(_1192407), 22596 ^ _780119 : [(22603 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192407), _1192409), _1192411)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1192407, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1192407), _1192409)), hAPP(c_SetInterval_Oord__class_OlessThan(_1192407), _1192411))))], (22597 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1192407, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1192407), _1192409)), hAPP(c_SetInterval_Oord__class_OlessThan(_1192407), _1192411))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192407), _1192409), _1192411)))]]], (34653 ^ _780119) ^ [_1430492, _1430494] : [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), _1430492), _1430494))), 34656 ^ _780119 : [(34663 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430494), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 34666 ^ _780119 : [(34675 ^ _780119) ^ [] : [-(c_Nitpick_Onorm__frac(_1430492, _1430494) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1430492), _1430494)), 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), _1430492))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1430494)))), -(_1430492 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1430494 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34667 ^ _780119) ^ [] : [34668 ^ _780119 : [(34671 ^ _780119) ^ [] : [_1430494 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (34669 ^ _780119) ^ [] : [_1430492 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1430492, _1430494) = 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)))]]], (34657 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430494), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1430492, _1430494) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1430492), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1430494)))]]], (43022 ^ _780119) ^ [_1632916, _1632918, _1632920] : [-(hBOOL(hAPP(hAPP(c_member(_1632916), _1632918), hAPP(c_List_Oset(_1632916), _1632920)))), -(c_List_Oremove1(_1632916, _1632918, _1632920) = _1632920)], (15540 ^ _780119) ^ [_1063362, _1063364, _1063366] : [class_Groups_Oordered__comm__monoid__add(_1063362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063362), _1063364), c_Groups_Ozero__class_Ozero(_1063362))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063362), _1063366), c_Groups_Ozero__class_Ozero(_1063362))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063362), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063362), _1063364), _1063366)), c_Groups_Ozero__class_Ozero(_1063362))))], (30089 ^ _780119) ^ [_1342479, _1342481, _1342483] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_1342479, _1342481, _1342483)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1342483)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12165 ^ _780119) ^ [_999445, _999447, _999449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999445), _999447)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999449), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999447), _999445)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999449), _999447)), _999445))], (21426 ^ _780119) ^ [_1170463, _1170465, _1170467, _1170469] : [class_Divides_Osemiring__div(_1170463), -(c_Divides_Odiv__class_Omod(_1170463, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170463), c_Divides_Odiv__class_Omod(_1170463, _1170465, _1170467)), _1170469), _1170467) = c_Divides_Odiv__class_Omod(_1170463, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170463), _1170465), _1170469), _1170467))], (28786 ^ _780119) ^ [_1312596, _1312598, _1312600] : [class_Orderings_Olinorder(_1312596), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312596), _1312598)), -(_1312598 = c_Orderings_Obot__class_Obot(tc_fun(_1312596, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312596), _1312600)), -(_1312600 = c_Orderings_Obot__class_Obot(tc_fun(_1312596, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1312596), c_Big__Operators_Olattice_OInf__fin(_1312596, c_Orderings_Oord__class_Omin(_1312596), _1312598)), c_Big__Operators_Olattice_OInf__fin(_1312596, c_Orderings_Oord__class_Omin(_1312596), _1312600)) = c_Big__Operators_Olattice_OInf__fin(_1312596, c_Orderings_Oord__class_Omin(_1312596), hAPP(c_Set_OCollect(_1312596), hAPP(hAPP(c_COMBB(tc_fun(_1312596, tc_HOL_Obool), tc_HOL_Obool, _1312596), c_HOL_OEx(_1312596)), hAPP(hAPP(c_COMBB(tc_fun(_1312596, tc_fun(_1312596, tc_HOL_Obool)), tc_fun(_1312596, tc_HOL_Obool), _1312596), hAPP(c_COMBB(tc_fun(_1312596, tc_HOL_Obool), tc_HOL_Obool, _1312596), c_HOL_OEx(_1312596))), hAPP(hAPP(c_COMBC(_1312596, tc_fun(_1312596, tc_fun(_1312596, tc_HOL_Obool)), tc_fun(_1312596, tc_fun(_1312596, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1312596, tc_fun(tc_fun(_1312596, tc_HOL_Obool), tc_fun(_1312596, tc_HOL_Obool))), tc_fun(tc_fun(_1312596, tc_fun(_1312596, tc_HOL_Obool)), tc_fun(_1312596, tc_fun(_1312596, tc_HOL_Obool))), _1312596), c_COMBS(_1312596, tc_fun(_1312596, tc_HOL_Obool), tc_fun(_1312596, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1312596, tc_fun(_1312596, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1312596, tc_fun(tc_fun(_1312596, tc_HOL_Obool), tc_fun(_1312596, tc_HOL_Obool))), _1312596), hAPP(c_COMBB(tc_fun(_1312596, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1312596, tc_HOL_Obool), tc_fun(_1312596, tc_HOL_Obool)), _1312596), c_COMBS(_1312596, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1312596, tc_fun(_1312596, tc_HOL_Obool)), tc_fun(_1312596, tc_fun(_1312596, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1312596), hAPP(c_COMBB(tc_fun(_1312596, tc_HOL_Obool), tc_fun(_1312596, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1312596), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1312596), c_fconj))), hAPP(hAPP(c_COMBC(_1312596, tc_fun(_1312596, tc_fun(_1312596, _1312596)), tc_fun(_1312596, tc_fun(_1312596, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1312596, _1312596), tc_fun(_1312596, tc_HOL_Obool)), tc_fun(tc_fun(_1312596, tc_fun(_1312596, _1312596)), tc_fun(_1312596, tc_fun(_1312596, tc_HOL_Obool))), _1312596), c_COMBB(tc_fun(_1312596, _1312596), tc_fun(_1312596, tc_HOL_Obool), _1312596)), hAPP(hAPP(c_COMBB(tc_fun(_1312596, tc_HOL_Obool), tc_fun(tc_fun(_1312596, _1312596), tc_fun(_1312596, tc_HOL_Obool)), _1312596), c_COMBB(_1312596, tc_HOL_Obool, _1312596)), c_fequal))), c_Orderings_Oord__class_Omax(_1312596)))))), hAPP(hAPP(c_COMBC(_1312596, tc_fun(_1312596, tc_HOL_Obool), tc_fun(_1312596, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1312596, tc_HOL_Obool), tc_fun(_1312596, tc_HOL_Obool)), _1312596), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1312596)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1312596), c_fconj), hAPP(hAPP(c_COMBC(_1312596, tc_fun(_1312596, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312596)), _1312598)))), hAPP(hAPP(c_COMBC(_1312596, tc_fun(_1312596, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312596)), _1312600))))))))], (39002 ^ _780119) ^ [_1536783, _1536785, _1536787, _1536789, _1536791, _1536793] : [c_Finite__Set_Ofolding(_1536783, _1536785, _1536787, _1536789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536783), _1536791)), -(hAPP(c_Fun_Ocomp(_1536785, _1536785, _1536785, hAPP(_1536787, _1536793)), hAPP(_1536789, _1536791)) = hAPP(c_Fun_Ocomp(_1536785, _1536785, _1536785, hAPP(_1536789, _1536791)), hAPP(_1536787, _1536793)))], (20334 ^ _780119) ^ [_1150062, _1150064, _1150066, _1150068] : [class_Fields_Olinordered__field__inverse__zero(_1150062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150062), _1150064), _1150066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150062), _1150068), c_Groups_Ozero__class_Ozero(_1150062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150062), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150062), _1150066), _1150068)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150062), _1150064), _1150068))))], (18388 ^ _780119) ^ [_1115652, _1115654, _1115656, _1115658] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1115652, _1115656)), c_Sum__Type_OPlus(_1115652, _1115656, _1115654, _1115658)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1115652), _1115654)), hAPP(c_Finite__Set_Ocard(_1115656), _1115658))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115652), _1115654)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115656), _1115658))], (7203 ^ _780119) ^ [_900017, _900019] : [c_Hoare__Mirabelle_Ostate__not__singleton, 7209 ^ _780119 : [(7212 ^ _780119) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _900017, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, 7208 ^ [_900017, _900019]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))], (7210 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), 7208 ^ [_900017, _900019]), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))]], hBOOL(hAPP(c_Com_OWT, _900019)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _900017, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _900019)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (36888 ^ _780119) ^ [_1481596, _1481598, _1481600, _1481602, _1481604] : [-(hAPP(c_Fun_Othe__inv__into(_1481596, _1481598, _1481600, _1481602), _1481604) = c_HOL_OThe(_1481596, hAPP(hAPP(c_COMBS(_1481596, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1481596), c_fconj), hAPP(hAPP(c_COMBC(_1481596, tc_fun(_1481596, tc_HOL_Obool), tc_HOL_Obool), c_member(_1481596)), _1481600))), hAPP(hAPP(c_COMBC(_1481596, _1481598, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1481598, tc_fun(_1481598, tc_HOL_Obool), _1481596), c_fequal), _1481602)), _1481604))))], (51161 ^ _780119) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (29568 ^ _780119) ^ [_1329001, _1329003] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1329001, 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(_1329001, tc_HOL_Obool)), tc_fun(_1329001, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1329001, tc_HOL_Obool)), tc_fun(_1329001, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1329001, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1329003)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1329001, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1329003))], (4802 ^ _780119) ^ [_853349, _853351, _853353, _853355, _853357, _853359, _853361, _853363] : [-(c_Lazy__Sequence_Oproduct(_853363, _853359, _853355, _853351) = c_Lazy__Sequence_Oproduct(_853361, _853357, _853353, _853349)), _853363 = _853361, _853359 = _853357, _853355 = _853353, _853351 = _853349], (35584 ^ _780119) ^ [_1452527, _1452529, _1452531, _1452533, _1452535, _1452537] : [c_Equiv__Relations_Oequiv(_1452527, _1452529, _1452531), hBOOL(hAPP(hAPP(c_member(_1452527), _1452533), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452527, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1452527, _1452527, _1452531), hAPP(hAPP(c_Set_Oinsert(_1452527), _1452535), c_Orderings_Obot__class_Obot(tc_fun(_1452527, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1452527, _1452527, _1452531), hAPP(hAPP(c_Set_Oinsert(_1452527), _1452537), c_Orderings_Obot__class_Obot(tc_fun(_1452527, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1452527, _1452527)), hAPP(hAPP(c_Product__Type_OPair(_1452527, _1452527), _1452535), _1452537)), _1452531)))], (36613 ^ _780119) ^ [_1475240, _1475242, _1475244, _1475246] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1475240), _1475242)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475244), _1475246)), 36620 ^ _780119 : [(36621 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1475240), _1475242)), hAPP(c_Finite__Set_Ocard(_1475244), _1475246)))), 36622 ^ _780119 : [(36623 ^ _780119) ^ [_1475451] : [c_Fun_Oinj__on(_1475240, _1475244, _1475451, _1475242), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475244, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1475240, _1475244, _1475451), _1475242)), _1475246))]]], (36631 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1475240), _1475242)), hAPP(c_Finite__Set_Ocard(_1475244), _1475246))), 36635 ^ _780119 : [(36638 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475244, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1475240, _1475244, 36634 ^ [_1475240, _1475242, _1475244, _1475246]), _1475242)), _1475246)))], (36636 ^ _780119) ^ [] : [-(c_Fun_Oinj__on(_1475240, _1475244, 36634 ^ [_1475240, _1475242, _1475244, _1475246], _1475242))]]]]], (25163 ^ _780119) ^ [_1240701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240701)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1240701)) = _1240701)], (766 ^ _780119) ^ [_791806, _791808, _791810, _791812, _791814, _791816] : [-(c_Enum_Oex__n__lists(_791814, _791810, _791806)), c_Enum_Oex__n__lists(_791816, _791812, _791808), _791816 = _791814, _791812 = _791810, _791808 = _791806], (21594 ^ _780119) ^ [_1174145, _1174147, _1174149] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1174145, tc_HOL_Obool)), _1174147), hAPP(c_Set_OPow(_1174145), _1174149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174145, tc_HOL_Obool)), _1174147), _1174149)))], (11469 ^ _780119) ^ [_985612, _985614, _985616, _985618] : [class_Rings_Ocomm__semiring__1(_985612), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985612), _985614), _985616)), _985618) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985612), _985614), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985612), _985616), _985618)))], (13770 ^ _780119) ^ [_1030591, _1030593, _1030595] : [class_Groups_Ocomm__monoid__mult(_1030591), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1030593, _1030591), _1030595), c_Orderings_Obot__class_Obot(tc_fun(_1030593, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1030591))], (46935 ^ _780119) ^ [_1726689, _1726691] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726689), _1726691))), -(c_List_Oupt(_1726689, _1726691) = c_List_Olist_ONil(tc_Nat_Onat))], (19420 ^ _780119) ^ [_1133057, _1133059, _1133061, _1133063] : [class_Divides_Osemiring__div(_1133057), -(_1133059 = c_Groups_Ozero__class_Ozero(_1133057)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133057), _1133061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133057), _1133063), _1133059))), _1133059) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133057), _1133063), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133057), _1133061), _1133059)))], (43370 ^ _780119) ^ [_1642130, _1642132, _1642134] : [hBOOL(hAPP(hAPP(c_member(_1642130), _1642132), hAPP(c_List_Oset(_1642130), _1642134))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642130)), c_List_Oremove1(_1642130, _1642132, _1642134)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642130)), _1642134)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10779 ^ _780119) ^ [_971234, _971236, _971238, _971240] : [class_Groups_Ocancel__semigroup__add(_971234), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971234), _971236), _971238) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971234), _971240), _971238), -(_971236 = _971240)], (44918 ^ _780119) ^ [_1680130, _1680132, _1680134] : [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), _1680130), _1680132))), -(hBOOL(hAPP(hAPP(_1680134, _1680130), _1680132))), 44925 ^ _780119 : [(44934 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1680134, 44923 ^ [_1680130, _1680132, _1680134]), 44924 ^ [_1680130, _1680132, _1680134]))], (44928 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 44923 ^ [_1680130, _1680132, _1680134]), 44924 ^ [_1680130, _1680132, _1680134])), -(hBOOL(hAPP(hAPP(_1680134, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 44923 ^ [_1680130, _1680132, _1680134]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 44924 ^ [_1680130, _1680132, _1680134])))], (44926 ^ _780119) ^ [] : [-(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), 44923 ^ [_1680130, _1680132, _1680134]), 44924 ^ [_1680130, _1680132, _1680134]))))]]], (45452 ^ _780119) ^ [_1693441, _1693443, _1693445, _1693447] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693441), tc_List_Olist(_1693441))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693441), tc_List_Olist(_1693441)), _1693443), _1693445)), c_List_Olistrel(_1693441, _1693447))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693441), tc_List_Olist(_1693441))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693441), tc_List_Olist(_1693441)), _1693443), _1693445)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1693441), c_List_Olistrel1(_1693441, _1693447)))))], (36093 ^ _780119) ^ [_1464694, _1464696] : [class_Groups_Oordered__ab__group__add(_1464694), -(c_Fun_Oinj__on(_1464694, _1464694, c_Groups_Ouminus__class_Ouminus(_1464694), _1464696))], (26593 ^ _780119) ^ [_1265586, _1265588, _1265590] : [class_Groups_Oordered__ab__group__add__abs(_1265586), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265586), hAPP(c_Groups_Oabs__class_Oabs(_1265586), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1265586), _1265588), _1265590))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1265586), hAPP(c_Groups_Oabs__class_Oabs(_1265586), _1265588)), hAPP(c_Groups_Oabs__class_Oabs(_1265586), _1265590)))))], (21372 ^ _780119) ^ [_1169432, _1169434] : [class_Divides_Osemiring__div(_1169432), -(c_Divides_Odiv__class_Omod(_1169432, c_Groups_Ozero__class_Ozero(_1169432), _1169434) = c_Groups_Ozero__class_Ozero(_1169432))], (23064 ^ _780119) ^ [_1201309, _1201311] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201309)), _1201311) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1201309), _1201311)))], (30435 ^ _780119) ^ [_1349114, _1349116] : [class_Int_Onumber__ring(_1349114), -(hBOOL(hAPP(hAPP(c_member(_1349114), hAPP(c_Int_Onumber__class_Onumber__of(_1349114), _1349116)), c_Int_Oring__1__class_OInts(_1349114))))], (21574 ^ _780119) ^ [_1173660, _1173662] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1173660), _1173662)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1173660, tc_HOL_Obool)), hAPP(c_Set_OPow(_1173660), _1173662))))], (7181 ^ _780119) ^ [_899214, _899216, _899218, _899220, _899222] : [class_Orderings_Oord(_899214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899216, _899214)), _899218), _899220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899214), hAPP(_899218, _899222)), hAPP(_899220, _899222))))], (45634 ^ _780119) ^ [_1698547, _1698549, _1698551, _1698553] : [-(hAPP(hAPP(c_List_Odrop(_1698547), _1698549), hAPP(hAPP(c_List_Otake(_1698547), _1698551), _1698553)) = hAPP(hAPP(c_List_Otake(_1698547), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1698551), _1698549)), hAPP(hAPP(c_List_Odrop(_1698547), _1698549), _1698553)))], (8778 ^ _780119) ^ [_931752, _931754, _931756] : [class_Orderings_Opreorder(_931752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931752), _931754), _931756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931752), _931756), _931754))], (47556 ^ _780119) ^ [_1739178, _1739180, _1739182] : [hAPP(c_List_Orev(_1739178), _1739180) = _1739182, -(_1739180 = hAPP(c_List_Orev(_1739178), _1739182))], (35432 ^ _780119) ^ [_1448593, _1448595] : [-(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), _1448593), _1448595)), 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), _1448595), _1448593)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (51523 ^ _780119) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (17039 ^ _780119) ^ [_1089624, _1089626, _1089628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1089624), _1089626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1089628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1089628), _1089624)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1089628), _1089626))))], (41435 ^ _780119) ^ [_1596238, _1596240, _1596242, _1596244, _1596246] : [_1596238 = c_Orderings_Obot__class_Obot(tc_fun(_1596240, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1596242, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596240, tc_fun(_1596242, tc_HOL_Obool)), _1596238), _1596244)), _1596246) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1596242, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1596242, tc_HOL_Obool))), _1596246))], (25406 ^ _780119) ^ [_1244778, _1244780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244780)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1244778), hAPP(c_Int_Onat, _1244780)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1244778, _1244780)))], (47919 ^ _780119) ^ [_1748227, _1748229, _1748231, _1748233] : [-(c_List_Oremdups(_1748227, hAPP(hAPP(c_List_Omap(_1748229, _1748227), _1748231), c_List_Oremdups(_1748229, _1748233))) = c_List_Oremdups(_1748227, hAPP(hAPP(c_List_Omap(_1748229, _1748227), _1748231), _1748233)))], (37924 ^ _780119) ^ [_1509664, _1509666, _1509668, _1509670] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1509664, _1509666)), hAPP(hAPP(c_Product__Type_OSigma(_1509664, _1509666), _1509668), hAPP(c_COMBK(tc_fun(_1509666, tc_HOL_Obool), _1509664), _1509670)))), -(_1509668 = c_Orderings_Obot__class_Obot(tc_fun(_1509664, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1509666), _1509670)))], (8208 ^ _780119) ^ [_921359, _921361, _921363, _921365] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921359, tc_HOL_Obool)), _921361), hAPP(hAPP(c_Set_Oinsert(_921359), _921363), _921365)))), 8211 ^ _780119 : [(8214 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921359, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921359, tc_HOL_Obool)), _921361), hAPP(hAPP(c_Set_Oinsert(_921359), _921363), c_Orderings_Obot__class_Obot(tc_fun(_921359, tc_HOL_Obool))))), _921365))], (8212 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_921359), _921363), _921361)))]], 8215 ^ _780119 : [(8218 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921359, tc_HOL_Obool)), _921361), _921365))], (8216 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_921359), _921363), _921361))]]], (46549 ^ _780119) ^ [_1718341, _1718343, _1718345, _1718347] : [-(hAPP(hAPP(c_List_Oappend(_1718341), _1718343), hAPP(hAPP(c_List_Olist_OCons(_1718341), _1718345), c_List_Olist_ONil(_1718341))) = _1718347), -(_1718347 = c_List_Olist_ONil(_1718341)), c_List_Obutlast(_1718341, _1718347) = _1718343, c_List_Olast(_1718341, _1718347) = _1718345], (10769 ^ _780119) ^ [_971067, _971069, _971071, _971073] : [class_Groups_Ocancel__ab__semigroup__add(_971067), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971067), _971069), _971071) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971067), _971069), _971073), -(_971071 = _971073)], (34199 ^ _780119) ^ [_1422213, _1422215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1422213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1422215)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1422213, _1422215), c_Divides_OposDivAlg(_1422213, _1422215))))], (43312 ^ _780119) ^ [_1640804, _1640806, _1640808] : [_1640804 = _1640806, 43315 ^ _780119 : [(43318 ^ _780119) ^ [_1640960] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1640808, _1640808)), _1640960), hAPP(c_List_Oset(tc_prod(_1640808, _1640808)), hAPP(hAPP(c_List_Ozip(_1640808, _1640808), _1640804), _1640806)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1640808, _1640808, tc_HOL_Obool), c_fequal), _1640960)))], (43316 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640808)), _1640804) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640808)), _1640806))]]], (14776 ^ _780119) ^ [_1051479] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1051479))))], (50975 ^ _780119) ^ [_1814180, _1814182] : [class_Lattices_Oboolean__algebra(_1814180), -(class_Lattices_Oboolean__algebra(tc_fun(_1814182, _1814180)))], (48223 ^ _780119) ^ [_1754574, _1754576, _1754578, _1754580] : [-(c_List_Opartition(_1754574, _1754576, hAPP(hAPP(c_List_Olist_OCons(_1754574), _1754578), _1754580)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1754574), tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1754574), tc_fun(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574))), tc_fun(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1754574), tc_fun(tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)))), tc_fun(tc_fun(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574))), tc_fun(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)))), tc_List_Olist(_1754574)), c_COMBS(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574))), tc_fun(tc_List_Olist(_1754574), tc_fun(tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)))), tc_List_Olist(_1754574)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)), tc_fun(tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574))), tc_List_Olist(_1754574)), hAPP(c_If(tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574))), hAPP(_1754576, _1754578)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1754574), tc_fun(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574))), tc_List_Olist(_1754574)), c_Product__Type_OPair(tc_List_Olist(_1754574), tc_List_Olist(_1754574))), hAPP(c_List_Olist_OCons(_1754574), _1754578))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1754574), tc_fun(tc_List_Olist(_1754574), tc_List_Olist(_1754574)), tc_fun(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574))), tc_fun(tc_fun(tc_List_Olist(_1754574), tc_List_Olist(_1754574)), tc_fun(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)))), tc_List_Olist(_1754574)), c_COMBB(tc_List_Olist(_1754574), tc_prod(tc_List_Olist(_1754574), tc_List_Olist(_1754574)), tc_List_Olist(_1754574))), c_Product__Type_OPair(tc_List_Olist(_1754574), tc_List_Olist(_1754574)))), hAPP(c_List_Olist_OCons(_1754574), _1754578)))), c_List_Opartition(_1754574, _1754576, _1754580)))], (46702 ^ _780119) ^ [_1721871, _1721873, _1721875] : [-(c_List_Omap__filter(_1721871, _1721873, _1721875, c_List_Olist_ONil(_1721871)) = c_List_Olist_ONil(_1721873))], (24071 ^ _780119) ^ [_1220715, _1220717, _1220719] : [class_Fields_Ofield(_1220715), -(_1220717 = c_Groups_Oone__class_Oone(_1220715)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220715), hAPP(c_Power_Opower__class_Opower(_1220715), _1220717)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1220719)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220715), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1220715), hAPP(hAPP(c_Power_Opower__class_Opower(_1220715), _1220717), _1220719)), c_Groups_Oone__class_Oone(_1220715))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1220715), _1220717), c_Groups_Oone__class_Oone(_1220715))))], (22883 ^ _780119) ^ [_1197999, _1198001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1197999), _1198001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197999)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198001))))], (16516 ^ _780119) ^ [_1080985, _1080987] : [class_Groups_Oordered__ab__group__add(_1080985), 16519 ^ _780119 : [(16526 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080985), _1080987), c_Groups_Ozero__class_Ozero(_1080985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080985), c_Groups_Ozero__class_Ozero(_1080985)), hAPP(c_Groups_Ouminus__class_Ouminus(_1080985), _1080987))))], (16520 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080985), c_Groups_Ozero__class_Ozero(_1080985)), hAPP(c_Groups_Ouminus__class_Ouminus(_1080985), _1080987))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080985), _1080987), c_Groups_Ozero__class_Ozero(_1080985))))]]], (15342 ^ _780119) ^ [_1060110] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060110), _1060110) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6353 ^ _780119) ^ [_882421, _882423, _882425, _882427, _882429] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882421, tc_HOL_Obool)), _882423), hAPP(c_Set_Oimage(_882425, _882421, _882427), _882429)))), 6354 ^ _780119 : [(6355 ^ _780119) ^ [_882501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882425, tc_HOL_Obool)), _882501), _882429)), _882423 = hAPP(c_Set_Oimage(_882425, _882421, _882427), _882501)]]], (5861 ^ _780119) ^ [_873077, _873079, _873081, _873083] : [5862 ^ _780119 : [(5865 ^ _780119) ^ [] : [_873079 = _873083], (5863 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873077), _873079), _873081))]], -(hBOOL(hAPP(hAPP(c_member(_873077), _873079), hAPP(hAPP(c_Set_Oinsert(_873077), _873083), _873081))))], (43693 ^ _780119) ^ [_1652362, _1652364, _1652366] : [hBOOL(hAPP(c_List_Odistinct(_1652362), _1652364)), -(hBOOL(hAPP(c_List_Odistinct(_1652362), c_List_Osublist(_1652362, _1652364, _1652366))))], (2344 ^ _780119) ^ [_814618, _814620, _814622, _814624, _814626, _814628, _814630, _814632] : [-(c_Nitpick_Oprod(_814632, _814628, _814624, _814620) = c_Nitpick_Oprod(_814630, _814626, _814622, _814618)), _814632 = _814630, _814628 = _814626, _814624 = _814622, _814620 = _814618], (41483 ^ _780119) ^ [_1597368, _1597370, _1597372, _1597374, _1597376] : [_1597368 = c_Orderings_Obot__class_Obot(tc_fun(_1597370, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597370, tc_fun(_1597372, tc_HOL_Obool)), _1597368), hAPP(hAPP(c_COMBB(tc_fun(_1597372, tc_HOL_Obool), tc_fun(_1597372, tc_HOL_Obool), _1597370), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1597372, tc_HOL_Obool)), _1597374)), _1597376)) = c_Orderings_Otop__class_Otop(tc_fun(_1597372, tc_HOL_Obool)))], (6583 ^ _780119) ^ [_887075, _887077, _887079] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887075, tc_HOL_Obool)), _887077), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887075, tc_HOL_Obool)), _887077), _887079)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887075, tc_HOL_Obool)), _887077), _887079))], (41447 ^ _780119) ^ [_1596548, _1596550, _1596552, _1596554, _1596556] : [_1596548 = c_Orderings_Obot__class_Obot(tc_fun(_1596550, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596550, tc_fun(_1596552, tc_HOL_Obool)), _1596548), hAPP(hAPP(c_COMBC(_1596550, tc_fun(_1596552, tc_HOL_Obool), tc_fun(_1596552, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1596552, tc_HOL_Obool), tc_fun(tc_fun(_1596552, tc_HOL_Obool), tc_fun(_1596552, tc_HOL_Obool)), _1596550), c_Groups_Ominus__class_Ominus(tc_fun(_1596552, tc_HOL_Obool))), _1596554)), _1596556)) = c_Orderings_Otop__class_Otop(tc_fun(_1596552, tc_HOL_Obool)))], (29943 ^ _780119) ^ [_1339416, _1339418, _1339420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1339416, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1339416, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29944 ^ [_1339416, _1339418, _1339420])), _1339418)), _1339420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1339416, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1339416, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1339418)), _1339420)))], (50394 ^ _780119) ^ [_1801922, _1801924, _1801926, _1801928] : [-(c_Lazy__Sequence_Ohb__bind(_1801922, _1801924, _1801926, _1801928) = c_Lazy__Sequence_Ohb__flat(_1801924, c_Lazy__Sequence_Ohb__map(_1801922, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1801924)), _1801928, _1801926)))], (34580 ^ _780119) ^ [_1429118, _1429120, _1429122] : [34582 ^ _780119 : [(34585 ^ _780119) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1429118, _1429120), 34581 ^ [_1429118, _1429120, _1429122]))], (34583 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1429120, 34581 ^ [_1429118, _1429120, _1429122]), _1429122)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1429118, _1429120), _1429122)))], (23125 ^ _780119) ^ [_1202436] : [-(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), _1202436))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50242 ^ _780119) ^ [_1798113, _1798115, _1798117] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1798113, _1798115), _1798117) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1798113, tc_Lazy__Sequence_Olazy__sequence(_1798113)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1798113, tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1798113, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_Nat_Onat)), _1798113), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1798113), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1798113)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1798113, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1798113), tc_Nat_Onat)), _1798113), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1798113))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1798113), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1798115))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1798113, _1798115))))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1798113), _1798117)))], (10248 ^ _780119) ^ [_959793, _959795, _959797, _959799] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959793, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_959793, tc_fun(_959793, tc_HOL_Obool), tc_HOL_Obool), c_member(_959793)), _959795)), hAPP(hAPP(c_COMBC(_959793, tc_fun(_959793, tc_HOL_Obool), tc_HOL_Obool), c_member(_959793)), _959797)), _959799)), -(hBOOL(hAPP(hAPP(c_member(_959793), _959799), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959793, tc_HOL_Obool)), _959795), _959797))))], (47448 ^ _780119) ^ [_1736890, _1736892, _1736894] : [_1736892 = hAPP(hAPP(c_List_Olist_OCons(_1736890), _1736894), c_List_Olist_ONil(_1736890)), -(hAPP(c_List_Orev(_1736890), _1736892) = hAPP(hAPP(c_List_Olist_OCons(_1736890), _1736894), c_List_Olist_ONil(_1736890)))], (42403 ^ _780119) ^ [_1618378, _1618380, _1618382, _1618384, _1618386, _1618388] : [hAPP(c_Map_Omap__add(_1618378, _1618380, _1618382, _1618384), _1618386) = hAPP(c_Option_Ooption_OSome(_1618380), _1618388), -(hAPP(_1618384, _1618386) = hAPP(c_Option_Ooption_OSome(_1618380), _1618388)), 42410 ^ _780119 : [(42413 ^ _780119) ^ [] : [-(hAPP(_1618382, _1618386) = hAPP(c_Option_Ooption_OSome(_1618380), _1618388))], (42411 ^ _780119) ^ [] : [-(hAPP(_1618384, _1618386) = c_Option_Ooption_ONone(_1618380))]]], (16228 ^ _780119) ^ [_1075865, _1075867, _1075869] : [class_Rings_Olinordered__ring__strict(_1075865), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075865), _1075867), c_Groups_Ozero__class_Ozero(_1075865))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075865), _1075869), c_Groups_Ozero__class_Ozero(_1075865))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075865), c_Groups_Ozero__class_Ozero(_1075865)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075865), _1075867), _1075869))))], (35757 ^ _780119) ^ [_1456327, _1456329, _1456331, _1456333, _1456335] : [c_Equiv__Relations_Oequiv(_1456327, _1456329, _1456331), hBOOL(hAPP(hAPP(c_member(_1456327), _1456333), _1456329)), hBOOL(hAPP(hAPP(c_member(_1456327), _1456335), _1456329)), 35768 ^ _780119 : [(35775 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1456327, _1456327)), hAPP(hAPP(c_Product__Type_OPair(_1456327, _1456327), _1456333), _1456335)), _1456331)), -(hAPP(c_Relation_OImage(_1456327, _1456327, _1456331), hAPP(hAPP(c_Set_Oinsert(_1456327), _1456333), c_Orderings_Obot__class_Obot(tc_fun(_1456327, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1456327, _1456327, _1456331), hAPP(hAPP(c_Set_Oinsert(_1456327), _1456335), c_Orderings_Obot__class_Obot(tc_fun(_1456327, tc_HOL_Obool)))))], (35769 ^ _780119) ^ [] : [hAPP(c_Relation_OImage(_1456327, _1456327, _1456331), hAPP(hAPP(c_Set_Oinsert(_1456327), _1456333), c_Orderings_Obot__class_Obot(tc_fun(_1456327, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1456327, _1456327, _1456331), hAPP(hAPP(c_Set_Oinsert(_1456327), _1456335), c_Orderings_Obot__class_Obot(tc_fun(_1456327, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1456327, _1456327)), hAPP(hAPP(c_Product__Type_OPair(_1456327, _1456327), _1456333), _1456335)), _1456331)))]]], (204 ^ _780119) ^ [_783353, _783355, _783357, _783359] : [-(c_Int_Oiszero(_783357, _783353)), c_Int_Oiszero(_783359, _783355), _783359 = _783357, _783355 = _783353], (19012 ^ _780119) ^ [_1126577, _1126579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126577)), -(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), _1126577), _1126579))))], (34939 ^ _780119) ^ [_1436219, _1436221, _1436223, _1436225, _1436227] : [hBOOL(hAPP(hAPP(_1436219, _1436221), _1436223)), -(hBOOL(hAPP(hAPP(_1436219, hAPP(c_Product__Type_Osnd(_1436225, _1436227), hAPP(hAPP(c_Product__Type_OPair(_1436225, _1436227), _1436223), _1436221))), hAPP(c_Product__Type_Ofst(_1436225, _1436227), hAPP(hAPP(c_Product__Type_OPair(_1436225, _1436227), _1436223), _1436221)))))], (36201 ^ _780119) ^ [_1466775, _1466777, _1466779, _1466781, _1466783, _1466785] : [c_Fun_Oinj__on(_1466775, _1466777, _1466779, _1466781), hAPP(_1466779, _1466783) = hAPP(_1466779, _1466785), hBOOL(hAPP(hAPP(c_member(_1466775), _1466783), _1466781)), hBOOL(hAPP(hAPP(c_member(_1466775), _1466785), _1466781)), -(_1466783 = _1466785)], (6282 ^ _780119) ^ [_880895, _880897, _880899, _880901] : [_880901 = c_Orderings_Obot__class_Obot(tc_fun(_880895, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_880895, _880897, _880899), _880901) = c_Orderings_Obot__class_Obot(tc_fun(_880897, tc_HOL_Obool)))], (9298 ^ _780119) ^ [_940032, _940034, _940036, _940038, _940040, _940042, _940044] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_940032, tc_Option_Ooption(_940034)), _940036), _940038), hAPP(c_Option_Ooption_OSome(_940034), _940040)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_940032, tc_Option_Ooption(_940034)), _940042), _940038), hAPP(c_Option_Ooption_OSome(_940034), _940044)), -(_940040 = _940044)], (18452 ^ _780119) ^ [_1116739, _1116741, _1116743] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1116739), _1116741)), _1116743) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116739), _1116743)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116741), _1116743)))], (13442 ^ _780119) ^ [_1024724, _1024726, _1024728] : [class_Groups_Oab__group__add(_1024724), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1024724), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024724), _1024726), _1024728)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024724), hAPP(c_Groups_Ouminus__class_Ouminus(_1024724), _1024726)), hAPP(c_Groups_Ouminus__class_Ouminus(_1024724), _1024728)))], (13436 ^ _780119) ^ [_1024585, _1024587, _1024589] : [class_Groups_Ogroup__add(_1024585), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1024585), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024585), _1024587), _1024589)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024585), hAPP(c_Groups_Ouminus__class_Ouminus(_1024585), _1024589)), hAPP(c_Groups_Ouminus__class_Ouminus(_1024585), _1024587)))], (1350 ^ _780119) ^ [_799718, _799720] : [-(class_Orderings_Otop(_799718)), _799720 = _799718, class_Orderings_Otop(_799720)], (11517 ^ _780119) ^ [_986756, _986758, _986760, _986762, _986764] : [class_Rings_Ocomm__semiring__1(_986756), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986756), _986758), _986760)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986756), _986762), _986764)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986756), _986758), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986756), _986760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986756), _986762), _986764))))], (7606 ^ _780119) ^ [_908144, _908146, _908148, _908150, _908152] : [c_Finite__Set_Ofolding__one__idem(_908144, _908146, _908148), hBOOL(hAPP(c_Finite__Set_Ofinite(_908144), _908150)), -(_908152 = c_Orderings_Obot__class_Obot(tc_fun(_908144, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908144, tc_HOL_Obool)), _908152), _908150)), -(hAPP(hAPP(_908146, hAPP(_908148, _908152)), hAPP(_908148, _908150)) = hAPP(_908148, _908150))], (15642 ^ _780119) ^ [_1065132, _1065134] : [class_Groups_Olinordered__ab__group__add(_1065132), 15645 ^ _780119 : [(15652 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065132), c_Groups_Ozero__class_Ozero(_1065132)), _1065134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065132), c_Groups_Ozero__class_Ozero(_1065132)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065132), _1065134), _1065134))))], (15646 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065132), c_Groups_Ozero__class_Ozero(_1065132)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065132), _1065134), _1065134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065132), c_Groups_Ozero__class_Ozero(_1065132)), _1065134)))]]], (14064 ^ _780119) ^ [_1036245, _1036247, _1036249, _1036251, _1036253] : [class_Groups_Ocomm__monoid__mult(_1036245), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036247), _1036249)), 14071 ^ _780119 : [(14078 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1036247), _1036251), _1036249))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1036247, _1036245), hAPP(hAPP(c_COMBC(_1036247, _1036245, _1036245), hAPP(hAPP(c_COMBS(_1036247, _1036245, tc_fun(_1036245, _1036245)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1036245, tc_fun(_1036245, _1036245)), _1036247), c_If(_1036245)), hAPP(hAPP(c_COMBC(_1036247, _1036247, tc_HOL_Obool), c_fequal), _1036251))), _1036253)), c_Groups_Oone__class_Oone(_1036245))), _1036249) = c_Groups_Oone__class_Oone(_1036245))], (14072 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1036247), _1036251), _1036249)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1036247, _1036245), hAPP(hAPP(c_COMBC(_1036247, _1036245, _1036245), hAPP(hAPP(c_COMBS(_1036247, _1036245, tc_fun(_1036245, _1036245)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1036245, tc_fun(_1036245, _1036245)), _1036247), c_If(_1036245)), hAPP(hAPP(c_COMBC(_1036247, _1036247, tc_HOL_Obool), c_fequal), _1036251))), _1036253)), c_Groups_Oone__class_Oone(_1036245))), _1036249) = hAPP(_1036253, _1036251))]]], (11963 ^ _780119) ^ [_995622, _995624, _995626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995622), _995624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995622), _995626)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995624), _995626))))], (38170 ^ _780119) ^ [_1517420, _1517422, _1517424, _1517426, _1517428, _1517430, _1517432, _1517434, _1517436, _1517438] : [hAPP(c_Set_Oimage(_1517420, _1517422, _1517424), _1517426) = _1517428, hAPP(c_Set_Oimage(_1517430, _1517432, _1517434), _1517436) = _1517438, -(hAPP(c_Set_Oimage(tc_prod(_1517420, _1517430), tc_prod(_1517422, _1517432), c_Product__Type_Omap__pair(_1517420, _1517422, _1517430, _1517432, _1517424, _1517434)), hAPP(hAPP(c_Product__Type_OSigma(_1517420, _1517430), _1517426), hAPP(c_COMBK(tc_fun(_1517430, tc_HOL_Obool), _1517420), _1517436))) = hAPP(hAPP(c_Product__Type_OSigma(_1517422, _1517432), _1517428), hAPP(c_COMBK(tc_fun(_1517432, tc_HOL_Obool), _1517422), _1517438)))], (39144 ^ _780119) ^ [_1540120, _1540122, _1540124, _1540126, _1540128, _1540130] : [class_Groups_Ocomm__monoid__add(_1540120), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540122), _1540124)), 39154 ^ _780119 : [(39162 ^ _780119) ^ [] : [-(hAPP(_1540126, 39153 ^ [_1540120, _1540122, _1540124, _1540126, _1540128, _1540130]) = hAPP(_1540126, 39156 ^ [_1540120, _1540122, _1540124, _1540126, _1540128, _1540130]))], (39160 ^ _780119) ^ [] : [39153 ^ [_1540120, _1540122, _1540124, _1540126, _1540128, _1540130] = 39156 ^ [_1540120, _1540122, _1540124, _1540126, _1540128, _1540130]], (39158 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540122), 39156 ^ [_1540120, _1540122, _1540124, _1540126, _1540128, _1540130]), _1540124)))], (39155 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540122), 39153 ^ [_1540120, _1540122, _1540124, _1540126, _1540128, _1540130]), _1540124)))], (39164 ^ _780119) ^ [] : [hAPP(_1540128, hAPP(_1540126, 39153 ^ [_1540120, _1540122, _1540124, _1540126, _1540128, _1540130])) = c_Groups_Ozero__class_Ozero(_1540120)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1540130, _1540120), _1540128), hAPP(c_Set_Oimage(_1540122, _1540130, _1540126), _1540124)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1540122, _1540120), hAPP(c_Fun_Ocomp(_1540130, _1540120, _1540122, _1540128), _1540126)), _1540124))], (35261 ^ _780119) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (44096 ^ _780119) ^ [_1662214, _1662216, _1662218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662214), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662216)), _1662218))), -(hBOOL(hAPP(hAPP(c_member(_1662216), hAPP(hAPP(c_List_Onth(_1662216), _1662218), _1662214)), hAPP(c_List_Oset(_1662216), _1662218))))], (50252 ^ _780119) ^ [_1798544, _1798546] : [-(hAPP(c_New__DSequence_Opos__empty(_1798544), _1798546) = c_Lazy__Sequence_Oempty(_1798544))], (14122 ^ _780119) ^ [_1037752, _1037754, _1037756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037752), _1037754)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037756), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037754), _1037752))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037756), _1037752)), hAPP(c_Nat_OSuc, _1037754)))], (1670 ^ _780119) ^ [_803718, _803720] : [-(class_Orderings_Opreorder(_803718)), _803720 = _803718, class_Orderings_Opreorder(_803720)], (47510 ^ _780119) ^ [_1738154, _1738156] : [_1738156 = c_List_Olist_ONil(_1738154), -(c_List_Olist_ONil(_1738154) = hAPP(c_List_Orev(_1738154), _1738156))], (33547 ^ _780119) ^ [_1404555, _1404557, _1404559, _1404561] : [-(c_Nitpick_Oprod(_1404555, _1404557, _1404559, _1404561) = hAPP(c_Set_OCollect(tc_prod(_1404555, _1404557)), hAPP(c_Product__Type_Oprod_Oprod__case(_1404555, _1404557, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1404555, tc_fun(_1404557, tc_HOL_Obool), tc_fun(_1404557, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1404557, tc_HOL_Obool), tc_fun(_1404557, tc_HOL_Obool)), _1404555), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1404557)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1404555), c_fconj), hAPP(hAPP(c_COMBC(_1404555, tc_fun(_1404555, tc_HOL_Obool), tc_HOL_Obool), c_member(_1404555)), _1404559)))), hAPP(hAPP(c_COMBC(_1404557, tc_fun(_1404557, tc_HOL_Obool), tc_HOL_Obool), c_member(_1404557)), _1404561)))))], (35857 ^ _780119) ^ [_1458930, _1458932] : [c_Equiv__Relations_Oequivp(_1458930, hAPP(hAPP(c_COMBC(_1458930, tc_fun(tc_prod(_1458930, _1458930), tc_HOL_Obool), tc_fun(_1458930, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458930, tc_fun(tc_fun(tc_prod(_1458930, _1458930), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1458930, _1458930), tc_HOL_Obool), tc_fun(_1458930, tc_HOL_Obool)), _1458930), c_COMBC(_1458930, tc_fun(tc_prod(_1458930, _1458930), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458930, tc_prod(_1458930, _1458930)), tc_fun(_1458930, tc_fun(tc_fun(tc_prod(_1458930, _1458930), tc_HOL_Obool), tc_HOL_Obool)), _1458930), hAPP(c_COMBB(tc_prod(_1458930, _1458930), tc_fun(tc_fun(tc_prod(_1458930, _1458930), tc_HOL_Obool), tc_HOL_Obool), _1458930), c_member(tc_prod(_1458930, _1458930)))), c_Product__Type_OPair(_1458930, _1458930)))), _1458932)), -(c_Equiv__Relations_Oequiv(_1458930, c_Orderings_Otop__class_Otop(tc_fun(_1458930, tc_HOL_Obool)), _1458932))], (11896 ^ _780119) ^ [_994247, _994249, _994251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994247), _994249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994247), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994249), _994251))))], (42318 ^ _780119) ^ [_1616740, _1616742, _1616744] : [c_Nitpick_Oless__eq__frac(_1616740, _1616742, _1616744), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1616740), c_Nitpick_Oplus__frac(_1616740, _1616742, c_Nitpick_Ouminus__frac(_1616740, _1616744)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26213 ^ _780119) ^ [_1258205, _1258207] : [class_Groups_Oordered__ab__group__add(_1258205), -(hAPP(c_Set_Oimage(_1258205, _1258205, c_Groups_Ouminus__class_Ouminus(_1258205)), hAPP(c_SetInterval_Oord__class_OatMost(_1258205), _1258207)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1258205), hAPP(c_Groups_Ouminus__class_Ouminus(_1258205), _1258207)))], (14008 ^ _780119) ^ [_1034983, _1034985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1034983)), _1034985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034983), _1034985)))], (2950 ^ _780119) ^ [_824037, _824039, _824041, _824043, _824045, _824047] : [-(c_Set_Ovimage(_824047, _824043, _824039) = c_Set_Ovimage(_824045, _824041, _824037)), _824047 = _824045, _824043 = _824041, _824039 = _824037], (20640 ^ _780119) ^ [_1155340, _1155342, _1155344, _1155346, _1155348] : [class_Fields_Olinordered__field(_1155340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155340), c_Groups_Ozero__class_Ozero(_1155340)), _1155342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155340), _1155342), _1155344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155340), c_Groups_Ozero__class_Ozero(_1155340)), _1155346)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155340), _1155346), _1155348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155340), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155340), _1155342), _1155348)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155340), _1155344), _1155346))))], (38264 ^ _780119) ^ [_1519675, _1519677, _1519679] : [c_Wellfounded_OwfP(_1519675, _1519677), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1519675, _1519677), _1519679)))], (23268 ^ _780119) ^ [_1205260, _1205262, _1205264, _1205266, _1205268, _1205270] : [-(hBOOL(hAPP(hAPP(c_member(_1205260), _1205262), c_SetInterval_Oord_OgreaterThanAtMost(_1205260, _1205264, _1205266, _1205268, _1205270)))), hBOOL(hAPP(hAPP(_1205266, _1205268), _1205262)), hBOOL(hAPP(hAPP(_1205264, _1205262), _1205270))], (40371 ^ _780119) ^ [_1570229, _1570231, _1570233] : [c_Relation_Osingle__valued(_1570229, _1570231, _1570233), 40374 ^ _780119 : [(40375 ^ _780119) ^ [_1570350, _1570352] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570229, _1570231)), hAPP(hAPP(c_Product__Type_OPair(_1570229, _1570231), _1570352), _1570350)), _1570233)), 40378 ^ _780119 : [(40379 ^ _780119) ^ [_1570476] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570229, _1570231)), hAPP(hAPP(c_Product__Type_OPair(_1570229, _1570231), _1570352), _1570476)), _1570233)), -(_1570350 = _1570476)]]]]], (13500 ^ _780119) ^ [_1025822, _1025824, _1025826] : [hBOOL(hAPP(hAPP(c_member(_1025822), _1025824), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025822, tc_HOL_Obool)), _1025826))), hBOOL(hAPP(hAPP(c_member(_1025822), _1025824), _1025826))], (29046 ^ _780119) ^ [_1318261, _1318263, _1318265] : [class_Orderings_Olinorder(_1318261), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318261), _1318263)), -(hBOOL(hAPP(hAPP(c_member(_1318261), _1318265), _1318263))), -(_1318263 = c_Orderings_Obot__class_Obot(tc_fun(_1318261, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1318261, c_Orderings_Oord__class_Omin(_1318261), hAPP(hAPP(c_Set_Oinsert(_1318261), _1318265), _1318263)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318261), _1318265), c_Big__Operators_Olattice_OInf__fin(_1318261, c_Orderings_Oord__class_Omin(_1318261), _1318263)))], (32307 ^ _780119) ^ [_1382508, _1382510] : [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), _1382508))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1382510)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1382508))) = 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), _1382510), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1382508)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (1010 ^ _780119) ^ [_795468, _795470] : [-(class_Lattices_Obounded__lattice(_795468)), _795470 = _795468, class_Lattices_Obounded__lattice(_795470)], (34591 ^ _780119) ^ [_1429348, _1429350, _1429352, _1429354, _1429356] : [hAPP(c_Product__Type_Osnd(_1429348, _1429350), hAPP(hAPP(c_Product__Type_OPair(_1429348, _1429350), _1429352), _1429354)) = _1429356, -(_1429354 = _1429356)], (19190 ^ _780119) ^ [_1129361, _1129363] : [class_Divides_Osemiring__div(_1129361), -(_1129363 = c_Groups_Ozero__class_Ozero(_1129361)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129361), _1129363), _1129363) = c_Groups_Oone__class_Oone(_1129361))], (36157 ^ _780119) ^ [_1466032, _1466034] : [-(c_Fun_Oinj__on(_1466032, _1466032, c_COMBI(_1466032), _1466034))], (38487 ^ _780119) ^ [_1524289, _1524291, _1524293] : [-(c_Relation_Orefl__on(_1524289, _1524291, _1524293)), 38491 ^ _780119 : [(38494 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1524289, _1524289, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1524289, tc_fun(_1524289, tc_HOL_Obool), tc_fun(_1524289, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1524289, tc_HOL_Obool), tc_fun(_1524289, tc_HOL_Obool)), _1524289), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1524289)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524289), c_fconj), hAPP(hAPP(c_COMBC(_1524289, tc_fun(_1524289, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524289)), _1524291)))), hAPP(hAPP(c_COMBC(_1524289, tc_fun(_1524289, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524289)), _1524291))), 38490 ^ [_1524289, _1524291, _1524293]))], (38492 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524289, _1524289)), 38490 ^ [_1524289, _1524291, _1524293]), _1524293)))]], 38496 ^ _780119 : [(38499 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524289, _1524289)), hAPP(hAPP(c_Product__Type_OPair(_1524289, _1524289), 38495 ^ [_1524289, _1524291, _1524293]), 38495 ^ [_1524289, _1524291, _1524293])), _1524293))], (38497 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524289), 38495 ^ [_1524289, _1524291, _1524293]), _1524291)))]]], (26839 ^ _780119) ^ [_1270912, _1270914, _1270916] : [class_Rings_Olinordered__idom(_1270912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270912), c_Groups_Ozero__class_Ozero(_1270912)), _1270914)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270912), hAPP(c_Groups_Oabs__class_Oabs(_1270912), _1270916)), _1270914) = hAPP(c_Groups_Oabs__class_Oabs(_1270912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270912), _1270916), _1270914)))], (23362 ^ _780119) ^ [_1207005, _1207007] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1207005), _1207007)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207005)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1207007))))], (19052 ^ _780119) ^ [_1127201] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127201) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48805 ^ _780119) ^ [_1767001, _1767003, _1767005] : [-(c_List_Olistsp(_1767001, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1767001, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1767001, tc_fun(_1767001, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767001)), _1767003)), hAPP(hAPP(c_COMBC(_1767001, tc_fun(_1767001, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767001)), _1767005))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1767001), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1767001), tc_fun(tc_List_Olist(_1767001), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1767001))), c_List_Olists(_1767001, _1767003))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1767001), tc_fun(tc_List_Olist(_1767001), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1767001))), c_List_Olists(_1767001, _1767005))))], (23084 ^ _780119) ^ [_1201729] : [_1201729 = 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), _1201729)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34539 ^ _780119) ^ [_1428303, _1428305, _1428307, _1428309, _1428311] : [-(hAPP(c_Product__Type_Osnd(_1428303, _1428305), hAPP(c_Product__Type_Oapsnd(_1428307, _1428305, _1428303, _1428309), _1428311)) = hAPP(_1428309, hAPP(c_Product__Type_Osnd(_1428303, _1428307), _1428311)))], (46309 ^ _780119) ^ [_1713787, _1713789, _1713791] : [-(_1713787 = c_List_Olist_ONil(_1713789)), -(c_List_Olast(_1713789, hAPP(hAPP(c_List_Olist_OCons(_1713789), _1713791), _1713787)) = c_List_Olast(_1713789, _1713787))], (27318 ^ _780119) ^ [_1284989, _1284991, _1284993] : [class_Orderings_Olinorder(_1284989), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284989), _1284991)), hBOOL(hAPP(hAPP(c_member(_1284989), _1284993), _1284991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284989), c_Big__Operators_Olinorder__class_OMin(_1284989, _1284991)), _1284993)))], (13978 ^ _780119) ^ [_1034446, _1034448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1034446)), _1034448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034446), _1034448)))], (51315 ^ _780119) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (12659 ^ _780119) ^ [_1009539, _1009541, _1009543, _1009545] : [-(c_Option_Ooption_Ooption__rec(_1009539, _1009541, _1009543, _1009545, c_Option_Ooption_ONone(_1009541)) = _1009543)], (36876 ^ _780119) ^ [_1481253, _1481255] : [-(c_Fun_Oinj__on(tc_fun(_1481253, _1481255), tc_fun(tc_prod(_1481253, _1481255), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1481253, _1481255), tc_HOL_Obool), tc_fun(tc_prod(_1481253, _1481255), tc_HOL_Obool), tc_fun(_1481253, _1481255)), c_Set_OCollect(tc_prod(_1481253, _1481255))), hAPP(hAPP(c_COMBB(tc_fun(_1481253, tc_fun(_1481255, tc_HOL_Obool)), tc_fun(tc_prod(_1481253, _1481255), tc_HOL_Obool), tc_fun(_1481253, _1481255)), c_Product__Type_Oprod_Oprod__case(_1481253, _1481255, tc_HOL_Obool)), hAPP(c_COMBB(_1481255, tc_fun(_1481255, tc_HOL_Obool), _1481253), hAPP(c_COMBC(_1481255, _1481255, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1481253, _1481255), tc_HOL_Obool))))], (49126 ^ _780119) ^ [_1774169, _1774171, _1774173, _1774175, _1774177] : [c_List_Olist__all2(_1774169, _1774171, _1774173, _1774175, _1774177), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774169)), _1774175) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774171)), _1774177))], (50220 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (33907 ^ _780119) ^ [_1416281, _1416283, _1416285, _1416287, _1416289, _1416291, _1416293] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1416281, _1416283, tc_fun(_1416285, tc_HOL_Obool)), _1416287), hAPP(hAPP(c_Product__Type_OPair(_1416281, _1416283), _1416289), _1416291)), _1416293)), -(hBOOL(hAPP(hAPP(hAPP(_1416287, _1416289), _1416291), _1416293)))], (23400 ^ _780119) ^ [_1207686, _1207688, _1207690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207686), _1207688)), -(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)), _1207686)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207690), _1207688)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1207690), _1207686)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1207688), _1207686)))], (8014 ^ _780119) ^ [_916958, _916960, _916962] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916958, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916958, tc_HOL_Obool)), _916960), _916962)), _916960)))], (11662 ^ _780119) ^ [_990043, _990045] : [class_Lattices_Olattice(_990043), hBOOL(hAPP(c_Finite__Set_Ofinite(_990043), _990045)), -(_990045 = c_Orderings_Obot__class_Obot(tc_fun(_990043, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_990043), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_990043), 11675 ^ [_990043, _990045]), 11676 ^ [_990043, _990045])), hAPP(hAPP(c_Set_Oinsert(_990043), 11675 ^ [_990043, _990045]), hAPP(hAPP(c_Set_Oinsert(_990043), 11676 ^ [_990043, _990045]), c_Orderings_Obot__class_Obot(tc_fun(_990043, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_990043), c_Big__Operators_Olattice__class_OInf__fin(_990043, _990045)), _990045)))], (16793 ^ _780119) ^ [_1085643, _1085645] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1085643, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1085643, tc_HOL_Obool)), _1085645)), _1085645) = c_Orderings_Otop__class_Otop(tc_fun(_1085643, tc_HOL_Obool)))], (26943 ^ _780119) ^ [_1272825, _1272827] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1272825), _1272827))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1272825))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1272827))))], (35468 ^ _780119) ^ [_1449751, _1449753] : [c_Relation_Oirrefl(_1449751, _1449753), 35471 ^ _780119 : [(35472 ^ _780119) ^ [_1449833] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1449751, _1449751)), hAPP(hAPP(c_Product__Type_OPair(_1449751, _1449751), _1449833), _1449833)), _1449753))]]], (48707 ^ _780119) ^ [_1764737, _1764739, _1764741] : [class_Enum_Oenum(_1764737), class_Enum_Oenum(_1764739), class_HOL_Oequal(_1764739), 48718 ^ _780119 : [(48725 ^ _780119) ^ [] : [c_Enum_Oex__n__lists(_1764737, hAPP(hAPP(c_COMBB(tc_fun(_1764739, _1764737), tc_HOL_Obool, tc_List_Olist(_1764737)), _1764741), hAPP(hAPP(c_COMBB(tc_fun(_1764739, tc_Option_Ooption(_1764737)), tc_fun(_1764739, _1764737), tc_List_Olist(_1764737)), c_Fun_Ocomp(tc_Option_Ooption(_1764737), _1764737, _1764739, c_Option_Othe(_1764737))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1764739, _1764737)), tc_fun(_1764739, tc_Option_Ooption(_1764737)), tc_List_Olist(_1764737)), c_Map_Omap__of(_1764739, _1764737)), hAPP(c_List_Ozip(_1764739, _1764737), c_Enum_Oenum__class_Oenum(_1764739))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764739)), c_Enum_Oenum__class_Oenum(_1764739))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1764739, _1764737)), _1764741)))], (48719 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1764739, _1764737)), _1764741)), -(c_Enum_Oex__n__lists(_1764737, hAPP(hAPP(c_COMBB(tc_fun(_1764739, _1764737), tc_HOL_Obool, tc_List_Olist(_1764737)), _1764741), hAPP(hAPP(c_COMBB(tc_fun(_1764739, tc_Option_Ooption(_1764737)), tc_fun(_1764739, _1764737), tc_List_Olist(_1764737)), c_Fun_Ocomp(tc_Option_Ooption(_1764737), _1764737, _1764739, c_Option_Othe(_1764737))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1764739, _1764737)), tc_fun(_1764739, tc_Option_Ooption(_1764737)), tc_List_Olist(_1764737)), c_Map_Omap__of(_1764739, _1764737)), hAPP(c_List_Ozip(_1764739, _1764737), c_Enum_Oenum__class_Oenum(_1764739))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764739)), c_Enum_Oenum__class_Oenum(_1764739))))]]], (14884 ^ _780119) ^ [_1053329, _1053331] : [class_Power_Opower(_1053329), class_Rings_Osemiring__0(_1053329), 14891 ^ _780119 : [(14898 ^ _780119) ^ [] : [-(_1053331 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1053329), c_Groups_Ozero__class_Ozero(_1053329)), _1053331) = c_Groups_Ozero__class_Ozero(_1053329))], (14892 ^ _780119) ^ [] : [_1053331 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1053329), c_Groups_Ozero__class_Ozero(_1053329)), _1053331) = c_Groups_Oone__class_Oone(_1053329))]]], (50008 ^ _780119) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25059 ^ _780119) ^ [_1239109] : [hAPP(c_Int_Onat, _1239109) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239109), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50901 ^ _780119) ^ [_1812944, _1812946, _1812948, _1812950, _1812952, _1812954, _1812956] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1812944, tc_fun(_1812946, tc_fun(_1812948, tc_HOL_Obool))), _1812950), _1812952), _1812954), _1812956)), 50905 ^ _780119 : [(50908 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1812952, 50904 ^ [_1812944, _1812946, _1812948, _1812950, _1812952, _1812954, _1812956]), _1812954), _1812956)))], (50906 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812944), 50904 ^ [_1812944, _1812946, _1812948, _1812950, _1812952, _1812954, _1812956]), _1812950)))]]], (51119 ^ _780119) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (3650 ^ _780119) ^ [_835003, _835005] : [_835005 = _835003, -(c_Lazy__Sequence_Ohb__not__seq(_835005) = c_Lazy__Sequence_Ohb__not__seq(_835003))], (43727 ^ _780119) ^ [_1653149, _1653151, _1653153] : [class_Groups_Omonoid__add(_1653149), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1653149), hAPP(hAPP(c_List_Omap(_1653151, _1653149), hAPP(c_COMBK(_1653149, _1653151), c_Groups_Ozero__class_Ozero(_1653149))), _1653153)) = c_Groups_Ozero__class_Ozero(_1653149))], (28710 ^ _780119) ^ [_1310590, _1310592, _1310594] : [class_Orderings_Olinorder(_1310590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310590), _1310592)), -(_1310592 = c_Orderings_Obot__class_Obot(tc_fun(_1310590, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310590), _1310594)), -(_1310594 = c_Orderings_Obot__class_Obot(tc_fun(_1310590, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310590, tc_HOL_Obool)), _1310592), _1310594) = c_Orderings_Obot__class_Obot(tc_fun(_1310590, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1310590, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310590, tc_HOL_Obool)), _1310592), _1310594)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310590), c_Big__Operators_Olinorder__class_OMin(_1310590, _1310592)), c_Big__Operators_Olinorder__class_OMin(_1310590, _1310594)))], (24289 ^ _780119) ^ [_1224883, _1224885, _1224887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224883)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1224885), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1224887)), 24296 ^ _780119 : [(24297 ^ _780119) ^ [_1225091] : [24299 ^ _780119 : [(24303 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24301 ^ [_1224883, _1224885, _1224887, _1225091]), _1224887)))], (24305 ^ _780119) ^ [] : [-(_1225091 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24301 ^ [_1224883, _1224885, _1224887, _1225091]), 24298 ^ [_1224883, _1224885, _1224887, _1225091]))], (24300 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24298 ^ [_1224883, _1224885, _1224887, _1225091]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1224883))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224885), _1225091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224885), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1225091), _1224883))))]]], (43733 ^ _780119) ^ [_1653274, _1653276, _1653278, _1653280, _1653282] : [class_Groups_Ocomm__monoid__add(_1653274), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1653274), hAPP(hAPP(c_List_Omap(_1653276, _1653274), hAPP(hAPP(c_COMBS(_1653276, _1653274, _1653274), hAPP(hAPP(c_COMBB(_1653274, tc_fun(_1653274, _1653274), _1653276), c_Groups_Oplus__class_Oplus(_1653274)), _1653278)), _1653280)), _1653282)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1653274), hAPP(c_List_Omonoid__add__class_Olistsum(_1653274), hAPP(hAPP(c_List_Omap(_1653276, _1653274), _1653278), _1653282))), hAPP(c_List_Omonoid__add__class_Olistsum(_1653274), hAPP(hAPP(c_List_Omap(_1653276, _1653274), _1653280), _1653282))))], (25895 ^ _780119) ^ [_1252694] : [c_Nat__Transfer_Onat__set(_1252694), -(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), _1252694)) = _1252694)], (18834 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39434 ^ _780119) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (23637 ^ _780119) ^ [_1212182, _1212184, _1212186, _1212188, _1212190] : [class_Orderings_Oorder(_1212182), 23640 ^ _780119 : [(23653 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1212182, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1212182, _1212184, _1212186)), c_SetInterval_Oord__class_OatLeastAtMost(_1212182, _1212188, _1212190)))), 23654 ^ _780119 : [(23657 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212182), _1212188), _1212184)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212182), _1212186), _1212190))], (23655 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212182), _1212184), _1212186)))]]], (23641 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1212182, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1212182, _1212184, _1212186)), c_SetInterval_Oord__class_OatLeastAtMost(_1212182, _1212188, _1212190))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212182), _1212184), _1212186)), 23648 ^ _780119 : [(23651 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212182), _1212186), _1212190)))], (23649 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212182), _1212188), _1212184)))]]]]], (9492 ^ _780119) ^ [_943382, _943384] : [class_Lattices_Olattice(_943382), hBOOL(hAPP(c_Finite__Set_Ofinite(_943382), _943384)), -(_943384 = c_Orderings_Obot__class_Obot(tc_fun(_943382, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_943382), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_943382), 9505 ^ [_943382, _943384]), 9506 ^ [_943382, _943384])), hAPP(hAPP(c_Set_Oinsert(_943382), 9505 ^ [_943382, _943384]), hAPP(hAPP(c_Set_Oinsert(_943382), 9506 ^ [_943382, _943384]), c_Orderings_Obot__class_Obot(tc_fun(_943382, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_943382), c_Big__Operators_Olattice__class_OSup__fin(_943382, _943384)), _943384)))], (31213 ^ _780119) ^ [_1363738, _1363740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1363738), _1363740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1363738)), c_Int_OBit1(_1363740))))], (4572 ^ _780119) ^ [_849490, _849492, _849494, _849496] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_849496, _849492) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_849494, _849490)), _849496 = _849494, _849492 = _849490], (31613 ^ _780119) ^ [_1370346] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370346), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370346)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1370346)))], (43585 ^ _780119) ^ [_1648814, _1648816, _1648818] : [-(hBOOL(hAPP(c_List_Odistinct(_1648814), hAPP(hAPP(c_List_Olist_OCons(_1648814), _1648816), _1648818)))), -(hBOOL(hAPP(hAPP(c_member(_1648814), _1648816), hAPP(c_List_Oset(_1648814), _1648818)))), hBOOL(hAPP(c_List_Odistinct(_1648814), _1648818))], (44272 ^ _780119) ^ [_1667028, _1667030, _1667032, _1667034] : [-(hAPP(hAPP(c_List_Otake(_1667028), hAPP(c_Nat_OSuc, _1667030)), hAPP(hAPP(c_List_Olist_OCons(_1667028), _1667032), _1667034)) = hAPP(hAPP(c_List_Olist_OCons(_1667028), _1667032), hAPP(hAPP(c_List_Otake(_1667028), _1667030), _1667034)))], (51235 ^ _780119) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (11523 ^ _780119) ^ [_986933, _986935, _986937, _986939, _986941] : [class_Rings_Ocomm__semiring__1(_986933), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986933), _986935), _986937)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986933), _986939), _986941)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986933), _986939), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986933), _986935), _986937)), _986941)))], (38986 ^ _780119) ^ [_1536303, _1536305, _1536307, _1536309, _1536311, _1536313] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1536303, _1536305), _1536303, tc_prod(_1536307, _1536309), c_Product__Type_Ofst(_1536303, _1536305)), c_Product__Type_Omap__pair(_1536307, _1536303, _1536309, _1536305, _1536311, _1536313)) = hAPP(c_Fun_Ocomp(_1536307, _1536303, tc_prod(_1536307, _1536309), _1536311), c_Product__Type_Ofst(_1536307, _1536309)))], (15424 ^ _780119) ^ [_1061310] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1061310), c_Orderings_Otop__class_Otop(tc_fun(_1061310, 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(_1061310), c_Orderings_Otop__class_Otop(tc_fun(_1061310, tc_HOL_Obool))))))], (11933 ^ _780119) ^ [_994985, _994987, _994989] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994985), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994987), _994989)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994985), _994987)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994985), _994989)))], (33441 ^ _780119) ^ [_1402976, _1402978] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1402976), _1402978) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1402976 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1402976 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (13732 ^ _780119) ^ [_1029714, _1029716, _1029718] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029714)), _1029716)), hAPP(c_Nat_OSuc, _1029718)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029714), _1029716)), _1029718))], (46244 ^ _780119) ^ [_1712249, _1712251, _1712253] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712249)), _1712251), c_Wellfounded_Oacc(tc_List_Olist(_1712249), c_List_Olistrel1(_1712249, _1712253)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712249)), _1712251), c_List_Olists(_1712249, c_Wellfounded_Oacc(_1712249, _1712253)))))], (26357 ^ _780119) ^ [_1261227, _1261229] : [-(hBOOL(hAPP(_1261229, 26358 ^ [_1261227, _1261229]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1261227, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1261227), _1261229))], (33087 ^ _780119) ^ [_1396684] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1396684, 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, _1396684, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (15830 ^ _780119) ^ [_1068517, _1068519, _1068521, _1068523] : [class_Rings_Oordered__comm__semiring(_1068517), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068517), _1068519), _1068521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068517), c_Groups_Ozero__class_Ozero(_1068517)), _1068523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068517), _1068523), _1068519)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068517), _1068523), _1068521))))], (44706 ^ _780119) ^ [_1675691, _1675693, _1675695] : [-(hAPP(hAPP(c_Map_Omap__of(_1675691, _1675693), c_List_Olist_ONil(tc_prod(_1675691, _1675693))), _1675695) = c_Option_Ooption_ONone(_1675693))], (3178 ^ _780119) ^ [_827555, _827557, _827559, _827561, _827563, _827565] : [-(c_Smallcheck_Ofull__small_H(_827565, _827561, _827557) = c_Smallcheck_Ofull__small_H(_827563, _827559, _827555)), _827565 = _827563, _827561 = _827559, _827557 = _827555], (37247 ^ _780119) ^ [_1492077, _1492079, _1492081] : [c_Wellfounded_Owf(_1492077, _1492079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1492077, _1492077), tc_HOL_Obool)), _1492081), _1492079)), -(c_Wellfounded_Owf(_1492077, _1492081))], (32319 ^ _780119) ^ [_1382737, _1382739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1382737), 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)))), _1382739)), 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)))), _1382737)) = 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), _1382739), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1382737))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (44262 ^ _780119) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (33063 ^ _780119) ^ [_1396243, _1396245] : [class_Rings_Oring__1(_1396243), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1396243), hAPP(c_Groups_Ouminus__class_Ouminus(_1396243), c_Groups_Oone__class_Oone(_1396243))), 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)))), _1396245)) = c_Groups_Oone__class_Oone(_1396243))], (38362 ^ _780119) ^ [_1521910, _1521912, _1521914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521910, _1521910), tc_HOL_Obool)), _1521912), hAPP(hAPP(c_Product__Type_OSigma(_1521910, _1521910), _1521914), hAPP(c_COMBK(tc_fun(_1521910, tc_HOL_Obool), _1521910), _1521914)))), 38368 ^ _780119 : [(38371 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1521910, _1521910)), hAPP(hAPP(c_Product__Type_OPair(_1521910, _1521910), 38367 ^ [_1521910, _1521912, _1521914]), 38367 ^ [_1521910, _1521912, _1521914])), _1521912))], (38369 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1521910), 38367 ^ [_1521910, _1521912, _1521914]), _1521914)))]], -(c_Relation_Orefl__on(_1521910, _1521914, _1521912))], (33605 ^ _780119) ^ [_1406345, _1406347, _1406349, _1406351, _1406353, _1406355] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1406345, _1406347)), hAPP(hAPP(c_Product__Type_OPair(_1406345, _1406347), _1406353), _1406355)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool)), _1406349), _1406351))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406345, tc_fun(_1406347, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1406345, tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_fun(_1406347, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1406347, tc_fun(tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_fun(_1406347, tc_HOL_Obool)), _1406345), c_COMBC(_1406347, tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1406347, tc_prod(_1406345, _1406347)), tc_fun(_1406347, tc_fun(tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_HOL_Obool)), _1406345), hAPP(c_COMBB(tc_prod(_1406345, _1406347), tc_fun(tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_HOL_Obool), _1406347), c_member(tc_prod(_1406345, _1406347)))), c_Product__Type_OPair(_1406345, _1406347)))), _1406349)), hAPP(hAPP(c_COMBC(_1406345, tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_fun(_1406347, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1406347, tc_fun(tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_fun(_1406347, tc_HOL_Obool)), _1406345), c_COMBC(_1406347, tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1406347, tc_prod(_1406345, _1406347)), tc_fun(_1406347, tc_fun(tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_HOL_Obool)), _1406345), hAPP(c_COMBB(tc_prod(_1406345, _1406347), tc_fun(tc_fun(tc_prod(_1406345, _1406347), tc_HOL_Obool), tc_HOL_Obool), _1406347), c_member(tc_prod(_1406345, _1406347)))), c_Product__Type_OPair(_1406345, _1406347)))), _1406351)), _1406353), _1406355)))], (33341 ^ _780119) ^ [] : [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)], (39168 ^ _780119) ^ [_1540857, _1540859, _1540861, _1540863, _1540865, _1540867] : [c_Finite__Set_Ofolding__idem(_1540857, _1540859, _1540861, _1540863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540857), _1540865)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540857), _1540867)), -(hAPP(_1540863, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1540857, tc_HOL_Obool)), _1540865), _1540867)) = hAPP(c_Fun_Ocomp(_1540859, _1540859, _1540859, hAPP(_1540863, _1540865)), hAPP(_1540863, _1540867)))], (23567 ^ _780119) ^ [_1210962, _1210964, _1210966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1210962), _1210964)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1210962), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1210964), _1210966)) = 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, _1210962), _1210964)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1210964), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1210964), _1210966))))], (8084 ^ _780119) ^ [_918276, _918278, _918280, _918282, _918284, _918286, _918288, _918290] : [c_Finite__Set_Ofolding__image__simple(_918276, _918278, _918280, _918282, _918284, _918286), hBOOL(hAPP(c_Finite__Set_Ofinite(_918278), _918288)), -(hAPP(_918286, hAPP(hAPP(c_Set_Oinsert(_918278), _918290), _918288)) = hAPP(hAPP(_918280, hAPP(_918284, _918290)), hAPP(_918286, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918278, tc_HOL_Obool)), _918288), hAPP(hAPP(c_Set_Oinsert(_918278), _918290), c_Orderings_Obot__class_Obot(tc_fun(_918278, tc_HOL_Obool)))))))], (37663 ^ _780119) ^ [_1501801, _1501803, _1501805, _1501807] : [-(hAPP(c_Relation_ODomain(_1501801, _1501803), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501801, _1501803), tc_HOL_Obool)), _1501805), _1501807)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501801, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1501801, _1501803), _1501805)), hAPP(c_Relation_ODomain(_1501801, _1501803), _1501807)))], (26009 ^ _780119) ^ [_1254519] : [c_Nat__Transfer_Onat__set(_1254519), 26012 ^ _780119 : [(26019 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1254519))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1254519)))], (26013 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1254519)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1254519))))]]], (30667 ^ _780119) ^ [_1353196, _1353198, _1353200, _1353202] : [class_Fields_Olinordered__field__inverse__zero(_1353196), class_Int_Onumber(_1353196), 30674 ^ _780119 : [(30675 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353196), _1353198), _1353200)), hAPP(c_Int_Onumber__class_Onumber__of(_1353196), _1353202))), 30678 ^ _780119 : [(30685 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), c_Groups_Ozero__class_Ozero(_1353196)), _1353200))), 30688 ^ _780119 : [(30695 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), _1353200), c_Groups_Ozero__class_Ozero(_1353196)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), c_Groups_Ozero__class_Ozero(_1353196)), hAPP(c_Int_Onumber__class_Onumber__of(_1353196), _1353202))))], (30689 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), _1353200), c_Groups_Ozero__class_Ozero(_1353196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353196), hAPP(c_Int_Onumber__class_Onumber__of(_1353196), _1353202)), _1353200)), _1353198)))]]], (30679 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), c_Groups_Ozero__class_Ozero(_1353196)), _1353200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), _1353198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353196), hAPP(c_Int_Onumber__class_Onumber__of(_1353196), _1353202)), _1353200))))]]], (30701 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353196), _1353198), _1353200)), hAPP(c_Int_Onumber__class_Onumber__of(_1353196), _1353202)))), 30704 ^ _780119 : [(30707 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), _1353198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353196), hAPP(c_Int_Onumber__class_Onumber__of(_1353196), _1353202)), _1353200)))], (30705 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), c_Groups_Ozero__class_Ozero(_1353196)), _1353200)))]], 30708 ^ _780119 : [(30711 ^ _780119) ^ [] : [30712 ^ _780119 : [(30715 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353196), hAPP(c_Int_Onumber__class_Onumber__of(_1353196), _1353202)), _1353200)), _1353198))], (30713 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), _1353200), c_Groups_Ozero__class_Ozero(_1353196))))]], 30716 ^ _780119 : [(30719 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), c_Groups_Ozero__class_Ozero(_1353196)), hAPP(c_Int_Onumber__class_Onumber__of(_1353196), _1353202)))], (30717 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), _1353200), c_Groups_Ozero__class_Ozero(_1353196)))]]], (30709 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353196), c_Groups_Ozero__class_Ozero(_1353196)), _1353200))]]]]], (47550 ^ _780119) ^ [_1739026, _1739028, _1739030] : [-(hAPP(c_List_Ofilter(_1739026, _1739028), c_List_Oconcat(_1739026, _1739030)) = c_List_Oconcat(_1739026, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1739026), tc_List_Olist(_1739026)), c_List_Ofilter(_1739026, _1739028)), _1739030)))], (34685 ^ _780119) ^ [_1430984, _1430986, _1430988] : [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), _1430984), _1430986))), -(hBOOL(hAPP(hAPP(_1430988, _1430984), _1430986))), 34692 ^ _780119 : [(34705 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1430988, 34690 ^ [_1430984, _1430986, _1430988]), 34691 ^ [_1430984, _1430986, _1430988]))], (34695 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1430988, 34690 ^ [_1430984, _1430986, _1430988]), 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)))), 34691 ^ [_1430984, _1430986, _1430988])))), -(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), 34690 ^ [_1430984, _1430986, _1430988]), 34691 ^ [_1430984, _1430986, _1430988])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 34691 ^ [_1430984, _1430986, _1430988]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34693 ^ _780119) ^ [] : [-(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), 34690 ^ [_1430984, _1430986, _1430988]), 34691 ^ [_1430984, _1430986, _1430988]))))]]], (7710 ^ _780119) ^ [_910817, _910819, _910821, _910823] : [c_Finite__Set_Ofolding__one__idem(_910817, _910819, _910821), -(hAPP(hAPP(_910819, _910823), _910823) = _910823)], (49084 ^ _780119) ^ [_1773376, _1773378, _1773380, _1773382, _1773384] : [c_List_Olist__all2(_1773376, _1773378, _1773380, _1773382, _1773384), -(c_List_Olist__all2(_1773376, _1773378, _1773380, hAPP(c_List_Orev(_1773376), _1773382), hAPP(c_List_Orev(_1773378), _1773384)))], (23889 ^ _780119) ^ [_1217071, _1217073] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1217071, _1217073)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1217073)), _1217071))], (45920 ^ _780119) ^ [_1704814, _1704816, _1704818] : [-(_1704814 = c_List_Olist_ONil(_1704816)), -(hAPP(c_List_Otl(_1704816), hAPP(hAPP(c_List_Oappend(_1704816), _1704814), _1704818)) = hAPP(hAPP(c_List_Oappend(_1704816), hAPP(c_List_Otl(_1704816), _1704814)), _1704818))], (9340 ^ _780119) ^ [_940796, _940798, _940800] : [class_Lattices_Olattice(_940796), hBOOL(hAPP(c_Finite__Set_Ofinite(_940796), _940798)), hBOOL(hAPP(hAPP(c_member(_940796), _940800), _940798)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_940796), _940800), c_Big__Operators_Olattice__class_OSup__fin(_940796, _940798)) = c_Big__Operators_Olattice__class_OSup__fin(_940796, _940798))], (18772 ^ _780119) ^ [_1122485] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1122485)) = _1122485)], (46608 ^ _780119) ^ [_1719693, _1719695, _1719697, _1719699] : [-(hAPP(c_List_Ofilter(_1719693, _1719695), c_List_Oremove1(_1719693, _1719697, _1719699)) = c_List_Oremove1(_1719693, _1719697, hAPP(c_List_Ofilter(_1719693, _1719695), _1719699)))], (13758 ^ _780119) ^ [_1030333, _1030335, _1030337, _1030339] : [class_Groups_Oab__group__add(_1030333), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1030335, _1030333), hAPP(hAPP(c_COMBB(_1030333, _1030333, _1030335), c_Groups_Ouminus__class_Ouminus(_1030333)), _1030337)), _1030339) = hAPP(c_Groups_Ouminus__class_Ouminus(_1030333), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1030335, _1030333), _1030337), _1030339)))], (43030 ^ _780119) ^ [_1633021, _1633023, _1633025] : [class_Orderings_Olinorder(_1633021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1633021), _1633023)), -(c_List_Olinorder__class_Osorted__list__of__set(_1633021, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1633021, tc_HOL_Obool)), _1633023), hAPP(hAPP(c_Set_Oinsert(_1633021), _1633025), c_Orderings_Obot__class_Obot(tc_fun(_1633021, tc_HOL_Obool))))) = c_List_Oremove1(_1633021, _1633025, c_List_Olinorder__class_Osorted__list__of__set(_1633021, _1633023)))], (32653 ^ _780119) ^ [_1388720, _1388722] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1388720)), c_Int_OBit1(_1388722)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1388720)), _1388722)))], (8070 ^ _780119) ^ [_918049, _918051] : [hBOOL(hAPP(c_Com_OWT, _918049)), hBOOL(hAPP(c_Com_OWT, _918051)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_918049, _918051))))], (12015 ^ _780119) ^ [_996640, _996642, _996644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996640), _996642)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996640), _996644)), 12022 ^ _780119 : [(12029 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996642), _996644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996642), _996640)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996644), _996640))))], (12023 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996642), _996640)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996644), _996640))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996642), _996644)))]]], (5634 ^ _780119) ^ [_866411, _866413] : [_866413 = _866411, -(c_member(_866413) = c_member(_866411))], (33227 ^ _780119) ^ [] : [-(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))], (51457 ^ _780119) ^ [] : [-(class_HOL_Oequal(tc_Code__Evaluation_Oterm))], (51509 ^ _780119) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (15872 ^ _780119) ^ [_1069324, _1069326, _1069328, _1069330, _1069332] : [class_Rings_Oordered__semiring(_1069324), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069324), _1069326), _1069328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069324), _1069330), _1069332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069324), c_Groups_Ozero__class_Ozero(_1069324)), _1069326)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069324), c_Groups_Ozero__class_Ozero(_1069324)), _1069330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069324), _1069326), _1069330)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069324), _1069328), _1069332))))], (33821 ^ _780119) ^ [_1414591, _1414593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414591), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1414593, _1414591) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1414593), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1414591)))], (50436 ^ _780119) ^ [_1802922, _1802924, _1802926, _1802928, _1802930] : [hBOOL(hAPP(hAPP(_1802926, _1802930), _1802928)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1802922, _1802924, _1802926), _1802928), _1802930)))], (37827 ^ _780119) ^ [_1507077, _1507079, _1507081, _1507083, _1507085] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1507077, _1507079), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507077, tc_HOL_Obool)), _1507081), _1507083)), _1507085) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1507077, _1507079), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1507077, _1507079), _1507081), _1507085)), hAPP(hAPP(c_Product__Type_OSigma(_1507077, _1507079), _1507083), _1507085)))], (6849 ^ _780119) ^ [_892977, _892979, _892981] : [-(hAPP(hAPP(c_Set_Oinsert(_892977), _892979), _892981) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892977, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_892977), _892979), c_Orderings_Obot__class_Obot(tc_fun(_892977, tc_HOL_Obool)))), _892981))], (12735 ^ _780119) ^ [_1010945, _1010947, _1010949] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1010945), _1010947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010945, tc_HOL_Obool)), _1010949), _1010947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1010945), _1010949)), hAPP(c_Finite__Set_Ocard(_1010945), _1010947))))], (43763 ^ _780119) ^ [_1654263, _1654265, _1654267, _1654269] : [class_Groups_Oab__group__add(_1654263), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1654263), hAPP(c_List_Omonoid__add__class_Olistsum(_1654263), hAPP(hAPP(c_List_Omap(_1654265, _1654263), _1654267), _1654269))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1654263), hAPP(hAPP(c_List_Omap(_1654265, _1654263), hAPP(c_Fun_Ocomp(_1654263, _1654263, _1654265, c_Groups_Ouminus__class_Ouminus(_1654263)), _1654267)), _1654269)))], (19200 ^ _780119) ^ [_1129475, _1129477, _1129479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129475), _1129477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129479), 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), _1129477), _1129479)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129475), _1129479))))], (43126 ^ _780119) ^ [_1635906, _1635908, _1635910, _1635912, _1635914, _1635916, _1635918, _1635920] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635906)), _1635908) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635910)), _1635912), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635906)), _1635914) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635910)), _1635912), -(hBOOL(hAPP(hAPP(c_member(_1635910), _1635916), hAPP(c_List_Oset(_1635910), _1635912)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1635910, tc_Option_Ooption(_1635906)), hAPP(c_Map_Omap__of(_1635910, _1635906), hAPP(hAPP(c_List_Ozip(_1635910, _1635906), _1635912), _1635908))), _1635916), hAPP(c_Option_Ooption_OSome(_1635906), _1635918)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1635910, tc_Option_Ooption(_1635906)), hAPP(c_Map_Omap__of(_1635910, _1635906), hAPP(hAPP(c_List_Ozip(_1635910, _1635906), _1635912), _1635914))), _1635916), hAPP(c_Option_Ooption_OSome(_1635906), _1635920)), -(hAPP(c_Map_Omap__of(_1635910, _1635906), hAPP(hAPP(c_List_Ozip(_1635910, _1635906), _1635912), _1635908)) = hAPP(c_Map_Omap__of(_1635910, _1635906), hAPP(hAPP(c_List_Ozip(_1635910, _1635906), _1635912), _1635914)))], (18298 ^ _780119) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1080 ^ _780119) ^ [_796343, _796345] : [-(class_Rings_Olinordered__semiring__1(_796343)), _796345 = _796343, class_Rings_Olinordered__semiring__1(_796345)], (19635 ^ _780119) ^ [_1137096, _1137098, _1137100, _1137102, _1137104] : [class_Groups_Oordered__ab__group__add(_1137096), hBOOL(hAPP(c_Finite__Set_Ofinite(_1137098), _1137100)), 19645 ^ _780119 : [(19648 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137096), c_Groups_Ozero__class_Ozero(_1137096)), hAPP(_1137102, 19644 ^ [_1137096, _1137098, _1137100, _1137102, _1137104])))], (19646 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1137098), 19644 ^ [_1137096, _1137098, _1137100, _1137102, _1137104]), _1137100)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1137098, _1137096), _1137102), _1137100) = c_Groups_Ozero__class_Ozero(_1137096), hBOOL(hAPP(hAPP(c_member(_1137098), _1137104), _1137100)), -(hAPP(_1137102, _1137104) = c_Groups_Ozero__class_Ozero(_1137096))], (44260 ^ _780119) ^ [_1666756, _1666758] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1666756)), hAPP(c_Code__Numeral_Oof__nat, _1666758)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1666756), _1666758)))], (21805 ^ _780119) ^ [_1178259, _1178261] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178259, _1178261) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178259, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178261)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178259, _1178261)), _1178261))], (13796 ^ _780119) ^ [_1030948, _1030950, _1030952] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1030948), _1030950)), 13799 ^ _780119 : [(13800 ^ _780119) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1030948, tc_Nat_Onat), _1030952), _1030950) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 13803 ^ _780119 : [(13804 ^ _780119) ^ [_1031110] : [hBOOL(hAPP(hAPP(c_member(_1030948), _1031110), _1030950)), -(hAPP(_1030952, _1031110) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (13810 ^ _780119) ^ [] : [13812 ^ _780119 : [(13815 ^ _780119) ^ [] : [hAPP(_1030952, 13811 ^ [_1030948, _1030950, _1030952]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (13813 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1030948), 13811 ^ [_1030948, _1030950, _1030952]), _1030950)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1030948, tc_Nat_Onat), _1030952), _1030950) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (25638 ^ _780119) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (24833 ^ _780119) ^ [_1235082, _1235084, _1235086, _1235088] : [class_Groups_Ocomm__monoid__add(_1235082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1235084), _1235086)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1235082), _1235088), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1235084, _1235086)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1235082), hAPP(_1235088, _1235084)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1235082), _1235088), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1235084, _1235086))))], (41770 ^ _780119) ^ [_1603837, _1603839, _1603841] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1603837, tc_HOL_Obool)), _1603839), _1603841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1603837, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1603837, tc_HOL_Obool), _1603841)), _1603839)))], (51193 ^ _780119) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (34599 ^ _780119) ^ [_1429515, _1429517] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1429515, _1429517) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1429515, _1429517)))], (11722 ^ _780119) ^ [_991299, _991301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991299), _991301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991299), _991301))), -(_991299 = _991301)], (25205 ^ _780119) ^ [_1241460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1241460))))], (17154 ^ _780119) ^ [_1091656, _1091658, _1091660] : [class_Groups_Oordered__comm__monoid__add(_1091656), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091656), c_Groups_Ozero__class_Ozero(_1091656)), _1091658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091656), c_Groups_Ozero__class_Ozero(_1091656)), _1091660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091656), c_Groups_Ozero__class_Ozero(_1091656)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091656), _1091658), _1091660))))], (14170 ^ _780119) ^ [_1038762, _1038764, _1038766, _1038768, _1038770] : [class_Groups_Ocomm__monoid__mult(_1038762), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038764), _1038766)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038764), _1038768)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038762), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038764, _1038762), _1038770), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1038764, tc_HOL_Obool)), _1038766), _1038768))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038764, _1038762), _1038770), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1038764, tc_HOL_Obool)), _1038766), _1038768))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038762), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038764, _1038762), _1038770), _1038766)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038764, _1038762), _1038770), _1038768)))], (3892 ^ _780119) ^ [_838812, _838814, _838816, _838818, _838820, _838822, _838824, _838826] : [-(c_List_Olist_Olist__case(_838826, _838822, _838818, _838814) = c_List_Olist_Olist__case(_838824, _838820, _838816, _838812)), _838826 = _838824, _838822 = _838820, _838818 = _838816, _838814 = _838812], (51229 ^ _780119) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (7786 ^ _780119) ^ [_912342, _912344, _912346, _912348, _912350] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_912342, _912344, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_912342)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_912342), hAPP(hAPP(c_COMBC(_912342, 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)), _912342), 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)), _912342), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _912346))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _912348))), c_Com_Ocom_OWhile(_912348, _912350)), _912346)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_912342), tc_HOL_Obool)))))], (32983 ^ _780119) ^ [_1394531, _1394533, _1394535] : [class_Rings_Olinordered__idom(_1394531), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394531), c_Groups_Ozero__class_Ozero(_1394531)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1394531), hAPP(hAPP(c_Power_Opower__class_Opower(_1394531), _1394533), 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(_1394531), _1394535), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (10532 ^ _780119) ^ [_966249, _966251, _966253, _966255, _966257, _966259, _966261] : [c_Big__Operators_Ocomm__monoid__big(_966249, _966251, _966253, _966255, _966257), 10535 ^ _780119 : [(10542 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_966251), _966259))), -(hAPP(hAPP(_966257, _966261), _966259) = _966255)], (10536 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_966251), _966259)), -(hAPP(hAPP(_966257, _966261), _966259) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_966249, _966251, _966253), _966261), _966255), _966259))]]], (28182 ^ _780119) ^ [_1300963, _1300965, _1300967, _1300969] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1300963), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300963), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300963), _1300965), _1300967)), _1300969) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300963), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300963), _1300965), _1300969)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300963), _1300967), _1300969)))], (39771 ^ _780119) ^ [_1555494, _1555496, _1555498, _1555500] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1555494, _1555494)), hAPP(hAPP(c_Product__Type_OPair(_1555494, _1555494), _1555496), _1555498)), c_Transitive__Closure_Ortrancl(_1555494, _1555500)))), 39772 ^ _780119 : [(39775 ^ _780119) ^ [] : [-(_1555496 = _1555498), hBOOL(hAPP(hAPP(c_member(tc_prod(_1555494, _1555494)), hAPP(hAPP(c_Product__Type_OPair(_1555494, _1555494), _1555496), _1555498)), c_Transitive__Closure_Otrancl(_1555494, _1555500)))], (39773 ^ _780119) ^ [] : [_1555496 = _1555498]]], (23827 ^ _780119) ^ [_1215808, _1215810, _1215812] : [-(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)), _1215808)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1215810, _1215812)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1215810), _1215808), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1215812), _1215808)))], (12123 ^ _780119) ^ [_998638, _998640, _998642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998638), _998642)), _998640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _998638), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998640), _998642))))], (12639 ^ _780119) ^ [_1009159, _1009161, _1009163, _1009165] : [-(hAPP(c_Option_Ooption_Ooption__case(_1009159, _1009161, _1009163, _1009165), c_Option_Ooption_ONone(_1009161)) = _1009163)], (51381 ^ _780119) ^ [_1818305] : [class_Finite__Set_Ofinite(_1818305), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1818305)))], (13280 ^ _780119) ^ [_1021796, _1021798] : [class_Lattices_Oboolean__algebra(_1021796), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1021796), hAPP(c_Groups_Ouminus__class_Ouminus(_1021796), _1021798)) = _1021798)], (25746 ^ _780119) ^ [_1250018, _1250020, _1250022] : [class_Rings_Olinordered__idom(_1250018), 25749 ^ _780119 : [(25756 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1250020), _1250022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250018), hAPP(c_Int_Oring__1__class_Oof__int(_1250018), _1250020)), hAPP(c_Int_Oring__1__class_Oof__int(_1250018), _1250022))))], (25750 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250018), hAPP(c_Int_Oring__1__class_Oof__int(_1250018), _1250020)), hAPP(c_Int_Oring__1__class_Oof__int(_1250018), _1250022))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1250020), _1250022)))]]], (20376 ^ _780119) ^ [_1150869, _1150871, _1150873] : [class_Fields_Olinordered__field(_1150869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150869), _1150871), c_Groups_Ozero__class_Ozero(_1150869))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150869), _1150873), c_Groups_Ozero__class_Ozero(_1150869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150869), c_Groups_Ozero__class_Ozero(_1150869)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150869), _1150871), _1150873))))], (32077 ^ _780119) ^ [_1377940, _1377942] : [hAPP(c_Nat_OSuc, _1377940) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377942), -(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(_1377942))), 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)), _1377940))))))], (46040 ^ _780119) ^ [_1707370, _1707372] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1707370), _1707372) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1707370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46046 ^ _780119 : [(46049 ^ _780119) ^ [] : [46045 ^ [_1707370, _1707372] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46047 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 46045 ^ [_1707370, _1707372]), hAPP(c_List_Oset(tc_Nat_Onat), _1707372))))]]], (10444 ^ _780119) ^ [_964429, _964431, _964433, _964435, _964437] : [class_Groups_Oab__group__add(_964429), hBOOL(hAPP(c_Finite__Set_Ofinite(_964431), _964433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_964431, tc_HOL_Obool)), _964435), _964433)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964431, _964429), _964437), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964431, tc_HOL_Obool)), _964433), _964435)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_964429), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964431, _964429), _964437), _964433)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964431, _964429), _964437), _964435)))], (5869 ^ _780119) ^ [_873254, _873256] : [hBOOL(hAPP(hAPP(c_member(_873254), _873256), c_Orderings_Obot__class_Obot(tc_fun(_873254, tc_HOL_Obool))))], (43797 ^ _780119) ^ [_1655031, _1655033, _1655035, _1655037] : [class_Groups_Ocomm__monoid__add(_1655031), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1655031), _1655033), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1655035, _1655037))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1655031), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1655031), _1655033), c_List_Oupto(_1655035, _1655037))))], (570 ^ _780119) ^ [_788894, _788896, _788898, _788900, _788902, _788904] : [-(c_Relation_Osingle__valued(_788902, _788898, _788894)), c_Relation_Osingle__valued(_788904, _788900, _788896), _788904 = _788902, _788900 = _788898, _788896 = _788894], (32631 ^ _780119) ^ [_1388325, _1388327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1388325), _1388327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1388325)), c_Int_OBit0(_1388327))))], (8940 ^ _780119) ^ [_934212, _934214, _934216] : [class_Orderings_Oorder(_934212), 8943 ^ _780119 : [(8944 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934212), _934214), _934216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934212), _934214), _934216))), -(_934214 = _934216)], (8954 ^ _780119) ^ [] : [8955 ^ _780119 : [(8958 ^ _780119) ^ [] : [_934214 = _934216], (8956 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934212), _934214), _934216))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934212), _934214), _934216)))]]], (6493 ^ _780119) ^ [_885258, _885260, _885262] : [class_Orderings_Obot(_885258), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_885260, _885258)), _885262) = c_Orderings_Obot__class_Obot(_885258))], (50472 ^ _780119) ^ [_1803624, _1803626, _1803628, _1803630] : [-(c_Predicate_Oconversep(_1803624, _1803626, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1803624, tc_fun(_1803626, tc_HOL_Obool))), _1803628), _1803630)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1803626, tc_fun(_1803624, tc_HOL_Obool))), c_Predicate_Oconversep(_1803624, _1803626, _1803628)), c_Predicate_Oconversep(_1803624, _1803626, _1803630)))], (24209 ^ _780119) ^ [_1223363, _1223365] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1223363), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1223365) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1223363, _1223365))], (29795 ^ _780119) ^ [_1335021, _1335023, _1335025, _1335027, _1335029, _1335031, _1335033] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335021, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335023, tc_fun(_1335021, tc_HOL_Obool)), _1335025), _1335027)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335029, tc_fun(_1335021, tc_HOL_Obool)), _1335031), _1335033)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335023, tc_fun(_1335021, tc_HOL_Obool)), _1335025), hAPP(hAPP(c_COMBB(tc_fun(_1335029, tc_fun(_1335021, tc_HOL_Obool)), tc_fun(_1335021, tc_HOL_Obool), _1335023), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335029, tc_fun(_1335021, tc_HOL_Obool)), _1335031)), hAPP(hAPP(c_COMBC(_1335023, tc_fun(_1335029, tc_fun(_1335021, tc_HOL_Obool)), tc_fun(_1335029, tc_fun(_1335021, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1335021, tc_HOL_Obool), tc_fun(_1335021, tc_HOL_Obool)), tc_fun(tc_fun(_1335029, tc_fun(_1335021, tc_HOL_Obool)), tc_fun(_1335029, tc_fun(_1335021, tc_HOL_Obool))), _1335023), c_COMBB(tc_fun(_1335021, tc_HOL_Obool), tc_fun(_1335021, tc_HOL_Obool), _1335029)), hAPP(hAPP(c_COMBB(tc_fun(_1335021, tc_HOL_Obool), tc_fun(tc_fun(_1335021, tc_HOL_Obool), tc_fun(_1335021, tc_HOL_Obool)), _1335023), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335021, tc_HOL_Obool))), _1335027))), _1335033))))], (51111 ^ _780119) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (10 ^ _780119) ^ [_780242, _780244, _780246] : [-(_780246 = _780242), _780246 = _780244, _780244 = _780242], (37042 ^ _780119) ^ [_1485946, _1485948, _1485950, _1485952, _1485954, _1485956, _1485958] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1485946, _1485948, _1485950), hAPP(hAPP(c_Relation_Orel__comp(_1485946, _1485952, _1485948), _1485954), _1485956)), _1485958) = hAPP(hAPP(c_Relation_Orel__comp(_1485946, _1485952, _1485950), _1485954), hAPP(hAPP(c_Relation_Orel__comp(_1485952, _1485948, _1485950), _1485956), _1485958)))], (19280 ^ _780119) ^ [_1130825, _1130827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130827), 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), _1130825), _1130827)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7247 ^ _780119) ^ [_901434, _901436, _901438, _901440, _901442] : [class_Lattices_Olattice(_901434), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901436, _901434)), _901438), _901440), _901442) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901434), hAPP(_901438, _901442)), hAPP(_901440, _901442)))], (2092 ^ _780119) ^ [_810566, _810568, _810570, _810572, _810574, _810576] : [-(c_SetInterval_Oord_OgreaterThan(_810576, _810572, _810568) = c_SetInterval_Oord_OgreaterThan(_810574, _810570, _810566)), _810576 = _810574, _810572 = _810570, _810568 = _810566], (7652 ^ _780119) ^ [_909139, _909141, _909143, _909145, _909147] : [c_Finite__Set_Ofolding__one__idem(_909139, _909141, _909143), hBOOL(hAPP(c_Finite__Set_Ofinite(_909139), _909145)), -(_909145 = c_Orderings_Obot__class_Obot(tc_fun(_909139, tc_HOL_Obool))), -(hAPP(_909143, hAPP(hAPP(c_Set_Oinsert(_909139), _909147), _909145)) = hAPP(hAPP(_909141, _909147), hAPP(_909143, _909145)))], (43619 ^ _780119) ^ [_1649650, _1649652, _1649654, _1649656] : [-(hAPP(c_Map_Omap__of(_1649650, _1649652), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1649650, _1649652)), _1649654), _1649656)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1649650, tc_Option_Ooption(_1649652)), hAPP(c_Map_Omap__of(_1649650, _1649652), _1649656)), hAPP(c_Product__Type_Ofst(_1649650, _1649652), _1649654)), hAPP(c_Option_Ooption_OSome(_1649652), hAPP(c_Product__Type_Osnd(_1649650, _1649652), _1649654))))], (28074 ^ _780119) ^ [_1298467, _1298469, _1298471] : [class_Orderings_Olinorder(_1298467), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298467), _1298469), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298467), _1298469), _1298471)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298467), _1298469), _1298471))], (50981 ^ _780119) ^ [_1814259, _1814261] : [class_Orderings_Opreorder(_1814259), -(class_Orderings_Opreorder(tc_fun(_1814261, _1814259)))], (6585 ^ _780119) ^ [_887135, _887137, _887139, _887141] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887135, tc_HOL_Obool)), _887137), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887135, tc_HOL_Obool)), _887139), _887141)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887135, tc_HOL_Obool)), _887139), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887135, tc_HOL_Obool)), _887137), _887141)))], (32427 ^ _780119) ^ [_1384737] : [_1384737 = c_Int_OPls, -(c_Int_OBit0(_1384737) = c_Int_OPls)], (13256 ^ _780119) ^ [_1021397, _1021399] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021397, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021397, tc_HOL_Obool)), _1021399)) = _1021399)], (35297 ^ _780119) ^ [_1444257, _1444259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1444257), _1444259)), -(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), _1444257), _1444259)), c_Wellfounded_Oless__than)))], (3068 ^ _780119) ^ [_825884, _825886, _825888, _825890] : [-(c_Nitpick_Oinverse__frac(_825890, _825886) = c_Nitpick_Oinverse__frac(_825888, _825884)), _825890 = _825888, _825886 = _825884], (26509 ^ _780119) ^ [_1264041, _1264043, _1264045, _1264047] : [class_Groups_Oordered__ab__group__add__abs(_1264041), -(hAPP(c_Groups_Oabs__class_Oabs(_1264041), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264043, _1264041), hAPP(hAPP(c_COMBB(_1264041, _1264041, _1264043), c_Groups_Oabs__class_Oabs(_1264041)), _1264045)), _1264047)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264043, _1264041), hAPP(hAPP(c_COMBB(_1264041, _1264041, _1264043), c_Groups_Oabs__class_Oabs(_1264041)), _1264045)), _1264047))], (2146 ^ _780119) ^ [_811477, _811479, _811481, _811483, _811485, _811487, _811489, _811491, _811493, _811495] : [-(c_SetInterval_Oord_OatLeastLessThan(_811495, _811491, _811487, _811483, _811479) = c_SetInterval_Oord_OatLeastLessThan(_811493, _811489, _811485, _811481, _811477)), _811495 = _811493, _811491 = _811489, _811487 = _811485, _811483 = _811481, _811479 = _811477], (21452 ^ _780119) ^ [_1171016, _1171018, _1171020, _1171022] : [class_Divides_Osemiring__div(_1171016), -(c_Divides_Odiv__class_Omod(_1171016, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171016), _1171018), _1171020), _1171022) = c_Divides_Odiv__class_Omod(_1171016, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171016), c_Divides_Odiv__class_Omod(_1171016, _1171018, _1171022)), _1171020), _1171022))], (10226 ^ _780119) ^ [_959280, _959282, _959284, _959286] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959280, tc_HOL_Obool)), _959282), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959280, tc_HOL_Obool)), _959284), _959286)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959280, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959280, tc_HOL_Obool)), _959282), _959284)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959280, tc_HOL_Obool)), _959282), _959286)))], (16638 ^ _780119) ^ [_1083108, _1083110, _1083112] : [class_Groups_Ocomm__monoid__add(_1083108), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083110, _1083108), _1083112), c_Orderings_Obot__class_Obot(tc_fun(_1083110, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1083108))], (42275 ^ _780119) ^ [_1615607, _1615609, _1615611, _1615613, _1615615, _1615617] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615607, _1615609)), _1615611), hAPP(hAPP(c_Relation_Orel__comp(_1615607, _1615613, _1615609), _1615615), _1615617))), 42281 ^ _780119 : [(42284 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615607, _1615613)), hAPP(hAPP(c_Product__Type_OPair(_1615607, _1615613), 42278 ^ [_1615607, _1615609, _1615611, _1615613, _1615615, _1615617]), 42279 ^ [_1615607, _1615609, _1615611, _1615613, _1615615, _1615617])), _1615615)))], (42286 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615613, _1615609)), hAPP(hAPP(c_Product__Type_OPair(_1615613, _1615609), 42279 ^ [_1615607, _1615609, _1615611, _1615613, _1615615, _1615617]), 42280 ^ [_1615607, _1615609, _1615611, _1615613, _1615615, _1615617])), _1615617)))], (42282 ^ _780119) ^ [] : [-(_1615611 = hAPP(hAPP(c_Product__Type_OPair(_1615607, _1615609), 42278 ^ [_1615607, _1615609, _1615611, _1615613, _1615615, _1615617]), 42280 ^ [_1615607, _1615609, _1615611, _1615613, _1615615, _1615617]))]]], (22907 ^ _780119) ^ [_1198508, _1198510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1198508), _1198510)), -(_1198510 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198508), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 22910 ^ [_1198508, _1198510])))], (32499 ^ _780119) ^ [_1385959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1385959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1385959))))], (43186 ^ _780119) ^ [_1637353, _1637355, _1637357, _1637359, _1637361] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637353), tc_List_Olist(_1637353))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637353), tc_List_Olist(_1637353)), _1637355), _1637357)), hAPP(c_List_Olexn(_1637353, _1637359), _1637361))), 43189 ^ _780119 : [(43192 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637353)), _1637357) = _1637361)], (43190 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637353)), _1637355) = _1637361)]]], (9952 ^ _780119) ^ [_953456, _953458, _953460] : [class_Lattices_Osemilattice__inf(_953456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953456), _953458), _953460)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_953456), _953458), _953460) = _953458)], (40744 ^ _780119) ^ [_1579057, _1579059, _1579061] : [class_Lattices_Olattice(_1579057), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579057), _1579059)), -(c_Big__Operators_Olattice__class_OSup__fin(_1579057, hAPP(hAPP(c_Set_Oinsert(_1579057), _1579061), _1579059)) = hAPP(hAPP(c_Finite__Set_Ofold(_1579057, _1579057, c_Lattices_Osemilattice__sup__class_Osup(_1579057)), _1579061), _1579059))], (41363 ^ _780119) ^ [_1593976, _1593978, _1593980, _1593982, _1593984, _1593986] : [-(hAPP(c_Set_Ovimage(_1593976, _1593978, _1593980), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593982, tc_fun(_1593978, tc_HOL_Obool)), _1593984), _1593986)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593982, tc_fun(_1593976, tc_HOL_Obool)), _1593984), hAPP(hAPP(c_COMBB(tc_fun(_1593978, tc_HOL_Obool), tc_fun(_1593976, tc_HOL_Obool), _1593982), c_Set_Ovimage(_1593976, _1593978, _1593980)), _1593986)))], (32377 ^ _780119) ^ [_1383899, _1383901] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1383899)), c_Int_OBit0(_1383901)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1383899), _1383901)))], (7564 ^ _780119) ^ [_907293, _907295, _907297, _907299] : [c_Finite__Set_Ofolding__one(_907293, _907295, _907297), hBOOL(hAPP(c_Finite__Set_Ofinite(_907293), _907299)), -(_907299 = c_Orderings_Obot__class_Obot(tc_fun(_907293, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_907293), hAPP(hAPP(_907295, 7577 ^ [_907293, _907295, _907297, _907299]), 7578 ^ [_907293, _907295, _907297, _907299])), hAPP(hAPP(c_Set_Oinsert(_907293), 7577 ^ [_907293, _907295, _907297, _907299]), hAPP(hAPP(c_Set_Oinsert(_907293), 7578 ^ [_907293, _907295, _907297, _907299]), c_Orderings_Obot__class_Obot(tc_fun(_907293, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_907293), hAPP(_907297, _907299)), _907299)))], (30235 ^ _780119) ^ [_1345004, _1345006, _1345008, _1345010, _1345012] : [c_Com_Ocom_OSemi(_1345004, _1345006) = c_Com_Ocom_OLocal(_1345008, _1345010, _1345012)], (11890 ^ _780119) ^ [_994136, _994138, _994140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994136), _994138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994136), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994140), _994138))))], (50945 ^ _780119) ^ [_1813785, _1813787] : [class_Lattices_Obounded__lattice(_1813785), -(class_Lattices_Obounded__lattice__top(tc_fun(_1813787, _1813785)))], (3406 ^ _780119) ^ [_831261, _831263, _831265, _831267, _831269, _831271, _831273, _831275] : [-(c_Map_Orestrict__map(_831275, _831271, _831267, _831263) = c_Map_Orestrict__map(_831273, _831269, _831265, _831261)), _831275 = _831273, _831271 = _831269, _831267 = _831265, _831263 = _831261], (7308 ^ _780119) ^ [_902559, _902561, _902563] : [class_Lattices_Osemilattice__sup(_902559), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902559), _902561), _902563) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902559), _902563), _902561))], (1820 ^ _780119) ^ [_805593, _805595] : [-(class_HOL_Oequal(_805593)), _805595 = _805593, class_HOL_Oequal(_805595)], (39737 ^ _780119) ^ [_1554754, _1554756] : [-(c_Transitive__Closure_Otrancl(_1554754, _1554756) = hAPP(hAPP(c_Relation_Orel__comp(_1554754, _1554754, _1554754), _1554756), c_Transitive__Closure_Ortrancl(_1554754, _1554756)))], (35053 ^ _780119) ^ [_1438551, _1438553, _1438555, _1438557, _1438559, _1438561, _1438563, _1438565] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1438551, _1438553), tc_prod(_1438551, _1438553))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1438551, _1438553), tc_prod(_1438551, _1438553)), hAPP(hAPP(c_Product__Type_OPair(_1438551, _1438553), _1438555), _1438557)), hAPP(hAPP(c_Product__Type_OPair(_1438551, _1438553), _1438559), _1438561))), c_Wellfounded_Olex__prod(_1438551, _1438553, _1438563, _1438565)))), 35054 ^ _780119 : [(35057 ^ _780119) ^ [] : [_1438555 = _1438559, hBOOL(hAPP(hAPP(c_member(tc_prod(_1438553, _1438553)), hAPP(hAPP(c_Product__Type_OPair(_1438553, _1438553), _1438557), _1438561)), _1438565))], (35055 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1438551, _1438551)), hAPP(hAPP(c_Product__Type_OPair(_1438551, _1438551), _1438555), _1438559)), _1438563))]]], (26443 ^ _780119) ^ [_1262686, _1262688, _1262690] : [class_Groups_Oordered__ab__group__add__abs(_1262686), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262686), hAPP(c_Groups_Oabs__class_Oabs(_1262686), _1262688)), _1262690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262686), _1262688), _1262690)))], (31869 ^ _780119) ^ [] : [-(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)))], (39080 ^ _780119) ^ [_1538397, _1538399, _1538401, _1538403, _1538405, _1538407] : [c_Finite__Set_Ofolding(_1538397, _1538399, _1538401, _1538403), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538397), _1538405)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538397), _1538407)), -(hAPP(c_Fun_Ocomp(_1538399, _1538399, _1538399, hAPP(_1538403, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1538397, tc_HOL_Obool)), _1538405), _1538407))), hAPP(_1538403, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1538397, tc_HOL_Obool)), _1538405), _1538407))) = hAPP(c_Fun_Ocomp(_1538399, _1538399, _1538399, hAPP(_1538403, _1538405)), hAPP(_1538403, _1538407)))], (32221 ^ _780119) ^ [_1381150] : [class_Rings_Osemiring__1(_1381150), -(c_Int_Oiszero(_1381150, c_Groups_Ozero__class_Ozero(_1381150)))], (40236 ^ _780119) ^ [_1566910, _1566912, _1566914] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566910, _1566910), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1566912)), _1566914) = hAPP(hAPP(c_Relation_Orel__comp(_1566910, _1566910, _1566910), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566910, _1566910), tc_HOL_Obool), _1566912), _1566914)), _1566914))], (21642 ^ _780119) ^ [_1175204, _1175206] : [class_Divides_Osemiring__div(_1175204), -(c_Divides_Odiv__class_Omod(_1175204, _1175206, c_Groups_Oone__class_Oone(_1175204)) = c_Groups_Ozero__class_Ozero(_1175204))], (49120 ^ _780119) ^ [_1774040, _1774042, _1774044, _1774046, _1774048, _1774050] : [c_List_Olist__all2(_1774040, _1774042, _1774044, _1774046, _1774048), -(c_List_Olist__all2(_1774040, _1774042, _1774044, hAPP(hAPP(c_List_Odrop(_1774040), _1774050), _1774046), hAPP(hAPP(c_List_Odrop(_1774042), _1774050), _1774048)))], (974 ^ _780119) ^ [_794930, _794932, _794934, _794936, _794938, _794940] : [-(c_Relation_Orefl__on(_794938, _794934, _794930)), c_Relation_Orefl__on(_794940, _794936, _794932), _794940 = _794938, _794936 = _794934, _794932 = _794930], (18476 ^ _780119) ^ [_1117203, _1117205, _1117207] : [class_Rings_Oring__1(_1117203), hBOOL(hAPP(hAPP(c_member(_1117203), _1117205), c_Int_Oring__1__class_OInts(_1117203))), hBOOL(hAPP(hAPP(c_member(_1117203), _1117207), c_Int_Oring__1__class_OInts(_1117203))), -(hBOOL(hAPP(hAPP(c_member(_1117203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117203), _1117205), _1117207)), c_Int_Oring__1__class_OInts(_1117203))))], (51233 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (26149 ^ _780119) ^ [_1256942, _1256944, _1256946] : [class_Orderings_Oorder(_1256942), 26152 ^ _780119 : [(26159 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256942), _1256944), _1256946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256942, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1256942), _1256944)), hAPP(c_SetInterval_Oord__class_OatMost(_1256942), _1256946))))], (26153 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256942, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1256942), _1256944)), hAPP(c_SetInterval_Oord__class_OatMost(_1256942), _1256946))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256942), _1256944), _1256946)))]]], (44352 ^ _780119) ^ [_1668484, _1668486, _1668488, _1668490] : [hBOOL(hAPP(c_List_Odistinct(_1668484), _1668486)), -(hBOOL(hAPP(hAPP(c_member(_1668484), _1668488), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1668484, tc_HOL_Obool)), hAPP(c_List_Oset(_1668484), _1668486)), hAPP(hAPP(c_Set_Oinsert(_1668484), hAPP(hAPP(c_List_Onth(_1668484), _1668486), _1668490)), c_Orderings_Obot__class_Obot(tc_fun(_1668484, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1668484), hAPP(hAPP(c_List_Olist__update(_1668484, _1668486), _1668490), _1668488))))], (30517 ^ _780119) ^ [_1350422, _1350424, _1350426, _1350428] : [class_Fields_Ofield__inverse__zero(_1350422), class_Int_Onumber(_1350422), 30524 ^ _780119 : [(30525 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1350422), _1350424) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350422), _1350426), _1350428), 30528 ^ _780119 : [(30535 ^ _780119) ^ [] : [_1350428 = c_Groups_Ozero__class_Ozero(_1350422), -(hAPP(c_Int_Onumber__class_Onumber__of(_1350422), _1350424) = c_Groups_Ozero__class_Ozero(_1350422))], (30529 ^ _780119) ^ [] : [-(_1350428 = c_Groups_Ozero__class_Ozero(_1350422)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350422), hAPP(c_Int_Onumber__class_Onumber__of(_1350422), _1350424)), _1350428) = _1350426)]]], (30541 ^ _780119) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1350422), _1350424) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350422), _1350426), _1350428)), 30544 ^ _780119 : [(30547 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350422), hAPP(c_Int_Onumber__class_Onumber__of(_1350422), _1350424)), _1350428) = _1350426], (30545 ^ _780119) ^ [] : [_1350428 = c_Groups_Ozero__class_Ozero(_1350422)]], 30548 ^ _780119 : [(30551 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1350422), _1350424) = c_Groups_Ozero__class_Ozero(_1350422)], (30549 ^ _780119) ^ [] : [-(_1350428 = c_Groups_Ozero__class_Ozero(_1350422))]]]]], (32671 ^ _780119) ^ [_1389171] : [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), _1389171))), 32674 ^ _780119 : [(32677 ^ _780119) ^ [] : [-(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(_1389171)))))], (32675 ^ _780119) ^ [] : [-(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(_1389171)))))]]], (17722 ^ _780119) ^ [_1102304, _1102306] : [-(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), _1102304), _1102306)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1102304)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1102306))], (46743 ^ _780119) ^ [_1722965, _1722967, _1722969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722965), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1722967))), c_List_Otranspose(_1722967, _1722969)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1722967)), c_List_Otranspose(_1722967, _1722969)), _1722965) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1722967), _1722967), hAPP(hAPP(c_COMBC(tc_List_Olist(_1722967), tc_Nat_Onat, _1722967), c_List_Onth(_1722967)), _1722965)), hAPP(c_List_Ofilter(tc_List_Olist(_1722967), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1722967)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722965)), c_Nat_Osize__class_Osize(tc_List_Olist(_1722967)))), _1722969)))], (44264 ^ _780119) ^ [_1666820, _1666822, _1666824, _1666826] : [-(hAPP(hAPP(c_List_Otake(_1666820), _1666822), hAPP(hAPP(c_List_Otake(_1666820), _1666824), _1666826)) = hAPP(hAPP(c_List_Otake(_1666820), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1666822), _1666824)), _1666826))], (13530 ^ _780119) ^ [_1026432, _1026434, _1026436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1026432, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026432, tc_HOL_Obool)), _1026434)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026432, tc_HOL_Obool)), _1026436))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1026432, tc_HOL_Obool)), _1026436), _1026434)))], (47404 ^ _780119) ^ [_1735684, _1735686] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1735684)), c_List_Otranspose__rel(_1735684)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1735684)), c_List_Olist_ONil(_1735684)), _1735686))), -(c_List_Otranspose(_1735684, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1735684)), c_List_Olist_ONil(_1735684)), _1735686)) = c_List_Otranspose(_1735684, _1735686))], (46714 ^ _780119) ^ [_1722132, _1722134] : [46716 ^ _780119 : [(46719 ^ _780119) ^ [] : [46715 ^ [_1722132, _1722134] = c_List_Olist_ONil(_1722132)], (46717 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1722132)), 46715 ^ [_1722132, _1722134]), hAPP(c_List_Oset(tc_List_Olist(_1722132)), _1722134))))]], -(c_List_Otranspose(_1722132, _1722134) = c_List_Olist_ONil(tc_List_Olist(_1722132)))], (33051 ^ _780119) ^ [_1395921, _1395923, _1395925] : [class_Rings_Ocomm__semiring__1(_1395921), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1395921), _1395923), 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)))), _1395925))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395921), _1395923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395921), hAPP(hAPP(c_Power_Opower__class_Opower(_1395921), _1395923), _1395925)), hAPP(hAPP(c_Power_Opower__class_Opower(_1395921), _1395923), _1395925))))], (20992 ^ _780119) ^ [_1161983, _1161985, _1161987, _1161989] : [class_Fields_Ofield(_1161983), -(_1161985 = c_Groups_Ozero__class_Ozero(_1161983)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161983), _1161987), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161983), _1161989), _1161985)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161983), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161983), _1161985), _1161987)), _1161989)), _1161985))], (47416 ^ _780119) ^ [_1735970, _1735972, _1735974] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1735970), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1735970))), _1735972))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735974), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1735970))), _1735972))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1735970), _1735970), hAPP(hAPP(c_COMBC(tc_List_Olist(_1735970), tc_Nat_Onat, _1735970), c_List_Onth(_1735970)), _1735974)), hAPP(c_List_Ofilter(tc_List_Olist(_1735970), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1735970)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735974)), c_Nat_Osize__class_Osize(tc_List_Olist(_1735970)))), c_List_Otranspose(_1735970, _1735972))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1735970)), _1735972), _1735974))], (40205 ^ _780119) ^ [_1566144, _1566146, _1566148] : [c_Wellfounded_Owf(_1566144, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566144, _1566144), tc_HOL_Obool), _1566146), _1566148)), -(c_Wellfounded_Owf(_1566144, _1566148))], (21689 ^ _780119) ^ [_1175972, _1175974] : [21690 ^ _780119 : [(21691 ^ _780119) ^ [_1176021] : [_1175972 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175974), _1176021)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1175972, _1175974) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10082 ^ _780119) ^ [_955704, _955706, _955708] : [class_Lattices_Olattice(_955704), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955704), _955706), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955704), _955706), _955708)) = _955706)], (50402 ^ _780119) ^ [_1802137, _1802139, _1802141] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802137)), c_List_Osplice(_1802137, _1802139, _1802141)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802137)), _1802139)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802137)), _1802141)))], (50680 ^ _780119) ^ [_1808027, _1808029, _1808031] : [-(_1808027 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1808029), c_List_Oreplicate(_1808029, _1808027, _1808031)) = hAPP(hAPP(c_Set_Oinsert(_1808029), _1808031), c_Orderings_Obot__class_Obot(tc_fun(_1808029, tc_HOL_Obool))))], (22205 ^ _780119) ^ [_1185469] : [class_Groups_Osgn__if(_1185469), -(c_Groups_Osgn__class_Osgn(_1185469, c_Groups_Ozero__class_Ozero(_1185469)) = c_Groups_Ozero__class_Ozero(_1185469))], (29439 ^ _780119) ^ [_1326591, _1326593] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1326591))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1326593)), hAPP(c_Int_Onat, _1326591)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1326593), _1326591)), 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)))], (34453 ^ _780119) ^ [_1426627, _1426629, _1426631, _1426633] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1426627, _1426629), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1426631), _1426633))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1426627), _1426629) = _1426631)], (7930 ^ _780119) ^ [_915177, _915179, _915181, _915183, _915185] : [class_Groups_Ominus(_915177), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915179, _915177)), _915181), _915183), _915185) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_915177), hAPP(_915181, _915185)), hAPP(_915183, _915185)))], (3672 ^ _780119) ^ [_835322, _835324, _835326, _835328, _835330, _835332] : [-(c_List_Olist_Olist__size(_835332, _835328, _835324) = c_List_Olist_Olist__size(_835330, _835326, _835322)), _835332 = _835330, _835328 = _835326, _835324 = _835322], (47804 ^ _780119) ^ [_1745992, _1745994, _1745996] : [47806 ^ _780119 : [(47809 ^ _780119) ^ [] : [hBOOL(hAPP(_1745994, 47805 ^ [_1745992, _1745994, _1745996]))], (47807 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745992), 47805 ^ [_1745992, _1745994, _1745996]), hAPP(c_List_Oset(_1745992), _1745996))))]], -(c_List_OtakeWhile(_1745992, _1745994, _1745996) = _1745996)], (23149 ^ _780119) ^ [_1202923, _1202925, _1202927] : [class_Rings_Oring__1(_1202923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1202925), _1202927)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1202923), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1202927), _1202925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1202923), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1202923), _1202927)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1202923), _1202925)))], (34417 ^ _780119) ^ [_1425928, _1425930, _1425932, _1425934, _1425936] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1425928, _1425930), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1425932), _1425934))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1425930)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1425936), _1425928), _1425930), 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), _1425936), _1425932)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1425936), _1425934)), _1425930))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1425936), _1425934), _1425930)))))], (11511 ^ _780119) ^ [_986613, _986615, _986617, _986619] : [class_Rings_Ocomm__semiring__1(_986613), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986613), _986615), _986617)), _986619) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986613), _986615), _986619)), _986617))], (1030 ^ _780119) ^ [_795718, _795720] : [-(class_Groups_Oordered__ab__group__add__abs(_795718)), _795720 = _795718, class_Groups_Oordered__ab__group__add__abs(_795720)], (6003 ^ _780119) ^ [_875559, _875561, _875563, _875565] : [-(hAPP(hAPP(c_Set_Oinsert(_875559), _875561), hAPP(hAPP(c_Set_Oinsert(_875559), _875563), _875565)) = hAPP(hAPP(c_Set_Oinsert(_875559), _875563), hAPP(hAPP(c_Set_Oinsert(_875559), _875561), _875565)))], (27025 ^ _780119) ^ [_1275609, _1275611] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1275609)), 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)), _1275609))), 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, _1275611))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5250 ^ _780119) ^ [_860423, _860425, _860427, _860429] : [-(c_Product__Type_OPair(_860429, _860425) = c_Product__Type_OPair(_860427, _860423)), _860429 = _860427, _860425 = _860423], (32729 ^ _780119) ^ [] : [-(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))))], (15788 ^ _780119) ^ [_1067724, _1067726, _1067728] : [class_Rings_Oordered__ring(_1067724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067724), _1067726), c_Groups_Ozero__class_Ozero(_1067724))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067724), _1067728), c_Groups_Ozero__class_Ozero(_1067724))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067724), c_Groups_Ozero__class_Ozero(_1067724)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067724), _1067726), _1067728))))], (194 ^ _780119) ^ [_783228, _783230] : [-(class_Fields_Olinordered__field__inverse__zero(_783228)), _783230 = _783228, class_Fields_Olinordered__field__inverse__zero(_783230)], (41810 ^ _780119) ^ [_1604908, _1604910] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1604908, tc_HOL_Obool), tc_HOL_Obool)), _1604910), hAPP(c_Set_OPow(_1604908), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1604908, tc_HOL_Obool), _1604910)))))], (28080 ^ _780119) ^ [_1298592, _1298594, _1298596] : [class_Orderings_Olinorder(_1298592), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298592), _1298594), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298592), _1298594), _1298596)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298592), _1298594), _1298596))], (16903 ^ _780119) ^ [_1087282, _1087284] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087282), _1087284) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 16906 ^ _780119 : [(16909 ^ _780119) ^ [] : [-(_1087284 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16907 ^ _780119) ^ [] : [-(_1087282 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (31377 ^ _780119) ^ [_1366640, _1366642, _1366644] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366640)))), 31380 ^ _780119 : [(31387 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366642)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366640)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366642)), _1366644)) = 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), _1366640), _1366642))), _1366644))], (31381 ^ _780119) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366642))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366640)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366642)), _1366644)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366640)), _1366644))]]], (17566 ^ _780119) ^ [_1099410, _1099412, _1099414, _1099416] : [class_Rings_Olinordered__semidom(_1099410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099410), hAPP(hAPP(c_Power_Opower__class_Opower(_1099410), _1099412), hAPP(c_Nat_OSuc, _1099414))), hAPP(hAPP(c_Power_Opower__class_Opower(_1099410), _1099416), hAPP(c_Nat_OSuc, _1099414)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099410), c_Groups_Ozero__class_Ozero(_1099410)), _1099416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099410), _1099412), _1099416)))], (8118 ^ _780119) ^ [_919199, _919201, _919203, _919205] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_919199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919199, tc_HOL_Obool)), _919201), hAPP(hAPP(c_Set_Oinsert(_919199), _919203), _919205)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_919199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919199, tc_HOL_Obool)), _919201), _919205))))], (23070 ^ _780119) ^ [_1201438, _1201440] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201438), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201440)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1201438), _1201440)))], (25093 ^ _780119) ^ [_1239654, _1239656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1239654)), hAPP(c_Int_Onat, _1239656))), 25096 ^ _780119 : [(25099 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239654), _1239656)))], (25097 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239656)))]]], (37509 ^ _780119) ^ [_1497917, _1497919] : [-(hAPP(c_List_Olexn(_1497917, _1497919), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1497917), tc_List_Olist(_1497917)), tc_HOL_Obool)))], (16943 ^ _780119) ^ [_1087914, _1087916, _1087918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1087914)), 16946 ^ _780119 : [(16953 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1087916), _1087918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087914), _1087916)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087914), _1087918))))], (16947 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087914), _1087916)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087914), _1087918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1087916), _1087918)))]]], (36293 ^ _780119) ^ [_1468400, _1468402, _1468404, _1468406] : [c_Fun_Oinj__on(_1468400, _1468402, _1468404, _1468406), -(hAPP(c_Finite__Set_Ocard(_1468402), hAPP(c_Set_Oimage(_1468400, _1468402, _1468404), _1468406)) = hAPP(c_Finite__Set_Ocard(_1468400), _1468406))], (16893 ^ _780119) ^ [_1087144, _1087146] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1087144, tc_HOL_Obool)), _1087146) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1087144, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1087144, tc_HOL_Obool))), _1087146))], (13392 ^ _780119) ^ [_1023781, _1023783, _1023785] : [class_Groups_Oordered__ab__group__add(_1023781), 13395 ^ _780119 : [(13402 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023781), hAPP(c_Groups_Ouminus__class_Ouminus(_1023781), _1023785)), _1023783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023781), hAPP(c_Groups_Ouminus__class_Ouminus(_1023781), _1023783)), _1023785)))], (13396 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023781), hAPP(c_Groups_Ouminus__class_Ouminus(_1023781), _1023783)), _1023785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023781), hAPP(c_Groups_Ouminus__class_Ouminus(_1023781), _1023785)), _1023783)))]]], (23455 ^ _780119) ^ [_1209030, _1209032] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1209030, _1209032))))], (31585 ^ _780119) ^ [_1369907] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369907), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369907)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1369907)))], (21002 ^ _780119) ^ [_1162161, _1162163, _1162165, _1162167] : [class_Fields_Ofield__inverse__zero(_1162161), -(_1162163 = c_Groups_Ozero__class_Ozero(_1162161)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162161), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162161), _1162165), _1162163)), _1162167) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162161), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162161), _1162165), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162161), _1162167), _1162163))), _1162163))], (34927 ^ _780119) ^ [_1435972, _1435974, _1435976, _1435978, _1435980, _1435982] : [hBOOL(hAPP(_1435972, _1435974)), hBOOL(hAPP(_1435976, _1435978)), 34934 ^ _780119 : [(34937 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1435976, hAPP(c_Product__Type_Osnd(_1435980, _1435982), hAPP(hAPP(c_Product__Type_OPair(_1435980, _1435982), _1435974), _1435978)))))], (34935 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1435972, hAPP(c_Product__Type_Ofst(_1435980, _1435982), hAPP(hAPP(c_Product__Type_OPair(_1435980, _1435982), _1435974), _1435978)))))]]], (4152 ^ _780119) ^ [_842876, _842878, _842880, _842882] : [-(c_List_Olistsp(_842882, _842878) = c_List_Olistsp(_842880, _842876)), _842882 = _842880, _842878 = _842876], (15270 ^ _780119) ^ [_1059078, _1059080] : [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), _1059078), _1059080))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1059078))), -(_1059080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26903 ^ _780119) ^ [_1272170, _1272172, _1272174] : [class_Rings_Olinordered__idom(_1272170), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272170), c_Groups_Ozero__class_Ozero(_1272170)), hAPP(hAPP(c_Power_Opower__class_Opower(_1272170), hAPP(c_Groups_Oabs__class_Oabs(_1272170), _1272172)), _1272174))))], (43040 ^ _780119) ^ [_1633246, _1633248, _1633250, _1633252, _1633254] : [hBOOL(hAPP(hAPP(c_member(_1633246), _1633248), hAPP(c_List_Oset(_1633246), _1633250))), -(hAPP(hAPP(c_Map_Omap__of(_1633246, _1633252), hAPP(hAPP(c_List_Ozip(_1633246, _1633252), _1633250), hAPP(hAPP(c_List_Omap(_1633246, _1633252), _1633254), _1633250))), _1633248) = hAPP(c_Option_Ooption_OSome(_1633252), hAPP(_1633254, _1633248)))], (10350 ^ _780119) ^ [_962304, _962306, _962308, _962310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962304, tc_HOL_Obool)), _962310), _962306)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962304, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962304, tc_HOL_Obool)), _962306), _962308)), _962310) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962304, tc_HOL_Obool)), _962306), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962304, tc_HOL_Obool)), _962308), _962310)))], (35617 ^ _780119) ^ [] : [-(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))], (42875 ^ _780119) ^ [_1629802, _1629804, _1629806, _1629808] : [hBOOL(hAPP(c_List_Odistinct(_1629802), hAPP(hAPP(c_List_Omap(_1629804, _1629802), _1629806), _1629808))), 42878 ^ _780119 : [(42881 ^ _780119) ^ [] : [-(c_Fun_Oinj__on(_1629804, _1629802, _1629806, hAPP(c_List_Oset(_1629804), _1629808)))], (42879 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1629804), _1629808)))]]], (33233 ^ _780119) ^ [_1399847] : [c_Int_OBit1(_1399847) = c_Int_OMin, -(_1399847 = c_Int_OMin)], (48114 ^ _780119) ^ [_1752003, _1752005, _1752007, _1752009, _1752011] : [c_List_OdropWhile(_1752003, _1752005, _1752007) = hAPP(hAPP(c_List_Olist_OCons(_1752003), _1752009), _1752011), 48117 ^ _780119 : [(48120 ^ _780119) ^ [] : [hBOOL(hAPP(_1752005, _1752009))], (48118 ^ _780119) ^ [] : [-(_1752007 = hAPP(hAPP(c_List_Oappend(_1752003), c_List_OtakeWhile(_1752003, _1752005, _1752007)), hAPP(hAPP(c_List_Olist_OCons(_1752003), _1752009), _1752011)))]]], (4934 ^ _780119) ^ [_855441, _855443, _855445, _855447, _855449, _855451, _855453, _855455] : [-(c_Option_Ooption_Ooption__case(_855455, _855451, _855447, _855443) = c_Option_Ooption_Ooption__case(_855453, _855449, _855445, _855441)), _855455 = _855453, _855451 = _855449, _855447 = _855445, _855443 = _855441], (13328 ^ _780119) ^ [_1022649, _1022651, _1022653] : [class_Groups_Oordered__ab__group__add(_1022649), 13331 ^ _780119 : [(13338 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022649), _1022653), _1022651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022649), hAPP(c_Groups_Ouminus__class_Ouminus(_1022649), _1022651)), hAPP(c_Groups_Ouminus__class_Ouminus(_1022649), _1022653))))], (13332 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022649), hAPP(c_Groups_Ouminus__class_Ouminus(_1022649), _1022651)), hAPP(c_Groups_Ouminus__class_Ouminus(_1022649), _1022653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022649), _1022653), _1022651)))]]], (360 ^ _780119) ^ [_785659, _785661, _785663, _785665, _785667, _785669, _785671, _785673] : [-(c_Equiv__Relations_Ocongruent(_785671, _785667, _785663, _785659)), c_Equiv__Relations_Ocongruent(_785673, _785669, _785665, _785661), _785673 = _785671, _785669 = _785667, _785665 = _785663, _785661 = _785659], (10088 ^ _780119) ^ [_955813, _955815, _955817, _955819] : [class_Lattices_Odistrib__lattice(_955813), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955813), _955815), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955813), _955817), _955819)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955813), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955813), _955815), _955817)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955813), _955815), _955819)))], (12787 ^ _780119) ^ [_1011912, _1011914, _1011916] : [-(hAPP(c_Finite__Set_Ofold1(_1011912, _1011914), _1011916) = c_HOL_OThe(_1011912, c_Finite__Set_Ofold1Set(_1011912, _1011914, _1011916)))], (51485 ^ _780119) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (25416 ^ _780119) ^ [_1244949, _1244951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244949)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244951)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1244949, _1244951)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1244949), hAPP(c_Int_Onat, _1244951)))], (44616 ^ _780119) ^ [_1674021, _1674023, _1674025, _1674027] : [hAPP(hAPP(c_List_Olist__update(_1674021, _1674023), _1674025), _1674027) = c_List_Olist_ONil(_1674021), -(_1674023 = c_List_Olist_ONil(_1674021))], (28134 ^ _780119) ^ [_1299875, _1299877, _1299879, _1299881] : [class_Orderings_Olinorder(_1299875), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299875), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299875), _1299877), _1299879)), _1299881) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299875), _1299877), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299875), _1299879), _1299881)))], (30429 ^ _780119) ^ [_1349003, _1349005] : [class_Int_Onumber__ring(_1349003), -(hAPP(c_Int_Onumber__class_Onumber__of(_1349003), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1349005)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1349003), hAPP(c_Int_Onumber__class_Onumber__of(_1349003), _1349005)))], (7171 ^ _780119) ^ [_899029, _899031, _899033, _899035, _899037] : [class_Orderings_Oord(_899029), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899031, _899029)), _899033), _899035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899029), hAPP(_899033, _899037)), hAPP(_899035, _899037))))], (18730 ^ _780119) ^ [_1121677, _1121679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121677), _1121679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121677), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1121679), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (32151 ^ _780119) ^ [_1379739] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379739))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379739)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9864 ^ _780119) ^ [_951757, _951759] : [class_Lattices_Osemilattice__inf(_951757), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951757), _951759), _951759) = _951759)], (15060 ^ _780119) ^ [_1056006, _1056008] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056006, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1056006, tc_HOL_Obool))), _1056008) = _1056008)], (42487 ^ _780119) ^ [_1620420, _1620422, _1620424] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1620420), _1620422))), -(c_Smallcheck_Osmall_H(_1620424, _1620420, _1620422) = 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(_1620424, _1620420, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1620422), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1620424, _1620422)))], (11830 ^ _780119) ^ [_993023, _993025, _993027] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993023), _993025) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993023), _993027), -(_993025 = _993027)], (42292 ^ _780119) ^ [_1616187, _1616189, _1616191] : [-(c_Nitpick_Oof__frac(_1616189, _1616187, _1616191) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1616187), hAPP(c_Int_Oring__1__class_Oof__int(_1616187), hAPP(c_Nitpick_Onum(_1616189), _1616191))), hAPP(c_Int_Oring__1__class_Oof__int(_1616187), hAPP(c_Nitpick_Odenom(_1616189), _1616191)))), class_Rings_Oinverse(_1616187), class_Rings_Oring__1(_1616187)], (36235 ^ _780119) ^ [_1467398, _1467400, _1467402, _1467404, _1467406] : [c_Fun_Oinj__on(_1467398, _1467400, _1467402, c_Orderings_Otop__class_Otop(tc_fun(_1467398, tc_HOL_Obool))), 36238 ^ _780119 : [(36245 ^ _780119) ^ [] : [_1467404 = _1467406, -(hAPP(_1467402, _1467404) = hAPP(_1467402, _1467406))], (36239 ^ _780119) ^ [] : [hAPP(_1467402, _1467404) = hAPP(_1467402, _1467406), -(_1467404 = _1467406)]]], (51139 ^ _780119) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (40940 ^ _780119) ^ [_1582839] : [class_Groups_Oab__semigroup__mult(_1582839), -(c_Finite__Set_Ofun__left__comm(_1582839, _1582839, c_Groups_Otimes__class_Otimes(_1582839)))], (41195 ^ _780119) ^ [_1588862, _1588864, _1588866, _1588868, _1588870] : [class_Complete__Lattice_Ocomplete__lattice(_1588862), 41198 ^ _780119 : [(41199 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1588862), _1588864), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1588866, _1588862), _1588868), _1588870))), 41202 ^ _780119 : [(41203 ^ _780119) ^ [_1589043] : [hBOOL(hAPP(hAPP(c_member(_1588866), _1589043), _1588868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1588862), _1588864), hAPP(_1588870, _1589043))))]]], (41209 ^ _780119) ^ [] : [41211 ^ _780119 : [(41214 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1588862), _1588864), hAPP(_1588870, 41210 ^ [_1588862, _1588864, _1588866, _1588868, _1588870])))], (41212 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588866), 41210 ^ [_1588862, _1588864, _1588866, _1588868, _1588870]), _1588868)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1588862), _1588864), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1588866, _1588862), _1588868), _1588870))))]]], (42564 ^ _780119) ^ [_1622373, _1622375, _1622377] : [c_Fun_Oinj__on(tc_List_Olist(_1622373), tc_List_Olist(_1622375), hAPP(c_List_Omap(_1622373, _1622375), _1622377), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1622373), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1622373, _1622375, _1622377, c_Orderings_Otop__class_Otop(tc_fun(_1622373, tc_HOL_Obool))))], (28086 ^ _780119) ^ [_1298717, _1298719, _1298721] : [class_Orderings_Olinorder(_1298717), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298717), _1298719), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298717), _1298719), _1298721)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298717), _1298719), _1298721))], (50390 ^ _780119) ^ [_1801801, _1801803, _1801805] : [-(c_Lazy__Sequence_Ohb__flat(_1801801, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1801801))), _1801803, _1801805)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(_1801801), hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1801801)), tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1801801)), c_Lazy__Sequence_Ohit__bound(_1801801), c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1801801)))), _1801803), c_Lazy__Sequence_Ohb__flat(_1801801, _1801805)))], (50330 ^ _780119) ^ [_1800666, _1800668, _1800670, _1800672] : [-(c_Lazy__Sequence_Oappend(_1800666, c_Lazy__Sequence_Olazy__sequence_OInsert(_1800666, _1800668, _1800670), _1800672) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1800666, _1800668, c_Lazy__Sequence_Oappend(_1800666, _1800670, _1800672)))], (20148 ^ _780119) ^ [_1146519, _1146521, _1146523, _1146525] : [class_Fields_Olinordered__field(_1146519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146519), _1146521), _1146523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146519), c_Groups_Ozero__class_Ozero(_1146519)), _1146525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146519), c_Groups_Ozero__class_Ozero(_1146519)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146519), _1146523), _1146521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146519), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146519), _1146525), _1146523)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146519), _1146525), _1146521))))], (51169 ^ _780119) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (27784 ^ _780119) ^ [_1293215, _1293217, _1293219, _1293221] : [class_Orderings_Olinorder(_1293215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293215), _1293217), _1293219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293215), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293215), _1293221), _1293217)), _1293219)))], (37837 ^ _780119) ^ [_1507548, _1507550, _1507552, _1507554] : [hBOOL(hAPP(c_Predicate_ODomainP(_1507548, _1507550, _1507552), _1507554)), -(hBOOL(hAPP(hAPP(_1507552, _1507554), 37840 ^ [_1507548, _1507550, _1507552, _1507554])))], (37550 ^ _780119) ^ [_1498823, _1498825, _1498827, _1498829] : [-(hAPP(c_Relation_ORange(_1498823, _1498825), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1498823, _1498825), tc_HOL_Obool)), _1498827), _1498829)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1498825, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1498823, _1498825), _1498827)), hAPP(c_Relation_ORange(_1498823, _1498825), _1498829)))], (50126 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (1420 ^ _780119) ^ [_800593, _800595] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_800593)), _800595 = _800593, class_Groups_Oordered__cancel__ab__semigroup__add(_800595)], (7942 ^ _780119) ^ [_915421, _915423, _915425, _915427] : [hBOOL(hAPP(hAPP(c_member(_915421), _915423), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915421, tc_HOL_Obool)), _915425), _915427))), hBOOL(hAPP(hAPP(c_member(_915421), _915423), _915427))], (14356 ^ _780119) ^ [_1042872, _1042874, _1042876, _1042878, _1042880, _1042882] : [class_Groups_Ocomm__monoid__mult(_1042872), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042874), _1042876)), 14363 ^ _780119 : [(14370 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1042874), _1042878), _1042876))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1042874, _1042872), hAPP(hAPP(c_COMBC(_1042874, _1042872, _1042872), hAPP(hAPP(c_COMBS(_1042874, _1042872, tc_fun(_1042872, _1042872)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1042872, tc_fun(_1042872, _1042872)), _1042874), c_If(_1042872)), hAPP(hAPP(c_COMBC(_1042874, _1042874, tc_HOL_Obool), c_fequal), _1042878))), _1042880)), _1042882)), _1042876) = hAPP(hAPP(c_Power_Opower__class_Opower(_1042872), _1042882), hAPP(c_Finite__Set_Ocard(_1042874), _1042876)))], (14364 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1042874), _1042878), _1042876)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1042874, _1042872), hAPP(hAPP(c_COMBC(_1042874, _1042872, _1042872), hAPP(hAPP(c_COMBS(_1042874, _1042872, tc_fun(_1042872, _1042872)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1042872, tc_fun(_1042872, _1042872)), _1042874), c_If(_1042872)), hAPP(hAPP(c_COMBC(_1042874, _1042874, tc_HOL_Obool), c_fequal), _1042878))), _1042880)), _1042882)), _1042876) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042872), hAPP(_1042880, _1042878)), hAPP(hAPP(c_Power_Opower__class_Opower(_1042872), _1042882), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1042874), _1042876)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (50957 ^ _780119) ^ [_1813943, _1813945] : [class_Lattices_Olattice(_1813943), -(class_Lattices_Osemilattice__sup(tc_fun(_1813945, _1813943)))], (35171 ^ _780119) ^ [_1441509, _1441511, _1441513, _1441515] : [c_Wellfounded_Omax__extp(_1441509, hAPP(hAPP(c_COMBC(_1441509, tc_fun(tc_prod(_1441509, _1441509), tc_HOL_Obool), tc_fun(_1441509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441509, tc_fun(tc_fun(tc_prod(_1441509, _1441509), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1441509, _1441509), tc_HOL_Obool), tc_fun(_1441509, tc_HOL_Obool)), _1441509), c_COMBC(_1441509, tc_fun(tc_prod(_1441509, _1441509), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441509, tc_prod(_1441509, _1441509)), tc_fun(_1441509, tc_fun(tc_fun(tc_prod(_1441509, _1441509), tc_HOL_Obool), tc_HOL_Obool)), _1441509), hAPP(c_COMBB(tc_prod(_1441509, _1441509), tc_fun(tc_fun(tc_prod(_1441509, _1441509), tc_HOL_Obool), tc_HOL_Obool), _1441509), c_member(tc_prod(_1441509, _1441509)))), c_Product__Type_OPair(_1441509, _1441509)))), _1441511), _1441513, _1441515), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1441509, tc_HOL_Obool), tc_fun(_1441509, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1441509, tc_HOL_Obool), tc_fun(_1441509, tc_HOL_Obool)), _1441513), _1441515)), c_Wellfounded_Omax__ext(_1441509, _1441511))))], (39933 ^ _780119) ^ [_1559292, _1559294, _1559296, _1559298, _1559300] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559292, _1559292)), hAPP(hAPP(c_Product__Type_OPair(_1559292, _1559292), _1559294), _1559296)), c_Transitive__Closure_Ortrancl(_1559292, _1559298))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559292, _1559292), tc_HOL_Obool)), _1559298), hAPP(hAPP(c_Product__Type_OSigma(_1559292, _1559292), _1559300), hAPP(c_COMBK(tc_fun(_1559292, tc_HOL_Obool), _1559292), _1559300)))), -(_1559294 = _1559296), -(hBOOL(hAPP(hAPP(c_member(_1559292), _1559294), _1559300)))], (8832 ^ _780119) ^ [_932591, _932593, _932595, _932597] : [class_Orderings_Oord(_932591), 8835 ^ _780119 : [(8844 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_932593, _932591)), _932595), _932597))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932593, _932591)), _932595), _932597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932593, _932591)), _932597), _932595)))], (8836 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_932593, _932591)), _932595), _932597)), 8839 ^ _780119 : [(8842 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932593, _932591)), _932597), _932595))], (8840 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932593, _932591)), _932595), _932597)))]]]]], (34570 ^ _780119) ^ [_1428932, _1428934, _1428936] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1428932, _1428934), _1428936)), 34573 ^ _780119 : [(34574 ^ _780119) ^ [_1429017] : [hBOOL(hAPP(hAPP(_1428934, _1429017), _1428936)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1428932, _1428934), _1429017)))]]], (49335 ^ _780119) ^ [_1778496, _1778498, _1778500, _1778502] : [-(c_List_Oconcat(_1778496, hAPP(hAPP(c_List_Omap(_1778498, tc_List_Olist(_1778496)), _1778500), _1778502)) = c_List_Omaps(_1778498, _1778496, _1778500, _1778502))], (38864 ^ _780119) ^ [_1533540, _1533542, _1533544, _1533546, _1533548] : [class_Groups_Ocomm__monoid__add(_1533540), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533542), _1533544)), c_Fun_Oinj__on(_1533542, _1533542, _1533546, _1533544), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1533542, _1533540), _1533548), hAPP(c_Set_Oimage(_1533542, _1533542, _1533546), _1533544)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1533542, _1533540), hAPP(c_Fun_Ocomp(_1533542, _1533540, _1533542, _1533548), _1533546)), _1533544))], (6803 ^ _780119) ^ [_891957, _891959, _891961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891957, tc_HOL_Obool)), _891959), _891961)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891957, tc_HOL_Obool)), _891959), _891961) = _891961)], (28306 ^ _780119) ^ [_1303397, _1303399] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1303397), hAPP(c_Nat_OSuc, _1303399)) = 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)), _1303399)), _1303397))], (44894 ^ _780119) ^ [_1679091, _1679093, _1679095, _1679097, _1679099] : [_1679091 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1679093, _1679095, _1679097), _1679091), _1679099) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679095), _1679093), c_List_Olist_ONil(_1679095)), _1679099))], (2534 ^ _780119) ^ [_817591, _817593, _817595, _817597] : [-(c_FunDef_Orp__inv__image(_817597, _817593) = c_FunDef_Orp__inv__image(_817595, _817591)), _817597 = _817595, _817593 = _817591], (30225 ^ _780119) ^ [_1344697, _1344699, _1344701, _1344703, _1344705] : [c_Com_Ocom_OLocal(_1344697, _1344699, _1344701) = c_Com_Ocom_OWhile(_1344703, _1344705)], (228 ^ _780119) ^ [_783671, _783673, _783675, _783677] : [-(c_Nitpick_Orefl_H(_783675, _783671)), c_Nitpick_Orefl_H(_783677, _783673), _783677 = _783675, _783673 = _783671], (8644 ^ _780119) ^ [_929638, _929640, _929642] : [class_Orderings_Opreorder(_929638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929638), _929640), _929642)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929638), _929642), _929640))], (34098 ^ _780119) ^ [_1420519] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1420519) = 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), _1420519), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (43577 ^ _780119) ^ [_1648647, _1648649, _1648651] : [hBOOL(hAPP(c_List_Odistinct(_1648647), hAPP(hAPP(c_List_Olist_OCons(_1648647), _1648649), _1648651))), 43580 ^ _780119 : [(43583 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1648647), _1648651)))], (43581 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1648647), _1648649), hAPP(c_List_Oset(_1648647), _1648651)))]]], (13825 ^ _780119) ^ [_1031487, _1031489, _1031491] : [class_Groups_Ogroup__add(_1031487), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031487), _1031489), _1031491) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031487), _1031489), hAPP(c_Groups_Ouminus__class_Ouminus(_1031487), _1031491)))], (7682 ^ _780119) ^ [_909959, _909961, _909963, _909965, _909967, _909969] : [c_Hoare__Mirabelle_Ohoare__derivs(_909959, _909961, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909959)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909959), _909963), _909965), _909967)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909959), tc_HOL_Obool)))), 7689 ^ _780119 : [(7692 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_909963, 7687 ^ [_909959, _909961, _909963, _909965, _909967, _909969]), 7688 ^ [_909959, _909961, _909963, _909965, _909967, _909969]))], (7690 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_909969, 7687 ^ [_909959, _909961, _909963, _909965, _909967, _909969]), 7688 ^ [_909959, _909961, _909963, _909965, _909967, _909969])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_909959, _909961, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909959)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909959), _909969), _909965), _909967)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909959), tc_HOL_Obool)))))], (31115 ^ _780119) ^ [_1361943, _1361945] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1361943))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1361943)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1361945)) = 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), _1361945)))], (20982 ^ _780119) ^ [_1161805, _1161807, _1161809, _1161811] : [class_Fields_Ofield__inverse__zero(_1161805), -(_1161807 = c_Groups_Ozero__class_Ozero(_1161805)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161805), _1161809), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161805), _1161811), _1161807)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161805), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161805), _1161811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161805), _1161809), _1161807))), _1161807))], (10208 ^ _780119) ^ [_958516, _958518, _958520] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958516, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958516, tc_HOL_Obool)), _958518), _958520)), _958518)))], (13600 ^ _780119) ^ [_1027604, _1027606] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027604), _1027606))), 13603 ^ _780119 : [(13610 ^ _780119) ^ [] : [_1027604 = _1027606, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027604), hAPP(c_Nat_OSuc, _1027606))))], (13604 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027604), hAPP(c_Nat_OSuc, _1027606))), -(_1027604 = _1027606)]]], (35418 ^ _780119) ^ [_1448171, _1448173, _1448175, _1448177] : [-(hAPP(c_Relation_OImage(_1448171, _1448173, _1448175), _1448177) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1448171, tc_fun(_1448173, tc_HOL_Obool)), _1448177), hAPP(hAPP(c_COMBB(tc_fun(_1448171, tc_HOL_Obool), tc_fun(_1448173, tc_HOL_Obool), _1448171), c_Relation_OImage(_1448171, _1448173, _1448175)), hAPP(hAPP(c_COMBC(_1448171, tc_fun(_1448171, tc_HOL_Obool), tc_fun(_1448171, tc_HOL_Obool)), c_Set_Oinsert(_1448171)), c_Orderings_Obot__class_Obot(tc_fun(_1448171, tc_HOL_Obool))))))], (51333 ^ _780119) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (50648 ^ _780119) ^ [_1807332, _1807334, _1807336, _1807338, _1807340] : [-(c_List_Oreplicate(_1807332, _1807334, _1807336) = c_List_Oreplicate(_1807332, _1807338, _1807340)), _1807334 = _1807338, 50653 ^ _780119 : [(50656 ^ _780119) ^ [] : [_1807336 = _1807340], (50654 ^ _780119) ^ [] : [_1807334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (13843 ^ _780119) ^ [_1031844, _1031846] : [class_Rings_Oring__1__no__zero__divisors(_1031844), 13846 ^ _780119 : [(13847 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031844), _1031846), _1031846) = c_Groups_Oone__class_Oone(_1031844), -(_1031846 = c_Groups_Oone__class_Oone(_1031844)), -(_1031846 = hAPP(c_Groups_Ouminus__class_Ouminus(_1031844), c_Groups_Oone__class_Oone(_1031844)))], (13857 ^ _780119) ^ [] : [13858 ^ _780119 : [(13861 ^ _780119) ^ [] : [_1031846 = hAPP(c_Groups_Ouminus__class_Ouminus(_1031844), c_Groups_Oone__class_Oone(_1031844))], (13859 ^ _780119) ^ [] : [_1031846 = c_Groups_Oone__class_Oone(_1031844)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031844), _1031846), _1031846) = c_Groups_Oone__class_Oone(_1031844))]]], (45193 ^ _780119) ^ [_1685962, _1685964, _1685966, _1685968] : [-(hAPP(hAPP(c_List_Oappend(_1685962), hAPP(hAPP(c_List_Oappend(_1685962), _1685964), _1685966)), _1685968) = hAPP(hAPP(c_List_Oappend(_1685962), _1685964), hAPP(hAPP(c_List_Oappend(_1685962), _1685966), _1685968)))], (41862 ^ _780119) ^ [_1606098, _1606100] : [class_Complete__Lattice_Ocomplete__lattice(_1606098), -(c_Complete__Lattice_OSup__class_OSup(_1606098, hAPP(hAPP(c_Set_Oinsert(_1606098), _1606100), c_Orderings_Obot__class_Obot(tc_fun(_1606098, tc_HOL_Obool)))) = _1606100)], (22781 ^ _780119) ^ [] : [-(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))))], (12643 ^ _780119) ^ [_1009243, _1009245, _1009247, _1009249] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1009243, tc_Option_Ooption(_1009245)), hAPP(c_COMBK(tc_Option_Ooption(_1009245), _1009243), c_Option_Ooption_ONone(_1009245))), _1009247), c_Option_Ooption_ONone(_1009245)), _1009249) = c_Option_Ooption_ONone(_1009245))], (6733 ^ _780119) ^ [_890482, _890484, _890486, _890488] : [hBOOL(hAPP(hAPP(c_member(_890482), _890484), _890486)), -(hBOOL(hAPP(hAPP(c_member(_890482), _890484), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890482, tc_HOL_Obool)), _890486), _890488))))], (19086 ^ _780119) ^ [_1127759, _1127761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1127759), 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)), _1127761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127759), _1127761)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (49249 ^ _780119) ^ [_1777014, _1777016, _1777018] : [-(hBOOL(hAPP(hAPP(c_member(_1777014), _1777016), hAPP(c_List_Oset(_1777014), _1777018)))), -(c_List_Oinsert(_1777014, _1777016, _1777018) = hAPP(hAPP(c_List_Olist_OCons(_1777014), _1777016), _1777018))], (9786 ^ _780119) ^ [_950130, _950132, _950134, _950136] : [class_Lattices_Osemilattice__inf(_950130), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950130), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950130), _950132), _950134)), _950136) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950130), _950132), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950130), _950134), _950136)))], (23587 ^ _780119) ^ [_1211394, _1211396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1211394), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1211396), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1211396), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1211394))))), -(_1211394 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1211396), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1211396), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1211394))))], (38570 ^ _780119) ^ [_1526595, _1526597, _1526599] : [c_Wellfounded_OwfP(_1526595, hAPP(_1526597, 38571 ^ [_1526595, _1526597, _1526599])), 38578 ^ _780119 : [(38581 ^ _780119) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1526595, tc_HOL_Obool)), c_Predicate_ODomainP(_1526595, _1526595, hAPP(_1526597, 38576 ^ [_1526595, _1526597, _1526599]))), c_Predicate_ORangeP(_1526595, _1526595, hAPP(_1526597, 38577 ^ [_1526595, _1526597, _1526599]))) = c_Orderings_Obot__class_Obot(tc_fun(_1526595, tc_HOL_Obool))], (38579 ^ _780119) ^ [] : [hAPP(_1526597, 38576 ^ [_1526595, _1526597, _1526599]) = hAPP(_1526597, 38577 ^ [_1526595, _1526597, _1526599])]], -(c_Wellfounded_OwfP(_1526595, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1526599, tc_fun(_1526595, tc_fun(_1526595, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1526599, tc_HOL_Obool))), _1526597)))], (7154 ^ _780119) ^ [_898683, _898685, _898687, _898689] : [class_Orderings_Oord(_898683), 7157 ^ _780119 : [(7164 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898683), hAPP(_898687, 7165 ^ [_898683, _898685, _898687, _898689])), hAPP(_898689, 7165 ^ [_898683, _898685, _898687, _898689]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898685, _898683)), _898687), _898689)))], (7158 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898685, _898683)), _898687), _898689)), 7161 ^ _780119 : [(7162 ^ _780119) ^ [_898840] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898683), hAPP(_898687, _898840)), hAPP(_898689, _898840))))]]]]], (37020 ^ _780119) ^ [_1484944, _1484946, _1484948, _1484950, _1484952] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1484944, _1484946, _1484948), _1484950), _1484952) = hAPP(c_Set_OCollect(tc_prod(_1484944, _1484948)), hAPP(c_Product__Type_Oprod_Oprod__case(_1484944, _1484948, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1484948, tc_fun(_1484946, tc_HOL_Obool)), tc_fun(_1484948, tc_HOL_Obool), _1484944), hAPP(c_COMBB(tc_fun(_1484946, tc_HOL_Obool), tc_HOL_Obool, _1484948), c_HOL_OEx(_1484946))), hAPP(hAPP(c_COMBC(_1484944, tc_fun(_1484948, tc_fun(_1484946, tc_HOL_Obool)), tc_fun(_1484948, tc_fun(_1484946, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1484946, tc_HOL_Obool), tc_fun(_1484946, tc_HOL_Obool)), tc_fun(tc_fun(_1484948, tc_fun(_1484946, tc_HOL_Obool)), tc_fun(_1484948, tc_fun(_1484946, tc_HOL_Obool))), _1484944), c_COMBB(tc_fun(_1484946, tc_HOL_Obool), tc_fun(_1484946, tc_HOL_Obool), _1484948)), hAPP(hAPP(c_COMBB(tc_fun(_1484946, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1484946, tc_HOL_Obool), tc_fun(_1484946, tc_HOL_Obool)), _1484944), c_COMBS(_1484946, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484946, tc_HOL_Obool), tc_fun(_1484946, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1484944), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1484946), c_fconj)), hAPP(hAPP(c_COMBC(_1484944, tc_fun(tc_prod(_1484944, _1484946), tc_HOL_Obool), tc_fun(_1484946, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484946, tc_fun(tc_fun(tc_prod(_1484944, _1484946), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484944, _1484946), tc_HOL_Obool), tc_fun(_1484946, tc_HOL_Obool)), _1484944), c_COMBC(_1484946, tc_fun(tc_prod(_1484944, _1484946), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484946, tc_prod(_1484944, _1484946)), tc_fun(_1484946, tc_fun(tc_fun(tc_prod(_1484944, _1484946), tc_HOL_Obool), tc_HOL_Obool)), _1484944), hAPP(c_COMBB(tc_prod(_1484944, _1484946), tc_fun(tc_fun(tc_prod(_1484944, _1484946), tc_HOL_Obool), tc_HOL_Obool), _1484946), c_member(tc_prod(_1484944, _1484946)))), c_Product__Type_OPair(_1484944, _1484946)))), _1484950))))), hAPP(hAPP(c_COMBC(_1484948, tc_fun(tc_prod(_1484946, _1484948), tc_HOL_Obool), tc_fun(_1484946, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484946, tc_fun(tc_fun(tc_prod(_1484946, _1484948), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484946, _1484948), tc_HOL_Obool), tc_fun(_1484946, tc_HOL_Obool)), _1484948), c_COMBC(_1484946, tc_fun(tc_prod(_1484946, _1484948), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484946, tc_prod(_1484946, _1484948)), tc_fun(_1484946, tc_fun(tc_fun(tc_prod(_1484946, _1484948), tc_HOL_Obool), tc_HOL_Obool)), _1484948), hAPP(c_COMBB(tc_prod(_1484946, _1484948), tc_fun(tc_fun(tc_prod(_1484946, _1484948), tc_HOL_Obool), tc_HOL_Obool), _1484946), c_member(tc_prod(_1484946, _1484948)))), hAPP(c_COMBC(_1484946, _1484948, tc_prod(_1484946, _1484948)), c_Product__Type_OPair(_1484946, _1484948))))), _1484952))))))], (26266 ^ _780119) ^ [_1259276, _1259278, _1259280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1259278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1259280), 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), _1259280), _1259278))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1259276)))))], (23422 ^ _780119) ^ [] : [-(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))))], (22903 ^ _780119) ^ [_1198387, _1198389] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198387)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198389)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198387), _1198389)))], (5646 ^ _780119) ^ [_866581, _866583] : [_866583 = _866581, -(tc_Option_Ooption(_866583) = tc_Option_Ooption(_866581))], (14692 ^ _780119) ^ [_1049846, _1049848, _1049850, _1049852, _1049854] : [hBOOL(hAPP(hAPP(c_member(_1049846), _1049848), c_Map_Oran(_1049850, _1049846, c_Map_Orestrict__map(_1049850, _1049846, _1049852, _1049854)))), 14696 ^ _780119 : [(14699 ^ _780119) ^ [] : [-(hAPP(_1049852, 14695 ^ [_1049846, _1049848, _1049850, _1049852, _1049854]) = hAPP(c_Option_Ooption_OSome(_1049846), _1049848))], (14697 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1049850), 14695 ^ [_1049846, _1049848, _1049850, _1049852, _1049854]), _1049854)))]]], (4872 ^ _780119) ^ [_854518, _854520, _854522, _854524, _854526, _854528] : [-(c_New__DSequence_Opos__union(_854528, _854524, _854520) = c_New__DSequence_Opos__union(_854526, _854522, _854518)), _854528 = _854526, _854524 = _854522, _854520 = _854518], (31903 ^ _780119) ^ [] : [-(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)))))], (21528 ^ _780119) ^ [_1172694, _1172696, _1172698] : [class_Divides_Oring__div(_1172694), -(c_Divides_Odiv__class_Omod(_1172694, hAPP(c_Groups_Ouminus__class_Ouminus(_1172694), _1172696), _1172698) = c_Divides_Odiv__class_Omod(_1172694, hAPP(c_Groups_Ouminus__class_Ouminus(_1172694), c_Divides_Odiv__class_Omod(_1172694, _1172696, _1172698)), _1172698))], (8830 ^ _780119) ^ [_932553, _932555, _932557, _932559] : [-(c_Nitpick_Ofold__graph_H(_932553, _932555, _932557, _932559, c_Orderings_Obot__class_Obot(tc_fun(_932553, tc_HOL_Obool)), _932559))], (51263 ^ _780119) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (23314 ^ _780119) ^ [_1206201, _1206203] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206201) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206203), -(_1206201 = _1206203)], (35183 ^ _780119) ^ [_1442285, _1442287, _1442289, _1442291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1442285), _1442287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1442289), _1442291)), -(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), _1442285), _1442289)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1442287), _1442291))), c_FunDef_Opair__leq)))], (41874 ^ _780119) ^ [_1606326, _1606328, _1606330, _1606332, _1606334] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606326, tc_fun(_1606328, tc_HOL_Obool)), _1606330), hAPP(hAPP(c_COMBS(_1606326, tc_fun(_1606328, tc_HOL_Obool), tc_fun(_1606328, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1606328, tc_HOL_Obool), tc_fun(tc_fun(_1606328, tc_HOL_Obool), tc_fun(_1606328, tc_HOL_Obool)), _1606326), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606328, tc_HOL_Obool))), _1606332)), _1606334)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606328, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1606328, tc_HOL_Obool), hAPP(c_Set_Oimage(_1606326, tc_fun(_1606328, tc_HOL_Obool), _1606332), _1606330))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1606328, tc_HOL_Obool), hAPP(c_Set_Oimage(_1606326, tc_fun(_1606328, tc_HOL_Obool), _1606334), _1606330))))], (27152 ^ _780119) ^ [_1280316, _1280318, _1280320, _1280322, _1280324, _1280326] : [-(hBOOL(hAPP(hAPP(c_member(_1280316), _1280318), _1280320))), -(hAPP(c_Fun_Ooverride__on(_1280316, _1280322, _1280324, _1280326, _1280320), _1280318) = hAPP(_1280324, _1280318))], (17668 ^ _780119) ^ [_1101286, _1101288, _1101290] : [-(hBOOL(hAPP(_1101286, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1101288), _1101290)))), 17671 ^ _780119 : [(17674 ^ _780119) ^ [] : [hBOOL(hAPP(_1101286, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17672 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101288), _1101290)))]], 17676 ^ _780119 : [(17679 ^ _780119) ^ [] : [hBOOL(hAPP(_1101286, 17675 ^ [_1101286, _1101288, _1101290]))], (17677 ^ _780119) ^ [] : [-(_1101288 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101290), 17675 ^ [_1101286, _1101288, _1101290]))]]], (6975 ^ _780119) ^ [_895323, _895325, _895327] : [class_Orderings_Oorder(_895323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895323), _895325), _895327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895323), _895327), _895325)), -(_895325 = _895327)], (49636 ^ _780119) ^ [_1786545, _1786547, _1786549] : [-(c_List_Olist__ex(_1786545, _1786547, _1786549)), 49637 ^ _780119 : [(49638 ^ _780119) ^ [_1786610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1786610), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786545)), _1786549))), hBOOL(hAPP(_1786547, hAPP(hAPP(c_List_Onth(_1786545), _1786549), _1786610)))]]], (12005 ^ _780119) ^ [_996453, _996455, _996457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996453), _996455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996453), _996457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996457), _996455)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996457), _996453))))], (51625 ^ _780119) ^ [_1821168, _1821170] : [hBOOL(hAPP(hAPP(c_fdisj, _1821168), _1821170)), -(hBOOL(_1821168)), -(hBOOL(_1821170))], (2588 ^ _780119) ^ [_818432, _818434, _818436, _818438] : [-(c_Wellfounded_Omin__ext(_818438, _818434) = c_Wellfounded_Omin__ext(_818436, _818432)), _818438 = _818436, _818434 = _818432], (38282 ^ _780119) ^ [_1519960, _1519962, _1519964, _1519966, _1519968] : [c_Relation_Orefl__on(_1519960, _1519962, _1519964), c_Relation_Orefl__on(_1519960, _1519966, _1519968), -(c_Relation_Orefl__on(_1519960, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1519960, tc_HOL_Obool)), _1519962), _1519966), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1519960, _1519960), tc_HOL_Obool)), _1519964), _1519968)))], (25456 ^ _780119) ^ [_1245714, _1245716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245716)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1245714)), hAPP(c_Int_Onat, _1245716)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1245714, _1245716)))], (31489 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (42749 ^ _780119) ^ [_1626744, _1626746, _1626748, _1626750, _1626752] : [hAPP(hAPP(c_List_Omap(_1626744, _1626746), _1626748), _1626750) = hAPP(hAPP(c_List_Omap(_1626744, _1626746), _1626752), _1626750), 42752 ^ _780119 : [(42753 ^ _780119) ^ [_1626867] : [hBOOL(hAPP(hAPP(c_member(_1626744), _1626867), hAPP(c_List_Oset(_1626744), _1626750))), -(hAPP(_1626748, _1626867) = hAPP(_1626752, _1626867))]]], (14314 ^ _780119) ^ [_1041882, _1041884, _1041886, _1041888, _1041890] : [class_Groups_Ocomm__monoid__mult(_1041882), hBOOL(hAPP(c_Finite__Set_Ofinite(_1041884), _1041886)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1041884), _1041888)), 14328 ^ _780119 : [(14331 ^ _780119) ^ [] : [hAPP(_1041890, 14327 ^ [_1041882, _1041884, _1041886, _1041888, _1041890]) = c_Groups_Oone__class_Oone(_1041882)], (14329 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1041884), 14327 ^ [_1041882, _1041884, _1041886, _1041888, _1041890]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1041884, tc_HOL_Obool)), _1041886), _1041888))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1041884, _1041882), _1041890), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1041884, tc_HOL_Obool)), _1041886), _1041888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041882), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1041884, _1041882), _1041890), _1041886)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1041884, _1041882), _1041890), _1041888)))], (22051 ^ _780119) ^ [_1182805, _1182807, _1182809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182805), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22054 ^ _780119 : [(22055 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1182807, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182809), _1182805)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182809, _1182805))), 22058 ^ _780119 : [(22059 ^ _780119) ^ [_1183015, _1183017] : [-(hBOOL(hAPP(hAPP(_1182807, _1183017), _1183015))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182805), _1183015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1183015), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1182809 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182805), _1183017)), _1183015)]]], (22073 ^ _780119) ^ [] : [22076 ^ _780119 : [(22077 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182805), 22075 ^ [_1182805, _1182807, _1182809])))], (22079 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 22075 ^ [_1182805, _1182807, _1182809]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22083 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1182807, 22074 ^ [_1182805, _1182807, _1182809]), 22075 ^ [_1182805, _1182807, _1182809]))], (22081 ^ _780119) ^ [] : [-(_1182809 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182805), 22074 ^ [_1182805, _1182807, _1182809])), 22075 ^ [_1182805, _1182807, _1182809]))]], -(hBOOL(hAPP(hAPP(_1182807, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182809), _1182805)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182809, _1182805))))]]], (11475 ^ _780119) ^ [_985755, _985757, _985759, _985761] : [class_Rings_Ocomm__semiring__1(_985755), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985755), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985755), _985757), _985759)), _985761) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985755), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985755), _985757), _985761)), _985759))], (16386 ^ _780119) ^ [_1078790] : [class_Rings_Olinordered__semidom(_1078790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078790), c_Groups_Oone__class_Oone(_1078790)), c_Groups_Ozero__class_Ozero(_1078790)))], (33539 ^ _780119) ^ [] : [-(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)))))], (7338 ^ _780119) ^ [_903186, _903188, _903190, _903192] : [class_Lattices_Olattice(_903186), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903186), _903188), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903186), _903190), _903192)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903186), _903190), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903186), _903188), _903192)))], (39262 ^ _780119) ^ [_1542864, _1542866, _1542868, _1542870, _1542872, _1542874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1542864, tc_HOL_Obool)), _1542866), _1542868)), 39268 ^ _780119 : [(39271 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1542870, tc_HOL_Obool)), hAPP(_1542872, 39267 ^ [_1542864, _1542866, _1542868, _1542870, _1542872, _1542874])), hAPP(_1542874, 39267 ^ [_1542864, _1542866, _1542868, _1542870, _1542872, _1542874])))], (39269 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542864), 39267 ^ [_1542864, _1542866, _1542868, _1542870, _1542872, _1542874]), _1542866)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542864, _1542870), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1542864, _1542870), _1542866), _1542872)), hAPP(hAPP(c_Product__Type_OSigma(_1542864, _1542870), _1542868), _1542874))))], (44748 ^ _780119) ^ [_1676431] : [-(hAPP(c_List_Oset(_1676431), c_List_Olist_ONil(_1676431)) = c_Orderings_Obot__class_Obot(tc_fun(_1676431, tc_HOL_Obool)))], (51635 ^ _780119) ^ [_1821262, _1821264] : [-(hBOOL(_1821262)), -(hBOOL(hAPP(hAPP(c_fimplies, _1821262), _1821264)))], (29633 ^ _780119) ^ [_1331044, _1331046, _1331048, _1331050, _1331052, _1331054] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331044, tc_fun(_1331046, tc_HOL_Obool)), _1331048), hAPP(hAPP(c_COMBC(_1331044, tc_fun(_1331050, tc_fun(_1331046, tc_HOL_Obool)), tc_fun(_1331046, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1331050, tc_HOL_Obool), tc_fun(tc_fun(_1331050, tc_fun(_1331046, tc_HOL_Obool)), tc_fun(_1331046, tc_HOL_Obool)), _1331044), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331050, tc_fun(_1331046, tc_HOL_Obool))), _1331052)), _1331054)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331050, tc_fun(_1331046, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331044, tc_fun(_1331050, tc_HOL_Obool)), _1331048), _1331052)), _1331054))], (50340 ^ _780119) ^ [_1800912, _1800914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1800912), _1800914)), -(c_Lazy__Sequence_Osmall__lazy_H(_1800912, _1800914) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (45396 ^ _780119) ^ [_1691522, _1691524, _1691526, _1691528, _1691530] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691522), tc_List_Olist(_1691522))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691522), tc_List_Olist(_1691522)), _1691524), _1691526)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1691522), c_List_Olistrel1(_1691522, _1691528)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691522), tc_List_Olist(_1691522))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691522), tc_List_Olist(_1691522)), hAPP(hAPP(c_List_Olist_OCons(_1691522), _1691530), _1691524)), hAPP(hAPP(c_List_Olist_OCons(_1691522), _1691530), _1691526))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1691522), c_List_Olistrel1(_1691522, _1691528)))))], (9982 ^ _780119) ^ [_953975, _953977, _953979, _953981] : [class_Lattices_Osemilattice__inf(_953975), 9985 ^ _780119 : [(9994 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953975), _953977), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_953975), _953979), _953981)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953975), _953977), _953979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953975), _953977), _953981))], (9986 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953975), _953977), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_953975), _953979), _953981))), 9989 ^ _780119 : [(9992 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953975), _953977), _953981)))], (9990 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953975), _953977), _953979)))]]]]], (45440 ^ _780119) ^ [_1692977, _1692979, _1692981, _1692983] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692977), tc_List_Olist(_1692977))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692977), tc_List_Olist(_1692977)), _1692979), _1692981)), c_List_Olistrel1(_1692977, hAPP(c_Relation_Oconverse(_1692977, _1692977), _1692983)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692977), tc_List_Olist(_1692977))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692977), tc_List_Olist(_1692977)), _1692979), _1692981)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1692977), tc_List_Olist(_1692977)), c_List_Olistrel1(_1692977, _1692983)))))], (17768 ^ _780119) ^ [_1103173, _1103175, _1103177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1103173)), 17771 ^ _780119 : [(17778 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1103175), _1103177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103173), _1103175)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103173), _1103177))))], (17772 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103173), _1103175)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103173), _1103177))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1103175), _1103177)))]]], (46923 ^ _780119) ^ [_1726470, _1726472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726470), _1726472)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1726470, _1726472)) = _1726470)], (39541 ^ _780119) ^ [_1549642, _1549644] : [-(c_Transitive__Closure_Otrancl(_1549642, _1549644) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1549642, _1549642), tc_HOL_Obool)), _1549644), hAPP(hAPP(c_Relation_Orel__comp(_1549642, _1549642, _1549642), c_Transitive__Closure_Otrancl(_1549642, _1549644)), _1549644)))], (38679 ^ _780119) ^ [_1529405, _1529407, _1529409, _1529411, _1529413, _1529415] : [-(hAPP(hAPP(c_Fun_Ocomp(_1529405, _1529407, _1529409, _1529411), _1529413), _1529415) = hAPP(_1529411, hAPP(_1529413, _1529415)))], (47939 ^ _780119) ^ [_1748556, _1748558] : [_1748558 = c_List_Olist_ONil(_1748556), -(c_List_Oremdups(_1748556, _1748558) = c_List_Olist_ONil(_1748556))], (34905 ^ _780119) ^ [_1435529, _1435531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1435529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435531), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1435529), _1435531) = 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), _1435529), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1435531)))))], (11641 ^ _780119) ^ [_989500, _989502, _989504, _989506, _989508] : [class_Groups_Ocomm__monoid__mult(_989500), hBOOL(hAPP(c_Finite__Set_Ofinite(_989502), _989504)), hBOOL(hAPP(c_Finite__Set_Ofinite(_989502), _989506)), 11655 ^ _780119 : [(11658 ^ _780119) ^ [] : [hAPP(_989508, 11654 ^ [_989500, _989502, _989504, _989506, _989508]) = c_Groups_Oone__class_Oone(_989500)], (11656 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_989502), 11654 ^ [_989500, _989502, _989504, _989506, _989508]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989502, tc_HOL_Obool)), _989504), _989506))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_989500, _989502, c_Groups_Otimes__class_Otimes(_989500)), _989508), c_Groups_Oone__class_Oone(_989500)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_989502, tc_HOL_Obool)), _989504), _989506)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989500), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_989500, _989502, c_Groups_Otimes__class_Otimes(_989500)), _989508), c_Groups_Oone__class_Oone(_989500)), _989504)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_989500, _989502, c_Groups_Otimes__class_Otimes(_989500)), _989508), c_Groups_Oone__class_Oone(_989500)), _989506)))], (35474 ^ _780119) ^ [_1449873, _1449875] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1449873, _1449873)), hAPP(hAPP(c_Product__Type_OPair(_1449873, _1449873), 35475 ^ [_1449873, _1449875]), 35475 ^ [_1449873, _1449875])), _1449875))), -(c_Relation_Oirrefl(_1449873, _1449875))], (51095 ^ _780119) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11003 ^ _780119) ^ [_975448, _975450, _975452, _975454, _975456] : [-(c_Map_Orestrict__map(_975448, _975450, c_Map_Orestrict__map(_975448, _975450, _975452, _975454), _975456) = c_Map_Orestrict__map(_975448, _975450, _975452, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975448, tc_HOL_Obool)), _975454), _975456)))], (36277 ^ _780119) ^ [_1468107, _1468109, _1468111, _1468113, _1468115] : [c_Fun_Oinj__on(_1468107, _1468109, _1468111, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468107, tc_HOL_Obool)), _1468113), _1468115)), 36280 ^ _780119 : [(36287 ^ _780119) ^ [] : [_1468113 = _1468115, -(hAPP(c_Set_Oimage(_1468107, _1468109, _1468111), _1468113) = hAPP(c_Set_Oimage(_1468107, _1468109, _1468111), _1468115))], (36281 ^ _780119) ^ [] : [hAPP(c_Set_Oimage(_1468107, _1468109, _1468111), _1468113) = hAPP(c_Set_Oimage(_1468107, _1468109, _1468111), _1468115), -(_1468113 = _1468115)]]], (47983 ^ _780119) ^ [_1749290, _1749292] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749290)), c_List_Oremdups(_1749290, _1749292)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749290)), _1749292), -(c_List_Oremdups(_1749290, _1749292) = _1749292)], (37417 ^ _780119) ^ [_1495545, _1495547] : [c_FunDef_Oreduction__pair(_1495545, _1495547), 37420 ^ _780119 : [(37423 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1495545, _1495545), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1495545, _1495545, _1495545), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1495545, _1495545), tc_HOL_Obool), tc_fun(tc_prod(_1495545, _1495545), tc_HOL_Obool)), _1495547)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1495545, _1495545), tc_HOL_Obool), tc_fun(tc_prod(_1495545, _1495545), tc_HOL_Obool)), _1495547))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1495545, _1495545), tc_HOL_Obool), tc_fun(tc_prod(_1495545, _1495545), tc_HOL_Obool)), _1495547))))], (37421 ^ _780119) ^ [] : [-(c_Wellfounded_Owf(_1495545, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1495545, _1495545), tc_HOL_Obool), tc_fun(tc_prod(_1495545, _1495545), tc_HOL_Obool)), _1495547)))]]], (34643 ^ _780119) ^ [_1430305, _1430307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430305), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430307), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1430305, _1430307) = 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), _1430305), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1430307)))))], (44222 ^ _780119) ^ [_1665996, _1665998, _1666000, _1666002] : [hBOOL(hAPP(hAPP(c_member(_1665996), _1665998), hAPP(c_List_Oset(_1665996), hAPP(hAPP(c_List_Otake(_1665996), _1666000), _1666002)))), -(hBOOL(hAPP(hAPP(c_member(_1665996), _1665998), hAPP(c_List_Oset(_1665996), _1666002))))], (40996 ^ _780119) ^ [_1583865, _1583867, _1583869, _1583871, _1583873, _1583875] : [c_Finite__Set_Ofun__left__comm(_1583865, _1583867, _1583869), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583865), _1583871)), -(hBOOL(hAPP(hAPP(c_member(_1583865), _1583873), _1583871))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1583865, _1583867, _1583869), _1583875), hAPP(hAPP(c_Set_Oinsert(_1583865), _1583873), _1583871)) = hAPP(hAPP(c_Finite__Set_Ofold(_1583865, _1583867, _1583869), hAPP(hAPP(_1583869, _1583873), _1583875)), _1583871))], (9882 ^ _780119) ^ [_952030, _952032, _952034, _952036, _952038, _952040] : [class_Groups_Ocomm__monoid__add(_952030), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_952032, _952030), hAPP(hAPP(c_COMBC(_952032, tc_fun(_952034, tc_HOL_Obool), _952030), hAPP(hAPP(c_COMBB(tc_fun(_952034, _952030), tc_fun(tc_fun(_952034, tc_HOL_Obool), _952030), _952032), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_952034, _952030)), _952036)), _952038)), _952040) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_952034, _952030), hAPP(hAPP(c_COMBC(_952034, tc_fun(_952032, tc_HOL_Obool), _952030), hAPP(hAPP(c_COMBB(tc_fun(_952032, _952030), tc_fun(tc_fun(_952032, tc_HOL_Obool), _952030), _952034), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_952032, _952030)), hAPP(c_COMBC(_952032, _952034, _952030), _952036))), _952040)), _952038))], (19056 ^ _780119) ^ [_1127270, _1127272] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127270), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1127272)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1127270)), _1127272))], (19496 ^ _780119) ^ [_1134541, _1134543, _1134545] : [-(hBOOL(hAPP(_1134541, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1134543), _1134545)))), 19499 ^ _780119 : [(19502 ^ _780119) ^ [] : [hBOOL(hAPP(_1134541, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (19500 ^ _780119) ^ [] : [-(_1134545 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 19505 ^ _780119 : [(19514 ^ _780119) ^ [] : [-(_1134543 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1134545), 19507 ^ [_1134541, _1134543, _1134545])), 19508 ^ [_1134541, _1134543, _1134545]))], (19512 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 19508 ^ [_1134541, _1134543, _1134545]), _1134545)))], (19510 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19508 ^ [_1134541, _1134543, _1134545])))], (19506 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134545)))], (19516 ^ _780119) ^ [] : [hBOOL(hAPP(_1134541, 19507 ^ [_1134541, _1134543, _1134545]))]], 19517 ^ _780119 : [(19526 ^ _780119) ^ [] : [-(_1134543 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1134545), 19519 ^ [_1134541, _1134543, _1134545])), 19520 ^ [_1134541, _1134543, _1134545]))], (19524 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 19520 ^ [_1134541, _1134543, _1134545]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19522 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1134545), 19520 ^ [_1134541, _1134543, _1134545])))], (19518 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1134545), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19528 ^ _780119) ^ [] : [hBOOL(hAPP(_1134541, 19519 ^ [_1134541, _1134543, _1134545]))]]], (46461 ^ _780119) ^ [_1716683, _1716685, _1716687] : [-(_1716683 = c_List_Olist_ONil(_1716685)), -(c_List_Obutlast(_1716685, hAPP(hAPP(c_List_Oappend(_1716685), _1716687), _1716683)) = hAPP(hAPP(c_List_Oappend(_1716685), _1716687), c_List_Obutlast(_1716685, _1716683)))], (11181 ^ _780119) ^ [_979196, _979198, _979200, _979202, _979204, _979206, _979208] : [c_Big__Operators_Ocomm__monoid__big(_979196, _979198, _979200, _979202, _979204), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979198), _979206))), -(hAPP(hAPP(_979204, _979208), _979206) = _979202)], (6270 ^ _780119) ^ [_880644, _880646] : [_880646 = c_Orderings_Obot__class_Obot(tc_fun(_880644, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880644, tc_HOL_Obool)), _880646), c_Orderings_Obot__class_Obot(tc_fun(_880644, tc_HOL_Obool)))))], (22292 ^ _780119) ^ [_1186802, _1186804, _1186806] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1186802), _1186804)), _1186806) = 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), _1186802), _1186806)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1186804), _1186806))), 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, _1186802, _1186806)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186804, _1186806))), _1186806)))], (39753 ^ _780119) ^ [_1555092, _1555094, _1555096] : [_1555094 = _1555096, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1555092, _1555092)), hAPP(hAPP(c_Product__Type_OPair(_1555092, _1555092), _1555094), _1555096)), c_Relation_OId(_1555092))))], (28572 ^ _780119) ^ [_1307914, _1307916, _1307918] : [class_Orderings_Olinorder(_1307914), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307914), _1307916)), -(hBOOL(hAPP(hAPP(c_member(_1307914), _1307918), _1307916))), -(_1307916 = c_Orderings_Obot__class_Obot(tc_fun(_1307914, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1307914, hAPP(hAPP(c_Set_Oinsert(_1307914), _1307918), _1307916)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1307914), _1307918), c_Big__Operators_Olinorder__class_OMin(_1307914, _1307916)))], (48317 ^ _780119) ^ [_1757149] : [class_Enum_Oenum(_1757149), -(c_Enum_Oenum__class_Oenum(tc_Option_Ooption(_1757149)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(_1757149)), c_Option_Ooption_ONone(_1757149)), hAPP(hAPP(c_List_Omap(_1757149, tc_Option_Ooption(_1757149)), c_Option_Ooption_OSome(_1757149)), c_Enum_Oenum__class_Oenum(_1757149))))], (47915 ^ _780119) ^ [_1748148, _1748150] : [-(hBOOL(hAPP(c_List_Odistinct(_1748148), c_List_Oremdups(_1748148, _1748150))))], (36768 ^ _780119) ^ [_1478984, _1478986, _1478988, _1478990, _1478992] : [hBOOL(hAPP(hAPP(c_member(_1478984), _1478986), hAPP(c_Set_Ovimage(_1478984, _1478988, _1478990), hAPP(hAPP(c_Set_Oinsert(_1478988), _1478992), c_Orderings_Obot__class_Obot(tc_fun(_1478988, tc_HOL_Obool)))))), -(hAPP(_1478990, _1478986) = _1478992)], (15010 ^ _780119) ^ [_1055220, _1055222, _1055224] : [class_Rings_Oring__no__zero__divisors(_1055220), 15013 ^ _780119 : [(15014 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055220), _1055222), _1055224) = c_Groups_Ozero__class_Ozero(_1055220), -(_1055222 = c_Groups_Ozero__class_Ozero(_1055220)), -(_1055224 = c_Groups_Ozero__class_Ozero(_1055220))], (15024 ^ _780119) ^ [] : [15025 ^ _780119 : [(15028 ^ _780119) ^ [] : [_1055224 = c_Groups_Ozero__class_Ozero(_1055220)], (15026 ^ _780119) ^ [] : [_1055222 = c_Groups_Ozero__class_Ozero(_1055220)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055220), _1055222), _1055224) = c_Groups_Ozero__class_Ozero(_1055220))]]], (13160 ^ _780119) ^ [_1019904] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1019904), hAPP(c_Nat_OSuc, _1019904))))], (26849 ^ _780119) ^ [_1271113, _1271115, _1271117, _1271119, _1271121] : [class_Groups_Oordered__ab__group__add__abs(_1271113), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271113), hAPP(c_Groups_Oabs__class_Oabs(_1271113), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1271113), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271113), _1271115), _1271117)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271113), _1271119), _1271121)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271113), hAPP(c_Groups_Oabs__class_Oabs(_1271113), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1271113), _1271115), _1271119))), hAPP(c_Groups_Oabs__class_Oabs(_1271113), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1271113), _1271117), _1271121))))))], (24627 ^ _780119) ^ [_1231311, _1231313, _1231315] : [class_Orderings_Oorder(_1231311), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231311), _1231313), _1231315)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1231311, _1231315, _1231313) = c_Orderings_Obot__class_Obot(tc_fun(_1231311, tc_HOL_Obool)))], (23829 ^ _780119) ^ [_1215865, _1215867, _1215869, _1215871, _1215873] : [class_Groups_Ocomm__monoid__add(_1215865), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1215867), _1215869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1215869), _1215871)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215865), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215865), _1215873), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1215867), _1215869))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215865), _1215873), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1215869), _1215871))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215865), _1215873), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1215867), _1215871)))], (51151 ^ _780119) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (7260 ^ _780119) ^ [_901682, _901684, _901686, _901688, _901690, _901692] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_901682, _901684, _901686, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_901682), _901688), _901690), _901692)) = hAPP(hAPP(hAPP(_901686, _901688), _901690), _901692))], (45235 ^ _780119) ^ [_1687107, _1687109, _1687111, _1687113] : [-(hAPP(hAPP(c_List_Onth(_1687107), hAPP(hAPP(c_List_Oappend(_1687107), _1687109), hAPP(hAPP(c_List_Olist_OCons(_1687107), _1687111), _1687113))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687107)), _1687109)) = _1687111)], (25722 ^ _780119) ^ [_1249687, _1249689] : [class_Int_Oring__char__0(_1249687), 25725 ^ _780119 : [(25732 ^ _780119) ^ [] : [_1249689 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1249687) = hAPP(c_Int_Oring__1__class_Oof__int(_1249687), _1249689))], (25726 ^ _780119) ^ [] : [c_Groups_Ozero__class_Ozero(_1249687) = hAPP(c_Int_Oring__1__class_Oof__int(_1249687), _1249689), -(_1249689 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (2650 ^ _780119) ^ [_819371, _819373, _819375, _819377] : [-(c_Nitpick_Onorm__frac(_819377, _819373) = c_Nitpick_Onorm__frac(_819375, _819371)), _819377 = _819375, _819373 = _819371], (26487 ^ _780119) ^ [_1263475] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1263475, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1263475), hAPP(c_COMBK(tc_HOL_Obool, _1263475), c_fFalse)))], (37223 ^ _780119) ^ [_1491734, _1491736] : [c_Wellfounded_Owf(_1491734, _1491736), -(c_Wellfounded_Owf(_1491734, hAPP(hAPP(c_Relation_Orel__comp(_1491734, _1491734, _1491734), _1491736), _1491736)))], (46664 ^ _780119) ^ [_1720745, _1720747] : [-(hAPP(c_List_Ofilter(_1720745, _1720747), c_List_Olist_ONil(_1720745)) = c_List_Olist_ONil(_1720745))], (35487 ^ _780119) ^ [_1450086] : [-(hAPP(c_Relation_OField(_1450086), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1450086, _1450086), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1450086, tc_HOL_Obool)))], (34839 ^ _780119) ^ [_1434149, _1434151, _1434153, _1434155, _1434157] : [hAPP(c_Product__Type_Ofst(_1434149, _1434151), hAPP(hAPP(c_Product__Type_OPair(_1434149, _1434151), _1434153), _1434155)) = _1434157, -(_1434153 = _1434157)], (26965 ^ _780119) ^ [_1273912, _1273914, _1273916, _1273918] : [_1273912 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1273914, _1273916), 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)), _1273918))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1273914), _1273912)))], (37575 ^ _780119) ^ [_1499463, _1499465, _1499467, _1499469] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1499463, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1499465, _1499463), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1499465, _1499463), tc_HOL_Obool)), _1499467), _1499469))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499463, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1499465, _1499463), _1499467)), hAPP(c_Relation_ORange(_1499465, _1499463), _1499469)))))], (11804 ^ _780119) ^ [_992554, _992556, _992558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992554), _992556)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992556), _992558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992554), _992558)))], (51547 ^ _780119) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (10805 ^ _780119) ^ [_971708, _971710, _971712, _971714] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_971708), 10808 ^ _780119 : [(10815 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971708), _971712), _971714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971708), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971708), _971710), _971712)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971708), _971710), _971714))))], (10809 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971708), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971708), _971710), _971712)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971708), _971710), _971714))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971708), _971712), _971714)))]]], (12405 ^ _780119) ^ [_1004232, _1004234] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004232), _1004234) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1004232 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1004234 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (41465 ^ _780119) ^ [_1597033, _1597035, _1597037, _1597039, _1597041] : [-(_1597033 = c_Orderings_Obot__class_Obot(tc_fun(_1597035, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1597037, tc_HOL_Obool)), _1597039), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1597035, tc_fun(_1597037, tc_HOL_Obool)), _1597033), _1597041)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597035, tc_fun(_1597037, tc_HOL_Obool)), _1597033), hAPP(hAPP(c_COMBB(tc_fun(_1597037, tc_HOL_Obool), tc_fun(_1597037, tc_HOL_Obool), _1597035), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1597037, tc_HOL_Obool)), _1597039)), _1597041)))], (41737 ^ _780119) ^ [_1603246, _1603248, _1603250] : [class_Complete__Lattice_Ocomplete__lattice(_1603246), class_Orderings_Olinorder(_1603246), 41744 ^ _780119 : [(41754 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1603246), _1603248), c_Complete__Lattice_OSup__class_OSup(_1603246, _1603250)))), 41755 ^ _780119 : [(41756 ^ _780119) ^ [_1603552] : [hBOOL(hAPP(hAPP(c_member(_1603246), _1603552), _1603250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1603246), _1603248), _1603552))]]], (41745 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1603246), _1603248), c_Complete__Lattice_OSup__class_OSup(_1603246, _1603250))), 41749 ^ _780119 : [(41752 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1603246), _1603248), 41748 ^ [_1603246, _1603248, _1603250])))], (41750 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1603246), 41748 ^ [_1603246, _1603248, _1603250]), _1603250)))]]]]], (50112 ^ _780119) ^ [_1795822, _1795824] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1795822)), _1795824) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1795822, tc_Lazy__Sequence_Olazy__sequence(_1795822)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1795822, tc_Lazy__Sequence_Olazy__sequence(_1795822), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1795822), tc_Nat_Onat), _1795822), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1795822), 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(_1795822)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1795822)))), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), hAPP(c_Lazy__Sequence_Oyield(_1795822), _1795824)))], (13996 ^ _780119) ^ [_1034764, _1034766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1034764), _1034766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034764), hAPP(c_Nat_OSuc, _1034766))))], (18694 ^ _780119) ^ [_1121013, _1121015, _1121017] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121013), _1121015)), _1121017) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121013), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121015), _1121017)))], (42592 ^ _780119) ^ [_1622926, _1622928, _1622930] : [c_Fun_Oinj__on(tc_List_Olist(_1622926), tc_List_Olist(_1622928), hAPP(c_List_Omap(_1622926, _1622928), _1622930), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1622926), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1622926, _1622928, _1622930, c_Orderings_Otop__class_Otop(tc_fun(_1622926, tc_HOL_Obool))))], (38028 ^ _780119) ^ [_1513856, _1513858] : [-(c_Product__Type_Oapfst(_1513856, _1513856, _1513858, c_Fun_Oid(_1513856)) = c_Fun_Oid(tc_prod(_1513856, _1513858)))], (702 ^ _780119) ^ [_790874, _790876, _790878, _790880, _790882, _790884] : [-(c_Finite__Set_Ofun__left__comm__idem(_790882, _790878, _790874)), c_Finite__Set_Ofun__left__comm__idem(_790884, _790880, _790876), _790884 = _790882, _790880 = _790878, _790876 = _790874], (49066 ^ _780119) ^ [_1773013, _1773015, _1773017, _1773019, _1773021] : [c_List_Olist__all2(_1773013, _1773015, _1773017, hAPP(c_List_Orev(_1773013), _1773019), _1773021), -(c_List_Olist__all2(_1773013, _1773015, _1773017, _1773019, hAPP(c_List_Orev(_1773015), _1773021)))], (41274 ^ _780119) ^ [_1590806, _1590808, _1590810, _1590812] : [c_Orderings_Otop__class_Otop(tc_fun(_1590806, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590808, tc_fun(_1590806, tc_HOL_Obool)), _1590810), _1590812), 41277 ^ _780119 : [(41278 ^ _780119) ^ [_1590922] : [hBOOL(hAPP(hAPP(c_member(_1590808), _1590922), _1590810)), -(hAPP(_1590812, _1590922) = c_Orderings_Otop__class_Otop(tc_fun(_1590806, tc_HOL_Obool)))]]], (3462 ^ _780119) ^ [_832153, _832155, _832157, _832159] : [-(c_List_Olistset(_832159, _832155) = c_List_Olistset(_832157, _832153)), _832159 = _832157, _832155 = _832153], (4924 ^ _780119) ^ [_855292, _855294, _855296, _855298] : [-(c_Wellfounded_Oaccp(_855298, _855294) = c_Wellfounded_Oaccp(_855296, _855292)), _855298 = _855296, _855294 = _855292], (43507 ^ _780119) ^ [_1647189, _1647191, _1647193, _1647195, _1647197] : [-(hAPP(hAPP(c_List_Olist_OCons(_1647189), _1647191), _1647193) = hAPP(hAPP(c_List_Olist_OCons(_1647189), _1647195), _1647197)), 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_1180845)]]], (21959 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180519), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 21962 ^ _780119 : [(21963 ^ _780119) ^ [_1181137, _1181139] : [-(hBOOL(hAPP(_1180515, _1181137))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180519), _1181137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181137), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1180517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180519), _1181139)), _1181137)]]], (21935 ^ _780119) ^ [] : [_1180519 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1180515, _1180517)))]]], (35434 ^ _780119) ^ [] : [-(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))))))], (12970 ^ _780119) ^ [_1015528, _1015530, _1015532] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1015528), _1015530)), -(hAPP(c_Finite__Set_Ocard(_1015528), hAPP(hAPP(c_Set_Oinsert(_1015528), _1015532), _1015530)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1015528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1015528, tc_HOL_Obool)), _1015530), hAPP(hAPP(c_Set_Oinsert(_1015528), _1015532), c_Orderings_Obot__class_Obot(tc_fun(_1015528, tc_HOL_Obool)))))))], (18770 ^ _780119) ^ [_1122445, _1122447] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1122445), _1122447) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122445), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1122447)))], (14727 ^ _780119) ^ [_1050510, _1050512, _1050514, _1050516, _1050518, _1050520] : [class_Rings_Olinordered__semiring__1__strict(_1050510), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050510), _1050512), _1050514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050510), _1050516), _1050514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050510), c_Groups_Ozero__class_Ozero(_1050510)), _1050518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050510), c_Groups_Ozero__class_Ozero(_1050510)), _1050520)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050510), _1050518), _1050520) = c_Groups_Oone__class_Oone(_1050510), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050510), _1050518), _1050512)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050510), _1050520), _1050516))), _1050514)))], (24015 ^ _780119) ^ [_1219465, _1219467, _1219469, _1219471] : [class_Groups_Ocomm__monoid__add(_1219465), 24018 ^ _780119 : [(24025 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1219467), _1219469))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219465), _1219471), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1219469), hAPP(c_Nat_OSuc, _1219467))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219465), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219465), _1219471), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1219469), _1219467))), hAPP(_1219471, _1219467)))], (24019 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1219467), _1219469)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219465), _1219471), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1219469), hAPP(c_Nat_OSuc, _1219467))) = c_Groups_Ozero__class_Ozero(_1219465))]]], (35524 ^ _780119) ^ [_1451133, _1451135, _1451137] : [_1451135 = c_Orderings_Obot__class_Obot(tc_fun(_1451133, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1451133, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1451133), _1451135), _1451137))], (39365 ^ _780119) ^ [_1545572, _1545574, _1545576, _1545578, _1545580, _1545582, _1545584] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1545572, _1545574, _1545576, _1545578), _1545580), _1545582), _1545584) = hAPP(hAPP(_1545582, hAPP(c_Product__Type_Ofst(_1545574, _1545576), hAPP(_1545580, _1545584))), hAPP(c_Product__Type_Osnd(_1545574, _1545576), hAPP(_1545580, _1545584))))], (35357 ^ _780119) ^ [_1446431, _1446433, _1446435] : [-(hAPP(c_Relation_OImage(_1446431, _1446433, _1446435), c_Orderings_Obot__class_Obot(tc_fun(_1446431, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1446433, tc_HOL_Obool)))], (21636 ^ _780119) ^ [_1175077, _1175079, _1175081, _1175083] : [class_Divides_Osemiring__div(_1175077), -(c_Divides_Odiv__class_Omod(_1175077, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1175077), _1175079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175077), _1175081), _1175083)), _1175083) = c_Divides_Odiv__class_Omod(_1175077, _1175079, _1175083))], (33213 ^ _780119) ^ [_1399548, _1399550] : [class_Int_Onumber__ring(_1399548), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1399548), hAPP(c_Int_Onumber__class_Onumber__of(_1399548), 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)))), _1399550)) = c_Groups_Oone__class_Oone(_1399548))], (29564 ^ _780119) ^ [] : [-(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)))], (4456 ^ _780119) ^ [_847522, _847524, _847526, _847528, _847530, _847532, _847534, _847536, _847538, _847540, _847542, _847544, _847546, _847548] : [-(c_New__Random__Sequence_Opos__decr__bind(_847548, _847544, _847540, _847536, _847532, _847528, _847524) = c_New__Random__Sequence_Opos__decr__bind(_847546, _847542, _847538, _847534, _847530, _847526, _847522)), _847548 = _847546, _847544 = _847542, _847540 = _847538, _847536 = _847534, _847532 = _847530, _847528 = _847526, _847524 = _847522], (11927 ^ _780119) ^ [_994856, _994858] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994856), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994856), _994858))))], (20946 ^ _780119) ^ [_1161087, _1161089, _1161091, _1161093] : [class_Fields_Olinordered__field(_1161087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161087), _1161089), _1161091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161087), c_Groups_Ozero__class_Ozero(_1161087)), _1161093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161087), c_Groups_Ozero__class_Ozero(_1161087)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161087), _1161091), _1161089))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161087), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161087), _1161093), _1161091)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161087), _1161093), _1161089))))], (47327 ^ _780119) ^ [_1733662, _1733664] : [class_Orderings_Olinorder(_1733662), 47330 ^ _780119 : [(47331 ^ _780119) ^ [] : [c_List_Olinorder__class_Osorted(_1733662, _1733664), 47334 ^ _780119 : [(47335 ^ _780119) ^ [_1733833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1733833), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733662)), _1733664))), 47338 ^ _780119 : [(47339 ^ _780119) ^ [_1733950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1733950), _1733833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1733662), hAPP(hAPP(c_List_Onth(_1733662), _1733664), _1733950)), hAPP(hAPP(c_List_Onth(_1733662), _1733664), _1733833))))]]]]], (47345 ^ _780119) ^ [] : [47347 ^ _780119 : [(47351 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47349 ^ [_1733662, _1733664]), 47346 ^ [_1733662, _1733664])))], (47353 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1733662), hAPP(hAPP(c_List_Onth(_1733662), _1733664), 47349 ^ [_1733662, _1733664])), hAPP(hAPP(c_List_Onth(_1733662), _1733664), 47346 ^ [_1733662, _1733664])))], (47348 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47346 ^ [_1733662, _1733664]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733662)), _1733664))))]], -(c_List_Olinorder__class_Osorted(_1733662, _1733664))]]], (45982 ^ _780119) ^ [_1706116, _1706118, _1706120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1706116), _1706118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1706116), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1706118), _1706120))))], (46636 ^ _780119) ^ [_1720213, _1720215, _1720217] : [46638 ^ _780119 : [(46641 ^ _780119) ^ [] : [hBOOL(hAPP(_1720215, 46637 ^ [_1720213, _1720215, _1720217]))], (46639 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720213), 46637 ^ [_1720213, _1720215, _1720217]), hAPP(c_List_Oset(_1720213), _1720217))))]], -(hAPP(c_List_Ofilter(_1720213, _1720215), _1720217) = _1720217)], (40203 ^ _780119) ^ [_1566085, _1566087, _1566089, _1566091] : [-(hAPP(_1566085, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1566087, _1566087), _1566089), _1566085), _1566091)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1566087, _1566087), _1566089), _1566085), hAPP(_1566085, _1566091)))], (19743 ^ _780119) ^ [_1139418, _1139420, _1139422, _1139424] : [class_Rings_Odivision__ring(_1139418), -(_1139420 = c_Groups_Ozero__class_Ozero(_1139418)), 19750 ^ _780119 : [(19757 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139418), _1139422), _1139420) = _1139424, -(_1139422 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139418), _1139424), _1139420))], (19751 ^ _780119) ^ [] : [_1139422 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139418), _1139424), _1139420), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139418), _1139422), _1139420) = _1139424)]]], (50045 ^ _780119) ^ [_1794756, _1794758, _1794760, _1794762] : [class_HOL_Oequal(_1794756), class_Enum_Oenum(_1794758), 50052 ^ _780119 : [(50053 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1794758, _1794756)), _1794760), _1794762)), 50056 ^ _780119 : [(50057 ^ _780119) ^ [_1794978] : [hBOOL(hAPP(hAPP(c_member(_1794758), _1794978), hAPP(c_List_Oset(_1794758), c_Enum_Oenum__class_Oenum(_1794758)))), -(hAPP(_1794760, _1794978) = hAPP(_1794762, _1794978))]]], (50063 ^ _780119) ^ [] : [50065 ^ _780119 : [(50068 ^ _780119) ^ [] : [hAPP(_1794760, 50064 ^ [_1794756, _1794758, _1794760, _1794762]) = hAPP(_1794762, 50064 ^ [_1794756, _1794758, _1794760, _1794762])], (50066 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1794758), 50064 ^ [_1794756, _1794758, _1794760, _1794762]), hAPP(c_List_Oset(_1794758), c_Enum_Oenum__class_Oenum(_1794758)))))]], -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1794758, _1794756)), _1794760), _1794762)))]]], (32115 ^ _780119) ^ [_1378887, _1378889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1378887)), hAPP(c_Nat_OSuc, _1378889))), -(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(_1378887))), 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)), _1378889)))))], (32409 ^ _780119) ^ [_1384494] : [c_Int_OPls = c_Int_OBit0(_1384494), -(c_Int_OPls = _1384494)], (41320 ^ _780119) ^ [_1592017, _1592019, _1592021, _1592023, _1592025, _1592027] : [class_Complete__Lattice_Ocomplete__lattice(_1592017), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592019, _1592017), _1592021), hAPP(hAPP(c_COMBB(tc_fun(_1592023, _1592017), _1592017, _1592019), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592023, _1592017), _1592025)), _1592027)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592023, _1592017), _1592025), hAPP(hAPP(c_COMBB(tc_fun(_1592019, _1592017), _1592017, _1592023), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592019, _1592017), _1592021)), hAPP(c_COMBC(_1592019, _1592023, _1592017), _1592027))))], (32385 ^ _780119) ^ [_1384058, _1384060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384058), _1384060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1384058)), c_Int_OBit0(_1384060))))], (47885 ^ _780119) ^ [_1747493, _1747495, _1747497, _1747499, _1747501] : [-(c_Map_Omap__upds(_1747493, _1747495, _1747497, _1747499, _1747501) = c_Map_Omap__add(_1747493, _1747495, _1747497, hAPP(c_Map_Omap__of(_1747493, _1747495), hAPP(c_List_Orev(tc_prod(_1747493, _1747495)), hAPP(hAPP(c_List_Ozip(_1747493, _1747495), _1747499), _1747501)))))], (6795 ^ _780119) ^ [_891709, _891711, _891713, _891715] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891709, tc_HOL_Obool)), _891711), hAPP(hAPP(c_Set_Oinsert(_891709), _891713), _891715)) = hAPP(hAPP(c_Set_Oinsert(_891709), _891713), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891709, tc_HOL_Obool)), _891711), _891715)))], (46869 ^ _780119) ^ [_1725502, _1725504, _1725506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1725502), _1725504)), _1725506)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1725504), c_List_Oupt(_1725502, _1725506)) = c_List_Oupt(_1725502, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1725502), _1725504)))], (15294 ^ _780119) ^ [_1059409, _1059411] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1059409), _1059411) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 15297 ^ _780119 : [(15300 ^ _780119) ^ [] : [-(_1059411 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15298 ^ _780119) ^ [] : [-(_1059409 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (45197 ^ _780119) ^ [_1686086, _1686088, _1686090, _1686092, _1686094] : [-(hAPP(hAPP(c_List_Omap(_1686086, _1686088), _1686090), hAPP(hAPP(c_List_Oappend(_1686086), _1686092), _1686094)) = hAPP(hAPP(c_List_Oappend(_1686088), hAPP(hAPP(c_List_Omap(_1686086, _1686088), _1686090), _1686092)), hAPP(hAPP(c_List_Omap(_1686086, _1686088), _1686090), _1686094)))], (43653 ^ _780119) ^ [_1650737, _1650739, _1650741] : [-(c_List_Oset__Cons(_1650737, _1650739, _1650741) = hAPP(c_Set_OCollect(tc_List_Olist(_1650737)), hAPP(hAPP(c_COMBB(tc_fun(_1650737, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1650737)), c_HOL_OEx(_1650737)), hAPP(hAPP(c_COMBB(tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool)), tc_fun(_1650737, tc_HOL_Obool), tc_List_Olist(_1650737)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), tc_HOL_Obool, _1650737), c_HOL_OEx(tc_List_Olist(_1650737)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1650737), tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool)), tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1650737, tc_fun(tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool))), tc_fun(tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool)), tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool))), tc_List_Olist(_1650737)), c_COMBS(_1650737, tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1650737, tc_fun(tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool))), tc_List_Olist(_1650737)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1650737), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool)), _1650737), c_COMBS(tc_List_Olist(_1650737), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool)), tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1650737)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), tc_fun(tc_List_Olist(_1650737), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1650737), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1650737)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1650737), tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_List_Olist(_1650737))), tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1650737), tc_List_Olist(_1650737)), tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool)), tc_fun(tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_List_Olist(_1650737))), tc_fun(_1650737, tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool))), tc_List_Olist(_1650737)), c_COMBB(tc_fun(tc_List_Olist(_1650737), tc_List_Olist(_1650737)), tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), _1650737)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1650737), tc_List_Olist(_1650737)), tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool)), tc_List_Olist(_1650737)), c_COMBB(tc_List_Olist(_1650737), tc_HOL_Obool, tc_List_Olist(_1650737))), c_fequal))), c_List_Olist_OCons(_1650737)))))), hAPP(hAPP(c_COMBC(_1650737, tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool)), _1650737), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1650737))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1650737), c_fconj), hAPP(hAPP(c_COMBC(_1650737, tc_fun(_1650737, tc_HOL_Obool), tc_HOL_Obool), c_member(_1650737)), _1650739)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1650737), tc_fun(tc_List_Olist(_1650737), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1650737))), _1650741)))))))], (45676 ^ _780119) ^ [_1699453, _1699455, _1699457, _1699459] : [-(hAPP(hAPP(c_List_Odrop(_1699453), _1699455), hAPP(hAPP(c_List_Oappend(_1699453), _1699457), _1699459)) = hAPP(hAPP(c_List_Oappend(_1699453), hAPP(hAPP(c_List_Odrop(_1699453), _1699455), _1699457)), hAPP(hAPP(c_List_Odrop(_1699453), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1699455), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699453)), _1699457))), _1699459)))], (30171 ^ _780119) ^ [_1343786, _1343788, _1343790] : [class_Int_Onumber(_1343786), 30174 ^ _780119 : [(30181 ^ _780119) ^ [] : [_1343790 = hAPP(c_Int_Onumber__class_Onumber__of(_1343786), _1343788), -(hAPP(c_Int_Onumber__class_Onumber__of(_1343786), _1343788) = _1343790)], (30175 ^ _780119) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1343786), _1343788) = _1343790, -(_1343790 = hAPP(c_Int_Onumber__class_Onumber__of(_1343786), _1343788))]]], (16795 ^ _780119) ^ [_1085692, _1085694] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1085692, tc_HOL_Obool)), _1085694), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1085692, tc_HOL_Obool)), _1085694)) = c_Orderings_Otop__class_Otop(tc_fun(_1085692, tc_HOL_Obool)))], (7758 ^ _780119) ^ [_911700, _911702, _911704, _911706, _911708, _911710, _911712] : [c_Hoare__Mirabelle_Ohoare__derivs(_911700, _911702, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_911700)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_911700), _911704), _911706), _911708)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_911700), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_911700, _911702, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_911700)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_911700), _911708), _911710), _911712)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_911700), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_911700, _911702, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_911700)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_911700), _911704), c_Com_Ocom_OSemi(_911706, _911710)), _911712)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_911700), tc_HOL_Obool)))))], (28230 ^ _780119) ^ [_1301948, _1301950] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1301948)), _1301950) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1301948), 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), _1301948)), _1301950))], (37046 ^ _780119) ^ [_1486112, _1486114, _1486116, _1486118, _1486120, _1486122] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1486112, _1486114, _1486116), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1486112, _1486114), tc_HOL_Obool)), _1486118), _1486120)), _1486122) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1486112, _1486116), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1486112, _1486114, _1486116), _1486118), _1486122)), hAPP(hAPP(c_Relation_Orel__comp(_1486112, _1486114, _1486116), _1486120), _1486122)))], (33859 ^ _780119) ^ [_1415258, _1415260, _1415262, _1415264, _1415266, _1415268] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415258, tc_fun(_1415260, tc_HOL_Obool))), _1415262), _1415264), _1415266), _1415268)), -(hBOOL(hAPP(hAPP(_1415262, _1415266), _1415268))), -(hBOOL(hAPP(hAPP(_1415264, _1415266), _1415268)))], (19160 ^ _780119) ^ [_1128909, _1128911, _1128913] : [class_Divides_Osemiring__div(_1128909), -(_1128911 = c_Groups_Ozero__class_Ozero(_1128909)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128909), _1128911), _1128913)), _1128911) = _1128913)], (22769 ^ _780119) ^ [_1196056] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1196056)), -(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)), _1196056))))], (40658 ^ _780119) ^ [_1577370, _1577372, _1577374, _1577376, _1577378] : [class_Complete__Lattice_Ocomplete__lattice(_1577370), hBOOL(hAPP(c_Finite__Set_Ofinite(_1577372), _1577374)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1577370), _1577376), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577372, _1577370), _1577374), _1577378)) = hAPP(hAPP(c_Finite__Set_Ofold(_1577372, _1577370, hAPP(hAPP(c_COMBB(_1577370, tc_fun(_1577370, _1577370), _1577372), c_Lattices_Osemilattice__sup__class_Osup(_1577370)), _1577378)), _1577376), _1577374))], (31131 ^ _780119) ^ [_1362211] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362211) = _1362211)], (5212 ^ _780119) ^ [_859870, _859872] : [_859872 = _859870, -(c_List_Onth(_859872) = c_List_Onth(_859870))], (5490 ^ _780119) ^ [_864205, _864207, _864209, _864211, _864213, _864215, _864217, _864219] : [-(c_Lazy__Sequence_Ohb__map(_864219, _864215, _864211, _864207) = c_Lazy__Sequence_Ohb__map(_864217, _864213, _864209, _864205)), _864219 = _864217, _864215 = _864213, _864211 = _864209, _864207 = _864205], (2918 ^ _780119) ^ [_823569, _823571] : [_823571 = _823569, -(c_Set_OBall(_823571) = c_Set_OBall(_823569))], (9852 ^ _780119) ^ [_951529, _951531, _951533, _951535, _951537] : [class_Lattices_Olattice(_951529), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_951531, _951529)), _951533), _951535), _951537) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951529), hAPP(_951533, _951537)), hAPP(_951535, _951537)))], (22950 ^ _780119) ^ [_1199228, _1199230] : [class_Rings_Olinordered__semidom(_1199228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199228), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1199228), _1199230)), c_Groups_Ozero__class_Ozero(_1199228)))], (23459 ^ _780119) ^ [_1209099, _1209101, _1209103] : [class_Orderings_Olinorder(_1209099), 23462 ^ _780119 : [(23469 ^ _780119) ^ [] : [_1209101 = _1209103, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1209099), _1209101) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1209099), _1209103))], (23463 ^ _780119) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1209099), _1209101) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1209099), _1209103), -(_1209101 = _1209103)]]], (38738 ^ _780119) ^ [_1530589, _1530591, _1530593, _1530595, _1530597, _1530599, _1530601, _1530603] : [hAPP(c_Fun_Ocomp(_1530589, _1530591, _1530593, _1530595), _1530597) = hAPP(c_Fun_Ocomp(_1530599, _1530591, _1530593, _1530601), _1530603), 38741 ^ _780119 : [(38742 ^ _780119) ^ [_1530704] : [-(hAPP(_1530595, hAPP(_1530597, _1530704)) = hAPP(_1530601, hAPP(_1530603, _1530704)))]]], (31121 ^ _780119) ^ [_1362060, _1362062] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362060)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1362060)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1362062)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362060)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1362062))))], (15894 ^ _780119) ^ [_1069747, _1069749, _1069751, _1069753, _1069755] : [class_Rings_Oordered__semiring(_1069747), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069747), _1069749), _1069751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069747), _1069753), _1069755)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069747), c_Groups_Ozero__class_Ozero(_1069747)), _1069751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069747), c_Groups_Ozero__class_Ozero(_1069747)), _1069753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069747), _1069749), _1069753)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069747), _1069751), _1069755))))], (18622 ^ _780119) ^ [_1119838, _1119840, _1119842, _1119844] : [c_Sum__Type_OPlus(_1119838, _1119840, _1119842, _1119844) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1119838, _1119840), tc_HOL_Obool)), 18625 ^ _780119 : [(18628 ^ _780119) ^ [] : [-(_1119844 = c_Orderings_Obot__class_Obot(tc_fun(_1119840, tc_HOL_Obool)))], (18626 ^ _780119) ^ [] : [-(_1119842 = c_Orderings_Obot__class_Obot(tc_fun(_1119838, tc_HOL_Obool)))]]], (40928 ^ _780119) ^ [_1582563, _1582565, _1582567, _1582569, _1582571] : [c_Finite__Set_Ofun__left__comm(_1582563, _1582565, _1582567), -(hAPP(c_Fun_Ocomp(_1582565, _1582565, _1582565, hAPP(_1582567, _1582569)), hAPP(_1582567, _1582571)) = hAPP(c_Fun_Ocomp(_1582565, _1582565, _1582565, hAPP(_1582567, _1582571)), hAPP(_1582567, _1582569)))], (40359 ^ _780119) ^ [_1570015, _1570017, _1570019, _1570021, _1570023] : [c_Relation_Osingle__valued(_1570015, _1570017, _1570019), c_Relation_Osingle__valued(_1570017, _1570021, _1570023), -(c_Relation_Osingle__valued(_1570015, _1570021, hAPP(hAPP(c_Relation_Orel__comp(_1570015, _1570017, _1570021), _1570019), _1570023)))], (2454 ^ _780119) ^ [_816281, _816283, _816285, _816287] : [-(c_Divides_OposDivAlg(_816287, _816283) = c_Divides_OposDivAlg(_816285, _816281)), _816287 = _816285, _816283 = _816281], (106 ^ _780119) ^ [_781914, _781916, _781918, _781920, _781922, _781924] : [-(c_Big__Operators_Osemilattice__big(_781922, _781918, _781914)), c_Big__Operators_Osemilattice__big(_781924, _781920, _781916), _781924 = _781922, _781920 = _781918, _781916 = _781914], (6799 ^ _780119) ^ [_891843, _891845, _891847] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891843, tc_HOL_Obool)), _891845), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891843, tc_HOL_Obool)), _891845), _891847))))], (21751 ^ _780119) ^ [_1177365, _1177367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177365)), -(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, _1177367, _1177365))))], (5929 ^ _780119) ^ [_874381, _874383, _874385, _874387] : [_874381 = _874383, 5932 ^ _780119 : [(5939 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874385), _874383), _874387)), -(hBOOL(hAPP(hAPP(c_member(_874385), _874381), _874387)))], (5933 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874385), _874381), _874387)), -(hBOOL(hAPP(hAPP(c_member(_874385), _874383), _874387)))]]], (50502 ^ _780119) ^ [_1804759, _1804761, _1804763] : [-(hAPP(hAPP(c_List_Oappend(_1804759), c_List_Oreplicate(_1804759, _1804761, _1804763)), hAPP(hAPP(c_List_Olist_OCons(_1804759), _1804763), c_List_Olist_ONil(_1804759))) = hAPP(hAPP(c_List_Olist_OCons(_1804759), _1804763), c_List_Oreplicate(_1804759, _1804761, _1804763)))], (24879 ^ _780119) ^ [_1236043, _1236045, _1236047] : [class_Orderings_Olinorder(_1236043), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236043), _1236045), _1236047)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1236043, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1236043, _1236045, _1236047)), hAPP(hAPP(c_Set_Oinsert(_1236043), _1236047), c_Orderings_Obot__class_Obot(tc_fun(_1236043, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1236043, _1236045, _1236047))], (12875 ^ _780119) ^ [_1013784, _1013786, _1013788] : [class_Lattices_Osemilattice__inf(_1013784), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013784), _1013786)), hBOOL(hAPP(hAPP(c_member(_1013784), _1013788), _1013786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013784), hAPP(c_Finite__Set_Ofold1(_1013784, c_Lattices_Osemilattice__inf__class_Oinf(_1013784)), _1013786)), _1013788)))], (33011 ^ _780119) ^ [_1395070, _1395072, _1395074] : [class_Rings_Olinordered__idom(_1395070), 33014 ^ _780119 : [(33015 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395070), c_Groups_Ozero__class_Ozero(_1395070)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1395070), hAPP(hAPP(c_Power_Opower__class_Opower(_1395070), _1395072), 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(_1395070), _1395074), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1395072 = c_Groups_Ozero__class_Ozero(_1395070), _1395074 = c_Groups_Ozero__class_Ozero(_1395070)], (33025 ^ _780119) ^ [] : [33026 ^ _780119 : [(33029 ^ _780119) ^ [] : [-(_1395074 = c_Groups_Ozero__class_Ozero(_1395070))], (33027 ^ _780119) ^ [] : [-(_1395072 = c_Groups_Ozero__class_Ozero(_1395070))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395070), c_Groups_Ozero__class_Ozero(_1395070)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1395070), hAPP(hAPP(c_Power_Opower__class_Opower(_1395070), _1395072), 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(_1395070), _1395074), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (37522 ^ _780119) ^ [_1498163] : [-(c_Nitpick_Ozero__frac(_1498163) = c_Nitpick_OAbs__Frac(_1498163, 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))))], (28742 ^ _780119) ^ [_1311168] : [class_Orderings_Olinorder(_1311168), -(c_Orderings_Oord_Omax(_1311168, hAPP(c_COMBC(_1311168, _1311168, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1311168))) = c_Orderings_Oord__class_Omin(_1311168))], (47518 ^ _780119) ^ [_1738283] : [-(hAPP(c_List_Orev(_1738283), c_List_Olist_ONil(_1738283)) = c_List_Olist_ONil(_1738283))], (41244 ^ _780119) ^ [_1589985, _1589987, _1589989, _1589991] : [_1589985 = c_Orderings_Obot__class_Obot(tc_fun(_1589987, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589987, tc_fun(_1589989, tc_HOL_Obool)), _1589985), hAPP(c_COMBK(tc_fun(_1589989, tc_HOL_Obool), _1589987), _1589991)) = c_Orderings_Otop__class_Otop(tc_fun(_1589989, tc_HOL_Obool)))], (1250 ^ _780119) ^ [_798468, _798470] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_798468)), _798470 = _798468, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_798470)], (22436 ^ _780119) ^ [_1189561, _1189563, _1189565] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1189561), _1189563)), 22442 ^ _780119 : [(22445 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1189565, 22441 ^ [_1189561, _1189563, _1189565])))], (22443 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1189561), 22441 ^ [_1189561, _1189563, _1189565]), _1189563)))]], -(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(_1189561, tc_Nat_Onat), _1189565), _1189563))))], (48417 ^ _780119) ^ [_1759197, _1759199] : [class_Orderings_Olinorder(_1759197), -(c_List_Olinorder__class_Osorted__list__of__set(_1759197, hAPP(c_List_Oset(_1759197), _1759199)) = c_List_Olinorder__class_Osort__key(_1759197, _1759197, c_COMBI(_1759197), c_List_Oremdups(_1759197, _1759199)))], (33647 ^ _780119) ^ [_1410730, _1410732, _1410734, _1410736] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1410730, tc_fun(_1410732, tc_HOL_Obool))), _1410734), _1410736)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1410730, _1410732)), hAPP(hAPP(c_Product__Type_OPair(_1410730, _1410732), _1410734), _1410736)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1410730, _1410732), tc_HOL_Obool)))))], (28152 ^ _780119) ^ [_1300304, _1300306, _1300308, _1300310] : [class_Orderings_Olinorder(_1300304), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300304), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300304), _1300306), _1300308)), _1300310) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300304), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300304), _1300306), _1300310)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300304), _1300308), _1300310)))], (19813 ^ _780119) ^ [_1140563, _1140565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1140563), _1140565)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1140563), _1140565) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23973 ^ _780119) ^ [_1218634, _1218636, _1218638] : [class_Groups_Ocomm__monoid__add(_1218634), hAPP(_1218636, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1218634), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218634), _1218636), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1218638)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218634), _1218636), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218638)))], (31881 ^ _780119) ^ [_1374512, _1374514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374512), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374512)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374514)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374514))], (42839 ^ _780119) ^ [_1628689, _1628691, _1628693, _1628695] : [c_Fun_Oinj__on(_1628689, _1628691, _1628693, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1628689, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1628689), tc_fun(_1628689, tc_HOL_Obool), c_List_Oset(_1628689)), _1628695))), -(c_Fun_Oinj__on(tc_List_Olist(_1628689), tc_List_Olist(_1628691), hAPP(c_List_Omap(_1628689, _1628691), _1628693), _1628695))], (50222 ^ _780119) ^ [_1797755, _1797757] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1797755)), c_Int_OBit0(_1797757))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1797755), _1797757)))], (45372 ^ _780119) ^ [_1690935, _1690937, _1690939, _1690941] : [hBOOL(hAPP(hAPP(c_member(_1690935), _1690937), c_Wellfounded_Oacc(_1690935, _1690939))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1690935)), _1690941), c_Wellfounded_Oacc(tc_List_Olist(_1690935), c_List_Olistrel1(_1690935, _1690939)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1690935)), hAPP(hAPP(c_List_Olist_OCons(_1690935), _1690937), _1690941)), c_Wellfounded_Oacc(tc_List_Olist(_1690935), c_List_Olistrel1(_1690935, _1690939)))))], (19220 ^ _780119) ^ [_1129843, _1129845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129843), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129845), _1129843)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129843), _1129845) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27136 ^ _780119) ^ [_1279987, _1279989, _1279991, _1279993, _1279995, _1279997] : [hBOOL(hAPP(hAPP(c_member(_1279987), _1279989), _1279991)), -(hAPP(c_Fun_Ooverride__on(_1279987, _1279993, _1279995, _1279997, _1279991), _1279989) = hAPP(_1279997, _1279989))], (10214 ^ _780119) ^ [_958787, _958789, _958791, _958793] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958787, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958787, tc_HOL_Obool)), _958789), _958791)), _958793) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958787, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958787, tc_HOL_Obool)), _958789), _958793)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958787, tc_HOL_Obool)), _958791), _958793)))], (26309 ^ _780119) ^ [_1260170, _1260172, _1260174] : [26310 ^ _780119 : [(26313 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1260170), hAPP(c_Set_OCollect(_1260170), _1260174)))], (26311 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1260170), hAPP(c_Set_OCollect(_1260170), _1260172)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260170), hAPP(c_Set_OCollect(_1260170), hAPP(hAPP(c_COMBS(_1260170, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260170), c_fconj), _1260172)), _1260174)))))], (38732 ^ _780119) ^ [_1530442, _1530444, _1530446, _1530448, _1530450, _1530452, _1530454, _1530456, _1530458] : [hAPP(c_Fun_Ocomp(_1530442, _1530444, _1530446, _1530448), _1530450) = hAPP(c_Fun_Ocomp(_1530452, _1530444, _1530446, _1530454), _1530456), -(hAPP(_1530448, hAPP(_1530450, _1530458)) = hAPP(_1530454, hAPP(_1530456, _1530458)))], (27410 ^ _780119) ^ [_1286424, _1286426] : [_1286424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1286426, _1286424) = _1286426)], (40317 ^ _780119) ^ [_1569090, _1569092, _1569094, _1569096, _1569098] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569090, _1569090)), hAPP(hAPP(c_Product__Type_OPair(_1569090, _1569090), _1569092), _1569094)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1569090, _1569090), tc_HOL_Obool), _1569096), _1569098))), 40322 ^ _780119 : [(40325 ^ _780119) ^ [] : [-(_1569092 = _1569094)], (40323 ^ _780119) ^ [] : [-(_1569096 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 40328 ^ _780119 : [(40331 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569090, _1569090)), hAPP(hAPP(c_Product__Type_OPair(_1569090, _1569090), _1569092), 40326 ^ [_1569090, _1569092, _1569094, _1569096, _1569098])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1569090, _1569090), tc_HOL_Obool), 40327 ^ [_1569090, _1569092, _1569094, _1569096, _1569098]), _1569098))))], (40333 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569090, _1569090)), hAPP(hAPP(c_Product__Type_OPair(_1569090, _1569090), 40326 ^ [_1569090, _1569092, _1569094, _1569096, _1569098]), _1569094)), _1569098)))], (40329 ^ _780119) ^ [] : [-(_1569096 = hAPP(c_Nat_OSuc, 40327 ^ [_1569090, _1569092, _1569094, _1569096, _1569098]))]]], (48191 ^ _780119) ^ [_1753927, _1753929, _1753931, _1753933, _1753935] : [c_List_Opartition(_1753927, _1753929, _1753931) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753927), tc_List_Olist(_1753927)), _1753933), _1753935), 48194 ^ _780119 : [(48201 ^ _780119) ^ [_1754189] : [hBOOL(hAPP(hAPP(c_member(_1753927), _1754189), hAPP(c_List_Oset(_1753927), _1753935))), hBOOL(hAPP(_1753929, _1754189))], (48195 ^ _780119) ^ [_1754080] : [hBOOL(hAPP(hAPP(c_member(_1753927), _1754080), hAPP(c_List_Oset(_1753927), _1753933))), -(hBOOL(hAPP(_1753929, _1754080)))]]], (16911 ^ _780119) ^ [_1087393, _1087395] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087393), _1087395) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1087393 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1087395 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24259 ^ _780119) ^ [_1224338, _1224340] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224338), _1224340))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1224340, _1224338) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1224340), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224340), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1224338)))], (15064 ^ _780119) ^ [_1056088, _1056090, _1056092] : [class_Groups_Ogroup__add(_1056088), 15067 ^ _780119 : [(15074 ^ _780119) ^ [] : [_1056090 = _1056092, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056088), _1056090), _1056092) = c_Groups_Ozero__class_Ozero(_1056088))], (15068 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056088), _1056090), _1056092) = c_Groups_Ozero__class_Ozero(_1056088), -(_1056090 = _1056092)]]], (14644 ^ _780119) ^ [_1048851] : [class_Power_Opower(_1048851), -(c_Power_Opower__class_Opower(_1048851) = c_Power_Opower_Opower(_1048851, c_Groups_Oone__class_Oone(_1048851), c_Groups_Otimes__class_Otimes(_1048851)))], (11055 ^ _780119) ^ [_976622, _976624, _976626, _976628, _976630] : [-(c_Map_Orestrict__map(_976622, _976624, _976626, hAPP(hAPP(c_Set_Oinsert(_976622), _976628), _976630)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_976622, tc_Option_Ooption(_976624)), c_Map_Orestrict__map(_976622, _976624, _976626, _976630)), _976628), hAPP(_976626, _976628)))], (16827 ^ _780119) ^ [_1086181, _1086183] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086181), _1086183) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 16832 ^ _780119 : [(16835 ^ _780119) ^ [] : [-(_1086183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16833 ^ _780119) ^ [] : [-(_1086181 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 16836 ^ _780119 : [(16839 ^ _780119) ^ [] : [-(_1086183 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16837 ^ _780119) ^ [] : [-(_1086181 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (26587 ^ _780119) ^ [_1265482, _1265484] : [class_Groups_Oordered__ab__group__add__abs(_1265482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265482), hAPP(c_Groups_Oabs__class_Oabs(_1265482), _1265484)), c_Groups_Ozero__class_Ozero(_1265482)))], (12669 ^ _780119) ^ [_1009677, _1009679, _1009681, _1009683] : [_1009677 = c_Finite__Set_Ofold1(_1009679, _1009681), -(hAPP(_1009677, hAPP(hAPP(c_Set_Oinsert(_1009679), _1009683), c_Orderings_Obot__class_Obot(tc_fun(_1009679, tc_HOL_Obool)))) = _1009683)], (38007 ^ _780119) ^ [_1513236, _1513238, _1513240, _1513242, _1513244, _1513246] : [class_Groups_Ocomm__monoid__mult(_1513236), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513238), _1513240)), 38017 ^ _780119 : [(38020 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513242), hAPP(_1513244, 38016 ^ [_1513236, _1513238, _1513240, _1513242, _1513244, _1513246])))], (38018 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513238), 38016 ^ [_1513236, _1513238, _1513240, _1513242, _1513244, _1513246]), _1513240)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1513236, _1513238, c_Groups_Otimes__class_Otimes(_1513236)), hAPP(hAPP(c_COMBS(_1513238, tc_fun(_1513242, tc_HOL_Obool), _1513236), hAPP(hAPP(c_COMBC(_1513238, _1513236, tc_fun(tc_fun(_1513242, tc_HOL_Obool), _1513236)), hAPP(hAPP(c_COMBB(tc_fun(_1513242, _1513236), tc_fun(_1513236, tc_fun(tc_fun(_1513242, tc_HOL_Obool), _1513236)), _1513238), c_Finite__Set_Ofold__image(_1513236, _1513242, c_Groups_Otimes__class_Otimes(_1513236))), _1513246)), c_Groups_Oone__class_Oone(_1513236))), _1513244)), c_Groups_Oone__class_Oone(_1513236)), _1513240) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1513236, tc_prod(_1513238, _1513242), c_Groups_Otimes__class_Otimes(_1513236)), hAPP(c_Product__Type_Oprod_Oprod__case(_1513238, _1513242, _1513236), _1513246)), c_Groups_Oone__class_Oone(_1513236)), hAPP(hAPP(c_Product__Type_OSigma(_1513238, _1513242), _1513240), _1513244)))], (34915 ^ _780119) ^ [_1435714, _1435716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435714), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435716), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1435714), _1435716) = 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), _1435714), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1435716)))))], (36453 ^ _780119) ^ [_1471623, _1471625, _1471627, _1471629, _1471631] : [c_Fun_Oinj__on(_1471623, _1471625, _1471627, c_Orderings_Otop__class_Otop(tc_fun(_1471623, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1471623, _1471625, _1471627), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471623, tc_HOL_Obool)), _1471629), _1471631)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471625, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471623, _1471625, _1471627), _1471629)), hAPP(c_Set_Oimage(_1471623, _1471625, _1471627), _1471631)))], (43437 ^ _780119) ^ [_1644708, _1644710, _1644712, _1644714] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644708), tc_List_Olist(_1644708))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644708), tc_List_Olist(_1644708)), _1644710), _1644712)), c_List_Olistrel(_1644708, _1644714))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644708)), _1644710) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644708)), _1644712))], (15402 ^ _780119) ^ [_1061028, _1061030] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061028), _1061030) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1061028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1061030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30973 ^ _780119) ^ [_1359158, _1359160, _1359162, _1359164] : [class_Fields_Olinordered__field__inverse__zero(_1359158), class_Int_Onumber(_1359158), 30980 ^ _780119 : [(30981 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359158), hAPP(c_Int_Onumber__class_Onumber__of(_1359158), _1359160)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359158), _1359162), _1359164))), 30984 ^ _780119 : [(30991 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359158), c_Groups_Ozero__class_Ozero(_1359158)), _1359164))), 30994 ^ _780119 : [(31001 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359158), _1359164), c_Groups_Ozero__class_Ozero(_1359158)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359158), hAPP(c_Int_Onumber__class_Onumber__of(_1359158), _1359160)), c_Groups_Ozero__class_Ozero(_1359158))))], (30995 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359158), _1359164), c_Groups_Ozero__class_Ozero(_1359158))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359158), _1359162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359158), hAPP(c_Int_Onumber__class_Onumber__of(_1359158), _1359160)), _1359164))))]]], (30985 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359158), c_Groups_Ozero__class_Ozero(_1359158)), _1359164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359158), hAPP(c_Int_Onumber__class_Onumber__of(_1359158), _1359160)), _1359164)), _1359162)))]]], (31007 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359158), hAPP(c_Int_Onumber__class_Onumber__of(_1359158), _1359160)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359158), _1359162), _1359164)))), 31010 ^ _780119 : [(31013 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359158), hAPP(c_Int_Onumber__class_Onumber__of(_1359158), _1359160)), _1359164)), _1359162))], (31011 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359158), c_Groups_Ozero__class_Ozero(_1359158)), _1359164)))]], 31014 ^ _780119 : [(31017 ^ _780119) ^ [] : [31018 ^ _780119 : [(31021 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359158), _1359162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359158), hAPP(c_Int_Onumber__class_Onumber__of(_1359158), _1359160)), _1359164)))], (31019 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359158), _1359164), c_Groups_Ozero__class_Ozero(_1359158))))]], 31022 ^ _780119 : [(31025 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359158), hAPP(c_Int_Onumber__class_Onumber__of(_1359158), _1359160)), c_Groups_Ozero__class_Ozero(_1359158)))], (31023 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359158), _1359164), c_Groups_Ozero__class_Ozero(_1359158)))]]], (31015 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359158), c_Groups_Ozero__class_Ozero(_1359158)), _1359164))]]]]], (15320 ^ _780119) ^ [_1059789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059789), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1059789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21022 ^ _780119) ^ [_1162517, _1162519, _1162521, _1162523, _1162525] : [class_Fields_Ofield(_1162517), -(_1162519 = c_Groups_Ozero__class_Ozero(_1162517)), -(_1162521 = c_Groups_Ozero__class_Ozero(_1162517)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162517), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162517), _1162523), _1162519)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162517), _1162525), _1162521)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162517), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162517), _1162523), _1162521)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162517), _1162525), _1162519))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162517), _1162519), _1162521)))], (17140 ^ _780119) ^ [_1091401, _1091403, _1091405] : [class_Groups_Oordered__comm__monoid__add(_1091401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091401), c_Groups_Ozero__class_Ozero(_1091401)), _1091403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091401), c_Groups_Ozero__class_Ozero(_1091401)), _1091405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091401), c_Groups_Ozero__class_Ozero(_1091401)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091401), _1091403), _1091405))))], (36299 ^ _780119) ^ [_1468519, _1468521, _1468523, _1468525, _1468527] : [c_Fun_Oinj__on(_1468519, _1468521, _1468523, _1468525), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1468519, tc_HOL_Obool)), _1468527), _1468525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1468521, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468519, _1468521, _1468523), _1468527)), hAPP(c_Set_Oimage(_1468519, _1468521, _1468523), _1468525))))], (20286 ^ _780119) ^ [_1149203, _1149205, _1149207] : [class_Fields_Olinordered__field__inverse__zero(_1149203), 20289 ^ _780119 : [(20304 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149203), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149203), _1149205), _1149207)), c_Groups_Ozero__class_Ozero(_1149203)))), 20305 ^ _780119 : [(20312 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149203), _1149205), c_Groups_Ozero__class_Ozero(_1149203))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149203), c_Groups_Ozero__class_Ozero(_1149203)), _1149207))], (20306 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149203), c_Groups_Ozero__class_Ozero(_1149203)), _1149205)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149203), _1149207), c_Groups_Ozero__class_Ozero(_1149203)))]]], (20290 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149203), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149203), _1149205), _1149207)), c_Groups_Ozero__class_Ozero(_1149203))), 20295 ^ _780119 : [(20298 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149203), _1149207), c_Groups_Ozero__class_Ozero(_1149203))))], (20296 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149203), c_Groups_Ozero__class_Ozero(_1149203)), _1149205)))]], 20299 ^ _780119 : [(20302 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149203), c_Groups_Ozero__class_Ozero(_1149203)), _1149207)))], (20300 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149203), _1149205), c_Groups_Ozero__class_Ozero(_1149203))))]]]]], (35247 ^ _780119) ^ [_1443509, _1443511, _1443513, _1443515] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1443509), _1443511)), 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)), _1443513), _1443509)), 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)), _1443515), _1443511)), 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)), _1443513), _1443515)), _1443511)), c_FunDef_Omax__strict)))], (23783 ^ _780119) ^ [_1214695, _1214697, _1214699, _1214701, _1214703] : [class_Groups_Ocomm__monoid__add(_1214695), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214695), _1214697), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1214699), _1214701)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1214703), _1214701))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214695), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1214695, tc_Nat_Onat), _1214697), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1214701))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1214699), _1214703)))], (9628 ^ _780119) ^ [_946595, _946597, _946599] : [class_Lattices_Olattice(_946595), hBOOL(hAPP(c_Finite__Set_Ofinite(_946595), _946597)), -(_946597 = c_Orderings_Obot__class_Obot(tc_fun(_946595, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_946595), _946599)), -(_946599 = c_Orderings_Obot__class_Obot(tc_fun(_946595, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946595, tc_HOL_Obool)), _946597), _946599) = c_Orderings_Obot__class_Obot(tc_fun(_946595, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_946595, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946595, tc_HOL_Obool)), _946597), _946599)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_946595), c_Big__Operators_Olattice__class_OSup__fin(_946595, _946597)), c_Big__Operators_Olattice__class_OSup__fin(_946595, _946599)))], (37880 ^ _780119) ^ [_1508587, _1508589, _1508591, _1508593, _1508595, _1508597] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1508587, _1508589)), hAPP(hAPP(c_Product__Type_OPair(_1508587, _1508589), _1508591), _1508593)), hAPP(hAPP(c_Product__Type_OSigma(_1508587, _1508589), _1508595), _1508597)))), hBOOL(hAPP(hAPP(c_member(_1508587), _1508591), _1508595)), hBOOL(hAPP(hAPP(c_member(_1508589), _1508593), hAPP(_1508597, _1508591)))], (7017 ^ _780119) ^ [_895982, _895984, _895986, _895988] : [class_Orderings_Oorder(_895982), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895982), _895984), _895986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895982), _895988), _895984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895982), _895988), _895986)))], (26517 ^ _780119) ^ [_1264253, _1264255, _1264257] : [-(hAPP(c_Set_OCollect(_1264253), hAPP(hAPP(c_COMBS(_1264253, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1264253), c_fdisj), _1264255)), _1264257)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264253, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1264253), _1264255)), hAPP(c_Set_OCollect(_1264253), _1264257)))], (37621 ^ _780119) ^ [_1500904, _1500906, _1500908] : [c_Wellfounded_Owf(_1500904, _1500906), c_Wellfounded_Owf(_1500904, _1500908), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500904, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1500904, _1500904), _1500906)), hAPP(c_Relation_ORange(_1500904, _1500904), _1500908)) = c_Orderings_Obot__class_Obot(tc_fun(_1500904, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1500904, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1500904, _1500904), tc_HOL_Obool)), _1500906), _1500908)))], (17632 ^ _780119) ^ [_1100664, _1100666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1100664)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1100666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100664), _1100666))))], (44380 ^ _780119) ^ [_1669056, _1669058, _1669060, _1669062, _1669064, _1669066, _1669068] : [-(hAPP(hAPP(c_List_Ozip(_1669056, _1669058), hAPP(hAPP(c_List_Olist__update(_1669056, _1669060), _1669062), _1669064)), hAPP(hAPP(c_List_Olist__update(_1669058, _1669066), _1669062), _1669068)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1669056, _1669058), hAPP(hAPP(c_List_Ozip(_1669056, _1669058), _1669060), _1669066)), _1669062), hAPP(hAPP(c_Product__Type_OPair(_1669056, _1669058), _1669064), _1669068)))], (5658 ^ _780119) ^ [_866751, _866753] : [_866753 = _866751, -(c_Option_Ooption_OSome(_866753) = c_Option_Ooption_OSome(_866751))], (23424 ^ _780119) ^ [_1208125, _1208127, _1208129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1208125, 23425 ^ [_1208125, _1208127, _1208129])), hAPP(_1208127, 23425 ^ [_1208125, _1208127, _1208129]))), -(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), _1208127), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1208129))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1208125), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1208129))) = 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)), _1208127)), _1208125)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1208129)))], (24201 ^ _780119) ^ [_1223227, _1223229] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1223227, _1223229))))], (40598 ^ _780119) ^ [_1576032, _1576034, _1576036, _1576038] : [class_Lattices_Osemilattice__sup(_1576032), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576032), _1576034)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1576032, _1576032, c_Lattices_Osemilattice__sup__class_Osup(_1576032)), _1576036), hAPP(hAPP(c_Set_Oinsert(_1576032), _1576038), _1576034)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1576032), _1576038), hAPP(hAPP(c_Finite__Set_Ofold(_1576032, _1576032, c_Lattices_Osemilattice__sup__class_Osup(_1576032)), _1576036), _1576034)))], (31747 ^ _780119) ^ [_1372471, _1372473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372471)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372473))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372471), _1372473))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372471), c_Int_OPls)))], (48033 ^ _780119) ^ [_1750370, _1750372, _1750374] : [hBOOL(hAPP(c_List_Odistinct(_1750370), _1750372)), hBOOL(hAPP(hAPP(c_member(_1750370), _1750374), hAPP(c_List_Oset(_1750370), _1750372))), -(c_List_OdropWhile(_1750370, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1750370), c_fNot), hAPP(hAPP(c_COMBC(_1750370, _1750370, tc_HOL_Obool), c_fequal), _1750374)), hAPP(c_List_Orev(_1750370), _1750372)) = hAPP(hAPP(c_List_Olist_OCons(_1750370), _1750374), hAPP(c_List_Orev(_1750370), c_List_OtakeWhile(_1750370, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1750370), c_fNot), hAPP(hAPP(c_COMBC(_1750370, _1750370, tc_HOL_Obool), c_fequal), _1750374)), _1750372))))], (8982 ^ _780119) ^ [_934750, _934752, _934754] : [class_Orderings_Olinorder(_934750), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934750), _934752), _934754))), 8989 ^ _780119 : [(8996 ^ _780119) ^ [] : [_934752 = _934754, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934750), _934752), _934754)))], (8990 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934750), _934752), _934754)), -(_934752 = _934754)]]], (8132 ^ _780119) ^ [_919616, _919618, _919620, _919622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919616, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919616, tc_HOL_Obool)), _919618), _919620)), _919622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919616, tc_HOL_Obool)), _919618), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_919616, tc_HOL_Obool)), _919620), _919622))))], (3448 ^ _780119) ^ [_831932, _831934, _831936, _831938, _831940, _831942] : [-(c_List_Oset__Cons(_831942, _831938, _831934) = c_List_Oset__Cons(_831940, _831936, _831932)), _831942 = _831940, _831938 = _831936, _831934 = _831932], (41591 ^ _780119) ^ [_1599728, _1599730, _1599732, _1599734, _1599736] : [41593 ^ _780119 : [(41596 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1599734, 41592 ^ [_1599728, _1599730, _1599732, _1599734, _1599736]), _1599736))], (41594 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1599728), 41592 ^ [_1599728, _1599730, _1599732, _1599734, _1599736]), _1599732)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599728, tc_fun(_1599730, tc_HOL_Obool)), _1599732), _1599734), _1599736)))], (5340 ^ _780119) ^ [_861820, _861822] : [_861822 = _861820, -(c_List_Oset(_861822) = c_List_Oset(_861820))], (14400 ^ _780119) ^ [_1044004, _1044006, _1044008] : [class_Rings_Ocomm__semiring__1(_1044004), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044004), _1044006), hAPP(hAPP(c_Power_Opower__class_Opower(_1044004), _1044006), _1044008)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1044004), _1044006), hAPP(c_Nat_OSuc, _1044008)))], (18442 ^ _780119) ^ [_1116508] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116508), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1116508)], (13925 ^ _780119) ^ [_1033498, _1033500, _1033502] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1033498, tc_HOL_Obool)), _1033500), _1033502) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1033498, tc_HOL_Obool)), _1033500), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033498, tc_HOL_Obool)), _1033502)))], (12585 ^ _780119) ^ [_1008164, _1008166, _1008168] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1008164), _1008166)), hBOOL(hAPP(hAPP(c_member(_1008164), _1008168), _1008166)), -(hAPP(c_Finite__Set_Ocard(_1008164), _1008166) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1008164), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008164, tc_HOL_Obool)), _1008166), hAPP(hAPP(c_Set_Oinsert(_1008164), _1008168), c_Orderings_Obot__class_Obot(tc_fun(_1008164, tc_HOL_Obool)))))))], (14242 ^ _780119) ^ [_1040163, _1040165, _1040167, _1040169, _1040171] : [class_Groups_Ocomm__monoid__mult(_1040163), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040165), _1040167)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1040165, _1040163), _1040169), hAPP(hAPP(c_Set_Oinsert(_1040165), _1040171), _1040167)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040163), hAPP(_1040169, _1040171)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1040165, _1040163), _1040169), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1040165, tc_HOL_Obool)), _1040167), hAPP(hAPP(c_Set_Oinsert(_1040165), _1040171), c_Orderings_Obot__class_Obot(tc_fun(_1040165, tc_HOL_Obool)))))))], (50416 ^ _780119) ^ [_1802498, _1802500, _1802502, _1802504, _1802506] : [-(c_List_Osplice(_1802498, hAPP(hAPP(c_List_Olist_OCons(_1802498), _1802500), _1802502), hAPP(hAPP(c_List_Olist_OCons(_1802498), _1802504), _1802506)) = hAPP(hAPP(c_List_Olist_OCons(_1802498), _1802500), hAPP(hAPP(c_List_Olist_OCons(_1802498), _1802504), c_List_Osplice(_1802498, _1802502, _1802506))))], (8886 ^ _780119) ^ [_933401, _933403, _933405] : [class_Orderings_Olinorder(_933401), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933401), _933403), _933405))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933401), _933405), _933403)))], (7720 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (13921 ^ _780119) ^ [_1033376, _1033378, _1033380] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033376, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1033376, tc_HOL_Obool)), _1033378), _1033380)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1033376, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033376, tc_HOL_Obool)), _1033378)), _1033380))], (40618 ^ _780119) ^ [_1576478, _1576480, _1576482, _1576484] : [class_Orderings_Olinorder(_1576478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576478), _1576480)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1576478, _1576478, c_Orderings_Oord__class_Omin(_1576478)), _1576482), hAPP(hAPP(c_Set_Oinsert(_1576478), _1576484), _1576480)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1576478), _1576484), hAPP(hAPP(c_Finite__Set_Ofold(_1576478, _1576478, c_Orderings_Oord__class_Omin(_1576478)), _1576482), _1576480)))], (4694 ^ _780119) ^ [_851605, _851607] : [_851607 = _851605, -(c_New__Random__Sequence_Opos__single(_851607) = c_New__Random__Sequence_Opos__single(_851605))], (1050 ^ _780119) ^ [_795968, _795970] : [-(class_Rings_Oring__1__no__zero__divisors(_795968)), _795970 = _795968, class_Rings_Oring__1__no__zero__divisors(_795970)], (48267 ^ _780119) ^ [_1756178, _1756180, _1756182, _1756184] : [class_Enum_Oenum(_1756178), class_Enum_Oenum(_1756180), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756180)), _1756182) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756178)), c_Enum_Oenum__class_Oenum(_1756178)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756180)), _1756184) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756178)), c_Enum_Oenum__class_Oenum(_1756178)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1756180), _1756180, _1756178, c_Option_Othe(_1756180)), hAPP(c_Map_Omap__of(_1756178, _1756180), hAPP(hAPP(c_List_Ozip(_1756178, _1756180), c_Enum_Oenum__class_Oenum(_1756178)), _1756182))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1756180), _1756180, _1756178, c_Option_Othe(_1756180)), hAPP(c_Map_Omap__of(_1756178, _1756180), hAPP(hAPP(c_List_Ozip(_1756178, _1756180), c_Enum_Oenum__class_Oenum(_1756178)), _1756184))), -(_1756182 = _1756184)], (13376 ^ _780119) ^ [_1023498, _1023500, _1023502] : [class_Groups_Oordered__ab__group__add(_1023498), 13379 ^ _780119 : [(13386 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023498), _1023502), hAPP(c_Groups_Ouminus__class_Ouminus(_1023498), _1023500))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023498), _1023500), hAPP(c_Groups_Ouminus__class_Ouminus(_1023498), _1023502))))], (13380 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023498), _1023500), hAPP(c_Groups_Ouminus__class_Ouminus(_1023498), _1023502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023498), _1023502), hAPP(c_Groups_Ouminus__class_Ouminus(_1023498), _1023500))))]]], (6667 ^ _780119) ^ [_889011, _889013, _889015, _889017] : [hBOOL(hAPP(_889011, _889013)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889015, tc_HOL_Obool)), _889017), _889011), _889013)))], (41912 ^ _780119) ^ [_1607245, _1607247, _1607249] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607245, tc_HOL_Obool)), _1607247), _1607249) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1607245, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1607245, tc_HOL_Obool)), _1607247), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1607245, tc_HOL_Obool)), _1607249), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1607245, tc_HOL_Obool), tc_HOL_Obool))))))], (29466 ^ _780119) ^ [_1327049, _1327051, _1327053, _1327055] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327049), _1327051)), 29469 ^ _780119 : [(29470 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327053), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1327049, tc_fun(_1327053, tc_HOL_Obool)), _1327051), _1327055))), 29473 ^ _780119 : [(29474 ^ _780119) ^ [_1327233] : [hBOOL(hAPP(hAPP(c_member(_1327049), _1327233), _1327051)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1327053), hAPP(_1327055, _1327233))))]]], (29480 ^ _780119) ^ [] : [29482 ^ _780119 : [(29485 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327053), hAPP(_1327055, 29481 ^ [_1327049, _1327051, _1327053, _1327055])))], (29483 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327049), 29481 ^ [_1327049, _1327051, _1327053, _1327055]), _1327051)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1327053), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1327049, tc_fun(_1327053, tc_HOL_Obool)), _1327051), _1327055))))]]], (23123 ^ _780119) ^ [_1202401] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1202401)) = 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), _1202401)))], (51201 ^ _780119) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (50734 ^ _780119) ^ [_1809128, _1809130, _1809132] : [hBOOL(hAPP(hAPP(c_List_Omember(_1809128), _1809130), _1809132)), -(hBOOL(hAPP(hAPP(c_member(_1809128), _1809132), hAPP(c_List_Oset(_1809128), _1809130))))], (7031 ^ _780119) ^ [_896215, _896217, _896219] : [class_Orderings_Olinorder(_896215), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896215), _896217), _896219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896215), _896219), _896217)))], (36682 ^ _780119) ^ [_1476965, _1476967] : [-(c_Fun_Oinj__on(_1476965, tc_Option_Ooption(_1476965), c_Option_Ooption_OSome(_1476965), _1476967))], (1450 ^ _780119) ^ [_800968, _800970] : [-(class_Groups_Olinordered__ab__semigroup__add(_800968)), _800970 = _800968, class_Groups_Olinordered__ab__semigroup__add(_800970)], (15346 ^ _780119) ^ [_1060168] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060168) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12745 ^ _780119) ^ [_1011136, _1011138, _1011140] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1011136), _1011138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1011136, tc_HOL_Obool)), _1011140), _1011138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1011136), _1011138)), hAPP(c_Finite__Set_Ocard(_1011136), _1011140))), -(_1011140 = _1011138)], (38832 ^ _780119) ^ [_1532794, _1532796, _1532798, _1532800, _1532802, _1532804, _1532806, _1532808] : [class_Groups_Ocomm__monoid__mult(_1532794), c_Fun_Oinj__on(_1532796, _1532798, _1532800, _1532802), _1532804 = hAPP(c_Set_Oimage(_1532796, _1532798, _1532800), _1532802), _1532806 = hAPP(c_Fun_Ocomp(_1532798, _1532794, _1532796, _1532808), _1532800), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1532798, _1532794), _1532808), _1532804) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1532796, _1532794), _1532806), _1532802))], (37101 ^ _780119) ^ [_1487743, _1487745, _1487747, _1487749] : [hBOOL(hAPP(hAPP(c_member(_1487743), _1487745), c_Wellfounded_Oacc(_1487743, _1487747))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1487743, _1487743)), hAPP(hAPP(c_Product__Type_OPair(_1487743, _1487743), _1487749), _1487745)), _1487747)), -(hBOOL(hAPP(hAPP(c_member(_1487743), _1487749), c_Wellfounded_Oacc(_1487743, _1487747))))], (2878 ^ _780119) ^ [_822965, _822967, _822969, _822971] : [-(c_Relation_OId__on(_822971, _822967) = c_Relation_OId__on(_822969, _822965)), _822971 = _822969, _822967 = _822965], (25596 ^ _780119) ^ [_1247961, _1247963] : [c_Nat__Transfer_Ois__nat(_1247961), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1247961, _1247963)))], (27856 ^ _780119) ^ [_1294485, _1294487, _1294489, _1294491] : [class_Orderings_Olinorder(_1294485), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294485), _1294487), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1294485), _1294489), _1294491))), 27863 ^ _780119 : [(27866 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294485), _1294487), _1294491)))], (27864 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294485), _1294487), _1294489)))]]], (14906 ^ _780119) ^ [_1053645] : [class_Finite__Set_Ofinite(_1053645), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1053645), c_Orderings_Otop__class_Otop(tc_fun(_1053645, tc_HOL_Obool)))))], (9716 ^ _780119) ^ [_948275, _948277, _948279, _948281, _948283, _948285, _948287] : [class_Rings_Osemiring__0(_948275), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948275), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_948277, _948275), _948279), _948281)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_948283, _948275), _948285), _948287)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_948277, _948275), hAPP(hAPP(c_COMBC(_948277, tc_fun(_948283, tc_HOL_Obool), _948275), hAPP(hAPP(c_COMBB(tc_fun(_948283, _948275), tc_fun(tc_fun(_948283, tc_HOL_Obool), _948275), _948277), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_948283, _948275)), hAPP(hAPP(c_COMBC(_948277, tc_fun(_948283, _948275), tc_fun(_948283, _948275)), hAPP(hAPP(c_COMBB(tc_fun(_948275, _948275), tc_fun(tc_fun(_948283, _948275), tc_fun(_948283, _948275)), _948277), c_COMBB(_948275, _948275, _948283)), hAPP(hAPP(c_COMBB(_948275, tc_fun(_948275, _948275), _948277), c_Groups_Otimes__class_Otimes(_948275)), _948279))), _948285))), _948287)), _948281))], (34861 ^ _780119) ^ [_1434543, _1434545, _1434547, _1434549, _1434551] : [-(hAPP(c_Product__Type_Ofst(_1434543, _1434545), hAPP(c_Product__Type_Oapsnd(_1434547, _1434545, _1434543, _1434549), _1434551)) = hAPP(c_Product__Type_Ofst(_1434543, _1434547), _1434551))], (47959 ^ _780119) ^ [_1748874, _1748876, _1748878] : [hBOOL(hAPP(c_List_Odistinct(_1748874), _1748876)), -(c_List_Oremove1(_1748874, _1748878, c_List_Oremdups(_1748874, _1748876)) = c_List_Oremdups(_1748874, c_List_Oremove1(_1748874, _1748878, _1748876)))], (7900 ^ _780119) ^ [_914608, _914610, _914612, _914614] : [c_Com_Ocom_OSemi(_914608, _914610) = c_Com_Ocom_OSemi(_914612, _914614), 7903 ^ _780119 : [(7906 ^ _780119) ^ [] : [-(_914610 = _914614)], (7904 ^ _780119) ^ [] : [-(_914608 = _914612)]]], (27252 ^ _780119) ^ [_1283789, _1283791] : [27253 ^ _780119 : [(27254 ^ _780119) ^ [_1283853, _1283855] : [_1283791 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1283789, _1283853), 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)), _1283855)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283789), _1283791)))], (39733 ^ _780119) ^ [_1554679, _1554681] : [-(c_Relation_Orefl__on(_1554679, c_Orderings_Otop__class_Otop(tc_fun(_1554679, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1554679, _1554681)))], (49689 ^ _780119) ^ [_1787520, _1787522, _1787524] : [c_List_Olist__ex(_1787520, _1787522, _1787524), -(c_List_Olist__ex(_1787520, _1787522, hAPP(c_List_Orev(_1787520), _1787524)))], (42113 ^ _780119) ^ [_1611759, _1611761, _1611763, _1611765] : [class_Orderings_Olinorder(_1611759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611759), _1611761)), 42123 ^ _780119 : [(42126 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1611759), 42122 ^ [_1611759, _1611761, _1611763, _1611765]), _1611763))], (42124 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611759), 42122 ^ [_1611759, _1611761, _1611763, _1611765]), _1611761)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1611759), hAPP(hAPP(c_Finite__Set_Ofold(_1611759, _1611759, c_Orderings_Oord__class_Omax(_1611759)), _1611765), _1611761)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1611759), _1611763), _1611765))))], (49000 ^ _780119) ^ [_1771419, _1771421, _1771423, _1771425, _1771427, _1771429, _1771431] : [-(c_List_Olist__all2(_1771419, _1771421, _1771423, hAPP(hAPP(c_List_Olist_OCons(_1771419), _1771425), _1771427), hAPP(hAPP(c_List_Olist_OCons(_1771421), _1771429), _1771431))), hBOOL(hAPP(hAPP(_1771423, _1771425), _1771429)), c_List_Olist__all2(_1771419, _1771421, _1771423, _1771427, _1771431)], (23789 ^ _780119) ^ [_1214886, _1214888, _1214890] : [class_Groups_Oordered__ab__group__add(_1214886), -(hAPP(c_Set_Oimage(_1214886, _1214886, c_Groups_Ouminus__class_Ouminus(_1214886)), c_SetInterval_Oord__class_OatLeastAtMost(_1214886, _1214888, _1214890)) = c_SetInterval_Oord__class_OatLeastAtMost(_1214886, hAPP(c_Groups_Ouminus__class_Ouminus(_1214886), _1214890), hAPP(c_Groups_Ouminus__class_Ouminus(_1214886), _1214888)))], (38322 ^ _780119) ^ [_1520740, _1520742, _1520744, _1520746, _1520748] : [c_Relation_Orefl__on(_1520740, _1520742, _1520744), hBOOL(hAPP(hAPP(c_member(tc_prod(_1520740, _1520740)), hAPP(hAPP(c_Product__Type_OPair(_1520740, _1520740), _1520746), _1520748)), _1520744)), -(hBOOL(hAPP(hAPP(c_member(_1520740), _1520746), _1520742)))], (20466 ^ _780119) ^ [_1152479, _1152481, _1152483] : [class_Fields_Olinordered__field__inverse__zero(_1152479), 20469 ^ _780119 : [(20484 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152479), c_Groups_Ozero__class_Ozero(_1152479)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152479), _1152481), _1152483)))), 20485 ^ _780119 : [(20492 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152479), _1152481), c_Groups_Ozero__class_Ozero(_1152479))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152479), _1152483), c_Groups_Ozero__class_Ozero(_1152479)))], (20486 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152479), c_Groups_Ozero__class_Ozero(_1152479)), _1152481)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152479), c_Groups_Ozero__class_Ozero(_1152479)), _1152483))]]], (20470 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152479), c_Groups_Ozero__class_Ozero(_1152479)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152479), _1152481), _1152483))), 20475 ^ _780119 : [(20478 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152479), c_Groups_Ozero__class_Ozero(_1152479)), _1152483)))], (20476 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152479), c_Groups_Ozero__class_Ozero(_1152479)), _1152481)))]], 20479 ^ _780119 : [(20482 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152479), _1152483), c_Groups_Ozero__class_Ozero(_1152479))))], (20480 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152479), _1152481), c_Groups_Ozero__class_Ozero(_1152479))))]]]]], (39473 ^ _780119) ^ [_1548002] : [-(c_Transitive__Closure_Otrancl(_1548002, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1548002, _1548002), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1548002, _1548002), tc_HOL_Obool)))], (22211 ^ _780119) ^ [_1185556, _1185558] : [class_Rings_Olinordered__idom(_1185556), 22214 ^ _780119 : [(22221 ^ _780119) ^ [] : [_1185558 = c_Groups_Ozero__class_Ozero(_1185556), -(c_Groups_Osgn__class_Osgn(_1185556, _1185558) = c_Groups_Ozero__class_Ozero(_1185556))], (22215 ^ _780119) ^ [] : [c_Groups_Osgn__class_Osgn(_1185556, _1185558) = c_Groups_Ozero__class_Ozero(_1185556), -(_1185558 = c_Groups_Ozero__class_Ozero(_1185556))]]], (7066 ^ _780119) ^ [_896776, _896778, _896780, _896782] : [hBOOL(hAPP(_896776, _896778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896780, tc_HOL_Obool)), _896776), _896782)), -(hBOOL(hAPP(_896782, _896778)))], (37044 ^ _780119) ^ [_1486021, _1486023, _1486025, _1486027, _1486029, _1486031] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1486021, _1486023, _1486025), _1486027), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1486023, _1486025), tc_HOL_Obool)), _1486029), _1486031)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1486021, _1486025), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1486021, _1486023, _1486025), _1486027), _1486029)), hAPP(hAPP(c_Relation_Orel__comp(_1486021, _1486023, _1486025), _1486027), _1486031)))], (33629 ^ _780119) ^ [_1408977, _1408979, _1408981, _1408983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool)), _1408981), _1408983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408977, tc_fun(_1408979, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1408977, tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_fun(_1408979, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408979, tc_fun(tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_fun(_1408979, tc_HOL_Obool)), _1408977), c_COMBC(_1408979, tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408979, tc_prod(_1408977, _1408979)), tc_fun(_1408979, tc_fun(tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_HOL_Obool)), _1408977), hAPP(c_COMBB(tc_prod(_1408977, _1408979), tc_fun(tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_HOL_Obool), _1408979), c_member(tc_prod(_1408977, _1408979)))), c_Product__Type_OPair(_1408977, _1408979)))), _1408981)), hAPP(hAPP(c_COMBC(_1408977, tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_fun(_1408979, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408979, tc_fun(tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_fun(_1408979, tc_HOL_Obool)), _1408977), c_COMBC(_1408979, tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408979, tc_prod(_1408977, _1408979)), tc_fun(_1408979, tc_fun(tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_HOL_Obool)), _1408977), hAPP(c_COMBB(tc_prod(_1408977, _1408979), tc_fun(tc_fun(tc_prod(_1408977, _1408979), tc_HOL_Obool), tc_HOL_Obool), _1408979), c_member(tc_prod(_1408977, _1408979)))), c_Product__Type_OPair(_1408977, _1408979)))), _1408983))))], (1230 ^ _780119) ^ [_798218, _798220] : [-(class_Rings_Oring(_798218)), _798220 = _798218, class_Rings_Oring(_798220)], (18736 ^ _780119) ^ [_1121788, _1121790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121788), _1121790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121788), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1121790)))], (22426 ^ _780119) ^ [_1189406, _1189408] : [class_Rings_Olinordered__idom(_1189406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189406), c_Groups_Ozero__class_Ozero(_1189406)), _1189408)), -(c_Groups_Osgn__class_Osgn(_1189406, _1189408) = c_Groups_Oone__class_Oone(_1189406))], (25153 ^ _780119) ^ [_1240554, _1240556] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1240554) = _1240556), _1240554 = hAPP(c_Int_Onat, _1240556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240556))], (51239 ^ _780119) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (4312 ^ _780119) ^ [_845346, _845348, _845350, _845352, _845354, _845356, _845358, _845360] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_845360, _845356, _845352, _845348) = c_New__Random__Sequence_Opos__not__random__dseq(_845358, _845354, _845350, _845346)), _845360 = _845358, _845356 = _845354, _845352 = _845350, _845348 = _845346], (41610 ^ _780119) ^ [_1600228, _1600230, _1600232, _1600234, _1600236, _1600238, _1600240] : [41612 ^ _780119 : [(41615 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1600236, 41611 ^ [_1600228, _1600230, _1600232, _1600234, _1600236, _1600238, _1600240]), _1600238), _1600240))], (41613 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1600228), 41611 ^ [_1600228, _1600230, _1600232, _1600234, _1600236, _1600238, _1600240]), _1600234)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600228, tc_fun(_1600230, tc_fun(_1600232, tc_HOL_Obool))), _1600234), _1600236), _1600238), _1600240)))], (46527 ^ _780119) ^ [_1717994, _1717996, _1717998, _1718000] : [-(_1717994 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717996)), _1717998)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1717996, hAPP(hAPP(c_List_Olist__update(_1717996, _1717998), _1717994), _1718000)) = hAPP(hAPP(c_List_Olist__update(_1717996, c_List_Obutlast(_1717996, _1717998)), _1717994), _1718000))], (9482 ^ _780119) ^ [_943226, _943228, _943230, _943232, _943234] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_943226, _943226, _943228, _943230, _943232), _943234)), -(hBOOL(hAPP(hAPP(c_member(_943226), _943230), _943232))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_943226, _943228, hAPP(hAPP(c_Set_Oinsert(_943226), _943230), _943232)), _943234)))], (45792 ^ _780119) ^ [_1702357, _1702359, _1702361, _1702363, _1702365] : [-(hAPP(hAPP(c_List_Ozip(_1702357, _1702359), _1702361), hAPP(hAPP(c_List_Oappend(_1702359), _1702363), _1702365)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1702357, _1702359)), hAPP(hAPP(c_List_Ozip(_1702357, _1702359), hAPP(hAPP(c_List_Otake(_1702357), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702359)), _1702363)), _1702361)), _1702363)), hAPP(hAPP(c_List_Ozip(_1702357, _1702359), hAPP(hAPP(c_List_Odrop(_1702357), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702359)), _1702363)), _1702361)), _1702365)))], (3858 ^ _780119) ^ [_838253, _838255, _838257, _838259, _838261, _838263, _838265, _838267, _838269, _838271] : [-(c_List_Ofoldr(_838271, _838267, _838263, _838259, _838255) = c_List_Ofoldr(_838269, _838265, _838261, _838257, _838253)), _838271 = _838269, _838267 = _838265, _838263 = _838261, _838259 = _838257, _838255 = _838253], (35145 ^ _780119) ^ [_1440755, _1440757, _1440759, _1440761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1440755), _1440757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1440759), _1440761)), -(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), _1440755), _1440759)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1440757), _1440761))), c_FunDef_Opair__less)))], (44912 ^ _780119) ^ [_1679816, _1679818, _1679820, _1679822] : [-(hAPP(c_List_Olist_Olist__case(_1679816, _1679818, _1679820, _1679822), c_List_Olist_ONil(_1679818)) = _1679820)], (16857 ^ _780119) ^ [_1086606, _1086608] : [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), _1086606), _1086608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1086606))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1086608)))], (34607 ^ _780119) ^ [_1429687, _1429689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429687), 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)), _1429689)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1429687, _1429689) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1429687, _1429689)))], (43713 ^ _780119) ^ [_1652776, _1652778, _1652780] : [-(c_Random_Oselect__weight(_1652776, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1652776)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1652776), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1652778)), _1652780)) = c_Random_Oselect__weight(_1652776, _1652780))], (8514 ^ _780119) ^ [_927985, _927987, _927989, _927991, _927993] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927985, _927987), _927989), _927991), _927993) = _927989, -(hAPP(_927989, _927991) = _927993)], (25019 ^ _780119) ^ [_1238469, _1238471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238471)), 25026 ^ _780119 : [(25033 ^ _780119) ^ [] : [_1238469 = _1238471, -(hAPP(c_Int_Onat, _1238469) = hAPP(c_Int_Onat, _1238471))], (25027 ^ _780119) ^ [] : [hAPP(c_Int_Onat, _1238469) = hAPP(c_Int_Onat, _1238471), -(_1238469 = _1238471)]]], (25356 ^ _780119) ^ [_1243829, _1243831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243831)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1243829), _1243831)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1243829)), hAPP(c_Int_Onat, _1243831)))], (34341 ^ _780119) ^ [_1424659, _1424661, _1424663] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1424659), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1424661)), _1424663)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1424659, _1424661), hAPP(c_Divides_OnegateSnd, _1424663))))], (23905 ^ _780119) ^ [_1217406, _1217408, _1217410, _1217412, _1217414] : [class_Orderings_Oorder(_1217406), 23908 ^ _780119 : [(23929 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1217406, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1217406, _1217408, _1217410)), c_SetInterval_Oord__class_OatLeastAtMost(_1217406, _1217412, _1217414)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217406), _1217412), _1217414)), 23932 ^ _780119 : [(23935 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217406), _1217412), _1217408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217406), _1217410), _1217414)), 23942 ^ _780119 : [(23945 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217406), _1217410), _1217414))], (23943 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217406), _1217412), _1217408))]]], (23933 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217406), _1217408), _1217410)))]]], (23909 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1217406, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1217406, _1217408, _1217410)), c_SetInterval_Oord__class_OatLeastAtMost(_1217406, _1217412, _1217414))), 23912 ^ _780119 : [(23913 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217406), _1217408), _1217410)), 23916 ^ _780119 : [(23919 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217406), _1217410), _1217414)))], (23921 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217406), _1217412), _1217408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217406), _1217410), _1217414)))], (23917 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217406), _1217412), _1217408)))]]], (23927 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217406), _1217412), _1217414)))]]]]], (13206 ^ _780119) ^ [_1020582, _1020584, _1020586] : [class_Groups_Ogroup__add(_1020582), 13209 ^ _780119 : [(13216 ^ _780119) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1020582), _1020586) = _1020584, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1020582), _1020584) = _1020586)], (13210 ^ _780119) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1020582), _1020584) = _1020586, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1020582), _1020586) = _1020584)]]], (40084 ^ _780119) ^ [_1562815, _1562817] : [-(c_Relation_Ototal__on(_1562815, c_Orderings_Obot__class_Obot(tc_fun(_1562815, tc_HOL_Obool)), _1562817))], (37006 ^ _780119) ^ [_1484199, _1484201, _1484203, _1484205] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1484199, _1484201, _1484203, c_Code__Numeral_OSuc__code__numeral(_1484205)) = hAPP(_1484203, _1484205))], (1680 ^ _780119) ^ [_803843, _803845] : [-(class_Orderings_Olinorder(_803843)), _803845 = _803843, class_Orderings_Olinorder(_803845)], (46079 ^ _780119) ^ [_1708131, _1708133, _1708135] : [class_Lattices_Olattice(_1708131), -(c_Big__Operators_Olattice__class_OInf__fin(_1708131, hAPP(c_List_Oset(_1708131), hAPP(hAPP(c_List_Olist_OCons(_1708131), _1708133), _1708135))) = hAPP(c_List_Ofoldl(_1708131, _1708131, c_Lattices_Osemilattice__inf__class_Oinf(_1708131), _1708133), _1708135))], (39479 ^ _780119) ^ [_1548139, _1548141] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548139, _1548139)), c_Transitive__Closure_Otrancl(_1548139, _1548141))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548139, _1548139)), _1548141)))], (23066 ^ _780119) ^ [_1201352, _1201354] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201352)), _1201354) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1201352), _1201354)))], (382 ^ _780119) ^ [_786012, _786014, _786016, _786018] : [-(c_Wellfounded_OwfP(_786016, _786012)), c_Wellfounded_OwfP(_786018, _786014), _786018 = _786016, _786014 = _786012], (49749 ^ _780119) ^ [_1788831, _1788833, _1788835] : [hBOOL(hAPP(hAPP(c_member(_1788831), _1788833), hAPP(c_List_Oset(_1788831), _1788835))), 49754 ^ _780119 : [(49757 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1788831), _1788833), hAPP(c_List_Oset(_1788831), 49752 ^ [_1788831, _1788833, _1788835])))], (49755 ^ _780119) ^ [] : [-(_1788835 = hAPP(hAPP(c_List_Oappend(_1788831), 49752 ^ [_1788831, _1788833, _1788835]), hAPP(hAPP(c_List_Olist_OCons(_1788831), _1788833), 49753 ^ [_1788831, _1788833, _1788835])))]]], (18520 ^ _780119) ^ [_1117981, _1117983, _1117985] : [class_Rings_Oring__1(_1117981), hBOOL(hAPP(hAPP(c_member(_1117981), _1117983), c_Int_Oring__1__class_OInts(_1117981))), -(hBOOL(hAPP(hAPP(c_member(_1117981), hAPP(hAPP(c_Power_Opower__class_Opower(_1117981), _1117983), _1117985)), c_Int_Oring__1__class_OInts(_1117981))))], (22035 ^ _780119) ^ [_1182531, _1182533] : [-(_1182531 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22038 ^ _780119 : [(22045 ^ _780119) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182533, _1182531) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182533), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182531)) = 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), _1182533), _1182531))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22039 ^ _780119) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182533, _1182531) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182533), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182531)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182533), _1182531)))]]], (25820 ^ _780119) ^ [_1251379, _1251381, _1251383] : [class_Rings_Oring__1(_1251379), -(hAPP(c_Int_Oring__1__class_Oof__int(_1251379), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1251381), _1251383)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1251379), hAPP(c_Int_Oring__1__class_Oof__int(_1251379), _1251381)), _1251383))], (12085 ^ _780119) ^ [_997896, _997898, _997900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997896), _997898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997896), _997900)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997898), _997896)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997900), _997896)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997898), _997900))], (38054 ^ _780119) ^ [_1514320, _1514322, _1514324, _1514326] : [class_Groups_Ocomm__monoid__mult(_1514320), c_Fun_Oinj__on(_1514322, _1514320, _1514324, _1514326), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514322, _1514320), _1514324), _1514326) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514320, _1514320), c_Fun_Oid(_1514320)), hAPP(c_Set_Oimage(_1514322, _1514320, _1514324), _1514326)))], (29973 ^ _780119) ^ [_1340152, _1340154] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1340152), _1340154)), 29979 ^ _780119 : [(29982 ^ _780119) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29980 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1340152), 29978 ^ [_1340152, _1340154]), _1340154)))]], -(hAPP(c_Finite__Set_Ocard(_1340152), _1340154) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45952 ^ _780119) ^ [_1705475, _1705477] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705475)), hAPP(c_List_Otl(_1705475), _1705477)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705475)), _1705477)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (29122 ^ _780119) ^ [_1319735, _1319737, _1319739] : [class_Orderings_Olinorder(_1319735), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319735), _1319737)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319735), _1319739)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319735, tc_HOL_Obool)), _1319737), _1319739) = c_Orderings_Obot__class_Obot(tc_fun(_1319735, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319735), c_Big__Operators_Olattice_OInf__fin(_1319735, c_Orderings_Oord__class_Omin(_1319735), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319735, tc_HOL_Obool)), _1319737), _1319739))), c_Big__Operators_Olattice_OInf__fin(_1319735, c_Orderings_Oord__class_Omin(_1319735), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319735, tc_HOL_Obool)), _1319737), _1319739))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319735), c_Big__Operators_Olattice_OInf__fin(_1319735, c_Orderings_Oord__class_Omin(_1319735), _1319737)), c_Big__Operators_Olattice_OInf__fin(_1319735, c_Orderings_Oord__class_Omin(_1319735), _1319739)))], (18774 ^ _780119) ^ [] : [-(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))], (47059 ^ _780119) ^ [_1728539, _1728541] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1728539, _1728541)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1728539), hAPP(c_Nat_OSuc, _1728541)))], (26272 ^ _780119) ^ [_1259423, _1259425, _1259427, _1259429, _1259431] : [class_Groups_Ocomm__monoid__add(_1259423), class_Groups_Ocomm__monoid__mult(_1259423), _1259425 = _1259427, c_Nat__Transfer_Onat__set(_1259427), 26290 ^ _780119 : [(26293 ^ _780119) ^ [] : [hAPP(_1259429, 26289 ^ [_1259423, _1259425, _1259427, _1259429, _1259431]) = hAPP(_1259431, 26289 ^ [_1259423, _1259425, _1259427, _1259429, _1259431])], (26291 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26289 ^ [_1259423, _1259425, _1259427, _1259429, _1259431])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1259423), _1259429), _1259425) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1259423), _1259431), _1259427))], (36119 ^ _780119) ^ [_1465142, _1465144, _1465146, _1465148] : [c_Fun_Oinj__on(_1465142, _1465144, _1465146, _1465148), 36122 ^ _780119 : [(36123 ^ _780119) ^ [_1465250] : [hBOOL(hAPP(hAPP(c_member(_1465142), _1465250), _1465148)), 36126 ^ _780119 : [(36127 ^ _780119) ^ [_1465352] : [hBOOL(hAPP(hAPP(c_member(_1465142), _1465352), _1465148)), hAPP(_1465146, _1465250) = hAPP(_1465146, _1465352), -(_1465250 = _1465352)]]]]], (24003 ^ _780119) ^ [_1219290, _1219292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1219290), _1219292)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1219290), hAPP(c_Nat_OSuc, _1219292)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1219292), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1219290), _1219292)))], (7474 ^ _780119) ^ [_905807, _905809, _905811, _905813] : [class_Lattices_Osemilattice__sup(_905807), 7477 ^ _780119 : [(7486 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905807), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_905807), _905809), _905811)), _905813))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905807), _905809), _905813)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905807), _905811), _905813))], (7478 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905807), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_905807), _905809), _905811)), _905813)), 7481 ^ _780119 : [(7484 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905807), _905811), _905813)))], (7482 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905807), _905809), _905813)))]]]]], (45162 ^ _780119) ^ [_1685243, _1685245, _1685247, _1685249, _1685251] : [hAPP(hAPP(c_List_Oappend(_1685243), _1685245), _1685247) = hAPP(hAPP(c_List_Oappend(_1685243), _1685249), _1685251), 45168 ^ _780119 : [(45171 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1685243), 45165 ^ [_1685243, _1685245, _1685247, _1685249, _1685251]), _1685247) = _1685251)], (45169 ^ _780119) ^ [] : [-(_1685245 = hAPP(hAPP(c_List_Oappend(_1685243), _1685249), 45165 ^ [_1685243, _1685245, _1685247, _1685249, _1685251]))]], 45172 ^ _780119 : [(45175 ^ _780119) ^ [] : [-(_1685247 = hAPP(hAPP(c_List_Oappend(_1685243), 45165 ^ [_1685243, _1685245, _1685247, _1685249, _1685251]), _1685251))], (45173 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1685243), _1685245), 45165 ^ [_1685243, _1685245, _1685247, _1685249, _1685251]) = _1685249)]]], (40215 ^ _780119) ^ [_1566347, _1566349, _1566351] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1566347, _1566347, _1566347), _1566349), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566347, _1566347), tc_HOL_Obool), _1566351), _1566349)) = hAPP(hAPP(c_Relation_Orel__comp(_1566347, _1566347, _1566347), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566347, _1566347), tc_HOL_Obool), _1566351), _1566349)), _1566349))], (28014 ^ _780119) ^ [_1297367, _1297369, _1297371] : [class_Groups_Olinordered__ab__group__add(_1297367), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1297367), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1297367), _1297369), _1297371)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1297367), hAPP(c_Groups_Ouminus__class_Ouminus(_1297367), _1297369)), hAPP(c_Groups_Ouminus__class_Ouminus(_1297367), _1297371)))], (44908 ^ _780119) ^ [_1679560, _1679562, _1679564, _1679566, _1679568] : [-(hAPP(hAPP(c_List_Ozip(_1679560, _1679562), hAPP(hAPP(c_List_Olist_OCons(_1679560), _1679564), _1679566)), _1679568) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1679560, _1679562)), _1679562, c_List_Olist_ONil(tc_prod(_1679560, _1679562)), hAPP(hAPP(c_COMBC(_1679562, tc_fun(tc_List_Olist(_1679562), tc_List_Olist(tc_prod(_1679560, _1679562))), tc_fun(tc_List_Olist(_1679562), tc_List_Olist(tc_prod(_1679560, _1679562)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1679560, _1679562)), tc_List_Olist(tc_prod(_1679560, _1679562))), tc_fun(tc_fun(tc_List_Olist(_1679562), tc_List_Olist(tc_prod(_1679560, _1679562))), tc_fun(tc_List_Olist(_1679562), tc_List_Olist(tc_prod(_1679560, _1679562)))), _1679562), c_COMBB(tc_List_Olist(tc_prod(_1679560, _1679562)), tc_List_Olist(tc_prod(_1679560, _1679562)), tc_List_Olist(_1679562))), hAPP(hAPP(c_COMBB(tc_prod(_1679560, _1679562), tc_fun(tc_List_Olist(tc_prod(_1679560, _1679562)), tc_List_Olist(tc_prod(_1679560, _1679562))), _1679562), c_List_Olist_OCons(tc_prod(_1679560, _1679562))), hAPP(c_Product__Type_OPair(_1679560, _1679562), _1679564)))), hAPP(c_List_Ozip(_1679560, _1679562), _1679566))), _1679568))], (35426 ^ _780119) ^ [] : [-(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))))))], (43064 ^ _780119) ^ [_1633744, _1633746] : [-(hAPP(hAPP(c_List_Ozip(_1633744, _1633744), _1633746), _1633746) = hAPP(hAPP(c_List_Omap(_1633744, tc_prod(_1633744, _1633744)), hAPP(hAPP(c_COMBS(_1633744, _1633744, tc_prod(_1633744, _1633744)), c_Product__Type_OPair(_1633744, _1633744)), c_COMBI(_1633744))), _1633746))], (39369 ^ _780119) ^ [_1545696, _1545698, _1545700, _1545702] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1545696, _1545698, _1545700, tc_prod(_1545698, _1545700)), _1545702), c_Product__Type_OPair(_1545698, _1545700)) = _1545702)], (19723 ^ _780119) ^ [_1138896, _1138898, _1138900] : [class_Rings_Odivision__ring(_1138896), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1138896), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138896), _1138898), _1138900)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138896), hAPP(c_Groups_Ouminus__class_Ouminus(_1138896), _1138898)), _1138900))], (51669 ^ _780119) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), v_F))], (9178 ^ _780119) ^ [_937709, _937711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937709, tc_HOL_Obool)), _937711), c_Orderings_Obot__class_Obot(tc_fun(_937709, tc_HOL_Obool))))], (12781 ^ _780119) ^ [_1011870] : [-(hAPP(c_Com_Obody, _1011870) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _1011870))))], (43479 ^ _780119) ^ [_1646575, _1646577, _1646579, _1646581] : [hBOOL(hAPP(hAPP(c_member(_1646575), _1646577), hAPP(c_List_Oset(_1646575), hAPP(hAPP(c_List_Olist_OCons(_1646575), _1646579), _1646581)))), -(_1646577 = _1646579), -(hBOOL(hAPP(hAPP(c_member(_1646575), _1646577), hAPP(c_List_Oset(_1646575), _1646581))))], (42655 ^ _780119) ^ [_1624461, _1624463, _1624465, _1624467] : [_1624467 = c_Option_Ooption_ONone(_1624461), -(hAPP(hAPP(c_Option_Omap(_1624461, _1624463), _1624465), _1624467) = c_Option_Ooption_ONone(_1624463))], (26521 ^ _780119) ^ [_1264399, _1264401, _1264403, _1264405] : [class_Fields_Olinordered__field(_1264399), -(hAPP(c_Groups_Oabs__class_Oabs(_1264399), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1264401, _1264399), _1264403), _1264405)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1264401, _1264399), hAPP(hAPP(c_COMBB(_1264399, _1264399, _1264401), c_Groups_Oabs__class_Oabs(_1264399)), _1264403)), _1264405))], (50969 ^ _780119) ^ [_1814101, _1814103] : [class_Lattices_Odistrib__lattice(_1814101), -(class_Lattices_Odistrib__lattice(tc_fun(_1814103, _1814101)))], (12990 ^ _780119) ^ [_1016004, _1016006, _1016008] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1016004), _1016006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1016004), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016004, tc_HOL_Obool)), _1016006), hAPP(hAPP(c_Set_Oinsert(_1016004), _1016008), c_Orderings_Obot__class_Obot(tc_fun(_1016004, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1016004), _1016006))))], (44540 ^ _780119) ^ [_1672381, _1672383] : [-(c_Code__Numeral_Onat__of__aux(_1672381, _1672383) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1672381)), _1672383))], (5368 ^ _780119) ^ [_862294, _862296, _862298, _862300, _862302, _862304, _862306, _862308, _862310, _862312] : [-(c_Nitpick_Opair__box_Opair__box__rec(_862312, _862308, _862304, _862300, _862296) = c_Nitpick_Opair__box_Opair__box__rec(_862310, _862306, _862302, _862298, _862294)), _862312 = _862310, _862308 = _862306, _862304 = _862302, _862300 = _862298, _862296 = _862294], (25263 ^ _780119) ^ [_1242332, _1242334] : [-(hAPP(c_Int_Onat, _1242332) = _1242334), 25266 ^ _780119 : [(25269 ^ _780119) ^ [] : [_1242332 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1242334)], (25267 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242332)))]], 25270 ^ _780119 : [(25273 ^ _780119) ^ [] : [_1242334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25271 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242332))]]], (34447 ^ _780119) ^ [_1426516, _1426518, _1426520, _1426522] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1426516, _1426518), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1426520), _1426522))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1426516, _1426518) = _1426522)], (5194 ^ _780119) ^ [_859615, _859617] : [_859617 = _859615, -(c_List_Ohd(_859617) = c_List_Ohd(_859615))], (11323 ^ _780119) ^ [_982111, _982113, _982115, _982117, _982119, _982121] : [class_Rings_Oordered__ring(_982111), 11326 ^ _780119 : [(11333 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982111), _982117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982111), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_982111), _982119), _982113)), _982115)), _982121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982111), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982111), _982113), _982115)), _982117)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982111), _982119), _982115)), _982121))))], (11327 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982111), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982111), _982113), _982115)), _982117)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982111), _982119), _982115)), _982121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982111), _982117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982111), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_982111), _982119), _982113)), _982115)), _982121))))]]], (40734 ^ _780119) ^ [_1578862, _1578864, _1578866] : [class_Lattices_Oab__semigroup__idem__mult(_1578862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578862), _1578864)), -(hAPP(c_Finite__Set_Ofold1(_1578862, c_Groups_Otimes__class_Otimes(_1578862)), hAPP(hAPP(c_Set_Oinsert(_1578862), _1578866), _1578864)) = hAPP(hAPP(c_Finite__Set_Ofold(_1578862, _1578862, c_Groups_Otimes__class_Otimes(_1578862)), _1578866), _1578864))], (1290 ^ _780119) ^ [_798968, _798970] : [-(class_Lattices_Obounded__lattice__bot(_798968)), _798970 = _798968, class_Lattices_Obounded__lattice__bot(_798970)], (32351 ^ _780119) ^ [_1383477, _1383479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1383477)), c_Int_OBit0(_1383479))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383477), _1383479)))], (17464 ^ _780119) ^ [_1097534, _1097536, _1097538] : [class_Rings_Olinordered__ring(_1097534), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097534), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097534), _1097536), _1097536)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097534), _1097538), _1097538))), c_Groups_Ozero__class_Ozero(_1097534)))], (21390 ^ _780119) ^ [_1169697, _1169699, _1169701] : [class_Divides_Osemiring__div(_1169697), -(c_Divides_Odiv__class_Omod(_1169697, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169697), _1169699), _1169701), _1169701) = c_Divides_Odiv__class_Omod(_1169697, _1169699, _1169701))], (28226 ^ _780119) ^ [_1301857, _1301859] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1301857), _1301859)), _1301859) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1301857), _1301859))], (11005 ^ _780119) ^ [_975505, _975507, _975509, _975511, _975513] : [class_Groups_Ocomm__monoid__add(_975505), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_975507, _975505), hAPP(hAPP(c_COMBS(_975507, _975505, _975505), hAPP(hAPP(c_COMBB(_975505, tc_fun(_975505, _975505), _975507), c_Groups_Oplus__class_Oplus(_975505)), _975509)), _975511)), _975513) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975505), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_975507, _975505), _975509), _975513)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_975507, _975505), _975511), _975513)))], (51065 ^ _780119) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (48381 ^ _780119) ^ [_1758269, _1758271, _1758273, _1758275] : [class_Orderings_Olinorder(_1758269), -(c_List_Olinorder__class_Osorted(_1758269, hAPP(hAPP(c_List_Omap(_1758271, _1758269), _1758273), c_List_Olinorder__class_Osort__key(_1758271, _1758269, _1758273, _1758275))))], (28956 ^ _780119) ^ [_1316725, _1316727, _1316729] : [class_Orderings_Olinorder(_1316725), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316725), _1316727)), -(_1316729 = c_Orderings_Obot__class_Obot(tc_fun(_1316725, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316725, tc_HOL_Obool)), _1316729), _1316727)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1316725), c_Big__Operators_Olattice_OSup__fin(_1316725, c_Orderings_Oord__class_Omax(_1316725), _1316729)), c_Big__Operators_Olattice_OSup__fin(_1316725, c_Orderings_Oord__class_Omax(_1316725), _1316727)) = c_Big__Operators_Olattice_OSup__fin(_1316725, c_Orderings_Oord__class_Omax(_1316725), _1316727))], (38700 ^ _780119) ^ [_1529779, _1529781] : [-(c_Hilbert__Choice_OEps(_1529779, hAPP(hAPP(c_COMBC(_1529779, _1529779, tc_HOL_Obool), c_fequal), _1529781)) = _1529781)], (45964 ^ _780119) ^ [_1705736, _1705738] : [class_Lattices_Oab__semigroup__idem__mult(_1705736), -(_1705738 = c_List_Olist_ONil(_1705736)), -(hAPP(c_Finite__Set_Ofold1(_1705736, c_Groups_Otimes__class_Otimes(_1705736)), hAPP(c_List_Oset(_1705736), _1705738)) = hAPP(c_List_Ofoldl(_1705736, _1705736, c_Groups_Otimes__class_Otimes(_1705736), hAPP(c_List_Ohd(_1705736), _1705738)), hAPP(c_List_Otl(_1705736), _1705738)))], (33069 ^ _780119) ^ [_1396367, _1396369] : [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), _1396367))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1396369))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1396367))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396369)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396367)))], (15478 ^ _780119) ^ [_1062280, _1062282] : [class_Lattices_Obounded__lattice__top(_1062280), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062280), c_Orderings_Otop__class_Otop(_1062280)), _1062282) = _1062282)], (10991 ^ _780119) ^ [_975234, _975236] : [class_Groups_Ocomm__monoid__mult(_975234), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975234), _975236), c_Groups_Oone__class_Oone(_975234)) = _975236)], (20500 ^ _780119) ^ [_1153069, _1153071, _1153073, _1153075] : [class_Fields_Ofield__inverse__zero(_1153069), 20503 ^ _780119 : [(20504 ^ _780119) ^ [] : [_1153071 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153069), _1153073), _1153075), 20507 ^ _780119 : [(20514 ^ _780119) ^ [] : [_1153075 = c_Groups_Ozero__class_Ozero(_1153069), -(_1153071 = c_Groups_Ozero__class_Ozero(_1153069))], (20508 ^ _780119) ^ [] : [-(_1153075 = c_Groups_Ozero__class_Ozero(_1153069)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153069), _1153071), _1153075) = _1153073)]]], (20520 ^ _780119) ^ [] : [-(_1153071 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153069), _1153073), _1153075)), 20523 ^ _780119 : [(20526 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153069), _1153071), _1153075) = _1153073], (20524 ^ _780119) ^ [] : [_1153075 = c_Groups_Ozero__class_Ozero(_1153069)]], 20527 ^ _780119 : [(20530 ^ _780119) ^ [] : [_1153071 = c_Groups_Ozero__class_Ozero(_1153069)], (20528 ^ _780119) ^ [] : [-(_1153075 = c_Groups_Ozero__class_Ozero(_1153069))]]]]], (44179 ^ _780119) ^ [_1664622, _1664624, _1664626, _1664628] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664622), tc_List_Olist(_1664622))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664622), tc_List_Olist(_1664622)), _1664624), _1664626)), c_List_Olexord(_1664622, _1664628))), 44184 ^ _780119 : [(44187 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1664622), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664622)), _1664624)), _1664626) = _1664624)], (44185 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664622)), _1664624)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664622)), _1664626))))]], 44189 ^ _780119 : [(44192 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1664622), 44188 ^ [_1664622, _1664624, _1664626, _1664628]), _1664624) = hAPP(hAPP(c_List_Otake(_1664622), 44188 ^ [_1664622, _1664624, _1664626, _1664628]), _1664626))], (44194 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1664622, _1664622)), hAPP(hAPP(c_Product__Type_OPair(_1664622, _1664622), hAPP(hAPP(c_List_Onth(_1664622), _1664624), 44188 ^ [_1664622, _1664624, _1664626, _1664628])), hAPP(hAPP(c_List_Onth(_1664622), _1664626), 44188 ^ [_1664622, _1664624, _1664626, _1664628]))), _1664628)))], (44190 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44188 ^ [_1664622, _1664624, _1664626, _1664628]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664622)), _1664624)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664622)), _1664626)))))]]], (39375 ^ _780119) ^ [_1545931, _1545933, _1545935, _1545937, _1545939, _1545941, _1545943] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1545931, _1545933, _1545935, _1545937), _1545939), _1545941), _1545943) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1545933, _1545935, _1545937), _1545941), hAPP(_1545939, _1545943)))], (46097 ^ _780119) ^ [_1708518, _1708520, _1708522] : [class_Orderings_Olinorder(_1708518), -(c_Big__Operators_Olattice_OInf__fin(_1708518, c_Orderings_Oord__class_Omin(_1708518), hAPP(c_List_Oset(_1708518), hAPP(hAPP(c_List_Olist_OCons(_1708518), _1708520), _1708522))) = hAPP(c_List_Ofoldl(_1708518, _1708518, c_Orderings_Oord__class_Omin(_1708518), _1708520), _1708522))], (48083 ^ _780119) ^ [_1751348, _1751350, _1751352] : [c_List_OdropWhile(_1751348, _1751350, _1751352) = c_List_Olist_ONil(_1751348), 48086 ^ _780119 : [(48087 ^ _780119) ^ [_1751439] : [hBOOL(hAPP(hAPP(c_member(_1751348), _1751439), hAPP(c_List_Oset(_1751348), _1751352))), -(hBOOL(hAPP(_1751350, _1751439)))]]], (40946 ^ _780119) ^ [_1582918, _1582920, _1582922, _1582924, _1582926] : [c_Finite__Set_Ofun__left__comm(_1582918, _1582920, _1582922), -(c_Finite__Set_Ofun__left__comm(_1582924, _1582920, hAPP(hAPP(c_COMBB(_1582918, tc_fun(_1582920, _1582920), _1582924), _1582922), _1582926)))], (9276 ^ _780119) ^ [_939578, _939580, _939582, _939584, _939586, _939588, _939590] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_939578, tc_Option_Ooption(_939580)), _939582), _939584), hAPP(c_Option_Ooption_OSome(_939580), _939586)), _939588) = hAPP(c_Option_Ooption_OSome(_939580), _939590)), 9277 ^ _780119 : [(9284 ^ _780119) ^ [] : [-(_939588 = _939584), hAPP(_939582, _939588) = hAPP(c_Option_Ooption_OSome(_939580), _939590)], (9278 ^ _780119) ^ [] : [_939588 = _939584, _939586 = _939590]]], (12059 ^ _780119) ^ [_997462, _997464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997462), _997464)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997464), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997464), _997462)) = _997462)], (51399 ^ _780119) ^ [_1818530, _1818532] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1818530, _1818532)))], (18784 ^ _780119) ^ [_1122665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1122665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122665)))], (7356 ^ _780119) ^ [_903615, _903617, _903619, _903621] : [class_Lattices_Olattice(_903615), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903615), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903615), _903617), _903619)), _903621) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903615), _903617), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903615), _903619), _903621)))], (19865 ^ _780119) ^ [_1141300, _1141302, _1141304] : [class_Rings_Odivision__ring(_1141300), -(_1141302 = c_Groups_Ozero__class_Ozero(_1141300)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1141300), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141300), _1141304), _1141302)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141300), _1141304), hAPP(c_Groups_Ouminus__class_Ouminus(_1141300), _1141302)))], (11686 ^ _780119) ^ [_990561, _990563, _990565] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990561), _990563)), _990565) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990561), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990563), _990565)))], (9396 ^ _780119) ^ [_941766, _941768, _941770] : [class_Lattices_Olattice(_941766), hBOOL(hAPP(c_Finite__Set_Ofinite(_941766), _941768)), -(_941768 = c_Orderings_Obot__class_Obot(tc_fun(_941766, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_941766), _941770)), -(_941770 = c_Orderings_Obot__class_Obot(tc_fun(_941766, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_941766, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941766, tc_HOL_Obool)), _941768), _941770)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_941766), c_Big__Operators_Olattice__class_OSup__fin(_941766, _941768)), c_Big__Operators_Olattice__class_OSup__fin(_941766, _941770)))], (36251 ^ _780119) ^ [_1467655, _1467657, _1467659, _1467661] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467655), hAPP(c_Set_Oimage(_1467657, _1467655, _1467659), _1467661))), c_Fun_Oinj__on(_1467657, _1467655, _1467659, _1467661), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1467657), _1467661)))], (3378 ^ _780119) ^ [_830857, _830859] : [_830859 = _830857, -(c_Random_Orange(_830859) = c_Random_Orange(_830857))], (51357 ^ _780119) ^ [_1817993, _1817995] : [-(class_Finite__Set_Ofinite(tc_sum(_1817993, _1817995))), class_Finite__Set_Ofinite(_1817993), class_Finite__Set_Ofinite(_1817995)], (35516 ^ _780119) ^ [_1450952, _1450954] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1450952), c_Orderings_Obot__class_Obot(tc_fun(_1450952, tc_HOL_Obool))), _1450954) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1450952, tc_HOL_Obool), tc_HOL_Obool)))], (2940 ^ _780119) ^ [_823888, _823890, _823892, _823894] : [-(c_Relation_ORange(_823894, _823890) = c_Relation_ORange(_823892, _823888)), _823894 = _823892, _823890 = _823888], (5809 ^ _780119) ^ [_872106, _872108] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, _872106))), _872108), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _872106)))), 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, _872108, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, _872106))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (26815 ^ _780119) ^ [_1270317, _1270319, _1270321] : [-(hAPP(c_Set_OCollect(_1270317), hAPP(hAPP(c_COMBS(_1270317, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1270317), c_fimplies), _1270319)), _1270321)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270317, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1270317, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1270317), _1270319))), hAPP(c_Set_OCollect(_1270317), _1270321)))], (7724 ^ _780119) ^ [_911018, _911020, _911022, _911024, _911026] : [c_Finite__Set_Ofolding__one__idem(_911018, _911020, _911022), hBOOL(hAPP(c_Finite__Set_Ofinite(_911018), _911024)), hBOOL(hAPP(hAPP(c_member(_911018), _911026), _911024)), -(hAPP(hAPP(_911020, _911026), hAPP(_911022, _911024)) = hAPP(_911022, _911024))], (41804 ^ _780119) ^ [_1604797, _1604799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1604797), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1604797, tc_HOL_Obool), _1604799))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1604797, tc_HOL_Obool)), _1604799)))], (40347 ^ _780119) ^ [_1569822] : [-(c_Relation_Osingle__valued(_1569822, _1569822, c_Relation_OId(_1569822)))], (18776 ^ _780119) ^ [_1122532] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1122532)), _1122532) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5218 ^ _780119) ^ [_859955, _859957] : [_859957 = _859955, -(c_List_Oappend(_859957) = c_List_Oappend(_859955))], (51009 ^ _780119) ^ [_1814625, _1814627] : [class_Orderings_Otop(_1814625), -(class_Orderings_Otop(tc_fun(_1814627, _1814625)))], (47640 ^ _780119) ^ [_1741145, _1741147, _1741149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741145), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741147)), _1741149))), -(hAPP(hAPP(c_List_Onth(_1741147), hAPP(c_List_Orev(_1741147), _1741149)), _1741145) = hAPP(hAPP(c_List_Onth(_1741147), _1741149), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741147)), _1741149)), hAPP(c_Nat_OSuc, _1741145))))], (51529 ^ _780119) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (50096 ^ _780119) ^ [_1795620, _1795622] : [class_HOL_Oequal(_1795620), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1795620), _1795622), _1795622)))], (32875 ^ _780119) ^ [_1392781, _1392783] : [class_Rings_Olinordered__idom(_1392781), 32878 ^ _780119 : [(32885 ^ _780119) ^ [] : [-(_1392783 = c_Groups_Ozero__class_Ozero(_1392781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1392781), c_Groups_Ozero__class_Ozero(_1392781)), hAPP(hAPP(c_Power_Opower__class_Opower(_1392781), _1392783), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (32879 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1392781), c_Groups_Ozero__class_Ozero(_1392781)), hAPP(hAPP(c_Power_Opower__class_Opower(_1392781), _1392783), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1392783 = c_Groups_Ozero__class_Ozero(_1392781)]]], (48171 ^ _780119) ^ [_1753401, _1753403, _1753405] : [-(c_Enum_On__lists(_1753401, hAPP(c_Nat_OSuc, _1753403), _1753405) = c_List_Oconcat(tc_List_Olist(_1753401), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753401), tc_List_Olist(tc_List_Olist(_1753401))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1753401), tc_List_Olist(_1753401), tc_List_Olist(tc_List_Olist(_1753401))), hAPP(hAPP(c_COMBB(tc_fun(_1753401, tc_List_Olist(_1753401)), tc_fun(tc_List_Olist(_1753401), tc_List_Olist(tc_List_Olist(_1753401))), tc_List_Olist(_1753401)), c_List_Omap(_1753401, tc_List_Olist(_1753401))), hAPP(c_COMBC(_1753401, tc_List_Olist(_1753401), tc_List_Olist(_1753401)), c_List_Olist_OCons(_1753401)))), _1753405)), c_Enum_On__lists(_1753401, _1753403, _1753405))))], (51259 ^ _780119) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (45126 ^ _780119) ^ [_1684461, _1684463, _1684465, _1684467, _1684469, _1684471] : [-(c_List_Ofoldr(_1684461, _1684463, _1684465, hAPP(hAPP(c_List_Oappend(_1684461), _1684467), _1684469), _1684471) = c_List_Ofoldr(_1684461, _1684463, _1684465, _1684467, c_List_Ofoldr(_1684461, _1684463, _1684465, _1684469, _1684471)))], (31703 ^ _780119) ^ [_1371741, _1371743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371741)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371743))), 31706 ^ _780119 : [(31707 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371741), _1371743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1371743)))], (31713 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371741), _1371743)))]]], (32619 ^ _780119) ^ [_1388102, _1388104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1388102), _1388104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1388102)), c_Int_OBit1(_1388104))))], (19070 ^ _780119) ^ [_1127511, _1127513] : [class_Divides_Osemiring__div(_1127511), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1127511), _1127513), c_Groups_Oone__class_Oone(_1127511)) = _1127513)], (22374 ^ _780119) ^ [_1188438, _1188440, _1188442] : [-(hBOOL(hAPP(_1188438, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1188440, _1188442)))), 22377 ^ _780119 : [(22380 ^ _780119) ^ [] : [hBOOL(hAPP(_1188438, _1188440))], (22378 ^ _780119) ^ [] : [-(_1188442 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 22381 ^ _780119 : [(22382 ^ _780119) ^ [] : [_1188442 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22386 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 22384 ^ [_1188438, _1188440, _1188442]), _1188442)))], (22390 ^ _780119) ^ [] : [hBOOL(hAPP(_1188438, 22384 ^ [_1188438, _1188440, _1188442]))], (22388 ^ _780119) ^ [] : [-(_1188440 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188442), 22383 ^ [_1188438, _1188440, _1188442])), 22384 ^ [_1188438, _1188440, _1188442]))]]], (33365 ^ _780119) ^ [_1401753] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1401753), c_Int_OMin) = c_Int_Osucc(_1401753))], (32403 ^ _780119) ^ [_1384388] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1384388)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1384388)))], (48173 ^ _780119) ^ [_1753521, _1753523, _1753525] : [-(c_List_Opartition(_1753521, _1753523, _1753525) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753521), tc_List_Olist(_1753521)), hAPP(c_List_Ofilter(_1753521, _1753523), _1753525)), hAPP(c_List_Ofilter(_1753521, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1753521, c_fNot), _1753523)), _1753525)))], (38862 ^ _780119) ^ [_1533462, _1533464, _1533466] : [-(c_Hilbert__Choice_OEps(tc_prod(_1533462, _1533464), _1533466) = c_Hilbert__Choice_OEps(tc_prod(_1533462, _1533464), hAPP(c_Product__Type_Oprod_Oprod__case(_1533462, _1533464, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1533464, tc_prod(_1533462, _1533464)), tc_fun(_1533464, tc_HOL_Obool), _1533462), hAPP(c_COMBB(tc_prod(_1533462, _1533464), tc_HOL_Obool, _1533464), _1533466)), c_Product__Type_OPair(_1533462, _1533464)))))], (31691 ^ _780119) ^ [_1371554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1371554))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1371554)))], (44077 ^ _780119) ^ [_1661790, _1661792, _1661794] : [hBOOL(hAPP(hAPP(c_member(_1661790), _1661792), hAPP(c_List_Oset(_1661790), _1661794))), 44081 ^ _780119 : [(44084 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1661790), _1661794), 44080 ^ [_1661790, _1661792, _1661794]) = _1661792)], (44082 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44080 ^ [_1661790, _1661792, _1661794]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661790)), _1661794))))]]], (12187 ^ _780119) ^ [_999871, _999873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999871), _999873)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999873), _999871)), _999871) = _999873)], (24843 ^ _780119) ^ [_1235301, _1235303] : [class_Orderings_Olinorder(_1235301), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235301, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1235301), _1235303), c_Orderings_Obot__class_Obot(tc_fun(_1235301, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1235301), _1235303)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1235301), _1235303))], (26855 ^ _780119) ^ [_1271334, _1271336, _1271338] : [class_Groups_Oordered__ab__group__add__abs(_1271334), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271334), hAPP(c_Groups_Oabs__class_Oabs(_1271334), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1271334), _1271336), _1271338))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271334), hAPP(c_Groups_Oabs__class_Oabs(_1271334), _1271336)), hAPP(c_Groups_Oabs__class_Oabs(_1271334), _1271338)))))], (6258 ^ _780119) ^ [_880403, _880405, _880407] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_880403), _880407)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_880403), hAPP(hAPP(c_Set_Oinsert(_880403), _880405), _880407))))], (29917 ^ _780119) ^ [_1338546, _1338548, _1338550, _1338552, _1338554] : [_1338546 = c_Orderings_Obot__class_Obot(tc_fun(_1338548, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338550, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338548, tc_fun(_1338550, tc_HOL_Obool)), _1338546), _1338552)), _1338554) = _1338554)], (31323 ^ _780119) ^ [_1365704, _1365706] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365704) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365706), 31326 ^ _780119 : [(31333 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365704)))), 31336 ^ _780119 : [(31343 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365706)))), -(_1365704 = _1365706)], (31337 ^ _780119) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365706))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365704) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (31327 ^ _780119) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365706)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (27952 ^ _780119) ^ [_1296153, _1296155, _1296157, _1296159] : [class_Orderings_Olinorder(_1296153), 27955 ^ _780119 : [(27964 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296153), _1296155), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1296153), _1296157), _1296159)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296153), _1296155), _1296157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296153), _1296155), _1296159))], (27956 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296153), _1296155), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1296153), _1296157), _1296159))), 27959 ^ _780119 : [(27962 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296153), _1296155), _1296159)))], (27960 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296153), _1296155), _1296157)))]]]]], (50310 ^ _780119) ^ [_1799956, _1799958, _1799960, _1799962] : [-(c_Lazy__Sequence_Oproduct(_1799956, _1799958, _1799960, _1799962) = hAPP(c_Lazy__Sequence_Obind(_1799956, tc_prod(_1799956, _1799958), _1799960), hAPP(hAPP(c_COMBB(tc_fun(_1799958, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1799956, _1799958))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1799956, _1799958)), _1799956), c_Lazy__Sequence_Obind(_1799958, tc_prod(_1799956, _1799958), _1799962)), hAPP(hAPP(c_COMBB(tc_fun(_1799958, tc_prod(_1799956, _1799958)), tc_fun(_1799958, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1799956, _1799958))), _1799956), hAPP(c_COMBB(tc_prod(_1799956, _1799958), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1799956, _1799958)), _1799958), c_Lazy__Sequence_Osingle(tc_prod(_1799956, _1799958)))), c_Product__Type_OPair(_1799956, _1799958)))))], (26109 ^ _780119) ^ [_1256298, _1256300, _1256302] : [class_Orderings_Olinorder(_1256298), 26112 ^ _780119 : [(26119 ^ _780119) ^ [] : [_1256300 = _1256302, -(hAPP(c_SetInterval_Oord__class_OatMost(_1256298), _1256300) = hAPP(c_SetInterval_Oord__class_OatMost(_1256298), _1256302))], (26113 ^ _780119) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1256298), _1256300) = hAPP(c_SetInterval_Oord__class_OatMost(_1256298), _1256302), -(_1256300 = _1256302)]]], (47602 ^ _780119) ^ [_1740161, _1740163, _1740165, _1740167] : [hAPP(c_List_Orev(_1740161), _1740163) = hAPP(hAPP(c_List_Olist_OCons(_1740161), _1740165), _1740167), -(_1740163 = hAPP(hAPP(c_List_Oappend(_1740161), hAPP(c_List_Orev(_1740161), _1740167)), hAPP(hAPP(c_List_Olist_OCons(_1740161), _1740165), c_List_Olist_ONil(_1740161))))], (15190 ^ _780119) ^ [_1057940] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1057940)], (42385 ^ _780119) ^ [_1618100, _1618102, _1618104, _1618106, _1618108] : [-(hBOOL(hAPP(hAPP(c_member(_1618100), _1618102), c_Map_Odom(_1618100, _1618104, _1618106)))), -(hAPP(c_Map_Omap__add(_1618100, _1618104, _1618106, _1618108), _1618102) = hAPP(_1618108, _1618102))], (38190 ^ _780119) ^ [_1517912, _1517914, _1517916, _1517918, _1517920, _1517922, _1517924, _1517926] : [c_Fun_Oinj__on(_1517912, _1517914, _1517916, _1517918), c_Fun_Oinj__on(_1517920, _1517922, _1517924, _1517926), -(c_Fun_Oinj__on(tc_prod(_1517912, _1517920), tc_prod(_1517914, _1517922), c_Product__Type_Omap__pair(_1517912, _1517914, _1517920, _1517922, _1517916, _1517924), hAPP(hAPP(c_Product__Type_OSigma(_1517912, _1517920), _1517918), hAPP(c_COMBK(tc_fun(_1517920, tc_HOL_Obool), _1517912), _1517926))))], (36684 ^ _780119) ^ [_1476996] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1476996))], (45414 ^ _780119) ^ [_1692191, _1692193, _1692195, _1692197] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692191), tc_List_Olist(_1692191))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692191), tc_List_Olist(_1692191)), _1692193), _1692195)), c_List_Olistrel1(_1692191, _1692197))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692191)), _1692193) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692191)), _1692195))], (28322 ^ _780119) ^ [_1303679, _1303681, _1303683] : [class_Orderings_Olinorder(_1303679), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303679), _1303681)), -(_1303681 = c_Orderings_Obot__class_Obot(tc_fun(_1303679, tc_HOL_Obool))), 28333 ^ _780119 : [(28334 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303679), _1303683), hAPP(c_Finite__Set_Ofold1(_1303679, c_Orderings_Oord__class_Omin(_1303679)), _1303681))), 28337 ^ _780119 : [(28338 ^ _780119) ^ [_1303972] : [hBOOL(hAPP(hAPP(c_member(_1303679), _1303972), _1303681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303679), _1303683), _1303972)))]]], (28344 ^ _780119) ^ [] : [28346 ^ _780119 : [(28349 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303679), _1303683), 28345 ^ [_1303679, _1303681, _1303683]))], (28347 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1303679), 28345 ^ [_1303679, _1303681, _1303683]), _1303681)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303679), _1303683), hAPP(c_Finite__Set_Ofold1(_1303679, c_Orderings_Oord__class_Omin(_1303679)), _1303681))))]]], (6031 ^ _780119) ^ [_876116, _876118, _876120] : [_876116 = _876118, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876120, tc_HOL_Obool)), _876116), _876118)))], (41888 ^ _780119) ^ [_1606655] : [class_Complete__Lattice_Ocomplete__lattice(_1606655), -(c_Complete__Lattice_OInf__class_OInf(_1606655, c_Orderings_Obot__class_Obot(tc_fun(_1606655, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1606655))], (41832 ^ _780119) ^ [_1605563, _1605565, _1605567] : [class_Complete__Lattice_Ocomplete__lattice(_1605563), hBOOL(hAPP(hAPP(c_member(_1605563), _1605565), _1605567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1605563), _1605565), c_Complete__Lattice_OSup__class_OSup(_1605563, _1605567))))], (11339 ^ _780119) ^ [_982550, _982552, _982554, _982556, _982558, _982560] : [class_Rings_Oordered__ring(_982550), 11342 ^ _780119 : [(11349 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982550), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_982550), _982552), _982558)), _982554)), _982556)), _982560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982550), _982552), _982554)), _982556)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982550), _982558), _982554)), _982560))))], (11343 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982550), _982552), _982554)), _982556)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982550), _982558), _982554)), _982560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982550), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_982550), _982552), _982558)), _982554)), _982556)), _982560)))]]], (50286 ^ _780119) ^ [_1799311, _1799313, _1799315, _1799317] : [-(c_New__Random__Sequence_Opos__map(_1799311, _1799313, _1799315, _1799317) = c_New__Random__Sequence_Opos__bind(_1799311, _1799313, _1799317, hAPP(c_Fun_Ocomp(_1799313, 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(_1799313))))), _1799311, c_New__Random__Sequence_Opos__single(_1799313)), _1799315)))], (9858 ^ _780119) ^ [_951666, _951668] : [class_Lattices_Osemilattice__inf(_951666), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951666), _951668), _951668) = _951668)], (39511 ^ _780119) ^ [_1548899, _1548901, _1548903, _1548905, _1548907] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548899, _1548899)), hAPP(hAPP(c_Product__Type_OPair(_1548899, _1548899), _1548901), _1548903)), _1548905)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1548899, _1548899)), hAPP(hAPP(c_Product__Type_OPair(_1548899, _1548899), _1548903), _1548907)), c_Transitive__Closure_Otrancl(_1548899, _1548905))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548899, _1548899)), hAPP(hAPP(c_Product__Type_OPair(_1548899, _1548899), _1548901), _1548907)), c_Transitive__Closure_Otrancl(_1548899, _1548905))))], (22404 ^ _780119) ^ [_1189052, _1189054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1189052)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1189052), _1189054)), _1189052) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (1370 ^ _780119) ^ [_799968, _799970] : [-(class_Groups_Ouminus(_799968)), _799970 = _799968, class_Groups_Ouminus(_799970)], (47442 ^ _780119) ^ [_1736765, _1736767, _1736769] : [hAPP(c_List_Orev(_1736765), _1736767) = hAPP(hAPP(c_List_Olist_OCons(_1736765), _1736769), c_List_Olist_ONil(_1736765)), -(_1736767 = hAPP(hAPP(c_List_Olist_OCons(_1736765), _1736769), c_List_Olist_ONil(_1736765)))], (22753 ^ _780119) ^ [_1195803, _1195805, _1195807] : [class_Nat_Osemiring__char__0(_1195803), 22756 ^ _780119 : [(22763 ^ _780119) ^ [] : [_1195805 = _1195807, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1195803), _1195805) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1195803), _1195807))], (22757 ^ _780119) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1195803), _1195805) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1195803), _1195807), -(_1195805 = _1195807)]]], (18151 ^ _780119) ^ [_1110744, _1110746] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1110744), _1110746))), -(hAPP(c_Finite__Set_Ocard(_1110744), _1110746) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35087 ^ _780119) ^ [_1439569] : [class_Rings_Osemiring__1(_1439569), -(hBOOL(hAPP(hAPP(c_member(_1439569), c_Groups_Ozero__class_Ozero(_1439569)), c_Nat_Osemiring__1__class_ONats(_1439569))))], (26789 ^ _780119) ^ [_1269682, _1269684] : [-(hAPP(c_Set_OCollect(_1269682), hAPP(hAPP(c_COMBC(_1269682, _1269682, tc_HOL_Obool), c_fequal), _1269684)) = hAPP(hAPP(c_Set_Oinsert(_1269682), _1269684), c_Orderings_Obot__class_Obot(tc_fun(_1269682, tc_HOL_Obool))))], (7862 ^ _780119) ^ [_913967, _913969, _913971] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913967), _913969)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_913967), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913967, tc_HOL_Obool)), _913969), _913971))))], (47426 ^ _780119) ^ [_1736297, _1736299] : [-(c_List_Oconcat(_1736297, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1736297), tc_List_Olist(_1736297)), c_List_Olist_Olist__case(tc_List_Olist(_1736297), _1736297, c_List_Olist_ONil(_1736297), hAPP(hAPP(c_COMBB(tc_List_Olist(_1736297), tc_fun(tc_List_Olist(_1736297), tc_List_Olist(_1736297)), _1736297), c_COMBK(tc_List_Olist(_1736297), tc_List_Olist(_1736297))), hAPP(hAPP(c_COMBC(_1736297, tc_List_Olist(_1736297), tc_List_Olist(_1736297)), c_List_Olist_OCons(_1736297)), c_List_Olist_ONil(_1736297))))), _1736299)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1736297), _1736297), c_List_Ohd(_1736297)), hAPP(c_List_Ofilter(tc_List_Olist(_1736297), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1736297)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1736297), tc_List_Olist(_1736297), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1736297)))), _1736299)))], (46165 ^ _780119) ^ [_1710427, _1710429, _1710431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1710427, tc_HOL_Obool)), _1710429), _1710431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1710427), tc_HOL_Obool)), c_List_Olists(_1710427, _1710429)), c_List_Olists(_1710427, _1710431))))], (44410 ^ _780119) ^ [_1669893, _1669895, _1669897, _1669899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669893), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669895)), _1669897))), -(hAPP(hAPP(c_List_Onth(_1669895), hAPP(hAPP(c_List_Olist__update(_1669895, _1669897), _1669893), _1669899)), _1669893) = _1669899)], (14454 ^ _780119) ^ [_1045084, _1045086, _1045088, _1045090] : [class_Rings_Olinordered__semidom(_1045084), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045084), c_Groups_Oone__class_Oone(_1045084)), _1045086)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045084), hAPP(hAPP(c_Power_Opower__class_Opower(_1045084), _1045086), _1045088)), hAPP(hAPP(c_Power_Opower__class_Opower(_1045084), _1045086), _1045090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045088), _1045090)))], (43210 ^ _780119) ^ [_1637915, _1637917] : [hAPP(c_Finite__Set_Ocard(_1637915), hAPP(c_List_Oset(_1637915), _1637917)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637915)), _1637917), -(hBOOL(hAPP(c_List_Odistinct(_1637915), _1637917)))], (4836 ^ _780119) ^ [_853884, _853886, _853888, _853890] : [-(c_Lazy__Sequence_Ohb__single(_853890, _853886) = c_Lazy__Sequence_Ohb__single(_853888, _853884)), _853890 = _853888, _853886 = _853884], (3298 ^ _780119) ^ [_829571, _829573, _829575, _829577, _829579, _829581, _829583, _829585] : [-(c_Wellfounded_Olex__prod(_829585, _829581, _829577, _829573) = c_Wellfounded_Olex__prod(_829583, _829579, _829575, _829571)), _829585 = _829583, _829581 = _829579, _829577 = _829575, _829573 = _829571], (51445 ^ _780119) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (19703 ^ _780119) ^ [_1138483, _1138485, _1138487, _1138489] : [class_Rings_Odivision__ring(_1138483), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138483), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1138483), _1138485), _1138487)), _1138489) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1138483), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138483), _1138485), _1138489)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138483), _1138487), _1138489)))], (38292 ^ _780119) ^ [_1520157, _1520159, _1520161, _1520163, _1520165] : [c_Relation_Orefl__on(_1520157, _1520159, _1520161), c_Relation_Orefl__on(_1520157, _1520163, _1520165), -(c_Relation_Orefl__on(_1520157, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520157, tc_HOL_Obool)), _1520159), _1520163), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1520157, _1520157), tc_HOL_Obool)), _1520161), _1520165)))], (49855 ^ _780119) ^ [_1791037, _1791039, _1791041] : [49857 ^ _780119 : [(49860 ^ _780119) ^ [] : [hBOOL(hAPP(_1791041, 49856 ^ [_1791037, _1791039, _1791041]))], (49858 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791037), 49856 ^ [_1791037, _1791039, _1791041]), hAPP(c_List_Oset(_1791037), _1791039))))]], -(c_List_Olist__all(_1791037, _1791041, _1791039))], (34060 ^ _780119) ^ [_1419845, _1419847] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1419845, _1419847) = 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), _1419845), _1419847)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1419845, _1419847)))], (46006 ^ _780119) ^ [_1706632, _1706634, _1706636, _1706638, _1706640, _1706642, _1706644] : [-(hAPP(c_List_Ofoldl(_1706632, _1706634, _1706636, _1706638), hAPP(hAPP(c_List_Omap(_1706640, _1706634), _1706642), _1706644)) = hAPP(c_List_Ofoldl(_1706632, _1706640, hAPP(hAPP(c_COMBC(_1706632, tc_fun(_1706640, _1706634), tc_fun(_1706640, _1706632)), hAPP(hAPP(c_COMBB(tc_fun(_1706634, _1706632), tc_fun(tc_fun(_1706640, _1706634), tc_fun(_1706640, _1706632)), _1706632), c_COMBB(_1706634, _1706632, _1706640)), _1706636)), _1706642), _1706638), _1706644))], (31597 ^ _780119) ^ [_1370074, _1370076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1370074)), _1370076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370074), _1370076)))], (49414 ^ _780119) ^ [_1780669, _1780671, _1780673, _1780675, _1780677, _1780679, _1780681, _1780683] : [49416 ^ _780119 : [(49419 ^ _780119) ^ [] : [hAPP(c_Fun_Ocomp(_1780673, _1780673, _1780675, hAPP(_1780677, 49415 ^ [_1780669, _1780671, _1780673, _1780675, _1780677, _1780679, _1780681, _1780683])), _1780679) = hAPP(c_Fun_Ocomp(_1780675, _1780673, _1780675, _1780679), hAPP(_1780681, 49415 ^ [_1780669, _1780671, _1780673, _1780675, _1780677, _1780679, _1780681, _1780683]))], (49417 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1780669), 49415 ^ [_1780669, _1780671, _1780673, _1780675, _1780677, _1780679, _1780681, _1780683]), hAPP(c_List_Oset(_1780669), _1780671))))]], -(hAPP(c_List_Ofoldl(_1780673, _1780669, hAPP(c_COMBC(_1780669, _1780673, _1780673), _1780677), hAPP(_1780679, _1780683)), _1780671) = hAPP(_1780679, hAPP(c_List_Ofoldl(_1780675, _1780669, hAPP(c_COMBC(_1780669, _1780675, _1780675), _1780681), _1780683), _1780671)))], (1130 ^ _780119) ^ [_796968, _796970] : [-(class_Groups_Oab__group__add(_796968)), _796970 = _796968, class_Groups_Oab__group__add(_796970)], (48924 ^ _780119) ^ [_1769691, _1769693, _1769695, _1769697, _1769699] : [c_List_Olist__all2(_1769691, _1769693, _1769695, _1769697, _1769699), 48927 ^ _780119 : [(48930 ^ _780119) ^ [_1769857] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1769691, _1769693)), _1769857), hAPP(c_List_Oset(tc_prod(_1769691, _1769693)), hAPP(hAPP(c_List_Ozip(_1769691, _1769693), _1769697), _1769699)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1769691, _1769693, tc_HOL_Obool), _1769695), _1769857)))], (48928 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769691)), _1769697) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769693)), _1769699))]]], (5178 ^ _780119) ^ [_859381, _859383, _859385, _859387] : [-(c_List_Olast(_859387, _859383) = c_List_Olast(_859385, _859381)), _859387 = _859385, _859383 = _859381], (50698 ^ _780119) ^ [_1808262, _1808264, _1808266] : [-(hAPP(c_List_Oset(_1808262), c_List_Oreplicate(_1808262, hAPP(c_Nat_OSuc, _1808264), _1808266)) = hAPP(hAPP(c_Set_Oinsert(_1808262), _1808266), c_Orderings_Obot__class_Obot(tc_fun(_1808262, tc_HOL_Obool))))], (9306 ^ _780119) ^ [_940237, _940239, _940241, _940243] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_940237, _940239, _940241, _940243, c_Orderings_Obot__class_Obot(tc_fun(_940237, tc_HOL_Obool))), _940243)))], (22789 ^ _780119) ^ [_1196364, _1196366, _1196368] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1196364, tc_Nat_Onat), _1196366), _1196368)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1196364, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1196364), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1196366)), _1196368))], (19150 ^ _780119) ^ [_1128781, _1128783, _1128785] : [class_Divides_Osemiring__div(_1128781), -(_1128783 = c_Groups_Ozero__class_Ozero(_1128781)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128781), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128781), _1128785), _1128783)), _1128783) = _1128785)], (42964 ^ _780119) ^ [_1631838, _1631840] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1631838, _1631840) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1631838, _1631840)))], (48888 ^ _780119) ^ [_1768908, _1768910, _1768912, _1768914] : [hBOOL(hAPP(c_List_Olistsp(_1768908, _1768910), hAPP(hAPP(c_List_Olist_OCons(_1768908), _1768912), _1768914))), 48891 ^ _780119 : [(48894 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1768908, _1768910), _1768914)))], (48892 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1768910, _1768912)))]]], (8444 ^ _780119) ^ [_926756, _926758, _926760, _926762, _926764, _926766] : [-(hBOOL(hAPP(hAPP(c_member(_926756), _926758), _926760))), -(hAPP(c_Set_Oimage(_926756, _926762, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_926756, _926762), _926764), _926758), _926766)), _926760) = hAPP(c_Set_Oimage(_926756, _926762, _926764), _926760))], (46845 ^ _780119) ^ [_1725159, _1725161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1725159), _1725161)), -(c_List_Oupt(_1725161, _1725159) = c_List_Olist_ONil(tc_Nat_Onat))], (36551 ^ _780119) ^ [_1473665, _1473667, _1473669, _1473671] : [c_Fun_Oinj__on(_1473665, _1473667, _1473669, c_Orderings_Otop__class_Otop(tc_fun(_1473665, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473667, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1473665, _1473667, _1473669), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1473665, tc_HOL_Obool)), _1473671))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1473667, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1473665, _1473667, _1473669), _1473671)))))], (23573 ^ _780119) ^ [_1211123] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1211123), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (28212 ^ _780119) ^ [_1301642, _1301644, _1301646] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1301642), _1301644)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1301646), _1301644)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1301642), _1301646)), _1301644))], (12301 ^ _780119) ^ [_1002504, _1002506, _1002508, _1002510, _1002512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002504), _1002506)), -(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), _1002504), _1002508)), _1002510)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002506), _1002508)), _1002512)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002510), 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), _1002506), _1002504)), _1002508)), _1002512)))], (50320 ^ _780119) ^ [_1800503, _1800505, _1800507] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1800503, _1800505), _1800507) = c_Lazy__Sequence_Oproduct(_1800503, _1800505, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1800503, _1800507), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1800505, _1800507))), class_Lazy__Sequence_Osmall__lazy(_1800503), class_Lazy__Sequence_Osmall__lazy(_1800505)], (18456 ^ _780119) ^ [_1116853] : [class_Rings_Oring__1(_1116853), -(hBOOL(hAPP(hAPP(c_member(_1116853), c_Groups_Ozero__class_Ozero(_1116853)), c_Int_Oring__1__class_OInts(_1116853))))], (15222 ^ _780119) ^ [_1058409, _1058411, _1058413] : [class_Rings_Oring__1__no__zero__divisors(_1058409), -(_1058411 = c_Groups_Ozero__class_Ozero(_1058409)), hAPP(hAPP(c_Power_Opower__class_Opower(_1058409), _1058411), _1058413) = c_Groups_Ozero__class_Ozero(_1058409)], (15318 ^ _780119) ^ [_1059752] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1059752)))], (7296 ^ _780119) ^ [_902341, _902343, _902345] : [class_Lattices_Osemilattice__sup(_902341), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902341), _902343), _902345) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902341), _902345), _902343))], (51447 ^ _780119) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (41643 ^ _780119) ^ [_1601333, _1601335] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1601333, tc_HOL_Obool), hAPP(c_Set_OPow(_1601333), _1601335)) = _1601335)], (6511 ^ _780119) ^ [_885598, _885600] : [-(hAPP(c_Option_Othe(_885598), hAPP(c_Option_Ooption_OSome(_885598), _885600)) = _885600)], (20077 ^ _780119) ^ [_1145206, _1145208, _1145210] : [hBOOL(hAPP(_1145206, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1145208), _1145210))), 20082 ^ _780119 : [(20085 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1145206, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20083 ^ _780119) ^ [] : [-(_1145210 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 20087 ^ _780119 : [(20090 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1145208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145210), hAPP(c_Nat_OSuc, 20086 ^ [_1145206, _1145208, _1145210])))))], (20092 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1145206, 20086 ^ [_1145206, _1145208, _1145210])))], (20088 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145210), 20086 ^ [_1145206, _1145208, _1145210])), _1145208)))]]], (22571 ^ _780119) ^ [_1192009, _1192011, _1192013, _1192015, _1192017] : [c_Com_Ocom_OCond(_1192009, _1192011, _1192013) = c_Com_Ocom_OSemi(_1192015, _1192017)], (24775 ^ _780119) ^ [_1233911, _1233913, _1233915, _1233917] : [class_Orderings_Oorder(_1233911), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1233911, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1233911, _1233913, _1233915)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1233911, _1233915, _1233917)) = c_Orderings_Obot__class_Obot(tc_fun(_1233911, tc_HOL_Obool)))], (51533 ^ _780119) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (19112 ^ _780119) ^ [_1128180, _1128182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1128180)), 19115 ^ _780119 : [(19122 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128182), 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), _1128182), _1128180)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19116 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1128182), _1128180)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128182), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (35440 ^ _780119) ^ [_1448820, _1448822] : [-(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), _1448820), _1448822)), 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), _1448820), _1448822))], (44698 ^ _780119) ^ [_1675555, _1675557, _1675559] : [-(hAPP(hAPP(c_List_Ozip(_1675555, _1675557), c_List_Olist_ONil(_1675555)), _1675559) = c_List_Olist_ONil(tc_prod(_1675555, _1675557)))], (5614 ^ _780119) ^ [_866105, _866107, _866109, _866111, _866113, _866115] : [-(c_COMBS(_866115, _866111, _866107) = c_COMBS(_866113, _866109, _866105)), _866115 = _866113, _866111 = _866109, _866107 = _866105], (44388 ^ _780119) ^ [_1669363, _1669365, _1669367, _1669369, _1669371] : [-(hAPP(hAPP(c_List_Olist__update(_1669363, hAPP(hAPP(c_List_Olist_OCons(_1669363), _1669365), _1669367)), _1669369), _1669371) = c_Nat_Onat_Onat__case(tc_List_Olist(_1669363), hAPP(hAPP(c_List_Olist_OCons(_1669363), _1669371), _1669367), hAPP(hAPP(c_COMBB(tc_List_Olist(_1669363), tc_List_Olist(_1669363), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1669363), _1669365)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1669363, tc_List_Olist(_1669363)), c_List_Olist__update(_1669363, _1669367)), _1669371)), _1669369))], (18073 ^ _780119) ^ [_1109321, _1109323, _1109325, _1109327] : [class_Groups_Ocomm__monoid__add(_1109321), 18076 ^ _780119 : [(18083 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1109323), _1109325))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1109323, _1109321), _1109327), _1109325) = c_Groups_Ozero__class_Ozero(_1109321))], (18077 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1109323), _1109325)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1109323, _1109321), _1109327), _1109325) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1109321, _1109323, c_Groups_Oplus__class_Oplus(_1109321)), _1109327), c_Groups_Ozero__class_Ozero(_1109321)), _1109325))]]], (42923 ^ _780119) ^ [_1630836, _1630838, _1630840, _1630842, _1630844] : [hBOOL(hAPP(c_List_Odistinct(_1630836), hAPP(hAPP(c_List_Omap(tc_prod(_1630836, _1630838), _1630836), c_Product__Type_Ofst(_1630836, _1630838)), _1630840))), 42926 ^ _780119 : [(42933 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630836, _1630838)), hAPP(hAPP(c_Product__Type_OPair(_1630836, _1630838), _1630842), _1630844)), hAPP(c_List_Oset(tc_prod(_1630836, _1630838)), _1630840))), -(hAPP(hAPP(c_Map_Omap__of(_1630836, _1630838), _1630840), _1630842) = hAPP(c_Option_Ooption_OSome(_1630838), _1630844))], (42927 ^ _780119) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1630836, _1630838), _1630840), _1630842) = hAPP(c_Option_Ooption_OSome(_1630838), _1630844), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630836, _1630838)), hAPP(hAPP(c_Product__Type_OPair(_1630836, _1630838), _1630842), _1630844)), hAPP(c_List_Oset(tc_prod(_1630836, _1630838)), _1630840))))]]], (164 ^ _780119) ^ [_782853, _782855] : [-(class_Rings_Odivision__ring(_782853)), _782855 = _782853, class_Rings_Odivision__ring(_782855)], (19875 ^ _780119) ^ [_1141448, _1141450, _1141452] : [class_Rings_Odivision__ring(_1141448), -(_1141450 = c_Groups_Ozero__class_Ozero(_1141448)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141448), hAPP(c_Groups_Ouminus__class_Ouminus(_1141448), _1141452)), hAPP(c_Groups_Ouminus__class_Ouminus(_1141448), _1141450)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141448), _1141452), _1141450))], (6745 ^ _780119) ^ [_890744, _890746] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890744, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_890744, tc_HOL_Obool))), _890746) = _890746)], (51117 ^ _780119) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (15472 ^ _780119) ^ [_1062181, _1062183] : [class_Lattices_Obounded__lattice__top(_1062181), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1062181), c_Orderings_Otop__class_Otop(_1062181)), _1062183) = c_Orderings_Otop__class_Otop(_1062181))], (37052 ^ _780119) ^ [_1486313, _1486315, _1486317, _1486319, _1486321, _1486323, _1486325] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1486313, _1486315, _1486317), _1486319), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486321, tc_fun(tc_prod(_1486315, _1486317), tc_HOL_Obool)), _1486323), _1486325)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486321, tc_fun(tc_prod(_1486313, _1486317), tc_HOL_Obool)), _1486323), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1486315, _1486317), tc_HOL_Obool), tc_fun(tc_prod(_1486313, _1486317), tc_HOL_Obool), _1486321), hAPP(c_Relation_Orel__comp(_1486313, _1486315, _1486317), _1486319)), _1486325)))], (45602 ^ _780119) ^ [_1697877, _1697879] : [-(hAPP(hAPP(c_List_Odrop(_1697877), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1697879) = _1697879)], (13302 ^ _780119) ^ [_1022187, _1022189, _1022191] : [class_Lattices_Oboolean__algebra(_1022187), 13305 ^ _780119 : [(13312 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022187), _1022191), _1022189)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022187), hAPP(c_Groups_Ouminus__class_Ouminus(_1022187), _1022189)), hAPP(c_Groups_Ouminus__class_Ouminus(_1022187), _1022191))))], (13306 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022187), hAPP(c_Groups_Ouminus__class_Ouminus(_1022187), _1022189)), hAPP(c_Groups_Ouminus__class_Ouminus(_1022187), _1022191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022187), _1022191), _1022189)))]]], (24253 ^ _780119) ^ [_1224249, _1224251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224249), _1224251)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1224251, _1224249) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (48446 ^ _780119) ^ [_1759727, _1759729, _1759731] : [class_Enum_Oenum(_1759727), 48449 ^ _780119 : [(48450 ^ _780119) ^ [] : [c_Enum_Oall__n__lists(_1759727, _1759729, _1759731), 48453 ^ _780119 : [(48454 ^ _780119) ^ [_1759877] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1759727)), _1759877), hAPP(c_List_Oset(tc_List_Olist(_1759727)), c_Enum_On__lists(_1759727, _1759731, c_Enum_Oenum__class_Oenum(_1759727))))), -(hBOOL(hAPP(_1759729, _1759877)))]]], (48460 ^ _780119) ^ [] : [48462 ^ _780119 : [(48465 ^ _780119) ^ [] : [hBOOL(hAPP(_1759729, 48461 ^ [_1759727, _1759729, _1759731]))], (48463 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1759727)), 48461 ^ [_1759727, _1759729, _1759731]), hAPP(c_List_Oset(tc_List_Olist(_1759727)), c_Enum_On__lists(_1759727, _1759731, c_Enum_Oenum__class_Oenum(_1759727))))))]], -(c_Enum_Oall__n__lists(_1759727, _1759729, _1759731))]]], (31165 ^ _780119) ^ [_1362852] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1362852))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1362852)))))], (36525 ^ _780119) ^ [_1473168, _1473170, _1473172, _1473174, _1473176, _1473178] : [c_Fun_Oinj__on(_1473168, _1473170, _1473172, _1473174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473170, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1473168, _1473170, _1473172), _1473174)), _1473176)), c_Fun_Oinj__on(_1473170, _1473168, _1473178, _1473176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473168, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1473170, _1473168, _1473178), _1473176)), _1473174)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473168), _1473174)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473170), _1473176)), -(hAPP(c_Finite__Set_Ocard(_1473168), _1473174) = hAPP(c_Finite__Set_Ocard(_1473170), _1473176))], (1520 ^ _780119) ^ [_801843, _801845] : [-(class_Groups_Ocancel__semigroup__add(_801843)), _801845 = _801843, class_Groups_Ocancel__semigroup__add(_801845)], (45247 ^ _780119) ^ [_1687490, _1687492, _1687494, _1687496, _1687498] : [-(hAPP(hAPP(c_List_Olist__update(_1687490, hAPP(hAPP(c_List_Oappend(_1687490), _1687492), hAPP(hAPP(c_List_Olist_OCons(_1687490), _1687494), _1687496))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687490)), _1687492)), _1687498) = hAPP(hAPP(c_List_Oappend(_1687490), _1687492), hAPP(hAPP(c_List_Olist_OCons(_1687490), _1687498), _1687496)))], (4952 ^ _780119) ^ [_855742, _855744] : [_855744 = _855742, -(c_Lazy__Sequence_Ohit__bound(_855744) = c_Lazy__Sequence_Ohit__bound(_855742))], (3500 ^ _780119) ^ [_832752, _832754, _832756, _832758] : [-(c_Nat_Ocompow(_832758, _832754) = c_Nat_Ocompow(_832756, _832752)), _832758 = _832756, _832754 = _832752], (51575 ^ _780119) ^ [] : [hBOOL(c_fFalse)], (33293 ^ _780119) ^ [_1400695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1400695)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400695), c_Int_OMin)))], (12383 ^ _780119) ^ [_1003843, _1003845] : [12384 ^ _780119 : [(12387 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003845), _1003843))], (12385 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003843), _1003845))]], _1003843 = _1003845], (26473 ^ _780119) ^ [_1263218, _1263220, _1263222] : [hBOOL(hAPP(hAPP(c_member(_1263218), _1263220), hAPP(c_Set_OCollect(_1263218), _1263222))), -(hBOOL(hAPP(_1263222, _1263220)))], (8016 ^ _780119) ^ [_917006, _917008, _917010, _917012] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917006, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917006, tc_HOL_Obool)), _917008), _917010)), _917012) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917006, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917006, tc_HOL_Obool)), _917008), _917012)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917006, tc_HOL_Obool)), _917010), _917012)))], (39905 ^ _780119) ^ [_1558618, _1558620, _1558622, _1558624] : [-(c_Wellfounded_Oacyclic(_1558618, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1558618, _1558618)), hAPP(hAPP(c_Product__Type_OPair(_1558618, _1558618), _1558620), _1558622)), _1558624))), c_Wellfounded_Oacyclic(_1558618, _1558624), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1558618, _1558618)), hAPP(hAPP(c_Product__Type_OPair(_1558618, _1558618), _1558622), _1558620)), c_Transitive__Closure_Ortrancl(_1558618, _1558624))))], (43070 ^ _780119) ^ [_1634017, _1634019, _1634021, _1634023, _1634025, _1634027, _1634029, _1634031] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1634017, _1634019), _1634021), _1634023), hAPP(hAPP(c_List_Ozip(_1634017, _1634019), _1634025), hAPP(hAPP(c_List_Omap(_1634027, _1634019), _1634029), _1634031))) = hAPP(hAPP(c_List_Omap(tc_prod(_1634017, _1634027), _1634021), hAPP(c_Product__Type_Oprod_Oprod__case(_1634017, _1634027, _1634021), hAPP(hAPP(c_COMBB(tc_fun(_1634027, tc_prod(_1634017, _1634019)), tc_fun(_1634027, _1634021), _1634017), hAPP(c_COMBB(tc_prod(_1634017, _1634019), _1634021, _1634027), _1634023)), hAPP(hAPP(c_COMBC(_1634017, tc_fun(_1634027, _1634019), tc_fun(_1634027, tc_prod(_1634017, _1634019))), hAPP(hAPP(c_COMBB(tc_fun(_1634019, tc_prod(_1634017, _1634019)), tc_fun(tc_fun(_1634027, _1634019), tc_fun(_1634027, tc_prod(_1634017, _1634019))), _1634017), c_COMBB(_1634019, tc_prod(_1634017, _1634019), _1634027)), c_Product__Type_OPair(_1634017, _1634019))), _1634029)))), hAPP(hAPP(c_List_Ozip(_1634017, _1634027), _1634025), _1634031)))], (37257 ^ _780119) ^ [_1492236, _1492238, _1492240] : [c_Wellfounded_Owf(_1492236, _1492238), -(c_Wellfounded_Owf(_1492236, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1492236, _1492236), tc_HOL_Obool)), _1492240), _1492238)))], (4516 ^ _780119) ^ [_848582, _848584, _848586, _848588, _848590, _848592] : [-(c_Lazy__Sequence_Oanamorph(_848592, _848588, _848584) = c_Lazy__Sequence_Oanamorph(_848590, _848586, _848582)), _848592 = _848590, _848588 = _848586, _848584 = _848582], (42156 ^ _780119) ^ [_1612703, _1612705, _1612707, _1612709] : [class_Lattices_Osemilattice__inf(_1612703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612703), _1612705)), 42166 ^ _780119 : [(42169 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612703), _1612707), 42165 ^ [_1612703, _1612705, _1612707, _1612709]))], (42167 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612703), 42165 ^ [_1612703, _1612705, _1612707, _1612709]), _1612705)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612703), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1612703), _1612707), _1612709)), hAPP(hAPP(c_Finite__Set_Ofold(_1612703, _1612703, c_Lattices_Osemilattice__inf__class_Oinf(_1612703)), _1612709), _1612705))))], (49114 ^ _780119) ^ [_1773911, _1773913, _1773915, _1773917, _1773919, _1773921] : [c_List_Olist__all2(_1773911, _1773913, _1773915, _1773917, _1773919), -(c_List_Olist__all2(_1773911, _1773913, _1773915, hAPP(hAPP(c_List_Otake(_1773911), _1773921), _1773917), hAPP(hAPP(c_List_Otake(_1773913), _1773921), _1773919)))], (49090 ^ _780119) ^ [_1773514, _1773516, _1773518, _1773520] : [c_List_Olist__all2(_1773514, _1773516, _1773518, _1773520, c_List_Olist_ONil(_1773516)), -(_1773520 = c_List_Olist_ONil(_1773514))], (10020 ^ _780119) ^ [_954611, _954613, _954615] : [class_Lattices_Osemilattice__inf(_954611), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954611), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_954611), _954613), _954615)), _954615)))], (44340 ^ _780119) ^ [_1668241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1668241)), _1668241 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3828 ^ _780119) ^ [_837798, _837800] : [_837800 = _837798, -(c_SetInterval_Oord__class_OatMost(_837800) = c_SetInterval_Oord__class_OatMost(_837798))], (33093 ^ _780119) ^ [_1396781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1396781)), -(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), _1396781), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (31697 ^ _780119) ^ [_1371637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1371637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1371637))))], (28294 ^ _780119) ^ [_1303195, _1303197] : [class_Orderings_Olinorder(_1303195), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303195), _1303197)), -(c_Big__Operators_Olinorder__class_OMin(_1303195, _1303197) = hAPP(c_Finite__Set_Ofold1(_1303195, c_Orderings_Oord__class_Omin(_1303195)), _1303197))], (22191 ^ _780119) ^ [_1185191, _1185193] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1185191), _1185193) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1185191, _1185193)), _1185193))], (51149 ^ _780119) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (13536 ^ _780119) ^ [_1026579, _1026581, _1026583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1026579, tc_HOL_Obool)), _1026583), _1026581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1026579, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026579, tc_HOL_Obool)), _1026581)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026579, tc_HOL_Obool)), _1026583))))], (24223 ^ _780119) ^ [_1223595, _1223597] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1223595)), _1223597) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1223595, _1223597))], (4330 ^ _780119) ^ [_845647, _845649] : [_845649 = _845647, -(c_New__DSequence_Opos__not__seq(_845649) = c_New__DSequence_Opos__not__seq(_845647))], (39747 ^ _780119) ^ [_1554975, _1554977, _1554979] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554975, _1554975)), hAPP(hAPP(c_Product__Type_OPair(_1554975, _1554975), _1554977), _1554979)), c_Relation_OId(_1554975))), -(_1554977 = _1554979)], (38044 ^ _780119) ^ [_1514127, _1514129, _1514131, _1514133] : [class_Groups_Ocomm__monoid__add(_1514127), c_Fun_Oinj__on(_1514129, _1514127, _1514131, _1514133), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514129, _1514127), _1514131), _1514133) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514127, _1514127), c_Fun_Oid(_1514127)), hAPP(c_Set_Oimage(_1514129, _1514127, _1514131), _1514133)))], (38200 ^ _780119) ^ [_1518139, _1518141, _1518143, _1518145, _1518147, _1518149, _1518151, _1518153] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1518139, _1518141)), _1518143), hAPP(c_Set_Oimage(tc_prod(_1518145, _1518147), tc_prod(_1518139, _1518141), c_Product__Type_Omap__pair(_1518145, _1518139, _1518147, _1518141, _1518149, _1518151)), _1518153))), 38205 ^ _780119 : [(38208 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1518145, _1518147)), hAPP(hAPP(c_Product__Type_OPair(_1518145, _1518147), 38203 ^ [_1518139, _1518141, _1518143, _1518145, _1518147, _1518149, _1518151, _1518153]), 38204 ^ [_1518139, _1518141, _1518143, _1518145, _1518147, _1518149, _1518151, _1518153])), _1518153)))], (38206 ^ _780119) ^ [] : [-(_1518143 = hAPP(hAPP(c_Product__Type_OPair(_1518139, _1518141), hAPP(_1518149, 38203 ^ [_1518139, _1518141, _1518143, _1518145, _1518147, _1518149, _1518151, _1518153])), hAPP(_1518151, 38204 ^ [_1518139, _1518141, _1518143, _1518145, _1518147, _1518149, _1518151, _1518153])))]]], (22284 ^ _780119) ^ [_1186640, _1186642, _1186644] : [-(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), _1186640), _1186642)), _1186644), _1186642) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186644, _1186642))], (31877 ^ _780119) ^ [] : [-(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))))))], (49337 ^ _780119) ^ [_1778544, _1778546, _1778548, _1778550] : [-(c_List_Omaps(_1778544, _1778546, _1778548, _1778550) = c_List_Oconcat(_1778546, hAPP(hAPP(c_List_Omap(_1778544, tc_List_Olist(_1778546)), _1778548), _1778550)))], (36700 ^ _780119) ^ [_1477364, _1477366, _1477368, _1477370, _1477372] : [hBOOL(hAPP(hAPP(c_member(_1477368), hAPP(_1477370, _1477366)), _1477372)), -(hBOOL(hAPP(hAPP(c_member(_1477364), _1477366), hAPP(c_Set_Ovimage(_1477364, _1477368, _1477370), _1477372))))], (22805 ^ _780119) ^ [] : [-(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))], (6815 ^ _780119) ^ [_892197, _892199, _892201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892197, tc_HOL_Obool)), _892199), _892201)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892197, tc_HOL_Obool)), _892199), _892201) = _892201)], (29801 ^ _780119) ^ [_1335423, _1335425, _1335427, _1335429, _1335431] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335423, tc_HOL_Obool)), _1335425), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335427, tc_fun(_1335423, tc_HOL_Obool)), _1335429), _1335431)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335427, tc_fun(_1335423, tc_HOL_Obool)), _1335429), hAPP(hAPP(c_COMBB(tc_fun(_1335423, tc_HOL_Obool), tc_fun(_1335423, tc_HOL_Obool), _1335427), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335423, tc_HOL_Obool)), _1335425)), _1335431)))], (42813 ^ _780119) ^ [_1628026, _1628028, _1628030, _1628032, _1628034, _1628036] : [-(hBOOL(hAPP(hAPP(c_member(_1628026), _1628028), hAPP(c_List_Oset(_1628026), _1628030)))), -(hAPP(hAPP(c_List_Omap(_1628026, _1628032), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1628026, _1628032), _1628034), _1628028), _1628036)), _1628030) = hAPP(hAPP(c_List_Omap(_1628026, _1628032), _1628034), _1628030))], (41111 ^ _780119) ^ [_1586254, _1586256, _1586258, _1586260] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1586258), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586254, tc_fun(_1586258, tc_HOL_Obool)), _1586256), _1586260)))), 41112 ^ _780119 : [(41113 ^ _780119) ^ [_1586328] : [hBOOL(hAPP(hAPP(c_member(_1586254), _1586328), _1586256)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1586258), hAPP(_1586260, _1586328)))]]], (27360 ^ _780119) ^ [_1285623, _1285625] : [class_Orderings_Olinorder(_1285623), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285623), _1285625)), -(_1285625 = c_Orderings_Obot__class_Obot(tc_fun(_1285623, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1285623), c_Big__Operators_Olinorder__class_OMax(_1285623, _1285625)), _1285625)))], (1770 ^ _780119) ^ [_804968, _804970] : [-(class_Groups_Ominus(_804968)), _804970 = _804968, class_Groups_Ominus(_804970)], (1110 ^ _780119) ^ [_796718, _796720] : [-(class_Rings_Olinordered__ring(_796718)), _796720 = _796718, class_Rings_Olinordered__ring(_796720)], (34889 ^ _780119) ^ [_1435253, _1435255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1435253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1435255)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1435253), _1435255) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1435253, _1435255)))], (34427 ^ _780119) ^ [_1426197, _1426199, _1426201, _1426203] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1426197, _1426199), _1426201)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1426197, _1426199), _1426203)), -(_1426201 = _1426203)], (31097 ^ _780119) ^ [_1361498] : [-(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), _1361498)) = 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), _1361498))))], (46582 ^ _780119) ^ [_1719177, _1719179, _1719181] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1719177, tc_HOL_Obool)), hAPP(c_List_Oset(_1719177), hAPP(c_List_Ofilter(_1719177, _1719179), _1719181))), hAPP(c_List_Oset(_1719177), _1719181))))], (47524 ^ _780119) ^ [_1738424, _1738426, _1738428, _1738430] : [-(hAPP(c_List_Orev(_1738424), hAPP(hAPP(c_List_Omap(_1738426, _1738424), _1738428), _1738430)) = hAPP(hAPP(c_List_Omap(_1738426, _1738424), _1738428), hAPP(c_List_Orev(_1738426), _1738430)))], (47216 ^ _780119) ^ [_1731534, _1731536] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1731534), hAPP(c_List_Onth(_1731534), _1731536)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731534)), _1731536))) = _1731536)], (21630 ^ _780119) ^ [_1174950, _1174952, _1174954, _1174956] : [class_Divides_Osemiring__div(_1174950), -(c_Divides_Odiv__class_Omod(_1174950, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1174950), _1174952), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174950), _1174954), _1174956)), _1174954) = c_Divides_Odiv__class_Omod(_1174950, _1174952, _1174954))], (51449 ^ _780119) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (34853 ^ _780119) ^ [_1434406, _1434408] : [_1434406 = _1434408, -(hAPP(c_Int_ORep__Integ, _1434406) = hAPP(c_Int_ORep__Integ, _1434408))], (43240 ^ _780119) ^ [_1638534, _1638536, _1638538, _1638540] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638534)), _1638536) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638538)), _1638540), -(hAPP(hAPP(c_List_Omap(tc_prod(_1638534, _1638538), _1638534), c_Product__Type_Ofst(_1638534, _1638538)), hAPP(hAPP(c_List_Ozip(_1638534, _1638538), _1638536), _1638540)) = _1638536)], (10919 ^ _780119) ^ [_973922, _973924, _973926, _973928] : [class_Groups_Oordered__cancel__ab__semigroup__add(_973922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973922), _973924), _973926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973922), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973922), _973924), _973928)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973922), _973926), _973928))))], (17112 ^ _780119) ^ [_1090899, _1090901, _1090903] : [-(c_Map_Odom(_1090899, _1090901, hAPP(hAPP(c_COMBB(_1090901, tc_Option_Ooption(_1090901), _1090899), c_Option_Ooption_OSome(_1090901)), _1090903)) = c_Orderings_Otop__class_Otop(tc_fun(_1090899, tc_HOL_Obool)))], (21606 ^ _780119) ^ [_1174401, _1174403, _1174405, _1174407, _1174409] : [hAPP(c_Set_Oimage(_1174401, _1174403, _1174405), _1174407) = _1174409, -(hAPP(c_Set_Oimage(tc_fun(_1174401, tc_HOL_Obool), tc_fun(_1174403, tc_HOL_Obool), c_Set_Oimage(_1174401, _1174403, _1174405)), hAPP(c_Set_OPow(_1174401), _1174407)) = hAPP(c_Set_OPow(_1174403), _1174409))], (7962 ^ _780119) ^ [_915880, _915882, _915884, _915886] : [-(hBOOL(hAPP(hAPP(c_member(_915880), _915882), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915880, tc_HOL_Obool)), _915884), _915886)))), hBOOL(hAPP(hAPP(c_member(_915880), _915882), _915884)), -(hBOOL(hAPP(hAPP(c_member(_915880), _915882), _915886)))], (42986 ^ _780119) ^ [_1632186, _1632188, _1632190] : [hBOOL(hAPP(c_List_Odistinct(_1632186), _1632188)), -(hAPP(c_List_Oset(_1632186), c_List_Oremove1(_1632186, _1632190, _1632188)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1632186, tc_HOL_Obool)), hAPP(c_List_Oset(_1632186), _1632188)), hAPP(hAPP(c_Set_Oinsert(_1632186), _1632190), c_Orderings_Obot__class_Obot(tc_fun(_1632186, tc_HOL_Obool)))))], (48251 ^ _780119) ^ [_1755861, _1755863] : [-(c_Enum_Oenum__the(_1755861, _1755863) = c_HOL_OThe(_1755861, _1755863))], (37032 ^ _780119) ^ [_1485679, _1485681, _1485683, _1485685, _1485687, _1485689, _1485691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1485679, _1485681), tc_HOL_Obool)), _1485683), _1485685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1485681, _1485687), tc_HOL_Obool)), _1485689), _1485691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1485679, _1485687), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1485679, _1485681, _1485687), _1485683), _1485689)), hAPP(hAPP(c_Relation_Orel__comp(_1485679, _1485681, _1485687), _1485685), _1485691))))], (23951 ^ _780119) ^ [_1218177, _1218179, _1218181] : [class_Orderings_Oorder(_1218177), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1218177, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1218177), _1218179)), c_SetInterval_Oord__class_OatLeastAtMost(_1218177, _1218179, _1218181)) = c_Orderings_Obot__class_Obot(tc_fun(_1218177, tc_HOL_Obool)))], (18768 ^ _780119) ^ [_1122405, _1122407] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122405), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1122407)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1122405), _1122407))], (7262 ^ _780119) ^ [_901740, _901742, _901744, _901746, _901748, _901750] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_901740, _901742, _901744, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_901740), _901746), _901748), _901750)) = hAPP(hAPP(hAPP(_901744, _901746), _901748), _901750))], (34018 ^ _780119) ^ [_1418652, _1418654, _1418656] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1418652, tc_HOL_Obool), tc_fun(_1418652, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1418652, tc_HOL_Obool), tc_fun(_1418652, tc_HOL_Obool)), _1418654), _1418656)), c_Wellfounded_Ofinite__psubset(_1418652)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1418652, tc_HOL_Obool)), _1418654), _1418656)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418652), _1418656))], (42022 ^ _780119) ^ [_1609666, _1609668] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1609666, tc_HOL_Obool), _1609668) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1609666, tc_HOL_Obool), tc_fun(_1609666, tc_HOL_Obool)), _1609668), c_COMBI(tc_fun(_1609666, tc_HOL_Obool))))], (5478 ^ _780119) ^ [_864035, _864037] : [_864037 = _864035, -(c_Nat_Osize__class_Osize(_864037) = c_Nat_Osize__class_Osize(_864035))], (44690 ^ _780119) ^ [_1675419] : [class_Orderings_Olinorder(_1675419), -(c_List_Olinorder__class_Osorted__list__of__set(_1675419, c_Orderings_Obot__class_Obot(tc_fun(_1675419, tc_HOL_Obool))) = c_List_Olist_ONil(_1675419))], (24061 ^ _780119) ^ [_1220424, _1220426, _1220428, _1220430, _1220432] : [class_Groups_Ocomm__monoid__add(_1220424), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220426), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220428), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220424), _1220430), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220426, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220428), _1220432))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220424), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220424), _1220430), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220426, _1220428))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220424), _1220430), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220428), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220428), _1220432)))))], (16582 ^ _780119) ^ [_1082098, _1082100, _1082102] : [class_Groups_Ogroup__add(_1082098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082098), _1082100), _1082102) = c_Groups_Ozero__class_Ozero(_1082098), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1082098), _1082100) = _1082102)], (37673 ^ _780119) ^ [_1502053, _1502055, _1502057, _1502059] : [hBOOL(hAPP(hAPP(c_member(_1502053), _1502055), hAPP(c_Relation_ODomain(_1502053, _1502057), _1502059))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1502053, _1502057)), hAPP(hAPP(c_Product__Type_OPair(_1502053, _1502057), _1502055), 37676 ^ [_1502053, _1502055, _1502057, _1502059])), _1502059)))], (37753 ^ _780119) ^ [_1504630, _1504632, _1504634, _1504636, _1504638, _1504640] : [class_Groups_Ocomm__monoid__add(_1504630), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1504632, _1504630), hAPP(hAPP(c_COMBC(_1504632, tc_fun(_1504634, tc_HOL_Obool), _1504630), hAPP(hAPP(c_COMBB(tc_fun(_1504634, _1504630), tc_fun(tc_fun(_1504634, tc_HOL_Obool), _1504630), _1504632), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1504634, _1504630)), _1504636)), _1504638)), _1504640) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1504632, _1504634), _1504630), hAPP(c_Product__Type_Oprod_Oprod__case(_1504632, _1504634, _1504630), _1504636)), hAPP(hAPP(c_Product__Type_OSigma(_1504632, _1504634), _1504640), hAPP(c_COMBK(tc_fun(_1504634, tc_HOL_Obool), _1504632), _1504638))))], (9870 ^ _780119) ^ [_951848, _951850] : [class_Lattices_Oab__semigroup__idem__mult(_951848), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951848), _951850), _951850) = _951850)], (1280 ^ _780119) ^ [_798843, _798845] : [-(class_Lattices_Obounded__lattice__top(_798843)), _798845 = _798843, class_Lattices_Obounded__lattice__top(_798845)], (12717 ^ _780119) ^ [_1010587, _1010589, _1010591, _1010593, _1010595] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1010587, tc_Option_Ooption(_1010589)), _1010591), _1010593), hAPP(c_Option_Ooption_OSome(_1010589), _1010595)) = hAPP(c_COMBK(tc_Option_Ooption(_1010589), _1010587), c_Option_Ooption_ONone(_1010589))], (16644 ^ _780119) ^ [_1083217, _1083219, _1083221, _1083223] : [class_Groups_Ocomm__monoid__add(_1083217), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1083219), _1083221))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083219, _1083217), _1083223), _1083221) = c_Groups_Ozero__class_Ozero(_1083217))], (32391 ^ _780119) ^ [_1384180, _1384182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1384180)), c_Int_OBit0(_1384182))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384180), _1384182)))], (23665 ^ _780119) ^ [_1212685, _1212687] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1212685), _1212687)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1212685)), hAPP(c_Nat_OSuc, _1212687)))], (25911 ^ _780119) ^ [_1252946, _1252948] : [c_Nat__Transfer_Onat__set(_1252946), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1252948), _1252946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252948)))], (26303 ^ _780119) ^ [_1260063, _1260065, _1260067] : [hBOOL(hAPP(_1260063, _1260065)), -(hBOOL(hAPP(hAPP(c_member(_1260067), _1260065), hAPP(c_Set_OCollect(_1260067), _1260063))))], (7362 ^ _780119) ^ [_903758, _903760, _903762, _903764] : [class_Lattices_Osemilattice__sup(_903758), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903758), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903758), _903760), _903762)), _903764) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903758), _903760), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903758), _903762), _903764)))], (47574 ^ _780119) ^ [_1739487, _1739489, _1739491] : [_1739489 = _1739491, -(hAPP(c_List_Orev(_1739487), _1739489) = hAPP(c_List_Orev(_1739487), _1739491))], (51015 ^ _780119) ^ [_1814704, _1814706] : [class_Orderings_Oord(_1814704), -(class_Orderings_Oord(tc_fun(_1814706, _1814704)))], (18696 ^ _780119) ^ [_1121064, _1121066, _1121068] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121064), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121066), _1121068)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121064), _1121068)))], (10997 ^ _780119) ^ [_975329, _975331, _975333, _975335, _975337] : [hBOOL(hAPP(hAPP(c_member(_975329), _975331), _975333)), -(hAPP(c_Map_Orestrict__map(_975329, _975335, _975337, _975333), _975331) = hAPP(_975337, _975331))], (22932 ^ _780119) ^ [_1198962, _1198964] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198962)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198964), 22935 ^ _780119 : [(22938 ^ _780119) ^ [] : [-(_1198964 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22936 ^ _780119) ^ [] : [-(_1198962 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25626 ^ _780119) ^ [_1248365, _1248367] : [c_Nat__Transfer_Ois__nat(_1248365), c_Nat__Transfer_Ois__nat(_1248367), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1248365), _1248367)))], (8498 ^ _780119) ^ [_927673, _927675, _927677, _927679, _927681, _927683] : [_927673 = _927675, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927677, _927679), _927681), _927675), _927683), _927673) = _927683)], (32743 ^ _780119) ^ [] : [-(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))))))], (22914 ^ _780119) ^ [_1198621, _1198623] : [22915 ^ _780119 : [(22916 ^ _780119) ^ [_1198674] : [_1198623 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198621), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198674))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1198621), _1198623)))], (50332 ^ _780119) ^ [_1800711, _1800713, _1800715, _1800717, _1800719] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1800711), _1800713), _1800715), _1800717), _1800719) = c_New__DSequence_Oneg__single(_1800711, _1800713))], (29741 ^ _780119) ^ [_1333480, _1333482, _1333484, _1333486] : [-(_1333480 = c_Orderings_Obot__class_Obot(tc_fun(_1333482, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1333482, tc_fun(_1333484, tc_HOL_Obool)), _1333480), hAPP(c_COMBK(tc_fun(_1333484, tc_HOL_Obool), _1333482), _1333486)) = _1333486)], (32663 ^ _780119) ^ [_1388981, _1388983] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1388981), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1388983))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1388981), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1388983))), 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))))], (31249 ^ _780119) ^ [_1364331] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1364331) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1364331)))], (14914 ^ _780119) ^ [_1053776, _1053778] : [class_Groups_Omonoid__add(_1053776), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053776), c_Groups_Ozero__class_Ozero(_1053776)), _1053778) = _1053778)], (45590 ^ _780119) ^ [_1697535, _1697537, _1697539] : [-(hAPP(hAPP(c_List_Odrop(_1697535), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1697535), _1697537), _1697539)) = _1697539)], (10172 ^ _780119) ^ [_957687, _957689, _957691, _957693] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957687, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_957687), _957689), _957691)), hAPP(hAPP(c_Set_Oinsert(_957687), _957689), _957693)) = hAPP(hAPP(c_Set_Oinsert(_957687), _957689), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957687, tc_HOL_Obool)), _957691), _957693)))], (41338 ^ _780119) ^ [_1592575, _1592577, _1592579, _1592581, _1592583] : [41340 ^ _780119 : [(41343 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1592575), _1592577), hAPP(_1592583, 41339 ^ [_1592575, _1592577, _1592579, _1592581, _1592583])))], (41341 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592579), 41339 ^ [_1592575, _1592577, _1592579, _1592581, _1592583]), _1592581)))]], -(hBOOL(hAPP(hAPP(c_member(_1592575), _1592577), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592579, tc_fun(_1592575, tc_HOL_Obool)), _1592581), _1592583))))], (18157 ^ _780119) ^ [_1110791, _1110793] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1110791), _1110793)), -(hAPP(c_Finite__Set_Ocard(_1110791), _1110793) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1110791, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1110791), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1110793))], (32569 ^ _780119) ^ [_1387228, _1387230] : [class_Int_Onumber__ring(_1387228), class_Int_Oring__char__0(_1387228), 32576 ^ _780119 : [(32583 ^ _780119) ^ [] : [c_Int_Oiszero(_1387228, hAPP(c_Int_Onumber__class_Onumber__of(_1387228), _1387230)), -(c_Int_Oiszero(_1387228, hAPP(c_Int_Onumber__class_Onumber__of(_1387228), c_Int_OBit0(_1387230))))], (32577 ^ _780119) ^ [] : [c_Int_Oiszero(_1387228, hAPP(c_Int_Onumber__class_Onumber__of(_1387228), c_Int_OBit0(_1387230))), -(c_Int_Oiszero(_1387228, hAPP(c_Int_Onumber__class_Onumber__of(_1387228), _1387230)))]]], (32727 ^ _780119) ^ [] : [-(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))))], (7041 ^ _780119) ^ [_896353, _896355, _896357] : [hBOOL(hAPP(hAPP(c_member(_896353), _896355), hAPP(c_fequal, _896357))), -(_896355 = _896357)], (9512 ^ _780119) ^ [_943856, _943858, _943860, _943862, _943864, _943866, _943868] : [c_Nitpick_Ofold__graph_H(_943856, _943858, _943860, _943862, _943864, hAPP(hAPP(_943860, _943866), _943868)), 9517 ^ _780119 : [(9520 ^ _780119) ^ [] : [-(hAPP(hAPP(_943860, _943866), _943868) = _943862)], (9518 ^ _780119) ^ [] : [-(_943864 = c_Orderings_Obot__class_Obot(tc_fun(_943856, tc_HOL_Obool)))]], 9523 ^ _780119 : [(9526 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_943856), 9521 ^ [_943856, _943858, _943860, _943862, _943864, _943866, _943868]), _943864)))], (9528 ^ _780119) ^ [] : [-(c_Nitpick_Ofold__graph_H(_943856, _943858, _943860, _943862, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943856, tc_HOL_Obool)), _943864), hAPP(hAPP(c_Set_Oinsert(_943856), 9521 ^ [_943856, _943858, _943860, _943862, _943864, _943866, _943868]), c_Orderings_Obot__class_Obot(tc_fun(_943856, tc_HOL_Obool)))), 9522 ^ [_943856, _943858, _943860, _943862, _943864, _943866, _943868]))], (9524 ^ _780119) ^ [] : [-(hAPP(hAPP(_943860, _943866), _943868) = hAPP(hAPP(_943860, 9521 ^ [_943856, _943858, _943860, _943862, _943864, _943866, _943868]), 9522 ^ [_943856, _943858, _943860, _943862, _943864, _943866, _943868]))]]], (26677 ^ _780119) ^ [_1267323, _1267325] : [class_Groups_Oordered__ab__group__add__abs(_1267323), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267323), hAPP(c_Groups_Ouminus__class_Ouminus(_1267323), _1267325)), hAPP(c_Groups_Oabs__class_Oabs(_1267323), _1267325))))], (22609 ^ _780119) ^ [_1192699, _1192701, _1192703] : [class_Groups_Ocomm__monoid__add(_1192699), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1192699), _1192701), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1192703))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192699), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1192699), _1192701), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1192703))), hAPP(_1192701, _1192703)))], (29776 ^ _780119) ^ [_1334310, _1334312, _1334314, _1334316, _1334318] : [29778 ^ _780119 : [(29781 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1334310, tc_HOL_Obool)), hAPP(_1334316, 29777 ^ [_1334310, _1334312, _1334314, _1334316, _1334318])), _1334318))], (29779 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1334312), 29777 ^ [_1334310, _1334312, _1334314, _1334316, _1334318]), _1334314)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1334310, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334312, tc_fun(_1334310, tc_HOL_Obool)), _1334314), _1334316)), _1334318)))], (2628 ^ _780119) ^ [_819052, _819054] : [_819054 = _819052, -(c_Nitpick_Ozero__frac(_819054) = c_Nitpick_Ozero__frac(_819052))], (32529 ^ _780119) ^ [_1386494, _1386496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1386494)), c_Int_OBit0(_1386496))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1386494), _1386496)))], (50102 ^ _780119) ^ [_1795709] : [class_HOL_Oequal(_1795709), -(c_HOL_Oequal__class_Oequal(_1795709) = c_fequal)], (30423 ^ _780119) ^ [_1348892, _1348894] : [class_Int_Onumber__ring(_1348892), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1348892), hAPP(c_Int_Onumber__class_Onumber__of(_1348892), _1348894)) = hAPP(c_Int_Onumber__class_Onumber__of(_1348892), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1348894)))], (7148 ^ _780119) ^ [_898590, _898592] : [class_Orderings_Obot(_898590), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898590), c_Orderings_Obot__class_Obot(_898590)), _898592)))], (4846 ^ _780119) ^ [_854033, _854035, _854037, _854039, _854041, _854043, _854045, _854047, _854049, _854051, _854053, _854055] : [-(c_New__Random__Sequence_Opos__union(_854055, _854051, _854047, _854043, _854039, _854035) = c_New__Random__Sequence_Opos__union(_854053, _854049, _854045, _854041, _854037, _854033)), _854055 = _854053, _854051 = _854049, _854047 = _854045, _854043 = _854041, _854039 = _854037, _854035 = _854033], (3150 ^ _780119) ^ [_827113, _827115, _827117, _827119, _827121, _827123] : [-(c_Smallcheck_Oorelse(_827123, _827119, _827115) = c_Smallcheck_Oorelse(_827121, _827117, _827113)), _827123 = _827121, _827119 = _827117, _827115 = _827113], (28764 ^ _780119) ^ [_1311479, _1311481, _1311483] : [class_Orderings_Olinorder(_1311479), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311479), _1311481)), -(_1311481 = c_Orderings_Obot__class_Obot(tc_fun(_1311479, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311479), _1311483)), -(_1311483 = c_Orderings_Obot__class_Obot(tc_fun(_1311479, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311479), c_Big__Operators_Olattice_OSup__fin(_1311479, c_Orderings_Oord__class_Omax(_1311479), _1311481)), c_Big__Operators_Olattice_OSup__fin(_1311479, c_Orderings_Oord__class_Omax(_1311479), _1311483)) = c_Big__Operators_Olattice_OSup__fin(_1311479, c_Orderings_Oord__class_Omax(_1311479), hAPP(c_Set_OCollect(_1311479), hAPP(hAPP(c_COMBB(tc_fun(_1311479, tc_HOL_Obool), tc_HOL_Obool, _1311479), c_HOL_OEx(_1311479)), hAPP(hAPP(c_COMBB(tc_fun(_1311479, tc_fun(_1311479, tc_HOL_Obool)), tc_fun(_1311479, tc_HOL_Obool), _1311479), hAPP(c_COMBB(tc_fun(_1311479, tc_HOL_Obool), tc_HOL_Obool, _1311479), c_HOL_OEx(_1311479))), hAPP(hAPP(c_COMBC(_1311479, tc_fun(_1311479, tc_fun(_1311479, tc_HOL_Obool)), tc_fun(_1311479, tc_fun(_1311479, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1311479, tc_fun(tc_fun(_1311479, tc_HOL_Obool), tc_fun(_1311479, tc_HOL_Obool))), tc_fun(tc_fun(_1311479, tc_fun(_1311479, tc_HOL_Obool)), tc_fun(_1311479, tc_fun(_1311479, tc_HOL_Obool))), _1311479), c_COMBS(_1311479, tc_fun(_1311479, tc_HOL_Obool), tc_fun(_1311479, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1311479, tc_fun(_1311479, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1311479, tc_fun(tc_fun(_1311479, tc_HOL_Obool), tc_fun(_1311479, tc_HOL_Obool))), _1311479), hAPP(c_COMBB(tc_fun(_1311479, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1311479, tc_HOL_Obool), tc_fun(_1311479, tc_HOL_Obool)), _1311479), c_COMBS(_1311479, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1311479, tc_fun(_1311479, tc_HOL_Obool)), tc_fun(_1311479, tc_fun(_1311479, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1311479), hAPP(c_COMBB(tc_fun(_1311479, tc_HOL_Obool), tc_fun(_1311479, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1311479), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1311479), c_fconj))), hAPP(hAPP(c_COMBC(_1311479, tc_fun(_1311479, tc_fun(_1311479, _1311479)), tc_fun(_1311479, tc_fun(_1311479, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1311479, _1311479), tc_fun(_1311479, tc_HOL_Obool)), tc_fun(tc_fun(_1311479, tc_fun(_1311479, _1311479)), tc_fun(_1311479, tc_fun(_1311479, tc_HOL_Obool))), _1311479), c_COMBB(tc_fun(_1311479, _1311479), tc_fun(_1311479, tc_HOL_Obool), _1311479)), hAPP(hAPP(c_COMBB(tc_fun(_1311479, tc_HOL_Obool), tc_fun(tc_fun(_1311479, _1311479), tc_fun(_1311479, tc_HOL_Obool)), _1311479), c_COMBB(_1311479, tc_HOL_Obool, _1311479)), c_fequal))), c_Orderings_Oord__class_Omin(_1311479)))))), hAPP(hAPP(c_COMBC(_1311479, tc_fun(_1311479, tc_HOL_Obool), tc_fun(_1311479, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1311479, tc_HOL_Obool), tc_fun(_1311479, tc_HOL_Obool)), _1311479), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1311479)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1311479), c_fconj), hAPP(hAPP(c_COMBC(_1311479, tc_fun(_1311479, tc_HOL_Obool), tc_HOL_Obool), c_member(_1311479)), _1311481)))), hAPP(hAPP(c_COMBC(_1311479, tc_fun(_1311479, tc_HOL_Obool), tc_HOL_Obool), c_member(_1311479)), _1311483))))))))], (26507 ^ _780119) ^ [_1263956, _1263958, _1263960] : [-(hAPP(hAPP(c_Set_Oinsert(_1263956), _1263958), hAPP(c_Set_OCollect(_1263956), _1263960)) = hAPP(c_Set_OCollect(_1263956), hAPP(hAPP(c_COMBS(_1263956, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263956), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1263956), c_fNot), hAPP(hAPP(c_COMBC(_1263956, _1263956, tc_HOL_Obool), c_fequal), _1263958)))), _1263960)))], (44268 ^ _780119) ^ [_1666955, _1666957, _1666959] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666955)), hAPP(hAPP(c_List_Otake(_1666955), _1666957), _1666959)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666955)), _1666959)), _1666957))], (21721 ^ _780119) ^ [_1176632, _1176634, _1176636, _1176638] : [class_Divides_Osemiring__div(_1176632), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176632), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1176632), _1176634), _1176636)), _1176636)), c_Divides_Odiv__class_Omod(_1176632, _1176634, _1176636))), _1176638) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176632), _1176634), _1176638))], (15430 ^ _780119) ^ [_1061427, _1061429, _1061431, _1061433] : [class_Rings_Olinordered__semidom(_1061427), hAPP(hAPP(c_Power_Opower__class_Opower(_1061427), _1061429), _1061431) = hAPP(hAPP(c_Power_Opower__class_Opower(_1061427), _1061433), _1061431), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061427), c_Groups_Ozero__class_Ozero(_1061427)), _1061429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061427), c_Groups_Ozero__class_Ozero(_1061427)), _1061433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1061431)), -(_1061429 = _1061433)], (8610 ^ _780119) ^ [_929197, _929199, _929201] : [class_Orderings_Olinorder(_929197), -(_929199 = _929201), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929197), _929199), _929201))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929197), _929201), _929199)))], (6175 ^ _780119) ^ [_878653, _878655, _878657, _878659, _878661, _878663] : [hBOOL(hAPP(hAPP(c_member(_878653), _878655), _878657)), _878659 = hAPP(_878661, _878655), -(hBOOL(hAPP(hAPP(c_member(_878663), _878659), hAPP(c_Set_Oimage(_878653, _878663, _878661), _878657))))], (2276 ^ _780119) ^ [_813602, _813604] : [_813604 = _813602, -(c_SetInterval_Oord__class_OatLeast(_813604) = c_SetInterval_Oord__class_OatLeast(_813602))], (37890 ^ _780119) ^ [_1508824, _1508826, _1508828, _1508830] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1508824, _1508826)), hAPP(hAPP(c_Product__Type_OSigma(_1508824, _1508826), hAPP(hAPP(c_Set_Oinsert(_1508824), _1508828), c_Orderings_Obot__class_Obot(tc_fun(_1508824, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1508826, tc_HOL_Obool), _1508824), _1508830))) = hAPP(c_Finite__Set_Ocard(_1508826), _1508830))], (12437 ^ _780119) ^ [_1004699, _1004701, _1004703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004699), _1004701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004699), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1004703), _1004701))))], (48255 ^ _780119) ^ [_1755931, _1755933, _1755935, _1755937] : [hBOOL(hAPP(c_List_Odistinct(_1755931), _1755933)), hBOOL(hAPP(c_List_Odistinct(_1755935), _1755937)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1755931, _1755935)), c_Enum_Oproduct(_1755931, _1755935, _1755933, _1755937))))], (38920 ^ _780119) ^ [_1534764, _1534766, _1534768, _1534770, _1534772, _1534774] : [c_Finite__Set_Ofolding(_1534764, _1534766, _1534768, _1534770), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534764), _1534772)), hBOOL(hAPP(hAPP(c_member(_1534764), _1534774), _1534772)), -(hAPP(_1534770, _1534772) = hAPP(c_Fun_Ocomp(_1534766, _1534766, _1534766, hAPP(_1534770, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1534764, tc_HOL_Obool)), _1534772), hAPP(hAPP(c_Set_Oinsert(_1534764), _1534774), c_Orderings_Obot__class_Obot(tc_fun(_1534764, tc_HOL_Obool)))))), hAPP(_1534768, _1534774)))], (4140 ^ _780119) ^ [_842706, _842708] : [_842708 = _842706, -(c_Enum_Oenum__class_Oenum__ex(_842708) = c_Enum_Oenum__class_Oenum__ex(_842706))], (32523 ^ _780119) ^ [_1386372, _1386374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1386372), _1386374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1386372)), c_Int_OBit0(_1386374))))], (12775 ^ _780119) ^ [_1011705, _1011707, _1011709, _1011711, _1011713] : [hAPP(_1011705, _1011707) = c_Option_Ooption_ONone(_1011709), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1011711, tc_HOL_Obool)), c_Map_Odom(_1011711, _1011709, _1011705)), hAPP(hAPP(c_Set_Oinsert(_1011711), _1011707), _1011713)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1011711, tc_HOL_Obool)), c_Map_Odom(_1011711, _1011709, _1011705)), _1011713))], (34829 ^ _780119) ^ [_1433962, _1433964, _1433966, _1433968] : [-(_1433962 = _1433964), hAPP(c_Product__Type_Ofst(_1433966, _1433968), _1433962) = hAPP(c_Product__Type_Ofst(_1433966, _1433968), _1433964), hAPP(c_Product__Type_Osnd(_1433966, _1433968), _1433962) = hAPP(c_Product__Type_Osnd(_1433966, _1433968), _1433964)], (11692 ^ _780119) ^ [_990714, _990716, _990718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990714), _990716)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990716), _990718)), _990714) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990716), _990714)), _990718))], (1886 ^ _780119) ^ [_807275, _807277, _807279, _807281, _807283, _807285, _807287, _807289] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_807289, _807285, _807281, _807277) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_807287, _807283, _807279, _807275)), _807289 = _807287, _807285 = _807283, _807281 = _807279, _807277 = _807275], (47614 ^ _780119) ^ [_1740465, _1740467] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740465)), c_List_Oconcat(_1740465, _1740467)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1740465), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1740465))), _1740467)))], (45862 ^ _780119) ^ [_1703661, _1703663, _1703665] : [-(_1703661 = c_List_Olist_ONil(_1703663)), -(hAPP(c_List_Ohd(_1703663), hAPP(c_List_Orotate(_1703663, _1703665), _1703661)) = hAPP(hAPP(c_List_Onth(_1703663), _1703661), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1703665, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703663)), _1703661))))], (45954 ^ _780119) ^ [_1705525, _1705527, _1705529] : [-(hAPP(c_List_Otl(_1705525), hAPP(hAPP(c_List_Otake(_1705525), _1705527), _1705529)) = hAPP(hAPP(c_List_Otake(_1705525), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1705527), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1705525), _1705529)))], (46422 ^ _780119) ^ [_1715744, _1715746, _1715748] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1715744)), _1715746), c_List_Olists(_1715744, _1715748)))), 46423 ^ _780119 : [(46426 ^ _780119) ^ [_1715872, _1715874] : [_1715746 = hAPP(hAPP(c_List_Olist_OCons(_1715744), _1715874), _1715872), hBOOL(hAPP(hAPP(c_member(_1715744), _1715874), _1715748)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1715744)), _1715872), c_List_Olists(_1715744, _1715748)))], (46424 ^ _780119) ^ [] : [_1715746 = c_List_Olist_ONil(_1715744)]]], (35546 ^ _780119) ^ [_1451647, _1451649, _1451651] : [-(hAPP(c_Relation_OImage(_1451647, _1451647, c_Relation_OId__on(_1451647, _1451649)), _1451651) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451647, tc_HOL_Obool)), _1451649), _1451651))], (23983 ^ _780119) ^ [_1218823, _1218825, _1218827, _1218829] : [class_Groups_Ocomm__monoid__add(_1218823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1218825), _1218827)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218823), _1218829), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218825), _1218827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218823), hAPP(_1218829, _1218825)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218823), _1218829), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1218825)), _1218827))))], (14552 ^ _780119) ^ [_1047014, _1047016, _1047018, _1047020] : [class_Groups_Ocomm__monoid__mult(_1047014), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1047014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047014), _1047016), _1047018)), _1047020) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047014), hAPP(hAPP(c_Power_Opower__class_Opower(_1047014), _1047016), _1047020)), hAPP(hAPP(c_Power_Opower__class_Opower(_1047014), _1047018), _1047020)))], (10224 ^ _780119) ^ [_959207, _959209, _959211, _959213] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959207, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959207, tc_HOL_Obool)), _959209), _959211)), _959213) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959207, tc_HOL_Obool)), _959209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959207, tc_HOL_Obool)), _959211), _959213)))], (12689 ^ _780119) ^ [_1010108, _1010110, _1010112, _1010114, _1010116] : [hBOOL(hAPP(hAPP(c_member(_1010108), _1010110), _1010112)), -(hAPP(c_Map_Orestrict__map(_1010108, _1010114, _1010116, _1010112), _1010110) = hAPP(_1010116, _1010110))], (21354 ^ _780119) ^ [_1169054, _1169056, _1169058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1169054, tc_HOL_Obool)), _1169056), _1169058)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1169054, tc_HOL_Obool)), _1169056), hAPP(c_Set_OPow(_1169054), _1169058))))], (48339 ^ _780119) ^ [_1757540] : [class_Enum_Oenum(_1757540), -(c_Orderings_Otop__class_Otop(tc_fun(_1757540, tc_HOL_Obool)) = hAPP(c_List_Oset(_1757540), c_Enum_Oenum__class_Oenum(_1757540)))], (32545 ^ _780119) ^ [_1386788] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1386788)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1386788)))], (44560 ^ _780119) ^ [_1672815, _1672817] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1672815, _1672817) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1672815), hAPP(c_Code__Numeral_Onat__of, _1672817))))], (41101 ^ _780119) ^ [_1586027, _1586029, _1586031, _1586033, _1586035, _1586037, _1586039, _1586041] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586027, tc_fun(_1586029, tc_fun(_1586031, tc_HOL_Obool))), _1586033), _1586035), _1586037), _1586039)), -(hBOOL(hAPP(hAPP(hAPP(_1586035, _1586041), _1586037), _1586039))), hBOOL(hAPP(hAPP(c_member(_1586027), _1586041), _1586033))], (34034 ^ _780119) ^ [_1419103, _1419105, _1419107, _1419109, _1419111] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1419103, _1419105, tc_HOL_Obool), _1419107), hAPP(hAPP(c_Product__Type_OPair(_1419103, _1419105), _1419109), _1419111))), -(hBOOL(hAPP(hAPP(_1419107, _1419109), _1419111)))], (48792 ^ _780119) ^ [_1766693, _1766695, _1766697, _1766699] : [48794 ^ _780119 : [(48797 ^ _780119) ^ [] : [hBOOL(hAPP(_1766695, hAPP(hAPP(c_List_Onth(_1766697), _1766699), 48793 ^ [_1766693, _1766695, _1766697, _1766699])))], (48795 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48793 ^ [_1766693, _1766695, _1766697, _1766699]), _1766693)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1766693), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766697)), _1766699))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1766693), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766697)), c_List_OtakeWhile(_1766697, _1766695, _1766699)))))], (51459 ^ _780119) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (5801 ^ _780119) ^ [_871939, _871941, _871943, _871945] : [c_Hoare__Mirabelle_Ohoare__derivs(_871939, _871941, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871939)), _871943), _871945)), 5804 ^ _780119 : [(5807 ^ _780119) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871939, _871941, _871945))], (5805 ^ _780119) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871939, _871941, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871939)), _871943), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871939), tc_HOL_Obool)))))]]], (37300 ^ _780119) ^ [_1493068, _1493070, _1493072] : [c_Wellfounded_Owf(_1493068, _1493070), hBOOL(hAPP(hAPP(c_member(tc_prod(_1493068, _1493068)), hAPP(hAPP(c_Product__Type_OPair(_1493068, _1493068), _1493072), _1493072)), _1493070))], (51067 ^ _780119) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (18123 ^ _780119) ^ [_1110142, _1110144] : [_1110142 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110142), _1110144) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37715 ^ _780119) ^ [_1503620, _1503622, _1503624, _1503626, _1503628, _1503630] : [-(hAPP(c_Set_Oimage(_1503620, tc_prod(_1503622, _1503624), hAPP(hAPP(c_COMBS(_1503620, _1503624, tc_prod(_1503622, _1503624)), hAPP(hAPP(c_COMBB(_1503622, tc_fun(_1503624, tc_prod(_1503622, _1503624)), _1503620), c_Product__Type_OPair(_1503622, _1503624)), _1503626)), _1503628)), _1503630) = hAPP(hAPP(c_Product__Type_OSigma(_1503622, _1503624), hAPP(c_Set_Oimage(_1503620, _1503622, _1503626), _1503630)), hAPP(hAPP(c_COMBB(tc_fun(_1503620, tc_HOL_Obool), tc_fun(_1503624, tc_HOL_Obool), _1503622), c_Set_Oimage(_1503620, _1503624, _1503628)), hAPP(hAPP(c_COMBC(_1503622, tc_fun(_1503620, tc_HOL_Obool), tc_fun(_1503620, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503620, tc_HOL_Obool), tc_fun(tc_fun(_1503620, tc_HOL_Obool), tc_fun(_1503620, tc_HOL_Obool)), _1503622), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1503620, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1503622, tc_HOL_Obool), tc_fun(_1503620, tc_HOL_Obool), _1503622), c_Set_Ovimage(_1503620, _1503622, _1503626)), hAPP(hAPP(c_COMBC(_1503622, tc_fun(_1503622, tc_HOL_Obool), tc_fun(_1503622, tc_HOL_Obool)), c_Set_Oinsert(_1503622)), c_Orderings_Obot__class_Obot(tc_fun(_1503622, tc_HOL_Obool)))))), _1503630))))], (8020 ^ _780119) ^ [_917150, _917152, _917154] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917150, tc_HOL_Obool)), _917152), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917150, tc_HOL_Obool)), _917154), _917152)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917150, tc_HOL_Obool)), _917152), _917154))], (14014 ^ _780119) ^ [_1035088, _1035090, _1035092, _1035094, _1035096] : [class_Groups_Ocomm__monoid__mult(_1035088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035090), _1035092)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1035090, _1035088), hAPP(hAPP(c_COMBS(_1035090, _1035088, _1035088), hAPP(hAPP(c_COMBB(_1035088, tc_fun(_1035088, _1035088), _1035090), c_Groups_Otimes__class_Otimes(_1035088)), _1035094)), _1035096)), _1035092) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035088), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1035090, _1035088), _1035094), _1035092)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1035090, _1035088), _1035096), _1035092)))], (51063 ^ _780119) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (45144 ^ _780119) ^ [_1684859, _1684861, _1684863, _1684865] : [_1684861 = _1684865, -(hAPP(hAPP(c_List_Oappend(_1684859), _1684861), _1684863) = hAPP(hAPP(c_List_Oappend(_1684859), _1684865), _1684863))], (46008 ^ _780119) ^ [_1706734, _1706736, _1706738, _1706740, _1706742, _1706744] : [-(hAPP(c_List_Ofoldl(_1706734, _1706736, _1706738, _1706740), hAPP(hAPP(c_List_Olist_OCons(_1706736), _1706742), _1706744)) = hAPP(c_List_Ofoldl(_1706734, _1706736, _1706738, hAPP(hAPP(_1706738, _1706740), _1706742)), _1706744))], (21765 ^ _780119) ^ [_1177595, _1177597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177595), _1177597)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1177595, _1177597) = _1177595)], (42083 ^ _780119) ^ [_1611141, _1611143, _1611145, _1611147, _1611149, _1611151] : [-(_1611141 = c_Orderings_Obot__class_Obot(tc_fun(_1611143, tc_HOL_Obool))), 42089 ^ _780119 : [(42092 ^ _780119) ^ [] : [c_Fun_Oinj__on(_1611145, _1611147, _1611149, hAPP(_1611151, 42088 ^ [_1611141, _1611143, _1611145, _1611147, _1611149, _1611151]))], (42090 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611143), 42088 ^ [_1611141, _1611143, _1611145, _1611147, _1611149, _1611151]), _1611141)))]], -(c_Fun_Oinj__on(_1611145, _1611147, _1611149, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611143, tc_fun(_1611145, tc_HOL_Obool)), _1611141), _1611151)))], (33417 ^ _780119) ^ [_1402613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1402613), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1402613)), c_Int_OMin)))], (26183 ^ _780119) ^ [] : [-(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))))], (27536 ^ _780119) ^ [_1288966, _1288968, _1288970, _1288972] : [class_Orderings_Olinorder(_1288966), 27539 ^ _780119 : [(27540 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288966), _1288968), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288966), _1288970), _1288972))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288966), _1288968), _1288970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288966), _1288968), _1288972)))], (27550 ^ _780119) ^ [] : [27551 ^ _780119 : [(27554 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288966), _1288968), _1288972))], (27552 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288966), _1288968), _1288970))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288966), _1288968), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288966), _1288970), _1288972))))]]], (45678 ^ _780119) ^ [_1699556, _1699558, _1699560, _1699562] : [hAPP(hAPP(c_List_Oappend(_1699556), _1699558), _1699560) = _1699562, 45681 ^ _780119 : [(45684 ^ _780119) ^ [] : [-(_1699560 = hAPP(hAPP(c_List_Odrop(_1699556), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699556)), _1699558)), _1699562))], (45682 ^ _780119) ^ [] : [-(_1699558 = hAPP(hAPP(c_List_Otake(_1699556), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699556)), _1699558)), _1699562))]]], (29963 ^ _780119) ^ [_1339929, _1339931, _1339933, _1339935, _1339937, _1339939, _1339941, _1339943] : [hBOOL(hAPP(hAPP(c_member(_1339929), _1339931), _1339933)), hBOOL(hAPP(hAPP(hAPP(_1339935, _1339931), _1339937), _1339939)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339929, tc_fun(_1339941, tc_fun(_1339943, tc_HOL_Obool))), _1339933), _1339935), _1339937), _1339939)))], (51175 ^ _780119) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (35121 ^ _780119) ^ [_1440174] : [class_Rings_Osemiring__1(_1440174), -(hBOOL(hAPP(hAPP(c_member(_1440174), c_Groups_Oone__class_Oone(_1440174)), c_Nat_Osemiring__1__class_ONats(_1440174))))], (6073 ^ _780119) ^ [_876925, _876927] : [-(_876927 = c_Orderings_Obot__class_Obot(tc_fun(_876925, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_876925), 6076 ^ [_876925, _876927]), _876927)))], (8474 ^ _780119) ^ [_927327, _927329, _927331, _927333, _927335, _927337] : [-(_927327 = _927329), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927331, _927333), _927335), _927329), _927337), _927327) = hAPP(_927335, _927327))], (23078 ^ _780119) ^ [_1201642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201642)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1201642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6212 ^ _780119) ^ [_879435, _879437, _879439] : [hAPP(hAPP(c_Set_Oinsert(_879435), _879437), c_Orderings_Obot__class_Obot(tc_fun(_879435, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_879435), _879439), c_Orderings_Obot__class_Obot(tc_fun(_879435, tc_HOL_Obool))), -(_879437 = _879439)], (25065 ^ _780119) ^ [_1239196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239196), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1239196) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10608 ^ _780119) ^ [_968004, _968006, _968008, _968010, _968012] : [class_Groups_Ocomm__monoid__add(_968004), class_Groups_Oordered__cancel__ab__semigroup__add(_968004), hBOOL(hAPP(c_Finite__Set_Ofinite(_968006), _968008)), -(_968008 = c_Orderings_Obot__class_Obot(tc_fun(_968006, tc_HOL_Obool))), 10626 ^ _780119 : [(10629 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968004), hAPP(_968010, 10625 ^ [_968004, _968006, _968008, _968010, _968012])), hAPP(_968012, 10625 ^ [_968004, _968006, _968008, _968010, _968012])))], (10627 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_968006), 10625 ^ [_968004, _968006, _968008, _968010, _968012]), _968008)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968004), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_968006, _968004), _968010), _968008)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_968006, _968004), _968012), _968008))))], (51455 ^ _780119) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (31529 ^ _780119) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (51039 ^ _780119) ^ [_1815020, _1815022] : [-(class_HOL_Oequal(tc_fun(_1815020, _1815022))), class_Enum_Oenum(_1815020), class_HOL_Oequal(_1815022)], (24757 ^ _780119) ^ [_1233514, _1233516, _1233518, _1233520] : [class_Orderings_Oorder(_1233514), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1233514, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1233514, _1233516, _1233518)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1233514, _1233518, _1233520)) = c_Orderings_Obot__class_Obot(tc_fun(_1233514, tc_HOL_Obool)))], (11884 ^ _780119) ^ [_994013, _994015, _994017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994013), _994015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994013), _994017)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994015), _994017))))], (23447 ^ _780119) ^ [_1208796, _1208798] : [class_Rings_Ocomm__semiring__1(_1208796), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208796), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208796), c_Groups_Oone__class_Oone(_1208796)), c_Groups_Oone__class_Oone(_1208796))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1208796), c_Nat_Osemiring__1__class_Oof__nat(_1208796)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1208798))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208796), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208796), _1208798)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208796), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208796), _1208798)), c_Groups_Oone__class_Oone(_1208796))))], (49243 ^ _780119) ^ [_1776839, _1776841, _1776843, _1776845, _1776847] : [c_Fun_Oinj__on(_1776839, _1776841, _1776843, hAPP(hAPP(c_Set_Oinsert(_1776839), _1776845), hAPP(c_List_Oset(_1776839), _1776847))), -(hAPP(hAPP(c_List_Omap(_1776839, _1776841), _1776843), hAPP(c_List_OremoveAll(_1776839, _1776845), _1776847)) = hAPP(c_List_OremoveAll(_1776841, hAPP(_1776843, _1776845)), hAPP(hAPP(c_List_Omap(_1776839, _1776841), _1776843), _1776847)))], (36802 ^ _780119) ^ [_1479796, _1479798, _1479800, _1479802] : [-(hAPP(c_Set_Oimage(_1479796, _1479798, _1479800), hAPP(c_Set_Ovimage(_1479796, _1479798, _1479800), _1479802)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479798, tc_HOL_Obool)), _1479802), hAPP(c_Set_Oimage(_1479796, _1479798, _1479800), c_Orderings_Otop__class_Otop(tc_fun(_1479796, tc_HOL_Obool)))))], (44686 ^ _780119) ^ [_1675330, _1675332, _1675334] : [hAPP(hAPP(c_List_Olist_OCons(_1675330), _1675332), _1675334) = c_List_Olist_ONil(_1675330)], (39232 ^ _780119) ^ [_1542159, _1542161, _1542163, _1542165, _1542167, _1542169, _1542171, _1542173] : [class_Groups_Ocomm__monoid__mult(_1542159), c_Fun_Oinj__on(_1542161, _1542163, _1542165, _1542167), _1542169 = hAPP(c_Set_Oimage(_1542161, _1542163, _1542165), _1542167), 39246 ^ _780119 : [(39249 ^ _780119) ^ [] : [hAPP(_1542171, 39245 ^ [_1542159, _1542161, _1542163, _1542165, _1542167, _1542169, _1542171, _1542173]) = hAPP(hAPP(c_Fun_Ocomp(_1542163, _1542159, _1542161, _1542173), _1542165), 39245 ^ [_1542159, _1542161, _1542163, _1542165, _1542167, _1542169, _1542171, _1542173])], (39247 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542161), 39245 ^ [_1542159, _1542161, _1542163, _1542165, _1542167, _1542169, _1542171, _1542173]), _1542167)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1542163, _1542159), _1542173), _1542169) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1542161, _1542159), _1542171), _1542167))], (50768 ^ _780119) ^ [_1809753, _1809755, _1809757, _1809759, _1809761, _1809763] : [-(c_Nitpick_Opair__box_Opair__box__size(_1809753, _1809755, _1809757, _1809759, c_Nitpick_Opair__box_OPairBox(_1809753, _1809755, _1809761, _1809763)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1809757, _1809761)), hAPP(_1809759, _1809763))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4746 ^ _780119) ^ [_852441, _852443, _852445, _852447, _852449, _852451, _852453, _852455] : [-(c_New__Random__Sequence_Oneg__bind(_852455, _852451, _852447, _852443) = c_New__Random__Sequence_Oneg__bind(_852453, _852449, _852445, _852441)), _852455 = _852453, _852451 = _852449, _852447 = _852445, _852443 = _852441], (5462 ^ _780119) ^ [_863801, _863803, _863805, _863807] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_863807, _863803) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_863805, _863801)), _863807 = _863805, _863803 = _863801], (42359 ^ _780119) ^ [_1617574, _1617576, _1617578, _1617580, _1617582] : [-(c_Map_Omap__add(_1617574, _1617576, _1617578, c_Map_Omap__add(_1617574, _1617576, _1617580, _1617582)) = c_Map_Omap__add(_1617574, _1617576, c_Map_Omap__add(_1617574, _1617576, _1617578, _1617580), _1617582))], (15234 ^ _780119) ^ [_1058611] : [-(_1058611 = 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)), _1058611)))], (41010 ^ _780119) ^ [_1584117, _1584119, _1584121, _1584123, _1584125, _1584127] : [c_Finite__Set_Ofun__left__comm(_1584117, _1584119, _1584121), hBOOL(hAPP(c_Finite__Set_Ofinite(_1584117), _1584123)), -(hBOOL(hAPP(hAPP(c_member(_1584117), _1584125), _1584123))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1584117, _1584119, _1584121), _1584127), hAPP(hAPP(c_Set_Oinsert(_1584117), _1584125), _1584123)) = hAPP(hAPP(_1584121, _1584125), hAPP(hAPP(c_Finite__Set_Ofold(_1584117, _1584119, _1584121), _1584127), _1584123)))], (4438 ^ _780119) ^ [_847267, _847269] : [_847269 = _847267, -(c_Int_Onumber__class_Onumber__of(_847269) = c_Int_Onumber__class_Onumber__of(_847267))], (45988 ^ _780119) ^ [_1706231, _1706233, _1706235] : [class_Groups_Oab__semigroup__add(_1706231), -(c_List_Ofoldr(_1706231, _1706231, c_Groups_Oplus__class_Oplus(_1706231), _1706233, _1706235) = hAPP(c_List_Ofoldl(_1706231, _1706231, c_Groups_Oplus__class_Oplus(_1706231), _1706235), _1706233))], (42511 ^ _780119) ^ [_1620820, _1620822, _1620824, _1620826] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1620822, _1620820)), _1620824), _1620826) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1620822), hAPP(hAPP(c_COMBC(_1620822, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1620820, 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))), _1620822), c_Smallcheck_Osmall__class_Osmall(_1620820)), hAPP(hAPP(c_COMBB(tc_fun(_1620820, tc_prod(_1620822, _1620820)), tc_fun(_1620820, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1620822), hAPP(c_COMBB(tc_prod(_1620822, _1620820), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1620820), _1620824)), c_Product__Type_OPair(_1620822, _1620820)))), _1620826)), _1620826)), class_Smallcheck_Osmall(_1620820), class_Smallcheck_Osmall(_1620822)], (50188 ^ _780119) ^ [_1797149, _1797151] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1797149), _1797151) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1797149), _1797151)))], (37694 ^ _780119) ^ [_1502658, _1502660, _1502662] : [-(hAPP(c_Relation_ODomain(_1502658, _1502660), hAPP(c_Set_OCollect(tc_prod(_1502658, _1502660)), hAPP(c_Product__Type_Oprod_Oprod__case(_1502658, _1502660, tc_HOL_Obool), _1502662))) = hAPP(c_Set_OCollect(_1502658), hAPP(hAPP(c_COMBB(tc_fun(_1502660, tc_HOL_Obool), tc_HOL_Obool, _1502658), c_HOL_OEx(_1502660)), _1502662)))], (13250 ^ _780119) ^ [_1021284, _1021286, _1021288] : [_1021286 = _1021288, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021284, tc_HOL_Obool)), _1021286) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021284, tc_HOL_Obool)), _1021288))], (12633 ^ _780119) ^ [_1009052, _1009054] : [12634 ^ _780119 : [(12635 ^ _780119) ^ [_1009100] : [_1009052 = hAPP(c_Option_Ooption_OSome(_1009054), _1009100)]], _1009052 = c_Option_Ooption_ONone(_1009054)], (30105 ^ _780119) ^ [_1342753, _1342755] : [class_Int_Onumber__ring(_1342753), -(hAPP(c_Int_Oring__1__class_Oof__int(_1342753), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1342755)) = hAPP(c_Int_Onumber__class_Onumber__of(_1342753), _1342755))], (22475 ^ _780119) ^ [_1190338] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1190338))))], (44266 ^ _780119) ^ [_1666879, _1666881, _1666883, _1666885, _1666887] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1666879, _1666881)), _1666883), hAPP(hAPP(c_List_Ozip(_1666879, _1666881), _1666885), _1666887)) = hAPP(hAPP(c_List_Ozip(_1666879, _1666881), hAPP(hAPP(c_List_Otake(_1666879), _1666883), _1666885)), hAPP(hAPP(c_List_Otake(_1666881), _1666883), _1666887)))], (41293 ^ _780119) ^ [_1591286, _1591288, _1591290, _1591292] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591286, tc_fun(_1591288, tc_HOL_Obool)), _1591290), _1591292) = c_Orderings_Otop__class_Otop(tc_fun(_1591288, tc_HOL_Obool)), 41296 ^ _780119 : [(41297 ^ _780119) ^ [_1591402] : [hBOOL(hAPP(hAPP(c_member(_1591286), _1591402), _1591290)), -(hAPP(_1591292, _1591402) = c_Orderings_Otop__class_Otop(tc_fun(_1591288, tc_HOL_Obool)))]]], (18210 ^ _780119) ^ [_1111853, _1111855, _1111857, _1111859, _1111861] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_1111853, _1111855, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1111853), _1111857), _1111859), _1111861)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4728 ^ _780119) ^ [_852140, _852142, _852144, _852146, _852148, _852150, _852152, _852154] : [-(c_New__Random__Sequence_Oneg__map(_852154, _852150, _852146, _852142) = c_New__Random__Sequence_Oneg__map(_852152, _852148, _852144, _852140)), _852154 = _852152, _852150 = _852148, _852146 = _852144, _852142 = _852140], (1840 ^ _780119) ^ [_805843, _805845] : [-(hBOOL(_805843)), _805845 = _805843, hBOOL(_805845)], (23026 ^ _780119) ^ [_1200548, _1200550, _1200552] : [class_Rings_Osemiring__1(_1200548), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200548), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1200550), _1200552)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200548), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200548), _1200550)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200548), _1200552)))], (39627 ^ _780119) ^ [_1552047, _1552049, _1552051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552047, _1552047), tc_HOL_Obool)), c_Relation_OId(_1552047)), _1552049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552047, _1552047), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1552047, _1552047, _1552047), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1552047, _1552047), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1552047, _1552051)), _1552049)), _1552051)), _1552049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552047, _1552047), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1552047, _1552051)), _1552049)))], (25139 ^ _780119) ^ [_1240380] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240380))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1240380)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15280 ^ _780119) ^ [_1059184, _1059186] : [15281 ^ _780119 : [(15284 ^ _780119) ^ [] : [_1059186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15282 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1059184))]], -(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), _1059184), _1059186))))], (47061 ^ _780119) ^ [_1728579, _1728581, _1728583, _1728585, _1728587] : [class_Orderings_Olinorder(_1728579), c_List_Olinorder__class_Osorted(_1728579, hAPP(hAPP(c_List_Omap(_1728581, _1728579), _1728583), _1728585)), -(c_List_Olinorder__class_Osorted(_1728579, hAPP(hAPP(c_List_Omap(_1728581, _1728579), _1728583), c_List_Oremove1(_1728581, _1728587, _1728585))))], (35420 ^ _780119) ^ [_1448262, _1448264, _1448266] : [class_Rings_Oring__1(_1448262), -(hAPP(c_Int_Oring__1__class_Oof__int(_1448262), 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), _1448264), _1448266)), 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(_1448262), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1448262), _1448264)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1448262), _1448266)))], (5508 ^ _780119) ^ [_864506, _864508, _864510, _864512, _864514, _864516] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_864516, _864512, _864508) = c_Lazy__Sequence_Olazy__sequence_OInsert(_864514, _864510, _864506)), _864516 = _864514, _864512 = _864510, _864508 = _864506], (27690 ^ _780119) ^ [_1291614, _1291616, _1291618, _1291620] : [class_Orderings_Olinorder(_1291614), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291614), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291614), _1291616), _1291618)), _1291620)), 27697 ^ _780119 : [(27700 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291614), _1291618), _1291620)))], (27698 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291614), _1291616), _1291620)))]]], (27724 ^ _780119) ^ [_1292186, _1292188, _1292190] : [class_Orderings_Olinorder(_1292186), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292186), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292186), _1292188), _1292190)), _1292188)))], (26919 ^ _780119) ^ [_1272504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1272504)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1272504 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14954 ^ _780119) ^ [_1054397, _1054399, _1054401] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1054397), 14957 ^ _780119 : [(14964 ^ _780119) ^ [] : [_1054401 = c_Groups_Ozero__class_Ozero(_1054397), -(_1054399 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054397), _1054399), _1054401))], (14958 ^ _780119) ^ [] : [_1054399 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054397), _1054399), _1054401), -(_1054401 = c_Groups_Ozero__class_Ozero(_1054397))]]], (41876 ^ _780119) ^ [_1606455, _1606457] : [class_Complete__Lattice_Ocomplete__lattice(_1606455), -(c_Complete__Lattice_OInf__class_OInf(_1606455, hAPP(hAPP(c_Set_Oinsert(_1606455), _1606457), c_Orderings_Obot__class_Obot(tc_fun(_1606455, tc_HOL_Obool)))) = _1606457)], (11405 ^ _780119) ^ [_984288, _984290, _984292, _984294, _984296, _984298] : [class_Rings_Oring(_984288), 11408 ^ _780119 : [(11415 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984288), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_984288), _984290), _984296)), _984292)), _984294) = _984298, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984288), _984290), _984292)), _984294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984288), _984296), _984292)), _984298))], (11409 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984288), _984290), _984292)), _984294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984288), _984296), _984292)), _984298), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984288), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_984288), _984290), _984296)), _984292)), _984294) = _984298)]]], (13430 ^ _780119) ^ [_1024466, _1024468, _1024470] : [class_Groups_Ogroup__add(_1024466), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024466), _1024468), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024466), hAPP(c_Groups_Ouminus__class_Ouminus(_1024466), _1024468)), _1024470)) = _1024470)], (33229 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (18754 ^ _780119) ^ [_1122143, _1122145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122143), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122145), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1122143), _1122145)))], (42970 ^ _780119) ^ [_1631938, _1631940] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1631938), _1631940) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1631938, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1631940), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (6037 ^ _780119) ^ [_876233, _876235, _876237] : [_876233 = _876235, 6040 ^ _780119 : [(6043 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876237, tc_HOL_Obool)), _876235), _876233)))], (6041 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876237, tc_HOL_Obool)), _876233), _876235)))]]], (47071 ^ _780119) ^ [_1728762, _1728764, _1728766, _1728768, _1728770] : [class_Orderings_Olinorder(_1728762), 47074 ^ _780119 : [(47081 ^ _780119) ^ [] : [c_List_Olinorder__class_Osorted(_1728762, hAPP(hAPP(c_List_Omap(_1728764, _1728762), _1728766), _1728770)), -(c_List_Olinorder__class_Osorted(_1728762, hAPP(hAPP(c_List_Omap(_1728764, _1728762), _1728766), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1728764, _1728762, _1728766), _1728768), _1728770))))], (47075 ^ _780119) ^ [] : [c_List_Olinorder__class_Osorted(_1728762, hAPP(hAPP(c_List_Omap(_1728764, _1728762), _1728766), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1728764, _1728762, _1728766), _1728768), _1728770))), -(c_List_Olinorder__class_Osorted(_1728762, hAPP(hAPP(c_List_Omap(_1728764, _1728762), _1728766), _1728770)))]]], (18504 ^ _780119) ^ [_1117713] : [class_Rings_Oring__1(_1117713), -(hBOOL(hAPP(hAPP(c_member(_1117713), c_Groups_Oone__class_Oone(_1117713)), c_Int_Oring__1__class_OInts(_1117713))))], (35233 ^ _780119) ^ [_1443228, _1443230, _1443232, _1443234] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1443228), _1443230)), 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)), _1443228), _1443232)), 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)), _1443230), _1443234)), 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)), _1443230), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1443232), _1443234))), c_FunDef_Omin__weak)))], (33677 ^ _780119) ^ [_1411322, _1411324, _1411326, _1411328, _1411330, _1411332] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1411322, _1411324), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1411326), _1411328))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1411322, _1411324), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1411330), _1411332))), -(_1411324 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1411326 = _1411330)], (21845 ^ _780119) ^ [_1178990, _1178992, _1178994, _1178996] : [_1178990 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178992), _1178994)), _1178996), -(_1178992 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178990, _1178992) = _1178996), 21852 ^ _780119 : [(21855 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178996), _1178992))], (21853 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178992)))]], 21860 ^ _780119 : [(21863 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178992), _1178996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178996), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21861 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178992))]]], (33391 ^ _780119) ^ [_1402200] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1402200), hAPP(c_Int_Onumber__class_Onumber__of(_1402200), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1402200)), class_Int_Onumber__ring(_1402200), class_Rings_Olinordered__idom(_1402200)], (5728 ^ _780119) ^ [_867818, _867820, _867822, _867824] : [-(tc_fun(_867824, _867820) = tc_fun(_867822, _867818)), _867824 = _867822, _867820 = _867818], (51257 ^ _780119) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (27230 ^ _780119) ^ [_1283157, _1283159, _1283161] : [class_Groups_Olinordered__ab__semigroup__add(_1283157), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283157), _1283159)), -(_1283159 = c_Orderings_Obot__class_Obot(tc_fun(_1283157, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1283157), _1283161), c_Big__Operators_Olinorder__class_OMin(_1283157, _1283159)) = c_Big__Operators_Olinorder__class_OMin(_1283157, hAPP(c_Set_OCollect(_1283157), hAPP(hAPP(c_COMBB(tc_fun(_1283157, tc_HOL_Obool), tc_HOL_Obool, _1283157), c_HOL_OEx(_1283157)), hAPP(hAPP(c_COMBC(_1283157, tc_fun(_1283157, tc_HOL_Obool), tc_fun(_1283157, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1283157, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1283157, tc_HOL_Obool), tc_fun(_1283157, tc_HOL_Obool)), _1283157), c_COMBS(_1283157, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1283157, tc_HOL_Obool), tc_fun(_1283157, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1283157), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1283157), c_fconj)), hAPP(hAPP(c_COMBC(_1283157, tc_fun(_1283157, _1283157), tc_fun(_1283157, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1283157, tc_HOL_Obool), tc_fun(tc_fun(_1283157, _1283157), tc_fun(_1283157, tc_HOL_Obool)), _1283157), c_COMBB(_1283157, tc_HOL_Obool, _1283157)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1283157), _1283161))))), hAPP(hAPP(c_COMBC(_1283157, tc_fun(_1283157, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283157)), _1283159))))))], (47544 ^ _780119) ^ [_1738921, _1738923] : [hBOOL(hAPP(c_List_Odistinct(_1738921), _1738923)), -(hBOOL(hAPP(c_List_Odistinct(_1738921), hAPP(c_List_Orev(_1738921), _1738923))))], (25392 ^ _780119) ^ [_1244489, _1244491] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1244489), _1244491) = 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)), _1244489)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1244491))))], (16616 ^ _780119) ^ [_1082711, _1082713, _1082715] : [class_Rings_Olinordered__semidom(_1082711), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082711), c_Groups_Ozero__class_Ozero(_1082711)), _1082713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082711), c_Groups_Ozero__class_Ozero(_1082711)), hAPP(hAPP(c_Power_Opower__class_Opower(_1082711), _1082713), _1082715))))], (42939 ^ _780119) ^ [_1631222, _1631224, _1631226, _1631228, _1631230] : [hBOOL(hAPP(c_List_Odistinct(_1631222), hAPP(hAPP(c_List_Omap(tc_prod(_1631222, _1631224), _1631222), c_Product__Type_Ofst(_1631222, _1631224)), _1631226))), 42942 ^ _780119 : [(42949 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631222, _1631224)), hAPP(hAPP(c_Product__Type_OPair(_1631222, _1631224), _1631230), _1631228)), hAPP(c_List_Oset(tc_prod(_1631222, _1631224)), _1631226))), -(hAPP(c_Option_Ooption_OSome(_1631224), _1631228) = hAPP(hAPP(c_Map_Omap__of(_1631222, _1631224), _1631226), _1631230))], (42943 ^ _780119) ^ [] : [hAPP(c_Option_Ooption_OSome(_1631224), _1631228) = hAPP(hAPP(c_Map_Omap__of(_1631222, _1631224), _1631226), _1631230), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631222, _1631224)), hAPP(hAPP(c_Product__Type_OPair(_1631222, _1631224), _1631230), _1631228)), hAPP(c_List_Oset(tc_prod(_1631222, _1631224)), _1631226))))]]], (7003 ^ _780119) ^ [_895769, _895771, _895773] : [class_Orderings_Oorder(_895769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895769), _895771), _895773)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895769), _895773), _895771)), -(_895773 = _895771)], (41579 ^ _780119) ^ [_1599396, _1599398, _1599400, _1599402] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1599396, tc_HOL_Obool), tc_fun(_1599398, tc_HOL_Obool)), _1599400), hAPP(hAPP(c_COMBC(tc_fun(_1599396, tc_HOL_Obool), tc_fun(_1599396, tc_fun(_1599398, tc_HOL_Obool)), tc_fun(_1599398, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599396, tc_fun(_1599398, tc_HOL_Obool))), _1599402)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599396, tc_fun(_1599398, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1599396, tc_HOL_Obool), _1599400)), _1599402))], (48403 ^ _780119) ^ [_1758830, _1758832] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1758830, _1758832)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1758832), tc_fun(_1758830, _1758832)), hAPP(hAPP(c_COMBB(tc_fun(_1758830, tc_Option_Ooption(_1758832)), tc_fun(_1758830, _1758832), tc_List_Olist(_1758832)), c_Fun_Ocomp(tc_Option_Ooption(_1758832), _1758832, _1758830, c_Option_Othe(_1758832))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1758830, _1758832)), tc_fun(_1758830, tc_Option_Ooption(_1758832)), tc_List_Olist(_1758832)), c_Map_Omap__of(_1758830, _1758832)), hAPP(c_List_Ozip(_1758830, _1758832), c_Enum_Oenum__class_Oenum(_1758830))))), c_Enum_On__lists(_1758832, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758830)), c_Enum_Oenum__class_Oenum(_1758830)), c_Enum_Oenum__class_Oenum(_1758832)))), class_Enum_Oenum(_1758830), class_HOL_Oequal(_1758830), class_Enum_Oenum(_1758832)], (20130 ^ _780119) ^ [_1146160, _1146162, _1146164, _1146166] : [class_Fields_Olinordered__field__inverse__zero(_1146160), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146160), _1146162), _1146164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146160), _1146166), c_Groups_Ozero__class_Ozero(_1146160))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146160), c_Groups_Ozero__class_Ozero(_1146160)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146160), _1146162), _1146164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146160), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146160), _1146166), _1146162)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146160), _1146166), _1146164))))], (10254 ^ _780119) ^ [_959992, _959994, _959996, _959998] : [hBOOL(hAPP(hAPP(c_member(_959992), _959998), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959992, tc_HOL_Obool)), _959994), _959996))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959992, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_959992, tc_fun(_959992, tc_HOL_Obool), tc_HOL_Obool), c_member(_959992)), _959994)), hAPP(hAPP(c_COMBC(_959992, tc_fun(_959992, tc_HOL_Obool), tc_HOL_Obool), c_member(_959992)), _959996)), _959998)))], (12620 ^ _780119) ^ [_1008891, _1008893] : [_1008891 = c_Option_Ooption_ONone(_1008893), 12623 ^ _780119 : [(12624 ^ _780119) ^ [_1008963] : [_1008891 = hAPP(c_Option_Ooption_OSome(_1008893), _1008963)]]], (39711 ^ _780119) ^ [_1554094, _1554096] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554094, _1554094), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1554094, _1554096)), c_Relation_OId(_1554094)) = c_Transitive__Closure_Ortrancl(_1554094, _1554096))], (48093 ^ _780119) ^ [_1751548, _1751550, _1751552] : [48095 ^ _780119 : [(48098 ^ _780119) ^ [] : [hBOOL(hAPP(_1751550, 48094 ^ [_1751548, _1751550, _1751552]))], (48096 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751548), 48094 ^ [_1751548, _1751550, _1751552]), hAPP(c_List_Oset(_1751548), _1751552))))]], -(c_List_OdropWhile(_1751548, _1751550, _1751552) = c_List_Olist_ONil(_1751548))], (46055 ^ _780119) ^ [_1707627, _1707629, _1707631, _1707633, _1707635] : [c_Finite__Set_Ofun__left__comm__idem(_1707627, _1707629, _1707631), -(hAPP(hAPP(c_Finite__Set_Ofold(_1707627, _1707629, _1707631), _1707633), hAPP(c_List_Oset(_1707627), _1707635)) = hAPP(c_List_Ofoldl(_1707629, _1707627, hAPP(c_COMBC(_1707627, _1707629, _1707629), _1707631), _1707633), _1707635))], (33919 ^ _780119) ^ [_1416553, _1416555, _1416557, _1416559, _1416561, _1416563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1416553, tc_fun(_1416555, tc_HOL_Obool))), _1416557), _1416559)), hBOOL(hAPP(hAPP(_1416557, _1416561), _1416563)), -(hBOOL(hAPP(hAPP(_1416559, _1416561), _1416563)))], (17470 ^ _780119) ^ [_1097678, _1097680, _1097682] : [class_Rings_Olinordered__ring__strict(_1097678), 17473 ^ _780119 : [(17474 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097678), c_Groups_Ozero__class_Ozero(_1097678)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097678), _1097680), _1097680)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097678), _1097682), _1097682)))), _1097680 = c_Groups_Ozero__class_Ozero(_1097678), _1097682 = c_Groups_Ozero__class_Ozero(_1097678)], (17484 ^ _780119) ^ [] : [17485 ^ _780119 : [(17488 ^ _780119) ^ [] : [-(_1097682 = c_Groups_Ozero__class_Ozero(_1097678))], (17486 ^ _780119) ^ [] : [-(_1097680 = c_Groups_Ozero__class_Ozero(_1097678))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097678), c_Groups_Ozero__class_Ozero(_1097678)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097678), _1097680), _1097680)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097678), _1097682), _1097682)))))]]], (22462 ^ _780119) ^ [_1190055, _1190057, _1190059, _1190061] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1190055, tc_Nat_Onat), _1190057), _1190059) = hAPP(c_Nat_OSuc, _1190061), 22466 ^ _780119 : [(22469 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1190057, 22465 ^ [_1190055, _1190057, _1190059, _1190061]))))], (22467 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1190055), 22465 ^ [_1190055, _1190057, _1190059, _1190061]), _1190059)))]]], (42665 ^ _780119) ^ [_1624702, _1624704, _1624706, _1624708, _1624710, _1624712] : [-(hAPP(hAPP(c_Option_Omap(_1624702, _1624704), _1624706), hAPP(hAPP(c_Option_Omap(_1624708, _1624702), _1624710), _1624712)) = hAPP(hAPP(c_Option_Omap(_1624708, _1624704), hAPP(c_Fun_Ocomp(_1624702, _1624704, _1624708, _1624706), _1624710)), _1624712))], (9740 ^ _780119) ^ [_949103, _949105] : [class_Lattices_Olattice(_949103), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949103), _949105), _949105) = _949105)], (29766 ^ _780119) ^ [_1334052, _1334054, _1334056, _1334058, _1334060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1334052, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334054, tc_fun(_1334052, tc_HOL_Obool)), _1334056), _1334058)), _1334060)), 29769 ^ _780119 : [(29770 ^ _780119) ^ [_1334185] : [hBOOL(hAPP(hAPP(c_member(_1334054), _1334185), _1334056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1334052, tc_HOL_Obool)), hAPP(_1334058, _1334185)), _1334060)))]]], (14715 ^ _780119) ^ [_1050298, _1050300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1050298)), _1050300)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050298), _1050300)))], (32335 ^ _780119) ^ [_1383169, _1383171] : [c_Int_OBit1(_1383169) = c_Int_OBit0(_1383171)], (18386 ^ _780119) ^ [_1115591, _1115593] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_1115591, _1115593)) = 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(_1115591)), c_Com_Ocom_Ocom__size(_1115593))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43609 ^ _780119) ^ [_1649315, _1649317, _1649319, _1649321, _1649323, _1649325] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649315, _1649315)), hAPP(hAPP(c_Product__Type_OPair(_1649315, _1649315), _1649317), _1649319)), _1649321)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649315), tc_List_Olist(_1649315))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649315), tc_List_Olist(_1649315)), _1649323), _1649325)), c_List_Olistrel(_1649315, _1649321))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649315), tc_List_Olist(_1649315))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649315), tc_List_Olist(_1649315)), hAPP(hAPP(c_List_Olist_OCons(_1649315), _1649317), _1649323)), hAPP(hAPP(c_List_Olist_OCons(_1649315), _1649319), _1649325))), c_List_Olistrel(_1649315, _1649321))))], (43962 ^ _780119) ^ [_1658944, _1658946, _1658948, _1658950] : [-(hAPP(hAPP(c_List_Onth(_1658944), hAPP(hAPP(c_List_Olist_OCons(_1658944), _1658946), _1658948)), _1658950) = c_Nat_Onat_Onat__case(_1658944, _1658946, hAPP(c_List_Onth(_1658944), _1658948), _1658950))], (31765 ^ _780119) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (39927 ^ _780119) ^ [_1559181, _1559183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1559181), _1559183)), -(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), _1559181), _1559183)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (27508 ^ _780119) ^ [_1288348] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1288348) = c_Orderings_Oord__class_Omin(_1288348)), class_Lattices_Osemilattice__inf(_1288348), class_Orderings_Olinorder(_1288348)], (23843 ^ _780119) ^ [_1216188, _1216190, _1216192, _1216194, _1216196] : [class_Groups_Oab__group__add(_1216188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216190), _1216192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216192), _1216194)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216188), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1216188), _1216196), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1216190), _1216194))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1216188), _1216196), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1216190), _1216192))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1216188), _1216196), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1216192), _1216194)))], (38154 ^ _780119) ^ [_1516968, _1516970, _1516972] : [-(hAPP(c_Product__Type_Omap__pair(_1516968, _1516968, _1516970, _1516970, c_COMBI(_1516968), c_COMBI(_1516970)), _1516972) = _1516972)], (38818 ^ _780119) ^ [_1532391, _1532393, _1532395, _1532397, _1532399, _1532401, _1532403, _1532405, _1532407, _1532409] : [-(c_Product__Type_Omap__pair(_1532391, _1532393, _1532395, _1532397, hAPP(c_Fun_Ocomp(_1532399, _1532393, _1532391, _1532401), _1532403), hAPP(c_Fun_Ocomp(_1532405, _1532397, _1532395, _1532407), _1532409)) = hAPP(c_Fun_Ocomp(tc_prod(_1532399, _1532405), tc_prod(_1532393, _1532397), tc_prod(_1532391, _1532395), c_Product__Type_Omap__pair(_1532399, _1532393, _1532405, _1532397, _1532401, _1532407)), c_Product__Type_Omap__pair(_1532391, _1532399, _1532395, _1532405, _1532403, _1532409)))], (39869 ^ _780119) ^ [_1557739, _1557741, _1557743, _1557745] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1557739, _1557739)), hAPP(hAPP(c_Product__Type_OPair(_1557739, _1557739), _1557741), _1557743)), c_Transitive__Closure_Ortrancl(_1557739, _1557745))), hBOOL(hAPP(hAPP(c_member(_1557739), _1557743), c_Wellfounded_Oacc(_1557739, _1557745))), -(hBOOL(hAPP(hAPP(c_member(_1557739), _1557741), c_Wellfounded_Oacc(_1557739, _1557745))))], (41395 ^ _780119) ^ [_1594961, _1594963, _1594965, _1594967, _1594969, _1594971] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594961, tc_fun(_1594963, tc_HOL_Obool)), _1594965), hAPP(hAPP(c_COMBC(_1594961, tc_fun(_1594967, tc_fun(_1594963, tc_HOL_Obool)), tc_fun(_1594963, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1594967, tc_HOL_Obool), tc_fun(tc_fun(_1594967, tc_fun(_1594963, tc_HOL_Obool)), tc_fun(_1594963, tc_HOL_Obool)), _1594961), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594967, tc_fun(_1594963, tc_HOL_Obool))), _1594969)), _1594971)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594967, tc_fun(_1594963, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1594961, tc_fun(_1594967, tc_HOL_Obool)), _1594965), _1594969)), _1594971))], (39953 ^ _780119) ^ [_1559752, _1559754, _1559756, _1559758, _1559760] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559752, _1559752)), hAPP(hAPP(c_Product__Type_OPair(_1559752, _1559752), hAPP(_1559754, hAPP(c_Nat_OSuc, 39954 ^ [_1559752, _1559754, _1559756, _1559758, _1559760]))), hAPP(_1559754, 39954 ^ [_1559752, _1559754, _1559756, _1559758, _1559760]))), c_Transitive__Closure_Ortrancl(_1559752, _1559756))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559752, _1559752)), hAPP(hAPP(c_Product__Type_OPair(_1559752, _1559752), hAPP(_1559754, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1559758), _1559760))), hAPP(_1559754, _1559758))), c_Transitive__Closure_Ortrancl(_1559752, _1559756))))], (46103 ^ _780119) ^ [_1708653, _1708655, _1708657] : [class_Orderings_Olinorder(_1708653), -(c_Big__Operators_Olattice_OSup__fin(_1708653, c_Orderings_Oord__class_Omax(_1708653), hAPP(c_List_Oset(_1708653), hAPP(hAPP(c_List_Olist_OCons(_1708653), _1708655), _1708657))) = hAPP(c_List_Ofoldl(_1708653, _1708653, c_Orderings_Oord__class_Omax(_1708653), _1708655), _1708657))], (20124 ^ _780119) ^ [_1146055, _1146057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146055), _1146057)), -(c_Nat__Transfer_Otsub(_1146057, _1146055) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1146057), _1146055))], (50626 ^ _780119) ^ [_1807027, _1807029, _1807031, _1807033] : [-(hAPP(hAPP(c_List_Otake(_1807027), _1807029), c_List_Oreplicate(_1807027, _1807031, _1807033)) = c_List_Oreplicate(_1807027, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1807029), _1807031), _1807033))], (46911 ^ _780119) ^ [_1726278, _1726280, _1726282] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1726278), c_List_Oupt(_1726280, _1726282)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1726280), _1726278), _1726282))], (41121 ^ _780119) ^ [_1586482, _1586484, _1586486, _1586488] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1586482, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1586484, tc_fun(_1586482, tc_HOL_Obool)), _1586486), _1586488)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1586484, tc_fun(_1586482, tc_HOL_Obool)), _1586486), hAPP(hAPP(c_COMBB(tc_fun(_1586482, tc_HOL_Obool), tc_fun(_1586482, tc_HOL_Obool), _1586484), c_Groups_Ouminus__class_Ouminus(tc_fun(_1586482, tc_HOL_Obool))), _1586488)))], (6689 ^ _780119) ^ [_889440, _889442, _889444, _889446, _889448, _889450, _889452] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_889440), _889442), _889444), _889446) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_889440), _889448), _889450), _889452)), _889442 = _889448, _889444 = _889450, _889446 = _889452], (13950 ^ _780119) ^ [_1033984, _1033986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1033984), _1033986)), 13953 ^ _780119 : [(13960 ^ _780119) ^ [] : [_1033986 = _1033984, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033986), hAPP(c_Nat_OSuc, _1033984))))], (13954 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033986), hAPP(c_Nat_OSuc, _1033984))), -(_1033986 = _1033984)]]], (9810 ^ _780119) ^ [_950702, _950704, _950706] : [class_Lattices_Osemilattice__inf(_950702), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950702), _950704), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950702), _950704), _950706)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950702), _950704), _950706))], (8634 ^ _780119) ^ [_929478, _929480, _929482] : [class_Orderings_Opreorder(_929478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929478), _929480), _929482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929478), _929482), _929480))], (37866 ^ _780119) ^ [_1508208, _1508210, _1508212, _1508214, _1508216, _1508218] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508208, _1508210)), hAPP(hAPP(c_Product__Type_OPair(_1508208, _1508210), _1508212), _1508214)), hAPP(hAPP(c_Product__Type_OSigma(_1508208, _1508210), _1508216), _1508218))), -(hBOOL(hAPP(hAPP(c_member(_1508208), _1508212), _1508216)))], (7496 ^ _780119) ^ [_906187, _906189, _906191] : [class_Lattices_Osemilattice__sup(_906187), 7499 ^ _780119 : [(7506 ^ _780119) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_906187), _906189), _906191) = _906191, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906187), _906189), _906191)))], (7500 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906187), _906189), _906191)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_906187), _906189), _906191) = _906191)]]], (39741 ^ _780119) ^ [_1554842, _1554844] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554842, _1554842), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1554842, _1554844)), c_Relation_OId(_1554842)) = c_Transitive__Closure_Ortrancl(_1554842, _1554844))], (31245 ^ _780119) ^ [_1364265] : [-(c_Int_OBit1(_1364265) = 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)), _1364265)), _1364265))], (35343 ^ _780119) ^ [_1445842, _1445844, _1445846, _1445848, _1445850] : [hBOOL(hAPP(hAPP(c_member(_1445842), _1445844), hAPP(c_Relation_OImage(_1445846, _1445842, _1445848), hAPP(hAPP(c_Set_Oinsert(_1445846), _1445850), c_Orderings_Obot__class_Obot(tc_fun(_1445846, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1445846, _1445842)), hAPP(hAPP(c_Product__Type_OPair(_1445846, _1445842), _1445850), _1445844)), _1445848)))], (50892 ^ _780119) ^ [_1812686, _1812688, _1812690, _1812692, _1812694, _1812696, _1812698] : [50894 ^ _780119 : [(50897 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1812690, 50893 ^ [_1812686, _1812688, _1812690, _1812692, _1812694, _1812696, _1812698]), _1812692), _1812694))], (50895 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812686), 50893 ^ [_1812686, _1812688, _1812690, _1812692, _1812694, _1812696, _1812698]), _1812688)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1812686, tc_fun(_1812696, tc_fun(_1812698, tc_HOL_Obool))), _1812688), _1812690), _1812692), _1812694)))], (22153 ^ _780119) ^ [_1184659, _1184661] : [class_Rings_Olinordered__idom(_1184659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184659), _1184661), c_Groups_Ozero__class_Ozero(_1184659))), -(c_Groups_Osgn__class_Osgn(_1184659, _1184661) = hAPP(c_Groups_Ouminus__class_Ouminus(_1184659), c_Groups_Oone__class_Oone(_1184659)))], (5973 ^ _780119) ^ [_875113, _875115] : [class_Finite__Set_Ofinite(_875113), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_875113), _875115)))], (33265 ^ _780119) ^ [_1400261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1400261)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400261), c_Int_OMin)))], (44594 ^ _780119) ^ [_1673526, _1673528, _1673530, _1673532, _1673534] : [-(c_Map_Odom(_1673526, _1673528, c_Map_Omap__upds(_1673526, _1673528, _1673530, _1673532, _1673534)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1673526, tc_HOL_Obool)), hAPP(c_List_Oset(_1673526), hAPP(hAPP(c_List_Otake(_1673526), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673528)), _1673534)), _1673532))), c_Map_Odom(_1673526, _1673528, _1673530)))], (33753 ^ _780119) ^ [_1413119, _1413121] : [-(_1413119 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1413121, _1413119), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1413121), _1413119)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1413121, _1413119)))))], (21408 ^ _780119) ^ [_1170050, _1170052, _1170054, _1170056] : [class_Divides_Osemiring__div(_1170050), -(c_Divides_Odiv__class_Omod(_1170050, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170050), _1170052), _1170054), _1170056) = c_Divides_Odiv__class_Omod(_1170050, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170050), c_Divides_Odiv__class_Omod(_1170050, _1170052, _1170056)), _1170054), _1170056))], (42803 ^ _780119) ^ [_1627807, _1627809, _1627811, _1627813, _1627815] : [hAPP(hAPP(c_List_Omap(_1627807, _1627809), _1627811), _1627813) = hAPP(hAPP(c_List_Omap(_1627807, _1627809), _1627811), _1627815), c_Fun_Oinj__on(_1627807, _1627809, _1627811, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1627807, tc_HOL_Obool)), hAPP(c_List_Oset(_1627807), _1627813)), hAPP(c_List_Oset(_1627807), _1627815))), -(_1627813 = _1627815)], (18322 ^ _780119) ^ [_1114221, _1114223, _1114225, _1114227] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_1114221)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1114221), _1114223), _1114225), _1114227)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32463 ^ _780119) ^ [_1385317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1385317), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1385317)), c_Int_OPls)))], (32089 ^ _780119) ^ [_1378207, _1378209] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1378207) = hAPP(c_Nat_OSuc, _1378209), -(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(_1378207))), 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)), _1378209))))))], (31481 ^ _780119) ^ [_1368384] : [c_Int_OPls = c_Int_OBit1(_1368384)], (8736 ^ _780119) ^ [_931067, _931069, _931071, _931073] : [class_Orderings_Oorder(_931067), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931067), _931069), _931071)), _931069 = _931073, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931067), _931073), _931071)))], (23278 ^ _780119) ^ [_1205480, _1205482, _1205484, _1205486, _1205488, _1205490] : [hBOOL(hAPP(hAPP(c_member(_1205480), _1205482), c_SetInterval_Oord_OatLeastLessThan(_1205480, _1205484, _1205486, _1205488, _1205490))), 23281 ^ _780119 : [(23284 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1205486, _1205482), _1205490)))], (23282 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1205484, _1205488), _1205482)))]]], (44286 ^ _780119) ^ [_1667337, _1667339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1667337), _1667339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1667337)), hAPP(c_Code__Numeral_Oof__nat, _1667339))))], (29572 ^ _780119) ^ [_1329179] : [-(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, _1329179))))))], (23286 ^ _780119) ^ [_1205633, _1205635, _1205637, _1205639, _1205641, _1205643] : [-(hBOOL(hAPP(hAPP(c_member(_1205633), _1205635), c_SetInterval_Oord_OatLeastLessThan(_1205633, _1205637, _1205639, _1205641, _1205643)))), hBOOL(hAPP(hAPP(_1205637, _1205641), _1205635)), hBOOL(hAPP(hAPP(_1205639, _1205635), _1205643))], (23046 ^ _780119) ^ [_1200994] : [class_Rings_Osemiring__1(_1200994), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200994), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1200994))], (47273 ^ _780119) ^ [_1732675, _1732677, _1732679, _1732681, _1732683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732675), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1732677), _1732679))), -(hAPP(hAPP(c_List_Onth(_1732681), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1732681), _1732683), c_List_Oupt(_1732679, _1732677))), _1732675) = hAPP(_1732683, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1732679), _1732675)))], (50512 ^ _780119) ^ [_1804956, _1804958, _1804960] : [_1804958 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1804956) = c_List_Oreplicate(_1804956, _1804958, _1804960))], (9168 ^ _780119) ^ [_937512, _937514, _937516, _937518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937512, tc_HOL_Obool)), _937514), _937516)), hBOOL(hAPP(hAPP(c_member(_937512), _937518), _937514)), -(hBOOL(hAPP(hAPP(c_member(_937512), _937518), _937516)))], (50566 ^ _780119) ^ [_1805913, _1805915, _1805917, _1805919] : [-(c_List_Oreplicate(_1805913, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1805915), _1805917), _1805919) = hAPP(hAPP(c_List_Oappend(_1805913), c_List_Oreplicate(_1805913, _1805915, _1805919)), c_List_Oreplicate(_1805913, _1805917, _1805919)))], (18766 ^ _780119) ^ [_1122359, _1122361] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122359), _1122361)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1122359)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1122361)))], (33147 ^ _780119) ^ [_1397920, _1397922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1397920)), -(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)))), _1397922)), 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)))), _1397920)) = 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, _1397922, _1397920))))], (3516 ^ _780119) ^ [_832986, _832988] : [_832988 = _832986, -(c_Fun_Oid(_832988) = c_Fun_Oid(_832986))], (50276 ^ _780119) ^ [_1799152, _1799154, _1799156, _1799158, _1799160] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1799152, _1799154, _1799156) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1799152, _1799158, _1799160)), _1799154 = _1799158, _1799156 = _1799160], (44039 ^ _780119) ^ [_1660905, _1660907] : [44041 ^ _780119 : [(44042 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44040 ^ [_1660905, _1660907]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660905)), _1660907))))], (44045 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44043 ^ [_1660905, _1660907]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660905)), _1660907))))], (44049 ^ _780119) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1660905), _1660907), 44040 ^ [_1660905, _1660907]) = hAPP(hAPP(c_List_Onth(_1660905), _1660907), 44043 ^ [_1660905, _1660907]))], (44047 ^ _780119) ^ [] : [44040 ^ [_1660905, _1660907] = 44043 ^ [_1660905, _1660907]]], -(hBOOL(hAPP(c_List_Odistinct(_1660905), _1660907)))], (6447 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (41565 ^ _780119) ^ [_1599042, _1599044, _1599046, _1599048] : [hBOOL(hAPP(hAPP(c_member(_1599042), _1599044), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1599042, tc_HOL_Obool), _1599046))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1599042, tc_HOL_Obool)), _1599048), _1599046)), -(hBOOL(hAPP(hAPP(c_member(_1599042), _1599044), _1599048)))], (43222 ^ _780119) ^ [_1638153, _1638155, _1638157, _1638159, _1638161] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638153)), _1638155) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638157)), _1638159), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638153)), _1638161) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638157)), _1638159), hBOOL(hAPP(c_List_Odistinct(_1638157), _1638159)), hAPP(c_Map_Omap__of(_1638157, _1638153), hAPP(hAPP(c_List_Ozip(_1638157, _1638153), _1638159), _1638155)) = hAPP(c_Map_Omap__of(_1638157, _1638153), hAPP(hAPP(c_List_Ozip(_1638157, _1638153), _1638159), _1638161)), -(_1638155 = _1638161)], (36932 ^ _780119) ^ [_1482908, _1482910, _1482912, _1482914, _1482916] : [c_Typedef_Otype__definition(_1482908, _1482910, _1482912, _1482914, _1482916), -(hAPP(c_Set_Oimage(_1482908, _1482910, _1482912), c_Orderings_Otop__class_Otop(tc_fun(_1482908, tc_HOL_Obool))) = _1482916)], (29590 ^ _780119) ^ [_1329716, _1329718, _1329720, _1329722, _1329724] : [29592 ^ _780119 : [(29595 ^ _780119) ^ [] : [hBOOL(hAPP(_1329724, 29591 ^ [_1329716, _1329718, _1329720, _1329722, _1329724]))], (29593 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329716), 29591 ^ [_1329716, _1329718, _1329720, _1329722, _1329724]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1329718, tc_fun(_1329716, tc_HOL_Obool)), _1329720), _1329722))))]], 29596 ^ _780119 : [(29597 ^ _780119) ^ [_1329938] : [hBOOL(hAPP(hAPP(c_member(_1329718), _1329938), _1329720)), 29600 ^ _780119 : [(29601 ^ _780119) ^ [_1330035] : [hBOOL(hAPP(hAPP(c_member(_1329716), _1330035), hAPP(_1329722, _1329938))), -(hBOOL(hAPP(_1329724, _1330035)))]]]]], (44642 ^ _780119) ^ [_1674493, _1674495] : [_1674495 = c_List_Olist_ONil(_1674493), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674493)), _1674495) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28188 ^ _780119) ^ [_1301122, _1301124] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1301122)), hAPP(c_Nat_OSuc, _1301124)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1301122), _1301124)))], (8004 ^ _780119) ^ [_916713, _916715, _916717, _916719, _916721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916713, tc_HOL_Obool)), _916715), _916717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916713, tc_HOL_Obool)), _916719), _916721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916713, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916713, tc_HOL_Obool)), _916715), _916721)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916713, tc_HOL_Obool)), _916717), _916719))))], (14586 ^ _780119) ^ [_1047685, _1047687, _1047689, _1047691] : [class_Rings_Olinordered__semidom(_1047685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047685), c_Groups_Oone__class_Oone(_1047685)), _1047687)), 14593 ^ _780119 : [(14600 ^ _780119) ^ [] : [_1047689 = _1047691, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1047685), _1047687), _1047689) = hAPP(hAPP(c_Power_Opower__class_Opower(_1047685), _1047687), _1047691))], (14594 ^ _780119) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1047685), _1047687), _1047689) = hAPP(hAPP(c_Power_Opower__class_Opower(_1047685), _1047687), _1047691), -(_1047689 = _1047691)]]], (14882 ^ _780119) ^ [_1053297, _1053299, _1053301] : [-(c_Nat_Onat_Onat__case(_1053297, _1053299, _1053301, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1053299)], (29064 ^ _780119) ^ [_1318510, _1318512, _1318514] : [class_Orderings_Olinorder(_1318510), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318510), _1318512)), -(hBOOL(hAPP(hAPP(c_member(_1318510), _1318514), _1318512))), -(_1318512 = c_Orderings_Obot__class_Obot(tc_fun(_1318510, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1318510, c_Orderings_Oord__class_Omax(_1318510), hAPP(hAPP(c_Set_Oinsert(_1318510), _1318514), _1318512)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1318510), _1318514), c_Big__Operators_Olattice_OSup__fin(_1318510, c_Orderings_Oord__class_Omax(_1318510), _1318512)))], (36878 ^ _780119) ^ [_1481373, _1481375, _1481377, _1481379, _1481381] : [c_Fun_Oinj__on(_1481373, _1481375, _1481377, c_Orderings_Otop__class_Otop(tc_fun(_1481373, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481375, tc_HOL_Obool)), _1481379), hAPP(c_Set_Oimage(_1481373, _1481375, _1481377), _1481381))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481373, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1481373, _1481375, _1481377), _1481379)), _1481381)))], (27448 ^ _780119) ^ [_1287104, _1287106, _1287108] : [class_Orderings_Olinorder(_1287104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287104), _1287106)), hBOOL(hAPP(hAPP(c_member(_1287104), _1287108), _1287106)), 27459 ^ _780119 : [(27466 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1287104, tc_HOL_Obool)), _1287106), hAPP(hAPP(c_Set_Oinsert(_1287104), _1287108), c_Orderings_Obot__class_Obot(tc_fun(_1287104, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1287104, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1287104, _1287106) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1287104), _1287108), c_Big__Operators_Olinorder__class_OMax(_1287104, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1287104, tc_HOL_Obool)), _1287106), hAPP(hAPP(c_Set_Oinsert(_1287104), _1287108), c_Orderings_Obot__class_Obot(tc_fun(_1287104, tc_HOL_Obool)))))))], (27460 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1287104, tc_HOL_Obool)), _1287106), hAPP(hAPP(c_Set_Oinsert(_1287104), _1287108), c_Orderings_Obot__class_Obot(tc_fun(_1287104, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1287104, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1287104, _1287106) = _1287108)]]], (25802 ^ _780119) ^ [_1251064, _1251066] : [class_Rings_Oring__1(_1251064), -(hAPP(c_Int_Oring__1__class_Oof__int(_1251064), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1251066)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1251064), _1251066))], (29566 ^ _780119) ^ [] : [-(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)))], (4898 ^ _780119) ^ [_854909, _854911, _854913, _854915] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_854915, _854911) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_854913, _854909)), _854915 = _854913, _854911 = _854909], (36774 ^ _780119) ^ [_1479123, _1479125, _1479127, _1479129, _1479131] : [hAPP(_1479129, _1479125) = _1479131, -(hBOOL(hAPP(hAPP(c_member(_1479123), _1479125), hAPP(c_Set_Ovimage(_1479123, _1479127, _1479129), hAPP(hAPP(c_Set_Oinsert(_1479127), _1479131), c_Orderings_Obot__class_Obot(tc_fun(_1479127, tc_HOL_Obool)))))))], (34339 ^ _780119) ^ [_1424615, _1424617] : [-(c_Divides_Odivmod__nat(_1424615, _1424617) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1424615), _1424617)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1424615, _1424617)))], (27258 ^ _780119) ^ [_1283925, _1283927, _1283929] : [27260 ^ _780119 : [(27263 ^ _780119) ^ [] : [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(_1283927, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 27259 ^ [_1283925, _1283927, _1283929]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1283927, 27259 ^ [_1283925, _1283927, _1283929])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (27261 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27259 ^ [_1283925, _1283927, _1283929]), _1283925)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1283927, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1283929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1283929), hAPP(_1283927, _1283925))), 27273 ^ _780119 : [(27276 ^ _780119) ^ [] : [-(hAPP(_1283927, 27272 ^ [_1283925, _1283927, _1283929]) = _1283929)], (27274 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27272 ^ [_1283925, _1283927, _1283929]), _1283925)))]]], (51249 ^ _780119) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (39389 ^ _780119) ^ [_1546196, _1546198, _1546200, _1546202, _1546204, _1546206, _1546208, _1546210] : [class_Groups_Ocomm__monoid__add(_1546196), class_Orderings_Oord(_1546198), _1546200 = _1546202, _1546204 = _1546206, 39407 ^ _780119 : [(39410 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1546198), 39406 ^ [_1546196, _1546198, _1546200, _1546202, _1546204, _1546206, _1546208, _1546210]), _1546206)))], (39412 ^ _780119) ^ [] : [hAPP(_1546208, 39406 ^ [_1546196, _1546198, _1546200, _1546202, _1546204, _1546206, _1546208, _1546210]) = hAPP(_1546210, 39406 ^ [_1546196, _1546198, _1546200, _1546202, _1546204, _1546206, _1546208, _1546210])], (39408 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1546198), _1546202), 39406 ^ [_1546196, _1546198, _1546200, _1546202, _1546204, _1546206, _1546208, _1546210])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1546198, _1546196), _1546208), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1546198, _1546200), _1546204)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1546198, _1546196), _1546210), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1546198, _1546202), _1546206)))], (15062 ^ _780119) ^ [_1056047, _1056049] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056047, tc_HOL_Obool)), _1056049), c_Orderings_Otop__class_Otop(tc_fun(_1056047, tc_HOL_Obool))) = _1056049)], (32589 ^ _780119) ^ [_1387521] : [-(c_Int_Osucc(c_Int_OBit0(_1387521)) = c_Int_OBit1(_1387521))], (20892 ^ _780119) ^ [_1160056, _1160058, _1160060, _1160062] : [class_Fields_Olinordered__field(_1160056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160056), c_Groups_Ozero__class_Ozero(_1160056)), _1160058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160056), _1160060), _1160058)), _1160062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160056), _1160060), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160056), _1160062), _1160058))))], (41796 ^ _780119) ^ [_1604627, _1604629, _1604631] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1604627, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1604627, tc_HOL_Obool)), _1604629), _1604631)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1604627, tc_HOL_Obool)), _1604629), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1604627, tc_HOL_Obool), _1604631)))], (51367 ^ _780119) ^ [_1818122, _1818124] : [-(class_HOL_Oequal(tc_sum(_1818122, _1818124)))], (51345 ^ _780119) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (5036 ^ _780119) ^ [_857132, _857134, _857136, _857138, _857140, _857142, _857144, _857146, _857148, _857150] : [-(c_New__DSequence_Oneg__map(_857150, _857146, _857142, _857138, _857134) = c_New__DSequence_Oneg__map(_857148, _857144, _857140, _857136, _857132)), _857150 = _857148, _857146 = _857144, _857142 = _857140, _857138 = _857136, _857134 = _857132], (48265 ^ _780119) ^ [_1756108, _1756110, _1756112, _1756114] : [-(hAPP(c_List_Oset(tc_prod(_1756108, _1756110)), c_Enum_Oproduct(_1756108, _1756110, _1756112, _1756114)) = hAPP(hAPP(c_Product__Type_OSigma(_1756108, _1756110), hAPP(c_List_Oset(_1756108), _1756112)), hAPP(c_COMBK(tc_fun(_1756110, tc_HOL_Obool), _1756108), hAPP(c_List_Oset(_1756110), _1756114))))], (18364 ^ _780119) ^ [_1115171, _1115173] : [class_Rings_Olinordered__idom(_1115171), hBOOL(hAPP(hAPP(c_member(_1115171), _1115173), c_Int_Oring__1__class_OInts(_1115171))), 18371 ^ _780119 : [(18378 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115171), _1115173), c_Groups_Ozero__class_Ozero(_1115171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115171), c_Groups_Oone__class_Oone(_1115171)), _1115173)), _1115173)), c_Groups_Ozero__class_Ozero(_1115171))))], (18372 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115171), c_Groups_Oone__class_Oone(_1115171)), _1115173)), _1115173)), c_Groups_Ozero__class_Ozero(_1115171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115171), _1115173), c_Groups_Ozero__class_Ozero(_1115171))))]]], (5234 ^ _780119) ^ [_860189, _860191, _860193, _860195] : [-(c_List_Ozip(_860195, _860191) = c_List_Ozip(_860193, _860189)), _860195 = _860193, _860191 = _860189], (23038 ^ _780119) ^ [_1200818, _1200820] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1200818, _1200820)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200818), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200820)))], (4002 ^ _780119) ^ [_840577, _840579] : [_840579 = _840577, -(c_List_Omonoid__add__class_Olistsum(_840579) = c_List_Omonoid__add__class_Olistsum(_840577))], (14564 ^ _780119) ^ [_1047272, _1047274, _1047276, _1047278] : [class_Groups_Omonoid__mult(_1047272), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1047272), _1047274), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047276), _1047278)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1047272), hAPP(hAPP(c_Power_Opower__class_Opower(_1047272), _1047274), _1047276)), _1047278))], (26333 ^ _780119) ^ [_1260745, _1260747, _1260749] : [class_Groups_Oordered__ab__group__add__abs(_1260745), -(hAPP(c_Groups_Oabs__class_Oabs(_1260745), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1260745), _1260747), _1260749)) = hAPP(c_Groups_Oabs__class_Oabs(_1260745), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1260745), _1260749), _1260747)))], (44520 ^ _780119) ^ [_1672040] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1672040)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (14288 ^ _780119) ^ [_1041222, _1041224, _1041226] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041222), _1041224)), -(hAPP(c_Finite__Set_Ocard(_1041222), hAPP(hAPP(c_Set_Oinsert(_1041222), _1041226), _1041224)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1041222), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1041222, tc_HOL_Obool)), _1041224), hAPP(hAPP(c_Set_Oinsert(_1041222), _1041226), c_Orderings_Obot__class_Obot(tc_fun(_1041222, tc_HOL_Obool)))))))], (21600 ^ _780119) ^ [_1174270, _1174272, _1174274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174270, tc_HOL_Obool)), _1174272), _1174274)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1174270, tc_HOL_Obool)), _1174272), hAPP(c_Set_OPow(_1174270), _1174274))))], (42618 ^ _780119) ^ [_1623496, _1623498, _1623500, _1623502, _1623504, _1623506] : [-(hAPP(hAPP(c_List_Omap(_1623496, _1623498), _1623500), hAPP(hAPP(c_List_Omap(_1623502, _1623496), _1623504), _1623506)) = hAPP(hAPP(c_List_Omap(_1623502, _1623498), hAPP(c_Fun_Ocomp(_1623496, _1623498, _1623502, _1623500), _1623504)), _1623506))], (47913 ^ _780119) ^ [_1748082, _1748084] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748082)), c_List_Oremdups(_1748082, c_List_Oconcat(_1748082, _1748084))) = hAPP(c_Finite__Set_Ocard(_1748082), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1748082), tc_fun(_1748082, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1748082)), _1748084)), c_List_Oset(_1748082))))], (46600 ^ _780119) ^ [_1719572, _1719574, _1719576, _1719578] : [-(hAPP(c_List_Ofilter(_1719572, _1719574), hAPP(c_List_Ofilter(_1719572, _1719576), _1719578)) = hAPP(c_List_Ofilter(_1719572, hAPP(hAPP(c_COMBS(_1719572, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1719572), c_fconj), _1719576)), _1719574)), _1719578))], (30205 ^ _780119) ^ [_1344339, _1344341, _1344343, _1344345] : [hAPP(c_Com_Ocom_OBODY, _1344339) = c_Com_Ocom_OLocal(_1344341, _1344343, _1344345)], (3910 ^ _780119) ^ [_839113, _839115, _839117, _839119] : [-(c_List_Otranspose(_839119, _839115) = c_List_Otranspose(_839117, _839113)), _839119 = _839117, _839115 = _839113], (15192 ^ _780119) ^ [_1057975] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1057975)], (18556 ^ _780119) ^ [_1118573, _1118575, _1118577, _1118579] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1118573, _1118575)), c_Sum__Type_OPlus(_1118573, _1118575, _1118577, _1118579))), 18559 ^ _780119 : [(18562 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1118575), _1118579)))], (18560 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1118573), _1118577)))]]], (21654 ^ _780119) ^ [_1175400, _1175402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1175400, _1175402)), _1175400)))], (21142 ^ _780119) ^ [_1164750, _1164752, _1164754, _1164756] : [class_Fields_Olinordered__field__inverse__zero(_1164750), 21145 ^ _780119 : [(21146 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164750), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1164750), _1164752), _1164754)), _1164756)), 21149 ^ _780119 : [(21156 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164750), c_Groups_Ozero__class_Ozero(_1164750)), _1164754))), 21159 ^ _780119 : [(21166 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164750), _1164754), c_Groups_Ozero__class_Ozero(_1164750)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164750), c_Groups_Ozero__class_Ozero(_1164750)), _1164756)))], (21160 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164750), _1164754), c_Groups_Ozero__class_Ozero(_1164750))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164750), _1164756), _1164754)), _1164752)))]]], (21150 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164750), c_Groups_Ozero__class_Ozero(_1164750)), _1164754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164750), _1164752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164750), _1164756), _1164754))))]]], (21172 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164750), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1164750), _1164752), _1164754)), _1164756))), 21175 ^ _780119 : [(21178 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164750), _1164752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164750), _1164756), _1164754)))], (21176 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164750), c_Groups_Ozero__class_Ozero(_1164750)), _1164754)))]], 21179 ^ _780119 : [(21182 ^ _780119) ^ [] : [21183 ^ _780119 : [(21186 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164750), _1164756), _1164754)), _1164752))], (21184 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164750), _1164754), c_Groups_Ozero__class_Ozero(_1164750))))]], 21187 ^ _780119 : [(21190 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164750), c_Groups_Ozero__class_Ozero(_1164750)), _1164756))], (21188 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164750), _1164754), c_Groups_Ozero__class_Ozero(_1164750)))]]], (21180 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164750), c_Groups_Ozero__class_Ozero(_1164750)), _1164754))]]]]], (2444 ^ _780119) ^ [_816132, _816134, _816136, _816138] : [-(c_Divides_OnegDivAlg(_816138, _816134) = c_Divides_OnegDivAlg(_816136, _816132)), _816138 = _816136, _816134 = _816132], (45070 ^ _780119) ^ [_1683442, _1683444, _1683446] : [hAPP(hAPP(c_List_Oappend(_1683442), _1683444), _1683446) = c_List_Olist_ONil(_1683442), 45073 ^ _780119 : [(45076 ^ _780119) ^ [] : [-(_1683446 = c_List_Olist_ONil(_1683442))], (45074 ^ _780119) ^ [] : [-(_1683444 = c_List_Olist_ONil(_1683442))]]], (47598 ^ _780119) ^ [_1740028, _1740030, _1740032] : [-(hAPP(c_List_Orev(_1740028), hAPP(c_List_Ofilter(_1740028, _1740030), _1740032)) = hAPP(c_List_Ofilter(_1740028, _1740030), hAPP(c_List_Orev(_1740028), _1740032)))], (23332 ^ _780119) ^ [_1206477, _1206479] : [_1206477 = _1206479, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206477) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206479))], (43841 ^ _780119) ^ [_1656167, _1656169, _1656171, _1656173, _1656175] : [class_Orderings_Olinorder(_1656167), -(hBOOL(hAPP(hAPP(c_member(_1656167), hAPP(_1656169, _1656171)), hAPP(c_Set_Oimage(_1656173, _1656167, _1656169), hAPP(c_List_Oset(_1656173), _1656175))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1656173, _1656167, _1656169, _1656171, _1656175) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1656173, _1656167, _1656169), _1656171), _1656175))], (17977 ^ _780119) ^ [_1107536, _1107538, _1107540] : [class_Rings_Olinordered__semidom(_1107536), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107536), c_Groups_Ozero__class_Ozero(_1107536)), _1107538)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107536), _1107538), c_Groups_Oone__class_Oone(_1107536))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107536), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107536), _1107538), hAPP(hAPP(c_Power_Opower__class_Opower(_1107536), _1107538), _1107540))), hAPP(hAPP(c_Power_Opower__class_Opower(_1107536), _1107538), _1107540))))], (45582 ^ _780119) ^ [_1697348, _1697350, _1697352, _1697354, _1697356] : [hAPP(hAPP(c_List_Odrop(_1697348), _1697350), _1697352) = hAPP(hAPP(c_List_Olist_OCons(_1697348), _1697354), _1697356), -(hAPP(hAPP(c_List_Onth(_1697348), _1697352), _1697350) = _1697354)], (44488 ^ _780119) ^ [_1671528, _1671530] : [hAPP(c_Code__Numeral_Onat__of, _1671528) = hAPP(c_Code__Numeral_Onat__of, _1671530), -(_1671528 = _1671530)], (5334 ^ _780119) ^ [_861735, _861737] : [_861737 = _861735, -(c_Groups_Oplus__class_Oplus(_861737) = c_Groups_Oplus__class_Oplus(_861735))], (45150 ^ _780119) ^ [_1684995, _1684997, _1684999, _1685001] : [hAPP(hAPP(c_List_Oappend(_1684995), _1684997), _1684999) = hAPP(hAPP(c_List_Oappend(_1684995), _1684997), _1685001), -(_1684999 = _1685001)], (30271 ^ _780119) ^ [_1345704, _1345706, _1345708, _1345710] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345704), hAPP(c_Int_Onumber__class_Onumber__of(_1345704), _1345706)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1345704), _1345708), _1345710)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1345704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345704), hAPP(c_Int_Onumber__class_Onumber__of(_1345704), _1345706)), _1345708)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345704), hAPP(c_Int_Onumber__class_Onumber__of(_1345704), _1345706)), _1345710))), class_Int_Onumber(_1345704), class_Rings_Osemiring(_1345704)], (51283 ^ _780119) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (11107 ^ _780119) ^ [_977813, _977815, _977817, _977819, _977821] : [class_Groups_Ocomm__monoid__add(_977813), hBOOL(hAPP(c_Finite__Set_Ofinite(_977815), _977817)), -(hBOOL(hAPP(hAPP(c_member(_977815), _977819), _977817))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977815, _977813), _977821), hAPP(hAPP(c_Set_Oinsert(_977815), _977819), _977817)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977813), hAPP(_977821, _977819)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977815, _977813), _977821), _977817)))], (23575 ^ _780119) ^ [_1211152] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211152) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1211152))], (6579 ^ _780119) ^ [_886990, _886992] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886990, tc_HOL_Obool)), _886992), _886992) = _886992)], (18005 ^ _780119) ^ [_1108080, _1108082, _1108084, _1108086] : [class_Rings_Olinordered__semidom(_1108080), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108082), _1108084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108080), c_Groups_Ozero__class_Ozero(_1108080)), _1108086)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108080), _1108086), c_Groups_Oone__class_Oone(_1108080))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108080), hAPP(hAPP(c_Power_Opower__class_Opower(_1108080), _1108086), _1108084)), hAPP(hAPP(c_Power_Opower__class_Opower(_1108080), _1108086), _1108082))))], (4146 ^ _780119) ^ [_842791, _842793] : [_842793 = _842791, -(c_Enum_Oenum__class_Oenum__all(_842793) = c_Enum_Oenum__class_Oenum__all(_842791))], (51221 ^ _780119) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (23127 ^ _780119) ^ [_1202470, _1202472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1202470), _1202472)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202472)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202470)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1202472), _1202470)))], (30361 ^ _780119) ^ [_1347487, _1347489, _1347491] : [class_Int_Onumber(_1347487), class_Orderings_Oord(_1347487), 30368 ^ _780119 : [(30375 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347487), hAPP(c_Int_Onumber__class_Onumber__of(_1347487), _1347489)), hAPP(c_Int_Onumber__class_Onumber__of(_1347487), _1347491)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347487), hAPP(c_Int_Onumber__class_Onumber__of(_1347487), _1347489)), hAPP(c_Int_Onumber__class_Onumber__of(_1347487), _1347491)) = hAPP(c_Int_Onumber__class_Onumber__of(_1347487), _1347489))], (30369 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347487), hAPP(c_Int_Onumber__class_Onumber__of(_1347487), _1347489)), hAPP(c_Int_Onumber__class_Onumber__of(_1347487), _1347491))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347487), hAPP(c_Int_Onumber__class_Onumber__of(_1347487), _1347489)), hAPP(c_Int_Onumber__class_Onumber__of(_1347487), _1347491)) = hAPP(c_Int_Onumber__class_Onumber__of(_1347487), _1347491))]]], (32913 ^ _780119) ^ [_1393380, _1393382] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1393380), hAPP(c_Int_Onumber__class_Onumber__of(_1393380), _1393382)), 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(_1393380), hAPP(c_Int_Onumber__class_Onumber__of(_1393380), _1393382)), hAPP(c_Int_Onumber__class_Onumber__of(_1393380), _1393382))), class_Groups_Omonoid__mult(_1393380), class_Int_Onumber(_1393380)], (41906 ^ _780119) ^ [_1606962, _1606964, _1606966] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606962, tc_HOL_Obool)), _1606964), _1606966) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1606962, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1606962, tc_HOL_Obool)), _1606964), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1606962, tc_HOL_Obool)), _1606966), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1606962, tc_HOL_Obool), tc_HOL_Obool))))))], (49408 ^ _780119) ^ [_1780498, _1780500, _1780502, _1780504, _1780506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1780498, _1780500)), hAPP(_1780498, _1780502))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780504, _1780504)), hAPP(hAPP(c_Product__Type_OPair(_1780504, _1780504), _1780500), _1780502)), c_List_Omeasures(_1780504, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1780504, tc_Nat_Onat)), _1780498), _1780506)))))], (48896 ^ _780119) ^ [_1769051, _1769053, _1769055, _1769057] : [-(hBOOL(hAPP(c_List_Olistsp(_1769051, _1769053), hAPP(hAPP(c_List_Olist_OCons(_1769051), _1769055), _1769057)))), hBOOL(hAPP(_1769053, _1769055)), hBOOL(hAPP(c_List_Olistsp(_1769051, _1769053), _1769057))], (3880 ^ _780119) ^ [_838642, _838644] : [_838644 = _838642, -(c_Orderings_Oord__class_Omax(_838644) = c_Orderings_Oord__class_Omax(_838642))], (26705 ^ _780119) ^ [_1267810, _1267812, _1267814] : [class_Fields_Olinordered__field(_1267810), -(_1267812 = c_Groups_Ozero__class_Ozero(_1267810)), -(hAPP(c_Groups_Oabs__class_Oabs(_1267810), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267810), _1267814), _1267812)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267810), hAPP(c_Groups_Oabs__class_Oabs(_1267810), _1267814)), hAPP(c_Groups_Oabs__class_Oabs(_1267810), _1267812)))], (51607 ^ _780119) ^ [_1820907, _1820909] : [hBOOL(hAPP(hAPP(c_fconj, _1820907), _1820909)), -(hBOOL(_1820909))], (1100 ^ _780119) ^ [_796593, _796595] : [-(class_Rings_Oordered__ring__abs(_796593)), _796595 = _796593, class_Rings_Oordered__ring__abs(_796595)], (42955 ^ _780119) ^ [_1631608, _1631610] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1631608, _1631610) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1631608), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1631610), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (14116 ^ _780119) ^ [_1037603, _1037605, _1037607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037603), _1037605)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037605), _1037603))), _1037607) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1037605)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037603), _1037607)))], (8046 ^ _780119) ^ [_917644, _917646] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_917644, _917646)], (44504 ^ _780119) ^ [_1671762] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1671762)) = _1671762)], (35657 ^ _780119) ^ [_1454213, _1454215, _1454217, _1454219, _1454221, _1454223, _1454225] : [c_Equiv__Relations_Oequiv(_1454213, _1454215, _1454217), hBOOL(hAPP(hAPP(c_member(tc_fun(_1454213, tc_HOL_Obool)), _1454219), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1454213), _1454215), _1454217))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1454213, tc_HOL_Obool)), _1454221), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1454213), _1454215), _1454217))), hBOOL(hAPP(hAPP(c_member(_1454213), _1454223), _1454219)), hBOOL(hAPP(hAPP(c_member(_1454213), _1454225), _1454221)), 35676 ^ _780119 : [(35683 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1454213, _1454213)), hAPP(hAPP(c_Product__Type_OPair(_1454213, _1454213), _1454223), _1454225)), _1454217)), -(_1454219 = _1454221)], (35677 ^ _780119) ^ [] : [_1454219 = _1454221, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1454213, _1454213)), hAPP(hAPP(c_Product__Type_OPair(_1454213, _1454213), _1454223), _1454225)), _1454217)))]]], (992 ^ _780119) ^ [_795199, _795201, _795203, _795205, _795207, _795209] : [-(c_List_Olist__ex1(_795207, _795203, _795199)), c_List_Olist__ex1(_795209, _795205, _795201), _795209 = _795207, _795205 = _795203, _795201 = _795199], (34627 ^ _780119) ^ [_1430007] : [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), _1430007))), -(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), _1430007)) = 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), _1430007))))], (33039 ^ _780119) ^ [_1395589, _1395591, _1395593] : [class_Int_Onumber__ring(_1395589), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1395589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1395589), _1395591), _1395593)), 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(_1395589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1395589), hAPP(hAPP(c_Power_Opower__class_Opower(_1395589), _1395591), 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(_1395589), _1395593), 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(_1395589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395589), hAPP(c_Int_Onumber__class_Onumber__of(_1395589), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1395591)), _1395593)))], (47921 ^ _780119) ^ [_1748283, _1748285] : [-(hAPP(c_List_Oset(_1748283), c_List_Oremdups(_1748283, _1748285)) = hAPP(c_List_Oset(_1748283), _1748285))], (36485 ^ _780119) ^ [_1472273, _1472275, _1472277, _1472279, _1472281, _1472283] : [c_Fun_Oinj__on(_1472273, _1472275, _1472277, _1472279), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472273, tc_HOL_Obool)), _1472281), _1472279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472273, tc_HOL_Obool)), _1472283), _1472279)), -(hAPP(c_Set_Oimage(_1472273, _1472275, _1472277), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472273, tc_HOL_Obool)), _1472281), _1472283)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472275, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1472273, _1472275, _1472277), _1472281)), hAPP(c_Set_Oimage(_1472273, _1472275, _1472277), _1472283)))], (36718 ^ _780119) ^ [_1477759, _1477761] : [-(hAPP(c_Set_Ovimage(_1477759, _1477759, c_COMBI(_1477759)), _1477761) = _1477761)], (14942 ^ _780119) ^ [_1054207, _1054209] : [class_Groups_Omonoid__add(_1054207), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054207), _1054209), c_Groups_Ozero__class_Ozero(_1054207)) = _1054209)], (33815 ^ _780119) ^ [_1414397, _1414399, _1414401, _1414403, _1414405, _1414407, _1414409] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1414397, _1414399)), hAPP(hAPP(c_Product__Type_OPair(_1414397, _1414399), _1414401), _1414403)), _1414405)), -(hBOOL(hAPP(hAPP(c_member(_1414407), hAPP(hAPP(_1414409, _1414401), _1414403)), hAPP(c_Set_Oimage(tc_prod(_1414397, _1414399), _1414407, hAPP(c_Product__Type_Oprod_Oprod__case(_1414397, _1414399, _1414407), _1414409)), _1414405))))], (29210 ^ _780119) ^ [_1321469, _1321471, _1321473] : [class_Orderings_Olinorder(_1321469), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321469), _1321471)), hBOOL(hAPP(hAPP(c_member(_1321469), _1321473), _1321471)), 29221 ^ _780119 : [(29228 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321469, tc_HOL_Obool)), _1321471), hAPP(hAPP(c_Set_Oinsert(_1321469), _1321473), c_Orderings_Obot__class_Obot(tc_fun(_1321469, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1321469, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1321469, c_Orderings_Oord__class_Omin(_1321469), _1321471) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321469), _1321473), c_Big__Operators_Olattice_OInf__fin(_1321469, c_Orderings_Oord__class_Omin(_1321469), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321469, tc_HOL_Obool)), _1321471), hAPP(hAPP(c_Set_Oinsert(_1321469), _1321473), c_Orderings_Obot__class_Obot(tc_fun(_1321469, tc_HOL_Obool)))))))], (29222 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321469, tc_HOL_Obool)), _1321471), hAPP(hAPP(c_Set_Oinsert(_1321469), _1321473), c_Orderings_Obot__class_Obot(tc_fun(_1321469, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1321469, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1321469, c_Orderings_Oord__class_Omin(_1321469), _1321471) = _1321473)]]], (8802 ^ _780119) ^ [_932047, _932049, _932051, _932053, _932055] : [class_Groups_Oordered__ab__group__add(_932047), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_932047), _932049), _932051) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_932047), _932053), _932055), 8809 ^ _780119 : [(8816 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932047), _932053), _932055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932047), _932049), _932051)))], (8810 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932047), _932049), _932051)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932047), _932053), _932055)))]]], (80 ^ _780119) ^ [_781469, _781471, _781473, _781475, _781477, _781479, _781481, _781483, _781485, _781487] : [-(c_Big__Operators_Ocomm__monoid__big(_781485, _781481, _781477, _781473, _781469)), c_Big__Operators_Ocomm__monoid__big(_781487, _781483, _781479, _781475, _781471), _781487 = _781485, _781483 = _781481, _781479 = _781477, _781475 = _781473, _781471 = _781469], (34811 ^ _780119) ^ [_1433605, _1433607, _1433609, _1433611] : [hAPP(c_Product__Type_Ofst(_1433605, _1433607), _1433609) = hAPP(c_Product__Type_Ofst(_1433605, _1433607), _1433611), hAPP(c_Product__Type_Osnd(_1433605, _1433607), _1433609) = hAPP(c_Product__Type_Osnd(_1433605, _1433607), _1433611), -(_1433609 = _1433611)], (22713 ^ _780119) ^ [_1195002, _1195004, _1195006, _1195008] : [hBOOL(hAPP(hAPP(_1195006, _1195004), _1195008)), -(hBOOL(hAPP(hAPP(c_member(_1195002), _1195004), c_SetInterval_Oord_OlessThan(_1195002, _1195006, _1195008))))], (35309 ^ _780119) ^ [_1444536, _1444538, _1444540, _1444542] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444536), _1444542) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444540), _1444538), -(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), _1444536), _1444538)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1444540), _1444542))), c_Int_Ointrel)))], (45764 ^ _780119) ^ [_1701709, _1701711, _1701713, _1701715] : [-(hAPP(c_List_Orotate1(_1701709), c_List_Olist_ONil(_1701709)) = c_List_Olist_ONil(_1701709))], (45956 ^ _780119) ^ [_1705580, _1705582, _1705584] : [-(_1705580 = c_List_Olist_ONil(_1705582)), -(hAPP(hAPP(c_List_Otake(_1705582), hAPP(c_Nat_OSuc, _1705584)), _1705580) = hAPP(hAPP(c_List_Olist_OCons(_1705582), hAPP(c_List_Ohd(_1705582), _1705580)), hAPP(hAPP(c_List_Otake(_1705582), _1705584), hAPP(c_List_Otl(_1705582), _1705580))))], (22565 ^ _780119) ^ [_1191832, _1191834, _1191836, _1191838, _1191840] : [c_Com_Ocom_OWhile(_1191832, _1191834) = c_Com_Ocom_OCond(_1191836, _1191838, _1191840)], (24207 ^ _780119) ^ [_1223322, _1223324] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1223322), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1223324), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1223322, _1223324))], (46797 ^ _780119) ^ [_1724327, _1724329, _1724331, _1724333, _1724335] : [class_Orderings_Olinorder(_1724327), c_List_Olinorder__class_Osorted(_1724327, hAPP(hAPP(c_List_Omap(_1724329, _1724327), _1724331), _1724333)), -(c_List_Olinorder__class_Osorted(_1724327, hAPP(hAPP(c_List_Omap(_1724329, _1724327), _1724331), hAPP(c_List_Ofilter(_1724329, _1724335), _1724333))))], (30099 ^ _780119) ^ [_1342658, _1342660] : [class_Int_Onumber__ring(_1342658), -(hAPP(c_Int_Onumber__class_Onumber__of(_1342658), _1342660) = hAPP(c_Int_Oring__1__class_Oof__int(_1342658), _1342660))], (34601 ^ _780119) ^ [_1429550, _1429552, _1429554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429550, tc_fun(_1429550, tc_HOL_Obool))), _1429552), _1429554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429550, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1429550, _1429554)), c_Wellfounded_Oaccp(_1429550, _1429552))))], (10218 ^ _780119) ^ [_958955, _958957, _958959, _958961] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958955, tc_HOL_Obool)), _958957), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958955, tc_HOL_Obool)), _958959), _958961)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958955, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958955, tc_HOL_Obool)), _958957), _958959)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958955, tc_HOL_Obool)), _958957), _958961)))], (47027 ^ _780119) ^ [_1728038, _1728040] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1728038, _1728040)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1728038), _1728040))], (4676 ^ _780119) ^ [_851304, _851306, _851308, _851310, _851312, _851314, _851316, _851318] : [-(c_New__DSequence_Oneg__decr__bind(_851318, _851314, _851310, _851306) = c_New__DSequence_Oneg__decr__bind(_851316, _851312, _851308, _851304)), _851318 = _851316, _851314 = _851312, _851310 = _851308, _851306 = _851304], (51559 ^ _780119) ^ [_1820243, _1820245, _1820247, _1820249, _1820251, _1820253] : [-(hAPP(hAPP(hAPP(c_COMBC(_1820243, _1820245, _1820247), _1820249), _1820251), _1820253) = hAPP(hAPP(_1820249, _1820253), _1820251))], (51255 ^ _780119) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (33555 ^ _780119) ^ [_1404769, _1404771] : [-(_1404769 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1404769, _1404771) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1404769), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1404771)))], (40230 ^ _780119) ^ [_1566759, _1566761, _1566763, _1566765] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566759, _1566759)), _1566761), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566759, _1566759), tc_HOL_Obool), _1566763), _1566765))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566759, _1566759)), _1566761), c_Transitive__Closure_Ortrancl(_1566759, _1566765))))], (15732 ^ _780119) ^ [_1066704, _1066706, _1066708] : [class_Rings_Oordered__cancel__semiring(_1066704), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066704), c_Groups_Ozero__class_Ozero(_1066704)), _1066706)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066704), c_Groups_Ozero__class_Ozero(_1066704)), _1066708)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066704), c_Groups_Ozero__class_Ozero(_1066704)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066704), _1066706), _1066708))))], (20926 ^ _780119) ^ [_1160706, _1160708, _1160710, _1160712] : [class_Fields_Olinordered__field(_1160706), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160706), _1160708), c_Groups_Ozero__class_Ozero(_1160706))), 20933 ^ _780119 : [(20940 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160706), _1160712), _1160708)), _1160710)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160706), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160706), _1160710), _1160708)), _1160712)))], (20934 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160706), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160706), _1160710), _1160708)), _1160712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160706), _1160712), _1160708)), _1160710)))]]], (37573 ^ _780119) ^ [_1499392, _1499394, _1499396, _1499398, _1499400] : [-(hAPP(c_Relation_ORange(_1499392, _1499394), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1499392, _1499394)), hAPP(hAPP(c_Product__Type_OPair(_1499392, _1499394), _1499396), _1499398)), _1499400)) = hAPP(hAPP(c_Set_Oinsert(_1499394), _1499398), hAPP(c_Relation_ORange(_1499392, _1499394), _1499400)))], (46365 ^ _780119) ^ [_1714495, _1714497, _1714499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714495), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714497)), _1714499))), -(c_List_Olast(_1714497, hAPP(hAPP(c_List_Odrop(_1714497), _1714495), _1714499)) = c_List_Olast(_1714497, _1714499))], (21827 ^ _780119) ^ [_1178601, _1178603, _1178605] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178601), _1178603)), _1178605) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178601), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1178603), _1178605))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178601), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178603, _1178605))), _1178605)))], (18620 ^ _780119) ^ [_1119781] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1119781)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1119781)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41041 ^ _780119) ^ [_1584753, _1584755, _1584757, _1584759] : [class_Complete__Lattice_Ocomplete__lattice(_1584753), hBOOL(hAPP(c_Finite__Set_Ofinite(_1584755), _1584757)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1584755, _1584753), _1584757), _1584759) = hAPP(hAPP(c_Finite__Set_Ofold(_1584755, _1584753, hAPP(hAPP(c_COMBB(_1584753, tc_fun(_1584753, _1584753), _1584755), c_Lattices_Osemilattice__inf__class_Oinf(_1584753)), _1584759)), c_Orderings_Otop__class_Otop(_1584753)), _1584757))], (37872 ^ _780119) ^ [_1508390, _1508392, _1508394, _1508396, _1508398, _1508400] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508390, _1508392)), hAPP(hAPP(c_Product__Type_OPair(_1508390, _1508392), _1508394), _1508396)), hAPP(hAPP(c_Product__Type_OSigma(_1508390, _1508392), _1508398), _1508400))), 37875 ^ _780119 : [(37878 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508392), _1508396), hAPP(_1508400, _1508394))))], (37876 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508390), _1508394), _1508398)))]]], (15534 ^ _780119) ^ [_1063235, _1063237, _1063239, _1063241, _1063243] : [_1063235 = hAPP(_1063237, _1063239), -(hBOOL(hAPP(hAPP(c_member(_1063241), _1063235), hAPP(c_Set_Oimage(_1063243, _1063241, _1063237), c_Orderings_Otop__class_Otop(tc_fun(_1063243, tc_HOL_Obool))))))], (43180 ^ _780119) ^ [_1637261, _1637263, _1637265] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637261)), _1637263) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637261)), _1637265)), _1637263 = _1637265], (34709 ^ _780119) ^ [_1431479, _1431481, _1431483] : [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), _1431479), _1431481))), -(hBOOL(hAPP(hAPP(_1431483, _1431479), _1431481))), 34716 ^ _780119 : [(34729 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1431483, 34714 ^ [_1431479, _1431481, _1431483]), 34715 ^ [_1431479, _1431481, _1431483]))], (34719 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1431483, 34714 ^ [_1431479, _1431481, _1431483]), 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)))), 34715 ^ [_1431479, _1431481, _1431483])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 34714 ^ [_1431479, _1431481, _1431483]), 34715 ^ [_1431479, _1431481, _1431483]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 34715 ^ [_1431479, _1431481, _1431483]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34717 ^ _780119) ^ [] : [-(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), 34714 ^ [_1431479, _1431481, _1431483]), 34715 ^ [_1431479, _1431481, _1431483]))))]]], (50200 ^ _780119) ^ [_1797370, _1797372] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1797370), _1797372)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1797370)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1797372))))], (45626 ^ _780119) ^ [_1698335, _1698337, _1698339, _1698341] : [hBOOL(hAPP(hAPP(c_member(_1698335), _1698337), hAPP(c_List_Oset(_1698335), hAPP(hAPP(c_List_Odrop(_1698335), _1698339), _1698341)))), -(hBOOL(hAPP(hAPP(c_member(_1698335), _1698337), hAPP(c_List_Oset(_1698335), _1698341))))], (15746 ^ _780119) ^ [_1066959, _1066961, _1066963] : [class_Rings_Oordered__cancel__semiring(_1066959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066959), c_Groups_Ozero__class_Ozero(_1066959)), _1066961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066959), _1066963), c_Groups_Ozero__class_Ozero(_1066959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066959), _1066961), _1066963)), c_Groups_Ozero__class_Ozero(_1066959))))], (51481 ^ _780119) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (3206 ^ _780119) ^ [_827997, _827999] : [_827999 = _827997, -(c_Smallcheck_Osmall__class_Osmall(_827999) = c_Smallcheck_Osmall__class_Osmall(_827997))], (13564 ^ _780119) ^ [_1027062, _1027064, _1027066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027062), _1027064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027064), _1027066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027062)), _1027066)))], (36736 ^ _780119) ^ [_1478167, _1478169, _1478171, _1478173] : [-(hAPP(c_Set_Ovimage(_1478167, _1478169, _1478171), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1478169, tc_HOL_Obool)), _1478173)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1478167, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1478167, _1478169, _1478171), _1478173)))], (24409 ^ _780119) ^ [_1227223, _1227225, _1227227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227223)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1227225), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1227227)), 24419 ^ _780119 : [(24423 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24421 ^ [_1227223, _1227225, _1227227]), _1227227)))], (24425 ^ _780119) ^ [] : [-(_1227225 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24421 ^ [_1227223, _1227225, _1227227]), 24418 ^ [_1227223, _1227225, _1227227]))], (24420 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24418 ^ [_1227223, _1227225, _1227227]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1227223))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1227225), _1227223) = _1227225)], (34042 ^ _780119) ^ [_1419300, _1419302, _1419304, _1419306] : [-(c_HOL_OThe(tc_prod(_1419300, _1419302), hAPP(c_Product__Type_Oprod_Oprod__case(_1419300, _1419302, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1419300, tc_fun(_1419302, tc_HOL_Obool), tc_fun(_1419302, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1419302, tc_HOL_Obool), tc_fun(_1419302, tc_HOL_Obool)), _1419300), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1419302)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1419300), c_fconj), hAPP(c_fequal, _1419304)))), hAPP(c_fequal, _1419306)))) = hAPP(hAPP(c_Product__Type_OPair(_1419300, _1419302), _1419304), _1419306))], (44584 ^ _780119) ^ [_1673247, _1673249, _1673251, _1673253, _1673255, _1673257] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673247)), _1673249) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673251)), _1673253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1673247, tc_HOL_Obool)), hAPP(c_List_Oset(_1673247), _1673249)), _1673255)), -(c_Map_Orestrict__map(_1673247, _1673251, c_Map_Omap__upds(_1673247, _1673251, _1673257, _1673249, _1673253), _1673255) = c_Map_Omap__upds(_1673247, _1673251, c_Map_Orestrict__map(_1673247, _1673251, _1673257, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1673247, tc_HOL_Obool)), _1673255), hAPP(c_List_Oset(_1673247), _1673249))), _1673249, _1673253))], (12789 ^ _780119) ^ [_1011952, _1011954] : [class_Lattices_Olattice(_1011952), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011952), _1011954)), -(c_Big__Operators_Olattice__class_OSup__fin(_1011952, _1011954) = hAPP(c_Finite__Set_Ofold1(_1011952, c_Lattices_Osemilattice__sup__class_Osup(_1011952)), _1011954))], (31509 ^ _780119) ^ [_1368745] : [class_Int_Onumber__ring(_1368745), -(c_Groups_Ozero__class_Ozero(_1368745) = hAPP(c_Int_Onumber__class_Onumber__of(_1368745), c_Int_OPls))], (12533 ^ _780119) ^ [_1007058, _1007060, _1007062] : [class_Groups_Oab__semigroup__mult(_1007058), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007058), _1007060)), -(_1007060 = c_Orderings_Obot__class_Obot(tc_fun(_1007058, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007058), _1007062)), -(_1007062 = c_Orderings_Obot__class_Obot(tc_fun(_1007058, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1007058, tc_HOL_Obool)), _1007060), _1007062) = c_Orderings_Obot__class_Obot(tc_fun(_1007058, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1007058, c_Groups_Otimes__class_Otimes(_1007058)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1007058, tc_HOL_Obool)), _1007060), _1007062)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007058), hAPP(c_Finite__Set_Ofold1(_1007058, c_Groups_Otimes__class_Otimes(_1007058)), _1007060)), hAPP(c_Finite__Set_Ofold1(_1007058, c_Groups_Otimes__class_Otimes(_1007058)), _1007062)))], (51207 ^ _780119) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (40471 ^ _780119) ^ [_1573072, _1573074, _1573076, _1573078, _1573080] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573072, _1573072)), hAPP(hAPP(c_Product__Type_OPair(_1573072, _1573072), _1573074), _1573076)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1573072, _1573072), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1573078)), _1573080))), 40475 ^ _780119 : [(40478 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573072, _1573072)), hAPP(hAPP(c_Product__Type_OPair(_1573072, _1573072), 40474 ^ [_1573072, _1573074, _1573076, _1573078, _1573080]), _1573076)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1573072, _1573072), tc_HOL_Obool), _1573078), _1573080))))], (40476 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573072, _1573072)), hAPP(hAPP(c_Product__Type_OPair(_1573072, _1573072), _1573074), 40474 ^ [_1573072, _1573074, _1573076, _1573078, _1573080])), _1573080)))]]], (51307 ^ _780119) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (51491 ^ _780119) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (24733 ^ _780119) ^ [_1233067, _1233069] : [class_Orderings_Olinorder(_1233067), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1233067, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1233067), _1233069)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1233067), _1233069))], (31091 ^ _780119) ^ [_1361440] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1361440)))), -(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), _1361440)) = 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), _1361440))))], (20011 ^ _780119) ^ [_1143913, _1143915, _1143917] : [-(hBOOL(hAPP(_1143913, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143915), _1143917)))), 20014 ^ _780119 : [(20017 ^ _780119) ^ [] : [hBOOL(hAPP(_1143913, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20015 ^ _780119) ^ [] : [-(_1143917 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 20018 ^ _780119 : [(20019 ^ _780119) ^ [] : [_1143917 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20023 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20021 ^ [_1143913, _1143915, _1143917]), _1143917)))], (20027 ^ _780119) ^ [] : [hBOOL(hAPP(_1143913, 20020 ^ [_1143913, _1143915, _1143917]))], (20025 ^ _780119) ^ [] : [-(_1143915 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143917), 20020 ^ [_1143913, _1143915, _1143917])), 20021 ^ [_1143913, _1143915, _1143917]))]]], (31773 ^ _780119) ^ [_1372834] : [-(c_Int_Osucc(_1372834) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1372834), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28808 ^ _780119) ^ [_1313713, _1313715, _1313717] : [class_Orderings_Olinorder(_1313713), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313713), _1313715)), -(_1313715 = c_Orderings_Obot__class_Obot(tc_fun(_1313713, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313713), _1313717), c_Big__Operators_Olattice_OSup__fin(_1313713, c_Orderings_Oord__class_Omax(_1313713), _1313715)) = c_Big__Operators_Olattice_OSup__fin(_1313713, c_Orderings_Oord__class_Omax(_1313713), hAPP(c_Set_OCollect(_1313713), hAPP(hAPP(c_COMBB(tc_fun(_1313713, tc_HOL_Obool), tc_HOL_Obool, _1313713), c_HOL_OEx(_1313713)), hAPP(hAPP(c_COMBC(_1313713, tc_fun(_1313713, tc_HOL_Obool), tc_fun(_1313713, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1313713, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1313713, tc_HOL_Obool), tc_fun(_1313713, tc_HOL_Obool)), _1313713), c_COMBS(_1313713, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1313713, tc_HOL_Obool), tc_fun(_1313713, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1313713), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1313713), c_fconj)), hAPP(hAPP(c_COMBC(_1313713, tc_fun(_1313713, _1313713), tc_fun(_1313713, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1313713, tc_HOL_Obool), tc_fun(tc_fun(_1313713, _1313713), tc_fun(_1313713, tc_HOL_Obool)), _1313713), c_COMBB(_1313713, tc_HOL_Obool, _1313713)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1313713), _1313717))))), hAPP(hAPP(c_COMBC(_1313713, tc_fun(_1313713, tc_HOL_Obool), tc_HOL_Obool), c_member(_1313713)), _1313715))))))], (6421 ^ _780119) ^ [_883896, _883898, _883900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883896, tc_HOL_Obool)), _883898), hAPP(hAPP(c_Set_Oinsert(_883896), _883900), c_Orderings_Obot__class_Obot(tc_fun(_883896, tc_HOL_Obool))))), -(_883898 = c_Orderings_Obot__class_Obot(tc_fun(_883896, tc_HOL_Obool))), -(_883898 = hAPP(hAPP(c_Set_Oinsert(_883896), _883900), c_Orderings_Obot__class_Obot(tc_fun(_883896, tc_HOL_Obool))))], (48861 ^ _780119) ^ [_1768342, _1768344, _1768346] : [48863 ^ _780119 : [(48866 ^ _780119) ^ [] : [hBOOL(hAPP(_1768344, 48862 ^ [_1768342, _1768344, _1768346]))], (48864 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1768342), 48862 ^ [_1768342, _1768344, _1768346]), hAPP(c_List_Oset(_1768342), _1768346))))]], -(hBOOL(hAPP(c_List_Olistsp(_1768342, _1768344), _1768346)))], (2862 ^ _780119) ^ [_822731, _822733, _822735, _822737] : [-(c_Random_Oinc__shift(_822737, _822733) = c_Random_Oinc__shift(_822735, _822731)), _822737 = _822735, _822733 = _822731], (32253 ^ _780119) ^ [_1381614] : [class_Int_Onumber__ring(_1381614), c_Int_Oiszero(_1381614, hAPP(c_Int_Onumber__class_Onumber__of(_1381614), c_Int_OBit1(c_Int_OPls)))], (45241 ^ _780119) ^ [_1687315, _1687317, _1687319, _1687321, _1687323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1687315), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687317)), _1687319))), -(hAPP(hAPP(c_List_Olist__update(_1687317, hAPP(hAPP(c_List_Oappend(_1687317), _1687319), _1687321)), _1687315), _1687323) = hAPP(hAPP(c_List_Oappend(_1687317), hAPP(hAPP(c_List_Olist__update(_1687317, _1687319), _1687315), _1687323)), _1687321))], (45980 ^ _780119) ^ [_1706060, _1706062, _1706064, _1706066, _1706068] : [-(c_List_Olist_Olist__size(_1706060, _1706062, hAPP(hAPP(c_List_Omap(_1706064, _1706060), _1706066), _1706068)) = c_List_Olist_Olist__size(_1706064, hAPP(c_Fun_Ocomp(_1706060, tc_Nat_Onat, _1706064, _1706062), _1706066), _1706068))], (15344 ^ _780119) ^ [_1060139] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060139), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1060139)], (50268 ^ _780119) ^ [_1799031, _1799033, _1799035, _1799037, _1799039] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1799031, _1799033, _1799035) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1799031, _1799037, _1799039), 50271 ^ _780119 : [(50274 ^ _780119) ^ [] : [-(_1799035 = _1799039)], (50272 ^ _780119) ^ [] : [-(_1799033 = _1799037)]]], (15512 ^ _780119) ^ [_1062797] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1062797), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1062797)), c_Option_Ooption_ONone(_1062797)), hAPP(c_Set_Oimage(_1062797, tc_Option_Ooption(_1062797), c_Option_Ooption_OSome(_1062797)), c_Orderings_Otop__class_Otop(tc_fun(_1062797, tc_HOL_Obool)))))], (35219 ^ _780119) ^ [_1442947, _1442949, _1442951, _1442953] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1442947), _1442949)), 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)), _1442951), _1442947)), 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)), _1442953), _1442949)), 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)), _1442951), _1442953)), _1442949)), c_FunDef_Omax__weak)))], (748 ^ _780119) ^ [_791537, _791539, _791541, _791543, _791545, _791547] : [-(c_Finite__Set_Ofun__left__comm(_791545, _791541, _791537)), c_Finite__Set_Ofun__left__comm(_791547, _791543, _791539), _791547 = _791545, _791543 = _791541, _791539 = _791537], (10212 ^ _780119) ^ [_958703, _958705, _958707, _958709] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958703, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958703, tc_HOL_Obool)), _958705), _958707)), _958709) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958703, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958703, tc_HOL_Obool)), _958705), _958709)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958703, tc_HOL_Obool)), _958707), _958709)))], (5104 ^ _780119) ^ [_858218, _858220, _858222, _858224] : [-(c_Relation_Oconverse(_858224, _858220) = c_Relation_Oconverse(_858222, _858218)), _858224 = _858222, _858220 = _858218], (30861 ^ _780119) ^ [_1356975, _1356977, _1356979, _1356981] : [class_Fields_Olinordered__field__inverse__zero(_1356975), class_Int_Onumber(_1356975), 30868 ^ _780119 : [(30869 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356975), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356975), _1356977), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979))), _1356981)), 30872 ^ _780119 : [(30879 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356975), c_Groups_Ozero__class_Ozero(_1356975)), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979)))), 30882 ^ _780119 : [(30889 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356975), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979)), c_Groups_Ozero__class_Ozero(_1356975)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356975), c_Groups_Ozero__class_Ozero(_1356975)), _1356981)))], (30883 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356975), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979)), c_Groups_Ozero__class_Ozero(_1356975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356975), _1356981), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979))), _1356977)))]]], (30873 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356975), c_Groups_Ozero__class_Ozero(_1356975)), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356975), _1356977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356975), _1356981), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979)))))]]], (30895 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356975), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356975), _1356977), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979))), _1356981))), 30898 ^ _780119 : [(30901 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356975), _1356977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356975), _1356981), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979))))], (30899 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356975), c_Groups_Ozero__class_Ozero(_1356975)), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979))))]], 30902 ^ _780119 : [(30905 ^ _780119) ^ [] : [30906 ^ _780119 : [(30909 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356975), _1356981), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979))), _1356977))], (30907 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356975), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979)), c_Groups_Ozero__class_Ozero(_1356975))))]], 30910 ^ _780119 : [(30913 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356975), c_Groups_Ozero__class_Ozero(_1356975)), _1356981))], (30911 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356975), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979)), c_Groups_Ozero__class_Ozero(_1356975)))]]], (30903 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356975), c_Groups_Ozero__class_Ozero(_1356975)), hAPP(c_Int_Onumber__class_Onumber__of(_1356975), _1356979)))]]]]], (44952 ^ _780119) ^ [_1681073, _1681075, _1681077, _1681079, _1681081] : [-(hAPP(hAPP(c_List_Oappend(_1681073), _1681075), hAPP(hAPP(c_List_Olist_OCons(_1681073), _1681077), c_List_Olist_ONil(_1681073))) = hAPP(hAPP(c_List_Oappend(_1681073), _1681079), hAPP(hAPP(c_List_Olist_OCons(_1681073), _1681081), c_List_Olist_ONil(_1681073)))), _1681075 = _1681079, _1681077 = _1681081], (23032 ^ _780119) ^ [_1200683, _1200685, _1200687] : [class_Rings_Osemiring__1(_1200683), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200683), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1200685), _1200687)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200683), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200683), _1200685)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1200683), _1200687)))], (50454 ^ _780119) ^ [_1803279, _1803281, _1803283] : [-(c_Predicate_Oconversep(_1803279, _1803281, c_Predicate_Oconversep(_1803281, _1803279, _1803283)) = _1803283)], (50770 ^ _780119) ^ [_1809833, _1809835, _1809837] : [c_List_Olist__ex1(_1809833, _1809835, _1809837), 50774 ^ _780119 : [(50777 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1809835, 50773 ^ [_1809833, _1809835, _1809837])))], (50779 ^ _780119) ^ [_1810079] : [-(_1810079 = 50773 ^ [_1809833, _1809835, _1809837]), hBOOL(hAPP(hAPP(c_member(_1809833), _1810079), hAPP(c_List_Oset(_1809833), _1809837))), hBOOL(hAPP(_1809835, _1810079))], (50775 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1809833), 50773 ^ [_1809833, _1809835, _1809837]), hAPP(c_List_Oset(_1809833), _1809837))))]]], (7924 ^ _780119) ^ [_915040, _915042, _915044, _915046, _915048] : [class_Groups_Ominus(_915040), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915042, _915040)), _915044), _915046), _915048) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_915040), hAPP(_915044, _915048)), hAPP(_915046, _915048)))], (36049 ^ _780119) ^ [_1463583, _1463585, _1463587, _1463589, _1463591, _1463593, _1463595] : [c_Equiv__Relations_Oequiv(_1463583, _1463585, _1463587), c_Equiv__Relations_Ocongruent(_1463583, tc_fun(_1463589, tc_HOL_Obool), _1463587, _1463591), hBOOL(hAPP(hAPP(c_member(tc_fun(_1463583, tc_HOL_Obool)), _1463593), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1463583), _1463585), _1463587))), 36063 ^ _780119 : [(36066 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1463589, tc_HOL_Obool)), hAPP(_1463591, 36062 ^ [_1463583, _1463585, _1463587, _1463589, _1463591, _1463593, _1463595])), _1463595))], (36064 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1463583), 36062 ^ [_1463583, _1463585, _1463587, _1463589, _1463591, _1463593, _1463595]), _1463585)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1463589, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1463583, tc_fun(_1463589, tc_HOL_Obool)), _1463593), _1463591)), _1463595)))], (6505 ^ _780119) ^ [_885481, _885483] : [hBOOL(hAPP(hAPP(c_member(_885481), _885483), c_Orderings_Obot__class_Obot(tc_fun(_885481, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_885481, tc_HOL_Obool)), _885483)))], (21550 ^ _780119) ^ [_1173107, _1173109, _1173111] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1173107), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1173109, _1173111)), _1173111) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1173107), _1173109), _1173111))], (8436 ^ _780119) ^ [_926492, _926494] : [-(hAPP(c_Set_Oimage(_926492, _926492, c_COMBI(_926492)), _926494) = _926494)], (22990 ^ _780119) ^ [_1199958, _1199960, _1199962] : [class_Rings_Olinordered__semidom(_1199958), 22993 ^ _780119 : [(23000 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1199960), _1199962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199958), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1199958), _1199960)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1199958), _1199962))))], (22994 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199958), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1199958), _1199960)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1199958), _1199962))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1199960), _1199962)))]]], (44248 ^ _780119) ^ [_1666580, _1666582] : [hAPP(c_Code__Numeral_Oof__nat, _1666580) = hAPP(c_Code__Numeral_Oof__nat, _1666582), -(_1666580 = _1666582)], (23595 ^ _780119) ^ [_1211581, _1211583, _1211585] : [class_Orderings_Oorder(_1211581), 23598 ^ _780119 : [(23605 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211581), _1211583), _1211585))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1211581, _1211583, _1211585) = c_Orderings_Obot__class_Obot(tc_fun(_1211581, tc_HOL_Obool)))], (23599 ^ _780119) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1211581, _1211583, _1211585) = c_Orderings_Obot__class_Obot(tc_fun(_1211581, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211581), _1211583), _1211585))]]], (3062 ^ _780119) ^ [_825799, _825801] : [_825801 = _825799, -(c_Int_Oring__1__class_Oof__int(_825801) = c_Int_Oring__1__class_Oof__int(_825799))], (26947 ^ _780119) ^ [_1272916, _1272918, _1272920, _1272922, _1272924, _1272926, _1272928] : [class_Groups_Ocomm__monoid__add(_1272916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272918), _1272920)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272922), _1272924)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1272918, _1272916), hAPP(hAPP(c_COMBS(_1272918, tc_fun(_1272922, tc_HOL_Obool), _1272916), hAPP(hAPP(c_COMBB(tc_fun(_1272922, _1272916), tc_fun(tc_fun(_1272922, tc_HOL_Obool), _1272916), _1272918), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1272922, _1272916)), _1272926)), hAPP(hAPP(c_COMBB(tc_fun(_1272922, tc_HOL_Obool), tc_fun(_1272922, tc_HOL_Obool), _1272918), c_Set_OCollect(_1272922)), hAPP(hAPP(c_COMBB(tc_fun(_1272922, tc_HOL_Obool), tc_fun(_1272922, tc_HOL_Obool), _1272918), hAPP(c_COMBS(_1272922, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1272922), c_fconj), hAPP(hAPP(c_COMBC(_1272922, tc_fun(_1272922, tc_HOL_Obool), tc_HOL_Obool), c_member(_1272922)), _1272924)))), _1272928)))), _1272920) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1272922, _1272916), hAPP(hAPP(c_COMBS(_1272922, tc_fun(_1272918, tc_HOL_Obool), _1272916), hAPP(hAPP(c_COMBB(tc_fun(_1272918, _1272916), tc_fun(tc_fun(_1272918, tc_HOL_Obool), _1272916), _1272922), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1272918, _1272916)), hAPP(c_COMBC(_1272918, _1272922, _1272916), _1272926))), hAPP(hAPP(c_COMBB(tc_fun(_1272918, tc_HOL_Obool), tc_fun(_1272918, tc_HOL_Obool), _1272922), c_Set_OCollect(_1272918)), hAPP(hAPP(c_COMBB(tc_fun(_1272918, tc_HOL_Obool), tc_fun(_1272918, tc_HOL_Obool), _1272922), hAPP(c_COMBS(_1272918, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1272918), c_fconj), hAPP(hAPP(c_COMBC(_1272918, tc_fun(_1272918, tc_HOL_Obool), tc_HOL_Obool), c_member(_1272918)), _1272920)))), hAPP(c_COMBC(_1272918, _1272922, tc_HOL_Obool), _1272928))))), _1272924))], (47694 ^ _780119) ^ [_1742976, _1742978, _1742980, _1742982] : [class_Orderings_Olinorder(_1742976), c_List_Olinorder__class_Osorted(_1742976, hAPP(c_List_Orev(_1742976), _1742978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1742980), _1742982)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1742982), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742976)), _1742978))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1742976), hAPP(hAPP(c_List_Onth(_1742976), _1742978), _1742982)), hAPP(hAPP(c_List_Onth(_1742976), _1742978), _1742980))))], (36511 ^ _780119) ^ [_1472921, _1472923, _1472925, _1472927, _1472929, _1472931] : [c_Fun_Oinj__on(_1472921, _1472923, _1472925, _1472927), -(hBOOL(hAPP(hAPP(c_member(_1472923), _1472929), hAPP(c_Set_Oimage(_1472921, _1472923, _1472925), _1472927)))), -(c_Fun_Oinj__on(_1472921, _1472923, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1472921, _1472923), _1472925), _1472931), _1472929), _1472927))], (50929 ^ _780119) ^ [_1813578, _1813580] : [-(c_Lazy__Sequence_Oappend(_1813578, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1813578), _1813580) = _1813580)], (24769 ^ _780119) ^ [_1233776, _1233778, _1233780] : [class_Groups_Oordered__ab__group__add(_1233776), -(hAPP(c_Set_Oimage(_1233776, _1233776, c_Groups_Ouminus__class_Ouminus(_1233776)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1233776, _1233778), _1233780)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1233776, hAPP(c_Groups_Ouminus__class_Ouminus(_1233776), _1233780), hAPP(c_Groups_Ouminus__class_Ouminus(_1233776), _1233778)))], (32771 ^ _780119) ^ [] : [-(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)))))], (50166 ^ _780119) ^ [_1796775] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1796775))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1796775)))], (25325 ^ _780119) ^ [_1243303, _1243305] : [hBOOL(hAPP(_1243303, hAPP(c_Int_Onat, _1243305))), 25328 ^ _780119 : [(25335 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243305), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1243303, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25329 ^ _780119) ^ [_1243403] : [_1243305 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243403), -(hBOOL(hAPP(_1243303, _1243403)))]]], (46586 ^ _780119) ^ [_1719297, _1719299, _1719301, _1719303] : [hBOOL(hAPP(_1719297, _1719299)), -(hAPP(c_List_Ofilter(_1719301, _1719297), hAPP(hAPP(c_List_Olist_OCons(_1719301), _1719299), _1719303)) = hAPP(hAPP(c_List_Olist_OCons(_1719301), _1719299), hAPP(c_List_Ofilter(_1719301, _1719297), _1719303)))], (50478 ^ _780119) ^ [_1803793, _1803795] : [-(c_List_Osplice(_1803793, c_List_Olist_ONil(_1803793), _1803795) = _1803795)], (2568 ^ _780119) ^ [_818126, _818128, _818130, _818132, _818134, _818136] : [-(c_Wellfounded_Omlex__prod(_818136, _818132, _818128) = c_Wellfounded_Omlex__prod(_818134, _818130, _818126)), _818136 = _818134, _818132 = _818130, _818128 = _818126], (4504 ^ _780119) ^ [_848412, _848414] : [_848414 = _848412, -(c_HOL_Oequal__class_Oequal(_848414) = c_HOL_Oequal__class_Oequal(_848412))], (11957 ^ _780119) ^ [_995511, _995513, _995515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995511), _995513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995511), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995515), _995513))))], (42610 ^ _780119) ^ [_1623284] : [-(hAPP(c_List_Omap(_1623284, _1623284), c_Fun_Oid(_1623284)) = c_Fun_Oid(tc_List_Olist(_1623284)))], (42546 ^ _780119) ^ [_1621844, _1621846, _1621848, _1621850, _1621852, _1621854, _1621856] : [c_Fun_Oinj__on(_1621844, _1621846, _1621848, c_Orderings_Otop__class_Otop(tc_fun(_1621844, tc_HOL_Obool))), hAPP(hAPP(c_Map_Omap__of(_1621844, _1621850), _1621852), _1621854) = hAPP(c_Option_Ooption_OSome(_1621850), _1621856), -(hAPP(hAPP(c_Map_Omap__of(_1621846, _1621850), hAPP(hAPP(c_List_Omap(tc_prod(_1621844, _1621850), tc_prod(_1621846, _1621850)), hAPP(c_Product__Type_Oprod_Oprod__case(_1621844, _1621850, tc_prod(_1621846, _1621850)), hAPP(hAPP(c_COMBB(_1621846, tc_fun(_1621850, tc_prod(_1621846, _1621850)), _1621844), c_Product__Type_OPair(_1621846, _1621850)), _1621848))), _1621852)), hAPP(_1621848, _1621854)) = hAPP(c_Option_Ooption_OSome(_1621850), _1621856))], (46692 ^ _780119) ^ [_1721485, _1721487, _1721489] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721485)), hAPP(c_List_Ofilter(_1721485, _1721487), _1721489)) = 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(_1721485)), _1721489)))), hAPP(hAPP(c_COMBB(_1721485, tc_HOL_Obool, tc_Nat_Onat), _1721487), hAPP(c_List_Onth(_1721485), _1721489))))))], (51569 ^ _780119) ^ [_1820439, _1820441] : [_1820439 = _1820441, -(hBOOL(hAPP(hAPP(c_fequal, _1820439), _1820441)))], (17900 ^ _780119) ^ [_1105788, _1105790, _1105792, _1105794, _1105796] : [class_Groups_Ocomm__monoid__add(_1105788), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105790), _1105792)), 17907 ^ _780119 : [(17914 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1105790), _1105794), _1105792))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105790, _1105788), hAPP(hAPP(c_COMBC(_1105790, _1105788, _1105788), hAPP(hAPP(c_COMBS(_1105790, _1105788, tc_fun(_1105788, _1105788)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1105788, tc_fun(_1105788, _1105788)), _1105790), c_If(_1105788)), hAPP(hAPP(c_COMBC(_1105790, _1105790, tc_HOL_Obool), c_fequal), _1105794))), _1105796)), c_Groups_Ozero__class_Ozero(_1105788))), _1105792) = c_Groups_Ozero__class_Ozero(_1105788))], (17908 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1105790), _1105794), _1105792)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105790, _1105788), hAPP(hAPP(c_COMBC(_1105790, _1105788, _1105788), hAPP(hAPP(c_COMBS(_1105790, _1105788, tc_fun(_1105788, _1105788)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1105788, tc_fun(_1105788, _1105788)), _1105790), c_If(_1105788)), hAPP(hAPP(c_COMBC(_1105790, _1105790, tc_HOL_Obool), c_fequal), _1105794))), _1105796)), c_Groups_Ozero__class_Ozero(_1105788))), _1105792) = hAPP(_1105796, _1105794))]]], (46741 ^ _780119) ^ [_1722902, _1722904] : [-(c_Random_Oselect__weight(_1722902, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1722902), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1722902, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1722902, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1722902)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1722904)) = c_Random_Oselect__weight(_1722902, _1722904))], (9792 ^ _780119) ^ [_950273, _950275, _950277, _950279] : [class_Lattices_Osemilattice__inf(_950273), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950273), _950275), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950273), _950277), _950279)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950273), _950277), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950273), _950275), _950279)))], (2224 ^ _780119) ^ [_812766, _812768, _812770, _812772, _812774, _812776, _812778, _812780, _812782, _812784] : [-(c_Fun_Ooverride__on(_812784, _812780, _812776, _812772, _812768) = c_Fun_Ooverride__on(_812782, _812778, _812774, _812770, _812766)), _812784 = _812782, _812780 = _812778, _812776 = _812774, _812772 = _812770, _812768 = _812766], (49380 ^ _780119) ^ [_1779721, _1779723, _1779725] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779721, _1779721)), hAPP(hAPP(c_Product__Type_OPair(_1779721, _1779721), _1779723), _1779725)), c_List_Omeasures(_1779721, c_List_Olist_ONil(tc_fun(_1779721, tc_Nat_Onat)))))], (24251 ^ _780119) ^ [_1224199, _1224201] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1224199, _1224201)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1224201), hAPP(c_Nat_OSuc, _1224199)))], (49759 ^ _780119) ^ [_1789086, _1789088, _1789090] : [-(hBOOL(hAPP(hAPP(c_member(_1789086), _1789088), hAPP(c_List_Oset(_1789086), _1789090)))), 49760 ^ _780119 : [(49761 ^ _780119) ^ [_1789175] : [49762 ^ _780119 : [(49763 ^ _780119) ^ [_1789248] : [_1789090 = hAPP(hAPP(c_List_Oappend(_1789086), _1789175), hAPP(hAPP(c_List_Olist_OCons(_1789086), _1789088), _1789248))]], -(hBOOL(hAPP(hAPP(c_member(_1789086), _1789088), hAPP(c_List_Oset(_1789086), _1789175))))]]], (44722 ^ _780119) ^ [_1675970, _1675972] : [-(c_List_Olistrelp(_1675970, _1675972, c_List_Olist_ONil(_1675970), c_List_Olist_ONil(_1675970)))], (41645 ^ _780119) ^ [_1601387, _1601389, _1601391] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1601387, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1601387, tc_HOL_Obool), _1601389)), _1601391) = c_Orderings_Obot__class_Obot(tc_fun(_1601387, tc_HOL_Obool)), 41648 ^ _780119 : [(41649 ^ _780119) ^ [_1601522] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1601387, tc_HOL_Obool)), _1601522), _1601389)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1601387, tc_HOL_Obool)), _1601522), _1601391) = c_Orderings_Obot__class_Obot(tc_fun(_1601387, tc_HOL_Obool)))]]], (350 ^ _780119) ^ [_785534, _785536] : [-(c_Nitpick_Ounknown(_785534)), _785536 = _785534, c_Nitpick_Ounknown(_785536)], (48061 ^ _780119) ^ [_1751001, _1751003, _1751005] : [class_Orderings_Olinorder(_1751001), c_List_Olinorder__class_Osorted(_1751001, _1751003), -(c_List_Olinorder__class_Osorted(_1751001, c_List_OdropWhile(_1751001, _1751005, _1751003)))], (20906 ^ _780119) ^ [_1160325, _1160327, _1160329, _1160331] : [class_Fields_Olinordered__field(_1160325), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160325), _1160327), c_Groups_Ozero__class_Ozero(_1160325))), 20913 ^ _780119 : [(20920 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160325), _1160331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160325), _1160329), _1160327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160325), _1160329), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160325), _1160331), _1160327))))], (20914 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160325), _1160329), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160325), _1160331), _1160327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160325), _1160331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160325), _1160329), _1160327))))]]], (13927 ^ _780119) ^ [_1033570, _1033572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033570), _1033572)), -(_1033572 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1033570), 13930 ^ [_1033570, _1033572])))], (23593 ^ _780119) ^ [_1211541, _1211543] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1211541), _1211543)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1211543), _1211541))], (38166 ^ _780119) ^ [_1517256, _1517258] : [-(c_Product__Type_Omap__pair(_1517256, _1517256, _1517258, _1517258, c_Fun_Oid(_1517256), c_Fun_Oid(_1517258)) = c_Fun_Oid(tc_prod(_1517256, _1517258)))], (32237 ^ _780119) ^ [_1381391] : [class_Int_Onumber__ring(_1381391), -(c_Int_Oiszero(_1381391, hAPP(c_Int_Onumber__class_Onumber__of(_1381391), c_Int_OPls)))], (46749 ^ _780119) ^ [_1723208, _1723210] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1723208))), c_List_Otranspose(_1723208, _1723210)) = c_List_Ofoldr(tc_List_Olist(_1723208), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1723208)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1723208))), _1723210, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14434 ^ _780119) ^ [_1044709, _1044711, _1044713, _1044715] : [class_Rings_Olinordered__semidom(_1044709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044709), c_Groups_Oone__class_Oone(_1044709)), _1044711)), 14441 ^ _780119 : [(14448 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044713), _1044715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044709), hAPP(hAPP(c_Power_Opower__class_Opower(_1044709), _1044711), _1044713)), hAPP(hAPP(c_Power_Opower__class_Opower(_1044709), _1044711), _1044715))))], (14442 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044709), hAPP(hAPP(c_Power_Opower__class_Opower(_1044709), _1044711), _1044713)), hAPP(hAPP(c_Power_Opower__class_Opower(_1044709), _1044711), _1044715))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044713), _1044715)))]]], (33317 ^ _780119) ^ [_1401087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1401087)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1401087), c_Int_OMin)))], (37332 ^ _780119) ^ [_1493732] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1493732)))], (39344 ^ _780119) ^ [_1545080, _1545082, _1545084, _1545086, _1545088, _1545090, _1545092, _1545094] : [class_Groups_Ocomm__monoid__add(_1545080), c_Fun_Oinj__on(_1545082, _1545084, _1545086, _1545088), _1545090 = hAPP(c_Set_Oimage(_1545082, _1545084, _1545086), _1545088), 39358 ^ _780119 : [(39361 ^ _780119) ^ [] : [hAPP(_1545092, 39357 ^ [_1545080, _1545082, _1545084, _1545086, _1545088, _1545090, _1545092, _1545094]) = hAPP(_1545094, hAPP(_1545086, 39357 ^ [_1545080, _1545082, _1545084, _1545086, _1545088, _1545090, _1545092, _1545094]))], (39359 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1545082), 39357 ^ [_1545080, _1545082, _1545084, _1545086, _1545088, _1545090, _1545092, _1545094]), _1545088)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545084, _1545080), _1545094), _1545090) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545082, _1545080), _1545092), _1545088))], (42778 ^ _780119) ^ [] : [42780 ^ _780119 : [(42783 ^ _780119) ^ [] : [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)), 42779 ^ []))], (42781 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 42779 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))]], -(c_Com_OWT__bodies)], (50260 ^ _780119) ^ [_1798790, _1798792, _1798794] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1798790)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1798790, _1798792, _1798794)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1798790)), _1798794)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25953 ^ _780119) ^ [_1253602, _1253604] : [class_Rings_Olinordered__idom(_1253602), 25956 ^ _780119 : [(25963 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1253604), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253602), hAPP(c_Int_Oring__1__class_Oof__int(_1253602), _1253604)), c_Groups_Ozero__class_Ozero(_1253602))))], (25957 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253602), hAPP(c_Int_Oring__1__class_Oof__int(_1253602), _1253604)), c_Groups_Ozero__class_Ozero(_1253602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1253604), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (14970 ^ _780119) ^ [_1054638, _1054640] : [class_Rings_Ocomm__semiring__1(_1054638), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054638), _1054640), c_Groups_Ozero__class_Ozero(_1054638)) = _1054640)], (8018 ^ _780119) ^ [_917090, _917092, _917094] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917090, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917090, tc_HOL_Obool)), _917092), _917094)), _917094) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917090, tc_HOL_Obool)), _917092), _917094))], (37789 ^ _780119) ^ [_1505738, _1505740, _1505742, _1505744, _1505746] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1505738, _1505740), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1505738, tc_HOL_Obool)), _1505742), _1505744)), _1505746) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1505738, _1505740), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1505738, _1505740), _1505742), _1505746)), hAPP(hAPP(c_Product__Type_OSigma(_1505738, _1505740), _1505744), _1505746)))], (42391 ^ _780119) ^ [_1618160, _1618162, _1618164, _1618166, _1618168] : [-(hBOOL(hAPP(hAPP(c_member(_1618160), _1618162), c_Map_Odom(_1618160, _1618164, _1618166)))), -(hAPP(c_Map_Omap__add(_1618160, _1618164, _1618168, _1618166), _1618162) = hAPP(_1618168, _1618162))], (46091 ^ _780119) ^ [_1708389, _1708391, _1708393] : [class_Orderings_Olinorder(_1708389), -(c_Big__Operators_Olinorder__class_OMax(_1708389, hAPP(c_List_Oset(_1708389), hAPP(hAPP(c_List_Olist_OCons(_1708389), _1708391), _1708393))) = hAPP(c_List_Ofoldl(_1708389, _1708389, c_Orderings_Oord__class_Omax(_1708389), _1708391), _1708393))], (20964 ^ _780119) ^ [_1161446, _1161448, _1161450, _1161452] : [class_Fields_Olinordered__field(_1161446), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161446), _1161448), _1161450)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161446), _1161452), c_Groups_Ozero__class_Ozero(_1161446))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161446), c_Groups_Ozero__class_Ozero(_1161446)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161446), _1161448), _1161450))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161446), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161446), _1161452), _1161448)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161446), _1161452), _1161450))))], (18173 ^ _780119) ^ [_1111084, _1111086] : [class_Rings_Olinordered__idom(_1111084), 18176 ^ _780119 : [(18183 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111084), _1111086), c_Groups_Ozero__class_Ozero(_1111084))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111084), _1111086), _1111086)), c_Groups_Ozero__class_Ozero(_1111084))))], (18177 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111084), _1111086), _1111086)), c_Groups_Ozero__class_Ozero(_1111084))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111084), _1111086), c_Groups_Ozero__class_Ozero(_1111084))))]]], (45217 ^ _780119) ^ [_1686684, _1686686, _1686688, _1686690, _1686692, _1686694] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686684)), _1686686) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686688)), _1686690), -(c_Map_Omap__upds(_1686684, _1686688, _1686692, hAPP(hAPP(c_List_Oappend(_1686684), _1686686), _1686694), _1686690) = c_Map_Omap__upds(_1686684, _1686688, _1686692, _1686686, _1686690))], (7220 ^ _780119) ^ [_900328, _900330, _900332] : [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(c_Hoare__Mirabelle_OMGT, _900328)), 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), _900330), _900328), _900332)), 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), _900330), _900328), _900332)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (39457 ^ _780119) ^ [_1547606, _1547608, _1547610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547606, _1547606), tc_HOL_Obool)), _1547608), _1547610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547606, _1547606), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1547606, _1547606, _1547606), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1547606, _1547606), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1547606, _1547608)), _1547610)), _1547608)), _1547610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547606, _1547606), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1547606, _1547608)), _1547610)))], (37956 ^ _780119) ^ [_1510496, _1510498, _1510500, _1510502] : [-(_1510496 = c_Orderings_Obot__class_Obot(tc_fun(_1510498, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1510498, _1510500), _1510500, c_Product__Type_Osnd(_1510498, _1510500)), hAPP(hAPP(c_Product__Type_OSigma(_1510498, _1510500), _1510496), hAPP(c_COMBK(tc_fun(_1510500, tc_HOL_Obool), _1510498), _1510502))) = _1510502)], (39637 ^ _780119) ^ [_1552322, _1552324, _1552326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1552322, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1552322, _1552322, _1552324), _1552326)), _1552326)), -(hAPP(c_Relation_OImage(_1552322, _1552322, c_Transitive__Closure_Ortrancl(_1552322, _1552324)), _1552326) = _1552326)], (34947 ^ _780119) ^ [_1436437, _1436439, _1436441] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1436437, _1436439), _1436441)), 34950 ^ _780119 : [(34953 ^ _780119) ^ [] : [_1436439 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1436441) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34959 ^ _780119) ^ [] : [-(_1436439 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34962 ^ _780119 : [(34971 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1436439))), 34974 ^ _780119 : [(34977 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1436441)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34975 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1436439), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1436441))))]]], (34963 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1436439)), 34966 ^ _780119 : [(34969 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1436441)), _1436439)))], (34967 ^ _780119) ^ [] : [-(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), _1436441))))]]]]], (34951 ^ _780119) ^ [] : [-(_1436437 = 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), _1436441)), _1436439)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1436441)))]]], (16774 ^ _780119) ^ [_1085353] : [_1085353 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1085353), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (31855 ^ _780119) ^ [_1374115] : [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), _1374115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1374115)))], (33081 ^ _780119) ^ [_1396593] : [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, _1396593, 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, _1396593, 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))], (5442 ^ _780119) ^ [_863503, _863505, _863507, _863509] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_863509, _863505) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_863507, _863503)), _863509 = _863507, _863505 = _863503], (32517 ^ _780119) ^ [_1386271, _1386273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1386271)), c_Int_OBit0(_1386273))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1386271), _1386273)))], (42190 ^ _780119) ^ [_1613446, _1613448] : [c_Wellfounded_Owf(_1613446, _1613448), 42193 ^ _780119 : [(42194 ^ _780119) ^ [_1613578] : [42195 ^ _780119 : [(42196 ^ _780119) ^ [_1613683] : [hBOOL(hAPP(hAPP(c_member(_1613446), _1613683), _1613578))]], 42198 ^ _780119 : [(42201 ^ _780119) ^ [_1613805] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613446, _1613446)), hAPP(hAPP(c_Product__Type_OPair(_1613446, _1613446), _1613805), 42197 ^ [_1613446, _1613448, _1613578])), _1613448)), hBOOL(hAPP(hAPP(c_member(_1613446), _1613805), _1613578))], (42199 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613446), 42197 ^ [_1613446, _1613448, _1613578]), _1613578)))]]]]], (38235 ^ _780119) ^ [_1519171, _1519173] : [c_Wellfounded_OwfP(_1519171, _1519173), -(c_Wellfounded_Owf(_1519171, hAPP(c_Set_OCollect(tc_prod(_1519171, _1519171)), hAPP(c_Product__Type_Oprod_Oprod__case(_1519171, _1519171, tc_HOL_Obool), _1519173))))], (18530 ^ _780119) ^ [_1118164, _1118166] : [-(c_Option_Ooption_Ooption__size(_1118164, _1118166, c_Option_Ooption_ONone(_1118164)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48140 ^ _780119) ^ [_1752635, _1752637, _1752639, _1752641, _1752643] : [class_Groups_Omonoid__add(_1752635), 48146 ^ _780119 : [(48149 ^ _780119) ^ [] : [hBOOL(hAPP(_1752641, 48145 ^ [_1752635, _1752637, _1752639, _1752641, _1752643]))], (48151 ^ _780119) ^ [] : [hAPP(_1752643, 48145 ^ [_1752635, _1752637, _1752639, _1752641, _1752643]) = c_Groups_Ozero__class_Ozero(_1752635)], (48147 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752637), 48145 ^ [_1752635, _1752637, _1752639, _1752641, _1752643]), hAPP(c_List_Oset(_1752637), _1752639))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1752635), hAPP(hAPP(c_List_Omap(_1752637, _1752635), _1752643), hAPP(c_List_Ofilter(_1752637, _1752641), _1752639))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1752635), hAPP(hAPP(c_List_Omap(_1752637, _1752635), _1752643), _1752639)))], (25175 ^ _780119) ^ [_1240912, _1240914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1240912)), _1240914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1240912), hAPP(c_Int_Onat, _1240914))))], (32445 ^ _780119) ^ [_1385038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1385038))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1385038)))], (10418 ^ _780119) ^ [_963799, _963801, _963803, _963805, _963807, _963809, _963811, _963813] : [c_Finite__Set_Ofolding__image__simple(_963799, _963801, _963803, _963805, _963807, _963809), hBOOL(hAPP(c_Finite__Set_Ofinite(_963801), _963811)), hBOOL(hAPP(c_Finite__Set_Ofinite(_963801), _963813)), -(hAPP(hAPP(_963803, hAPP(_963809, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963801, tc_HOL_Obool)), _963811), _963813))), hAPP(_963809, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963801, tc_HOL_Obool)), _963811), _963813))) = hAPP(hAPP(_963803, hAPP(_963809, _963811)), hAPP(_963809, _963813)))], (9314 ^ _780119) ^ [_940388, _940390, _940392, _940394, _940396, _940398] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_940388, _940390, _940392, _940394, _940396), _940398)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_940388), _940396)))], (33827 ^ _780119) ^ [_1414697, _1414699] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414697), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 33830 ^ _780119 : [(33839 ^ _780119) ^ [] : [-(c_Nitpick_Onorm__frac(_1414699, _1414697) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1414699), _1414697)), 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), _1414699))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1414697)))), -(_1414699 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1414697 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33831 ^ _780119) ^ [] : [33832 ^ _780119 : [(33835 ^ _780119) ^ [] : [_1414697 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (33833 ^ _780119) ^ [] : [_1414699 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1414699, _1414697) = 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)))]]], (25293 ^ _780119) ^ [_1242763, _1242765] : [-(_1242763 = hAPP(c_Int_Onat, _1242765)), 25296 ^ _780119 : [(25299 ^ _780119) ^ [] : [_1242765 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1242763)], (25297 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242765)))]], 25300 ^ _780119 : [(25303 ^ _780119) ^ [] : [_1242763 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25301 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242765))]]], (12035 ^ _780119) ^ [_996993, _996995, _996997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996993), _996995)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996997), _996993)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996993), _996997)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996995), _996997))))], (44688 ^ _780119) ^ [_1675382, _1675384, _1675386] : [c_List_Olist_ONil(_1675382) = hAPP(hAPP(c_List_Olist_OCons(_1675382), _1675384), _1675386)], (12425 ^ _780119) ^ [_1004530, _1004532] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004530), _1004532)), _1004530 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1004532 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (11999 ^ _780119) ^ [_996342, _996344, _996346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996342), _996344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996342), _996346)), _996344)))], (44602 ^ _780119) ^ [_1673660, _1673662] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1673660)), hAPP(c_Code__Numeral_Oof__nat, _1673662)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1673660), _1673662)))], (20220 ^ _780119) ^ [_1147909, _1147911, _1147913, _1147915] : [class_Fields_Olinordered__field(_1147909), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147909), c_Groups_Ozero__class_Ozero(_1147909)), _1147911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147909), _1147913), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147909), _1147915), _1147911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147909), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147909), _1147913), _1147911)), _1147915)))], (44792 ^ _780119) ^ [_1677103, _1677105, _1677107] : [-(hAPP(hAPP(c_List_Otake(_1677103), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1677103), _1677105), _1677107)) = hAPP(hAPP(c_List_Olist_OCons(_1677103), _1677105), c_List_Olist_ONil(_1677103)))], (670 ^ _780119) ^ [_790396, _790398, _790400, _790402, _790404, _790406, _790408, _790410] : [-(c_List_Olistrelp(_790408, _790404, _790400, _790396)), c_List_Olistrelp(_790410, _790406, _790402, _790398), _790410 = _790408, _790406 = _790404, _790402 = _790400, _790398 = _790396], (44280 ^ _780119) ^ [_1667232, _1667234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1667232)), hAPP(c_Code__Numeral_Oof__nat, _1667234))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1667232), _1667234)))], (35263 ^ _780119) ^ [_1443808] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1443808)), -(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))), _1443808)), c_FunDef_Omax__weak)))], (13524 ^ _780119) ^ [_1026263, _1026265, _1026267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1026263, tc_HOL_Obool)), _1026265), _1026267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1026263, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026263, tc_HOL_Obool)), _1026267)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026263, tc_HOL_Obool)), _1026265))))], (48001 ^ _780119) ^ [_1749641, _1749643, _1749645] : [hBOOL(hAPP(hAPP(c_member(_1749641), _1749643), hAPP(c_List_Oset(_1749641), _1749645))), -(c_List_Oremdups(_1749641, hAPP(hAPP(c_List_Olist_OCons(_1749641), _1749643), _1749645)) = c_List_Oremdups(_1749641, _1749645))], (2414 ^ _780119) ^ [_815685, _815687, _815689, _815691] : [-(c_Nitpick_Onat__gcd(_815691, _815687) = c_Nitpick_Onat__gcd(_815689, _815685)), _815691 = _815689, _815687 = _815685], (12695 ^ _780119) ^ [_1010221, _1010223, _1010225, _1010227, _1010229] : [-(hBOOL(hAPP(hAPP(c_member(_1010221), _1010223), _1010225))), -(hAPP(c_Map_Orestrict__map(_1010221, _1010227, _1010229, _1010225), _1010223) = c_Option_Ooption_ONone(_1010227))], (17943 ^ _780119) ^ [_1106762, _1106764, _1106766, _1106768, _1106770] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1106762)), hAPP(c_Set_Oimage(_1106764, tc_Option_Ooption(_1106762), _1106766), c_Orderings_Otop__class_Otop(tc_fun(_1106764, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1106762)), hAPP(c_Set_Oimage(_1106764, tc_Option_Ooption(_1106762), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1106764, tc_Option_Ooption(_1106762)), _1106766), _1106768), hAPP(c_Option_Ooption_OSome(_1106762), _1106770))), c_Orderings_Otop__class_Otop(tc_fun(_1106764, tc_HOL_Obool))))))], (34867 ^ _780119) ^ [_1434690, _1434692, _1434694, _1434696, _1434698] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1434690, _1434692, _1434694), _1434696), _1434698) = hAPP(hAPP(_1434696, hAPP(c_Product__Type_Ofst(_1434690, _1434692), _1434698)), hAPP(c_Product__Type_Osnd(_1434690, _1434692), _1434698)))], (27472 ^ _780119) ^ [_1287610, _1287612, _1287614] : [27474 ^ _780119 : [(27477 ^ _780119) ^ [] : [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(_1287612, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 27473 ^ [_1287610, _1287612, _1287614]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1287612, 27473 ^ [_1287610, _1287612, _1287614])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (27475 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27473 ^ [_1287610, _1287612, _1287614]), _1287610)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1287612, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1287614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1287614), hAPP(_1287612, _1287610))), 27487 ^ _780119 : [(27490 ^ _780119) ^ [] : [-(hAPP(_1287612, 27486 ^ [_1287610, _1287612, _1287614]) = _1287614)], (27488 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27486 ^ [_1287610, _1287612, _1287614]), _1287610)))]]], (45106 ^ _780119) ^ [_1684061, _1684063, _1684065] : [_1684063 = c_List_Olist_ONil(_1684061), -(hAPP(hAPP(c_List_Oappend(_1684061), _1684063), _1684065) = _1684065)], (38659 ^ _780119) ^ [_1528987, _1528989, _1528991, _1528993, _1528995, _1528997, _1528999] : [hAPP(c_Fun_Ocomp(_1528987, _1528989, _1528991, _1528993), _1528995) = hAPP(c_Fun_Ocomp(_1528989, _1528989, _1528991, c_Fun_Oid(_1528989)), _1528997), -(hAPP(_1528993, hAPP(_1528995, _1528999)) = hAPP(_1528997, _1528999))], (14054 ^ _780119) ^ [_1036044, _1036046, _1036048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036046), _1036048)), -(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, _1036044)), _1036046)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1036044)), _1036048))))], (48132 ^ _780119) ^ [_1752398, _1752400, _1752402] : [-(c_List_OdropWhile(_1752398, _1752400, _1752402) = hAPP(hAPP(c_List_Odrop(_1752398), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752398)), c_List_OtakeWhile(_1752398, _1752400, _1752402))), _1752402))], (50554 ^ _780119) ^ [_1805678, _1805680, _1805682, _1805684] : [-(hBOOL(hAPP(hAPP(c_member(_1805678), _1805680), hAPP(c_List_Oset(_1805678), c_List_Oreplicate(_1805678, _1805682, _1805684))))), _1805680 = _1805684, -(_1805682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33165 ^ _780119) ^ [_1398252] : [-(_1398252 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 33168 ^ _780119 : [(33175 ^ _780119) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1398252, 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, _1398252) = 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), _1398252), 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)))], (33169 ^ _780119) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1398252, 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, _1398252) = 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), _1398252), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (36177 ^ _780119) ^ [_1466374, _1466376, _1466378, _1466380, _1466382, _1466384] : [c_Fun_Oinj__on(_1466374, _1466376, _1466378, _1466380), hBOOL(hAPP(hAPP(c_member(_1466374), _1466382), _1466380)), hBOOL(hAPP(hAPP(c_member(_1466374), _1466384), _1466380)), 36188 ^ _780119 : [(36195 ^ _780119) ^ [] : [_1466382 = _1466384, -(hAPP(_1466378, _1466382) = hAPP(_1466378, _1466384))], (36189 ^ _780119) ^ [] : [hAPP(_1466378, _1466382) = hAPP(_1466378, _1466384), -(_1466382 = _1466384)]]], (21709 ^ _780119) ^ [_1176297] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1176297), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13664 ^ _780119) ^ [_1028628, _1028630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028628)), _1028630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028628), _1028630)))], (39994 ^ _780119) ^ [_1560734, _1560736, _1560738, _1560740] : [-(hAPP(c_Relation_Oconverse(_1560734, _1560734), hAPP(hAPP(c_Relation_Oinv__image(_1560736, _1560734), _1560738), _1560740)) = hAPP(hAPP(c_Relation_Oinv__image(_1560736, _1560734), hAPP(c_Relation_Oconverse(_1560736, _1560736), _1560738)), _1560740))], (17580 ^ _780119) ^ [_1099691, _1099693, _1099695, _1099697] : [hAPP(c_Set_Oimage(_1099691, _1099693, _1099695), c_Orderings_Otop__class_Otop(tc_fun(_1099691, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1099693, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099693, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1099693, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1099691, _1099693, _1099695), _1099697))), hAPP(c_Set_Oimage(_1099691, _1099693, _1099695), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1099691, tc_HOL_Obool)), _1099697)))))], (9200 ^ _780119) ^ [_938125, _938127, _938129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938125, tc_HOL_Obool)), _938127), _938129)), 9203 ^ _780119 : [(9206 ^ _780119) ^ [] : [_938127 = _938129], (9204 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938125, tc_HOL_Obool)), _938127), _938129)))]]], (38302 ^ _780119) ^ [_1520354, _1520356, _1520358, _1520360] : [c_Relation_Orefl__on(_1520354, _1520356, _1520358), hBOOL(hAPP(hAPP(c_member(_1520354), _1520360), _1520356)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1520354, _1520354)), hAPP(hAPP(c_Product__Type_OPair(_1520354, _1520354), _1520360), _1520360)), _1520358)))], (26971 ^ _780119) ^ [_1274042, _1274044] : [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), _1274042)), _1274044))), _1274042 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1274044 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25307 ^ _780119) ^ [_1242987, _1242989] : [25308 ^ _780119 : [(25311 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242989))], (25309 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242987))]], 25312 ^ _780119 : [(25319 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1242987), _1242989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1242987)), hAPP(c_Int_Onat, _1242989))))], (25313 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1242987)), hAPP(c_Int_Onat, _1242989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1242987), _1242989)))]]], (32969 ^ _780119) ^ [_1394268, _1394270, _1394272] : [class_Rings_Olinordered__semidom(_1394268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394268), hAPP(hAPP(c_Power_Opower__class_Opower(_1394268), _1394270), 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(_1394268), _1394272), 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(_1394268), c_Groups_Ozero__class_Ozero(_1394268)), _1394272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394268), _1394270), _1394272)))], (22410 ^ _780119) ^ [_1189159, _1189161] : [class_Rings_Olinordered__idom(_1189159), 22413 ^ _780119 : [(22420 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189159), c_Groups_Ozero__class_Ozero(_1189159)), _1189161)), -(c_Groups_Osgn__class_Osgn(_1189159, _1189161) = c_Groups_Oone__class_Oone(_1189159))], (22414 ^ _780119) ^ [] : [c_Groups_Osgn__class_Osgn(_1189159, _1189161) = c_Groups_Oone__class_Oone(_1189159), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189159), c_Groups_Ozero__class_Ozero(_1189159)), _1189161)))]]], (39416 ^ _780119) ^ [_1546840, _1546842] : [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), _1546840), _1546842)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1546840), _1546842)))], (8144 ^ _780119) ^ [_919944, _919946, _919948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919944, tc_HOL_Obool)), _919946), _919948)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_919944, tc_HOL_Obool)), _919946), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919944, tc_HOL_Obool)), _919948), _919946)) = _919948)], (39984 ^ _780119) ^ [_1560510, _1560512] : [c_Wellfounded_Oacyclic(_1560510, _1560512), -(c_Wellfounded_Oacyclic(_1560510, hAPP(c_Relation_Oconverse(_1560510, _1560510), _1560512)))], (51339 ^ _780119) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (14650 ^ _780119) ^ [_1048944, _1048946, _1048948, _1048950, _1048952] : [class_Groups_Ocomm__monoid__mult(_1048944), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048946), _1048948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1048946, tc_HOL_Obool)), _1048950), _1048948)), 14664 ^ _780119 : [(14667 ^ _780119) ^ [] : [hAPP(_1048952, 14663 ^ [_1048944, _1048946, _1048948, _1048950, _1048952]) = c_Groups_Oone__class_Oone(_1048944)], (14665 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1048946), 14663 ^ [_1048944, _1048946, _1048948, _1048950, _1048952]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048946, tc_HOL_Obool)), _1048948), _1048950))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1048946, _1048944), _1048952), _1048948) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1048946, _1048944), _1048952), _1048950))], (16468 ^ _780119) ^ [_1080175, _1080177] : [class_Groups_Olinordered__ab__group__add(_1080175), 16471 ^ _780119 : [(16478 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080175), c_Groups_Ozero__class_Ozero(_1080175)), _1080177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080175), hAPP(c_Groups_Ouminus__class_Ouminus(_1080175), _1080177)), _1080177)))], (16472 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080175), hAPP(c_Groups_Ouminus__class_Ouminus(_1080175), _1080177)), _1080177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080175), c_Groups_Ozero__class_Ozero(_1080175)), _1080177)))]]], (46861 ^ _780119) ^ [_1725369, _1725371] : [46862 ^ _780119 : [(46865 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1725371), _1725369))], (46863 ^ _780119) ^ [] : [_1725371 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1725369, _1725371) = c_List_Olist_ONil(tc_Nat_Onat))], (30093 ^ _780119) ^ [_1342563, _1342565, _1342567] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1342563, _1342565, _1342567))), -(hBOOL(hAPP(c_Com_OWT, _1342567)))], (16070 ^ _780119) ^ [_1072967, _1072969, _1072971, _1072973] : [class_Rings_Olinordered__ring__strict(_1072967), 16073 ^ _780119 : [(16088 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072967), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072967), _1072969), _1072971)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072967), _1072969), _1072973)))), 16089 ^ _780119 : [(16096 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072967), _1072969), c_Groups_Ozero__class_Ozero(_1072967))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072967), _1072973), _1072971))], (16090 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072967), c_Groups_Ozero__class_Ozero(_1072967)), _1072969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072967), _1072971), _1072973))]]], (16074 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072967), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072967), _1072969), _1072971)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072967), _1072969), _1072973))), 16079 ^ _780119 : [(16082 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072967), _1072971), _1072973)))], (16080 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072967), c_Groups_Ozero__class_Ozero(_1072967)), _1072969)))]], 16083 ^ _780119 : [(16086 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072967), _1072973), _1072971)))], (16084 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072967), _1072969), c_Groups_Ozero__class_Ozero(_1072967))))]]]]], (50448 ^ _780119) ^ [_1803166, _1803168, _1803170, _1803172, _1803174] : [hBOOL(hAPP(hAPP(_1803170, _1803174), _1803172)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1803166, _1803168, _1803170), _1803172), _1803174)))], (50858 ^ _780119) ^ [_1811689, _1811691, _1811693, _1811695] : [class_Groups_Ocomm__monoid__add(_1811689), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1811691, tc_HOL_Obool)), _1811693)), 50868 ^ _780119 : [(50871 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1811691), 50867 ^ [_1811689, _1811691, _1811693, _1811695]))], (50869 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1811691, tc_HOL_Obool)), 50867 ^ [_1811689, _1811691, _1811693, _1811695]), _1811693)))]], 50875 ^ _780119 : [(50886 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1811691), 50882 ^ [_1811689, _1811691, _1811693, _1811695]), 50877 ^ [_1811689, _1811691, _1811693, _1811695])))], (50881 ^ _780119) ^ [] : [50874 ^ [_1811689, _1811691, _1811693, _1811695] = 50877 ^ [_1811689, _1811691, _1811693, _1811695]], (50884 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1811691), 50882 ^ [_1811689, _1811691, _1811693, _1811695]), 50874 ^ [_1811689, _1811691, _1811693, _1811695])))], (50888 ^ _780119) ^ [] : [hAPP(_1811695, 50882 ^ [_1811689, _1811691, _1811693, _1811695]) = c_Groups_Ozero__class_Ozero(_1811689)], (50876 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1811691, tc_HOL_Obool)), 50874 ^ [_1811689, _1811691, _1811693, _1811695]), _1811693)))], (50879 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1811691, tc_HOL_Obool)), 50877 ^ [_1811689, _1811691, _1811693, _1811695]), _1811693)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1811691, _1811689), _1811695), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1811691, tc_HOL_Obool), _1811693)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1811691, tc_HOL_Obool), _1811689), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1811691, _1811689), _1811695)), _1811693))], (16452 ^ _780119) ^ [_1079901, _1079903] : [class_Groups_Oordered__ab__group__add(_1079901), 16455 ^ _780119 : [(16462 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079901), c_Groups_Ozero__class_Ozero(_1079901)), _1079903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079901), hAPP(c_Groups_Ouminus__class_Ouminus(_1079901), _1079903)), c_Groups_Ozero__class_Ozero(_1079901))))], (16456 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079901), hAPP(c_Groups_Ouminus__class_Ouminus(_1079901), _1079903)), c_Groups_Ozero__class_Ozero(_1079901))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079901), c_Groups_Ozero__class_Ozero(_1079901)), _1079903)))]]], (42353 ^ _780119) ^ [_1617433, _1617435, _1617437, _1617439, _1617441] : [-(hAPP(c_Map_Omap__add(_1617433, _1617435, _1617437, _1617439), _1617441) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1617435), _1617435, hAPP(_1617437, _1617441), c_Option_Ooption_OSome(_1617435)), hAPP(_1617439, _1617441)))], (23159 ^ _780119) ^ [_1203122, _1203124, _1203126, _1203128] : [class_Rings_Osemiring__1(_1203122), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1203124, _1203122), hAPP(c_COMBK(_1203122, _1203124), _1203126)), _1203128) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1203122), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203122), hAPP(c_Finite__Set_Ocard(_1203124), _1203128))), _1203126))], (45458 ^ _780119) ^ [_1693652, _1693654, _1693656, _1693658] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693652), tc_List_Olist(_1693652))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693652), tc_List_Olist(_1693652)), _1693654), _1693656)), c_List_Olistrel1(_1693652, _1693658))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693652), tc_List_Olist(_1693652))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693652), tc_List_Olist(_1693652)), _1693654), _1693656)), c_List_Olistrel(_1693652, c_Transitive__Closure_Ortrancl(_1693652, _1693658)))))], (12611 ^ _780119) ^ [_1008804, _1008806] : [hAPP(c_Option_Ooption_OSome(_1008804), _1008806) = c_Option_Ooption_ONone(_1008804)], (43809 ^ _780119) ^ [_1655333, _1655335, _1655337, _1655339, _1655341] : [class_Groups_Ocomm__monoid__add(_1655333), hBOOL(hAPP(hAPP(c_member(_1655335), _1655337), hAPP(c_List_Oset(_1655335), _1655339))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1655333), hAPP(hAPP(c_List_Omap(_1655335, _1655333), _1655341), _1655339)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655333), hAPP(_1655341, _1655337)), hAPP(c_List_Omonoid__add__class_Olistsum(_1655333), hAPP(hAPP(c_List_Omap(_1655335, _1655333), _1655341), c_List_Oremove1(_1655335, _1655337, _1655339)))))], (45500 ^ _780119) ^ [_1694897, _1694899, _1694901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1694897, _1694897), tc_HOL_Obool)), _1694899), _1694901)), c_Relation_Orefl__on(_1694897, c_Orderings_Otop__class_Otop(tc_fun(_1694897, tc_HOL_Obool)), _1694901), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1694897), tc_List_Olist(_1694897)), tc_HOL_Obool)), c_List_Olistrel1(_1694897, _1694899)), c_List_Olistrel(_1694897, _1694901))))], (50208 ^ _780119) ^ [_1797514, _1797516] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1797514)), c_Int_OBit1(_1797516))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1797514), _1797516)))], (29893 ^ _780119) ^ [_1337935, _1337937, _1337939, _1337941, _1337943] : [_1337935 = c_Orderings_Obot__class_Obot(tc_fun(_1337937, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337937, tc_fun(_1337939, tc_HOL_Obool)), _1337935), hAPP(hAPP(c_COMBC(_1337937, tc_fun(_1337939, tc_HOL_Obool), tc_fun(_1337939, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1337939, tc_HOL_Obool), tc_fun(tc_fun(_1337939, tc_HOL_Obool), tc_fun(_1337939, tc_HOL_Obool)), _1337937), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337939, tc_HOL_Obool))), _1337941)), _1337943)) = c_Orderings_Obot__class_Obot(tc_fun(_1337939, tc_HOL_Obool)))], (18462 ^ _780119) ^ [_1116948, _1116950, _1116952] : [class_Rings_Oring__1(_1116948), hBOOL(hAPP(hAPP(c_member(_1116948), _1116950), c_Int_Oring__1__class_OInts(_1116948))), hBOOL(hAPP(hAPP(c_member(_1116948), _1116952), c_Int_Oring__1__class_OInts(_1116948))), -(hBOOL(hAPP(hAPP(c_member(_1116948), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116948), _1116950), _1116952)), c_Int_Oring__1__class_OInts(_1116948))))], (10216 ^ _780119) ^ [_958871, _958873, _958875, _958877] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958871, tc_HOL_Obool)), _958873), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958871, tc_HOL_Obool)), _958875), _958877)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958871, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958871, tc_HOL_Obool)), _958873), _958875)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958871, tc_HOL_Obool)), _958873), _958877)))], (35428 ^ _780119) ^ [_1448439, _1448441, _1448443, _1448445] : [-(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), _1448439), _1448441)), 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), _1448443), _1448445)), 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), _1448439), _1448443)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1448441), _1448445))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1448439), _1448445)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1448441), _1448443)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (17742 ^ _780119) ^ [_1102654, _1102656, _1102658] : [17743 ^ _780119 : [(17746 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102656), _1102658))], (17744 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102654)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102654), _1102656)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102654), _1102658))))], (6647 ^ _780119) ^ [_888547, _888549, _888551, _888553] : [6651 ^ _780119 : [(6654 ^ _780119) ^ [] : [hBOOL(hAPP(_888553, 6650 ^ [_888547, _888549, _888551, _888553]))], (6652 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_888547), 6650 ^ [_888547, _888549, _888551, _888553]), _888549)))]], 6656 ^ _780119 : [(6659 ^ _780119) ^ [] : [hBOOL(hAPP(_888553, 6655 ^ [_888547, _888549, _888551, _888553]))], (6657 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_888547), 6655 ^ [_888547, _888549, _888551, _888553]), _888551)))]], 6660 ^ _780119 : [(6661 ^ _780119) ^ [_888880] : [hBOOL(hAPP(hAPP(c_member(_888547), _888880), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888547, tc_HOL_Obool)), _888549), _888551))), -(hBOOL(hAPP(_888553, _888880)))]]], (37769 ^ _780119) ^ [_1505058, _1505060, _1505062, _1505064] : [37770 ^ _780119 : [(37773 ^ _780119) ^ [] : [_1505064 = c_Orderings_Obot__class_Obot(tc_fun(_1505060, tc_HOL_Obool))], (37771 ^ _780119) ^ [] : [_1505062 = c_Orderings_Obot__class_Obot(tc_fun(_1505058, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1505058, _1505060), _1505062), hAPP(c_COMBK(tc_fun(_1505060, tc_HOL_Obool), _1505058), _1505064)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1505058, _1505060), tc_HOL_Obool)))], (47089 ^ _780119) ^ [_1729106, _1729108, _1729110] : [class_Orderings_Olinorder(_1729106), 47092 ^ _780119 : [(47105 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1729106, hAPP(hAPP(c_List_Olist_OCons(_1729106), _1729108), _1729110))), c_List_Olinorder__class_Osorted(_1729106, _1729110), 47111 ^ _780119 : [(47114 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1729106), _1729108), 47110 ^ [_1729106, _1729108, _1729110]))], (47112 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1729106), 47110 ^ [_1729106, _1729108, _1729110]), hAPP(c_List_Oset(_1729106), _1729110))))]]], (47093 ^ _780119) ^ [] : [c_List_Olinorder__class_Osorted(_1729106, hAPP(hAPP(c_List_Olist_OCons(_1729106), _1729108), _1729110)), 47096 ^ _780119 : [(47099 ^ _780119) ^ [_1729292] : [hBOOL(hAPP(hAPP(c_member(_1729106), _1729292), hAPP(c_List_Oset(_1729106), _1729110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1729106), _1729108), _1729292)))], (47097 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1729106, _1729110))]]]]], (9816 ^ _780119) ^ [_950827, _950829, _950831] : [class_Lattices_Olattice(_950827), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950827), _950829), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950827), _950829), _950831)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950827), _950829), _950831))], (13616 ^ _780119) ^ [_1027853, _1027855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027853)), hAPP(c_Nat_OSuc, _1027855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027853), _1027855)))], (1360 ^ _780119) ^ [_799843, _799845] : [-(class_Orderings_Obot(_799843)), _799845 = _799843, class_Orderings_Obot(_799845)], (44622 ^ _780119) ^ [_1674124, _1674126, _1674128, _1674130] : [_1674126 = c_List_Olist_ONil(_1674124), -(hAPP(hAPP(c_List_Olist__update(_1674124, _1674126), _1674128), _1674130) = c_List_Olist_ONil(_1674124))], (42598 ^ _780119) ^ [_1623057, _1623059, _1623061, _1623063, _1623065] : [hAPP(hAPP(c_List_Omap(_1623057, _1623059), _1623061), _1623063) = hAPP(hAPP(c_List_Omap(_1623057, _1623059), _1623061), _1623065), c_Fun_Oinj__on(_1623057, _1623059, _1623061, c_Orderings_Otop__class_Otop(tc_fun(_1623057, tc_HOL_Obool))), -(_1623063 = _1623065)], (33663 ^ _780119) ^ [_1411118, _1411120, _1411122, _1411124, _1411126, _1411128] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1411118, _1411120), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1411122), _1411124))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1411118, _1411120), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1411126), _1411128))), -(_1411120 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1411124 = _1411128)], (41894 ^ _780119) ^ [_1606748] : [class_Complete__Lattice_Ocomplete__lattice(_1606748), -(c_Complete__Lattice_OInf__class_OInf(_1606748, c_Orderings_Otop__class_Otop(tc_fun(_1606748, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1606748))], (1400 ^ _780119) ^ [_800343, _800345] : [-(class_Smallcheck_Osmall(_800343)), _800345 = _800343, class_Smallcheck_Osmall(_800345)], (51033 ^ _780119) ^ [_1814941, _1814943] : [class_Groups_Ominus(_1814941), -(class_Groups_Ominus(tc_fun(_1814943, _1814941)))], (21616 ^ _780119) ^ [_1174673, _1174675, _1174677] : [-(hAPP(c_Set_OPow(_1174673), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1174673, tc_HOL_Obool)), _1174675), _1174677)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1174673, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1174673), _1174675)), hAPP(c_Set_OPow(_1174673), _1174677)))], (18454 ^ _780119) ^ [_1116796, _1116798, _1116800] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116796), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1116798), _1116800)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116796), _1116798)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116796), _1116800)))], (11371 ^ _780119) ^ [_983428, _983430, _983432, _983434, _983436, _983438] : [class_Rings_Oordered__ring(_983428), 11374 ^ _780119 : [(11381 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983428), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_983428), _983430), _983436)), _983432)), _983434)), _983438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983428), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983428), _983430), _983432)), _983434)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983428), _983436), _983432)), _983438))))], (11375 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983428), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983428), _983430), _983432)), _983434)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983428), _983436), _983432)), _983438))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983428), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_983428), _983430), _983436)), _983432)), _983434)), _983438)))]]], (40848 ^ _780119) ^ [_1581107, _1581109, _1581111] : [class_Lattices_Olattice(_1581107), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581107), _1581109)), -(hBOOL(hAPP(hAPP(c_member(_1581107), _1581111), _1581109))), -(c_Big__Operators_Olattice__class_OSup__fin(_1581107, hAPP(hAPP(c_Set_Oinsert(_1581107), _1581111), _1581109)) = hAPP(hAPP(c_Finite__Set_Ofold(_1581107, _1581107, c_Lattices_Osemilattice__sup__class_Osup(_1581107)), _1581111), _1581109))], (13907 ^ _780119) ^ [_1033007, _1033009] : [_1033009 = c_Orderings_Obot__class_Obot(tc_fun(_1033007, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033007, tc_HOL_Obool)), _1033009), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033007, tc_HOL_Obool)), _1033009))))], (13168 ^ _780119) ^ [_1019991, _1019993] : [hAPP(c_Nat_OSuc, _1019991) = hAPP(c_Nat_OSuc, _1019993), -(_1019991 = _1019993)], (22272 ^ _780119) ^ [_1186532, _1186534] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186532), _1186534))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186532, _1186534) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1186532), _1186534), _1186534))], (46725 ^ _780119) ^ [_1722370, _1722372, _1722374, _1722376, _1722378, _1722380] : [hAPP(hAPP(c_Map_Omap__of(_1722370, _1722372), _1722374), _1722376) = hAPP(c_Option_Ooption_OSome(_1722372), _1722378), hBOOL(hAPP(hAPP(_1722380, _1722376), _1722378)), -(hAPP(hAPP(c_Map_Omap__of(_1722370, _1722372), hAPP(c_List_Ofilter(tc_prod(_1722370, _1722372), hAPP(c_Product__Type_Oprod_Oprod__case(_1722370, _1722372, tc_HOL_Obool), _1722380)), _1722374)), _1722376) = hAPP(c_Option_Ooption_OSome(_1722372), _1722378))], (36499 ^ _780119) ^ [_1472608, _1472610, _1472612, _1472614, _1472616] : [c_Fun_Oinj__on(_1472608, _1472610, _1472612, c_Orderings_Otop__class_Otop(tc_fun(_1472608, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1472608, _1472610, _1472612), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472608, tc_HOL_Obool)), _1472614), _1472616)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472610, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1472608, _1472610, _1472612), _1472614)), hAPP(c_Set_Oimage(_1472608, _1472610, _1472612), _1472616)))], (14184 ^ _780119) ^ [_1039123, _1039125, _1039127, _1039129] : [class_Groups_Ocomm__monoid__mult(_1039123), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039125), _1039127)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1039125, _1039123), _1039129), _1039127) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1039123, _1039125, c_Groups_Otimes__class_Otimes(_1039123)), _1039129), c_Groups_Oone__class_Oone(_1039123)), _1039127))], (47780 ^ _780119) ^ [_1745354, _1745356] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1745354), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1745354))), _1745356))), -(c_List_Otranspose(_1745354, c_List_Otranspose(_1745354, _1745356)) = c_List_OtakeWhile(tc_List_Olist(_1745354), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1745354)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1745354), tc_List_Olist(_1745354), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1745354))), _1745356))], (25650 ^ _780119) ^ [_1248678, _1248680] : [c_Nat__Transfer_Ois__nat(_1248678), c_Nat__Transfer_Ois__nat(_1248680), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1248678, _1248680)))], (1590 ^ _780119) ^ [_802718, _802720] : [-(class_Rings_Ono__zero__divisors(_802718)), _802720 = _802718, class_Rings_Ono__zero__divisors(_802720)], (41236 ^ _780119) ^ [_1589766, _1589768, _1589770, _1589772, _1589774] : [-(_1589766 = c_Orderings_Obot__class_Obot(tc_fun(_1589768, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589770, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589768, tc_fun(_1589770, tc_HOL_Obool)), _1589766), _1589772)), _1589774) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589768, tc_fun(_1589770, tc_HOL_Obool)), _1589766), hAPP(hAPP(c_COMBC(_1589768, tc_fun(_1589770, tc_HOL_Obool), tc_fun(_1589770, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1589770, tc_HOL_Obool), tc_fun(tc_fun(_1589770, tc_HOL_Obool), tc_fun(_1589770, tc_HOL_Obool)), _1589768), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589770, tc_HOL_Obool))), _1589772)), _1589774)))], (16138 ^ _780119) ^ [_1074209, _1074211, _1074213] : [class_Rings_Olinordered__semiring__strict(_1074209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074209), c_Groups_Ozero__class_Ozero(_1074209)), _1074211)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074209), _1074213), c_Groups_Ozero__class_Ozero(_1074209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074209), _1074211), _1074213)), c_Groups_Ozero__class_Ozero(_1074209))))], (16666 ^ _780119) ^ [_1083506] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1083506, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1083506, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1083506, tc_HOL_Obool)))], (23549 ^ _780119) ^ [_1210655, _1210657, _1210659, _1210661, _1210663] : [class_Orderings_Olinorder(_1210655), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1210655, _1210657), _1210659) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1210655, _1210661), _1210663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210655), _1210657), _1210659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210655), _1210661), _1210663)), -(_1210659 = _1210663)], (3028 ^ _780119) ^ [_825272, _825274, _825276, _825278, _825280, _825282] : [-(c_Nitpick_Otimes__frac(_825282, _825278, _825274) = c_Nitpick_Otimes__frac(_825280, _825276, _825272)), _825282 = _825280, _825278 = _825276, _825274 = _825272], (47786 ^ _780119) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (9570 ^ _780119) ^ [_945217, _945219, _945221, _945223] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_945217), _945219)), -(hAPP(c_Set_Oimage(_945217, _945221, _945223), _945219) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_945221, tc_HOL_Obool), _945217, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945221, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_945217, tc_fun(_945221, tc_HOL_Obool), tc_fun(_945221, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_945221, tc_fun(tc_fun(_945221, tc_HOL_Obool), tc_fun(_945221, tc_HOL_Obool)), _945217), c_Set_Oinsert(_945221)), _945223)), c_Orderings_Obot__class_Obot(tc_fun(_945221, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_945221, tc_HOL_Obool))), _945219))], (34156 ^ _780119) ^ [_1421541, _1421543] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1421541, _1421541)), hAPP(hAPP(c_Product__Type_OPair(_1421541, _1421541), 34157 ^ [_1421541, _1421543]), 34157 ^ [_1421541, _1421543])), _1421543)), -(c_Nitpick_Orefl_H(_1421541, _1421543))], (38124 ^ _780119) ^ [_1516091, _1516093, _1516095, _1516097, _1516099] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516091, _1516093)), _1516095), hAPP(hAPP(c_Product__Type_OSigma(_1516091, _1516093), _1516097), _1516099))), 38128 ^ _780119 : [(38132 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1516093), 38130 ^ [_1516091, _1516093, _1516095, _1516097, _1516099]), hAPP(_1516099, 38127 ^ [_1516091, _1516093, _1516095, _1516097, _1516099]))))], (38134 ^ _780119) ^ [] : [-(_1516095 = hAPP(hAPP(c_Product__Type_OPair(_1516091, _1516093), 38127 ^ [_1516091, _1516093, _1516095, _1516097, _1516099]), 38130 ^ [_1516091, _1516093, _1516095, _1516097, _1516099]))], (38129 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1516091), 38127 ^ [_1516091, _1516093, _1516095, _1516097, _1516099]), _1516097)))]]], (22877 ^ _780119) ^ [_1197894, _1197896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197894)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197896))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1197894), _1197896)))], (26999 ^ _780119) ^ [_1274736, _1274738, _1274740, _1274742, _1274744, _1274746] : [class_Groups_Ocomm__monoid__add(_1274736), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274738), _1274740)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1274738, _1274736), _1274742), _1274740) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1274744, _1274736), hAPP(hAPP(c_COMBB(tc_fun(_1274738, tc_HOL_Obool), _1274736, _1274744), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1274738, _1274736), _1274742)), hAPP(hAPP(c_COMBB(tc_fun(_1274738, tc_HOL_Obool), tc_fun(_1274738, tc_HOL_Obool), _1274744), c_Set_OCollect(_1274738)), hAPP(hAPP(c_COMBB(tc_fun(_1274738, tc_HOL_Obool), tc_fun(_1274738, tc_HOL_Obool), _1274744), hAPP(c_COMBS(_1274738, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1274738), c_fconj), hAPP(hAPP(c_COMBC(_1274738, tc_fun(_1274738, tc_HOL_Obool), tc_HOL_Obool), c_member(_1274738)), _1274740)))), hAPP(c_COMBC(_1274738, _1274744, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1274744, tc_fun(_1274744, tc_HOL_Obool), _1274738), c_fequal), _1274746)))))), hAPP(c_Set_Oimage(_1274738, _1274744, _1274746), _1274740)))], (35927 ^ _780119) ^ [_1460397, _1460399, _1460401, _1460403, _1460405, _1460407, _1460409, _1460411] : [c_Equiv__Relations_Oequiv(_1460397, _1460399, _1460401), c_Equiv__Relations_Ocongruent2(_1460397, _1460403, _1460405, _1460401, _1460407, _1460409), hBOOL(hAPP(hAPP(c_member(_1460397), _1460411), _1460399)), -(c_Equiv__Relations_Ocongruent(_1460403, _1460405, _1460407, hAPP(_1460409, _1460411)))], (45046 ^ _780119) ^ [_1683014, _1683016, _1683018] : [_1683014 = hAPP(hAPP(c_List_Oappend(_1683016), _1683014), _1683018), -(_1683018 = c_List_Olist_ONil(_1683016))], (31767 ^ _780119) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28510 ^ _780119) ^ [_1306979, _1306981, _1306983] : [class_Orderings_Olinorder(_1306979), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306979), _1306981)), -(_1306981 = c_Orderings_Obot__class_Obot(tc_fun(_1306979, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306979), _1306983)), -(_1306983 = c_Orderings_Obot__class_Obot(tc_fun(_1306979, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1306979, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306979, tc_HOL_Obool)), _1306981), _1306983)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306979), c_Big__Operators_Olinorder__class_OMax(_1306979, _1306981)), c_Big__Operators_Olinorder__class_OMax(_1306979, _1306983)))], (44650 ^ _780119) ^ [_1674643, _1674645, _1674647, _1674649] : [hAPP(hAPP(c_List_Omap(_1674643, _1674645), _1674647), _1674649) = c_List_Olist_ONil(_1674645), -(_1674649 = c_List_Olist_ONil(_1674643))], (26683 ^ _780119) ^ [_1267432, _1267434, _1267436] : [class_Rings_Olinordered__idom(_1267432), 26686 ^ _780119 : [(26695 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267432), hAPP(c_Groups_Oabs__class_Oabs(_1267432), _1267434)), _1267436))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267432), _1267434), _1267436)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267432), hAPP(c_Groups_Ouminus__class_Ouminus(_1267432), _1267434)), _1267436))], (26687 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267432), hAPP(c_Groups_Oabs__class_Oabs(_1267432), _1267434)), _1267436)), 26690 ^ _780119 : [(26693 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267432), hAPP(c_Groups_Ouminus__class_Ouminus(_1267432), _1267434)), _1267436)))], (26691 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267432), _1267434), _1267436)))]]]]], (18342 ^ _780119) ^ [_1114704, _1114706, _1114708] : [-(hAPP(c_Finite__Set_Ocard(_1114704), _1114706) = hAPP(c_Nat_OSuc, _1114708)), 18343 ^ _780119 : [(18344 ^ _780119) ^ [_1114804, _1114806] : [_1114706 = hAPP(hAPP(c_Set_Oinsert(_1114704), _1114806), _1114804), -(hBOOL(hAPP(hAPP(c_member(_1114704), _1114806), _1114804))), hAPP(c_Finite__Set_Ocard(_1114704), _1114804) = _1114708, 18355 ^ _780119 : [(18358 ^ _780119) ^ [] : [_1114804 = c_Orderings_Obot__class_Obot(tc_fun(_1114704, tc_HOL_Obool))], (18356 ^ _780119) ^ [] : [-(_1114708 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (15376 ^ _780119) ^ [_1060597, _1060599, _1060601] : [15377 ^ _780119 : [(15380 ^ _780119) ^ [] : [_1060599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15378 ^ _780119) ^ [] : [_1060597 = _1060601]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060597), _1060599) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060601), _1060599))], (18111 ^ _780119) ^ [_1109991, _1109993] : [_1109991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109991), _1109993) = _1109993)], (32559 ^ _780119) ^ [_1387067] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1387067))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1387067)))))], (51323 ^ _780119) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (14296 ^ _780119) ^ [_1041443, _1041445] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041443), hAPP(c_Nat_OSuc, _1041445)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041443), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1041445))], (47228 ^ _780119) ^ [_1731796, _1731798, _1731800, _1731802] : [class_Groups_Ocomm__monoid__add(_1731796), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1731796), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1731796), _1731798), c_List_Oupt(_1731800, _1731802))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1731796), _1731798), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1731800, _1731802))))], (51397 ^ _780119) ^ [_1818503, _1818505] : [-(class_HOL_Oequal(tc_Nitpick_Opair__box(_1818503, _1818505)))], (44508 ^ _780119) ^ [_1671824, _1671826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1671824), _1671826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1671824)), hAPP(c_Code__Numeral_Onat__of, _1671826))))], (2434 ^ _780119) ^ [_815983, _815985, _815987, _815989] : [-(c_Divides_Odivmod__int(_815989, _815985) = c_Divides_Odivmod__int(_815987, _815983)), _815989 = _815987, _815985 = _815983], (24045 ^ _780119) ^ [_1220088, _1220090, _1220092, _1220094] : [class_Groups_Ocomm__monoid__add(_1220088), 24048 ^ _780119 : [(24055 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220090)), _1220092))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220088), _1220094), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220092, hAPP(c_Nat_OSuc, _1220090))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220088), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220088), _1220094), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220092, _1220090))), hAPP(_1220094, hAPP(c_Nat_OSuc, _1220090))))], (24049 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220090)), _1220092)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220088), _1220094), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220092, hAPP(c_Nat_OSuc, _1220090))) = c_Groups_Ozero__class_Ozero(_1220088))]]], (16881 ^ _780119) ^ [_1086954, _1086956] : [class_Rings_Ocomm__semiring__1(_1086954), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1086954), _1086956), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1086954))], (23763 ^ _780119) ^ [_1214247, _1214249, _1214251, _1214253] : [class_Groups_Ocomm__monoid__add(_1214247), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214247), _1214249), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1214251)), hAPP(c_Nat_OSuc, _1214253))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214247), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1214247, tc_Nat_Onat), _1214249), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1214251), _1214253)))], (22247 ^ _780119) ^ [_1186103, _1186105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186105, _1186103)), _1186103)))], (27019 ^ _780119) ^ [_1275526, _1275528] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1275526))), -(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)), _1275526))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1275528)))) = 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)), _1275526))), 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, _1275528))))))], (23260 ^ _780119) ^ [_1205107, _1205109, _1205111, _1205113, _1205115, _1205117] : [hBOOL(hAPP(hAPP(c_member(_1205107), _1205109), c_SetInterval_Oord_OgreaterThanAtMost(_1205107, _1205111, _1205113, _1205115, _1205117))), 23263 ^ _780119 : [(23266 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1205111, _1205109), _1205117)))], (23264 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1205113, _1205115), _1205109)))]]], (18688 ^ _780119) ^ [_1120890, _1120892, _1120894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120890), _1120892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120890), _1120894)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120892), _1120894))))], (14820 ^ _780119) ^ [_1052175] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1052175)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1052175), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052175), c_Orderings_Otop__class_Otop(tc_fun(_1052175, tc_HOL_Obool)))))], (14252 ^ _780119) ^ [_1040432, _1040434, _1040436, _1040438, _1040440] : [class_Groups_Ocomm__monoid__mult(_1040432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040434), _1040436)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040434), _1040438)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040434, tc_HOL_Obool)), _1040436), _1040438) = c_Orderings_Obot__class_Obot(tc_fun(_1040434, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1040434, _1040432), _1040440), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040434, tc_HOL_Obool)), _1040436), _1040438)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040432), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1040434, _1040432), _1040440), _1040436)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1040434, _1040432), _1040440), _1040438)))], (37723 ^ _780119) ^ [_1503922, _1503924, _1503926, _1503928, _1503930, _1503932] : [hBOOL(hAPP(hAPP(c_member(_1503922), _1503924), _1503926)), hBOOL(hAPP(hAPP(c_member(_1503928), _1503930), hAPP(_1503932, _1503924))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1503922, _1503928)), hAPP(hAPP(c_Product__Type_OPair(_1503922, _1503928), _1503924), _1503930)), hAPP(hAPP(c_Product__Type_OSigma(_1503922, _1503928), _1503926), _1503932))))], (34597 ^ _780119) ^ [_1429461, _1429463, _1429465] : [-(hAPP(c_Product__Type_Osnd(_1429461, _1429463), _1429465) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1429461, _1429463, _1429463), hAPP(c_COMBK(tc_fun(_1429463, _1429463), _1429461), c_COMBI(_1429463))), _1429465))], (5536 ^ _780119) ^ [_864948, _864950] : [_864950 = _864948, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_864950) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_864948))], (40904 ^ _780119) ^ [_1581963, _1581965, _1581967, _1581969, _1581971, _1581973] : [c_Finite__Set_Ofun__left__comm(_1581963, _1581965, _1581967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581963), _1581969)), hBOOL(hAPP(hAPP(c_member(_1581963), _1581971), _1581969)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1581963, _1581965, _1581967), _1581973), _1581969) = hAPP(hAPP(_1581967, _1581971), hAPP(hAPP(c_Finite__Set_Ofold(_1581963, _1581965, _1581967), _1581973), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1581963, tc_HOL_Obool)), _1581969), hAPP(hAPP(c_Set_Oinsert(_1581963), _1581971), c_Orderings_Obot__class_Obot(tc_fun(_1581963, tc_HOL_Obool)))))))], (26479 ^ _780119) ^ [_1263321, _1263323, _1263325] : [hBOOL(hAPP(_1263325, _1263323)), -(hBOOL(hAPP(hAPP(c_member(_1263321), _1263323), hAPP(c_Set_OCollect(_1263321), _1263325))))], (46929 ^ _780119) ^ [_1726578, _1726580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726578), _1726580)), -(c_List_Oupt(_1726578, _1726580) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1726578), c_List_Oupt(hAPP(c_Nat_OSuc, _1726578), _1726580)))], (23406 ^ _780119) ^ [_1207838, _1207840, _1207842] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207838), _1207840))), 23409 ^ _780119 : [(23416 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207842), _1207840))), -(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)), _1207838)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207842), _1207840)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23410 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207842), _1207840)), -(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)), _1207838)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207842), _1207840)) = 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))))]]], (43353 ^ _780119) ^ [_1641734, _1641736, _1641738, _1641740, _1641742] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641734)), _1641736) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641738)), _1641740), 43356 ^ _780119 : [(43364 ^ _780119) ^ [] : [43365 ^ _780119 : [(43366 ^ _780119) ^ [_1642026] : [hAPP(hAPP(c_Map_Omap__of(_1641734, _1641738), hAPP(hAPP(c_List_Ozip(_1641734, _1641738), _1641736), _1641740)), _1641742) = hAPP(c_Option_Ooption_OSome(_1641738), _1642026)]], -(hBOOL(hAPP(hAPP(c_member(_1641734), _1641742), hAPP(c_List_Oset(_1641734), _1641736))))], (43357 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1641734), _1641742), hAPP(c_List_Oset(_1641734), _1641736))), -(hAPP(hAPP(c_Map_Omap__of(_1641734, _1641738), hAPP(hAPP(c_List_Ozip(_1641734, _1641738), _1641736), _1641740)), _1641742) = hAPP(c_Option_Ooption_OSome(_1641738), 43360 ^ [_1641734, _1641736, _1641738, _1641740, _1641742]))]]], (39759 ^ _780119) ^ [_1555236, _1555238, _1555240, _1555242] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1555236, _1555236)), hAPP(hAPP(c_Product__Type_OPair(_1555236, _1555236), _1555238), _1555240)), c_Transitive__Closure_Ortrancl(_1555236, _1555242))), -(_1555238 = _1555240), 39766 ^ _780119 : [(39769 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1555236, _1555236)), hAPP(hAPP(c_Product__Type_OPair(_1555236, _1555236), _1555238), _1555240)), c_Transitive__Closure_Otrancl(_1555236, _1555242))))], (39767 ^ _780119) ^ [] : [_1555238 = _1555240]]], (6218 ^ _780119) ^ [_879590, _879592, _879594, _879596, _879598] : [hAPP(hAPP(c_Set_Oinsert(_879590), _879592), hAPP(hAPP(c_Set_Oinsert(_879590), _879594), c_Orderings_Obot__class_Obot(tc_fun(_879590, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_879590), _879596), hAPP(hAPP(c_Set_Oinsert(_879590), _879598), c_Orderings_Obot__class_Obot(tc_fun(_879590, tc_HOL_Obool)))), 6223 ^ _780119 : [(6226 ^ _780119) ^ [] : [-(_879594 = _879598)], (6224 ^ _780119) ^ [] : [-(_879592 = _879596)]], 6227 ^ _780119 : [(6230 ^ _780119) ^ [] : [-(_879594 = _879596)], (6228 ^ _780119) ^ [] : [-(_879592 = _879598)]]], (15232 ^ _780119) ^ [_1058577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1058577), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8278 ^ _780119) ^ [_922945, _922947, _922949, _922951, _922953] : [class_Groups_Oordered__ab__group__add(_922945), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_922945), _922947), _922949) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_922945), _922951), _922953), 8285 ^ _780119 : [(8292 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922945), _922951), _922953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922945), _922947), _922949)))], (8286 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922945), _922947), _922949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922945), _922951), _922953)))]]], (37082 ^ _780119) ^ [_1487250, _1487252, _1487254] : [hBOOL(hAPP(hAPP(c_member(_1487250), _1487252), c_Wellfounded_Oacc(_1487250, _1487254))), 37085 ^ _780119 : [(37086 ^ _780119) ^ [_1487364] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1487250, _1487250)), hAPP(hAPP(c_Product__Type_OPair(_1487250, _1487250), _1487364), _1487252)), _1487254)), -(hBOOL(hAPP(hAPP(c_member(_1487250), _1487364), c_Wellfounded_Oacc(_1487250, _1487254))))]]], (16284 ^ _780119) ^ [_1076927, _1076929, _1076931, _1076933] : [class_Rings_Olinordered__ring__strict(_1076927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076927), _1076929), _1076931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076927), _1076933), c_Groups_Ozero__class_Ozero(_1076927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076927), _1076931), _1076933)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076927), _1076929), _1076933))))], (9112 ^ _780119) ^ [_936580, _936582, _936584, _936586] : [class_Orderings_Opreorder(_936580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936580), _936582), _936584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936580), _936584), _936586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936580), _936582), _936586)))], (17049 ^ _780119) ^ [_1089805, _1089807] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1089805), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089805), _1089807)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50582 ^ _780119) ^ [_1806271, _1806273, _1806275, _1806277] : [50590 ^ _780119 : [(50593 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1806277, 50589 ^ [_1806271, _1806273, _1806275, _1806277])))], (50591 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806271), 50589 ^ [_1806271, _1806273, _1806275, _1806277]), hAPP(c_List_Oset(_1806271), c_List_Oreplicate(_1806271, _1806273, _1806275)))))]], hBOOL(hAPP(_1806277, _1806275)), -(_1806273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29378 ^ _780119) ^ [_1325135, _1325137, _1325139] : [class_Orderings_Olinorder(_1325135), hAPP(_1325137, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1325135), 29383 ^ [_1325135, _1325137, _1325139]), 29384 ^ [_1325135, _1325137, _1325139])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1325135), hAPP(_1325137, 29383 ^ [_1325135, _1325137, _1325139])), hAPP(_1325137, 29384 ^ [_1325135, _1325137, _1325139])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325135), _1325139)), -(_1325139 = c_Orderings_Obot__class_Obot(tc_fun(_1325135, tc_HOL_Obool))), -(hAPP(_1325137, c_Big__Operators_Olinorder__class_OMax(_1325135, _1325139)) = c_Big__Operators_Olinorder__class_OMax(_1325135, hAPP(c_Set_Oimage(_1325135, _1325135, _1325137), _1325139)))], (37686 ^ _780119) ^ [_1502370, _1502372, _1502374, _1502376, _1502378] : [-(hAPP(c_Relation_ODomain(_1502370, _1502372), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1502370, _1502372)), hAPP(hAPP(c_Product__Type_OPair(_1502370, _1502372), _1502374), _1502376)), _1502378)) = hAPP(hAPP(c_Set_Oinsert(_1502370), _1502374), hAPP(c_Relation_ODomain(_1502370, _1502372), _1502378)))], (16344 ^ _780119) ^ [_1078031, _1078033] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078031, tc_HOL_Obool)), _1078033), c_Orderings_Otop__class_Otop(tc_fun(_1078031, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1078031, tc_HOL_Obool)))], (9804 ^ _780119) ^ [_950559, _950561, _950563, _950565] : [class_Lattices_Osemilattice__inf(_950559), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950559), _950561), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950559), _950563), _950565)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950559), _950563), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950559), _950561), _950565)))], (38595 ^ _780119) ^ [_1527304, _1527306, _1527308] : [38597 ^ _780119 : [(38600 ^ _780119) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1527304, hAPP(c_Nat_OSuc, _1527308), 38596 ^ [_1527304, _1527306, _1527308])], (38598 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1527304)), 38596 ^ [_1527304, _1527306, _1527308]), _1527306)))]], 38601 ^ _780119 : [(38602 ^ _780119) ^ [_1527477] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1527304)), _1527477), _1527306)), -(c_Hoare__Mirabelle_Otriple__valid(_1527304, _1527308, _1527477))]]], (45818 ^ _780119) ^ [_1703161, _1703163, _1703165] : [-(hAPP(c_List_Ohd(_1703161), hAPP(hAPP(c_List_Olist_OCons(_1703161), _1703163), _1703165)) = _1703163)], (25211 ^ _780119) ^ [_1241551, _1241553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241551)), 25214 ^ _780119 : [(25221 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241551), _1241553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1241551)), hAPP(c_Int_Onat, _1241553))))], (25215 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1241551)), hAPP(c_Int_Onat, _1241553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241551), _1241553)))]]], (6200 ^ _780119) ^ [_879185, _879187, _879189, _879191, _879193] : [-(hBOOL(hAPP(hAPP(c_member(_879185), _879187), hAPP(c_Set_Oimage(_879189, _879185, _879191), _879193)))), 6201 ^ _780119 : [(6202 ^ _780119) ^ [_879255] : [hBOOL(hAPP(hAPP(c_member(_879189), _879255), _879193)), _879187 = hAPP(_879191, _879255)]]], (13222 ^ _780119) ^ [_1020823, _1020825, _1020827] : [class_Groups_Ogroup__add(_1020823), 13225 ^ _780119 : [(13232 ^ _780119) ^ [] : [_1020827 = hAPP(c_Groups_Ouminus__class_Ouminus(_1020823), _1020825), -(_1020825 = hAPP(c_Groups_Ouminus__class_Ouminus(_1020823), _1020827))], (13226 ^ _780119) ^ [] : [_1020825 = hAPP(c_Groups_Ouminus__class_Ouminus(_1020823), _1020827), -(_1020827 = hAPP(c_Groups_Ouminus__class_Ouminus(_1020823), _1020825))]]], (14996 ^ _780119) ^ [_1055000, _1055002, _1055004] : [class_Rings_Ono__zero__divisors(_1055000), -(_1055002 = c_Groups_Ozero__class_Ozero(_1055000)), -(_1055004 = c_Groups_Ozero__class_Ozero(_1055000)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055000), _1055002), _1055004) = c_Groups_Ozero__class_Ozero(_1055000)], (6725 ^ _780119) ^ [_890297, _890299, _890301, _890303] : [6726 ^ _780119 : [(6729 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890297), _890299), _890303))], (6727 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890297), _890299), _890301))]], -(hBOOL(hAPP(hAPP(c_member(_890297), _890299), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890297, tc_HOL_Obool)), _890301), _890303))))], (50910 ^ _780119) ^ [_1813170, _1813172] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1813170)), _1813172)), 50914 ^ _780119 : [(50915 ^ _780119) ^ [_1813271] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1813170)), _1813271), _1813172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1813170)), _1813271)), 50913 ^ [_1813170, _1813172])))]]], (18616 ^ _780119) ^ [_1119695, _1119697] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1119695, _1119697)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1119697)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31487 ^ _780119) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (46897 ^ _780119) ^ [_1726025, _1726027, _1726029, _1726031] : [class_Orderings_Olinorder(_1726025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726025), _1726027), _1726029)), c_List_Olinorder__class_Osorted(_1726025, hAPP(hAPP(c_List_Olist_OCons(_1726025), _1726029), _1726031)), -(c_List_Olinorder__class_Osorted(_1726025, hAPP(hAPP(c_List_Olist_OCons(_1726025), _1726027), hAPP(hAPP(c_List_Olist_OCons(_1726025), _1726029), _1726031))))], (20390 ^ _780119) ^ [_1151124, _1151126, _1151128] : [class_Fields_Olinordered__field(_1151124), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151124), _1151126), c_Groups_Ozero__class_Ozero(_1151124))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151124), c_Groups_Ozero__class_Ozero(_1151124)), _1151128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151124), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151124), _1151126), _1151128)), c_Groups_Ozero__class_Ozero(_1151124))))], (43711 ^ _780119) ^ [_1652725, _1652727, _1652729] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1652725, tc_HOL_Obool)), hAPP(c_List_Oset(_1652725), c_List_Osublist(_1652725, _1652727, _1652729))), hAPP(c_List_Oset(_1652725), _1652727))))], (41764 ^ _780119) ^ [_1603706, _1603708, _1603710] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1603706, tc_HOL_Obool)), _1603708), _1603710)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1603706, tc_HOL_Obool)), _1603708), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1603706, tc_HOL_Obool), _1603710))))], (10432 ^ _780119) ^ [_964147, _964149, _964151, _964153] : [hBOOL(hAPP(hAPP(c_member(_964147), _964149), _964151)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964147, tc_Nat_Onat), _964153), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964147, tc_HOL_Obool)), _964151), hAPP(hAPP(c_Set_Oinsert(_964147), _964149), c_Orderings_Obot__class_Obot(tc_fun(_964147, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964147, tc_Nat_Onat), _964153), _964151)), hAPP(_964153, _964149)))], (13286 ^ _780119) ^ [_1021891, _1021893, _1021895, _1021897] : [class_Groups_Ouminus(_1021891), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021893, _1021891)), _1021895), _1021897) = hAPP(c_Groups_Ouminus__class_Ouminus(_1021891), hAPP(_1021895, _1021897)))], (44696 ^ _780119) ^ [_1675512, _1675514, _1675516] : [-(hAPP(hAPP(c_List_Ozip(_1675512, _1675514), _1675516), c_List_Olist_ONil(_1675514)) = c_List_Olist_ONil(tc_prod(_1675512, _1675514)))], (6889 ^ _780119) ^ [_894002, _894004, _894006] : [class_Orderings_Opreorder(_894002), _894004 = _894006, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894002), _894004), _894006)))], (11824 ^ _780119) ^ [_992866, _992868] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _992866), _992868) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _992868), _992866))], (44634 ^ _780119) ^ [_1674350, _1674352, _1674354, _1674356] : [-(c_Map_Omap__upds(_1674350, _1674352, _1674354, c_List_Olist_ONil(_1674350), _1674356) = _1674354)], (33045 ^ _780119) ^ [_1395804, _1395806, _1395808] : [class_Rings_Olinordered__idom(_1395804), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395804), c_Groups_Ozero__class_Ozero(_1395804)), hAPP(hAPP(c_Power_Opower__class_Opower(_1395804), _1395806), 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)))), _1395808)))))], (23388 ^ _780119) ^ [_1207476, _1207478, _1207480] : [class_Rings_Osemiring__1(_1207476), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1207476, _1207478, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1207480) = _1207480)], (16975 ^ _780119) ^ [_1088465, _1088467] : [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), _1088465), _1088467))), 16978 ^ _780119 : [(16981 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1088467)))], (16979 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1088465)))]]], (50636 ^ _780119) ^ [_1807196, _1807198, _1807200, _1807202, _1807204] : [c_List_Oreplicate(_1807196, _1807198, _1807200) = c_List_Oreplicate(_1807196, _1807202, _1807204), 50639 ^ _780119 : [(50642 ^ _780119) ^ [] : [-(_1807198 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1807200 = _1807204)], (50640 ^ _780119) ^ [] : [-(_1807198 = _1807202)]]], (25071 ^ _780119) ^ [_1239289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239289), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1239289) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5751 ^ _780119) ^ [_871098, _871100] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871098, _871100, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871098), tc_HOL_Obool))))], (28190 ^ _780119) ^ [_1301168, _1301170] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1301168)), hAPP(c_Nat_OSuc, _1301170)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1301168), _1301170)))], (12435 ^ _780119) ^ [_1004673] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1004673) = _1004673)], (2528 ^ _780119) ^ [_817506, _817508] : [_817508 = _817506, -(c_Nat_Osemiring__1__class_ONats(_817508) = c_Nat_Osemiring__1__class_ONats(_817506))], (1904 ^ _780119) ^ [_807576, _807578, _807580, _807582, _807584, _807586] : [-(c_Partial__Function_Oflat__lub(_807586, _807582, _807578) = c_Partial__Function_Oflat__lub(_807584, _807580, _807576)), _807586 = _807584, _807582 = _807580, _807578 = _807576], (50692 ^ _780119) ^ [_1808200, _1808202, _1808204] : [-(_1808200 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1808202), c_List_Oreplicate(_1808202, _1808200, _1808204)) = hAPP(hAPP(c_Set_Oinsert(_1808202), _1808204), c_Orderings_Obot__class_Obot(tc_fun(_1808202, tc_HOL_Obool))))], (40986 ^ _780119) ^ [_1583678, _1583680, _1583682, _1583684, _1583686] : [c_Finite__Set_Ofun__left__comm(_1583678, _1583680, _1583682), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583678), _1583684)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1583678, _1583680, _1583682, _1583686, _1583684), hAPP(hAPP(c_Finite__Set_Ofold(_1583678, _1583680, _1583682), _1583686), _1583684))))], (45962 ^ _780119) ^ [_1705657, _1705659, _1705661] : [-(hAPP(c_List_Orotate(_1705657, _1705659), _1705661) = hAPP(hAPP(c_List_Oappend(_1705657), hAPP(hAPP(c_List_Odrop(_1705657), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1705659, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705657)), _1705661))), _1705661)), hAPP(hAPP(c_List_Otake(_1705657), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1705659, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705657)), _1705661))), _1705661)))], (18706 ^ _780119) ^ [_1121290, _1121292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121290), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121292), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121290), _1121292))), -(_1121290 = _1121292)], (32023 ^ _780119) ^ [_1376921, _1376923, _1376925] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376921), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376921)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376923)), _1376925)) = 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), _1376921), _1376923))), _1376925))], (8764 ^ _780119) ^ [_931519, _931521, _931523, _931525] : [class_Orderings_Oorder(_931519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931519), _931521), _931523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931519), _931525), _931521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931519), _931525), _931523)))], (44736 ^ _780119) ^ [_1676231, _1676233] : [c_Orderings_Obot__class_Obot(tc_fun(_1676231, tc_HOL_Obool)) = hAPP(c_List_Oset(_1676231), _1676233), -(_1676233 = c_List_Olist_ONil(_1676231))], (6232 ^ _780119) ^ [_879852, _879854, _879856, _879858, _879860] : [-(hAPP(hAPP(c_Set_Oinsert(_879852), _879854), hAPP(hAPP(c_Set_Oinsert(_879852), _879856), c_Orderings_Obot__class_Obot(tc_fun(_879852, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_879852), _879858), hAPP(hAPP(c_Set_Oinsert(_879852), _879860), c_Orderings_Obot__class_Obot(tc_fun(_879852, tc_HOL_Obool))))), 6233 ^ _780119 : [(6240 ^ _780119) ^ [] : [_879854 = _879860, _879856 = _879858], (6234 ^ _780119) ^ [] : [_879854 = _879858, _879856 = _879860]]], (42461 ^ _780119) ^ [_1619595, _1619597, _1619599, _1619601] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1619595)), hAPP(c_Set_Oimage(_1619597, tc_Option_Ooption(_1619595), _1619599), c_Orderings_Otop__class_Otop(tc_fun(_1619597, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1619595)), hAPP(c_Set_Oimage(_1619597, tc_Option_Ooption(_1619595), c_Map_Omap__add(_1619597, _1619595, _1619599, hAPP(c_Map_Omap__of(_1619597, _1619595), _1619601))), c_Orderings_Otop__class_Otop(tc_fun(_1619597, tc_HOL_Obool))))))], (21560 ^ _780119) ^ [_1173344, _1173346] : [-(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, _1173344, _1173346)), _1173346) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1173344), _1173346))], (29234 ^ _780119) ^ [_1321993, _1321995, _1321997] : [class_Orderings_Olinorder(_1321993), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321993), _1321995)), hBOOL(hAPP(hAPP(c_member(_1321993), _1321997), _1321995)), 29245 ^ _780119 : [(29252 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321993, tc_HOL_Obool)), _1321995), hAPP(hAPP(c_Set_Oinsert(_1321993), _1321997), c_Orderings_Obot__class_Obot(tc_fun(_1321993, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1321993, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1321993, c_Orderings_Oord__class_Omax(_1321993), _1321995) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1321993), _1321997), c_Big__Operators_Olattice_OSup__fin(_1321993, c_Orderings_Oord__class_Omax(_1321993), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321993, tc_HOL_Obool)), _1321995), hAPP(hAPP(c_Set_Oinsert(_1321993), _1321997), c_Orderings_Obot__class_Obot(tc_fun(_1321993, tc_HOL_Obool)))))))], (29246 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321993, tc_HOL_Obool)), _1321995), hAPP(hAPP(c_Set_Oinsert(_1321993), _1321997), c_Orderings_Obot__class_Obot(tc_fun(_1321993, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1321993, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1321993, c_Orderings_Oord__class_Omax(_1321993), _1321995) = _1321997)]]], (39996 ^ _780119) ^ [_1560811, _1560813, _1560815] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560811, _1560813)), hAPP(c_Relation_Oconverse(_1560813, _1560811), _1560815))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560813, _1560811)), _1560815)))], (37643 ^ _780119) ^ [_1501374, _1501376, _1501378] : [hAPP(c_Relation_ODomain(_1501374, _1501376), _1501378) = c_Orderings_Obot__class_Obot(tc_fun(_1501374, tc_HOL_Obool)), -(_1501378 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501374, _1501376), tc_HOL_Obool)))], (15254 ^ _780119) ^ [_1058846] : [-(_1058846 = 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)), _1058846)))], (44136 ^ _780119) ^ [_1663190, _1663192, _1663194, _1663196] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663190), tc_List_Olist(_1663190))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663190), tc_List_Olist(_1663190)), _1663192), _1663194)), c_List_Olex(_1663190, _1663196))), 44139 ^ _780119 : [(44142 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663190)), _1663192) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663190)), _1663194))], (44140 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663190), tc_List_Olist(_1663190))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663190), tc_List_Olist(_1663190)), _1663192), _1663194)), c_List_Olexord(_1663190, _1663196))))]]], (1580 ^ _780119) ^ [_802593, _802595] : [-(class_Rings_Oordered__semiring(_802593)), _802595 = _802593, class_Rings_Oordered__semiring(_802595)], (8654 ^ _780119) ^ [_929798, _929800, _929802] : [class_Orderings_Oorder(_929798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929798), _929800), _929802)), _929800 = _929802], (16410 ^ _780119) ^ [_1079172, _1079174] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1079172), c_Orderings_Otop__class_Otop(tc_fun(_1079172, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1079172), _1079174) = hAPP(c_Finite__Set_Ocard(_1079172), c_Orderings_Otop__class_Otop(tc_fun(_1079172, tc_HOL_Obool))), -(_1079174 = c_Orderings_Otop__class_Otop(tc_fun(_1079172, tc_HOL_Obool)))], (51299 ^ _780119) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (27570 ^ _780119) ^ [_1289529, _1289531, _1289533] : [class_Orderings_Olinorder(_1289529), 27573 ^ _780119 : [(27580 ^ _780119) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289529), _1289531), _1289533) = _1289533, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289529), _1289531), _1289533)))], (27574 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289529), _1289531), _1289533)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289529), _1289531), _1289533) = _1289533)]]], (37211 ^ _780119) ^ [_1491536, _1491538, _1491540, _1491542] : [c_Wellfounded_Owf(_1491536, _1491538), c_Wellfounded_Owf(_1491540, _1491542), -(c_Wellfounded_Owf(tc_prod(_1491536, _1491540), c_Wellfounded_Olex__prod(_1491536, _1491540, _1491538, _1491542)))], (51551 ^ _780119) ^ [_1820099] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1820099)))], (46511 ^ _780119) ^ [_1717610, _1717612, _1717614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1717610), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717612)), _1717614))), -(hAPP(hAPP(c_List_Otake(_1717612), _1717610), c_List_Obutlast(_1717612, _1717614)) = hAPP(hAPP(c_List_Otake(_1717612), _1717610), _1717614))], (47118 ^ _780119) ^ [_1729631, _1729633, _1729635] : [class_Orderings_Olinorder(_1729631), 47121 ^ _780119 : [(47140 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1729631, hAPP(hAPP(c_List_Oappend(_1729631), _1729633), _1729635))), c_List_Olinorder__class_Osorted(_1729631, _1729633), c_List_Olinorder__class_Osorted(_1729631, _1729635), 47150 ^ _780119 : [(47154 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1729631), 47152 ^ [_1729631, _1729633, _1729635]), hAPP(c_List_Oset(_1729631), _1729635))))], (47156 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1729631), 47149 ^ [_1729631, _1729633, _1729635]), 47152 ^ [_1729631, _1729633, _1729635]))], (47151 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1729631), 47149 ^ [_1729631, _1729633, _1729635]), hAPP(c_List_Oset(_1729631), _1729633))))]]], (47122 ^ _780119) ^ [] : [c_List_Olinorder__class_Osorted(_1729631, hAPP(hAPP(c_List_Oappend(_1729631), _1729633), _1729635)), 47125 ^ _780119 : [(47128 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1729631, _1729635))], (47130 ^ _780119) ^ [_1729867] : [hBOOL(hAPP(hAPP(c_member(_1729631), _1729867), hAPP(c_List_Oset(_1729631), _1729633))), 47133 ^ _780119 : [(47134 ^ _780119) ^ [_1729977] : [hBOOL(hAPP(hAPP(c_member(_1729631), _1729977), hAPP(c_List_Oset(_1729631), _1729635))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1729631), _1729867), _1729977)))]]], (47126 ^ _780119) ^ [] : [-(c_List_Olinorder__class_Osorted(_1729631, _1729633))]]]]], (26125 ^ _780119) ^ [_1256539] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1256539) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1256539))], (37759 ^ _780119) ^ [_1504896, _1504898, _1504900, _1504902] : [hAPP(hAPP(c_Product__Type_OSigma(_1504896, _1504898), _1504900), hAPP(c_COMBK(tc_fun(_1504898, tc_HOL_Obool), _1504896), _1504902)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1504896, _1504898), tc_HOL_Obool)), -(_1504900 = c_Orderings_Obot__class_Obot(tc_fun(_1504896, tc_HOL_Obool))), -(_1504902 = c_Orderings_Obot__class_Obot(tc_fun(_1504898, tc_HOL_Obool)))], (34821 ^ _780119) ^ [_1433811, _1433813, _1433815, _1433817] : [_1433811 = _1433813, 34824 ^ _780119 : [(34827 ^ _780119) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1433815, _1433817), _1433811) = hAPP(c_Product__Type_Osnd(_1433815, _1433817), _1433813))], (34825 ^ _780119) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1433815, _1433817), _1433811) = hAPP(c_Product__Type_Ofst(_1433815, _1433817), _1433813))]]], (4134 ^ _780119) ^ [_842621, _842623] : [_842623 = _842621, -(c_Option_Ooption_ONone(_842623) = c_Option_Ooption_ONone(_842621))], (3996 ^ _780119) ^ [_840492, _840494] : [_840494 = _840492, -(c_List_Oembed__list(_840494) = c_List_Oembed__list(_840492))], (27774 ^ _780119) ^ [_1293036, _1293038, _1293040, _1293042] : [class_Orderings_Olinorder(_1293036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293036), _1293038), _1293040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293036), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293036), _1293038), _1293042)), _1293040)))], (14294 ^ _780119) ^ [_1041399, _1041401] : [-(c_Map_Oran(_1041399, _1041401, hAPP(c_COMBK(tc_Option_Ooption(_1041401), _1041399), c_Option_Ooption_ONone(_1041401))) = c_Orderings_Obot__class_Obot(tc_fun(_1041401, tc_HOL_Obool)))], (28884 ^ _780119) ^ [_1315514, _1315516] : [class_Orderings_Olinorder(_1315514), -(c_Big__Operators_Olattice_OSup__fin(_1315514, c_Orderings_Oord__class_Omax(_1315514), hAPP(hAPP(c_Set_Oinsert(_1315514), _1315516), c_Orderings_Obot__class_Obot(tc_fun(_1315514, tc_HOL_Obool)))) = _1315516)], (37581 ^ _780119) ^ [_1499631, _1499633, _1499635, _1499637] : [hBOOL(hAPP(c_Predicate_ORangeP(_1499631, _1499633, hAPP(hAPP(c_COMBC(_1499631, tc_fun(tc_prod(_1499631, _1499633), tc_HOL_Obool), tc_fun(_1499633, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499633, tc_fun(tc_fun(tc_prod(_1499631, _1499633), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499631, _1499633), tc_HOL_Obool), tc_fun(_1499633, tc_HOL_Obool)), _1499631), c_COMBC(_1499633, tc_fun(tc_prod(_1499631, _1499633), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499633, tc_prod(_1499631, _1499633)), tc_fun(_1499633, tc_fun(tc_fun(tc_prod(_1499631, _1499633), tc_HOL_Obool), tc_HOL_Obool)), _1499631), hAPP(c_COMBB(tc_prod(_1499631, _1499633), tc_fun(tc_fun(tc_prod(_1499631, _1499633), tc_HOL_Obool), tc_HOL_Obool), _1499633), c_member(tc_prod(_1499631, _1499633)))), c_Product__Type_OPair(_1499631, _1499633)))), _1499635)), _1499637)), -(hBOOL(hAPP(hAPP(c_member(_1499633), _1499637), hAPP(c_Relation_ORange(_1499631, _1499633), _1499635))))], (46240 ^ _780119) ^ [_1712121, _1712123] : [-(c_List_Olists(_1712121, _1712123) = hAPP(c_Set_OCollect(tc_List_Olist(_1712121)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1712121), tc_fun(_1712121, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1712121, tc_HOL_Obool), tc_fun(tc_fun(_1712121, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1712121)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1712121, tc_HOL_Obool))), c_List_Oset(_1712121))), _1712123)))], (42994 ^ _780119) ^ [_1632394, _1632396, _1632398] : [hBOOL(hAPP(c_List_Odistinct(_1632394), _1632396)), -(hBOOL(hAPP(c_List_Odistinct(_1632394), c_List_Oremove1(_1632394, _1632398, _1632396))))], (45249 ^ _780119) ^ [_1687584, _1687586, _1687588, _1687590] : [hBOOL(hAPP(hAPP(c_member(_1687584), _1687586), hAPP(c_List_Oset(_1687584), _1687588))), -(c_List_Oremove1(_1687584, _1687586, hAPP(hAPP(c_List_Oappend(_1687584), _1687588), _1687590)) = hAPP(hAPP(c_List_Oappend(_1687584), c_List_Oremove1(_1687584, _1687586, _1687588)), _1687590))], (45928 ^ _780119) ^ [_1704936, _1704938, _1704940] : [-(hAPP(c_List_Orotate1(_1704936), hAPP(c_List_Orotate(_1704936, _1704938), _1704940)) = hAPP(c_List_Orotate(_1704936, _1704938), hAPP(c_List_Orotate1(_1704936), _1704940)))], (18648 ^ _780119) ^ [_1120328] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1120328) = _1120328)], (50963 ^ _780119) ^ [_1814022, _1814024] : [class_Lattices_Olattice(_1814022), -(class_Lattices_Osemilattice__inf(tc_fun(_1814024, _1814022)))], (49382 ^ _780119) ^ [_1779775, _1779777] : [-(c_List_Omeasures(_1779775, _1779777) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1779775), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1779775, tc_List_Olist(tc_fun(_1779775, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779775, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1779775, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1779775), c_List_Omap(tc_fun(_1779775, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1779775, tc_Nat_Onat), _1779775, tc_Nat_Onat), c_COMBI(tc_fun(_1779775, tc_Nat_Onat))))), _1779777)))], (6747 ^ _780119) ^ [_890785, _890787] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890785, tc_HOL_Obool)), _890787), c_Orderings_Obot__class_Obot(tc_fun(_890785, tc_HOL_Obool))) = _890787)], (48134 ^ _780119) ^ [_1752448, _1752450, _1752452, _1752454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752448), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752450)), c_List_OdropWhile(_1752450, _1752452, _1752454)))), -(hAPP(hAPP(c_List_Onth(_1752450), c_List_OdropWhile(_1752450, _1752452, _1752454)), _1752448) = hAPP(hAPP(c_List_Onth(_1752450), _1752454), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1752448), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752450)), c_List_OtakeWhile(_1752450, _1752452, _1752454)))))], (41854 ^ _780119) ^ [_1605935] : [class_Complete__Lattice_Ocomplete__lattice(_1605935), -(c_Complete__Lattice_OSup__class_OSup(_1605935, c_Orderings_Obot__class_Obot(tc_fun(_1605935, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1605935))], (35582 ^ _780119) ^ [_1452440, _1452442, _1452444] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1452440), hAPP(hAPP(c_Set_Oinsert(_1452440), _1452442), c_Orderings_Obot__class_Obot(tc_fun(_1452440, tc_HOL_Obool)))), _1452444) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1452440, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1452440, _1452440, _1452444), hAPP(hAPP(c_Set_Oinsert(_1452440), _1452442), c_Orderings_Obot__class_Obot(tc_fun(_1452440, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1452440, tc_HOL_Obool), tc_HOL_Obool))))], (27586 ^ _780119) ^ [_1289785, _1289787, _1289789, _1289791] : [class_Orderings_Olinorder(_1289785), 27589 ^ _780119 : [(27598 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289785), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289785), _1289787), _1289789)), _1289791))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289785), _1289787), _1289791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289785), _1289789), _1289791))], (27590 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289785), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289785), _1289787), _1289789)), _1289791)), 27593 ^ _780119 : [(27596 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289785), _1289789), _1289791)))], (27594 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289785), _1289787), _1289791)))]]]]], (9354 ^ _780119) ^ [_941030, _941032, _941034, _941036, _941038, _941040, _941042] : [-(hBOOL(hAPP(hAPP(c_member(_941030), _941032), _941034))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_941030, _941036, _941038, _941040, _941034), _941042)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_941030, _941036, _941038, _941040, hAPP(hAPP(c_Set_Oinsert(_941030), _941032), _941034)), hAPP(hAPP(_941038, _941032), _941042))))], (19891 ^ _780119) ^ [_1141717, _1141719, _1141721] : [-(_1141717 = 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), _1141717), _1141719)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1141717), _1141721)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1141719), _1141721))], (47534 ^ _780119) ^ [_1738695, _1738697, _1738699] : [-(c_List_Oconcat(_1738695, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1738695)), _1738697), _1738699)) = hAPP(hAPP(c_List_Oappend(_1738695), c_List_Oconcat(_1738695, _1738697)), c_List_Oconcat(_1738695, _1738699)))], (1660 ^ _780119) ^ [_803593, _803595] : [-(class_Rings_Ozero__neq__one(_803593)), _803595 = _803593, class_Rings_Ozero__neq__one(_803595)], (25524 ^ _780119) ^ [_1246886, _1246888] : [class_Rings_Oring__1(_1246886), 25527 ^ _780119 : [(25534 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246888), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1246886), _1246888) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1246886), hAPP(c_Int_Onat, _1246888)))], (25528 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246888), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1246886), _1246888) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246886), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1246886), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246888)))))]]], (10316 ^ _780119) ^ [_961489, _961491, _961493, _961495] : [-(hBOOL(hAPP(hAPP(c_member(_961489), _961491), _961493))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961489, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_961489), _961491), _961495)), _961493) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961489, tc_HOL_Obool)), _961495), _961493))], (37852 ^ _780119) ^ [_1507842, _1507844, _1507846, _1507848, _1507850, _1507852] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1507842, _1507844)), hAPP(hAPP(c_Product__Type_OPair(_1507842, _1507844), _1507846), _1507848)), hAPP(hAPP(c_Product__Type_OSigma(_1507842, _1507844), _1507850), _1507852))), 37855 ^ _780119 : [(37858 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1507844), _1507848), hAPP(_1507852, _1507846))))], (37856 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1507842), _1507846), _1507850)))]]], (41139 ^ _780119) ^ [_1587429, _1587431, _1587433, _1587435] : [-(hAPP(c_Set_OCollect(_1587429), hAPP(hAPP(c_COMBB(tc_fun(_1587431, tc_HOL_Obool), tc_HOL_Obool, _1587429), c_HOL_OAll(_1587431)), hAPP(hAPP(c_COMBB(tc_fun(_1587431, tc_HOL_Obool), tc_fun(_1587431, tc_HOL_Obool), _1587429), hAPP(c_COMBS(_1587431, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1587431), c_fimplies), hAPP(hAPP(c_COMBC(_1587431, tc_fun(_1587431, tc_HOL_Obool), tc_HOL_Obool), c_member(_1587431)), _1587433)))), _1587435))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1587431, tc_fun(_1587429, tc_HOL_Obool)), _1587433), hAPP(hAPP(c_COMBB(tc_fun(_1587429, tc_HOL_Obool), tc_fun(_1587429, tc_HOL_Obool), _1587431), c_Set_OCollect(_1587429)), hAPP(c_COMBC(_1587429, _1587431, tc_HOL_Obool), _1587435))))], (22731 ^ _780119) ^ [_1195386, _1195388, _1195390, _1195392, _1195394] : [hBOOL(hAPP(hAPP(c_member(_1195386), _1195388), c_SetInterval_Oord_OatLeastAtMost(_1195386, _1195390, _1195392, _1195394))), 22734 ^ _780119 : [(22737 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1195390, _1195388), _1195394)))], (22735 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1195390, _1195392), _1195388)))]]], (42857 ^ _780119) ^ [_1629094, _1629096, _1629098, _1629100] : [hAPP(c_List_Oset(_1629094), _1629096) = c_Map_Odom(_1629094, _1629098, _1629100), -(hAPP(c_Map_Omap__of(_1629094, _1629098), hAPP(hAPP(c_List_Omap(_1629094, tc_prod(_1629094, _1629098)), hAPP(hAPP(c_COMBS(_1629094, _1629098, tc_prod(_1629094, _1629098)), c_Product__Type_OPair(_1629094, _1629098)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1629098), _1629098, _1629094), c_Option_Othe(_1629098)), _1629100))), _1629096)) = _1629100)], (18840 ^ _780119) ^ [_1123557, _1123559, _1123561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1123557)), _1123557 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123557), _1123561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1123559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123561), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (43545 ^ _780119) ^ [_1647940, _1647942, _1647944, _1647946, _1647948, _1647950] : [-(c_List_Ofoldr(_1647940, _1647942, _1647944, hAPP(hAPP(c_List_Olist_OCons(_1647940), _1647946), _1647948), _1647950) = hAPP(hAPP(_1647944, _1647946), c_List_Ofoldr(_1647940, _1647942, _1647944, _1647948, _1647950)))], (31591 ^ _780119) ^ [_1369977, _1369979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1369977), _1369979)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1369977)), _1369979)))], (45652 ^ _780119) ^ [_1698905, _1698907, _1698909, _1698911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1698905), _1698907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1698909, tc_HOL_Obool)), hAPP(c_List_Oset(_1698909), hAPP(hAPP(c_List_Odrop(_1698909), _1698907), _1698911))), hAPP(c_List_Oset(_1698909), hAPP(hAPP(c_List_Odrop(_1698909), _1698905), _1698911)))))], (43068 ^ _780119) ^ [_1633874, _1633876, _1633878, _1633880, _1633882, _1633884, _1633886, _1633888] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1633874, _1633876), _1633878), _1633880), hAPP(hAPP(c_List_Ozip(_1633874, _1633876), hAPP(hAPP(c_List_Omap(_1633882, _1633874), _1633884), _1633886)), _1633888)) = hAPP(hAPP(c_List_Omap(tc_prod(_1633882, _1633876), _1633878), hAPP(c_Product__Type_Oprod_Oprod__case(_1633882, _1633876, _1633878), hAPP(hAPP(c_COMBB(tc_fun(_1633876, tc_prod(_1633874, _1633876)), tc_fun(_1633876, _1633878), _1633882), hAPP(c_COMBB(tc_prod(_1633874, _1633876), _1633878, _1633876), _1633880)), hAPP(hAPP(c_COMBB(_1633874, tc_fun(_1633876, tc_prod(_1633874, _1633876)), _1633882), c_Product__Type_OPair(_1633874, _1633876)), _1633884)))), hAPP(hAPP(c_List_Ozip(_1633882, _1633876), _1633886), _1633888)))], (33219 ^ _780119) ^ [_1399668] : [c_Int_OBit0(_1399668) = c_Int_OMin], (1760 ^ _780119) ^ [_804843, _804845] : [-(class_Orderings_Oord(_804843)), _804845 = _804843, class_Orderings_Oord(_804845)], (10961 ^ _780119) ^ [_974731, _974733, _974735] : [class_Groups_Ogroup__add(_974731), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974731), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974731), _974733), _974735)), _974735) = _974733)], (35135 ^ _780119) ^ [_1440450, _1440452, _1440454, _1440456, _1440458, _1440460, _1440462] : [hBOOL(hAPP(_1440450, _1440452)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1440454, _1440454)), hAPP(hAPP(c_Product__Type_OPair(_1440454, _1440454), _1440456), _1440458)), hAPP(_1440460, _1440452))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1440462, _1440454), tc_prod(_1440462, _1440454))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1440462, _1440454), tc_prod(_1440462, _1440454)), hAPP(hAPP(c_Product__Type_OPair(_1440462, _1440454), _1440452), _1440456)), hAPP(hAPP(c_Product__Type_OPair(_1440462, _1440454), _1440452), _1440458))), c_Recdef_Osame__fst(_1440462, _1440454, _1440450, _1440460))))], (4886 ^ _780119) ^ [_854739, _854741] : [_854741 = _854739, -(c_Lazy__Sequence_Oempty(_854741) = c_Lazy__Sequence_Oempty(_854739))], (45600 ^ _780119) ^ [_1697818, _1697820, _1697822, _1697824] : [-(hAPP(hAPP(c_List_Odrop(_1697818), _1697820), hAPP(hAPP(c_List_Odrop(_1697818), _1697822), _1697824)) = hAPP(hAPP(c_List_Odrop(_1697818), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1697820), _1697822)), _1697824))], (43940 ^ _780119) ^ [_1658220, _1658222, _1658224, _1658226] : [-(hAPP(c_List_Oset(tc_prod(_1658220, _1658222)), hAPP(hAPP(c_List_Ozip(_1658220, _1658222), _1658224), _1658226)) = hAPP(c_Set_OCollect(tc_prod(_1658220, _1658222)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1658220, _1658222)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1658220, _1658222), 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(_1658220, _1658222)), 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(_1658220, _1658222)), 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(_1658220, _1658222), tc_fun(tc_Nat_Onat, tc_prod(_1658220, _1658222)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1658220, _1658222), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1658220, _1658222)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1658220, _1658222)), c_COMBB(tc_prod(_1658220, _1658222), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1658222, tc_prod(_1658220, _1658222)), hAPP(hAPP(c_COMBB(_1658220, tc_fun(_1658222, tc_prod(_1658220, _1658222)), tc_Nat_Onat), c_Product__Type_OPair(_1658220, _1658222)), hAPP(c_List_Onth(_1658220), _1658224))), hAPP(c_List_Onth(_1658222), _1658226)))))), 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(_1658220)), _1658224)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658222)), _1658226)))))))], (51135 ^ _780119) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (6587 ^ _780119) ^ [_887208, _887210, _887212, _887214] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887208, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887208, tc_HOL_Obool)), _887210), _887212)), _887214) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887208, tc_HOL_Obool)), _887210), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887208, tc_HOL_Obool)), _887212), _887214)))], (38158 ^ _780119) ^ [_1517069, _1517071, _1517073, _1517075, _1517077, _1517079, _1517081] : [-(hAPP(c_Product__Type_Osnd(_1517069, _1517071), hAPP(c_Product__Type_Omap__pair(_1517073, _1517069, _1517075, _1517071, _1517077, _1517079), _1517081)) = hAPP(_1517079, hAPP(c_Product__Type_Osnd(_1517073, _1517075), _1517081)))], (31411 ^ _780119) ^ [_1367223, _1367225] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367223)))), 31414 ^ _780119 : [(31421 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367225)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367223), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367225)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367223), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367225))))], (31415 ^ _780119) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367225))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367223), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367225)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367223))]]], (28278 ^ _780119) ^ [_1302895, _1302897, _1302899, _1302901] : [class_Orderings_Olinorder(_1302895), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302895, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1302895), _1302897)), c_SetInterval_Oord__class_OatLeastAtMost(_1302895, _1302899, _1302901)) = c_SetInterval_Oord__class_OatLeastAtMost(_1302895, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1302895), _1302897), _1302899), _1302901))], (44144 ^ _780119) ^ [_1663441, _1663443, _1663445, _1663447] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663441), tc_List_Olist(_1663441))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663441), tc_List_Olist(_1663441)), _1663443), _1663445)), c_List_Olex(_1663441, _1663447)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663441), tc_List_Olist(_1663441))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663441), tc_List_Olist(_1663441)), _1663443), _1663445)), c_List_Olexord(_1663441, _1663447))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663441)), _1663443) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663441)), _1663445)], (50128 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OPls))], (51303 ^ _780119) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (17069 ^ _780119) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50300 ^ _780119) ^ [_1799569, _1799571, _1799573, _1799575, _1799577, _1799579, _1799581] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1799569, _1799571, _1799573, _1799575, _1799577, _1799579, _1799581) = c_New__DSequence_Oneg__decr__bind(_1799569, _1799571, hAPP(hAPP(hAPP(_1799573, _1799577), _1799579), _1799581), hAPP(hAPP(c_COMBC(_1799569, 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(_1799571)))), hAPP(hAPP(c_COMBC(_1799569, 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(_1799571))))), hAPP(hAPP(c_COMBC(_1799569, 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(_1799571)))))), _1799575), _1799577)), _1799579)), _1799581)))], (48375 ^ _780119) ^ [_1758144, _1758146, _1758148, _1758150, _1758152] : [class_Orderings_Olinorder(_1758144), -(hAPP(c_List_Ofilter(_1758146, _1758148), c_List_Olinorder__class_Osort__key(_1758146, _1758144, _1758150, _1758152)) = c_List_Olinorder__class_Osort__key(_1758146, _1758144, _1758150, hAPP(c_List_Ofilter(_1758146, _1758148), _1758152)))], (21297 ^ _780119) ^ [_1167863, _1167865] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1167863), _1167865)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1167863, tc_HOL_Obool)), hAPP(c_Set_OPow(_1167863), _1167865)) = 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(_1167863), _1167865)))], (51495 ^ _780119) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (43757 ^ _780119) ^ [_1654122, _1654124] : [class_Groups_Oordered__ab__group__add__abs(_1654122), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1654122), hAPP(c_Groups_Oabs__class_Oabs(_1654122), hAPP(c_List_Omonoid__add__class_Olistsum(_1654122), _1654124))), hAPP(c_List_Omonoid__add__class_Olistsum(_1654122), hAPP(hAPP(c_List_Omap(_1654122, _1654122), c_Groups_Oabs__class_Oabs(_1654122)), _1654124)))))], (44542 ^ _780119) ^ [_1672418, _1672420, _1672422, _1672424, _1672426, _1672428, _1672430] : [-(c_Map_Omap__upds(_1672418, _1672420, _1672422, hAPP(hAPP(c_List_Olist_OCons(_1672418), _1672424), _1672426), hAPP(hAPP(c_List_Olist_OCons(_1672420), _1672428), _1672430)) = c_Map_Omap__upds(_1672418, _1672420, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1672418, tc_Option_Ooption(_1672420)), _1672422), _1672424), hAPP(c_Option_Ooption_OSome(_1672420), _1672428)), _1672426, _1672430))], (7922 ^ _780119) ^ [_914980, _914982, _914984] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914980, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914980, tc_HOL_Obool)), _914982), _914984)), _914984) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914980, tc_HOL_Obool)), _914982), _914984))], (5831 ^ _780119) ^ [_872559, _872561, _872563, _872565, _872567, _872569] : [_872559 = hAPP(_872561, _872563), hBOOL(hAPP(hAPP(c_member(_872565), _872563), _872567)), -(hBOOL(hAPP(hAPP(c_member(_872569), _872559), hAPP(c_Set_Oimage(_872565, _872569, _872561), _872567))))], (6145 ^ _780119) ^ [_878098, _878100, _878102, _878104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878098, tc_HOL_Obool)), _878100), _878102)), hBOOL(hAPP(hAPP(c_member(_878098), _878104), _878100)), -(hBOOL(hAPP(hAPP(c_member(_878098), _878104), _878102)))], (9530 ^ _780119) ^ [_944293, _944295, _944297, _944299, _944301, _944303, _944305] : [-(c_Nitpick_Ofold__graph_H(_944293, _944295, _944297, _944299, _944301, hAPP(hAPP(_944297, _944303), _944305))), 9531 ^ _780119 : [(9538 ^ _780119) ^ [_944522, _944524] : [hAPP(hAPP(_944297, _944303), _944305) = hAPP(hAPP(_944297, _944524), _944522), hBOOL(hAPP(hAPP(c_member(_944293), _944524), _944301)), c_Nitpick_Ofold__graph_H(_944293, _944295, _944297, _944299, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_944293, tc_HOL_Obool)), _944301), hAPP(hAPP(c_Set_Oinsert(_944293), _944524), c_Orderings_Obot__class_Obot(tc_fun(_944293, tc_HOL_Obool)))), _944522)], (9532 ^ _780119) ^ [] : [_944301 = c_Orderings_Obot__class_Obot(tc_fun(_944293, tc_HOL_Obool)), hAPP(hAPP(_944297, _944303), _944305) = _944299]]], (16180 ^ _780119) ^ [_1074974, _1074976, _1074978] : [class_Rings_Olinordered__semiring__strict(_1074974), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074974), c_Groups_Ozero__class_Ozero(_1074974)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074974), _1074976), _1074978))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074974), c_Groups_Ozero__class_Ozero(_1074974)), _1074978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074974), c_Groups_Ozero__class_Ozero(_1074974)), _1074976)))], (36151 ^ _780119) ^ [_1465919, _1465921, _1465923, _1465925, _1465927] : [c_Fun_Oinj__on(_1465919, _1465921, _1465923, _1465925), -(c_Fun_Oinj__on(_1465919, _1465921, _1465923, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1465919, tc_HOL_Obool)), _1465925), _1465927)))], (38716 ^ _780119) ^ [_1530069, _1530071, _1530073] : [hBOOL(hAPP(_1530069, _1530071)), -(hBOOL(hAPP(_1530069, c_Hilbert__Choice_OEps(_1530073, _1530069))))], (44312 ^ _780119) ^ [] : [-(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))], (4958 ^ _780119) ^ [_855827, _855829, _855831, _855833, _855835, _855837, _855839, _855841] : [-(c_Lazy__Sequence_Ohb__bind(_855841, _855837, _855833, _855829) = c_Lazy__Sequence_Ohb__bind(_855839, _855835, _855831, _855827)), _855841 = _855839, _855837 = _855835, _855833 = _855831, _855829 = _855827], (17492 ^ _780119) ^ [_1098053, _1098055, _1098057] : [class_Rings_Olinordered__idom(_1098053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098053), c_Groups_Ozero__class_Ozero(_1098053)), _1098055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098053), c_Groups_Ozero__class_Ozero(_1098053)), _1098057)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098053), _1098057), c_Groups_Oone__class_Oone(_1098053))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098053), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098053), _1098055), _1098057)), _1098055)))], (12839 ^ _780119) ^ [_1012938, _1012940, _1012942] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1012938), _1012940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012938, tc_HOL_Obool)), _1012940), _1012942)), -(hAPP(c_Finite__Set_Ocard(_1012938), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012938, tc_HOL_Obool)), _1012942), _1012940)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1012938), _1012942)), hAPP(c_Finite__Set_Ocard(_1012938), _1012940)))], (13740 ^ _780119) ^ [_1029900, _1029902, _1029904] : [_1029902 = _1029904, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029900)), _1029902) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029900)), _1029904))], (26364 ^ _780119) ^ [_1261299, _1261301] : [hAPP(c_Set_OCollect(_1261299), _1261301) = c_Orderings_Obot__class_Obot(tc_fun(_1261299, tc_HOL_Obool)), 26367 ^ _780119 : [(26368 ^ _780119) ^ [_1261384] : [hBOOL(hAPP(_1261301, _1261384))]]], (50568 ^ _780119) ^ [_1805968, _1805970, _1805972] : [-(hAPP(c_List_Orev(_1805968), c_List_Oreplicate(_1805968, _1805970, _1805972)) = c_List_Oreplicate(_1805968, _1805970, _1805972))], (28170 ^ _780119) ^ [_1300713, _1300715] : [class_Orderings_Olinorder(_1300713), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300713), _1300715), _1300715) = _1300715)], (35909 ^ _780119) ^ [_1460045, _1460047] : [-(c_Equiv__Relations_Oequivp(_1460045, _1460047)), 35914 ^ _780119 : [(35917 ^ _780119) ^ [] : [hAPP(_1460047, 35910 ^ [_1460045, _1460047]) = hAPP(_1460047, 35911 ^ [_1460045, _1460047])], (35915 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1460047, 35910 ^ [_1460045, _1460047]), 35911 ^ [_1460045, _1460047])))]], 35918 ^ _780119 : [(35921 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1460047, 35910 ^ [_1460045, _1460047]), 35911 ^ [_1460045, _1460047]))], (35919 ^ _780119) ^ [] : [-(hAPP(_1460047, 35910 ^ [_1460045, _1460047]) = hAPP(_1460047, 35911 ^ [_1460045, _1460047]))]]], (50678 ^ _780119) ^ [_1807982, _1807984, _1807986] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1807982), hAPP(c_COMBK(_1807982, tc_Nat_Onat), _1807984)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1807986)) = c_List_Oreplicate(_1807982, _1807986, _1807984))], (45768 ^ _780119) ^ [_1701821, _1701823, _1701825, _1701827] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1701821) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1701823), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1701821)), hAPP(hAPP(c_List_Olist_OCons(_1701823), _1701825), _1701827)) = hAPP(hAPP(c_List_Olist_OCons(_1701823), _1701825), _1701827))], (50288 ^ _780119) ^ [_1799392, _1799394, _1799396, _1799398, _1799400] : [_1799392 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1799394, _1799396, _1799398, _1799400), _1799392) = c_Lazy__Sequence_Ohit__bound(_1799396))], (33385 ^ _780119) ^ [_1402103] : [class_Int_Onumber__ring(_1402103), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1402103), c_Groups_Oone__class_Oone(_1402103)) = hAPP(c_Int_Onumber__class_Onumber__of(_1402103), c_Int_OMin))], (45044 ^ _780119) ^ [_1682961, _1682963] : [-(hAPP(hAPP(c_List_Oappend(_1682961), _1682963), c_List_Olist_ONil(_1682961)) = _1682963)], (26467 ^ _780119) ^ [_1263093, _1263095, _1263097] : [hBOOL(hAPP(hAPP(c_member(_1263093), _1263095), hAPP(c_Set_OCollect(_1263093), _1263097))), -(hBOOL(hAPP(_1263097, _1263095)))], (28762 ^ _780119) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (23171 ^ _780119) ^ [_1203364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203364)), -(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), _1203364))))], (21534 ^ _780119) ^ [_1172815, _1172817, _1172819, _1172821] : [class_Divides_Oring__div(_1172815), c_Divides_Odiv__class_Omod(_1172815, _1172817, _1172819) = c_Divides_Odiv__class_Omod(_1172815, _1172821, _1172819), -(c_Divides_Odiv__class_Omod(_1172815, hAPP(c_Groups_Ouminus__class_Ouminus(_1172815), _1172817), _1172819) = c_Divides_Odiv__class_Omod(_1172815, hAPP(c_Groups_Ouminus__class_Ouminus(_1172815), _1172821), _1172819))], (49230 ^ _780119) ^ [_1776543, _1776545, _1776547, _1776549] : [49232 ^ _780119 : [(49235 ^ _780119) ^ [] : [hBOOL(hAPP(_1776547, hAPP(hAPP(c_List_Onth(_1776543), _1776545), 49231 ^ [_1776543, _1776545, _1776547, _1776549])))], (49233 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49231 ^ [_1776543, _1776545, _1776547, _1776549]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776543)), _1776545))))]], hBOOL(hAPP(hAPP(c_member(_1776543), _1776549), hAPP(c_List_Oset(_1776543), _1776545))), -(hBOOL(hAPP(_1776547, _1776549)))], (28228 ^ _780119) ^ [_1301900, _1301902] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1301900), hAPP(c_Nat_OSuc, _1301902)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1301902), 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)), _1301902)), _1301900))], (21624 ^ _780119) ^ [_1174845, _1174847, _1174849] : [class_Divides_Osemiring__div(_1174845), -(c_Divides_Odiv__class_Omod(_1174845, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174845), _1174847), _1174849), _1174849) = c_Groups_Ozero__class_Ozero(_1174845))], (9002 ^ _780119) ^ [_935053, _935055, _935057] : [class_Orderings_Oorder(_935053), -(_935055 = _935057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935053), _935055), _935057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935053), _935055), _935057)))], (40128 ^ _780119) ^ [_1564145, _1564147, _1564149] : [hAPP(hAPP(c_Relation_Orel__comp(_1564145, _1564145, _1564145), hAPP(c_Relation_Oconverse(_1564145, _1564145), _1564147)), _1564147) = _1564147, hAPP(c_Relation_ODomain(_1564145, _1564145), _1564147) = _1564149, -(c_Equiv__Relations_Oequiv(_1564145, _1564149, _1564147))], (41471 ^ _780119) ^ [_1597141, _1597143, _1597145, _1597147, _1597149] : [class_Complete__Lattice_Ocomplete__lattice(_1597141), hBOOL(hAPP(hAPP(c_member(_1597143), _1597145), _1597147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1597141), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597143, _1597141), _1597147), _1597149)), hAPP(_1597149, _1597145))))], (37751 ^ _780119) ^ [_1504559, _1504561, _1504563, _1504565] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1504559, _1504561)), hAPP(hAPP(c_Product__Type_OSigma(_1504559, _1504561), _1504563), hAPP(c_COMBK(tc_fun(_1504561, tc_HOL_Obool), _1504559), _1504565))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1504559), _1504563)), hAPP(c_Finite__Set_Ocard(_1504561), _1504565)))], (34028 ^ _780119) ^ [_1418881, _1418883, _1418885, _1418887, _1418889, _1418891, _1418893, _1418895] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1418881, _1418883, _1418885), _1418887), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1418889, _1418891, tc_prod(_1418881, _1418883)), _1418893), _1418895)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1418889, _1418891, _1418885), hAPP(hAPP(c_COMBB(tc_fun(_1418891, tc_prod(_1418881, _1418883)), tc_fun(_1418891, _1418885), _1418889), hAPP(c_COMBB(tc_prod(_1418881, _1418883), _1418885, _1418891), hAPP(c_Product__Type_Oprod_Oprod__case(_1418881, _1418883, _1418885), _1418887))), _1418893)), _1418895))], (47863 ^ _780119) ^ [_1747014, _1747016, _1747018, _1747020, _1747022] : [hBOOL(hAPP(hAPP(c_member(_1747014), _1747016), hAPP(c_List_Oset(_1747014), _1747018))), -(hBOOL(hAPP(_1747020, _1747016))), -(c_List_OtakeWhile(_1747014, _1747020, hAPP(hAPP(c_List_Oappend(_1747014), _1747018), _1747022)) = c_List_OtakeWhile(_1747014, _1747020, _1747018))], (25784 ^ _780119) ^ [_1250707, _1250709, _1250711] : [class_Rings_Oring__1(_1250707), -(hAPP(c_Int_Oring__1__class_Oof__int(_1250707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1250709), _1250711)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250707), hAPP(c_Int_Oring__1__class_Oof__int(_1250707), _1250709)), hAPP(c_Int_Oring__1__class_Oof__int(_1250707), _1250711)))], (45402 ^ _780119) ^ [_1691777, _1691779, _1691781, _1691783, _1691785] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691777), tc_List_Olist(_1691777))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691777), tc_List_Olist(_1691777)), _1691779), _1691781)), c_List_Olistrel1(_1691777, _1691783))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691777), tc_List_Olist(_1691777))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691777), tc_List_Olist(_1691777)), hAPP(hAPP(c_List_Olist_OCons(_1691777), _1691785), _1691779)), hAPP(hAPP(c_List_Olist_OCons(_1691777), _1691785), _1691781))), c_List_Olistrel1(_1691777, _1691783))))], (33329 ^ _780119) ^ [_1401295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1401295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1401295)))], (44802 ^ _780119) ^ [_1677437, _1677439, _1677441, _1677443] : [-(hAPP(hAPP(c_List_Otake(_1677437), _1677439), hAPP(hAPP(c_List_Olist_OCons(_1677437), _1677441), _1677443)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1677437), c_List_Olist_ONil(_1677437), hAPP(hAPP(c_COMBB(tc_List_Olist(_1677437), tc_List_Olist(_1677437), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1677437), _1677441)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1677437), tc_List_Olist(_1677437)), c_List_Otake(_1677437)), _1677443)), _1677439))], (44786 ^ _780119) ^ [_1677054, _1677056] : [-(_1677056 = c_List_Olist_ONil(_1677054)), -(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(_1677054)), _1677056))))], (42443 ^ _780119) ^ [_1619202, _1619204, _1619206, _1619208] : [c_Fun_Oinj__on(_1619202, tc_Option_Ooption(_1619204), c_Map_Omap__add(_1619202, _1619204, _1619206, _1619208), c_Map_Odom(_1619202, _1619204, _1619208)), -(c_Fun_Oinj__on(_1619202, tc_Option_Ooption(_1619204), _1619208, c_Map_Odom(_1619202, _1619204, _1619208)))], (34187 ^ _780119) ^ [_1422118, _1422120] : [-(c_Divides_OposDivAlg(_1422118, _1422120) = hAPP(c_Divides_Oadjust(_1422120), c_Divides_OposDivAlg(_1422118, 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)))), _1422120)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422118), _1422120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1422120), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47738 ^ _780119) ^ [_1744160, _1744162] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1744160), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1744160))), _1744162))), 47741 ^ _780119 : [(47748 ^ _780119) ^ [] : [-(_1744162 = c_List_Olist_ONil(tc_List_Olist(_1744160))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1744160))), c_List_Otranspose(_1744160, _1744162)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744160)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1744160)), _1744162), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47742 ^ _780119) ^ [] : [_1744162 = c_List_Olist_ONil(tc_List_Olist(_1744160)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1744160))), c_List_Otranspose(_1744160, _1744162)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11059 ^ _780119) ^ [_976741, _976743, _976745, _976747] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976741), _976743)), hBOOL(hAPP(c_Finite__Set_Ofinite(_976741), _976745)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_976741, tc_Nat_Onat), _976747), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_976741, tc_HOL_Obool)), _976743), _976745)) = 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(_976741, tc_Nat_Onat), _976747), _976743)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_976741, tc_Nat_Onat), _976747), _976745))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_976741, tc_Nat_Onat), _976747), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976741, tc_HOL_Obool)), _976743), _976745))))], (11505 ^ _780119) ^ [_986470, _986472, _986474, _986476] : [class_Rings_Ocomm__semiring__1(_986470), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986470), _986472), _986474)), _986476) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986470), _986472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986470), _986474), _986476)))], (51103 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (49806 ^ _780119) ^ [_1790138, _1790140, _1790142] : [c_List_Olist__all(_1790138, _1790140, _1790142), 49809 ^ _780119 : [(49810 ^ _780119) ^ [_1790219] : [hBOOL(hAPP(hAPP(c_member(_1790138), _1790219), hAPP(c_List_Oset(_1790138), _1790142))), -(hBOOL(hAPP(_1790140, _1790219)))]]], (44844 ^ _780119) ^ [_1678163, _1678165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678163)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678165))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678163), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678165)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678163)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678163)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678165))))], (23006 ^ _780119) ^ [] : [-(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)))], (35497 ^ _780119) ^ [_1450339, _1450341] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1450339, _1450339)), _1450341)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1450339), hAPP(c_Relation_OField(_1450339), _1450341))))], (49144 ^ _780119) ^ [_1774472, _1774474, _1774476, _1774478, _1774480, _1774482] : [c_List_Olist__all2(_1774472, _1774474, _1774476, _1774478, _1774480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1774482), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774474)), _1774480))), -(hBOOL(hAPP(hAPP(_1774476, hAPP(hAPP(c_List_Onth(_1774472), _1774478), _1774482)), hAPP(hAPP(c_List_Onth(_1774474), _1774480), _1774482))))], (11011 ^ _780119) ^ [_975706, _975708, _975710, _975712, _975714] : [class_Groups_Oordered__cancel__ab__semigroup__add(_975706), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975706), _975708), _975710)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975706), _975712), _975714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975706), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975706), _975708), _975712)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975706), _975710), _975714))))], (4370 ^ _780119) ^ [_846259, _846261, _846263, _846265, _846267, _846269] : [-(c_List_Olinorder__class_Oinsort__key(_846269, _846265, _846261) = c_List_Olinorder__class_Oinsort__key(_846267, _846263, _846259)), _846269 = _846267, _846265 = _846263, _846261 = _846259], (5738 ^ _780119) ^ [_867963, _867965] : [_867965 = _867963, -(tc_Hoare__Mirabelle_Otriple(_867965) = tc_Hoare__Mirabelle_Otriple(_867963))], (39669 ^ _780119) ^ [_1553066, _1553068, _1553070] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1553066, _1553068, _1553068), _1553070), c_Relation_OId(_1553068)) = _1553070)], (27099 ^ _780119) ^ [_1278860, _1278862] : [-(hAPP(c_Set_OPow(_1278860), _1278862) = hAPP(c_Set_OCollect(tc_fun(_1278860, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1278860, tc_HOL_Obool), tc_fun(_1278860, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1278860, tc_HOL_Obool))), _1278862)))], (35536 ^ _780119) ^ [_1451391, _1451393, _1451395] : [_1451393 = c_Orderings_Obot__class_Obot(tc_fun(_1451391, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1451391), _1451393), _1451395) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1451391, tc_HOL_Obool), tc_HOL_Obool)))], (32963 ^ _780119) ^ [_1394137, _1394139, _1394141] : [class_Rings_Oring__1(_1394137), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1394137), hAPP(c_Groups_Ouminus__class_Ouminus(_1394137), _1394139)), 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)))), _1394141)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1394137), _1394139), 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)))), _1394141)))], (18798 ^ _780119) ^ [_1122859] : [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)), _1122859)), _1122859)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122859), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6250 ^ _780119) ^ [_880238, _880240, _880242] : [c_Orderings_Obot__class_Obot(tc_fun(_880238, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_880238), _880240), _880242)], (13990 ^ _780119) ^ [_1034665, _1034667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034665), hAPP(c_Nat_OSuc, _1034667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1034665), _1034667)))], (47309 ^ _780119) ^ [_1733335, _1733337, _1733339, _1733341] : [class_Orderings_Olinorder(_1733335), c_List_Olinorder__class_Osorted(_1733335, _1733337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1733339), _1733341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1733341), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733335)), _1733337))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1733335), hAPP(hAPP(c_List_Onth(_1733335), _1733337), _1733339)), hAPP(hAPP(c_List_Onth(_1733335), _1733337), _1733341))))], (15120 ^ _780119) ^ [_1056924] : [class_Groups_Ogroup__add(_1056924), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1056924), c_Groups_Ozero__class_Ozero(_1056924)) = c_Groups_Ozero__class_Ozero(_1056924))], (25762 ^ _780119) ^ [_1250295, _1250297, _1250299] : [class_Rings_Olinordered__idom(_1250295), 25765 ^ _780119 : [(25772 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250297), _1250299)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250295), hAPP(c_Int_Oring__1__class_Oof__int(_1250295), _1250297)), hAPP(c_Int_Oring__1__class_Oof__int(_1250295), _1250299))))], (25766 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250295), hAPP(c_Int_Oring__1__class_Oof__int(_1250295), _1250297)), hAPP(c_Int_Oring__1__class_Oof__int(_1250295), _1250299))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250297), _1250299)))]]], (33335 ^ _780119) ^ [_1401378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1401378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1401378))))], (22567 ^ _780119) ^ [_1191891, _1191893, _1191895, _1191897, _1191899] : [c_Com_Ocom_OCond(_1191891, _1191893, _1191895) = c_Com_Ocom_OWhile(_1191897, _1191899)], (42616 ^ _780119) ^ [_1623425, _1623427, _1623429, _1623431, _1623433] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1623425), tc_List_Olist(_1623427), tc_List_Olist(_1623429), hAPP(c_List_Omap(_1623425, _1623427), _1623431)), hAPP(c_List_Omap(_1623429, _1623425), _1623433)) = hAPP(c_List_Omap(_1623429, _1623427), hAPP(c_Fun_Ocomp(_1623425, _1623427, _1623429, _1623431), _1623433)))], (7624 ^ _780119) ^ [_908474, _908476, _908478, _908480] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_908474), _908476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908474, tc_HOL_Obool)), _908476), _908478)), hBOOL(hAPP(_908480, c_Orderings_Obot__class_Obot(tc_fun(_908474, tc_HOL_Obool)))), 7639 ^ _780119 : [(7646 ^ _780119) ^ [] : [-(hBOOL(hAPP(_908480, 7638 ^ [_908474, _908476, _908478, _908480])))], (7644 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_908474), 7637 ^ [_908474, _908476, _908478, _908480]), 7638 ^ [_908474, _908476, _908478, _908480]))], (7642 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_908474), 7637 ^ [_908474, _908476, _908478, _908480]), _908478)))], (7640 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_908474), 7638 ^ [_908474, _908476, _908478, _908480])))], (7648 ^ _780119) ^ [] : [hBOOL(hAPP(_908480, hAPP(hAPP(c_Set_Oinsert(_908474), 7637 ^ [_908474, _908476, _908478, _908480]), 7638 ^ [_908474, _908476, _908478, _908480])))]], -(hBOOL(hAPP(_908480, _908476)))], (49217 ^ _780119) ^ [_1776204, _1776206, _1776208, _1776210, _1776212] : [49219 ^ _780119 : [(49222 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1776204, _1776206, tc_HOL_Obool), _1776212), 49218 ^ [_1776204, _1776206, _1776208, _1776210, _1776212]))], (49220 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776204, _1776206)), 49218 ^ [_1776204, _1776206, _1776208, _1776210, _1776212]), hAPP(c_List_Oset(tc_prod(_1776204, _1776206)), hAPP(hAPP(c_List_Ozip(_1776204, _1776206), _1776208), _1776210)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776204)), _1776208) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776206)), _1776210), -(c_List_Olist__all2(_1776204, _1776206, _1776212, _1776208, _1776210))], (50029 ^ _780119) ^ [_1794472, _1794474] : [-(c_FunDef_Ois__measure(_1794472, _1794474))], (32133 ^ _780119) ^ [_1379307, _1379309] : [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(_1379309))), 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), _1379307)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1379307)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379309))))], (49078 ^ _780119) ^ [_1773265, _1773267, _1773269, _1773271, _1773273] : [c_List_Olist__all2(_1773265, _1773267, _1773269, hAPP(c_List_Orev(_1773265), _1773271), hAPP(c_List_Orev(_1773267), _1773273)), -(c_List_Olist__all2(_1773265, _1773267, _1773269, _1773271, _1773273))], (6276 ^ _780119) ^ [_880784, _880786, _880788, _880790] : [hAPP(c_Set_Oimage(_880784, _880786, _880788), _880790) = c_Orderings_Obot__class_Obot(tc_fun(_880786, tc_HOL_Obool)), -(_880790 = c_Orderings_Obot__class_Obot(tc_fun(_880784, tc_HOL_Obool)))], (21833 ^ _780119) ^ [_1178768, _1178770] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178768), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1178770), _1178768)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178770), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178770, _1178768)))], (3522 ^ _780119) ^ [_833071, _833073, _833075, _833077] : [-(c_Finite__Set_Ofold1(_833077, _833073) = c_Finite__Set_Ofold1(_833075, _833071)), _833077 = _833075, _833073 = _833071], (51145 ^ _780119) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (35629 ^ _780119) ^ [_1453634, _1453636, _1453638, _1453640, _1453642] : [c_Equiv__Relations_Oequiv(_1453634, _1453636, _1453638), hBOOL(hAPP(hAPP(c_member(tc_fun(_1453634, tc_HOL_Obool)), _1453640), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1453634), _1453636), _1453638))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1453634, tc_HOL_Obool)), _1453642), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1453634), _1453636), _1453638))), -(_1453640 = _1453642), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453634, tc_HOL_Obool)), _1453640), _1453642) = c_Orderings_Obot__class_Obot(tc_fun(_1453634, tc_HOL_Obool)))], (9252 ^ _780119) ^ [_939073, _939075, _939077, _939079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939073, tc_HOL_Obool)), _939075), _939077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_939073, tc_HOL_Obool)), _939077), _939079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_939073, tc_HOL_Obool)), _939075), _939079)))], (20 ^ _780119) ^ [_780379, _780381, _780383, _780385, _780387, _780389, _780391, _780393, _780395, _780397, _780399, _780401] : [-(c_Finite__Set_Ofolding__image__simple__idem(_780399, _780395, _780391, _780387, _780383, _780379)), c_Finite__Set_Ofolding__image__simple__idem(_780401, _780397, _780393, _780389, _780385, _780381), _780401 = _780399, _780397 = _780395, _780393 = _780391, _780389 = _780387, _780385 = _780383, _780381 = _780379], (1270 ^ _780119) ^ [_798718, _798720] : [-(class_Complete__Lattice_Ocomplete__lattice(_798718)), _798720 = _798718, class_Complete__Lattice_Ocomplete__lattice(_798720)], (47532 ^ _780119) ^ [_1738643, _1738645, _1738647] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1738643), tc_List_Olist(_1738643), c_List_Oappend(_1738643), _1738645), _1738647) = hAPP(hAPP(c_List_Oappend(_1738643), _1738645), c_List_Oconcat(_1738643, _1738647)))], (37495 ^ _780119) ^ [_1497685, _1497687] : [c_Wellfounded_Owf(_1497685, _1497687), -(c_Wellfounded_Owf(tc_List_Olist(_1497685), c_List_Olex(_1497685, _1497687)))], (17132 ^ _780119) ^ [_1091236, _1091238] : [class_Lattices_Oboolean__algebra(_1091236), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1091236), _1091238), hAPP(c_Groups_Ouminus__class_Ouminus(_1091236), _1091238)) = c_Orderings_Otop__class_Otop(_1091236))], (11951 ^ _780119) ^ [_995400, _995402, _995404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995400), _995402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995400), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995402), _995404))))], (31579 ^ _780119) ^ [_1369810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369810), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369810)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (50244 ^ _780119) ^ [_1798308, _1798310, _1798312, _1798314, _1798316, _1798318, _1798320] : [-(c_New__Random__Sequence_Opos__decr__bind(_1798308, _1798310, _1798312, _1798314, _1798316, _1798318, _1798320) = c_New__DSequence_Opos__decr__bind(_1798308, _1798310, hAPP(hAPP(hAPP(_1798312, _1798316), _1798318), _1798320), hAPP(hAPP(c_COMBC(_1798308, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1798310))), hAPP(hAPP(c_COMBC(_1798308, 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(_1798310)))), hAPP(hAPP(c_COMBC(_1798308, 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(_1798310))))), _1798314), _1798316)), _1798318)), _1798320)))], (19897 ^ _780119) ^ [_1141781, _1141783, _1141785, _1141787] : [class_Fields_Ofield(_1141781), -(_1141783 = c_Groups_Ozero__class_Ozero(_1141781)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1141781), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141781), _1141785), _1141783)), _1141787) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141781), hAPP(hAPP(c_Power_Opower__class_Opower(_1141781), _1141785), _1141787)), hAPP(hAPP(c_Power_Opower__class_Opower(_1141781), _1141783), _1141787)))], (24819 ^ _780119) ^ [_1234817, _1234819, _1234821, _1234823] : [class_Orderings_Olinorder(_1234817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234817), _1234819), _1234821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234817), _1234821), _1234823)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234817, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1234817, _1234819, _1234821)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1234817, _1234821, _1234823)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1234817, _1234819, _1234823))], (39371 ^ _780119) ^ [_1545742, _1545744, _1545746, _1545748, _1545750, _1545752, _1545754, _1545756, _1545758] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1545742, _1545744, _1545746, _1545748), hAPP(hAPP(c_Product__Type_Oscomp(_1545742, _1545750, _1545752, tc_prod(_1545744, _1545746)), _1545754), _1545756)), _1545758) = hAPP(hAPP(c_Product__Type_Oscomp(_1545742, _1545750, _1545752, _1545748), _1545754), hAPP(hAPP(c_COMBC(_1545750, tc_fun(_1545744, tc_fun(_1545746, _1545748)), tc_fun(_1545752, _1545748)), hAPP(hAPP(c_COMBB(tc_fun(_1545752, tc_prod(_1545744, _1545746)), tc_fun(tc_fun(_1545744, tc_fun(_1545746, _1545748)), tc_fun(_1545752, _1545748)), _1545750), c_Product__Type_Oscomp(_1545752, _1545744, _1545746, _1545748)), _1545756)), _1545758)))], (1800 ^ _780119) ^ [_805343, _805345] : [-(class_Int_Onumber(_805343)), _805345 = _805343, class_Int_Onumber(_805345)], (11621 ^ _780119) ^ [_989136, _989138] : [class_Rings_Olinordered__semidom(_989136), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989136), _989138), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_989136), _989138), c_Groups_Oone__class_Oone(_989136)))))], (43751 ^ _780119) ^ [_1653891, _1653893, _1653895, _1653897, _1653899] : [class_Groups_Oab__group__add(_1653891), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1653891), hAPP(hAPP(c_List_Omap(_1653893, _1653891), hAPP(hAPP(c_COMBS(_1653893, _1653891, _1653891), hAPP(hAPP(c_COMBB(_1653891, tc_fun(_1653891, _1653891), _1653893), c_Groups_Ominus__class_Ominus(_1653891)), _1653895)), _1653897)), _1653899)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1653891), hAPP(c_List_Omonoid__add__class_Olistsum(_1653891), hAPP(hAPP(c_List_Omap(_1653893, _1653891), _1653895), _1653899))), hAPP(c_List_Omonoid__add__class_Olistsum(_1653891), hAPP(hAPP(c_List_Omap(_1653893, _1653891), _1653897), _1653899))))], (29881 ^ _780119) ^ [_1337640, _1337642, _1337644, _1337646, _1337648] : [_1337640 = c_Orderings_Obot__class_Obot(tc_fun(_1337642, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337642, tc_fun(_1337644, tc_HOL_Obool)), _1337640), hAPP(hAPP(c_COMBB(tc_fun(_1337644, tc_HOL_Obool), tc_fun(_1337644, tc_HOL_Obool), _1337642), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337644, tc_HOL_Obool)), _1337646)), _1337648)) = c_Orderings_Obot__class_Obot(tc_fun(_1337644, tc_HOL_Obool)))], (12976 ^ _780119) ^ [_1015705, _1015707, _1015709] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1015705), _1015707)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015705), _1015709)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1015705, tc_HOL_Obool)), _1015707), _1015709) = c_Orderings_Obot__class_Obot(tc_fun(_1015705, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1015705), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1015705, tc_HOL_Obool)), _1015707), _1015709)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1015705), _1015707)), hAPP(c_Finite__Set_Ocard(_1015705), _1015709)))], (45388 ^ _780119) ^ [_1691318, _1691320, _1691322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1691318, _1691318), tc_HOL_Obool)), _1691320), _1691322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1691318), tc_List_Olist(_1691318)), tc_HOL_Obool)), c_List_Olistrel1(_1691318, _1691320)), c_List_Olistrel1(_1691318, _1691322))))], (12613 ^ _780119) ^ [_1008845, _1008847] : [-(_1008845 = hAPP(c_Option_Ooption_OSome(_1008847), 12614 ^ [_1008845, _1008847])), -(_1008845 = c_Option_Ooption_ONone(_1008847))], (44678 ^ _780119) ^ [_1675161, _1675163] : [-(c_List_Osublist(_1675161, _1675163, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1675161))], (31979 ^ _780119) ^ [_1376105, _1376107] : [class_Int_Onumber__ring(_1376105), class_Rings_Olinordered__idom(_1376105), 31986 ^ _780119 : [(31993 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376107), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376105), hAPP(c_Int_Onumber__class_Onumber__of(_1376105), _1376107)), c_Groups_Oone__class_Oone(_1376105))))], (31987 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376105), hAPP(c_Int_Onumber__class_Onumber__of(_1376105), _1376107)), c_Groups_Oone__class_Oone(_1376105))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376107), c_Int_OBit1(c_Int_OPls))))]]], (23304 ^ _780119) ^ [_1205999, _1206001, _1206003, _1206005, _1206007] : [-(hBOOL(hAPP(hAPP(c_member(_1205999), _1206001), c_SetInterval_Oord_OgreaterThanLessThan(_1205999, _1206003, _1206005, _1206007)))), hBOOL(hAPP(hAPP(_1206003, _1206005), _1206001)), hBOOL(hAPP(hAPP(_1206003, _1206001), _1206007))], (39591 ^ _780119) ^ [_1550435, _1550437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1550435)), -(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(_1550435), _1550437))), _1550435)))], (20240 ^ _780119) ^ [_1148355, _1148357, _1148359] : [class_Fields_Ofield__inverse__zero(_1148355), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148355), hAPP(c_Groups_Ouminus__class_Ouminus(_1148355), _1148357)), hAPP(c_Groups_Ouminus__class_Ouminus(_1148355), _1148359)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148355), _1148357), _1148359))], (46723 ^ _780119) ^ [_1722327, _1722329] : [-(c_List_Otranspose(_1722327, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1722327)), c_List_Olist_ONil(_1722327)), _1722329)) = c_List_Otranspose(_1722327, _1722329))], (50713 ^ _780119) ^ [_1808592, _1808594, _1808596, _1808598, _1808600] : [50715 ^ _780119 : [(50718 ^ _780119) ^ [] : [c_Relation_Orefl__on(_1808596, hAPP(_1808598, 50714 ^ [_1808592, _1808594, _1808596, _1808598, _1808600]), hAPP(_1808600, 50714 ^ [_1808592, _1808594, _1808596, _1808598, _1808600]))], (50716 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808592), 50714 ^ [_1808592, _1808594, _1808596, _1808598, _1808600]), _1808594)))]], -(c_Relation_Orefl__on(_1808596, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1808592, tc_fun(_1808596, tc_HOL_Obool)), _1808594), _1808598), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1808592, tc_fun(tc_prod(_1808596, _1808596), tc_HOL_Obool)), _1808594), _1808600)))], (6961 ^ _780119) ^ [_895104, _895106, _895108, _895110] : [class_Orderings_Oorder(_895104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895104), _895106), _895108)), _895106 = _895110, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895104), _895110), _895108)))], (24493 ^ _780119) ^ [_1228781, _1228783, _1228785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228781)), 24496 ^ _780119 : [(24497 ^ _780119) ^ [_1228915] : [24499 ^ _780119 : [(24503 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24501 ^ [_1228781, _1228783, _1228785, _1228915]), _1228783)))], (24505 ^ _780119) ^ [] : [-(_1228915 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24501 ^ [_1228781, _1228783, _1228785, _1228915]), 24498 ^ [_1228781, _1228783, _1228785, _1228915]))], (24500 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24498 ^ [_1228781, _1228783, _1228785, _1228915]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1228781))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228785), _1228915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228785), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228915), _1228781))))]]], (24955 ^ _780119) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2786 ^ _780119) ^ [_821541, _821543, _821545, _821547] : [-(c_Com_Ocom_OWhile(_821547, _821543) = c_Com_Ocom_OWhile(_821545, _821541)), _821547 = _821545, _821543 = _821541], (35303 ^ _780119) ^ [_1444389, _1444391, _1444393, _1444395] : [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), _1444389), _1444391)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1444393), _1444395))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444389), _1444395) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444393), _1444391))], (36694 ^ _780119) ^ [_1477237, _1477239, _1477241, _1477243, _1477245] : [hBOOL(hAPP(hAPP(c_member(_1477237), _1477239), hAPP(c_Set_Ovimage(_1477237, _1477241, _1477243), _1477245))), -(hBOOL(hAPP(hAPP(c_member(_1477241), hAPP(_1477243, _1477239)), _1477245)))], (45100 ^ _780119) ^ [_1683966, _1683968, _1683970] : [hAPP(hAPP(c_List_Oappend(_1683966), _1683968), _1683970) = _1683970, -(_1683968 = c_List_Olist_ONil(_1683966))], (48509 ^ _780119) ^ [_1761262, _1761264] : [class_Enum_Oenum(_1761262), 48512 ^ _780119 : [(48520 ^ _780119) ^ [] : [48521 ^ _780119 : [(48522 ^ _780119) ^ [_1761442] : [hBOOL(hAPP(_1761264, _1761442))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1761262), _1761264)))], (48513 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1761262), _1761264)), -(hBOOL(hAPP(_1761264, 48516 ^ [_1761262, _1761264])))]]], (50570 ^ _780119) ^ [_1806029, _1806031, _1806033, _1806035] : [50577 ^ _780119 : [(50580 ^ _780119) ^ [] : [_1806031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50578 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1806035, _1806033)))]], 50571 ^ _780119 : [(50572 ^ _780119) ^ [_1806101] : [hBOOL(hAPP(hAPP(c_member(_1806029), _1806101), hAPP(c_List_Oset(_1806029), c_List_Oreplicate(_1806029, _1806031, _1806033)))), hBOOL(hAPP(_1806035, _1806101))]]], (29936 ^ _780119) ^ [_1339136, _1339138, _1339140, _1339142] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1339136, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29937 ^ [_1339136, _1339138, _1339140, _1339142])), _1339138) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1339136, 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), 29937 ^ [_1339136, _1339138, _1339140, _1339142]), _1339140))), _1339142), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1339136, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1339138) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1339136, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1339142))], (32747 ^ _780119) ^ [_1390501] : [-(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)))), _1390501) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1390501)))], (39442 ^ _780119) ^ [_1547300, _1547302] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547300, _1547300)), hAPP(hAPP(c_Product__Type_OPair(_1547300, _1547300), 39443 ^ [_1547300, _1547302]), 39443 ^ [_1547300, _1547302])), c_Transitive__Closure_Otrancl(_1547300, _1547302)))), -(c_Wellfounded_Oacyclic(_1547300, _1547302))], (21070 ^ _780119) ^ [_1163367, _1163369, _1163371] : [class_Fields_Olinordered__field(_1163367), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163367), _1163369), _1163371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163367), _1163369), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163367), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163367), _1163369), _1163371)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163367), c_Groups_Oone__class_Oone(_1163367)), c_Groups_Oone__class_Oone(_1163367))))))], (6290 ^ _780119) ^ [_881077, _881079, _881081, _881083] : [c_Orderings_Obot__class_Obot(tc_fun(_881077, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_881079, _881077, _881081), _881083), -(_881083 = c_Orderings_Obot__class_Obot(tc_fun(_881079, tc_HOL_Obool)))], (32681 ^ _780119) ^ [_1389328, _1389330, _1389332] : [class_Int_Onumber__ring(_1389328), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1389328), hAPP(c_Int_Onumber__class_Onumber__of(_1389328), _1389330)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1389332))) = hAPP(hAPP(c_HOL_OLet(_1389328, _1389328), hAPP(hAPP(c_Power_Opower__class_Opower(_1389328), hAPP(c_Int_Onumber__class_Onumber__of(_1389328), _1389330)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1389332))), hAPP(hAPP(c_COMBS(_1389328, _1389328, _1389328), c_Groups_Otimes__class_Otimes(_1389328)), c_COMBI(_1389328))))], (32773 ^ _780119) ^ [] : [-(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)))))], (50392 ^ _780119) ^ [_1801874, _1801876, _1801878, _1801880] : [-(hAPP(c_New__DSequence_Oneg__union(_1801874, _1801876, _1801878), _1801880) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(_1801874), hAPP(_1801876, _1801880), hAPP(_1801878, _1801880)))], (42469 ^ _780119) ^ [_1619813, _1619815, _1619817] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1619813), c_Map_Odom(_1619813, _1619815, hAPP(c_Map_Omap__of(_1619813, _1619815), _1619817)))))], (40072 ^ _780119) ^ [_1562567, _1562569, _1562571] : [c_Equiv__Relations_Oequiv(_1562567, _1562569, _1562571), -(hAPP(hAPP(c_Relation_Orel__comp(_1562567, _1562567, _1562567), hAPP(c_Relation_Oconverse(_1562567, _1562567), _1562571)), _1562571) = _1562571)], (51285 ^ _780119) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (26389 ^ _780119) ^ [_1261660, _1261662] : [class_Groups_Oordered__ab__group__add__abs(_1261660), 26392 ^ _780119 : [(26399 ^ _780119) ^ [] : [_1261662 = c_Groups_Ozero__class_Ozero(_1261660), -(hAPP(c_Groups_Oabs__class_Oabs(_1261660), _1261662) = c_Groups_Ozero__class_Ozero(_1261660))], (26393 ^ _780119) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1261660), _1261662) = c_Groups_Ozero__class_Ozero(_1261660), -(_1261662 = c_Groups_Ozero__class_Ozero(_1261660))]]], (38772 ^ _780119) ^ [_1531379, _1531381, _1531383, _1531385, _1531387, _1531389] : [c_Fun_Oinj__on(_1531379, _1531381, hAPP(c_Fun_Ocomp(_1531383, _1531381, _1531379, _1531385), _1531387), _1531389), -(c_Fun_Oinj__on(_1531383, _1531381, _1531385, hAPP(c_Set_Oimage(_1531379, _1531383, _1531387), _1531389)))], (46377 ^ _780119) ^ [_1714684, _1714686] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1714684), _1714686) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1714684, 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)))), _1714686))))], (31919 ^ _780119) ^ [_1375181, _1375183] : [class_Int_Onumber__ring(_1375181), class_Rings_Olinordered__idom(_1375181), 31926 ^ _780119 : [(31933 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1375183), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375181), hAPP(c_Int_Onumber__class_Onumber__of(_1375181), _1375183)), c_Groups_Oone__class_Oone(_1375181))))], (31927 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375181), hAPP(c_Int_Onumber__class_Onumber__of(_1375181), _1375183)), c_Groups_Oone__class_Oone(_1375181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1375183), c_Int_OBit1(c_Int_OPls))))]]], (25197 ^ _780119) ^ [_1241320, _1241322] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1241320), _1241322)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1241322), _1241320)))], (47504 ^ _780119) ^ [_1738063, _1738065] : [c_List_Olist_ONil(_1738063) = hAPP(c_List_Orev(_1738063), _1738065), -(_1738065 = c_List_Olist_ONil(_1738063))], (28194 ^ _780119) ^ [_1301240] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1301240), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4356 ^ _780119) ^ [_846038, _846040, _846042, _846044, _846046, _846048] : [-(c_List_OtakeWhile(_846048, _846044, _846040) = c_List_OtakeWhile(_846046, _846042, _846038)), _846048 = _846046, _846044 = _846042, _846040 = _846038], (10458 ^ _780119) ^ [_964767, _964769, _964771, _964773] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_964767, _964769, hAPP(hAPP(c_Set_Oinsert(_964767), _964771), c_Orderings_Obot__class_Obot(tc_fun(_964767, tc_HOL_Obool)))), _964773)), -(_964771 = _964773)], (49911 ^ _780119) ^ [_1792124, _1792126, _1792128, _1792130] : [-(c_List_Olist__ex1(_1792124, _1792126, hAPP(hAPP(c_List_Olist_OCons(_1792124), _1792128), _1792130))), 49914 ^ _780119 : [(49917 ^ _780119) ^ [] : [c_List_Olist__all(_1792124, hAPP(hAPP(c_COMBS(_1792124, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1792124), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1792124), c_fNot), _1792126))), hAPP(c_fequal, _1792128)), _1792130)], (49915 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1792126, _1792128)))]], 49918 ^ _780119 : [(49921 ^ _780119) ^ [] : [c_List_Olist__ex1(_1792124, _1792126, _1792130)], (49919 ^ _780119) ^ [] : [hBOOL(hAPP(_1792126, _1792128))]]], (28474 ^ _780119) ^ [_1306351, _1306353, _1306355] : [class_Orderings_Olinorder(_1306351), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306351), _1306353)), -(_1306355 = c_Orderings_Obot__class_Obot(tc_fun(_1306351, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306351, tc_HOL_Obool)), _1306355), _1306353)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306351), c_Big__Operators_Olinorder__class_OMax(_1306351, _1306355)), c_Big__Operators_Olinorder__class_OMax(_1306351, _1306353)) = c_Big__Operators_Olinorder__class_OMax(_1306351, _1306353))], (37092 ^ _780119) ^ [_1487503, _1487505, _1487507] : [37094 ^ _780119 : [(37097 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1487503), 37093 ^ [_1487503, _1487505, _1487507]), c_Wellfounded_Oacc(_1487503, _1487507)))], (37095 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1487503, _1487503)), hAPP(hAPP(c_Product__Type_OPair(_1487503, _1487503), 37093 ^ [_1487503, _1487505, _1487507]), _1487505)), _1487507)))]], -(hBOOL(hAPP(hAPP(c_member(_1487503), _1487505), c_Wellfounded_Oacc(_1487503, _1487507))))], (47692 ^ _780119) ^ [_1742889, _1742891, _1742893, _1742895] : [-(c_List_Oconcat(_1742889, hAPP(hAPP(c_List_Omap(_1742891, tc_List_Olist(_1742889)), hAPP(hAPP(c_COMBC(_1742891, tc_List_Olist(_1742889), tc_List_Olist(_1742889)), hAPP(hAPP(c_COMBB(_1742889, tc_fun(tc_List_Olist(_1742889), tc_List_Olist(_1742889)), _1742891), c_List_Olist_OCons(_1742889)), _1742893)), c_List_Olist_ONil(_1742889))), _1742895)) = hAPP(hAPP(c_List_Omap(_1742891, _1742889), _1742893), _1742895))], (3336 ^ _780119) ^ [_830170, _830172, _830174, _830176, _830178, _830180, _830182, _830184] : [-(c_Nitpick_Osetsum_H(_830184, _830180, _830176, _830172) = c_Nitpick_Osetsum_H(_830182, _830178, _830174, _830170)), _830184 = _830182, _830180 = _830178, _830176 = _830174, _830172 = _830170], (19697 ^ _780119) ^ [_1138340, _1138342, _1138344, _1138346] : [class_Rings_Odivision__ring(_1138340), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138340), _1138342), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138340), _1138344), _1138346)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138340), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138340), _1138342), _1138344)), _1138346))], (39449 ^ _780119) ^ [_1547374, _1547376, _1547378, _1547380] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547374, _1547374)), hAPP(hAPP(c_Product__Type_OPair(_1547374, _1547374), _1547376), _1547378)), _1547380)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547374, _1547374)), hAPP(hAPP(c_Product__Type_OPair(_1547374, _1547374), _1547376), _1547378)), c_Transitive__Closure_Otrancl(_1547374, _1547380))))], (46655 ^ _780119) ^ [_1720628, _1720630, _1720632] : [46657 ^ _780119 : [(46660 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1720630, 46656 ^ [_1720628, _1720630, _1720632])))], (46658 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720628), 46656 ^ [_1720628, _1720630, _1720632]), hAPP(c_List_Oset(_1720628), _1720632))))]], -(hAPP(c_List_Ofilter(_1720628, _1720630), _1720632) = c_List_Olist_ONil(_1720628))], (3620 ^ _780119) ^ [_834556, _834558, _834560, _834562] : [-(c_List_Olistrel(_834562, _834558) = c_List_Olistrel(_834560, _834556)), _834562 = _834560, _834558 = _834556], (46131 ^ _780119) ^ [_1709329, _1709331, _1709333, _1709335, _1709337] : [hBOOL(hAPP(hAPP(c_member(_1709329), _1709331), hAPP(c_List_Oset(_1709329), _1709333))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1709335), hAPP(_1709337, _1709331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1709335), c_List_Olist_Olist__size(_1709329, _1709337, _1709333))))], (16104 ^ _780119) ^ [_1073573, _1073575, _1073577, _1073579] : [class_Rings_Olinordered__ring__strict(_1073573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073573), c_Groups_Ozero__class_Ozero(_1073573)), _1073575)), 16111 ^ _780119 : [(16118 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073573), _1073577), _1073579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073573), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073573), _1073575), _1073577)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073573), _1073575), _1073579))))], (16112 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073573), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073573), _1073575), _1073577)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073573), _1073575), _1073579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073573), _1073577), _1073579)))]]], (42647 ^ _780119) ^ [_1624297, _1624299, _1624301] : [-(hAPP(hAPP(c_Option_Omap(_1624297, _1624299), _1624301), c_Option_Ooption_ONone(_1624297)) = c_Option_Ooption_ONone(_1624299))], (47764 ^ _780119) ^ [_1744779, _1744781] : [-(c_List_Oconcat(tc_List_Olist(_1744779), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1744779), tc_List_Olist(tc_List_Olist(_1744779))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1744779)), _1744779, c_List_Olist_ONil(tc_List_Olist(_1744779)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1744779), tc_List_Olist(tc_List_Olist(_1744779))), _1744779), hAPP(hAPP(c_COMBC(tc_List_Olist(_1744779), tc_List_Olist(tc_List_Olist(_1744779)), tc_List_Olist(tc_List_Olist(_1744779))), c_List_Olist_OCons(tc_List_Olist(_1744779))), c_List_Olist_ONil(tc_List_Olist(_1744779)))))), _1744781)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1744779), tc_List_Olist(_1744779)), c_List_Otl(_1744779)), hAPP(c_List_Ofilter(tc_List_Olist(_1744779), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1744779)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1744779), tc_List_Olist(_1744779), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1744779)))), _1744781)))], (13919 ^ _780119) ^ [_1033303, _1033305, _1033307] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033303, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1033303, tc_HOL_Obool)), _1033305), _1033307)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1033303, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033303, tc_HOL_Obool)), _1033305)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033303, tc_HOL_Obool)), _1033307)))], (51549 ^ _780119) ^ [_1820075] : [-(class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(_1820075)))], (7524 ^ _780119) ^ [_906657, _906659, _906661] : [class_Lattices_Osemilattice__sup(_906657), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906657), _906659), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_906657), _906659), _906661))))], (33223 ^ _780119) ^ [] : [c_Int_OPls = c_Int_OMin], (32797 ^ _780119) ^ [_1391401, _1391403] : [class_Fields_Olinordered__field__inverse__zero(_1391401), class_Int_Onumber__ring(_1391401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391401), c_Groups_Ozero__class_Ozero(_1391401)), _1391403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391401), c_Groups_Ozero__class_Ozero(_1391401)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391401), _1391403), hAPP(c_Int_Onumber__class_Onumber__of(_1391401), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (16921 ^ _780119) ^ [_1087551, _1087553] : [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), _1087551), _1087553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1087553), _1087551)))], (22783 ^ _780119) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (7264 ^ _780119) ^ [_901798, _901800] : [-(c_Option_Oset(_901798, hAPP(c_Option_Ooption_OSome(_901798), _901800)) = hAPP(hAPP(c_Set_Oinsert(_901798), _901800), c_Orderings_Obot__class_Obot(tc_fun(_901798, tc_HOL_Obool))))], (13966 ^ _780119) ^ [_1034225, _1034227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034225), _1034227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1034225)), _1034227)))], (50266 ^ _780119) ^ [_1798950, _1798952, _1798954] : [-(hAPP(c_Lazy__Sequence_Oyield(_1798950), c_Lazy__Sequence_Olazy__sequence_OInsert(_1798950, _1798952, _1798954)) = hAPP(c_Option_Ooption_OSome(tc_prod(_1798950, tc_Lazy__Sequence_Olazy__sequence(_1798950))), hAPP(hAPP(c_Product__Type_OPair(_1798950, tc_Lazy__Sequence_Olazy__sequence(_1798950)), _1798952), _1798954)))], (21402 ^ _780119) ^ [_1169915, _1169917, _1169919, _1169921] : [class_Divides_Osemiring__div(_1169915), -(c_Divides_Odiv__class_Omod(_1169915, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169915), _1169917), _1169919), _1169921) = c_Divides_Odiv__class_Omod(_1169915, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169915), _1169917), c_Divides_Odiv__class_Omod(_1169915, _1169919, _1169921)), _1169921))], (23187 ^ _780119) ^ [_1203657] : [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, _1203657)))))], (41993 ^ _780119) ^ [_1608884, _1608886, _1608888] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1608884, tc_HOL_Obool)), _1608886)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608884), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1608884, tc_HOL_Obool), _1608886))), 42003 ^ _780119 : [(42006 ^ _780119) ^ [] : [hAPP(c_Finite__Set_Ocard(_1608884), 42002 ^ [_1608884, _1608886, _1608888]) = _1608888], (42004 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1608884, tc_HOL_Obool)), 42002 ^ [_1608884, _1608886, _1608888]), _1608886)))]], 42010 ^ _780119 : [(42011 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1608884, tc_HOL_Obool)), 42009 ^ [_1608884, _1608886, _1608888]), _1608886)))], (42014 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1608884, tc_HOL_Obool)), 42012 ^ [_1608884, _1608886, _1608888]), _1608886)))], (42018 ^ _780119) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1608884, tc_HOL_Obool)), 42009 ^ [_1608884, _1608886, _1608888]), 42012 ^ [_1608884, _1608886, _1608888]) = c_Orderings_Obot__class_Obot(tc_fun(_1608884, tc_HOL_Obool))], (42016 ^ _780119) ^ [] : [42009 ^ [_1608884, _1608886, _1608888] = 42012 ^ [_1608884, _1608886, _1608888]]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1608888), hAPP(c_Finite__Set_Ocard(tc_fun(_1608884, tc_HOL_Obool)), _1608886)) = hAPP(c_Finite__Set_Ocard(_1608884), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1608884, tc_HOL_Obool), _1608886)))], (39897 ^ _780119) ^ [_1558423, _1558425, _1558427, _1558429] : [c_Wellfounded_Oacyclic(_1558423, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1558423, _1558423)), hAPP(hAPP(c_Product__Type_OPair(_1558423, _1558423), _1558425), _1558427)), _1558429)), 39900 ^ _780119 : [(39903 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1558423, _1558423)), hAPP(hAPP(c_Product__Type_OPair(_1558423, _1558423), _1558427), _1558425)), c_Transitive__Closure_Ortrancl(_1558423, _1558429)))], (39901 ^ _780119) ^ [] : [-(c_Wellfounded_Oacyclic(_1558423, _1558429))]]], (13039 ^ _780119) ^ [_1017129, _1017131, _1017133] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1017129), _1017131)), hBOOL(hAPP(hAPP(c_member(_1017129), _1017133), _1017131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1017129), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017129, tc_HOL_Obool)), _1017131), hAPP(hAPP(c_Set_Oinsert(_1017129), _1017133), c_Orderings_Obot__class_Obot(tc_fun(_1017129, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1017129), _1017131))))], (14300 ^ _780119) ^ [_1041518] : [-(hAPP(c_Nat_OSuc, _1041518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041518), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (49845 ^ _780119) ^ [_1790858, _1790860, _1790862, _1790864] : [-(c_List_Olist__all(_1790858, _1790860, hAPP(hAPP(c_List_Oappend(_1790858), _1790862), _1790864))), c_List_Olist__all(_1790858, _1790860, _1790862), c_List_Olist__all(_1790858, _1790860, _1790864)], (45211 ^ _780119) ^ [_1686531, _1686533, _1686535, _1686537, _1686539, _1686541] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686531)), _1686533) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686535)), _1686537), -(c_Map_Omap__upds(_1686531, _1686535, _1686539, _1686533, hAPP(hAPP(c_List_Oappend(_1686535), _1686537), _1686541)) = c_Map_Omap__upds(_1686531, _1686535, _1686539, _1686533, _1686537))], (50240 ^ _780119) ^ [_1798086] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1798086)))], (45930 ^ _780119) ^ [_1704985, _1704987] : [-(c_List_Orotate(_1704985, _1704987) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1704985), tc_List_Olist(_1704985)), _1704987), c_List_Orotate1(_1704985)))], (18650 ^ _780119) ^ [_1120354, _1120356, _1120358, _1120360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120354), _1120356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120358), _1120360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120354), _1120358)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120356), _1120360))))], (51325 ^ _780119) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (36325 ^ _780119) ^ [_1469043, _1469045, _1469047, _1469049] : [c_Fun_Oinj__on(_1469043, _1469045, _1469047, c_Orderings_Otop__class_Otop(tc_fun(_1469043, tc_HOL_Obool))), 36328 ^ _780119 : [(36342 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1469045), _1469049), hAPP(c_Set_Oimage(_1469043, _1469045, _1469047), c_Orderings_Otop__class_Otop(tc_fun(_1469043, tc_HOL_Obool)))))), 36343 ^ _780119 : [(36344 ^ _780119) ^ [_1469446] : [_1469049 = hAPP(_1469047, _1469446), 36348 ^ _780119 : [(36351 ^ _780119) ^ [] : [36347 ^ [_1469043, _1469045, _1469047, _1469049, _1469446] = _1469446], (36349 ^ _780119) ^ [] : [-(_1469049 = hAPP(_1469047, 36347 ^ [_1469043, _1469045, _1469047, _1469049, _1469446]))]]]]], (36329 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1469045), _1469049), hAPP(c_Set_Oimage(_1469043, _1469045, _1469047), c_Orderings_Otop__class_Otop(tc_fun(_1469043, tc_HOL_Obool))))), 36333 ^ _780119 : [(36336 ^ _780119) ^ [_1469308] : [_1469049 = hAPP(_1469047, _1469308), -(_1469308 = 36332 ^ [_1469043, _1469045, _1469047, _1469049])], (36334 ^ _780119) ^ [] : [-(_1469049 = hAPP(_1469047, 36332 ^ [_1469043, _1469045, _1469047, _1469049]))]]]]], (36099 ^ _780119) ^ [_1464777, _1464779, _1464781, _1464783, _1464785] : [c_Fun_Oinj__on(_1464777, _1464779, _1464781, _1464783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1464777, tc_HOL_Obool)), _1464785), _1464783)), -(c_Fun_Oinj__on(_1464777, _1464779, _1464781, _1464785))], (7197 ^ _780119) ^ [_899496, _899498, _899500, _899502, _899504] : [c_Hoare__Mirabelle_Ohoare__valids(_899496, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_899496), tc_HOL_Obool)), _899498), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_899496), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_899496)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_899496))), hAPP(hAPP(c_COMBB(tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_899496))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_899496)), _899500)), c_Com_Ocom_OBODY)), _899502)), _899504)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_899496), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_899496)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_899496))), hAPP(hAPP(c_COMBB(tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_899496))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_899496)), _899500)), 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))), _899502)), _899504)), -(c_Hoare__Mirabelle_Ohoare__valids(_899496, _899498, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_899496), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_899496)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_899496))), hAPP(hAPP(c_COMBB(tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_899496, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_899496))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_899496)), _899500)), c_Com_Ocom_OBODY)), _899502)), _899504)))], (11097 ^ _780119) ^ [_977498, _977500, _977502, _977504, _977506] : [class_Groups_Ocomm__monoid__mult(_977498), hBOOL(hAPP(c_Finite__Set_Ofinite(_977500), _977502)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_977498, _977500, c_Groups_Otimes__class_Otimes(_977498)), hAPP(hAPP(c_COMBS(_977500, _977498, _977498), hAPP(hAPP(c_COMBB(_977498, tc_fun(_977498, _977498), _977500), c_Groups_Otimes__class_Otimes(_977498)), _977504)), _977506)), c_Groups_Oone__class_Oone(_977498)), _977502) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977498), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_977498, _977500, c_Groups_Otimes__class_Otimes(_977498)), _977504), c_Groups_Oone__class_Oone(_977498)), _977502)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_977498, _977500, c_Groups_Otimes__class_Otimes(_977498)), _977506), c_Groups_Oone__class_Oone(_977498)), _977502)))], (31665 ^ _780119) ^ [_1371136] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371136), c_Int_OPls)))], (25183 ^ _780119) ^ [_1241055, _1241057] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1241055, _1241057) = 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), _1241055), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241057))))], (50302 ^ _780119) ^ [_1799686, _1799688, _1799690, _1799692, _1799694] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1799686), _1799688), _1799690), _1799692), _1799694) = c_New__DSequence_Opos__single(_1799686, _1799688))], (15196 ^ _780119) ^ [_1058045] : [hAPP(c_Nat_OSuc, _1058045) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30835 ^ _780119) ^ [_1356448, _1356450] : [class_Int_Onumber__ring(_1356448), class_Rings_Olinordered__idom(_1356448), 30842 ^ _780119 : [(30849 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356448), hAPP(c_Int_Onumber__class_Onumber__of(_1356448), _1356450)), c_Groups_Ozero__class_Ozero(_1356448)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1356448), hAPP(c_Int_Onumber__class_Onumber__of(_1356448), _1356450)) = hAPP(c_Int_Onumber__class_Onumber__of(_1356448), _1356450))], (30843 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356448), hAPP(c_Int_Onumber__class_Onumber__of(_1356448), _1356450)), c_Groups_Ozero__class_Ozero(_1356448))), -(hAPP(c_Groups_Oabs__class_Oabs(_1356448), hAPP(c_Int_Onumber__class_Onumber__of(_1356448), _1356450)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1356448), hAPP(c_Int_Onumber__class_Onumber__of(_1356448), _1356450)))]]], (4102 ^ _780119) ^ [_842099, _842101, _842103, _842105, _842107, _842109, _842111, _842113] : [-(c_List_Olinorder__class_Osort__key(_842113, _842109, _842105, _842101) = c_List_Olinorder__class_Osort__key(_842111, _842107, _842103, _842099)), _842113 = _842111, _842109 = _842107, _842105 = _842103, _842101 = _842099], (41824 ^ _780119) ^ [_1605318, _1605320, _1605322] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1605318, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1605318, tc_HOL_Obool), tc_HOL_Obool)), _1605320), _1605322)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605318, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1605318, tc_HOL_Obool), _1605320)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1605318, tc_HOL_Obool), _1605322)))], (50676 ^ _780119) ^ [_1807910, _1807912, _1807914, _1807916, _1807918, _1807920] : [-(hAPP(hAPP(c_List_Ozip(_1807910, _1807912), c_List_Oreplicate(_1807910, _1807914, _1807916)), c_List_Oreplicate(_1807912, _1807918, _1807920)) = c_List_Oreplicate(tc_prod(_1807910, _1807912), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1807914), _1807918), hAPP(hAPP(c_Product__Type_OPair(_1807910, _1807912), _1807916), _1807920)))], (39992 ^ _780119) ^ [_1560693, _1560695] : [-(hAPP(c_Relation_OField(_1560693), hAPP(c_Relation_Oconverse(_1560693, _1560693), _1560695)) = hAPP(c_Relation_OField(_1560693), _1560695))], (50818 ^ _780119) ^ [_1810891, _1810893, _1810895, _1810897, _1810899, _1810901] : [-(c_Nitpick_Opair__box_OPairBox(_1810891, _1810893, _1810895, _1810897) = c_Nitpick_Opair__box_OPairBox(_1810891, _1810893, _1810899, _1810901)), _1810895 = _1810899, _1810897 = _1810901], (42992 ^ _780119) ^ [_1632349, _1632351, _1632353, _1632355] : [-(c_List_Oremove1(_1632349, _1632351, c_List_Oremove1(_1632349, _1632353, _1632355)) = c_List_Oremove1(_1632349, _1632353, c_List_Oremove1(_1632349, _1632351, _1632355)))], (23811 ^ _780119) ^ [_1215359, _1215361] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1215359, _1215361)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1215359), hAPP(c_Nat_OSuc, _1215361)))], (38152 ^ _780119) ^ [_1516897, _1516899, _1516901, _1516903, _1516905, _1516907, _1516909, _1516911] : [-(hAPP(c_Product__Type_Omap__pair(_1516897, _1516899, _1516901, _1516903, _1516905, _1516907), hAPP(hAPP(c_Product__Type_OPair(_1516897, _1516901), _1516909), _1516911)) = hAPP(hAPP(c_Product__Type_OPair(_1516899, _1516903), hAPP(_1516905, _1516909)), hAPP(_1516907, _1516911)))], (9698 ^ _780119) ^ [_947911, _947913, _947915, _947917] : [hBOOL(hAPP(hAPP(c_member(_947911), _947913), _947915)), hBOOL(hAPP(hAPP(c_member(_947911), _947913), _947917)), -(hBOOL(hAPP(hAPP(c_member(_947911), _947913), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947911, tc_HOL_Obool)), _947915), _947917))))], (40398 ^ _780119) ^ [_1570973, _1570975, _1570977, _1570979, _1570981, _1570983] : [c_Relation_Osingle__valued(_1570973, _1570975, _1570977), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570973, _1570975)), hAPP(hAPP(c_Product__Type_OPair(_1570973, _1570975), _1570979), _1570981)), _1570977)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570973, _1570975)), hAPP(hAPP(c_Product__Type_OPair(_1570973, _1570975), _1570979), _1570983)), _1570977)), -(_1570981 = _1570983)], (2924 ^ _780119) ^ [_823654, _823656] : [_823656 = _823654, -(c_SetInterval_Oord__class_OgreaterThan(_823656) = c_SetInterval_Oord__class_OgreaterThan(_823654))], (39543 ^ _780119) ^ [_1549697, _1549699, _1549701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1549697, _1549697), tc_HOL_Obool)), _1549699), hAPP(hAPP(c_Product__Type_OSigma(_1549697, _1549697), _1549701), hAPP(c_COMBK(tc_fun(_1549697, tc_HOL_Obool), _1549697), _1549701)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1549697, _1549697), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1549697, _1549699)), hAPP(hAPP(c_Product__Type_OSigma(_1549697, _1549697), _1549701), hAPP(c_COMBK(tc_fun(_1549697, tc_HOL_Obool), _1549697), _1549701)))))], (45034 ^ _780119) ^ [_1682798, _1682800, _1682802] : [-(c_List_Olist_ONil(_1682798) = hAPP(hAPP(c_List_Oappend(_1682798), _1682800), _1682802)), _1682800 = c_List_Olist_ONil(_1682798), _1682802 = c_List_Olist_ONil(_1682798)], (32679 ^ _780119) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34331 ^ _780119) ^ [_1424473, _1424475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1424473), _1424475)), -(c_Divides_Odivmod__nat(_1424473, _1424475) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1424473))], (46149 ^ _780119) ^ [_1709944, _1709946, _1709948] : [-(c_List_Olist_Olist__size(_1709944, _1709946, _1709948) = 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(_1709944, tc_Nat_Onat), _1709946), _1709948))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709944)), _1709948)))], (26459 ^ _780119) ^ [_1262954] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1262954)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1262954))], (4416 ^ _780119) ^ [_846948, _846950, _846952, _846954] : [-(c_Product__Type_Osnd(_846954, _846950) = c_Product__Type_Osnd(_846952, _846948)), _846954 = _846952, _846950 = _846948], (15760 ^ _780119) ^ [_1067214, _1067216, _1067218] : [class_Rings_Oordered__cancel__semiring(_1067214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067214), c_Groups_Ozero__class_Ozero(_1067214)), _1067216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067214), _1067218), c_Groups_Ozero__class_Ozero(_1067214))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067214), _1067218), _1067216)), c_Groups_Ozero__class_Ozero(_1067214))))], (36159 ^ _780119) ^ [_1466061, _1466063, _1466065, _1466067, _1466069, _1466071] : [c_Fun_Oinj__on(_1466061, _1466063, _1466065, _1466067), -(_1466069 = _1466071), hBOOL(hAPP(hAPP(c_member(_1466061), _1466069), _1466067)), hBOOL(hAPP(hAPP(c_member(_1466061), _1466071), _1466067)), hAPP(_1466065, _1466069) = hAPP(_1466065, _1466071)], (16404 ^ _780119) ^ [_1079076] : [class_Rings_Olinordered__semidom(_1079076), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079076), c_Groups_Oone__class_Oone(_1079076)), c_Groups_Ozero__class_Ozero(_1079076)))], (1992 ^ _780119) ^ [_808998, _809000, _809002, _809004, _809006, _809008] : [-(c_Option_Ooption_Ooption__size(_809008, _809004, _809000) = c_Option_Ooption_Ooption__size(_809006, _809002, _808998)), _809008 = _809006, _809004 = _809002, _809000 = _808998], (5692 ^ _780119) ^ [_867278, _867280, _867282, _867284, _867286, _867288] : [-(c_Map_Odom(_867288, _867284, _867280) = c_Map_Odom(_867286, _867282, _867278)), _867288 = _867286, _867284 = _867282, _867280 = _867278], (49874 ^ _780119) ^ [_1791409, _1791411] : [-(c_List_Olist__all(_1791409, _1791411, c_List_Olist_ONil(_1791409)))], (13895 ^ _780119) ^ [_1032734, _1032736, _1032738] : [class_Lattices_Oboolean__algebra(_1032734), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1032734), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1032734), _1032736), _1032738)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1032734), hAPP(c_Groups_Ouminus__class_Ouminus(_1032734), _1032736)), hAPP(c_Groups_Ouminus__class_Ouminus(_1032734), _1032738)))], (28196 ^ _780119) ^ [_1301269] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1301269) = _1301269)], (26419 ^ _780119) ^ [_1262166, _1262168] : [class_Rings_Olinordered__idom(_1262166), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262166), hAPP(c_Groups_Oabs__class_Oabs(_1262166), _1262168)), hAPP(c_Groups_Oabs__class_Oabs(_1262166), _1262168)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262166), _1262168), _1262168))], (23899 ^ _780119) ^ [_1217283, _1217285] : [hAPP(_1217283, 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), _1217283), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217285)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1217283), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1217285)))], (4782 ^ _780119) ^ [_853043, _853045] : [_853045 = _853043, -(c_If(_853045) = c_If(_853043))], (13408 ^ _780119) ^ [_1024064, _1024066, _1024068] : [class_Groups_Oordered__ab__group__add(_1024064), 13411 ^ _780119 : [(13418 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024064), _1024068), _1024066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024064), hAPP(c_Groups_Ouminus__class_Ouminus(_1024064), _1024066)), hAPP(c_Groups_Ouminus__class_Ouminus(_1024064), _1024068))))], (13412 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024064), hAPP(c_Groups_Ouminus__class_Ouminus(_1024064), _1024066)), hAPP(c_Groups_Ouminus__class_Ouminus(_1024064), _1024068))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024064), _1024068), _1024066)))]]], (51517 ^ _780119) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (13026 ^ _780119) ^ [_1016756, _1016758, _1016760, _1016762] : [c_Map_Odom(_1016756, _1016758, _1016760) = hAPP(hAPP(c_Set_Oinsert(_1016756), _1016762), c_Orderings_Obot__class_Obot(tc_fun(_1016756, tc_HOL_Obool))), -(_1016760 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1016756, tc_Option_Ooption(_1016758)), hAPP(c_COMBK(tc_Option_Ooption(_1016758), _1016756), c_Option_Ooption_ONone(_1016758))), _1016762), hAPP(c_Option_Ooption_OSome(_1016758), 13029 ^ [_1016756, _1016758, _1016760, _1016762])))], (37690 ^ _780119) ^ [_1502523, _1502525, _1502527, _1502529] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502523, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1502523, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1502523, _1502525), _1502527)), hAPP(c_Relation_ODomain(_1502523, _1502525), _1502529))), hAPP(c_Relation_ODomain(_1502523, _1502525), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1502523, _1502525), tc_HOL_Obool)), _1502527), _1502529)))))], (42768 ^ _780119) ^ [] : [c_Com_OWT__bodies, 42771 ^ _780119 : [(42772 ^ _780119) ^ [_1627291] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1627291), 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)), _1627291)))]]], (35715 ^ _780119) ^ [_1455394, _1455396, _1455398, _1455400, _1455402] : [c_Equiv__Relations_Oequiv(_1455394, _1455396, _1455398), 35718 ^ _780119 : [(35729 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1455394, _1455394)), hAPP(hAPP(c_Product__Type_OPair(_1455394, _1455394), _1455400), _1455402)), _1455398))), hAPP(c_Relation_OImage(_1455394, _1455394, _1455398), hAPP(hAPP(c_Set_Oinsert(_1455394), _1455400), c_Orderings_Obot__class_Obot(tc_fun(_1455394, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1455394, _1455394, _1455398), hAPP(hAPP(c_Set_Oinsert(_1455394), _1455402), c_Orderings_Obot__class_Obot(tc_fun(_1455394, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1455394), _1455400), _1455396)), hBOOL(hAPP(hAPP(c_member(_1455394), _1455402), _1455396))], (35719 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1455394, _1455394)), hAPP(hAPP(c_Product__Type_OPair(_1455394, _1455394), _1455400), _1455402)), _1455398)), 35722 ^ _780119 : [(35725 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1455394), _1455400), _1455396)))], (35727 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1455394), _1455402), _1455396)))], (35723 ^ _780119) ^ [] : [-(hAPP(c_Relation_OImage(_1455394, _1455394, _1455398), hAPP(hAPP(c_Set_Oinsert(_1455394), _1455400), c_Orderings_Obot__class_Obot(tc_fun(_1455394, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1455394, _1455394, _1455398), hAPP(hAPP(c_Set_Oinsert(_1455394), _1455402), c_Orderings_Obot__class_Obot(tc_fun(_1455394, tc_HOL_Obool)))))]]]]], (38677 ^ _780119) ^ [_1529355, _1529357, _1529359, _1529361, _1529363, _1529365] : [-(hAPP(hAPP(c_Fun_Ocomp(_1529355, _1529357, _1529359, hAPP(c_COMBK(_1529357, _1529355), _1529361)), _1529363), _1529365) = _1529361)], (4034 ^ _780119) ^ [_841053, _841055, _841057, _841059] : [-(c_HOL_OLet(_841059, _841055) = c_HOL_OLet(_841057, _841053)), _841059 = _841057, _841055 = _841053], (51541 ^ _780119) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (23320 ^ _780119) ^ [_1206286, _1206288] : [_1206286 = _1206288, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206286) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206288))], (37823 ^ _780119) ^ [_1506852, _1506854, _1506856, _1506858, _1506860] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1506852, _1506854), _1506856), hAPP(hAPP(c_COMBS(_1506852, tc_fun(_1506854, tc_HOL_Obool), tc_fun(_1506854, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506854, tc_HOL_Obool), tc_fun(tc_fun(_1506854, tc_HOL_Obool), tc_fun(_1506854, tc_HOL_Obool)), _1506852), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506854, tc_HOL_Obool))), _1506858)), _1506860)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1506852, _1506854), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1506852, _1506854), _1506856), _1506858)), hAPP(hAPP(c_Product__Type_OSigma(_1506852, _1506854), _1506856), _1506860)))], (36938 ^ _780119) ^ [_1483021, _1483023, _1483025, _1483027, _1483029] : [c_Typedef_Otype__definition(_1483021, _1483023, _1483025, _1483027, _1483029), -(hAPP(c_Set_Oimage(_1483023, _1483021, _1483027), _1483029) = c_Orderings_Otop__class_Otop(tc_fun(_1483021, tc_HOL_Obool)))], (29562 ^ _780119) ^ [] : [-(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)))], (33291 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (35177 ^ _780119) ^ [_1441894, _1441896, _1441898, _1441900] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1441894, tc_HOL_Obool), tc_fun(_1441894, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1441894, tc_HOL_Obool), tc_fun(_1441894, tc_HOL_Obool)), _1441898), _1441900)), c_Wellfounded_Omax__ext(_1441894, _1441896))), -(c_Wellfounded_Omax__extp(_1441894, hAPP(hAPP(c_COMBC(_1441894, tc_fun(tc_prod(_1441894, _1441894), tc_HOL_Obool), tc_fun(_1441894, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441894, tc_fun(tc_fun(tc_prod(_1441894, _1441894), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1441894, _1441894), tc_HOL_Obool), tc_fun(_1441894, tc_HOL_Obool)), _1441894), c_COMBC(_1441894, tc_fun(tc_prod(_1441894, _1441894), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441894, tc_prod(_1441894, _1441894)), tc_fun(_1441894, tc_fun(tc_fun(tc_prod(_1441894, _1441894), tc_HOL_Obool), tc_HOL_Obool)), _1441894), hAPP(c_COMBB(tc_prod(_1441894, _1441894), tc_fun(tc_fun(tc_prod(_1441894, _1441894), tc_HOL_Obool), tc_HOL_Obool), _1441894), c_member(tc_prod(_1441894, _1441894)))), c_Product__Type_OPair(_1441894, _1441894)))), _1441896), _1441898, _1441900))], (19180 ^ _780119) ^ [_1129199, _1129201, _1129203, _1129205] : [class_Divides_Osemiring__div(_1129199), -(_1129201 = c_Groups_Ozero__class_Ozero(_1129199)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129199), _1129201), _1129203)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129199), _1129201), _1129205)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129199), _1129203), _1129205))], (30207 ^ _780119) ^ [_1344393, _1344395, _1344397] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1344393, _1344395, _1344397))), -(hBOOL(hAPP(c_Com_OWT, _1344397)))], (50458 ^ _780119) ^ [_1803359, _1803361, _1803363] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1803359, _1803359, hAPP(hAPP(c_COMBB(tc_fun(_1803359, tc_HOL_Obool), tc_fun(_1803359, tc_HOL_Obool), _1803359), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1803359), c_fNot)), c_fequal)), _1803361), _1803363)), _1803361 = _1803363], (47580 ^ _780119) ^ [_1739588, _1739590] : [class_Groups_Ocomm__monoid__add(_1739588), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1739588), hAPP(c_List_Orev(_1739588), _1739590)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1739588), _1739590))], (35594 ^ _780119) ^ [_1452828, _1452830, _1452832, _1452834, _1452836] : [c_Equiv__Relations_Oequiv(_1452828, _1452830, _1452832), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452828, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1452828, _1452828, _1452832), hAPP(hAPP(c_Set_Oinsert(_1452828), _1452834), c_Orderings_Obot__class_Obot(tc_fun(_1452828, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1452828, _1452828, _1452832), hAPP(hAPP(c_Set_Oinsert(_1452828), _1452836), c_Orderings_Obot__class_Obot(tc_fun(_1452828, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1452828), _1452834), _1452830)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1452828, _1452828)), hAPP(hAPP(c_Product__Type_OPair(_1452828, _1452828), _1452836), _1452834)), _1452832)))], (45094 ^ _780119) ^ [_1683847, _1683849, _1683851] : [_1683851 = c_List_Olist_ONil(_1683847), -(hAPP(hAPP(c_List_Oappend(_1683847), _1683849), _1683851) = _1683849)], (46959 ^ _780119) ^ [_1727036, _1727038] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1727036, _1727038)))], (18618 ^ _780119) ^ [_1119733, _1119735] : [-(c_Sum__Type_OPlus(_1119733, _1119735, c_Orderings_Otop__class_Otop(tc_fun(_1119733, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1119735, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1119733, _1119735), tc_HOL_Obool)))], (45309 ^ _780119) ^ [_1689000, _1689002, _1689004, _1689006, _1689008] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689000), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689002)), _1689004)))), -(hAPP(hAPP(c_List_Olist__update(_1689002, hAPP(hAPP(c_List_Oappend(_1689002), _1689004), _1689006)), _1689000), _1689008) = hAPP(hAPP(c_List_Oappend(_1689002), _1689004), hAPP(hAPP(c_List_Olist__update(_1689002, _1689006), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1689000), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689002)), _1689004))), _1689008)))], (10200 ^ _780119) ^ [_958347, _958349, _958351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958347, tc_HOL_Obool)), _958349), _958351)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958347, tc_HOL_Obool)), _958349), _958351) = _958349)], (286 ^ _780119) ^ [_784602, _784604, _784606, _784608, _784610, _784612, _784614, _784616] : [-(c_Wellfounded_Omax__extp(_784614, _784610, _784606, _784602)), c_Wellfounded_Omax__extp(_784616, _784612, _784608, _784604), _784616 = _784614, _784612 = _784610, _784608 = _784606, _784604 = _784602], (37860 ^ _780119) ^ [_1508047, _1508049, _1508051, _1508053, _1508055, _1508057] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508047, _1508049)), hAPP(hAPP(c_Product__Type_OPair(_1508047, _1508049), _1508051), _1508053)), hAPP(hAPP(c_Product__Type_OSigma(_1508047, _1508049), _1508055), _1508057))), -(hBOOL(hAPP(hAPP(c_member(_1508049), _1508053), hAPP(_1508057, _1508051))))], (8112 ^ _780119) ^ [_918945, _918947, _918949] : [-(hAPP(hAPP(c_Set_Oinsert(_918945), _918947), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918945, tc_HOL_Obool)), _918949), hAPP(hAPP(c_Set_Oinsert(_918945), _918947), c_Orderings_Obot__class_Obot(tc_fun(_918945, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_918945), _918947), _918949))], (44522 ^ _780119) ^ [_1672071] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1672071)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1672071))], (47686 ^ _780119) ^ [_1742690, _1742692, _1742694, _1742696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1742690), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742692)), _1742694))), -(hAPP(c_List_Orev(_1742692), hAPP(hAPP(c_List_Olist__update(_1742692, _1742694), _1742690), _1742696)) = hAPP(hAPP(c_List_Olist__update(_1742692, hAPP(c_List_Orev(_1742692), _1742694)), 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(_1742692)), _1742694)), _1742690)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1742696))], (35955 ^ _780119) ^ [_1460985, _1460987, _1460989, _1460991, _1460993, _1460995] : [c_Equiv__Relations_Ocongruent(_1460985, _1460987, _1460989, _1460991), hBOOL(hAPP(hAPP(c_member(tc_prod(_1460985, _1460985)), hAPP(hAPP(c_Product__Type_OPair(_1460985, _1460985), _1460993), _1460995)), _1460989)), -(hAPP(_1460991, _1460993) = hAPP(_1460991, _1460995))], (32693 ^ _780119) ^ [_1389636, _1389638] : [class_Int_Onumber__ring(_1389636), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389636), hAPP(c_Int_Onumber__class_Onumber__of(_1389636), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1389638) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389636), _1389638), _1389638))], (37326 ^ _780119) ^ [_1493614, _1493616, _1493618] : [c_Wellfounded_Owf(_1493614, _1493616), hBOOL(hAPP(hAPP(c_member(tc_prod(_1493614, _1493614)), hAPP(hAPP(c_Product__Type_OPair(_1493614, _1493614), _1493618), _1493618)), _1493616))], (14606 ^ _780119) ^ [_1048024, _1048026, _1048028] : [class_Power_Opower(_1048024), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1048024), _1048026), hAPP(c_Nat_OSuc, _1048028)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048024), _1048026), hAPP(hAPP(c_Power_Opower__class_Opower(_1048024), _1048026), _1048028)))], (242 ^ _780119) ^ [_783864, _783866, _783868, _783870] : [-(c_Equiv__Relations_Oequivp(_783868, _783864)), c_Equiv__Relations_Oequivp(_783870, _783866), _783870 = _783868, _783866 = _783864], (896 ^ _780119) ^ [_793797, _793799, _793801, _793803, _793805, _793807] : [-(c_List_Olist__all(_793805, _793801, _793797)), c_List_Olist__all(_793807, _793803, _793799), _793807 = _793805, _793803 = _793801, _793799 = _793797], (12355 ^ _780119) ^ [_1003611, _1003613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003611), _1003613)), _1003613 = _1003611], (46453 ^ _780119) ^ [_1716513, _1716515, _1716517, _1716519] : [-(hAPP(hAPP(c_List_Omap(_1716513, _1716515), _1716517), c_List_Obutlast(_1716513, _1716519)) = c_List_Obutlast(_1716515, hAPP(hAPP(c_List_Omap(_1716513, _1716515), _1716517), _1716519)))], (48755 ^ _780119) ^ [_1765939, _1765941, _1765943, _1765945] : [class_Enum_Oenum(_1765939), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765941)), _1765943) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765939)), c_Enum_Oenum__class_Oenum(_1765939)), -(hAPP(hAPP(c_Map_Omap__of(_1765939, _1765941), hAPP(hAPP(c_List_Ozip(_1765939, _1765941), c_Enum_Oenum__class_Oenum(_1765939)), _1765943)), _1765945) = hAPP(c_Option_Ooption_OSome(_1765941), 48762 ^ [_1765939, _1765941, _1765943, _1765945]))], (43525 ^ _780119) ^ [_1647548, _1647550, _1647552, _1647554, _1647556, _1647558] : [-(c_List_Olistrelp(_1647548, _1647550, hAPP(hAPP(c_List_Olist_OCons(_1647548), _1647552), _1647554), hAPP(hAPP(c_List_Olist_OCons(_1647548), _1647556), _1647558))), hBOOL(hAPP(hAPP(_1647550, _1647552), _1647556)), c_List_Olistrelp(_1647548, _1647550, _1647554, _1647558)], (41868 ^ _780119) ^ [_1606205, _1606207, _1606209] : [class_Complete__Lattice_Ocomplete__lattice(_1606205), -(c_Complete__Lattice_OSup__class_OSup(_1606205, hAPP(hAPP(c_Set_Oinsert(_1606205), _1606207), _1606209)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1606205), _1606207), c_Complete__Lattice_OSup__class_OSup(_1606205, _1606209)))], (12373 ^ _780119) ^ [_1003794, _1003796] : [-(_1003794 = _1003796), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003794), _1003796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003796), _1003794)))], (36858 ^ _780119) ^ [_1480890, _1480892, _1480894, _1480896] : [c_Fun_Oinj__on(_1480890, _1480892, _1480894, _1480896), -(hAPP(c_Set_Oimage(_1480892, _1480890, c_Fun_Othe__inv__into(_1480890, _1480892, _1480896, _1480894)), hAPP(c_Set_Oimage(_1480890, _1480892, _1480894), _1480896)) = _1480896)], (27492 ^ _780119) ^ [_1288060, _1288062, _1288064, _1288066, _1288068] : [class_Orderings_Olinorder(_1288060), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288060, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1288060, _1288062, _1288064)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1288060, _1288066, _1288068)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1288060, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288060), _1288062), _1288066), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288060), _1288064), _1288068)))], (34925 ^ _780119) ^ [_1435905, _1435907, _1435909, _1435911, _1435913] : [-(c_Product__Type_Oprod_Oprod__size(_1435905, _1435907, _1435909, _1435911, _1435913) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1435909, hAPP(c_Product__Type_Ofst(_1435905, _1435907), _1435913))), hAPP(_1435911, hAPP(c_Product__Type_Osnd(_1435905, _1435907), _1435913)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26405 ^ _780119) ^ [_1261892, _1261894] : [class_Groups_Oordered__ab__group__add__abs(_1261892), -(hAPP(c_Groups_Oabs__class_Oabs(_1261892), hAPP(c_Groups_Oabs__class_Oabs(_1261892), _1261894)) = hAPP(c_Groups_Oabs__class_Oabs(_1261892), _1261894))], (43705 ^ _780119) ^ [_1652601, _1652603, _1652605, _1652607] : [-(hBOOL(hAPP(hAPP(c_member(_1652601), _1652603), hAPP(c_List_Oset(_1652601), _1652605)))), hBOOL(hAPP(hAPP(c_member(_1652601), _1652603), hAPP(c_List_Oset(_1652601), c_List_Osublist(_1652601, _1652605, _1652607))))], (17683 ^ _780119) ^ [_1101597, _1101599, _1101601] : [hBOOL(hAPP(_1101597, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1101599), _1101601))), 17686 ^ _780119 : [(17693 ^ _780119) ^ [_1101782] : [_1101599 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101601), _1101782), -(hBOOL(hAPP(_1101597, _1101782)))], (17687 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101599), _1101601)), -(hBOOL(hAPP(_1101597, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (17616 ^ _780119) ^ [_1100396, _1100398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1100396), hAPP(c_Nat_OSuc, _1100398))), _1100396)))], (35554 ^ _780119) ^ [_1451887, _1451889, _1451891, _1451893] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1451887, _1451887)), hAPP(hAPP(c_Product__Type_OPair(_1451887, _1451887), _1451889), _1451891)), c_Relation_OId__on(_1451887, _1451893))), 35557 ^ _780119 : [(35560 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451887), _1451889), _1451893)))], (35558 ^ _780119) ^ [] : [-(_1451889 = _1451891)]]], (12934 ^ _780119) ^ [_1014869, _1014871, _1014873] : [class_Lattices_Oab__semigroup__idem__mult(_1014869), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014869), _1014871)), -(_1014871 = c_Orderings_Obot__class_Obot(tc_fun(_1014869, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014869), _1014873)), -(_1014873 = c_Orderings_Obot__class_Obot(tc_fun(_1014869, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1014869, c_Groups_Otimes__class_Otimes(_1014869)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014869, tc_HOL_Obool)), _1014871), _1014873)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014869), hAPP(c_Finite__Set_Ofold1(_1014869, c_Groups_Otimes__class_Otimes(_1014869)), _1014871)), hAPP(c_Finite__Set_Ofold1(_1014869, c_Groups_Otimes__class_Otimes(_1014869)), _1014873)))], (24231 ^ _780119) ^ [_1223764, _1223766] : [-(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)), _1223764)), 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), _1223766), _1223764))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1223764), _1223766))], (15514 ^ _780119) ^ [_1062855, _1062857, _1062859, _1062861] : [class_Rings_Olinordered__semidom(_1062855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062855), _1062857), _1062859)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062855), c_Groups_Ozero__class_Ozero(_1062855)), _1062857)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062855), hAPP(hAPP(c_Power_Opower__class_Opower(_1062855), _1062857), _1062861)), hAPP(hAPP(c_Power_Opower__class_Opower(_1062855), _1062859), _1062861))))], (40054 ^ _780119) ^ [_1562118, _1562120, _1562122, _1562124, _1562126] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562118, _1562120)), hAPP(hAPP(c_Product__Type_OPair(_1562118, _1562120), _1562122), _1562124)), _1562126)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562120, _1562118)), hAPP(hAPP(c_Product__Type_OPair(_1562120, _1562118), _1562124), _1562122)), hAPP(c_Relation_Oconverse(_1562118, _1562120), _1562126))))], (7738 ^ _780119) ^ [_911265, _911267, _911269, _911271, _911273] : [c_Finite__Set_Ofolding__one__idem(_911265, _911267, _911269), hAPP(_911271, hAPP(hAPP(_911267, 7743 ^ [_911265, _911267, _911269, _911271, _911273]), 7744 ^ [_911265, _911267, _911269, _911271, _911273])) = hAPP(hAPP(_911267, hAPP(_911271, 7743 ^ [_911265, _911267, _911269, _911271, _911273])), hAPP(_911271, 7744 ^ [_911265, _911267, _911269, _911271, _911273])), hBOOL(hAPP(c_Finite__Set_Ofinite(_911265), _911273)), -(_911273 = c_Orderings_Obot__class_Obot(tc_fun(_911265, tc_HOL_Obool))), -(hAPP(_911271, hAPP(_911269, _911273)) = hAPP(_911269, hAPP(c_Set_Oimage(_911265, _911265, _911271), _911273)))], (46022 ^ _780119) ^ [_1707025, _1707027] : [class_Groups_Omonoid__add(_1707025), -(hAPP(c_List_Ofoldl(_1707025, _1707025, c_Groups_Oplus__class_Oplus(_1707025), c_Groups_Ozero__class_Ozero(_1707025)), _1707027) = c_List_Ofoldr(_1707025, _1707025, c_Groups_Oplus__class_Oplus(_1707025), _1707027, c_Groups_Ozero__class_Ozero(_1707025)))], (50019 ^ _780119) ^ [] : [-(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))))], (36557 ^ _780119) ^ [_1473864, _1473866, _1473868, _1473870, _1473872] : [c_Fun_Oinj__on(_1473864, _1473866, _1473868, hAPP(hAPP(c_Set_Oinsert(_1473864), _1473870), _1473872)), 36560 ^ _780119 : [(36563 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1473866), hAPP(_1473868, _1473870)), hAPP(c_Set_Oimage(_1473864, _1473866, _1473868), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1473864, tc_HOL_Obool)), _1473872), hAPP(hAPP(c_Set_Oinsert(_1473864), _1473870), c_Orderings_Obot__class_Obot(tc_fun(_1473864, tc_HOL_Obool)))))))], (36561 ^ _780119) ^ [] : [-(c_Fun_Oinj__on(_1473864, _1473866, _1473868, _1473872))]]], (42441 ^ _780119) ^ [_1619100, _1619102, _1619104, _1619106, _1619108, _1619110] : [-(c_Map_Omap__add(_1619100, _1619102, _1619104, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1619100, tc_Option_Ooption(_1619102)), _1619106), _1619108), hAPP(c_Option_Ooption_OSome(_1619102), _1619110))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1619100, tc_Option_Ooption(_1619102)), c_Map_Omap__add(_1619100, _1619102, _1619104, _1619106)), _1619108), hAPP(c_Option_Ooption_OSome(_1619102), _1619110)))], (50933 ^ _780119) ^ [_1813627, _1813629] : [class_Lattices_Obounded__lattice(_1813627), -(class_Lattices_Obounded__lattice(tc_fun(_1813629, _1813627)))], (35323 ^ _780119) ^ [_1444806, _1444808, _1444810] : [-(c_Wellfounded_Omlex__prod(_1444806, _1444808, _1444810) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1444806), _1444806), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1444806, c_Wellfounded_Oless__than, _1444810)), hAPP(hAPP(c_COMBS(_1444806, _1444806, tc_prod(tc_Nat_Onat, _1444806)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1444806, tc_prod(tc_Nat_Onat, _1444806)), _1444806), c_Product__Type_OPair(tc_Nat_Onat, _1444806)), _1444808)), c_COMBI(_1444806))))], (28822 ^ _780119) ^ [_1314211, _1314213, _1314215] : [class_Orderings_Olinorder(_1314211), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314211), _1314213)), -(_1314213 = c_Orderings_Obot__class_Obot(tc_fun(_1314211, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1314211), _1314215), c_Big__Operators_Olattice_OInf__fin(_1314211, c_Orderings_Oord__class_Omin(_1314211), _1314213)) = c_Big__Operators_Olattice_OInf__fin(_1314211, c_Orderings_Oord__class_Omin(_1314211), hAPP(c_Set_OCollect(_1314211), hAPP(hAPP(c_COMBB(tc_fun(_1314211, tc_HOL_Obool), tc_HOL_Obool, _1314211), c_HOL_OEx(_1314211)), hAPP(hAPP(c_COMBC(_1314211, tc_fun(_1314211, tc_HOL_Obool), tc_fun(_1314211, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1314211, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1314211, tc_HOL_Obool), tc_fun(_1314211, tc_HOL_Obool)), _1314211), c_COMBS(_1314211, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1314211, tc_HOL_Obool), tc_fun(_1314211, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1314211), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1314211), c_fconj)), hAPP(hAPP(c_COMBC(_1314211, tc_fun(_1314211, _1314211), tc_fun(_1314211, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1314211, tc_HOL_Obool), tc_fun(tc_fun(_1314211, _1314211), tc_fun(_1314211, tc_HOL_Obool)), _1314211), c_COMBB(_1314211, tc_HOL_Obool, _1314211)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1314211), _1314215))))), hAPP(hAPP(c_COMBC(_1314211, tc_fun(_1314211, tc_HOL_Obool), tc_HOL_Obool), c_member(_1314211)), _1314213))))))], (45118 ^ _780119) ^ [_1684261, _1684263, _1684265] : [class_Groups_Omonoid__add(_1684261), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1684261), hAPP(hAPP(c_List_Oappend(_1684261), _1684263), _1684265)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1684261), hAPP(c_List_Omonoid__add__class_Olistsum(_1684261), _1684263)), hAPP(c_List_Omonoid__add__class_Olistsum(_1684261), _1684265)))], (23380 ^ _780119) ^ [_1207341, _1207343] : [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)), _1207341)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1207343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1207341), _1207343)))], (35339 ^ _780119) ^ [_1445684] : [-(c_Wellfounded_Omeasure(_1445684) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1445684), c_Wellfounded_Oless__than))], (36748 ^ _780119) ^ [_1478535] : [class_Nat_Osemiring__char__0(_1478535), -(c_Fun_Oinj__on(tc_Nat_Onat, _1478535, c_Nat_Osemiring__1__class_Oof__nat(_1478535), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (12609 ^ _780119) ^ [_1008760, _1008762] : [c_Option_Ooption_ONone(_1008760) = hAPP(c_Option_Ooption_OSome(_1008760), _1008762)], (7918 ^ _780119) ^ [_914892, _914894, _914896, _914898] : [c_Com_Ocom_OWhile(_914892, _914894) = c_Com_Ocom_OSemi(_914896, _914898)], (16030 ^ _780119) ^ [_1072251, _1072253] : [class_Rings_Olinordered__ring(_1072251), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072251), _1072253), _1072253)), c_Groups_Ozero__class_Ozero(_1072251)))], (14110 ^ _780119) ^ [_1037454, _1037456, _1037458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1037454, tc_HOL_Obool)), _1037456), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1037454, tc_HOL_Obool)), _1037458))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1037454, tc_HOL_Obool)), _1037456), _1037458) = c_Orderings_Obot__class_Obot(tc_fun(_1037454, tc_HOL_Obool)))], (16684 ^ _780119) ^ [_1083825, _1083827] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1083825), c_Groups_Ozero__class_Ozero(_1083825)), hAPP(c_Nat_OSuc, _1083827)) = c_Groups_Ozero__class_Ozero(_1083825)), class_Power_Opower(_1083825), class_Rings_Osemiring__0(_1083825)], (13646 ^ _780119) ^ [_1028348, _1028350] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028348), _1028350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028350), hAPP(c_Nat_OSuc, _1028348))))], (1570 ^ _780119) ^ [_802468, _802470] : [-(class_Groups_Oab__semigroup__add(_802468)), _802470 = _802468, class_Groups_Oab__semigroup__add(_802470)], (2898 ^ _780119) ^ [_823263, _823265] : [_823265 = _823263, -(c_Relation_OId(_823265) = c_Relation_OId(_823263))], (29526 ^ _780119) ^ [_1328516] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1328516))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328516)))], (41826 ^ _780119) ^ [_1605388, _1605390, _1605392] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1605388, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1605388, tc_HOL_Obool)), _1605390), _1605392)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1605388, tc_HOL_Obool)), _1605390), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1605388, tc_HOL_Obool), _1605392)))], (46645 ^ _780119) ^ [_1720423, _1720425, _1720427] : [hAPP(c_List_Ofilter(_1720423, _1720425), _1720427) = c_List_Olist_ONil(_1720423), 46648 ^ _780119 : [(46649 ^ _780119) ^ [_1720520] : [hBOOL(hAPP(hAPP(c_member(_1720423), _1720520), hAPP(c_List_Oset(_1720423), _1720427))), hBOOL(hAPP(_1720425, _1720520))]]], (18868 ^ _780119) ^ [_1124015, _1124017, _1124019, _1124021, _1124023, _1124025] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1124015), _1124017)), _1124019) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1124021), _1124023)), _1124025), 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), _1124021), _1124023)), _1124025)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124019), _1124015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1124025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1124021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124021), _1124015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124023), _1124017)))], (46256 ^ _780119) ^ [_1712606, _1712608, _1712610] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712606), tc_List_Olist(_1712606))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712606), tc_List_Olist(_1712606)), c_List_Olist_ONil(_1712606)), _1712608)), c_List_Olexord(_1712606, _1712610))), -(_1712608 = hAPP(hAPP(c_List_Olist_OCons(_1712606), 46259 ^ [_1712606, _1712608, _1712610]), 46260 ^ [_1712606, _1712608, _1712610]))], (7374 ^ _780119) ^ [_904024, _904026, _904028] : [_904028 = hAPP(c_Option_Ooption_OSome(_904024), _904026), -(hBOOL(hAPP(hAPP(c_member(_904024), _904026), c_Option_Oset(_904024, _904028))))], (50456 ^ _780119) ^ [_1803314] : [-(c_Predicate_Oconversep(_1803314, _1803314, c_fequal) = c_fequal)], (33057 ^ _780119) ^ [_1396090, _1396092, _1396094] : [class_Groups_Omonoid__mult(_1396090), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1396090), _1396092), 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)))), _1396094))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396090), _1396092), hAPP(hAPP(c_Power_Opower__class_Opower(_1396090), hAPP(hAPP(c_Power_Opower__class_Opower(_1396090), _1396092), _1396094)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (6775 ^ _780119) ^ [_891349, _891351, _891353] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_891349), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891349, tc_HOL_Obool)), _891351), _891353)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_891349), _891351)), hBOOL(hAPP(c_Finite__Set_Ofinite(_891349), _891353))], (51489 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (33543 ^ _780119) ^ [_1404491] : [-(c_Int_Oint__ge__less__than2(_1404491) = 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), _1404491)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (40030 ^ _780119) ^ [_1561566, _1561568, _1561570] : [c_Relation_Orefl__on(_1561566, _1561568, hAPP(c_Relation_Oconverse(_1561566, _1561566), _1561570)), -(c_Relation_Orefl__on(_1561566, _1561568, _1561570))], (51253 ^ _780119) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (28850 ^ _780119) ^ [_1314907, _1314909, _1314911] : [class_Orderings_Olinorder(_1314907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314907), _1314909)), hBOOL(hAPP(hAPP(c_member(_1314907), _1314911), _1314909)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314907), _1314911), c_Big__Operators_Olattice_OInf__fin(_1314907, c_Orderings_Oord__class_Omin(_1314907), _1314909)) = c_Big__Operators_Olattice_OInf__fin(_1314907, c_Orderings_Oord__class_Omin(_1314907), _1314909))], (38728 ^ _780119) ^ [_1530325, _1530327, _1530329, _1530331, _1530333, _1530335, _1530337] : [-(hAPP(c_Fun_Ocomp(_1530325, _1530327, _1530329, _1530331), hAPP(c_Fun_Ocomp(_1530333, _1530325, _1530329, _1530335), _1530337)) = hAPP(c_Fun_Ocomp(_1530333, _1530327, _1530329, hAPP(c_Fun_Ocomp(_1530325, _1530327, _1530333, _1530331), _1530335)), _1530337))], (45078 ^ _780119) ^ [_1683571, _1683573, _1683575] : [-(hAPP(hAPP(c_List_Oappend(_1683571), _1683573), _1683575) = c_List_Olist_ONil(_1683571)), _1683573 = c_List_Olist_ONil(_1683571), _1683575 = c_List_Olist_ONil(_1683571)], (35450 ^ _780119) ^ [_1449124, _1449126, _1449128, _1449130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1449124), _1449130)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1449128), _1449126))), -(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), _1449124), _1449126)), 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), _1449128), _1449130)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (50660 ^ _780119) ^ [_1807531, _1807533, _1807535, _1807537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1807531), _1807533)), -(hAPP(hAPP(c_List_Onth(_1807535), c_List_Oreplicate(_1807535, _1807533, _1807537)), _1807531) = _1807537)], (31313 ^ _780119) ^ [_1365524, _1365526] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1365524) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365526)), _1365524 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365526)), 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), _1365526)))], (33641 ^ _780119) ^ [_1410154, _1410156, _1410158, _1410160] : [_1410158 = _1410160, -(hAPP(hAPP(c_COMBC(_1410154, tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_fun(_1410156, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410156, tc_fun(tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_fun(_1410156, tc_HOL_Obool)), _1410154), c_COMBC(_1410156, tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410156, tc_prod(_1410154, _1410156)), tc_fun(_1410156, tc_fun(tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_HOL_Obool)), _1410154), hAPP(c_COMBB(tc_prod(_1410154, _1410156), tc_fun(tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_HOL_Obool), _1410156), c_member(tc_prod(_1410154, _1410156)))), c_Product__Type_OPair(_1410154, _1410156)))), _1410158) = hAPP(hAPP(c_COMBC(_1410154, tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_fun(_1410156, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410156, tc_fun(tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_fun(_1410156, tc_HOL_Obool)), _1410154), c_COMBC(_1410156, tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410156, tc_prod(_1410154, _1410156)), tc_fun(_1410156, tc_fun(tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_HOL_Obool)), _1410154), hAPP(c_COMBB(tc_prod(_1410154, _1410156), tc_fun(tc_fun(tc_prod(_1410154, _1410156), tc_HOL_Obool), tc_HOL_Obool), _1410156), c_member(tc_prod(_1410154, _1410156)))), c_Product__Type_OPair(_1410154, _1410156)))), _1410160))], (29512 ^ _780119) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (44362 ^ _780119) ^ [_1668702, _1668704, _1668706] : [-(hAPP(hAPP(c_List_Olist__update(_1668702, _1668704), _1668706), hAPP(hAPP(c_List_Onth(_1668702), _1668704), _1668706)) = _1668704)], (51469 ^ _780119) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (36523 ^ _780119) ^ [_1473137] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1473137)), c_Int_OInteg)))], (19076 ^ _780119) ^ [_1127606, _1127608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127606)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127608)), -(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), _1127606), _1127608))))], (18606 ^ _780119) ^ [_1119509, _1119511] : [class_Int_Oring__char__0(_1119509), hBOOL(hAPP(hAPP(c_member(_1119509), _1119511), c_Int_Oring__1__class_OInts(_1119509))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119509), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119509), c_Groups_Oone__class_Oone(_1119509)), _1119511)), _1119511) = c_Groups_Ozero__class_Ozero(_1119509)], (51479 ^ _780119) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (35291 ^ _780119) ^ [_1444152, _1444154] : [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), _1444152), _1444154)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1444152), _1444154)))], (32705 ^ _780119) ^ [_1389860] : [class_Rings_Osemiring__1(_1389860), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1389860), c_Groups_Ozero__class_Ozero(_1389860)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1389860))], (44500 ^ _780119) ^ [_1671704] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1671704)) = _1671704)], (50760 ^ _780119) ^ [_1809588, _1809590, _1809592, _1809594] : [50761 ^ _780119 : [(50764 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1809588), _1809592), _1809594))], (50762 ^ _780119) ^ [] : [_1809590 = _1809594]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1809588), hAPP(hAPP(c_List_Olist_OCons(_1809588), _1809590), _1809592)), _1809594)))], (30855 ^ _780119) ^ [_1356800, _1356802, _1356804, _1356806] : [class_Int_Onumber__ring(_1356800), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356800), hAPP(c_Int_Onumber__class_Onumber__of(_1356800), _1356802)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1356800), _1356804), hAPP(c_Int_Onumber__class_Onumber__of(_1356800), _1356806))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356800), hAPP(c_Int_Onumber__class_Onumber__of(_1356800), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1356802), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1356806)))), _1356804))], (35107 ^ _780119) ^ [_1439919, _1439921, _1439923] : [class_Rings_Osemiring__1(_1439919), hBOOL(hAPP(hAPP(c_member(_1439919), _1439921), c_Nat_Osemiring__1__class_ONats(_1439919))), hBOOL(hAPP(hAPP(c_member(_1439919), _1439923), c_Nat_Osemiring__1__class_ONats(_1439919))), -(hBOOL(hAPP(hAPP(c_member(_1439919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1439919), _1439921), _1439923)), c_Nat_Osemiring__1__class_ONats(_1439919))))], (28308 ^ _780119) ^ [_1303442, _1303444, _1303446] : [class_Orderings_Olinorder(_1303442), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303442), _1303444)), hBOOL(hAPP(hAPP(c_member(_1303442), _1303446), _1303444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303442), hAPP(c_Finite__Set_Ofold1(_1303442, c_Orderings_Oord__class_Omin(_1303442)), _1303444)), _1303446)))], (6375 ^ _780119) ^ [_882918, _882920, _882922] : [_882920 = _882922, -(hBOOL(hAPP(hAPP(c_member(_882918), _882920), hAPP(hAPP(c_Set_Oinsert(_882918), _882922), c_Orderings_Obot__class_Obot(tc_fun(_882918, tc_HOL_Obool))))))], (11575 ^ _780119) ^ [_988182, _988184, _988186, _988188] : [class_Rings_Ocomm__semiring__1(_988182), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988182), _988184), _988186)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988182), _988188), _988186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988182), _988184), _988188)), _988186))], (50182 ^ _780119) ^ [_1797054, _1797056] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1797054), _1797056)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1797054), _1797056) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19737 ^ _780119) ^ [_1139235, _1139237, _1139239, _1139241, _1139243] : [class_Fields_Ofield(_1139235), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139235), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1139237, _1139235), _1139239), _1139241)), _1139243) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1139237, _1139235), hAPP(hAPP(c_COMBC(_1139237, _1139235, _1139235), hAPP(hAPP(c_COMBB(_1139235, tc_fun(_1139235, _1139235), _1139237), c_Rings_Oinverse__class_Odivide(_1139235)), _1139239)), _1139243)), _1139241))], (48215 ^ _780119) ^ [_1754481, _1754483] : [-(_1754481 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1754483, _1754481, c_List_Olist_ONil(_1754483)) = c_List_Olist_ONil(tc_List_Olist(_1754483)))], (44750 ^ _780119) ^ [_1676466] : [class_Groups_Omonoid__add(_1676466), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676466), c_List_Olist_ONil(_1676466)) = c_Groups_Ozero__class_Ozero(_1676466))], (24791 ^ _780119) ^ [_1234233, _1234235, _1234237] : [class_Orderings_Oorder(_1234233), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1234233, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1234233, _1234235, _1234237)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1234233), _1234237)) = c_Orderings_Obot__class_Obot(tc_fun(_1234233, tc_HOL_Obool)))], (16867 ^ _780119) ^ [_1086716, _1086718] : [16868 ^ _780119 : [(16871 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1086718))], (16869 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1086716))]], -(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), _1086716), _1086718))))], (27130 ^ _780119) ^ [_1279924, _1279926, _1279928, _1279930, _1279932, _1279934] : [-(hBOOL(hAPP(hAPP(c_member(_1279924), _1279926), _1279928))), -(hAPP(c_Fun_Ooverride__on(_1279924, _1279930, _1279932, _1279934, _1279928), _1279926) = hAPP(_1279932, _1279926))], (51243 ^ _780119) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (39293 ^ _780119) ^ [_1543740, _1543742, _1543744, _1543746] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1543740, tc_HOL_Obool), tc_fun(_1543740, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1543740, tc_HOL_Obool), tc_fun(_1543740, tc_HOL_Obool)), _1543742), _1543744)), c_Wellfounded_Omax__ext(_1543740, _1543746))), 39296 ^ _780119 : [(39297 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1543740), _1543742)))], (39299 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1543740), _1543744)))], (39303 ^ _780119) ^ [_1544034] : [hBOOL(hAPP(hAPP(c_member(_1543740), _1544034), _1543742)), 39307 ^ _780119 : [(39310 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1543740, _1543740)), hAPP(hAPP(c_Product__Type_OPair(_1543740, _1543740), _1544034), 39306 ^ [_1543740, _1543742, _1543744, _1543746, _1544034])), _1543746)))], (39308 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543740), 39306 ^ [_1543740, _1543742, _1543744, _1543746, _1544034]), _1543744)))]]], (39301 ^ _780119) ^ [] : [_1543744 = c_Orderings_Obot__class_Obot(tc_fun(_1543740, tc_HOL_Obool))]]], (30229 ^ _780119) ^ [_1344818, _1344820, _1344822, _1344824, _1344826, _1344828] : [c_Com_Ocom_OLocal(_1344818, _1344820, _1344822) = c_Com_Ocom_OCond(_1344824, _1344826, _1344828)], (22318 ^ _780119) ^ [_1187305, _1187307] : [class_Rings_Olinordered__idom(_1187305), 22321 ^ _780119 : [(22328 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187305), c_Groups_Ozero__class_Ozero(_1187305)), _1187307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187305), c_Groups_Ozero__class_Ozero(_1187305)), c_Groups_Osgn__class_Osgn(_1187305, _1187307))))], (22322 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187305), c_Groups_Ozero__class_Ozero(_1187305)), c_Groups_Osgn__class_Osgn(_1187305, _1187307))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187305), c_Groups_Ozero__class_Ozero(_1187305)), _1187307)))]]], (39012 ^ _780119) ^ [_1536996, _1536998, _1537000, _1537002, _1537004, _1537006, _1537008, _1537010] : [c_Finite__Set_Ofolding(_1536996, _1536998, _1537000, _1537002), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536996), _1537004)), -(hAPP(c_Fun_Ocomp(_1536998, _1536998, _1537006, hAPP(_1537000, _1537008)), hAPP(c_Fun_Ocomp(_1536998, _1536998, _1537006, hAPP(_1537002, _1537004)), _1537010)) = hAPP(c_Fun_Ocomp(_1536998, _1536998, _1537006, hAPP(_1537002, _1537004)), hAPP(c_Fun_Ocomp(_1536998, _1536998, _1537006, hAPP(_1537000, _1537008)), _1537010)))], (15658 ^ _780119) ^ [_1065415, _1065417] : [class_Rings_Olinordered__ring(_1065415), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065415), c_Groups_Ozero__class_Ozero(_1065415)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065415), _1065417), _1065417))))], (25640 ^ _780119) ^ [_1248543, _1248545] : [c_Nat__Transfer_Ois__nat(_1248543), c_Nat__Transfer_Ois__nat(_1248545), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1248543), _1248545)))], (36403 ^ _780119) ^ [_1470557, _1470559] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1470557), c_Orderings_Otop__class_Otop(tc_fun(_1470557, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1470557, _1470557, _1470559), c_Orderings_Otop__class_Otop(tc_fun(_1470557, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1470557, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1470557, _1470557, _1470559, c_Orderings_Otop__class_Otop(tc_fun(_1470557, tc_HOL_Obool))))], (2388 ^ _780119) ^ [_815302, _815304, _815306, _815308] : [-(c_Groups_Osgn__class_Osgn(_815308, _815304) = c_Groups_Osgn__class_Osgn(_815306, _815302)), _815308 = _815306, _815304 = _815302], (10366 ^ _780119) ^ [_962712, _962714, _962716, _962718] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_962712, tc_HOL_Obool)), _962714), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962712, tc_HOL_Obool)), _962716), _962718)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962712, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_962712, tc_HOL_Obool)), _962714), _962716)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_962712, tc_HOL_Obool)), _962714), _962718)))], (40668 ^ _780119) ^ [_1577601, _1577603, _1577605, _1577607, _1577609] : [c_Finite__Set_Ofolding__one__idem(_1577601, _1577603, _1577605), hBOOL(hAPP(c_Finite__Set_Ofinite(_1577601), _1577607)), -(hAPP(_1577605, hAPP(hAPP(c_Set_Oinsert(_1577601), _1577609), _1577607)) = hAPP(hAPP(c_Finite__Set_Ofold(_1577601, _1577601, _1577603), _1577609), _1577607))], (29704 ^ _780119) ^ [_1332656, _1332658, _1332660, _1332662] : [class_Complete__Lattice_Ocomplete__lattice(_1332656), -(_1332658 = c_Orderings_Obot__class_Obot(tc_fun(_1332660, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1332660, _1332656), _1332658), hAPP(c_COMBK(_1332656, _1332660), _1332662)) = _1332662)], (29797 ^ _780119) ^ [_1335224, _1335226, _1335228, _1335230, _1335232] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335224, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335226, tc_fun(_1335224, tc_HOL_Obool)), _1335228), _1335230)), _1335232) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1335226, tc_fun(_1335224, tc_HOL_Obool)), _1335228), hAPP(hAPP(c_COMBC(_1335226, tc_fun(_1335224, tc_HOL_Obool), tc_fun(_1335224, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1335224, tc_HOL_Obool), tc_fun(tc_fun(_1335224, tc_HOL_Obool), tc_fun(_1335224, tc_HOL_Obool)), _1335226), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335224, tc_HOL_Obool))), _1335230)), _1335232)))], (11732 ^ _780119) ^ [_991405, _991407] : [11733 ^ _780119 : [(11736 ^ _780119) ^ [] : [_991405 = _991407], (11734 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991405), _991407))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991405), _991407)))], (25277 ^ _780119) ^ [_1242571, _1242573] : [_1242571 = hAPP(c_Int_Onat, _1242573), 25280 ^ _780119 : [(25287 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242573))), -(_1242571 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25281 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242573)), -(_1242573 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1242571))]]], (41938 ^ _780119) ^ [_1607866, _1607868] : [class_Complete__Lattice_Ocomplete__lattice(_1607866), hBOOL(hAPP(c_Finite__Set_Ofinite(_1607866), _1607868)), -(_1607868 = c_Orderings_Obot__class_Obot(tc_fun(_1607866, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1607866, _1607868) = c_Complete__Lattice_OSup__class_OSup(_1607866, _1607868))], (50400 ^ _780119) ^ [_1802092, _1802094, _1802096, _1802098, _1802100] : [-(c_New__DSequence_Oneg__map(_1802092, _1802094, _1802096, _1802098, _1802100) = c_Lazy__Sequence_Ohb__map(_1802092, _1802094, _1802096, hAPP(_1802098, _1802100)))], (24669 ^ _780119) ^ [_1231912, _1231914, _1231916, _1231918] : [class_Orderings_Olinorder(_1231912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231912), _1231914), _1231916)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231912), _1231916), _1231918)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1231912, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1231912, _1231914, _1231916)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1231912, _1231916, _1231918)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1231912, _1231914, _1231918))], (19410 ^ _780119) ^ [_1132879, _1132881, _1132883, _1132885] : [class_Divides_Osemiring__div(_1132879), -(_1132881 = c_Groups_Ozero__class_Ozero(_1132879)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132879), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132879), _1132883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132879), _1132881), _1132885))), _1132881) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132879), _1132885), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132879), _1132883), _1132881)))], (29550 ^ _780119) ^ [_1328824] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1328824)), -(hAPP(c_Int_Onat, _1328824) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21775 ^ _780119) ^ [_1177746, _1177748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177746), 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, _1177748, _1177746)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (43861 ^ _780119) ^ [_1656519] : [43863 ^ _780119 : [(43866 ^ _780119) ^ [] : [43862 ^ [_1656519] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43864 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43862 ^ [_1656519]), hAPP(c_List_Oset(tc_Nat_Onat), _1656519))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1656519) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51219 ^ _780119) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (38608 ^ _780119) ^ [_1527602, _1527604, _1527606] : [c_Hoare__Mirabelle_Ohoare__valids(_1527602, _1527604, _1527606), 38611 ^ _780119 : [(38612 ^ _780119) ^ [_1527711] : [38614 ^ _780119 : [(38617 ^ _780119) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1527602, _1527711, 38613 ^ [_1527602, _1527604, _1527606, _1527711])], (38615 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1527602)), 38613 ^ [_1527602, _1527604, _1527606, _1527711]), _1527604)))]], 38618 ^ _780119 : [(38619 ^ _780119) ^ [_1527883] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1527602)), _1527883), _1527606)), -(c_Hoare__Mirabelle_Otriple__valid(_1527602, _1527711, _1527883))]]]]], (42361 ^ _780119) ^ [_1617625, _1617627, _1617629, _1617631, _1617633, _1617635] : [hAPP(_1617625, _1617627) = hAPP(c_Option_Ooption_OSome(_1617629), _1617631), -(hAPP(c_Map_Omap__add(_1617633, _1617629, _1617635, _1617625), _1617627) = hAPP(c_Option_Ooption_OSome(_1617629), _1617631))], (14032 ^ _780119) ^ [_1035543, _1035545, _1035547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035545), _1035547)), -(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, _1035543)), _1035545)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1035543)), _1035547))))], (14418 ^ _780119) ^ [_1044421, _1044423, _1044425] : [c_Hoare__Mirabelle_Otriple__valid(_1044421, hAPP(c_Nat_OSuc, _1044423), _1044425), -(c_Hoare__Mirabelle_Otriple__valid(_1044421, _1044423, _1044425))], (38356 ^ _780119) ^ [_1521789, _1521791] : [c_Relation_Orefl__on(_1521789, c_Orderings_Otop__class_Otop(tc_fun(_1521789, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1521789, _1521789)), hAPP(c_Product__Type_Oprod_Oprod__case(_1521789, _1521789, tc_HOL_Obool), _1521791))), -(c_Predicate_Oreflp(_1521789, _1521791))], (32363 ^ _780119) ^ [_1383700, _1383702] : [c_Int_OBit0(_1383700) = c_Int_OBit0(_1383702), -(_1383700 = _1383702)], (2904 ^ _780119) ^ [_823348, _823350, _823352, _823354, _823356, _823358] : [-(c_Finite__Set_Ofold__image(_823358, _823354, _823350) = c_Finite__Set_Ofold__image(_823356, _823352, _823348)), _823358 = _823356, _823354 = _823352, _823350 = _823348], (14024 ^ _780119) ^ [_1035355, _1035357] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035355), _1035357)), hAPP(c_Nat_OSuc, _1035355))))], (28116 ^ _780119) ^ [_1299414, _1299416, _1299418, _1299420] : [class_Orderings_Olinorder(_1299414), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299414), _1299416), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299414), _1299418), _1299420)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299414), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299414), _1299416), _1299418)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299414), _1299416), _1299420)))], (11615 ^ _780119) ^ [_989041, _989043] : [class_Rings_Ocomm__semiring__1(_989041), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989041), _989043), c_Groups_Oone__class_Oone(_989041)) = _989043)], (51545 ^ _780119) ^ [] : [-(class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))], (39597 ^ _780119) ^ [_1550542, _1550544, _1550546, _1550548] : [-(c_Transitive__Closure_Otrancl(_1550542, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1550542, _1550542)), hAPP(hAPP(c_Product__Type_OPair(_1550542, _1550542), _1550544), _1550546)), _1550548)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1550542, _1550542), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1550542, _1550548)), hAPP(c_Set_OCollect(tc_prod(_1550542, _1550542)), hAPP(c_Product__Type_Oprod_Oprod__case(_1550542, _1550542, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1550542, tc_fun(_1550542, tc_HOL_Obool), tc_fun(_1550542, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1550542, tc_HOL_Obool), tc_fun(_1550542, tc_HOL_Obool)), _1550542), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1550542)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550542), c_fconj), hAPP(hAPP(c_COMBC(_1550542, tc_fun(tc_prod(_1550542, _1550542), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1550542, _1550542), tc_fun(tc_fun(tc_prod(_1550542, _1550542), tc_HOL_Obool), tc_HOL_Obool), _1550542), c_member(tc_prod(_1550542, _1550542))), hAPP(hAPP(c_COMBC(_1550542, _1550542, tc_prod(_1550542, _1550542)), c_Product__Type_OPair(_1550542, _1550542)), _1550544))), c_Transitive__Closure_Ortrancl(_1550542, _1550548))))), hAPP(hAPP(c_COMBC(_1550542, tc_fun(tc_prod(_1550542, _1550542), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1550542, _1550542), tc_fun(tc_fun(tc_prod(_1550542, _1550542), tc_HOL_Obool), tc_HOL_Obool), _1550542), c_member(tc_prod(_1550542, _1550542))), hAPP(c_Product__Type_OPair(_1550542, _1550542), _1550546))), c_Transitive__Closure_Ortrancl(_1550542, _1550548)))))))], (9154 ^ _780119) ^ [_937279, _937281, _937283, _937285] : [class_Orderings_Oorder(_937279), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937279), _937281), _937283)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937279), _937285), _937281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937279), _937285), _937283)))], (25859 ^ _780119) ^ [_1252010, _1252012, _1252014] : [class_Groups_Ocomm__monoid__add(_1252010), class_Groups_Ocomm__monoid__mult(_1252010), c_Nat__Transfer_Onat__set(_1252012), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1252010), _1252014), _1252012) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1252010), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1252010, tc_Nat_Onat), _1252014), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1252012)))], (15220 ^ _780119) ^ [_1058383] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1058383) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51153 ^ _780119) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (43535 ^ _780119) ^ [_1647745, _1647747, _1647749, _1647751, _1647753, _1647755] : [hBOOL(hAPP(hAPP(_1647745, _1647747), _1647749)), c_List_Olistrelp(_1647751, _1647745, _1647753, _1647755), -(c_List_Olistrelp(_1647751, _1647745, hAPP(hAPP(c_List_Olist_OCons(_1647751), _1647747), _1647753), hAPP(hAPP(c_List_Olist_OCons(_1647751), _1647749), _1647755)))], (2730 ^ _780119) ^ [_820633, _820635, _820637, _820639, _820641, _820643, _820645, _820647] : [-(c_Product__Type_Oapsnd(_820647, _820643, _820639, _820635) = c_Product__Type_Oapsnd(_820645, _820641, _820637, _820633)), _820647 = _820645, _820643 = _820641, _820639 = _820637, _820635 = _820633], (2266 ^ _780119) ^ [_813453, _813455, _813457, _813459] : [-(c_Orderings_Oord_Omin(_813459, _813455) = c_Orderings_Oord_Omin(_813457, _813453)), _813459 = _813457, _813455 = _813453], (45596 ^ _780119) ^ [_1697677, _1697679, _1697681, _1697683, _1697685] : [-(hAPP(hAPP(c_List_Odrop(_1697677), _1697679), hAPP(hAPP(c_List_Omap(_1697681, _1697677), _1697683), _1697685)) = hAPP(hAPP(c_List_Omap(_1697681, _1697677), _1697683), hAPP(hAPP(c_List_Odrop(_1697681), _1697679), _1697685)))], (15326 ^ _780119) ^ [_1059870] : [_1059870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059870), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24944 ^ _780119) ^ [_1237292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237292)), 24948 ^ _780119 : [(24951 ^ _780119) ^ [] : [-(_1237292 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 24947 ^ [_1237292]))], (24949 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24947 ^ [_1237292])))]]], (11393 ^ _780119) ^ [_983998, _984000, _984002] : [class_Rings_Ocomm__semiring__1(_983998), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983998), _984000), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983998), _984002), _984000)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983998), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983998), _984002), c_Groups_Oone__class_Oone(_983998))), _984000))], (44850 ^ _780119) ^ [_1678322, _1678324] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678322)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678324)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678322), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1678324)) = c_List_Olist_ONil(tc_Int_Oint))], (34209 ^ _780119) ^ [_1422366, _1422368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1422366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1422368)), -(c_Divides_OposDivAlg(_1422366, _1422368) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1422366), _1422368)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1422366, _1422368)))], (32811 ^ _780119) ^ [_1391642, _1391644] : [class_Fields_Olinordered__field__inverse__zero(_1391642), class_Int_Onumber__ring(_1391642), 32818 ^ _780119 : [(32825 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391642), c_Groups_Ozero__class_Ozero(_1391642)), _1391644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391642), c_Groups_Ozero__class_Ozero(_1391642)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391642), _1391644), hAPP(c_Int_Onumber__class_Onumber__of(_1391642), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (32819 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391642), c_Groups_Ozero__class_Ozero(_1391642)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391642), _1391644), hAPP(c_Int_Onumber__class_Onumber__of(_1391642), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391642), c_Groups_Ozero__class_Ozero(_1391642)), _1391644)))]]], (33599 ^ _780119) ^ [_1405688, _1405690, _1405692, _1405694, _1405696, _1405698] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405688, tc_fun(_1405690, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1405688, tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_fun(_1405690, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405690, tc_fun(tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_fun(_1405690, tc_HOL_Obool)), _1405688), c_COMBC(_1405690, tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405690, tc_prod(_1405688, _1405690)), tc_fun(_1405690, tc_fun(tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_HOL_Obool)), _1405688), hAPP(c_COMBB(tc_prod(_1405688, _1405690), tc_fun(tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_HOL_Obool), _1405690), c_member(tc_prod(_1405688, _1405690)))), c_Product__Type_OPair(_1405688, _1405690)))), _1405692)), hAPP(hAPP(c_COMBC(_1405688, tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_fun(_1405690, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405690, tc_fun(tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_fun(_1405690, tc_HOL_Obool)), _1405688), c_COMBC(_1405690, tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405690, tc_prod(_1405688, _1405690)), tc_fun(_1405690, tc_fun(tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_HOL_Obool)), _1405688), hAPP(c_COMBB(tc_prod(_1405688, _1405690), tc_fun(tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool), tc_HOL_Obool), _1405690), c_member(tc_prod(_1405688, _1405690)))), c_Product__Type_OPair(_1405688, _1405690)))), _1405694)), _1405696), _1405698)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1405688, _1405690)), hAPP(hAPP(c_Product__Type_OPair(_1405688, _1405690), _1405696), _1405698)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1405688, _1405690), tc_HOL_Obool)), _1405692), _1405694))))], (11529 ^ _780119) ^ [_987110, _987112, _987114, _987116, _987118] : [class_Rings_Ocomm__semiring__1(_987110), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987110), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987110), _987112), _987114)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987110), _987116), _987118)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987110), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987110), _987112), _987116)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987110), _987114), _987118)))], (7126 ^ _780119) ^ [_897765, _897767, _897769, _897771, _897773, _897775] : [c_Hoare__Mirabelle_Ohoare__derivs(_897765, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_897765), tc_HOL_Obool)), _897767), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_897765), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_897765, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897765)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_897765, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897765))), hAPP(hAPP(c_COMBB(tc_fun(_897765, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_897765, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897765))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_897765)), _897769)), c_Com_Ocom_OBODY)), _897771)), _897773)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_897765), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_897765, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897765)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_897765, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897765))), hAPP(hAPP(c_COMBB(tc_fun(_897765, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_897765, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897765))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_897765)), _897769)), 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))), _897771)), _897773)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _897775), _897773)), -(c_Hoare__Mirabelle_Ohoare__derivs(_897765, _897767, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_897765)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_897765), hAPP(_897769, _897775)), hAPP(c_Com_Ocom_OBODY, _897775)), hAPP(_897771, _897775))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_897765), tc_HOL_Obool)))))], (13488 ^ _780119) ^ [_1025569, _1025571, _1025573] : [class_Rings_Oring(_1025569), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1025569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025569), _1025571), _1025573)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025569), _1025571), hAPP(c_Groups_Ouminus__class_Ouminus(_1025569), _1025573)))], (31607 ^ _780119) ^ [_1370249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370249), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370249)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37373 ^ _780119) ^ [_1494681, _1494683] : [c_Wellfounded_Owf(_1494681, _1494683), 37377 ^ _780119 : [(37378 ^ _780119) ^ [_1494817] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494681, _1494681)), hAPP(hAPP(c_Product__Type_OPair(_1494681, _1494681), hAPP(_1494817, hAPP(c_Nat_OSuc, 37376 ^ [_1494681, _1494683, _1494817]))), hAPP(_1494817, 37376 ^ [_1494681, _1494683, _1494817]))), _1494683))]]], (19907 ^ _780119) ^ [_1141959, _1141961, _1141963] : [class_Fields_Ofield__inverse__zero(_1141959), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141959), c_Groups_Oone__class_Oone(_1141959)), hAPP(hAPP(c_Power_Opower__class_Opower(_1141959), _1141961), _1141963)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1141959), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141959), c_Groups_Oone__class_Oone(_1141959)), _1141961)), _1141963))], (48155 ^ _780119) ^ [_1753026, _1753028] : [class_Orderings_Olinorder(_1753026), 48162 ^ _780119 : [(48165 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48161 ^ [_1753026, _1753028]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753026)), _1753028))))], (48167 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1753026), hAPP(hAPP(c_List_Onth(_1753026), _1753028), 48160 ^ [_1753026, _1753028])), hAPP(hAPP(c_List_Onth(_1753026), _1753028), 48161 ^ [_1753026, _1753028])))], (48163 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 48160 ^ [_1753026, _1753028]), 48161 ^ [_1753026, _1753028])))]], -(c_List_Olinorder__class_Osorted(_1753026, _1753028))], (10100 ^ _780119) ^ [_956131, _956133, _956135, _956137] : [class_Lattices_Odistrib__lattice(_956131), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956131), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_956131), _956133), _956135)), _956137) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_956131), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956131), _956133), _956137)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956131), _956135), _956137)))], (35069 ^ _780119) ^ [_1439093, _1439095, _1439097, _1439099, _1439101, _1439103] : [hAPP(c_Product__Type_Oapfst(_1439093, _1439095, _1439097, _1439099), _1439101) = hAPP(c_Product__Type_Oapfst(_1439093, _1439095, _1439097, _1439103), _1439101), -(hAPP(_1439099, hAPP(c_Product__Type_Ofst(_1439093, _1439097), _1439101)) = hAPP(_1439103, hAPP(c_Product__Type_Ofst(_1439093, _1439097), _1439101)))], (46171 ^ _780119) ^ [_1710583, _1710585, _1710587, _1710589] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710583)), hAPP(hAPP(c_List_Oappend(_1710583), _1710585), _1710587)), c_List_Olists(_1710583, _1710589))), 46174 ^ _780119 : [(46177 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710583)), _1710587), c_List_Olists(_1710583, _1710589))))], (46175 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710583)), _1710585), c_List_Olists(_1710583, _1710589))))]]], (49108 ^ _780119) ^ [_1773814, _1773816, _1773818, _1773820] : [_1773820 = c_List_Olist_ONil(_1773816), -(c_List_Olist__all2(_1773814, _1773816, _1773818, c_List_Olist_ONil(_1773814), _1773820))], (44578 ^ _780119) ^ [_1673196] : [-(_1673196 = 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, _1673196)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1673196))))], (6296 ^ _780119) ^ [_881188, _881190, _881192, _881194] : [_881194 = c_Orderings_Obot__class_Obot(tc_fun(_881190, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_881188, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_881190, _881188, _881192), _881194))], (41928 ^ _780119) ^ [_1607681, _1607683, _1607685] : [class_Complete__Lattice_Ocomplete__lattice(_1607681), hBOOL(hAPP(c_Finite__Set_Ofinite(_1607681), _1607683)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1607681), _1607685), c_Complete__Lattice_OSup__class_OSup(_1607681, _1607683)) = hAPP(hAPP(c_Finite__Set_Ofold(_1607681, _1607681, c_Lattices_Osemilattice__sup__class_Osup(_1607681)), _1607685), _1607683))], (19679 ^ _780119) ^ [_1137983, _1137985] : [class_Rings_Odivision__ring(_1137983), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137983), c_Groups_Ozero__class_Ozero(_1137983)), _1137985) = c_Groups_Ozero__class_Ozero(_1137983))], (47240 ^ _780119) ^ [_1732070, _1732072] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1732070, _1732072) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1732070), hAPP(c_Nat_OSuc, _1732072))))], (43052 ^ _780119) ^ [_1633502, _1633504, _1633506, _1633508] : [hBOOL(hAPP(c_List_Odistinct(_1633502), _1633504)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1633506, _1633502)), hAPP(hAPP(c_List_Ozip(_1633506, _1633502), _1633508), _1633504))))], (39825 ^ _780119) ^ [_1556829, _1556831, _1556833, _1556835, _1556837] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1556829, _1556829)), hAPP(hAPP(c_Product__Type_OPair(_1556829, _1556829), _1556831), _1556833)), c_Transitive__Closure_Ortrancl(_1556829, _1556835))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1556829, _1556829)), hAPP(hAPP(c_Product__Type_OPair(_1556829, _1556829), _1556833), _1556837)), c_Transitive__Closure_Otrancl(_1556829, _1556835))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556829, _1556829)), hAPP(hAPP(c_Product__Type_OPair(_1556829, _1556829), _1556831), _1556837)), c_Transitive__Closure_Otrancl(_1556829, _1556835))))], (46991 ^ _780119) ^ [_1727508, _1727510, _1727512] : [class_Orderings_Olinorder(_1727508), c_List_Olinorder__class_Osorted(_1727508, _1727510), hBOOL(hAPP(c_List_Odistinct(_1727508), _1727510)), c_List_Olinorder__class_Osorted(_1727508, _1727512), hBOOL(hAPP(c_List_Odistinct(_1727508), _1727512)), hAPP(c_List_Oset(_1727508), _1727510) = hAPP(c_List_Oset(_1727508), _1727512), -(_1727510 = _1727512)], (41224 ^ _780119) ^ [_1589507, _1589509, _1589511, _1589513, _1589515] : [-(_1589507 = c_Orderings_Obot__class_Obot(tc_fun(_1589509, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589511, tc_HOL_Obool)), _1589513), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589509, tc_fun(_1589511, tc_HOL_Obool)), _1589507), _1589515)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589509, tc_fun(_1589511, tc_HOL_Obool)), _1589507), hAPP(hAPP(c_COMBB(tc_fun(_1589511, tc_HOL_Obool), tc_fun(_1589511, tc_HOL_Obool), _1589509), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589511, tc_HOL_Obool)), _1589513)), _1589515)))], (33153 ^ _780119) ^ [_1398047, _1398049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1398047)), -(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)))), _1398049))), 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)))), _1398047)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1398049), _1398047))], (18490 ^ _780119) ^ [_1117458, _1117460, _1117462] : [class_Rings_Oring__1(_1117458), hBOOL(hAPP(hAPP(c_member(_1117458), _1117460), c_Int_Oring__1__class_OInts(_1117458))), hBOOL(hAPP(hAPP(c_member(_1117458), _1117462), c_Int_Oring__1__class_OInts(_1117458))), -(hBOOL(hAPP(hAPP(c_member(_1117458), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117458), _1117460), _1117462)), c_Int_Oring__1__class_OInts(_1117458))))], (40028 ^ _780119) ^ [_1561479, _1561481, _1561483, _1561485, _1561487] : [-(hAPP(c_Relation_Oconverse(_1561479, _1561481), hAPP(hAPP(c_Relation_Orel__comp(_1561479, _1561483, _1561481), _1561485), _1561487)) = hAPP(hAPP(c_Relation_Orel__comp(_1561481, _1561483, _1561479), hAPP(c_Relation_Oconverse(_1561483, _1561481), _1561487)), hAPP(c_Relation_Oconverse(_1561479, _1561483), _1561485)))], (28008 ^ _780119) ^ [_1297228, _1297230, _1297232] : [class_Groups_Olinordered__ab__group__add(_1297228), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1297228), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1297228), _1297230), _1297232)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1297228), hAPP(c_Groups_Ouminus__class_Ouminus(_1297228), _1297230)), hAPP(c_Groups_Ouminus__class_Ouminus(_1297228), _1297232)))], (19210 ^ _780119) ^ [_1129662, _1129664, _1129666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129662), _1129664)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129662), _1129666)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129664), _1129666))))], (44116 ^ _780119) ^ [_1662692, _1662694, _1662696, _1662698] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662692) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1662694), hAPP(hAPP(c_List_Olist_OCons(_1662694), _1662696), _1662698)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662692)) = _1662696)], (39699 ^ _780119) ^ [_1553787, _1553789, _1553791, _1553793, _1553795] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553787, _1553787)), hAPP(hAPP(c_Product__Type_OPair(_1553787, _1553787), _1553789), _1553791)), c_Transitive__Closure_Ortrancl(_1553787, _1553793))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1553787, _1553787)), hAPP(hAPP(c_Product__Type_OPair(_1553787, _1553787), _1553791), _1553795)), c_Transitive__Closure_Ortrancl(_1553787, _1553793))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1553787, _1553787)), hAPP(hAPP(c_Product__Type_OPair(_1553787, _1553787), _1553789), _1553795)), c_Transitive__Closure_Ortrancl(_1553787, _1553793))))], (50536 ^ _780119) ^ [_1805369, _1805371, _1805373, _1805375] : [-(hBOOL(hAPP(_1805369, _1805371))), -(hAPP(c_List_Ofilter(_1805373, _1805369), c_List_Oreplicate(_1805373, _1805375, _1805371)) = c_List_Olist_ONil(_1805373))], (40272 ^ _780119) ^ [_1567977, _1567979, _1567981, _1567983] : [-(hAPP(hAPP(c_Nat_Ocompow(_1567977, _1567977), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1567979), _1567981)), _1567983) = hAPP(c_Fun_Ocomp(_1567977, _1567977, _1567977, hAPP(hAPP(c_Nat_Ocompow(_1567977, _1567977), _1567979), _1567983)), hAPP(hAPP(c_Nat_Ocompow(_1567977, _1567977), _1567981), _1567983)))], (38164 ^ _780119) ^ [_1517213, _1517215, _1517217, _1517219] : [-(c_Product__Type_Oapsnd(_1517213, _1517215, _1517217, _1517219) = c_Product__Type_Omap__pair(_1517217, _1517217, _1517213, _1517215, c_Fun_Oid(_1517217), _1517219))], (23058 ^ _780119) ^ [_1201184, _1201186, _1201188] : [class_Rings_Osemiring__1(_1201184), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201184), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1201186), _1201188)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1201184), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201184), _1201186)), _1201188))], (11688 ^ _780119) ^ [_990612, _990614, _990616] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990612), _990614)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990612), _990616)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990614), _990616))], (25436 ^ _780119) ^ [_1245299, _1245301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245299)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1245299), _1245301)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1245299)), hAPP(c_Int_Onat, _1245301)))], (26461 ^ _780119) ^ [_1262986, _1262988, _1262990] : [hBOOL(hAPP(hAPP(c_member(_1262986), _1262988), hAPP(c_Set_OCollect(_1262986), _1262990))), -(hBOOL(hAPP(_1262990, _1262988)))], (22838 ^ _780119) ^ [_1197172] : [22839 ^ _780119 : [(22840 ^ _780119) ^ [_1197229] : [hBOOL(hAPP(_1197172, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197229)))]], 22842 ^ _780119 : [(22845 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1197172, 22841 ^ [_1197172])))], (22843 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22841 ^ [_1197172])))]]], (22531 ^ _780119) ^ [_1191218] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1191218)) = 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), _1191218))))], (42661 ^ _780119) ^ [_1624570, _1624572, _1624574, _1624576, _1624578] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1624570), tc_Option_Ooption(_1624572), _1624574, hAPP(c_Option_Omap(_1624570, _1624572), _1624576)), hAPP(c_COMBK(tc_Option_Ooption(_1624570), _1624574), c_Option_Ooption_ONone(_1624570))), _1624578) = c_Option_Ooption_ONone(_1624572))], (11039 ^ _780119) ^ [_976248, _976250] : [class_Lattices_Olattice(_976248), -(c_Big__Operators_Olattice__class_OInf__fin(_976248, hAPP(hAPP(c_Set_Oinsert(_976248), _976250), c_Orderings_Obot__class_Obot(tc_fun(_976248, tc_HOL_Obool)))) = _976250)], (41489 ^ _780119) ^ [_1597537, _1597539, _1597541, _1597543, _1597545] : [-(_1597537 = c_Orderings_Obot__class_Obot(tc_fun(_1597539, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597539, tc_fun(_1597541, tc_HOL_Obool)), _1597537), hAPP(hAPP(c_COMBB(tc_fun(_1597541, tc_HOL_Obool), tc_fun(_1597541, tc_HOL_Obool), _1597539), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1597541, tc_HOL_Obool)), _1597543)), _1597545)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1597541, tc_HOL_Obool)), _1597543), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1597539, tc_fun(_1597541, tc_HOL_Obool)), _1597537), _1597545)))], (14406 ^ _780119) ^ [_1044135, _1044137, _1044139] : [class_Rings_Ocomm__semiring__1(_1044135), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044135), hAPP(hAPP(c_Power_Opower__class_Opower(_1044135), _1044137), _1044139)), _1044137) = hAPP(hAPP(c_Power_Opower__class_Opower(_1044135), _1044137), hAPP(c_Nat_OSuc, _1044139)))], (3970 ^ _780119) ^ [_840101, _840103] : [_840103 = _840101, -(c_Finite__Set_Ocard(_840103) = c_Finite__Set_Ocard(_840101))], (8170 ^ _780119) ^ [_920521, _920523, _920525] : [hBOOL(hAPP(hAPP(c_member(_920521), _920523), _920525)), -(hAPP(hAPP(c_Set_Oinsert(_920521), _920523), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920521, tc_HOL_Obool)), _920525), hAPP(hAPP(c_Set_Oinsert(_920521), _920523), c_Orderings_Obot__class_Obot(tc_fun(_920521, tc_HOL_Obool))))) = _920525)], (41664 ^ _780119) ^ [_1601918, _1601920, _1601922] : [class_Complete__Lattice_Ocomplete__lattice(_1601918), 41667 ^ _780119 : [(41668 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1601918), _1601920), c_Complete__Lattice_OInf__class_OInf(_1601918, _1601922))), 41671 ^ _780119 : [(41672 ^ _780119) ^ [_1602076] : [hBOOL(hAPP(hAPP(c_member(_1601918), _1602076), _1601922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1601918), _1601920), _1602076)))]]], (41678 ^ _780119) ^ [] : [41680 ^ _780119 : [(41683 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1601918), _1601920), 41679 ^ [_1601918, _1601920, _1601922]))], (41681 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601918), 41679 ^ [_1601918, _1601920, _1601922]), _1601922)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1601918), _1601920), c_Complete__Lattice_OInf__class_OInf(_1601918, _1601922))))]]], (5188 ^ _780119) ^ [_859530, _859532] : [_859532 = _859530, -(c_List_Otake(_859532) = c_List_Otake(_859530))], (124 ^ _780119) ^ [_782183, _782185, _782187, _782189, _782191, _782193, _782195, _782197, _782199, _782201, _782203, _782205] : [-(c_Finite__Set_Ofolding__image__simple(_782203, _782199, _782195, _782191, _782187, _782183)), c_Finite__Set_Ofolding__image__simple(_782205, _782201, _782197, _782193, _782189, _782185), _782205 = _782203, _782201 = _782199, _782197 = _782195, _782193 = _782191, _782189 = _782187, _782185 = _782183], (41168 ^ _780119) ^ [_1588344, _1588346, _1588348, _1588350, _1588352] : [class_Complete__Lattice_Ocomplete__lattice(_1588344), class_Orderings_Olinorder(_1588344), 41175 ^ _780119 : [(41185 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1588344), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1588346, _1588344), _1588348), _1588350)), _1588352))), 41186 ^ _780119 : [(41187 ^ _780119) ^ [_1588692] : [hBOOL(hAPP(hAPP(c_member(_1588346), _1588692), _1588348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1588344), hAPP(_1588350, _1588692)), _1588352))]]], (41176 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1588344), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1588346, _1588344), _1588348), _1588350)), _1588352)), 41180 ^ _780119 : [(41183 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1588344), hAPP(_1588350, 41179 ^ [_1588344, _1588346, _1588348, _1588350, _1588352])), _1588352)))], (41181 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588346), 41179 ^ [_1588344, _1588346, _1588348, _1588350, _1588352]), _1588348)))]]]]], (42714 ^ _780119) ^ [_1625981, _1625983, _1625985, _1625987, _1625989, _1625991] : [c_Map_Omap__comp(_1625981, _1625983, _1625985, _1625987, _1625989, _1625991) = c_Option_Ooption_ONone(_1625983), -(hAPP(_1625989, _1625991) = c_Option_Ooption_ONone(_1625981)), 42722 ^ _780119 : [(42725 ^ _780119) ^ [] : [-(hAPP(_1625987, 42721 ^ [_1625981, _1625983, _1625985, _1625987, _1625989, _1625991]) = c_Option_Ooption_ONone(_1625983))], (42723 ^ _780119) ^ [] : [-(hAPP(_1625989, _1625991) = hAPP(c_Option_Ooption_OSome(_1625981), 42721 ^ [_1625981, _1625983, _1625985, _1625987, _1625989, _1625991]))]]], (41230 ^ _780119) ^ [_1589633, _1589635, _1589637, _1589639, _1589641] : [_1589633 = c_Orderings_Obot__class_Obot(tc_fun(_1589635, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589637, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589635, tc_fun(_1589637, tc_HOL_Obool)), _1589633), _1589639)), _1589641) = _1589641)], (45008 ^ _780119) ^ [_1682269, _1682271, _1682273, _1682275, _1682277] : [-(hAPP(hAPP(c_List_Oappend(_1682269), _1682271), _1682273) = hAPP(hAPP(c_List_Olist_OCons(_1682269), _1682275), _1682277)), 45009 ^ _780119 : [(45016 ^ _780119) ^ [_1682452] : [_1682271 = hAPP(hAPP(c_List_Olist_OCons(_1682269), _1682275), _1682452), hAPP(hAPP(c_List_Oappend(_1682269), _1682452), _1682273) = _1682277], (45010 ^ _780119) ^ [] : [_1682271 = c_List_Olist_ONil(_1682269), _1682273 = hAPP(hAPP(c_List_Olist_OCons(_1682269), _1682275), _1682277)]]], (47586 ^ _780119) ^ [_1739693, _1739695, _1739697, _1739699, _1739701] : [-(c_List_Ofoldr(_1739693, _1739695, _1739697, _1739699, _1739701) = hAPP(c_List_Ofoldl(_1739695, _1739693, hAPP(c_COMBC(_1739693, _1739695, _1739695), _1739697), _1739701), hAPP(c_List_Orev(_1739693), _1739699)))], (22827 ^ _780119) ^ [_1197002] : [-(hBOOL(hAPP(_1197002, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 22834 ^ [_1197002])))), 22828 ^ _780119 : [(22829 ^ _780119) ^ [_1197054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197054)), hBOOL(hAPP(_1197002, _1197054))]]], (36672 ^ _780119) ^ [_1476772, _1476774, _1476776, _1476778, _1476780, _1476782] : [hAPP(_1476772, _1476774) = _1476776, hBOOL(hAPP(hAPP(c_member(_1476778), _1476776), _1476780)), -(hBOOL(hAPP(hAPP(c_member(_1476782), _1476774), hAPP(c_Set_Ovimage(_1476782, _1476778, _1476772), _1476780))))], (48071 ^ _780119) ^ [_1751155, _1751157, _1751159, _1751161] : [hBOOL(hAPP(_1751155, _1751157)), -(c_List_OdropWhile(_1751159, _1751155, hAPP(hAPP(c_List_Olist_OCons(_1751159), _1751157), _1751161)) = c_List_OdropWhile(_1751159, _1751155, _1751161))], (184 ^ _780119) ^ [_783103, _783105] : [-(c_Nat__Transfer_Ois__nat(_783103)), _783105 = _783103, c_Nat__Transfer_Ois__nat(_783105)], (22529 ^ _780119) ^ [_1191189] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1191189)) = _1191189)], (50039 ^ _780119) ^ [_1794639, _1794641, _1794643] : [c_FunDef_Ois__measure(_1794639, _1794641), -(c_FunDef_Ois__measure(tc_prod(_1794643, _1794639), hAPP(hAPP(c_COMBB(_1794639, tc_Nat_Onat, tc_prod(_1794643, _1794639)), _1794641), c_Product__Type_Osnd(_1794643, _1794639))))], (35456 ^ _780119) ^ [_1449344, _1449346, _1449348, _1449350] : [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), _1449344), _1449346)), 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), _1449348), _1449350)), 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), _1449344), _1449350)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1449348), _1449346))))], (41218 ^ _780119) ^ [_1589374, _1589376, _1589378, _1589380, _1589382] : [_1589374 = c_Orderings_Obot__class_Obot(tc_fun(_1589376, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589378, tc_HOL_Obool)), _1589380), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589376, tc_fun(_1589378, tc_HOL_Obool)), _1589374), _1589382)) = _1589380)], (42683 ^ _780119) ^ [_1625175, _1625177, _1625179, _1625181, _1625183, _1625185, _1625187] : [c_Map_Omap__comp(_1625175, _1625177, _1625179, _1625181, _1625183, _1625185) = hAPP(c_Option_Ooption_OSome(_1625177), _1625187), 42687 ^ _780119 : [(42690 ^ _780119) ^ [] : [-(hAPP(_1625181, 42686 ^ [_1625175, _1625177, _1625179, _1625181, _1625183, _1625185, _1625187]) = hAPP(c_Option_Ooption_OSome(_1625177), _1625187))], (42688 ^ _780119) ^ [] : [-(hAPP(_1625183, _1625185) = hAPP(c_Option_Ooption_OSome(_1625175), 42686 ^ [_1625175, _1625177, _1625179, _1625181, _1625183, _1625185, _1625187]))]]], (11149 ^ _780119) ^ [_978674, _978676, _978678] : [class_Lattices_Olattice(_978674), hBOOL(hAPP(c_Finite__Set_Ofinite(_978674), _978676)), -(_978676 = c_Orderings_Obot__class_Obot(tc_fun(_978674, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_978674, hAPP(hAPP(c_Set_Oinsert(_978674), _978678), _978676)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978674), _978678), c_Big__Operators_Olattice__class_OInf__fin(_978674, _978676)))], (19030 ^ _780119) ^ [_1126845, _1126847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126847)), -(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), _1126845), _1126847))))], (51531 ^ _780119) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (8750 ^ _780119) ^ [_931286, _931288, _931290, _931292] : [class_Orderings_Opreorder(_931286), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931286), _931288), _931290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931286), _931290), _931292)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931286), _931288), _931292)))], (39501 ^ _780119) ^ [_1548632, _1548634, _1548636, _1548638, _1548640] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548632, _1548632)), hAPP(hAPP(c_Product__Type_OPair(_1548632, _1548632), _1548634), _1548636)), c_Transitive__Closure_Otrancl(_1548632, _1548638))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1548632, _1548632)), hAPP(hAPP(c_Product__Type_OPair(_1548632, _1548632), _1548636), _1548640)), _1548638)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548632, _1548632)), hAPP(hAPP(c_Product__Type_OPair(_1548632, _1548632), _1548634), _1548640)), c_Transitive__Closure_Otrancl(_1548632, _1548638))))], (22286 ^ _780119) ^ [_1186687, _1186689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186687), _1186689)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186689, _1186687) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1186689), _1186687), _1186687))], (40720 ^ _780119) ^ [_1578595, _1578597, _1578599, _1578601] : [class_Orderings_Olinorder(_1578595), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578595), _1578597)), hBOOL(hAPP(hAPP(c_member(_1578595), _1578599), _1578597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1578595), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1578595), _1578599), _1578601)), hAPP(hAPP(c_Finite__Set_Ofold(_1578595, _1578595, c_Orderings_Oord__class_Omax(_1578595)), _1578601), _1578597))))], (18972 ^ _780119) ^ [_1125986, _1125988] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125986), _1125988))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125988), _1125986)))], (36690 ^ _780119) ^ [_1477095, _1477097, _1477099] : [-(hAPP(c_Set_Ovimage(_1477095, _1477097, _1477099), c_Orderings_Obot__class_Obot(tc_fun(_1477097, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1477095, tc_HOL_Obool)))], (39485 ^ _780119) ^ [_1548246, _1548248] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548246, _1548246)), _1548248)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548246, _1548246)), c_Transitive__Closure_Otrancl(_1548246, _1548248))))], (43453 ^ _780119) ^ [_1645216, _1645218, _1645220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1645216, _1645216), tc_HOL_Obool)), _1645218), _1645220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1645216), tc_List_Olist(_1645216)), tc_HOL_Obool)), c_List_Olistrel(_1645216, _1645218)), c_List_Olistrel(_1645216, _1645220))))], (8722 ^ _780119) ^ [_930848, _930850, _930852, _930854] : [class_Orderings_Oord(_930848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930848), _930850), _930852)), _930852 = _930854, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930848), _930850), _930854)))], (46739 ^ _780119) ^ [_1722839, _1722841] : [-(c_Random_Opick(_1722839, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1722839), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1722839, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1722839, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1722839)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1722841)) = c_Random_Opick(_1722839, _1722841))], (51157 ^ _780119) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (33125 ^ _780119) ^ [_1397481, _1397483] : [class_Rings_Oring__1(_1397481), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1397481), hAPP(c_Groups_Ouminus__class_Ouminus(_1397481), c_Groups_Oone__class_Oone(_1397481))), 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)))), _1397483))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1397481), c_Groups_Oone__class_Oone(_1397481)))], (5300 ^ _780119) ^ [_861176, _861178] : [_861178 = _861176, -(c_List_Olist_OCons(_861178) = c_List_Olist_OCons(_861176))], (44448 ^ _780119) ^ [_1670622, _1670624, _1670626, _1670628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670622), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670624)), _1670626))), -(hBOOL(hAPP(hAPP(c_member(_1670624), _1670628), hAPP(c_List_Oset(_1670624), hAPP(hAPP(c_List_Olist__update(_1670624, _1670626), _1670622), _1670628)))))], (32063 ^ _780119) ^ [_1377616, _1377618] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377616)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377618)) = 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)))), _1377616)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377618)))], (4008 ^ _780119) ^ [_840662, _840664, _840666, _840668, _840670, _840672] : [-(c_List_Opartition(_840672, _840668, _840664) = c_List_Opartition(_840670, _840666, _840662)), _840672 = _840670, _840668 = _840666, _840664 = _840662], (44524 ^ _780119) ^ [] : [-(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))], (18912 ^ _780119) ^ [_1124875, _1124877, _1124879, _1124881, _1124883, _1124885] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1124875), _1124877)), _1124879) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1124881), _1124883)), _1124885), 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), _1124881), _1124883)), _1124885))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124885), _1124881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1124879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1124881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124881), _1124875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124877), _1124883)))], (26413 ^ _780119) ^ [_1262027, _1262029, _1262031] : [class_Rings_Olinordered__idom(_1262027), -(hAPP(c_Groups_Oabs__class_Oabs(_1262027), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262027), _1262029), _1262031)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262027), hAPP(c_Groups_Oabs__class_Oabs(_1262027), _1262029)), hAPP(c_Groups_Oabs__class_Oabs(_1262027), _1262031)))], (47160 ^ _780119) ^ [_1730488, _1730490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730488)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730490))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730488), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730490)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730488)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730488)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730490))))], (34100 ^ _780119) ^ [_1420563, _1420565] : [34101 ^ _780119 : [(34104 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420565), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34102 ^ _780119) ^ [] : [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), _1420563), _1420565)))]], -(c_Divides_OnegDivAlg(_1420563, _1420565) = 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), _1420563), _1420565)))], (22775 ^ _780119) ^ [_1196141] : [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)), _1196141))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1196141)))], (34763 ^ _780119) ^ [_1432539, _1432541, _1432543] : [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), _1432539), _1432541))), -(hBOOL(hAPP(hAPP(_1432543, _1432539), _1432541))), 34770 ^ _780119 : [(34779 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(_1432543, 34768 ^ [_1432539, _1432541, _1432543]), 34769 ^ [_1432539, _1432541, _1432543]))], (34773 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 34769 ^ [_1432539, _1432541, _1432543]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1432543, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 34768 ^ [_1432539, _1432541, _1432543])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 34769 ^ [_1432539, _1432541, _1432543]))))], (34771 ^ _780119) ^ [] : [-(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), 34768 ^ [_1432539, _1432541, _1432543]), 34769 ^ [_1432539, _1432541, _1432543]))))]]], (12269 ^ _780119) ^ [_1001722, _1001724, _1001726, _1001728, _1001730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001722), _1001724)), 12272 ^ _780119 : [(12279 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001728), 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), _1001724), _1001722)), _1001726)), _1001730))), -(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), _1001722), _1001726)), _1001728)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001724), _1001726)), _1001730))))], (12273 ^ _780119) ^ [] : [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), _1001722), _1001726)), _1001728)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001724), _1001726)), _1001730))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001728), 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), _1001724), _1001722)), _1001726)), _1001730))))]]], (41051 ^ _780119) ^ [_1584968, _1584970, _1584972, _1584974, _1584976, _1584978] : [hBOOL(hAPP(hAPP(c_member(_1584968), _1584970), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1584972, tc_fun(_1584968, tc_HOL_Obool)), _1584974), _1584976))), -(hBOOL(hAPP(hAPP(c_member(_1584968), _1584970), hAPP(_1584976, _1584978)))), hBOOL(hAPP(hAPP(c_member(_1584972), _1584978), _1584974))], (40952 ^ _780119) ^ [_1583031, _1583033, _1583035, _1583037, _1583039, _1583041, _1583043] : [c_Finite__Set_Ofun__left__comm(_1583031, _1583033, _1583035), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1583031, _1583033, _1583035, _1583037, _1583039), _1583041)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1583031, _1583033, _1583035, _1583037, _1583039), _1583043)), -(_1583043 = _1583041)], (12047 ^ _780119) ^ [_997216, _997218, _997220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997216), _997218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997220), _997218)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997220), _997216))))], (33353 ^ _780119) ^ [_1401605] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1401605) = c_Int_Opred(_1401605))], (9746 ^ _780119) ^ [_949194, _949196, _949198, _949200] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949194, tc_HOL_Obool)), _949196), _949198), _949200)), -(hBOOL(hAPP(_949198, _949200)))], (27974 ^ _780119) ^ [_1296533, _1296535, _1296537, _1296539] : [class_Orderings_Olinorder(_1296533), 27977 ^ _780119 : [(27978 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296533), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1296533), _1296535), _1296537)), _1296539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296533), _1296535), _1296539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296533), _1296537), _1296539)))], (27988 ^ _780119) ^ [] : [27989 ^ _780119 : [(27992 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296533), _1296537), _1296539))], (27990 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296533), _1296535), _1296539))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296533), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1296533), _1296535), _1296537)), _1296539)))]]], (38988 ^ _780119) ^ [_1536374, _1536376, _1536378, _1536380, _1536382, _1536384] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1536374, _1536376), _1536376, tc_prod(_1536378, _1536380), c_Product__Type_Osnd(_1536374, _1536376)), c_Product__Type_Omap__pair(_1536378, _1536374, _1536380, _1536376, _1536382, _1536384)) = hAPP(c_Fun_Ocomp(_1536380, _1536376, tc_prod(_1536378, _1536380), _1536384), c_Product__Type_Osnd(_1536378, _1536380)))], (48577 ^ _780119) ^ [_1762254, _1762256] : [class_Enum_Oenum(_1762254), 48580 ^ _780119 : [(48589 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1762254)), _1762256))), hBOOL(hAPP(_1762256, c_Option_Ooption_ONone(_1762254))), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1762254), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1762254), tc_HOL_Obool, _1762254), _1762256), c_Option_Ooption_OSome(_1762254))))], (48581 ^ _780119) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1762254)), _1762256)), 48584 ^ _780119 : [(48587 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1762254), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1762254), tc_HOL_Obool, _1762254), _1762256), c_Option_Ooption_OSome(_1762254)))))], (48585 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1762256, c_Option_Ooption_ONone(_1762254))))]]]]], (29338 ^ _780119) ^ [_1324305, _1324307, _1324309] : [class_Orderings_Olinorder(_1324305), hAPP(_1324307, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324305), 29343 ^ [_1324305, _1324307, _1324309]), 29344 ^ [_1324305, _1324307, _1324309])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324305), hAPP(_1324307, 29343 ^ [_1324305, _1324307, _1324309])), hAPP(_1324307, 29344 ^ [_1324305, _1324307, _1324309])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324305), _1324309)), -(_1324309 = c_Orderings_Obot__class_Obot(tc_fun(_1324305, tc_HOL_Obool))), -(hAPP(_1324307, c_Big__Operators_Olattice_OSup__fin(_1324305, c_Orderings_Oord__class_Omax(_1324305), _1324309)) = c_Big__Operators_Olattice_OSup__fin(_1324305, c_Orderings_Oord__class_Omax(_1324305), hAPP(c_Set_Oimage(_1324305, _1324305, _1324307), _1324309)))], (26961 ^ _780119) ^ [_1273609, _1273611, _1273613, _1273615, _1273617, _1273619] : [-(hAPP(c_Set_Oimage(_1273609, _1273611, hAPP(hAPP(c_COMBS(_1273609, _1273611, _1273611), hAPP(hAPP(c_COMBS(_1273609, _1273611, tc_fun(_1273611, _1273611)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1273611, tc_fun(_1273611, _1273611)), _1273609), c_If(_1273611)), _1273613)), _1273615)), _1273617)), _1273619) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273611, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1273609, _1273611, _1273615), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1273609, tc_HOL_Obool)), _1273619), hAPP(c_Set_OCollect(_1273609), _1273613)))), hAPP(c_Set_Oimage(_1273609, _1273611, _1273617), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1273609, tc_HOL_Obool)), _1273619), hAPP(c_Set_OCollect(_1273609), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1273609), c_fNot), _1273613))))))], (32127 ^ _780119) ^ [_1379162, _1379164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1379162)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379164))), -(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(_1379164))), 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), _1379162)), c_Int_Onat))))))], (43928 ^ _780119) ^ [_1657847, _1657849, _1657851, _1657853, _1657855, _1657857] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657847), tc_List_Olist(_1657847))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657847), tc_List_Olist(_1657847)), hAPP(hAPP(c_List_Olist_OCons(_1657847), _1657849), _1657851)), hAPP(hAPP(c_List_Olist_OCons(_1657847), _1657853), _1657855))), c_List_Olexord(_1657847, _1657857)))), 43929 ^ _780119 : [(43932 ^ _780119) ^ [] : [_1657849 = _1657853, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657847), tc_List_Olist(_1657847))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657847), tc_List_Olist(_1657847)), _1657851), _1657855)), c_List_Olexord(_1657847, _1657857)))], (43930 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1657847, _1657847)), hAPP(hAPP(c_Product__Type_OPair(_1657847, _1657847), _1657849), _1657853)), _1657857))]]], (7936 ^ _780119) ^ [_915314, _915316, _915318, _915320, _915322, _915324, _915326] : [c_Finite__Set_Ofolding__image__simple__idem(_915314, _915316, _915318, _915320, _915322, _915324), -(hAPP(hAPP(_915318, _915326), _915326) = _915326)], (51109 ^ _780119) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (11541 ^ _780119) ^ [_987446, _987448, _987450, _987452, _987454] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_987446), 11544 ^ _780119 : [(11545 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987446), _987448), _987452)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987446), _987450), _987454)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987446), _987448), _987454)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987446), _987450), _987452)), -(_987448 = _987450), -(_987452 = _987454)], (11555 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987446), _987448), _987452)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987446), _987450), _987454)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987446), _987448), _987454)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987446), _987450), _987452))), 11558 ^ _780119 : [(11561 ^ _780119) ^ [] : [_987452 = _987454], (11559 ^ _780119) ^ [] : [_987448 = _987450]]]]], (12729 ^ _780119) ^ [_1010812, _1010814, _1010816] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1010812), _1010814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1010812), _1010814)), hAPP(c_Finite__Set_Ocard(_1010812), hAPP(hAPP(c_Set_Oinsert(_1010812), _1010816), _1010814)))))], (44314 ^ _780119) ^ [_1667763, _1667765, _1667767, _1667769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667763), _1667765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1667767, tc_HOL_Obool)), hAPP(c_List_Oset(_1667767), hAPP(hAPP(c_List_Otake(_1667767), _1667763), _1667769))), hAPP(c_List_Oset(_1667767), hAPP(hAPP(c_List_Otake(_1667767), _1667765), _1667769)))))], (30321 ^ _780119) ^ [_1346764, _1346766, _1346768] : [class_Int_Onumber__ring(_1346764), class_Rings_Olinordered__idom(_1346764), 30328 ^ _780119 : [(30335 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1346766), _1346768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346764), hAPP(c_Int_Onumber__class_Onumber__of(_1346764), _1346766)), hAPP(c_Int_Onumber__class_Onumber__of(_1346764), _1346768))))], (30329 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346764), hAPP(c_Int_Onumber__class_Onumber__of(_1346764), _1346766)), hAPP(c_Int_Onumber__class_Onumber__of(_1346764), _1346768))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1346766), _1346768)))]]], (31867 ^ _780119) ^ [] : [-(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)))))], (15412 ^ _780119) ^ [_1061126, _1061128] : [15413 ^ _780119 : [(15416 ^ _780119) ^ [] : [_1061128 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15414 ^ _780119) ^ [] : [_1061126 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061126), _1061128) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38990 ^ _780119) ^ [_1536445, _1536447, _1536449, _1536451, _1536453, _1536455, _1536457, _1536459] : [c_Finite__Set_Ofolding__image(_1536445, _1536447, _1536449, _1536451, _1536453), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536447), _1536455)), -(hAPP(hAPP(_1536453, hAPP(hAPP(c_COMBS(_1536447, _1536445, _1536445), hAPP(hAPP(c_COMBB(_1536445, tc_fun(_1536445, _1536445), _1536447), _1536449), _1536457)), _1536459)), _1536455) = hAPP(hAPP(_1536449, hAPP(hAPP(_1536453, _1536457), _1536455)), hAPP(hAPP(_1536453, _1536459), _1536455)))], (33661 ^ _780119) ^ [_1411093] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1411093)], (12065 ^ _780119) ^ [_997573, _997575, _997577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997573), _997575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997573), _997577)), 12072 ^ _780119 : [(12079 ^ _780119) ^ [] : [_997575 = _997577, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997575), _997573) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997577), _997573))], (12073 ^ _780119) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997575), _997573) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997577), _997573), -(_997575 = _997577)]]], (1300 ^ _780119) ^ [_799093, _799095] : [-(class_Lattices_Osemilattice__sup(_799093)), _799095 = _799093, class_Lattices_Osemilattice__sup(_799095)], (13877 ^ _780119) ^ [_1032371, _1032373] : [class_Lattices_Oboolean__algebra(_1032371), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1032371), _1032373), hAPP(c_Groups_Ouminus__class_Ouminus(_1032371), _1032373)) = c_Orderings_Obot__class_Obot(_1032371))], (25404 ^ _780119) ^ [_1244720, _1244722, _1244724] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1244720, tc_Nat_Onat), _1244722), _1244724) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1244720, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1244720), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1244722)), _1244724)))], (23667 ^ _780119) ^ [_1212731, _1212733, _1212735] : [class_Orderings_Oorder(_1212731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212731), _1212733), _1212735)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1212731, _1212735), _1212733) = c_Orderings_Obot__class_Obot(tc_fun(_1212731, tc_HOL_Obool)))], (3990 ^ _780119) ^ [_840407, _840409] : [_840409 = _840407, -(c_List_Oreturn__list(_840409) = c_List_Oreturn__list(_840407))], (46686 ^ _780119) ^ [_1721330, _1721332, _1721334] : [hBOOL(hAPP(c_List_Odistinct(_1721330), _1721332)), -(hAPP(c_List_Ofilter(_1721330, hAPP(hAPP(c_COMBC(_1721330, tc_fun(_1721330, tc_HOL_Obool), tc_HOL_Obool), c_member(_1721330)), hAPP(c_List_Oset(_1721330), c_List_Osublist(_1721330, _1721332, _1721334)))), _1721332) = c_List_Osublist(_1721330, _1721332, _1721334))], (51183 ^ _780119) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (41535 ^ _780119) ^ [_1598440, _1598442] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1598440), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1598440, tc_HOL_Obool), _1598442)))), 41536 ^ _780119 : [(41537 ^ _780119) ^ [_1598504] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1598440, tc_HOL_Obool)), _1598504), _1598442)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598440), _1598504))]]], (2888 ^ _780119) ^ [_823114, _823116, _823118, _823120] : [-(c_Transitive__Closure_Otrancl(_823120, _823116) = c_Transitive__Closure_Otrancl(_823118, _823114)), _823120 = _823118, _823116 = _823114], (42608 ^ _780119) ^ [_1623248, _1623250] : [-(hAPP(hAPP(c_List_Omap(_1623248, _1623248), c_COMBI(_1623248)), _1623250) = _1623250)], (46497 ^ _780119) ^ [_1717239, _1717241, _1717243] : [-(hAPP(hAPP(c_List_Odrop(_1717239), _1717241), c_List_Obutlast(_1717239, _1717243)) = c_List_Obutlast(_1717239, hAPP(hAPP(c_List_Odrop(_1717239), _1717241), _1717243)))], (22847 ^ _780119) ^ [_1197321] : [-(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), _1197321))))], (37294 ^ _780119) ^ [_1492979, _1492981] : [c_Wellfounded_Owf(_1492979, _1492981), -(c_Wellfounded_Owf(tc_fun(_1492979, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1492979, _1492981)))], (45291 ^ _780119) ^ [_1688575, _1688577, _1688579, _1688581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688575), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688577)), _1688579))), -(hAPP(hAPP(c_List_Onth(_1688577), hAPP(hAPP(c_List_Oappend(_1688577), _1688579), _1688581)), _1688575) = hAPP(hAPP(c_List_Onth(_1688577), _1688579), _1688575))], (48185 ^ _780119) ^ [_1753792, _1753794, _1753796, _1753798] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1753792)), _1753794), hAPP(c_List_Oset(tc_List_Olist(_1753792)), c_Enum_On__lists(_1753792, _1753796, _1753798)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753792)), _1753794) = _1753796)], (2464 ^ _780119) ^ [_816430, _816432, _816434, _816436, _816438, _816440, _816442, _816444, _816446, _816448] : [-(c_Product__Type_Oprod_Oprod__size(_816448, _816444, _816440, _816436, _816432) = c_Product__Type_Oprod_Oprod__size(_816446, _816442, _816438, _816434, _816430)), _816448 = _816446, _816444 = _816442, _816440 = _816438, _816436 = _816434, _816432 = _816430], (13638 ^ _780119) ^ [_1028196, _1028198] : [13639 ^ _780119 : [(13642 ^ _780119) ^ [] : [_1028196 = _1028198], (13640 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028196), _1028198))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028196), hAPP(c_Nat_OSuc, _1028198))))], (38413 ^ _780119) ^ [_1522832, _1522834] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1522832, _1522832)), _1522834)), 38416 ^ _780119 : [(38423 ^ _780119) ^ [] : [c_Wellfounded_Oacyclic(_1522832, _1522834), -(c_Wellfounded_Owf(_1522832, _1522834))], (38417 ^ _780119) ^ [] : [c_Wellfounded_Owf(_1522832, _1522834), -(c_Wellfounded_Oacyclic(_1522832, _1522834))]]], (32487 ^ _780119) ^ [_1385757, _1385759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1385757), _1385759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1385757)), c_Int_OBit1(_1385759))))], (25814 ^ _780119) ^ [_1251276, _1251278] : [class_Rings_Oring__1(_1251276), -(hBOOL(hAPP(hAPP(c_member(_1251276), hAPP(c_Int_Oring__1__class_Oof__int(_1251276), _1251278)), c_Int_Oring__1__class_OInts(_1251276))))], (47971 ^ _780119) ^ [_1749091, _1749093] : [hBOOL(hAPP(c_List_Odistinct(_1749091), _1749093)), -(c_List_Oremdups(_1749091, _1749093) = _1749093)], (27160 ^ _780119) ^ [_1280475] : [-(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)))), _1280475)) = 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), _1280475), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (5484 ^ _780119) ^ [_864120, _864122] : [_864122 = _864120, -(c_Groups_Ozero__class_Ozero(_864122) = c_Groups_Ozero__class_Ozero(_864120))], (21715 ^ _780119) ^ [_1176435, _1176437, _1176439, _1176441, _1176443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1176435, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1176437, _1176435, _1176439), _1176441)), _1176443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1176435, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1176437, tc_HOL_Obool), tc_fun(_1176435, tc_HOL_Obool), c_Set_Oimage(_1176437, _1176435, _1176439)), hAPP(c_Set_OPow(_1176437), _1176441))), hAPP(c_Set_OPow(_1176435), _1176443))))], (44610 ^ _780119) ^ [_1673853, _1673855, _1673857] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1673853), tc_List_Olist(_1673853))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1673853), tc_List_Olist(_1673853)), c_List_Olist_ONil(_1673853)), _1673855)), c_List_Olistrel(_1673853, _1673857))), -(_1673855 = c_List_Olist_ONil(_1673853))], (47861 ^ _780119) ^ [_1746986] : [-(c_List_Oreturn__list(_1746986) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1746986))], (11399 ^ _780119) ^ [_984143, _984145, _984147] : [class_Rings_Ocomm__semiring__1(_984143), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984143), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984143), _984145), _984147)), _984147) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984143), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984143), _984145), c_Groups_Oone__class_Oone(_984143))), _984147))], (38503 ^ _780119) ^ [_1524930, _1524932] : [38505 ^ _780119 : [(38508 ^ _780119) ^ [] : [hBOOL(hAPP(_1524930, hAPP(c_Int_OAbs__Integ, 38504 ^ [_1524930, _1524932])))], (38506 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 38504 ^ [_1524930, _1524932]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1524930, _1524932)))], (15554 ^ _780119) ^ [_1063617, _1063619, _1063621, _1063623] : [class_Groups_Oordered__comm__monoid__add(_1063617), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063617), c_Groups_Ozero__class_Ozero(_1063617)), _1063619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063617), _1063621), _1063623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063617), _1063621), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063617), _1063623), _1063619))))], (38042 ^ _780119) ^ [_1514084, _1514086] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1514084, _1514086, tc_prod(_1514084, _1514086)), c_Product__Type_OPair(_1514084, _1514086)) = c_Fun_Oid(tc_prod(_1514084, _1514086)))], (34367 ^ _780119) ^ [_1425046, _1425048] : [_1425046 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1425048, _1425046) = 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), _1425048)))], (39887 ^ _780119) ^ [_1558176, _1558178, _1558180, _1558182] : [-(c_Wellfounded_Owf(_1558176, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1558176, _1558176)), hAPP(hAPP(c_Product__Type_OPair(_1558176, _1558176), _1558178), _1558180)), _1558182))), c_Wellfounded_Owf(_1558176, _1558182), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1558176, _1558176)), hAPP(hAPP(c_Product__Type_OPair(_1558176, _1558176), _1558180), _1558178)), c_Transitive__Closure_Ortrancl(_1558176, _1558182))))], (18790 ^ _780119) ^ [_1122744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1122744)))], (31491 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (32869 ^ _780119) ^ [_1392671, _1392673] : [class_Rings_Olinordered__idom(_1392671), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1392671), hAPP(hAPP(c_Power_Opower__class_Opower(_1392671), _1392673), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1392671)))], (47999 ^ _780119) ^ [_1749601] : [-(c_List_Oembed__list(_1749601) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1749601))], (28446 ^ _780119) ^ [_1305935, _1305937, _1305939] : [class_Orderings_Olinorder(_1305935), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305935), _1305937)), -(_1305937 = c_Orderings_Obot__class_Obot(tc_fun(_1305935, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1305935, hAPP(hAPP(c_Set_Oinsert(_1305935), _1305939), _1305937)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305935), _1305939), c_Big__Operators_Olinorder__class_OMax(_1305935, _1305937)))], (32613 ^ _780119) ^ [_1388001, _1388003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1388001)), c_Int_OBit1(_1388003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1388001), _1388003)))], (44656 ^ _780119) ^ [_1674746, _1674748, _1674750, _1674752] : [_1674752 = c_List_Olist_ONil(_1674746), -(hAPP(hAPP(c_List_Omap(_1674746, _1674748), _1674750), _1674752) = c_List_Olist_ONil(_1674748))], (51021 ^ _780119) ^ [_1814783, _1814785] : [class_Orderings_Obot(_1814783), -(class_Orderings_Obot(tc_fun(_1814785, _1814783)))], (864 ^ _780119) ^ [_793335, _793337, _793339, _793341] : [-(c_List_Olinorder__class_Osorted(_793339, _793335)), c_List_Olinorder__class_Osorted(_793341, _793337), _793341 = _793339, _793337 = _793335], (42070 ^ _780119) ^ [_1610880, _1610882, _1610884] : [42072 ^ _780119 : [(42075 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610880, tc_HOL_Obool)), 42071 ^ [_1610880, _1610882, _1610884]), _1610884))], (42073 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1610880, tc_HOL_Obool)), 42071 ^ [_1610880, _1610882, _1610884]), _1610882)))]], -(_1610882 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1610880, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610880, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1610880, tc_HOL_Obool), _1610882)), _1610884)))], (44454 ^ _780119) ^ [_1670793, _1670795, _1670797, _1670799, _1670801, _1670803, _1670805] : [hBOOL(hAPP(hAPP(c_member(_1670793), _1670795), hAPP(c_List_Oset(_1670793), hAPP(hAPP(c_List_Otake(_1670793), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670797)), _1670799)), _1670801)))), -(c_Map_Omap__upds(_1670793, _1670797, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1670793, tc_Option_Ooption(_1670797)), _1670803), _1670795), hAPP(c_Option_Ooption_OSome(_1670797), _1670805)), _1670801, _1670799) = c_Map_Omap__upds(_1670793, _1670797, _1670803, _1670801, _1670799))], (33439 ^ _780119) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (2030 ^ _780119) ^ [_809605, _809607, _809609, _809611] : [-(c_SMT_Oz3div(_809611, _809607) = c_SMT_Oz3div(_809609, _809605)), _809611 = _809609, _809607 = _809605], (43046 ^ _780119) ^ [_1633417, _1633419, _1633421, _1633423, _1633425] : [-(hBOOL(hAPP(hAPP(c_member(_1633417), _1633419), hAPP(c_List_Oset(_1633417), _1633421)))), -(hAPP(hAPP(c_Map_Omap__of(_1633417, _1633423), hAPP(hAPP(c_List_Ozip(_1633417, _1633423), _1633421), hAPP(hAPP(c_List_Omap(_1633417, _1633423), _1633425), _1633421))), _1633419) = c_Option_Ooption_ONone(_1633423))], (33571 ^ _780119) ^ [_1405012] : [-(c_Wellfounded_Ofinite__psubset(_1405012) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1405012, tc_HOL_Obool), tc_fun(_1405012, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1405012, tc_HOL_Obool), tc_fun(_1405012, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1405012, tc_HOL_Obool), tc_fun(tc_fun(_1405012, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1405012, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1405012, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1405012, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1405012, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1405012, tc_HOL_Obool)), c_COMBS(tc_fun(_1405012, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1405012, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1405012, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1405012, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1405012, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1405012, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1405012)))))], (35530 ^ _780119) ^ [_1451274, _1451276, _1451278] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1451274), _1451276), _1451278) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1451274, tc_HOL_Obool), tc_HOL_Obool)), -(_1451276 = c_Orderings_Obot__class_Obot(tc_fun(_1451274, tc_HOL_Obool)))], (35743 ^ _780119) ^ [_1455994, _1455996, _1455998, _1456000, _1456002] : [hAPP(c_Relation_OImage(_1455994, _1455994, _1455996), hAPP(hAPP(c_Set_Oinsert(_1455994), _1455998), c_Orderings_Obot__class_Obot(tc_fun(_1455994, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1455994, _1455994, _1455996), hAPP(hAPP(c_Set_Oinsert(_1455994), _1456000), c_Orderings_Obot__class_Obot(tc_fun(_1455994, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1455994, _1456002, _1455996), hBOOL(hAPP(hAPP(c_member(_1455994), _1456000), _1456002)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1455994, _1455994)), hAPP(hAPP(c_Product__Type_OPair(_1455994, _1455994), _1455998), _1456000)), _1455996)))], (4628 ^ _780119) ^ [_850414, _850416, _850418, _850420, _850422, _850424, _850426, _850428] : [-(c_New__Random__Sequence_Opos__bind(_850428, _850424, _850420, _850416) = c_New__Random__Sequence_Opos__bind(_850426, _850422, _850418, _850414)), _850428 = _850426, _850424 = _850422, _850420 = _850418, _850416 = _850414], (19304 ^ _780119) ^ [_1131229, _1131231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131229)), 19307 ^ _780119 : [(19316 ^ _780119) ^ [] : [-(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), _1131229), _1131231)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131231), _1131229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131231))], (19308 ^ _780119) ^ [] : [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), _1131229), _1131231))), 19311 ^ _780119 : [(19314 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131231)))], (19312 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131231), _1131229)))]]]]], (42727 ^ _780119) ^ [_1626207, _1626209, _1626211, _1626213, _1626215, _1626217] : [-(c_Map_Omap__comp(_1626207, _1626209, _1626211, _1626213, _1626215, _1626217) = c_Option_Ooption_ONone(_1626209)), 42728 ^ _780119 : [(42731 ^ _780119) ^ [_1626319] : [hAPP(_1626215, _1626217) = hAPP(c_Option_Ooption_OSome(_1626207), _1626319), hAPP(_1626213, _1626319) = c_Option_Ooption_ONone(_1626209)], (42729 ^ _780119) ^ [] : [hAPP(_1626215, _1626217) = c_Option_Ooption_ONone(_1626207)]]], (27278 ^ _780119) ^ [_1284375, _1284377] : [class_Groups_Olinordered__ab__group__add(_1284375), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284375), _1284377)), -(_1284377 = c_Orderings_Obot__class_Obot(tc_fun(_1284375, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1284375), c_Big__Operators_Olinorder__class_OMin(_1284375, _1284377)) = c_Big__Operators_Olinorder__class_OMax(_1284375, hAPP(c_Set_Oimage(_1284375, _1284375, c_Groups_Ouminus__class_Ouminus(_1284375)), _1284377)))], (26743 ^ _780119) ^ [_1268592, _1268594, _1268596] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1268592, tc_HOL_Obool)), _1268594), _1268596) = hAPP(c_Set_OCollect(_1268592), hAPP(hAPP(c_COMBS(_1268592, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268592), c_fdisj), hAPP(hAPP(c_COMBC(_1268592, tc_fun(_1268592, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268592)), _1268594))), hAPP(hAPP(c_COMBC(_1268592, tc_fun(_1268592, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268592)), _1268596))))], (28158 ^ _780119) ^ [_1300463, _1300465, _1300467, _1300469] : [class_Orderings_Olinorder(_1300463), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300463), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300463), _1300465), _1300467)), _1300469) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300463), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300463), _1300465), _1300469)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300463), _1300467), _1300469)))], (34385 ^ _780119) ^ [_1425272, _1425274] : [-(_1425272 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34388 ^ _780119 : [(34395 ^ _780119) ^ [] : [-(_1425274 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1425272, _1425274) = 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, _1425274))), 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, _1425272)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1425274))), c_Divides_Opdivmod(_1425272, _1425274)), 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), _1425274))))), c_Divides_Opdivmod(_1425272, _1425274)))))], (34389 ^ _780119) ^ [] : [_1425274 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1425272, _1425274) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1425272))]]], (40784 ^ _780119) ^ [_1579797, _1579799, _1579801] : [class_Orderings_Olinorder(_1579797), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579797), _1579799)), -(c_Big__Operators_Olattice_OInf__fin(_1579797, c_Orderings_Oord__class_Omin(_1579797), hAPP(hAPP(c_Set_Oinsert(_1579797), _1579801), _1579799)) = hAPP(hAPP(c_Finite__Set_Ofold(_1579797, _1579797, c_Orderings_Oord__class_Omin(_1579797)), _1579801), _1579799))], (31521 ^ _780119) ^ [_1368933, _1368935] : [class_Int_Onumber__ring(_1368933), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1368933), hAPP(c_Int_Onumber__class_Onumber__of(_1368933), c_Int_OPls)), _1368935) = _1368935)], (36599 ^ _780119) ^ [_1474965, _1474967, _1474969, _1474971, _1474973] : [c_Fun_Oinj__on(_1474965, _1474967, _1474969, _1474971), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474967, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1474965, _1474967, _1474969), _1474971)), _1474973)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474967), _1474973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1474965), _1474971)), hAPP(c_Finite__Set_Ocard(_1474967), _1474973))))], (37316 ^ _780119) ^ [_1493400, _1493402, _1493404, _1493406] : [c_Wellfounded_Owf(_1493400, _1493402), hBOOL(hAPP(hAPP(c_member(tc_prod(_1493400, _1493400)), hAPP(hAPP(c_Product__Type_OPair(_1493400, _1493400), _1493404), _1493406)), _1493402)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1493400, _1493400)), hAPP(hAPP(c_Product__Type_OPair(_1493400, _1493400), _1493406), _1493404)), _1493402))], (21090 ^ _780119) ^ [_1163797, _1163799, _1163801, _1163803] : [class_Fields_Olinordered__field__inverse__zero(_1163797), 21093 ^ _780119 : [(21094 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163797), _1163799), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163797), _1163801), _1163803))), 21097 ^ _780119 : [(21104 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163797), c_Groups_Ozero__class_Ozero(_1163797)), _1163803))), 21107 ^ _780119 : [(21114 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163797), _1163803), c_Groups_Ozero__class_Ozero(_1163797)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163797), _1163799), c_Groups_Ozero__class_Ozero(_1163797))))], (21108 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163797), _1163803), c_Groups_Ozero__class_Ozero(_1163797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163797), _1163801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163797), _1163799), _1163803))))]]], (21098 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163797), c_Groups_Ozero__class_Ozero(_1163797)), _1163803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163797), _1163799), _1163803)), _1163801)))]]], (21120 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163797), _1163799), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163797), _1163801), _1163803)))), 21123 ^ _780119 : [(21126 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163797), _1163799), _1163803)), _1163801))], (21124 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163797), c_Groups_Ozero__class_Ozero(_1163797)), _1163803)))]], 21127 ^ _780119 : [(21130 ^ _780119) ^ [] : [21131 ^ _780119 : [(21134 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163797), _1163801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163797), _1163799), _1163803)))], (21132 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163797), _1163803), c_Groups_Ozero__class_Ozero(_1163797))))]], 21135 ^ _780119 : [(21138 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163797), _1163799), c_Groups_Ozero__class_Ozero(_1163797)))], (21136 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163797), _1163803), c_Groups_Ozero__class_Ozero(_1163797)))]]], (21128 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163797), c_Groups_Ozero__class_Ozero(_1163797)), _1163803))]]]]], (44556 ^ _780119) ^ [_1672723, _1672725] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1672723), _1672725) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1672723)), hAPP(c_Code__Numeral_Onat__of, _1672725))))], (31541 ^ _780119) ^ [_1369207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1369207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1369207))))], (8492 ^ _780119) ^ [_927558, _927560, _927562, _927564, _927566, _927568, _927570] : [-(_927558 = _927560), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927562, _927564), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927562, _927564), _927566), _927558), _927568)), _927560), _927570) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927562, _927564), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927562, _927564), _927566), _927560), _927570)), _927558), _927568))], (43404 ^ _780119) ^ [_1643115, _1643117] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1643115), _1643117))), -(c_Nitpick_Ocard_H(_1643115, _1643117) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40385 ^ _780119) ^ [_1570603, _1570605, _1570607] : [40388 ^ _780119 : [(40392 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570603, _1570605)), hAPP(hAPP(c_Product__Type_OPair(_1570603, _1570605), 40386 ^ [_1570603, _1570605, _1570607]), 40390 ^ [_1570603, _1570605, _1570607])), _1570607)))], (40394 ^ _780119) ^ [] : [40387 ^ [_1570603, _1570605, _1570607] = 40390 ^ [_1570603, _1570605, _1570607]], (40389 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570603, _1570605)), hAPP(hAPP(c_Product__Type_OPair(_1570603, _1570605), 40386 ^ [_1570603, _1570605, _1570607]), 40387 ^ [_1570603, _1570605, _1570607])), _1570607)))]], -(c_Relation_Osingle__valued(_1570603, _1570605, _1570607))], (38513 ^ _780119) ^ [_1525097] : [-(_1525097 = hAPP(c_Int_OAbs__Integ, 38511 ^ [_1525097]))], (12759 ^ _780119) ^ [_1011381, _1011383, _1011385, _1011387] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1011381), _1011383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1011385), hAPP(c_Set_Oimage(_1011381, _1011385, _1011387), _1011383))), hAPP(c_Finite__Set_Ocard(_1011381), _1011383))))], (28415 ^ _780119) ^ [_1305357, _1305359, _1305361] : [class_Orderings_Olinorder(_1305357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305357), _1305359)), -(_1305359 = c_Orderings_Obot__class_Obot(tc_fun(_1305357, tc_HOL_Obool))), 28426 ^ _780119 : [(28427 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305357), _1305361), hAPP(c_Finite__Set_Ofold1(_1305357, c_Orderings_Oord__class_Omin(_1305357)), _1305359))), 28430 ^ _780119 : [(28431 ^ _780119) ^ [_1305650] : [hBOOL(hAPP(hAPP(c_member(_1305357), _1305650), _1305359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305357), _1305361), _1305650)))]]], (28437 ^ _780119) ^ [] : [28439 ^ _780119 : [(28442 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305357), _1305361), 28438 ^ [_1305357, _1305359, _1305361]))], (28440 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305357), 28438 ^ [_1305357, _1305359, _1305361]), _1305359)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305357), _1305361), hAPP(c_Finite__Set_Ofold1(_1305357, c_Orderings_Oord__class_Omin(_1305357)), _1305359))))]]], (27608 ^ _780119) ^ [_1290165, _1290167, _1290169, _1290171] : [class_Orderings_Olinorder(_1290165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290165), _1290167), _1290169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290165), _1290167), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290165), _1290169), _1290171))))], (32243 ^ _780119) ^ [_1381474, _1381476] : [c_Int_Oiszero(_1381474, hAPP(c_Int_Onumber__class_Onumber__of(_1381474), c_Int_OBit1(_1381476))), class_Int_Onumber__ring(_1381474), class_Int_Oring__char__0(_1381474)], (3960 ^ _780119) ^ [_839952, _839954, _839956, _839958] : [-(c_List_Obutlast(_839958, _839954) = c_List_Obutlast(_839956, _839952)), _839958 = _839956, _839954 = _839952], (46501 ^ _780119) ^ [_1717337, _1717339, _1717341, _1717343] : [46502 ^ _780119 : [(46505 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1717337), _1717339), hAPP(c_List_Oset(_1717337), c_List_Obutlast(_1717337, _1717343))))], (46503 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1717337), _1717339), hAPP(c_List_Oset(_1717337), c_List_Obutlast(_1717337, _1717341))))]], -(hBOOL(hAPP(hAPP(c_member(_1717337), _1717339), hAPP(c_List_Oset(_1717337), c_List_Obutlast(_1717337, hAPP(hAPP(c_List_Oappend(_1717337), _1717341), _1717343))))))], (10356 ^ _780119) ^ [_962495, _962497, _962499, _962501] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_962495, _962497, _962499), _962501)), _962499 = c_Orderings_Obot__class_Obot(tc_fun(_962495, tc_HOL_Obool))], (1964 ^ _780119) ^ [_808556, _808558, _808560, _808562, _808564, _808566] : [-(c_Power_Opower_Opower(_808566, _808562, _808558) = c_Power_Opower_Opower(_808564, _808560, _808556)), _808566 = _808564, _808562 = _808560, _808558 = _808556], (37950 ^ _780119) ^ [_1510339, _1510341, _1510343, _1510345] : [_1510339 = c_Orderings_Obot__class_Obot(tc_fun(_1510341, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1510341, _1510343), _1510343, c_Product__Type_Osnd(_1510341, _1510343)), hAPP(hAPP(c_Product__Type_OSigma(_1510341, _1510343), _1510339), hAPP(c_COMBK(tc_fun(_1510343, tc_HOL_Obool), _1510341), _1510345))) = c_Orderings_Obot__class_Obot(tc_fun(_1510343, tc_HOL_Obool)))], (6797 ^ _780119) ^ [_891776, _891778, _891780, _891782] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891776, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_891776), _891778), _891780)), _891782) = hAPP(hAPP(c_Set_Oinsert(_891776), _891778), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891776, tc_HOL_Obool)), _891780), _891782)))], (23453 ^ _780119) ^ [_1208997, _1208999] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1208997), _1208999))))], (35408 ^ _780119) ^ [_1447946, _1447948, _1447950, _1447952, _1447954, _1447956] : [hBOOL(hAPP(hAPP(c_member(_1447946), _1447948), _1447950)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1447946, _1447952)), hAPP(hAPP(c_Product__Type_OPair(_1447946, _1447952), _1447948), _1447954)), _1447956)), -(hBOOL(hAPP(hAPP(c_member(_1447952), _1447954), hAPP(c_Relation_OImage(_1447946, _1447952, _1447956), _1447950))))], (36393 ^ _780119) ^ [_1470378, _1470380, _1470382] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1470378), _1470380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470378, tc_HOL_Obool)), _1470380), hAPP(c_Set_Oimage(_1470378, _1470378, _1470382), _1470380))), -(c_Fun_Oinj__on(_1470378, _1470378, _1470382, _1470380))], (38471 ^ _780119) ^ [_1523670, _1523672, _1523674] : [c_Relation_Orefl__on(_1523670, _1523672, _1523674), 38474 ^ _780119 : [(38481 ^ _780119) ^ [_1524154] : [hBOOL(hAPP(hAPP(c_member(_1523670), _1524154), _1523672)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523670, _1523670)), hAPP(hAPP(c_Product__Type_OPair(_1523670, _1523670), _1524154), _1524154)), _1523674)))], (38475 ^ _780119) ^ [_1523881] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523670, _1523670)), _1523881), _1523674)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1523670, _1523670, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1523670, tc_fun(_1523670, tc_HOL_Obool), tc_fun(_1523670, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1523670, tc_HOL_Obool), tc_fun(_1523670, tc_HOL_Obool)), _1523670), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1523670)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523670), c_fconj), hAPP(hAPP(c_COMBC(_1523670, tc_fun(_1523670, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523670)), _1523672)))), hAPP(hAPP(c_COMBC(_1523670, tc_fun(_1523670, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523670)), _1523672))), _1523881)))]]], (27332 ^ _780119) ^ [_1285216, _1285218, _1285220] : [class_Orderings_Olinorder(_1285216), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285216), _1285218)), hBOOL(hAPP(hAPP(c_member(_1285216), _1285220), _1285218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285216), _1285220), c_Big__Operators_Olinorder__class_OMax(_1285216, _1285218))))], (28736 ^ _780119) ^ [_1311067] : [class_Orderings_Olinorder(_1311067), -(c_Orderings_Oord_Omin(_1311067, hAPP(c_COMBC(_1311067, _1311067, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1311067))) = c_Orderings_Oord__class_Omax(_1311067))], (12135 ^ _780119) ^ [_998812, _998814, _998816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998812), _998814)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998816), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _998814), _998812)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998816), _998812)), _998814))], (39915 ^ _780119) ^ [_1558844, _1558846] : [-(c_Relation_Orefl__on(_1558844, c_Orderings_Otop__class_Otop(tc_fun(_1558844, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1558844, _1558844), tc_HOL_Obool)), _1558846), c_Relation_OId(_1558844))))], (20626 ^ _780119) ^ [_1155085, _1155087, _1155089] : [class_Fields_Olinordered__field(_1155085), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155085), c_Groups_Ozero__class_Ozero(_1155085)), _1155087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155085), _1155089), c_Groups_Ozero__class_Ozero(_1155085))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155085), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155085), _1155087), _1155089)), c_Groups_Ozero__class_Ozero(_1155085))))], (39579 ^ _780119) ^ [_1550311, _1550313] : [_1550311 = _1550313, -(c_Random_Oinc__shift(_1550311, _1550313) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (27530 ^ _780119) ^ [_1288807, _1288809, _1288811, _1288813, _1288815] : [class_Orderings_Olinorder(_1288807), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288807, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1288807, _1288809, _1288811)), c_SetInterval_Oord__class_OatLeastAtMost(_1288807, _1288813, _1288815)) = c_SetInterval_Oord__class_OatLeastAtMost(_1288807, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288807), _1288809), _1288813), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288807), _1288811), _1288815)))], (25131 ^ _780119) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46539 ^ _780119) ^ [_1718152, _1718154, _1718156, _1718158] : [hAPP(hAPP(c_List_Oappend(_1718152), _1718154), hAPP(hAPP(c_List_Olist_OCons(_1718152), _1718156), c_List_Olist_ONil(_1718152))) = _1718158, 46542 ^ _780119 : [(46545 ^ _780119) ^ [] : [-(c_List_Obutlast(_1718152, _1718158) = _1718154)], (46547 ^ _780119) ^ [] : [-(c_List_Olast(_1718152, _1718158) = _1718156)], (46543 ^ _780119) ^ [] : [_1718158 = c_List_Olist_ONil(_1718152)]]], (8124 ^ _780119) ^ [_919352, _919354, _919356, _919358] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_919352), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919352, tc_HOL_Obool)), _919354), _919358))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_919352), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919352, tc_HOL_Obool)), _919354), hAPP(hAPP(c_Set_Oinsert(_919352), _919356), _919358)))))], (5791 ^ _780119) ^ [_871742, _871744, _871746, _871748] : [c_Hoare__Mirabelle_Ohoare__derivs(_871742, _871744, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871742)), _871746), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871742), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_871742, _871744, _871748), -(c_Hoare__Mirabelle_Ohoare__derivs(_871742, _871744, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871742)), _871746), _871748)))], (4826 ^ _780119) ^ [_853735, _853737, _853739, _853741] : [-(c_New__DSequence_Oneg__single(_853741, _853737) = c_New__DSequence_Oneg__single(_853739, _853735)), _853741 = _853739, _853737 = _853735], (17784 ^ _780119) ^ [_1103465, _1103467] : [_1103465 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1103467), _1103465) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (26225 ^ _780119) ^ [_1258471, _1258473, _1258475] : [class_Orderings_Olinorder(_1258471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258471), _1258473), _1258475)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258471, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1258471), _1258473)), c_SetInterval_Oord__class_OatLeastAtMost(_1258471, _1258473, _1258475)) = hAPP(c_SetInterval_Oord__class_OatMost(_1258471), _1258475))], (33277 ^ _780119) ^ [_1400469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1400469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1400469)))], (41976 ^ _780119) ^ [_1608395, _1608397, _1608399, _1608401, _1608403, _1608405, _1608407, _1608409] : [c_Fun_Oinj__on(_1608395, _1608397, _1608399, _1608401), 41982 ^ _780119 : [(41985 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1608395, tc_HOL_Obool)), hAPP(_1608407, 41981 ^ [_1608395, _1608397, _1608399, _1608401, _1608403, _1608405, _1608407, _1608409])), _1608401))], (41983 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608403), 41981 ^ [_1608395, _1608397, _1608399, _1608401, _1608403, _1608405, _1608407, _1608409]), _1608405)))]], hBOOL(hAPP(hAPP(c_member(_1608403), _1608409), _1608405)), -(hAPP(c_Set_Oimage(_1608395, _1608397, _1608399), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608403, tc_fun(_1608395, tc_HOL_Obool)), _1608405), _1608407)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608403, tc_fun(_1608397, tc_HOL_Obool)), _1608405), hAPP(hAPP(c_COMBB(tc_fun(_1608395, tc_HOL_Obool), tc_fun(_1608397, tc_HOL_Obool), _1608403), c_Set_Oimage(_1608395, _1608397, _1608399)), _1608407)))], (51483 ^ _780119) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (33429 ^ _780119) ^ [_1402809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1402809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1402809))))], (13542 ^ _780119) ^ [_1026732, _1026734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1026732)), hAPP(c_Nat_OSuc, _1026734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026732), _1026734)))], (32551 ^ _780119) ^ [_1386907, _1386909] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1386907))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1386909))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1386907)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1386909)))], (15174 ^ _780119) ^ [_1057705, _1057707] : [class_Groups_Olinordered__ab__group__add(_1057705), 15177 ^ _780119 : [(15184 ^ _780119) ^ [] : [_1057707 = c_Groups_Ozero__class_Ozero(_1057705), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1057705), _1057707) = _1057707)], (15178 ^ _780119) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1057705), _1057707) = _1057707, -(_1057707 = c_Groups_Ozero__class_Ozero(_1057705))]]], (31251 ^ _780119) ^ [_1364369] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1364369))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1364369)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33739 ^ _780119) ^ [_1412918, _1412920, _1412922, _1412924] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1412918, _1412920), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1412922), _1412924))), -(_1412920 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1412918), _1412920) = _1412922)], (36944 ^ _780119) ^ [_1483134, _1483136, _1483138, _1483140, _1483142, _1483144] : [c_Typedef_Otype__definition(_1483134, _1483136, _1483138, _1483140, _1483142), -(hBOOL(hAPP(hAPP(c_member(_1483136), hAPP(_1483138, _1483144)), _1483142)))], (38681 ^ _780119) ^ [_1529455, _1529457] : [38682 ^ _780119 : [(38683 ^ _780119) ^ [_1529501] : [hBOOL(hAPP(_1529455, _1529501))]], -(hBOOL(hAPP(_1529455, c_Hilbert__Choice_OEps(_1529457, _1529455))))], (26555 ^ _780119) ^ [_1265009, _1265011] : [class_Groups_Oordered__ab__group__add__abs(_1265009), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265009), c_Groups_Ozero__class_Ozero(_1265009)), hAPP(c_Groups_Oabs__class_Oabs(_1265009), _1265011))))], (51107 ^ _780119) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (38820 ^ _780119) ^ [_1532486, _1532488, _1532490, _1532492, _1532494, _1532496, _1532498, _1532500, _1532502, _1532504] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1532486, _1532488), tc_prod(_1532490, _1532492), tc_prod(_1532494, _1532496), c_Product__Type_Omap__pair(_1532486, _1532490, _1532488, _1532492, _1532498, _1532500)), c_Product__Type_Omap__pair(_1532494, _1532486, _1532496, _1532488, _1532502, _1532504)) = c_Product__Type_Omap__pair(_1532494, _1532490, _1532496, _1532492, hAPP(c_Fun_Ocomp(_1532486, _1532490, _1532494, _1532498), _1532502), hAPP(c_Fun_Ocomp(_1532488, _1532492, _1532496, _1532500), _1532504)))], (17796 ^ _780119) ^ [_1103610, _1103612, _1103614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1103610), _1103612)), 17799 ^ _780119 : [(17819 ^ _780119) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1103610, tc_Nat_Onat), _1103614), _1103612) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 17820 ^ _780119 : [(17821 ^ _780119) ^ [_1104091] : [hBOOL(hAPP(hAPP(c_member(_1103610), _1104091), _1103612)), hAPP(_1103614, _1104091) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 17829 ^ _780119 : [(17832 ^ _780119) ^ [] : [_1104091 = 17828 ^ [_1103610, _1103612, _1103614, _1104091]], (17834 ^ _780119) ^ [] : [hAPP(_1103614, 17828 ^ [_1103610, _1103612, _1103614, _1104091]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17830 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1103610), 17828 ^ [_1103610, _1103612, _1103614, _1104091]), _1103612)))]]]]], (17800 ^ _780119) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1103610, tc_Nat_Onat), _1103614), _1103612) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 17804 ^ _780119 : [(17807 ^ _780119) ^ [] : [-(hAPP(_1103614, 17803 ^ [_1103610, _1103612, _1103614]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17809 ^ _780119) ^ [_1103930] : [hBOOL(hAPP(hAPP(c_member(_1103610), _1103930), _1103612)), -(17803 ^ [_1103610, _1103612, _1103614] = _1103930), -(hAPP(_1103614, _1103930) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17805 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1103610), 17803 ^ [_1103610, _1103612, _1103614]), _1103612)))]]]]], (24199 ^ _780119) ^ [_1223196, _1223198] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1223196, _1223198))))], (18642 ^ _780119) ^ [_1120210, _1120212] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1120210)), hAPP(c_Option_Ooption_OSome(_1120210), _1120212)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10909 ^ _780119) ^ [_973727, _973729, _973731, _973733] : [class_Groups_Oordered__cancel__ab__semigroup__add(_973727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973727), _973729), _973731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973727), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973727), _973733), _973729)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973727), _973733), _973731))))], (21255 ^ _780119) ^ [_1166961, _1166963, _1166965, _1166967, _1166969] : [class_Groups_Ocomm__monoid__add(_1166961), hBOOL(hAPP(c_Finite__Set_Ofinite(_1166963), _1166965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1166963, tc_HOL_Obool)), _1166967), _1166965)), 21269 ^ _780119 : [(21272 ^ _780119) ^ [] : [hAPP(_1166969, 21268 ^ [_1166961, _1166963, _1166965, _1166967, _1166969]) = c_Groups_Ozero__class_Ozero(_1166961)], (21270 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1166963), 21268 ^ [_1166961, _1166963, _1166965, _1166967, _1166969]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1166963, tc_HOL_Obool)), _1166965), _1166967))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1166963, _1166961), _1166969), _1166965) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1166963, _1166961), _1166969), _1166967))], (6581 ^ _780119) ^ [_887026, _887028, _887030] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887026, tc_HOL_Obool)), _887028), _887030) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887026, tc_HOL_Obool)), _887030), _887028))], (34046 ^ _780119) ^ [_1419484] : [-(c_Divides_Oadjust(_1419484) = 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)), _1419484))))), 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)), _1419484))))), 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))))))))], (2604 ^ _780119) ^ [_818666, _818668] : [_818668 = _818666, -(c_Int_Oint__ge__less__than(_818668) = c_Int_Oint__ge__less__than(_818666))], (50248 ^ _780119) ^ [_1798447, _1798449, _1798451, _1798453, _1798455] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1798447, _1798449, _1798451, _1798453, _1798455) = hAPP(c_Option_Ooption_Ooption__case(_1798447, tc_prod(_1798449, tc_Lazy__Sequence_Olazy__sequence(_1798449)), _1798451, hAPP(c_Product__Type_Oprod_Oprod__case(_1798449, tc_Lazy__Sequence_Olazy__sequence(_1798449), _1798447), _1798453)), hAPP(c_Lazy__Sequence_Oyield(_1798449), _1798455)))], (8266 ^ _780119) ^ [_922709, _922711, _922713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922709, tc_HOL_Obool)), _922711), hAPP(hAPP(c_Set_Oinsert(_922709), _922713), c_Orderings_Obot__class_Obot(tc_fun(_922709, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_922709, _922713, _922711) = _922713)], (23237 ^ _780119) ^ [_1204563, _1204565] : [class_Rings_Osemiring__1(_1204563), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1204563), _1204565) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1204563, hAPP(hAPP(c_COMBC(_1204563, _1204563, _1204563), c_Groups_Oplus__class_Oplus(_1204563)), c_Groups_Oone__class_Oone(_1204563)), _1204565, c_Groups_Ozero__class_Ozero(_1204563)))], (43202 ^ _780119) ^ [_1637759, _1637761, _1637763] : [class_Orderings_Olinorder(_1637759), -(c_List_Oremove1(_1637759, _1637761, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1637759, _1637759, c_COMBI(_1637759)), _1637761), _1637763)) = _1637763)], (23223 ^ _780119) ^ [_1204288, _1204290, _1204292] : [-(hBOOL(hAPP(_1204288, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1204290), _1204292))))), 23226 ^ _780119 : [(23229 ^ _780119) ^ [] : [hBOOL(hAPP(_1204288, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204290)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204292))))], (23227 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204292), _1204290)))]], 23230 ^ _780119 : [(23233 ^ _780119) ^ [] : [hBOOL(hAPP(_1204288, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23231 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204290), _1204292)))]]], (49656 ^ _780119) ^ [_1786900, _1786902, _1786904, _1786906] : [49657 ^ _780119 : [(49660 ^ _780119) ^ [] : [c_List_Olist__ex(_1786900, _1786902, _1786906)], (49658 ^ _780119) ^ [] : [hBOOL(hAPP(_1786902, _1786904))]], -(c_List_Olist__ex(_1786900, _1786902, hAPP(hAPP(c_List_Olist_OCons(_1786900), _1786904), _1786906)))], (19731 ^ _780119) ^ [_1139076, _1139078, _1139080, _1139082] : [class_Fields_Ofield__inverse__zero(_1139076), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1139076), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139076), _1139078), _1139080)), _1139082) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139076), hAPP(hAPP(c_Power_Opower__class_Opower(_1139076), _1139078), _1139082)), hAPP(hAPP(c_Power_Opower__class_Opower(_1139076), _1139080), _1139082)))], (37147 ^ _780119) ^ [_1490280, _1490282, _1490284, _1490286] : [c_Wellfounded_Omax__extp(_1490280, _1490282, _1490284, _1490286), 37150 ^ _780119 : [(37151 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1490280), _1490284)))], (37153 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1490280), _1490286)))], (37157 ^ _780119) ^ [_1490496] : [hBOOL(hAPP(hAPP(c_member(_1490280), _1490496), _1490284)), 37161 ^ _780119 : [(37164 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(_1490282, _1490496), 37160 ^ [_1490280, _1490282, _1490284, _1490286, _1490496])))], (37162 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490280), 37160 ^ [_1490280, _1490282, _1490284, _1490286, _1490496]), _1490286)))]]], (37155 ^ _780119) ^ [] : [_1490286 = c_Orderings_Obot__class_Obot(tc_fun(_1490280, tc_HOL_Obool))]]], (13819 ^ _780119) ^ [_1031368, _1031370, _1031372] : [class_Rings_Ocomm__ring__1(_1031368), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031368), _1031370), _1031372) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031368), _1031370), hAPP(c_Groups_Ouminus__class_Ouminus(_1031368), _1031372)))], (17991 ^ _780119) ^ [_1107819, _1107821, _1107823] : [class_Rings_Olinordered__semidom(_1107819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107819), c_Groups_Ozero__class_Ozero(_1107819)), _1107821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107819), _1107821), c_Groups_Oone__class_Oone(_1107819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107819), hAPP(hAPP(c_Power_Opower__class_Opower(_1107819), _1107821), hAPP(c_Nat_OSuc, _1107823))), c_Groups_Oone__class_Oone(_1107819))))], (33435 ^ _780119) ^ [_1402898] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1402898, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24637 ^ _780119) ^ [_1231474, _1231476, _1231478] : [class_Orderings_Oorder(_1231474), 24640 ^ _780119 : [(24647 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231474), _1231476), _1231478))), -(c_Orderings_Obot__class_Obot(tc_fun(_1231474, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1231474, _1231476, _1231478))], (24641 ^ _780119) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1231474, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1231474, _1231476, _1231478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231474), _1231476), _1231478))]]], (6055 ^ _780119) ^ [_876549, _876551] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876549, tc_HOL_Obool)), _876551), _876551)))], (31201 ^ _780119) ^ [_1363515, _1363517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1363515), _1363517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1363515)), c_Int_OBit1(_1363517))))], (39841 ^ _780119) ^ [] : [-(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))))], (4530 ^ _780119) ^ [_848803, _848805, _848807, _848809, _848811, _848813, _848815, _848817] : [-(c_New__Random__Sequence_Opos__empty(_848817, _848813, _848809, _848805) = c_New__Random__Sequence_Opos__empty(_848815, _848811, _848807, _848803)), _848817 = _848815, _848813 = _848811, _848809 = _848807, _848805 = _848803], (26981 ^ _780119) ^ [_1274191, _1274193] : [26982 ^ _780119 : [(26985 ^ _780119) ^ [] : [_1274193 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26983 ^ _780119) ^ [] : [-(_1274191 = 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), _1274191)), _1274193))))], (22266 ^ _780119) ^ [_1186443, _1186445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186443), _1186445)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186443, _1186445) = _1186443)], (43252 ^ _780119) ^ [_1638848, _1638850, _1638852, _1638854, _1638856] : [class_Orderings_Olinorder(_1638848), 43255 ^ _780119 : [(43264 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1638850), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1638850, _1638848, _1638852), _1638854), _1638856)))), -(hBOOL(hAPP(hAPP(c_member(_1638850), _1638854), hAPP(c_List_Oset(_1638850), _1638856)))), hBOOL(hAPP(c_List_Odistinct(_1638850), _1638856))], (43256 ^ _780119) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1638850), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1638850, _1638848, _1638852), _1638854), _1638856))), 43259 ^ _780119 : [(43262 ^ _780119) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1638850), _1638856)))], (43260 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1638850), _1638854), hAPP(c_List_Oset(_1638850), _1638856)))]]]]], (48363 ^ _780119) ^ [_1757932, _1757934, _1757936] : [class_Orderings_Olinorder(_1757932), -(c_List_Olinorder__class_Osort__key(_1757934, _1757932, _1757936, c_List_Olist_ONil(_1757934)) = c_List_Olist_ONil(_1757934))], (29631 ^ _780119) ^ [_1330925, _1330927, _1330929, _1330931, _1330933, _1330935] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330925, tc_fun(_1330927, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330929, tc_fun(_1330925, tc_HOL_Obool)), _1330931), _1330933)), _1330935) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330929, tc_fun(_1330927, tc_HOL_Obool)), _1330931), hAPP(hAPP(c_COMBC(_1330929, tc_fun(_1330925, tc_fun(_1330927, tc_HOL_Obool)), tc_fun(_1330927, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1330925, tc_HOL_Obool), tc_fun(tc_fun(_1330925, tc_fun(_1330927, tc_HOL_Obool)), tc_fun(_1330927, tc_HOL_Obool)), _1330929), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330925, tc_fun(_1330927, tc_HOL_Obool))), _1330933)), _1330935)))], (11828 ^ _780119) ^ [_992954, _992956, _992958] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _992954), _992956)), _992958) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _992954), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _992956), _992958)))], (35325 ^ _780119) ^ [_1444888, _1444890] : [-(c_FunDef_Orp__inv__image(_1444888, _1444890) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool), tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool), tc_fun(tc_fun(_1444890, _1444888), tc_prod(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool), tc_fun(tc_fun(_1444890, _1444888), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool), tc_fun(tc_fun(_1444890, _1444888), tc_prod(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1444890, _1444888), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)), tc_fun(tc_fun(_1444890, _1444888), tc_prod(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool), tc_fun(tc_fun(_1444890, _1444888), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool), tc_fun(tc_fun(_1444890, _1444888), tc_prod(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool))))), tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1444890, _1444888), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)), tc_fun(tc_fun(_1444890, _1444888), tc_prod(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool))), tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1444890, _1444888), tc_fun(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1444890, _1444888), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)), tc_fun(tc_fun(_1444890, _1444888), tc_prod(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)))), tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool)), c_COMBS(tc_fun(_1444890, _1444888), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1444890, _1444888), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)), tc_fun(tc_fun(_1444890, _1444888), tc_fun(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)))), tc_fun(tc_prod(_1444888, _1444888), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool))), tc_fun(_1444890, _1444888)), c_Product__Type_OPair(tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool), tc_fun(tc_prod(_1444890, _1444890), tc_HOL_Obool)))), c_Relation_Oinv__image(_1444888, _1444890))))), c_Relation_Oinv__image(_1444888, _1444890))))], (5841 ^ _780119) ^ [_872752, _872754, _872756, _872758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872752, tc_HOL_Obool)), _872754), _872756)), hBOOL(hAPP(hAPP(c_member(_872752), _872758), _872754)), -(hBOOL(hAPP(hAPP(c_member(_872752), _872758), _872756)))], (44390 ^ _780119) ^ [_1669460, _1669462, _1669464, _1669466, _1669468] : [-(hAPP(hAPP(c_List_Olist__update(_1669460, hAPP(hAPP(c_List_Olist__update(_1669460, _1669462), _1669464), _1669466)), _1669464), _1669468) = hAPP(hAPP(c_List_Olist__update(_1669460, _1669462), _1669464), _1669468))], (8468 ^ _780119) ^ [_927218, _927220, _927222, _927224, _927226, _927228] : [_927218 = _927220, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_927222, _927224), _927226), _927220), _927228), _927218) = _927228)], (4222 ^ _780119) ^ [_843927, _843929, _843931, _843933, _843935, _843937] : [-(c_List_Oinsert(_843937, _843933, _843929) = c_List_Oinsert(_843935, _843931, _843927)), _843937 = _843935, _843933 = _843931, _843929 = _843927], (38542 ^ _780119) ^ [_1525669, _1525671, _1525673, _1525675] : [c_Equiv__Relations_Ocongruent(_1525669, _1525671, _1525673, _1525675), 38545 ^ _780119 : [(38546 ^ _780119) ^ [_1525814] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1525669, _1525669)), _1525814), _1525673)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1525669, _1525669, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1525669, tc_fun(_1525669, _1525671), tc_fun(_1525669, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525671, tc_HOL_Obool), tc_fun(tc_fun(_1525669, _1525671), tc_fun(_1525669, tc_HOL_Obool)), _1525669), c_COMBB(_1525671, tc_HOL_Obool, _1525669)), hAPP(hAPP(c_COMBB(_1525671, tc_fun(_1525671, tc_HOL_Obool), _1525669), c_fequal), _1525675))), _1525675)), _1525814)))]]], (49895 ^ _780119) ^ [_1791848, _1791850, _1791852, _1791854] : [c_List_Olist__ex1(_1791848, _1791850, hAPP(hAPP(c_List_Olist_OCons(_1791848), _1791852), _1791854)), 49898 ^ _780119 : [(49905 ^ _780119) ^ [] : [-(hBOOL(hAPP(_1791850, _1791852))), -(c_List_Olist__ex1(_1791848, _1791850, _1791854))], (49899 ^ _780119) ^ [] : [hBOOL(hAPP(_1791850, _1791852)), -(c_List_Olist__all(_1791848, hAPP(hAPP(c_COMBS(_1791848, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1791848), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1791848), c_fNot), _1791850))), hAPP(c_fequal, _1791852)), _1791854))]]], (9444 ^ _780119) ^ [_942519, _942521, _942523] : [class_Lattices_Olattice(_942519), hBOOL(hAPP(c_Finite__Set_Ofinite(_942519), _942521)), -(hBOOL(hAPP(hAPP(c_member(_942519), _942523), _942521))), -(_942521 = c_Orderings_Obot__class_Obot(tc_fun(_942519, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_942519, hAPP(hAPP(c_Set_Oinsert(_942519), _942523), _942521)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_942519), _942523), c_Big__Operators_Olattice__class_OSup__fin(_942519, _942521)))], (24999 ^ _780119) ^ [_1238118] : [hBOOL(hAPP(_1238118, 25000 ^ [_1238118])), 25003 ^ _780119 : [(25004 ^ _780119) ^ [_1238212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238212)), -(hBOOL(hAPP(_1238118, hAPP(c_Int_Onat, _1238212))))]]], (10633 ^ _780119) ^ [_968535, _968537, _968539, _968541, _968543] : [class_Groups_Ocomm__monoid__add(_968535), hBOOL(hAPP(c_Finite__Set_Ofinite(_968537), _968539)), hBOOL(hAPP(hAPP(c_member(_968537), _968541), _968539)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_968537, _968535), _968543), _968539) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968535), hAPP(_968543, _968541)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_968537, _968535), _968543), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968537, tc_HOL_Obool)), _968539), hAPP(hAPP(c_Set_Oinsert(_968537), _968541), c_Orderings_Obot__class_Obot(tc_fun(_968537, tc_HOL_Obool)))))))], (46485 ^ _780119) ^ [_1717072, _1717074, _1717076] : [_1717072 = c_List_Olist_ONil(_1717074), -(c_List_Obutlast(_1717074, hAPP(hAPP(c_List_Olist_OCons(_1717074), _1717076), _1717072)) = c_List_Olist_ONil(_1717074))], (32407 ^ _780119) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (5883 ^ _780119) ^ [_873576, _873578, _873580, _873582] : [-(_873576 = c_Orderings_Obot__class_Obot(tc_fun(_873578, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_873578, _873580, hAPP(c_COMBK(_873580, _873578), _873582)), _873576) = hAPP(hAPP(c_Set_Oinsert(_873580), _873582), c_Orderings_Obot__class_Obot(tc_fun(_873580, tc_HOL_Obool))))], (37501 ^ _780119) ^ [_1497772, _1497774, _1497776] : [c_Wellfounded_Owf(_1497772, _1497774), -(c_Wellfounded_Owf(tc_List_Olist(_1497772), hAPP(c_List_Olexn(_1497772, _1497774), _1497776)))], (37229 ^ _780119) ^ [_1491827, _1491829] : [c_Wellfounded_Owf(_1491827, hAPP(hAPP(c_Relation_Orel__comp(_1491827, _1491827, _1491827), _1491829), _1491829)), -(c_Wellfounded_Owf(_1491827, _1491829))], (16500 ^ _780119) ^ [_1080711, _1080713] : [class_Groups_Oordered__ab__group__add(_1080711), 16503 ^ _780119 : [(16510 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080711), c_Groups_Ozero__class_Ozero(_1080711)), _1080713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080711), hAPP(c_Groups_Ouminus__class_Ouminus(_1080711), _1080713)), c_Groups_Ozero__class_Ozero(_1080711))))], (16504 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080711), hAPP(c_Groups_Ouminus__class_Ouminus(_1080711), _1080713)), c_Groups_Ozero__class_Ozero(_1080711))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080711), c_Groups_Ozero__class_Ozero(_1080711)), _1080713)))]]], (21580 ^ _780119) ^ [_1173771, _1173773, _1173775] : [-(hAPP(c_Set_OPow(_1173771), hAPP(hAPP(c_Set_Oinsert(_1173771), _1173773), _1173775)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1173771, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1173771), _1173775)), hAPP(c_Set_Oimage(tc_fun(_1173771, tc_HOL_Obool), tc_fun(_1173771, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1173771), _1173773)), hAPP(c_Set_OPow(_1173771), _1173775))))], (46339 ^ _780119) ^ [_1714181, _1714183, _1714185] : [_1714181 = c_List_Olist_ONil(_1714183), -(c_List_Olast(_1714183, hAPP(hAPP(c_List_Oappend(_1714183), _1714185), _1714181)) = c_List_Olast(_1714183, _1714185))], (15484 ^ _780119) ^ [_1062375, _1062377] : [class_Lattices_Obounded__lattice__top(_1062375), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062375), _1062377), c_Orderings_Otop__class_Otop(_1062375)) = _1062377)], (20858 ^ _780119) ^ [_1159406, _1159408, _1159410, _1159412] : [class_Fields_Olinordered__field(_1159406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159406), c_Groups_Ozero__class_Ozero(_1159406)), _1159408)), 20865 ^ _780119 : [(20872 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159406), _1159410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159406), _1159412), _1159408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159406), _1159410), _1159408)), _1159412)))], (20866 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159406), _1159410), _1159408)), _1159412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159406), _1159410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159406), _1159412), _1159408))))]]], (37593 ^ _780119) ^ [_1500339, _1500341, _1500343, _1500345, _1500347] : [hBOOL(hAPP(hAPP(_1500339, _1500341), _1500343)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1500345, _1500347, _1500339), _1500343)))], (33493 ^ _780119) ^ [] : [-(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))], (47608 ^ _780119) ^ [_1740310, _1740312, _1740314, _1740316] : [_1740312 = hAPP(hAPP(c_List_Oappend(_1740310), hAPP(c_List_Orev(_1740310), _1740316)), hAPP(hAPP(c_List_Olist_OCons(_1740310), _1740314), c_List_Olist_ONil(_1740310))), -(hAPP(c_List_Orev(_1740310), _1740312) = hAPP(hAPP(c_List_Olist_OCons(_1740310), _1740314), _1740316))], (42355 ^ _780119) ^ [_1617490, _1617492, _1617494] : [-(c_Map_Omap__add(_1617490, _1617492, hAPP(c_COMBK(tc_Option_Ooption(_1617492), _1617490), c_Option_Ooption_ONone(_1617492)), _1617494) = _1617494)], (49837 ^ _780119) ^ [_1790733, _1790735, _1790737, _1790739] : [c_List_Olist__all(_1790733, _1790735, hAPP(hAPP(c_List_Oappend(_1790733), _1790737), _1790739)), 49840 ^ _780119 : [(49843 ^ _780119) ^ [] : [-(c_List_Olist__all(_1790733, _1790735, _1790739))], (49841 ^ _780119) ^ [] : [-(c_List_Olist__all(_1790733, _1790735, _1790737))]]], (34004 ^ _780119) ^ [_1418314, _1418316, _1418318, _1418320, _1418322, _1418324] : [_1418314 = _1418316, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1418318, _1418320, _1418322), _1418324), _1418314) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1418318, _1418320, _1418322), _1418324), _1418316))], (43473 ^ _780119) ^ [_1646439, _1646441, _1646443, _1646445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646439)), _1646441)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646439)), _1646443))), _1646441 = hAPP(hAPP(c_List_Olist_OCons(_1646439), _1646445), _1646443)], (51167 ^ _780119) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (43621 ^ _780119) ^ [_1649760, _1649762, _1649764, _1649766, _1649768, _1649770] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649760), tc_List_Olist(_1649760))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649760), tc_List_Olist(_1649760)), hAPP(hAPP(c_List_Olist_OCons(_1649760), _1649762), _1649764)), hAPP(hAPP(c_List_Olist_OCons(_1649760), _1649766), _1649768))), c_List_Olex(_1649760, _1649770))), 43626 ^ _780119 : [(43629 ^ _780119) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649760)), _1649764) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649760)), _1649768))], (43627 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1649760, _1649760)), hAPP(hAPP(c_Product__Type_OPair(_1649760, _1649760), _1649762), _1649766)), _1649770)))]], 43630 ^ _780119 : [(43633 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649760), tc_List_Olist(_1649760))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649760), tc_List_Olist(_1649760)), _1649764), _1649768)), c_List_Olex(_1649760, _1649770))))], (43631 ^ _780119) ^ [] : [-(_1649762 = _1649766)]]], (32789 ^ _780119) ^ [_1391233] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1391233)), 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, _1391233, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (8256 ^ _780119) ^ [_922482, _922484, _922486, _922488, _922490, _922492, _922494, _922496] : [c_Finite__Set_Ofolding__image__simple__idem(_922482, _922484, _922486, _922488, _922490, _922492), hBOOL(hAPP(c_Finite__Set_Ofinite(_922484), _922494)), -(hAPP(_922492, hAPP(hAPP(c_Set_Oinsert(_922484), _922496), _922494)) = hAPP(hAPP(_922486, hAPP(_922490, _922496)), hAPP(_922492, _922494)))], (3326 ^ _780119) ^ [_830021, _830023, _830025, _830027] : [-(c_Hilbert__Choice_OEps(_830027, _830023) = c_Hilbert__Choice_OEps(_830025, _830021)), _830027 = _830025, _830023 = _830021], (11493 ^ _780119) ^ [_986184, _986186, _986188, _986190] : [class_Rings_Ocomm__semiring__1(_986184), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986184), _986186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986184), _986188), _986190)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986184), _986188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986184), _986186), _986190)))], (25851 ^ _780119) ^ [_1251906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251906)), -(c_Nat__Transfer_Ois__nat(_1251906))], (21470 ^ _780119) ^ [_1171437, _1171439, _1171441, _1171443] : [class_Divides_Osemiring__div(_1171437), -(c_Divides_Odiv__class_Omod(_1171437, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171437), _1171439), _1171441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171437), _1171443), _1171441)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171437), c_Divides_Odiv__class_Omod(_1171437, _1171439, _1171443)), _1171441))], (36754 ^ _780119) ^ [] : [-(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))))], (51071 ^ _780119) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (11848 ^ _780119) ^ [_993344, _993346, _993348] : [_993344 = _993348, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993344), _993346) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993348), _993346))], (34757 ^ _780119) ^ [_1432386, _1432388, _1432390, _1432392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1432392, _1432388)), hAPP(_1432392, _1432390))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1432386, _1432386)), hAPP(hAPP(c_Product__Type_OPair(_1432386, _1432386), _1432388), _1432390)), hAPP(c_Wellfounded_Omeasure(_1432386), _1432392))))], (44916 ^ _780119) ^ [_1679903, _1679905, _1679907, _1679909, _1679911] : [-(hAPP(hAPP(c_List_Ozip(_1679903, _1679905), _1679907), hAPP(hAPP(c_List_Olist_OCons(_1679905), _1679909), _1679911)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1679903, _1679905)), _1679903, c_List_Olist_ONil(tc_prod(_1679903, _1679905)), hAPP(hAPP(c_COMBC(_1679903, tc_fun(tc_List_Olist(_1679903), tc_List_Olist(tc_prod(_1679903, _1679905))), tc_fun(tc_List_Olist(_1679903), tc_List_Olist(tc_prod(_1679903, _1679905)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1679903, _1679905)), tc_List_Olist(tc_prod(_1679903, _1679905))), tc_fun(tc_fun(tc_List_Olist(_1679903), tc_List_Olist(tc_prod(_1679903, _1679905))), tc_fun(tc_List_Olist(_1679903), tc_List_Olist(tc_prod(_1679903, _1679905)))), _1679903), c_COMBB(tc_List_Olist(tc_prod(_1679903, _1679905)), tc_List_Olist(tc_prod(_1679903, _1679905)), tc_List_Olist(_1679903))), hAPP(hAPP(c_COMBB(tc_prod(_1679903, _1679905), tc_fun(tc_List_Olist(tc_prod(_1679903, _1679905)), tc_List_Olist(tc_prod(_1679903, _1679905))), _1679903), c_List_Olist_OCons(tc_prod(_1679903, _1679905))), hAPP(hAPP(c_COMBC(_1679903, _1679905, tc_prod(_1679903, _1679905)), c_Product__Type_OPair(_1679903, _1679905)), _1679909)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1679903), tc_List_Olist(_1679905), tc_List_Olist(tc_prod(_1679903, _1679905))), c_List_Ozip(_1679903, _1679905)), _1679911))), _1679907))], (5821 ^ _780119) ^ [_872376, _872378] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872376, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_872376, tc_HOL_Obool))), _872378)))], (38657 ^ _780119) ^ [_1528950, _1528952, _1528954] : [-(hAPP(c_Fun_Ocomp(_1528950, _1528952, _1528950, _1528954), c_Fun_Oid(_1528950)) = _1528954)], (27144 ^ _780119) ^ [_1280150] : [-(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)))), _1280150))))], (16797 ^ _780119) ^ [_1085756, _1085758] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085756), _1085758), 16802 ^ _780119 : [(16805 ^ _780119) ^ [] : [-(_1085758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16803 ^ _780119) ^ [] : [-(_1085756 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 16806 ^ _780119 : [(16809 ^ _780119) ^ [] : [-(_1085758 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16807 ^ _780119) ^ [] : [-(_1085756 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (38561 ^ _780119) ^ [_1526420, _1526422] : [38563 ^ _780119 : [(38566 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1526422), 38562 ^ [_1526420, _1526422]))], (38564 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 38562 ^ [_1526420, _1526422]), _1526420)))]], -(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)), _1526422), _1526420))], (27518 ^ _780119) ^ [_1288477, _1288479, _1288481, _1288483, _1288485] : [class_Orderings_Olinorder(_1288477), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288477, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1288477, _1288479, _1288481)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1288477, _1288483, _1288485)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1288477, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288477), _1288479), _1288483), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288477), _1288481), _1288485)))], (39739 ^ _780119) ^ [_1554795, _1554797] : [-(c_Transitive__Closure_Otrancl(_1554795, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554795, _1554795), tc_HOL_Obool)), _1554797), c_Relation_OId(_1554795))) = c_Transitive__Closure_Ortrancl(_1554795, _1554797))], (14812 ^ _780119) ^ [_1051999, _1052001, _1052003, _1052005] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1051999, _1052001, _1052003), _1052005), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1052001)], (22920 ^ _780119) ^ [_1198741, _1198743] : [class_Rings_Olinordered__semidom(_1198741), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198741), c_Groups_Ozero__class_Ozero(_1198741)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1198741), _1198743))))], (25790 ^ _780119) ^ [_1250842] : [class_Rings_Oring__1(_1250842), -(hAPP(c_Int_Oring__1__class_Oof__int(_1250842), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1250842))], (25041 ^ _780119) ^ [_1238772, _1238774] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1238772), _1238774) = 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)), _1238772)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238774))))], (10118 ^ _780119) ^ [_956580, _956582, _956584, _956586] : [hBOOL(hAPP(hAPP(c_member(_956580), _956582), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956580, tc_HOL_Obool)), _956584), _956586))), -(hBOOL(hAPP(hAPP(c_member(_956580), _956582), _956584)))], (18564 ^ _780119) ^ [_1118716, _1118718, _1118720, _1118722] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1118716, _1118718)), c_Sum__Type_OPlus(_1118716, _1118718, _1118720, _1118722)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1118716), _1118720)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1118718), _1118722))], (45938 ^ _780119) ^ [_1705191, _1705193, _1705195] : [-(c_List_Orotate(_1705191, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1705193), _1705195)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1705191), tc_List_Olist(_1705191), tc_List_Olist(_1705191), c_List_Orotate(_1705191, _1705193)), c_List_Orotate(_1705191, _1705195)))], (14128 ^ _780119) ^ [_1037901, _1037903, _1037905, _1037907, _1037909] : [class_Groups_Ocomm__monoid__mult(_1037901), hBOOL(hAPP(c_Finite__Set_Ofinite(_1037903), _1037905)), -(hBOOL(hAPP(hAPP(c_member(_1037903), _1037907), _1037905))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1037903, _1037901), _1037909), hAPP(hAPP(c_Set_Oinsert(_1037903), _1037907), _1037905)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037901), hAPP(_1037909, _1037907)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1037903, _1037901), _1037909), _1037905)))], (7380 ^ _780119) ^ [_904135, _904137, _904139, _904141] : [class_Lattices_Osemilattice__sup(_904135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904135), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_904135), _904137), _904139)), _904141)), 7387 ^ _780119 : [(7390 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904135), _904139), _904141)))], (7388 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904135), _904137), _904141)))]]], (31257 ^ _780119) ^ [_1364458] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1364458)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1364458)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1364458)), 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)))))], (31641 ^ _780119) ^ [_1370758] : [class_Int_Onumber__ring(_1370758), -(c_Groups_Oone__class_Oone(_1370758) = hAPP(c_Int_Onumber__class_Onumber__of(_1370758), c_Int_OBit1(c_Int_OPls)))], (44392 ^ _780119) ^ [_1669514, _1669516, _1669518, _1669520, _1669522, _1669524] : [-(_1669514 = _1669516), -(hAPP(hAPP(c_List_Olist__update(_1669518, hAPP(hAPP(c_List_Olist__update(_1669518, _1669520), _1669514), _1669522)), _1669516), _1669524) = hAPP(hAPP(c_List_Olist__update(_1669518, hAPP(hAPP(c_List_Olist__update(_1669518, _1669520), _1669516), _1669524)), _1669514), _1669522))], (9888 ^ _780119) ^ [_952303, _952305, _952307, _952309] : [class_Lattices_Osemilattice__inf(_952303), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952303), _952305), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952303), _952307), _952309))), 9895 ^ _780119 : [(9898 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952303), _952305), _952309)))], (9896 ^ _780119) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952303), _952305), _952307)))]]], (45209 ^ _780119) ^ [_1686469, _1686471, _1686473] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686469)), hAPP(hAPP(c_List_Oappend(_1686469), _1686471), _1686473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686469)), _1686471)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686469)), _1686473)))], (6067 ^ _780119) ^ [_876816, _876818] : [6068 ^ _780119 : [(6069 ^ _780119) ^ [_876869] : [hBOOL(hAPP(hAPP(c_member(_876816), _876869), _876818))]], _876818 = c_Orderings_Obot__class_Obot(tc_fun(_876816, tc_HOL_Obool))], (9228 ^ _780119) ^ [_938598, _938600, _938602] : [9229 ^ _780119 : [(9232 ^ _780119) ^ [] : [_938600 = _938602], (9230 ^ _780119) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938598, tc_HOL_Obool)), _938600), _938602))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938598, tc_HOL_Obool)), _938600), _938602)))]], input).
% 226.14/217.82 ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, v_y)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))],start(51671 ^ 0)).
% 226.14/217.82 ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, v_y)), 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(c_Hoare__Mirabelle_OMGT, v_y)), 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, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))],extension(5781 ^ 1,bind([[_871599, _871601, _871603, _871605], [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(c_Hoare__Mirabelle_OMGT, v_y)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))]]))).
% 226.14/217.82 ncf('1.1.1',plain,[-(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(c_Hoare__Mirabelle_OMGT, v_y)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))), c_Hoare__Mirabelle_Ostate__not__singleton, c_Com_OWT__bodies, hBOOL(hAPP(c_Com_OWT, v_y))],extension(6449 ^ 2,bind([[_884400], [v_y]]))).
% 226.14/217.82 ncf('1.1.1.1',plain,[-(c_Hoare__Mirabelle_Ostate__not__singleton)],extension(51657 ^ 3)).
% 226.14/217.82 ncf('1.1.1.2',plain,[-(c_Com_OWT__bodies)],extension(51659 ^ 3)).
% 226.14/217.82 ncf('1.1.1.3',plain,[-(hBOOL(hAPP(c_Com_OWT, v_y))), c_Com_OWT__bodies, hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y)],extension(7116 ^ 3,bind([[_897626, _897628], [v_pn, v_y]]))).
% 226.14/217.82 ncf('1.1.1.3.1',plain,[-(c_Com_OWT__bodies)],lemmata('[1, 1].x')).
% 226.14/217.82 ncf('1.1.1.3.2',plain,[-(hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))],extension(51667 ^ 4)).
% 226.14/217.82 ncf('1.1.2',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), 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, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _393020), c_Com_Ocom_OSKIP), _393020)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))), 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, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _393020), c_Com_Ocom_OSKIP), _393020)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))],extension(5781 ^ 2,bind([[_871599, _871601, _871603, _871605], [tc_Com_Ostate, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _393020), c_Com_Ocom_OSKIP), _393020)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))]]))).
% 226.14/217.82 ncf('1.1.2.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _393020), c_Com_Ocom_OSKIP), _393020)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))],extension(5753 ^ 3,bind([[_871131, _871133], [tc_Com_Ostate, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _393020), c_Com_Ocom_OSKIP), _393020)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))]]))).
% 226.14/217.82 ncf('1.1.2.2',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _393020), c_Com_Ocom_OSKIP), _393020)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))],extension(7676 ^ 3,bind([[_909777, _909779, _909781], [tc_Com_Ostate, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), _393020]]))).
% 226.14/217.82 %-----------------------------------------------------
% 226.14/217.82 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------